id	sid	tid	token	lemma	pos
ejpam-2666	1	1	european	european	PROPN
ejpam-2666	1	2	journal	journal	PROPN
ejpam-2666	1	3	of	of	ADP
ejpam-2666	1	4	pure	pure	ADJ
ejpam-2666	1	5	and	and	CCONJ
ejpam-2666	1	6	applied	apply	VERB
ejpam-2666	1	7	mathematics	mathematic	NOUN
ejpam-2666	1	8	vol	vol	NOUN
ejpam-2666	1	9	.	.	PROPN
ejpam-2666	2	1	10	10	NUM
ejpam-2666	2	2	,	,	PUNCT
ejpam-2666	2	3	no	no	INTJ
ejpam-2666	2	4	.	.	NOUN
ejpam-2666	2	5	2	2	NUM
ejpam-2666	2	6	,	,	PUNCT
ejpam-2666	2	7	2017	2017	NUM
ejpam-2666	2	8	,	,	PUNCT
ejpam-2666	2	9	392	392	NUM
ejpam-2666	2	10	-	-	SYM
ejpam-2666	2	11	409	409	NUM
ejpam-2666	2	12	issn	issn	PROPN
ejpam-2666	2	13	1307	1307	NUM
ejpam-2666	2	14	-	-	SYM
ejpam-2666	2	15	5543	5543	NUM
ejpam-2666	2	16	–	–	PUNCT
ejpam-2666	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2666	2	18	published	publish	VERB
ejpam-2666	2	19	by	by	ADP
ejpam-2666	2	20	new	new	PROPN
ejpam-2666	2	21	york	york	PROPN
ejpam-2666	2	22	business	business	PROPN
ejpam-2666	2	23	global	global	PROPN
ejpam-2666	2	24	z2	z2	PROPN
ejpam-2666	2	25	-	-	PUNCT
ejpam-2666	2	26	triple	triple	ADJ
ejpam-2666	2	27	cyclic	cyclic	ADJ
ejpam-2666	2	28	codes	code	NOUN
ejpam-2666	2	29	and	and	CCONJ
ejpam-2666	2	30	their	their	PRON
ejpam-2666	2	31	duals	dual	NOUN
ejpam-2666	2	32	srinivasulu	srinivasulu	ADP
ejpam-2666	2	33	b1	b1	PROPN
ejpam-2666	2	34	,	,	PUNCT
ejpam-2666	2	35	maheshanand	maheshanand	NOUN
ejpam-2666	2	36	bhaintwal2	bhaintwal2	NOUN
ejpam-2666	2	37	1,2	1,2	NUM
ejpam-2666	2	38	department	department	NOUN
ejpam-2666	2	39	of	of	ADP
ejpam-2666	2	40	mathematics	mathematics	PROPN
ejpam-2666	2	41	,	,	PUNCT
ejpam-2666	2	42	indian	indian	PROPN
ejpam-2666	2	43	institute	institute	PROPN
ejpam-2666	2	44	of	of	ADP
ejpam-2666	2	45	technology	technology	PROPN
ejpam-2666	2	46	roorkee	roorkee	PROPN
ejpam-2666	2	47	,	,	PUNCT
ejpam-2666	2	48	roorkee	roorkee	PROPN
ejpam-2666	2	49	,	,	PUNCT
ejpam-2666	2	50	india	india	PROPN
ejpam-2666	2	51	.	.	PUNCT
ejpam-2666	2	52	abstract	abstract	PROPN
ejpam-2666	2	53	.	.	PUNCT
ejpam-2666	3	1	a	a	DET
ejpam-2666	3	2	z2	z2	NUM
ejpam-2666	3	3	-	-	PUNCT
ejpam-2666	3	4	triple	triple	ADJ
ejpam-2666	3	5	cyclic	cyclic	ADJ
ejpam-2666	3	6	code	code	NOUN
ejpam-2666	3	7	of	of	ADP
ejpam-2666	3	8	block	block	NOUN
ejpam-2666	3	9	length	length	NOUN
ejpam-2666	3	10	(	(	PUNCT
ejpam-2666	3	11	r	r	NOUN
ejpam-2666	3	12	,	,	PUNCT
ejpam-2666	3	13	s	s	PROPN
ejpam-2666	3	14	,	,	PUNCT
ejpam-2666	3	15	t	t	PROPN
ejpam-2666	3	16	)	)	PUNCT
ejpam-2666	3	17	is	be	AUX
ejpam-2666	3	18	a	a	DET
ejpam-2666	3	19	binary	binary	ADJ
ejpam-2666	3	20	code	code	NOUN
ejpam-2666	3	21	of	of	ADP
ejpam-2666	3	22	length	length	NOUN
ejpam-2666	3	23	r+	r+	PUNCT
ejpam-2666	3	24	s+	s+	PUNCT
ejpam-2666	3	25	t	t	NOUN
ejpam-2666	3	26	such	such	ADJ
ejpam-2666	3	27	that	that	SCONJ
ejpam-2666	3	28	the	the	DET
ejpam-2666	3	29	code	code	NOUN
ejpam-2666	3	30	is	be	AUX
ejpam-2666	3	31	partitioned	partition	VERB
ejpam-2666	3	32	into	into	ADP
ejpam-2666	3	33	three	three	NUM
ejpam-2666	3	34	parts	part	NOUN
ejpam-2666	3	35	of	of	ADP
ejpam-2666	3	36	lengths	length	NOUN
ejpam-2666	3	37	r	r	NOUN
ejpam-2666	3	38	,	,	PUNCT
ejpam-2666	3	39	s	s	PART
ejpam-2666	3	40	and	and	CCONJ
ejpam-2666	3	41	t	t	PROPN
ejpam-2666	3	42	such	such	ADJ
ejpam-2666	3	43	that	that	SCONJ
ejpam-2666	3	44	each	each	DET
ejpam-2666	3	45	part	part	NOUN
ejpam-2666	3	46	is	be	AUX
ejpam-2666	3	47	invariant	invariant	ADJ
ejpam-2666	3	48	under	under	ADP
ejpam-2666	3	49	the	the	DET
ejpam-2666	3	50	cyclic	cyclic	ADJ
ejpam-2666	3	51	shifts	shift	NOUN
ejpam-2666	3	52	of	of	ADP
ejpam-2666	3	53	the	the	DET
ejpam-2666	3	54	coordinates	coordinate	NOUN
ejpam-2666	3	55	.	.	PUNCT
ejpam-2666	4	1	such	such	DET
ejpam-2666	4	2	a	a	DET
ejpam-2666	4	3	code	code	NOUN
ejpam-2666	4	4	can	can	AUX
ejpam-2666	4	5	be	be	AUX
ejpam-2666	4	6	viewed	view	VERB
ejpam-2666	4	7	as	as	ADP
ejpam-2666	4	8	z2[x]-submodules	z2[x]-submodules	PROPN
ejpam-2666	4	9	of	of	ADP
ejpam-2666	4	10	z2[x	z2[x	PROPN
ejpam-2666	4	11	]	]	PUNCT
ejpam-2666	5	1	〈	〈	PROPN
ejpam-2666	5	2	xr−1	xr−1	PROPN
ejpam-2666	5	3	〉	〉	PROPN
ejpam-2666	5	4	×	×	PROPN
ejpam-2666	5	5	z2[x	z2[x	X
ejpam-2666	5	6	]	]	PUNCT
ejpam-2666	6	1	〈	〈	PROPN
ejpam-2666	6	2	xs−1	xs−1	PROPN
ejpam-2666	6	3	〉	〉	PROPN
ejpam-2666	6	4	×	×	NOUN
ejpam-2666	6	5	z2[x	z2[x	X
ejpam-2666	6	6	]	]	PUNCT
ejpam-2666	7	1	〈	〈	PROPN
ejpam-2666	7	2	xt−1	xt−1	PROPN
ejpam-2666	7	3	〉	〉	PROPN
ejpam-2666	7	4	,	,	PUNCT
ejpam-2666	7	5	in	in	ADP
ejpam-2666	7	6	polynomial	polynomial	ADJ
ejpam-2666	7	7	representation	representation	NOUN
ejpam-2666	7	8	.	.	PUNCT
ejpam-2666	8	1	in	in	ADP
ejpam-2666	8	2	this	this	DET
ejpam-2666	8	3	paper	paper	NOUN
ejpam-2666	8	4	,	,	PUNCT
ejpam-2666	8	5	we	we	PRON
ejpam-2666	8	6	determine	determine	VERB
ejpam-2666	8	7	the	the	DET
ejpam-2666	8	8	structure	structure	NOUN
ejpam-2666	8	9	of	of	ADP
ejpam-2666	8	10	these	these	DET
ejpam-2666	8	11	codes	code	NOUN
ejpam-2666	8	12	.	.	PUNCT
ejpam-2666	9	1	we	we	PRON
ejpam-2666	9	2	have	have	AUX
ejpam-2666	9	3	obtained	obtain	VERB
ejpam-2666	9	4	the	the	DET
ejpam-2666	9	5	form	form	NOUN
ejpam-2666	9	6	of	of	ADP
ejpam-2666	9	7	the	the	DET
ejpam-2666	9	8	generators	generator	NOUN
ejpam-2666	9	9	for	for	ADP
ejpam-2666	9	10	such	such	ADJ
ejpam-2666	9	11	codes	code	NOUN
ejpam-2666	9	12	.	.	PUNCT
ejpam-2666	10	1	further	far	ADV
ejpam-2666	10	2	,	,	PUNCT
ejpam-2666	10	3	a	a	DET
ejpam-2666	10	4	minimal	minimal	ADJ
ejpam-2666	10	5	generating	generating	NOUN
ejpam-2666	10	6	set	set	NOUN
ejpam-2666	10	7	for	for	ADP
ejpam-2666	10	8	such	such	ADJ
ejpam-2666	10	9	codes	code	NOUN
ejpam-2666	10	10	is	be	AUX
ejpam-2666	10	11	obtained	obtain	VERB
ejpam-2666	10	12	.	.	PUNCT
ejpam-2666	11	1	also	also	ADV
ejpam-2666	11	2	,	,	PUNCT
ejpam-2666	11	3	we	we	PRON
ejpam-2666	11	4	study	study	VERB
ejpam-2666	11	5	the	the	DET
ejpam-2666	11	6	structure	structure	NOUN
ejpam-2666	11	7	of	of	ADP
ejpam-2666	11	8	the	the	DET
ejpam-2666	11	9	duals	dual	NOUN
ejpam-2666	11	10	of	of	ADP
ejpam-2666	11	11	these	these	DET
ejpam-2666	11	12	codes	code	NOUN
ejpam-2666	11	13	via	via	ADP
ejpam-2666	11	14	the	the	DET
ejpam-2666	11	15	generators	generator	NOUN
ejpam-2666	11	16	of	of	ADP
ejpam-2666	11	17	the	the	DET
ejpam-2666	11	18	codes	code	NOUN
ejpam-2666	11	19	.	.	PUNCT
ejpam-2666	12	1	2010	2010	NUM
ejpam-2666	12	2	mathematics	mathematic	NOUN
ejpam-2666	12	3	subject	subject	NOUN
ejpam-2666	12	4	classifications	classification	NOUN
ejpam-2666	12	5	:	:	PUNCT
ejpam-2666	12	6	94b05	94b05	NUM
ejpam-2666	12	7	,	,	PUNCT
ejpam-2666	12	8	94b60	94b60	NUM
ejpam-2666	12	9	key	key	ADJ
ejpam-2666	12	10	words	word	NOUN
ejpam-2666	12	11	and	and	CCONJ
ejpam-2666	12	12	phrases	phrase	NOUN
ejpam-2666	12	13	:	:	PUNCT
ejpam-2666	12	14	triple	triple	ADJ
ejpam-2666	12	15	cyclic	cyclic	ADJ
ejpam-2666	12	16	codes	code	NOUN
ejpam-2666	12	17	,	,	PUNCT
ejpam-2666	12	18	minimal	minimal	ADJ
ejpam-2666	12	19	spanning	span	VERB
ejpam-2666	12	20	sets	set	NOUN
ejpam-2666	12	21	,	,	PUNCT
ejpam-2666	12	22	dual	dual	ADJ
ejpam-2666	12	23	codes	code	NOUN
ejpam-2666	12	24	1	1	NUM
ejpam-2666	12	25	.	.	PUNCT
ejpam-2666	13	1	introduction	introduction	NOUN
ejpam-2666	13	2	codes	code	NOUN
ejpam-2666	13	3	over	over	ADP
ejpam-2666	13	4	rings	ring	NOUN
ejpam-2666	13	5	were	be	AUX
ejpam-2666	13	6	introduced	introduce	VERB
ejpam-2666	13	7	in	in	ADP
ejpam-2666	13	8	early	early	ADJ
ejpam-2666	13	9	1970s	1970	NOUN
ejpam-2666	13	10	.	.	PUNCT
ejpam-2666	14	1	among	among	ADP
ejpam-2666	14	2	them	they	PRON
ejpam-2666	14	3	,	,	PUNCT
ejpam-2666	14	4	cyclic	cyclic	ADJ
ejpam-2666	14	5	codes	code	NOUN
ejpam-2666	14	6	are	be	AUX
ejpam-2666	14	7	an	an	DET
ejpam-2666	14	8	important	important	ADJ
ejpam-2666	14	9	class	class	NOUN
ejpam-2666	14	10	of	of	ADP
ejpam-2666	14	11	linear	linear	PROPN
ejpam-2666	14	12	codes	code	NOUN
ejpam-2666	14	13	because	because	SCONJ
ejpam-2666	14	14	of	of	ADP
ejpam-2666	14	15	their	their	PRON
ejpam-2666	14	16	richness	richness	NOUN
ejpam-2666	14	17	in	in	ADP
ejpam-2666	14	18	algebraic	algebraic	ADJ
ejpam-2666	14	19	structure	structure	NOUN
ejpam-2666	14	20	and	and	CCONJ
ejpam-2666	14	21	practical	practical	ADJ
ejpam-2666	14	22	use	use	NOUN
ejpam-2666	14	23	.	.	PUNCT
ejpam-2666	15	1	cyclic	cyclic	ADJ
ejpam-2666	15	2	codes	code	NOUN
ejpam-2666	15	3	over	over	ADP
ejpam-2666	15	4	finite	finite	ADJ
ejpam-2666	15	5	fields	field	NOUN
ejpam-2666	15	6	are	be	AUX
ejpam-2666	15	7	well	well	ADV
ejpam-2666	15	8	studied	study	VERB
ejpam-2666	15	9	[	[	X
ejpam-2666	15	10	15	15	NUM
ejpam-2666	15	11	]	]	PUNCT
ejpam-2666	15	12	and	and	CCONJ
ejpam-2666	15	13	they	they	PRON
ejpam-2666	15	14	have	have	AUX
ejpam-2666	15	15	been	be	AUX
ejpam-2666	15	16	extended	extend	VERB
ejpam-2666	15	17	to	to	ADP
ejpam-2666	15	18	various	various	ADJ
ejpam-2666	15	19	finite	finite	ADJ
ejpam-2666	15	20	rings	ring	NOUN
ejpam-2666	16	1	[	[	X
ejpam-2666	16	2	11	11	NUM
ejpam-2666	16	3	]	]	PUNCT
ejpam-2666	16	4	.	.	PUNCT
ejpam-2666	17	1	the	the	DET
ejpam-2666	17	2	search	search	NOUN
ejpam-2666	17	3	for	for	ADP
ejpam-2666	17	4	new	new	ADJ
ejpam-2666	17	5	codes	code	NOUN
ejpam-2666	17	6	with	with	ADP
ejpam-2666	17	7	good	good	ADJ
ejpam-2666	17	8	parameters	parameter	NOUN
ejpam-2666	17	9	encourages	encourage	VERB
ejpam-2666	17	10	researchers	researcher	NOUN
ejpam-2666	17	11	to	to	PART
ejpam-2666	17	12	introduce	introduce	VERB
ejpam-2666	17	13	various	various	ADJ
ejpam-2666	17	14	families	family	NOUN
ejpam-2666	17	15	of	of	ADP
ejpam-2666	17	16	linear	linear	PROPN
ejpam-2666	17	17	codes	code	NOUN
ejpam-2666	17	18	.	.	PUNCT
ejpam-2666	18	1	in	in	ADP
ejpam-2666	18	2	1973	1973	NUM
ejpam-2666	18	3	,	,	PUNCT
ejpam-2666	18	4	delsarte	delsarte	NOUN
ejpam-2666	18	5	and	and	CCONJ
ejpam-2666	18	6	levenshtein	levenshtein	NOUN
ejpam-2666	18	7	[	[	X
ejpam-2666	18	8	10	10	NUM
ejpam-2666	18	9	]	]	SYM
ejpam-2666	18	10	defined	define	VERB
ejpam-2666	18	11	additive	additive	ADJ
ejpam-2666	18	12	codes	code	NOUN
ejpam-2666	18	13	in	in	ADP
ejpam-2666	18	14	terms	term	NOUN
ejpam-2666	18	15	of	of	ADP
ejpam-2666	18	16	association	association	NOUN
ejpam-2666	18	17	schemes	scheme	NOUN
ejpam-2666	18	18	as	as	ADP
ejpam-2666	18	19	the	the	DET
ejpam-2666	18	20	subgroups	subgroup	NOUN
ejpam-2666	18	21	of	of	ADP
ejpam-2666	18	22	the	the	DET
ejpam-2666	18	23	underlying	underlying	ADJ
ejpam-2666	18	24	abelian	abelian	ADJ
ejpam-2666	18	25	group	group	NOUN
ejpam-2666	18	26	.	.	PUNCT
ejpam-2666	19	1	under	under	ADP
ejpam-2666	19	2	binary	binary	ADJ
ejpam-2666	19	3	hamming	hamming	NOUN
ejpam-2666	19	4	scheme	scheme	NOUN
ejpam-2666	19	5	,	,	PUNCT
ejpam-2666	19	6	the	the	DET
ejpam-2666	19	7	underlying	underlie	VERB
ejpam-2666	19	8	group	group	NOUN
ejpam-2666	19	9	of	of	ADP
ejpam-2666	19	10	order	order	NOUN
ejpam-2666	19	11	2k	2k	NOUN
ejpam-2666	19	12	is	be	AUX
ejpam-2666	19	13	isomorphic	isomorphic	ADJ
ejpam-2666	19	14	to	to	ADP
ejpam-2666	19	15	zα2	zα2	PROPN
ejpam-2666	19	16	×zβ4	×zβ4	PUNCT
ejpam-2666	19	17	,	,	PUNCT
ejpam-2666	19	18	where	where	SCONJ
ejpam-2666	19	19	α	α	NOUN
ejpam-2666	19	20	and	and	CCONJ
ejpam-2666	19	21	β	β	X
ejpam-2666	19	22	are	be	AUX
ejpam-2666	19	23	non	non	ADJ
ejpam-2666	19	24	-	-	ADJ
ejpam-2666	19	25	negative	negative	ADJ
ejpam-2666	19	26	integers	integer	NOUN
ejpam-2666	19	27	.	.	PUNCT
ejpam-2666	20	1	the	the	DET
ejpam-2666	20	2	subgroups	subgroup	NOUN
ejpam-2666	20	3	of	of	ADP
ejpam-2666	20	4	underlying	underlie	VERB
ejpam-2666	20	5	group	group	NOUN
ejpam-2666	20	6	are	be	AUX
ejpam-2666	20	7	called	call	VERB
ejpam-2666	20	8	z2z4	z2z4	ADJ
ejpam-2666	20	9	-	-	ADJ
ejpam-2666	20	10	additive	additive	ADJ
ejpam-2666	20	11	codes	code	NOUN
ejpam-2666	20	12	.	.	PUNCT
ejpam-2666	21	1	borges	borge	NOUN
ejpam-2666	21	2	et	et	PROPN
ejpam-2666	21	3	al	al	PROPN
ejpam-2666	21	4	.	.	PUNCT
ejpam-2666	22	1	[	[	X
ejpam-2666	22	2	5	5	NUM
ejpam-2666	22	3	]	]	PUNCT
ejpam-2666	22	4	have	have	AUX
ejpam-2666	22	5	studied	study	VERB
ejpam-2666	22	6	z2z4	z2z4	ADJ
ejpam-2666	22	7	-	-	ADJ
ejpam-2666	22	8	additive	additive	ADJ
ejpam-2666	22	9	codes	code	NOUN
ejpam-2666	22	10	by	by	ADP
ejpam-2666	22	11	deriving	derive	VERB
ejpam-2666	22	12	their	their	PRON
ejpam-2666	22	13	generator	generator	NOUN
ejpam-2666	22	14	matrices	matrix	NOUN
ejpam-2666	22	15	and	and	CCONJ
ejpam-2666	22	16	parity	parity	NOUN
ejpam-2666	22	17	check	check	NOUN
ejpam-2666	22	18	matrices	matrix	NOUN
ejpam-2666	22	19	.	.	PUNCT
ejpam-2666	23	1	in	in	ADP
ejpam-2666	23	2	[	[	X
ejpam-2666	23	3	1	1	NUM
ejpam-2666	23	4	]	]	PUNCT
ejpam-2666	23	5	,	,	PUNCT
ejpam-2666	23	6	z2z4	z2z4	ADJ
ejpam-2666	23	7	-	-	ADJ
ejpam-2666	23	8	cyclic	cyclic	ADJ
ejpam-2666	23	9	codes	code	NOUN
ejpam-2666	23	10	of	of	ADP
ejpam-2666	23	11	block	block	NOUN
ejpam-2666	23	12	length	length	NOUN
ejpam-2666	23	13	(	(	PUNCT
ejpam-2666	23	14	r	r	NOUN
ejpam-2666	23	15	,	,	PUNCT
ejpam-2666	23	16	t	t	PROPN
ejpam-2666	23	17	)	)	PUNCT
ejpam-2666	23	18	for	for	ADP
ejpam-2666	23	19	odd	odd	ADJ
ejpam-2666	23	20	t	t	PROPN
ejpam-2666	23	21	have	have	AUX
ejpam-2666	23	22	been	be	AUX
ejpam-2666	23	23	defined	define	VERB
ejpam-2666	23	24	as	as	ADP
ejpam-2666	23	25	z4submodules	z4submodule	NOUN
ejpam-2666	23	26	of	of	ADP
ejpam-2666	23	27	zr2	zr2	PROPN
ejpam-2666	23	28	×	×	PROPN
ejpam-2666	23	29	zt4	zt4	PROPN
ejpam-2666	23	30	,	,	PUNCT
ejpam-2666	23	31	and	and	CCONJ
ejpam-2666	23	32	a	a	DET
ejpam-2666	23	33	minimal	minimal	ADJ
ejpam-2666	23	34	spanning	span	VERB
ejpam-2666	23	35	set	set	NOUN
ejpam-2666	23	36	for	for	ADP
ejpam-2666	23	37	these	these	DET
ejpam-2666	23	38	codes	code	NOUN
ejpam-2666	23	39	has	have	AUX
ejpam-2666	23	40	been	be	AUX
ejpam-2666	23	41	determined	determine	VERB
ejpam-2666	23	42	.	.	PUNCT
ejpam-2666	24	1	extending	extend	VERB
ejpam-2666	24	2	this	this	DET
ejpam-2666	24	3	work	work	NOUN
ejpam-2666	24	4	,	,	PUNCT
ejpam-2666	24	5	borges	borge	NOUN
ejpam-2666	24	6	et	et	NOUN
ejpam-2666	24	7	al	al	PROPN
ejpam-2666	24	8	.	.	PUNCT
ejpam-2666	25	1	[	[	X
ejpam-2666	25	2	6	6	NUM
ejpam-2666	25	3	]	]	PUNCT
ejpam-2666	25	4	gave	give	VERB
ejpam-2666	25	5	duals	dual	NOUN
ejpam-2666	25	6	of	of	ADP
ejpam-2666	25	7	z2z4	z2z4	NOUN
ejpam-2666	25	8	-	-	ADJ
ejpam-2666	25	9	cyclic	cyclic	ADJ
ejpam-2666	25	10	codes	code	NOUN
ejpam-2666	25	11	of	of	ADP
ejpam-2666	25	12	block	block	NOUN
ejpam-2666	25	13	length	length	NOUN
ejpam-2666	25	14	(	(	PUNCT
ejpam-2666	25	15	r	r	NOUN
ejpam-2666	25	16	,	,	PUNCT
ejpam-2666	25	17	t	t	PROPN
ejpam-2666	25	18	)	)	PUNCT
ejpam-2666	25	19	for	for	ADP
ejpam-2666	25	20	odd	odd	ADJ
ejpam-2666	25	21	t.	t.	NOUN
ejpam-2666	25	22	recently	recently	ADV
ejpam-2666	25	23	aydogdu	aydogdu	ADV
ejpam-2666	25	24	et	et	PROPN
ejpam-2666	25	25	al	al	PROPN
ejpam-2666	25	26	.	.	PUNCT
ejpam-2666	26	1	[	[	X
ejpam-2666	26	2	3	3	X
ejpam-2666	26	3	]	]	PUNCT
ejpam-2666	26	4	have	have	AUX
ejpam-2666	26	5	studied	study	VERB
ejpam-2666	26	6	a	a	DET
ejpam-2666	26	7	new	new	ADJ
ejpam-2666	26	8	class	class	NOUN
ejpam-2666	26	9	of	of	ADP
ejpam-2666	26	10	codes	code	NOUN
ejpam-2666	26	11	over	over	ADP
ejpam-2666	26	12	the	the	DET
ejpam-2666	26	13	structure	structure	NOUN
ejpam-2666	26	14	z2z2[u	z2z2[u	PROPN
ejpam-2666	26	15	]	]	X
ejpam-2666	26	16	,	,	PUNCT
ejpam-2666	26	17	where	where	SCONJ
ejpam-2666	26	18	z2[u	z2[u	X
ejpam-2666	26	19	]	]	X
ejpam-2666	26	20	=	=	SYM
ejpam-2666	26	21	z2	z2	PROPN
ejpam-2666	26	22	+	+	CCONJ
ejpam-2666	26	23	uz2	uz2	PROPN
ejpam-2666	26	24	,	,	PUNCT
ejpam-2666	26	25	u	u	NOUN
ejpam-2666	26	26	2	2	NUM
ejpam-2666	26	27	=	=	SYM
ejpam-2666	26	28	0	0	NUM
ejpam-2666	26	29	.	.	PUNCT
ejpam-2666	27	1	they	they	PRON
ejpam-2666	27	2	have	have	AUX
ejpam-2666	27	3	defined	define	VERB
ejpam-2666	27	4	z2z2[u]-additive	z2z2[u]-additive	PROPN
ejpam-2666	27	5	codes	code	NOUN
ejpam-2666	27	6	as	as	ADP
ejpam-2666	27	7	z2[u]-submodules	z2[u]-submodule	NOUN
ejpam-2666	27	8	of	of	ADP
ejpam-2666	27	9	zs2	zs2	NOUN
ejpam-2666	27	10	×	×	PROPN
ejpam-2666	27	11	z2[u]t	z2[u]t	PROPN
ejpam-2666	27	12	,	,	PUNCT
ejpam-2666	27	13	and	and	CCONJ
ejpam-2666	27	14	obtained	obtain	VERB
ejpam-2666	27	15	their	their	PRON
ejpam-2666	27	16	generator	generator	NOUN
ejpam-2666	27	17	and	and	CCONJ
ejpam-2666	27	18	parity	parity	NOUN
ejpam-2666	27	19	check	check	NOUN
ejpam-2666	27	20	matrices	matrix	NOUN
ejpam-2666	27	21	.	.	PUNCT
ejpam-2666	28	1	they	they	PRON
ejpam-2666	28	2	have	have	AUX
ejpam-2666	28	3	also	also	ADV
ejpam-2666	28	4	defined	define	VERB
ejpam-2666	28	5	the	the	DET
ejpam-2666	28	6	type	type	NOUN
ejpam-2666	28	7	of	of	ADP
ejpam-2666	28	8	these	these	DET
ejpam-2666	28	9	codes	code	NOUN
ejpam-2666	28	10	and	and	CCONJ
ejpam-2666	28	11	have	have	AUX
ejpam-2666	28	12	shown	show	VERB
ejpam-2666	28	13	that	that	SCONJ
ejpam-2666	28	14	some	some	DET
ejpam-2666	28	15	optimal	optimal	ADJ
ejpam-2666	28	16	binary	binary	ADJ
ejpam-2666	28	17	codes	code	NOUN
ejpam-2666	28	18	are	be	AUX
ejpam-2666	28	19	gray	gray	ADJ
ejpam-2666	28	20	images	image	NOUN
ejpam-2666	28	21	of	of	ADP
ejpam-2666	28	22	z2z2[u]-additive	z2z2[u]-additive	PROPN
ejpam-2666	28	23	codes	code	NOUN
ejpam-2666	28	24	.	.	PUNCT
ejpam-2666	29	1	email	email	NOUN
ejpam-2666	29	2	addresses	address	NOUN
ejpam-2666	29	3	:	:	PUNCT
ejpam-2666	29	4	bslu1981@gmail.com	bslu1981@gmail.com	X
ejpam-2666	30	1	(	(	PUNCT
ejpam-2666	30	2	srinivasulu	srinivasulu	PROPN
ejpam-2666	30	3	b	b	PROPN
ejpam-2666	30	4	)	)	PUNCT
ejpam-2666	30	5	,	,	PUNCT
ejpam-2666	30	6	mahesfma@iitr.ac.in	mahesfma@iitr.ac.in	PROPN
ejpam-2666	30	7	(	(	PUNCT
ejpam-2666	30	8	m.	m.	NOUN
ejpam-2666	30	9	bhaintwal	bhaintwal	NOUN
ejpam-2666	30	10	)	)	PUNCT
ejpam-2666	30	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2666	31	1	392	392	NUM
ejpam-2666	31	2	c	c	AUX
ejpam-2666	31	3	©	©	PROPN
ejpam-2666	31	4	2017	2017	NUM
ejpam-2666	31	5	ejpam	ejpam	VERB
ejpam-2666	31	6	all	all	DET
ejpam-2666	31	7	rights	right	NOUN
ejpam-2666	31	8	reserved	reserve	VERB
ejpam-2666	31	9	.	.	PUNCT
ejpam-2666	32	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	32	2	b	b	NUM
ejpam-2666	32	3	,	,	PUNCT
ejpam-2666	32	4	maheshanand	maheshanand	NOUN
ejpam-2666	32	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	32	6	/	/	SYM
ejpam-2666	32	7	eur	eur	PROPN
ejpam-2666	32	8	.	.	PUNCT
ejpam-2666	33	1	j.	j.	PROPN
ejpam-2666	33	2	pure	pure	PROPN
ejpam-2666	33	3	appl	appl	PROPN
ejpam-2666	33	4	.	.	PROPN
ejpam-2666	33	5	math	math	PROPN
ejpam-2666	33	6	,	,	PUNCT
ejpam-2666	33	7	10	10	NUM
ejpam-2666	33	8	(	(	PUNCT
ejpam-2666	33	9	2	2	NUM
ejpam-2666	33	10	)	)	PUNCT
ejpam-2666	33	11	(	(	PUNCT
ejpam-2666	33	12	2017	2017	NUM
ejpam-2666	33	13	)	)	PUNCT
ejpam-2666	33	14	,	,	PUNCT
ejpam-2666	33	15	392	392	NUM
ejpam-2666	33	16	-	-	SYM
ejpam-2666	33	17	409	409	NUM
ejpam-2666	33	18	393	393	NUM
ejpam-2666	33	19	extending	extend	VERB
ejpam-2666	33	20	the	the	DET
ejpam-2666	33	21	concepts	concept	NOUN
ejpam-2666	33	22	given	give	VERB
ejpam-2666	33	23	in	in	ADP
ejpam-2666	33	24	[	[	X
ejpam-2666	33	25	6	6	NUM
ejpam-2666	33	26	]	]	PUNCT
ejpam-2666	33	27	,	,	PUNCT
ejpam-2666	33	28	recently	recently	ADV
ejpam-2666	33	29	aydogdu	aydogdu	ADV
ejpam-2666	33	30	and	and	CCONJ
ejpam-2666	33	31	siap	siap	PROPN
ejpam-2666	33	32	have	have	AUX
ejpam-2666	33	33	studied	study	VERB
ejpam-2666	33	34	[	[	PUNCT
ejpam-2666	33	35	2	2	X
ejpam-2666	33	36	]	]	PUNCT
ejpam-2666	33	37	the	the	DET
ejpam-2666	33	38	algebraic	algebraic	ADJ
ejpam-2666	33	39	structure	structure	NOUN
ejpam-2666	33	40	of	of	ADP
ejpam-2666	33	41	zprzps	zprzps	NOUN
ejpam-2666	33	42	-	-	PUNCT
ejpam-2666	33	43	additive	additive	ADJ
ejpam-2666	33	44	codes	code	NOUN
ejpam-2666	33	45	.	.	PUNCT
ejpam-2666	34	1	they	they	PRON
ejpam-2666	34	2	have	have	AUX
ejpam-2666	34	3	determined	determine	VERB
ejpam-2666	34	4	the	the	DET
ejpam-2666	34	5	generator	generator	NOUN
ejpam-2666	34	6	and	and	CCONJ
ejpam-2666	34	7	parity	parity	NOUN
ejpam-2666	34	8	check	check	NOUN
ejpam-2666	34	9	matrices	matrix	NOUN
ejpam-2666	34	10	for	for	ADP
ejpam-2666	34	11	these	these	DET
ejpam-2666	34	12	codes	code	NOUN
ejpam-2666	34	13	.	.	PUNCT
ejpam-2666	35	1	borges	borge	NOUN
ejpam-2666	35	2	et	et	PROPN
ejpam-2666	35	3	al	al	PROPN
ejpam-2666	35	4	.	.	PUNCT
ejpam-2666	36	1	[	[	X
ejpam-2666	36	2	4	4	X
ejpam-2666	36	3	]	]	PUNCT
ejpam-2666	36	4	have	have	AUX
ejpam-2666	36	5	derived	derive	VERB
ejpam-2666	36	6	the	the	DET
ejpam-2666	36	7	structure	structure	NOUN
ejpam-2666	36	8	of	of	ADP
ejpam-2666	36	9	z2	z2	NOUN
ejpam-2666	36	10	-	-	PUNCT
ejpam-2666	36	11	double	double	ADJ
ejpam-2666	36	12	cyclic	cyclic	NOUN
ejpam-2666	36	13	codes	code	NOUN
ejpam-2666	36	14	.	.	PUNCT
ejpam-2666	37	1	they	they	PRON
ejpam-2666	37	2	have	have	AUX
ejpam-2666	37	3	determined	determine	VERB
ejpam-2666	37	4	generating	generating	NOUN
ejpam-2666	37	5	polynomials	polynomial	NOUN
ejpam-2666	37	6	for	for	ADP
ejpam-2666	37	7	these	these	DET
ejpam-2666	37	8	codes	code	NOUN
ejpam-2666	37	9	and	and	CCONJ
ejpam-2666	37	10	derived	derive	VERB
ejpam-2666	37	11	the	the	DET
ejpam-2666	37	12	relationship	relationship	NOUN
ejpam-2666	37	13	between	between	ADP
ejpam-2666	37	14	the	the	DET
ejpam-2666	37	15	codes	code	NOUN
ejpam-2666	37	16	and	and	CCONJ
ejpam-2666	37	17	their	their	PRON
ejpam-2666	37	18	duals	dual	NOUN
ejpam-2666	37	19	.	.	PUNCT
ejpam-2666	38	1	similarly	similarly	ADV
ejpam-2666	38	2	structure	structure	NOUN
ejpam-2666	38	3	of	of	ADP
ejpam-2666	38	4	double	double	ADJ
ejpam-2666	38	5	cyclic	cyclic	NOUN
ejpam-2666	38	6	codes	code	NOUN
ejpam-2666	38	7	over	over	ADP
ejpam-2666	38	8	the	the	DET
ejpam-2666	38	9	rings	ring	NOUN
ejpam-2666	38	10	z4	z4	PROPN
ejpam-2666	38	11	and	and	CCONJ
ejpam-2666	38	12	f2	f2	PROPN
ejpam-2666	38	13	+	+	CCONJ
ejpam-2666	38	14	uf2	uf2	NOUN
ejpam-2666	38	15	+	+	CCONJ
ejpam-2666	38	16	u2f2	u2f2	PROPN
ejpam-2666	38	17	,	,	PUNCT
ejpam-2666	38	18	u	u	NOUN
ejpam-2666	38	19	3	3	NUM
ejpam-2666	38	20	=	=	SYM
ejpam-2666	38	21	0	0	NUM
ejpam-2666	38	22	have	have	AUX
ejpam-2666	38	23	been	be	AUX
ejpam-2666	38	24	studied	study	VERB
ejpam-2666	38	25	in	in	ADP
ejpam-2666	38	26	[	[	X
ejpam-2666	38	27	14][17	14][17	PROPN
ejpam-2666	38	28	]	]	X
ejpam-2666	38	29	.	.	PUNCT
ejpam-2666	39	1	in	in	ADP
ejpam-2666	39	2	[	[	X
ejpam-2666	39	3	14	14	NUM
ejpam-2666	39	4	]	]	PUNCT
ejpam-2666	39	5	,	,	PUNCT
ejpam-2666	39	6	gao	gao	PROPN
ejpam-2666	39	7	et	et	PROPN
ejpam-2666	39	8	al	al	PROPN
ejpam-2666	39	9	.	.	PROPN
ejpam-2666	39	10	have	have	AUX
ejpam-2666	39	11	obtained	obtain	VERB
ejpam-2666	39	12	some	some	DET
ejpam-2666	39	13	optimal	optimal	ADJ
ejpam-2666	39	14	or	or	CCONJ
ejpam-2666	39	15	suboptimal	suboptimal	ADJ
ejpam-2666	39	16	non	non	ADJ
ejpam-2666	39	17	-	-	ADJ
ejpam-2666	39	18	linear	linear	ADJ
ejpam-2666	39	19	binary	binary	ADJ
ejpam-2666	39	20	codes	code	NOUN
ejpam-2666	39	21	.	.	PUNCT
ejpam-2666	40	1	a	a	DET
ejpam-2666	40	2	double	double	ADJ
ejpam-2666	40	3	cyclic	cyclic	NOUN
ejpam-2666	40	4	code	code	NOUN
ejpam-2666	40	5	is	be	AUX
ejpam-2666	40	6	in	in	ADP
ejpam-2666	40	7	fact	fact	NOUN
ejpam-2666	40	8	a	a	DET
ejpam-2666	40	9	generalized	generalized	ADJ
ejpam-2666	40	10	quasi	quasi	NOUN
ejpam-2666	40	11	-	-	ADJ
ejpam-2666	40	12	cyclic	cyclic	ADJ
ejpam-2666	40	13	(	(	PUNCT
ejpam-2666	40	14	gqc	gqc	PROPN
ejpam-2666	40	15	)	)	PUNCT
ejpam-2666	40	16	code	code	NOUN
ejpam-2666	40	17	of	of	ADP
ejpam-2666	40	18	index	index	NOUN
ejpam-2666	40	19	two	two	NUM
ejpam-2666	40	20	.	.	PUNCT
ejpam-2666	41	1	siap	siap	PROPN
ejpam-2666	41	2	and	and	CCONJ
ejpam-2666	41	3	kulhan[16	kulhan[16	PROPN
ejpam-2666	41	4	]	]	PUNCT
ejpam-2666	41	5	introduced	introduce	VERB
ejpam-2666	41	6	gqc	gqc	PROPN
ejpam-2666	41	7	codes	code	NOUN
ejpam-2666	41	8	over	over	ADP
ejpam-2666	41	9	finite	finite	ADJ
ejpam-2666	41	10	fields	field	NOUN
ejpam-2666	41	11	and	and	CCONJ
ejpam-2666	41	12	the	the	DET
ejpam-2666	41	13	study	study	NOUN
ejpam-2666	41	14	has	have	AUX
ejpam-2666	41	15	been	be	AUX
ejpam-2666	41	16	extended	extend	VERB
ejpam-2666	41	17	to	to	ADP
ejpam-2666	41	18	various	various	ADJ
ejpam-2666	41	19	finite	finite	NOUN
ejpam-2666	41	20	rings	ring	NOUN
ejpam-2666	41	21	by	by	ADP
ejpam-2666	41	22	many	many	ADJ
ejpam-2666	41	23	authors	author	NOUN
ejpam-2666	41	24	[	[	X
ejpam-2666	41	25	7	7	NUM
ejpam-2666	41	26	,	,	PUNCT
ejpam-2666	41	27	8	8	NUM
ejpam-2666	41	28	,	,	PUNCT
ejpam-2666	41	29	9	9	NUM
ejpam-2666	41	30	,	,	PUNCT
ejpam-2666	41	31	12	12	NUM
ejpam-2666	41	32	,	,	PUNCT
ejpam-2666	41	33	13	13	NUM
ejpam-2666	41	34	]	]	PUNCT
ejpam-2666	41	35	.	.	PUNCT
ejpam-2666	42	1	most	most	ADJ
ejpam-2666	42	2	of	of	ADP
ejpam-2666	42	3	these	these	DET
ejpam-2666	42	4	studies	study	NOUN
ejpam-2666	42	5	focused	focus	VERB
ejpam-2666	42	6	on	on	ADP
ejpam-2666	42	7	exploring	explore	VERB
ejpam-2666	42	8	1	1	NUM
ejpam-2666	42	9	-	-	PUNCT
ejpam-2666	42	10	generator	generator	NOUN
ejpam-2666	42	11	gqc	gqc	NOUN
ejpam-2666	42	12	codes	code	NOUN
ejpam-2666	42	13	where	where	SCONJ
ejpam-2666	42	14	they	they	PRON
ejpam-2666	42	15	have	have	AUX
ejpam-2666	42	16	succeeded	succeed	VERB
ejpam-2666	42	17	in	in	ADP
ejpam-2666	42	18	finding	find	VERB
ejpam-2666	42	19	their	their	PRON
ejpam-2666	42	20	duals	dual	NOUN
ejpam-2666	42	21	and	and	CCONJ
ejpam-2666	42	22	obtained	obtain	VERB
ejpam-2666	42	23	a	a	DET
ejpam-2666	42	24	good	good	ADJ
ejpam-2666	42	25	number	number	NOUN
ejpam-2666	42	26	of	of	ADP
ejpam-2666	42	27	optimal	optimal	ADJ
ejpam-2666	42	28	codes	code	NOUN
ejpam-2666	42	29	.	.	PUNCT
ejpam-2666	43	1	in	in	ADP
ejpam-2666	43	2	this	this	DET
ejpam-2666	43	3	paper	paper	NOUN
ejpam-2666	43	4	,	,	PUNCT
ejpam-2666	43	5	extending	extend	VERB
ejpam-2666	43	6	the	the	DET
ejpam-2666	43	7	concepts	concept	NOUN
ejpam-2666	43	8	of	of	ADP
ejpam-2666	43	9	[	[	X
ejpam-2666	43	10	4	4	NUM
ejpam-2666	43	11	]	]	PUNCT
ejpam-2666	43	12	and	and	CCONJ
ejpam-2666	43	13	[	[	X
ejpam-2666	43	14	17	17	NUM
ejpam-2666	43	15	]	]	X
ejpam-2666	43	16	we	we	PRON
ejpam-2666	43	17	introduce	introduce	VERB
ejpam-2666	43	18	z2	z2	ADJ
ejpam-2666	43	19	-	-	PUNCT
ejpam-2666	43	20	triple	triple	ADJ
ejpam-2666	43	21	cyclic	cyclic	ADJ
ejpam-2666	43	22	codes	code	NOUN
ejpam-2666	43	23	and	and	CCONJ
ejpam-2666	43	24	study	study	VERB
ejpam-2666	43	25	their	their	PRON
ejpam-2666	43	26	algebraic	algebraic	ADJ
ejpam-2666	43	27	structure	structure	NOUN
ejpam-2666	43	28	.	.	PUNCT
ejpam-2666	44	1	we	we	PRON
ejpam-2666	44	2	give	give	VERB
ejpam-2666	44	3	a	a	DET
ejpam-2666	44	4	minimal	minimal	ADJ
ejpam-2666	44	5	spanning	span	VERB
ejpam-2666	44	6	set	set	NOUN
ejpam-2666	44	7	for	for	ADP
ejpam-2666	44	8	these	these	DET
ejpam-2666	44	9	codes	code	NOUN
ejpam-2666	44	10	.	.	PUNCT
ejpam-2666	45	1	further	far	ADV
ejpam-2666	45	2	we	we	PRON
ejpam-2666	45	3	present	present	VERB
ejpam-2666	45	4	the	the	DET
ejpam-2666	45	5	structure	structure	NOUN
ejpam-2666	45	6	of	of	ADP
ejpam-2666	45	7	duals	dual	NOUN
ejpam-2666	45	8	of	of	ADP
ejpam-2666	45	9	these	these	DET
ejpam-2666	45	10	codes	code	NOUN
ejpam-2666	45	11	via	via	ADP
ejpam-2666	45	12	their	their	PRON
ejpam-2666	45	13	generators	generator	NOUN
ejpam-2666	45	14	.	.	PUNCT
ejpam-2666	46	1	the	the	DET
ejpam-2666	46	2	paper	paper	NOUN
ejpam-2666	46	3	is	be	AUX
ejpam-2666	46	4	organized	organize	VERB
ejpam-2666	46	5	as	as	SCONJ
ejpam-2666	46	6	follows	follow	VERB
ejpam-2666	46	7	.	.	PUNCT
ejpam-2666	47	1	in	in	ADP
ejpam-2666	47	2	section	section	NOUN
ejpam-2666	47	3	2	2	NUM
ejpam-2666	47	4	,	,	PUNCT
ejpam-2666	47	5	we	we	PRON
ejpam-2666	47	6	introduce	introduce	VERB
ejpam-2666	47	7	some	some	DET
ejpam-2666	47	8	basic	basic	ADJ
ejpam-2666	47	9	notations	notation	NOUN
ejpam-2666	47	10	and	and	CCONJ
ejpam-2666	47	11	definitions	definition	NOUN
ejpam-2666	47	12	of	of	ADP
ejpam-2666	47	13	z2	z2	NOUN
ejpam-2666	47	14	-	-	PUNCT
ejpam-2666	47	15	triple	triple	ADJ
ejpam-2666	47	16	cyclic	cyclic	ADJ
ejpam-2666	47	17	codes	code	NOUN
ejpam-2666	47	18	and	and	CCONJ
ejpam-2666	47	19	derive	derive	VERB
ejpam-2666	47	20	the	the	DET
ejpam-2666	47	21	form	form	NOUN
ejpam-2666	47	22	of	of	ADP
ejpam-2666	47	23	their	their	PRON
ejpam-2666	47	24	generators	generator	NOUN
ejpam-2666	47	25	.	.	PUNCT
ejpam-2666	48	1	in	in	ADP
ejpam-2666	48	2	this	this	DET
ejpam-2666	48	3	section	section	NOUN
ejpam-2666	48	4	,	,	PUNCT
ejpam-2666	48	5	we	we	PRON
ejpam-2666	48	6	also	also	ADV
ejpam-2666	48	7	determine	determine	VERB
ejpam-2666	48	8	a	a	DET
ejpam-2666	48	9	minimal	minimal	ADJ
ejpam-2666	48	10	spanning	span	VERB
ejpam-2666	48	11	set	set	NOUN
ejpam-2666	48	12	for	for	ADP
ejpam-2666	48	13	z2	z2	NOUN
ejpam-2666	48	14	-	-	PUNCT
ejpam-2666	48	15	triple	triple	ADJ
ejpam-2666	48	16	cyclic	cyclic	ADJ
ejpam-2666	48	17	codes	code	NOUN
ejpam-2666	48	18	.	.	PUNCT
ejpam-2666	49	1	in	in	ADP
ejpam-2666	49	2	section	section	NOUN
ejpam-2666	49	3	3	3	NUM
ejpam-2666	49	4	,	,	PUNCT
ejpam-2666	49	5	we	we	PRON
ejpam-2666	49	6	study	study	VERB
ejpam-2666	49	7	the	the	DET
ejpam-2666	49	8	duals	dual	NOUN
ejpam-2666	49	9	of	of	ADP
ejpam-2666	49	10	z2	z2	NOUN
ejpam-2666	49	11	-	-	PUNCT
ejpam-2666	49	12	triple	triple	ADJ
ejpam-2666	49	13	cyclic	cyclic	ADJ
ejpam-2666	49	14	codes	code	NOUN
ejpam-2666	49	15	.	.	PUNCT
ejpam-2666	50	1	2	2	X
ejpam-2666	50	2	.	.	X
ejpam-2666	50	3	z2	z2	ADJ
ejpam-2666	50	4	-	-	PUNCT
ejpam-2666	50	5	triple	triple	ADJ
ejpam-2666	50	6	cyclic	cyclic	ADJ
ejpam-2666	50	7	codes	code	NOUN
ejpam-2666	50	8	let	let	VERB
ejpam-2666	50	9	r	r	NOUN
ejpam-2666	50	10	,	,	PUNCT
ejpam-2666	50	11	s	s	PART
ejpam-2666	50	12	and	and	CCONJ
ejpam-2666	50	13	t	t	PROPN
ejpam-2666	50	14	be	be	VERB
ejpam-2666	50	15	three	three	NUM
ejpam-2666	50	16	positive	positive	ADJ
ejpam-2666	50	17	integers	integer	NOUN
ejpam-2666	50	18	and	and	CCONJ
ejpam-2666	50	19	n	n	NOUN
ejpam-2666	50	20	=	=	SYM
ejpam-2666	51	1	r	r	NOUN
ejpam-2666	51	2	+	+	SYM
ejpam-2666	51	3	s	s	PART
ejpam-2666	51	4	+	+	X
ejpam-2666	51	5	t.	t.	NOUN
ejpam-2666	51	6	let	let	VERB
ejpam-2666	51	7	c	c	PRON
ejpam-2666	51	8	be	be	AUX
ejpam-2666	51	9	a	a	DET
ejpam-2666	51	10	binary	binary	ADJ
ejpam-2666	51	11	linear	linear	PROPN
ejpam-2666	51	12	code	code	NOUN
ejpam-2666	51	13	of	of	ADP
ejpam-2666	51	14	length	length	NOUN
ejpam-2666	51	15	n.	n.	PROPN
ejpam-2666	51	16	the	the	DET
ejpam-2666	51	17	n	n	NOUN
ejpam-2666	51	18	coordinates	coordinate	NOUN
ejpam-2666	51	19	of	of	ADP
ejpam-2666	51	20	each	each	DET
ejpam-2666	51	21	codeword	codeword	NOUN
ejpam-2666	51	22	of	of	ADP
ejpam-2666	51	23	c	c	PROPN
ejpam-2666	51	24	can	can	AUX
ejpam-2666	51	25	be	be	AUX
ejpam-2666	51	26	partitioned	partition	VERB
ejpam-2666	51	27	into	into	ADP
ejpam-2666	51	28	three	three	NUM
ejpam-2666	51	29	sets	set	NOUN
ejpam-2666	51	30	of	of	ADP
ejpam-2666	51	31	size	size	NOUN
ejpam-2666	51	32	r	r	NOUN
ejpam-2666	51	33	,	,	PUNCT
ejpam-2666	51	34	s	s	PART
ejpam-2666	51	35	and	and	CCONJ
ejpam-2666	51	36	t.	t.	PROPN
ejpam-2666	51	37	therefore	therefore	ADV
ejpam-2666	51	38	c	c	PROPN
ejpam-2666	51	39	is	be	AUX
ejpam-2666	51	40	a	a	DET
ejpam-2666	51	41	z2	z2	NUM
ejpam-2666	51	42	-	-	PUNCT
ejpam-2666	51	43	submodule	submodule	NOUN
ejpam-2666	51	44	of	of	ADP
ejpam-2666	51	45	zr2	zr2	PROPN
ejpam-2666	51	46	×	×	PROPN
ejpam-2666	51	47	zs2	zs2	PROPN
ejpam-2666	51	48	×	×	PROPN
ejpam-2666	51	49	zt2	zt2	PROPN
ejpam-2666	51	50	.	.	PUNCT
ejpam-2666	51	51	definition	definition	NOUN
ejpam-2666	51	52	1	1	NUM
ejpam-2666	51	53	.	.	PUNCT
ejpam-2666	52	1	for	for	ADP
ejpam-2666	52	2	any	any	DET
ejpam-2666	52	3	three	three	NUM
ejpam-2666	52	4	positive	positive	ADJ
ejpam-2666	52	5	integers	integer	NOUN
ejpam-2666	52	6	r	r	NOUN
ejpam-2666	52	7	,	,	PUNCT
ejpam-2666	52	8	s	s	PART
ejpam-2666	52	9	and	and	CCONJ
ejpam-2666	52	10	t	t	PROPN
ejpam-2666	52	11	,	,	PUNCT
ejpam-2666	52	12	a	a	DET
ejpam-2666	52	13	z2	z2	ADJ
ejpam-2666	52	14	-	-	PUNCT
ejpam-2666	52	15	triple	triple	ADJ
ejpam-2666	52	16	cyclic	cyclic	ADJ
ejpam-2666	52	17	code	code	NOUN
ejpam-2666	52	18	c	c	PROPN
ejpam-2666	52	19	of	of	ADP
ejpam-2666	52	20	block	block	NOUN
ejpam-2666	52	21	length	length	NOUN
ejpam-2666	52	22	(	(	PUNCT
ejpam-2666	52	23	r	r	NOUN
ejpam-2666	52	24	,	,	PUNCT
ejpam-2666	52	25	s	s	PROPN
ejpam-2666	52	26	,	,	PUNCT
ejpam-2666	52	27	t	t	PROPN
ejpam-2666	52	28	)	)	PUNCT
ejpam-2666	52	29	is	be	AUX
ejpam-2666	52	30	a	a	DET
ejpam-2666	52	31	binary	binary	ADJ
ejpam-2666	52	32	linear	linear	PROPN
ejpam-2666	52	33	code	code	NOUN
ejpam-2666	52	34	of	of	ADP
ejpam-2666	52	35	length	length	NOUN
ejpam-2666	53	1	n	n	NOUN
ejpam-2666	53	2	=	=	SYM
ejpam-2666	53	3	r	r	NOUN
ejpam-2666	54	1	+	+	CCONJ
ejpam-2666	54	2	s+	s+	ADP
ejpam-2666	54	3	t	t	NOUN
ejpam-2666	54	4	such	such	ADJ
ejpam-2666	54	5	that	that	SCONJ
ejpam-2666	54	6	σ(c	σ(c	PROPN
ejpam-2666	54	7	)	)	PUNCT
ejpam-2666	55	1	=	=	SYM
ejpam-2666	55	2	(	(	PUNCT
ejpam-2666	55	3	c1,r−1	c1,r−1	PROPN
ejpam-2666	55	4	,	,	PUNCT
ejpam-2666	55	5	c1,0	c1,0	PROPN
ejpam-2666	55	6	,	,	PUNCT
ejpam-2666	55	7	·	·	PUNCT
ejpam-2666	55	8	·	·	PUNCT
ejpam-2666	55	9	·	·	PUNCT
ejpam-2666	55	10	,	,	PUNCT
ejpam-2666	55	11	c1,r−2	c1,r−2	ADJ
ejpam-2666	55	12	|	|	ADP
ejpam-2666	55	13	c2,s−1	c2,s−1	NOUN
ejpam-2666	55	14	,	,	PUNCT
ejpam-2666	55	15	c2,0	c2,0	PROPN
ejpam-2666	55	16	,	,	PUNCT
ejpam-2666	55	17	·	·	PUNCT
ejpam-2666	55	18	·	·	PUNCT
ejpam-2666	55	19	·	·	PUNCT
ejpam-2666	55	20	,	,	PUNCT
ejpam-2666	55	21	c2,s−2	c2,s−2	VERB
ejpam-2666	55	22	|	|	ADV
ejpam-2666	55	23	c3,t−1	c3,t−1	NOUN
ejpam-2666	55	24	,	,	PUNCT
ejpam-2666	55	25	c3,0	c3,0	X
ejpam-2666	55	26	,	,	PUNCT
ejpam-2666	55	27	·	·	PUNCT
ejpam-2666	55	28	·	·	PUNCT
ejpam-2666	55	29	·	·	PUNCT
ejpam-2666	55	30	,	,	PUNCT
ejpam-2666	55	31	c3,t−2	c3,t−2	NOUN
ejpam-2666	55	32	)	)	PUNCT
ejpam-2666	55	33	∈	∈	PROPN
ejpam-2666	56	1	c	c	X
ejpam-2666	56	2	,	,	PUNCT
ejpam-2666	56	3	whenever	whenever	SCONJ
ejpam-2666	56	4	c	c	X
ejpam-2666	56	5	=	=	SYM
ejpam-2666	56	6	(	(	PUNCT
ejpam-2666	56	7	c1,0	c1,0	PROPN
ejpam-2666	56	8	,	,	PUNCT
ejpam-2666	56	9	c1,1	c1,1	PROPN
ejpam-2666	56	10	,	,	PUNCT
ejpam-2666	56	11	·	·	PUNCT
ejpam-2666	56	12	·	·	PUNCT
ejpam-2666	56	13	·	·	PUNCT
ejpam-2666	56	14	,	,	PUNCT
ejpam-2666	56	15	c1,r−1	c1,r−1	PROPN
ejpam-2666	56	16	|	|	ADV
ejpam-2666	56	17	c2,0	c2,0	PROPN
ejpam-2666	56	18	,	,	PUNCT
ejpam-2666	56	19	c2,1	c2,1	PROPN
ejpam-2666	56	20	,	,	PUNCT
ejpam-2666	56	21	·	·	PUNCT
ejpam-2666	56	22	·	·	PUNCT
ejpam-2666	56	23	·	·	PUNCT
ejpam-2666	56	24	,	,	PUNCT
ejpam-2666	56	25	c2,s−1	c2,s−1	NOUN
ejpam-2666	56	26	|	|	ADV
ejpam-2666	56	27	c3,0	c3,0	ADV
ejpam-2666	56	28	,	,	PUNCT
ejpam-2666	56	29	c3,1	c3,1	PROPN
ejpam-2666	56	30	,	,	PUNCT
ejpam-2666	56	31	·	·	PUNCT
ejpam-2666	56	32	·	·	PUNCT
ejpam-2666	56	33	·	·	PUNCT
ejpam-2666	56	34	,	,	PUNCT
ejpam-2666	56	35	c3,t−1	c3,t−1	NOUN
ejpam-2666	56	36	)	)	PUNCT
ejpam-2666	56	37	∈	∈	PROPN
ejpam-2666	56	38	c.	c.	NOUN
ejpam-2666	56	39	let	let	VERB
ejpam-2666	56	40	c	c	NOUN
ejpam-2666	56	41	be	be	AUX
ejpam-2666	56	42	a	a	DET
ejpam-2666	56	43	z2	z2	ADJ
ejpam-2666	56	44	-	-	PUNCT
ejpam-2666	56	45	triple	triple	ADJ
ejpam-2666	56	46	cyclic	cyclic	ADJ
ejpam-2666	56	47	code	code	NOUN
ejpam-2666	56	48	of	of	ADP
ejpam-2666	56	49	block	block	NOUN
ejpam-2666	56	50	length	length	NOUN
ejpam-2666	56	51	(	(	PUNCT
ejpam-2666	56	52	r	r	NOUN
ejpam-2666	56	53	,	,	PUNCT
ejpam-2666	56	54	s	s	PROPN
ejpam-2666	56	55	,	,	PUNCT
ejpam-2666	56	56	t	t	PROPN
ejpam-2666	56	57	)	)	PUNCT
ejpam-2666	56	58	.	.	PUNCT
ejpam-2666	57	1	let	let	VERB
ejpam-2666	57	2	cr	cr	NOUN
ejpam-2666	57	3	be	be	AUX
ejpam-2666	57	4	the	the	DET
ejpam-2666	57	5	canonical	canonical	ADJ
ejpam-2666	57	6	projection	projection	NOUN
ejpam-2666	57	7	of	of	ADP
ejpam-2666	57	8	c	c	PROPN
ejpam-2666	57	9	on	on	ADP
ejpam-2666	57	10	the	the	DET
ejpam-2666	57	11	first	first	ADJ
ejpam-2666	57	12	r	r	NOUN
ejpam-2666	57	13	coordinates	coordinate	NOUN
ejpam-2666	57	14	,	,	PUNCT
ejpam-2666	57	15	cs	cs	X
ejpam-2666	57	16	be	be	VERB
ejpam-2666	57	17	the	the	DET
ejpam-2666	57	18	projection	projection	NOUN
ejpam-2666	57	19	of	of	ADP
ejpam-2666	57	20	c	c	PROPN
ejpam-2666	57	21	on	on	ADP
ejpam-2666	57	22	next	next	PROPN
ejpam-2666	57	23	s	s	PART
ejpam-2666	57	24	coordinates	coordinate	NOUN
ejpam-2666	57	25	and	and	CCONJ
ejpam-2666	57	26	ct	ct	PRON
ejpam-2666	57	27	be	be	AUX
ejpam-2666	57	28	the	the	DET
ejpam-2666	57	29	projection	projection	NOUN
ejpam-2666	57	30	of	of	ADP
ejpam-2666	57	31	c	c	PROPN
ejpam-2666	57	32	on	on	ADP
ejpam-2666	57	33	the	the	DET
ejpam-2666	57	34	last	last	ADJ
ejpam-2666	57	35	t	t	NOUN
ejpam-2666	57	36	coordinates	coordinate	NOUN
ejpam-2666	57	37	.	.	PUNCT
ejpam-2666	58	1	it	it	PRON
ejpam-2666	58	2	is	be	AUX
ejpam-2666	58	3	easy	easy	ADJ
ejpam-2666	58	4	to	to	PART
ejpam-2666	58	5	see	see	VERB
ejpam-2666	58	6	that	that	SCONJ
ejpam-2666	58	7	these	these	DET
ejpam-2666	58	8	projections	projection	NOUN
ejpam-2666	58	9	cr	cr	ADP
ejpam-2666	58	10	,	,	PUNCT
ejpam-2666	58	11	cs	cs	PROPN
ejpam-2666	58	12	and	and	CCONJ
ejpam-2666	58	13	ct	ct	PROPN
ejpam-2666	58	14	are	be	AUX
ejpam-2666	58	15	binary	binary	ADJ
ejpam-2666	58	16	cyclic	cyclic	ADJ
ejpam-2666	58	17	codes	code	NOUN
ejpam-2666	58	18	of	of	ADP
ejpam-2666	58	19	lengths	length	NOUN
ejpam-2666	58	20	r	r	NOUN
ejpam-2666	58	21	,	,	PUNCT
ejpam-2666	58	22	s	s	X
ejpam-2666	58	23	and	and	CCONJ
ejpam-2666	58	24	t	t	PROPN
ejpam-2666	58	25	,	,	PUNCT
ejpam-2666	58	26	respectively	respectively	ADV
ejpam-2666	58	27	.	.	PUNCT
ejpam-2666	59	1	c	c	PROPN
ejpam-2666	59	2	is	be	AUX
ejpam-2666	59	3	called	call	VERB
ejpam-2666	59	4	separable	separable	ADJ
ejpam-2666	59	5	if	if	SCONJ
ejpam-2666	59	6	c	c	NOUN
ejpam-2666	59	7	=	=	SYM
ejpam-2666	59	8	cr	cr	PROPN
ejpam-2666	59	9	×	×	PROPN
ejpam-2666	59	10	cs	cs	PROPN
ejpam-2666	59	11	×	×	PROPN
ejpam-2666	59	12	ct	ct	PROPN
ejpam-2666	59	13	.	.	PUNCT
ejpam-2666	60	1	the	the	DET
ejpam-2666	60	2	dual	dual	ADJ
ejpam-2666	60	3	c⊥	c⊥	NOUN
ejpam-2666	60	4	of	of	ADP
ejpam-2666	60	5	a	a	DET
ejpam-2666	60	6	z2	z2	ADJ
ejpam-2666	60	7	-	-	PUNCT
ejpam-2666	60	8	triple	triple	ADJ
ejpam-2666	60	9	cyclic	cyclic	ADJ
ejpam-2666	60	10	code	code	NOUN
ejpam-2666	60	11	c	c	PROPN
ejpam-2666	60	12	of	of	ADP
ejpam-2666	60	13	block	block	NOUN
ejpam-2666	60	14	length	length	NOUN
ejpam-2666	60	15	(	(	PUNCT
ejpam-2666	60	16	r	r	NOUN
ejpam-2666	60	17	,	,	PUNCT
ejpam-2666	60	18	s	s	PROPN
ejpam-2666	60	19	,	,	PUNCT
ejpam-2666	60	20	t	t	PROPN
ejpam-2666	60	21	)	)	PUNCT
ejpam-2666	60	22	is	be	AUX
ejpam-2666	60	23	defined	define	VERB
ejpam-2666	60	24	as	as	ADP
ejpam-2666	60	25	c⊥	c⊥	NOUN
ejpam-2666	60	26	=	=	PUNCT
ejpam-2666	60	27	{	{	PUNCT
ejpam-2666	60	28	v′	v′	NOUN
ejpam-2666	60	29	∈	∈	PROPN
ejpam-2666	61	1	zr2	zr2	PROPN
ejpam-2666	61	2	×	×	PROPN
ejpam-2666	61	3	zs2	zs2	NOUN
ejpam-2666	61	4	×	×	NOUN
ejpam-2666	61	5	zt2	zt2	PROPN
ejpam-2666	62	1	|	|	ADV
ejpam-2666	62	2	v	v	X
ejpam-2666	62	3	·	·	PUNCT
ejpam-2666	62	4	v′	v′	X
ejpam-2666	62	5	=	=	SYM
ejpam-2666	62	6	0	0	NUM
ejpam-2666	62	7	for	for	ADP
ejpam-2666	62	8	all	all	PRON
ejpam-2666	62	9	v	v	ADP
ejpam-2666	62	10	∈	∈	ADJ
ejpam-2666	62	11	c	c	NOUN
ejpam-2666	62	12	}	}	PUNCT
ejpam-2666	62	13	,	,	PUNCT
ejpam-2666	62	14	where	where	SCONJ
ejpam-2666	62	15	v	v	X
ejpam-2666	62	16	·	·	PUNCT
ejpam-2666	62	17	v′	v′	NOUN
ejpam-2666	62	18	is	be	AUX
ejpam-2666	62	19	the	the	DET
ejpam-2666	62	20	usual	usual	ADJ
ejpam-2666	62	21	inner	inner	ADJ
ejpam-2666	62	22	product	product	NOUN
ejpam-2666	62	23	over	over	ADP
ejpam-2666	62	24	z2	z2	PROPN
ejpam-2666	62	25	.	.	PUNCT
ejpam-2666	63	1	let	let	VERB
ejpam-2666	63	2	m	m	NOUN
ejpam-2666	63	3	=	=	SYM
ejpam-2666	63	4	lcm(r	lcm(r	PROPN
ejpam-2666	63	5	,	,	PUNCT
ejpam-2666	63	6	s	s	PROPN
ejpam-2666	63	7	,	,	PUNCT
ejpam-2666	63	8	t	t	PROPN
ejpam-2666	63	9	)	)	PUNCT
ejpam-2666	63	10	.	.	PUNCT
ejpam-2666	64	1	the	the	DET
ejpam-2666	64	2	following	follow	VERB
ejpam-2666	64	3	result	result	NOUN
ejpam-2666	64	4	shows	show	VERB
ejpam-2666	64	5	that	that	SCONJ
ejpam-2666	64	6	the	the	DET
ejpam-2666	64	7	dual	dual	NOUN
ejpam-2666	64	8	of	of	ADP
ejpam-2666	64	9	a	a	DET
ejpam-2666	64	10	z2	z2	ADJ
ejpam-2666	64	11	-	-	PUNCT
ejpam-2666	64	12	triple	triple	ADJ
ejpam-2666	64	13	cyclic	cyclic	ADJ
ejpam-2666	64	14	code	code	NOUN
ejpam-2666	64	15	of	of	ADP
ejpam-2666	64	16	block	block	NOUN
ejpam-2666	64	17	length	length	NOUN
ejpam-2666	64	18	(	(	PUNCT
ejpam-2666	64	19	r	r	NOUN
ejpam-2666	64	20	,	,	PUNCT
ejpam-2666	64	21	s	s	PROPN
ejpam-2666	64	22	,	,	PUNCT
ejpam-2666	64	23	t	t	PROPN
ejpam-2666	64	24	)	)	PUNCT
ejpam-2666	64	25	is	be	AUX
ejpam-2666	64	26	also	also	ADV
ejpam-2666	64	27	a	a	DET
ejpam-2666	64	28	z2	z2	NUM
ejpam-2666	64	29	-	-	PUNCT
ejpam-2666	64	30	triple	triple	ADJ
ejpam-2666	64	31	cyclic	cyclic	ADJ
ejpam-2666	64	32	code	code	NOUN
ejpam-2666	64	33	of	of	ADP
ejpam-2666	64	34	same	same	ADJ
ejpam-2666	64	35	block	block	NOUN
ejpam-2666	64	36	length	length	NOUN
ejpam-2666	64	37	.	.	PUNCT
ejpam-2666	65	1	theorem	theorem	NOUN
ejpam-2666	65	2	1	1	NUM
ejpam-2666	65	3	.	.	PUNCT
ejpam-2666	66	1	if	if	SCONJ
ejpam-2666	66	2	c	c	PROPN
ejpam-2666	66	3	is	be	AUX
ejpam-2666	66	4	a	a	DET
ejpam-2666	66	5	z2	z2	ADJ
ejpam-2666	66	6	-	-	PUNCT
ejpam-2666	66	7	triple	triple	ADJ
ejpam-2666	66	8	cyclic	cyclic	ADJ
ejpam-2666	66	9	code	code	NOUN
ejpam-2666	66	10	of	of	ADP
ejpam-2666	66	11	block	block	NOUN
ejpam-2666	66	12	length	length	NOUN
ejpam-2666	66	13	(	(	PUNCT
ejpam-2666	66	14	r	r	NOUN
ejpam-2666	66	15	,	,	PUNCT
ejpam-2666	66	16	s	s	PROPN
ejpam-2666	66	17	,	,	PUNCT
ejpam-2666	66	18	t	t	PROPN
ejpam-2666	66	19	)	)	PUNCT
ejpam-2666	66	20	,	,	PUNCT
ejpam-2666	66	21	then	then	ADV
ejpam-2666	66	22	c⊥	c⊥	PROPN
ejpam-2666	66	23	is	be	AUX
ejpam-2666	66	24	also	also	ADV
ejpam-2666	66	25	z2	z2	ADJ
ejpam-2666	66	26	-	-	PUNCT
ejpam-2666	66	27	triple	triple	ADJ
ejpam-2666	66	28	cyclic	cyclic	ADJ
ejpam-2666	66	29	code	code	NOUN
ejpam-2666	66	30	of	of	ADP
ejpam-2666	66	31	block	block	NOUN
ejpam-2666	66	32	length	length	NOUN
ejpam-2666	66	33	(	(	PUNCT
ejpam-2666	66	34	r	r	NOUN
ejpam-2666	66	35	,	,	PUNCT
ejpam-2666	66	36	s	s	PROPN
ejpam-2666	66	37	,	,	PUNCT
ejpam-2666	66	38	t	t	PROPN
ejpam-2666	66	39	)	)	PUNCT
ejpam-2666	66	40	.	.	PUNCT
ejpam-2666	67	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	67	2	b	b	PROPN
ejpam-2666	67	3	,	,	PUNCT
ejpam-2666	67	4	maheshanand	maheshanand	NOUN
ejpam-2666	67	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	67	6	/	/	SYM
ejpam-2666	67	7	eur	eur	PROPN
ejpam-2666	67	8	.	.	PUNCT
ejpam-2666	68	1	j.	j.	PROPN
ejpam-2666	68	2	pure	pure	PROPN
ejpam-2666	68	3	appl	appl	PROPN
ejpam-2666	68	4	.	.	PROPN
ejpam-2666	68	5	math	math	PROPN
ejpam-2666	68	6	,	,	PUNCT
ejpam-2666	68	7	10	10	NUM
ejpam-2666	68	8	(	(	PUNCT
ejpam-2666	68	9	2	2	NUM
ejpam-2666	68	10	)	)	PUNCT
ejpam-2666	68	11	(	(	PUNCT
ejpam-2666	68	12	2017	2017	NUM
ejpam-2666	68	13	)	)	PUNCT
ejpam-2666	68	14	,	,	PUNCT
ejpam-2666	68	15	392	392	NUM
ejpam-2666	68	16	-	-	SYM
ejpam-2666	68	17	409	409	NUM
ejpam-2666	68	18	394	394	NUM
ejpam-2666	68	19	proof	proof	NOUN
ejpam-2666	68	20	.	.	PUNCT
ejpam-2666	69	1	let	let	VERB
ejpam-2666	69	2	u	u	PRON
ejpam-2666	69	3	∈	∈	PROPN
ejpam-2666	69	4	c⊥	c⊥	NOUN
ejpam-2666	69	5	and	and	CCONJ
ejpam-2666	69	6	v	v	ADP
ejpam-2666	69	7	∈	∈	PROPN
ejpam-2666	69	8	c.	c.	NOUN
ejpam-2666	69	9	since	since	SCONJ
ejpam-2666	69	10	c	c	PROPN
ejpam-2666	69	11	is	be	AUX
ejpam-2666	69	12	invariant	invariant	ADJ
ejpam-2666	69	13	under	under	ADP
ejpam-2666	69	14	σ	σ	PROPN
ejpam-2666	69	15	,	,	PUNCT
ejpam-2666	69	16	σm−1(v	σm−1(v	ADJ
ejpam-2666	69	17	)	)	PUNCT
ejpam-2666	69	18	∈	∈	PROPN
ejpam-2666	69	19	c.	c.	NOUN
ejpam-2666	69	20	therefore	therefore	ADV
ejpam-2666	69	21	0	0	X
ejpam-2666	69	22	=	=	SYM
ejpam-2666	69	23	u	u	PROPN
ejpam-2666	69	24	·	·	PUNCT
ejpam-2666	69	25	σm−1(v	σm−1(v	NUM
ejpam-2666	69	26	)	)	PUNCT
ejpam-2666	69	27	=	=	PUNCT
ejpam-2666	70	1	(	(	PUNCT
ejpam-2666	70	2	u1,0v1,1	u1,0v1,1	PUNCT
ejpam-2666	70	3	+	+	PROPN
ejpam-2666	70	4	·	·	PUNCT
ejpam-2666	70	5	·	·	PUNCT
ejpam-2666	70	6	·	·	PUNCT
ejpam-2666	70	7	+	+	NUM
ejpam-2666	70	8	u1,r−2v1,r−1	u1,r−2v1,r−1	NOUN
ejpam-2666	70	9	+	+	NUM
ejpam-2666	70	10	u1,r−1v1,0	u1,r−1v1,0	PROPN
ejpam-2666	70	11	)	)	PUNCT
ejpam-2666	71	1	+	+	CCONJ
ejpam-2666	71	2	(	(	PUNCT
ejpam-2666	71	3	u2,0v2,1	u2,0v2,1	NUM
ejpam-2666	71	4	+	+	CCONJ
ejpam-2666	71	5	·	·	PUNCT
ejpam-2666	71	6	·	·	PUNCT
ejpam-2666	71	7	·	·	PUNCT
ejpam-2666	71	8	+	+	NUM
ejpam-2666	71	9	u2,s−1v2,0	u2,s−1v2,0	PROPN
ejpam-2666	71	10	)	)	PUNCT
ejpam-2666	72	1	+	+	CCONJ
ejpam-2666	72	2	(	(	PUNCT
ejpam-2666	72	3	u3,0v3,1	u3,0v3,1	NUM
ejpam-2666	72	4	+	+	CCONJ
ejpam-2666	72	5	·	·	PUNCT
ejpam-2666	72	6	·	·	PUNCT
ejpam-2666	72	7	·	·	PUNCT
ejpam-2666	72	8	+	+	NUM
ejpam-2666	72	9	u3,t−1v3,0	u3,t−1v3,0	SYM
ejpam-2666	72	10	)	)	PUNCT
ejpam-2666	72	11	=	=	SYM
ejpam-2666	72	12	(	(	PUNCT
ejpam-2666	72	13	u1,r−1v1,0	u1,r−1v1,0	PROPN
ejpam-2666	72	14	+	+	CCONJ
ejpam-2666	72	15	u1,0v1,1	u1,0v1,1	PROPN
ejpam-2666	72	16	+	+	PROPN
ejpam-2666	72	17	·	·	PUNCT
ejpam-2666	72	18	·	·	PUNCT
ejpam-2666	72	19	·	·	PUNCT
ejpam-2666	72	20	+	+	NUM
ejpam-2666	72	21	u1,r−2v1,r−1	u1,r−2v1,r−1	NUM
ejpam-2666	72	22	)	)	PUNCT
ejpam-2666	73	1	+	+	CCONJ
ejpam-2666	73	2	(	(	PUNCT
ejpam-2666	73	3	u2,s−1v2,0	u2,s−1v2,0	PROPN
ejpam-2666	73	4	+	+	X
ejpam-2666	73	5	·	·	PUNCT
ejpam-2666	73	6	·	·	PUNCT
ejpam-2666	73	7	·	·	PUNCT
ejpam-2666	73	8	+	+	NUM
ejpam-2666	73	9	u2,s−2v2,s−1	u2,s−2v2,s−1	PRON
ejpam-2666	73	10	)	)	PUNCT
ejpam-2666	74	1	+	+	CCONJ
ejpam-2666	74	2	(	(	PUNCT
ejpam-2666	74	3	u3,t−1v3,0	u3,t−1v3,0	PROPN
ejpam-2666	74	4	+	+	CCONJ
ejpam-2666	74	5	·	·	PUNCT
ejpam-2666	74	6	·	·	PUNCT
ejpam-2666	74	7	·	·	PUNCT
ejpam-2666	74	8	+	+	NUM
ejpam-2666	74	9	u3,t−2v3,t−1	u3,t−2v3,t−1	SYM
ejpam-2666	74	10	)	)	PUNCT
ejpam-2666	74	11	=	=	SYM
ejpam-2666	74	12	σ(u	σ(u	NOUN
ejpam-2666	74	13	)	)	PUNCT
ejpam-2666	74	14	·	·	PUNCT
ejpam-2666	75	1	v.	v.	CCONJ
ejpam-2666	75	2	as	as	SCONJ
ejpam-2666	75	3	u	u	NOUN
ejpam-2666	75	4	is	be	AUX
ejpam-2666	75	5	an	an	DET
ejpam-2666	75	6	arbitrary	arbitrary	ADJ
ejpam-2666	75	7	element	element	NOUN
ejpam-2666	75	8	of	of	ADP
ejpam-2666	75	9	c⊥	c⊥	PROPN
ejpam-2666	75	10	,	,	PUNCT
ejpam-2666	75	11	the	the	DET
ejpam-2666	75	12	result	result	NOUN
ejpam-2666	75	13	follows	follow	VERB
ejpam-2666	75	14	.	.	PUNCT
ejpam-2666	76	1	now	now	ADV
ejpam-2666	76	2	we	we	PRON
ejpam-2666	76	3	determine	determine	VERB
ejpam-2666	76	4	the	the	DET
ejpam-2666	76	5	generators	generator	NOUN
ejpam-2666	76	6	for	for	ADP
ejpam-2666	76	7	a	a	DET
ejpam-2666	76	8	z2	z2	ADJ
ejpam-2666	76	9	-	-	PUNCT
ejpam-2666	76	10	triple	triple	ADJ
ejpam-2666	76	11	cyclic	cyclic	ADJ
ejpam-2666	76	12	code	code	NOUN
ejpam-2666	76	13	c	c	PROPN
ejpam-2666	76	14	of	of	ADP
ejpam-2666	76	15	block	block	NOUN
ejpam-2666	76	16	length	length	NOUN
ejpam-2666	76	17	(	(	PUNCT
ejpam-2666	76	18	r	r	NOUN
ejpam-2666	76	19	,	,	PUNCT
ejpam-2666	76	20	s	s	PROPN
ejpam-2666	76	21	,	,	PUNCT
ejpam-2666	76	22	t	t	PROPN
ejpam-2666	76	23	)	)	PUNCT
ejpam-2666	76	24	.	.	PUNCT
ejpam-2666	77	1	for	for	ADP
ejpam-2666	77	2	this	this	PRON
ejpam-2666	77	3	,	,	PUNCT
ejpam-2666	77	4	we	we	PRON
ejpam-2666	77	5	first	first	ADV
ejpam-2666	77	6	consider	consider	VERB
ejpam-2666	77	7	the	the	DET
ejpam-2666	77	8	algebraic	algebraic	ADJ
ejpam-2666	77	9	structure	structure	NOUN
ejpam-2666	77	10	of	of	ADP
ejpam-2666	77	11	c	c	PROPN
ejpam-2666	77	12	in	in	ADP
ejpam-2666	77	13	z2[x	z2[x	PROPN
ejpam-2666	77	14	]	]	PUNCT
ejpam-2666	78	1	〈	〈	PROPN
ejpam-2666	78	2	xr−1	xr−1	PROPN
ejpam-2666	78	3	〉	〉	PROPN
ejpam-2666	78	4	×	×	PROPN
ejpam-2666	78	5	z2[x	z2[x	X
ejpam-2666	78	6	]	]	PUNCT
ejpam-2666	79	1	〈	〈	PROPN
ejpam-2666	79	2	xs−1	xs−1	PROPN
ejpam-2666	79	3	〉	〉	PROPN
ejpam-2666	79	4	×	×	NOUN
ejpam-2666	79	5	z2[x	z2[x	X
ejpam-2666	79	6	]	]	PUNCT
ejpam-2666	79	7	〈	〈	PROPN
ejpam-2666	79	8	xt−1	xt−1	PROPN
ejpam-2666	79	9	〉	〉	PROPN
ejpam-2666	79	10	.	.	PUNCT
ejpam-2666	80	1	let	let	VERB
ejpam-2666	80	2	rr	rr	VERB
ejpam-2666	80	3	,	,	PUNCT
ejpam-2666	80	4	s	s	X
ejpam-2666	80	5	,	,	PUNCT
ejpam-2666	80	6	t[x	t[x	NOUN
ejpam-2666	80	7	]	]	X
ejpam-2666	80	8	=	=	SYM
ejpam-2666	80	9	z2[x	z2[x	PROPN
ejpam-2666	80	10	]	]	PUNCT
ejpam-2666	81	1	〈	〈	PROPN
ejpam-2666	81	2	xr−1	xr−1	PROPN
ejpam-2666	81	3	〉	〉	PROPN
ejpam-2666	81	4	×	×	PROPN
ejpam-2666	81	5	z2[x	z2[x	X
ejpam-2666	81	6	]	]	PUNCT
ejpam-2666	82	1	〈	〈	PROPN
ejpam-2666	82	2	xs−1	xs−1	PROPN
ejpam-2666	82	3	〉	〉	PROPN
ejpam-2666	82	4	×	×	NOUN
ejpam-2666	82	5	z2[x	z2[x	X
ejpam-2666	82	6	]	]	PUNCT
ejpam-2666	83	1	〈	〈	PROPN
ejpam-2666	83	2	xt−1	xt−1	PROPN
ejpam-2666	83	3	〉	〉	PROPN
ejpam-2666	83	4	,	,	PUNCT
ejpam-2666	83	5	z2,r[x	z2,r[x	PROPN
ejpam-2666	83	6	]	]	PUNCT
ejpam-2666	84	1	=	=	SYM
ejpam-2666	84	2	z2[x	z2[x	PROPN
ejpam-2666	84	3	]	]	PUNCT
ejpam-2666	85	1	〈	〈	PROPN
ejpam-2666	85	2	xr−1	xr−1	PROPN
ejpam-2666	85	3	〉	〉	PROPN
ejpam-2666	85	4	,	,	PUNCT
ejpam-2666	85	5	z2,s[x	z2,s[x	PROPN
ejpam-2666	85	6	]	]	X
ejpam-2666	85	7	=	=	SYM
ejpam-2666	85	8	z2[x	z2[x	PROPN
ejpam-2666	85	9	]	]	PUNCT
ejpam-2666	85	10	〈	〈	PROPN
ejpam-2666	85	11	xs−1	xs−1	PROPN
ejpam-2666	85	12	〉	〉	PROPN
ejpam-2666	85	13	and	and	CCONJ
ejpam-2666	85	14	z2,t[x	z2,t[x	PROPN
ejpam-2666	85	15	]	]	X
ejpam-2666	85	16	=	=	SYM
ejpam-2666	85	17	z2[x	z2[x	PROPN
ejpam-2666	85	18	]	]	PUNCT
ejpam-2666	86	1	〈	〈	PROPN
ejpam-2666	86	2	xt−1	xt−1	PROPN
ejpam-2666	86	3	〉	〉	PROPN
ejpam-2666	86	4	.	.	PUNCT
ejpam-2666	87	1	by	by	ADP
ejpam-2666	87	2	identifying	identify	VERB
ejpam-2666	87	3	each	each	DET
ejpam-2666	87	4	c	c	NOUN
ejpam-2666	87	5	=	=	SYM
ejpam-2666	87	6	(	(	PUNCT
ejpam-2666	87	7	c1	c1	PROPN
ejpam-2666	87	8	|	|	ADV
ejpam-2666	87	9	c2	c2	PROPN
ejpam-2666	87	10	|	|	PROPN
ejpam-2666	87	11	c3	c3	PROPN
ejpam-2666	87	12	)	)	PUNCT
ejpam-2666	87	13	∈	∈	PROPN
ejpam-2666	87	14	zr2	zr2	PROPN
ejpam-2666	87	15	×	×	PROPN
ejpam-2666	87	16	zs2	zs2	PROPN
ejpam-2666	87	17	×	×	PROPN
ejpam-2666	87	18	zt2	zt2	NOUN
ejpam-2666	87	19	with	with	ADP
ejpam-2666	87	20	a	a	DET
ejpam-2666	87	21	triplet	triplet	NOUN
ejpam-2666	87	22	of	of	ADP
ejpam-2666	87	23	polynomials	polynomial	NOUN
ejpam-2666	87	24	(	(	PUNCT
ejpam-2666	87	25	c1(x	c1(x	NOUN
ejpam-2666	87	26	)	)	PUNCT
ejpam-2666	87	27	|	|	ADV
ejpam-2666	87	28	c2(x	c2(x	NOUN
ejpam-2666	87	29	)	)	PUNCT
ejpam-2666	87	30	|	|	ADV
ejpam-2666	87	31	c3(x	c3(x	NOUN
ejpam-2666	87	32	)	)	PUNCT
ejpam-2666	87	33	)	)	PUNCT
ejpam-2666	87	34	∈	∈	PROPN
ejpam-2666	87	35	rr	rr	PROPN
ejpam-2666	87	36	,	,	PUNCT
ejpam-2666	87	37	s	s	PROPN
ejpam-2666	87	38	,	,	PUNCT
ejpam-2666	87	39	t[x	t[x	NOUN
ejpam-2666	87	40	]	]	SYM
ejpam-2666	87	41	,	,	PUNCT
ejpam-2666	87	42	where	where	SCONJ
ejpam-2666	87	43	c1(x	c1(x	NOUN
ejpam-2666	87	44	)	)	PUNCT
ejpam-2666	87	45	=	=	SYM
ejpam-2666	87	46	∑r−1	∑r−1	PROPN
ejpam-2666	87	47	j=0	j=0	PROPN
ejpam-2666	87	48	c1,jx	c1,jx	PROPN
ejpam-2666	87	49	j	j	PROPN
ejpam-2666	87	50	,	,	PUNCT
ejpam-2666	87	51	c2(x	c2(x	PROPN
ejpam-2666	87	52	)	)	PUNCT
ejpam-2666	87	53	=	=	SYM
ejpam-2666	87	54	∑s−1	∑s−1	PROPN
ejpam-2666	87	55	j=0	j=0	PROPN
ejpam-2666	87	56	c2,jx	c2,jx	PROPN
ejpam-2666	87	57	j	j	PROPN
ejpam-2666	87	58	and	and	CCONJ
ejpam-2666	87	59	c3(x	c3(x	NOUN
ejpam-2666	87	60	)	)	PUNCT
ejpam-2666	87	61	=	=	SYM
ejpam-2666	87	62	∑t−1	∑t−1	NOUN
ejpam-2666	87	63	k=0	k=0	PROPN
ejpam-2666	87	64	c3,jx	c3,jx	PROPN
ejpam-2666	87	65	j	j	NOUN
ejpam-2666	87	66	,	,	PUNCT
ejpam-2666	87	67	we	we	PRON
ejpam-2666	87	68	get	get	VERB
ejpam-2666	87	69	a	a	DET
ejpam-2666	87	70	z2	z2	ADJ
ejpam-2666	87	71	-	-	PUNCT
ejpam-2666	87	72	module	module	NOUN
ejpam-2666	87	73	isomorphism	isomorphism	NOUN
ejpam-2666	87	74	between	between	ADP
ejpam-2666	87	75	zr2×zs2×zt2	zr2×zs2×zt2	PROPN
ejpam-2666	87	76	and	and	CCONJ
ejpam-2666	87	77	rr	rr	PROPN
ejpam-2666	87	78	,	,	PUNCT
ejpam-2666	87	79	s	s	PROPN
ejpam-2666	87	80	,	,	PUNCT
ejpam-2666	87	81	t[x	t[x	NOUN
ejpam-2666	87	82	]	]	PUNCT
ejpam-2666	87	83	.	.	PUNCT
ejpam-2666	88	1	also	also	ADV
ejpam-2666	88	2	for	for	ADP
ejpam-2666	88	3	any	any	DET
ejpam-2666	88	4	f(x	f(x	PROPN
ejpam-2666	88	5	)	)	PUNCT
ejpam-2666	88	6	∈	∈	PROPN
ejpam-2666	88	7	z2[x	z2[x	PROPN
ejpam-2666	88	8	]	]	PUNCT
ejpam-2666	88	9	and	and	CCONJ
ejpam-2666	88	10	c	c	X
ejpam-2666	88	11	=	=	SYM
ejpam-2666	88	12	(	(	PUNCT
ejpam-2666	88	13	c1(x	c1(x	NOUN
ejpam-2666	88	14	)	)	PUNCT
ejpam-2666	88	15	|	|	ADV
ejpam-2666	88	16	c2(x	c2(x	NOUN
ejpam-2666	88	17	)	)	PUNCT
ejpam-2666	88	18	|	|	ADV
ejpam-2666	88	19	c3(x	c3(x	NOUN
ejpam-2666	88	20	)	)	PUNCT
ejpam-2666	88	21	)	)	PUNCT
ejpam-2666	89	1	∈	∈	PROPN
ejpam-2666	89	2	rr	rr	PROPN
ejpam-2666	89	3	,	,	PUNCT
ejpam-2666	89	4	s	s	PROPN
ejpam-2666	89	5	,	,	PUNCT
ejpam-2666	89	6	t[x	t[x	NOUN
ejpam-2666	89	7	]	]	PUNCT
ejpam-2666	89	8	,	,	PUNCT
ejpam-2666	89	9	we	we	PRON
ejpam-2666	89	10	define	define	VERB
ejpam-2666	89	11	the	the	DET
ejpam-2666	89	12	product	product	NOUN
ejpam-2666	89	13	f(x	f(x	PROPN
ejpam-2666	89	14	)	)	PUNCT
ejpam-2666	89	15	∗	∗	NOUN
ejpam-2666	89	16	(	(	PUNCT
ejpam-2666	89	17	c1(x	c1(x	NOUN
ejpam-2666	89	18	)	)	PUNCT
ejpam-2666	89	19	|	|	ADV
ejpam-2666	89	20	c2(x	c2(x	NOUN
ejpam-2666	89	21	)	)	PUNCT
ejpam-2666	89	22	|	|	ADV
ejpam-2666	89	23	c3(x	c3(x	NOUN
ejpam-2666	89	24	)	)	PUNCT
ejpam-2666	89	25	)	)	PUNCT
ejpam-2666	90	1	=	=	SYM
ejpam-2666	90	2	(	(	PUNCT
ejpam-2666	90	3	f(x)c1(x	f(x)c1(x	NOUN
ejpam-2666	90	4	)	)	PUNCT
ejpam-2666	90	5	|	|	ADV
ejpam-2666	90	6	f(x)c2(x	f(x)c2(x	ADJ
ejpam-2666	90	7	)	)	PUNCT
ejpam-2666	90	8	|	|	CCONJ
ejpam-2666	90	9	f(x)c3(x	f(x)c3(x	NOUN
ejpam-2666	90	10	)	)	PUNCT
ejpam-2666	90	11	)	)	PUNCT
ejpam-2666	91	1	∈	∈	PROPN
ejpam-2666	91	2	rr	rr	PROPN
ejpam-2666	91	3	,	,	PUNCT
ejpam-2666	91	4	s	s	PROPN
ejpam-2666	91	5	,	,	PUNCT
ejpam-2666	91	6	t[x	t[x	NOUN
ejpam-2666	91	7	]	]	SYM
ejpam-2666	91	8	,	,	PUNCT
ejpam-2666	91	9	where	where	SCONJ
ejpam-2666	91	10	f(x)ci(x	f(x)ci(x	NOUN
ejpam-2666	91	11	)	)	PUNCT
ejpam-2666	91	12	is	be	AUX
ejpam-2666	91	13	determined	determine	VERB
ejpam-2666	91	14	in	in	ADP
ejpam-2666	91	15	the	the	DET
ejpam-2666	91	16	corresponding	corresponding	ADJ
ejpam-2666	91	17	residue	residue	NOUN
ejpam-2666	91	18	ring	ring	NOUN
ejpam-2666	91	19	.	.	PUNCT
ejpam-2666	92	1	clearly	clearly	ADV
ejpam-2666	92	2	this	this	DET
ejpam-2666	92	3	product	product	NOUN
ejpam-2666	92	4	is	be	AUX
ejpam-2666	92	5	well	well	ADV
ejpam-2666	92	6	defined	define	VERB
ejpam-2666	92	7	.	.	PUNCT
ejpam-2666	93	1	therefore	therefore	ADV
ejpam-2666	93	2	rr	rr	VERB
ejpam-2666	93	3	,	,	PUNCT
ejpam-2666	93	4	s	s	X
ejpam-2666	93	5	,	,	PUNCT
ejpam-2666	93	6	t[x	t[x	NOUN
ejpam-2666	93	7	]	]	PUNCT
ejpam-2666	93	8	is	be	AUX
ejpam-2666	93	9	a	a	DET
ejpam-2666	93	10	z2[x]-module	z2[x]-module	NOUN
ejpam-2666	93	11	with	with	ADP
ejpam-2666	93	12	respect	respect	NOUN
ejpam-2666	93	13	to	to	ADP
ejpam-2666	93	14	this	this	DET
ejpam-2666	93	15	product	product	NOUN
ejpam-2666	93	16	.	.	PUNCT
ejpam-2666	94	1	we	we	PRON
ejpam-2666	94	2	note	note	VERB
ejpam-2666	94	3	that	that	SCONJ
ejpam-2666	94	4	,	,	PUNCT
ejpam-2666	94	5	in	in	ADP
ejpam-2666	94	6	polynomial	polynomial	ADJ
ejpam-2666	94	7	representation	representation	NOUN
ejpam-2666	94	8	,	,	PUNCT
ejpam-2666	94	9	x(c1(x	x(c1(x	PROPN
ejpam-2666	94	10	)	)	PUNCT
ejpam-2666	95	1	|	|	ADV
ejpam-2666	95	2	c2(x	c2(x	NOUN
ejpam-2666	95	3	)	)	PUNCT
ejpam-2666	95	4	|	|	ADV
ejpam-2666	95	5	c3(x	c3(x	NOUN
ejpam-2666	95	6	)	)	PUNCT
ejpam-2666	95	7	)	)	PUNCT
ejpam-2666	96	1	=	=	PRON
ejpam-2666	96	2	(	(	PUNCT
ejpam-2666	96	3	xc1(x	xc1(x	PROPN
ejpam-2666	96	4	)	)	PUNCT
ejpam-2666	96	5	|	|	ADV
ejpam-2666	96	6	xc2(x	xc2(x	PROPN
ejpam-2666	96	7	)	)	PUNCT
ejpam-2666	96	8	|	|	ADV
ejpam-2666	96	9	xc3(x	xc3(x	PROPN
ejpam-2666	96	10	)	)	PUNCT
ejpam-2666	96	11	)	)	PUNCT
ejpam-2666	96	12	represents	represent	VERB
ejpam-2666	96	13	σ(c	σ(c	PROPN
ejpam-2666	96	14	)	)	PUNCT
ejpam-2666	96	15	for	for	ADP
ejpam-2666	96	16	the	the	DET
ejpam-2666	96	17	corresponding	corresponding	ADJ
ejpam-2666	96	18	element	element	NOUN
ejpam-2666	96	19	c	c	PROPN
ejpam-2666	96	20	=	=	PUNCT
ejpam-2666	96	21	(	(	PUNCT
ejpam-2666	96	22	c1	c1	PROPN
ejpam-2666	96	23	|	|	ADV
ejpam-2666	96	24	c2	c2	PROPN
ejpam-2666	96	25	|	|	PROPN
ejpam-2666	96	26	c3	c3	PROPN
ejpam-2666	96	27	)	)	PUNCT
ejpam-2666	96	28	∈	∈	PROPN
ejpam-2666	96	29	zr2	zr2	PROPN
ejpam-2666	96	30	×zs2	×zs2	X
ejpam-2666	96	31	×zt2	×zt2	PUNCT
ejpam-2666	96	32	.	.	PUNCT
ejpam-2666	97	1	the	the	DET
ejpam-2666	97	2	codes	code	NOUN
ejpam-2666	97	3	in	in	ADP
ejpam-2666	97	4	the	the	DET
ejpam-2666	97	5	present	present	ADJ
ejpam-2666	97	6	setting	setting	NOUN
ejpam-2666	97	7	are	be	AUX
ejpam-2666	97	8	in	in	ADP
ejpam-2666	97	9	fact	fact	NOUN
ejpam-2666	97	10	the	the	DET
ejpam-2666	97	11	extensions	extension	NOUN
ejpam-2666	97	12	of	of	ADP
ejpam-2666	97	13	both	both	CCONJ
ejpam-2666	97	14	binary	binary	PROPN
ejpam-2666	97	15	cyclic	cyclic	PROPN
ejpam-2666	97	16	codes	code	NOUN
ejpam-2666	97	17	and	and	CCONJ
ejpam-2666	97	18	z2	z2	ADJ
ejpam-2666	97	19	-	-	PUNCT
ejpam-2666	97	20	double	double	ADJ
ejpam-2666	97	21	cyclic	cyclic	NOUN
ejpam-2666	97	22	codes	code	NOUN
ejpam-2666	97	23	that	that	PRON
ejpam-2666	97	24	defined	define	VERB
ejpam-2666	97	25	in	in	ADP
ejpam-2666	97	26	[	[	X
ejpam-2666	97	27	4	4	NUM
ejpam-2666	97	28	]	]	PUNCT
ejpam-2666	97	29	.	.	PUNCT
ejpam-2666	98	1	we	we	PRON
ejpam-2666	98	2	denote	denote	VERB
ejpam-2666	98	3	f	f	PROPN
ejpam-2666	98	4	∗	∗	NOUN
ejpam-2666	98	5	g	g	PROPN
ejpam-2666	98	6	simply	simply	ADV
ejpam-2666	98	7	by	by	ADP
ejpam-2666	98	8	fg	fg	PRON
ejpam-2666	98	9	.	.	PUNCT
ejpam-2666	99	1	the	the	DET
ejpam-2666	99	2	following	following	ADJ
ejpam-2666	99	3	result	result	NOUN
ejpam-2666	99	4	follows	follow	VERB
ejpam-2666	99	5	immediately	immediately	ADV
ejpam-2666	99	6	from	from	ADP
ejpam-2666	99	7	the	the	DET
ejpam-2666	99	8	previous	previous	ADJ
ejpam-2666	99	9	discussion	discussion	NOUN
ejpam-2666	99	10	.	.	PUNCT
ejpam-2666	100	1	theorem	theorem	NOUN
ejpam-2666	100	2	2	2	NUM
ejpam-2666	100	3	.	.	PUNCT
ejpam-2666	101	1	let	let	VERB
ejpam-2666	101	2	c	c	PRON
ejpam-2666	101	3	be	be	AUX
ejpam-2666	101	4	a	a	DET
ejpam-2666	101	5	binary	binary	ADJ
ejpam-2666	101	6	linear	linear	PROPN
ejpam-2666	101	7	code	code	NOUN
ejpam-2666	101	8	of	of	ADP
ejpam-2666	101	9	length	length	NOUN
ejpam-2666	101	10	r+s+	r+s+	NOUN
ejpam-2666	102	1	t.	t.	PROPN
ejpam-2666	102	2	then	then	ADV
ejpam-2666	102	3	c	c	PROPN
ejpam-2666	102	4	is	be	AUX
ejpam-2666	102	5	a	a	DET
ejpam-2666	102	6	z2	z2	ADJ
ejpam-2666	102	7	-	-	PUNCT
ejpam-2666	102	8	triple	triple	ADJ
ejpam-2666	102	9	cyclic	cyclic	ADJ
ejpam-2666	102	10	code	code	NOUN
ejpam-2666	102	11	in	in	ADP
ejpam-2666	102	12	zr2	zr2	PROPN
ejpam-2666	102	13	×	×	PROPN
ejpam-2666	102	14	zs2	zs2	NOUN
ejpam-2666	102	15	×	×	NOUN
ejpam-2666	102	16	zt2	zt2	INTJ
ejpam-2666	103	1	if	if	SCONJ
ejpam-2666	103	2	and	and	CCONJ
ejpam-2666	103	3	only	only	ADV
ejpam-2666	103	4	if	if	SCONJ
ejpam-2666	103	5	c	c	PROPN
ejpam-2666	103	6	is	be	AUX
ejpam-2666	103	7	a	a	DET
ejpam-2666	103	8	z2[x]-submodule	z2[x]-submodule	PROPN
ejpam-2666	103	9	of	of	ADP
ejpam-2666	103	10	rr	rr	PROPN
ejpam-2666	103	11	,	,	PUNCT
ejpam-2666	103	12	s	s	PROPN
ejpam-2666	103	13	,	,	PUNCT
ejpam-2666	103	14	t[x	t[x	NOUN
ejpam-2666	103	15	]	]	PUNCT
ejpam-2666	103	16	.	.	PUNCT
ejpam-2666	104	1	since	since	SCONJ
ejpam-2666	104	2	both	both	CCONJ
ejpam-2666	104	3	the	the	DET
ejpam-2666	104	4	modules	module	NOUN
ejpam-2666	104	5	zr2	zr2	PROPN
ejpam-2666	104	6	×	×	PROPN
ejpam-2666	104	7	zs2	zs2	NOUN
ejpam-2666	104	8	and	and	CCONJ
ejpam-2666	104	9	zt2	zt2	PROPN
ejpam-2666	104	10	can	can	AUX
ejpam-2666	104	11	be	be	AUX
ejpam-2666	104	12	obtained	obtain	VERB
ejpam-2666	104	13	by	by	ADP
ejpam-2666	104	14	projecting	project	VERB
ejpam-2666	104	15	zr2	zr2	PROPN
ejpam-2666	104	16	×	×	PROPN
ejpam-2666	104	17	zs2	zs2	PROPN
ejpam-2666	104	18	×	×	PROPN
ejpam-2666	104	19	zt2	zt2	PROPN
ejpam-2666	104	20	on	on	ADP
ejpam-2666	104	21	first	first	ADJ
ejpam-2666	104	22	r	r	NOUN
ejpam-2666	104	23	+	+	CCONJ
ejpam-2666	104	24	s	s	NOUN
ejpam-2666	104	25	coordinates	coordinate	NOUN
ejpam-2666	104	26	and	and	CCONJ
ejpam-2666	104	27	last	last	ADJ
ejpam-2666	104	28	t	t	NOUN
ejpam-2666	104	29	coordinates	coordinate	NOUN
ejpam-2666	104	30	,	,	PUNCT
ejpam-2666	104	31	respectively	respectively	ADV
ejpam-2666	104	32	,	,	PUNCT
ejpam-2666	104	33	we	we	PRON
ejpam-2666	104	34	make	make	VERB
ejpam-2666	104	35	use	use	NOUN
ejpam-2666	104	36	of	of	ADP
ejpam-2666	104	37	the	the	DET
ejpam-2666	104	38	cyclic	cyclic	ADJ
ejpam-2666	104	39	structures	structure	NOUN
ejpam-2666	104	40	of	of	ADP
ejpam-2666	104	41	both	both	DET
ejpam-2666	104	42	binary	binary	ADJ
ejpam-2666	104	43	codes	code	NOUN
ejpam-2666	104	44	and	and	CCONJ
ejpam-2666	104	45	z2	z2	ADJ
ejpam-2666	104	46	-	-	PUNCT
ejpam-2666	104	47	double	double	ADJ
ejpam-2666	104	48	cyclic	cyclic	NOUN
ejpam-2666	104	49	codes	code	NOUN
ejpam-2666	104	50	as	as	SCONJ
ejpam-2666	104	51	given	give	VERB
ejpam-2666	104	52	in	in	ADP
ejpam-2666	104	53	[	[	NOUN
ejpam-2666	104	54	4	4	NUM
ejpam-2666	104	55	]	]	PUNCT
ejpam-2666	104	56	to	to	PART
ejpam-2666	104	57	find	find	VERB
ejpam-2666	104	58	the	the	DET
ejpam-2666	104	59	generator	generator	NOUN
ejpam-2666	104	60	polynomials	polynomial	NOUN
ejpam-2666	104	61	for	for	ADP
ejpam-2666	104	62	a	a	DET
ejpam-2666	104	63	z2	z2	ADJ
ejpam-2666	104	64	-	-	PUNCT
ejpam-2666	104	65	triple	triple	ADJ
ejpam-2666	104	66	cyclic	cyclic	ADJ
ejpam-2666	104	67	code	code	NOUN
ejpam-2666	104	68	c	c	PROPN
ejpam-2666	104	69	of	of	ADP
ejpam-2666	104	70	block	block	NOUN
ejpam-2666	104	71	length	length	NOUN
ejpam-2666	104	72	(	(	PUNCT
ejpam-2666	104	73	r	r	NOUN
ejpam-2666	104	74	,	,	PUNCT
ejpam-2666	104	75	s	s	PROPN
ejpam-2666	104	76	,	,	PUNCT
ejpam-2666	104	77	t	t	PROPN
ejpam-2666	104	78	)	)	PUNCT
ejpam-2666	104	79	in	in	ADP
ejpam-2666	104	80	rr	rr	PROPN
ejpam-2666	104	81	,	,	PUNCT
ejpam-2666	104	82	s	s	X
ejpam-2666	104	83	,	,	PUNCT
ejpam-2666	104	84	t[x	t[x	NOUN
ejpam-2666	104	85	]	]	PUNCT
ejpam-2666	104	86	.	.	PUNCT
ejpam-2666	105	1	the	the	DET
ejpam-2666	105	2	following	follow	VERB
ejpam-2666	105	3	theorem	theorem	NOUN
ejpam-2666	105	4	gives	give	VERB
ejpam-2666	105	5	the	the	DET
ejpam-2666	105	6	generators	generator	NOUN
ejpam-2666	105	7	for	for	ADP
ejpam-2666	105	8	a	a	DET
ejpam-2666	105	9	z2	z2	ADJ
ejpam-2666	105	10	-	-	PUNCT
ejpam-2666	105	11	double	double	ADJ
ejpam-2666	105	12	cyclic	cyclic	NOUN
ejpam-2666	105	13	code	code	NOUN
ejpam-2666	105	14	of	of	ADP
ejpam-2666	105	15	block	block	NOUN
ejpam-2666	105	16	length	length	NOUN
ejpam-2666	105	17	(	(	PUNCT
ejpam-2666	105	18	r	r	NOUN
ejpam-2666	105	19	,	,	PUNCT
ejpam-2666	105	20	s	s	PART
ejpam-2666	105	21	)	)	PUNCT
ejpam-2666	105	22	,	,	PUNCT
ejpam-2666	105	23	which	which	PRON
ejpam-2666	105	24	is	be	AUX
ejpam-2666	105	25	useful	useful	ADJ
ejpam-2666	105	26	for	for	ADP
ejpam-2666	105	27	the	the	DET
ejpam-2666	105	28	rest	rest	NOUN
ejpam-2666	105	29	of	of	ADP
ejpam-2666	105	30	our	our	PRON
ejpam-2666	105	31	study	study	NOUN
ejpam-2666	105	32	.	.	PUNCT
ejpam-2666	106	1	theorem	theorem	NOUN
ejpam-2666	106	2	3	3	NUM
ejpam-2666	106	3	.	.	PUNCT
ejpam-2666	107	1	[	[	X
ejpam-2666	107	2	4	4	NUM
ejpam-2666	107	3	,	,	PUNCT
ejpam-2666	107	4	theorem	theorem	VERB
ejpam-2666	107	5	3.1	3.1	NUM
ejpam-2666	107	6	]	]	PUNCT
ejpam-2666	107	7	the	the	DET
ejpam-2666	107	8	z2[x]-module	z2[x]-module	PROPN
ejpam-2666	107	9	rr	rr	PROPN
ejpam-2666	107	10	,	,	PUNCT
ejpam-2666	107	11	s	s	PART
ejpam-2666	107	12	=	=	X
ejpam-2666	107	13	z2[x	z2[x	X
ejpam-2666	107	14	]	]	X
ejpam-2666	108	1	〈	〈	PROPN
ejpam-2666	108	2	xr−1	xr−1	PROPN
ejpam-2666	108	3	〉	〉	PROPN
ejpam-2666	108	4	×	×	PROPN
ejpam-2666	108	5	z2[x	z2[x	X
ejpam-2666	108	6	]	]	X
ejpam-2666	109	1	〈	〈	PROPN
ejpam-2666	109	2	xs−1	xs−1	PROPN
ejpam-2666	109	3	〉	〉	PROPN
ejpam-2666	109	4	is	be	AUX
ejpam-2666	109	5	a	a	DET
ejpam-2666	109	6	noetherian	noetherian	ADJ
ejpam-2666	109	7	module	module	NOUN
ejpam-2666	109	8	,	,	PUNCT
ejpam-2666	109	9	and	and	CCONJ
ejpam-2666	109	10	every	every	DET
ejpam-2666	109	11	submodule	submodule	NOUN
ejpam-2666	109	12	c	c	PROPN
ejpam-2666	109	13	of	of	ADP
ejpam-2666	109	14	rr	rr	PROPN
ejpam-2666	109	15	,	,	PUNCT
ejpam-2666	109	16	s	s	PART
ejpam-2666	109	17	can	can	AUX
ejpam-2666	109	18	be	be	AUX
ejpam-2666	109	19	written	write	VERB
ejpam-2666	109	20	as	as	ADP
ejpam-2666	109	21	c	c	PROPN
ejpam-2666	109	22	=	=	SYM
ejpam-2666	109	23	〈	〈	PROPN
ejpam-2666	109	24	(	(	PUNCT
ejpam-2666	109	25	b(x	b(x	NOUN
ejpam-2666	109	26	)	)	PUNCT
ejpam-2666	109	27	|	|	ADV
ejpam-2666	109	28	0	0	NUM
ejpam-2666	109	29	)	)	PUNCT
ejpam-2666	109	30	,	,	PUNCT
ejpam-2666	109	31	(	(	PUNCT
ejpam-2666	109	32	l(x	l(x	PROPN
ejpam-2666	109	33	)	)	PUNCT
ejpam-2666	110	1	|	|	ADV
ejpam-2666	110	2	a(x	a(x	NOUN
ejpam-2666	110	3	)	)	PUNCT
ejpam-2666	110	4	〉	〉	PROPN
ejpam-2666	110	5	,	,	PUNCT
ejpam-2666	110	6	where	where	SCONJ
ejpam-2666	110	7	b(x	b(x	NOUN
ejpam-2666	110	8	)	)	PUNCT
ejpam-2666	110	9	,	,	PUNCT
ejpam-2666	110	10	l(x	l(x	PROPN
ejpam-2666	110	11	)	)	PUNCT
ejpam-2666	110	12	∈	∈	PROPN
ejpam-2666	110	13	z2[x]/〈xr	z2[x]/〈xr	PROPN
ejpam-2666	110	14	−	−	PROPN
ejpam-2666	111	1	1	1	NUM
ejpam-2666	111	2	〉	〉	NOUN
ejpam-2666	111	3	with	with	ADP
ejpam-2666	111	4	b(x	b(x	NOUN
ejpam-2666	111	5	)	)	PUNCT
ejpam-2666	111	6	|	|	ADV
ejpam-2666	111	7	(	(	PUNCT
ejpam-2666	111	8	xr	xr	PROPN
ejpam-2666	111	9	−	−	PROPN
ejpam-2666	111	10	1	1	NUM
ejpam-2666	111	11	)	)	PUNCT
ejpam-2666	111	12	and	and	CCONJ
ejpam-2666	111	13	a(x	a(x	PROPN
ejpam-2666	111	14	)	)	PUNCT
ejpam-2666	111	15	∈	∈	NOUN
ejpam-2666	111	16	z2[x]/〈xs	z2[x]/〈xs	NOUN
ejpam-2666	111	17	−	−	PROPN
ejpam-2666	111	18	1	1	NUM
ejpam-2666	111	19	〉	〉	NOUN
ejpam-2666	111	20	with	with	ADP
ejpam-2666	111	21	a(x	a(x	NOUN
ejpam-2666	111	22	)	)	PUNCT
ejpam-2666	111	23	|	|	ADV
ejpam-2666	111	24	(	(	PUNCT
ejpam-2666	111	25	xs	xs	PROPN
ejpam-2666	111	26	−	−	PROPN
ejpam-2666	111	27	1	1	NUM
ejpam-2666	111	28	)	)	PUNCT
ejpam-2666	111	29	.	.	PUNCT
ejpam-2666	112	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	112	2	b	b	PROPN
ejpam-2666	112	3	,	,	PUNCT
ejpam-2666	112	4	maheshanand	maheshanand	NOUN
ejpam-2666	112	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	112	6	/	/	SYM
ejpam-2666	112	7	eur	eur	PROPN
ejpam-2666	112	8	.	.	PUNCT
ejpam-2666	113	1	j.	j.	PROPN
ejpam-2666	113	2	pure	pure	PROPN
ejpam-2666	113	3	appl	appl	PROPN
ejpam-2666	113	4	.	.	PROPN
ejpam-2666	113	5	math	math	PROPN
ejpam-2666	113	6	,	,	PUNCT
ejpam-2666	113	7	10	10	NUM
ejpam-2666	113	8	(	(	PUNCT
ejpam-2666	113	9	2	2	NUM
ejpam-2666	113	10	)	)	PUNCT
ejpam-2666	113	11	(	(	PUNCT
ejpam-2666	113	12	2017	2017	NUM
ejpam-2666	113	13	)	)	PUNCT
ejpam-2666	113	14	,	,	PUNCT
ejpam-2666	113	15	392	392	NUM
ejpam-2666	113	16	-	-	SYM
ejpam-2666	113	17	409	409	NUM
ejpam-2666	113	18	395	395	NUM
ejpam-2666	113	19	theorem	theorem	NOUN
ejpam-2666	113	20	4	4	NUM
ejpam-2666	113	21	.	.	PUNCT
ejpam-2666	114	1	[	[	X
ejpam-2666	114	2	4	4	NUM
ejpam-2666	114	3	,	,	PUNCT
ejpam-2666	114	4	proposition	proposition	NOUN
ejpam-2666	114	5	3.2	3.2	NUM
ejpam-2666	114	6	.	.	PUNCT
ejpam-2666	114	7	]	]	PUNCT
ejpam-2666	115	1	let	let	VERB
ejpam-2666	115	2	c	c	PRON
ejpam-2666	115	3	be	be	AUX
ejpam-2666	115	4	a	a	DET
ejpam-2666	115	5	z2	z2	ADJ
ejpam-2666	115	6	-	-	PUNCT
ejpam-2666	115	7	double	double	ADJ
ejpam-2666	115	8	cyclic	cyclic	NOUN
ejpam-2666	115	9	code	code	NOUN
ejpam-2666	115	10	of	of	ADP
ejpam-2666	115	11	block	block	NOUN
ejpam-2666	115	12	length	length	NOUN
ejpam-2666	115	13	(	(	PUNCT
ejpam-2666	115	14	r	r	NOUN
ejpam-2666	115	15	,	,	PUNCT
ejpam-2666	115	16	s	s	PART
ejpam-2666	115	17	)	)	PUNCT
ejpam-2666	115	18	,	,	PUNCT
ejpam-2666	116	1	such	such	ADJ
ejpam-2666	116	2	that	that	SCONJ
ejpam-2666	116	3	c	c	NOUN
ejpam-2666	116	4	=	=	SYM
ejpam-2666	116	5	〈	〈	PROPN
ejpam-2666	116	6	(	(	PUNCT
ejpam-2666	116	7	b(x	b(x	NOUN
ejpam-2666	116	8	)	)	PUNCT
ejpam-2666	116	9	|	|	ADV
ejpam-2666	116	10	0	0	NUM
ejpam-2666	116	11	)	)	PUNCT
ejpam-2666	116	12	,	,	PUNCT
ejpam-2666	116	13	(	(	PUNCT
ejpam-2666	116	14	l(x	l(x	PROPN
ejpam-2666	116	15	)	)	PUNCT
ejpam-2666	116	16	|	|	ADV
ejpam-2666	116	17	a(x	a(x	NOUN
ejpam-2666	116	18	)	)	PUNCT
ejpam-2666	116	19	)	)	PUNCT
ejpam-2666	116	20	〉	〉	PROPN
ejpam-2666	116	21	,	,	PUNCT
ejpam-2666	116	22	where	where	SCONJ
ejpam-2666	116	23	b(x)|xr	b(x)|xr	NOUN
ejpam-2666	116	24	−	−	PROPN
ejpam-2666	116	25	1	1	NUM
ejpam-2666	116	26	,	,	PUNCT
ejpam-2666	116	27	a(x)|xs	a(x)|xs	PRON
ejpam-2666	116	28	−	−	NOUN
ejpam-2666	116	29	1	1	NUM
ejpam-2666	116	30	over	over	ADP
ejpam-2666	116	31	z2	z2	PROPN
ejpam-2666	116	32	.	.	PUNCT
ejpam-2666	117	1	if	if	SCONJ
ejpam-2666	117	2	deg(b(x	deg(b(x	NOUN
ejpam-2666	117	3	)	)	PUNCT
ejpam-2666	117	4	)	)	PUNCT
ejpam-2666	118	1	=	=	SYM
ejpam-2666	118	2	t1	t1	NOUN
ejpam-2666	118	3	and	and	CCONJ
ejpam-2666	118	4	deg(a(x	deg(a(x	NOUN
ejpam-2666	118	5	)	)	PUNCT
ejpam-2666	118	6	)	)	PUNCT
ejpam-2666	119	1	=	=	SYM
ejpam-2666	119	2	t2	t2	PROPN
ejpam-2666	119	3	,	,	PUNCT
ejpam-2666	119	4	then	then	ADV
ejpam-2666	119	5	a	a	DET
ejpam-2666	119	6	minimal	minimal	ADJ
ejpam-2666	119	7	spanning	span	VERB
ejpam-2666	119	8	set	set	NOUN
ejpam-2666	119	9	for	for	ADP
ejpam-2666	119	10	c	c	PROPN
ejpam-2666	119	11	is	be	AUX
ejpam-2666	119	12	s′	s′	ADJ
ejpam-2666	119	13	=	=	PUNCT
ejpam-2666	119	14	s′1	s′1	NOUN
ejpam-2666	119	15	∪	∪	ADJ
ejpam-2666	119	16	s′2	s′2	NOUN
ejpam-2666	119	17	,	,	PUNCT
ejpam-2666	119	18	where	where	SCONJ
ejpam-2666	119	19	s′1	s′1	NOUN
ejpam-2666	119	20	=	=	PUNCT
ejpam-2666	119	21	r−t1−1⋃	r−t1−1⋃	X
ejpam-2666	119	22	i=0	i=0	PROPN
ejpam-2666	119	23	xi	xi	PROPN
ejpam-2666	119	24	∗	∗	PROPN
ejpam-2666	119	25	(	(	PUNCT
ejpam-2666	119	26	b(x	b(x	NOUN
ejpam-2666	119	27	)	)	PUNCT
ejpam-2666	119	28	|	|	ADV
ejpam-2666	119	29	0	0	X
ejpam-2666	119	30	)	)	PUNCT
ejpam-2666	119	31	s′2	s′2	NOUN
ejpam-2666	119	32	=	=	PUNCT
ejpam-2666	119	33	s−t2−1⋃	s−t2−1⋃	NOUN
ejpam-2666	120	1	i=0	i=0	PROPN
ejpam-2666	120	2	xi	xi	PROPN
ejpam-2666	120	3	∗	∗	PROPN
ejpam-2666	120	4	(	(	PUNCT
ejpam-2666	120	5	l(x	l(x	PROPN
ejpam-2666	120	6	)	)	PUNCT
ejpam-2666	120	7	|	|	ADV
ejpam-2666	120	8	a(x	a(x	NOUN
ejpam-2666	120	9	)	)	PUNCT
ejpam-2666	120	10	)	)	PUNCT
ejpam-2666	120	11	.	.	PUNCT
ejpam-2666	121	1	in	in	ADP
ejpam-2666	121	2	the	the	DET
ejpam-2666	121	3	following	following	NOUN
ejpam-2666	121	4	theorem	theorem	NOUN
ejpam-2666	121	5	,	,	PUNCT
ejpam-2666	121	6	we	we	PRON
ejpam-2666	121	7	determine	determine	VERB
ejpam-2666	121	8	the	the	DET
ejpam-2666	121	9	generator	generator	NOUN
ejpam-2666	121	10	polynomials	polynomial	NOUN
ejpam-2666	121	11	for	for	ADP
ejpam-2666	121	12	z2	z2	NOUN
ejpam-2666	121	13	-	-	PUNCT
ejpam-2666	121	14	triple	triple	ADJ
ejpam-2666	121	15	cyclic	cyclic	ADJ
ejpam-2666	121	16	codes	code	NOUN
ejpam-2666	121	17	of	of	ADP
ejpam-2666	121	18	block	block	NOUN
ejpam-2666	121	19	length	length	NOUN
ejpam-2666	121	20	(	(	PUNCT
ejpam-2666	121	21	r	r	NOUN
ejpam-2666	121	22	,	,	PUNCT
ejpam-2666	121	23	s	s	PROPN
ejpam-2666	121	24	,	,	PUNCT
ejpam-2666	121	25	t	t	PROPN
ejpam-2666	121	26	)	)	PUNCT
ejpam-2666	121	27	.	.	PUNCT
ejpam-2666	122	1	theorem	theorem	NOUN
ejpam-2666	122	2	5	5	NUM
ejpam-2666	122	3	.	.	PUNCT
ejpam-2666	123	1	let	let	VERB
ejpam-2666	123	2	c	c	PRON
ejpam-2666	123	3	be	be	AUX
ejpam-2666	123	4	a	a	DET
ejpam-2666	123	5	z2	z2	ADJ
ejpam-2666	123	6	-	-	PUNCT
ejpam-2666	123	7	triple	triple	ADJ
ejpam-2666	123	8	cyclic	cyclic	ADJ
ejpam-2666	123	9	code	code	NOUN
ejpam-2666	123	10	of	of	ADP
ejpam-2666	123	11	block	block	NOUN
ejpam-2666	123	12	length	length	NOUN
ejpam-2666	123	13	(	(	PUNCT
ejpam-2666	123	14	r	r	NOUN
ejpam-2666	123	15	,	,	PUNCT
ejpam-2666	123	16	s	s	PROPN
ejpam-2666	123	17	,	,	PUNCT
ejpam-2666	123	18	t	t	PROPN
ejpam-2666	123	19	)	)	PUNCT
ejpam-2666	123	20	.	.	PUNCT
ejpam-2666	124	1	then	then	ADV
ejpam-2666	124	2	c	c	X
ejpam-2666	124	3	=	=	SYM
ejpam-2666	124	4	〈	〈	PROPN
ejpam-2666	124	5	(	(	PUNCT
ejpam-2666	124	6	b(x	b(x	NOUN
ejpam-2666	124	7	)	)	PUNCT
ejpam-2666	124	8	|	|	ADV
ejpam-2666	124	9	0	0	NUM
ejpam-2666	125	1	|	|	ADV
ejpam-2666	125	2	0	0	NUM
ejpam-2666	125	3	)	)	PUNCT
ejpam-2666	125	4	,	,	PUNCT
ejpam-2666	125	5	(	(	PUNCT
ejpam-2666	125	6	l(x	l(x	PROPN
ejpam-2666	125	7	)	)	PUNCT
ejpam-2666	126	1	|	|	ADV
ejpam-2666	126	2	a(x	a(x	NOUN
ejpam-2666	126	3	)	)	PUNCT
ejpam-2666	126	4	|	|	ADV
ejpam-2666	126	5	0	0	NUM
ejpam-2666	126	6	)	)	PUNCT
ejpam-2666	126	7	,	,	PUNCT
ejpam-2666	126	8	(	(	PUNCT
ejpam-2666	126	9	g1(x	g1(x	NOUN
ejpam-2666	126	10	)	)	PUNCT
ejpam-2666	126	11	|	|	ADV
ejpam-2666	126	12	g2(x	g2(x	NOUN
ejpam-2666	126	13	)	)	PUNCT
ejpam-2666	126	14	|	|	PROPN
ejpam-2666	126	15	g3(x	g3(x	PROPN
ejpam-2666	126	16	)	)	PUNCT
ejpam-2666	126	17	)	)	PUNCT
ejpam-2666	126	18	〉	〉	PROPN
ejpam-2666	126	19	,	,	PUNCT
ejpam-2666	126	20	where	where	SCONJ
ejpam-2666	126	21	b(x	b(x	NOUN
ejpam-2666	126	22	)	)	PUNCT
ejpam-2666	126	23	,	,	PUNCT
ejpam-2666	126	24	l(x	l(x	PROPN
ejpam-2666	126	25	)	)	PUNCT
ejpam-2666	126	26	,	,	PUNCT
ejpam-2666	126	27	g1(x	g1(x	NOUN
ejpam-2666	126	28	)	)	PUNCT
ejpam-2666	126	29	∈	∈	PROPN
ejpam-2666	126	30	z2,r[x	z2,r[x	PROPN
ejpam-2666	126	31	]	]	PUNCT
ejpam-2666	126	32	with	with	ADP
ejpam-2666	126	33	b(x)|xr−	b(x)|xr−	PROPN
ejpam-2666	126	34	1	1	NUM
ejpam-2666	126	35	and	and	CCONJ
ejpam-2666	126	36	a(x	a(x	NOUN
ejpam-2666	126	37	)	)	PUNCT
ejpam-2666	126	38	,	,	PUNCT
ejpam-2666	126	39	g2(x	g2(x	X
ejpam-2666	126	40	)	)	PUNCT
ejpam-2666	126	41	∈	∈	PROPN
ejpam-2666	126	42	z2,s[x	z2,s[x	PROPN
ejpam-2666	126	43	]	]	PUNCT
ejpam-2666	126	44	with	with	ADP
ejpam-2666	126	45	a(x)|xs−	a(x)|xs−	PROPN
ejpam-2666	126	46	1	1	NUM
ejpam-2666	126	47	and	and	CCONJ
ejpam-2666	126	48	g3(x	g3(x	PROPN
ejpam-2666	126	49	)	)	PUNCT
ejpam-2666	126	50	∈	∈	PROPN
ejpam-2666	126	51	z2,t[x	z2,t[x	PROPN
ejpam-2666	126	52	]	]	PUNCT
ejpam-2666	126	53	with	with	ADP
ejpam-2666	126	54	g3(x)|xt−	g3(x)|xt−	PROPN
ejpam-2666	126	55	1	1	NUM
ejpam-2666	126	56	.	.	PUNCT
ejpam-2666	126	57	proof	proof	NOUN
ejpam-2666	126	58	.	.	PUNCT
ejpam-2666	127	1	consider	consider	VERB
ejpam-2666	127	2	the	the	DET
ejpam-2666	127	3	canonical	canonical	ADJ
ejpam-2666	127	4	projection	projection	NOUN
ejpam-2666	127	5	πt	πt	INTJ
ejpam-2666	127	6	:	:	PUNCT
ejpam-2666	127	7	c→	c→	PROPN
ejpam-2666	127	8	z2,t[x	z2,t[x	PROPN
ejpam-2666	127	9	]	]	PUNCT
ejpam-2666	127	10	such	such	ADJ
ejpam-2666	127	11	that	that	SCONJ
ejpam-2666	127	12	(	(	PUNCT
ejpam-2666	127	13	c1	c1	PROPN
ejpam-2666	127	14	|	|	ADV
ejpam-2666	127	15	c2	c2	PROPN
ejpam-2666	127	16	|	|	PROPN
ejpam-2666	127	17	c3	c3	PROPN
ejpam-2666	127	18	)	)	PUNCT
ejpam-2666	127	19	7→	7→	PROPN
ejpam-2666	127	20	c3	c3	NOUN
ejpam-2666	127	21	.	.	PUNCT
ejpam-2666	128	1	it	it	PRON
ejpam-2666	128	2	is	be	AUX
ejpam-2666	128	3	easy	easy	ADJ
ejpam-2666	128	4	to	to	PART
ejpam-2666	128	5	see	see	VERB
ejpam-2666	128	6	that	that	DET
ejpam-2666	128	7	πt	πt	NOUN
ejpam-2666	128	8	is	be	AUX
ejpam-2666	128	9	a	a	DET
ejpam-2666	128	10	z2[x]-module	z2[x]-module	PROPN
ejpam-2666	128	11	homomorphism	homomorphism	NOUN
ejpam-2666	128	12	with	with	ADP
ejpam-2666	128	13	kernel	kernel	PROPN
ejpam-2666	128	14	kerc(πt	kerc(πt	PROPN
ejpam-2666	128	15	)	)	PUNCT
ejpam-2666	129	1	=	=	PRON
ejpam-2666	129	2	{	{	PUNCT
ejpam-2666	129	3	(	(	PUNCT
ejpam-2666	129	4	c1	c1	PROPN
ejpam-2666	129	5	|	|	ADV
ejpam-2666	129	6	c2	c2	PROPN
ejpam-2666	129	7	|	|	ADV
ejpam-2666	129	8	0	0	NUM
ejpam-2666	129	9	)	)	PUNCT
ejpam-2666	129	10	∈	∈	PROPN
ejpam-2666	129	11	c	c	NOUN
ejpam-2666	129	12	}	}	PUNCT
ejpam-2666	129	13	,	,	PUNCT
ejpam-2666	129	14	and	and	CCONJ
ejpam-2666	129	15	therefore	therefore	ADV
ejpam-2666	129	16	the	the	DET
ejpam-2666	129	17	set	set	NOUN
ejpam-2666	129	18	k	k	PROPN
ejpam-2666	130	1	=	=	PRON
ejpam-2666	130	2	{	{	PUNCT
ejpam-2666	130	3	(	(	PUNCT
ejpam-2666	130	4	c1	c1	PROPN
ejpam-2666	130	5	|	|	PROPN
ejpam-2666	130	6	c2	c2	PROPN
ejpam-2666	130	7	)	)	PUNCT
ejpam-2666	130	8	∈	∈	PROPN
ejpam-2666	130	9	c	c	NOUN
ejpam-2666	130	10	:	:	PUNCT
ejpam-2666	130	11	(	(	PUNCT
ejpam-2666	130	12	c1	c1	PROPN
ejpam-2666	130	13	|	|	ADV
ejpam-2666	130	14	c2	c2	PROPN
ejpam-2666	130	15	|	|	ADV
ejpam-2666	130	16	0	0	NUM
ejpam-2666	130	17	)	)	PUNCT
ejpam-2666	130	18	∈	∈	NOUN
ejpam-2666	130	19	c	c	AUX
ejpam-2666	130	20	}	}	PUNCT
ejpam-2666	130	21	is	be	AUX
ejpam-2666	130	22	a	a	DET
ejpam-2666	130	23	z2	z2	ADJ
ejpam-2666	130	24	-	-	PUNCT
ejpam-2666	130	25	double	double	ADJ
ejpam-2666	130	26	cyclic	cyclic	NOUN
ejpam-2666	130	27	code	code	NOUN
ejpam-2666	130	28	of	of	ADP
ejpam-2666	130	29	block	block	NOUN
ejpam-2666	130	30	length	length	NOUN
ejpam-2666	130	31	(	(	PUNCT
ejpam-2666	130	32	r	r	NOUN
ejpam-2666	130	33	,	,	PUNCT
ejpam-2666	130	34	s	s	PART
ejpam-2666	130	35	)	)	PUNCT
ejpam-2666	130	36	in	in	ADP
ejpam-2666	130	37	rr	rr	PROPN
ejpam-2666	130	38	,	,	PUNCT
ejpam-2666	130	39	s[x	s[x	PROPN
ejpam-2666	130	40	]	]	PUNCT
ejpam-2666	130	41	.	.	PUNCT
ejpam-2666	131	1	from	from	ADP
ejpam-2666	131	2	theorem	theorem	ADJ
ejpam-2666	131	3	3	3	NUM
ejpam-2666	131	4	,	,	PUNCT
ejpam-2666	131	5	there	there	PRON
ejpam-2666	131	6	exist	exist	VERB
ejpam-2666	131	7	b	b	NUM
ejpam-2666	131	8	,	,	PUNCT
ejpam-2666	131	9	l	l	PROPN
ejpam-2666	131	10	∈	∈	PROPN
ejpam-2666	131	11	z2,r[x	z2,r[x	PROPN
ejpam-2666	131	12	]	]	PUNCT
ejpam-2666	131	13	and	and	CCONJ
ejpam-2666	131	14	a	a	DET
ejpam-2666	131	15	∈	∈	PROPN
ejpam-2666	131	16	z2,s[x	z2,s[x	PROPN
ejpam-2666	131	17	]	]	PUNCT
ejpam-2666	131	18	such	such	ADJ
ejpam-2666	131	19	that	that	SCONJ
ejpam-2666	131	20	k	k	PROPN
ejpam-2666	131	21	=	=	SYM
ejpam-2666	131	22	〈	〈	PROPN
ejpam-2666	131	23	(	(	PUNCT
ejpam-2666	131	24	b	b	NOUN
ejpam-2666	131	25	|	|	ADJ
ejpam-2666	131	26	0	0	NUM
ejpam-2666	131	27	)	)	PUNCT
ejpam-2666	131	28	,	,	PUNCT
ejpam-2666	131	29	(	(	PUNCT
ejpam-2666	131	30	l	l	NOUN
ejpam-2666	131	31	|	|	ADV
ejpam-2666	131	32	a	a	X
ejpam-2666	131	33	)	)	PUNCT
ejpam-2666	131	34	〉	〉	NOUN
ejpam-2666	131	35	,	,	PUNCT
ejpam-2666	131	36	with	with	ADP
ejpam-2666	131	37	b|xr	b|xr	NOUN
ejpam-2666	131	38	−	−	PROPN
ejpam-2666	131	39	1	1	NUM
ejpam-2666	131	40	and	and	CCONJ
ejpam-2666	131	41	a|xs	a|xs	NUM
ejpam-2666	131	42	−	−	PROPN
ejpam-2666	132	1	1	1	X
ejpam-2666	132	2	.	.	PUNCT
ejpam-2666	133	1	this	this	PRON
ejpam-2666	133	2	implies	imply	VERB
ejpam-2666	133	3	that	that	DET
ejpam-2666	133	4	kerc(πt	kerc(πt	NOUN
ejpam-2666	133	5	)	)	PUNCT
ejpam-2666	133	6	=	=	SYM
ejpam-2666	133	7	〈	〈	PROPN
ejpam-2666	133	8	(	(	PUNCT
ejpam-2666	133	9	b	b	NOUN
ejpam-2666	133	10	|	|	NOUN
ejpam-2666	133	11	0	0	NUM
ejpam-2666	133	12	|	|	NOUN
ejpam-2666	133	13	0	0	NUM
ejpam-2666	133	14	)	)	PUNCT
ejpam-2666	133	15	,	,	PUNCT
ejpam-2666	133	16	(	(	PUNCT
ejpam-2666	133	17	l	l	NOUN
ejpam-2666	133	18	|	|	ADV
ejpam-2666	133	19	a	a	DET
ejpam-2666	133	20	|	|	NOUN
ejpam-2666	133	21	0	0	NUM
ejpam-2666	133	22	)	)	PUNCT
ejpam-2666	133	23	〉	〉	PROPN
ejpam-2666	133	24	.	.	PUNCT
ejpam-2666	134	1	on	on	ADP
ejpam-2666	134	2	the	the	DET
ejpam-2666	134	3	other	other	ADJ
ejpam-2666	134	4	hand	hand	NOUN
ejpam-2666	134	5	the	the	DET
ejpam-2666	134	6	image	image	NOUN
ejpam-2666	134	7	of	of	ADP
ejpam-2666	134	8	c	c	PROPN
ejpam-2666	134	9	under	under	ADP
ejpam-2666	134	10	πt	πt	NOUN
ejpam-2666	134	11	is	be	AUX
ejpam-2666	134	12	an	an	DET
ejpam-2666	134	13	ideal	ideal	NOUN
ejpam-2666	134	14	of	of	ADP
ejpam-2666	134	15	z2,t[x	z2,t[x	PROPN
ejpam-2666	134	16	]	]	PUNCT
ejpam-2666	134	17	and	and	CCONJ
ejpam-2666	134	18	as	as	ADP
ejpam-2666	134	19	z2,t[x	z2,t[x	PROPN
ejpam-2666	134	20	]	]	PUNCT
ejpam-2666	134	21	is	be	AUX
ejpam-2666	134	22	a	a	DET
ejpam-2666	134	23	pid	pid	NOUN
ejpam-2666	134	24	,	,	PUNCT
ejpam-2666	134	25	there	there	PRON
ejpam-2666	134	26	exists	exist	VERB
ejpam-2666	134	27	g3	g3	PROPN
ejpam-2666	134	28	∈	∈	PROPN
ejpam-2666	134	29	z2,t[x	z2,t[x	PROPN
ejpam-2666	134	30	]	]	PUNCT
ejpam-2666	134	31	such	such	ADJ
ejpam-2666	134	32	that	that	SCONJ
ejpam-2666	134	33	πt(c	πt(c	PUNCT
ejpam-2666	134	34	)	)	PUNCT
ejpam-2666	134	35	=	=	PUNCT
ejpam-2666	134	36	〈	〈	PROPN
ejpam-2666	134	37	g3	g3	PROPN
ejpam-2666	134	38	〉	〉	PROPN
ejpam-2666	134	39	.	.	PUNCT
ejpam-2666	135	1	therefore	therefore	ADV
ejpam-2666	135	2	we	we	PRON
ejpam-2666	135	3	have	have	VERB
ejpam-2666	135	4	c	c	PROPN
ejpam-2666	135	5	kerc(πt	kerc(πt	NOUN
ejpam-2666	135	6	)	)	PUNCT
ejpam-2666	135	7	∼=	∼=	PROPN
ejpam-2666	135	8	πt(c	πt(c	NUM
ejpam-2666	135	9	)	)	PUNCT
ejpam-2666	135	10	,	,	PUNCT
ejpam-2666	135	11	and	and	CCONJ
ejpam-2666	135	12	hence	hence	ADV
ejpam-2666	135	13	c	c	X
ejpam-2666	135	14	=	=	SYM
ejpam-2666	135	15	〈	〈	PROPN
ejpam-2666	135	16	(	(	PUNCT
ejpam-2666	135	17	b	b	NOUN
ejpam-2666	135	18	|	|	NOUN
ejpam-2666	135	19	0	0	NUM
ejpam-2666	136	1	|	|	NOUN
ejpam-2666	136	2	0	0	NUM
ejpam-2666	136	3	)	)	PUNCT
ejpam-2666	136	4	,	,	PUNCT
ejpam-2666	137	1	(	(	PUNCT
ejpam-2666	137	2	l	l	NOUN
ejpam-2666	137	3	|	|	ADV
ejpam-2666	137	4	a	a	DET
ejpam-2666	137	5	|	|	NOUN
ejpam-2666	137	6	0	0	NUM
ejpam-2666	137	7	)	)	PUNCT
ejpam-2666	137	8	,	,	PUNCT
ejpam-2666	137	9	(	(	PUNCT
ejpam-2666	137	10	g1	g1	VERB
ejpam-2666	137	11	|	|	ADV
ejpam-2666	137	12	g2	g2	PROPN
ejpam-2666	137	13	|	|	CCONJ
ejpam-2666	137	14	g3	g3	PROPN
ejpam-2666	137	15	)	)	PUNCT
ejpam-2666	137	16	〉	〉	NOUN
ejpam-2666	137	17	for	for	ADP
ejpam-2666	137	18	some	some	DET
ejpam-2666	137	19	g1	g1	PROPN
ejpam-2666	137	20	∈	∈	PROPN
ejpam-2666	137	21	z2,r[x	z2,r[x	PROPN
ejpam-2666	137	22	]	]	PUNCT
ejpam-2666	137	23	and	and	CCONJ
ejpam-2666	137	24	g2	g2	PROPN
ejpam-2666	137	25	∈	∈	PROPN
ejpam-2666	137	26	z2,s[x	z2,s[x	PROPN
ejpam-2666	137	27	]	]	X
ejpam-2666	137	28	.	.	PUNCT
ejpam-2666	138	1	hence	hence	ADV
ejpam-2666	138	2	the	the	DET
ejpam-2666	138	3	theorem	theorem	NOUN
ejpam-2666	138	4	.	.	PUNCT
ejpam-2666	139	1	let	let	VERB
ejpam-2666	139	2	(	(	PUNCT
ejpam-2666	139	3	c1	c1	NOUN
ejpam-2666	139	4	|	|	ADV
ejpam-2666	139	5	0	0	NUM
ejpam-2666	140	1	|	|	ADV
ejpam-2666	140	2	0	0	NUM
ejpam-2666	140	3	)	)	PUNCT
ejpam-2666	140	4	∈	∈	PROPN
ejpam-2666	140	5	c.	c.	NOUN
ejpam-2666	140	6	then	then	ADV
ejpam-2666	140	7	(	(	PUNCT
ejpam-2666	140	8	c1	c1	NOUN
ejpam-2666	140	9	|	|	ADV
ejpam-2666	140	10	0	0	NUM
ejpam-2666	140	11	)	)	PUNCT
ejpam-2666	140	12	∈	∈	PROPN
ejpam-2666	141	1	k	k	NOUN
ejpam-2666	141	2	=	=	PRON
ejpam-2666	141	3	{	{	PUNCT
ejpam-2666	141	4	(	(	PUNCT
ejpam-2666	141	5	c1	c1	PROPN
ejpam-2666	141	6	|	|	PROPN
ejpam-2666	141	7	c2	c2	PROPN
ejpam-2666	141	8	)	)	PUNCT
ejpam-2666	141	9	∈	∈	PROPN
ejpam-2666	141	10	c	c	NOUN
ejpam-2666	141	11	:	:	PUNCT
ejpam-2666	141	12	(	(	PUNCT
ejpam-2666	141	13	c1	c1	PROPN
ejpam-2666	141	14	|	|	ADV
ejpam-2666	141	15	c2	c2	PROPN
ejpam-2666	141	16	|	|	ADV
ejpam-2666	141	17	0	0	NUM
ejpam-2666	141	18	)	)	PUNCT
ejpam-2666	141	19	∈	∈	PROPN
ejpam-2666	141	20	c	c	NOUN
ejpam-2666	141	21	}	}	PUNCT
ejpam-2666	141	22	.	.	PUNCT
ejpam-2666	142	1	also	also	ADV
ejpam-2666	142	2	,	,	PUNCT
ejpam-2666	142	3	from	from	ADP
ejpam-2666	142	4	theorem	theorem	NOUN
ejpam-2666	142	5	5	5	NUM
ejpam-2666	142	6	,	,	PUNCT
ejpam-2666	142	7	we	we	PRON
ejpam-2666	142	8	have	have	VERB
ejpam-2666	142	9	k	k	NOUN
ejpam-2666	142	10	=	=	SYM
ejpam-2666	142	11	〈	〈	PROPN
ejpam-2666	142	12	(	(	PUNCT
ejpam-2666	142	13	b	b	NOUN
ejpam-2666	142	14	|	|	ADJ
ejpam-2666	142	15	0	0	NUM
ejpam-2666	142	16	)	)	PUNCT
ejpam-2666	142	17	,	,	PUNCT
ejpam-2666	142	18	(	(	PUNCT
ejpam-2666	142	19	l	l	NOUN
ejpam-2666	142	20	|	|	ADV
ejpam-2666	142	21	a	a	X
ejpam-2666	142	22	)	)	PUNCT
ejpam-2666	142	23	〉	〉	NOUN
ejpam-2666	142	24	.	.	PUNCT
ejpam-2666	143	1	therefore	therefore	ADV
ejpam-2666	143	2	c1	c1	PROPN
ejpam-2666	143	3	∈	∈	PROPN
ejpam-2666	143	4	〈	〈	PROPN
ejpam-2666	143	5	b	b	PROPN
ejpam-2666	143	6	〉	〉	PROPN
ejpam-2666	143	7	.	.	PUNCT
ejpam-2666	144	1	hence	hence	ADV
ejpam-2666	144	2	(	(	PUNCT
ejpam-2666	144	3	c1	c1	PROPN
ejpam-2666	144	4	|	|	ADV
ejpam-2666	144	5	0	0	NUM
ejpam-2666	145	1	|	|	ADV
ejpam-2666	145	2	0	0	X
ejpam-2666	145	3	)	)	PUNCT
ejpam-2666	145	4	∈	∈	PROPN
ejpam-2666	145	5	c	c	NOUN
ejpam-2666	145	6	implies	imply	VERB
ejpam-2666	145	7	that	that	SCONJ
ejpam-2666	145	8	c1	c1	PROPN
ejpam-2666	145	9	∈	∈	PROPN
ejpam-2666	145	10	〈	〈	PROPN
ejpam-2666	145	11	b	b	PROPN
ejpam-2666	145	12	〉	〉	PROPN
ejpam-2666	145	13	.	.	PUNCT
ejpam-2666	146	1	the	the	DET
ejpam-2666	146	2	following	follow	VERB
ejpam-2666	146	3	results	result	NOUN
ejpam-2666	146	4	are	be	AUX
ejpam-2666	146	5	useful	useful	ADJ
ejpam-2666	146	6	to	to	PART
ejpam-2666	146	7	understand	understand	VERB
ejpam-2666	146	8	the	the	DET
ejpam-2666	146	9	structure	structure	NOUN
ejpam-2666	146	10	of	of	ADP
ejpam-2666	146	11	z2	z2	NOUN
ejpam-2666	146	12	-	-	PUNCT
ejpam-2666	146	13	triple	triple	ADJ
ejpam-2666	146	14	cyclic	cyclic	ADJ
ejpam-2666	146	15	code	code	NOUN
ejpam-2666	146	16	and	and	CCONJ
ejpam-2666	146	17	to	to	PART
ejpam-2666	146	18	determine	determine	VERB
ejpam-2666	146	19	their	their	PRON
ejpam-2666	146	20	minimal	minimal	ADJ
ejpam-2666	146	21	spanning	span	VERB
ejpam-2666	146	22	sets	set	NOUN
ejpam-2666	146	23	.	.	PUNCT
ejpam-2666	147	1	the	the	DET
ejpam-2666	147	2	minimal	minimal	ADJ
ejpam-2666	147	3	spanning	span	VERB
ejpam-2666	147	4	set	set	NOUN
ejpam-2666	147	5	of	of	ADP
ejpam-2666	147	6	a	a	DET
ejpam-2666	147	7	z2	z2	ADJ
ejpam-2666	147	8	-	-	PUNCT
ejpam-2666	147	9	triple	triple	ADJ
ejpam-2666	147	10	cyclic	cyclic	ADJ
ejpam-2666	147	11	code	code	NOUN
ejpam-2666	147	12	can	can	AUX
ejpam-2666	147	13	be	be	AUX
ejpam-2666	147	14	used	use	VERB
ejpam-2666	147	15	to	to	PART
ejpam-2666	147	16	determine	determine	VERB
ejpam-2666	147	17	its	its	PRON
ejpam-2666	147	18	cardinality	cardinality	NOUN
ejpam-2666	147	19	and	and	CCONJ
ejpam-2666	147	20	the	the	DET
ejpam-2666	147	21	generator	generator	NOUN
ejpam-2666	147	22	matrix	matrix	NOUN
ejpam-2666	147	23	.	.	PUNCT
ejpam-2666	148	1	in	in	ADP
ejpam-2666	148	2	the	the	DET
ejpam-2666	148	3	rest	rest	NOUN
ejpam-2666	148	4	of	of	ADP
ejpam-2666	148	5	the	the	DET
ejpam-2666	148	6	paper	paper	NOUN
ejpam-2666	148	7	we	we	PRON
ejpam-2666	148	8	consider	consider	VERB
ejpam-2666	148	9	the	the	DET
ejpam-2666	148	10	z2	z2	NUM
ejpam-2666	148	11	-	-	PUNCT
ejpam-2666	148	12	triple	triple	ADJ
ejpam-2666	148	13	cyclic	cyclic	ADJ
ejpam-2666	148	14	code	code	NOUN
ejpam-2666	148	15	as	as	SCONJ
ejpam-2666	148	16	defined	define	VERB
ejpam-2666	148	17	in	in	ADP
ejpam-2666	148	18	theorem	theorem	NOUN
ejpam-2666	148	19	5	5	NUM
ejpam-2666	148	20	.	.	PUNCT
ejpam-2666	149	1	lemma	lemma	PROPN
ejpam-2666	149	2	1	1	X
ejpam-2666	149	3	.	.	PUNCT
ejpam-2666	150	1	let	let	VERB
ejpam-2666	150	2	c	c	NOUN
ejpam-2666	150	3	=	=	SYM
ejpam-2666	150	4	〈	〈	PROPN
ejpam-2666	150	5	(	(	PUNCT
ejpam-2666	150	6	b	b	NOUN
ejpam-2666	150	7	|	|	NOUN
ejpam-2666	150	8	0	0	NUM
ejpam-2666	151	1	|	|	NOUN
ejpam-2666	151	2	0	0	NUM
ejpam-2666	151	3	)	)	PUNCT
ejpam-2666	151	4	,	,	PUNCT
ejpam-2666	152	1	(	(	PUNCT
ejpam-2666	152	2	l	l	NOUN
ejpam-2666	152	3	|	|	ADV
ejpam-2666	152	4	a	a	DET
ejpam-2666	152	5	|	|	NOUN
ejpam-2666	152	6	0	0	NUM
ejpam-2666	152	7	)	)	PUNCT
ejpam-2666	152	8	,	,	PUNCT
ejpam-2666	152	9	(	(	PUNCT
ejpam-2666	152	10	g1	g1	VERB
ejpam-2666	152	11	|	|	ADV
ejpam-2666	152	12	g2	g2	PROPN
ejpam-2666	152	13	|	|	CCONJ
ejpam-2666	152	14	g3	g3	PROPN
ejpam-2666	152	15	)	)	PUNCT
ejpam-2666	152	16	〉	〉	PROPN
ejpam-2666	152	17	be	be	AUX
ejpam-2666	152	18	a	a	DET
ejpam-2666	152	19	z2	z2	ADJ
ejpam-2666	152	20	-	-	PUNCT
ejpam-2666	152	21	triple	triple	ADJ
ejpam-2666	152	22	cyclic	cyclic	ADJ
ejpam-2666	152	23	code	code	NOUN
ejpam-2666	152	24	of	of	ADP
ejpam-2666	152	25	block	block	NOUN
ejpam-2666	152	26	length	length	NOUN
ejpam-2666	152	27	(	(	PUNCT
ejpam-2666	152	28	r	r	NOUN
ejpam-2666	152	29	,	,	PUNCT
ejpam-2666	152	30	s	s	PROPN
ejpam-2666	152	31	,	,	PUNCT
ejpam-2666	152	32	t	t	PROPN
ejpam-2666	152	33	)	)	PUNCT
ejpam-2666	152	34	.	.	PUNCT
ejpam-2666	153	1	then	then	ADV
ejpam-2666	153	2	deg(l	deg(l	NUM
ejpam-2666	153	3	)	)	PUNCT
ejpam-2666	153	4	<	<	X
ejpam-2666	153	5	deg(b	deg(b	PROPN
ejpam-2666	153	6	)	)	PUNCT
ejpam-2666	153	7	and	and	CCONJ
ejpam-2666	153	8	deg(g1	deg(g1	NOUN
ejpam-2666	153	9	)	)	PUNCT
ejpam-2666	153	10	<	<	X
ejpam-2666	153	11	deg(b	deg(b	PROPN
ejpam-2666	153	12	)	)	PUNCT
ejpam-2666	153	13	.	.	PUNCT
ejpam-2666	154	1	proof	proof	NOUN
ejpam-2666	154	2	.	.	PUNCT
ejpam-2666	155	1	assume	assume	VERB
ejpam-2666	155	2	deg(l	deg(l	NUM
ejpam-2666	155	3	)	)	PUNCT
ejpam-2666	155	4	≥	≥	NOUN
ejpam-2666	155	5	deg(b	deg(b	NUM
ejpam-2666	155	6	)	)	PUNCT
ejpam-2666	155	7	.	.	PUNCT
ejpam-2666	156	1	by	by	ADP
ejpam-2666	156	2	applying	apply	VERB
ejpam-2666	156	3	division	division	NOUN
ejpam-2666	156	4	algorithm	algorithm	NOUN
ejpam-2666	156	5	,	,	PUNCT
ejpam-2666	156	6	there	there	PRON
ejpam-2666	156	7	exist	exist	VERB
ejpam-2666	156	8	polynomials	polynomial	NOUN
ejpam-2666	156	9	q	q	NOUN
ejpam-2666	156	10	and	and	CCONJ
ejpam-2666	156	11	r	r	NOUN
ejpam-2666	156	12	in	in	ADP
ejpam-2666	156	13	z2[x	z2[x	PROPN
ejpam-2666	156	14	]	]	PUNCT
ejpam-2666	156	15	such	such	ADJ
ejpam-2666	156	16	that	that	SCONJ
ejpam-2666	156	17	l	l	NOUN
ejpam-2666	156	18	=	=	PUNCT
ejpam-2666	156	19	bq	bq	X
ejpam-2666	156	20	+	+	CCONJ
ejpam-2666	156	21	r	r	NOUN
ejpam-2666	156	22	,	,	PUNCT
ejpam-2666	156	23	where	where	SCONJ
ejpam-2666	156	24	r	r	NOUN
ejpam-2666	156	25	=	=	SYM
ejpam-2666	156	26	0	0	NUM
ejpam-2666	156	27	or	or	CCONJ
ejpam-2666	156	28	deg(r	deg(r	PROPN
ejpam-2666	156	29	)	)	PUNCT
ejpam-2666	156	30	<	<	X
ejpam-2666	156	31	deg(b	deg(b	PROPN
ejpam-2666	156	32	)	)	PUNCT
ejpam-2666	156	33	.	.	PUNCT
ejpam-2666	157	1	then	then	ADV
ejpam-2666	157	2	〈	〈	PROPN
ejpam-2666	157	3	(	(	PUNCT
ejpam-2666	157	4	b	b	NOUN
ejpam-2666	157	5	|	|	NOUN
ejpam-2666	157	6	0	0	NUM
ejpam-2666	157	7	|	|	NOUN
ejpam-2666	157	8	0	0	NUM
ejpam-2666	157	9	)	)	PUNCT
ejpam-2666	157	10	,	,	PUNCT
ejpam-2666	157	11	(	(	PUNCT
ejpam-2666	157	12	l	l	NOUN
ejpam-2666	157	13	|	|	ADV
ejpam-2666	157	14	a	a	DET
ejpam-2666	157	15	|	|	NOUN
ejpam-2666	157	16	0	0	NUM
ejpam-2666	157	17	)	)	PUNCT
ejpam-2666	157	18	〉	〉	NOUN
ejpam-2666	157	19	=	=	SYM
ejpam-2666	157	20	〈	〈	PROPN
ejpam-2666	157	21	(	(	PUNCT
ejpam-2666	157	22	b	b	NOUN
ejpam-2666	157	23	|	|	NOUN
ejpam-2666	157	24	0	0	NUM
ejpam-2666	157	25	|	|	NOUN
ejpam-2666	157	26	0	0	NUM
ejpam-2666	157	27	)	)	PUNCT
ejpam-2666	157	28	,	,	PUNCT
ejpam-2666	157	29	(	(	PUNCT
ejpam-2666	157	30	bq	bq	INTJ
ejpam-2666	157	31	+	+	NUM
ejpam-2666	157	32	r	r	NOUN
ejpam-2666	157	33	|	|	ADV
ejpam-2666	157	34	a	a	DET
ejpam-2666	157	35	|	|	NOUN
ejpam-2666	157	36	0	0	NUM
ejpam-2666	157	37	)	)	PUNCT
ejpam-2666	157	38	〉	〉	NOUN
ejpam-2666	157	39	=	=	SYM
ejpam-2666	157	40	〈	〈	PROPN
ejpam-2666	157	41	(	(	PUNCT
ejpam-2666	157	42	b	b	NOUN
ejpam-2666	157	43	|	|	NOUN
ejpam-2666	157	44	0	0	NUM
ejpam-2666	157	45	|	|	NOUN
ejpam-2666	157	46	0	0	NUM
ejpam-2666	157	47	)	)	PUNCT
ejpam-2666	157	48	,	,	PUNCT
ejpam-2666	157	49	(	(	PUNCT
ejpam-2666	157	50	r	r	NOUN
ejpam-2666	157	51	|	|	ADV
ejpam-2666	157	52	a	a	DET
ejpam-2666	157	53	|	|	NOUN
ejpam-2666	157	54	0	0	NUM
ejpam-2666	157	55	)	)	PUNCT
ejpam-2666	157	56	〉	〉	PROPN
ejpam-2666	157	57	.	.	PUNCT
ejpam-2666	158	1	hence	hence	ADV
ejpam-2666	158	2	,	,	PUNCT
ejpam-2666	158	3	we	we	PRON
ejpam-2666	158	4	may	may	AUX
ejpam-2666	158	5	assume	assume	VERB
ejpam-2666	158	6	that	that	SCONJ
ejpam-2666	158	7	deg(l	deg(l	PROPN
ejpam-2666	158	8	)	)	PUNCT
ejpam-2666	158	9	<	<	X
ejpam-2666	158	10	deg(b	deg(b	PROPN
ejpam-2666	158	11	)	)	PUNCT
ejpam-2666	158	12	.	.	PUNCT
ejpam-2666	159	1	similarly	similarly	ADV
ejpam-2666	159	2	,	,	PUNCT
ejpam-2666	159	3	we	we	PRON
ejpam-2666	159	4	can	can	AUX
ejpam-2666	159	5	show	show	VERB
ejpam-2666	159	6	deg(g1	deg(g1	PROPN
ejpam-2666	159	7	)	)	PUNCT
ejpam-2666	159	8	<	<	X
ejpam-2666	159	9	deg(b	deg(b	PROPN
ejpam-2666	159	10	)	)	PUNCT
ejpam-2666	159	11	.	.	PUNCT
ejpam-2666	160	1	lemma	lemma	PROPN
ejpam-2666	160	2	2	2	X
ejpam-2666	160	3	.	.	PUNCT
ejpam-2666	161	1	let	let	VERB
ejpam-2666	161	2	c	c	NOUN
ejpam-2666	161	3	=	=	SYM
ejpam-2666	161	4	〈	〈	PROPN
ejpam-2666	161	5	(	(	PUNCT
ejpam-2666	161	6	b	b	NOUN
ejpam-2666	161	7	|	|	NOUN
ejpam-2666	161	8	0	0	NUM
ejpam-2666	162	1	|	|	NOUN
ejpam-2666	162	2	0	0	NUM
ejpam-2666	162	3	)	)	PUNCT
ejpam-2666	162	4	,	,	PUNCT
ejpam-2666	163	1	(	(	PUNCT
ejpam-2666	163	2	l	l	NOUN
ejpam-2666	163	3	|	|	ADV
ejpam-2666	163	4	a	a	DET
ejpam-2666	163	5	|	|	NOUN
ejpam-2666	163	6	0	0	NUM
ejpam-2666	163	7	)	)	PUNCT
ejpam-2666	163	8	,	,	PUNCT
ejpam-2666	163	9	(	(	PUNCT
ejpam-2666	163	10	g1	g1	VERB
ejpam-2666	163	11	|	|	ADV
ejpam-2666	163	12	g2	g2	PROPN
ejpam-2666	163	13	|	|	CCONJ
ejpam-2666	163	14	g3	g3	PROPN
ejpam-2666	163	15	)	)	PUNCT
ejpam-2666	163	16	〉	〉	PROPN
ejpam-2666	163	17	be	be	AUX
ejpam-2666	163	18	a	a	DET
ejpam-2666	163	19	z2	z2	ADJ
ejpam-2666	163	20	-	-	PUNCT
ejpam-2666	163	21	triple	triple	ADJ
ejpam-2666	163	22	cyclic	cyclic	ADJ
ejpam-2666	163	23	code	code	NOUN
ejpam-2666	163	24	of	of	ADP
ejpam-2666	163	25	block	block	NOUN
ejpam-2666	163	26	length	length	NOUN
ejpam-2666	163	27	(	(	PUNCT
ejpam-2666	163	28	r	r	NOUN
ejpam-2666	163	29	,	,	PUNCT
ejpam-2666	163	30	s	s	PROPN
ejpam-2666	163	31	,	,	PUNCT
ejpam-2666	163	32	t	t	PROPN
ejpam-2666	163	33	)	)	PUNCT
ejpam-2666	163	34	.	.	PUNCT
ejpam-2666	164	1	then	then	ADV
ejpam-2666	164	2	srinivasulu	srinivasulu	PROPN
ejpam-2666	164	3	b	b	PROPN
ejpam-2666	164	4	,	,	PUNCT
ejpam-2666	164	5	maheshanand	maheshanand	NOUN
ejpam-2666	164	6	bhaintwal	bhaintwal	NOUN
ejpam-2666	164	7	/	/	SYM
ejpam-2666	164	8	eur	eur	PROPN
ejpam-2666	164	9	.	.	PUNCT
ejpam-2666	165	1	j.	j.	PROPN
ejpam-2666	165	2	pure	pure	PROPN
ejpam-2666	165	3	appl	appl	PROPN
ejpam-2666	165	4	.	.	PROPN
ejpam-2666	165	5	math	math	PROPN
ejpam-2666	165	6	,	,	PUNCT
ejpam-2666	165	7	10	10	NUM
ejpam-2666	165	8	(	(	PUNCT
ejpam-2666	165	9	2	2	NUM
ejpam-2666	165	10	)	)	PUNCT
ejpam-2666	165	11	(	(	PUNCT
ejpam-2666	165	12	2017	2017	NUM
ejpam-2666	165	13	)	)	PUNCT
ejpam-2666	165	14	,	,	PUNCT
ejpam-2666	165	15	392	392	NUM
ejpam-2666	165	16	-	-	SYM
ejpam-2666	165	17	409	409	NUM
ejpam-2666	165	18	396	396	NUM
ejpam-2666	165	19	(	(	PUNCT
ejpam-2666	165	20	i	i	NOUN
ejpam-2666	165	21	)	)	PUNCT
ejpam-2666	165	22	b|xs−1a	b|xs−1a	PROPN
ejpam-2666	165	23	l	l	NOUN
ejpam-2666	165	24	;	;	PUNCT
ejpam-2666	165	25	(	(	PUNCT
ejpam-2666	165	26	ii	ii	NOUN
ejpam-2666	165	27	)	)	PUNCT
ejpam-2666	165	28	a|xt−1g3	a|xt−1g3	PROPN
ejpam-2666	165	29	g2	g2	PROPN
ejpam-2666	165	30	and	and	CCONJ
ejpam-2666	165	31	if	if	SCONJ
ejpam-2666	165	32	g2	g2	PROPN
ejpam-2666	165	33	=	=	SYM
ejpam-2666	165	34	0	0	NUM
ejpam-2666	165	35	,	,	PUNCT
ejpam-2666	165	36	then	then	ADV
ejpam-2666	165	37	b|xt−1g3	b|xt−1g3	PROPN
ejpam-2666	165	38	g1	g1	PROPN
ejpam-2666	165	39	;	;	PUNCT
ejpam-2666	165	40	(	(	PUNCT
ejpam-2666	165	41	iii	iii	X
ejpam-2666	165	42	)	)	PUNCT
ejpam-2666	165	43	b	b	NOUN
ejpam-2666	165	44	divides	divide	VERB
ejpam-2666	165	45	xt−1	xt−1	PROPN
ejpam-2666	165	46	g3a	g3a	PROPN
ejpam-2666	165	47	lg2	lg2	X
ejpam-2666	165	48	+	+	CCONJ
ejpam-2666	165	49	xt−1	xt−1	PROPN
ejpam-2666	165	50	g3	g3	NOUN
ejpam-2666	165	51	g1	g1	PROPN
ejpam-2666	165	52	.	.	PUNCT
ejpam-2666	166	1	proof	proof	NOUN
ejpam-2666	166	2	.	.	PUNCT
ejpam-2666	167	1	we	we	PRON
ejpam-2666	167	2	have	have	VERB
ejpam-2666	167	3	xs−1	xs−1	PROPN
ejpam-2666	167	4	a	a	PRON
ejpam-2666	167	5	(	(	PUNCT
ejpam-2666	167	6	l	l	NOUN
ejpam-2666	167	7	|	|	ADV
ejpam-2666	167	8	a	a	DET
ejpam-2666	167	9	|	|	NOUN
ejpam-2666	167	10	0	0	NUM
ejpam-2666	167	11	)	)	PUNCT
ejpam-2666	167	12	=	=	SYM
ejpam-2666	168	1	(	(	PUNCT
ejpam-2666	168	2	xs−1	xs−1	X
ejpam-2666	168	3	a	a	DET
ejpam-2666	168	4	l	l	NOUN
ejpam-2666	169	1	|	|	NOUN
ejpam-2666	169	2	0	0	NUM
ejpam-2666	170	1	|	|	ADV
ejpam-2666	170	2	0	0	X
ejpam-2666	170	3	)	)	PUNCT
ejpam-2666	171	1	∈	∈	PROPN
ejpam-2666	171	2	c.	c.	NOUN
ejpam-2666	171	3	this	this	PRON
ejpam-2666	171	4	implies	imply	VERB
ejpam-2666	171	5	that	that	SCONJ
ejpam-2666	171	6	xs−1	xs−1	PROPN
ejpam-2666	171	7	a	a	DET
ejpam-2666	171	8	l	l	NOUN
ejpam-2666	171	9	∈	∈	PROPN
ejpam-2666	171	10	〈	〈	PROPN
ejpam-2666	171	11	b	b	PROPN
ejpam-2666	171	12	〉	〉	PROPN
ejpam-2666	171	13	and	and	CCONJ
ejpam-2666	171	14	hence	hence	ADV
ejpam-2666	171	15	b|xs−1a	b|xs−1a	PROPN
ejpam-2666	171	16	l.	l.	PROPN
ejpam-2666	171	17	similarly	similarly	ADV
ejpam-2666	171	18	,	,	PUNCT
ejpam-2666	171	19	we	we	PRON
ejpam-2666	171	20	can	can	AUX
ejpam-2666	171	21	prove	prove	VERB
ejpam-2666	171	22	the	the	DET
ejpam-2666	171	23	second	second	ADJ
ejpam-2666	171	24	result	result	NOUN
ejpam-2666	171	25	.	.	PUNCT
ejpam-2666	172	1	for	for	ADP
ejpam-2666	172	2	result	result	NOUN
ejpam-2666	172	3	(	(	PUNCT
ejpam-2666	172	4	3	3	NUM
ejpam-2666	172	5	)	)	PUNCT
ejpam-2666	172	6	,	,	PUNCT
ejpam-2666	172	7	as	as	ADP
ejpam-2666	172	8	a|xt−1g3	a|xt−1g3	PROPN
ejpam-2666	172	9	g2	g2	PROPN
ejpam-2666	172	10	,	,	PUNCT
ejpam-2666	172	11	we	we	PRON
ejpam-2666	172	12	have	have	VERB
ejpam-2666	172	13	xt−1	xt−1	PROPN
ejpam-2666	172	14	g3	g3	PROPN
ejpam-2666	172	15	g2	g2	PROPN
ejpam-2666	172	16	=	=	SYM
ejpam-2666	172	17	ka	ka	PROPN
ejpam-2666	172	18	for	for	ADP
ejpam-2666	172	19	some	some	DET
ejpam-2666	172	20	k	k	PROPN
ejpam-2666	172	21	∈	∈	PROPN
ejpam-2666	172	22	z2[x	z2[x	PROPN
ejpam-2666	172	23	]	]	X
ejpam-2666	172	24	.	.	PUNCT
ejpam-2666	173	1	also	also	ADV
ejpam-2666	173	2	as	as	ADP
ejpam-2666	173	3	(	(	PUNCT
ejpam-2666	173	4	kl	kl	INTJ
ejpam-2666	173	5	|	|	ADV
ejpam-2666	173	6	ka	ka	PROPN
ejpam-2666	174	1	|	|	ADV
ejpam-2666	174	2	0	0	NUM
ejpam-2666	174	3	)	)	PUNCT
ejpam-2666	175	1	,	,	PUNCT
ejpam-2666	175	2	(	(	PUNCT
ejpam-2666	175	3	x	x	SYM
ejpam-2666	175	4	t−1	t−1	PROPN
ejpam-2666	175	5	g3	g3	PROPN
ejpam-2666	175	6	g1	g1	PROPN
ejpam-2666	175	7	|	|	ADV
ejpam-2666	175	8	x	x	SYM
ejpam-2666	175	9	t−1	t−1	PROPN
ejpam-2666	175	10	g3	g3	PROPN
ejpam-2666	175	11	g2	g2	PROPN
ejpam-2666	175	12	|	|	ADV
ejpam-2666	175	13	0	0	NUM
ejpam-2666	175	14	)	)	PUNCT
ejpam-2666	175	15	∈	∈	PROPN
ejpam-2666	175	16	c	c	NOUN
ejpam-2666	175	17	,	,	PUNCT
ejpam-2666	175	18	implies	imply	VERB
ejpam-2666	175	19	that	that	SCONJ
ejpam-2666	175	20	(	(	PUNCT
ejpam-2666	175	21	kl	kl	INTJ
ejpam-2666	175	22	|	|	ADV
ejpam-2666	175	23	ka	ka	PROPN
ejpam-2666	175	24	|	|	ADV
ejpam-2666	175	25	0	0	NUM
ejpam-2666	175	26	)	)	PUNCT
ejpam-2666	176	1	+	+	CCONJ
ejpam-2666	176	2	(	(	PUNCT
ejpam-2666	176	3	x	x	SYM
ejpam-2666	176	4	t−1	t−1	PROPN
ejpam-2666	176	5	g3	g3	PROPN
ejpam-2666	176	6	g1	g1	PROPN
ejpam-2666	176	7	|	|	ADV
ejpam-2666	176	8	x	x	SYM
ejpam-2666	176	9	t−1	t−1	PROPN
ejpam-2666	176	10	g3	g3	PROPN
ejpam-2666	176	11	g2	g2	PROPN
ejpam-2666	176	12	|	|	ADV
ejpam-2666	176	13	0	0	NUM
ejpam-2666	176	14	)	)	PUNCT
ejpam-2666	177	1	=	=	PRON
ejpam-2666	178	1	(	(	PUNCT
ejpam-2666	178	2	kl	kl	INTJ
ejpam-2666	178	3	+	+	CCONJ
ejpam-2666	178	4	xt−1	xt−1	PROPN
ejpam-2666	178	5	g3	g3	PROPN
ejpam-2666	178	6	g1	g1	PROPN
ejpam-2666	178	7	|	|	ADV
ejpam-2666	178	8	0	0	NUM
ejpam-2666	179	1	|	|	NOUN
ejpam-2666	179	2	0	0	NUM
ejpam-2666	179	3	)	)	PUNCT
ejpam-2666	179	4	∈	∈	PROPN
ejpam-2666	179	5	c.	c.	NOUN
ejpam-2666	180	1	the	the	DET
ejpam-2666	180	2	result	result	NOUN
ejpam-2666	180	3	follows	follow	VERB
ejpam-2666	180	4	as	as	ADP
ejpam-2666	180	5	kl	kl	PROPN
ejpam-2666	180	6	+	+	PROPN
ejpam-2666	180	7	xt−1	xt−1	PROPN
ejpam-2666	180	8	g3	g3	PROPN
ejpam-2666	180	9	g1	g1	PROPN
ejpam-2666	180	10	∈	∈	PROPN
ejpam-2666	180	11	〈	〈	PROPN
ejpam-2666	180	12	b	b	PROPN
ejpam-2666	180	13	〉	〉	PROPN
ejpam-2666	180	14	.	.	PUNCT
ejpam-2666	181	1	in	in	ADP
ejpam-2666	181	2	the	the	DET
ejpam-2666	181	3	following	follow	VERB
ejpam-2666	181	4	theorem	theorem	NOUN
ejpam-2666	181	5	we	we	PRON
ejpam-2666	181	6	determine	determine	VERB
ejpam-2666	181	7	a	a	DET
ejpam-2666	181	8	minimal	minimal	ADJ
ejpam-2666	181	9	spanning	span	VERB
ejpam-2666	181	10	set	set	NOUN
ejpam-2666	181	11	for	for	ADP
ejpam-2666	181	12	a	a	DET
ejpam-2666	181	13	z2	z2	ADJ
ejpam-2666	181	14	-	-	PUNCT
ejpam-2666	181	15	triple	triple	ADJ
ejpam-2666	181	16	cyclic	cyclic	ADJ
ejpam-2666	181	17	code	code	NOUN
ejpam-2666	181	18	.	.	PUNCT
ejpam-2666	182	1	theorem	theorem	VERB
ejpam-2666	182	2	6	6	NUM
ejpam-2666	182	3	.	.	PUNCT
ejpam-2666	183	1	let	let	VERB
ejpam-2666	183	2	c	c	NOUN
ejpam-2666	183	3	=	=	SYM
ejpam-2666	183	4	〈	〈	PROPN
ejpam-2666	183	5	(	(	PUNCT
ejpam-2666	183	6	b	b	NOUN
ejpam-2666	183	7	|	|	NOUN
ejpam-2666	183	8	0	0	NUM
ejpam-2666	184	1	|	|	NOUN
ejpam-2666	184	2	0	0	NUM
ejpam-2666	184	3	)	)	PUNCT
ejpam-2666	184	4	,	,	PUNCT
ejpam-2666	185	1	(	(	PUNCT
ejpam-2666	185	2	l	l	NOUN
ejpam-2666	185	3	|	|	ADV
ejpam-2666	185	4	a	a	DET
ejpam-2666	185	5	|	|	NOUN
ejpam-2666	185	6	0	0	NUM
ejpam-2666	185	7	)	)	PUNCT
ejpam-2666	185	8	,	,	PUNCT
ejpam-2666	185	9	(	(	PUNCT
ejpam-2666	185	10	g1	g1	VERB
ejpam-2666	185	11	|	|	ADV
ejpam-2666	185	12	g2	g2	PROPN
ejpam-2666	185	13	|	|	CCONJ
ejpam-2666	185	14	g3	g3	PROPN
ejpam-2666	185	15	)	)	PUNCT
ejpam-2666	185	16	〉	〉	PROPN
ejpam-2666	185	17	be	be	AUX
ejpam-2666	185	18	a	a	DET
ejpam-2666	185	19	z2	z2	ADJ
ejpam-2666	185	20	-	-	PUNCT
ejpam-2666	185	21	triple	triple	ADJ
ejpam-2666	185	22	cyclic	cyclic	ADJ
ejpam-2666	185	23	code	code	NOUN
ejpam-2666	185	24	of	of	ADP
ejpam-2666	185	25	block	block	NOUN
ejpam-2666	185	26	length	length	NOUN
ejpam-2666	185	27	(	(	PUNCT
ejpam-2666	185	28	r	r	NOUN
ejpam-2666	185	29	,	,	PUNCT
ejpam-2666	185	30	s	s	PROPN
ejpam-2666	185	31	,	,	PUNCT
ejpam-2666	185	32	t	t	PROPN
ejpam-2666	185	33	)	)	PUNCT
ejpam-2666	185	34	such	such	ADJ
ejpam-2666	185	35	that	that	DET
ejpam-2666	185	36	b	b	NOUN
ejpam-2666	185	37	,	,	PUNCT
ejpam-2666	185	38	l	l	NOUN
ejpam-2666	185	39	,	,	PUNCT
ejpam-2666	185	40	g1	g1	PROPN
ejpam-2666	185	41	∈	∈	PROPN
ejpam-2666	185	42	z2,r[x	z2,r[x	PROPN
ejpam-2666	185	43	]	]	X
ejpam-2666	185	44	,	,	PUNCT
ejpam-2666	185	45	a	a	PRON
ejpam-2666	185	46	,	,	PUNCT
ejpam-2666	185	47	g2	g2	PROPN
ejpam-2666	185	48	∈	∈	PROPN
ejpam-2666	185	49	z2,s[x	z2,s[x	PROPN
ejpam-2666	185	50	]	]	X
ejpam-2666	185	51	,	,	PUNCT
ejpam-2666	185	52	g3	g3	PROPN
ejpam-2666	185	53	∈	∈	PROPN
ejpam-2666	185	54	z2,t[x	z2,t[x	PROPN
ejpam-2666	185	55	]	]	PUNCT
ejpam-2666	185	56	with	with	ADP
ejpam-2666	185	57	b|xr−	b|xr−	NUM
ejpam-2666	185	58	1	1	NUM
ejpam-2666	185	59	,	,	PUNCT
ejpam-2666	185	60	a|xs−	a|xs−	ADJ
ejpam-2666	185	61	1	1	NUM
ejpam-2666	185	62	and	and	CCONJ
ejpam-2666	185	63	g3|xt	g3|xt	PROPN
ejpam-2666	185	64	−	−	PROPN
ejpam-2666	186	1	1	1	X
ejpam-2666	186	2	.	.	PUNCT
ejpam-2666	187	1	let	let	VERB
ejpam-2666	187	2	h1	h1	VERB
ejpam-2666	187	3	=	=	PROPN
ejpam-2666	187	4	xr−1	xr−1	PROPN
ejpam-2666	187	5	b	b	PROPN
ejpam-2666	187	6	,	,	PUNCT
ejpam-2666	187	7	h2	h2	PROPN
ejpam-2666	187	8	=	=	SYM
ejpam-2666	187	9	xs−1	xs−1	PROPN
ejpam-2666	187	10	a	a	PRON
ejpam-2666	187	11	and	and	CCONJ
ejpam-2666	187	12	h3	h3	NOUN
ejpam-2666	187	13	=	=	SYM
ejpam-2666	187	14	xt−1	xt−1	PROPN
ejpam-2666	187	15	g3	g3	PROPN
ejpam-2666	187	16	.	.	PUNCT
ejpam-2666	188	1	if	if	SCONJ
ejpam-2666	188	2	deg(b	deg(b	PROPN
ejpam-2666	188	3	)	)	PUNCT
ejpam-2666	188	4	=	=	SYM
ejpam-2666	188	5	t1	t1	PROPN
ejpam-2666	188	6	,	,	PUNCT
ejpam-2666	188	7	deg(a	deg(a	PROPN
ejpam-2666	188	8	)	)	PUNCT
ejpam-2666	188	9	=	=	NOUN
ejpam-2666	188	10	t2	t2	NOUN
ejpam-2666	188	11	and	and	CCONJ
ejpam-2666	188	12	deg(g3	deg(g3	NOUN
ejpam-2666	188	13	)	)	PUNCT
ejpam-2666	188	14	=	=	SYM
ejpam-2666	188	15	t3	t3	PROPN
ejpam-2666	188	16	,	,	PUNCT
ejpam-2666	188	17	then	then	ADV
ejpam-2666	188	18	a	a	DET
ejpam-2666	188	19	minimal	minimal	ADJ
ejpam-2666	188	20	spanning	span	VERB
ejpam-2666	188	21	set	set	NOUN
ejpam-2666	188	22	for	for	ADP
ejpam-2666	188	23	c	c	PROPN
ejpam-2666	188	24	is	be	AUX
ejpam-2666	188	25	s	s	NOUN
ejpam-2666	188	26	=	=	NOUN
ejpam-2666	188	27	s1	s1	PROPN
ejpam-2666	188	28	∪	∪	ADP
ejpam-2666	188	29	s2	s2	PROPN
ejpam-2666	188	30	∪	∪	X
ejpam-2666	188	31	s3	s3	PROPN
ejpam-2666	188	32	,	,	PUNCT
ejpam-2666	188	33	where	where	SCONJ
ejpam-2666	188	34	s1	s1	PROPN
ejpam-2666	188	35	=	=	PROPN
ejpam-2666	188	36	r−t1−1⋃	r−t1−1⋃	X
ejpam-2666	189	1	i=0	i=0	PROPN
ejpam-2666	189	2	xi	xi	PROPN
ejpam-2666	189	3	∗	∗	PROPN
ejpam-2666	189	4	(	(	PUNCT
ejpam-2666	189	5	b	b	NOUN
ejpam-2666	189	6	|	|	ADV
ejpam-2666	189	7	0	0	NUM
ejpam-2666	190	1	|	|	NOUN
ejpam-2666	190	2	0	0	NUM
ejpam-2666	190	3	)	)	PUNCT
ejpam-2666	190	4	s2	s2	NOUN
ejpam-2666	190	5	=	=	PUNCT
ejpam-2666	190	6	s−t2−1⋃	s−t2−1⋃	NOUN
ejpam-2666	190	7	i=0	i=0	PROPN
ejpam-2666	190	8	xi	xi	PROPN
ejpam-2666	190	9	∗	∗	PROPN
ejpam-2666	190	10	(	(	PUNCT
ejpam-2666	190	11	l	l	NOUN
ejpam-2666	190	12	|	|	ADV
ejpam-2666	190	13	a	a	DET
ejpam-2666	190	14	|	|	NOUN
ejpam-2666	190	15	0	0	NUM
ejpam-2666	190	16	)	)	PUNCT
ejpam-2666	190	17	s3	s3	NOUN
ejpam-2666	190	18	=	=	PROPN
ejpam-2666	190	19	t−t3−1⋃	t−t3−1⋃	NOUN
ejpam-2666	190	20	i=0	i=0	PROPN
ejpam-2666	190	21	xi	xi	PROPN
ejpam-2666	190	22	∗	∗	PROPN
ejpam-2666	190	23	(	(	PUNCT
ejpam-2666	190	24	g1	g1	PROPN
ejpam-2666	190	25	|	|	ADV
ejpam-2666	190	26	g2	g2	PROPN
ejpam-2666	190	27	|	|	CCONJ
ejpam-2666	190	28	g3	g3	PROPN
ejpam-2666	190	29	)	)	PUNCT
ejpam-2666	190	30	.	.	PUNCT
ejpam-2666	191	1	moreover	moreover	ADV
ejpam-2666	191	2	,	,	PUNCT
ejpam-2666	191	3	|	|	ADV
ejpam-2666	191	4	c	c	NOUN
ejpam-2666	191	5	|=	|=	NOUN
ejpam-2666	191	6	2r+s+t−deg(b)−deg(a)−deg(g3	2r+s+t−deg(b)−deg(a)−deg(g3	NUM
ejpam-2666	191	7	)	)	PUNCT
ejpam-2666	191	8	.	.	PUNCT
ejpam-2666	192	1	proof	proof	NOUN
ejpam-2666	192	2	.	.	PUNCT
ejpam-2666	193	1	let	let	VERB
ejpam-2666	193	2	c	c	PRON
ejpam-2666	193	3	be	be	AUX
ejpam-2666	193	4	a	a	DET
ejpam-2666	193	5	codeword	codeword	NOUN
ejpam-2666	193	6	in	in	ADP
ejpam-2666	193	7	c.	c.	PROPN
ejpam-2666	193	8	then	then	ADV
ejpam-2666	193	9	there	there	PRON
ejpam-2666	193	10	exist	exist	VERB
ejpam-2666	193	11	d1	d1	PROPN
ejpam-2666	193	12	,	,	PUNCT
ejpam-2666	193	13	d2	d2	PROPN
ejpam-2666	193	14	,	,	PUNCT
ejpam-2666	193	15	d3	d3	PROPN
ejpam-2666	193	16	∈	∈	PROPN
ejpam-2666	193	17	z2[x	z2[x	PROPN
ejpam-2666	193	18	]	]	PUNCT
ejpam-2666	194	1	such	such	ADJ
ejpam-2666	194	2	that	that	SCONJ
ejpam-2666	194	3	c	c	NOUN
ejpam-2666	194	4	=	=	SYM
ejpam-2666	194	5	d1	d1	PROPN
ejpam-2666	194	6	∗	∗	NOUN
ejpam-2666	194	7	(	(	PUNCT
ejpam-2666	194	8	b	b	NOUN
ejpam-2666	194	9	|	|	ADV
ejpam-2666	194	10	0	0	NUM
ejpam-2666	194	11	|	|	ADV
ejpam-2666	194	12	0	0	NUM
ejpam-2666	194	13	)	)	PUNCT
ejpam-2666	194	14	+	+	CCONJ
ejpam-2666	194	15	d2	d2	PROPN
ejpam-2666	194	16	∗	∗	NOUN
ejpam-2666	194	17	(	(	PUNCT
ejpam-2666	194	18	l	l	NOUN
ejpam-2666	194	19	|	|	ADV
ejpam-2666	194	20	a	a	DET
ejpam-2666	194	21	|	|	NOUN
ejpam-2666	194	22	0	0	NUM
ejpam-2666	194	23	)	)	PUNCT
ejpam-2666	194	24	+	+	CCONJ
ejpam-2666	194	25	d3	d3	PROPN
ejpam-2666	194	26	∗	∗	NOUN
ejpam-2666	194	27	(	(	PUNCT
ejpam-2666	194	28	g1	g1	PROPN
ejpam-2666	194	29	|	|	ADV
ejpam-2666	194	30	g2	g2	PROPN
ejpam-2666	194	31	|	|	CCONJ
ejpam-2666	194	32	g3	g3	PROPN
ejpam-2666	194	33	)	)	PUNCT
ejpam-2666	194	34	(	(	PUNCT
ejpam-2666	194	35	1	1	X
ejpam-2666	194	36	)	)	PUNCT
ejpam-2666	194	37	=	=	SYM
ejpam-2666	194	38	(	(	PUNCT
ejpam-2666	194	39	d1b	d1b	NOUN
ejpam-2666	194	40	|	|	ADV
ejpam-2666	194	41	0	0	NUM
ejpam-2666	195	1	|	|	ADV
ejpam-2666	195	2	0	0	NUM
ejpam-2666	195	3	)	)	PUNCT
ejpam-2666	196	1	+	+	CCONJ
ejpam-2666	196	2	(	(	PUNCT
ejpam-2666	196	3	d2l	d2l	ADV
ejpam-2666	197	1	|	|	INTJ
ejpam-2666	197	2	d2a	d2a	PROPN
ejpam-2666	197	3	|	|	NOUN
ejpam-2666	197	4	0	0	NUM
ejpam-2666	197	5	)	)	PUNCT
ejpam-2666	198	1	+	+	CCONJ
ejpam-2666	198	2	(	(	PUNCT
ejpam-2666	198	3	d3g1	d3g1	X
ejpam-2666	198	4	|	|	NOUN
ejpam-2666	198	5	d3g2	d3g2	PROPN
ejpam-2666	198	6	|	|	ADV
ejpam-2666	198	7	d3g3	d3g3	NOUN
ejpam-2666	198	8	)	)	PUNCT
ejpam-2666	198	9	we	we	PRON
ejpam-2666	198	10	first	first	ADV
ejpam-2666	198	11	show	show	VERB
ejpam-2666	198	12	that	that	SCONJ
ejpam-2666	198	13	d1	d1	PROPN
ejpam-2666	198	14	∗	∗	NOUN
ejpam-2666	198	15	(	(	PUNCT
ejpam-2666	198	16	b	b	NOUN
ejpam-2666	199	1	|	|	ADV
ejpam-2666	199	2	0	0	NUM
ejpam-2666	200	1	|	|	NOUN
ejpam-2666	200	2	0	0	NUM
ejpam-2666	200	3	)	)	PUNCT
ejpam-2666	200	4	∈	∈	PROPN
ejpam-2666	200	5	span(s1	span(s1	NOUN
ejpam-2666	200	6	)	)	PUNCT
ejpam-2666	200	7	.	.	PUNCT
ejpam-2666	201	1	if	if	SCONJ
ejpam-2666	201	2	deg(d1	deg(d1	NOUN
ejpam-2666	201	3	)	)	PUNCT
ejpam-2666	201	4	<	<	X
ejpam-2666	201	5	r	r	NOUN
ejpam-2666	201	6	−	−	PROPN
ejpam-2666	201	7	t1	t1	NOUN
ejpam-2666	201	8	,	,	PUNCT
ejpam-2666	201	9	then	then	ADV
ejpam-2666	201	10	obviously	obviously	ADV
ejpam-2666	201	11	d1	d1	PROPN
ejpam-2666	201	12	∗	∗	NOUN
ejpam-2666	201	13	(	(	PUNCT
ejpam-2666	201	14	b	b	NOUN
ejpam-2666	201	15	|	|	ADV
ejpam-2666	201	16	0	0	NUM
ejpam-2666	202	1	|	|	NOUN
ejpam-2666	202	2	0	0	NUM
ejpam-2666	202	3	)	)	PUNCT
ejpam-2666	202	4	∈	∈	PROPN
ejpam-2666	202	5	span(s1	span(s1	NOUN
ejpam-2666	202	6	)	)	PUNCT
ejpam-2666	202	7	.	.	PUNCT
ejpam-2666	203	1	let	let	VERB
ejpam-2666	203	2	deg(d1	deg(d1	NOUN
ejpam-2666	203	3	)	)	PUNCT
ejpam-2666	203	4	≥	≥	PROPN
ejpam-2666	203	5	r	r	NOUN
ejpam-2666	203	6	−	−	PROPN
ejpam-2666	203	7	t1	t1	NOUN
ejpam-2666	203	8	.	.	PUNCT
ejpam-2666	204	1	by	by	ADP
ejpam-2666	204	2	division	division	NOUN
ejpam-2666	204	3	algorithm	algorithm	NOUN
ejpam-2666	204	4	,	,	PUNCT
ejpam-2666	204	5	there	there	PRON
ejpam-2666	204	6	exist	exist	VERB
ejpam-2666	204	7	q1,r1∈	q1,r1∈	PROPN
ejpam-2666	204	8	z2[x	z2[x	PROPN
ejpam-2666	204	9	]	]	PUNCT
ejpam-2666	204	10	such	such	ADJ
ejpam-2666	204	11	that	that	SCONJ
ejpam-2666	204	12	d1	d1	PROPN
ejpam-2666	204	13	=	=	SYM
ejpam-2666	204	14	q1	q1	PROPN
ejpam-2666	204	15	xr−1	xr−1	PROPN
ejpam-2666	204	16	b	b	PROPN
ejpam-2666	205	1	+	+	PUNCT
ejpam-2666	205	2	r1	r1	PROPN
ejpam-2666	205	3	with	with	ADP
ejpam-2666	205	4	r1	r1	PROPN
ejpam-2666	205	5	=	=	SYM
ejpam-2666	205	6	0	0	NUM
ejpam-2666	205	7	or	or	CCONJ
ejpam-2666	205	8	deg(r1	deg(r1	NOUN
ejpam-2666	205	9	)	)	PUNCT
ejpam-2666	205	10	<	<	X
ejpam-2666	205	11	r	r	NOUN
ejpam-2666	205	12	−	−	PROPN
ejpam-2666	205	13	t1	t1	NOUN
ejpam-2666	205	14	.	.	PUNCT
ejpam-2666	206	1	then	then	ADV
ejpam-2666	206	2	(	(	PUNCT
ejpam-2666	206	3	d1b	d1b	VERB
ejpam-2666	206	4	|	|	ADV
ejpam-2666	206	5	0	0	NUM
ejpam-2666	206	6	|	|	NOUN
ejpam-2666	206	7	0	0	NUM
ejpam-2666	206	8	)	)	PUNCT
ejpam-2666	206	9	=	=	SYM
ejpam-2666	207	1	(	(	PUNCT
ejpam-2666	207	2	(	(	PUNCT
ejpam-2666	207	3	q1	q1	PROPN
ejpam-2666	207	4	xr	xr	PROPN
ejpam-2666	207	5	−	−	PROPN
ejpam-2666	208	1	1	1	NUM
ejpam-2666	208	2	b	b	X
ejpam-2666	208	3	+	+	NOUN
ejpam-2666	208	4	r1	r1	NOUN
ejpam-2666	208	5	)	)	PUNCT
ejpam-2666	208	6	b	b	NOUN
ejpam-2666	209	1	|	|	ADV
ejpam-2666	209	2	0	0	NUM
ejpam-2666	210	1	|	|	ADV
ejpam-2666	210	2	0	0	X
ejpam-2666	210	3	)	)	PUNCT
ejpam-2666	211	1	=	=	PUNCT
ejpam-2666	211	2	(	(	PUNCT
ejpam-2666	212	1	q1(x	q1(x	NOUN
ejpam-2666	212	2	r	r	NOUN
ejpam-2666	212	3	−	−	NOUN
ejpam-2666	212	4	1	1	NUM
ejpam-2666	212	5	)	)	PUNCT
ejpam-2666	213	1	+	+	ADP
ejpam-2666	213	2	r1b	r1b	PROPN
ejpam-2666	213	3	|	|	NOUN
ejpam-2666	213	4	0	0	NUM
ejpam-2666	214	1	|	|	ADV
ejpam-2666	214	2	0	0	NUM
ejpam-2666	214	3	)	)	PUNCT
ejpam-2666	215	1	=	=	PUNCT
ejpam-2666	216	1	q1(x	q1(x	NOUN
ejpam-2666	216	2	r	r	NOUN
ejpam-2666	216	3	−	−	NOUN
ejpam-2666	216	4	1	1	NUM
ejpam-2666	217	1	|	|	ADV
ejpam-2666	217	2	0	0	NUM
ejpam-2666	218	1	|	|	ADV
ejpam-2666	218	2	0	0	X
ejpam-2666	218	3	)	)	PUNCT
ejpam-2666	219	1	+	+	NOUN
ejpam-2666	219	2	r1(b	r1(b	PROPN
ejpam-2666	219	3	|	|	ADV
ejpam-2666	219	4	0	0	NUM
ejpam-2666	220	1	|	|	ADV
ejpam-2666	220	2	0	0	NUM
ejpam-2666	220	3	)	)	PUNCT
ejpam-2666	221	1	=	=	VERB
ejpam-2666	221	2	r1(b	r1(b	PROPN
ejpam-2666	222	1	|	|	ADV
ejpam-2666	222	2	0	0	NUM
ejpam-2666	223	1	|	|	ADV
ejpam-2666	223	2	0	0	NUM
ejpam-2666	223	3	)	)	PUNCT
ejpam-2666	223	4	∈	∈	PROPN
ejpam-2666	223	5	span(s1	span(s1	NOUN
ejpam-2666	223	6	)	)	PUNCT
ejpam-2666	223	7	.	.	PUNCT
ejpam-2666	224	1	next	next	ADV
ejpam-2666	224	2	we	we	PRON
ejpam-2666	224	3	show	show	VERB
ejpam-2666	224	4	that	that	SCONJ
ejpam-2666	224	5	d2	d2	PROPN
ejpam-2666	224	6	∗	∗	NOUN
ejpam-2666	224	7	(	(	PUNCT
ejpam-2666	224	8	l	l	NOUN
ejpam-2666	224	9	|	|	ADV
ejpam-2666	224	10	a	a	DET
ejpam-2666	224	11	|	|	NOUN
ejpam-2666	224	12	0	0	NUM
ejpam-2666	224	13	)	)	PUNCT
ejpam-2666	224	14	∈	∈	PROPN
ejpam-2666	224	15	span(s1	span(s1	ADJ
ejpam-2666	224	16	∪	∪	X
ejpam-2666	224	17	s2	s2	PROPN
ejpam-2666	224	18	)	)	PUNCT
ejpam-2666	224	19	.	.	PUNCT
ejpam-2666	225	1	we	we	PRON
ejpam-2666	225	2	have	have	VERB
ejpam-2666	225	3	by	by	ADP
ejpam-2666	225	4	division	division	NOUN
ejpam-2666	225	5	algorithm	algorithm	NOUN
ejpam-2666	225	6	d2	d2	PROPN
ejpam-2666	225	7	=	=	SYM
ejpam-2666	225	8	q2h2	q2h2	PROPN
ejpam-2666	225	9	+	+	ADJ
ejpam-2666	225	10	r2	r2	NOUN
ejpam-2666	225	11	with	with	ADP
ejpam-2666	225	12	r2	r2	PROPN
ejpam-2666	225	13	=	=	SYM
ejpam-2666	225	14	0	0	NUM
ejpam-2666	225	15	or	or	CCONJ
ejpam-2666	225	16	deg(r2	deg(r2	NOUN
ejpam-2666	225	17	)	)	PUNCT
ejpam-2666	225	18	<	<	X
ejpam-2666	225	19	s−	s−	PROPN
ejpam-2666	225	20	t2	t2	PROPN
ejpam-2666	225	21	,	,	PUNCT
ejpam-2666	225	22	q2	q2	NOUN
ejpam-2666	225	23	,	,	PUNCT
ejpam-2666	225	24	r2	r2	PROPN
ejpam-2666	225	25	∈	∈	PROPN
ejpam-2666	225	26	z2[x	z2[x	PROPN
ejpam-2666	225	27	]	]	PUNCT
ejpam-2666	225	28	.	.	PUNCT
ejpam-2666	226	1	therefore	therefore	ADV
ejpam-2666	226	2	d2	d2	PROPN
ejpam-2666	226	3	∗	∗	NOUN
ejpam-2666	226	4	(	(	PUNCT
ejpam-2666	226	5	l	l	NOUN
ejpam-2666	226	6	|	|	ADV
ejpam-2666	226	7	a	a	DET
ejpam-2666	226	8	|	|	NOUN
ejpam-2666	226	9	0	0	NUM
ejpam-2666	226	10	)	)	PUNCT
ejpam-2666	226	11	=	=	NOUN
ejpam-2666	227	1	(	(	PUNCT
ejpam-2666	227	2	q2h2	q2h2	X
ejpam-2666	227	3	+	+	NOUN
ejpam-2666	227	4	r2)(l	r2)(l	NOUN
ejpam-2666	227	5	|	|	ADV
ejpam-2666	227	6	a	a	DET
ejpam-2666	227	7	|	|	NOUN
ejpam-2666	227	8	0	0	NUM
ejpam-2666	227	9	)	)	PUNCT
ejpam-2666	227	10	srinivasulu	srinivasulu	ADP
ejpam-2666	227	11	b	b	NUM
ejpam-2666	227	12	,	,	PUNCT
ejpam-2666	227	13	maheshanand	maheshanand	NOUN
ejpam-2666	227	14	bhaintwal	bhaintwal	NOUN
ejpam-2666	227	15	/	/	SYM
ejpam-2666	227	16	eur	eur	PROPN
ejpam-2666	227	17	.	.	PUNCT
ejpam-2666	228	1	j.	j.	PROPN
ejpam-2666	228	2	pure	pure	PROPN
ejpam-2666	228	3	appl	appl	PROPN
ejpam-2666	228	4	.	.	PROPN
ejpam-2666	228	5	math	math	PROPN
ejpam-2666	228	6	,	,	PUNCT
ejpam-2666	228	7	10	10	NUM
ejpam-2666	228	8	(	(	PUNCT
ejpam-2666	228	9	2	2	NUM
ejpam-2666	228	10	)	)	PUNCT
ejpam-2666	228	11	(	(	PUNCT
ejpam-2666	228	12	2017	2017	NUM
ejpam-2666	228	13	)	)	PUNCT
ejpam-2666	228	14	,	,	PUNCT
ejpam-2666	228	15	392	392	NUM
ejpam-2666	228	16	-	-	SYM
ejpam-2666	228	17	409	409	NUM
ejpam-2666	228	18	397	397	NUM
ejpam-2666	228	19	=	=	SYM
ejpam-2666	228	20	q2(lh2	q2(lh2	ADJ
ejpam-2666	228	21	|	|	NOUN
ejpam-2666	228	22	0	0	NUM
ejpam-2666	228	23	|	|	NOUN
ejpam-2666	228	24	0	0	NUM
ejpam-2666	228	25	)	)	PUNCT
ejpam-2666	229	1	+	+	CCONJ
ejpam-2666	229	2	r2(l	r2(l	PROPN
ejpam-2666	229	3	|	|	ADV
ejpam-2666	229	4	a	a	DET
ejpam-2666	229	5	|	|	NOUN
ejpam-2666	229	6	0	0	NUM
ejpam-2666	229	7	)	)	PUNCT
ejpam-2666	229	8	.	.	PUNCT
ejpam-2666	230	1	(	(	PUNCT
ejpam-2666	230	2	2	2	X
ejpam-2666	230	3	)	)	PUNCT
ejpam-2666	230	4	since	since	SCONJ
ejpam-2666	230	5	0	0	NUM
ejpam-2666	230	6	≤	≤	NUM
ejpam-2666	230	7	deg(r2	deg(r2	NOUN
ejpam-2666	230	8	)	)	PUNCT
ejpam-2666	230	9	≤	≤	PROPN
ejpam-2666	230	10	s	s	PART
ejpam-2666	230	11	−	−	PROPN
ejpam-2666	230	12	t2	t2	NOUN
ejpam-2666	230	13	−	−	PROPN
ejpam-2666	230	14	1	1	NUM
ejpam-2666	230	15	,	,	PUNCT
ejpam-2666	230	16	we	we	PRON
ejpam-2666	230	17	have	have	VERB
ejpam-2666	230	18	r2(l	r2(l	NOUN
ejpam-2666	230	19	|	|	ADV
ejpam-2666	230	20	a	a	DET
ejpam-2666	230	21	|	|	NOUN
ejpam-2666	230	22	0	0	NUM
ejpam-2666	230	23	)	)	PUNCT
ejpam-2666	230	24	∈	∈	PROPN
ejpam-2666	230	25	span(s2	span(s2	NOUN
ejpam-2666	230	26	)	)	PUNCT
ejpam-2666	230	27	.	.	PUNCT
ejpam-2666	231	1	also	also	ADV
ejpam-2666	231	2	from	from	ADP
ejpam-2666	231	3	lemma	lemma	PROPN
ejpam-2666	231	4	2	2	NUM
ejpam-2666	231	5	,	,	PUNCT
ejpam-2666	231	6	we	we	PRON
ejpam-2666	231	7	have	have	VERB
ejpam-2666	231	8	b	b	NOUN
ejpam-2666	231	9	|	|	ADV
ejpam-2666	231	10	h2l	h2l	PROPN
ejpam-2666	231	11	,	,	PUNCT
ejpam-2666	231	12	which	which	PRON
ejpam-2666	231	13	implies	imply	VERB
ejpam-2666	231	14	that	that	SCONJ
ejpam-2666	231	15	q2(lh2	q2(lh2	ADJ
ejpam-2666	231	16	|	|	NOUN
ejpam-2666	231	17	0	0	NUM
ejpam-2666	231	18	|	|	NOUN
ejpam-2666	231	19	0	0	NUM
ejpam-2666	231	20	)	)	PUNCT
ejpam-2666	231	21	∈	∈	PROPN
ejpam-2666	231	22	span(s1	span(s1	NOUN
ejpam-2666	231	23	)	)	PUNCT
ejpam-2666	231	24	.	.	PUNCT
ejpam-2666	232	1	therefore	therefore	ADV
ejpam-2666	232	2	from	from	ADP
ejpam-2666	232	3	(	(	PUNCT
ejpam-2666	232	4	2	2	X
ejpam-2666	232	5	)	)	PUNCT
ejpam-2666	232	6	we	we	PRON
ejpam-2666	232	7	get	get	VERB
ejpam-2666	232	8	d2	d2	NOUN
ejpam-2666	232	9	∗	∗	NOUN
ejpam-2666	232	10	(	(	PUNCT
ejpam-2666	232	11	l	l	NOUN
ejpam-2666	232	12	|	|	ADV
ejpam-2666	232	13	a	a	DET
ejpam-2666	232	14	|	|	NOUN
ejpam-2666	232	15	0	0	NUM
ejpam-2666	232	16	)	)	PUNCT
ejpam-2666	232	17	∈	∈	PROPN
ejpam-2666	232	18	span(s1	span(s1	ADJ
ejpam-2666	232	19	∪	∪	X
ejpam-2666	232	20	s2	s2	PROPN
ejpam-2666	232	21	)	)	PUNCT
ejpam-2666	232	22	.	.	PUNCT
ejpam-2666	233	1	finally	finally	ADV
ejpam-2666	233	2	we	we	PRON
ejpam-2666	233	3	show	show	VERB
ejpam-2666	233	4	that	that	SCONJ
ejpam-2666	233	5	d3	d3	PROPN
ejpam-2666	233	6	∗	∗	NOUN
ejpam-2666	233	7	(	(	PUNCT
ejpam-2666	233	8	g1	g1	PROPN
ejpam-2666	233	9	|	|	ADV
ejpam-2666	233	10	g2	g2	PROPN
ejpam-2666	233	11	|	|	CCONJ
ejpam-2666	233	12	g3	g3	PROPN
ejpam-2666	233	13	)	)	PUNCT
ejpam-2666	233	14	belongs	belong	VERB
ejpam-2666	233	15	to	to	ADP
ejpam-2666	233	16	span(s1	span(s1	ADJ
ejpam-2666	233	17	∪	∪	PROPN
ejpam-2666	233	18	s2	s2	PROPN
ejpam-2666	233	19	∪	∪	X
ejpam-2666	233	20	s3	s3	PROPN
ejpam-2666	233	21	)	)	PUNCT
ejpam-2666	233	22	.	.	PUNCT
ejpam-2666	234	1	again	again	ADV
ejpam-2666	234	2	by	by	ADP
ejpam-2666	234	3	the	the	DET
ejpam-2666	234	4	division	division	NOUN
ejpam-2666	234	5	algorithm	algorithm	NOUN
ejpam-2666	234	6	,	,	PUNCT
ejpam-2666	234	7	we	we	PRON
ejpam-2666	234	8	have	have	VERB
ejpam-2666	234	9	d3	d3	PROPN
ejpam-2666	234	10	=	=	SYM
ejpam-2666	234	11	q3h3	q3h3	PROPN
ejpam-2666	234	12	+	+	NUM
ejpam-2666	234	13	r3	r3	PROPN
ejpam-2666	234	14	with	with	ADP
ejpam-2666	234	15	r3	r3	PROPN
ejpam-2666	234	16	=	=	SYM
ejpam-2666	234	17	0	0	NUM
ejpam-2666	234	18	or	or	CCONJ
ejpam-2666	234	19	deg(r3	deg(r3	NOUN
ejpam-2666	234	20	)	)	PUNCT
ejpam-2666	234	21	<	<	X
ejpam-2666	234	22	t	t	PROPN
ejpam-2666	235	1	−	−	PROPN
ejpam-2666	235	2	t3	t3	PROPN
ejpam-2666	235	3	,	,	PUNCT
ejpam-2666	235	4	where	where	SCONJ
ejpam-2666	235	5	q3	q3	NOUN
ejpam-2666	235	6	and	and	CCONJ
ejpam-2666	235	7	r3	r3	PROPN
ejpam-2666	235	8	∈	∈	PROPN
ejpam-2666	235	9	z2[x	z2[x	PROPN
ejpam-2666	235	10	]	]	PUNCT
ejpam-2666	235	11	.	.	PUNCT
ejpam-2666	236	1	then	then	ADV
ejpam-2666	236	2	d3	d3	PROPN
ejpam-2666	236	3	∗	∗	NOUN
ejpam-2666	236	4	(	(	PUNCT
ejpam-2666	236	5	g1	g1	PROPN
ejpam-2666	236	6	|	|	ADV
ejpam-2666	236	7	g2	g2	PROPN
ejpam-2666	236	8	|	|	CCONJ
ejpam-2666	236	9	g3	g3	PROPN
ejpam-2666	236	10	)	)	PUNCT
ejpam-2666	236	11	=	=	PRON
ejpam-2666	236	12	(	(	PUNCT
ejpam-2666	236	13	q3h3	q3h3	PROPN
ejpam-2666	236	14	+	+	NOUN
ejpam-2666	236	15	r3	r3	NOUN
ejpam-2666	236	16	)	)	PUNCT
ejpam-2666	236	17	(	(	PUNCT
ejpam-2666	236	18	g1	g1	VERB
ejpam-2666	236	19	|	|	ADV
ejpam-2666	236	20	g2	g2	PROPN
ejpam-2666	236	21	|	|	CCONJ
ejpam-2666	236	22	g3	g3	PROPN
ejpam-2666	236	23	)	)	PUNCT
ejpam-2666	237	1	=	=	PRON
ejpam-2666	237	2	q3h3(g1	q3h3(g1	NUM
ejpam-2666	238	1	|	|	ADV
ejpam-2666	238	2	g2	g2	VERB
ejpam-2666	238	3	|	|	ADV
ejpam-2666	238	4	0	0	NUM
ejpam-2666	238	5	)	)	PUNCT
ejpam-2666	239	1	+	+	NOUN
ejpam-2666	239	2	r3(g1	r3(g1	VERB
ejpam-2666	239	3	|	|	ADV
ejpam-2666	239	4	g2	g2	PROPN
ejpam-2666	239	5	|	|	CCONJ
ejpam-2666	239	6	g3	g3	PROPN
ejpam-2666	239	7	)	)	PUNCT
ejpam-2666	239	8	.	.	PUNCT
ejpam-2666	240	1	(	(	PUNCT
ejpam-2666	240	2	3	3	X
ejpam-2666	240	3	)	)	PUNCT
ejpam-2666	240	4	it	it	PRON
ejpam-2666	240	5	easy	easy	ADJ
ejpam-2666	240	6	to	to	PART
ejpam-2666	240	7	see	see	VERB
ejpam-2666	240	8	that	that	DET
ejpam-2666	240	9	q3h3(g1	q3h3(g1	NOUN
ejpam-2666	240	10	|	|	ADV
ejpam-2666	240	11	g2	g2	VERB
ejpam-2666	240	12	|	|	ADV
ejpam-2666	240	13	0	0	NUM
ejpam-2666	240	14	)	)	PUNCT
ejpam-2666	240	15	∈	∈	PROPN
ejpam-2666	240	16	c	c	NOUN
ejpam-2666	240	17	and	and	CCONJ
ejpam-2666	240	18	hence	hence	ADV
ejpam-2666	240	19	q3h3(g1	q3h3(g1	VERB
ejpam-2666	240	20	|	|	ADV
ejpam-2666	240	21	g2	g2	PROPN
ejpam-2666	240	22	)	)	PUNCT
ejpam-2666	241	1	∈	∈	PROPN
ejpam-2666	242	1	k	k	NOUN
ejpam-2666	242	2	=	=	PRON
ejpam-2666	242	3	{	{	PUNCT
ejpam-2666	242	4	(	(	PUNCT
ejpam-2666	242	5	c1	c1	PROPN
ejpam-2666	242	6	|	|	PROPN
ejpam-2666	242	7	c2	c2	PROPN
ejpam-2666	242	8	)	)	PUNCT
ejpam-2666	242	9	:	:	PUNCT
ejpam-2666	242	10	(	(	PUNCT
ejpam-2666	242	11	c1	c1	PROPN
ejpam-2666	242	12	|	|	ADV
ejpam-2666	242	13	c2	c2	PROPN
ejpam-2666	242	14	|	|	ADV
ejpam-2666	242	15	0	0	NUM
ejpam-2666	242	16	)	)	PUNCT
ejpam-2666	242	17	∈	∈	PROPN
ejpam-2666	242	18	kerc(πt	kerc(πt	NOUN
ejpam-2666	242	19	)	)	PUNCT
ejpam-2666	242	20	}	}	PUNCT
ejpam-2666	242	21	.	.	PUNCT
ejpam-2666	243	1	from	from	ADP
ejpam-2666	243	2	theorem	theorem	ADJ
ejpam-2666	243	3	4	4	NUM
ejpam-2666	243	4	,	,	PUNCT
ejpam-2666	243	5	we	we	PRON
ejpam-2666	243	6	have	have	AUX
ejpam-2666	243	7	q3h3(g1	q3h3(g1	VERB
ejpam-2666	243	8	|	|	ADV
ejpam-2666	243	9	g2	g2	PROPN
ejpam-2666	243	10	)	)	PUNCT
ejpam-2666	243	11	∈	∈	PROPN
ejpam-2666	243	12	span(s′1	span(s′1	VERB
ejpam-2666	243	13	∪	∪	ADP
ejpam-2666	243	14	s′2	s′2	NOUN
ejpam-2666	243	15	)	)	PUNCT
ejpam-2666	243	16	.	.	PUNCT
ejpam-2666	244	1	this	this	PRON
ejpam-2666	244	2	implies	imply	VERB
ejpam-2666	244	3	that	that	SCONJ
ejpam-2666	244	4	,	,	PUNCT
ejpam-2666	244	5	q3h3(g1	q3h3(g1	CCONJ
ejpam-2666	244	6	|	|	ADV
ejpam-2666	244	7	g2	g2	VERB
ejpam-2666	244	8	|	|	ADV
ejpam-2666	244	9	0	0	NUM
ejpam-2666	244	10	)	)	PUNCT
ejpam-2666	244	11	∈	∈	PROPN
ejpam-2666	244	12	span(s1	span(s1	ADJ
ejpam-2666	244	13	∪	∪	X
ejpam-2666	244	14	s2	s2	PROPN
ejpam-2666	244	15	)	)	PUNCT
ejpam-2666	244	16	.	.	PUNCT
ejpam-2666	245	1	also	also	ADV
ejpam-2666	245	2	,	,	PUNCT
ejpam-2666	245	3	r3(g1	r3(g1	ADJ
ejpam-2666	245	4	|	|	NOUN
ejpam-2666	245	5	g2	g2	PROPN
ejpam-2666	245	6	|	|	CCONJ
ejpam-2666	245	7	g3	g3	PROPN
ejpam-2666	245	8	)	)	PUNCT
ejpam-2666	245	9	∈	∈	PROPN
ejpam-2666	245	10	span(s3	span(s3	NOUN
ejpam-2666	245	11	)	)	PUNCT
ejpam-2666	245	12	,	,	PUNCT
ejpam-2666	245	13	as	as	ADP
ejpam-2666	245	14	deg(r3	deg(r3	NOUN
ejpam-2666	245	15	)	)	PUNCT
ejpam-2666	245	16	<	<	X
ejpam-2666	245	17	t	t	PROPN
ejpam-2666	245	18	−	−	PROPN
ejpam-2666	245	19	t3	t3	PROPN
ejpam-2666	245	20	.	.	PUNCT
ejpam-2666	246	1	therefore	therefore	ADV
ejpam-2666	246	2	,	,	PUNCT
ejpam-2666	246	3	from	from	ADP
ejpam-2666	246	4	(	(	PUNCT
ejpam-2666	246	5	3	3	NUM
ejpam-2666	246	6	)	)	PUNCT
ejpam-2666	246	7	,	,	PUNCT
ejpam-2666	246	8	d3	d3	PROPN
ejpam-2666	246	9	∗	∗	NOUN
ejpam-2666	246	10	(	(	PUNCT
ejpam-2666	246	11	g1	g1	PROPN
ejpam-2666	246	12	|	|	ADV
ejpam-2666	246	13	g2	g2	PROPN
ejpam-2666	246	14	|	|	CCONJ
ejpam-2666	246	15	g3	g3	PROPN
ejpam-2666	246	16	)	)	PUNCT
ejpam-2666	246	17	∈	∈	PROPN
ejpam-2666	246	18	span(s1	span(s1	ADJ
ejpam-2666	246	19	∪	∪	PROPN
ejpam-2666	246	20	s2	s2	PROPN
ejpam-2666	246	21	∪	∪	X
ejpam-2666	246	22	s3	s3	PROPN
ejpam-2666	246	23	)	)	PUNCT
ejpam-2666	246	24	.	.	PUNCT
ejpam-2666	247	1	hence	hence	ADV
ejpam-2666	247	2	c	c	PROPN
ejpam-2666	247	3	∈	∈	PROPN
ejpam-2666	247	4	span(s1	span(s1	VERB
ejpam-2666	247	5	∪	∪	PROPN
ejpam-2666	247	6	s2	s2	PROPN
ejpam-2666	247	7	∪	∪	X
ejpam-2666	247	8	s3	s3	PROPN
ejpam-2666	247	9	)	)	PUNCT
ejpam-2666	247	10	.	.	PUNCT
ejpam-2666	248	1	the	the	DET
ejpam-2666	248	2	second	second	ADJ
ejpam-2666	248	3	result	result	NOUN
ejpam-2666	248	4	follows	follow	VERB
ejpam-2666	248	5	as	as	SCONJ
ejpam-2666	248	6	s	s	NOUN
ejpam-2666	248	7	is	be	AUX
ejpam-2666	248	8	linearly	linearly	ADV
ejpam-2666	248	9	independent	independent	ADJ
ejpam-2666	248	10	.	.	PUNCT
ejpam-2666	249	1	the	the	DET
ejpam-2666	249	2	following	follow	VERB
ejpam-2666	249	3	example	example	NOUN
ejpam-2666	249	4	illustrates	illustrate	VERB
ejpam-2666	249	5	this	this	PRON
ejpam-2666	249	6	.	.	PUNCT
ejpam-2666	250	1	example	example	NOUN
ejpam-2666	251	1	1	1	NUM
ejpam-2666	251	2	.	.	PUNCT
ejpam-2666	251	3	let	let	VERB
ejpam-2666	251	4	r	r	NOUN
ejpam-2666	251	5	=	=	SYM
ejpam-2666	251	6	s	s	PART
ejpam-2666	251	7	=	=	X
ejpam-2666	251	8	t	t	NOUN
ejpam-2666	251	9	=	=	SYM
ejpam-2666	251	10	7	7	X
ejpam-2666	251	11	.	.	X
ejpam-2666	252	1	we	we	PRON
ejpam-2666	252	2	have	have	AUX
ejpam-2666	252	3	x7	x7	VERB
ejpam-2666	252	4	−	−	PROPN
ejpam-2666	252	5	1	1	NUM
ejpam-2666	252	6	=	=	SYM
ejpam-2666	252	7	(	(	PUNCT
ejpam-2666	252	8	x	x	X
ejpam-2666	253	1	+	+	PUNCT
ejpam-2666	253	2	1)(x3	1)(x3	NUM
ejpam-2666	254	1	+	+	CCONJ
ejpam-2666	254	2	x	x	SYM
ejpam-2666	255	1	+	+	NUM
ejpam-2666	255	2	1)(x3	1)(x3	NUM
ejpam-2666	255	3	+	+	CCONJ
ejpam-2666	255	4	x2	x2	PROPN
ejpam-2666	256	1	+	+	CCONJ
ejpam-2666	256	2	1	1	X
ejpam-2666	256	3	)	)	PUNCT
ejpam-2666	256	4	over	over	ADP
ejpam-2666	256	5	z2	z2	PROPN
ejpam-2666	256	6	.	.	PUNCT
ejpam-2666	257	1	let	let	VERB
ejpam-2666	257	2	c	c	NOUN
ejpam-2666	257	3	=	=	SYM
ejpam-2666	257	4	〈	〈	PROPN
ejpam-2666	257	5	(	(	PUNCT
ejpam-2666	257	6	b	b	NOUN
ejpam-2666	257	7	|	|	NOUN
ejpam-2666	257	8	0	0	NUM
ejpam-2666	258	1	|	|	NOUN
ejpam-2666	258	2	0	0	NUM
ejpam-2666	258	3	)	)	PUNCT
ejpam-2666	258	4	,	,	PUNCT
ejpam-2666	259	1	(	(	PUNCT
ejpam-2666	259	2	l	l	NOUN
ejpam-2666	259	3	|	|	ADV
ejpam-2666	259	4	a	a	DET
ejpam-2666	259	5	|	|	NOUN
ejpam-2666	259	6	0	0	NUM
ejpam-2666	259	7	)	)	PUNCT
ejpam-2666	259	8	,	,	PUNCT
ejpam-2666	259	9	(	(	PUNCT
ejpam-2666	259	10	g1	g1	VERB
ejpam-2666	259	11	|	|	ADV
ejpam-2666	259	12	g2	g2	PROPN
ejpam-2666	259	13	|	|	CCONJ
ejpam-2666	259	14	g3	g3	PROPN
ejpam-2666	259	15	)	)	PUNCT
ejpam-2666	259	16	〉	〉	PROPN
ejpam-2666	259	17	,	,	PUNCT
ejpam-2666	259	18	where	where	SCONJ
ejpam-2666	259	19	b	b	X
ejpam-2666	260	1	=	=	PRON
ejpam-2666	261	1	(	(	PUNCT
ejpam-2666	261	2	x	x	PROPN
ejpam-2666	261	3	+	+	PUNCT
ejpam-2666	261	4	1)(x3	1)(x3	NUM
ejpam-2666	261	5	+	+	CCONJ
ejpam-2666	261	6	x2	x2	PROPN
ejpam-2666	262	1	+	+	CCONJ
ejpam-2666	262	2	1	1	NUM
ejpam-2666	262	3	)	)	PUNCT
ejpam-2666	262	4	,	,	PUNCT
ejpam-2666	263	1	l	l	NOUN
ejpam-2666	263	2	=	=	SYM
ejpam-2666	263	3	(	(	PUNCT
ejpam-2666	263	4	x+	x+	PROPN
ejpam-2666	263	5	1)2	1)2	NUM
ejpam-2666	263	6	,	,	PUNCT
ejpam-2666	263	7	a	a	PRON
ejpam-2666	263	8	=	=	X
ejpam-2666	263	9	(	(	PUNCT
ejpam-2666	263	10	x+	x+	X
ejpam-2666	263	11	1)(x3	1)(x3	NUM
ejpam-2666	264	1	+	+	ADJ
ejpam-2666	264	2	x+	x+	ADJ
ejpam-2666	264	3	1	1	NUM
ejpam-2666	264	4	)	)	PUNCT
ejpam-2666	264	5	,	,	PUNCT
ejpam-2666	264	6	g1	g1	PROPN
ejpam-2666	264	7	=	=	PUNCT
ejpam-2666	264	8	x+	x+	X
ejpam-2666	264	9	1	1	NUM
ejpam-2666	264	10	,	,	PUNCT
ejpam-2666	264	11	g2	g2	PROPN
ejpam-2666	264	12	=	=	PUNCT
ejpam-2666	265	1	x2	x2	INTJ
ejpam-2666	266	1	+	+	ADJ
ejpam-2666	266	2	x	x	NOUN
ejpam-2666	266	3	and	and	CCONJ
ejpam-2666	266	4	g3	g3	PROPN
ejpam-2666	266	5	=	=	SYM
ejpam-2666	266	6	(	(	PUNCT
ejpam-2666	266	7	x+	x+	X
ejpam-2666	266	8	1)(x3	1)(x3	NUM
ejpam-2666	266	9	+	+	NOUN
ejpam-2666	266	10	x2	x2	PROPN
ejpam-2666	266	11	+	+	ADJ
ejpam-2666	266	12	1	1	NUM
ejpam-2666	266	13	)	)	PUNCT
ejpam-2666	266	14	.	.	PUNCT
ejpam-2666	267	1	then	then	ADV
ejpam-2666	267	2	,	,	PUNCT
ejpam-2666	267	3	c	c	PROPN
ejpam-2666	267	4	satisfies	satisfy	VERB
ejpam-2666	267	5	all	all	DET
ejpam-2666	267	6	the	the	DET
ejpam-2666	267	7	conditions	condition	NOUN
ejpam-2666	267	8	of	of	ADP
ejpam-2666	267	9	lemma	lemma	PROPN
ejpam-2666	267	10	1	1	NUM
ejpam-2666	267	11	and	and	CCONJ
ejpam-2666	267	12	lemma	lemma	PROPN
ejpam-2666	267	13	2	2	NUM
ejpam-2666	267	14	.	.	PUNCT
ejpam-2666	268	1	therefore	therefore	ADV
ejpam-2666	268	2	,	,	PUNCT
ejpam-2666	268	3	c	c	PROPN
ejpam-2666	268	4	is	be	AUX
ejpam-2666	268	5	a	a	DET
ejpam-2666	268	6	z2	z2	ADJ
ejpam-2666	268	7	-	-	PUNCT
ejpam-2666	268	8	triple	triple	ADJ
ejpam-2666	268	9	cyclic	cyclic	ADJ
ejpam-2666	268	10	code	code	NOUN
ejpam-2666	268	11	of	of	ADP
ejpam-2666	268	12	block	block	NOUN
ejpam-2666	268	13	length	length	NOUN
ejpam-2666	268	14	(	(	PUNCT
ejpam-2666	268	15	7	7	NUM
ejpam-2666	268	16	,	,	PUNCT
ejpam-2666	268	17	7	7	NUM
ejpam-2666	268	18	,	,	PUNCT
ejpam-2666	268	19	7	7	NUM
ejpam-2666	268	20	)	)	PUNCT
ejpam-2666	268	21	.	.	PUNCT
ejpam-2666	269	1	also	also	ADV
ejpam-2666	269	2	,	,	PUNCT
ejpam-2666	269	3	s	s	PART
ejpam-2666	269	4	=	=	NOUN
ejpam-2666	269	5	s1	s1	PROPN
ejpam-2666	269	6	∪	∪	ADP
ejpam-2666	269	7	s2	s2	PROPN
ejpam-2666	269	8	∪	∪	ADP
ejpam-2666	269	9	s3	s3	PROPN
ejpam-2666	269	10	forms	form	NOUN
ejpam-2666	269	11	a	a	DET
ejpam-2666	269	12	generating	generate	VERB
ejpam-2666	269	13	set	set	NOUN
ejpam-2666	269	14	for	for	ADP
ejpam-2666	269	15	c	c	NOUN
ejpam-2666	269	16	,	,	PUNCT
ejpam-2666	269	17	where	where	SCONJ
ejpam-2666	269	18	s1	s1	NOUN
ejpam-2666	269	19	=	=	SYM
ejpam-2666	269	20	∪2i=0x	∪2i=0x	PUNCT
ejpam-2666	269	21	i(x4	i(x4	NOUN
ejpam-2666	269	22	+	+	CCONJ
ejpam-2666	269	23	x2	x2	PROPN
ejpam-2666	270	1	+	+	CCONJ
ejpam-2666	270	2	x	x	SYM
ejpam-2666	271	1	+	+	NUM
ejpam-2666	271	2	1	1	NUM
ejpam-2666	271	3	|	|	ADV
ejpam-2666	271	4	0	0	NUM
ejpam-2666	272	1	|	|	NOUN
ejpam-2666	272	2	0	0	NUM
ejpam-2666	272	3	)	)	PUNCT
ejpam-2666	273	1	,	,	PUNCT
ejpam-2666	273	2	s2	s2	NOUN
ejpam-2666	273	3	=	=	SYM
ejpam-2666	273	4	∪2i=0x	∪2i=0x	NOUN
ejpam-2666	273	5	i(x2	i(x2	NOUN
ejpam-2666	273	6	+	+	CCONJ
ejpam-2666	273	7	1	1	NUM
ejpam-2666	273	8	|	|	ADV
ejpam-2666	273	9	x4	x4	PROPN
ejpam-2666	274	1	+	+	CCONJ
ejpam-2666	275	1	x3	x3	ADJ
ejpam-2666	276	1	+	+	CCONJ
ejpam-2666	276	2	x2	x2	PROPN
ejpam-2666	277	1	+	+	CCONJ
ejpam-2666	277	2	1	1	NUM
ejpam-2666	277	3	|	|	ADV
ejpam-2666	277	4	0	0	NUM
ejpam-2666	277	5	)	)	PUNCT
ejpam-2666	277	6	and	and	CCONJ
ejpam-2666	277	7	s3	s3	PROPN
ejpam-2666	277	8	=	=	SYM
ejpam-2666	278	1	∪2i=0x	∪2i=0x	PROPN
ejpam-2666	278	2	i(x+	i(x+	PROPN
ejpam-2666	278	3	1	1	NUM
ejpam-2666	278	4	|	|	ADV
ejpam-2666	278	5	x+	x+	ADJ
ejpam-2666	279	1	x2	x2	PROPN
ejpam-2666	279	2	|	|	ADV
ejpam-2666	279	3	x4	x4	PROPN
ejpam-2666	280	1	+	+	CCONJ
ejpam-2666	280	2	x2	x2	PROPN
ejpam-2666	281	1	+	+	CCONJ
ejpam-2666	281	2	x+	x+	ADJ
ejpam-2666	281	3	1	1	NUM
ejpam-2666	281	4	)	)	PUNCT
ejpam-2666	281	5	.	.	PUNCT
ejpam-2666	282	1	the	the	DET
ejpam-2666	282	2	cardinality	cardinality	NOUN
ejpam-2666	282	3	of	of	ADP
ejpam-2666	282	4	c	c	PROPN
ejpam-2666	282	5	is	be	AUX
ejpam-2666	282	6	29	29	NUM
ejpam-2666	282	7	.	.	PUNCT
ejpam-2666	283	1	also	also	ADV
ejpam-2666	283	2	,	,	PUNCT
ejpam-2666	283	3	c	c	PROPN
ejpam-2666	283	4	is	be	AUX
ejpam-2666	283	5	generated	generate	VERB
ejpam-2666	283	6	by	by	ADP
ejpam-2666	283	7	the	the	DET
ejpam-2666	283	8	generator	generator	NOUN
ejpam-2666	283	9	matrix	matrix	NOUN
ejpam-2666	283	10	g	g	NOUN
ejpam-2666	283	11	,	,	PUNCT
ejpam-2666	283	12	where	where	SCONJ
ejpam-2666	283	13	g	g	NOUN
ejpam-2666	283	14	=	=	PUNCT
ejpam-2666	283	15			VERB
ejpam-2666	283	16	1	1	NUM
ejpam-2666	283	17	1	1	NUM
ejpam-2666	283	18	1	1	NUM
ejpam-2666	283	19	0	0	NUM
ejpam-2666	283	20	1	1	NUM
ejpam-2666	283	21	0	0	NUM
ejpam-2666	283	22	0	0	NUM
ejpam-2666	283	23	0	0	NUM
ejpam-2666	283	24	0	0	NUM
ejpam-2666	283	25	0	0	NUM
ejpam-2666	283	26	0	0	NUM
ejpam-2666	283	27	0	0	NUM
ejpam-2666	283	28	0	0	NUM
ejpam-2666	283	29	0	0	NUM
ejpam-2666	283	30	0	0	NUM
ejpam-2666	283	31	0	0	NUM
ejpam-2666	283	32	0	0	NUM
ejpam-2666	283	33	0	0	NUM
ejpam-2666	283	34	0	0	NUM
ejpam-2666	283	35	0	0	NUM
ejpam-2666	283	36	0	0	NUM
ejpam-2666	283	37	0	0	NUM
ejpam-2666	283	38	1	1	NUM
ejpam-2666	283	39	1	1	NUM
ejpam-2666	283	40	1	1	NUM
ejpam-2666	283	41	0	0	NUM
ejpam-2666	283	42	1	1	NUM
ejpam-2666	283	43	0	0	NUM
ejpam-2666	283	44	0	0	NUM
ejpam-2666	283	45	0	0	NUM
ejpam-2666	283	46	0	0	NUM
ejpam-2666	283	47	0	0	NUM
ejpam-2666	283	48	0	0	NUM
ejpam-2666	283	49	0	0	NUM
ejpam-2666	283	50	0	0	NUM
ejpam-2666	283	51	0	0	NUM
ejpam-2666	283	52	0	0	NUM
ejpam-2666	283	53	0	0	NUM
ejpam-2666	283	54	0	0	NUM
ejpam-2666	283	55	0	0	NUM
ejpam-2666	283	56	0	0	NUM
ejpam-2666	283	57	0	0	NUM
ejpam-2666	283	58	0	0	NUM
ejpam-2666	283	59	0	0	NUM
ejpam-2666	283	60	1	1	NUM
ejpam-2666	283	61	1	1	NUM
ejpam-2666	283	62	1	1	NUM
ejpam-2666	283	63	0	0	NUM
ejpam-2666	283	64	1	1	NUM
ejpam-2666	283	65	0	0	NUM
ejpam-2666	283	66	0	0	NUM
ejpam-2666	283	67	0	0	NUM
ejpam-2666	283	68	0	0	NUM
ejpam-2666	283	69	0	0	NUM
ejpam-2666	283	70	0	0	NUM
ejpam-2666	283	71	0	0	NUM
ejpam-2666	283	72	0	0	NUM
ejpam-2666	283	73	0	0	NUM
ejpam-2666	283	74	0	0	NUM
ejpam-2666	283	75	0	0	NUM
ejpam-2666	283	76	0	0	NUM
ejpam-2666	283	77	0	0	NUM
ejpam-2666	283	78	0	0	NUM
ejpam-2666	283	79	1	1	NUM
ejpam-2666	283	80	0	0	NUM
ejpam-2666	283	81	1	1	NUM
ejpam-2666	283	82	0	0	NUM
ejpam-2666	283	83	0	0	NUM
ejpam-2666	283	84	0	0	NUM
ejpam-2666	283	85	0	0	NUM
ejpam-2666	283	86	1	1	NUM
ejpam-2666	283	87	0	0	NUM
ejpam-2666	283	88	1	1	NUM
ejpam-2666	283	89	1	1	NUM
ejpam-2666	283	90	1	1	NUM
ejpam-2666	283	91	0	0	NUM
ejpam-2666	283	92	0	0	NUM
ejpam-2666	283	93	0	0	NUM
ejpam-2666	283	94	0	0	NUM
ejpam-2666	283	95	0	0	NUM
ejpam-2666	283	96	0	0	NUM
ejpam-2666	283	97	0	0	NUM
ejpam-2666	283	98	0	0	NUM
ejpam-2666	283	99	0	0	NUM
ejpam-2666	283	100	0	0	NUM
ejpam-2666	283	101	1	1	NUM
ejpam-2666	283	102	0	0	NUM
ejpam-2666	283	103	1	1	NUM
ejpam-2666	283	104	0	0	NUM
ejpam-2666	283	105	0	0	NUM
ejpam-2666	283	106	0	0	NUM
ejpam-2666	283	107	0	0	NUM
ejpam-2666	283	108	1	1	NUM
ejpam-2666	283	109	0	0	NUM
ejpam-2666	283	110	1	1	NUM
ejpam-2666	283	111	1	1	NUM
ejpam-2666	283	112	1	1	NUM
ejpam-2666	283	113	0	0	NUM
ejpam-2666	283	114	0	0	NUM
ejpam-2666	283	115	0	0	NUM
ejpam-2666	283	116	0	0	NUM
ejpam-2666	283	117	0	0	NUM
ejpam-2666	283	118	0	0	NUM
ejpam-2666	283	119	0	0	NUM
ejpam-2666	283	120	0	0	NUM
ejpam-2666	283	121	0	0	NUM
ejpam-2666	283	122	0	0	NUM
ejpam-2666	283	123	1	1	NUM
ejpam-2666	283	124	0	0	NUM
ejpam-2666	283	125	1	1	NUM
ejpam-2666	283	126	0	0	NUM
ejpam-2666	283	127	0	0	NUM
ejpam-2666	283	128	0	0	NUM
ejpam-2666	283	129	0	0	NUM
ejpam-2666	283	130	1	1	NUM
ejpam-2666	283	131	0	0	NUM
ejpam-2666	283	132	1	1	NUM
ejpam-2666	283	133	1	1	NUM
ejpam-2666	283	134	1	1	NUM
ejpam-2666	283	135	0	0	NUM
ejpam-2666	283	136	0	0	NUM
ejpam-2666	283	137	0	0	NUM
ejpam-2666	283	138	0	0	NUM
ejpam-2666	283	139	0	0	NUM
ejpam-2666	283	140	0	0	NUM
ejpam-2666	283	141	0	0	NUM
ejpam-2666	283	142	1	1	NUM
ejpam-2666	283	143	1	1	NUM
ejpam-2666	283	144	0	0	NUM
ejpam-2666	283	145	0	0	NUM
ejpam-2666	283	146	0	0	NUM
ejpam-2666	283	147	0	0	NUM
ejpam-2666	283	148	0	0	NUM
ejpam-2666	283	149	0	0	NUM
ejpam-2666	283	150	1	1	NUM
ejpam-2666	283	151	1	1	NUM
ejpam-2666	283	152	0	0	NUM
ejpam-2666	283	153	0	0	NUM
ejpam-2666	283	154	0	0	NUM
ejpam-2666	283	155	0	0	NUM
ejpam-2666	283	156	1	1	NUM
ejpam-2666	283	157	1	1	NUM
ejpam-2666	283	158	1	1	NUM
ejpam-2666	283	159	0	0	NUM
ejpam-2666	283	160	1	1	NUM
ejpam-2666	283	161	0	0	NUM
ejpam-2666	283	162	0	0	NUM
ejpam-2666	283	163	0	0	NUM
ejpam-2666	283	164	1	1	NUM
ejpam-2666	283	165	1	1	NUM
ejpam-2666	283	166	0	0	NUM
ejpam-2666	283	167	0	0	NUM
ejpam-2666	283	168	0	0	NUM
ejpam-2666	283	169	0	0	NUM
ejpam-2666	283	170	0	0	NUM
ejpam-2666	283	171	0	0	NUM
ejpam-2666	283	172	1	1	NUM
ejpam-2666	283	173	1	1	NUM
ejpam-2666	283	174	0	0	NUM
ejpam-2666	283	175	0	0	NUM
ejpam-2666	283	176	0	0	NUM
ejpam-2666	283	177	0	0	NUM
ejpam-2666	283	178	1	1	NUM
ejpam-2666	283	179	1	1	NUM
ejpam-2666	283	180	1	1	NUM
ejpam-2666	283	181	0	0	NUM
ejpam-2666	283	182	1	1	NUM
ejpam-2666	283	183	0	0	NUM
ejpam-2666	283	184	0	0	NUM
ejpam-2666	283	185	0	0	NUM
ejpam-2666	283	186	1	1	NUM
ejpam-2666	283	187	1	1	NUM
ejpam-2666	283	188	0	0	NUM
ejpam-2666	283	189	0	0	NUM
ejpam-2666	283	190	0	0	NUM
ejpam-2666	283	191	0	0	NUM
ejpam-2666	283	192	0	0	NUM
ejpam-2666	283	193	0	0	NUM
ejpam-2666	283	194	1	1	NUM
ejpam-2666	283	195	1	1	NUM
ejpam-2666	283	196	0	0	NUM
ejpam-2666	283	197	0	0	NUM
ejpam-2666	283	198	0	0	NUM
ejpam-2666	283	199	0	0	NUM
ejpam-2666	283	200	1	1	NUM
ejpam-2666	283	201	1	1	NUM
ejpam-2666	283	202	1	1	NUM
ejpam-2666	283	203	0	0	NUM
ejpam-2666	283	204	1	1	NUM
ejpam-2666	283	205			NOUN
ejpam-2666	283	206	.	.	PUNCT
ejpam-2666	284	1	further	far	ADV
ejpam-2666	284	2	,	,	PUNCT
ejpam-2666	284	3	the	the	DET
ejpam-2666	284	4	minimum	minimum	ADJ
ejpam-2666	284	5	hamming	hamming	NOUN
ejpam-2666	284	6	distance	distance	NOUN
ejpam-2666	284	7	of	of	ADP
ejpam-2666	284	8	c	c	PROPN
ejpam-2666	284	9	is	be	AUX
ejpam-2666	284	10	4	4	NUM
ejpam-2666	284	11	and	and	CCONJ
ejpam-2666	284	12	therefore	therefore	ADV
ejpam-2666	284	13	,	,	PUNCT
ejpam-2666	284	14	c	c	PROPN
ejpam-2666	284	15	is	be	AUX
ejpam-2666	284	16	a	a	DET
ejpam-2666	284	17	[	[	X
ejpam-2666	284	18	21	21	NUM
ejpam-2666	284	19	,	,	PUNCT
ejpam-2666	284	20	9	9	NUM
ejpam-2666	284	21	,	,	PUNCT
ejpam-2666	284	22	4	4	NUM
ejpam-2666	284	23	]	]	X
ejpam-2666	284	24	binary	binary	ADJ
ejpam-2666	284	25	linear	linear	PROPN
ejpam-2666	284	26	code	code	PROPN
ejpam-2666	284	27	with	with	ADP
ejpam-2666	284	28	the	the	DET
ejpam-2666	284	29	hamming	hamming	ADJ
ejpam-2666	284	30	weight	weight	NOUN
ejpam-2666	284	31	distribution	distribution	NOUN
ejpam-2666	284	32	given	give	VERB
ejpam-2666	284	33	by	by	ADP
ejpam-2666	284	34	[	[	X
ejpam-2666	284	35	<	<	X
ejpam-2666	284	36	0	0	NUM
ejpam-2666	284	37	,	,	PUNCT
ejpam-2666	284	38	1	1	NUM
ejpam-2666	284	39	>	>	PUNCT
ejpam-2666	284	40	,	,	PUNCT
ejpam-2666	284	41	<	<	X
ejpam-2666	284	42	4	4	NUM
ejpam-2666	284	43	,	,	PUNCT
ejpam-2666	284	44	7	7	NUM
ejpam-2666	284	45	>	>	PUNCT
ejpam-2666	284	46	,	,	PUNCT
ejpam-2666	284	47	<	<	X
ejpam-2666	284	48	6	6	NUM
ejpam-2666	284	49	,	,	PUNCT
ejpam-2666	284	50	21	21	NUM
ejpam-2666	284	51	>	>	X
ejpam-2666	284	52	,	,	PUNCT
ejpam-2666	284	53	<	<	X
ejpam-2666	284	54	8	8	NUM
ejpam-2666	284	55	,	,	PUNCT
ejpam-2666	284	56	98	98	NUM
ejpam-2666	284	57	>	>	PUNCT
ejpam-2666	284	58	,	,	PUNCT
ejpam-2666	284	59	<	<	X
ejpam-2666	284	60	10	10	NUM
ejpam-2666	284	61	,	,	PUNCT
ejpam-2666	284	62	154	154	NUM
ejpam-2666	284	63	>	>	PUNCT
ejpam-2666	284	64	,	,	PUNCT
ejpam-2666	284	65	<	<	X
ejpam-2666	284	66	12	12	NUM
ejpam-2666	284	67	,	,	PUNCT
ejpam-2666	284	68	175	175	NUM
ejpam-2666	284	69	>	>	X
ejpam-2666	284	70	,	,	PUNCT
ejpam-2666	284	71	<	<	X
ejpam-2666	284	72	14	14	NUM
ejpam-2666	284	73	,	,	PUNCT
ejpam-2666	284	74	49	49	NUM
ejpam-2666	284	75	>	>	PUNCT
ejpam-2666	284	76	,	,	PUNCT
ejpam-2666	284	77	<	<	X
ejpam-2666	284	78	16	16	NUM
ejpam-2666	284	79	,	,	PUNCT
ejpam-2666	284	80	7	7	NUM
ejpam-2666	284	81	>	>	PUNCT
ejpam-2666	284	82	]	]	PUNCT
ejpam-2666	284	83	.	.	PUNCT
ejpam-2666	285	1	3	3	X
ejpam-2666	285	2	.	.	X
ejpam-2666	285	3	duals	dual	NOUN
ejpam-2666	285	4	of	of	ADP
ejpam-2666	285	5	z2	z2	NOUN
ejpam-2666	285	6	-	-	PUNCT
ejpam-2666	285	7	triple	triple	ADJ
ejpam-2666	285	8	cyclic	cyclic	ADJ
ejpam-2666	285	9	codes	code	NOUN
ejpam-2666	285	10	in	in	ADP
ejpam-2666	285	11	this	this	DET
ejpam-2666	285	12	section	section	NOUN
ejpam-2666	285	13	,	,	PUNCT
ejpam-2666	285	14	we	we	PRON
ejpam-2666	285	15	determine	determine	VERB
ejpam-2666	285	16	the	the	DET
ejpam-2666	285	17	duals	dual	NOUN
ejpam-2666	285	18	of	of	ADP
ejpam-2666	285	19	z2	z2	NOUN
ejpam-2666	285	20	-	-	PUNCT
ejpam-2666	285	21	triple	triple	ADJ
ejpam-2666	285	22	cyclic	cyclic	ADJ
ejpam-2666	285	23	codes	code	NOUN
ejpam-2666	285	24	of	of	ADP
ejpam-2666	285	25	block	block	NOUN
ejpam-2666	285	26	length	length	NOUN
ejpam-2666	285	27	(	(	PUNCT
ejpam-2666	285	28	r	r	NOUN
ejpam-2666	285	29	,	,	PUNCT
ejpam-2666	285	30	s	s	PROPN
ejpam-2666	285	31	,	,	PUNCT
ejpam-2666	285	32	t	t	PROPN
ejpam-2666	285	33	)	)	PUNCT
ejpam-2666	285	34	.	.	PUNCT
ejpam-2666	286	1	in	in	ADP
ejpam-2666	286	2	theorem	theorem	NOUN
ejpam-2666	286	3	1	1	NUM
ejpam-2666	286	4	,	,	PUNCT
ejpam-2666	286	5	it	it	PRON
ejpam-2666	286	6	is	be	AUX
ejpam-2666	286	7	shown	show	VERB
ejpam-2666	286	8	that	that	SCONJ
ejpam-2666	286	9	the	the	DET
ejpam-2666	286	10	dual	dual	ADJ
ejpam-2666	286	11	c⊥	c⊥	NOUN
ejpam-2666	286	12	of	of	ADP
ejpam-2666	286	13	a	a	DET
ejpam-2666	286	14	z2	z2	ADJ
ejpam-2666	286	15	-	-	PUNCT
ejpam-2666	286	16	triple	triple	ADJ
ejpam-2666	286	17	cyclic	cyclic	ADJ
ejpam-2666	286	18	code	code	NOUN
ejpam-2666	286	19	c	c	NOUN
ejpam-2666	286	20	is	be	AUX
ejpam-2666	286	21	also	also	ADV
ejpam-2666	286	22	a	a	DET
ejpam-2666	286	23	z2	z2	NUM
ejpam-2666	286	24	-	-	PUNCT
ejpam-2666	286	25	triple	triple	ADJ
ejpam-2666	286	26	srinivasulu	srinivasulu	ADJ
ejpam-2666	286	27	b	b	NOUN
ejpam-2666	286	28	,	,	PUNCT
ejpam-2666	286	29	maheshanand	maheshanand	NOUN
ejpam-2666	286	30	bhaintwal	bhaintwal	NOUN
ejpam-2666	286	31	/	/	SYM
ejpam-2666	286	32	eur	eur	PROPN
ejpam-2666	286	33	.	.	PUNCT
ejpam-2666	287	1	j.	j.	PROPN
ejpam-2666	287	2	pure	pure	PROPN
ejpam-2666	287	3	appl	appl	PROPN
ejpam-2666	287	4	.	.	PROPN
ejpam-2666	287	5	math	math	PROPN
ejpam-2666	287	6	,	,	PUNCT
ejpam-2666	287	7	10	10	NUM
ejpam-2666	287	8	(	(	PUNCT
ejpam-2666	287	9	2	2	NUM
ejpam-2666	287	10	)	)	PUNCT
ejpam-2666	287	11	(	(	PUNCT
ejpam-2666	287	12	2017	2017	NUM
ejpam-2666	287	13	)	)	PUNCT
ejpam-2666	287	14	,	,	PUNCT
ejpam-2666	287	15	392	392	NUM
ejpam-2666	287	16	-	-	SYM
ejpam-2666	287	17	409	409	NUM
ejpam-2666	287	18	398	398	NUM
ejpam-2666	287	19	cyclic	cyclic	ADJ
ejpam-2666	287	20	code	code	NOUN
ejpam-2666	287	21	.	.	PUNCT
ejpam-2666	288	1	therefore	therefore	ADV
ejpam-2666	288	2	,	,	PUNCT
ejpam-2666	288	3	we	we	PRON
ejpam-2666	288	4	may	may	AUX
ejpam-2666	288	5	let	let	VERB
ejpam-2666	288	6	c⊥	c⊥	VERB
ejpam-2666	288	7	=	=	SYM
ejpam-2666	288	8	〈	〈	PROPN
ejpam-2666	288	9	(	(	PUNCT
ejpam-2666	288	10	b̂	b̂	NOUN
ejpam-2666	288	11	|	|	ADV
ejpam-2666	288	12	0	0	NUM
ejpam-2666	289	1	|	|	NOUN
ejpam-2666	289	2	0	0	NUM
ejpam-2666	289	3	)	)	PUNCT
ejpam-2666	290	1	,	,	PUNCT
ejpam-2666	290	2	(	(	PUNCT
ejpam-2666	290	3	l̂	l̂	X
ejpam-2666	290	4	|	|	ADV
ejpam-2666	290	5	â	â	X
ejpam-2666	290	6	|	|	NOUN
ejpam-2666	290	7	0	0	NUM
ejpam-2666	290	8	)	)	PUNCT
ejpam-2666	290	9	,	,	PUNCT
ejpam-2666	290	10	(	(	PUNCT
ejpam-2666	290	11	ĝ1	ĝ1	NOUN
ejpam-2666	290	12	|	|	ADV
ejpam-2666	290	13	ĝ2	ĝ2	NOUN
ejpam-2666	290	14	|	|	ADV
ejpam-2666	290	15	ĝ3	ĝ3	PROPN
ejpam-2666	290	16	)	)	PUNCT
ejpam-2666	290	17	〉	〉	NOUN
ejpam-2666	290	18	with	with	ADP
ejpam-2666	290	19	b̂|xr	b̂|xr	PUNCT
ejpam-2666	290	20	−	−	PROPN
ejpam-2666	290	21	1	1	NUM
ejpam-2666	290	22	,	,	PUNCT
ejpam-2666	290	23	â|xs	â|xs	PUNCT
ejpam-2666	290	24	−	−	PROPN
ejpam-2666	290	25	1	1	NUM
ejpam-2666	290	26	and	and	CCONJ
ejpam-2666	290	27	ĝ3|xt	ĝ3|xt	ADJ
ejpam-2666	290	28	−	−	NOUN
ejpam-2666	290	29	1	1	NUM
ejpam-2666	290	30	over	over	ADP
ejpam-2666	290	31	z2	z2	PROPN
ejpam-2666	290	32	.	.	PUNCT
ejpam-2666	291	1	further	far	ADV
ejpam-2666	291	2	,	,	PUNCT
ejpam-2666	291	3	let	let	VERB
ejpam-2666	291	4	m	m	NOUN
ejpam-2666	291	5	=	=	SYM
ejpam-2666	291	6	lcm(r	lcm(r	PROPN
ejpam-2666	291	7	,	,	PUNCT
ejpam-2666	291	8	s	s	PROPN
ejpam-2666	291	9	,	,	PUNCT
ejpam-2666	291	10	t	t	PROPN
ejpam-2666	291	11	)	)	PUNCT
ejpam-2666	291	12	and	and	CCONJ
ejpam-2666	291	13	denote	denote	VERB
ejpam-2666	291	14	the	the	DET
ejpam-2666	291	15	polynomial	polynomial	ADJ
ejpam-2666	291	16	∑m−1	∑m−1	ADJ
ejpam-2666	291	17	i=0	i=0	PROPN
ejpam-2666	291	18	xi	xi	NUM
ejpam-2666	291	19	by	by	ADP
ejpam-2666	291	20	θm(x	θm(x	NOUN
ejpam-2666	291	21	)	)	PUNCT
ejpam-2666	291	22	.	.	PUNCT
ejpam-2666	292	1	then	then	ADV
ejpam-2666	292	2	by	by	ADP
ejpam-2666	292	3	[	[	X
ejpam-2666	292	4	4	4	NUM
ejpam-2666	292	5	,	,	PUNCT
ejpam-2666	292	6	preposition	preposition	NOUN
ejpam-2666	292	7	4.2	4.2	NUM
ejpam-2666	292	8	]	]	PUNCT
ejpam-2666	292	9	,	,	PUNCT
ejpam-2666	292	10	we	we	PRON
ejpam-2666	292	11	have	have	VERB
ejpam-2666	292	12	the	the	DET
ejpam-2666	292	13	following	follow	VERB
ejpam-2666	292	14	result	result	NOUN
ejpam-2666	292	15	.	.	PUNCT
ejpam-2666	293	1	proposition	proposition	NOUN
ejpam-2666	293	2	1	1	NUM
ejpam-2666	293	3	.	.	PUNCT
ejpam-2666	294	1	let	let	VERB
ejpam-2666	294	2	r	r	NOUN
ejpam-2666	294	3	,	,	PUNCT
ejpam-2666	294	4	s	s	PROPN
ejpam-2666	294	5	,	,	PUNCT
ejpam-2666	294	6	t	t	PROPN
ejpam-2666	294	7	∈	∈	PROPN
ejpam-2666	294	8	n	n	PROPN
ejpam-2666	294	9	and	and	CCONJ
ejpam-2666	294	10	m	m	PROPN
ejpam-2666	295	1	=	=	SYM
ejpam-2666	295	2	lcm(r	lcm(r	PROPN
ejpam-2666	295	3	,	,	PUNCT
ejpam-2666	295	4	s	s	PROPN
ejpam-2666	295	5	,	,	PUNCT
ejpam-2666	295	6	t	t	PROPN
ejpam-2666	295	7	)	)	PUNCT
ejpam-2666	295	8	.	.	PUNCT
ejpam-2666	296	1	then	then	ADV
ejpam-2666	296	2	,	,	PUNCT
ejpam-2666	296	3	xm	xm	PROPN
ejpam-2666	296	4	−	−	PROPN
ejpam-2666	297	1	1	1	NUM
ejpam-2666	297	2	=	=	SYM
ejpam-2666	297	3	θm	θm	PROPN
ejpam-2666	297	4	r	r	NOUN
ejpam-2666	297	5	(	(	PUNCT
ejpam-2666	297	6	xr)(xr	xr)(xr	PUNCT
ejpam-2666	297	7	−	−	PROPN
ejpam-2666	297	8	1	1	X
ejpam-2666	297	9	)	)	PUNCT
ejpam-2666	297	10	=	=	PUNCT
ejpam-2666	298	1	θm	θm	PROPN
ejpam-2666	298	2	s	s	X
ejpam-2666	298	3	(	(	PUNCT
ejpam-2666	298	4	xs)(xs	xs)(xs	PUNCT
ejpam-2666	298	5	−	−	PROPN
ejpam-2666	298	6	1	1	NUM
ejpam-2666	298	7	)	)	PUNCT
ejpam-2666	298	8	=	=	VERB
ejpam-2666	298	9	θm	θm	PROPN
ejpam-2666	298	10	t	t	PROPN
ejpam-2666	298	11	(	(	PUNCT
ejpam-2666	298	12	xt)(xt	xt)(xt	PROPN
ejpam-2666	298	13	−	−	PROPN
ejpam-2666	298	14	1	1	NUM
ejpam-2666	298	15	)	)	PUNCT
ejpam-2666	298	16	.	.	PUNCT
ejpam-2666	299	1	for	for	ADP
ejpam-2666	299	2	any	any	DET
ejpam-2666	299	3	polynomials	polynomial	NOUN
ejpam-2666	299	4	f	f	NOUN
ejpam-2666	299	5	,	,	PUNCT
ejpam-2666	299	6	g	g	PROPN
ejpam-2666	299	7	∈	∈	PROPN
ejpam-2666	299	8	z2[x	z2[x	PROPN
ejpam-2666	299	9	]	]	X
ejpam-2666	299	10	,	,	PUNCT
ejpam-2666	299	11	we	we	PRON
ejpam-2666	299	12	denote	denote	VERB
ejpam-2666	299	13	the	the	DET
ejpam-2666	299	14	g.c.d	g.c.d	NOUN
ejpam-2666	299	15	.	.	PUNCT
ejpam-2666	300	1	of	of	ADP
ejpam-2666	300	2	f	f	PROPN
ejpam-2666	300	3	and	and	CCONJ
ejpam-2666	300	4	g	g	PROPN
ejpam-2666	300	5	by	by	ADP
ejpam-2666	300	6	(	(	PUNCT
ejpam-2666	300	7	f	f	X
ejpam-2666	300	8	,	,	PUNCT
ejpam-2666	300	9	g	g	NOUN
ejpam-2666	300	10	)	)	PUNCT
ejpam-2666	300	11	,	,	PUNCT
ejpam-2666	301	1	and	and	CCONJ
ejpam-2666	301	2	we	we	PRON
ejpam-2666	301	3	extend	extend	VERB
ejpam-2666	301	4	this	this	DET
ejpam-2666	301	5	notation	notation	NOUN
ejpam-2666	301	6	for	for	ADP
ejpam-2666	301	7	three	three	NUM
ejpam-2666	301	8	or	or	CCONJ
ejpam-2666	301	9	more	more	ADJ
ejpam-2666	301	10	polynomials	polynomial	NOUN
ejpam-2666	301	11	.	.	PUNCT
ejpam-2666	302	1	for	for	ADP
ejpam-2666	302	2	any	any	DET
ejpam-2666	302	3	polynomial	polynomial	ADJ
ejpam-2666	302	4	f	f	PROPN
ejpam-2666	302	5	of	of	ADP
ejpam-2666	302	6	degree	degree	NOUN
ejpam-2666	302	7	n	n	CCONJ
ejpam-2666	302	8	the	the	DET
ejpam-2666	302	9	reciprocal	reciprocal	NOUN
ejpam-2666	302	10	of	of	ADP
ejpam-2666	302	11	f	f	PROPN
ejpam-2666	302	12	is	be	AUX
ejpam-2666	302	13	defined	define	VERB
ejpam-2666	302	14	as	as	ADP
ejpam-2666	302	15	f∗	f∗	NOUN
ejpam-2666	302	16	=	=	SYM
ejpam-2666	302	17	xnf	xnf	PROPN
ejpam-2666	302	18	(	(	PUNCT
ejpam-2666	302	19	1x	1x	NUM
ejpam-2666	302	20	)	)	PUNCT
ejpam-2666	302	21	.	.	PUNCT
ejpam-2666	303	1	the	the	DET
ejpam-2666	303	2	following	follow	VERB
ejpam-2666	303	3	result	result	NOUN
ejpam-2666	303	4	is	be	AUX
ejpam-2666	303	5	usefull	usefull	ADJ
ejpam-2666	303	6	for	for	ADP
ejpam-2666	303	7	our	our	PRON
ejpam-2666	303	8	study	study	NOUN
ejpam-2666	303	9	.	.	PUNCT
ejpam-2666	304	1	theorem	theorem	ADJ
ejpam-2666	304	2	7	7	NUM
ejpam-2666	304	3	.	.	PUNCT
ejpam-2666	305	1	let	let	VERB
ejpam-2666	305	2	f	f	PROPN
ejpam-2666	305	3	and	and	CCONJ
ejpam-2666	305	4	g	g	PROPN
ejpam-2666	305	5	be	be	AUX
ejpam-2666	305	6	two	two	NUM
ejpam-2666	305	7	binary	binary	ADJ
ejpam-2666	305	8	polynomials	polynomial	NOUN
ejpam-2666	305	9	,	,	PUNCT
ejpam-2666	305	10	such	such	ADJ
ejpam-2666	305	11	that	that	SCONJ
ejpam-2666	305	12	deg(f	deg(f	PROPN
ejpam-2666	305	13	)	)	PUNCT
ejpam-2666	305	14	≥	≥	NOUN
ejpam-2666	305	15	deg(g	deg(g	PROPN
ejpam-2666	305	16	)	)	PUNCT
ejpam-2666	305	17	.	.	PUNCT
ejpam-2666	306	1	then	then	ADV
ejpam-2666	306	2	(	(	PUNCT
ejpam-2666	306	3	i	i	NOUN
ejpam-2666	306	4	)	)	PUNCT
ejpam-2666	306	5	deg(f	deg(f	PROPN
ejpam-2666	306	6	)	)	PUNCT
ejpam-2666	306	7	≥	≥	NOUN
ejpam-2666	306	8	deg(f∗	deg(f∗	PROPN
ejpam-2666	306	9	)	)	PUNCT
ejpam-2666	306	10	,	,	PUNCT
ejpam-2666	306	11	and	and	CCONJ
ejpam-2666	306	12	equality	equality	NOUN
ejpam-2666	306	13	holds	hold	VERB
ejpam-2666	306	14	if	if	SCONJ
ejpam-2666	306	15	x	x	PROPN
ejpam-2666	306	16	f	f	X
ejpam-2666	306	17	;	;	PUNCT
ejpam-2666	306	18	(	(	PUNCT
ejpam-2666	306	19	ii	ii	NOUN
ejpam-2666	306	20	)	)	PUNCT
ejpam-2666	307	1	(	(	PUNCT
ejpam-2666	307	2	fg)∗	fg)∗	PROPN
ejpam-2666	307	3	=	=	SYM
ejpam-2666	307	4	f∗g∗	f∗g∗	PROPN
ejpam-2666	307	5	;	;	PUNCT
ejpam-2666	307	6	(	(	PUNCT
ejpam-2666	307	7	iii	iii	X
ejpam-2666	307	8	)	)	PUNCT
ejpam-2666	307	9	(	(	PUNCT
ejpam-2666	307	10	f	f	X
ejpam-2666	307	11	+	+	PROPN
ejpam-2666	307	12	g)∗	g)∗	NOUN
ejpam-2666	307	13	=	=	SYM
ejpam-2666	307	14	f∗	f∗	NOUN
ejpam-2666	307	15	+	+	CCONJ
ejpam-2666	307	16	xdeg(f)−deg(g)g∗	xdeg(f)−deg(g)g∗	NOUN
ejpam-2666	307	17	;	;	PUNCT
ejpam-2666	307	18	(	(	PUNCT
ejpam-2666	307	19	iv	iv	X
ejpam-2666	307	20	)	)	PUNCT
ejpam-2666	307	21	g	g	NOUN
ejpam-2666	308	1	|	|	ADV
ejpam-2666	308	2	f	f	PROPN
ejpam-2666	308	3	⇒	⇒	NOUN
ejpam-2666	308	4	g∗	g∗	VERB
ejpam-2666	308	5	|	|	ADV
ejpam-2666	308	6	f∗	f∗	NOUN
ejpam-2666	308	7	and	and	CCONJ
ejpam-2666	308	8	(	(	PUNCT
ejpam-2666	308	9	v	v	NOUN
ejpam-2666	308	10	)	)	PUNCT
ejpam-2666	308	11	(	(	PUNCT
ejpam-2666	308	12	f∗	f∗	NOUN
ejpam-2666	308	13	,	,	PUNCT
ejpam-2666	308	14	g∗	g∗	PROPN
ejpam-2666	308	15	)	)	PUNCT
ejpam-2666	308	16	=	=	PUNCT
ejpam-2666	309	1	(	(	PUNCT
ejpam-2666	309	2	f	f	X
ejpam-2666	309	3	,	,	PUNCT
ejpam-2666	309	4	g)∗.	g)∗.	NOUN
ejpam-2666	309	5	proof	proof	NOUN
ejpam-2666	309	6	.	.	PUNCT
ejpam-2666	310	1	the	the	DET
ejpam-2666	310	2	proofs	proof	NOUN
ejpam-2666	310	3	of	of	ADP
ejpam-2666	310	4	1	1	NUM
ejpam-2666	310	5	,	,	PUNCT
ejpam-2666	310	6	2	2	NUM
ejpam-2666	310	7	and	and	CCONJ
ejpam-2666	310	8	3	3	NUM
ejpam-2666	310	9	are	be	AUX
ejpam-2666	310	10	straight	straight	ADV
ejpam-2666	310	11	forward	forward	ADV
ejpam-2666	310	12	.	.	PUNCT
ejpam-2666	311	1	for	for	ADP
ejpam-2666	311	2	4	4	NUM
ejpam-2666	311	3	,	,	PUNCT
ejpam-2666	311	4	let	let	VERB
ejpam-2666	311	5	g	g	NOUN
ejpam-2666	311	6	|	|	ADV
ejpam-2666	311	7	f	f	PROPN
ejpam-2666	311	8	,	,	PUNCT
ejpam-2666	311	9	so	so	SCONJ
ejpam-2666	311	10	that	that	SCONJ
ejpam-2666	311	11	f	f	X
ejpam-2666	311	12	=	=	PUNCT
ejpam-2666	311	13	kg	kg	PROPN
ejpam-2666	311	14	for	for	ADP
ejpam-2666	311	15	some	some	DET
ejpam-2666	311	16	k	k	PROPN
ejpam-2666	311	17	∈	∈	PROPN
ejpam-2666	311	18	z2[x	z2[x	PROPN
ejpam-2666	311	19	]	]	PUNCT
ejpam-2666	311	20	.	.	PUNCT
ejpam-2666	312	1	then	then	ADV
ejpam-2666	312	2	f∗	f∗	NOUN
ejpam-2666	312	3	=	=	SYM
ejpam-2666	312	4	k∗g∗.	k∗g∗.	PROPN
ejpam-2666	312	5	therefore	therefore	ADV
ejpam-2666	312	6	g∗	g∗	VERB
ejpam-2666	312	7	|	|	ADV
ejpam-2666	312	8	f∗.	f∗.	NOUN
ejpam-2666	312	9	from	from	ADP
ejpam-2666	312	10	the	the	DET
ejpam-2666	312	11	definition	definition	NOUN
ejpam-2666	312	12	of	of	ADP
ejpam-2666	312	13	g.c.d	g.c.d	NOUN
ejpam-2666	312	14	.	.	PUNCT
ejpam-2666	313	1	,	,	PUNCT
ejpam-2666	313	2	there	there	PRON
ejpam-2666	313	3	exist	exist	VERB
ejpam-2666	313	4	m1,m2	m1,m2	PROPN
ejpam-2666	313	5	∈	∈	PROPN
ejpam-2666	313	6	z2[x	z2[x	PROPN
ejpam-2666	313	7	]	]	PUNCT
ejpam-2666	313	8	such	such	ADJ
ejpam-2666	313	9	that	that	SCONJ
ejpam-2666	313	10	(	(	PUNCT
ejpam-2666	313	11	f	f	X
ejpam-2666	313	12	,	,	PUNCT
ejpam-2666	313	13	g	g	NOUN
ejpam-2666	313	14	)	)	PUNCT
ejpam-2666	313	15	=	=	PUNCT
ejpam-2666	313	16	m1f	m1f	PROPN
ejpam-2666	313	17	+	+	NOUN
ejpam-2666	313	18	m2	m2	PROPN
ejpam-2666	313	19	g.	g.	PROPN
ejpam-2666	313	20	assuming	assume	VERB
ejpam-2666	313	21	deg(m1f	deg(m1f	PROPN
ejpam-2666	313	22	)	)	PUNCT
ejpam-2666	313	23	≥	≥	NOUN
ejpam-2666	313	24	deg(m2	deg(m2	NOUN
ejpam-2666	313	25	g	g	NOUN
ejpam-2666	313	26	)	)	PUNCT
ejpam-2666	313	27	,	,	PUNCT
ejpam-2666	313	28	we	we	PRON
ejpam-2666	313	29	get	get	VERB
ejpam-2666	313	30	(	(	PUNCT
ejpam-2666	313	31	f	f	X
ejpam-2666	313	32	,	,	PUNCT
ejpam-2666	313	33	g)∗	g)∗	PROPN
ejpam-2666	314	1	=	=	PUNCT
ejpam-2666	314	2	m∗1f	m∗1f	PROPN
ejpam-2666	314	3	∗	∗	NOUN
ejpam-2666	314	4	+	+	NUM
ejpam-2666	314	5	xdeg(m1f)−deg(m2g)m∗2	xdeg(m1f)−deg(m2g)m∗2	NOUN
ejpam-2666	314	6	g	g	NOUN
ejpam-2666	314	7	∗.	∗.	NOUN
ejpam-2666	314	8	again	again	ADV
ejpam-2666	314	9	as	as	ADP
ejpam-2666	314	10	(	(	PUNCT
ejpam-2666	314	11	f∗	f∗	NOUN
ejpam-2666	314	12	,	,	PUNCT
ejpam-2666	314	13	g∗	g∗	PROPN
ejpam-2666	314	14	)	)	PUNCT
ejpam-2666	314	15	|	|	ADV
ejpam-2666	314	16	f∗	f∗	NOUN
ejpam-2666	314	17	and	and	CCONJ
ejpam-2666	314	18	(	(	PUNCT
ejpam-2666	314	19	f∗	f∗	NOUN
ejpam-2666	314	20	,	,	PUNCT
ejpam-2666	314	21	g∗	g∗	PROPN
ejpam-2666	314	22	)	)	PUNCT
ejpam-2666	314	23	|	|	ADV
ejpam-2666	314	24	g∗	g∗	VERB
ejpam-2666	314	25	,	,	PUNCT
ejpam-2666	314	26	so	so	CCONJ
ejpam-2666	314	27	(	(	PUNCT
ejpam-2666	314	28	f∗	f∗	NOUN
ejpam-2666	314	29	,	,	PUNCT
ejpam-2666	314	30	g∗	g∗	PROPN
ejpam-2666	314	31	)	)	PUNCT
ejpam-2666	315	1	|	|	ADV
ejpam-2666	316	1	(	(	PUNCT
ejpam-2666	316	2	f	f	X
ejpam-2666	316	3	,	,	PUNCT
ejpam-2666	316	4	g)∗.	g)∗.	PROPN
ejpam-2666	316	5	on	on	ADP
ejpam-2666	316	6	the	the	DET
ejpam-2666	316	7	other	other	ADJ
ejpam-2666	316	8	hand	hand	NOUN
ejpam-2666	316	9	,	,	PUNCT
ejpam-2666	316	10	(	(	PUNCT
ejpam-2666	316	11	f	f	X
ejpam-2666	316	12	,	,	PUNCT
ejpam-2666	316	13	g	g	NOUN
ejpam-2666	316	14	)	)	PUNCT
ejpam-2666	316	15	|	|	ADV
ejpam-2666	316	16	f	f	PROPN
ejpam-2666	316	17	implies	imply	VERB
ejpam-2666	316	18	that	that	SCONJ
ejpam-2666	316	19	(	(	PUNCT
ejpam-2666	316	20	f	f	X
ejpam-2666	316	21	,	,	PUNCT
ejpam-2666	316	22	g)∗	g)∗	PROPN
ejpam-2666	316	23	|	|	ADV
ejpam-2666	316	24	f∗.	f∗.	VERB
ejpam-2666	316	25	similarly	similarly	ADV
ejpam-2666	316	26	(	(	PUNCT
ejpam-2666	316	27	f	f	X
ejpam-2666	316	28	,	,	PUNCT
ejpam-2666	316	29	g)∗	g)∗	PROPN
ejpam-2666	316	30	|	|	ADV
ejpam-2666	316	31	g∗.	g∗.	ADV
ejpam-2666	316	32	hence	hence	ADV
ejpam-2666	316	33	(	(	PUNCT
ejpam-2666	316	34	f	f	X
ejpam-2666	316	35	,	,	PUNCT
ejpam-2666	316	36	g)∗	g)∗	PROPN
ejpam-2666	316	37	|	|	ADV
ejpam-2666	316	38	(	(	PUNCT
ejpam-2666	316	39	f∗	f∗	NOUN
ejpam-2666	316	40	,	,	PUNCT
ejpam-2666	316	41	g∗	g∗	PROPN
ejpam-2666	316	42	)	)	PUNCT
ejpam-2666	316	43	.	.	PUNCT
ejpam-2666	317	1	the	the	DET
ejpam-2666	317	2	result	result	NOUN
ejpam-2666	317	3	follows	follow	VERB
ejpam-2666	317	4	.	.	PUNCT
ejpam-2666	318	1	remark	remark	PROPN
ejpam-2666	318	2	1	1	NUM
ejpam-2666	318	3	.	.	PUNCT
ejpam-2666	319	1	if	if	SCONJ
ejpam-2666	319	2	x	x	SYM
ejpam-2666	319	3	f	f	PROPN
ejpam-2666	319	4	or	or	CCONJ
ejpam-2666	319	5	x	x	NOUN
ejpam-2666	319	6	g	g	NOUN
ejpam-2666	319	7	,	,	PUNCT
ejpam-2666	319	8	then	then	ADV
ejpam-2666	319	9	it	it	PRON
ejpam-2666	319	10	is	be	AUX
ejpam-2666	319	11	easy	easy	ADJ
ejpam-2666	319	12	to	to	PART
ejpam-2666	319	13	prove	prove	VERB
ejpam-2666	319	14	that	that	DET
ejpam-2666	319	15	deg(f∗	deg(f∗	NOUN
ejpam-2666	319	16	,	,	PUNCT
ejpam-2666	319	17	g∗	g∗	PROPN
ejpam-2666	319	18	)	)	PUNCT
ejpam-2666	319	19	=	=	SYM
ejpam-2666	320	1	deg(f	deg(f	PROPN
ejpam-2666	320	2	,	,	PUNCT
ejpam-2666	320	3	g)∗	g)∗	NOUN
ejpam-2666	321	1	=	=	SYM
ejpam-2666	321	2	deg(f	deg(f	PROPN
ejpam-2666	321	3	,	,	PUNCT
ejpam-2666	321	4	g	g	NOUN
ejpam-2666	321	5	)	)	PUNCT
ejpam-2666	321	6	.	.	PUNCT
ejpam-2666	322	1	now	now	ADV
ejpam-2666	322	2	we	we	PRON
ejpam-2666	322	3	define	define	VERB
ejpam-2666	322	4	a	a	DET
ejpam-2666	322	5	mapping	mapping	NOUN
ejpam-2666	322	6	ψ	ψ	X
ejpam-2666	322	7	:	:	PUNCT
ejpam-2666	322	8	rr	rr	PROPN
ejpam-2666	322	9	,	,	PUNCT
ejpam-2666	322	10	s	s	PROPN
ejpam-2666	322	11	,	,	PUNCT
ejpam-2666	322	12	t[x]×	t[x]×	PROPN
ejpam-2666	322	13	rr	rr	PROPN
ejpam-2666	322	14	,	,	PUNCT
ejpam-2666	322	15	s	s	PART
ejpam-2666	322	16	,	,	PUNCT
ejpam-2666	322	17	t[x]→	t[x]→	PROPN
ejpam-2666	322	18	z2[x	z2[x	PROPN
ejpam-2666	322	19	]	]	PUNCT
ejpam-2666	323	1	〈	〈	PROPN
ejpam-2666	323	2	xm−1	xm−1	PROPN
ejpam-2666	323	3	〉	〉	PROPN
ejpam-2666	323	4	such	such	ADJ
ejpam-2666	323	5	that	that	PRON
ejpam-2666	323	6	ψ(u	ψ(u	PROPN
ejpam-2666	323	7	,	,	PUNCT
ejpam-2666	323	8	v	v	NOUN
ejpam-2666	323	9	)	)	PUNCT
ejpam-2666	323	10	=	=	SYM
ejpam-2666	323	11	u1θm	u1θm	X
ejpam-2666	323	12	r	r	NOUN
ejpam-2666	323	13	(	(	PUNCT
ejpam-2666	323	14	xr)xm−deg(v1)−1v∗1	xr)xm−deg(v1)−1v∗1	PROPN
ejpam-2666	323	15	+	+	NUM
ejpam-2666	323	16	u2θm	u2θm	PRON
ejpam-2666	323	17	s	s	X
ejpam-2666	323	18	(	(	PUNCT
ejpam-2666	323	19	xs)xm−deg(v2)−1v∗2	xs)xm−deg(v2)−1v∗2	PROPN
ejpam-2666	323	20	+	+	NUM
ejpam-2666	323	21	u3θm	u3θm	ADJ
ejpam-2666	323	22	r	r	NOUN
ejpam-2666	323	23	(	(	PUNCT
ejpam-2666	323	24	xr)xm−deg(v3)−1v∗3	xr)xm−deg(v3)−1v∗3	PROPN
ejpam-2666	323	25	,	,	PUNCT
ejpam-2666	323	26	(	(	PUNCT
ejpam-2666	323	27	4	4	X
ejpam-2666	323	28	)	)	PUNCT
ejpam-2666	323	29	where	where	SCONJ
ejpam-2666	323	30	u	u	NOUN
ejpam-2666	323	31	=	=	PUNCT
ejpam-2666	323	32	(	(	PUNCT
ejpam-2666	323	33	u1	u1	NOUN
ejpam-2666	323	34	|	|	ADV
ejpam-2666	323	35	u2	u2	PROPN
ejpam-2666	323	36	|	|	NOUN
ejpam-2666	323	37	u3	u3	NOUN
ejpam-2666	323	38	)	)	PUNCT
ejpam-2666	323	39	,	,	PUNCT
ejpam-2666	323	40	v	v	NOUN
ejpam-2666	323	41	=	=	SYM
ejpam-2666	323	42	(	(	PUNCT
ejpam-2666	323	43	v1	v1	VERB
ejpam-2666	323	44	|	|	ADV
ejpam-2666	323	45	v2	v2	PROPN
ejpam-2666	323	46	|	|	CCONJ
ejpam-2666	323	47	v3	v3	PROPN
ejpam-2666	323	48	)	)	PUNCT
ejpam-2666	323	49	∈	∈	PROPN
ejpam-2666	323	50	rr	rr	PROPN
ejpam-2666	323	51	,	,	PUNCT
ejpam-2666	323	52	s	s	PROPN
ejpam-2666	323	53	,	,	PUNCT
ejpam-2666	323	54	t[x	t[x	NOUN
ejpam-2666	323	55	]	]	PUNCT
ejpam-2666	323	56	.	.	PUNCT
ejpam-2666	324	1	the	the	DET
ejpam-2666	324	2	map	map	NOUN
ejpam-2666	324	3	ψ	ψ	NOUN
ejpam-2666	324	4	is	be	AUX
ejpam-2666	324	5	a	a	DET
ejpam-2666	324	6	bilinear	bilinear	NOUN
ejpam-2666	324	7	map	map	NOUN
ejpam-2666	324	8	between	between	ADP
ejpam-2666	324	9	the	the	DET
ejpam-2666	324	10	two	two	NUM
ejpam-2666	324	11	z2[x]-modules	z2[x]-module	NOUN
ejpam-2666	324	12	.	.	PUNCT
ejpam-2666	325	1	ψ	ψ	NOUN
ejpam-2666	325	2	is	be	AUX
ejpam-2666	325	3	a	a	DET
ejpam-2666	325	4	generalization	generalization	NOUN
ejpam-2666	325	5	of	of	ADP
ejpam-2666	325	6	a	a	DET
ejpam-2666	325	7	similar	similar	ADJ
ejpam-2666	325	8	map	map	NOUN
ejpam-2666	325	9	defined	define	VERB
ejpam-2666	325	10	in	in	ADP
ejpam-2666	325	11	[	[	X
ejpam-2666	325	12	4	4	NUM
ejpam-2666	325	13	]	]	PUNCT
ejpam-2666	325	14	for	for	ADP
ejpam-2666	325	15	z2	z2	NOUN
ejpam-2666	325	16	-	-	PUNCT
ejpam-2666	325	17	double	double	ADJ
ejpam-2666	325	18	cyclic	cyclic	NOUN
ejpam-2666	325	19	codes	code	NOUN
ejpam-2666	325	20	.	.	PUNCT
ejpam-2666	326	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	326	2	b	b	NUM
ejpam-2666	326	3	,	,	PUNCT
ejpam-2666	326	4	maheshanand	maheshanand	NOUN
ejpam-2666	326	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	326	6	/	/	SYM
ejpam-2666	326	7	eur	eur	PROPN
ejpam-2666	326	8	.	.	PUNCT
ejpam-2666	327	1	j.	j.	PROPN
ejpam-2666	327	2	pure	pure	PROPN
ejpam-2666	327	3	appl	appl	PROPN
ejpam-2666	327	4	.	.	PROPN
ejpam-2666	327	5	math	math	PROPN
ejpam-2666	327	6	,	,	PUNCT
ejpam-2666	327	7	10	10	NUM
ejpam-2666	327	8	(	(	PUNCT
ejpam-2666	327	9	2	2	NUM
ejpam-2666	327	10	)	)	PUNCT
ejpam-2666	327	11	(	(	PUNCT
ejpam-2666	327	12	2017	2017	NUM
ejpam-2666	327	13	)	)	PUNCT
ejpam-2666	327	14	,	,	PUNCT
ejpam-2666	327	15	392	392	NUM
ejpam-2666	327	16	-	-	SYM
ejpam-2666	327	17	409	409	NUM
ejpam-2666	327	18	399	399	NUM
ejpam-2666	327	19	lemma	lemma	PROPN
ejpam-2666	327	20	3	3	X
ejpam-2666	327	21	.	.	PUNCT
ejpam-2666	328	1	let	let	VERB
ejpam-2666	328	2	u	u	PRON
ejpam-2666	328	3	=	=	PUNCT
ejpam-2666	328	4	(	(	PUNCT
ejpam-2666	328	5	u1	u1	NOUN
ejpam-2666	328	6	|	|	ADV
ejpam-2666	328	7	u2	u2	PROPN
ejpam-2666	328	8	|	|	NOUN
ejpam-2666	328	9	u3	u3	NOUN
ejpam-2666	328	10	)	)	PUNCT
ejpam-2666	328	11	,	,	PUNCT
ejpam-2666	328	12	v	v	NOUN
ejpam-2666	328	13	=	=	SYM
ejpam-2666	328	14	(	(	PUNCT
ejpam-2666	328	15	v1	v1	VERB
ejpam-2666	328	16	|	|	ADV
ejpam-2666	328	17	v2	v2	PROPN
ejpam-2666	328	18	|	|	NOUN
ejpam-2666	328	19	v3	v3	PROPN
ejpam-2666	328	20	)	)	PUNCT
ejpam-2666	328	21	be	be	AUX
ejpam-2666	328	22	elements	element	NOUN
ejpam-2666	328	23	in	in	ADP
ejpam-2666	328	24	zr2	zr2	PROPN
ejpam-2666	328	25	×	×	PROPN
ejpam-2666	328	26	zs2	zs2	PROPN
ejpam-2666	328	27	×	×	PROPN
ejpam-2666	328	28	zt2	zt2	PROPN
ejpam-2666	328	29	with	with	ADP
ejpam-2666	328	30	associated	associate	VERB
ejpam-2666	328	31	polynomials	polynomial	NOUN
ejpam-2666	328	32	u(x	u(x	NOUN
ejpam-2666	328	33	)	)	PUNCT
ejpam-2666	329	1	=	=	SYM
ejpam-2666	329	2	(	(	PUNCT
ejpam-2666	329	3	u1(x	u1(x	NOUN
ejpam-2666	329	4	)	)	PUNCT
ejpam-2666	329	5	|	|	ADV
ejpam-2666	329	6	u2(x	u2(x	NUM
ejpam-2666	329	7	)	)	PUNCT
ejpam-2666	329	8	|	|	ADV
ejpam-2666	329	9	u3(x	u3(x	NOUN
ejpam-2666	329	10	)	)	PUNCT
ejpam-2666	329	11	)	)	PUNCT
ejpam-2666	329	12	and	and	CCONJ
ejpam-2666	329	13	v(x	v(x	NUM
ejpam-2666	329	14	)	)	PUNCT
ejpam-2666	330	1	=	=	PRON
ejpam-2666	330	2	(	(	PUNCT
ejpam-2666	330	3	v1(x	v1(x	NOUN
ejpam-2666	330	4	)	)	PUNCT
ejpam-2666	330	5	|	|	ADV
ejpam-2666	330	6	v2(x	v2(x	NOUN
ejpam-2666	330	7	)	)	PUNCT
ejpam-2666	330	8	|	|	PRON
ejpam-2666	330	9	v3(x	v3(x	NOUN
ejpam-2666	330	10	)	)	PUNCT
ejpam-2666	330	11	)	)	PUNCT
ejpam-2666	331	1	in	in	ADP
ejpam-2666	331	2	rr	rr	PROPN
ejpam-2666	331	3	,	,	PUNCT
ejpam-2666	331	4	s	s	X
ejpam-2666	331	5	,	,	PUNCT
ejpam-2666	331	6	t[x	t[x	NOUN
ejpam-2666	331	7	]	]	PUNCT
ejpam-2666	331	8	.	.	PUNCT
ejpam-2666	332	1	then	then	ADV
ejpam-2666	332	2	u	u	PRON
ejpam-2666	332	3	is	be	AUX
ejpam-2666	332	4	orthogonal	orthogonal	ADJ
ejpam-2666	332	5	to	to	ADP
ejpam-2666	332	6	v	v	NOUN
ejpam-2666	332	7	and	and	CCONJ
ejpam-2666	332	8	all	all	DET
ejpam-2666	332	9	its	its	PRON
ejpam-2666	332	10	cyclic	cyclic	ADJ
ejpam-2666	332	11	shifts	shift	NOUN
ejpam-2666	332	12	if	if	SCONJ
ejpam-2666	332	13	and	and	CCONJ
ejpam-2666	332	14	only	only	ADV
ejpam-2666	332	15	if	if	SCONJ
ejpam-2666	332	16	ψ(u	ψ(u	PROPN
ejpam-2666	332	17	,	,	PUNCT
ejpam-2666	332	18	v	v	NOUN
ejpam-2666	332	19	)	)	PUNCT
ejpam-2666	332	20	=	=	SYM
ejpam-2666	333	1	0	0	X
ejpam-2666	333	2	.	.	PUNCT
ejpam-2666	333	3	proof	proof	NOUN
ejpam-2666	333	4	.	.	PUNCT
ejpam-2666	334	1	let	let	VERB
ejpam-2666	334	2	u	u	PRON
ejpam-2666	334	3	=	=	SYM
ejpam-2666	334	4	(	(	PUNCT
ejpam-2666	334	5	u1,0	u1,0	PROPN
ejpam-2666	334	6	,	,	PUNCT
ejpam-2666	334	7	u1,1	u1,1	ADJ
ejpam-2666	334	8	,	,	PUNCT
ejpam-2666	334	9	·	·	PUNCT
ejpam-2666	334	10	·	·	PUNCT
ejpam-2666	334	11	·	·	PUNCT
ejpam-2666	334	12	,	,	PUNCT
ejpam-2666	334	13	u1,r−1	u1,r−1	ADJ
ejpam-2666	334	14	|	|	NOUN
ejpam-2666	334	15	u2,0	u2,0	PROPN
ejpam-2666	334	16	,	,	PUNCT
ejpam-2666	334	17	u2,1	u2,1	PROPN
ejpam-2666	334	18	,	,	PUNCT
ejpam-2666	334	19	·	·	PUNCT
ejpam-2666	334	20	·	·	PUNCT
ejpam-2666	334	21	·	·	PUNCT
ejpam-2666	334	22	,	,	PUNCT
ejpam-2666	334	23	u2,s−1	u2,s−1	ADJ
ejpam-2666	334	24	|	|	ADV
ejpam-2666	334	25	u3,0	u3,0	ADV
ejpam-2666	334	26	,	,	PUNCT
ejpam-2666	334	27	u3,1	u3,1	PROPN
ejpam-2666	334	28	,	,	PUNCT
ejpam-2666	334	29	·	·	PUNCT
ejpam-2666	334	30	·	·	PUNCT
ejpam-2666	334	31	·	·	PUNCT
ejpam-2666	334	32	,	,	PUNCT
ejpam-2666	334	33	u3,t−1	u3,t−1	NOUN
ejpam-2666	334	34	)	)	PUNCT
ejpam-2666	334	35	and	and	CCONJ
ejpam-2666	334	36	v	v	NOUN
ejpam-2666	334	37	=	=	SYM
ejpam-2666	334	38	(	(	PUNCT
ejpam-2666	334	39	v1,0	v1,0	PROPN
ejpam-2666	334	40	,	,	PUNCT
ejpam-2666	334	41	v1,1	v1,1	PROPN
ejpam-2666	334	42	,	,	PUNCT
ejpam-2666	334	43	·	·	PUNCT
ejpam-2666	334	44	·	·	PUNCT
ejpam-2666	334	45	·	·	PUNCT
ejpam-2666	334	46	,	,	PUNCT
ejpam-2666	334	47	v1,r−1	v1,r−1	ADV
ejpam-2666	334	48	|	|	PROPN
ejpam-2666	334	49	v2,0	v2,0	NOUN
ejpam-2666	334	50	,	,	PUNCT
ejpam-2666	334	51	v2,1	v2,1	PROPN
ejpam-2666	334	52	,	,	PUNCT
ejpam-2666	334	53	·	·	PUNCT
ejpam-2666	334	54	·	·	PUNCT
ejpam-2666	334	55	·	·	PUNCT
ejpam-2666	334	56	,	,	PUNCT
ejpam-2666	334	57	v2,s−1	v2,s−1	NOUN
ejpam-2666	334	58	|	|	ADV
ejpam-2666	334	59	v3,0	v3,0	PROPN
ejpam-2666	334	60	,	,	PUNCT
ejpam-2666	334	61	v3,1	v3,1	NOUN
ejpam-2666	334	62	,	,	PUNCT
ejpam-2666	334	63	·	·	PUNCT
ejpam-2666	334	64	·	·	PUNCT
ejpam-2666	334	65	·	·	PUNCT
ejpam-2666	334	66	,	,	PUNCT
ejpam-2666	334	67	v3,t−1	v3,t−1	NOUN
ejpam-2666	334	68	)	)	PUNCT
ejpam-2666	334	69	be	be	VERB
ejpam-2666	334	70	two	two	NUM
ejpam-2666	334	71	elements	element	NOUN
ejpam-2666	334	72	in	in	ADP
ejpam-2666	334	73	zr2	zr2	PROPN
ejpam-2666	334	74	×	×	PROPN
ejpam-2666	334	75	zs2	zs2	PROPN
ejpam-2666	334	76	×	×	PROPN
ejpam-2666	334	77	zt2	zt2	PROPN
ejpam-2666	334	78	.	.	PUNCT
ejpam-2666	335	1	let	let	VERB
ejpam-2666	335	2	σ(i)(v	σ(i)(v	X
ejpam-2666	335	3	)	)	PUNCT
ejpam-2666	336	1	be	be	AUX
ejpam-2666	336	2	the	the	DET
ejpam-2666	336	3	i	i	PROPN
ejpam-2666	336	4	-	-	PUNCT
ejpam-2666	336	5	th	th	VERB
ejpam-2666	336	6	shift	shift	NOUN
ejpam-2666	336	7	of	of	ADP
ejpam-2666	336	8	v.	v.	ADP
ejpam-2666	336	9	then	then	ADV
ejpam-2666	336	10	σ(i)(v	σ(i)(v	X
ejpam-2666	336	11	)	)	PUNCT
ejpam-2666	337	1	=	=	SYM
ejpam-2666	337	2	(	(	PUNCT
ejpam-2666	337	3	v1,0+i	v1,0+i	PROPN
ejpam-2666	337	4	,	,	PUNCT
ejpam-2666	337	5	v1,1+i	v1,1+i	NOUN
ejpam-2666	337	6	,	,	PUNCT
ejpam-2666	337	7	·	·	PUNCT
ejpam-2666	337	8	·	·	PUNCT
ejpam-2666	337	9	·	·	PUNCT
ejpam-2666	337	10	,	,	PUNCT
ejpam-2666	337	11	v1,i−1	v1,i−1	PROPN
ejpam-2666	337	12	|	|	ADP
ejpam-2666	337	13	v2,0+i	v2,0+i	PROPN
ejpam-2666	337	14	,	,	PUNCT
ejpam-2666	337	15	v2,1+i	v2,1+i	NOUN
ejpam-2666	337	16	,	,	PUNCT
ejpam-2666	337	17	·	·	PUNCT
ejpam-2666	337	18	·	·	PUNCT
ejpam-2666	337	19	·	·	PUNCT
ejpam-2666	337	20	,	,	PUNCT
ejpam-2666	337	21	v2,i−1	v2,i−1	VERB
ejpam-2666	337	22	|	|	ADV
ejpam-2666	337	23	v3,0+i	v3,0+i	NOUN
ejpam-2666	337	24	,	,	PUNCT
ejpam-2666	337	25	v3,1+i	v3,1+i	NOUN
ejpam-2666	337	26	,	,	PUNCT
ejpam-2666	337	27	·	·	PUNCT
ejpam-2666	337	28	·	·	PUNCT
ejpam-2666	337	29	·	·	PUNCT
ejpam-2666	337	30	,	,	PUNCT
ejpam-2666	337	31	v3,i−1	v3,i−1	PROPN
ejpam-2666	337	32	)	)	PUNCT
ejpam-2666	337	33	for	for	ADP
ejpam-2666	337	34	1	1	NUM
ejpam-2666	337	35	≤	≤	NUM
ejpam-2666	337	36	i	i	PRON
ejpam-2666	337	37	≤	≤	NOUN
ejpam-2666	337	38	m	m	VERB
ejpam-2666	337	39	−	−	PROPN
ejpam-2666	337	40	1	1	NUM
ejpam-2666	337	41	.	.	PUNCT
ejpam-2666	338	1	under	under	ADP
ejpam-2666	338	2	polynomial	polynomial	ADJ
ejpam-2666	338	3	representation	representation	NOUN
ejpam-2666	338	4	we	we	PRON
ejpam-2666	338	5	have	have	VERB
ejpam-2666	338	6	ψ(u	ψ(u	PROPN
ejpam-2666	338	7	,	,	PUNCT
ejpam-2666	338	8	σ(i)(v	σ(i)(v	X
ejpam-2666	338	9	)	)	PUNCT
ejpam-2666	338	10	)	)	PUNCT
ejpam-2666	339	1	=	=	PUNCT
ejpam-2666	340	1	r−1∑	r−1∑	PROPN
ejpam-2666	340	2	p=0	p=0	PROPN
ejpam-2666	340	3	θm	θm	NOUN
ejpam-2666	340	4	r	r	NOUN
ejpam-2666	340	5	(	(	PUNCT
ejpam-2666	340	6	xr	xr	X
ejpam-2666	340	7	)	)	PUNCT
ejpam-2666	340	8	r−1∑	r−1∑	PROPN
ejpam-2666	340	9	j=0	j=0	PROPN
ejpam-2666	340	10	u1,jv1,p+jx	u1,jv1,p+jx	PROPN
ejpam-2666	340	11	m−1−p	m−1−p	PROPN
ejpam-2666	340	12	+	+	PROPN
ejpam-2666	340	13	s−1∑	s−1∑	NUM
ejpam-2666	340	14	q=0	q=0	NOUN
ejpam-2666	341	1	(	(	PUNCT
ejpam-2666	341	2	θm	θm	PROPN
ejpam-2666	341	3	s	s	X
ejpam-2666	341	4	(	(	PUNCT
ejpam-2666	341	5	xs	xs	PROPN
ejpam-2666	341	6	)	)	PUNCT
ejpam-2666	341	7	s−1∑	s−1∑	NUM
ejpam-2666	341	8	k=0	k=0	PROPN
ejpam-2666	341	9	u2,kv2,q+kx	u2,kv2,q+kx	NOUN
ejpam-2666	341	10	m−1−q	m−1−q	PUNCT
ejpam-2666	341	11	)	)	PUNCT
ejpam-2666	342	1	+	+	CCONJ
ejpam-2666	342	2	t−1∑	t−1∑	NUM
ejpam-2666	342	3	l=0	l=0	PROPN
ejpam-2666	342	4	(	(	PUNCT
ejpam-2666	342	5	θm	θm	PROPN
ejpam-2666	342	6	t	t	PROPN
ejpam-2666	342	7	(	(	PUNCT
ejpam-2666	342	8	xt	xt	ADJ
ejpam-2666	342	9	)	)	PUNCT
ejpam-2666	342	10	t−1∑	t−1∑	VERB
ejpam-2666	342	11	w=0	w=0	PROPN
ejpam-2666	342	12	u3,wv3,l+wx	u3,wv3,l+wx	NOUN
ejpam-2666	342	13	m−1−l	m−1−l	ADV
ejpam-2666	342	14	)	)	PUNCT
ejpam-2666	342	15	.	.	PUNCT
ejpam-2666	343	1	rearranging	rearrange	VERB
ejpam-2666	343	2	the	the	DET
ejpam-2666	343	3	terms	term	NOUN
ejpam-2666	343	4	in	in	ADP
ejpam-2666	343	5	the	the	DET
ejpam-2666	343	6	summation	summation	NOUN
ejpam-2666	343	7	we	we	PRON
ejpam-2666	343	8	get	get	VERB
ejpam-2666	343	9	ψ(u	ψ(u	PROPN
ejpam-2666	343	10	,	,	PUNCT
ejpam-2666	343	11	σ(i)(v	σ(i)(v	X
ejpam-2666	343	12	)	)	PUNCT
ejpam-2666	343	13	)	)	PUNCT
ejpam-2666	344	1	=	=	PUNCT
ejpam-2666	344	2	m−1∑	m−1∑	PROPN
ejpam-2666	344	3	i=0	i=0	PROPN
ejpam-2666	344	4	six	six	NUM
ejpam-2666	344	5	m−1−i	m−1−i	ADJ
ejpam-2666	344	6	mod(xm	mod(xm	NOUN
ejpam-2666	344	7	−	−	PROPN
ejpam-2666	344	8	1	1	NUM
ejpam-2666	344	9	)	)	PUNCT
ejpam-2666	344	10	,	,	PUNCT
ejpam-2666	344	11	where	where	SCONJ
ejpam-2666	344	12	si	si	PROPN
ejpam-2666	344	13	=	=	PUNCT
ejpam-2666	344	14	∑r−1	∑r−1	PROPN
ejpam-2666	344	15	j=0	j=0	PROPN
ejpam-2666	344	16	u1,jv1,i+j+	u1,jv1,i+j+	NOUN
ejpam-2666	344	17	∑s−1	∑s−1	NOUN
ejpam-2666	344	18	k=0	k=0	X
ejpam-2666	344	19	u2,kv2,i+k+	u2,kv2,i+k+	PROPN
ejpam-2666	344	20	∑t−1	∑t−1	X
ejpam-2666	344	21	l=0	l=0	PROPN
ejpam-2666	344	22	u1,lv2,i+l	u1,lv2,i+l	PROPN
ejpam-2666	344	23	.	.	PUNCT
ejpam-2666	345	1	on	on	ADP
ejpam-2666	345	2	the	the	DET
ejpam-2666	345	3	other	other	ADJ
ejpam-2666	345	4	hand	hand	NOUN
ejpam-2666	345	5	,	,	PUNCT
ejpam-2666	345	6	we	we	PRON
ejpam-2666	345	7	have	have	VERB
ejpam-2666	345	8	u·σ(i)(v	u·σ(i)(v	VERB
ejpam-2666	345	9	)	)	PUNCT
ejpam-2666	345	10	=	=	SYM
ejpam-2666	346	1	∑r−1	∑r−1	PROPN
ejpam-2666	346	2	j=0	j=0	PROPN
ejpam-2666	346	3	u1,jv1,i+j+	u1,jv1,i+j+	NOUN
ejpam-2666	346	4	∑s−1	∑s−1	NOUN
ejpam-2666	346	5	k=0	k=0	X
ejpam-2666	346	6	u2,kv2,i+k+	u2,kv2,i+k+	PROPN
ejpam-2666	346	7	∑t−1	∑t−1	NOUN
ejpam-2666	346	8	l=0	l=0	PROPN
ejpam-2666	346	9	u1,lv2,i+l	u1,lv2,i+l	INTJ
ejpam-2666	347	1	=	=	PUNCT
ejpam-2666	347	2	si	si	X
ejpam-2666	347	3	.	.	PUNCT
ejpam-2666	347	4	thus	thus	ADV
ejpam-2666	347	5	,	,	PUNCT
ejpam-2666	347	6	ψ(u	ψ(u	PROPN
ejpam-2666	347	7	,	,	PUNCT
ejpam-2666	347	8	σ(i)(v	σ(i)(v	X
ejpam-2666	347	9	)	)	PUNCT
ejpam-2666	347	10	)	)	PUNCT
ejpam-2666	348	1	=	=	SYM
ejpam-2666	348	2	0	0	PUNCT
ejpam-2666	349	1	if	if	SCONJ
ejpam-2666	349	2	and	and	CCONJ
ejpam-2666	349	3	only	only	ADV
ejpam-2666	349	4	if	if	SCONJ
ejpam-2666	349	5	si	si	PROPN
ejpam-2666	349	6	=	=	SYM
ejpam-2666	349	7	0	0	NUM
ejpam-2666	349	8	for	for	ADP
ejpam-2666	349	9	all	all	DET
ejpam-2666	349	10	1	1	NUM
ejpam-2666	349	11	≤	≤	NUM
ejpam-2666	350	1	i	i	PRON
ejpam-2666	350	2	≤	≤	ADJ
ejpam-2666	350	3	m−	m−	PROPN
ejpam-2666	350	4	1	1	NUM
ejpam-2666	350	5	.	.	PUNCT
ejpam-2666	351	1	hence	hence	ADV
ejpam-2666	351	2	the	the	DET
ejpam-2666	351	3	result	result	NOUN
ejpam-2666	351	4	.	.	PUNCT
ejpam-2666	352	1	lemma	lemma	PROPN
ejpam-2666	352	2	4	4	X
ejpam-2666	352	3	.	.	PUNCT
ejpam-2666	353	1	let	let	VERB
ejpam-2666	353	2	u	u	PRON
ejpam-2666	353	3	=	=	PUNCT
ejpam-2666	353	4	(	(	PUNCT
ejpam-2666	353	5	u1	u1	NOUN
ejpam-2666	353	6	|	|	ADV
ejpam-2666	353	7	u2	u2	PROPN
ejpam-2666	353	8	|	|	NOUN
ejpam-2666	353	9	u3	u3	NOUN
ejpam-2666	353	10	)	)	PUNCT
ejpam-2666	353	11	and	and	CCONJ
ejpam-2666	353	12	v	v	NOUN
ejpam-2666	353	13	=	=	SYM
ejpam-2666	353	14	(	(	PUNCT
ejpam-2666	353	15	v1	v1	VERB
ejpam-2666	353	16	|	|	ADV
ejpam-2666	353	17	v2	v2	PROPN
ejpam-2666	353	18	|	|	NOUN
ejpam-2666	353	19	v3	v3	PROPN
ejpam-2666	353	20	)	)	PUNCT
ejpam-2666	353	21	in	in	ADP
ejpam-2666	353	22	rr	rr	PROPN
ejpam-2666	353	23	,	,	PUNCT
ejpam-2666	353	24	s	s	X
ejpam-2666	353	25	,	,	PUNCT
ejpam-2666	353	26	t[x	t[x	NOUN
ejpam-2666	353	27	]	]	PUNCT
ejpam-2666	354	1	such	such	ADJ
ejpam-2666	354	2	that	that	SCONJ
ejpam-2666	354	3	ψ(u	ψ(u	PROPN
ejpam-2666	354	4	,	,	PUNCT
ejpam-2666	354	5	v	v	NOUN
ejpam-2666	354	6	)	)	PUNCT
ejpam-2666	354	7	=	=	SYM
ejpam-2666	354	8	0	0	X
ejpam-2666	354	9	.	.	PUNCT
ejpam-2666	355	1	then	then	ADV
ejpam-2666	355	2	(	(	PUNCT
ejpam-2666	355	3	i	i	NOUN
ejpam-2666	355	4	)	)	PUNCT
ejpam-2666	355	5	if	if	SCONJ
ejpam-2666	355	6	u2	u2	NOUN
ejpam-2666	355	7	=	=	NOUN
ejpam-2666	355	8	0	0	NUM
ejpam-2666	355	9	or	or	CCONJ
ejpam-2666	355	10	v2	v2	ADJ
ejpam-2666	355	11	=	=	SYM
ejpam-2666	355	12	0	0	NUM
ejpam-2666	355	13	and	and	CCONJ
ejpam-2666	355	14	u3	u3	NOUN
ejpam-2666	355	15	=	=	SYM
ejpam-2666	355	16	0	0	NUM
ejpam-2666	355	17	or	or	CCONJ
ejpam-2666	355	18	v3	v3	PROPN
ejpam-2666	355	19	=	=	SYM
ejpam-2666	355	20	0	0	PROPN
ejpam-2666	355	21	,	,	PUNCT
ejpam-2666	355	22	then	then	ADV
ejpam-2666	355	23	u1v	u1v	NUM
ejpam-2666	355	24	∗	∗	NOUN
ejpam-2666	355	25	1	1	NUM
ejpam-2666	355	26	=	=	SYM
ejpam-2666	355	27	0	0	NUM
ejpam-2666	356	1	(	(	PUNCT
ejpam-2666	356	2	mod	mod	PROPN
ejpam-2666	356	3	xr	xr	PROPN
ejpam-2666	356	4	−	−	PROPN
ejpam-2666	356	5	1	1	NUM
ejpam-2666	356	6	)	)	PUNCT
ejpam-2666	356	7	.	.	PUNCT
ejpam-2666	357	1	(	(	PUNCT
ejpam-2666	357	2	ii	ii	NOUN
ejpam-2666	357	3	)	)	PUNCT
ejpam-2666	357	4	if	if	SCONJ
ejpam-2666	357	5	u1	u1	NOUN
ejpam-2666	357	6	=	=	SYM
ejpam-2666	357	7	0	0	NUM
ejpam-2666	357	8	or	or	CCONJ
ejpam-2666	357	9	v1	v1	VERB
ejpam-2666	357	10	=	=	SYM
ejpam-2666	357	11	0	0	NUM
ejpam-2666	357	12	and	and	CCONJ
ejpam-2666	357	13	u3	u3	NOUN
ejpam-2666	357	14	=	=	SYM
ejpam-2666	357	15	0	0	NUM
ejpam-2666	357	16	or	or	CCONJ
ejpam-2666	357	17	v3	v3	PROPN
ejpam-2666	357	18	=	=	SYM
ejpam-2666	357	19	0	0	PROPN
ejpam-2666	357	20	,	,	PUNCT
ejpam-2666	357	21	then	then	ADV
ejpam-2666	357	22	u2v	u2v	ADJ
ejpam-2666	357	23	∗	∗	NOUN
ejpam-2666	357	24	2	2	NUM
ejpam-2666	357	25	=	=	SYM
ejpam-2666	357	26	0	0	NUM
ejpam-2666	358	1	(	(	PUNCT
ejpam-2666	358	2	mod	mod	PROPN
ejpam-2666	358	3	xs	xs	PROPN
ejpam-2666	358	4	−	−	PROPN
ejpam-2666	358	5	1	1	NUM
ejpam-2666	358	6	)	)	PUNCT
ejpam-2666	358	7	.	.	PUNCT
ejpam-2666	359	1	(	(	PUNCT
ejpam-2666	359	2	iii	iii	X
ejpam-2666	359	3	)	)	PUNCT
ejpam-2666	359	4	if	if	SCONJ
ejpam-2666	359	5	u1	u1	NOUN
ejpam-2666	359	6	=	=	SYM
ejpam-2666	359	7	0	0	NUM
ejpam-2666	359	8	or	or	CCONJ
ejpam-2666	359	9	v1	v1	VERB
ejpam-2666	359	10	=	=	SYM
ejpam-2666	359	11	0	0	NUM
ejpam-2666	359	12	and	and	CCONJ
ejpam-2666	359	13	u2	u2	PROPN
ejpam-2666	359	14	=	=	SYM
ejpam-2666	359	15	0	0	NUM
ejpam-2666	359	16	or	or	CCONJ
ejpam-2666	359	17	v2	v2	ADJ
ejpam-2666	359	18	=	=	SYM
ejpam-2666	359	19	0	0	NUM
ejpam-2666	359	20	,	,	PUNCT
ejpam-2666	359	21	then	then	ADV
ejpam-2666	359	22	u3v	u3v	PUNCT
ejpam-2666	359	23	∗	∗	VERB
ejpam-2666	359	24	3	3	NUM
ejpam-2666	359	25	=	=	SYM
ejpam-2666	359	26	0	0	NUM
ejpam-2666	360	1	(	(	PUNCT
ejpam-2666	360	2	mod	mod	PROPN
ejpam-2666	360	3	xt	xt	PROPN
ejpam-2666	360	4	−	−	PROPN
ejpam-2666	360	5	1	1	NUM
ejpam-2666	360	6	)	)	PUNCT
ejpam-2666	360	7	.	.	PUNCT
ejpam-2666	361	1	proof	proof	NOUN
ejpam-2666	361	2	.	.	PUNCT
ejpam-2666	362	1	let	let	VERB
ejpam-2666	362	2	u2	u2	NOUN
ejpam-2666	362	3	=	=	VERB
ejpam-2666	362	4	0	0	NUM
ejpam-2666	362	5	or	or	CCONJ
ejpam-2666	362	6	v2	v2	ADJ
ejpam-2666	362	7	=	=	SYM
ejpam-2666	362	8	0	0	NUM
ejpam-2666	362	9	and	and	CCONJ
ejpam-2666	362	10	u3	u3	NOUN
ejpam-2666	362	11	=	=	SYM
ejpam-2666	362	12	0	0	NUM
ejpam-2666	362	13	or	or	CCONJ
ejpam-2666	362	14	v3	v3	PROPN
ejpam-2666	362	15	=	=	SYM
ejpam-2666	363	1	0	0	PROPN
ejpam-2666	363	2	.	.	PUNCT
ejpam-2666	364	1	then	then	ADV
ejpam-2666	364	2	from	from	ADP
ejpam-2666	364	3	the	the	DET
ejpam-2666	364	4	definition	definition	NOUN
ejpam-2666	364	5	of	of	ADP
ejpam-2666	364	6	ψ	ψ	PROPN
ejpam-2666	364	7	,	,	PUNCT
ejpam-2666	364	8	we	we	PRON
ejpam-2666	364	9	have	have	VERB
ejpam-2666	364	10	ψ(u	ψ(u	PROPN
ejpam-2666	364	11	,	,	PUNCT
ejpam-2666	364	12	v	v	NOUN
ejpam-2666	364	13	)	)	PUNCT
ejpam-2666	364	14	=	=	SYM
ejpam-2666	365	1	u1θm	u1θm	X
ejpam-2666	365	2	r	r	NOUN
ejpam-2666	365	3	(	(	PUNCT
ejpam-2666	365	4	xr)xm−deg(v1)−1v∗1	xr)xm−deg(v1)−1v∗1	PROPN
ejpam-2666	365	5	=	=	SYM
ejpam-2666	365	6	0	0	PUNCT
ejpam-2666	366	1	(	(	PUNCT
ejpam-2666	366	2	mod	mod	PROPN
ejpam-2666	366	3	xm	xm	PROPN
ejpam-2666	366	4	−	−	NOUN
ejpam-2666	366	5	1	1	NUM
ejpam-2666	366	6	)	)	PUNCT
ejpam-2666	366	7	.	.	PUNCT
ejpam-2666	367	1	this	this	PRON
ejpam-2666	367	2	implies	imply	VERB
ejpam-2666	367	3	that	that	SCONJ
ejpam-2666	367	4	u1θm	u1θm	X
ejpam-2666	368	1	r	r	NOUN
ejpam-2666	368	2	(	(	PUNCT
ejpam-2666	368	3	xr)xm−deg(v1)−1v∗1	xr)xm−deg(v1)−1v∗1	PROPN
ejpam-2666	368	4	=	=	SYM
ejpam-2666	368	5	(	(	PUNCT
ejpam-2666	368	6	xm	xm	PROPN
ejpam-2666	368	7	−	−	PROPN
ejpam-2666	368	8	1)g	1)g	PROPN
ejpam-2666	368	9	for	for	ADP
ejpam-2666	368	10	some	some	DET
ejpam-2666	368	11	g	g	PROPN
ejpam-2666	368	12	∈	∈	PROPN
ejpam-2666	368	13	z2[x	z2[x	PROPN
ejpam-2666	368	14	]	]	PUNCT
ejpam-2666	368	15	.	.	PUNCT
ejpam-2666	369	1	taking	take	VERB
ejpam-2666	369	2	f	f	PROPN
ejpam-2666	369	3	=	=	PUNCT
ejpam-2666	369	4	xdeg(v1)+1	xdeg(v1)+1	PROPN
ejpam-2666	369	5	g	g	NOUN
ejpam-2666	369	6	,	,	PUNCT
ejpam-2666	369	7	we	we	PRON
ejpam-2666	369	8	get	get	VERB
ejpam-2666	369	9	u1θm	u1θm	X
ejpam-2666	369	10	r	r	NOUN
ejpam-2666	369	11	(	(	PUNCT
ejpam-2666	369	12	xr)xmv∗1	xr)xmv∗1	PROPN
ejpam-2666	369	13	=	=	PUNCT
ejpam-2666	369	14	f(xm	f(xm	PROPN
ejpam-2666	369	15	−	−	PROPN
ejpam-2666	369	16	1	1	NUM
ejpam-2666	369	17	)	)	PUNCT
ejpam-2666	369	18	and	and	CCONJ
ejpam-2666	369	19	therefore	therefore	ADV
ejpam-2666	369	20	u1(x	u1(x	ADV
ejpam-2666	369	21	m	m	NUM
ejpam-2666	369	22	−	−	NOUN
ejpam-2666	369	23	1)xmv∗1	1)xmv∗1	NUM
ejpam-2666	369	24	=	=	SYM
ejpam-2666	369	25	(	(	PUNCT
ejpam-2666	369	26	xm	xm	PROPN
ejpam-2666	369	27	−	−	PROPN
ejpam-2666	369	28	1)(xr	1)(xr	NUM
ejpam-2666	369	29	−	−	PROPN
ejpam-2666	369	30	1)f	1)f	NUM
ejpam-2666	369	31	.	.	PUNCT
ejpam-2666	370	1	since	since	SCONJ
ejpam-2666	370	2	x	x	PROPN
ejpam-2666	370	3	and	and	CCONJ
ejpam-2666	370	4	xr	xr	PROPN
ejpam-2666	370	5	−	−	PROPN
ejpam-2666	370	6	1	1	NUM
ejpam-2666	370	7	are	be	AUX
ejpam-2666	370	8	relatively	relatively	ADV
ejpam-2666	370	9	prime	prime	ADJ
ejpam-2666	370	10	,	,	PUNCT
ejpam-2666	370	11	we	we	PRON
ejpam-2666	370	12	have	have	VERB
ejpam-2666	370	13	u1v	u1v	NOUN
ejpam-2666	370	14	∗	∗	NOUN
ejpam-2666	370	15	1	1	NUM
ejpam-2666	370	16	=	=	SYM
ejpam-2666	370	17	0	0	NUM
ejpam-2666	371	1	(	(	PUNCT
ejpam-2666	371	2	mod	mod	PROPN
ejpam-2666	371	3	xr	xr	PROPN
ejpam-2666	371	4	−	−	PROPN
ejpam-2666	371	5	1	1	NUM
ejpam-2666	371	6	)	)	PUNCT
ejpam-2666	371	7	.	.	PUNCT
ejpam-2666	372	1	other	other	ADJ
ejpam-2666	372	2	results	result	NOUN
ejpam-2666	372	3	can	can	AUX
ejpam-2666	372	4	be	be	AUX
ejpam-2666	372	5	proved	prove	VERB
ejpam-2666	372	6	similarly	similarly	ADV
ejpam-2666	372	7	.	.	PUNCT
ejpam-2666	373	1	now	now	ADV
ejpam-2666	373	2	we	we	PRON
ejpam-2666	373	3	determine	determine	VERB
ejpam-2666	373	4	the	the	DET
ejpam-2666	373	5	form	form	NOUN
ejpam-2666	373	6	of	of	ADP
ejpam-2666	373	7	generator	generator	NOUN
ejpam-2666	373	8	matrix	matrix	NOUN
ejpam-2666	373	9	of	of	ADP
ejpam-2666	373	10	a	a	DET
ejpam-2666	373	11	z2	z2	ADJ
ejpam-2666	373	12	-	-	PUNCT
ejpam-2666	373	13	triple	triple	ADJ
ejpam-2666	373	14	cyclic	cyclic	ADJ
ejpam-2666	373	15	code	code	NOUN
ejpam-2666	373	16	.	.	PUNCT
ejpam-2666	374	1	the	the	DET
ejpam-2666	374	2	generator	generator	NOUN
ejpam-2666	374	3	matrix	matrix	NOUN
ejpam-2666	374	4	of	of	ADP
ejpam-2666	374	5	a	a	DET
ejpam-2666	374	6	z2	z2	ADJ
ejpam-2666	374	7	-	-	PUNCT
ejpam-2666	374	8	triple	triple	ADJ
ejpam-2666	374	9	cyclic	cyclic	ADJ
ejpam-2666	374	10	code	code	NOUN
ejpam-2666	374	11	c	c	NOUN
ejpam-2666	374	12	determines	determine	VERB
ejpam-2666	374	13	the	the	DET
ejpam-2666	374	14	cardinalities	cardinality	NOUN
ejpam-2666	374	15	of	of	ADP
ejpam-2666	374	16	the	the	DET
ejpam-2666	374	17	projections	projection	NOUN
ejpam-2666	374	18	cr	cr	PROPN
ejpam-2666	374	19	,	,	PUNCT
ejpam-2666	374	20	cs	cs	PROPN
ejpam-2666	374	21	and	and	CCONJ
ejpam-2666	374	22	ct	ct	PROPN
ejpam-2666	374	23	and	and	CCONJ
ejpam-2666	374	24	their	their	PRON
ejpam-2666	374	25	duals	dual	NOUN
ejpam-2666	374	26	,	,	PUNCT
ejpam-2666	374	27	and	and	CCONJ
ejpam-2666	374	28	these	these	PRON
ejpam-2666	374	29	are	be	AUX
ejpam-2666	374	30	further	far	ADV
ejpam-2666	374	31	be	be	AUX
ejpam-2666	374	32	used	use	VERB
ejpam-2666	374	33	to	to	PART
ejpam-2666	374	34	obtain	obtain	VERB
ejpam-2666	374	35	the	the	DET
ejpam-2666	374	36	duals	dual	NOUN
ejpam-2666	374	37	of	of	ADP
ejpam-2666	374	38	a	a	DET
ejpam-2666	374	39	z2	z2	ADJ
ejpam-2666	374	40	-	-	PUNCT
ejpam-2666	374	41	triple	triple	ADJ
ejpam-2666	374	42	cyclic	cyclic	ADJ
ejpam-2666	374	43	codes	code	NOUN
ejpam-2666	374	44	.	.	PUNCT
ejpam-2666	375	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	375	2	b	b	NUM
ejpam-2666	375	3	,	,	PUNCT
ejpam-2666	375	4	maheshanand	maheshanand	NOUN
ejpam-2666	375	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	375	6	/	/	SYM
ejpam-2666	375	7	eur	eur	PROPN
ejpam-2666	375	8	.	.	PUNCT
ejpam-2666	376	1	j.	j.	PROPN
ejpam-2666	376	2	pure	pure	PROPN
ejpam-2666	376	3	appl	appl	PROPN
ejpam-2666	376	4	.	.	PROPN
ejpam-2666	376	5	math	math	PROPN
ejpam-2666	376	6	,	,	PUNCT
ejpam-2666	376	7	10	10	NUM
ejpam-2666	376	8	(	(	PUNCT
ejpam-2666	376	9	2	2	NUM
ejpam-2666	376	10	)	)	PUNCT
ejpam-2666	376	11	(	(	PUNCT
ejpam-2666	376	12	2017	2017	NUM
ejpam-2666	376	13	)	)	PUNCT
ejpam-2666	376	14	,	,	PUNCT
ejpam-2666	376	15	392	392	NUM
ejpam-2666	376	16	-	-	SYM
ejpam-2666	376	17	409	409	NUM
ejpam-2666	376	18	400	400	NUM
ejpam-2666	376	19	let	let	VERB
ejpam-2666	376	20	c	c	NOUN
ejpam-2666	376	21	=	=	SYM
ejpam-2666	376	22	〈	〈	PROPN
ejpam-2666	376	23	(	(	PUNCT
ejpam-2666	376	24	b	b	NOUN
ejpam-2666	376	25	|	|	NOUN
ejpam-2666	376	26	0	0	NUM
ejpam-2666	377	1	|	|	NOUN
ejpam-2666	377	2	0	0	NUM
ejpam-2666	377	3	)	)	PUNCT
ejpam-2666	377	4	,	,	PUNCT
ejpam-2666	378	1	(	(	PUNCT
ejpam-2666	378	2	l	l	NOUN
ejpam-2666	378	3	|	|	ADV
ejpam-2666	378	4	a	a	DET
ejpam-2666	378	5	|	|	NOUN
ejpam-2666	378	6	0	0	NUM
ejpam-2666	378	7	)	)	PUNCT
ejpam-2666	378	8	,	,	PUNCT
ejpam-2666	378	9	(	(	PUNCT
ejpam-2666	378	10	g1	g1	VERB
ejpam-2666	378	11	|	|	ADV
ejpam-2666	378	12	g2	g2	PROPN
ejpam-2666	378	13	|	|	CCONJ
ejpam-2666	378	14	g3	g3	PROPN
ejpam-2666	378	15	)	)	PUNCT
ejpam-2666	378	16	〉	〉	PROPN
ejpam-2666	378	17	be	be	AUX
ejpam-2666	378	18	a	a	DET
ejpam-2666	378	19	z2	z2	ADJ
ejpam-2666	378	20	-	-	PUNCT
ejpam-2666	378	21	triple	triple	ADJ
ejpam-2666	378	22	cyclic	cyclic	ADJ
ejpam-2666	378	23	code	code	NOUN
ejpam-2666	378	24	of	of	ADP
ejpam-2666	378	25	block	block	NOUN
ejpam-2666	378	26	length	length	NOUN
ejpam-2666	378	27	(	(	PUNCT
ejpam-2666	378	28	r	r	NOUN
ejpam-2666	378	29	,	,	PUNCT
ejpam-2666	378	30	s	s	PROPN
ejpam-2666	378	31	,	,	PUNCT
ejpam-2666	378	32	t	t	PROPN
ejpam-2666	378	33	)	)	PUNCT
ejpam-2666	378	34	and	and	CCONJ
ejpam-2666	378	35	c⊥	c⊥	PROPN
ejpam-2666	378	36	be	be	AUX
ejpam-2666	378	37	its	its	PRON
ejpam-2666	378	38	dual	dual	ADJ
ejpam-2666	378	39	.	.	PUNCT
ejpam-2666	379	1	then	then	ADV
ejpam-2666	379	2	from	from	ADP
ejpam-2666	379	3	theorem	theorem	ADJ
ejpam-2666	379	4	6	6	NUM
ejpam-2666	379	5	,	,	PUNCT
ejpam-2666	379	6	c	c	PROPN
ejpam-2666	379	7	is	be	AUX
ejpam-2666	379	8	spanned	span	VERB
ejpam-2666	379	9	by	by	ADP
ejpam-2666	379	10	s	s	NOUN
ejpam-2666	379	11	=	=	NOUN
ejpam-2666	379	12	s1	s1	PROPN
ejpam-2666	379	13	∪	∪	ADP
ejpam-2666	379	14	s2	s2	PROPN
ejpam-2666	379	15	∪	∪	X
ejpam-2666	379	16	s3	s3	PROPN
ejpam-2666	379	17	and	and	CCONJ
ejpam-2666	379	18	therefore	therefore	ADV
ejpam-2666	379	19	c	c	PROPN
ejpam-2666	379	20	is	be	AUX
ejpam-2666	379	21	generated	generate	VERB
ejpam-2666	379	22	by	by	ADP
ejpam-2666	379	23	the	the	DET
ejpam-2666	379	24	matrix	matrix	NOUN
ejpam-2666	379	25	whose	whose	DET
ejpam-2666	379	26	rows	row	NOUN
ejpam-2666	379	27	are	be	AUX
ejpam-2666	379	28	the	the	DET
ejpam-2666	379	29	elements	element	NOUN
ejpam-2666	379	30	of	of	ADP
ejpam-2666	379	31	the	the	DET
ejpam-2666	379	32	set	set	NOUN
ejpam-2666	379	33	s.	s.	PROPN
ejpam-2666	379	34	let	let	VERB
ejpam-2666	379	35	c1	c1	PROPN
ejpam-2666	379	36	,	,	PUNCT
ejpam-2666	379	37	c2	c2	PROPN
ejpam-2666	379	38	and	and	CCONJ
ejpam-2666	379	39	c3	c3	PROPN
ejpam-2666	379	40	be	be	VERB
ejpam-2666	379	41	the	the	DET
ejpam-2666	379	42	subcodes	subcode	NOUN
ejpam-2666	379	43	of	of	ADP
ejpam-2666	379	44	c	c	NOUN
ejpam-2666	379	45	generated	generate	VERB
ejpam-2666	379	46	by	by	ADP
ejpam-2666	379	47	s1	s1	PROPN
ejpam-2666	379	48	,	,	PUNCT
ejpam-2666	379	49	s2	s2	NOUN
ejpam-2666	379	50	and	and	CCONJ
ejpam-2666	379	51	s3	s3	PROPN
ejpam-2666	379	52	,	,	PUNCT
ejpam-2666	379	53	respectively	respectively	ADV
ejpam-2666	379	54	,	,	PUNCT
ejpam-2666	379	55	and	and	CCONJ
ejpam-2666	379	56	let	let	VERB
ejpam-2666	379	57	g1	g1	PROPN
ejpam-2666	379	58	,	,	PUNCT
ejpam-2666	379	59	g2	g2	PROPN
ejpam-2666	379	60	and	and	CCONJ
ejpam-2666	379	61	g3	g3	PROPN
ejpam-2666	379	62	be	be	AUX
ejpam-2666	379	63	their	their	PRON
ejpam-2666	379	64	generator	generator	NOUN
ejpam-2666	379	65	matrices	matrix	NOUN
ejpam-2666	379	66	,	,	PUNCT
ejpam-2666	379	67	where	where	SCONJ
ejpam-2666	379	68	g1	g1	PROPN
ejpam-2666	379	69	=	=	SYM
ejpam-2666	379	70	(	(	PUNCT
ejpam-2666	379	71	ir−deg(b	ir−deg(b	X
ejpam-2666	379	72	)	)	PUNCT
ejpam-2666	379	73	a	a	DET
ejpam-2666	379	74	|	|	NOUN
ejpam-2666	379	75	0	0	NUM
ejpam-2666	380	1	|	|	NOUN
ejpam-2666	380	2	0),g2	0),g2	NUM
ejpam-2666	381	1	=	=	SYM
ejpam-2666	381	2	(	(	PUNCT
ejpam-2666	381	3	b	b	X
ejpam-2666	381	4	|	|	ADV
ejpam-2666	381	5	c	c	PROPN
ejpam-2666	381	6	ir−deg(a	ir−deg(a	PROPN
ejpam-2666	381	7	)	)	PUNCT
ejpam-2666	382	1	|	|	ADV
ejpam-2666	382	2	0),g3	0),g3	NUM
ejpam-2666	382	3	=	=	SYM
ejpam-2666	383	1	(	(	PUNCT
ejpam-2666	383	2	d	d	X
ejpam-2666	383	3	|	|	NOUN
ejpam-2666	384	1	e	e	NOUN
ejpam-2666	385	1	|	|	ADV
ejpam-2666	385	2	f	f	PROPN
ejpam-2666	385	3	it−deg(g3	it−deg(g3	NOUN
ejpam-2666	385	4	)	)	PUNCT
ejpam-2666	385	5	)	)	PUNCT
ejpam-2666	385	6	.	.	PUNCT
ejpam-2666	386	1	then	then	ADV
ejpam-2666	386	2	,	,	PUNCT
ejpam-2666	386	3	the	the	DET
ejpam-2666	386	4	matrix	matrix	NOUN
ejpam-2666	386	5	g	g	NOUN
ejpam-2666	386	6	=	=	SYM
ejpam-2666	386	7			PROPN
ejpam-2666	386	8	g1	g1	PROPN
ejpam-2666	386	9	g2	g2	PROPN
ejpam-2666	386	10	g3	g3	PROPN
ejpam-2666	386	11			PROPN
ejpam-2666	386	12	forms	form	VERB
ejpam-2666	386	13	a	a	DET
ejpam-2666	386	14	generator	generator	NOUN
ejpam-2666	386	15	matrix	matrix	NOUN
ejpam-2666	386	16	for	for	ADP
ejpam-2666	386	17	c.	c.	NOUN
ejpam-2666	386	18	we	we	PRON
ejpam-2666	386	19	obtain	obtain	VERB
ejpam-2666	386	20	an	an	DET
ejpam-2666	386	21	equivalent	equivalent	ADJ
ejpam-2666	386	22	form	form	NOUN
ejpam-2666	386	23	of	of	ADP
ejpam-2666	386	24	the	the	DET
ejpam-2666	386	25	matrix	matrix	NOUN
ejpam-2666	386	26	g	g	NOUN
ejpam-2666	386	27	by	by	ADP
ejpam-2666	386	28	adjusting	adjust	VERB
ejpam-2666	386	29	its	its	PRON
ejpam-2666	386	30	rows	row	NOUN
ejpam-2666	386	31	,	,	PUNCT
ejpam-2666	386	32	so	so	SCONJ
ejpam-2666	386	33	that	that	SCONJ
ejpam-2666	386	34	we	we	PRON
ejpam-2666	386	35	can	can	AUX
ejpam-2666	386	36	make	make	VERB
ejpam-2666	386	37	use	use	NOUN
ejpam-2666	386	38	of	of	ADP
ejpam-2666	386	39	this	this	DET
ejpam-2666	386	40	equivalent	equivalent	ADJ
ejpam-2666	386	41	form	form	NOUN
ejpam-2666	386	42	to	to	PART
ejpam-2666	386	43	find	find	VERB
ejpam-2666	386	44	the	the	DET
ejpam-2666	386	45	cardinalities	cardinality	NOUN
ejpam-2666	386	46	of	of	ADP
ejpam-2666	386	47	the	the	DET
ejpam-2666	386	48	respective	respective	ADJ
ejpam-2666	386	49	projections	projection	NOUN
ejpam-2666	386	50	cr	cr	ADP
ejpam-2666	386	51	,	,	PUNCT
ejpam-2666	386	52	cs	cs	PROPN
ejpam-2666	386	53	and	and	CCONJ
ejpam-2666	386	54	ct	ct	INTJ
ejpam-2666	386	55	.	.	PUNCT
ejpam-2666	387	1	it	it	PRON
ejpam-2666	387	2	is	be	AUX
ejpam-2666	387	3	easy	easy	ADJ
ejpam-2666	387	4	to	to	PART
ejpam-2666	387	5	see	see	VERB
ejpam-2666	387	6	that	that	SCONJ
ejpam-2666	387	7	cr	cr	PROPN
ejpam-2666	387	8	is	be	AUX
ejpam-2666	387	9	generated	generate	VERB
ejpam-2666	387	10	by	by	ADP
ejpam-2666	387	11	(	(	PUNCT
ejpam-2666	387	12	b	b	PROPN
ejpam-2666	387	13	,	,	PUNCT
ejpam-2666	387	14	l	l	NOUN
ejpam-2666	387	15	,	,	PUNCT
ejpam-2666	387	16	g1	g1	PROPN
ejpam-2666	387	17	)	)	PUNCT
ejpam-2666	387	18	,	,	PUNCT
ejpam-2666	387	19	and	and	CCONJ
ejpam-2666	387	20	this	this	PRON
ejpam-2666	387	21	implies	imply	VERB
ejpam-2666	387	22	that	that	SCONJ
ejpam-2666	387	23	the	the	DET
ejpam-2666	387	24	dimension	dimension	NOUN
ejpam-2666	387	25	of	of	ADP
ejpam-2666	387	26	cr	cr	PROPN
ejpam-2666	387	27	is	be	AUX
ejpam-2666	387	28	r	r	NOUN
ejpam-2666	387	29	−	−	PROPN
ejpam-2666	387	30	deg(b	deg(b	PROPN
ejpam-2666	387	31	,	,	PUNCT
ejpam-2666	387	32	l	l	NOUN
ejpam-2666	387	33	,	,	PUNCT
ejpam-2666	387	34	g1	g1	PROPN
ejpam-2666	387	35	)	)	PUNCT
ejpam-2666	387	36	,	,	PUNCT
ejpam-2666	387	37	which	which	PRON
ejpam-2666	387	38	is	be	AUX
ejpam-2666	387	39	greater	great	ADJ
ejpam-2666	387	40	than	than	ADP
ejpam-2666	387	41	or	or	CCONJ
ejpam-2666	387	42	equal	equal	ADJ
ejpam-2666	387	43	to	to	ADP
ejpam-2666	387	44	r	r	NOUN
ejpam-2666	387	45	−	−	PROPN
ejpam-2666	387	46	deg(b	deg(b	NUM
ejpam-2666	387	47	)	)	PUNCT
ejpam-2666	387	48	.	.	PUNCT
ejpam-2666	388	1	therefore	therefore	ADV
ejpam-2666	388	2	,	,	PUNCT
ejpam-2666	388	3	the	the	DET
ejpam-2666	388	4	matrices	matrix	NOUN
ejpam-2666	388	5	b	b	NOUN
ejpam-2666	388	6	and	and	CCONJ
ejpam-2666	388	7	d	d	PROPN
ejpam-2666	388	8	must	must	AUX
ejpam-2666	388	9	have	have	VERB
ejpam-2666	388	10	submatrices	submatrice	NOUN
ejpam-2666	388	11	,	,	PUNCT
ejpam-2666	388	12	say	say	VERB
ejpam-2666	388	13	bε1	bε1	NOUN
ejpam-2666	388	14	and	and	CCONJ
ejpam-2666	388	15	dε2	dε2	NOUN
ejpam-2666	388	16	of	of	ADP
ejpam-2666	388	17	full	full	ADJ
ejpam-2666	388	18	ranks	rank	NOUN
ejpam-2666	388	19	ε1	ε1	PROPN
ejpam-2666	388	20	and	and	CCONJ
ejpam-2666	388	21	ε2	ε2	ADJ
ejpam-2666	388	22	,	,	PUNCT
ejpam-2666	388	23	respectively	respectively	ADV
ejpam-2666	388	24	,	,	PUNCT
ejpam-2666	388	25	such	such	ADJ
ejpam-2666	388	26	that	that	PRON
ejpam-2666	388	27	ε1	ε1	PROPN
ejpam-2666	388	28	+	+	CCONJ
ejpam-2666	388	29	ε2	ε2	ADJ
ejpam-2666	388	30	=	=	SYM
ejpam-2666	388	31	deg(b	deg(b	PROPN
ejpam-2666	388	32	)	)	PUNCT
ejpam-2666	388	33	−	−	PROPN
ejpam-2666	388	34	deg(b	deg(b	PROPN
ejpam-2666	388	35	,	,	PUNCT
ejpam-2666	388	36	l	l	NOUN
ejpam-2666	388	37	,	,	PUNCT
ejpam-2666	388	38	g1	g1	PROPN
ejpam-2666	388	39	)	)	PUNCT
ejpam-2666	388	40	.	.	PUNCT
ejpam-2666	389	1	add	add	VERB
ejpam-2666	389	2	the	the	DET
ejpam-2666	389	3	corresponding	correspond	VERB
ejpam-2666	389	4	rows	row	NOUN
ejpam-2666	389	5	of	of	ADP
ejpam-2666	389	6	g2	g2	PROPN
ejpam-2666	389	7	and	and	CCONJ
ejpam-2666	389	8	g3	g3	PROPN
ejpam-2666	389	9	that	that	PRON
ejpam-2666	389	10	contain	contain	VERB
ejpam-2666	389	11	bε1	bε1	ADJ
ejpam-2666	389	12	and	and	CCONJ
ejpam-2666	389	13	dε2	dε2	NOUN
ejpam-2666	389	14	,	,	PUNCT
ejpam-2666	389	15	to	to	PART
ejpam-2666	389	16	g1	g1	VERB
ejpam-2666	389	17	.	.	PUNCT
ejpam-2666	390	1	as	as	ADP
ejpam-2666	390	2	a	a	DET
ejpam-2666	390	3	result	result	NOUN
ejpam-2666	390	4	,	,	PUNCT
ejpam-2666	390	5	g2	g2	PROPN
ejpam-2666	390	6	and	and	CCONJ
ejpam-2666	390	7	g3	g3	PROPN
ejpam-2666	390	8	are	be	AUX
ejpam-2666	390	9	now	now	ADV
ejpam-2666	390	10	reduced	reduce	VERB
ejpam-2666	390	11	to	to	ADP
ejpam-2666	390	12	the	the	DET
ejpam-2666	390	13	matrices	matrix	NOUN
ejpam-2666	390	14	of	of	ADP
ejpam-2666	390	15	the	the	DET
ejpam-2666	390	16	form	form	NOUN
ejpam-2666	390	17	g′2	g′2	NOUN
ejpam-2666	390	18	=	=	PUNCT
ejpam-2666	390	19	(	(	PUNCT
ejpam-2666	390	20	0	0	NUM
ejpam-2666	390	21	|	|	ADV
ejpam-2666	390	22	c1	c1	PROPN
ejpam-2666	390	23	ir−deg(a)−ε1	ir−deg(a)−ε1	PROPN
ejpam-2666	390	24	|	|	ADV
ejpam-2666	390	25	0	0	NUM
ejpam-2666	390	26	)	)	PUNCT
ejpam-2666	390	27	and	and	CCONJ
ejpam-2666	390	28	g′3	g′3	VERB
ejpam-2666	391	1	=	=	PUNCT
ejpam-2666	391	2	(	(	PUNCT
ejpam-2666	391	3	0	0	NUM
ejpam-2666	391	4	|	|	ADV
ejpam-2666	391	5	e1	e1	VERB
ejpam-2666	391	6	|	|	ADV
ejpam-2666	391	7	f1	f1	NOUN
ejpam-2666	391	8	it−deg(g3)−ε2	it−deg(g3)−ε2	NUM
ejpam-2666	391	9	)	)	PUNCT
ejpam-2666	391	10	.	.	PUNCT
ejpam-2666	392	1	similarly	similarly	ADV
ejpam-2666	392	2	the	the	DET
ejpam-2666	392	3	dimension	dimension	NOUN
ejpam-2666	392	4	of	of	ADP
ejpam-2666	392	5	cs	cs	PROPN
ejpam-2666	392	6	is	be	AUX
ejpam-2666	392	7	s−	s−	PROPN
ejpam-2666	392	8	deg(a	deg(a	PROPN
ejpam-2666	392	9	,	,	PUNCT
ejpam-2666	392	10	g2	g2	PROPN
ejpam-2666	392	11	)	)	PUNCT
ejpam-2666	392	12	,	,	PUNCT
ejpam-2666	392	13	as	as	SCONJ
ejpam-2666	392	14	cs	cs	PROPN
ejpam-2666	392	15	is	be	AUX
ejpam-2666	392	16	generated	generate	VERB
ejpam-2666	392	17	by	by	ADP
ejpam-2666	392	18	(	(	PUNCT
ejpam-2666	392	19	a	a	PRON
ejpam-2666	392	20	,	,	PUNCT
ejpam-2666	392	21	g2	g2	PROPN
ejpam-2666	392	22	)	)	PUNCT
ejpam-2666	392	23	.	.	PUNCT
ejpam-2666	393	1	therefore	therefore	ADV
ejpam-2666	393	2	,	,	PUNCT
ejpam-2666	393	3	the	the	DET
ejpam-2666	393	4	matrix	matrix	NOUN
ejpam-2666	393	5	e1	e1	NOUN
ejpam-2666	393	6	must	must	AUX
ejpam-2666	393	7	have	have	VERB
ejpam-2666	393	8	a	a	DET
ejpam-2666	393	9	submatrix	submatrix	NOUN
ejpam-2666	393	10	,	,	PUNCT
ejpam-2666	393	11	say	say	VERB
ejpam-2666	393	12	ek1	ek1	NOUN
ejpam-2666	393	13	,	,	PUNCT
ejpam-2666	393	14	of	of	ADP
ejpam-2666	393	15	full	full	ADJ
ejpam-2666	393	16	rank	rank	NOUN
ejpam-2666	393	17	k1	k1	NOUN
ejpam-2666	393	18	=	=	PUNCT
ejpam-2666	393	19	deg(a)−	deg(a)−	NOUN
ejpam-2666	393	20	ε2−	ε2−	PROPN
ejpam-2666	393	21	deg(a	deg(a	PROPN
ejpam-2666	393	22	,	,	PUNCT
ejpam-2666	393	23	g2	g2	PROPN
ejpam-2666	393	24	)	)	PUNCT
ejpam-2666	393	25	.	.	PUNCT
ejpam-2666	394	1	again	again	ADV
ejpam-2666	394	2	,	,	PUNCT
ejpam-2666	394	3	adding	add	VERB
ejpam-2666	394	4	the	the	DET
ejpam-2666	394	5	rows	row	NOUN
ejpam-2666	394	6	that	that	PRON
ejpam-2666	394	7	contain	contain	VERB
ejpam-2666	394	8	the	the	DET
ejpam-2666	394	9	matrix	matrix	NOUN
ejpam-2666	394	10	ek1	ek1	NOUN
ejpam-2666	394	11	,	,	PUNCT
ejpam-2666	394	12	to	to	PART
ejpam-2666	394	13	g′2	g′2	VERB
ejpam-2666	394	14	,	,	PUNCT
ejpam-2666	394	15	we	we	PRON
ejpam-2666	394	16	get	get	VERB
ejpam-2666	394	17	the	the	DET
ejpam-2666	394	18	remaining	remain	VERB
ejpam-2666	394	19	part	part	NOUN
ejpam-2666	394	20	of	of	ADP
ejpam-2666	394	21	the	the	DET
ejpam-2666	394	22	generating	generate	VERB
ejpam-2666	394	23	matrix	matrix	NOUN
ejpam-2666	394	24	g	g	NOUN
ejpam-2666	394	25	of	of	ADP
ejpam-2666	394	26	c	c	PROPN
ejpam-2666	394	27	as	as	ADP
ejpam-2666	394	28	(	(	PUNCT
ejpam-2666	394	29	0	0	NUM
ejpam-2666	395	1	|	|	NOUN
ejpam-2666	395	2	0	0	NUM
ejpam-2666	396	1	|	|	ADV
ejpam-2666	396	2	f	f	PROPN
ejpam-2666	396	3	′1	′1	X
ejpam-2666	396	4	it−deg(g3)−ε2−k1	it−deg(g3)−ε2−k1	PROPN
ejpam-2666	396	5	)	)	PUNCT
ejpam-2666	396	6	.	.	PUNCT
ejpam-2666	397	1	let	let	VERB
ejpam-2666	397	2	k2	k2	PROPN
ejpam-2666	397	3	=	=	SYM
ejpam-2666	397	4	deg(g3)+ε2+k1	deg(g3)+ε2+k1	NOUN
ejpam-2666	398	1	=	=	SYM
ejpam-2666	398	2	deg(a)+deg(g3)−deg(a	deg(a)+deg(g3)−deg(a	PROPN
ejpam-2666	398	3	,	,	PUNCT
ejpam-2666	398	4	g2	g2	PROPN
ejpam-2666	398	5	)	)	PUNCT
ejpam-2666	398	6	.	.	PUNCT
ejpam-2666	399	1	therefore	therefore	ADV
ejpam-2666	399	2	,	,	PUNCT
ejpam-2666	399	3	the	the	DET
ejpam-2666	399	4	generator	generator	NOUN
ejpam-2666	399	5	matrix	matrix	NOUN
ejpam-2666	399	6	g	g	NOUN
ejpam-2666	399	7	of	of	ADP
ejpam-2666	399	8	c	c	PROPN
ejpam-2666	399	9	is	be	AUX
ejpam-2666	399	10	permutation	permutation	NOUN
ejpam-2666	399	11	equivalent	equivalent	ADJ
ejpam-2666	399	12	to	to	ADP
ejpam-2666	399	13	the	the	DET
ejpam-2666	399	14	matrix	matrix	NOUN
ejpam-2666	399	15	g′	g′	NOUN
ejpam-2666	399	16	,	,	PUNCT
ejpam-2666	399	17	where	where	SCONJ
ejpam-2666	399	18	g	g	NOUN
ejpam-2666	399	19	′	′	NOUN
ejpam-2666	399	20	=	=	SYM
ejpam-2666	399	21			NOUN
ejpam-2666	399	22	ir−deg(b	ir−deg(b	X
ejpam-2666	399	23	)	)	PUNCT
ejpam-2666	399	24	a1	a1	NOUN
ejpam-2666	399	25	a2	a2	PROPN
ejpam-2666	399	26	a3	a3	NOUN
ejpam-2666	399	27	bε1	bε1	PROPN
ejpam-2666	399	28	b1	b1	NOUN
ejpam-2666	399	29	b2	b2	NOUN
ejpam-2666	399	30	c11	c11	NOUN
ejpam-2666	399	31	iε1	iε1	NOUN
ejpam-2666	399	32	0	0	NUM
ejpam-2666	399	33	0	0	NUM
ejpam-2666	399	34	c21	c21	NOUN
ejpam-2666	399	35	r1	r1	PROPN
ejpam-2666	399	36	is−deg(a)−ε1	is−deg(a)−ε1	PROPN
ejpam-2666	399	37	0	0	NUM
ejpam-2666	399	38	0	0	NUM
ejpam-2666	399	39	dε2	dε2	NOUN
ejpam-2666	399	40	d11	d11	PROPN
ejpam-2666	399	41	e11	e11	PROPN
ejpam-2666	399	42	e12	e12	NOUN
ejpam-2666	399	43	eε2	eε2	NOUN
ejpam-2666	399	44	e14	e14	PROPN
ejpam-2666	399	45	f11	f11	PROPN
ejpam-2666	399	46	iε2	iε2	PROPN
ejpam-2666	399	47	e21	e21	X
ejpam-2666	399	48	e22	e22	PROPN
ejpam-2666	399	49	ek1	ek1	NOUN
ejpam-2666	399	50	e24	e24	PROPN
ejpam-2666	399	51	f21	f21	PROPN
ejpam-2666	399	52	r2	r2	PROPN
ejpam-2666	399	53	ik1	ik1	VERB
ejpam-2666	399	54	f31	f31	PROPN
ejpam-2666	399	55	f32	f32	NOUN
ejpam-2666	399	56	r3	r3	PROPN
ejpam-2666	399	57	it−k2	it−k2	NOUN
ejpam-2666	399	58			NOUN
ejpam-2666	399	59	.	.	PUNCT
ejpam-2666	400	1	the	the	DET
ejpam-2666	400	2	cardinalities	cardinality	NOUN
ejpam-2666	400	3	of	of	ADP
ejpam-2666	400	4	cr	cr	PROPN
ejpam-2666	400	5	,	,	PUNCT
ejpam-2666	400	6	cs	cs	PROPN
ejpam-2666	400	7	and	and	CCONJ
ejpam-2666	400	8	ct	ct	PROPN
ejpam-2666	400	9	and	and	CCONJ
ejpam-2666	400	10	their	their	PRON
ejpam-2666	400	11	duals	dual	NOUN
ejpam-2666	400	12	follow	follow	VERB
ejpam-2666	400	13	from	from	ADP
ejpam-2666	400	14	g′.	g′.	ADP
ejpam-2666	400	15	the	the	DET
ejpam-2666	400	16	cardinalities	cardinality	NOUN
ejpam-2666	400	17	of	of	ADP
ejpam-2666	400	18	(	(	PUNCT
ejpam-2666	400	19	c⊥)r	c⊥)r	PROPN
ejpam-2666	400	20	,	,	PUNCT
ejpam-2666	400	21	(	(	PUNCT
ejpam-2666	400	22	c⊥)s	c⊥)s	NOUN
ejpam-2666	400	23	and	and	CCONJ
ejpam-2666	400	24	(	(	PUNCT
ejpam-2666	400	25	c⊥)t	c⊥)t	NOUN
ejpam-2666	400	26	can	can	AUX
ejpam-2666	400	27	be	be	AUX
ejpam-2666	400	28	obtained	obtain	VERB
ejpam-2666	400	29	by	by	ADP
ejpam-2666	400	30	projecting	project	VERB
ejpam-2666	400	31	the	the	DET
ejpam-2666	400	32	parity	parity	NOUN
ejpam-2666	400	33	check	check	NOUN
ejpam-2666	400	34	matrix	matrix	NOUN
ejpam-2666	400	35	of	of	ADP
ejpam-2666	400	36	c	c	PROPN
ejpam-2666	400	37	on	on	ADP
ejpam-2666	400	38	first	first	ADJ
ejpam-2666	400	39	r	r	NOUN
ejpam-2666	400	40	coordinates	coordinate	NOUN
ejpam-2666	400	41	,	,	PUNCT
ejpam-2666	400	42	next	next	PROPN
ejpam-2666	400	43	s	s	PART
ejpam-2666	400	44	coordinates	coordinate	NOUN
ejpam-2666	400	45	and	and	CCONJ
ejpam-2666	400	46	remaining	remain	VERB
ejpam-2666	400	47	last	last	ADJ
ejpam-2666	400	48	t	t	NOUN
ejpam-2666	400	49	coordinates	coordinate	NOUN
ejpam-2666	400	50	,	,	PUNCT
ejpam-2666	400	51	respectively	respectively	ADV
ejpam-2666	400	52	.	.	PUNCT
ejpam-2666	401	1	the	the	DET
ejpam-2666	401	2	results	result	NOUN
ejpam-2666	401	3	are	be	AUX
ejpam-2666	401	4	summarized	summarize	VERB
ejpam-2666	401	5	in	in	ADP
ejpam-2666	401	6	the	the	DET
ejpam-2666	401	7	following	follow	VERB
ejpam-2666	401	8	theorem	theorem	NOUN
ejpam-2666	401	9	.	.	PUNCT
ejpam-2666	401	10	theorem	theorem	NOUN
ejpam-2666	401	11	8	8	NUM
ejpam-2666	401	12	.	.	PUNCT
ejpam-2666	402	1	let	let	VERB
ejpam-2666	402	2	c	c	NOUN
ejpam-2666	402	3	=	=	SYM
ejpam-2666	402	4	〈	〈	PROPN
ejpam-2666	402	5	(	(	PUNCT
ejpam-2666	402	6	b	b	NOUN
ejpam-2666	402	7	|	|	NOUN
ejpam-2666	402	8	0	0	NUM
ejpam-2666	403	1	|	|	NOUN
ejpam-2666	403	2	0	0	NUM
ejpam-2666	403	3	)	)	PUNCT
ejpam-2666	403	4	,	,	PUNCT
ejpam-2666	404	1	(	(	PUNCT
ejpam-2666	404	2	l	l	NOUN
ejpam-2666	404	3	|	|	ADV
ejpam-2666	404	4	a	a	DET
ejpam-2666	404	5	|	|	NOUN
ejpam-2666	404	6	0	0	NUM
ejpam-2666	404	7	)	)	PUNCT
ejpam-2666	404	8	,	,	PUNCT
ejpam-2666	404	9	(	(	PUNCT
ejpam-2666	404	10	g1	g1	VERB
ejpam-2666	404	11	|	|	ADV
ejpam-2666	404	12	g2	g2	PROPN
ejpam-2666	404	13	|	|	CCONJ
ejpam-2666	404	14	g3	g3	PROPN
ejpam-2666	404	15	)	)	PUNCT
ejpam-2666	404	16	〉	〉	PROPN
ejpam-2666	404	17	be	be	AUX
ejpam-2666	404	18	a	a	DET
ejpam-2666	404	19	z2	z2	ADJ
ejpam-2666	404	20	-	-	PUNCT
ejpam-2666	404	21	triple	triple	ADJ
ejpam-2666	404	22	cyclic	cyclic	ADJ
ejpam-2666	404	23	code	code	NOUN
ejpam-2666	404	24	of	of	ADP
ejpam-2666	404	25	block	block	NOUN
ejpam-2666	404	26	length	length	NOUN
ejpam-2666	404	27	(	(	PUNCT
ejpam-2666	404	28	r	r	NOUN
ejpam-2666	404	29	,	,	PUNCT
ejpam-2666	404	30	s	s	PROPN
ejpam-2666	404	31	,	,	PUNCT
ejpam-2666	404	32	t	t	PROPN
ejpam-2666	404	33	)	)	PUNCT
ejpam-2666	404	34	.	.	PUNCT
ejpam-2666	405	1	then	then	ADV
ejpam-2666	405	2	,	,	PUNCT
ejpam-2666	405	3	|	|	ADV
ejpam-2666	405	4	cr	cr	VERB
ejpam-2666	405	5	|	|	ADV
ejpam-2666	405	6	=	=	SYM
ejpam-2666	406	1	2r−deg(b)+ε	2r−deg(b)+ε	NUM
ejpam-2666	406	2	|	|	ADV
ejpam-2666	406	3	(	(	PUNCT
ejpam-2666	406	4	cr	cr	NOUN
ejpam-2666	406	5	)	)	PUNCT
ejpam-2666	406	6	⊥	⊥	NOUN
ejpam-2666	407	1	|	|	NOUN
ejpam-2666	407	2	=	=	SYM
ejpam-2666	407	3	2deg(b	2deg(b	NUM
ejpam-2666	407	4	,	,	PUNCT
ejpam-2666	407	5	l	l	NOUN
ejpam-2666	407	6	,	,	PUNCT
ejpam-2666	407	7	g1	g1	NOUN
ejpam-2666	407	8	)	)	PUNCT
ejpam-2666	407	9	|	|	CCONJ
ejpam-2666	407	10	(	(	PUNCT
ejpam-2666	407	11	c⊥)r	c⊥)r	PROPN
ejpam-2666	407	12	|	|	NOUN
ejpam-2666	407	13	=	=	SYM
ejpam-2666	407	14	2deg(b	2deg(b	NUM
ejpam-2666	407	15	)	)	PUNCT
ejpam-2666	407	16	,	,	PUNCT
ejpam-2666	407	17	|	|	ADV
ejpam-2666	407	18	cs	cs	X
ejpam-2666	407	19	|	|	ADV
ejpam-2666	407	20	=	=	SYM
ejpam-2666	407	21	2r−deg(a	2r−deg(a	NUM
ejpam-2666	407	22	,	,	PUNCT
ejpam-2666	407	23	g2	g2	PROPN
ejpam-2666	407	24	)	)	PUNCT
ejpam-2666	408	1	|	|	ADV
ejpam-2666	408	2	(	(	PUNCT
ejpam-2666	408	3	cs	cs	PROPN
ejpam-2666	408	4	)	)	PUNCT
ejpam-2666	408	5	⊥	⊥	NOUN
ejpam-2666	408	6	|	|	NOUN
ejpam-2666	408	7	=	=	SYM
ejpam-2666	408	8	2deg(a	2deg(a	NUM
ejpam-2666	408	9	,	,	PUNCT
ejpam-2666	408	10	g2	g2	PROPN
ejpam-2666	408	11	)	)	PUNCT
ejpam-2666	409	1	|	|	ADV
ejpam-2666	409	2	(	(	PUNCT
ejpam-2666	409	3	c⊥)s	c⊥)s	NOUN
ejpam-2666	409	4	|	|	ADV
ejpam-2666	410	1	=	=	SYM
ejpam-2666	411	1	2deg(a)+ε1	2deg(a)+ε1	PROPN
ejpam-2666	412	1	and	and	CCONJ
ejpam-2666	412	2	|	|	ADV
ejpam-2666	412	3	ct	ct	PRON
ejpam-2666	413	1	|	|	NOUN
ejpam-2666	413	2	=	=	SYM
ejpam-2666	414	1	2r−deg(g3	2r−deg(g3	X
ejpam-2666	414	2	)	)	PUNCT
ejpam-2666	415	1	|	|	ADV
ejpam-2666	415	2	(	(	PUNCT
ejpam-2666	415	3	ct	ct	NOUN
ejpam-2666	415	4	)	)	PUNCT
ejpam-2666	415	5	⊥	⊥	NOUN
ejpam-2666	416	1	|	|	NOUN
ejpam-2666	416	2	=	=	SYM
ejpam-2666	416	3	2deg(g3	2deg(g3	NUM
ejpam-2666	416	4	)	)	PUNCT
ejpam-2666	416	5	|	|	ADV
ejpam-2666	416	6	(	(	PUNCT
ejpam-2666	416	7	c⊥)t	c⊥)t	VERB
ejpam-2666	416	8	|	|	NOUN
ejpam-2666	416	9	=	=	SYM
ejpam-2666	416	10	2k2	2k2	NUM
ejpam-2666	416	11	,	,	PUNCT
ejpam-2666	416	12	where	where	SCONJ
ejpam-2666	416	13	ε	ε	PROPN
ejpam-2666	416	14	=	=	SYM
ejpam-2666	416	15	deg(b)−	deg(b)−	PROPN
ejpam-2666	416	16	deg(b	deg(b	PROPN
ejpam-2666	416	17	,	,	PUNCT
ejpam-2666	416	18	l	l	NOUN
ejpam-2666	416	19	,	,	PUNCT
ejpam-2666	416	20	g1	g1	PROPN
ejpam-2666	416	21	)	)	PUNCT
ejpam-2666	416	22	and	and	CCONJ
ejpam-2666	416	23	k2	k2	PROPN
ejpam-2666	416	24	=	=	SYM
ejpam-2666	416	25	deg(a	deg(a	PROPN
ejpam-2666	416	26	)	)	PUNCT
ejpam-2666	416	27	+	+	NUM
ejpam-2666	416	28	deg(g3)−	deg(g3)−	X
ejpam-2666	416	29	deg(a	deg(a	PROPN
ejpam-2666	416	30	,	,	PUNCT
ejpam-2666	416	31	g2	g2	PROPN
ejpam-2666	416	32	)	)	PUNCT
ejpam-2666	416	33	.	.	PUNCT
ejpam-2666	417	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	417	2	b	b	PROPN
ejpam-2666	417	3	,	,	PUNCT
ejpam-2666	417	4	maheshanand	maheshanand	NOUN
ejpam-2666	417	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	417	6	/	/	SYM
ejpam-2666	417	7	eur	eur	PROPN
ejpam-2666	417	8	.	.	PUNCT
ejpam-2666	418	1	j.	j.	PROPN
ejpam-2666	418	2	pure	pure	PROPN
ejpam-2666	418	3	appl	appl	PROPN
ejpam-2666	418	4	.	.	PROPN
ejpam-2666	418	5	math	math	PROPN
ejpam-2666	418	6	,	,	PUNCT
ejpam-2666	418	7	10	10	NUM
ejpam-2666	418	8	(	(	PUNCT
ejpam-2666	418	9	2	2	NUM
ejpam-2666	418	10	)	)	PUNCT
ejpam-2666	418	11	(	(	PUNCT
ejpam-2666	418	12	2017	2017	NUM
ejpam-2666	418	13	)	)	PUNCT
ejpam-2666	418	14	,	,	PUNCT
ejpam-2666	418	15	392	392	NUM
ejpam-2666	418	16	-	-	SYM
ejpam-2666	418	17	409	409	NUM
ejpam-2666	418	18	401	401	NUM
ejpam-2666	418	19	theorem	theorem	NOUN
ejpam-2666	418	20	9	9	NUM
ejpam-2666	418	21	.	.	PUNCT
ejpam-2666	419	1	let	let	VERB
ejpam-2666	419	2	c	c	NOUN
ejpam-2666	419	3	=	=	SYM
ejpam-2666	419	4	〈	〈	PROPN
ejpam-2666	419	5	(	(	PUNCT
ejpam-2666	419	6	b	b	NOUN
ejpam-2666	419	7	|	|	NOUN
ejpam-2666	419	8	0	0	NUM
ejpam-2666	420	1	|	|	NOUN
ejpam-2666	420	2	0	0	NUM
ejpam-2666	420	3	)	)	PUNCT
ejpam-2666	420	4	,	,	PUNCT
ejpam-2666	421	1	(	(	PUNCT
ejpam-2666	421	2	l	l	NOUN
ejpam-2666	421	3	|	|	ADV
ejpam-2666	421	4	a	a	DET
ejpam-2666	421	5	|	|	NOUN
ejpam-2666	421	6	0	0	NUM
ejpam-2666	421	7	)	)	PUNCT
ejpam-2666	421	8	,	,	PUNCT
ejpam-2666	421	9	(	(	PUNCT
ejpam-2666	421	10	g1	g1	VERB
ejpam-2666	421	11	|	|	ADV
ejpam-2666	421	12	g2	g2	PROPN
ejpam-2666	421	13	|	|	CCONJ
ejpam-2666	421	14	g3	g3	PROPN
ejpam-2666	421	15	)	)	PUNCT
ejpam-2666	421	16	〉	〉	PROPN
ejpam-2666	421	17	be	be	AUX
ejpam-2666	421	18	a	a	DET
ejpam-2666	421	19	z2	z2	ADJ
ejpam-2666	421	20	-	-	PUNCT
ejpam-2666	421	21	triple	triple	ADJ
ejpam-2666	421	22	cyclic	cyclic	ADJ
ejpam-2666	421	23	code	code	NOUN
ejpam-2666	421	24	of	of	ADP
ejpam-2666	421	25	block	block	NOUN
ejpam-2666	421	26	length	length	NOUN
ejpam-2666	421	27	(	(	PUNCT
ejpam-2666	421	28	r	r	NOUN
ejpam-2666	421	29	,	,	PUNCT
ejpam-2666	421	30	s	s	PROPN
ejpam-2666	421	31	,	,	PUNCT
ejpam-2666	421	32	t	t	PROPN
ejpam-2666	421	33	)	)	PUNCT
ejpam-2666	421	34	and	and	CCONJ
ejpam-2666	421	35	c⊥	c⊥	X
ejpam-2666	422	1	=	=	SYM
ejpam-2666	422	2	〈	〈	PROPN
ejpam-2666	422	3	(	(	PUNCT
ejpam-2666	422	4	b̂	b̂	NOUN
ejpam-2666	422	5	|	|	ADV
ejpam-2666	422	6	0	0	NUM
ejpam-2666	423	1	|	|	NOUN
ejpam-2666	423	2	0	0	NUM
ejpam-2666	423	3	)	)	PUNCT
ejpam-2666	423	4	,	,	PUNCT
ejpam-2666	423	5	(	(	PUNCT
ejpam-2666	423	6	l̂	l̂	X
ejpam-2666	423	7	|	|	ADV
ejpam-2666	423	8	â	â	X
ejpam-2666	423	9	|	|	NOUN
ejpam-2666	423	10	0	0	NUM
ejpam-2666	423	11	)	)	PUNCT
ejpam-2666	423	12	,	,	PUNCT
ejpam-2666	423	13	(	(	PUNCT
ejpam-2666	423	14	ĝ1	ĝ1	NOUN
ejpam-2666	423	15	|	|	ADV
ejpam-2666	423	16	ĝ2	ĝ2	NOUN
ejpam-2666	423	17	|	|	ADV
ejpam-2666	423	18	ĝ3	ĝ3	NOUN
ejpam-2666	423	19	)	)	PUNCT
ejpam-2666	423	20	〉	〉	NOUN
ejpam-2666	423	21	be	be	AUX
ejpam-2666	423	22	the	the	DET
ejpam-2666	423	23	dual	dual	ADJ
ejpam-2666	423	24	of	of	ADP
ejpam-2666	423	25	c.	c.	NOUN
ejpam-2666	423	26	then	then	ADV
ejpam-2666	423	27	b̂	b̂	NOUN
ejpam-2666	423	28	=	=	SYM
ejpam-2666	423	29	xr	xr	PROPN
ejpam-2666	424	1	−	−	PROPN
ejpam-2666	424	2	1	1	NUM
ejpam-2666	424	3	(	(	PUNCT
ejpam-2666	424	4	b	b	NOUN
ejpam-2666	424	5	,	,	PUNCT
ejpam-2666	424	6	l	l	NOUN
ejpam-2666	424	7	,	,	PUNCT
ejpam-2666	424	8	g1)∗	g1)∗	ADJ
ejpam-2666	424	9	.	.	PUNCT
ejpam-2666	425	1	proof	proof	NOUN
ejpam-2666	425	2	.	.	PUNCT
ejpam-2666	426	1	first	first	ADV
ejpam-2666	426	2	we	we	PRON
ejpam-2666	426	3	determine	determine	VERB
ejpam-2666	426	4	the	the	DET
ejpam-2666	426	5	degree	degree	NOUN
ejpam-2666	426	6	of	of	ADP
ejpam-2666	426	7	b̂.	b̂.	NOUN
ejpam-2666	426	8	from	from	ADP
ejpam-2666	426	9	the	the	DET
ejpam-2666	426	10	definition	definition	NOUN
ejpam-2666	426	11	of	of	ADP
ejpam-2666	426	12	c⊥	c⊥	PROPN
ejpam-2666	426	13	,	,	PUNCT
ejpam-2666	426	14	it	it	PRON
ejpam-2666	426	15	is	be	AUX
ejpam-2666	426	16	easy	easy	ADJ
ejpam-2666	426	17	to	to	PART
ejpam-2666	426	18	show	show	VERB
ejpam-2666	426	19	that	that	SCONJ
ejpam-2666	426	20	(	(	PUNCT
ejpam-2666	426	21	cr	cr	NOUN
ejpam-2666	426	22	)	)	PUNCT
ejpam-2666	426	23	⊥	⊥	NOUN
ejpam-2666	426	24	=	=	PUNCT
ejpam-2666	426	25	〈	〈	PROPN
ejpam-2666	426	26	b̂	b̂	NOUN
ejpam-2666	426	27	〉	〉	PROPN
ejpam-2666	426	28	.	.	PUNCT
ejpam-2666	427	1	this	this	PRON
ejpam-2666	427	2	implies	imply	VERB
ejpam-2666	427	3	that	that	SCONJ
ejpam-2666	427	4	|	|	INTJ
ejpam-2666	427	5	(	(	PUNCT
ejpam-2666	427	6	cr	cr	NOUN
ejpam-2666	427	7	)	)	PUNCT
ejpam-2666	427	8	⊥	⊥	NUM
ejpam-2666	427	9	|=	|=	NUM
ejpam-2666	427	10	2r−deg(b̂	2r−deg(b̂	NUM
ejpam-2666	427	11	)	)	PUNCT
ejpam-2666	427	12	.	.	PUNCT
ejpam-2666	428	1	from	from	ADP
ejpam-2666	428	2	theorem	theorem	ADJ
ejpam-2666	428	3	8	8	NUM
ejpam-2666	428	4	,	,	PUNCT
ejpam-2666	428	5	we	we	PRON
ejpam-2666	428	6	have	have	VERB
ejpam-2666	428	7	|	|	ADV
ejpam-2666	428	8	(	(	PUNCT
ejpam-2666	428	9	cr	cr	NOUN
ejpam-2666	428	10	)	)	PUNCT
ejpam-2666	428	11	⊥	⊥	NUM
ejpam-2666	428	12	|=	|=	X
ejpam-2666	428	13	2deg(b	2deg(b	NUM
ejpam-2666	428	14	,	,	PUNCT
ejpam-2666	428	15	l	l	NOUN
ejpam-2666	428	16	,	,	PUNCT
ejpam-2666	428	17	g1	g1	PROPN
ejpam-2666	428	18	)	)	PUNCT
ejpam-2666	428	19	.	.	PUNCT
ejpam-2666	429	1	therefore	therefore	ADV
ejpam-2666	429	2	deg(b̂	deg(b̂	ADJ
ejpam-2666	429	3	)	)	PUNCT
ejpam-2666	430	1	=	=	SYM
ejpam-2666	430	2	r	r	NOUN
ejpam-2666	430	3	−	−	PROPN
ejpam-2666	430	4	deg(b	deg(b	PROPN
ejpam-2666	430	5	,	,	PUNCT
ejpam-2666	430	6	l	l	NOUN
ejpam-2666	430	7	,	,	PUNCT
ejpam-2666	430	8	g1	g1	PROPN
ejpam-2666	430	9	)	)	PUNCT
ejpam-2666	430	10	.	.	PUNCT
ejpam-2666	431	1	(	(	PUNCT
ejpam-2666	431	2	5	5	X
ejpam-2666	431	3	)	)	PUNCT
ejpam-2666	431	4	now	now	ADV
ejpam-2666	431	5	,	,	PUNCT
ejpam-2666	431	6	as	as	ADP
ejpam-2666	431	7	(	(	PUNCT
ejpam-2666	431	8	b̂	b̂	NOUN
ejpam-2666	431	9	|	|	ADV
ejpam-2666	431	10	0	0	NUM
ejpam-2666	432	1	|	|	NOUN
ejpam-2666	432	2	0	0	NUM
ejpam-2666	432	3	)	)	PUNCT
ejpam-2666	432	4	∈	∈	PROPN
ejpam-2666	432	5	c⊥	c⊥	PROPN
ejpam-2666	432	6	,	,	PUNCT
ejpam-2666	432	7	from	from	ADP
ejpam-2666	432	8	the	the	DET
ejpam-2666	432	9	definition	definition	NOUN
ejpam-2666	432	10	of	of	ADP
ejpam-2666	432	11	ψ	ψ	PROPN
ejpam-2666	432	12	,	,	PUNCT
ejpam-2666	432	13	we	we	PRON
ejpam-2666	432	14	have	have	VERB
ejpam-2666	432	15	ψ	ψ	X
ejpam-2666	432	16	(	(	PUNCT
ejpam-2666	432	17	(	(	PUNCT
ejpam-2666	432	18	b̂	b̂	NOUN
ejpam-2666	432	19	|	|	ADV
ejpam-2666	432	20	0	0	NUM
ejpam-2666	433	1	|	|	NOUN
ejpam-2666	433	2	0	0	NUM
ejpam-2666	433	3	)	)	PUNCT
ejpam-2666	433	4	,	,	PUNCT
ejpam-2666	434	1	(	(	PUNCT
ejpam-2666	434	2	b	b	X
ejpam-2666	434	3	|	|	ADV
ejpam-2666	434	4	0	0	NUM
ejpam-2666	434	5	|	|	NOUN
ejpam-2666	434	6	0	0	NUM
ejpam-2666	434	7	)	)	PUNCT
ejpam-2666	434	8	)	)	PUNCT
ejpam-2666	435	1	=	=	SYM
ejpam-2666	435	2	ψ	ψ	X
ejpam-2666	435	3	(	(	PUNCT
ejpam-2666	435	4	(	(	PUNCT
ejpam-2666	435	5	b̂	b̂	NOUN
ejpam-2666	435	6	|	|	ADV
ejpam-2666	435	7	0	0	NUM
ejpam-2666	436	1	|	|	NOUN
ejpam-2666	436	2	0	0	NUM
ejpam-2666	436	3	)	)	PUNCT
ejpam-2666	436	4	,	,	PUNCT
ejpam-2666	436	5	(	(	PUNCT
ejpam-2666	436	6	l	l	NOUN
ejpam-2666	436	7	|	|	ADV
ejpam-2666	436	8	a	a	DET
ejpam-2666	436	9	|	|	NOUN
ejpam-2666	436	10	0	0	NUM
ejpam-2666	436	11	)	)	PUNCT
ejpam-2666	436	12	)	)	PUNCT
ejpam-2666	437	1	=	=	SYM
ejpam-2666	437	2	ψ	ψ	X
ejpam-2666	437	3	(	(	PUNCT
ejpam-2666	437	4	(	(	PUNCT
ejpam-2666	437	5	b̂	b̂	NOUN
ejpam-2666	437	6	|	|	ADV
ejpam-2666	437	7	0	0	NUM
ejpam-2666	438	1	|	|	NOUN
ejpam-2666	438	2	0	0	NUM
ejpam-2666	438	3	)	)	PUNCT
ejpam-2666	439	1	,	,	PUNCT
ejpam-2666	439	2	(	(	PUNCT
ejpam-2666	439	3	g1	g1	VERB
ejpam-2666	439	4	|	|	ADV
ejpam-2666	439	5	g2	g2	PROPN
ejpam-2666	439	6	|	|	CCONJ
ejpam-2666	439	7	g3	g3	PROPN
ejpam-2666	439	8	)	)	PUNCT
ejpam-2666	439	9	)	)	PUNCT
ejpam-2666	440	1	=	=	SYM
ejpam-2666	440	2	0	0	X
ejpam-2666	440	3	,	,	PUNCT
ejpam-2666	440	4	all	all	PRON
ejpam-2666	440	5	modulo	modulo	ADJ
ejpam-2666	440	6	(	(	PUNCT
ejpam-2666	440	7	xm	xm	NOUN
ejpam-2666	440	8	−	−	NOUN
ejpam-2666	440	9	1	1	NUM
ejpam-2666	440	10	)	)	PUNCT
ejpam-2666	440	11	.	.	PUNCT
ejpam-2666	441	1	this	this	PRON
ejpam-2666	441	2	implies	imply	VERB
ejpam-2666	441	3	that	that	SCONJ
ejpam-2666	441	4	b̂	b̂	NOUN
ejpam-2666	441	5	b∗	b∗	ADJ
ejpam-2666	441	6	=	=	SYM
ejpam-2666	441	7	b̂	b̂	NOUN
ejpam-2666	441	8	l∗	l∗	PROPN
ejpam-2666	441	9	=	=	SYM
ejpam-2666	441	10	b̂	b̂	NOUN
ejpam-2666	441	11	g∗1	g∗1	PROPN
ejpam-2666	441	12	=	=	PROPN
ejpam-2666	441	13	0	0	PUNCT
ejpam-2666	442	1	(	(	PUNCT
ejpam-2666	442	2	mod	mod	PROPN
ejpam-2666	442	3	xr	xr	PROPN
ejpam-2666	442	4	−	−	PROPN
ejpam-2666	442	5	1	1	NUM
ejpam-2666	442	6	)	)	PUNCT
ejpam-2666	442	7	.	.	PUNCT
ejpam-2666	443	1	therefore	therefore	ADV
ejpam-2666	443	2	,	,	PUNCT
ejpam-2666	443	3	b̂	b̂	NOUN
ejpam-2666	443	4	gcd(b∗	gcd(b∗	PROPN
ejpam-2666	443	5	,	,	PUNCT
ejpam-2666	443	6	l∗	l∗	PROPN
ejpam-2666	443	7	,	,	PUNCT
ejpam-2666	443	8	g∗1	g∗1	PROPN
ejpam-2666	443	9	)	)	PUNCT
ejpam-2666	443	10	=	=	SYM
ejpam-2666	443	11	0	0	PUNCT
ejpam-2666	443	12	(	(	PUNCT
ejpam-2666	443	13	mod	mod	PROPN
ejpam-2666	443	14	xr	xr	PROPN
ejpam-2666	443	15	−	−	PROPN
ejpam-2666	443	16	1	1	NUM
ejpam-2666	443	17	)	)	PUNCT
ejpam-2666	443	18	.	.	PUNCT
ejpam-2666	444	1	since	since	SCONJ
ejpam-2666	444	2	(	(	PUNCT
ejpam-2666	444	3	b∗	b∗	ADJ
ejpam-2666	444	4	,	,	PUNCT
ejpam-2666	444	5	l∗	l∗	PROPN
ejpam-2666	444	6	,	,	PUNCT
ejpam-2666	444	7	g∗1	g∗1	PROPN
ejpam-2666	444	8	)	)	PUNCT
ejpam-2666	444	9	=	=	PUNCT
ejpam-2666	444	10	(	(	PUNCT
ejpam-2666	444	11	b	b	NOUN
ejpam-2666	444	12	,	,	PUNCT
ejpam-2666	444	13	l	l	NOUN
ejpam-2666	444	14	,	,	PUNCT
ejpam-2666	444	15	g1	g1	NOUN
ejpam-2666	444	16	)	)	PUNCT
ejpam-2666	444	17	∗	∗	NOUN
ejpam-2666	444	18	,	,	PUNCT
ejpam-2666	444	19	we	we	PRON
ejpam-2666	444	20	have	have	VERB
ejpam-2666	444	21	b̂	b̂	NUM
ejpam-2666	444	22	gcd(b	gcd(b	PROPN
ejpam-2666	444	23	,	,	PUNCT
ejpam-2666	444	24	l	l	NOUN
ejpam-2666	444	25	,	,	PUNCT
ejpam-2666	444	26	g1	g1	NOUN
ejpam-2666	444	27	)	)	PUNCT
ejpam-2666	444	28	∗	∗	NOUN
ejpam-2666	444	29	=	=	SYM
ejpam-2666	444	30	0	0	PUNCT
ejpam-2666	444	31	(	(	PUNCT
ejpam-2666	444	32	mod	mod	PROPN
ejpam-2666	444	33	xr	xr	PROPN
ejpam-2666	444	34	−	−	PROPN
ejpam-2666	444	35	1	1	NUM
ejpam-2666	444	36	)	)	PUNCT
ejpam-2666	444	37	.	.	PUNCT
ejpam-2666	445	1	then	then	ADV
ejpam-2666	445	2	there	there	PRON
ejpam-2666	445	3	exists	exist	VERB
ejpam-2666	445	4	λ	λ	PROPN
ejpam-2666	445	5	∈	∈	PROPN
ejpam-2666	445	6	z2[x	z2[x	PROPN
ejpam-2666	445	7	]	]	PUNCT
ejpam-2666	445	8	such	such	ADJ
ejpam-2666	445	9	that	that	SCONJ
ejpam-2666	445	10	,	,	PUNCT
ejpam-2666	445	11	b̂	b̂	X
ejpam-2666	445	12	(	(	PUNCT
ejpam-2666	445	13	b	b	X
ejpam-2666	445	14	,	,	PUNCT
ejpam-2666	445	15	l	l	NOUN
ejpam-2666	445	16	,	,	PUNCT
ejpam-2666	445	17	g1	g1	NOUN
ejpam-2666	445	18	)	)	PUNCT
ejpam-2666	445	19	∗	∗	NOUN
ejpam-2666	445	20	=	=	PUNCT
ejpam-2666	445	21	λ(xr	λ(xr	NOUN
ejpam-2666	445	22	−	−	ADP
ejpam-2666	445	23	1	1	NUM
ejpam-2666	445	24	)	)	PUNCT
ejpam-2666	445	25	(	(	PUNCT
ejpam-2666	445	26	6	6	NUM
ejpam-2666	445	27	)	)	PUNCT
ejpam-2666	445	28	from	from	ADP
ejpam-2666	445	29	equations	equation	NOUN
ejpam-2666	445	30	(	(	PUNCT
ejpam-2666	445	31	5	5	NUM
ejpam-2666	445	32	)	)	PUNCT
ejpam-2666	445	33	and	and	CCONJ
ejpam-2666	445	34	(	(	PUNCT
ejpam-2666	445	35	6	6	NUM
ejpam-2666	445	36	)	)	PUNCT
ejpam-2666	445	37	,	,	PUNCT
ejpam-2666	445	38	we	we	PRON
ejpam-2666	445	39	get	get	VERB
ejpam-2666	445	40	λ	λ	X
ejpam-2666	445	41	=	=	SYM
ejpam-2666	445	42	1	1	NUM
ejpam-2666	445	43	and	and	CCONJ
ejpam-2666	445	44	hence	hence	ADV
ejpam-2666	445	45	b̂	b̂	NOUN
ejpam-2666	445	46	(	(	PUNCT
ejpam-2666	445	47	b	b	X
ejpam-2666	445	48	,	,	PUNCT
ejpam-2666	445	49	l	l	NOUN
ejpam-2666	445	50	,	,	PUNCT
ejpam-2666	445	51	g1	g1	NOUN
ejpam-2666	445	52	)	)	PUNCT
ejpam-2666	445	53	∗	∗	NOUN
ejpam-2666	445	54	=	=	SYM
ejpam-2666	445	55	(	(	PUNCT
ejpam-2666	445	56	xr	xr	PROPN
ejpam-2666	445	57	−	−	PROPN
ejpam-2666	445	58	1	1	NUM
ejpam-2666	445	59	)	)	PUNCT
ejpam-2666	445	60	.	.	PUNCT
ejpam-2666	446	1	lemma	lemma	PROPN
ejpam-2666	446	2	5	5	X
ejpam-2666	446	3	.	.	PUNCT
ejpam-2666	447	1	let	let	VERB
ejpam-2666	447	2	c	c	NOUN
ejpam-2666	447	3	=	=	SYM
ejpam-2666	447	4	〈	〈	PROPN
ejpam-2666	447	5	(	(	PUNCT
ejpam-2666	447	6	b	b	NOUN
ejpam-2666	447	7	|	|	NOUN
ejpam-2666	447	8	0	0	NUM
ejpam-2666	448	1	|	|	NOUN
ejpam-2666	448	2	0	0	NUM
ejpam-2666	448	3	)	)	PUNCT
ejpam-2666	448	4	,	,	PUNCT
ejpam-2666	449	1	(	(	PUNCT
ejpam-2666	449	2	l	l	NOUN
ejpam-2666	449	3	|	|	ADV
ejpam-2666	449	4	a	a	DET
ejpam-2666	449	5	|	|	NOUN
ejpam-2666	449	6	0	0	NUM
ejpam-2666	449	7	)	)	PUNCT
ejpam-2666	449	8	,	,	PUNCT
ejpam-2666	449	9	(	(	PUNCT
ejpam-2666	449	10	g1	g1	VERB
ejpam-2666	449	11	|	|	ADV
ejpam-2666	449	12	g2	g2	PROPN
ejpam-2666	449	13	|	|	CCONJ
ejpam-2666	449	14	g3	g3	PROPN
ejpam-2666	449	15	)	)	PUNCT
ejpam-2666	449	16	〉	〉	PROPN
ejpam-2666	449	17	be	be	AUX
ejpam-2666	449	18	a	a	DET
ejpam-2666	449	19	z2	z2	ADJ
ejpam-2666	449	20	-	-	PUNCT
ejpam-2666	449	21	triple	triple	ADJ
ejpam-2666	449	22	cyclic	cyclic	ADJ
ejpam-2666	449	23	code	code	NOUN
ejpam-2666	449	24	of	of	ADP
ejpam-2666	449	25	block	block	NOUN
ejpam-2666	449	26	length	length	NOUN
ejpam-2666	449	27	(	(	PUNCT
ejpam-2666	449	28	r	r	NOUN
ejpam-2666	449	29	,	,	PUNCT
ejpam-2666	449	30	s	s	PROPN
ejpam-2666	449	31	,	,	PUNCT
ejpam-2666	449	32	t	t	PROPN
ejpam-2666	449	33	)	)	PUNCT
ejpam-2666	449	34	.	.	PUNCT
ejpam-2666	450	1	then	then	ADV
ejpam-2666	450	2	(	(	PUNCT
ejpam-2666	450	3	0	0	NUM
ejpam-2666	450	4	|	|	ADV
ejpam-2666	450	5	0	0	NUM
ejpam-2666	451	1	|	|	ADV
ejpam-2666	451	2	abg3	abg3	ADJ
ejpam-2666	451	3	(	(	PUNCT
ejpam-2666	451	4	a	a	PRON
ejpam-2666	451	5	,	,	PUNCT
ejpam-2666	451	6	g2	g2	PROPN
ejpam-2666	451	7	)	)	PUNCT
ejpam-2666	451	8	)	)	PUNCT
ejpam-2666	452	1	∈	∈	PROPN
ejpam-2666	452	2	c.	c.	NOUN
ejpam-2666	452	3	proof	proof	NOUN
ejpam-2666	452	4	.	.	PUNCT
ejpam-2666	453	1	since	since	SCONJ
ejpam-2666	453	2	(	(	PUNCT
ejpam-2666	453	3	b	b	X
ejpam-2666	453	4	|	|	NOUN
ejpam-2666	453	5	0	0	NUM
ejpam-2666	453	6	|	|	NOUN
ejpam-2666	453	7	0	0	NUM
ejpam-2666	453	8	)	)	PUNCT
ejpam-2666	453	9	,	,	PUNCT
ejpam-2666	453	10	(	(	PUNCT
ejpam-2666	453	11	l	l	NOUN
ejpam-2666	453	12	|	|	ADV
ejpam-2666	453	13	a	a	DET
ejpam-2666	453	14	|	|	NOUN
ejpam-2666	453	15	0	0	NUM
ejpam-2666	453	16	)	)	PUNCT
ejpam-2666	453	17	∈	∈	PROPN
ejpam-2666	453	18	c	c	NOUN
ejpam-2666	453	19	,	,	PUNCT
ejpam-2666	453	20	so	so	ADV
ejpam-2666	453	21	l(b	l(b	PROPN
ejpam-2666	453	22	|	|	ADV
ejpam-2666	453	23	0	0	NUM
ejpam-2666	453	24	|	|	ADV
ejpam-2666	453	25	0	0	NUM
ejpam-2666	453	26	)	)	PUNCT
ejpam-2666	453	27	+	+	CCONJ
ejpam-2666	453	28	b(l	b(l	PROPN
ejpam-2666	454	1	|	|	ADV
ejpam-2666	454	2	a	a	DET
ejpam-2666	454	3	|	|	NOUN
ejpam-2666	454	4	0	0	NUM
ejpam-2666	454	5	)	)	PUNCT
ejpam-2666	454	6	=	=	SYM
ejpam-2666	455	1	(	(	PUNCT
ejpam-2666	455	2	0	0	NUM
ejpam-2666	455	3	|	|	ADV
ejpam-2666	456	1	ab	ab	PROPN
ejpam-2666	457	1	|	|	ADV
ejpam-2666	457	2	0	0	NUM
ejpam-2666	457	3	)	)	PUNCT
ejpam-2666	457	4	∈	∈	PROPN
ejpam-2666	457	5	c.	c.	NOUN
ejpam-2666	457	6	similarly	similarly	ADV
ejpam-2666	457	7	(	(	PUNCT
ejpam-2666	457	8	b	b	X
ejpam-2666	458	1	|	|	ADV
ejpam-2666	458	2	0	0	NUM
ejpam-2666	459	1	|	|	NOUN
ejpam-2666	459	2	0	0	NUM
ejpam-2666	459	3	)	)	PUNCT
ejpam-2666	459	4	,	,	PUNCT
ejpam-2666	459	5	(	(	PUNCT
ejpam-2666	459	6	g1	g1	VERB
ejpam-2666	459	7	|	|	ADV
ejpam-2666	459	8	g2	g2	PROPN
ejpam-2666	459	9	|	|	CCONJ
ejpam-2666	459	10	g3	g3	PROPN
ejpam-2666	459	11	)	)	PUNCT
ejpam-2666	459	12	∈	∈	PROPN
ejpam-2666	459	13	c	c	NOUN
ejpam-2666	459	14	implies	imply	VERB
ejpam-2666	459	15	that	that	SCONJ
ejpam-2666	459	16	(	(	PUNCT
ejpam-2666	459	17	0	0	NUM
ejpam-2666	459	18	|	|	ADV
ejpam-2666	459	19	bg2	bg2	PROPN
ejpam-2666	459	20	|	|	NOUN
ejpam-2666	459	21	bg3	bg3	PROPN
ejpam-2666	459	22	)	)	PUNCT
ejpam-2666	459	23	∈	∈	PROPN
ejpam-2666	459	24	c.	c.	NOUN
ejpam-2666	459	25	therefore	therefore	ADV
ejpam-2666	459	26	,	,	PUNCT
ejpam-2666	459	27	as	as	ADP
ejpam-2666	459	28	(	(	PUNCT
ejpam-2666	459	29	0	0	NUM
ejpam-2666	460	1	|	|	ADV
ejpam-2666	460	2	ab	ab	PROPN
ejpam-2666	460	3	|	|	ADV
ejpam-2666	460	4	0	0	NUM
ejpam-2666	460	5	)	)	PUNCT
ejpam-2666	460	6	,	,	PUNCT
ejpam-2666	460	7	(	(	PUNCT
ejpam-2666	460	8	0	0	NUM
ejpam-2666	460	9	|	|	ADV
ejpam-2666	460	10	bg2	bg2	PROPN
ejpam-2666	460	11	|	|	NOUN
ejpam-2666	460	12	bg3	bg3	VERB
ejpam-2666	460	13	)	)	PUNCT
ejpam-2666	460	14	∈	∈	PROPN
ejpam-2666	461	1	c	c	X
ejpam-2666	461	2	,	,	PUNCT
ejpam-2666	461	3	we	we	PRON
ejpam-2666	461	4	have	have	VERB
ejpam-2666	461	5	g2	g2	PROPN
ejpam-2666	461	6	(	(	PUNCT
ejpam-2666	461	7	a	a	PRON
ejpam-2666	461	8	,	,	PUNCT
ejpam-2666	461	9	g2	g2	PROPN
ejpam-2666	461	10	)	)	PUNCT
ejpam-2666	462	1	(	(	PUNCT
ejpam-2666	462	2	0	0	X
ejpam-2666	462	3	|	|	ADV
ejpam-2666	463	1	ab	ab	PROPN
ejpam-2666	464	1	|	|	ADV
ejpam-2666	464	2	0	0	NUM
ejpam-2666	464	3	)	)	PUNCT
ejpam-2666	465	1	+	+	CCONJ
ejpam-2666	465	2	a	a	DET
ejpam-2666	465	3	(	(	PUNCT
ejpam-2666	465	4	a	a	PRON
ejpam-2666	465	5	,	,	PUNCT
ejpam-2666	465	6	g2	g2	PROPN
ejpam-2666	465	7	)	)	PUNCT
ejpam-2666	465	8	(	(	PUNCT
ejpam-2666	465	9	0	0	NUM
ejpam-2666	465	10	|	|	ADV
ejpam-2666	465	11	bg2	bg2	PROPN
ejpam-2666	465	12	|	|	NOUN
ejpam-2666	465	13	bg3	bg3	PROPN
ejpam-2666	465	14	)	)	PUNCT
ejpam-2666	465	15	=(	=(	NOUN
ejpam-2666	465	16	0	0	NUM
ejpam-2666	466	1	|	|	ADV
ejpam-2666	466	2	0	0	NUM
ejpam-2666	467	1	|	|	ADV
ejpam-2666	467	2	abg3	abg3	ADJ
ejpam-2666	467	3	(	(	PUNCT
ejpam-2666	467	4	a	a	PRON
ejpam-2666	467	5	,	,	PUNCT
ejpam-2666	467	6	g2	g2	PROPN
ejpam-2666	467	7	)	)	PUNCT
ejpam-2666	467	8	)	)	PUNCT
ejpam-2666	468	1	∈	∈	PROPN
ejpam-2666	468	2	c.	c.	PROPN
ejpam-2666	468	3	theorem	theorem	VERB
ejpam-2666	468	4	10	10	NUM
ejpam-2666	468	5	.	.	PUNCT
ejpam-2666	469	1	let	let	VERB
ejpam-2666	469	2	c	c	NOUN
ejpam-2666	469	3	=	=	SYM
ejpam-2666	469	4	〈	〈	PROPN
ejpam-2666	469	5	(	(	PUNCT
ejpam-2666	469	6	b	b	NOUN
ejpam-2666	469	7	|	|	NOUN
ejpam-2666	469	8	0	0	NUM
ejpam-2666	470	1	|	|	NOUN
ejpam-2666	470	2	0	0	NUM
ejpam-2666	470	3	)	)	PUNCT
ejpam-2666	470	4	,	,	PUNCT
ejpam-2666	471	1	(	(	PUNCT
ejpam-2666	471	2	l	l	NOUN
ejpam-2666	471	3	|	|	ADV
ejpam-2666	471	4	a	a	DET
ejpam-2666	471	5	|	|	NOUN
ejpam-2666	471	6	0	0	NUM
ejpam-2666	471	7	)	)	PUNCT
ejpam-2666	471	8	,	,	PUNCT
ejpam-2666	471	9	(	(	PUNCT
ejpam-2666	471	10	g1	g1	VERB
ejpam-2666	471	11	|	|	ADV
ejpam-2666	471	12	g2	g2	PROPN
ejpam-2666	471	13	|	|	CCONJ
ejpam-2666	471	14	g3	g3	PROPN
ejpam-2666	471	15	)	)	PUNCT
ejpam-2666	471	16	〉	〉	PROPN
ejpam-2666	471	17	be	be	AUX
ejpam-2666	471	18	a	a	DET
ejpam-2666	471	19	z2	z2	ADJ
ejpam-2666	471	20	-	-	PUNCT
ejpam-2666	471	21	triple	triple	ADJ
ejpam-2666	471	22	cyclic	cyclic	ADJ
ejpam-2666	471	23	code	code	NOUN
ejpam-2666	471	24	of	of	ADP
ejpam-2666	471	25	block	block	NOUN
ejpam-2666	471	26	length	length	NOUN
ejpam-2666	471	27	(	(	PUNCT
ejpam-2666	471	28	r	r	NOUN
ejpam-2666	471	29	,	,	PUNCT
ejpam-2666	471	30	s	s	PROPN
ejpam-2666	471	31	,	,	PUNCT
ejpam-2666	471	32	t	t	PROPN
ejpam-2666	471	33	)	)	PUNCT
ejpam-2666	471	34	and	and	CCONJ
ejpam-2666	471	35	c⊥	c⊥	X
ejpam-2666	472	1	=	=	SYM
ejpam-2666	472	2	〈	〈	PROPN
ejpam-2666	472	3	(	(	PUNCT
ejpam-2666	472	4	b̂	b̂	NOUN
ejpam-2666	472	5	|	|	ADV
ejpam-2666	472	6	0	0	NUM
ejpam-2666	473	1	|	|	NOUN
ejpam-2666	473	2	0	0	NUM
ejpam-2666	473	3	)	)	PUNCT
ejpam-2666	473	4	,	,	PUNCT
ejpam-2666	473	5	(	(	PUNCT
ejpam-2666	473	6	l̂	l̂	X
ejpam-2666	473	7	|	|	ADV
ejpam-2666	473	8	â	â	X
ejpam-2666	473	9	|	|	NOUN
ejpam-2666	473	10	0	0	NUM
ejpam-2666	473	11	)	)	PUNCT
ejpam-2666	473	12	,	,	PUNCT
ejpam-2666	473	13	(	(	PUNCT
ejpam-2666	473	14	ĝ1	ĝ1	NOUN
ejpam-2666	473	15	|	|	ADV
ejpam-2666	473	16	ĝ2	ĝ2	NOUN
ejpam-2666	473	17	|	|	ADV
ejpam-2666	473	18	ĝ3	ĝ3	NOUN
ejpam-2666	473	19	)	)	PUNCT
ejpam-2666	473	20	〉	〉	NOUN
ejpam-2666	473	21	be	be	AUX
ejpam-2666	473	22	the	the	DET
ejpam-2666	473	23	dual	dual	ADJ
ejpam-2666	473	24	of	of	ADP
ejpam-2666	473	25	c.	c.	NOUN
ejpam-2666	473	26	then	then	ADV
ejpam-2666	473	27	ĝ3	ĝ3	VERB
ejpam-2666	473	28	=	=	SYM
ejpam-2666	474	1	(	(	PUNCT
ejpam-2666	474	2	xt	xt	NUM
ejpam-2666	474	3	−	−	NOUN
ejpam-2666	474	4	1)(a	1)(a	NUM
ejpam-2666	474	5	,	,	PUNCT
ejpam-2666	474	6	g2	g2	PROPN
ejpam-2666	474	7	)	)	PUNCT
ejpam-2666	474	8	∗	∗	NOUN
ejpam-2666	474	9	a∗g∗3	a∗g∗3	PUNCT
ejpam-2666	474	10	.	.	PUNCT
ejpam-2666	475	1	proof	proof	NOUN
ejpam-2666	475	2	.	.	PUNCT
ejpam-2666	476	1	again	again	ADV
ejpam-2666	476	2	,	,	PUNCT
ejpam-2666	476	3	first	first	ADV
ejpam-2666	476	4	we	we	PRON
ejpam-2666	476	5	determine	determine	VERB
ejpam-2666	476	6	the	the	DET
ejpam-2666	476	7	degree	degree	NOUN
ejpam-2666	476	8	of	of	ADP
ejpam-2666	476	9	ĝ3	ĝ3	PROPN
ejpam-2666	476	10	.	.	PUNCT
ejpam-2666	477	1	from	from	ADP
ejpam-2666	477	2	the	the	DET
ejpam-2666	477	3	definition	definition	NOUN
ejpam-2666	477	4	of	of	ADP
ejpam-2666	477	5	c⊥	c⊥	PROPN
ejpam-2666	477	6	,	,	PUNCT
ejpam-2666	477	7	it	it	PRON
ejpam-2666	477	8	is	be	AUX
ejpam-2666	477	9	easy	easy	ADJ
ejpam-2666	477	10	to	to	PART
ejpam-2666	477	11	show	show	VERB
ejpam-2666	477	12	that	that	SCONJ
ejpam-2666	477	13	(	(	PUNCT
ejpam-2666	477	14	c⊥)s	c⊥)s	NOUN
ejpam-2666	477	15	=	=	SYM
ejpam-2666	477	16	〈	〈	PROPN
ejpam-2666	477	17	ĝ3	ĝ3	NOUN
ejpam-2666	477	18	〉	〉	NOUN
ejpam-2666	477	19	and	and	CCONJ
ejpam-2666	477	20	this	this	PRON
ejpam-2666	477	21	implies	imply	VERB
ejpam-2666	477	22	that	that	SCONJ
ejpam-2666	478	1	|	|	INTJ
ejpam-2666	478	2	(	(	PUNCT
ejpam-2666	478	3	c⊥)s	c⊥)s	X
ejpam-2666	478	4	|=	|=	X
ejpam-2666	478	5	2t−deg(ĝ3	2t−deg(ĝ3	NUM
ejpam-2666	478	6	)	)	PUNCT
ejpam-2666	478	7	.	.	PUNCT
ejpam-2666	479	1	also	also	ADV
ejpam-2666	479	2	from	from	ADP
ejpam-2666	479	3	theorem	theorem	ADJ
ejpam-2666	479	4	8	8	NUM
ejpam-2666	479	5	,	,	PUNCT
ejpam-2666	479	6	we	we	PRON
ejpam-2666	479	7	have	have	VERB
ejpam-2666	479	8	|	|	ADV
ejpam-2666	479	9	(	(	PUNCT
ejpam-2666	479	10	c⊥)s	c⊥)s	X
ejpam-2666	479	11	|=	|=	X
ejpam-2666	479	12	2k2	2k2	NUM
ejpam-2666	479	13	.	.	PUNCT
ejpam-2666	480	1	therefore	therefore	ADV
ejpam-2666	480	2	deg(ĝ3	deg(ĝ3	ADJ
ejpam-2666	480	3	)	)	PUNCT
ejpam-2666	480	4	=	=	SYM
ejpam-2666	480	5	t−	t−	PROPN
ejpam-2666	480	6	deg(g3)−	deg(g3)−	X
ejpam-2666	480	7	deg(a	deg(a	PROPN
ejpam-2666	480	8	)	)	PUNCT
ejpam-2666	480	9	+	+	CCONJ
ejpam-2666	480	10	deg(a	deg(a	PROPN
ejpam-2666	480	11	,	,	PUNCT
ejpam-2666	480	12	g2	g2	PROPN
ejpam-2666	480	13	)	)	PUNCT
ejpam-2666	480	14	.	.	PUNCT
ejpam-2666	481	1	(	(	PUNCT
ejpam-2666	481	2	7	7	X
ejpam-2666	481	3	)	)	PUNCT
ejpam-2666	481	4	srinivasulu	srinivasulu	ADV
ejpam-2666	481	5	b	b	NUM
ejpam-2666	481	6	,	,	PUNCT
ejpam-2666	481	7	maheshanand	maheshanand	NOUN
ejpam-2666	481	8	bhaintwal	bhaintwal	NOUN
ejpam-2666	481	9	/	/	SYM
ejpam-2666	481	10	eur	eur	PROPN
ejpam-2666	481	11	.	.	PUNCT
ejpam-2666	482	1	j.	j.	PROPN
ejpam-2666	482	2	pure	pure	PROPN
ejpam-2666	482	3	appl	appl	PROPN
ejpam-2666	482	4	.	.	PROPN
ejpam-2666	482	5	math	math	PROPN
ejpam-2666	482	6	,	,	PUNCT
ejpam-2666	482	7	10	10	NUM
ejpam-2666	482	8	(	(	PUNCT
ejpam-2666	482	9	2	2	NUM
ejpam-2666	482	10	)	)	PUNCT
ejpam-2666	482	11	(	(	PUNCT
ejpam-2666	482	12	2017	2017	NUM
ejpam-2666	482	13	)	)	PUNCT
ejpam-2666	482	14	,	,	PUNCT
ejpam-2666	482	15	392	392	NUM
ejpam-2666	482	16	-	-	SYM
ejpam-2666	482	17	409	409	NUM
ejpam-2666	482	18	402	402	NUM
ejpam-2666	482	19	now	now	ADV
ejpam-2666	482	20	from	from	ADP
ejpam-2666	482	21	lemma	lemma	PROPN
ejpam-2666	482	22	5	5	NUM
ejpam-2666	482	23	,	,	PUNCT
ejpam-2666	482	24	we	we	PRON
ejpam-2666	482	25	have	have	VERB
ejpam-2666	482	26	(	(	PUNCT
ejpam-2666	482	27	0	0	NUM
ejpam-2666	482	28	|	|	ADV
ejpam-2666	482	29	0	0	NUM
ejpam-2666	483	1	|	|	ADV
ejpam-2666	483	2	abg3	abg3	ADJ
ejpam-2666	483	3	(	(	PUNCT
ejpam-2666	483	4	a	a	PRON
ejpam-2666	483	5	,	,	PUNCT
ejpam-2666	483	6	g2	g2	PROPN
ejpam-2666	483	7	)	)	PUNCT
ejpam-2666	483	8	)	)	PUNCT
ejpam-2666	484	1	∈	∈	PROPN
ejpam-2666	484	2	c	c	NOUN
ejpam-2666	484	3	and	and	CCONJ
ejpam-2666	484	4	also	also	ADV
ejpam-2666	484	5	,	,	PUNCT
ejpam-2666	484	6	as	as	ADP
ejpam-2666	484	7	(	(	PUNCT
ejpam-2666	484	8	ĝ1	ĝ1	NOUN
ejpam-2666	484	9	|	|	ADV
ejpam-2666	484	10	ĝ2	ĝ2	NOUN
ejpam-2666	484	11	|	|	ADV
ejpam-2666	484	12	ĝ3	ĝ3	PRON
ejpam-2666	484	13	)	)	PUNCT
ejpam-2666	484	14	∈	∈	PROPN
ejpam-2666	484	15	c⊥	c⊥	PROPN
ejpam-2666	484	16	,	,	PUNCT
ejpam-2666	484	17	we	we	PRON
ejpam-2666	484	18	have	have	VERB
ejpam-2666	484	19	ψ	ψ	X
ejpam-2666	484	20	(	(	PUNCT
ejpam-2666	484	21	(	(	PUNCT
ejpam-2666	484	22	0	0	NUM
ejpam-2666	484	23	|	|	NOUN
ejpam-2666	484	24	0	0	NUM
ejpam-2666	485	1	|	|	ADV
ejpam-2666	485	2	abg3	abg3	ADJ
ejpam-2666	485	3	(	(	PUNCT
ejpam-2666	485	4	a	a	PRON
ejpam-2666	485	5	,	,	PUNCT
ejpam-2666	485	6	g2	g2	PROPN
ejpam-2666	485	7	)	)	PUNCT
ejpam-2666	485	8	)	)	PUNCT
ejpam-2666	485	9	,	,	PUNCT
ejpam-2666	485	10	(	(	PUNCT
ejpam-2666	485	11	ĝ1	ĝ1	NOUN
ejpam-2666	485	12	|	|	ADV
ejpam-2666	485	13	ĝ2	ĝ2	NOUN
ejpam-2666	485	14	|	|	ADV
ejpam-2666	485	15	ĝ3	ĝ3	VERB
ejpam-2666	485	16	)	)	PUNCT
ejpam-2666	485	17	)	)	PUNCT
ejpam-2666	486	1	=	=	SYM
ejpam-2666	486	2	0	0	PUNCT
ejpam-2666	487	1	(	(	PUNCT
ejpam-2666	487	2	mod	mod	PROPN
ejpam-2666	487	3	xm	xm	PROPN
ejpam-2666	487	4	−	−	NOUN
ejpam-2666	487	5	1	1	NUM
ejpam-2666	487	6	)	)	PUNCT
ejpam-2666	487	7	.	.	PUNCT
ejpam-2666	488	1	this	this	PRON
ejpam-2666	488	2	implies	imply	VERB
ejpam-2666	488	3	that	that	SCONJ
ejpam-2666	488	4	ĝ3	ĝ3	VERB
ejpam-2666	488	5	a∗b∗g∗3	a∗b∗g∗3	NOUN
ejpam-2666	488	6	(	(	PUNCT
ejpam-2666	488	7	a	a	PRON
ejpam-2666	488	8	,	,	PUNCT
ejpam-2666	488	9	g2)∗	g2)∗	ADJ
ejpam-2666	488	10	=	=	SYM
ejpam-2666	488	11	0	0	PUNCT
ejpam-2666	488	12	(	(	PUNCT
ejpam-2666	488	13	mod	mod	PROPN
ejpam-2666	488	14	xt	xt	PROPN
ejpam-2666	488	15	−	−	PROPN
ejpam-2666	488	16	1	1	NUM
ejpam-2666	488	17	)	)	PUNCT
ejpam-2666	488	18	,	,	PUNCT
ejpam-2666	488	19	and	and	CCONJ
ejpam-2666	488	20	therefore	therefore	ADV
ejpam-2666	488	21	ĝ3	ĝ3	VERB
ejpam-2666	488	22	a∗g∗3	a∗g∗3	NOUN
ejpam-2666	488	23	(	(	PUNCT
ejpam-2666	488	24	a	a	PRON
ejpam-2666	488	25	,	,	PUNCT
ejpam-2666	488	26	g2)∗	g2)∗	ADJ
ejpam-2666	488	27	=	=	SYM
ejpam-2666	488	28	0	0	PUNCT
ejpam-2666	488	29	(	(	PUNCT
ejpam-2666	488	30	mod	mod	PROPN
ejpam-2666	488	31	xt	xt	PROPN
ejpam-2666	488	32	−	−	PROPN
ejpam-2666	488	33	1	1	NUM
ejpam-2666	488	34	)	)	PUNCT
ejpam-2666	488	35	.	.	PUNCT
ejpam-2666	489	1	hence	hence	ADV
ejpam-2666	489	2	ĝ3	ĝ3	VERB
ejpam-2666	489	3	a∗g∗3	a∗g∗3	NOUN
ejpam-2666	489	4	(	(	PUNCT
ejpam-2666	489	5	a	a	DET
ejpam-2666	489	6	,	,	PUNCT
ejpam-2666	489	7	g2)∗	g2)∗	ADJ
ejpam-2666	489	8	=	=	PUNCT
ejpam-2666	489	9	λ′(xt	λ′(xt	NOUN
ejpam-2666	489	10	−	−	NOUN
ejpam-2666	489	11	1	1	NUM
ejpam-2666	489	12	)	)	PUNCT
ejpam-2666	489	13	for	for	ADP
ejpam-2666	489	14	some	some	DET
ejpam-2666	489	15	λ′	λ′	X
ejpam-2666	489	16	∈	∈	PROPN
ejpam-2666	489	17	z2[x	z2[x	PROPN
ejpam-2666	489	18	]	]	X
ejpam-2666	489	19	.	.	PUNCT
ejpam-2666	490	1	from	from	ADP
ejpam-2666	490	2	the	the	DET
ejpam-2666	490	3	degree	degree	NOUN
ejpam-2666	490	4	consideration	consideration	NOUN
ejpam-2666	490	5	of	of	ADP
ejpam-2666	490	6	ĝ3	ĝ3	VERB
ejpam-2666	490	7	i.e.	i.e.	X
ejpam-2666	490	8	from	from	ADP
ejpam-2666	490	9	(	(	PUNCT
ejpam-2666	490	10	7	7	NUM
ejpam-2666	490	11	)	)	PUNCT
ejpam-2666	490	12	,	,	PUNCT
ejpam-2666	490	13	we	we	PRON
ejpam-2666	490	14	get	get	VERB
ejpam-2666	490	15	λ′	λ′	NOUN
ejpam-2666	490	16	=	=	NOUN
ejpam-2666	490	17	1	1	X
ejpam-2666	490	18	.	.	PUNCT
ejpam-2666	491	1	the	the	DET
ejpam-2666	491	2	result	result	NOUN
ejpam-2666	491	3	follows	follow	VERB
ejpam-2666	491	4	.	.	PUNCT
ejpam-2666	492	1	theorem	theorem	NOUN
ejpam-2666	492	2	11	11	NUM
ejpam-2666	492	3	.	.	PUNCT
ejpam-2666	493	1	let	let	VERB
ejpam-2666	493	2	c	c	NOUN
ejpam-2666	493	3	=	=	SYM
ejpam-2666	493	4	〈	〈	PROPN
ejpam-2666	493	5	(	(	PUNCT
ejpam-2666	493	6	b	b	NOUN
ejpam-2666	493	7	|	|	NOUN
ejpam-2666	493	8	0	0	NUM
ejpam-2666	494	1	|	|	NOUN
ejpam-2666	494	2	0	0	NUM
ejpam-2666	494	3	)	)	PUNCT
ejpam-2666	494	4	,	,	PUNCT
ejpam-2666	495	1	(	(	PUNCT
ejpam-2666	495	2	l	l	NOUN
ejpam-2666	495	3	|	|	ADV
ejpam-2666	495	4	a	a	DET
ejpam-2666	495	5	|	|	NOUN
ejpam-2666	495	6	0	0	NUM
ejpam-2666	495	7	)	)	PUNCT
ejpam-2666	495	8	,	,	PUNCT
ejpam-2666	495	9	(	(	PUNCT
ejpam-2666	495	10	g1	g1	VERB
ejpam-2666	495	11	|	|	ADV
ejpam-2666	495	12	g2	g2	PROPN
ejpam-2666	495	13	|	|	CCONJ
ejpam-2666	495	14	g3	g3	PROPN
ejpam-2666	495	15	)	)	PUNCT
ejpam-2666	495	16	〉	〉	PROPN
ejpam-2666	495	17	be	be	AUX
ejpam-2666	495	18	a	a	DET
ejpam-2666	495	19	z2	z2	ADJ
ejpam-2666	495	20	-	-	PUNCT
ejpam-2666	495	21	triple	triple	ADJ
ejpam-2666	495	22	cyclic	cyclic	ADJ
ejpam-2666	495	23	code	code	NOUN
ejpam-2666	495	24	of	of	ADP
ejpam-2666	495	25	block	block	NOUN
ejpam-2666	495	26	length	length	NOUN
ejpam-2666	495	27	(	(	PUNCT
ejpam-2666	495	28	r	r	NOUN
ejpam-2666	495	29	,	,	PUNCT
ejpam-2666	495	30	s	s	PROPN
ejpam-2666	495	31	,	,	PUNCT
ejpam-2666	495	32	t	t	PROPN
ejpam-2666	495	33	)	)	PUNCT
ejpam-2666	495	34	and	and	CCONJ
ejpam-2666	495	35	c⊥	c⊥	X
ejpam-2666	496	1	=	=	SYM
ejpam-2666	496	2	〈	〈	PROPN
ejpam-2666	496	3	(	(	PUNCT
ejpam-2666	496	4	b̂	b̂	NOUN
ejpam-2666	496	5	|	|	ADV
ejpam-2666	496	6	0	0	NUM
ejpam-2666	497	1	|	|	NOUN
ejpam-2666	497	2	0	0	NUM
ejpam-2666	497	3	)	)	PUNCT
ejpam-2666	497	4	,	,	PUNCT
ejpam-2666	497	5	(	(	PUNCT
ejpam-2666	497	6	l̂	l̂	X
ejpam-2666	497	7	|	|	ADV
ejpam-2666	497	8	â	â	X
ejpam-2666	497	9	|	|	NOUN
ejpam-2666	497	10	0	0	NUM
ejpam-2666	497	11	)	)	PUNCT
ejpam-2666	497	12	,	,	PUNCT
ejpam-2666	497	13	(	(	PUNCT
ejpam-2666	497	14	ĝ1	ĝ1	NOUN
ejpam-2666	497	15	|	|	ADV
ejpam-2666	497	16	ĝ2	ĝ2	NOUN
ejpam-2666	497	17	|	|	ADV
ejpam-2666	497	18	ĝ3	ĝ3	NOUN
ejpam-2666	497	19	)	)	PUNCT
ejpam-2666	497	20	〉	〉	NOUN
ejpam-2666	497	21	be	be	AUX
ejpam-2666	497	22	the	the	DET
ejpam-2666	497	23	dual	dual	ADJ
ejpam-2666	497	24	of	of	ADP
ejpam-2666	497	25	c.	c.	NOUN
ejpam-2666	497	26	then	then	ADV
ejpam-2666	497	27	,	,	PUNCT
ejpam-2666	497	28	for	for	ADP
ejpam-2666	497	29	some	some	DET
ejpam-2666	497	30	λ1	λ1	ADJ
ejpam-2666	497	31	,	,	PUNCT
ejpam-2666	497	32	λ2	λ2	PROPN
ejpam-2666	497	33	∈	∈	PROPN
ejpam-2666	497	34	z2[x	z2[x	PROPN
ejpam-2666	497	35	]	]	X
ejpam-2666	497	36	,	,	PUNCT
ejpam-2666	497	37	we	we	PRON
ejpam-2666	497	38	have	have	VERB
ejpam-2666	497	39	ĝ1	ĝ1	PROPN
ejpam-2666	497	40	b	b	NOUN
ejpam-2666	497	41	∗	∗	NOUN
ejpam-2666	497	42	=	=	SYM
ejpam-2666	498	1	λ1(x	λ1(x	PUNCT
ejpam-2666	498	2	r	r	NOUN
ejpam-2666	498	3	−	−	NOUN
ejpam-2666	498	4	1	1	NUM
ejpam-2666	498	5	)	)	PUNCT
ejpam-2666	498	6	and	and	CCONJ
ejpam-2666	498	7	ĝ2	ĝ2	NOUN
ejpam-2666	498	8	a	a	DET
ejpam-2666	498	9	∗b∗	∗b∗	NUM
ejpam-2666	499	1	=	=	SYM
ejpam-2666	500	1	λ2(x	λ2(x	X
ejpam-2666	500	2	s	s	X
ejpam-2666	500	3	−	−	PROPN
ejpam-2666	500	4	1)(b	1)(b	NUM
ejpam-2666	500	5	,	,	PUNCT
ejpam-2666	500	6	l	l	NOUN
ejpam-2666	500	7	,	,	PUNCT
ejpam-2666	500	8	g1	g1	PROPN
ejpam-2666	500	9	)	)	PUNCT
ejpam-2666	500	10	∗.	∗.	PROPN
ejpam-2666	500	11	proof	proof	NOUN
ejpam-2666	500	12	.	.	PUNCT
ejpam-2666	501	1	from	from	ADP
ejpam-2666	501	2	the	the	DET
ejpam-2666	501	3	definitions	definition	NOUN
ejpam-2666	501	4	of	of	ADP
ejpam-2666	501	5	c	c	PROPN
ejpam-2666	501	6	and	and	CCONJ
ejpam-2666	501	7	c⊥	c⊥	PROPN
ejpam-2666	501	8	,	,	PUNCT
ejpam-2666	501	9	we	we	PRON
ejpam-2666	501	10	have	have	AUX
ejpam-2666	501	11	ψ((ĝ1	ψ((ĝ1	VERB
ejpam-2666	501	12	|	|	ADV
ejpam-2666	501	13	ĝ2	ĝ2	NOUN
ejpam-2666	501	14	|	|	ADV
ejpam-2666	501	15	ĝ3	ĝ3	VERB
ejpam-2666	501	16	)	)	PUNCT
ejpam-2666	501	17	,	,	PUNCT
ejpam-2666	501	18	(	(	PUNCT
ejpam-2666	501	19	b	b	X
ejpam-2666	501	20	|	|	ADV
ejpam-2666	501	21	0	0	NUM
ejpam-2666	501	22	|	|	NOUN
ejpam-2666	501	23	0	0	NUM
ejpam-2666	501	24	)	)	PUNCT
ejpam-2666	501	25	)	)	PUNCT
ejpam-2666	502	1	=	=	SYM
ejpam-2666	502	2	0	0	PUNCT
ejpam-2666	503	1	(	(	PUNCT
ejpam-2666	503	2	mod	mod	PROPN
ejpam-2666	503	3	xm	xm	PROPN
ejpam-2666	503	4	−	−	NOUN
ejpam-2666	503	5	1	1	NUM
ejpam-2666	503	6	)	)	PUNCT
ejpam-2666	503	7	.	.	PUNCT
ejpam-2666	504	1	this	this	PRON
ejpam-2666	504	2	implies	imply	VERB
ejpam-2666	504	3	that	that	SCONJ
ejpam-2666	504	4	ĝ1	ĝ1	PROPN
ejpam-2666	504	5	b	b	NOUN
ejpam-2666	504	6	∗	∗	NOUN
ejpam-2666	504	7	=	=	SYM
ejpam-2666	504	8	λ1(x	λ1(x	PUNCT
ejpam-2666	504	9	r	r	NOUN
ejpam-2666	504	10	−	−	NOUN
ejpam-2666	504	11	1	1	NUM
ejpam-2666	504	12	)	)	PUNCT
ejpam-2666	504	13	for	for	ADP
ejpam-2666	504	14	some	some	DET
ejpam-2666	504	15	λ1	λ1	PROPN
ejpam-2666	504	16	∈	∈	PROPN
ejpam-2666	504	17	z2[x	z2[x	NOUN
ejpam-2666	504	18	]	]	X
ejpam-2666	504	19	.	.	PUNCT
ejpam-2666	505	1	on	on	ADP
ejpam-2666	505	2	the	the	DET
ejpam-2666	505	3	other	other	ADJ
ejpam-2666	505	4	hand	hand	NOUN
ejpam-2666	505	5	,	,	PUNCT
ejpam-2666	505	6	it	it	PRON
ejpam-2666	505	7	is	be	AUX
ejpam-2666	505	8	easy	easy	ADJ
ejpam-2666	505	9	to	to	PART
ejpam-2666	505	10	show	show	VERB
ejpam-2666	505	11	that	that	SCONJ
ejpam-2666	505	12	(	(	PUNCT
ejpam-2666	505	13	0	0	NUM
ejpam-2666	505	14	|	|	ADV
ejpam-2666	505	15	ab	ab	PROPN
ejpam-2666	505	16	(	(	PUNCT
ejpam-2666	505	17	b	b	PROPN
ejpam-2666	505	18	,	,	PUNCT
ejpam-2666	505	19	l	l	NOUN
ejpam-2666	505	20	,	,	PUNCT
ejpam-2666	505	21	g1	g1	NOUN
ejpam-2666	505	22	)	)	PUNCT
ejpam-2666	506	1	|	|	ADV
ejpam-2666	506	2	0	0	X
ejpam-2666	506	3	)	)	PUNCT
ejpam-2666	506	4	∈	∈	PROPN
ejpam-2666	506	5	c.	c.	PROPN
ejpam-2666	506	6	therefore	therefore	ADV
ejpam-2666	506	7	,	,	PUNCT
ejpam-2666	506	8	ψ	ψ	X
ejpam-2666	506	9	(	(	PUNCT
ejpam-2666	506	10	(	(	PUNCT
ejpam-2666	506	11	0	0	NUM
ejpam-2666	506	12	|	|	ADV
ejpam-2666	506	13	ab	ab	PROPN
ejpam-2666	506	14	(	(	PUNCT
ejpam-2666	506	15	b	b	PROPN
ejpam-2666	506	16	,	,	PUNCT
ejpam-2666	506	17	l	l	NOUN
ejpam-2666	506	18	,	,	PUNCT
ejpam-2666	506	19	g1	g1	NOUN
ejpam-2666	506	20	)	)	PUNCT
ejpam-2666	506	21	|	|	ADV
ejpam-2666	506	22	0	0	NUM
ejpam-2666	506	23	)	)	PUNCT
ejpam-2666	506	24	,	,	PUNCT
ejpam-2666	506	25	(	(	PUNCT
ejpam-2666	506	26	ĝ1	ĝ1	NOUN
ejpam-2666	506	27	|	|	ADV
ejpam-2666	506	28	ĝ2	ĝ2	NOUN
ejpam-2666	506	29	|	|	ADV
ejpam-2666	506	30	ĝ3	ĝ3	VERB
ejpam-2666	506	31	)	)	PUNCT
ejpam-2666	506	32	)	)	PUNCT
ejpam-2666	507	1	=	=	SYM
ejpam-2666	507	2	0	0	PUNCT
ejpam-2666	508	1	(	(	PUNCT
ejpam-2666	508	2	mod	mod	PROPN
ejpam-2666	508	3	xm	xm	PROPN
ejpam-2666	508	4	−	−	NOUN
ejpam-2666	508	5	1	1	NUM
ejpam-2666	508	6	)	)	PUNCT
ejpam-2666	508	7	.	.	PUNCT
ejpam-2666	509	1	this	this	PRON
ejpam-2666	509	2	implies	imply	VERB
ejpam-2666	509	3	that	that	SCONJ
ejpam-2666	509	4	ĝ2	ĝ2	NOUN
ejpam-2666	509	5	a	a	DET
ejpam-2666	509	6	∗b∗	∗b∗	NUM
ejpam-2666	509	7	=	=	SYM
ejpam-2666	510	1	λ2(x	λ2(x	X
ejpam-2666	510	2	s	s	X
ejpam-2666	510	3	−	−	PROPN
ejpam-2666	510	4	1)(b	1)(b	NUM
ejpam-2666	510	5	,	,	PUNCT
ejpam-2666	510	6	l	l	NOUN
ejpam-2666	510	7	,	,	PUNCT
ejpam-2666	510	8	g1	g1	NOUN
ejpam-2666	510	9	)	)	PUNCT
ejpam-2666	510	10	∗	∗	NOUN
ejpam-2666	510	11	for	for	ADP
ejpam-2666	510	12	some	some	DET
ejpam-2666	510	13	λ2	λ2	PROPN
ejpam-2666	510	14	∈	∈	PROPN
ejpam-2666	510	15	z2[x	z2[x	PROPN
ejpam-2666	510	16	]	]	X
ejpam-2666	510	17	.	.	PUNCT
ejpam-2666	511	1	in	in	ADP
ejpam-2666	511	2	the	the	DET
ejpam-2666	511	3	following	following	NOUN
ejpam-2666	511	4	theorem	theorem	NOUN
ejpam-2666	511	5	,	,	PUNCT
ejpam-2666	511	6	we	we	PRON
ejpam-2666	511	7	obtain	obtain	VERB
ejpam-2666	511	8	the	the	DET
ejpam-2666	511	9	explicit	explicit	ADJ
ejpam-2666	511	10	forms	form	NOUN
ejpam-2666	511	11	for	for	ADP
ejpam-2666	511	12	λ1	λ1	ADJ
ejpam-2666	511	13	and	and	CCONJ
ejpam-2666	511	14	λ2	λ2	NOUN
ejpam-2666	511	15	that	that	PRON
ejpam-2666	511	16	are	be	AUX
ejpam-2666	511	17	given	give	VERB
ejpam-2666	511	18	in	in	ADP
ejpam-2666	511	19	theorem	theorem	ADJ
ejpam-2666	511	20	11	11	NUM
ejpam-2666	511	21	.	.	PUNCT
ejpam-2666	512	1	theorem	theorem	NOUN
ejpam-2666	512	2	12	12	NUM
ejpam-2666	512	3	.	.	PUNCT
ejpam-2666	513	1	let	let	VERB
ejpam-2666	513	2	c	c	NOUN
ejpam-2666	513	3	=	=	SYM
ejpam-2666	513	4	〈	〈	PROPN
ejpam-2666	513	5	(	(	PUNCT
ejpam-2666	513	6	b	b	NOUN
ejpam-2666	513	7	|	|	NOUN
ejpam-2666	513	8	0	0	NUM
ejpam-2666	514	1	|	|	NOUN
ejpam-2666	514	2	0	0	NUM
ejpam-2666	514	3	)	)	PUNCT
ejpam-2666	514	4	,	,	PUNCT
ejpam-2666	515	1	(	(	PUNCT
ejpam-2666	515	2	l	l	NOUN
ejpam-2666	515	3	|	|	ADV
ejpam-2666	515	4	a	a	DET
ejpam-2666	515	5	|	|	NOUN
ejpam-2666	515	6	0	0	NUM
ejpam-2666	515	7	)	)	PUNCT
ejpam-2666	515	8	,	,	PUNCT
ejpam-2666	515	9	(	(	PUNCT
ejpam-2666	515	10	g1	g1	VERB
ejpam-2666	515	11	|	|	ADV
ejpam-2666	515	12	g2	g2	PROPN
ejpam-2666	515	13	|	|	CCONJ
ejpam-2666	515	14	g3	g3	PROPN
ejpam-2666	515	15	)	)	PUNCT
ejpam-2666	515	16	〉	〉	PROPN
ejpam-2666	515	17	be	be	AUX
ejpam-2666	515	18	a	a	DET
ejpam-2666	515	19	z2	z2	ADJ
ejpam-2666	515	20	-	-	PUNCT
ejpam-2666	515	21	triple	triple	ADJ
ejpam-2666	515	22	cyclic	cyclic	ADJ
ejpam-2666	515	23	code	code	NOUN
ejpam-2666	515	24	of	of	ADP
ejpam-2666	515	25	block	block	NOUN
ejpam-2666	515	26	length	length	NOUN
ejpam-2666	515	27	(	(	PUNCT
ejpam-2666	515	28	r	r	NOUN
ejpam-2666	515	29	,	,	PUNCT
ejpam-2666	515	30	s	s	PROPN
ejpam-2666	515	31	,	,	PUNCT
ejpam-2666	515	32	t	t	PROPN
ejpam-2666	515	33	)	)	PUNCT
ejpam-2666	515	34	and	and	CCONJ
ejpam-2666	515	35	c⊥	c⊥	X
ejpam-2666	516	1	=	=	SYM
ejpam-2666	516	2	〈	〈	PROPN
ejpam-2666	516	3	(	(	PUNCT
ejpam-2666	516	4	b̂	b̂	NOUN
ejpam-2666	516	5	|	|	ADV
ejpam-2666	516	6	0	0	NUM
ejpam-2666	517	1	|	|	NOUN
ejpam-2666	517	2	0	0	NUM
ejpam-2666	517	3	)	)	PUNCT
ejpam-2666	517	4	,	,	PUNCT
ejpam-2666	517	5	(	(	PUNCT
ejpam-2666	517	6	l̂	l̂	X
ejpam-2666	517	7	|	|	ADV
ejpam-2666	517	8	â	â	X
ejpam-2666	517	9	|	|	NOUN
ejpam-2666	517	10	0	0	NUM
ejpam-2666	517	11	)	)	PUNCT
ejpam-2666	517	12	,	,	PUNCT
ejpam-2666	517	13	(	(	PUNCT
ejpam-2666	517	14	ĝ1	ĝ1	NOUN
ejpam-2666	517	15	|	|	ADV
ejpam-2666	517	16	ĝ2	ĝ2	NOUN
ejpam-2666	517	17	|	|	ADV
ejpam-2666	517	18	ĝ3	ĝ3	NOUN
ejpam-2666	517	19	)	)	PUNCT
ejpam-2666	517	20	〉	〉	NOUN
ejpam-2666	517	21	be	be	AUX
ejpam-2666	517	22	the	the	DET
ejpam-2666	517	23	dual	dual	ADJ
ejpam-2666	517	24	code	code	NOUN
ejpam-2666	517	25	of	of	ADP
ejpam-2666	517	26	c.	c.	PROPN
ejpam-2666	517	27	let	let	VERB
ejpam-2666	517	28	ρ1	ρ1	NOUN
ejpam-2666	517	29	=	=	PUNCT
ejpam-2666	518	1	l∗	l∗	PROPN
ejpam-2666	518	2	(	(	PUNCT
ejpam-2666	518	3	b	b	NOUN
ejpam-2666	518	4	,	,	PUNCT
ejpam-2666	518	5	l	l	NOUN
ejpam-2666	518	6	,	,	PUNCT
ejpam-2666	518	7	g1)∗	g1)∗	ADJ
ejpam-2666	518	8	and	and	CCONJ
ejpam-2666	518	9	ρ2	ρ2	NOUN
ejpam-2666	518	10	=	=	SYM
ejpam-2666	518	11	g∗2	g∗2	NOUN
ejpam-2666	518	12	(	(	PUNCT
ejpam-2666	518	13	a	a	DET
ejpam-2666	518	14	,	,	PUNCT
ejpam-2666	518	15	g2)∗	g2)∗	NOUN
ejpam-2666	518	16	.	.	PUNCT
ejpam-2666	519	1	then	then	ADV
ejpam-2666	519	2	ĝ1b	ĝ1b	VERB
ejpam-2666	519	3	∗	∗	NOUN
ejpam-2666	519	4	=	=	PUNCT
ejpam-2666	520	1	λ1(x	λ1(x	PUNCT
ejpam-2666	520	2	r	r	NOUN
ejpam-2666	520	3	−	−	NOUN
ejpam-2666	520	4	1	1	NUM
ejpam-2666	520	5	)	)	PUNCT
ejpam-2666	520	6	and	and	CCONJ
ejpam-2666	520	7	ĝ2	ĝ2	NOUN
ejpam-2666	520	8	a	a	DET
ejpam-2666	520	9	∗b∗	∗b∗	NUM
ejpam-2666	521	1	=	=	SYM
ejpam-2666	522	1	λ2(x	λ2(x	X
ejpam-2666	522	2	s	s	X
ejpam-2666	522	3	−	−	PROPN
ejpam-2666	522	4	1)(b	1)(b	NUM
ejpam-2666	522	5	,	,	PUNCT
ejpam-2666	522	6	l	l	NOUN
ejpam-2666	522	7	,	,	PUNCT
ejpam-2666	522	8	g1	g1	NOUN
ejpam-2666	522	9	)	)	PUNCT
ejpam-2666	522	10	∗	∗	NOUN
ejpam-2666	522	11	,	,	PUNCT
ejpam-2666	522	12	where	where	SCONJ
ejpam-2666	522	13	λ1	λ1	ADJ
ejpam-2666	522	14	=	=	SYM
ejpam-2666	522	15	(	(	PUNCT
ejpam-2666	522	16	ρ1	ρ1	PROPN
ejpam-2666	522	17	)	)	PUNCT
ejpam-2666	522	18	−1	−1	NOUN
ejpam-2666	522	19	(	(	PUNCT
ejpam-2666	522	20	ρ2	ρ2	NOUN
ejpam-2666	522	21	)	)	PUNCT
ejpam-2666	522	22	−1	−1	NOUN
ejpam-2666	522	23	b∗	b∗	ADJ
ejpam-2666	522	24	(	(	PUNCT
ejpam-2666	522	25	b	b	NOUN
ejpam-2666	522	26	,	,	PUNCT
ejpam-2666	522	27	l	l	NOUN
ejpam-2666	522	28	,	,	PUNCT
ejpam-2666	522	29	g1)∗	g1)∗	VERB
ejpam-2666	522	30	x2m+deg(l)−deg(a)+deg(g2)−deg(g3	x2m+deg(l)−deg(a)+deg(g2)−deg(g3	X
ejpam-2666	522	31	)	)	PUNCT
ejpam-2666	522	32	(	(	PUNCT
ejpam-2666	522	33	mod	mod	X
ejpam-2666	522	34	(	(	PUNCT
ejpam-2666	522	35	(	(	PUNCT
ejpam-2666	522	36	b	b	NOUN
ejpam-2666	522	37	,	,	PUNCT
ejpam-2666	522	38	g1	g1	PROPN
ejpam-2666	522	39	)	)	PUNCT
ejpam-2666	522	40	∗	∗	NOUN
ejpam-2666	522	41	(	(	PUNCT
ejpam-2666	522	42	b	b	NOUN
ejpam-2666	522	43	,	,	PUNCT
ejpam-2666	522	44	l	l	NOUN
ejpam-2666	522	45	,	,	PUNCT
ejpam-2666	522	46	g1)∗	g1)∗	NOUN
ejpam-2666	522	47	,	,	PUNCT
ejpam-2666	522	48	a∗	a∗	PROPN
ejpam-2666	522	49	(	(	PUNCT
ejpam-2666	522	50	a	a	PRON
ejpam-2666	522	51	,	,	PUNCT
ejpam-2666	522	52	g2)∗	g2)∗	ADJ
ejpam-2666	522	53	)	)	PUNCT
ejpam-2666	522	54	)	)	PUNCT
ejpam-2666	522	55	and	and	CCONJ
ejpam-2666	522	56	λ2	λ2	NOUN
ejpam-2666	522	57	=	=	SYM
ejpam-2666	522	58	(	(	PUNCT
ejpam-2666	522	59	g∗2	g∗2	NOUN
ejpam-2666	522	60	(	(	PUNCT
ejpam-2666	522	61	a	a	PRON
ejpam-2666	522	62	,	,	PUNCT
ejpam-2666	522	63	g2)∗	g2)∗	ADJ
ejpam-2666	522	64	)	)	PUNCT
ejpam-2666	522	65	−1	−1	NOUN
ejpam-2666	522	66	b∗	b∗	ADJ
ejpam-2666	522	67	(	(	PUNCT
ejpam-2666	522	68	b	b	NOUN
ejpam-2666	522	69	,	,	PUNCT
ejpam-2666	522	70	l	l	NOUN
ejpam-2666	522	71	,	,	PUNCT
ejpam-2666	522	72	g1)∗	g1)∗	VERB
ejpam-2666	522	73	x2m+deg(g2)−deg(g3	x2m+deg(g2)−deg(g3	NOUN
ejpam-2666	522	74	)	)	PUNCT
ejpam-2666	522	75	(	(	PUNCT
ejpam-2666	522	76	mod	mod	PROPN
ejpam-2666	522	77	a∗	a∗	PROPN
ejpam-2666	522	78	(	(	PUNCT
ejpam-2666	522	79	a	a	PRON
ejpam-2666	522	80	,	,	PUNCT
ejpam-2666	522	81	g2)∗	g2)∗	ADJ
ejpam-2666	522	82	)	)	PUNCT
ejpam-2666	522	83	.	.	PUNCT
ejpam-2666	523	1	proof	proof	NOUN
ejpam-2666	523	2	.	.	PUNCT
ejpam-2666	524	1	since	since	SCONJ
ejpam-2666	524	2	(	(	PUNCT
ejpam-2666	524	3	l	l	NOUN
ejpam-2666	524	4	|	|	ADV
ejpam-2666	524	5	a	a	DET
ejpam-2666	524	6	|	|	NOUN
ejpam-2666	524	7	0	0	NUM
ejpam-2666	524	8	)	)	PUNCT
ejpam-2666	524	9	,	,	PUNCT
ejpam-2666	524	10	(	(	PUNCT
ejpam-2666	524	11	g1	g1	VERB
ejpam-2666	524	12	|	|	ADV
ejpam-2666	524	13	g2	g2	PROPN
ejpam-2666	524	14	|	|	CCONJ
ejpam-2666	524	15	g3	g3	PROPN
ejpam-2666	524	16	)	)	PUNCT
ejpam-2666	524	17	∈	∈	PROPN
ejpam-2666	524	18	c	c	PROPN
ejpam-2666	524	19	and	and	CCONJ
ejpam-2666	524	20	(	(	PUNCT
ejpam-2666	524	21	ĝ1	ĝ1	NOUN
ejpam-2666	524	22	|	|	ADV
ejpam-2666	524	23	ĝ2	ĝ2	NOUN
ejpam-2666	524	24	|	|	ADV
ejpam-2666	524	25	ĝ3	ĝ3	PRON
ejpam-2666	524	26	)	)	PUNCT
ejpam-2666	525	1	∈	∈	PROPN
ejpam-2666	525	2	c⊥	c⊥	PROPN
ejpam-2666	525	3	,	,	PUNCT
ejpam-2666	525	4	we	we	PRON
ejpam-2666	525	5	have	have	AUX
ejpam-2666	525	6	ψ((ĝ1	ψ((ĝ1	VERB
ejpam-2666	525	7	|	|	ADV
ejpam-2666	525	8	ĝ2	ĝ2	NOUN
ejpam-2666	525	9	|	|	ADV
ejpam-2666	525	10	ĝ3	ĝ3	VERB
ejpam-2666	525	11	)	)	PUNCT
ejpam-2666	525	12	,	,	PUNCT
ejpam-2666	525	13	(	(	PUNCT
ejpam-2666	525	14	l	l	NOUN
ejpam-2666	525	15	|	|	ADV
ejpam-2666	525	16	a	a	DET
ejpam-2666	525	17	|	|	NOUN
ejpam-2666	525	18	0	0	NUM
ejpam-2666	525	19	)	)	PUNCT
ejpam-2666	525	20	)	)	PUNCT
ejpam-2666	526	1	=	=	PUNCT
ejpam-2666	526	2	ψ(ĝ1	ψ(ĝ1	NOUN
ejpam-2666	527	1	|	|	ADV
ejpam-2666	527	2	ĝ2	ĝ2	NOUN
ejpam-2666	527	3	|	|	ADV
ejpam-2666	527	4	ĝ3	ĝ3	VERB
ejpam-2666	527	5	)	)	PUNCT
ejpam-2666	527	6	,	,	PUNCT
ejpam-2666	527	7	(	(	PUNCT
ejpam-2666	527	8	g1	g1	VERB
ejpam-2666	527	9	|	|	ADV
ejpam-2666	527	10	g2	g2	PROPN
ejpam-2666	527	11	|	|	CCONJ
ejpam-2666	527	12	g3	g3	PROPN
ejpam-2666	527	13	)	)	PUNCT
ejpam-2666	527	14	)	)	PUNCT
ejpam-2666	528	1	=	=	SYM
ejpam-2666	528	2	0	0	PUNCT
ejpam-2666	529	1	(	(	PUNCT
ejpam-2666	529	2	mod	mod	PROPN
ejpam-2666	529	3	xm	xm	PROPN
ejpam-2666	529	4	−	−	NOUN
ejpam-2666	529	5	1	1	NUM
ejpam-2666	529	6	)	)	PUNCT
ejpam-2666	529	7	.	.	PUNCT
ejpam-2666	530	1	this	this	PRON
ejpam-2666	530	2	implies	imply	VERB
ejpam-2666	530	3	that	that	SCONJ
ejpam-2666	530	4	ĝ1θm	ĝ1θm	NOUN
ejpam-2666	530	5	r	r	NOUN
ejpam-2666	530	6	(	(	PUNCT
ejpam-2666	530	7	xr)xm−1−deg(l)l∗	xr)xm−1−deg(l)l∗	PROPN
ejpam-2666	530	8	+	+	NUM
ejpam-2666	530	9	ĝ2θm	ĝ2θm	PROPN
ejpam-2666	530	10	s	s	PART
ejpam-2666	530	11	(	(	PUNCT
ejpam-2666	530	12	xs)xm−1−deg(a)a∗	xs)xm−1−deg(a)a∗	X
ejpam-2666	530	13	=	=	SYM
ejpam-2666	530	14	0	0	NUM
ejpam-2666	531	1	(	(	PUNCT
ejpam-2666	531	2	mod	mod	PROPN
ejpam-2666	531	3	xm	xm	PROPN
ejpam-2666	531	4	−	−	NOUN
ejpam-2666	531	5	1	1	NUM
ejpam-2666	531	6	)	)	PUNCT
ejpam-2666	531	7	(	(	PUNCT
ejpam-2666	531	8	8)	8)	NUM
ejpam-2666	531	9	and	and	CCONJ
ejpam-2666	531	10	ĝ1θm	ĝ1θm	NOUN
ejpam-2666	531	11	r	r	NOUN
ejpam-2666	531	12	(	(	PUNCT
ejpam-2666	531	13	xr)xm−1−deg(g1)g∗1	xr)xm−1−deg(g1)g∗1	PROPN
ejpam-2666	531	14	+	+	CCONJ
ejpam-2666	531	15	ĝ2θm	ĝ2θm	PROPN
ejpam-2666	531	16	s	s	PART
ejpam-2666	531	17	(	(	PUNCT
ejpam-2666	531	18	xs)xm−1−deg(g2)g∗2	xs)xm−1−deg(g2)g∗2	NOUN
ejpam-2666	531	19	+	+	CCONJ
ejpam-2666	531	20	ĝ3θm	ĝ3θm	ADJ
ejpam-2666	531	21	t	t	NOUN
ejpam-2666	531	22	(	(	PUNCT
ejpam-2666	531	23	xt)xm−1−deg(g3)g∗3	xt)xm−1−deg(g3)g∗3	NOUN
ejpam-2666	531	24	=	=	SYM
ejpam-2666	531	25	0	0	PUNCT
ejpam-2666	531	26	(	(	PUNCT
ejpam-2666	531	27	mod	mod	PROPN
ejpam-2666	531	28	xm	xm	PROPN
ejpam-2666	531	29	−	−	NOUN
ejpam-2666	532	1	1	1	NUM
ejpam-2666	532	2	)	)	PUNCT
ejpam-2666	532	3	(	(	PUNCT
ejpam-2666	532	4	9	9	NUM
ejpam-2666	532	5	)	)	PUNCT
ejpam-2666	532	6	srinivasulu	srinivasulu	ADV
ejpam-2666	532	7	b	b	NUM
ejpam-2666	532	8	,	,	PUNCT
ejpam-2666	532	9	maheshanand	maheshanand	NOUN
ejpam-2666	532	10	bhaintwal	bhaintwal	NOUN
ejpam-2666	532	11	/	/	SYM
ejpam-2666	532	12	eur	eur	PROPN
ejpam-2666	532	13	.	.	PUNCT
ejpam-2666	533	1	j.	j.	PROPN
ejpam-2666	533	2	pure	pure	PROPN
ejpam-2666	533	3	appl	appl	PROPN
ejpam-2666	533	4	.	.	PROPN
ejpam-2666	533	5	math	math	PROPN
ejpam-2666	533	6	,	,	PUNCT
ejpam-2666	533	7	10	10	NUM
ejpam-2666	533	8	(	(	PUNCT
ejpam-2666	533	9	2	2	NUM
ejpam-2666	533	10	)	)	PUNCT
ejpam-2666	533	11	(	(	PUNCT
ejpam-2666	533	12	2017	2017	NUM
ejpam-2666	533	13	)	)	PUNCT
ejpam-2666	533	14	,	,	PUNCT
ejpam-2666	533	15	392	392	NUM
ejpam-2666	533	16	-	-	SYM
ejpam-2666	533	17	409	409	NUM
ejpam-2666	533	18	403	403	NUM
ejpam-2666	533	19	substituting	substitute	VERB
ejpam-2666	533	20	ĝ1	ĝ1	NOUN
ejpam-2666	533	21	and	and	CCONJ
ejpam-2666	533	22	ĝ2	ĝ2	NOUN
ejpam-2666	533	23	from	from	ADP
ejpam-2666	533	24	theorem	theorem	ADJ
ejpam-2666	533	25	11	11	NUM
ejpam-2666	533	26	,	,	PUNCT
ejpam-2666	533	27	in	in	ADP
ejpam-2666	533	28	(	(	PUNCT
ejpam-2666	533	29	8)	8)	NUM
ejpam-2666	533	30	and	and	CCONJ
ejpam-2666	533	31	(	(	PUNCT
ejpam-2666	533	32	9	9	NUM
ejpam-2666	533	33	)	)	PUNCT
ejpam-2666	533	34	,	,	PUNCT
ejpam-2666	533	35	and	and	CCONJ
ejpam-2666	533	36	rearranging	rearrange	VERB
ejpam-2666	533	37	the	the	DET
ejpam-2666	533	38	terms	term	NOUN
ejpam-2666	533	39	,	,	PUNCT
ejpam-2666	533	40	we	we	PRON
ejpam-2666	533	41	get	get	VERB
ejpam-2666	533	42	(	(	PUNCT
ejpam-2666	533	43	xm	xm	NOUN
ejpam-2666	533	44	−	−	NOUN
ejpam-2666	533	45	1	1	X
ejpam-2666	533	46	)	)	PUNCT
ejpam-2666	533	47	l∗	l∗	NOUN
ejpam-2666	534	1	b∗	b∗	ADV
ejpam-2666	534	2	xm−1−deg(l)λ1	xm−1−deg(l)λ1	PUNCT
ejpam-2666	535	1	+	+	CCONJ
ejpam-2666	535	2	(	(	PUNCT
ejpam-2666	535	3	xm	xm	NOUN
ejpam-2666	535	4	−	−	PROPN
ejpam-2666	535	5	1	1	NUM
ejpam-2666	535	6	)	)	PUNCT
ejpam-2666	535	7	(	(	PUNCT
ejpam-2666	535	8	b	b	X
ejpam-2666	535	9	,	,	PUNCT
ejpam-2666	535	10	l	l	NOUN
ejpam-2666	535	11	,	,	PUNCT
ejpam-2666	535	12	g1	g1	NOUN
ejpam-2666	535	13	)	)	PUNCT
ejpam-2666	535	14	∗	∗	NOUN
ejpam-2666	535	15	b∗	b∗	ADV
ejpam-2666	535	16	xm−1−deg(a)λ2	xm−1−deg(a)λ2	PUNCT
ejpam-2666	536	1	=	=	SYM
ejpam-2666	536	2	0	0	PUNCT
ejpam-2666	537	1	(	(	PUNCT
ejpam-2666	537	2	mod	mod	PROPN
ejpam-2666	537	3	xm	xm	PROPN
ejpam-2666	537	4	−	−	NOUN
ejpam-2666	537	5	1	1	NUM
ejpam-2666	537	6	)	)	PUNCT
ejpam-2666	537	7	(	(	PUNCT
ejpam-2666	537	8	10	10	NUM
ejpam-2666	537	9	)	)	PUNCT
ejpam-2666	537	10	and	and	CCONJ
ejpam-2666	537	11	(	(	PUNCT
ejpam-2666	537	12	xm	xm	NOUN
ejpam-2666	537	13	−	−	NOUN
ejpam-2666	537	14	1	1	X
ejpam-2666	537	15	)	)	PUNCT
ejpam-2666	537	16	g∗1	g∗1	PROPN
ejpam-2666	537	17	b∗	b∗	PROPN
ejpam-2666	537	18	xm−1−deg(g1)λ1	xm−1−deg(g1)λ1	PROPN
ejpam-2666	538	1	+	+	CCONJ
ejpam-2666	538	2	(	(	PUNCT
ejpam-2666	538	3	xm	xm	PROPN
ejpam-2666	538	4	−	−	PROPN
ejpam-2666	538	5	1	1	NUM
ejpam-2666	538	6	)	)	PUNCT
ejpam-2666	538	7	(	(	PUNCT
ejpam-2666	538	8	b	b	X
ejpam-2666	538	9	,	,	PUNCT
ejpam-2666	538	10	l	l	NOUN
ejpam-2666	538	11	,	,	PUNCT
ejpam-2666	538	12	g1	g1	NOUN
ejpam-2666	538	13	)	)	PUNCT
ejpam-2666	538	14	∗g∗2	∗g∗2	PROPN
ejpam-2666	538	15	a∗b∗	a∗b∗	NOUN
ejpam-2666	538	16	xm−1−deg(g2)λ2	xm−1−deg(g2)λ2	PROPN
ejpam-2666	539	1	+	+	CCONJ
ejpam-2666	539	2	(	(	PUNCT
ejpam-2666	539	3	xm	xm	PROPN
ejpam-2666	539	4	−	−	PROPN
ejpam-2666	539	5	1	1	NUM
ejpam-2666	539	6	)	)	PUNCT
ejpam-2666	539	7	(	(	PUNCT
ejpam-2666	539	8	a	a	PRON
ejpam-2666	539	9	,	,	PUNCT
ejpam-2666	539	10	g2	g2	PROPN
ejpam-2666	539	11	)	)	PUNCT
ejpam-2666	539	12	∗	∗	NOUN
ejpam-2666	539	13	a∗	a∗	PROPN
ejpam-2666	539	14	xm−1−deg(g3	xm−1−deg(g3	PROPN
ejpam-2666	539	15	)	)	PUNCT
ejpam-2666	540	1	=	=	SYM
ejpam-2666	540	2	0	0	PUNCT
ejpam-2666	541	1	(	(	PUNCT
ejpam-2666	541	2	mod	mod	PROPN
ejpam-2666	541	3	xm	xm	PROPN
ejpam-2666	541	4	−	−	NOUN
ejpam-2666	541	5	1	1	NUM
ejpam-2666	541	6	)	)	PUNCT
ejpam-2666	541	7	(	(	PUNCT
ejpam-2666	541	8	11	11	NUM
ejpam-2666	541	9	)	)	PUNCT
ejpam-2666	541	10	from	from	ADP
ejpam-2666	541	11	(	(	PUNCT
ejpam-2666	541	12	10	10	NUM
ejpam-2666	541	13	)	)	PUNCT
ejpam-2666	541	14	and	and	CCONJ
ejpam-2666	541	15	(	(	PUNCT
ejpam-2666	541	16	11	11	NUM
ejpam-2666	541	17	)	)	PUNCT
ejpam-2666	541	18	,	,	PUNCT
ejpam-2666	541	19	we	we	PRON
ejpam-2666	541	20	get	get	VERB
ejpam-2666	541	21	(	(	PUNCT
ejpam-2666	541	22	xm−1	xm−1	PROPN
ejpam-2666	541	23	)	)	PUNCT
ejpam-2666	542	1	(	(	PUNCT
ejpam-2666	542	2	b	b	X
ejpam-2666	542	3	,	,	PUNCT
ejpam-2666	542	4	l	l	NOUN
ejpam-2666	542	5	,	,	PUNCT
ejpam-2666	542	6	g1	g1	NOUN
ejpam-2666	542	7	)	)	PUNCT
ejpam-2666	542	8	∗g∗1	∗g∗1	VERB
ejpam-2666	542	9	b∗	b∗	PROPN
ejpam-2666	542	10	x2m−2−deg(a)−deg(g1)λ2+(xm−1	x2m−2−deg(a)−deg(g1)λ2+(xm−1	PROPN
ejpam-2666	542	11	)	)	PUNCT
ejpam-2666	543	1	(	(	PUNCT
ejpam-2666	543	2	b	b	X
ejpam-2666	543	3	,	,	PUNCT
ejpam-2666	543	4	l	l	NOUN
ejpam-2666	543	5	,	,	PUNCT
ejpam-2666	543	6	g1	g1	NOUN
ejpam-2666	543	7	)	)	PUNCT
ejpam-2666	543	8	∗	∗	NOUN
ejpam-2666	543	9	a∗b∗	a∗b∗	NOUN
ejpam-2666	543	10	g∗2l	g∗2l	NOUN
ejpam-2666	543	11	∗	∗	NOUN
ejpam-2666	543	12	x2m−2−deg(l)−deg(g2)λ2	x2m−2−deg(l)−deg(g2)λ2	ADJ
ejpam-2666	543	13	+	+	CCONJ
ejpam-2666	544	1	(	(	PUNCT
ejpam-2666	544	2	xm	xm	NOUN
ejpam-2666	544	3	−	−	PROPN
ejpam-2666	544	4	1	1	NUM
ejpam-2666	544	5	)	)	PUNCT
ejpam-2666	544	6	(	(	PUNCT
ejpam-2666	544	7	a	a	PRON
ejpam-2666	544	8	,	,	PUNCT
ejpam-2666	544	9	g2	g2	PROPN
ejpam-2666	544	10	)	)	PUNCT
ejpam-2666	544	11	∗	∗	VERB
ejpam-2666	544	12	a∗	a∗	PROPN
ejpam-2666	544	13	l∗	l∗	PROPN
ejpam-2666	544	14	x2m−2−deg(l)−deg(g3	x2m−2−deg(l)−deg(g3	PROPN
ejpam-2666	544	15	)	)	PUNCT
ejpam-2666	545	1	=	=	SYM
ejpam-2666	545	2	0	0	PUNCT
ejpam-2666	546	1	(	(	PUNCT
ejpam-2666	546	2	mod	mod	PROPN
ejpam-2666	546	3	xm	xm	PROPN
ejpam-2666	546	4	−	−	NOUN
ejpam-2666	546	5	1	1	NUM
ejpam-2666	546	6	)	)	PUNCT
ejpam-2666	546	7	.	.	PUNCT
ejpam-2666	547	1	(	(	PUNCT
ejpam-2666	547	2	12	12	NUM
ejpam-2666	547	3	)	)	PUNCT
ejpam-2666	547	4	equation	equation	NOUN
ejpam-2666	547	5	(	(	PUNCT
ejpam-2666	547	6	12	12	NUM
ejpam-2666	547	7	)	)	PUNCT
ejpam-2666	547	8	can	can	AUX
ejpam-2666	547	9	be	be	AUX
ejpam-2666	547	10	rewritten	rewrite	VERB
ejpam-2666	547	11	as	as	ADP
ejpam-2666	547	12	(	(	PUNCT
ejpam-2666	547	13	xm	xm	PROPN
ejpam-2666	547	14	−	−	NOUN
ejpam-2666	547	15	1	1	NUM
ejpam-2666	547	16	)	)	PUNCT
ejpam-2666	547	17	(	(	PUNCT
ejpam-2666	547	18	b	b	X
ejpam-2666	547	19	,	,	PUNCT
ejpam-2666	547	20	l	l	NOUN
ejpam-2666	547	21	,	,	PUNCT
ejpam-2666	547	22	g1	g1	NOUN
ejpam-2666	547	23	)	)	PUNCT
ejpam-2666	547	24	∗	∗	NOUN
ejpam-2666	547	25	b∗	b∗	ADJ
ejpam-2666	547	26	(	(	PUNCT
ejpam-2666	547	27	a	a	PRON
ejpam-2666	547	28	,	,	PUNCT
ejpam-2666	547	29	g2	g2	PROPN
ejpam-2666	547	30	)	)	PUNCT
ejpam-2666	547	31	∗	∗	NOUN
ejpam-2666	547	32	a∗	a∗	X
ejpam-2666	547	33	[	[	PUNCT
ejpam-2666	547	34	g∗1a	g∗1a	NOUN
ejpam-2666	547	35	∗	∗	NOUN
ejpam-2666	547	36	(	(	PUNCT
ejpam-2666	547	37	a	a	DET
ejpam-2666	547	38	,	,	PUNCT
ejpam-2666	547	39	g2)∗	g2)∗	ADJ
ejpam-2666	547	40	x2m−2−deg(a)−deg(g1)λ2	x2m−2−deg(a)−deg(g1)λ2	NOUN
ejpam-2666	547	41	+	+	CCONJ
ejpam-2666	547	42	g∗2	g∗2	NOUN
ejpam-2666	547	43	(	(	PUNCT
ejpam-2666	547	44	a	a	DET
ejpam-2666	547	45	,	,	PUNCT
ejpam-2666	547	46	g2)∗	g2)∗	ADJ
ejpam-2666	547	47	l∗	l∗	NOUN
ejpam-2666	547	48	x2m−2−deg(l)−deg(g2)λ2	x2m−2−deg(l)−deg(g2)λ2	VERB
ejpam-2666	547	49	+	+	CCONJ
ejpam-2666	547	50	b∗	b∗	ADJ
ejpam-2666	547	51	(	(	PUNCT
ejpam-2666	547	52	b	b	NOUN
ejpam-2666	547	53	,	,	PUNCT
ejpam-2666	547	54	l	l	NOUN
ejpam-2666	547	55	,	,	PUNCT
ejpam-2666	547	56	g1)∗	g1)∗	VERB
ejpam-2666	547	57	l∗	l∗	PROPN
ejpam-2666	547	58	x2m−2−deg(l)−deg(g3	x2m−2−deg(l)−deg(g3	PROPN
ejpam-2666	547	59	)	)	PUNCT
ejpam-2666	547	60	]	]	PUNCT
ejpam-2666	548	1	=	=	PUNCT
ejpam-2666	548	2	0	0	PUNCT
ejpam-2666	548	3	(	(	PUNCT
ejpam-2666	548	4	mod	mod	PROPN
ejpam-2666	548	5	xm	xm	PROPN
ejpam-2666	548	6	−	−	NOUN
ejpam-2666	548	7	1	1	NUM
ejpam-2666	548	8	)	)	PUNCT
ejpam-2666	548	9	.	.	PUNCT
ejpam-2666	549	1	(	(	PUNCT
ejpam-2666	549	2	13	13	NUM
ejpam-2666	549	3	)	)	PUNCT
ejpam-2666	549	4	this	this	PRON
ejpam-2666	549	5	implies	imply	VERB
ejpam-2666	549	6	that	that	SCONJ
ejpam-2666	549	7	[	[	PUNCT
ejpam-2666	549	8	g∗1a	g∗1a	NOUN
ejpam-2666	549	9	∗	∗	NOUN
ejpam-2666	549	10	(	(	PUNCT
ejpam-2666	549	11	a	a	DET
ejpam-2666	549	12	,	,	PUNCT
ejpam-2666	549	13	g2)∗	g2)∗	ADJ
ejpam-2666	549	14	x2m−2−deg(a)−deg(g1)λ2	x2m−2−deg(a)−deg(g1)λ2	NOUN
ejpam-2666	549	15	+	+	CCONJ
ejpam-2666	549	16	g∗2	g∗2	NOUN
ejpam-2666	549	17	(	(	PUNCT
ejpam-2666	549	18	a	a	DET
ejpam-2666	549	19	,	,	PUNCT
ejpam-2666	549	20	g2)∗	g2)∗	ADJ
ejpam-2666	549	21	l∗	l∗	NOUN
ejpam-2666	549	22	x2m−2−deg(l)−deg(g2)λ2	x2m−2−deg(l)−deg(g2)λ2	VERB
ejpam-2666	549	23	+	+	CCONJ
ejpam-2666	549	24	b∗	b∗	ADJ
ejpam-2666	549	25	(	(	PUNCT
ejpam-2666	549	26	b	b	NOUN
ejpam-2666	549	27	,	,	PUNCT
ejpam-2666	549	28	l	l	NOUN
ejpam-2666	549	29	,	,	PUNCT
ejpam-2666	549	30	g1)∗	g1)∗	VERB
ejpam-2666	549	31	l∗	l∗	PROPN
ejpam-2666	549	32	x2m−2−deg(l)−deg(g3	x2m−2−deg(l)−deg(g3	PROPN
ejpam-2666	549	33	)	)	PUNCT
ejpam-2666	549	34	]	]	PUNCT
ejpam-2666	550	1	=	=	PUNCT
ejpam-2666	550	2	0	0	PUNCT
ejpam-2666	550	3	(	(	PUNCT
ejpam-2666	550	4	mod	mod	PROPN
ejpam-2666	550	5	xm	xm	PROPN
ejpam-2666	550	6	−	−	NOUN
ejpam-2666	550	7	1	1	NUM
ejpam-2666	550	8	)	)	PUNCT
ejpam-2666	550	9	.	.	PUNCT
ejpam-2666	551	1	since	since	SCONJ
ejpam-2666	551	2	a∗	a∗	PROPN
ejpam-2666	551	3	(	(	PUNCT
ejpam-2666	551	4	a	a	PRON
ejpam-2666	551	5	,	,	PUNCT
ejpam-2666	551	6	g2)∗	g2)∗	ADJ
ejpam-2666	551	7	divides	divide	VERB
ejpam-2666	551	8	xm	xm	PROPN
ejpam-2666	551	9	−	−	PROPN
ejpam-2666	551	10	1	1	NUM
ejpam-2666	551	11	,	,	PUNCT
ejpam-2666	551	12	we	we	PRON
ejpam-2666	551	13	get	get	VERB
ejpam-2666	551	14	g∗2	g∗2	NOUN
ejpam-2666	551	15	(	(	PUNCT
ejpam-2666	551	16	a	a	DET
ejpam-2666	551	17	,	,	PUNCT
ejpam-2666	551	18	g2)∗	g2)∗	ADJ
ejpam-2666	551	19	x2m−2−deg(l)−deg(g2)λ2	x2m−2−deg(l)−deg(g2)λ2	ADJ
ejpam-2666	552	1	+	+	CCONJ
ejpam-2666	552	2	b∗	b∗	ADJ
ejpam-2666	552	3	(	(	PUNCT
ejpam-2666	552	4	b	b	NOUN
ejpam-2666	552	5	,	,	PUNCT
ejpam-2666	552	6	l	l	NOUN
ejpam-2666	552	7	,	,	PUNCT
ejpam-2666	552	8	g1)∗	g1)∗	VERB
ejpam-2666	552	9	x2m−2−deg(l)−deg(g3	x2m−2−deg(l)−deg(g3	NOUN
ejpam-2666	552	10	)	)	PUNCT
ejpam-2666	552	11	=	=	SYM
ejpam-2666	552	12	0	0	NUM
ejpam-2666	552	13	mod	mod	NOUN
ejpam-2666	552	14	(	(	PUNCT
ejpam-2666	552	15	a∗	a∗	PROPN
ejpam-2666	552	16	(	(	PUNCT
ejpam-2666	552	17	a	a	PRON
ejpam-2666	552	18	,	,	PUNCT
ejpam-2666	552	19	g2)∗	g2)∗	ADJ
ejpam-2666	552	20	)	)	PUNCT
ejpam-2666	552	21	.	.	PUNCT
ejpam-2666	553	1	(	(	PUNCT
ejpam-2666	553	2	14	14	NUM
ejpam-2666	553	3	)	)	PUNCT
ejpam-2666	553	4	since	since	SCONJ
ejpam-2666	553	5	a∗	a∗	NOUN
ejpam-2666	553	6	(	(	PUNCT
ejpam-2666	553	7	a	a	PRON
ejpam-2666	553	8	,	,	PUNCT
ejpam-2666	553	9	g2)∗	g2)∗	ADJ
ejpam-2666	553	10	and	and	CCONJ
ejpam-2666	553	11	g∗2	g∗2	NOUN
ejpam-2666	553	12	(	(	PUNCT
ejpam-2666	553	13	a	a	DET
ejpam-2666	553	14	,	,	PUNCT
ejpam-2666	553	15	g2)∗	g2)∗	ADJ
ejpam-2666	553	16	are	be	AUX
ejpam-2666	553	17	relatively	relatively	ADV
ejpam-2666	553	18	prime	prime	ADJ
ejpam-2666	553	19	,	,	PUNCT
ejpam-2666	553	20	we	we	PRON
ejpam-2666	553	21	get	get	VERB
ejpam-2666	553	22	from	from	ADP
ejpam-2666	553	23	(	(	PUNCT
ejpam-2666	553	24	14	14	NUM
ejpam-2666	553	25	)	)	PUNCT
ejpam-2666	553	26	λ2	λ2	NOUN
ejpam-2666	553	27	=	=	SYM
ejpam-2666	553	28	(	(	PUNCT
ejpam-2666	553	29	g∗2	g∗2	NOUN
ejpam-2666	553	30	(	(	PUNCT
ejpam-2666	553	31	a	a	PRON
ejpam-2666	553	32	,	,	PUNCT
ejpam-2666	553	33	g2)∗	g2)∗	ADJ
ejpam-2666	553	34	)	)	PUNCT
ejpam-2666	553	35	−1	−1	NOUN
ejpam-2666	553	36	b∗	b∗	ADJ
ejpam-2666	553	37	(	(	PUNCT
ejpam-2666	553	38	b	b	NOUN
ejpam-2666	553	39	,	,	PUNCT
ejpam-2666	553	40	l	l	NOUN
ejpam-2666	553	41	,	,	PUNCT
ejpam-2666	553	42	g1)∗	g1)∗	VERB
ejpam-2666	553	43	x2m+deg(g2)−deg(g3	x2m+deg(g2)−deg(g3	NOUN
ejpam-2666	553	44	)	)	PUNCT
ejpam-2666	553	45	(	(	PUNCT
ejpam-2666	553	46	mod	mod	PROPN
ejpam-2666	553	47	a∗	a∗	PROPN
ejpam-2666	553	48	(	(	PUNCT
ejpam-2666	553	49	a	a	PRON
ejpam-2666	553	50	,	,	PUNCT
ejpam-2666	553	51	g2)∗	g2)∗	ADJ
ejpam-2666	553	52	)	)	PUNCT
ejpam-2666	553	53	.	.	PUNCT
ejpam-2666	554	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	554	2	b	b	NUM
ejpam-2666	554	3	,	,	PUNCT
ejpam-2666	554	4	maheshanand	maheshanand	NOUN
ejpam-2666	554	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	554	6	/	/	SYM
ejpam-2666	554	7	eur	eur	PROPN
ejpam-2666	554	8	.	.	PUNCT
ejpam-2666	555	1	j.	j.	PROPN
ejpam-2666	555	2	pure	pure	PROPN
ejpam-2666	555	3	appl	appl	PROPN
ejpam-2666	555	4	.	.	PROPN
ejpam-2666	555	5	math	math	PROPN
ejpam-2666	555	6	,	,	PUNCT
ejpam-2666	555	7	10	10	NUM
ejpam-2666	555	8	(	(	PUNCT
ejpam-2666	555	9	2	2	NUM
ejpam-2666	555	10	)	)	PUNCT
ejpam-2666	555	11	(	(	PUNCT
ejpam-2666	555	12	2017	2017	NUM
ejpam-2666	555	13	)	)	PUNCT
ejpam-2666	555	14	,	,	PUNCT
ejpam-2666	555	15	392	392	NUM
ejpam-2666	555	16	-	-	SYM
ejpam-2666	555	17	409	409	NUM
ejpam-2666	555	18	404	404	NUM
ejpam-2666	555	19	.	.	PUNCT
ejpam-2666	556	1	using	use	VERB
ejpam-2666	556	2	the	the	DET
ejpam-2666	556	3	similar	similar	ADJ
ejpam-2666	556	4	arguments	argument	NOUN
ejpam-2666	556	5	that	that	PRON
ejpam-2666	556	6	are	be	AUX
ejpam-2666	556	7	given	give	VERB
ejpam-2666	556	8	in	in	ADP
ejpam-2666	556	9	finding	find	VERB
ejpam-2666	556	10	λ1	λ1	ADJ
ejpam-2666	556	11	,	,	PUNCT
ejpam-2666	556	12	we	we	PRON
ejpam-2666	556	13	therefore	therefore	ADV
ejpam-2666	556	14	get	get	VERB
ejpam-2666	556	15	λ1	λ1	ADJ
ejpam-2666	556	16	=	=	SYM
ejpam-2666	556	17	(	(	PUNCT
ejpam-2666	556	18	ρ1	ρ1	PROPN
ejpam-2666	556	19	)	)	PUNCT
ejpam-2666	556	20	−1	−1	NOUN
ejpam-2666	556	21	(	(	PUNCT
ejpam-2666	556	22	ρ2	ρ2	NOUN
ejpam-2666	556	23	)	)	PUNCT
ejpam-2666	557	1	−1	−1	NOUN
ejpam-2666	557	2	b∗	b∗	ADJ
ejpam-2666	557	3	(	(	PUNCT
ejpam-2666	557	4	b	b	NOUN
ejpam-2666	557	5	,	,	PUNCT
ejpam-2666	557	6	l	l	NOUN
ejpam-2666	557	7	,	,	PUNCT
ejpam-2666	557	8	g1)∗	g1)∗	VERB
ejpam-2666	557	9	x2m−deg(g3)−deg(a)+deg(g2)+deg(l	x2m−deg(g3)−deg(a)+deg(g2)+deg(l	NOUN
ejpam-2666	557	10	)	)	PUNCT
ejpam-2666	557	11	(	(	PUNCT
ejpam-2666	557	12	mod	mod	X
ejpam-2666	557	13	(	(	PUNCT
ejpam-2666	557	14	(	(	PUNCT
ejpam-2666	557	15	b	b	NOUN
ejpam-2666	557	16	,	,	PUNCT
ejpam-2666	557	17	g1	g1	PROPN
ejpam-2666	557	18	)	)	PUNCT
ejpam-2666	557	19	∗	∗	NOUN
ejpam-2666	557	20	(	(	PUNCT
ejpam-2666	557	21	b	b	NOUN
ejpam-2666	557	22	,	,	PUNCT
ejpam-2666	557	23	l	l	NOUN
ejpam-2666	557	24	,	,	PUNCT
ejpam-2666	557	25	g1)∗	g1)∗	NOUN
ejpam-2666	557	26	,	,	PUNCT
ejpam-2666	557	27	a∗	a∗	PROPN
ejpam-2666	557	28	(	(	PUNCT
ejpam-2666	557	29	a	a	PRON
ejpam-2666	557	30	,	,	PUNCT
ejpam-2666	557	31	g2)∗	g2)∗	ADJ
ejpam-2666	557	32	)	)	PUNCT
ejpam-2666	557	33	)	)	PUNCT
ejpam-2666	557	34	,	,	PUNCT
ejpam-2666	557	35	where	where	SCONJ
ejpam-2666	557	36	ρ1	ρ1	NOUN
ejpam-2666	557	37	=	=	SYM
ejpam-2666	557	38	l∗	l∗	PROPN
ejpam-2666	557	39	(	(	PUNCT
ejpam-2666	557	40	b	b	NOUN
ejpam-2666	557	41	,	,	PUNCT
ejpam-2666	557	42	l	l	NOUN
ejpam-2666	557	43	,	,	PUNCT
ejpam-2666	557	44	g1)∗	g1)∗	ADJ
ejpam-2666	557	45	and	and	CCONJ
ejpam-2666	557	46	ρ2	ρ2	NOUN
ejpam-2666	557	47	=	=	SYM
ejpam-2666	557	48	g∗2	g∗2	NOUN
ejpam-2666	557	49	(	(	PUNCT
ejpam-2666	557	50	a	a	PRON
ejpam-2666	557	51	,	,	PUNCT
ejpam-2666	557	52	g2)∗	g2)∗	ADJ
ejpam-2666	557	53	.	.	PUNCT
ejpam-2666	558	1	hence	hence	ADV
ejpam-2666	558	2	the	the	DET
ejpam-2666	558	3	result	result	NOUN
ejpam-2666	558	4	.	.	PUNCT
ejpam-2666	559	1	theorem	theorem	ADJ
ejpam-2666	559	2	13	13	NUM
ejpam-2666	559	3	.	.	PUNCT
ejpam-2666	560	1	let	let	VERB
ejpam-2666	560	2	c	c	NOUN
ejpam-2666	560	3	=	=	SYM
ejpam-2666	560	4	〈	〈	PROPN
ejpam-2666	560	5	(	(	PUNCT
ejpam-2666	560	6	b	b	NOUN
ejpam-2666	560	7	|	|	NOUN
ejpam-2666	560	8	0	0	NUM
ejpam-2666	561	1	|	|	NOUN
ejpam-2666	561	2	0	0	NUM
ejpam-2666	561	3	)	)	PUNCT
ejpam-2666	561	4	,	,	PUNCT
ejpam-2666	562	1	(	(	PUNCT
ejpam-2666	562	2	l	l	NOUN
ejpam-2666	562	3	|	|	ADV
ejpam-2666	562	4	a	a	DET
ejpam-2666	562	5	|	|	NOUN
ejpam-2666	562	6	0	0	NUM
ejpam-2666	562	7	)	)	PUNCT
ejpam-2666	562	8	,	,	PUNCT
ejpam-2666	562	9	(	(	PUNCT
ejpam-2666	562	10	g1	g1	VERB
ejpam-2666	562	11	|	|	ADV
ejpam-2666	562	12	g2	g2	PROPN
ejpam-2666	562	13	|	|	CCONJ
ejpam-2666	562	14	g3	g3	PROPN
ejpam-2666	562	15	)	)	PUNCT
ejpam-2666	562	16	〉	〉	PROPN
ejpam-2666	562	17	be	be	AUX
ejpam-2666	562	18	a	a	DET
ejpam-2666	562	19	z2	z2	ADJ
ejpam-2666	562	20	-	-	PUNCT
ejpam-2666	562	21	triple	triple	ADJ
ejpam-2666	562	22	cyclic	cyclic	ADJ
ejpam-2666	562	23	code	code	NOUN
ejpam-2666	562	24	of	of	ADP
ejpam-2666	562	25	block	block	NOUN
ejpam-2666	562	26	length	length	NOUN
ejpam-2666	562	27	(	(	PUNCT
ejpam-2666	562	28	r	r	NOUN
ejpam-2666	562	29	,	,	PUNCT
ejpam-2666	562	30	s	s	PROPN
ejpam-2666	562	31	,	,	PUNCT
ejpam-2666	562	32	t	t	PROPN
ejpam-2666	562	33	)	)	PUNCT
ejpam-2666	562	34	and	and	CCONJ
ejpam-2666	562	35	c⊥	c⊥	X
ejpam-2666	563	1	=	=	SYM
ejpam-2666	563	2	〈	〈	PROPN
ejpam-2666	563	3	(	(	PUNCT
ejpam-2666	563	4	b̂	b̂	NOUN
ejpam-2666	563	5	|	|	ADV
ejpam-2666	563	6	0	0	NUM
ejpam-2666	564	1	|	|	NOUN
ejpam-2666	564	2	0	0	NUM
ejpam-2666	564	3	)	)	PUNCT
ejpam-2666	564	4	,	,	PUNCT
ejpam-2666	564	5	(	(	PUNCT
ejpam-2666	564	6	l̂	l̂	X
ejpam-2666	564	7	|	|	ADV
ejpam-2666	564	8	â	â	X
ejpam-2666	564	9	|	|	NOUN
ejpam-2666	564	10	0	0	NUM
ejpam-2666	564	11	)	)	PUNCT
ejpam-2666	564	12	,	,	PUNCT
ejpam-2666	564	13	(	(	PUNCT
ejpam-2666	564	14	ĝ1	ĝ1	NOUN
ejpam-2666	564	15	|	|	ADV
ejpam-2666	564	16	ĝ2	ĝ2	NOUN
ejpam-2666	564	17	|	|	ADV
ejpam-2666	564	18	ĝ3	ĝ3	NOUN
ejpam-2666	564	19	)	)	PUNCT
ejpam-2666	564	20	〉	〉	NOUN
ejpam-2666	564	21	be	be	AUX
ejpam-2666	564	22	the	the	DET
ejpam-2666	564	23	dual	dual	ADJ
ejpam-2666	564	24	code	code	NOUN
ejpam-2666	564	25	of	of	ADP
ejpam-2666	564	26	c.	c.	PROPN
ejpam-2666	564	27	then	then	ADV
ejpam-2666	564	28	â	â	PROPN
ejpam-2666	564	29	b∗(a	b∗(a	PROPN
ejpam-2666	564	30	,	,	PUNCT
ejpam-2666	564	31	g2	g2	PROPN
ejpam-2666	564	32	)	)	PUNCT
ejpam-2666	564	33	∗	∗	NOUN
ejpam-2666	564	34	=	=	SYM
ejpam-2666	564	35	(	(	PUNCT
ejpam-2666	564	36	xs	xs	PROPN
ejpam-2666	564	37	−	−	PROPN
ejpam-2666	564	38	1)(b	1)(b	PROPN
ejpam-2666	564	39	,	,	PUNCT
ejpam-2666	564	40	l	l	NOUN
ejpam-2666	564	41	,	,	PUNCT
ejpam-2666	564	42	g1	g1	PROPN
ejpam-2666	564	43	)	)	PUNCT
ejpam-2666	564	44	∗.	∗.	PROPN
ejpam-2666	564	45	proof	proof	NOUN
ejpam-2666	564	46	.	.	PUNCT
ejpam-2666	565	1	first	first	ADV
ejpam-2666	565	2	we	we	PRON
ejpam-2666	565	3	determine	determine	VERB
ejpam-2666	565	4	the	the	DET
ejpam-2666	565	5	degree	degree	NOUN
ejpam-2666	565	6	of	of	ADP
ejpam-2666	565	7	â.	â.	ADJ
ejpam-2666	565	8	we	we	PRON
ejpam-2666	565	9	note	note	VERB
ejpam-2666	565	10	that	that	DET
ejpam-2666	565	11	dim(c⊥	dim(c⊥	NOUN
ejpam-2666	565	12	)	)	PUNCT
ejpam-2666	565	13	=	=	PUNCT
ejpam-2666	566	1	(	(	PUNCT
ejpam-2666	566	2	r	r	NOUN
ejpam-2666	566	3	+	+	SYM
ejpam-2666	566	4	s	s	PART
ejpam-2666	566	5	+	+	NUM
ejpam-2666	566	6	t	t	NOUN
ejpam-2666	566	7	)	)	PUNCT
ejpam-2666	566	8	−	−	PROPN
ejpam-2666	566	9	(	(	PUNCT
ejpam-2666	566	10	deg(b̂	deg(b̂	PROPN
ejpam-2666	566	11	)	)	PUNCT
ejpam-2666	566	12	+	+	NUM
ejpam-2666	566	13	deg(â	deg(â	NOUN
ejpam-2666	566	14	)	)	PUNCT
ejpam-2666	566	15	+	+	CCONJ
ejpam-2666	566	16	deg(ĝ3	deg(ĝ3	ADJ
ejpam-2666	566	17	)	)	PUNCT
ejpam-2666	566	18	)	)	PUNCT
ejpam-2666	566	19	.	.	PUNCT
ejpam-2666	567	1	also	also	ADV
ejpam-2666	567	2	,	,	PUNCT
ejpam-2666	567	3	since	since	SCONJ
ejpam-2666	567	4	dim(c	dim(c	PROPN
ejpam-2666	567	5	)	)	PUNCT
ejpam-2666	567	6	=	=	PUNCT
ejpam-2666	567	7	(	(	PUNCT
ejpam-2666	567	8	r+	r+	PUNCT
ejpam-2666	567	9	s+	s+	PUNCT
ejpam-2666	567	10	t)−	t)−	PROPN
ejpam-2666	567	11	(	(	PUNCT
ejpam-2666	567	12	deg(b	deg(b	PROPN
ejpam-2666	567	13	)	)	PUNCT
ejpam-2666	567	14	+	+	NUM
ejpam-2666	567	15	deg(a	deg(a	PROPN
ejpam-2666	567	16	)	)	PUNCT
ejpam-2666	567	17	+	+	CCONJ
ejpam-2666	567	18	deg(g3	deg(g3	NOUN
ejpam-2666	567	19	)	)	PUNCT
ejpam-2666	567	20	)	)	PUNCT
ejpam-2666	567	21	implies	imply	VERB
ejpam-2666	567	22	that	that	DET
ejpam-2666	567	23	dim(c⊥	dim(c⊥	NOUN
ejpam-2666	567	24	)	)	PUNCT
ejpam-2666	567	25	=	=	SYM
ejpam-2666	567	26	deg(b)+deg(a)+deg(g3	deg(b)+deg(a)+deg(g3	NOUN
ejpam-2666	567	27	)	)	PUNCT
ejpam-2666	567	28	.	.	PUNCT
ejpam-2666	568	1	therefore	therefore	ADV
ejpam-2666	568	2	from	from	ADP
ejpam-2666	568	3	theorem	theorem	ADJ
ejpam-2666	568	4	9	9	NUM
ejpam-2666	568	5	and	and	CCONJ
ejpam-2666	568	6	theorem	theorem	VERB
ejpam-2666	568	7	10	10	NUM
ejpam-2666	568	8	,	,	PUNCT
ejpam-2666	568	9	we	we	PRON
ejpam-2666	568	10	get	get	VERB
ejpam-2666	568	11	deg(â	deg(â	NOUN
ejpam-2666	568	12	)	)	PUNCT
ejpam-2666	569	1	=	=	SYM
ejpam-2666	569	2	s−	s−	PROPN
ejpam-2666	569	3	b−	b−	PROPN
ejpam-2666	569	4	(	(	PUNCT
ejpam-2666	569	5	a	a	PRON
ejpam-2666	569	6	,	,	PUNCT
ejpam-2666	569	7	g2	g2	PROPN
ejpam-2666	569	8	)	)	PUNCT
ejpam-2666	570	1	+	+	CCONJ
ejpam-2666	570	2	(	(	PUNCT
ejpam-2666	570	3	b	b	X
ejpam-2666	570	4	,	,	PUNCT
ejpam-2666	570	5	l	l	NOUN
ejpam-2666	570	6	,	,	PUNCT
ejpam-2666	570	7	g1	g1	PROPN
ejpam-2666	570	8	)	)	PUNCT
ejpam-2666	570	9	.	.	PUNCT
ejpam-2666	571	1	(	(	PUNCT
ejpam-2666	571	2	15	15	NUM
ejpam-2666	571	3	)	)	PUNCT
ejpam-2666	571	4	now	now	ADV
ejpam-2666	571	5	since	since	SCONJ
ejpam-2666	571	6	(	(	PUNCT
ejpam-2666	571	7	0	0	NUM
ejpam-2666	571	8	|	|	ADV
ejpam-2666	571	9	ab	ab	PROPN
ejpam-2666	571	10	(	(	PUNCT
ejpam-2666	571	11	b	b	PROPN
ejpam-2666	571	12	,	,	PUNCT
ejpam-2666	571	13	l	l	NOUN
ejpam-2666	571	14	,	,	PUNCT
ejpam-2666	571	15	g1	g1	NOUN
ejpam-2666	571	16	)	)	PUNCT
ejpam-2666	571	17	|	|	ADV
ejpam-2666	571	18	0	0	NUM
ejpam-2666	571	19	)	)	PUNCT
ejpam-2666	571	20	and	and	CCONJ
ejpam-2666	571	21	(	(	PUNCT
ejpam-2666	571	22	0	0	NUM
ejpam-2666	571	23	|	|	ADV
ejpam-2666	571	24	bg2	bg2	PROPN
ejpam-2666	571	25	(	(	PUNCT
ejpam-2666	571	26	b	b	PROPN
ejpam-2666	571	27	,	,	PUNCT
ejpam-2666	571	28	l	l	NOUN
ejpam-2666	571	29	,	,	PUNCT
ejpam-2666	571	30	g1	g1	NOUN
ejpam-2666	571	31	)	)	PUNCT
ejpam-2666	572	1	|	|	ADV
ejpam-2666	572	2	bg3	bg3	NOUN
ejpam-2666	572	3	(	(	PUNCT
ejpam-2666	572	4	b	b	NOUN
ejpam-2666	572	5	,	,	PUNCT
ejpam-2666	572	6	l	l	NOUN
ejpam-2666	572	7	,	,	PUNCT
ejpam-2666	572	8	g1	g1	PROPN
ejpam-2666	572	9	)	)	PUNCT
ejpam-2666	572	10	)	)	PUNCT
ejpam-2666	572	11	are	be	AUX
ejpam-2666	572	12	in	in	ADP
ejpam-2666	572	13	c	c	NOUN
ejpam-2666	572	14	,	,	PUNCT
ejpam-2666	572	15	and	and	CCONJ
ejpam-2666	572	16	(	(	PUNCT
ejpam-2666	572	17	l̂	l̂	X
ejpam-2666	572	18	|	|	ADV
ejpam-2666	572	19	â	â	ADP
ejpam-2666	572	20	|	|	NOUN
ejpam-2666	572	21	0	0	X
ejpam-2666	572	22	)	)	PUNCT
ejpam-2666	572	23	∈	∈	PROPN
ejpam-2666	572	24	c⊥	c⊥	PROPN
ejpam-2666	572	25	,	,	PUNCT
ejpam-2666	572	26	we	we	PRON
ejpam-2666	572	27	have	have	VERB
ejpam-2666	572	28	ψ	ψ	X
ejpam-2666	572	29	(	(	PUNCT
ejpam-2666	572	30	(	(	PUNCT
ejpam-2666	572	31	l̂	l̂	X
ejpam-2666	572	32	|	|	ADV
ejpam-2666	572	33	â	â	X
ejpam-2666	572	34	|	|	NOUN
ejpam-2666	572	35	0	0	NUM
ejpam-2666	572	36	)	)	PUNCT
ejpam-2666	572	37	,	,	PUNCT
ejpam-2666	572	38	(	(	PUNCT
ejpam-2666	572	39	0	0	NUM
ejpam-2666	572	40	|	|	ADV
ejpam-2666	573	1	ab	ab	PROPN
ejpam-2666	574	1	(	(	PUNCT
ejpam-2666	574	2	b	b	PROPN
ejpam-2666	574	3	,	,	PUNCT
ejpam-2666	574	4	l	l	NOUN
ejpam-2666	574	5	,	,	PUNCT
ejpam-2666	574	6	g1	g1	NOUN
ejpam-2666	574	7	)	)	PUNCT
ejpam-2666	575	1	|	|	ADV
ejpam-2666	575	2	0	0	NUM
ejpam-2666	575	3	)	)	PUNCT
ejpam-2666	575	4	)	)	PUNCT
ejpam-2666	576	1	=	=	SYM
ejpam-2666	576	2	ψ	ψ	X
ejpam-2666	576	3	(	(	PUNCT
ejpam-2666	576	4	(	(	PUNCT
ejpam-2666	576	5	l̂	l̂	X
ejpam-2666	576	6	|	|	ADV
ejpam-2666	576	7	â	â	X
ejpam-2666	576	8	|	|	NOUN
ejpam-2666	576	9	0	0	NUM
ejpam-2666	576	10	)	)	PUNCT
ejpam-2666	576	11	,	,	PUNCT
ejpam-2666	576	12	(	(	PUNCT
ejpam-2666	576	13	0	0	NUM
ejpam-2666	576	14	|	|	ADV
ejpam-2666	576	15	bg2	bg2	PROPN
ejpam-2666	576	16	(	(	PUNCT
ejpam-2666	576	17	b	b	PROPN
ejpam-2666	576	18	,	,	PUNCT
ejpam-2666	576	19	l	l	NOUN
ejpam-2666	576	20	,	,	PUNCT
ejpam-2666	576	21	g1	g1	NOUN
ejpam-2666	576	22	)	)	PUNCT
ejpam-2666	577	1	|	|	ADV
ejpam-2666	577	2	bg3	bg3	NOUN
ejpam-2666	577	3	(	(	PUNCT
ejpam-2666	577	4	b	b	NOUN
ejpam-2666	577	5	,	,	PUNCT
ejpam-2666	577	6	l	l	NOUN
ejpam-2666	577	7	,	,	PUNCT
ejpam-2666	577	8	g1	g1	PROPN
ejpam-2666	577	9	)	)	PUNCT
ejpam-2666	577	10	)	)	PUNCT
ejpam-2666	577	11	)	)	PUNCT
ejpam-2666	578	1	=	=	PUNCT
ejpam-2666	578	2	0	0	X
ejpam-2666	578	3	.	.	PUNCT
ejpam-2666	579	1	this	this	PRON
ejpam-2666	579	2	implies	imply	VERB
ejpam-2666	579	3	that	that	SCONJ
ejpam-2666	579	4	â	â	ADP
ejpam-2666	579	5	a∗b∗	a∗b∗	PROPN
ejpam-2666	579	6	(	(	PUNCT
ejpam-2666	579	7	b	b	NOUN
ejpam-2666	579	8	,	,	PUNCT
ejpam-2666	579	9	l	l	NOUN
ejpam-2666	579	10	,	,	PUNCT
ejpam-2666	579	11	g1)∗	g1)∗	NOUN
ejpam-2666	579	12	=	=	SYM
ejpam-2666	579	13	â	â	X
ejpam-2666	579	14	g∗2b	g∗2b	NOUN
ejpam-2666	579	15	∗	∗	NOUN
ejpam-2666	579	16	(	(	PUNCT
ejpam-2666	579	17	b	b	NOUN
ejpam-2666	579	18	,	,	PUNCT
ejpam-2666	579	19	l	l	NOUN
ejpam-2666	579	20	,	,	PUNCT
ejpam-2666	579	21	g1)∗	g1)∗	ADJ
ejpam-2666	579	22	=	=	SYM
ejpam-2666	579	23	0	0	NUM
ejpam-2666	579	24	(	(	PUNCT
ejpam-2666	579	25	mod	mod	PROPN
ejpam-2666	579	26	(	(	PUNCT
ejpam-2666	579	27	xs	xs	PROPN
ejpam-2666	579	28	−	−	PROPN
ejpam-2666	579	29	1	1	NUM
ejpam-2666	579	30	)	)	PUNCT
ejpam-2666	579	31	)	)	PUNCT
ejpam-2666	579	32	and	and	CCONJ
ejpam-2666	579	33	hence	hence	ADV
ejpam-2666	579	34	â	â	X
ejpam-2666	579	35	(	(	PUNCT
ejpam-2666	579	36	a	a	DET
ejpam-2666	579	37	,	,	PUNCT
ejpam-2666	579	38	g2)∗b∗	g2)∗b∗	X
ejpam-2666	579	39	(	(	PUNCT
ejpam-2666	579	40	b	b	X
ejpam-2666	579	41	,	,	PUNCT
ejpam-2666	579	42	l	l	NOUN
ejpam-2666	579	43	,	,	PUNCT
ejpam-2666	579	44	g1)∗	g1)∗	ADJ
ejpam-2666	579	45	=	=	SYM
ejpam-2666	579	46	0	0	NUM
ejpam-2666	579	47	(	(	PUNCT
ejpam-2666	579	48	mod	mod	PROPN
ejpam-2666	579	49	(	(	PUNCT
ejpam-2666	579	50	xs	xs	PROPN
ejpam-2666	579	51	−	−	PROPN
ejpam-2666	579	52	1	1	NUM
ejpam-2666	579	53	)	)	PUNCT
ejpam-2666	579	54	)	)	PUNCT
ejpam-2666	579	55	.	.	PUNCT
ejpam-2666	580	1	therefore	therefore	ADV
ejpam-2666	580	2	,	,	PUNCT
ejpam-2666	580	3	for	for	ADP
ejpam-2666	580	4	some	some	DET
ejpam-2666	580	5	γ	γ	PROPN
ejpam-2666	580	6	∈	∈	PROPN
ejpam-2666	580	7	z2[x	z2[x	PROPN
ejpam-2666	580	8	]	]	X
ejpam-2666	580	9	,	,	PUNCT
ejpam-2666	580	10	we	we	PRON
ejpam-2666	580	11	have	have	VERB
ejpam-2666	580	12	â	â	X
ejpam-2666	580	13	(	(	PUNCT
ejpam-2666	580	14	a	a	PRON
ejpam-2666	580	15	,	,	PUNCT
ejpam-2666	580	16	g2	g2	PROPN
ejpam-2666	580	17	)	)	PUNCT
ejpam-2666	580	18	∗b∗	∗b∗	NUM
ejpam-2666	580	19	(	(	PUNCT
ejpam-2666	580	20	b	b	NOUN
ejpam-2666	580	21	,	,	PUNCT
ejpam-2666	580	22	l	l	NOUN
ejpam-2666	580	23	,	,	PUNCT
ejpam-2666	580	24	g1)∗	g1)∗	VERB
ejpam-2666	580	25	=	=	SYM
ejpam-2666	580	26	γ(xs	γ(xs	X
ejpam-2666	580	27	−	−	PROPN
ejpam-2666	580	28	1	1	NUM
ejpam-2666	580	29	)	)	PUNCT
ejpam-2666	580	30	.	.	PUNCT
ejpam-2666	581	1	(	(	PUNCT
ejpam-2666	581	2	16	16	NUM
ejpam-2666	581	3	)	)	PUNCT
ejpam-2666	581	4	from	from	ADP
ejpam-2666	581	5	equation	equation	NOUN
ejpam-2666	581	6	(	(	PUNCT
ejpam-2666	581	7	15	15	NUM
ejpam-2666	581	8	)	)	PUNCT
ejpam-2666	581	9	and	and	CCONJ
ejpam-2666	581	10	equation	equation	NOUN
ejpam-2666	581	11	(	(	PUNCT
ejpam-2666	581	12	16	16	NUM
ejpam-2666	581	13	)	)	PUNCT
ejpam-2666	581	14	,	,	PUNCT
ejpam-2666	581	15	we	we	PRON
ejpam-2666	581	16	get	get	VERB
ejpam-2666	581	17	γ	γ	X
ejpam-2666	581	18	=	=	SYM
ejpam-2666	581	19	1	1	NUM
ejpam-2666	581	20	and	and	CCONJ
ejpam-2666	581	21	hence	hence	ADV
ejpam-2666	581	22	â	â	PROPN
ejpam-2666	581	23	b∗(a	b∗(a	PROPN
ejpam-2666	581	24	,	,	PUNCT
ejpam-2666	581	25	g2	g2	PROPN
ejpam-2666	581	26	)	)	PUNCT
ejpam-2666	581	27	∗	∗	NOUN
ejpam-2666	581	28	=	=	SYM
ejpam-2666	581	29	(	(	PUNCT
ejpam-2666	581	30	xs	xs	PROPN
ejpam-2666	582	1	−	−	PROPN
ejpam-2666	582	2	1)(b	1)(b	PROPN
ejpam-2666	582	3	,	,	PUNCT
ejpam-2666	582	4	l	l	NOUN
ejpam-2666	582	5	,	,	PUNCT
ejpam-2666	582	6	g1	g1	PROPN
ejpam-2666	582	7	)	)	PUNCT
ejpam-2666	582	8	∗.	∗.	PROPN
ejpam-2666	582	9	theorem	theorem	VERB
ejpam-2666	582	10	14	14	NUM
ejpam-2666	582	11	.	.	PUNCT
ejpam-2666	583	1	let	let	VERB
ejpam-2666	583	2	c	c	NOUN
ejpam-2666	583	3	=	=	SYM
ejpam-2666	583	4	〈	〈	PROPN
ejpam-2666	583	5	(	(	PUNCT
ejpam-2666	583	6	b	b	NOUN
ejpam-2666	583	7	|	|	NOUN
ejpam-2666	583	8	0	0	NUM
ejpam-2666	584	1	|	|	NOUN
ejpam-2666	584	2	0	0	NUM
ejpam-2666	584	3	)	)	PUNCT
ejpam-2666	584	4	,	,	PUNCT
ejpam-2666	585	1	(	(	PUNCT
ejpam-2666	585	2	l	l	NOUN
ejpam-2666	585	3	|	|	ADV
ejpam-2666	585	4	a	a	DET
ejpam-2666	585	5	|	|	NOUN
ejpam-2666	585	6	0	0	NUM
ejpam-2666	585	7	)	)	PUNCT
ejpam-2666	585	8	,	,	PUNCT
ejpam-2666	585	9	(	(	PUNCT
ejpam-2666	585	10	g1	g1	VERB
ejpam-2666	585	11	|	|	ADV
ejpam-2666	585	12	g2	g2	PROPN
ejpam-2666	585	13	|	|	CCONJ
ejpam-2666	585	14	g3	g3	PROPN
ejpam-2666	585	15	)	)	PUNCT
ejpam-2666	585	16	〉	〉	PROPN
ejpam-2666	585	17	be	be	AUX
ejpam-2666	585	18	a	a	DET
ejpam-2666	585	19	z2	z2	ADJ
ejpam-2666	585	20	-	-	PUNCT
ejpam-2666	585	21	triple	triple	ADJ
ejpam-2666	585	22	cyclic	cyclic	ADJ
ejpam-2666	585	23	code	code	NOUN
ejpam-2666	585	24	of	of	ADP
ejpam-2666	585	25	block	block	NOUN
ejpam-2666	585	26	length	length	NOUN
ejpam-2666	585	27	(	(	PUNCT
ejpam-2666	585	28	r	r	NOUN
ejpam-2666	585	29	,	,	PUNCT
ejpam-2666	585	30	s	s	PROPN
ejpam-2666	585	31	,	,	PUNCT
ejpam-2666	585	32	t	t	PROPN
ejpam-2666	585	33	)	)	PUNCT
ejpam-2666	585	34	and	and	CCONJ
ejpam-2666	585	35	c⊥	c⊥	X
ejpam-2666	586	1	=	=	SYM
ejpam-2666	586	2	〈	〈	PROPN
ejpam-2666	586	3	(	(	PUNCT
ejpam-2666	586	4	b̂	b̂	NOUN
ejpam-2666	586	5	|	|	ADV
ejpam-2666	586	6	0	0	NUM
ejpam-2666	587	1	|	|	NOUN
ejpam-2666	587	2	0	0	NUM
ejpam-2666	587	3	)	)	PUNCT
ejpam-2666	587	4	,	,	PUNCT
ejpam-2666	587	5	(	(	PUNCT
ejpam-2666	587	6	l̂	l̂	X
ejpam-2666	587	7	|	|	ADV
ejpam-2666	587	8	â	â	X
ejpam-2666	587	9	|	|	NOUN
ejpam-2666	587	10	0	0	NUM
ejpam-2666	587	11	)	)	PUNCT
ejpam-2666	587	12	,	,	PUNCT
ejpam-2666	587	13	(	(	PUNCT
ejpam-2666	587	14	ĝ1	ĝ1	NOUN
ejpam-2666	587	15	|	|	ADV
ejpam-2666	587	16	ĝ2	ĝ2	NOUN
ejpam-2666	587	17	|	|	ADV
ejpam-2666	587	18	ĝ3	ĝ3	NOUN
ejpam-2666	587	19	)	)	PUNCT
ejpam-2666	587	20	〉	〉	NOUN
ejpam-2666	587	21	be	be	AUX
ejpam-2666	587	22	the	the	DET
ejpam-2666	587	23	dual	dual	ADJ
ejpam-2666	587	24	code	code	NOUN
ejpam-2666	587	25	of	of	ADP
ejpam-2666	587	26	c.	c.	PROPN
ejpam-2666	587	27	then	then	ADV
ejpam-2666	587	28	l̂	l̂	VERB
ejpam-2666	587	29	b∗	b∗	ADJ
ejpam-2666	587	30	=	=	PUNCT
ejpam-2666	587	31	β(xr	β(xr	PROPN
ejpam-2666	587	32	−	−	NOUN
ejpam-2666	587	33	1	1	NUM
ejpam-2666	587	34	)	)	PUNCT
ejpam-2666	587	35	,	,	PUNCT
ejpam-2666	587	36	where	where	SCONJ
ejpam-2666	587	37	β	β	X
ejpam-2666	587	38	=	=	SYM
ejpam-2666	587	39	(	(	PUNCT
ejpam-2666	587	40	l∗	l∗	PROPN
ejpam-2666	587	41	(	(	PUNCT
ejpam-2666	587	42	b	b	NOUN
ejpam-2666	587	43	,	,	PUNCT
ejpam-2666	587	44	l	l	NOUN
ejpam-2666	587	45	,	,	PUNCT
ejpam-2666	587	46	g1)∗	g1)∗	NOUN
ejpam-2666	587	47	)	)	PUNCT
ejpam-2666	587	48	−1	−1	NOUN
ejpam-2666	587	49	a∗	a∗	NOUN
ejpam-2666	587	50	(	(	PUNCT
ejpam-2666	587	51	a	a	DET
ejpam-2666	587	52	,	,	PUNCT
ejpam-2666	587	53	g2)∗	g2)∗	ADJ
ejpam-2666	587	54	xm+deg(l)−deg(a	xm+deg(l)−deg(a	PROPN
ejpam-2666	587	55	)	)	PUNCT
ejpam-2666	587	56	(	(	PUNCT
ejpam-2666	587	57	mod	mod	X
ejpam-2666	587	58	(	(	PUNCT
ejpam-2666	587	59	b	b	NOUN
ejpam-2666	587	60	,	,	PUNCT
ejpam-2666	587	61	g1)∗	g1)∗	NOUN
ejpam-2666	587	62	(	(	PUNCT
ejpam-2666	587	63	b	b	NOUN
ejpam-2666	587	64	,	,	PUNCT
ejpam-2666	587	65	l	l	NOUN
ejpam-2666	587	66	,	,	PUNCT
ejpam-2666	587	67	g1)∗	g1)∗	NOUN
ejpam-2666	587	68	)	)	PUNCT
ejpam-2666	587	69	.	.	PUNCT
ejpam-2666	588	1	proof	proof	NOUN
ejpam-2666	588	2	.	.	PUNCT
ejpam-2666	589	1	since	since	SCONJ
ejpam-2666	589	2	(	(	PUNCT
ejpam-2666	589	3	b	b	X
ejpam-2666	589	4	|	|	NOUN
ejpam-2666	589	5	0	0	NUM
ejpam-2666	589	6	|	|	NOUN
ejpam-2666	589	7	0	0	X
ejpam-2666	589	8	)	)	PUNCT
ejpam-2666	589	9	∈	∈	PROPN
ejpam-2666	589	10	c	c	PROPN
ejpam-2666	589	11	and	and	CCONJ
ejpam-2666	589	12	(	(	PUNCT
ejpam-2666	589	13	l̂	l̂	X
ejpam-2666	589	14	|	|	ADV
ejpam-2666	589	15	â	â	ADP
ejpam-2666	589	16	|	|	NOUN
ejpam-2666	589	17	0	0	X
ejpam-2666	589	18	)	)	PUNCT
ejpam-2666	589	19	∈	∈	PROPN
ejpam-2666	589	20	c⊥	c⊥	PROPN
ejpam-2666	589	21	,	,	PUNCT
ejpam-2666	589	22	we	we	PRON
ejpam-2666	589	23	have	have	AUX
ejpam-2666	589	24	l̂b∗	l̂b∗	VERB
ejpam-2666	589	25	=	=	SYM
ejpam-2666	589	26	0	0	PUNCT
ejpam-2666	590	1	(	(	PUNCT
ejpam-2666	590	2	mod	mod	PROPN
ejpam-2666	590	3	xr	xr	PROPN
ejpam-2666	590	4	−	−	PROPN
ejpam-2666	590	5	1	1	NUM
ejpam-2666	590	6	)	)	PUNCT
ejpam-2666	590	7	.	.	PUNCT
ejpam-2666	591	1	therefore	therefore	ADV
ejpam-2666	591	2	l̂	l̂	VERB
ejpam-2666	591	3	b∗	b∗	ADJ
ejpam-2666	591	4	=	=	PUNCT
ejpam-2666	591	5	β(xr	β(xr	PROPN
ejpam-2666	591	6	−	−	NOUN
ejpam-2666	591	7	1	1	NUM
ejpam-2666	591	8	)	)	PUNCT
ejpam-2666	591	9	for	for	ADP
ejpam-2666	591	10	some	some	DET
ejpam-2666	591	11	β	β	X
ejpam-2666	591	12	∈	∈	PROPN
ejpam-2666	591	13	z2[x	z2[x	PROPN
ejpam-2666	591	14	]	]	PUNCT
ejpam-2666	591	15	.	.	PUNCT
ejpam-2666	592	1	again	again	ADV
ejpam-2666	592	2	,	,	PUNCT
ejpam-2666	592	3	as	as	ADP
ejpam-2666	592	4	(	(	PUNCT
ejpam-2666	592	5	l̂	l̂	X
ejpam-2666	592	6	|	|	ADV
ejpam-2666	592	7	â	â	ADP
ejpam-2666	592	8	|	|	NOUN
ejpam-2666	592	9	0	0	X
ejpam-2666	592	10	)	)	PUNCT
ejpam-2666	592	11	∈	∈	PROPN
ejpam-2666	592	12	c⊥	c⊥	PROPN
ejpam-2666	592	13	and	and	CCONJ
ejpam-2666	592	14	(	(	PUNCT
ejpam-2666	592	15	l	l	NOUN
ejpam-2666	592	16	|	|	ADV
ejpam-2666	592	17	a	a	DET
ejpam-2666	592	18	|	|	NOUN
ejpam-2666	592	19	0	0	NUM
ejpam-2666	592	20	)	)	PUNCT
ejpam-2666	592	21	∈	∈	PROPN
ejpam-2666	592	22	c	c	X
ejpam-2666	592	23	,	,	PUNCT
ejpam-2666	592	24	so	so	SCONJ
ejpam-2666	592	25	ψ	ψ	X
ejpam-2666	592	26	(	(	PUNCT
ejpam-2666	592	27	(	(	PUNCT
ejpam-2666	592	28	l̂	l̂	X
ejpam-2666	593	1	|	|	ADV
ejpam-2666	593	2	â	â	X
ejpam-2666	593	3	|	|	NOUN
ejpam-2666	593	4	0	0	NUM
ejpam-2666	593	5	)	)	PUNCT
ejpam-2666	593	6	,	,	PUNCT
ejpam-2666	593	7	(	(	PUNCT
ejpam-2666	593	8	l	l	NOUN
ejpam-2666	593	9	|	|	ADV
ejpam-2666	593	10	a	a	DET
ejpam-2666	593	11	|	|	NOUN
ejpam-2666	593	12	0	0	NUM
ejpam-2666	593	13	)	)	PUNCT
ejpam-2666	593	14	)	)	PUNCT
ejpam-2666	594	1	=	=	SYM
ejpam-2666	594	2	0	0	PUNCT
ejpam-2666	594	3	(	(	PUNCT
ejpam-2666	594	4	mod	mod	NOUN
ejpam-2666	594	5	xm−	xm−	PROPN
ejpam-2666	594	6	1	1	NUM
ejpam-2666	594	7	)	)	PUNCT
ejpam-2666	594	8	.	.	PUNCT
ejpam-2666	595	1	this	this	PRON
ejpam-2666	595	2	implies	imply	VERB
ejpam-2666	595	3	that	that	SCONJ
ejpam-2666	595	4	srinivasulu	srinivasulu	PROPN
ejpam-2666	595	5	b	b	PROPN
ejpam-2666	595	6	,	,	PUNCT
ejpam-2666	595	7	maheshanand	maheshanand	NOUN
ejpam-2666	595	8	bhaintwal	bhaintwal	NOUN
ejpam-2666	595	9	/	/	SYM
ejpam-2666	595	10	eur	eur	PROPN
ejpam-2666	595	11	.	.	PUNCT
ejpam-2666	596	1	j.	j.	PROPN
ejpam-2666	596	2	pure	pure	PROPN
ejpam-2666	596	3	appl	appl	PROPN
ejpam-2666	596	4	.	.	PROPN
ejpam-2666	596	5	math	math	PROPN
ejpam-2666	596	6	,	,	PUNCT
ejpam-2666	596	7	10	10	NUM
ejpam-2666	596	8	(	(	PUNCT
ejpam-2666	596	9	2	2	NUM
ejpam-2666	596	10	)	)	PUNCT
ejpam-2666	596	11	(	(	PUNCT
ejpam-2666	596	12	2017	2017	NUM
ejpam-2666	596	13	)	)	PUNCT
ejpam-2666	596	14	,	,	PUNCT
ejpam-2666	596	15	392	392	NUM
ejpam-2666	596	16	-	-	SYM
ejpam-2666	596	17	409	409	NUM
ejpam-2666	596	18	405	405	NUM
ejpam-2666	596	19	l̂θm	l̂θm	NOUN
ejpam-2666	596	20	r	r	NOUN
ejpam-2666	596	21	(	(	PUNCT
ejpam-2666	596	22	xr)xm−1−deg(l)l∗	xr)xm−1−deg(l)l∗	PROPN
ejpam-2666	596	23	+	+	CCONJ
ejpam-2666	596	24	âθm	âθm	NOUN
ejpam-2666	596	25	s	s	X
ejpam-2666	596	26	(	(	PUNCT
ejpam-2666	596	27	xs)xm−1−deg(a)a∗	xs)xm−1−deg(a)a∗	X
ejpam-2666	596	28	=	=	SYM
ejpam-2666	596	29	0	0	NUM
ejpam-2666	597	1	(	(	PUNCT
ejpam-2666	597	2	mod	mod	PROPN
ejpam-2666	597	3	xm	xm	PROPN
ejpam-2666	597	4	−	−	NOUN
ejpam-2666	597	5	1	1	NUM
ejpam-2666	597	6	)	)	PUNCT
ejpam-2666	597	7	.	.	PUNCT
ejpam-2666	598	1	(	(	PUNCT
ejpam-2666	598	2	17	17	NUM
ejpam-2666	598	3	)	)	PUNCT
ejpam-2666	598	4	substituting	substitute	VERB
ejpam-2666	598	5	l̂	l̂	VERB
ejpam-2666	598	6	and	and	CCONJ
ejpam-2666	598	7	â	â	X
ejpam-2666	598	8	in	in	ADP
ejpam-2666	598	9	equation	equation	NOUN
ejpam-2666	598	10	(	(	PUNCT
ejpam-2666	598	11	17	17	NUM
ejpam-2666	598	12	)	)	PUNCT
ejpam-2666	598	13	,	,	PUNCT
ejpam-2666	598	14	we	we	PRON
ejpam-2666	598	15	get	get	VERB
ejpam-2666	598	16	(	(	PUNCT
ejpam-2666	598	17	xm	xm	NOUN
ejpam-2666	598	18	−	−	NOUN
ejpam-2666	598	19	1	1	X
ejpam-2666	598	20	)	)	PUNCT
ejpam-2666	598	21	l∗	l∗	NOUN
ejpam-2666	598	22	b∗	b∗	ADV
ejpam-2666	598	23	xm−1−deg(l)β	xm−1−deg(l)β	PUNCT
ejpam-2666	599	1	+	+	CCONJ
ejpam-2666	599	2	(	(	PUNCT
ejpam-2666	599	3	xm	xm	PROPN
ejpam-2666	599	4	−	−	PROPN
ejpam-2666	599	5	1	1	NUM
ejpam-2666	599	6	)	)	PUNCT
ejpam-2666	599	7	(	(	PUNCT
ejpam-2666	599	8	b	b	X
ejpam-2666	599	9	,	,	PUNCT
ejpam-2666	599	10	l	l	NOUN
ejpam-2666	599	11	,	,	PUNCT
ejpam-2666	599	12	g1	g1	NOUN
ejpam-2666	599	13	)	)	PUNCT
ejpam-2666	599	14	∗	∗	NOUN
ejpam-2666	599	15	b∗(a	b∗(a	PROPN
ejpam-2666	599	16	,	,	PUNCT
ejpam-2666	599	17	g2)∗	g2)∗	ADJ
ejpam-2666	599	18	a∗xm−1−deg(a	a∗xm−1−deg(a	PROPN
ejpam-2666	599	19	)	)	PUNCT
ejpam-2666	599	20	=	=	SYM
ejpam-2666	600	1	0	0	PUNCT
ejpam-2666	601	1	(	(	PUNCT
ejpam-2666	601	2	mod	mod	PROPN
ejpam-2666	601	3	xm	xm	PROPN
ejpam-2666	601	4	−	−	NOUN
ejpam-2666	601	5	1	1	NUM
ejpam-2666	601	6	)	)	PUNCT
ejpam-2666	601	7	.	.	PUNCT
ejpam-2666	602	1	(	(	PUNCT
ejpam-2666	602	2	18	18	NUM
ejpam-2666	602	3	)	)	PUNCT
ejpam-2666	602	4	rearranging	rearrange	VERB
ejpam-2666	602	5	the	the	DET
ejpam-2666	602	6	terms	term	NOUN
ejpam-2666	602	7	in	in	ADP
ejpam-2666	602	8	equation	equation	NOUN
ejpam-2666	602	9	(	(	PUNCT
ejpam-2666	602	10	18	18	NUM
ejpam-2666	602	11	)	)	PUNCT
ejpam-2666	602	12	,	,	PUNCT
ejpam-2666	602	13	we	we	PRON
ejpam-2666	602	14	get	get	VERB
ejpam-2666	602	15	(	(	PUNCT
ejpam-2666	602	16	xm−1	xm−1	PROPN
ejpam-2666	602	17	)	)	PUNCT
ejpam-2666	603	1	(	(	PUNCT
ejpam-2666	603	2	b	b	X
ejpam-2666	603	3	,	,	PUNCT
ejpam-2666	603	4	l	l	NOUN
ejpam-2666	603	5	,	,	PUNCT
ejpam-2666	603	6	g1	g1	NOUN
ejpam-2666	603	7	)	)	PUNCT
ejpam-2666	603	8	∗	∗	NOUN
ejpam-2666	603	9	b∗	b∗	ADJ
ejpam-2666	603	10	[	[	PUNCT
ejpam-2666	603	11	l∗	l∗	PROPN
ejpam-2666	603	12	(	(	PUNCT
ejpam-2666	603	13	b	b	NOUN
ejpam-2666	603	14	,	,	PUNCT
ejpam-2666	603	15	l	l	NOUN
ejpam-2666	603	16	,	,	PUNCT
ejpam-2666	603	17	g1)∗	g1)∗	ADJ
ejpam-2666	603	18	xm−1−deg(l)β	xm−1−deg(l)β	NOUN
ejpam-2666	603	19	+	+	CCONJ
ejpam-2666	603	20	a∗	a∗	PROPN
ejpam-2666	603	21	(	(	PUNCT
ejpam-2666	603	22	a	a	PRON
ejpam-2666	603	23	,	,	PUNCT
ejpam-2666	603	24	g2)∗	g2)∗	ADJ
ejpam-2666	603	25	xm−1−deg(a	xm−1−deg(a	NUM
ejpam-2666	603	26	)	)	PUNCT
ejpam-2666	603	27	]	]	PUNCT
ejpam-2666	604	1	=	=	PUNCT
ejpam-2666	604	2	0	0	PUNCT
ejpam-2666	604	3	(	(	PUNCT
ejpam-2666	604	4	mod	mod	PROPN
ejpam-2666	604	5	xm−1	xm−1	PROPN
ejpam-2666	604	6	)	)	PUNCT
ejpam-2666	604	7	.	.	PUNCT
ejpam-2666	605	1	(	(	PUNCT
ejpam-2666	605	2	19	19	NUM
ejpam-2666	605	3	)	)	PUNCT
ejpam-2666	605	4	with	with	ADP
ejpam-2666	605	5	similar	similar	ADJ
ejpam-2666	605	6	arguments	argument	NOUN
ejpam-2666	605	7	as	as	ADP
ejpam-2666	605	8	in	in	ADP
ejpam-2666	605	9	theorem	theorem	NOUN
ejpam-2666	605	10	12	12	NUM
ejpam-2666	605	11	,	,	PUNCT
ejpam-2666	605	12	we	we	PRON
ejpam-2666	605	13	get	get	VERB
ejpam-2666	605	14	β	β	X
ejpam-2666	605	15	=	=	SYM
ejpam-2666	605	16	(	(	PUNCT
ejpam-2666	605	17	l∗	l∗	PROPN
ejpam-2666	605	18	(	(	PUNCT
ejpam-2666	605	19	b	b	NOUN
ejpam-2666	605	20	,	,	PUNCT
ejpam-2666	605	21	l	l	NOUN
ejpam-2666	605	22	,	,	PUNCT
ejpam-2666	605	23	g1)∗	g1)∗	NOUN
ejpam-2666	605	24	)	)	PUNCT
ejpam-2666	605	25	−1	−1	NOUN
ejpam-2666	605	26	a∗	a∗	NOUN
ejpam-2666	605	27	(	(	PUNCT
ejpam-2666	605	28	a	a	DET
ejpam-2666	605	29	,	,	PUNCT
ejpam-2666	605	30	g2)∗	g2)∗	ADJ
ejpam-2666	605	31	xm+deg(l)−deg(a	xm+deg(l)−deg(a	PROPN
ejpam-2666	605	32	)	)	PUNCT
ejpam-2666	605	33	(	(	PUNCT
ejpam-2666	605	34	mod	mod	X
ejpam-2666	605	35	(	(	PUNCT
ejpam-2666	605	36	b	b	NOUN
ejpam-2666	605	37	,	,	PUNCT
ejpam-2666	605	38	g1	g1	PROPN
ejpam-2666	605	39	)	)	PUNCT
ejpam-2666	605	40	∗	∗	NOUN
ejpam-2666	605	41	(	(	PUNCT
ejpam-2666	605	42	b	b	NOUN
ejpam-2666	605	43	,	,	PUNCT
ejpam-2666	605	44	l	l	NOUN
ejpam-2666	605	45	,	,	PUNCT
ejpam-2666	605	46	g1)∗	g1)∗	NOUN
ejpam-2666	605	47	)	)	PUNCT
ejpam-2666	605	48	.	.	PUNCT
ejpam-2666	606	1	(	(	PUNCT
ejpam-2666	606	2	20	20	NUM
ejpam-2666	606	3	)	)	PUNCT
ejpam-2666	606	4	hence	hence	ADV
ejpam-2666	606	5	the	the	DET
ejpam-2666	606	6	result	result	NOUN
ejpam-2666	606	7	.	.	PUNCT
ejpam-2666	607	1	summarising	summarise	VERB
ejpam-2666	607	2	the	the	DET
ejpam-2666	607	3	previous	previous	ADJ
ejpam-2666	607	4	results	result	NOUN
ejpam-2666	607	5	we	we	PRON
ejpam-2666	607	6	have	have	VERB
ejpam-2666	607	7	the	the	DET
ejpam-2666	607	8	following	follow	VERB
ejpam-2666	607	9	theorem	theorem	VERB
ejpam-2666	607	10	.	.	PUNCT
ejpam-2666	607	11	theorem	theorem	PROPN
ejpam-2666	607	12	15	15	NUM
ejpam-2666	607	13	.	.	PUNCT
ejpam-2666	608	1	let	let	VERB
ejpam-2666	608	2	c	c	NOUN
ejpam-2666	608	3	=	=	SYM
ejpam-2666	608	4	〈	〈	PROPN
ejpam-2666	608	5	(	(	PUNCT
ejpam-2666	608	6	b	b	NOUN
ejpam-2666	608	7	|	|	NOUN
ejpam-2666	608	8	0	0	NUM
ejpam-2666	609	1	|	|	NOUN
ejpam-2666	609	2	0	0	NUM
ejpam-2666	609	3	)	)	PUNCT
ejpam-2666	609	4	,	,	PUNCT
ejpam-2666	610	1	(	(	PUNCT
ejpam-2666	610	2	l	l	NOUN
ejpam-2666	610	3	|	|	ADV
ejpam-2666	610	4	a	a	DET
ejpam-2666	610	5	|	|	NOUN
ejpam-2666	610	6	0	0	NUM
ejpam-2666	610	7	)	)	PUNCT
ejpam-2666	610	8	,	,	PUNCT
ejpam-2666	610	9	(	(	PUNCT
ejpam-2666	610	10	g1	g1	VERB
ejpam-2666	610	11	|	|	ADV
ejpam-2666	610	12	g2	g2	PROPN
ejpam-2666	610	13	|	|	CCONJ
ejpam-2666	610	14	g3	g3	PROPN
ejpam-2666	610	15	)	)	PUNCT
ejpam-2666	610	16	〉	〉	PROPN
ejpam-2666	610	17	be	be	AUX
ejpam-2666	610	18	a	a	DET
ejpam-2666	610	19	z2	z2	ADJ
ejpam-2666	610	20	-	-	PUNCT
ejpam-2666	610	21	triple	triple	ADJ
ejpam-2666	610	22	cyclic	cyclic	ADJ
ejpam-2666	610	23	code	code	NOUN
ejpam-2666	610	24	of	of	ADP
ejpam-2666	610	25	block	block	NOUN
ejpam-2666	610	26	length	length	NOUN
ejpam-2666	610	27	(	(	PUNCT
ejpam-2666	610	28	r	r	NOUN
ejpam-2666	610	29	,	,	PUNCT
ejpam-2666	610	30	s	s	PROPN
ejpam-2666	610	31	,	,	PUNCT
ejpam-2666	610	32	t	t	PROPN
ejpam-2666	610	33	)	)	PUNCT
ejpam-2666	610	34	and	and	CCONJ
ejpam-2666	610	35	c⊥	c⊥	X
ejpam-2666	611	1	=	=	SYM
ejpam-2666	611	2	〈	〈	PROPN
ejpam-2666	611	3	(	(	PUNCT
ejpam-2666	611	4	b̂	b̂	NOUN
ejpam-2666	611	5	|	|	ADV
ejpam-2666	611	6	0	0	NUM
ejpam-2666	612	1	|	|	NOUN
ejpam-2666	612	2	0	0	NUM
ejpam-2666	612	3	)	)	PUNCT
ejpam-2666	612	4	,	,	PUNCT
ejpam-2666	612	5	(	(	PUNCT
ejpam-2666	612	6	l̂	l̂	X
ejpam-2666	612	7	|	|	ADV
ejpam-2666	612	8	â	â	X
ejpam-2666	612	9	|	|	NOUN
ejpam-2666	612	10	0	0	NUM
ejpam-2666	612	11	)	)	PUNCT
ejpam-2666	612	12	,	,	PUNCT
ejpam-2666	612	13	(	(	PUNCT
ejpam-2666	612	14	ĝ1	ĝ1	NOUN
ejpam-2666	612	15	|	|	ADV
ejpam-2666	612	16	ĝ2	ĝ2	NOUN
ejpam-2666	612	17	|	|	ADV
ejpam-2666	612	18	ĝ3	ĝ3	NOUN
ejpam-2666	612	19	)	)	PUNCT
ejpam-2666	612	20	〉	〉	NOUN
ejpam-2666	612	21	be	be	AUX
ejpam-2666	612	22	the	the	DET
ejpam-2666	612	23	dual	dual	ADJ
ejpam-2666	612	24	code	code	NOUN
ejpam-2666	612	25	of	of	ADP
ejpam-2666	612	26	c.	c.	PROPN
ejpam-2666	612	27	let	let	VERB
ejpam-2666	612	28	ρ1	ρ1	NOUN
ejpam-2666	612	29	=	=	PUNCT
ejpam-2666	613	1	l∗	l∗	PROPN
ejpam-2666	613	2	(	(	PUNCT
ejpam-2666	613	3	b	b	NOUN
ejpam-2666	613	4	,	,	PUNCT
ejpam-2666	613	5	l	l	NOUN
ejpam-2666	613	6	,	,	PUNCT
ejpam-2666	613	7	g1)∗	g1)∗	ADJ
ejpam-2666	613	8	and	and	CCONJ
ejpam-2666	613	9	ρ2	ρ2	NOUN
ejpam-2666	613	10	=	=	SYM
ejpam-2666	613	11	g∗2	g∗2	NOUN
ejpam-2666	613	12	(	(	PUNCT
ejpam-2666	613	13	a	a	DET
ejpam-2666	613	14	,	,	PUNCT
ejpam-2666	613	15	g2)∗	g2)∗	NOUN
ejpam-2666	613	16	.	.	PUNCT
ejpam-2666	614	1	then	then	ADV
ejpam-2666	614	2	(	(	PUNCT
ejpam-2666	614	3	i	i	NOUN
ejpam-2666	614	4	)	)	PUNCT
ejpam-2666	614	5	b̂	b̂	NOUN
ejpam-2666	614	6	=	=	SYM
ejpam-2666	614	7	xr−1	xr−1	PROPN
ejpam-2666	614	8	(	(	PUNCT
ejpam-2666	614	9	b	b	NOUN
ejpam-2666	614	10	,	,	PUNCT
ejpam-2666	614	11	l	l	NOUN
ejpam-2666	614	12	,	,	PUNCT
ejpam-2666	614	13	g1)∗	g1)∗	VERB
ejpam-2666	614	14	;	;	PUNCT
ejpam-2666	614	15	(	(	PUNCT
ejpam-2666	614	16	ii	ii	NOUN
ejpam-2666	614	17	)	)	PUNCT
ejpam-2666	614	18	ĝ3	ĝ3	X
ejpam-2666	615	1	=	=	PUNCT
ejpam-2666	616	1	(	(	PUNCT
ejpam-2666	616	2	xt−1)(a	xt−1)(a	ADJ
ejpam-2666	616	3	,	,	PUNCT
ejpam-2666	616	4	g2)∗	g2)∗	ADJ
ejpam-2666	616	5	a∗g∗3	a∗g∗3	NUM
ejpam-2666	616	6	;	;	PUNCT
ejpam-2666	616	7	(	(	PUNCT
ejpam-2666	616	8	iii	iii	NOUN
ejpam-2666	616	9	)	)	PUNCT
ejpam-2666	616	10	â	â	X
ejpam-2666	617	1	=	=	PUNCT
ejpam-2666	617	2	(	(	PUNCT
ejpam-2666	617	3	xs−1)(b	xs−1)(b	ADJ
ejpam-2666	617	4	,	,	PUNCT
ejpam-2666	617	5	l	l	NOUN
ejpam-2666	617	6	,	,	PUNCT
ejpam-2666	617	7	g1)∗	g1)∗	NOUN
ejpam-2666	617	8	(	(	PUNCT
ejpam-2666	617	9	a	a	DET
ejpam-2666	617	10	,	,	PUNCT
ejpam-2666	617	11	g2)∗b∗	g2)∗b∗	NOUN
ejpam-2666	617	12	;	;	PUNCT
ejpam-2666	617	13	(	(	PUNCT
ejpam-2666	617	14	iv	iv	X
ejpam-2666	617	15	)	)	PUNCT
ejpam-2666	617	16	ĝ1	ĝ1	NOUN
ejpam-2666	618	1	=	=	SYM
ejpam-2666	618	2	λ1	λ1	PROPN
ejpam-2666	618	3	(	(	PUNCT
ejpam-2666	618	4	xr−1	xr−1	PROPN
ejpam-2666	618	5	)	)	PUNCT
ejpam-2666	618	6	b∗	b∗	ADJ
ejpam-2666	618	7	,	,	PUNCT
ejpam-2666	618	8	ĝ2	ĝ2	NOUN
ejpam-2666	618	9	=	=	SYM
ejpam-2666	618	10	λ2	λ2	PROPN
ejpam-2666	618	11	(	(	PUNCT
ejpam-2666	618	12	xs−1)(b	xs−1)(b	ADJ
ejpam-2666	618	13	,	,	PUNCT
ejpam-2666	618	14	l	l	NOUN
ejpam-2666	618	15	,	,	PUNCT
ejpam-2666	618	16	g1)∗	g1)∗	ADJ
ejpam-2666	618	17	a∗b∗	a∗b∗	NOUN
ejpam-2666	618	18	,	,	PUNCT
ejpam-2666	618	19	where	where	SCONJ
ejpam-2666	618	20	λ1	λ1	ADJ
ejpam-2666	618	21	=	=	SYM
ejpam-2666	618	22	(	(	PUNCT
ejpam-2666	618	23	ρ1	ρ1	PROPN
ejpam-2666	618	24	)	)	PUNCT
ejpam-2666	618	25	−1	−1	NOUN
ejpam-2666	618	26	(	(	PUNCT
ejpam-2666	618	27	ρ2	ρ2	NOUN
ejpam-2666	618	28	)	)	PUNCT
ejpam-2666	618	29	−1	−1	NOUN
ejpam-2666	618	30	b∗	b∗	ADJ
ejpam-2666	618	31	(	(	PUNCT
ejpam-2666	618	32	b	b	NOUN
ejpam-2666	618	33	,	,	PUNCT
ejpam-2666	618	34	l	l	NOUN
ejpam-2666	618	35	,	,	PUNCT
ejpam-2666	618	36	g1)∗	g1)∗	VERB
ejpam-2666	618	37	x2m+deg(l)−deg(a)+deg(g2)−deg(g3	x2m+deg(l)−deg(a)+deg(g2)−deg(g3	X
ejpam-2666	618	38	)	)	PUNCT
ejpam-2666	618	39	(	(	PUNCT
ejpam-2666	618	40	mod	mod	X
ejpam-2666	618	41	(	(	PUNCT
ejpam-2666	618	42	(	(	PUNCT
ejpam-2666	618	43	b	b	NOUN
ejpam-2666	618	44	,	,	PUNCT
ejpam-2666	618	45	g∗1	g∗1	PROPN
ejpam-2666	618	46	)	)	PUNCT
ejpam-2666	618	47	(	(	PUNCT
ejpam-2666	618	48	b	b	X
ejpam-2666	618	49	,	,	PUNCT
ejpam-2666	618	50	l	l	NOUN
ejpam-2666	618	51	,	,	PUNCT
ejpam-2666	618	52	g1)∗	g1)∗	NOUN
ejpam-2666	618	53	,	,	PUNCT
ejpam-2666	618	54	a∗	a∗	PROPN
ejpam-2666	618	55	(	(	PUNCT
ejpam-2666	618	56	a	a	PRON
ejpam-2666	618	57	,	,	PUNCT
ejpam-2666	618	58	g2)∗	g2)∗	ADJ
ejpam-2666	618	59	)	)	PUNCT
ejpam-2666	618	60	)	)	PUNCT
ejpam-2666	618	61	and	and	CCONJ
ejpam-2666	618	62	λ2	λ2	NOUN
ejpam-2666	618	63	=	=	SYM
ejpam-2666	618	64	(	(	PUNCT
ejpam-2666	618	65	g∗2	g∗2	NOUN
ejpam-2666	618	66	(	(	PUNCT
ejpam-2666	618	67	a	a	PRON
ejpam-2666	618	68	,	,	PUNCT
ejpam-2666	618	69	g2)∗	g2)∗	ADJ
ejpam-2666	618	70	)	)	PUNCT
ejpam-2666	618	71	−1	−1	NOUN
ejpam-2666	618	72	b∗	b∗	ADJ
ejpam-2666	618	73	(	(	PUNCT
ejpam-2666	618	74	b	b	NOUN
ejpam-2666	618	75	,	,	PUNCT
ejpam-2666	618	76	l	l	NOUN
ejpam-2666	618	77	,	,	PUNCT
ejpam-2666	618	78	g1)∗	g1)∗	VERB
ejpam-2666	618	79	x2m+deg(g2)−deg(g3	x2m+deg(g2)−deg(g3	NOUN
ejpam-2666	618	80	)	)	PUNCT
ejpam-2666	618	81	(	(	PUNCT
ejpam-2666	618	82	mod	mod	PROPN
ejpam-2666	618	83	a∗	a∗	PROPN
ejpam-2666	618	84	(	(	PUNCT
ejpam-2666	618	85	a	a	PRON
ejpam-2666	618	86	,	,	PUNCT
ejpam-2666	618	87	g2)∗	g2)∗	ADJ
ejpam-2666	618	88	)	)	PUNCT
ejpam-2666	618	89	.	.	PUNCT
ejpam-2666	619	1	(	(	PUNCT
ejpam-2666	619	2	v	v	NOUN
ejpam-2666	619	3	)	)	PUNCT
ejpam-2666	619	4	l̂	l̂	VERB
ejpam-2666	620	1	b∗	b∗	ADJ
ejpam-2666	620	2	=	=	SYM
ejpam-2666	620	3	β(xr	β(xr	PROPN
ejpam-2666	621	1	−	−	NOUN
ejpam-2666	621	2	1	1	NUM
ejpam-2666	621	3	)	)	PUNCT
ejpam-2666	621	4	,	,	PUNCT
ejpam-2666	621	5	where	where	SCONJ
ejpam-2666	621	6	β	β	X
ejpam-2666	621	7	=	=	SYM
ejpam-2666	621	8	(	(	PUNCT
ejpam-2666	621	9	l∗	l∗	PROPN
ejpam-2666	621	10	(	(	PUNCT
ejpam-2666	621	11	b	b	NOUN
ejpam-2666	621	12	,	,	PUNCT
ejpam-2666	621	13	l	l	NOUN
ejpam-2666	621	14	,	,	PUNCT
ejpam-2666	621	15	g1)∗	g1)∗	NOUN
ejpam-2666	621	16	)	)	PUNCT
ejpam-2666	621	17	−1	−1	NOUN
ejpam-2666	621	18	a∗	a∗	NOUN
ejpam-2666	621	19	(	(	PUNCT
ejpam-2666	621	20	a	a	DET
ejpam-2666	621	21	,	,	PUNCT
ejpam-2666	621	22	g2)∗	g2)∗	ADJ
ejpam-2666	621	23	xm+deg(l)−deg(a	xm+deg(l)−deg(a	PROPN
ejpam-2666	621	24	)	)	PUNCT
ejpam-2666	621	25	(	(	PUNCT
ejpam-2666	621	26	mod	mod	X
ejpam-2666	621	27	(	(	PUNCT
ejpam-2666	621	28	b	b	NOUN
ejpam-2666	621	29	,	,	PUNCT
ejpam-2666	621	30	g1)∗	g1)∗	NOUN
ejpam-2666	621	31	(	(	PUNCT
ejpam-2666	621	32	b	b	NOUN
ejpam-2666	621	33	,	,	PUNCT
ejpam-2666	621	34	l	l	NOUN
ejpam-2666	621	35	,	,	PUNCT
ejpam-2666	621	36	g1)∗	g1)∗	NOUN
ejpam-2666	621	37	)	)	PUNCT
ejpam-2666	621	38	.	.	PUNCT
ejpam-2666	622	1	srinivasulu	srinivasulu	PROPN
ejpam-2666	622	2	b	b	NUM
ejpam-2666	622	3	,	,	PUNCT
ejpam-2666	622	4	maheshanand	maheshanand	NOUN
ejpam-2666	622	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	622	6	/	/	SYM
ejpam-2666	622	7	eur	eur	PROPN
ejpam-2666	622	8	.	.	PUNCT
ejpam-2666	623	1	j.	j.	PROPN
ejpam-2666	623	2	pure	pure	PROPN
ejpam-2666	623	3	appl	appl	PROPN
ejpam-2666	623	4	.	.	PROPN
ejpam-2666	623	5	math	math	PROPN
ejpam-2666	623	6	,	,	PUNCT
ejpam-2666	623	7	10	10	NUM
ejpam-2666	623	8	(	(	PUNCT
ejpam-2666	623	9	2	2	NUM
ejpam-2666	623	10	)	)	PUNCT
ejpam-2666	623	11	(	(	PUNCT
ejpam-2666	623	12	2017	2017	NUM
ejpam-2666	623	13	)	)	PUNCT
ejpam-2666	623	14	,	,	PUNCT
ejpam-2666	623	15	392	392	NUM
ejpam-2666	623	16	-	-	SYM
ejpam-2666	623	17	409	409	NUM
ejpam-2666	623	18	406	406	NUM
ejpam-2666	623	19	example	example	NOUN
ejpam-2666	623	20	2	2	NUM
ejpam-2666	623	21	.	.	PUNCT
ejpam-2666	624	1	let	let	VERB
ejpam-2666	624	2	r	r	NOUN
ejpam-2666	624	3	=	=	SYM
ejpam-2666	624	4	10	10	NUM
ejpam-2666	624	5	,	,	PUNCT
ejpam-2666	624	6	s	s	PART
ejpam-2666	624	7	=	=	SYM
ejpam-2666	624	8	12	12	NUM
ejpam-2666	624	9	and	and	CCONJ
ejpam-2666	624	10	t	t	NOUN
ejpam-2666	624	11	=	=	SYM
ejpam-2666	624	12	15	15	X
ejpam-2666	624	13	.	.	PUNCT
ejpam-2666	625	1	let	let	VERB
ejpam-2666	625	2	c	c	NOUN
ejpam-2666	625	3	=	=	SYM
ejpam-2666	625	4	〈	〈	PROPN
ejpam-2666	625	5	(	(	PUNCT
ejpam-2666	625	6	b	b	NOUN
ejpam-2666	625	7	|	|	NOUN
ejpam-2666	625	8	0	0	NUM
ejpam-2666	626	1	|	|	NOUN
ejpam-2666	626	2	0	0	NUM
ejpam-2666	626	3	)	)	PUNCT
ejpam-2666	626	4	,	,	PUNCT
ejpam-2666	627	1	(	(	PUNCT
ejpam-2666	627	2	l	l	NOUN
ejpam-2666	627	3	|	|	ADV
ejpam-2666	627	4	a	a	DET
ejpam-2666	627	5	|	|	NOUN
ejpam-2666	627	6	0	0	NUM
ejpam-2666	627	7	)	)	PUNCT
ejpam-2666	627	8	,	,	PUNCT
ejpam-2666	627	9	(	(	PUNCT
ejpam-2666	627	10	g1	g1	VERB
ejpam-2666	627	11	|	|	ADV
ejpam-2666	627	12	g2	g2	PROPN
ejpam-2666	627	13	|	|	CCONJ
ejpam-2666	627	14	g3	g3	PROPN
ejpam-2666	627	15	)	)	PUNCT
ejpam-2666	627	16	〉	〉	PROPN
ejpam-2666	627	17	,	,	PUNCT
ejpam-2666	627	18	where	where	SCONJ
ejpam-2666	627	19	b	b	NOUN
ejpam-2666	627	20	=	=	SYM
ejpam-2666	627	21	x6	x6	PROPN
ejpam-2666	627	22	+	+	CCONJ
ejpam-2666	627	23	x5	x5	NOUN
ejpam-2666	627	24	+	+	CCONJ
ejpam-2666	627	25	x+	x+	PROPN
ejpam-2666	627	26	1	1	NUM
ejpam-2666	627	27	,	,	PUNCT
ejpam-2666	627	28	l	l	NOUN
ejpam-2666	627	29	=	=	SYM
ejpam-2666	627	30	x5	x5	PROPN
ejpam-2666	627	31	+	+	CCONJ
ejpam-2666	627	32	1	1	NUM
ejpam-2666	627	33	,	,	PUNCT
ejpam-2666	627	34	a	a	DET
ejpam-2666	627	35	=	=	SYM
ejpam-2666	627	36	x6	x6	PROPN
ejpam-2666	627	37	+	+	CCONJ
ejpam-2666	627	38	1	1	NUM
ejpam-2666	627	39	,	,	PUNCT
ejpam-2666	627	40	g1	g1	NOUN
ejpam-2666	627	41	=	=	SYM
ejpam-2666	627	42	x5	x5	PROPN
ejpam-2666	628	1	+	+	CCONJ
ejpam-2666	628	2	1	1	NUM
ejpam-2666	628	3	,	,	PUNCT
ejpam-2666	628	4	g2	g2	PROPN
ejpam-2666	628	5	=	=	SYM
ejpam-2666	628	6	x5	x5	PROPN
ejpam-2666	628	7	+	+	CCONJ
ejpam-2666	628	8	x4	x4	PROPN
ejpam-2666	629	1	+	+	CCONJ
ejpam-2666	629	2	x2	x2	PROPN
ejpam-2666	629	3	+	+	CCONJ
ejpam-2666	629	4	x	x	NOUN
ejpam-2666	629	5	and	and	CCONJ
ejpam-2666	629	6	g3	g3	PROPN
ejpam-2666	629	7	=	=	SYM
ejpam-2666	629	8	x12	x12	PROPN
ejpam-2666	630	1	+	+	NUM
ejpam-2666	630	2	x9	x9	NOUN
ejpam-2666	630	3	+	+	CCONJ
ejpam-2666	630	4	x6	x6	PROPN
ejpam-2666	630	5	+	+	CCONJ
ejpam-2666	630	6	x5	x5	PROPN
ejpam-2666	630	7	+	+	CCONJ
ejpam-2666	630	8	x4	x4	PROPN
ejpam-2666	631	1	+	+	CCONJ
ejpam-2666	631	2	x2	x2	PROPN
ejpam-2666	632	1	+	+	CCONJ
ejpam-2666	632	2	x+	x+	ADJ
ejpam-2666	632	3	1	1	X
ejpam-2666	632	4	.	.	X
ejpam-2666	632	5	c	c	NOUN
ejpam-2666	632	6	satisfies	satisfy	VERB
ejpam-2666	632	7	all	all	DET
ejpam-2666	632	8	the	the	DET
ejpam-2666	632	9	conditions	condition	NOUN
ejpam-2666	632	10	given	give	VERB
ejpam-2666	632	11	in	in	ADP
ejpam-2666	632	12	lemma	lemma	PROPN
ejpam-2666	632	13	1	1	NUM
ejpam-2666	632	14	and	and	CCONJ
ejpam-2666	632	15	lemma	lemma	PROPN
ejpam-2666	632	16	2	2	NUM
ejpam-2666	632	17	.	.	PUNCT
ejpam-2666	633	1	therefore	therefore	ADV
ejpam-2666	633	2	,	,	PUNCT
ejpam-2666	633	3	c	c	PROPN
ejpam-2666	633	4	is	be	AUX
ejpam-2666	633	5	a	a	DET
ejpam-2666	633	6	z2	z2	ADJ
ejpam-2666	633	7	-	-	PUNCT
ejpam-2666	633	8	triple	triple	ADJ
ejpam-2666	633	9	cyclic	cyclic	ADJ
ejpam-2666	633	10	code	code	NOUN
ejpam-2666	633	11	of	of	ADP
ejpam-2666	633	12	block	block	NOUN
ejpam-2666	633	13	length	length	NOUN
ejpam-2666	633	14	(	(	PUNCT
ejpam-2666	633	15	10	10	NUM
ejpam-2666	633	16	,	,	PUNCT
ejpam-2666	633	17	12	12	NUM
ejpam-2666	633	18	,	,	PUNCT
ejpam-2666	633	19	15	15	NUM
ejpam-2666	633	20	)	)	PUNCT
ejpam-2666	633	21	.	.	PUNCT
ejpam-2666	634	1	also	also	ADV
ejpam-2666	634	2	,	,	PUNCT
ejpam-2666	634	3	s	s	PART
ejpam-2666	634	4	=	=	NOUN
ejpam-2666	634	5	s1	s1	PROPN
ejpam-2666	634	6	∪	∪	ADP
ejpam-2666	634	7	s2	s2	PROPN
ejpam-2666	634	8	∪	∪	ADP
ejpam-2666	634	9	s3	s3	PROPN
ejpam-2666	634	10	forms	form	NOUN
ejpam-2666	634	11	a	a	DET
ejpam-2666	634	12	generating	generate	VERB
ejpam-2666	634	13	set	set	NOUN
ejpam-2666	634	14	for	for	ADP
ejpam-2666	634	15	c	c	NOUN
ejpam-2666	634	16	,	,	PUNCT
ejpam-2666	634	17	where	where	SCONJ
ejpam-2666	634	18	s1	s1	NOUN
ejpam-2666	634	19	=	=	SYM
ejpam-2666	634	20	∪3i=0x	∪3i=0x	PROPN
ejpam-2666	634	21	i(x6	i(x6	NOUN
ejpam-2666	634	22	+	+	CCONJ
ejpam-2666	634	23	x5	x5	NOUN
ejpam-2666	634	24	+	+	CCONJ
ejpam-2666	634	25	x+	x+	SYM
ejpam-2666	634	26	1	1	NUM
ejpam-2666	634	27	|	|	NOUN
ejpam-2666	634	28	0	0	NUM
ejpam-2666	635	1	|	|	NOUN
ejpam-2666	635	2	0	0	NUM
ejpam-2666	635	3	)	)	PUNCT
ejpam-2666	636	1	,	,	PUNCT
ejpam-2666	636	2	s2	s2	NOUN
ejpam-2666	636	3	=	=	PUNCT
ejpam-2666	636	4	∪5i=0x	∪5i=0x	PROPN
ejpam-2666	636	5	i(x5	i(x5	ADJ
ejpam-2666	636	6	+	+	CCONJ
ejpam-2666	636	7	1	1	NUM
ejpam-2666	636	8	|	|	ADV
ejpam-2666	636	9	x6	x6	NUM
ejpam-2666	636	10	+	+	CCONJ
ejpam-2666	636	11	1	1	NUM
ejpam-2666	636	12	|	|	ADV
ejpam-2666	636	13	0	0	NUM
ejpam-2666	636	14	)	)	PUNCT
ejpam-2666	636	15	and	and	CCONJ
ejpam-2666	636	16	s3	s3	PROPN
ejpam-2666	636	17	=	=	SYM
ejpam-2666	636	18	∪2i=0x	∪2i=0x	PROPN
ejpam-2666	636	19	i(x5	i(x5	ADP
ejpam-2666	636	20	+	+	CCONJ
ejpam-2666	636	21	1	1	NUM
ejpam-2666	636	22	|	|	NOUN
ejpam-2666	636	23	x5	x5	PROPN
ejpam-2666	636	24	+	+	CCONJ
ejpam-2666	636	25	x4	x4	PROPN
ejpam-2666	637	1	+	+	CCONJ
ejpam-2666	637	2	x2	x2	PROPN
ejpam-2666	638	1	+	+	CCONJ
ejpam-2666	638	2	x	x	SYM
ejpam-2666	638	3	|	|	ADV
ejpam-2666	638	4	x12	x12	NUM
ejpam-2666	638	5	+	+	NUM
ejpam-2666	638	6	x9	x9	NOUN
ejpam-2666	638	7	+	+	CCONJ
ejpam-2666	638	8	x6	x6	PROPN
ejpam-2666	638	9	+	+	CCONJ
ejpam-2666	638	10	x5	x5	PROPN
ejpam-2666	638	11	+	+	CCONJ
ejpam-2666	638	12	x4	x4	PROPN
ejpam-2666	639	1	+	+	CCONJ
ejpam-2666	639	2	x2	x2	PROPN
ejpam-2666	640	1	+	+	CCONJ
ejpam-2666	640	2	x+	x+	ADJ
ejpam-2666	640	3	1	1	NUM
ejpam-2666	640	4	)	)	PUNCT
ejpam-2666	640	5	.	.	PUNCT
ejpam-2666	641	1	the	the	DET
ejpam-2666	641	2	cardinality	cardinality	NOUN
ejpam-2666	641	3	of	of	ADP
ejpam-2666	641	4	c	c	PROPN
ejpam-2666	641	5	is	be	AUX
ejpam-2666	641	6	213	213	NUM
ejpam-2666	641	7	.	.	PUNCT
ejpam-2666	642	1	a	a	DET
ejpam-2666	642	2	generator	generator	NOUN
ejpam-2666	642	3	matrix	matrix	NOUN
ejpam-2666	642	4	of	of	ADP
ejpam-2666	642	5	c	c	PROPN
ejpam-2666	642	6	is	be	AUX
ejpam-2666	642	7	g	g	NOUN
ejpam-2666	642	8	=	=	PUNCT
ejpam-2666	642	9			NOUN
ejpam-2666	642	10	1100011000	1100011000	NUM
ejpam-2666	642	11	000000000000	000000000000	NUM
ejpam-2666	642	12	000000000000000	000000000000000	NUM
ejpam-2666	642	13	0110001100	0110001100	NUM
ejpam-2666	642	14	000000000000	000000000000	NUM
ejpam-2666	642	15	000000000000000	000000000000000	NUM
ejpam-2666	642	16	0011000110	0011000110	NUM
ejpam-2666	642	17	000000000000	000000000000	NUM
ejpam-2666	642	18	000000000000000	000000000000000	NUM
ejpam-2666	642	19	0001100011	0001100011	NUM
ejpam-2666	642	20	000000000000	000000000000	NUM
ejpam-2666	642	21	000000000000000	000000000000000	NUM
ejpam-2666	642	22	1000010000	1000010000	NUM
ejpam-2666	642	23	100000100000	100000100000	NUM
ejpam-2666	642	24	000000000000000	000000000000000	NUM
ejpam-2666	642	25	0100001000	0100001000	NUM
ejpam-2666	642	26	010000010000	010000010000	NUM
ejpam-2666	642	27	000000000000000	000000000000000	NUM
ejpam-2666	642	28	0010000100	0010000100	NUM
ejpam-2666	642	29	001000001000	001000001000	NUM
ejpam-2666	642	30	000000000000000	000000000000000	NUM
ejpam-2666	643	1	0001000010	0001000010	NUM
ejpam-2666	643	2	000100000100	000100000100	NUM
ejpam-2666	643	3	000000000000000	000000000000000	NUM
ejpam-2666	643	4	0000100001	0000100001	NUM
ejpam-2666	643	5	000010000010	000010000010	NUM
ejpam-2666	643	6	000000000000000	000000000000000	NUM
ejpam-2666	643	7	1000010000	1000010000	NUM
ejpam-2666	643	8	000001000001	000001000001	NUM
ejpam-2666	643	9	000000000000000	000000000000000	NUM
ejpam-2666	643	10	1000010000	1000010000	NUM
ejpam-2666	643	11	011011000000	011011000000	NUM
ejpam-2666	643	12	111011100100100	111011100100100	NUM
ejpam-2666	643	13	0100001000	0100001000	NUM
ejpam-2666	643	14	001101100000	001101100000	NUM
ejpam-2666	643	15	011101110010010	011101110010010	NUM
ejpam-2666	643	16	0010000100	0010000100	NUM
ejpam-2666	643	17	000110110000	000110110000	NUM
ejpam-2666	643	18	001110111001001	001110111001001	NUM
ejpam-2666	643	19			NOUN
ejpam-2666	643	20	.	.	PUNCT
ejpam-2666	644	1	further	far	ADV
ejpam-2666	644	2	,	,	PUNCT
ejpam-2666	644	3	the	the	DET
ejpam-2666	644	4	minimum	minimum	ADJ
ejpam-2666	644	5	hamming	hamming	NOUN
ejpam-2666	644	6	distance	distance	NOUN
ejpam-2666	644	7	of	of	ADP
ejpam-2666	644	8	c	c	PROPN
ejpam-2666	644	9	is	be	AUX
ejpam-2666	644	10	4	4	NUM
ejpam-2666	644	11	and	and	CCONJ
ejpam-2666	644	12	therefore	therefore	ADV
ejpam-2666	644	13	,	,	PUNCT
ejpam-2666	644	14	c	c	PROPN
ejpam-2666	644	15	is	be	AUX
ejpam-2666	644	16	a	a	PRON
ejpam-2666	644	17	[	[	X
ejpam-2666	644	18	37	37	NUM
ejpam-2666	644	19	,	,	PUNCT
ejpam-2666	644	20	13	13	NUM
ejpam-2666	644	21	,	,	PUNCT
ejpam-2666	644	22	4	4	NUM
ejpam-2666	644	23	]	]	SYM
ejpam-2666	644	24	binary	binary	ADJ
ejpam-2666	644	25	linear	linear	PROPN
ejpam-2666	644	26	code	code	PROPN
ejpam-2666	644	27	.	.	PUNCT
ejpam-2666	645	1	from	from	ADP
ejpam-2666	645	2	theorem	theorem	ADJ
ejpam-2666	645	3	15	15	NUM
ejpam-2666	645	4	,	,	PUNCT
ejpam-2666	645	5	we	we	PRON
ejpam-2666	645	6	have	have	VERB
ejpam-2666	645	7	the	the	DET
ejpam-2666	645	8	dual	dual	ADJ
ejpam-2666	645	9	code	code	NOUN
ejpam-2666	645	10	of	of	ADP
ejpam-2666	645	11	c	c	PROPN
ejpam-2666	645	12	as	as	ADP
ejpam-2666	645	13	c⊥	c⊥	PROPN
ejpam-2666	645	14	=	=	SYM
ejpam-2666	645	15	〈	〈	PROPN
ejpam-2666	645	16	(	(	PUNCT
ejpam-2666	645	17	b̂	b̂	NOUN
ejpam-2666	645	18	|	|	ADV
ejpam-2666	645	19	0	0	NUM
ejpam-2666	646	1	|	|	NOUN
ejpam-2666	646	2	0	0	NUM
ejpam-2666	646	3	)	)	PUNCT
ejpam-2666	647	1	,	,	PUNCT
ejpam-2666	647	2	(	(	PUNCT
ejpam-2666	647	3	l̂	l̂	X
ejpam-2666	647	4	|	|	ADV
ejpam-2666	647	5	â	â	X
ejpam-2666	647	6	|	|	NOUN
ejpam-2666	647	7	0	0	NUM
ejpam-2666	647	8	)	)	PUNCT
ejpam-2666	647	9	,	,	PUNCT
ejpam-2666	647	10	(	(	PUNCT
ejpam-2666	647	11	ĝ1	ĝ1	NOUN
ejpam-2666	647	12	|	|	ADV
ejpam-2666	647	13	ĝ2	ĝ2	NOUN
ejpam-2666	647	14	|	|	ADV
ejpam-2666	647	15	ĝ3	ĝ3	PROPN
ejpam-2666	647	16	)	)	PUNCT
ejpam-2666	647	17	〉	〉	PROPN
ejpam-2666	647	18	,	,	PUNCT
ejpam-2666	647	19	where	where	SCONJ
ejpam-2666	647	20	b̂	b̂	NOUN
ejpam-2666	647	21	=	=	SYM
ejpam-2666	647	22	(	(	PUNCT
ejpam-2666	647	23	x	x	SYM
ejpam-2666	647	24	+	+	PUNCT
ejpam-2666	647	25	1)(x4	1)(x4	ADJ
ejpam-2666	647	26	+	+	X
ejpam-2666	647	27	x3	x3	ADJ
ejpam-2666	647	28	+	+	CCONJ
ejpam-2666	648	1	x2	x2	PROPN
ejpam-2666	649	1	+	+	CCONJ
ejpam-2666	649	2	x	x	SYM
ejpam-2666	649	3	+	+	ADJ
ejpam-2666	649	4	1	1	NUM
ejpam-2666	649	5	)	)	PUNCT
ejpam-2666	649	6	,	,	PUNCT
ejpam-2666	649	7	â	â	X
ejpam-2666	649	8	=	=	PUNCT
ejpam-2666	649	9	(	(	PUNCT
ejpam-2666	649	10	x	x	SYM
ejpam-2666	649	11	+	+	NUM
ejpam-2666	649	12	1)(x2	1)(x2	NOUN
ejpam-2666	650	1	+	+	CCONJ
ejpam-2666	650	2	x	x	SYM
ejpam-2666	650	3	+	+	NUM
ejpam-2666	650	4	1)3	1)3	NUM
ejpam-2666	650	5	,	,	PUNCT
ejpam-2666	650	6	ĝ3	ĝ3	PUNCT
ejpam-2666	651	1	=	=	PUNCT
ejpam-2666	651	2	x+	x+	ADJ
ejpam-2666	651	3	1	1	NUM
ejpam-2666	651	4	,	,	PUNCT
ejpam-2666	651	5	ĝ1	ĝ1	NOUN
ejpam-2666	651	6	=	=	PUNCT
ejpam-2666	652	1	l̂	l̂	X
ejpam-2666	652	2	=	=	SYM
ejpam-2666	652	3	0	0	NUM
ejpam-2666	652	4	and	and	CCONJ
ejpam-2666	652	5	ĝ2	ĝ2	NOUN
ejpam-2666	652	6	=	=	SYM
ejpam-2666	652	7	(	(	PUNCT
ejpam-2666	652	8	x+	x+	ADJ
ejpam-2666	652	9	1)(x2	1)(x2	NOUN
ejpam-2666	653	1	+	+	CCONJ
ejpam-2666	653	2	x+	x+	PROPN
ejpam-2666	653	3	1)2	1)2	NUM
ejpam-2666	653	4	.	.	PUNCT
ejpam-2666	654	1	let	let	VERB
ejpam-2666	654	2	t	t	NOUN
ejpam-2666	654	3	=	=	SYM
ejpam-2666	654	4	0	0	X
ejpam-2666	654	5	.	.	PUNCT
ejpam-2666	655	1	then	then	ADV
ejpam-2666	655	2	by	by	ADP
ejpam-2666	655	3	taking	take	VERB
ejpam-2666	655	4	g1	g1	NOUN
ejpam-2666	655	5	=	=	SYM
ejpam-2666	655	6	g2	g2	PROPN
ejpam-2666	655	7	=	=	SYM
ejpam-2666	655	8	g3	g3	PROPN
ejpam-2666	655	9	=	=	SYM
ejpam-2666	655	10	0	0	NUM
ejpam-2666	655	11	,	,	PUNCT
ejpam-2666	655	12	we	we	PRON
ejpam-2666	655	13	have	have	VERB
ejpam-2666	655	14	(	(	PUNCT
ejpam-2666	655	15	b	b	NOUN
ejpam-2666	655	16	,	,	PUNCT
ejpam-2666	655	17	l	l	NOUN
ejpam-2666	655	18	,	,	PUNCT
ejpam-2666	655	19	g1	g1	NOUN
ejpam-2666	655	20	)	)	PUNCT
ejpam-2666	655	21	=	=	SYM
ejpam-2666	655	22	(	(	PUNCT
ejpam-2666	655	23	b	b	NOUN
ejpam-2666	655	24	,	,	PUNCT
ejpam-2666	655	25	l	l	NOUN
ejpam-2666	655	26	)	)	PUNCT
ejpam-2666	655	27	and	and	CCONJ
ejpam-2666	655	28	(	(	PUNCT
ejpam-2666	655	29	b	b	NOUN
ejpam-2666	655	30	,	,	PUNCT
ejpam-2666	655	31	g1	g1	NOUN
ejpam-2666	655	32	)	)	PUNCT
ejpam-2666	656	1	=	=	SYM
ejpam-2666	656	2	b	b	NOUN
ejpam-2666	656	3	and	and	CCONJ
ejpam-2666	656	4	hence	hence	ADV
ejpam-2666	656	5	from	from	ADP
ejpam-2666	656	6	theorem	theorem	ADJ
ejpam-2666	656	7	(	(	PUNCT
ejpam-2666	656	8	15	15	NUM
ejpam-2666	656	9	)	)	PUNCT
ejpam-2666	656	10	,	,	PUNCT
ejpam-2666	656	11	we	we	PRON
ejpam-2666	656	12	see	see	VERB
ejpam-2666	656	13	that	that	SCONJ
ejpam-2666	656	14	z2	z2	NUM
ejpam-2666	656	15	-	-	PUNCT
ejpam-2666	656	16	double	double	ADJ
ejpam-2666	656	17	cyclic	cyclic	NOUN
ejpam-2666	656	18	codes	code	NOUN
ejpam-2666	656	19	are	be	AUX
ejpam-2666	656	20	special	special	ADJ
ejpam-2666	656	21	case	case	NOUN
ejpam-2666	656	22	of	of	ADP
ejpam-2666	656	23	the	the	DET
ejpam-2666	656	24	family	family	NOUN
ejpam-2666	656	25	of	of	ADP
ejpam-2666	656	26	codes	code	NOUN
ejpam-2666	656	27	that	that	SCONJ
ejpam-2666	656	28	we	we	PRON
ejpam-2666	656	29	are	be	AUX
ejpam-2666	656	30	considering	consider	VERB
ejpam-2666	656	31	when	when	SCONJ
ejpam-2666	656	32	t	t	PROPN
ejpam-2666	656	33	=	=	SYM
ejpam-2666	656	34	0	0	NUM
ejpam-2666	656	35	.	.	PUNCT
ejpam-2666	657	1	thus	thus	ADV
ejpam-2666	657	2	we	we	PRON
ejpam-2666	657	3	have	have	VERB
ejpam-2666	657	4	the	the	DET
ejpam-2666	657	5	following	follow	VERB
ejpam-2666	657	6	result	result	NOUN
ejpam-2666	657	7	.	.	PUNCT
ejpam-2666	658	1	corollary	corollary	ADJ
ejpam-2666	658	2	1	1	NUM
ejpam-2666	658	3	.	.	PUNCT
ejpam-2666	659	1	let	let	VERB
ejpam-2666	659	2	c	c	NOUN
ejpam-2666	659	3	=	=	SYM
ejpam-2666	659	4	〈	〈	PROPN
ejpam-2666	659	5	(	(	PUNCT
ejpam-2666	659	6	b	b	NOUN
ejpam-2666	659	7	|	|	NOUN
ejpam-2666	659	8	0	0	NUM
ejpam-2666	660	1	|	|	NOUN
ejpam-2666	660	2	0	0	NUM
ejpam-2666	660	3	)	)	PUNCT
ejpam-2666	660	4	,	,	PUNCT
ejpam-2666	661	1	(	(	PUNCT
ejpam-2666	661	2	l	l	NOUN
ejpam-2666	661	3	|	|	ADV
ejpam-2666	661	4	a	a	DET
ejpam-2666	661	5	|	|	NOUN
ejpam-2666	661	6	0	0	NUM
ejpam-2666	661	7	)	)	PUNCT
ejpam-2666	661	8	〉	〉	NOUN
ejpam-2666	661	9	be	be	AUX
ejpam-2666	661	10	a	a	DET
ejpam-2666	661	11	z2	z2	ADJ
ejpam-2666	661	12	-	-	PUNCT
ejpam-2666	661	13	double	double	ADJ
ejpam-2666	661	14	cyclic	cyclic	NOUN
ejpam-2666	661	15	code	code	NOUN
ejpam-2666	661	16	of	of	ADP
ejpam-2666	661	17	block	block	NOUN
ejpam-2666	661	18	length	length	NOUN
ejpam-2666	661	19	(	(	PUNCT
ejpam-2666	661	20	r	r	NOUN
ejpam-2666	661	21	,	,	PUNCT
ejpam-2666	661	22	s	s	PART
ejpam-2666	661	23	)	)	PUNCT
ejpam-2666	661	24	and	and	CCONJ
ejpam-2666	661	25	c⊥	c⊥	X
ejpam-2666	662	1	=	=	SYM
ejpam-2666	662	2	〈	〈	PROPN
ejpam-2666	662	3	(	(	PUNCT
ejpam-2666	662	4	b̂	b̂	NOUN
ejpam-2666	662	5	|	|	ADV
ejpam-2666	662	6	0	0	NUM
ejpam-2666	663	1	|	|	NOUN
ejpam-2666	663	2	0	0	NUM
ejpam-2666	663	3	)	)	PUNCT
ejpam-2666	664	1	,	,	PUNCT
ejpam-2666	664	2	(	(	PUNCT
ejpam-2666	664	3	l̂	l̂	X
ejpam-2666	664	4	|	|	ADV
ejpam-2666	664	5	â	â	ADP
ejpam-2666	664	6	|	|	NOUN
ejpam-2666	664	7	0	0	NUM
ejpam-2666	664	8	)	)	PUNCT
ejpam-2666	664	9	〉	〉	NOUN
ejpam-2666	664	10	be	be	AUX
ejpam-2666	664	11	the	the	DET
ejpam-2666	664	12	dual	dual	ADJ
ejpam-2666	664	13	code	code	NOUN
ejpam-2666	664	14	of	of	ADP
ejpam-2666	664	15	c.	c.	PROPN
ejpam-2666	664	16	then	then	ADV
ejpam-2666	664	17	(	(	PUNCT
ejpam-2666	664	18	i	i	NOUN
ejpam-2666	664	19	)	)	PUNCT
ejpam-2666	664	20	b̂	b̂	NOUN
ejpam-2666	665	1	=	=	SYM
ejpam-2666	665	2	xr−1	xr−1	PROPN
ejpam-2666	665	3	(	(	PUNCT
ejpam-2666	665	4	b	b	NOUN
ejpam-2666	665	5	,	,	PUNCT
ejpam-2666	665	6	l)∗	l)∗	NOUN
ejpam-2666	665	7	;	;	PUNCT
ejpam-2666	665	8	(	(	PUNCT
ejpam-2666	665	9	ii	ii	NOUN
ejpam-2666	665	10	)	)	PUNCT
ejpam-2666	665	11	â	â	X
ejpam-2666	665	12	a∗b∗	a∗b∗	NOUN
ejpam-2666	666	1	=	=	SYM
ejpam-2666	666	2	(	(	PUNCT
ejpam-2666	666	3	xs	xs	PROPN
ejpam-2666	666	4	−	−	PROPN
ejpam-2666	666	5	1)(b	1)(b	PROPN
ejpam-2666	666	6	,	,	PUNCT
ejpam-2666	666	7	l)∗	l)∗	PROPN
ejpam-2666	666	8	;	;	PUNCT
ejpam-2666	666	9	(	(	PUNCT
ejpam-2666	666	10	iii	iii	NOUN
ejpam-2666	666	11	)	)	PUNCT
ejpam-2666	666	12	l̂	l̂	VERB
ejpam-2666	666	13	b∗	b∗	ADJ
ejpam-2666	666	14	=	=	SYM
ejpam-2666	666	15	β(xr	β(xr	PROPN
ejpam-2666	666	16	−	−	NOUN
ejpam-2666	666	17	1	1	NUM
ejpam-2666	666	18	)	)	PUNCT
ejpam-2666	666	19	,	,	PUNCT
ejpam-2666	666	20	where	where	SCONJ
ejpam-2666	666	21	β	β	X
ejpam-2666	666	22	=	=	SYM
ejpam-2666	666	23	(	(	PUNCT
ejpam-2666	666	24	l∗	l∗	PROPN
ejpam-2666	666	25	(	(	PUNCT
ejpam-2666	666	26	b	b	NOUN
ejpam-2666	666	27	,	,	PUNCT
ejpam-2666	666	28	l)∗	l)∗	NOUN
ejpam-2666	666	29	)	)	PUNCT
ejpam-2666	666	30	−1	−1	NOUN
ejpam-2666	666	31	xm−deg(a)+deg(l	xm−deg(a)+deg(l	PROPN
ejpam-2666	666	32	)	)	PUNCT
ejpam-2666	666	33	(	(	PUNCT
ejpam-2666	666	34	mod	mod	X
ejpam-2666	666	35	(	(	PUNCT
ejpam-2666	666	36	b∗	b∗	ADJ
ejpam-2666	666	37	(	(	PUNCT
ejpam-2666	666	38	b	b	NOUN
ejpam-2666	666	39	,	,	PUNCT
ejpam-2666	666	40	l)∗	l)∗	NOUN
ejpam-2666	666	41	)	)	PUNCT
ejpam-2666	666	42	)	)	PUNCT
ejpam-2666	666	43	.	.	PUNCT
ejpam-2666	667	1	let	let	VERB
ejpam-2666	667	2	c	c	NOUN
ejpam-2666	667	3	=	=	SYM
ejpam-2666	667	4	〈	〈	PROPN
ejpam-2666	667	5	(	(	PUNCT
ejpam-2666	667	6	b	b	NOUN
ejpam-2666	667	7	|	|	NOUN
ejpam-2666	667	8	0	0	NUM
ejpam-2666	668	1	|	|	NOUN
ejpam-2666	668	2	0	0	NUM
ejpam-2666	668	3	)	)	PUNCT
ejpam-2666	668	4	,	,	PUNCT
ejpam-2666	669	1	(	(	PUNCT
ejpam-2666	669	2	l	l	NOUN
ejpam-2666	669	3	|	|	ADV
ejpam-2666	669	4	a	a	DET
ejpam-2666	669	5	|	|	NOUN
ejpam-2666	669	6	0	0	NUM
ejpam-2666	669	7	)	)	PUNCT
ejpam-2666	669	8	,	,	PUNCT
ejpam-2666	669	9	(	(	PUNCT
ejpam-2666	669	10	g1	g1	VERB
ejpam-2666	669	11	|	|	ADV
ejpam-2666	669	12	g2	g2	PROPN
ejpam-2666	669	13	|	|	CCONJ
ejpam-2666	669	14	g3	g3	PROPN
ejpam-2666	669	15	)	)	PUNCT
ejpam-2666	669	16	〉	〉	PROPN
ejpam-2666	669	17	be	be	AUX
ejpam-2666	669	18	a	a	DET
ejpam-2666	669	19	z2	z2	ADJ
ejpam-2666	669	20	-	-	PUNCT
ejpam-2666	669	21	triple	triple	ADJ
ejpam-2666	669	22	cyclic	cyclic	ADJ
ejpam-2666	669	23	code	code	NOUN
ejpam-2666	669	24	of	of	ADP
ejpam-2666	669	25	block	block	NOUN
ejpam-2666	669	26	length	length	NOUN
ejpam-2666	669	27	(	(	PUNCT
ejpam-2666	669	28	r	r	NOUN
ejpam-2666	669	29	,	,	PUNCT
ejpam-2666	669	30	s	s	PROPN
ejpam-2666	669	31	,	,	PUNCT
ejpam-2666	669	32	t	t	PROPN
ejpam-2666	669	33	)	)	PUNCT
ejpam-2666	669	34	as	as	ADP
ejpam-2666	669	35	in	in	ADP
ejpam-2666	669	36	theorem	theorem	NOUN
ejpam-2666	669	37	(	(	PUNCT
ejpam-2666	669	38	3	3	NUM
ejpam-2666	669	39	)	)	PUNCT
ejpam-2666	669	40	.	.	PUNCT
ejpam-2666	670	1	if	if	SCONJ
ejpam-2666	670	2	b|l	b|l	PROPN
ejpam-2666	670	3	,	,	PUNCT
ejpam-2666	670	4	b|g1	b|g1	PROPN
ejpam-2666	670	5	and	and	CCONJ
ejpam-2666	670	6	a|g2	a|g2	PROPN
ejpam-2666	670	7	,	,	PUNCT
ejpam-2666	670	8	then	then	ADV
ejpam-2666	670	9	c	c	X
ejpam-2666	670	10	=	=	SYM
ejpam-2666	670	11	〈	〈	PROPN
ejpam-2666	670	12	(	(	PUNCT
ejpam-2666	670	13	b	b	NOUN
ejpam-2666	670	14	|	|	NOUN
ejpam-2666	670	15	0	0	NUM
ejpam-2666	670	16	|	|	NOUN
ejpam-2666	670	17	0	0	NUM
ejpam-2666	670	18	)	)	PUNCT
ejpam-2666	670	19	,	,	PUNCT
ejpam-2666	670	20	(	(	PUNCT
ejpam-2666	670	21	0	0	NUM
ejpam-2666	670	22	|	|	ADV
ejpam-2666	670	23	a	a	DET
ejpam-2666	670	24	|	|	NOUN
ejpam-2666	670	25	0	0	NUM
ejpam-2666	670	26	)	)	PUNCT
ejpam-2666	670	27	,	,	PUNCT
ejpam-2666	670	28	(	(	PUNCT
ejpam-2666	670	29	0	0	NUM
ejpam-2666	671	1	|	|	NOUN
ejpam-2666	671	2	0	0	NUM
ejpam-2666	671	3	|	|	CCONJ
ejpam-2666	671	4	g3	g3	PROPN
ejpam-2666	671	5	)	)	PUNCT
ejpam-2666	671	6	〉	〉	PROPN
ejpam-2666	671	7	.	.	PUNCT
ejpam-2666	672	1	we	we	PRON
ejpam-2666	672	2	note	note	VERB
ejpam-2666	672	3	that	that	SCONJ
ejpam-2666	672	4	cr	cr	PROPN
ejpam-2666	672	5	=	=	PUNCT
ejpam-2666	672	6	〈	〈	PROPN
ejpam-2666	672	7	b	b	PROPN
ejpam-2666	672	8	〉	〉	PROPN
ejpam-2666	672	9	,	,	PUNCT
ejpam-2666	672	10	cs	cs	PROPN
ejpam-2666	672	11	=	=	SYM
ejpam-2666	672	12	〈	〈	PROPN
ejpam-2666	672	13	a	a	DET
ejpam-2666	672	14	〉	〉	NOUN
ejpam-2666	672	15	and	and	CCONJ
ejpam-2666	672	16	ct	ct	NOUN
ejpam-2666	672	17	=	=	SYM
ejpam-2666	672	18	〈	〈	PROPN
ejpam-2666	672	19	g3	g3	PROPN
ejpam-2666	672	20	〉	〉	PROPN
ejpam-2666	672	21	and	and	CCONJ
ejpam-2666	672	22	c	c	NOUN
ejpam-2666	672	23	=	=	SYM
ejpam-2666	672	24	cr	cr	PROPN
ejpam-2666	672	25	×	×	PROPN
ejpam-2666	672	26	cs	cs	PROPN
ejpam-2666	673	1	×	×	PROPN
ejpam-2666	673	2	ct	ct	PROPN
ejpam-2666	673	3	.	.	PUNCT
ejpam-2666	674	1	hence	hence	ADV
ejpam-2666	674	2	c	c	PROPN
ejpam-2666	674	3	is	be	AUX
ejpam-2666	674	4	srinivasulu	srinivasulu	ADV
ejpam-2666	674	5	b	b	NUM
ejpam-2666	674	6	,	,	PUNCT
ejpam-2666	674	7	maheshanand	maheshanand	NOUN
ejpam-2666	674	8	bhaintwal	bhaintwal	NOUN
ejpam-2666	674	9	/	/	SYM
ejpam-2666	674	10	eur	eur	PROPN
ejpam-2666	674	11	.	.	PUNCT
ejpam-2666	675	1	j.	j.	PROPN
ejpam-2666	675	2	pure	pure	PROPN
ejpam-2666	675	3	appl	appl	PROPN
ejpam-2666	675	4	.	.	PROPN
ejpam-2666	675	5	math	math	PROPN
ejpam-2666	675	6	,	,	PUNCT
ejpam-2666	675	7	10	10	NUM
ejpam-2666	675	8	(	(	PUNCT
ejpam-2666	675	9	2	2	NUM
ejpam-2666	675	10	)	)	PUNCT
ejpam-2666	675	11	(	(	PUNCT
ejpam-2666	675	12	2017	2017	NUM
ejpam-2666	675	13	)	)	PUNCT
ejpam-2666	675	14	,	,	PUNCT
ejpam-2666	675	15	392	392	NUM
ejpam-2666	675	16	-	-	SYM
ejpam-2666	675	17	409	409	NUM
ejpam-2666	675	18	407	407	NUM
ejpam-2666	675	19	separable	separable	NOUN
ejpam-2666	675	20	.	.	PUNCT
ejpam-2666	676	1	a	a	DET
ejpam-2666	676	2	generator	generator	NOUN
ejpam-2666	676	3	matrix	matrix	NOUN
ejpam-2666	676	4	of	of	ADP
ejpam-2666	676	5	c	c	PROPN
ejpam-2666	676	6	is	be	AUX
ejpam-2666	676	7	permutation	permutation	NOUN
ejpam-2666	676	8	equivalent	equivalent	ADJ
ejpam-2666	676	9	to	to	ADP
ejpam-2666	676	10	the	the	DET
ejpam-2666	676	11	matrix	matrix	NOUN
ejpam-2666	676	12	g	g	NOUN
ejpam-2666	676	13	=	=	PUNCT
ejpam-2666	676	14			PROPN
ejpam-2666	676	15	ir−deg(b	ir−deg(b	PROPN
ejpam-2666	676	16	)	)	PUNCT
ejpam-2666	676	17	a	a	DET
ejpam-2666	676	18	0	0	NUM
ejpam-2666	676	19	0	0	NUM
ejpam-2666	676	20	0	0	NUM
ejpam-2666	676	21	0	0	NUM
ejpam-2666	676	22	0	0	NUM
ejpam-2666	676	23	0	0	NUM
ejpam-2666	676	24	is−deg(a	is−deg(a	PROPN
ejpam-2666	676	25	)	)	PUNCT
ejpam-2666	676	26	b	b	NOUN
ejpam-2666	676	27	0	0	NUM
ejpam-2666	676	28	0	0	NUM
ejpam-2666	676	29	0	0	NUM
ejpam-2666	676	30	0	0	NUM
ejpam-2666	676	31	0	0	NUM
ejpam-2666	676	32	0	0	PUNCT
ejpam-2666	676	33	c	c	PROPN
ejpam-2666	676	34	it−deg(g3	it−deg(g3	NOUN
ejpam-2666	676	35	)	)	PUNCT
ejpam-2666	676	36			PROPN
ejpam-2666	676	37	.	.	PUNCT
ejpam-2666	677	1	the	the	DET
ejpam-2666	677	2	following	follow	VERB
ejpam-2666	677	3	theorem	theorem	NOUN
ejpam-2666	677	4	shows	show	VERB
ejpam-2666	677	5	that	that	SCONJ
ejpam-2666	677	6	the	the	DET
ejpam-2666	677	7	dual	dual	NOUN
ejpam-2666	677	8	of	of	ADP
ejpam-2666	677	9	a	a	DET
ejpam-2666	677	10	separable	separable	ADJ
ejpam-2666	677	11	z2	z2	ADJ
ejpam-2666	677	12	-	-	PUNCT
ejpam-2666	677	13	triple	triple	ADJ
ejpam-2666	677	14	cyclic	cyclic	ADJ
ejpam-2666	677	15	code	code	NOUN
ejpam-2666	677	16	is	be	AUX
ejpam-2666	677	17	also	also	ADV
ejpam-2666	677	18	separable	separable	ADJ
ejpam-2666	677	19	.	.	PUNCT
ejpam-2666	678	1	theorem	theorem	VERB
ejpam-2666	678	2	16	16	NUM
ejpam-2666	678	3	.	.	PUNCT
ejpam-2666	679	1	let	let	VERB
ejpam-2666	679	2	c	c	NOUN
ejpam-2666	679	3	=	=	SYM
ejpam-2666	679	4	〈	〈	PROPN
ejpam-2666	679	5	(	(	PUNCT
ejpam-2666	679	6	b	b	NOUN
ejpam-2666	679	7	|	|	NOUN
ejpam-2666	679	8	0	0	NUM
ejpam-2666	680	1	|	|	NOUN
ejpam-2666	680	2	0	0	NUM
ejpam-2666	680	3	)	)	PUNCT
ejpam-2666	681	1	,	,	PUNCT
ejpam-2666	681	2	(	(	PUNCT
ejpam-2666	681	3	0	0	NUM
ejpam-2666	681	4	|	|	ADV
ejpam-2666	681	5	a	a	DET
ejpam-2666	681	6	|	|	NOUN
ejpam-2666	681	7	0	0	NUM
ejpam-2666	681	8	)	)	PUNCT
ejpam-2666	681	9	,	,	PUNCT
ejpam-2666	681	10	(	(	PUNCT
ejpam-2666	681	11	0	0	NUM
ejpam-2666	682	1	|	|	NOUN
ejpam-2666	682	2	0	0	NUM
ejpam-2666	682	3	|	|	CCONJ
ejpam-2666	682	4	g3	g3	NOUN
ejpam-2666	682	5	)	)	PUNCT
ejpam-2666	682	6	〉	〉	PROPN
ejpam-2666	682	7	be	be	AUX
ejpam-2666	682	8	a	a	DET
ejpam-2666	682	9	separable	separable	ADJ
ejpam-2666	682	10	z2	z2	NUM
ejpam-2666	682	11	-	-	PUNCT
ejpam-2666	682	12	triple	triple	ADJ
ejpam-2666	682	13	cyclic	cyclic	ADJ
ejpam-2666	682	14	code	code	NOUN
ejpam-2666	682	15	of	of	ADP
ejpam-2666	682	16	block	block	NOUN
ejpam-2666	682	17	length	length	NOUN
ejpam-2666	682	18	(	(	PUNCT
ejpam-2666	682	19	r	r	NOUN
ejpam-2666	682	20	,	,	PUNCT
ejpam-2666	682	21	s	s	PROPN
ejpam-2666	682	22	,	,	PUNCT
ejpam-2666	682	23	t	t	PROPN
ejpam-2666	682	24	)	)	PUNCT
ejpam-2666	682	25	.	.	PUNCT
ejpam-2666	683	1	then	then	ADV
ejpam-2666	683	2	(	(	PUNCT
ejpam-2666	683	3	i	i	NOUN
ejpam-2666	683	4	)	)	PUNCT
ejpam-2666	683	5	c⊥	c⊥	PROPN
ejpam-2666	683	6	is	be	AUX
ejpam-2666	683	7	also	also	ADV
ejpam-2666	683	8	a	a	DET
ejpam-2666	683	9	separable	separable	ADJ
ejpam-2666	683	10	z2	z2	ADJ
ejpam-2666	683	11	-	-	PUNCT
ejpam-2666	683	12	triple	triple	ADJ
ejpam-2666	683	13	cyclic	cyclic	ADJ
ejpam-2666	683	14	code	code	NOUN
ejpam-2666	683	15	of	of	ADP
ejpam-2666	683	16	block	block	NOUN
ejpam-2666	683	17	length	length	NOUN
ejpam-2666	683	18	(	(	PUNCT
ejpam-2666	683	19	r	r	NOUN
ejpam-2666	683	20	,	,	PUNCT
ejpam-2666	683	21	s	s	PROPN
ejpam-2666	683	22	,	,	PUNCT
ejpam-2666	683	23	t	t	PROPN
ejpam-2666	683	24	)	)	PUNCT
ejpam-2666	683	25	,	,	PUNCT
ejpam-2666	683	26	(	(	PUNCT
ejpam-2666	683	27	ii	ii	NOUN
ejpam-2666	683	28	)	)	PUNCT
ejpam-2666	683	29	c⊥	c⊥	PROPN
ejpam-2666	684	1	=	=	SYM
ejpam-2666	684	2	〈	〈	PROPN
ejpam-2666	684	3	(	(	PUNCT
ejpam-2666	684	4	xr−1	xr−1	PROPN
ejpam-2666	684	5	b	b	PROPN
ejpam-2666	685	1	|	|	NOUN
ejpam-2666	685	2	0	0	NUM
ejpam-2666	686	1	|	|	ADV
ejpam-2666	686	2	0	0	NUM
ejpam-2666	686	3	)	)	PUNCT
ejpam-2666	687	1	,	,	PUNCT
ejpam-2666	687	2	(	(	PUNCT
ejpam-2666	687	3	0	0	NUM
ejpam-2666	687	4	|	|	ADV
ejpam-2666	687	5	xs−1a	xs−1a	PROPN
ejpam-2666	688	1	|	|	ADV
ejpam-2666	688	2	0	0	NUM
ejpam-2666	688	3	)	)	PUNCT
ejpam-2666	689	1	,	,	PUNCT
ejpam-2666	689	2	(	(	PUNCT
ejpam-2666	689	3	0	0	NUM
ejpam-2666	689	4	|	|	NOUN
ejpam-2666	689	5	0	0	NUM
ejpam-2666	690	1	|	|	ADV
ejpam-2666	690	2	xt−1g3	xt−1g3	PROPN
ejpam-2666	690	3	)	)	PUNCT
ejpam-2666	690	4	〉	〉	NOUN
ejpam-2666	690	5	,	,	PUNCT
ejpam-2666	690	6	and	and	CCONJ
ejpam-2666	690	7	(	(	PUNCT
ejpam-2666	690	8	iii	iii	NOUN
ejpam-2666	690	9	)	)	PUNCT
ejpam-2666	690	10	dmin(c	dmin(c	NOUN
ejpam-2666	690	11	)	)	PUNCT
ejpam-2666	690	12	=	=	SYM
ejpam-2666	690	13	min{dmin(cr	min{dmin(cr	PROPN
ejpam-2666	690	14	)	)	PUNCT
ejpam-2666	690	15	,	,	PUNCT
ejpam-2666	690	16	dmin(cs	dmin(cs	PROPN
ejpam-2666	690	17	)	)	PUNCT
ejpam-2666	690	18	,	,	PUNCT
ejpam-2666	690	19	dmin(ct	dmin(ct	NOUN
ejpam-2666	690	20	)	)	PUNCT
ejpam-2666	690	21	}	}	PUNCT
ejpam-2666	690	22	.	.	PUNCT
ejpam-2666	691	1	proof	proof	NOUN
ejpam-2666	691	2	.	.	PUNCT
ejpam-2666	692	1	as	as	ADP
ejpam-2666	692	2	l	l	NOUN
ejpam-2666	692	3	=	=	PUNCT
ejpam-2666	692	4	g1	g1	NOUN
ejpam-2666	692	5	=	=	SYM
ejpam-2666	692	6	g2	g2	PROPN
ejpam-2666	692	7	=	=	SYM
ejpam-2666	692	8	0	0	PROPN
ejpam-2666	692	9	,	,	PUNCT
ejpam-2666	692	10	the	the	DET
ejpam-2666	692	11	proof	proof	NOUN
ejpam-2666	692	12	follows	follow	VERB
ejpam-2666	692	13	from	from	ADP
ejpam-2666	692	14	theorem	theorem	ADJ
ejpam-2666	692	15	15	15	NUM
ejpam-2666	692	16	.	.	PUNCT
ejpam-2666	692	17	remark	remark	NOUN
ejpam-2666	692	18	2	2	NUM
ejpam-2666	692	19	.	.	PUNCT
ejpam-2666	693	1	if	if	SCONJ
ejpam-2666	693	2	c	c	PROPN
ejpam-2666	693	3	is	be	AUX
ejpam-2666	693	4	a	a	DET
ejpam-2666	693	5	non	non	ADJ
ejpam-2666	693	6	-	-	ADJ
ejpam-2666	693	7	separable	separable	ADJ
ejpam-2666	693	8	z2	z2	ADJ
ejpam-2666	693	9	-	-	PUNCT
ejpam-2666	693	10	triple	triple	ADJ
ejpam-2666	693	11	cyclic	cyclic	ADJ
ejpam-2666	693	12	code	code	NOUN
ejpam-2666	693	13	of	of	ADP
ejpam-2666	693	14	block	block	NOUN
ejpam-2666	693	15	length	length	NOUN
ejpam-2666	693	16	(	(	PUNCT
ejpam-2666	693	17	r	r	NOUN
ejpam-2666	693	18	,	,	PUNCT
ejpam-2666	693	19	s	s	PROPN
ejpam-2666	693	20	,	,	PUNCT
ejpam-2666	693	21	t	t	PROPN
ejpam-2666	693	22	)	)	PUNCT
ejpam-2666	693	23	,	,	PUNCT
ejpam-2666	693	24	then	then	ADV
ejpam-2666	693	25	dmin(c	dmin(c	PROPN
ejpam-2666	693	26	)	)	PUNCT
ejpam-2666	693	27	≥	≥	PROPN
ejpam-2666	693	28	min{dmin(cr	min{dmin(cr	PROPN
ejpam-2666	693	29	)	)	PUNCT
ejpam-2666	693	30	,	,	PUNCT
ejpam-2666	693	31	dmin(cs	dmin(cs	PROPN
ejpam-2666	693	32	)	)	PUNCT
ejpam-2666	693	33	,	,	PUNCT
ejpam-2666	693	34	dmin(ct	dmin(ct	NOUN
ejpam-2666	693	35	)	)	PUNCT
ejpam-2666	693	36	}	}	PUNCT
ejpam-2666	693	37	.	.	PUNCT
ejpam-2666	694	1	example	example	NOUN
ejpam-2666	695	1	3	3	X
ejpam-2666	695	2	.	.	PUNCT
ejpam-2666	695	3	let	let	VERB
ejpam-2666	695	4	r	r	NOUN
ejpam-2666	695	5	=	=	SYM
ejpam-2666	695	6	6	6	NUM
ejpam-2666	695	7	,	,	PUNCT
ejpam-2666	695	8	s	s	PART
ejpam-2666	695	9	=	=	SYM
ejpam-2666	695	10	4	4	NUM
ejpam-2666	695	11	and	and	CCONJ
ejpam-2666	695	12	t	t	NOUN
ejpam-2666	696	1	=	=	SYM
ejpam-2666	696	2	5	5	X
ejpam-2666	696	3	.	.	PUNCT
ejpam-2666	696	4	let	let	VERB
ejpam-2666	696	5	c	c	NOUN
ejpam-2666	696	6	=	=	SYM
ejpam-2666	696	7	〈	〈	PROPN
ejpam-2666	696	8	(	(	PUNCT
ejpam-2666	696	9	b	b	NOUN
ejpam-2666	696	10	|	|	NOUN
ejpam-2666	696	11	0	0	NUM
ejpam-2666	697	1	|	|	NOUN
ejpam-2666	697	2	0	0	NUM
ejpam-2666	697	3	)	)	PUNCT
ejpam-2666	698	1	,	,	PUNCT
ejpam-2666	698	2	(	(	PUNCT
ejpam-2666	698	3	0	0	NUM
ejpam-2666	698	4	|	|	ADV
ejpam-2666	698	5	a	a	DET
ejpam-2666	698	6	|	|	NOUN
ejpam-2666	698	7	0	0	NUM
ejpam-2666	698	8	)	)	PUNCT
ejpam-2666	698	9	,	,	PUNCT
ejpam-2666	698	10	(	(	PUNCT
ejpam-2666	698	11	0	0	NUM
ejpam-2666	699	1	|	|	NOUN
ejpam-2666	699	2	0	0	NUM
ejpam-2666	699	3	|	|	CCONJ
ejpam-2666	699	4	g3	g3	PROPN
ejpam-2666	699	5	)	)	PUNCT
ejpam-2666	699	6	〉	〉	PROPN
ejpam-2666	699	7	,	,	PUNCT
ejpam-2666	699	8	where	where	SCONJ
ejpam-2666	699	9	b	b	X
ejpam-2666	699	10	=	=	PRON
ejpam-2666	699	11	(	(	PUNCT
ejpam-2666	699	12	x	x	SYM
ejpam-2666	699	13	+	+	NUM
ejpam-2666	699	14	1)(x2	1)(x2	NOUN
ejpam-2666	700	1	+	+	CCONJ
ejpam-2666	700	2	x	x	PUNCT
ejpam-2666	701	1	+	+	NUM
ejpam-2666	701	2	1)2	1)2	NUM
ejpam-2666	701	3	,	,	PUNCT
ejpam-2666	701	4	a	a	PRON
ejpam-2666	701	5	=	=	X
ejpam-2666	701	6	(	(	PUNCT
ejpam-2666	701	7	x	x	PROPN
ejpam-2666	701	8	+	+	CCONJ
ejpam-2666	701	9	1)3	1)3	PROPN
ejpam-2666	701	10	and	and	CCONJ
ejpam-2666	701	11	g3	g3	PROPN
ejpam-2666	701	12	=	=	SYM
ejpam-2666	701	13	x4	x4	PROPN
ejpam-2666	702	1	+	+	CCONJ
ejpam-2666	702	2	x3	x3	ADJ
ejpam-2666	702	3	+	+	CCONJ
ejpam-2666	702	4	x2	x2	PROPN
ejpam-2666	703	1	+	+	CCONJ
ejpam-2666	703	2	x	x	SYM
ejpam-2666	703	3	+	+	NUM
ejpam-2666	703	4	1	1	X
ejpam-2666	703	5	.	.	PUNCT
ejpam-2666	704	1	then	then	ADV
ejpam-2666	704	2	c	c	PROPN
ejpam-2666	704	3	is	be	AUX
ejpam-2666	704	4	a	a	DET
ejpam-2666	704	5	z2	z2	ADJ
ejpam-2666	704	6	-	-	PUNCT
ejpam-2666	704	7	triple	triple	ADJ
ejpam-2666	704	8	cyclic	cyclic	ADJ
ejpam-2666	704	9	code	code	NOUN
ejpam-2666	704	10	of	of	ADP
ejpam-2666	704	11	block	block	NOUN
ejpam-2666	704	12	length	length	NOUN
ejpam-2666	704	13	(	(	PUNCT
ejpam-2666	704	14	6	6	NUM
ejpam-2666	704	15	,	,	PUNCT
ejpam-2666	704	16	4	4	NUM
ejpam-2666	704	17	,	,	PUNCT
ejpam-2666	704	18	5	5	NUM
ejpam-2666	704	19	)	)	PUNCT
ejpam-2666	704	20	.	.	PUNCT
ejpam-2666	705	1	the	the	DET
ejpam-2666	705	2	set	set	NOUN
ejpam-2666	705	3	s	s	PART
ejpam-2666	705	4	=	=	X
ejpam-2666	705	5	{	{	PUNCT
ejpam-2666	705	6	(	(	PUNCT
ejpam-2666	705	7	x5	x5	NOUN
ejpam-2666	705	8	+	+	CCONJ
ejpam-2666	705	9	x4	x4	PROPN
ejpam-2666	705	10	+	+	CCONJ
ejpam-2666	705	11	x3	x3	ADJ
ejpam-2666	705	12	+	+	CCONJ
ejpam-2666	705	13	x2	x2	PROPN
ejpam-2666	706	1	+	+	CCONJ
ejpam-2666	706	2	x+	x+	SYM
ejpam-2666	706	3	1	1	NUM
ejpam-2666	706	4	|	|	NOUN
ejpam-2666	706	5	0	0	NUM
ejpam-2666	707	1	|	|	ADV
ejpam-2666	707	2	0	0	NUM
ejpam-2666	707	3	)	)	PUNCT
ejpam-2666	708	1	,	,	PUNCT
ejpam-2666	708	2	(	(	PUNCT
ejpam-2666	708	3	0	0	NUM
ejpam-2666	708	4	|	|	ADV
ejpam-2666	708	5	x3	x3	VERB
ejpam-2666	708	6	+	+	CCONJ
ejpam-2666	708	7	x2	x2	PROPN
ejpam-2666	709	1	+	+	CCONJ
ejpam-2666	709	2	x	x	SYM
ejpam-2666	709	3	+	+	NUM
ejpam-2666	709	4	1	1	NUM
ejpam-2666	709	5	|	|	ADV
ejpam-2666	709	6	0	0	NUM
ejpam-2666	709	7	)	)	PUNCT
ejpam-2666	710	1	,	,	PUNCT
ejpam-2666	710	2	(	(	PUNCT
ejpam-2666	710	3	0	0	NUM
ejpam-2666	710	4	|	|	NOUN
ejpam-2666	710	5	0	0	NUM
ejpam-2666	710	6	|	|	ADV
ejpam-2666	711	1	x4	x4	PROPN
ejpam-2666	712	1	+	+	CCONJ
ejpam-2666	712	2	x3	x3	ADJ
ejpam-2666	712	3	+	+	CCONJ
ejpam-2666	712	4	x2	x2	PROPN
ejpam-2666	713	1	+	+	CCONJ
ejpam-2666	713	2	x	x	SYM
ejpam-2666	713	3	+	+	ADJ
ejpam-2666	713	4	1	1	NUM
ejpam-2666	713	5	)	)	PUNCT
ejpam-2666	713	6	}	}	PUNCT
ejpam-2666	713	7	forms	form	VERB
ejpam-2666	713	8	a	a	DET
ejpam-2666	713	9	generating	generate	VERB
ejpam-2666	713	10	set	set	NOUN
ejpam-2666	713	11	for	for	ADP
ejpam-2666	713	12	c.	c.	PROPN
ejpam-2666	713	13	the	the	DET
ejpam-2666	713	14	cardinality	cardinality	NOUN
ejpam-2666	713	15	of	of	ADP
ejpam-2666	713	16	c	c	PROPN
ejpam-2666	713	17	is	be	AUX
ejpam-2666	713	18	23	23	NUM
ejpam-2666	713	19	.	.	PUNCT
ejpam-2666	714	1	further	far	ADV
ejpam-2666	714	2	,	,	PUNCT
ejpam-2666	714	3	the	the	DET
ejpam-2666	714	4	minimum	minimum	ADJ
ejpam-2666	714	5	hamming	hamming	NOUN
ejpam-2666	714	6	distance	distance	NOUN
ejpam-2666	714	7	of	of	ADP
ejpam-2666	714	8	c	c	PROPN
ejpam-2666	714	9	is	be	AUX
ejpam-2666	714	10	4	4	NUM
ejpam-2666	714	11	and	and	CCONJ
ejpam-2666	714	12	therefore	therefore	ADV
ejpam-2666	714	13	c	c	PROPN
ejpam-2666	714	14	is	be	AUX
ejpam-2666	714	15	a	a	DET
ejpam-2666	714	16	[	[	X
ejpam-2666	714	17	15	15	NUM
ejpam-2666	714	18	,	,	PUNCT
ejpam-2666	714	19	3	3	NUM
ejpam-2666	714	20	,	,	PUNCT
ejpam-2666	714	21	4	4	NUM
ejpam-2666	714	22	]	]	X
ejpam-2666	714	23	binary	binary	ADJ
ejpam-2666	714	24	linear	linear	PROPN
ejpam-2666	714	25	code	code	PROPN
ejpam-2666	714	26	with	with	ADP
ejpam-2666	714	27	the	the	DET
ejpam-2666	714	28	hamming	hamming	NOUN
ejpam-2666	714	29	weight	weight	NOUN
ejpam-2666	714	30	distribution	distribution	NOUN
ejpam-2666	715	1	[	[	X
ejpam-2666	715	2	<	<	X
ejpam-2666	715	3	0	0	NUM
ejpam-2666	715	4	,	,	PUNCT
ejpam-2666	715	5	1	1	NUM
ejpam-2666	715	6	>	>	PUNCT
ejpam-2666	715	7	,	,	PUNCT
ejpam-2666	715	8	<	<	X
ejpam-2666	715	9	4	4	NUM
ejpam-2666	715	10	,	,	PUNCT
ejpam-2666	715	11	1	1	NUM
ejpam-2666	715	12	>	>	PUNCT
ejpam-2666	715	13	,	,	PUNCT
ejpam-2666	715	14	<	<	X
ejpam-2666	715	15	5	5	NUM
ejpam-2666	715	16	,	,	PUNCT
ejpam-2666	715	17	1	1	NUM
ejpam-2666	715	18	>	>	PUNCT
ejpam-2666	715	19	,	,	PUNCT
ejpam-2666	715	20	<	<	X
ejpam-2666	715	21	6	6	NUM
ejpam-2666	715	22	,	,	PUNCT
ejpam-2666	715	23	1	1	NUM
ejpam-2666	715	24	>	>	PUNCT
ejpam-2666	715	25	,	,	PUNCT
ejpam-2666	715	26	<	<	X
ejpam-2666	715	27	9	9	NUM
ejpam-2666	715	28	,	,	PUNCT
ejpam-2666	715	29	1	1	NUM
ejpam-2666	715	30	>	>	PUNCT
ejpam-2666	715	31	,	,	PUNCT
ejpam-2666	715	32	<	<	X
ejpam-2666	715	33	10	10	NUM
ejpam-2666	715	34	,	,	PUNCT
ejpam-2666	715	35	1	1	NUM
ejpam-2666	715	36	>	>	PUNCT
ejpam-2666	715	37	,	,	PUNCT
ejpam-2666	715	38	<	<	X
ejpam-2666	715	39	11	11	NUM
ejpam-2666	715	40	,	,	PUNCT
ejpam-2666	715	41	1	1	NUM
ejpam-2666	715	42	>	>	PUNCT
ejpam-2666	715	43	,	,	PUNCT
ejpam-2666	715	44	<	<	X
ejpam-2666	715	45	15	15	NUM
ejpam-2666	715	46	,	,	PUNCT
ejpam-2666	715	47	1	1	NUM
ejpam-2666	715	48	>	>	PUNCT
ejpam-2666	715	49	]	]	PUNCT
ejpam-2666	715	50	.	.	PUNCT
ejpam-2666	716	1	the	the	DET
ejpam-2666	716	2	dual	dual	ADJ
ejpam-2666	716	3	of	of	ADP
ejpam-2666	716	4	c	c	PROPN
ejpam-2666	716	5	is	be	AUX
ejpam-2666	716	6	also	also	ADV
ejpam-2666	716	7	a	a	DET
ejpam-2666	716	8	separable	separable	ADJ
ejpam-2666	716	9	z2	z2	ADJ
ejpam-2666	716	10	-	-	PUNCT
ejpam-2666	716	11	triple	triple	ADJ
ejpam-2666	716	12	cyclic	cyclic	ADJ
ejpam-2666	716	13	code	code	NOUN
ejpam-2666	716	14	of	of	ADP
ejpam-2666	716	15	block	block	NOUN
ejpam-2666	716	16	length	length	NOUN
ejpam-2666	716	17	(	(	PUNCT
ejpam-2666	716	18	6	6	NUM
ejpam-2666	716	19	,	,	PUNCT
ejpam-2666	716	20	4	4	NUM
ejpam-2666	716	21	,	,	PUNCT
ejpam-2666	716	22	5	5	NUM
ejpam-2666	716	23	)	)	PUNCT
ejpam-2666	717	1	such	such	ADJ
ejpam-2666	717	2	that	that	PRON
ejpam-2666	717	3	c⊥	c⊥	PROPN
ejpam-2666	717	4	=	=	SYM
ejpam-2666	717	5	〈	〈	PROPN
ejpam-2666	717	6	(	(	PUNCT
ejpam-2666	717	7	x+	x+	X
ejpam-2666	717	8	1	1	NUM
ejpam-2666	717	9	|	|	NOUN
ejpam-2666	717	10	0	0	NUM
ejpam-2666	718	1	|	|	ADV
ejpam-2666	718	2	0	0	NUM
ejpam-2666	718	3	)	)	PUNCT
ejpam-2666	719	1	,	,	PUNCT
ejpam-2666	719	2	(	(	PUNCT
ejpam-2666	719	3	0	0	NUM
ejpam-2666	719	4	|	|	ADV
ejpam-2666	719	5	x+	x+	ADJ
ejpam-2666	719	6	1	1	NUM
ejpam-2666	719	7	|	|	NOUN
ejpam-2666	719	8	0	0	NUM
ejpam-2666	719	9	)	)	PUNCT
ejpam-2666	719	10	,	,	PUNCT
ejpam-2666	719	11	(	(	PUNCT
ejpam-2666	719	12	0	0	NUM
ejpam-2666	719	13	|	|	NOUN
ejpam-2666	719	14	0	0	NUM
ejpam-2666	720	1	|	|	ADV
ejpam-2666	720	2	x+	x+	ADJ
ejpam-2666	720	3	1	1	X
ejpam-2666	720	4	)	)	PUNCT
ejpam-2666	720	5	〉	〉	NOUN
ejpam-2666	720	6	with	with	ADP
ejpam-2666	720	7	minimum	minimum	ADJ
ejpam-2666	720	8	hamming	hamming	NOUN
ejpam-2666	720	9	distance	distance	NOUN
ejpam-2666	720	10	2	2	NUM
ejpam-2666	721	1	and	and	CCONJ
ejpam-2666	721	2	therefore	therefore	ADV
ejpam-2666	721	3	it	it	PRON
ejpam-2666	721	4	is	be	AUX
ejpam-2666	721	5	a	a	DET
ejpam-2666	721	6	[	[	X
ejpam-2666	721	7	15	15	NUM
ejpam-2666	721	8	,	,	PUNCT
ejpam-2666	721	9	12	12	NUM
ejpam-2666	721	10	,	,	PUNCT
ejpam-2666	721	11	2	2	NUM
ejpam-2666	721	12	]	]	X
ejpam-2666	721	13	binary	binary	PROPN
ejpam-2666	721	14	code	code	PROPN
ejpam-2666	721	15	.	.	PUNCT
ejpam-2666	722	1	4	4	X
ejpam-2666	722	2	.	.	X
ejpam-2666	722	3	conclusion	conclusion	NOUN
ejpam-2666	722	4	in	in	ADP
ejpam-2666	722	5	this	this	DET
ejpam-2666	722	6	paper	paper	NOUN
ejpam-2666	722	7	we	we	PRON
ejpam-2666	722	8	have	have	AUX
ejpam-2666	722	9	considered	consider	VERB
ejpam-2666	722	10	z2	z2	NUM
ejpam-2666	722	11	-	-	PUNCT
ejpam-2666	722	12	triple	triple	ADJ
ejpam-2666	722	13	cyclic	cyclic	ADJ
ejpam-2666	722	14	codes	code	NOUN
ejpam-2666	722	15	of	of	ADP
ejpam-2666	722	16	block	block	NOUN
ejpam-2666	722	17	length	length	NOUN
ejpam-2666	722	18	(	(	PUNCT
ejpam-2666	722	19	r	r	NOUN
ejpam-2666	722	20	,	,	PUNCT
ejpam-2666	722	21	s	s	PROPN
ejpam-2666	722	22	,	,	PUNCT
ejpam-2666	722	23	t	t	PROPN
ejpam-2666	722	24	)	)	PUNCT
ejpam-2666	722	25	.	.	PUNCT
ejpam-2666	723	1	we	we	PRON
ejpam-2666	723	2	have	have	AUX
ejpam-2666	723	3	studied	study	VERB
ejpam-2666	723	4	the	the	DET
ejpam-2666	723	5	structure	structure	NOUN
ejpam-2666	723	6	these	these	DET
ejpam-2666	723	7	codes	code	NOUN
ejpam-2666	723	8	and	and	CCONJ
ejpam-2666	723	9	determined	determine	VERB
ejpam-2666	723	10	the	the	DET
ejpam-2666	723	11	form	form	NOUN
ejpam-2666	723	12	of	of	ADP
ejpam-2666	723	13	their	their	PRON
ejpam-2666	723	14	generators	generator	NOUN
ejpam-2666	723	15	of	of	ADP
ejpam-2666	723	16	these	these	DET
ejpam-2666	723	17	codes	code	NOUN
ejpam-2666	723	18	.	.	PUNCT
ejpam-2666	724	1	we	we	PRON
ejpam-2666	724	2	have	have	AUX
ejpam-2666	724	3	determined	determine	VERB
ejpam-2666	724	4	the	the	DET
ejpam-2666	724	5	size	size	NOUN
ejpam-2666	724	6	of	of	ADP
ejpam-2666	724	7	z2	z2	NOUN
ejpam-2666	724	8	-	-	PUNCT
ejpam-2666	724	9	triple	triple	ADJ
ejpam-2666	724	10	cyclic	cyclic	ADJ
ejpam-2666	724	11	codes	code	NOUN
ejpam-2666	724	12	by	by	ADP
ejpam-2666	724	13	giving	give	VERB
ejpam-2666	724	14	a	a	DET
ejpam-2666	724	15	minimal	minimal	ADJ
ejpam-2666	724	16	spanning	span	VERB
ejpam-2666	724	17	set	set	NOUN
ejpam-2666	724	18	.	.	PUNCT
ejpam-2666	725	1	we	we	PRON
ejpam-2666	725	2	also	also	ADV
ejpam-2666	725	3	studied	study	VERB
ejpam-2666	725	4	the	the	DET
ejpam-2666	725	5	relationship	relationship	NOUN
ejpam-2666	725	6	between	between	ADP
ejpam-2666	725	7	the	the	DET
ejpam-2666	725	8	generators	generator	NOUN
ejpam-2666	725	9	of	of	ADP
ejpam-2666	725	10	z2	z2	ADJ
ejpam-2666	725	11	-	-	PUNCT
ejpam-2666	725	12	triple	triple	ADJ
ejpam-2666	725	13	cyclic	cyclic	ADJ
ejpam-2666	725	14	codes	code	NOUN
ejpam-2666	725	15	and	and	CCONJ
ejpam-2666	725	16	their	their	PRON
ejpam-2666	725	17	duals	dual	NOUN
ejpam-2666	725	18	and	and	CCONJ
ejpam-2666	725	19	determined	determine	VERB
ejpam-2666	725	20	the	the	DET
ejpam-2666	725	21	generators	generator	NOUN
ejpam-2666	725	22	for	for	ADP
ejpam-2666	725	23	dual	dual	ADJ
ejpam-2666	725	24	of	of	ADP
ejpam-2666	725	25	a	a	DET
ejpam-2666	725	26	z2	z2	ADJ
ejpam-2666	725	27	-	-	PUNCT
ejpam-2666	725	28	triple	triple	ADJ
ejpam-2666	725	29	cyclic	cyclic	ADJ
ejpam-2666	725	30	code	code	NOUN
ejpam-2666	725	31	.	.	PUNCT
ejpam-2666	726	1	references	reference	NOUN
ejpam-2666	726	2	408	408	NUM
ejpam-2666	726	3	references	reference	NOUN
ejpam-2666	726	4	[	[	X
ejpam-2666	726	5	1	1	NUM
ejpam-2666	726	6	]	]	PUNCT
ejpam-2666	726	7	t.	t.	PROPN
ejpam-2666	726	8	abualrub	abualrub	PROPN
ejpam-2666	726	9	,	,	PUNCT
ejpam-2666	726	10	i.	i.	PROPN
ejpam-2666	726	11	siap	siap	PROPN
ejpam-2666	726	12	and	and	CCONJ
ejpam-2666	726	13	n.	n.	PROPN
ejpam-2666	726	14	aydin	aydin	PROPN
ejpam-2666	726	15	.	.	PUNCT
ejpam-2666	727	1	z2z4	z2z4	X
ejpam-2666	727	2	-	-	ADJ
ejpam-2666	727	3	additive	additive	ADJ
ejpam-2666	727	4	cyclic	cyclic	NOUN
ejpam-2666	727	5	codes	code	NOUN
ejpam-2666	727	6	.	.	PUNCT
ejpam-2666	728	1	ieee	ieee	PROPN
ejpam-2666	728	2	trans	trans	PROPN
ejpam-2666	728	3	.	.	PUNCT
ejpam-2666	729	1	inform	inform	NOUN
ejpam-2666	729	2	.	.	PUNCT
ejpam-2666	730	1	theory	theory	NOUN
ejpam-2666	730	2	,	,	PUNCT
ejpam-2666	730	3	60(3	60(3	NOUN
ejpam-2666	730	4	)	)	PUNCT
ejpam-2666	730	5	:	:	PUNCT
ejpam-2666	731	1	1508−	1508−	NUM
ejpam-2666	731	2	1514	1514	NUM
ejpam-2666	731	3	,	,	PUNCT
ejpam-2666	731	4	2014	2014	NUM
ejpam-2666	731	5	.	.	PUNCT
ejpam-2666	732	1	[	[	X
ejpam-2666	732	2	2	2	NUM
ejpam-2666	732	3	]	]	PUNCT
ejpam-2666	732	4	i.	i.	NOUN
ejpam-2666	732	5	aydogdu	aydogdu	PROPN
ejpam-2666	732	6	and	and	CCONJ
ejpam-2666	732	7	i.	i.	PROPN
ejpam-2666	732	8	siap	siap	PROPN
ejpam-2666	732	9	.	.	PUNCT
ejpam-2666	733	1	zprzps	zprzp	NOUN
ejpam-2666	733	2	-	-	PUNCT
ejpam-2666	733	3	additive	additive	ADJ
ejpam-2666	733	4	codes	code	NOUN
ejpam-2666	733	5	.	.	PUNCT
ejpam-2666	734	1	linear	linear	PROPN
ejpam-2666	734	2	multilinear	multilinear	PROPN
ejpam-2666	734	3	algebra	algebra	PROPN
ejpam-2666	734	4	,	,	PUNCT
ejpam-2666	734	5	63(10	63(10	NOUN
ejpam-2666	734	6	)	)	PUNCT
ejpam-2666	734	7	:	:	PUNCT
ejpam-2666	735	1	2089−	2089−	NUM
ejpam-2666	735	2	2102	2102	NUM
ejpam-2666	735	3	,	,	PUNCT
ejpam-2666	735	4	2014	2014	NUM
ejpam-2666	735	5	.	.	PUNCT
ejpam-2666	736	1	[	[	X
ejpam-2666	736	2	3	3	NUM
ejpam-2666	736	3	]	]	X
ejpam-2666	736	4	i.	i.	NOUN
ejpam-2666	736	5	aydogdu	aydogdu	PROPN
ejpam-2666	736	6	,	,	PUNCT
ejpam-2666	736	7	t.	t.	PROPN
ejpam-2666	736	8	abualrub	abualrub	NOUN
ejpam-2666	736	9	and	and	CCONJ
ejpam-2666	736	10	i.	i.	PROPN
ejpam-2666	736	11	siap	siap	PROPN
ejpam-2666	736	12	.	.	PUNCT
ejpam-2666	737	1	on	on	ADP
ejpam-2666	737	2	z2z2[u]-additive	z2z2[u]-additive	PROPN
ejpam-2666	737	3	codes	code	NOUN
ejpam-2666	737	4	.	.	PUNCT
ejpam-2666	738	1	int	int	NOUN
ejpam-2666	738	2	.	.	PUNCT
ejpam-2666	739	1	j.	j.	PROPN
ejpam-2666	739	2	of	of	ADP
ejpam-2666	739	3	comput	comput	PROPN
ejpam-2666	739	4	.	.	PUNCT
ejpam-2666	740	1	math	math	NOUN
ejpam-2666	740	2	.	.	PUNCT
ejpam-2666	740	3	,	,	PUNCT
ejpam-2666	740	4	92(9	92(9	NUM
ejpam-2666	740	5	)	)	PUNCT
ejpam-2666	740	6	:	:	PUNCT
ejpam-2666	741	1	1806−	1806−	NUM
ejpam-2666	741	2	1814	1814	NUM
ejpam-2666	741	3	,	,	PUNCT
ejpam-2666	741	4	2013	2013	NUM
ejpam-2666	741	5	.	.	PUNCT
ejpam-2666	742	1	[	[	X
ejpam-2666	742	2	4	4	X
ejpam-2666	742	3	]	]	PUNCT
ejpam-2666	742	4	j.	j.	PROPN
ejpam-2666	742	5	borges	borges	PROPN
ejpam-2666	742	6	,	,	PUNCT
ejpam-2666	742	7	c.	c.	PROPN
ejpam-2666	742	8	fernàndez	fernàndez	PROPN
ejpam-2666	742	9	-	-	PUNCT
ejpam-2666	742	10	còrdoba	còrdoba	PROPN
ejpam-2666	742	11	and	and	CCONJ
ejpam-2666	742	12	r.	r.	PROPN
ejpam-2666	742	13	ten	ten	NUM
ejpam-2666	742	14	-	-	PUNCT
ejpam-2666	742	15	valls	vall	NOUN
ejpam-2666	742	16	.	.	PUNCT
ejpam-2666	743	1	z2	z2	ADJ
ejpam-2666	743	2	-	-	PUNCT
ejpam-2666	743	3	double	double	ADJ
ejpam-2666	743	4	cyclic	cyclic	NOUN
ejpam-2666	743	5	codes	code	NOUN
ejpam-2666	743	6	,	,	PUNCT
ejpam-2666	743	7	arxiv	arxiv	PROPN
ejpam-2666	743	8	:	:	PUNCT
ejpam-2666	744	1	1410.5604v1	1410.5604v1	X
ejpam-2666	744	2	.	.	PUNCT
ejpam-2666	745	1	[	[	X
ejpam-2666	745	2	5	5	X
ejpam-2666	745	3	]	]	PUNCT
ejpam-2666	745	4	j.	j.	PROPN
ejpam-2666	745	5	borges	borges	PROPN
ejpam-2666	745	6	,	,	PUNCT
ejpam-2666	745	7	c.	c.	PROPN
ejpam-2666	745	8	fernàndez	fernàndez	PROPN
ejpam-2666	745	9	-	-	PUNCT
ejpam-2666	745	10	còrdoba	còrdoba	PROPN
ejpam-2666	745	11	,	,	PUNCT
ejpam-2666	745	12	j.	j.	PROPN
ejpam-2666	745	13	pujol	pujol	PROPN
ejpam-2666	745	14	,	,	PUNCT
ejpam-2666	745	15	j.	j.	PROPN
ejpam-2666	745	16	rifà	rifà	PROPN
ejpam-2666	745	17	and	and	CCONJ
ejpam-2666	745	18	m.	m.	PROPN
ejpam-2666	745	19	villanueva	villanueva	PROPN
ejpam-2666	745	20	.	.	PUNCT
ejpam-2666	746	1	z2z4	z2z4	ADJ
ejpam-2666	746	2	-	-	ADJ
ejpam-2666	746	3	linear	linear	ADJ
ejpam-2666	746	4	codes	code	NOUN
ejpam-2666	746	5	:	:	PUNCT
ejpam-2666	746	6	generator	generator	NOUN
ejpam-2666	746	7	matrices	matrix	NOUN
ejpam-2666	746	8	and	and	CCONJ
ejpam-2666	746	9	duality	duality	NOUN
ejpam-2666	746	10	,	,	PUNCT
ejpam-2666	746	11	des	des	PROPN
ejpam-2666	746	12	.	.	PROPN
ejpam-2666	746	13	codes	code	NOUN
ejpam-2666	746	14	crypt	crypt	NOUN
ejpam-2666	746	15	.	.	PUNCT
ejpam-2666	746	16	,	,	PUNCT
ejpam-2666	746	17	54(2	54(2	NUM
ejpam-2666	746	18	)	)	PUNCT
ejpam-2666	746	19	:	:	PUNCT
ejpam-2666	746	20	167−	167−	NUM
ejpam-2666	746	21	179	179	NUM
ejpam-2666	746	22	,	,	PUNCT
ejpam-2666	746	23	2009	2009	NUM
ejpam-2666	746	24	.	.	PUNCT
ejpam-2666	747	1	[	[	X
ejpam-2666	747	2	6	6	NUM
ejpam-2666	747	3	]	]	PUNCT
ejpam-2666	747	4	j.	j.	PROPN
ejpam-2666	747	5	borges	borges	PROPN
ejpam-2666	747	6	,	,	PUNCT
ejpam-2666	747	7	c.	c.	PROPN
ejpam-2666	747	8	fernàndez	fernàndez	PROPN
ejpam-2666	747	9	-	-	PUNCT
ejpam-2666	747	10	còrdoba	còrdoba	PROPN
ejpam-2666	747	11	and	and	CCONJ
ejpam-2666	747	12	r.	r.	PROPN
ejpam-2666	747	13	ten	ten	NUM
ejpam-2666	747	14	-	-	PUNCT
ejpam-2666	747	15	valls	vall	NOUN
ejpam-2666	747	16	.	.	PUNCT
ejpam-2666	748	1	z2z4	z2z4	X
ejpam-2666	748	2	-	-	ADJ
ejpam-2666	748	3	additive	additive	ADJ
ejpam-2666	748	4	cyclic	cyclic	NOUN
ejpam-2666	748	5	codes	code	NOUN
ejpam-2666	748	6	,	,	PUNCT
ejpam-2666	748	7	generator	generator	NOUN
ejpam-2666	748	8	polynomials	polynomial	NOUN
ejpam-2666	748	9	and	and	CCONJ
ejpam-2666	748	10	dual	dual	ADJ
ejpam-2666	748	11	codes	code	NOUN
ejpam-2666	748	12	.	.	PUNCT
ejpam-2666	749	1	ieee	ieee	PROPN
ejpam-2666	749	2	trans	trans	PROPN
ejpam-2666	749	3	.	.	PUNCT
ejpam-2666	750	1	inform	inform	NOUN
ejpam-2666	750	2	.	.	PUNCT
ejpam-2666	751	1	theory	theory	NOUN
ejpam-2666	751	2	,	,	PUNCT
ejpam-2666	751	3	62(11	62(11	NUM
ejpam-2666	751	4	)	)	PUNCT
ejpam-2666	751	5	:	:	PUNCT
ejpam-2666	751	6	6348	6348	NUM
ejpam-2666	751	7	−	−	NOUN
ejpam-2666	751	8	6354	6354	NUM
ejpam-2666	751	9	,	,	PUNCT
ejpam-2666	751	10	2016	2016	NUM
ejpam-2666	751	11	.	.	PUNCT
ejpam-2666	752	1	[	[	X
ejpam-2666	752	2	7	7	X
ejpam-2666	752	3	]	]	PUNCT
ejpam-2666	752	4	m.	m.	NOUN
ejpam-2666	752	5	bhaintwal	bhaintwal	NOUN
ejpam-2666	752	6	and	and	CCONJ
ejpam-2666	752	7	s.	s.	PROPN
ejpam-2666	752	8	wasan	wasan	PROPN
ejpam-2666	752	9	.	.	PUNCT
ejpam-2666	753	1	on	on	ADP
ejpam-2666	753	2	quasi	quasi	ADJ
ejpam-2666	753	3	-	-	ADJ
ejpam-2666	753	4	cyclic	cyclic	ADJ
ejpam-2666	753	5	codes	code	NOUN
ejpam-2666	753	6	over	over	ADP
ejpam-2666	753	7	zq	zq	PROPN
ejpam-2666	753	8	.	.	PUNCT
ejpam-2666	753	9	appl	appl	PROPN
ejpam-2666	753	10	.	.	PUNCT
ejpam-2666	754	1	algebra	algebra	PROPN
ejpam-2666	754	2	engrg	engrg	PROPN
ejpam-2666	754	3	.	.	PROPN
ejpam-2666	754	4	comm	comm	NOUN
ejpam-2666	754	5	.	.	PUNCT
ejpam-2666	755	1	comput	comput	NOUN
ejpam-2666	755	2	.	.	PUNCT
ejpam-2666	755	3	,	,	PUNCT
ejpam-2666	755	4	20(5	20(5	NUM
ejpam-2666	755	5	)	)	PUNCT
ejpam-2666	755	6	:	:	PUNCT
ejpam-2666	755	7	459−	459−	NOUN
ejpam-2666	755	8	480	480	NUM
ejpam-2666	755	9	,	,	PUNCT
ejpam-2666	755	10	2009	2009	NUM
ejpam-2666	755	11	.	.	PUNCT
ejpam-2666	756	1	[	[	X
ejpam-2666	756	2	8	8	NUM
ejpam-2666	756	3	]	]	X
ejpam-2666	756	4	y.	y.	PROPN
ejpam-2666	756	5	cao	cao	PROPN
ejpam-2666	756	6	.	.	PUNCT
ejpam-2666	757	1	structural	structural	ADJ
ejpam-2666	757	2	properties	property	NOUN
ejpam-2666	757	3	and	and	CCONJ
ejpam-2666	757	4	enumeration	enumeration	NOUN
ejpam-2666	757	5	of	of	ADP
ejpam-2666	757	6	1	1	NUM
ejpam-2666	757	7	-	-	PUNCT
ejpam-2666	757	8	generator	generator	NOUN
ejpam-2666	757	9	generalized	generalize	VERB
ejpam-2666	757	10	quasi	quasi	ADJ
ejpam-2666	757	11	-	-	ADJ
ejpam-2666	757	12	cyclic	cyclic	ADJ
ejpam-2666	757	13	codes	code	NOUN
ejpam-2666	757	14	.	.	PUNCT
ejpam-2666	758	1	des	des	PROPN
ejpam-2666	758	2	.	.	PROPN
ejpam-2666	758	3	codes	code	NOUN
ejpam-2666	758	4	cryptogr	cryptogr	NOUN
ejpam-2666	758	5	.	.	PUNCT
ejpam-2666	758	6	,	,	PUNCT
ejpam-2666	758	7	60(1	60(1	NUM
ejpam-2666	758	8	)	)	PUNCT
ejpam-2666	758	9	:	:	PUNCT
ejpam-2666	758	10	67−	67−	NOUN
ejpam-2666	758	11	79	79	NUM
ejpam-2666	758	12	,	,	PUNCT
ejpam-2666	758	13	2011	2011	NUM
ejpam-2666	758	14	.	.	PUNCT
ejpam-2666	759	1	[	[	X
ejpam-2666	759	2	9	9	NUM
ejpam-2666	759	3	]	]	X
ejpam-2666	759	4	y.	y.	PROPN
ejpam-2666	759	5	cao	cao	PROPN
ejpam-2666	759	6	.	.	PUNCT
ejpam-2666	760	1	generalized	generalize	VERB
ejpam-2666	760	2	quasi	quasi	ADJ
ejpam-2666	760	3	-	-	ADJ
ejpam-2666	760	4	cyclic	cyclic	ADJ
ejpam-2666	760	5	codes	code	NOUN
ejpam-2666	760	6	over	over	ADP
ejpam-2666	760	7	galois	galois	PROPN
ejpam-2666	760	8	rings	ring	NOUN
ejpam-2666	760	9	:	:	PUNCT
ejpam-2666	760	10	structural	structural	ADJ
ejpam-2666	760	11	properties	property	NOUN
ejpam-2666	760	12	and	and	CCONJ
ejpam-2666	760	13	enumeration	enumeration	NOUN
ejpam-2666	760	14	.	.	PUNCT
ejpam-2666	761	1	appl	appl	PROPN
ejpam-2666	761	2	.	.	PUNCT
ejpam-2666	762	1	algebra	algebra	PROPN
ejpam-2666	762	2	eng	eng	PROPN
ejpam-2666	762	3	.	.	PUNCT
ejpam-2666	762	4	commun	commun	PROPN
ejpam-2666	762	5	.	.	PUNCT
ejpam-2666	763	1	comput	comput	PROPN
ejpam-2666	763	2	.	.	PUNCT
ejpam-2666	763	3	,	,	PUNCT
ejpam-2666	763	4	22(3	22(3	NUM
ejpam-2666	763	5	)	)	PUNCT
ejpam-2666	763	6	:	:	PUNCT
ejpam-2666	763	7	219−	219−	NUM
ejpam-2666	763	8	233	233	NUM
ejpam-2666	763	9	,	,	PUNCT
ejpam-2666	763	10	2011	2011	NUM
ejpam-2666	763	11	.	.	PUNCT
ejpam-2666	764	1	[	[	X
ejpam-2666	764	2	10	10	NUM
ejpam-2666	764	3	]	]	PUNCT
ejpam-2666	764	4	p.	p.	NOUN
ejpam-2666	764	5	delsarte	delsarte	PROPN
ejpam-2666	764	6	and	and	CCONJ
ejpam-2666	764	7	v.	v.	PROPN
ejpam-2666	764	8	i.	i.	PROPN
ejpam-2666	764	9	levenshtein	levenshtein	PROPN
ejpam-2666	764	10	.	.	PUNCT
ejpam-2666	765	1	association	association	NOUN
ejpam-2666	765	2	schemes	scheme	NOUN
ejpam-2666	765	3	and	and	CCONJ
ejpam-2666	765	4	coding	code	VERB
ejpam-2666	765	5	theory	theory	NOUN
ejpam-2666	765	6	.	.	PUNCT
ejpam-2666	766	1	ieee	ieee	PROPN
ejpam-2666	766	2	trans	trans	PROPN
ejpam-2666	766	3	.	.	PUNCT
ejpam-2666	767	1	inform	inform	NOUN
ejpam-2666	767	2	.	.	PUNCT
ejpam-2666	768	1	theory	theory	NOUN
ejpam-2666	768	2	,	,	PUNCT
ejpam-2666	768	3	44(6	44(6	NOUN
ejpam-2666	768	4	)	)	PUNCT
ejpam-2666	768	5	:	:	PUNCT
ejpam-2666	769	1	2477−	2477−	NUM
ejpam-2666	769	2	2504	2504	NUM
ejpam-2666	769	3	,	,	PUNCT
ejpam-2666	769	4	1998	1998	NUM
ejpam-2666	769	5	.	.	PUNCT
ejpam-2666	770	1	[	[	X
ejpam-2666	770	2	11	11	NUM
ejpam-2666	770	3	]	]	PUNCT
ejpam-2666	770	4	h.	h.	PROPN
ejpam-2666	770	5	q.	q.	PROPN
ejpam-2666	770	6	dinh	dinh	PROPN
ejpam-2666	770	7	and	and	CCONJ
ejpam-2666	770	8	s.	s.	PROPN
ejpam-2666	770	9	r.	r.	PROPN
ejpam-2666	770	10	loṕez	loṕez	PROPN
ejpam-2666	770	11	-	-	PUNCT
ejpam-2666	770	12	permouth	permouth	NOUN
ejpam-2666	770	13	.	.	PUNCT
ejpam-2666	771	1	cyclic	cyclic	ADJ
ejpam-2666	771	2	and	and	CCONJ
ejpam-2666	771	3	negacyclic	negacyclic	ADJ
ejpam-2666	771	4	codes	code	NOUN
ejpam-2666	771	5	over	over	ADP
ejpam-2666	771	6	finite	finite	ADJ
ejpam-2666	771	7	chain	chain	NOUN
ejpam-2666	771	8	rings	ring	NOUN
ejpam-2666	771	9	.	.	PUNCT
ejpam-2666	772	1	ieee	ieee	PROPN
ejpam-2666	772	2	trans	trans	PROPN
ejpam-2666	772	3	.	.	PUNCT
ejpam-2666	773	1	inform	inform	VERB
ejpam-2666	773	2	.	.	PUNCT
ejpam-2666	774	1	theory	theory	NOUN
ejpam-2666	774	2	.	.	PUNCT
ejpam-2666	774	3	,	,	PUNCT
ejpam-2666	774	4	50(8	50(8	NUM
ejpam-2666	774	5	)	)	PUNCT
ejpam-2666	774	6	:	:	PUNCT
ejpam-2666	774	7	1728−	1728−	NUM
ejpam-2666	774	8	1743	1743	NUM
ejpam-2666	774	9	,	,	PUNCT
ejpam-2666	774	10	2004	2004	NUM
ejpam-2666	774	11	.	.	PUNCT
ejpam-2666	775	1	[	[	X
ejpam-2666	775	2	12	12	NUM
ejpam-2666	775	3	]	]	PUNCT
ejpam-2666	775	4	m.	m.	NOUN
ejpam-2666	775	5	esmaeili	esmaeili	NOUN
ejpam-2666	775	6	and	and	CCONJ
ejpam-2666	775	7	s.	s.	PROPN
ejpam-2666	775	8	yari	yari	PROPN
ejpam-2666	775	9	.	.	PUNCT
ejpam-2666	776	1	generalized	generalize	VERB
ejpam-2666	776	2	quasi	quasi	ADJ
ejpam-2666	776	3	-	-	ADJ
ejpam-2666	776	4	cyclic	cyclic	ADJ
ejpam-2666	776	5	codes	code	NOUN
ejpam-2666	776	6	:	:	PUNCT
ejpam-2666	776	7	structural	structural	ADJ
ejpam-2666	776	8	properties	property	NOUN
ejpam-2666	776	9	and	and	CCONJ
ejpam-2666	776	10	code	code	NOUN
ejpam-2666	776	11	construction	construction	NOUN
ejpam-2666	776	12	.	.	PUNCT
ejpam-2666	777	1	appl	appl	PROPN
ejpam-2666	777	2	.	.	PUNCT
ejpam-2666	778	1	algebra	algebra	PROPN
ejpam-2666	778	2	eng	eng	PROPN
ejpam-2666	778	3	.	.	PUNCT
ejpam-2666	778	4	commun	commun	PROPN
ejpam-2666	778	5	.	.	PUNCT
ejpam-2666	779	1	comput	comput	PROPN
ejpam-2666	779	2	.	.	PUNCT
ejpam-2666	779	3	,	,	PUNCT
ejpam-2666	779	4	20(2	20(2	NUM
ejpam-2666	779	5	)	)	PUNCT
ejpam-2666	779	6	:	:	PUNCT
ejpam-2666	780	1	159−	159−	NUM
ejpam-2666	780	2	173	173	NUM
ejpam-2666	780	3	,	,	PUNCT
ejpam-2666	780	4	2009	2009	NUM
ejpam-2666	780	5	.	.	PUNCT
ejpam-2666	781	1	[	[	X
ejpam-2666	781	2	13	13	NUM
ejpam-2666	781	3	]	]	PUNCT
ejpam-2666	781	4	j.	j.	PROPN
ejpam-2666	781	5	gao	gao	PROPN
ejpam-2666	781	6	,	,	PUNCT
ejpam-2666	781	7	f	f	PROPN
ejpam-2666	781	8	-	-	PUNCT
ejpam-2666	781	9	w.	w.	PROPN
ejpam-2666	781	10	fu	fu	PROPN
ejpam-2666	781	11	,	,	PUNCT
ejpam-2666	781	12	l.	l.	PROPN
ejpam-2666	781	13	shen	shen	PROPN
ejpam-2666	781	14	and	and	CCONJ
ejpam-2666	781	15	w.	w.	PROPN
ejpam-2666	781	16	ren	ren	PROPN
ejpam-2666	781	17	.	.	PUNCT
ejpam-2666	782	1	some	some	DET
ejpam-2666	782	2	results	result	NOUN
ejpam-2666	782	3	on	on	ADP
ejpam-2666	782	4	generalized	generalized	ADJ
ejpam-2666	782	5	quasi	quasi	ADJ
ejpam-2666	782	6	-	-	ADJ
ejpam-2666	782	7	cyclic	cyclic	ADJ
ejpam-2666	782	8	codes	code	NOUN
ejpam-2666	782	9	over	over	ADP
ejpam-2666	782	10	fq	fq	PROPN
ejpam-2666	782	11	+	+	CCONJ
ejpam-2666	782	12	ufq	ufq	PROPN
ejpam-2666	782	13	.	.	PROPN
ejpam-2666	783	1	ieice	ieice	PROPN
ejpam-2666	783	2	trans	trans	PROPN
ejpam-2666	783	3	.	.	PUNCT
ejpam-2666	784	1	fund	fund	PROPN
ejpam-2666	784	2	.	.	PUNCT
ejpam-2666	784	3	,	,	PUNCT
ejpam-2666	784	4	97(4	97(4	NUM
ejpam-2666	784	5	)	)	PUNCT
ejpam-2666	784	6	:	:	PUNCT
ejpam-2666	784	7	1005−	1005−	NUM
ejpam-2666	784	8	1011	1011	NUM
ejpam-2666	784	9	,	,	PUNCT
ejpam-2666	784	10	2014	2014	NUM
ejpam-2666	784	11	.	.	PUNCT
ejpam-2666	785	1	[	[	X
ejpam-2666	785	2	14	14	NUM
ejpam-2666	785	3	]	]	PUNCT
ejpam-2666	785	4	j.	j.	PROPN
ejpam-2666	785	5	gao	gao	PROPN
ejpam-2666	785	6	,	,	PUNCT
ejpam-2666	785	7	m.	m.	PROPN
ejpam-2666	785	8	shi	shi	PROPN
ejpam-2666	785	9	,	,	PUNCT
ejpam-2666	785	10	t.	t.	PROPN
ejpam-2666	785	11	wu	wu	PROPN
ejpam-2666	785	12	and	and	CCONJ
ejpam-2666	785	13	f	f	PROPN
ejpam-2666	785	14	-	-	PUNCT
ejpam-2666	785	15	w.	w.	PROPN
ejpam-2666	785	16	fu	fu	PROPN
ejpam-2666	785	17	.	.	PUNCT
ejpam-2666	786	1	on	on	ADP
ejpam-2666	786	2	double	double	ADJ
ejpam-2666	786	3	cyclic	cyclic	NOUN
ejpam-2666	786	4	codes	code	NOUN
ejpam-2666	786	5	over	over	ADP
ejpam-2666	786	6	z4	z4	PROPN
ejpam-2666	786	7	.	.	PUNCT
ejpam-2666	787	1	finite	finite	PROPN
ejpam-2666	787	2	fields	fields	PROPN
ejpam-2666	787	3	appl	appl	PROPN
ejpam-2666	788	1	.	.	PROPN
ejpam-2666	788	2	,	,	PUNCT
ejpam-2666	788	3	39	39	NUM
ejpam-2666	788	4	:	:	PUNCT
ejpam-2666	788	5	233−	233−	PROPN
ejpam-2666	788	6	250	250	NUM
ejpam-2666	788	7	2016	2016	NUM
ejpam-2666	788	8	.	.	PUNCT
ejpam-2666	789	1	[	[	X
ejpam-2666	789	2	15	15	NUM
ejpam-2666	789	3	]	]	X
ejpam-2666	789	4	f.	f.	PROPN
ejpam-2666	789	5	j.	j.	PROPN
ejpam-2666	789	6	macwilliams	macwilliams	PROPN
ejpam-2666	789	7	and	and	CCONJ
ejpam-2666	789	8	n.	n.	PROPN
ejpam-2666	789	9	j.	j.	PROPN
ejpam-2666	789	10	a.	a.	PROPN
ejpam-2666	789	11	sloane	sloane	PROPN
ejpam-2666	789	12	.	.	PUNCT
ejpam-2666	790	1	the	the	DET
ejpam-2666	790	2	theory	theory	NOUN
ejpam-2666	790	3	of	of	ADP
ejpam-2666	790	4	error	error	NOUN
ejpam-2666	790	5	correcting	correct	VERB
ejpam-2666	790	6	codes	code	NOUN
ejpam-2666	790	7	.	.	PUNCT
ejpam-2666	791	1	north	north	NOUN
ejpam-2666	791	2	holland	holland	PROPN
ejpam-2666	791	3	,	,	PUNCT
ejpam-2666	791	4	amsterdam	amsterdam	PROPN
ejpam-2666	791	5	,	,	PUNCT
ejpam-2666	791	6	1977	1977	NUM
ejpam-2666	791	7	.	.	PUNCT
ejpam-2666	792	1	references	reference	NOUN
ejpam-2666	792	2	409	409	NUM
ejpam-2666	793	1	[	[	X
ejpam-2666	793	2	16	16	NUM
ejpam-2666	793	3	]	]	X
ejpam-2666	793	4	i.	i.	PROPN
ejpam-2666	793	5	siap	siap	PROPN
ejpam-2666	793	6	and	and	CCONJ
ejpam-2666	793	7	n.	n.	PROPN
ejpam-2666	793	8	kulhan	kulhan	PROPN
ejpam-2666	793	9	.	.	PUNCT
ejpam-2666	794	1	the	the	DET
ejpam-2666	794	2	structure	structure	NOUN
ejpam-2666	794	3	of	of	ADP
ejpam-2666	794	4	generalized	generalized	ADJ
ejpam-2666	794	5	quasi	quasi	ADJ
ejpam-2666	794	6	-	-	ADJ
ejpam-2666	794	7	cyclic	cyclic	ADJ
ejpam-2666	794	8	codes	code	NOUN
ejpam-2666	794	9	.	.	PUNCT
ejpam-2666	795	1	appl	appl	PROPN
ejpam-2666	795	2	.	.	PUNCT
ejpam-2666	795	3	math	math	NOUN
ejpam-2666	795	4	.	.	PUNCT
ejpam-2666	796	1	e	e	X
ejpam-2666	796	2	-	-	NOUN
ejpam-2666	796	3	notes	note	NOUN
ejpam-2666	796	4	,	,	PUNCT
ejpam-2666	796	5	5	5	NUM
ejpam-2666	796	6	:	:	PUNCT
ejpam-2666	796	7	24−	24−	NUM
ejpam-2666	796	8	30	30	NUM
ejpam-2666	796	9	,	,	PUNCT
ejpam-2666	796	10	2005	2005	NUM
ejpam-2666	796	11	.	.	PUNCT
ejpam-2666	797	1	[	[	X
ejpam-2666	797	2	17	17	NUM
ejpam-2666	797	3	]	]	PUNCT
ejpam-2666	797	4	t.	t.	PROPN
ejpam-2666	797	5	yao	yao	PROPN
ejpam-2666	797	6	,	,	PUNCT
ejpam-2666	797	7	m.	m.	NOUN
ejpam-2666	797	8	shi	shi	PROPN
ejpam-2666	797	9	and	and	CCONJ
ejpam-2666	797	10	p.	p.	NOUN
ejpam-2666	797	11	solé.	solé.	PROPN
ejpam-2666	797	12	double	double	ADJ
ejpam-2666	797	13	cyclic	cyclic	NOUN
ejpam-2666	797	14	codes	code	NOUN
ejpam-2666	797	15	over	over	ADP
ejpam-2666	797	16	fq	fq	PROPN
ejpam-2666	797	17	+	+	CCONJ
ejpam-2666	797	18	ufq	ufq	PROPN
ejpam-2666	797	19	+	+	NUM
ejpam-2666	797	20	u2fq	u2fq	X
ejpam-2666	797	21	.	.	PUNCT
ejpam-2666	798	1	int	int	NOUN
ejpam-2666	798	2	.	.	PUNCT
ejpam-2666	799	1	j.	j.	PROPN
ejpam-2666	799	2	inf	inf	PROPN
ejpam-2666	799	3	.	.	PUNCT
ejpam-2666	800	1	coding	code	VERB
ejpam-2666	800	2	theory	theory	NOUN
ejpam-2666	800	3	,	,	PUNCT
ejpam-2666	800	4	3(2	3(2	NUM
ejpam-2666	800	5	)	)	PUNCT
ejpam-2666	800	6	:	:	PUNCT
ejpam-2666	801	1	145−	145−	NUM
ejpam-2666	801	2	157	157	NUM
ejpam-2666	801	3	,	,	PUNCT
ejpam-2666	801	4	2015	2015	NUM
ejpam-2666	801	5	.	.	PUNCT