id	sid	tid	token	lemma	pos
ejpam-2245	1	1	compile	compile	NOUN
ejpam-2245	1	2	/	/	SYM
ejpam-2245	1	3	output.dvi	output.dvi	NOUN
ejpam-2245	1	4	european	european	ADJ
ejpam-2245	1	5	journal	journal	NOUN
ejpam-2245	1	6	of	of	ADP
ejpam-2245	1	7	pure	pure	ADJ
ejpam-2245	1	8	and	and	CCONJ
ejpam-2245	1	9	applied	apply	VERB
ejpam-2245	1	10	mathematics	mathematic	NOUN
ejpam-2245	1	11	vol	vol	NOUN
ejpam-2245	1	12	.	.	PROPN
ejpam-2245	1	13	8	8	NUM
ejpam-2245	1	14	,	,	PUNCT
ejpam-2245	1	15	no	no	INTJ
ejpam-2245	1	16	.	.	NOUN
ejpam-2245	1	17	1	1	NUM
ejpam-2245	1	18	,	,	PUNCT
ejpam-2245	1	19	2015	2015	NUM
ejpam-2245	1	20	,	,	PUNCT
ejpam-2245	1	21	64	64	NUM
ejpam-2245	1	22	-	-	SYM
ejpam-2245	1	23	80	80	NUM
ejpam-2245	1	24	issn	issn	PROPN
ejpam-2245	1	25	1307	1307	NUM
ejpam-2245	1	26	-	-	SYM
ejpam-2245	1	27	5543	5543	NUM
ejpam-2245	1	28	–	–	PUNCT
ejpam-2245	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2245	1	30	cyclic	cyclic	ADJ
ejpam-2245	1	31	isodual	isodual	ADJ
ejpam-2245	1	32	and	and	CCONJ
ejpam-2245	1	33	formally	formally	ADV
ejpam-2245	1	34	self	self	NOUN
ejpam-2245	1	35	-	-	PUNCT
ejpam-2245	1	36	dual	dual	ADJ
ejpam-2245	1	37	codes	code	NOUN
ejpam-2245	1	38	over	over	ADP
ejpam-2245	1	39	fq	fq	PROPN
ejpam-2245	1	40	+	+	CCONJ
ejpam-2245	1	41	vfq	vfq	PROPN
ejpam-2245	1	42	aicha	aicha	PROPN
ejpam-2245	1	43	batoul1	batoul1	PROPN
ejpam-2245	1	44	,	,	PUNCT
ejpam-2245	1	45	kenza	kenza	PROPN
ejpam-2245	1	46	guenda1	guenda1	PROPN
ejpam-2245	1	47	,	,	PUNCT
ejpam-2245	1	48	abidin	abidin	PROPN
ejpam-2245	1	49	kaya2	kaya2	PROPN
ejpam-2245	1	50	,	,	PUNCT
ejpam-2245	1	51	bahattin	bahattin	PROPN
ejpam-2245	1	52	yildiz2,∗	yildiz2,∗	NUM
ejpam-2245	1	53	1	1	NUM
ejpam-2245	1	54	faculty	faculty	NOUN
ejpam-2245	1	55	of	of	ADP
ejpam-2245	1	56	mathematics	mathematic	NOUN
ejpam-2245	1	57	usthb	usthb	ADJ
ejpam-2245	1	58	,	,	PUNCT
ejpam-2245	1	59	university	university	NOUN
ejpam-2245	1	60	of	of	ADP
ejpam-2245	1	61	science	science	NOUN
ejpam-2245	1	62	and	and	CCONJ
ejpam-2245	1	63	technology	technology	NOUN
ejpam-2245	1	64	of	of	ADP
ejpam-2245	1	65	algiers	algiers	PROPN
ejpam-2245	1	66	,	,	PUNCT
ejpam-2245	1	67	algeria	algeria	PROPN
ejpam-2245	1	68	2	2	NUM
ejpam-2245	1	69	department	department	NOUN
ejpam-2245	1	70	of	of	ADP
ejpam-2245	1	71	mathematics	mathematics	PROPN
ejpam-2245	1	72	,	,	PUNCT
ejpam-2245	1	73	fatih	fatih	PROPN
ejpam-2245	1	74	university	university	PROPN
ejpam-2245	1	75	,	,	PUNCT
ejpam-2245	1	76	istanbul	istanbul	PROPN
ejpam-2245	1	77	,	,	PUNCT
ejpam-2245	1	78	turkey	turkey	PROPN
ejpam-2245	1	79	.	.	PUNCT
ejpam-2245	2	1	abstract	abstract	ADJ
ejpam-2245	2	2	.	.	PUNCT
ejpam-2245	3	1	in	in	ADP
ejpam-2245	3	2	this	this	DET
ejpam-2245	3	3	paper	paper	NOUN
ejpam-2245	3	4	,	,	PUNCT
ejpam-2245	3	5	we	we	PRON
ejpam-2245	3	6	investigate	investigate	VERB
ejpam-2245	3	7	the	the	DET
ejpam-2245	3	8	structure	structure	NOUN
ejpam-2245	3	9	and	and	CCONJ
ejpam-2245	3	10	properties	property	NOUN
ejpam-2245	3	11	of	of	ADP
ejpam-2245	3	12	duadic	duadic	ADJ
ejpam-2245	3	13	,	,	PUNCT
ejpam-2245	3	14	isodual	isodual	ADJ
ejpam-2245	3	15	cyclic	cyclic	NOUN
ejpam-2245	3	16	and	and	CCONJ
ejpam-2245	3	17	formally	formally	ADV
ejpam-2245	3	18	self	self	NOUN
ejpam-2245	3	19	-	-	PUNCT
ejpam-2245	3	20	dual	dual	ADJ
ejpam-2245	3	21	codes	code	NOUN
ejpam-2245	3	22	over	over	ADP
ejpam-2245	3	23	the	the	DET
ejpam-2245	3	24	ring	ring	NOUN
ejpam-2245	3	25	r	r	NOUN
ejpam-2245	3	26	=	=	SYM
ejpam-2245	3	27	fq	fq	PROPN
ejpam-2245	3	28	+	+	CCONJ
ejpam-2245	3	29	vfq	vfq	NOUN
ejpam-2245	3	30	with	with	ADP
ejpam-2245	3	31	v2	v2	PROPN
ejpam-2245	4	1	=	=	PUNCT
ejpam-2245	5	1	v.	v.	CCONJ
ejpam-2245	5	2	in	in	ADP
ejpam-2245	5	3	addition	addition	NOUN
ejpam-2245	5	4	to	to	ADP
ejpam-2245	5	5	the	the	DET
ejpam-2245	5	6	theoretical	theoretical	ADJ
ejpam-2245	5	7	work	work	NOUN
ejpam-2245	5	8	on	on	ADP
ejpam-2245	5	9	the	the	DET
ejpam-2245	5	10	structure	structure	NOUN
ejpam-2245	5	11	of	of	ADP
ejpam-2245	5	12	these	these	DET
ejpam-2245	5	13	codes	code	NOUN
ejpam-2245	5	14	,	,	PUNCT
ejpam-2245	5	15	we	we	PRON
ejpam-2245	5	16	construct	construct	VERB
ejpam-2245	5	17	examples	example	NOUN
ejpam-2245	5	18	of	of	ADP
ejpam-2245	5	19	good	good	ADJ
ejpam-2245	5	20	codes	code	NOUN
ejpam-2245	5	21	over	over	ADP
ejpam-2245	5	22	different	different	ADJ
ejpam-2245	5	23	alphabets	alphabet	NOUN
ejpam-2245	5	24	from	from	ADP
ejpam-2245	5	25	cyclic	cyclic	ADJ
ejpam-2245	5	26	self	self	NOUN
ejpam-2245	5	27	-	-	PUNCT
ejpam-2245	5	28	dual	dual	ADJ
ejpam-2245	5	29	and	and	CCONJ
ejpam-2245	5	30	formally	formally	ADV
ejpam-2245	5	31	self	self	NOUN
ejpam-2245	5	32	-	-	PUNCT
ejpam-2245	5	33	dual	dual	ADJ
ejpam-2245	5	34	codes	code	NOUN
ejpam-2245	5	35	over	over	ADP
ejpam-2245	5	36	r.	r.	PROPN
ejpam-2245	5	37	2010	2010	NUM
ejpam-2245	5	38	mathematics	mathematics	PROPN
ejpam-2245	5	39	subject	subject	NOUN
ejpam-2245	5	40	classifications	classification	NOUN
ejpam-2245	5	41	:	:	PUNCT
ejpam-2245	5	42	94b15	94b15	NUM
ejpam-2245	5	43	,	,	PUNCT
ejpam-2245	5	44	94b05	94b05	NUM
ejpam-2245	5	45	key	key	ADJ
ejpam-2245	5	46	words	word	NOUN
ejpam-2245	5	47	and	and	CCONJ
ejpam-2245	5	48	phrases	phrase	NOUN
ejpam-2245	5	49	:	:	PUNCT
ejpam-2245	5	50	isodual	isodual	ADJ
ejpam-2245	5	51	codes	code	NOUN
ejpam-2245	5	52	,	,	PUNCT
ejpam-2245	5	53	duadic	duadic	ADJ
ejpam-2245	5	54	codes	code	NOUN
ejpam-2245	5	55	,	,	PUNCT
ejpam-2245	5	56	formally	formally	ADV
ejpam-2245	5	57	self	self	NOUN
ejpam-2245	5	58	-	-	PUNCT
ejpam-2245	5	59	dual	dual	ADJ
ejpam-2245	5	60	codes	code	NOUN
ejpam-2245	5	61	,	,	PUNCT
ejpam-2245	5	62	cyclic	cyclic	ADJ
ejpam-2245	5	63	codes	code	NOUN
ejpam-2245	5	64	1	1	NUM
ejpam-2245	5	65	.	.	PUNCT
ejpam-2245	6	1	introduction	introduction	NOUN
ejpam-2245	6	2	duadic	duadic	ADJ
ejpam-2245	6	3	codes	code	NOUN
ejpam-2245	6	4	over	over	ADP
ejpam-2245	6	5	finite	finite	ADJ
ejpam-2245	6	6	fields	field	NOUN
ejpam-2245	6	7	form	form	VERB
ejpam-2245	6	8	an	an	DET
ejpam-2245	6	9	important	important	ADJ
ejpam-2245	6	10	class	class	NOUN
ejpam-2245	6	11	of	of	ADP
ejpam-2245	6	12	linear	linear	PROPN
ejpam-2245	6	13	codes	code	NOUN
ejpam-2245	6	14	for	for	ADP
ejpam-2245	6	15	both	both	CCONJ
ejpam-2245	6	16	theoretical	theoretical	ADJ
ejpam-2245	6	17	and	and	CCONJ
ejpam-2245	6	18	practical	practical	ADJ
ejpam-2245	6	19	reasons	reason	NOUN
ejpam-2245	6	20	in	in	ADP
ejpam-2245	6	21	error	error	NOUN
ejpam-2245	6	22	-	-	PUNCT
ejpam-2245	6	23	correcting	correct	VERB
ejpam-2245	6	24	codes	code	NOUN
ejpam-2245	6	25	.	.	PUNCT
ejpam-2245	7	1	they	they	PRON
ejpam-2245	7	2	were	be	AUX
ejpam-2245	7	3	first	first	ADV
ejpam-2245	7	4	introduced	introduce	VERB
ejpam-2245	7	5	by	by	ADP
ejpam-2245	7	6	leon	leon	PROPN
ejpam-2245	7	7	et	et	PROPN
ejpam-2245	7	8	al	al	PROPN
ejpam-2245	7	9	.	.	PUNCT
ejpam-2245	8	1	[	[	X
ejpam-2245	8	2	10	10	NUM
ejpam-2245	8	3	]	]	PUNCT
ejpam-2245	8	4	as	as	ADP
ejpam-2245	8	5	generalized	generalized	ADJ
ejpam-2245	8	6	quadratic	quadratic	ADJ
ejpam-2245	8	7	residue	residue	NOUN
ejpam-2245	8	8	cyclic	cyclic	NOUN
ejpam-2245	8	9	codes	code	NOUN
ejpam-2245	8	10	over	over	ADP
ejpam-2245	8	11	fields	field	NOUN
ejpam-2245	8	12	.	.	PUNCT
ejpam-2245	9	1	rushanan	rushanan	PROPN
ejpam-2245	10	1	[	[	X
ejpam-2245	10	2	12	12	NUM
ejpam-2245	10	3	]	]	PUNCT
ejpam-2245	10	4	generalized	generalize	VERB
ejpam-2245	10	5	them	they	PRON
ejpam-2245	10	6	to	to	ADP
ejpam-2245	10	7	duadic	duadic	ADJ
ejpam-2245	10	8	abelian	abelian	ADJ
ejpam-2245	10	9	codes	code	NOUN
ejpam-2245	10	10	.	.	PUNCT
ejpam-2245	11	1	duadic	duadic	ADJ
ejpam-2245	11	2	codes	code	NOUN
ejpam-2245	11	3	over	over	ADP
ejpam-2245	11	4	rings	ring	NOUN
ejpam-2245	11	5	were	be	AUX
ejpam-2245	11	6	introduced	introduce	VERB
ejpam-2245	11	7	by	by	ADP
ejpam-2245	11	8	langevin	langevin	PROPN
ejpam-2245	11	9	et	et	PROPN
ejpam-2245	11	10	al	al	PROPN
ejpam-2245	11	11	.	.	PUNCT
ejpam-2245	12	1	[	[	X
ejpam-2245	12	2	9	9	NUM
ejpam-2245	12	3	]	]	PUNCT
ejpam-2245	12	4	and	and	CCONJ
ejpam-2245	12	5	over	over	ADP
ejpam-2245	12	6	f2	f2	PROPN
ejpam-2245	12	7	+	+	CCONJ
ejpam-2245	12	8	uf2	uf2	NOUN
ejpam-2245	12	9	by	by	ADP
ejpam-2245	12	10	san	san	PROPN
ejpam-2245	12	11	ling	ling	PROPN
ejpam-2245	12	12	et	et	PROPN
ejpam-2245	12	13	al	al	PROPN
ejpam-2245	12	14	.	.	PUNCT
ejpam-2245	13	1	[	[	X
ejpam-2245	13	2	11	11	NUM
ejpam-2245	13	3	]	]	PUNCT
ejpam-2245	13	4	.	.	PUNCT
ejpam-2245	14	1	codes	code	NOUN
ejpam-2245	14	2	over	over	ADP
ejpam-2245	14	3	fp	fp	PROPN
ejpam-2245	14	4	+	+	NUM
ejpam-2245	14	5	vfp	vfp	NOUN
ejpam-2245	14	6	,	,	PUNCT
ejpam-2245	14	7	p	p	X
ejpam-2245	14	8	a	a	DET
ejpam-2245	14	9	prime	prime	ADJ
ejpam-2245	14	10	integer	integer	NOUN
ejpam-2245	14	11	,	,	PUNCT
ejpam-2245	14	12	were	be	AUX
ejpam-2245	14	13	first	first	ADV
ejpam-2245	14	14	introduced	introduce	VERB
ejpam-2245	14	15	by	by	ADP
ejpam-2245	14	16	bachoc	bachoc	NOUN
ejpam-2245	14	17	in	in	ADP
ejpam-2245	14	18	[	[	X
ejpam-2245	14	19	1	1	NUM
ejpam-2245	14	20	]	]	PUNCT
ejpam-2245	14	21	together	together	ADV
ejpam-2245	14	22	with	with	ADP
ejpam-2245	14	23	a	a	DET
ejpam-2245	14	24	new	new	ADJ
ejpam-2245	14	25	weight	weight	NOUN
ejpam-2245	14	26	.	.	PUNCT
ejpam-2245	15	1	they	they	PRON
ejpam-2245	15	2	are	be	AUX
ejpam-2245	15	3	shown	show	VERB
ejpam-2245	15	4	to	to	PART
ejpam-2245	15	5	be	be	AUX
ejpam-2245	15	6	connected	connect	VERB
ejpam-2245	15	7	to	to	ADP
ejpam-2245	15	8	lattices	lattice	NOUN
ejpam-2245	15	9	and	and	CCONJ
ejpam-2245	15	10	have	have	AUX
ejpam-2245	15	11	since	since	SCONJ
ejpam-2245	15	12	then	then	ADV
ejpam-2245	15	13	generated	generate	VERB
ejpam-2245	15	14	interest	interest	NOUN
ejpam-2245	15	15	among	among	ADP
ejpam-2245	15	16	coding	code	VERB
ejpam-2245	15	17	theorists	theorist	NOUN
ejpam-2245	15	18	.	.	PUNCT
ejpam-2245	16	1	for	for	ADP
ejpam-2245	16	2	some	some	PRON
ejpam-2245	16	3	of	of	ADP
ejpam-2245	16	4	the	the	DET
ejpam-2245	16	5	work	work	NOUN
ejpam-2245	16	6	in	in	ADP
ejpam-2245	16	7	the	the	DET
ejpam-2245	16	8	literature	literature	NOUN
ejpam-2245	16	9	about	about	ADP
ejpam-2245	16	10	these	these	DET
ejpam-2245	16	11	codes	code	NOUN
ejpam-2245	16	12	and	and	CCONJ
ejpam-2245	16	13	related	related	ADJ
ejpam-2245	16	14	codes	code	NOUN
ejpam-2245	16	15	we	we	PRON
ejpam-2245	16	16	refer	refer	VERB
ejpam-2245	16	17	the	the	DET
ejpam-2245	16	18	readers	reader	NOUN
ejpam-2245	16	19	to	to	ADP
ejpam-2245	16	20	[	[	X
ejpam-2245	16	21	6	6	NUM
ejpam-2245	16	22	,	,	PUNCT
ejpam-2245	16	23	11–13	11–13	NUM
ejpam-2245	16	24	,	,	PUNCT
ejpam-2245	16	25	16	16	NUM
ejpam-2245	16	26	]	]	PUNCT
ejpam-2245	16	27	.	.	PUNCT
ejpam-2245	17	1	recently	recently	ADV
ejpam-2245	17	2	,	,	PUNCT
ejpam-2245	17	3	zhu	zhu	PROPN
ejpam-2245	17	4	et	et	PROPN
ejpam-2245	17	5	al	al	PROPN
ejpam-2245	17	6	.	.	PROPN
ejpam-2245	17	7	considered	consider	VERB
ejpam-2245	17	8	the	the	DET
ejpam-2245	17	9	structure	structure	NOUN
ejpam-2245	17	10	of	of	ADP
ejpam-2245	17	11	cyclic	cyclic	ADJ
ejpam-2245	17	12	codes	code	NOUN
ejpam-2245	17	13	over	over	ADP
ejpam-2245	17	14	f2	f2	PROPN
ejpam-2245	17	15	+	+	CCONJ
ejpam-2245	17	16	vf2	vf2	NOUN
ejpam-2245	17	17	in	in	ADP
ejpam-2245	17	18	[	[	X
ejpam-2245	17	19	17	17	NUM
ejpam-2245	17	20	]	]	PUNCT
ejpam-2245	17	21	.	.	PUNCT
ejpam-2245	18	1	formally	formally	ADV
ejpam-2245	18	2	self	self	NOUN
ejpam-2245	18	3	-	-	PUNCT
ejpam-2245	18	4	dual	dual	ADJ
ejpam-2245	18	5	codes	code	NOUN
ejpam-2245	18	6	are	be	AUX
ejpam-2245	18	7	also	also	ADV
ejpam-2245	18	8	an	an	DET
ejpam-2245	18	9	important	important	ADJ
ejpam-2245	18	10	class	class	NOUN
ejpam-2245	18	11	of	of	ADP
ejpam-2245	18	12	codes	code	NOUN
ejpam-2245	18	13	that	that	PRON
ejpam-2245	18	14	have	have	AUX
ejpam-2245	18	15	generated	generate	VERB
ejpam-2245	18	16	a	a	DET
ejpam-2245	18	17	lot	lot	NOUN
ejpam-2245	18	18	of	of	ADP
ejpam-2245	18	19	interest	interest	NOUN
ejpam-2245	18	20	since	since	SCONJ
ejpam-2245	18	21	they	they	PRON
ejpam-2245	18	22	have	have	VERB
ejpam-2245	18	23	weight	weight	NOUN
ejpam-2245	18	24	enumerators	enumerator	NOUN
ejpam-2245	18	25	that	that	PRON
ejpam-2245	18	26	are	be	AUX
ejpam-2245	18	27	invariant	invariant	ADJ
ejpam-2245	18	28	under	under	ADP
ejpam-2245	18	29	the	the	DET
ejpam-2245	18	30	macwilliams	macwilliam	NOUN
ejpam-2245	18	31	transform	transform	VERB
ejpam-2245	18	32	and	and	CCONJ
ejpam-2245	18	33	sometimes	sometimes	ADV
ejpam-2245	18	34	have	have	VERB
ejpam-2245	18	35	better	well	ADJ
ejpam-2245	18	36	parameters	parameter	NOUN
ejpam-2245	18	37	than	than	ADP
ejpam-2245	18	38	self	self	NOUN
ejpam-2245	18	39	-	-	PUNCT
ejpam-2245	18	40	dual	dual	ADJ
ejpam-2245	18	41	codes	code	NOUN
ejpam-2245	18	42	.	.	PUNCT
ejpam-2245	19	1	this	this	PRON
ejpam-2245	19	2	gives	give	VERB
ejpam-2245	19	3	them	they	PRON
ejpam-2245	19	4	a	a	DET
ejpam-2245	19	5	potential	potential	NOUN
ejpam-2245	19	6	for	for	ADP
ejpam-2245	19	7	applications	application	NOUN
ejpam-2245	19	8	to	to	ADP
ejpam-2245	19	9	such	such	ADJ
ejpam-2245	19	10	areas	area	NOUN
ejpam-2245	19	11	as	as	ADP
ejpam-2245	19	12	invariant	invariant	ADJ
ejpam-2245	19	13	theory	theory	NOUN
ejpam-2245	19	14	,	,	PUNCT
ejpam-2245	19	15	lattices	lattice	NOUN
ejpam-2245	19	16	and	and	CCONJ
ejpam-2245	19	17	designs	design	NOUN
ejpam-2245	19	18	.	.	PUNCT
ejpam-2245	20	1	the	the	DET
ejpam-2245	20	2	aim	aim	NOUN
ejpam-2245	20	3	of	of	ADP
ejpam-2245	20	4	this	this	DET
ejpam-2245	20	5	paper	paper	NOUN
ejpam-2245	20	6	is	be	AUX
ejpam-2245	20	7	to	to	PART
ejpam-2245	20	8	introduce	introduce	VERB
ejpam-2245	20	9	and	and	CCONJ
ejpam-2245	20	10	study	study	VERB
ejpam-2245	20	11	duadic	duadic	ADJ
ejpam-2245	20	12	codes	code	NOUN
ejpam-2245	20	13	,	,	PUNCT
ejpam-2245	20	14	isodual	isodual	ADJ
ejpam-2245	20	15	cyclic	cyclic	NOUN
ejpam-2245	20	16	codes	code	NOUN
ejpam-2245	20	17	and	and	CCONJ
ejpam-2245	20	18	formally	formally	ADV
ejpam-2245	20	19	self	self	NOUN
ejpam-2245	20	20	-	-	PUNCT
ejpam-2245	20	21	dual	dual	ADJ
ejpam-2245	20	22	codes	code	NOUN
ejpam-2245	20	23	over	over	ADP
ejpam-2245	20	24	the	the	DET
ejpam-2245	20	25	ring	ring	NOUN
ejpam-2245	20	26	fq	fq	PROPN
ejpam-2245	20	27	+	+	CCONJ
ejpam-2245	20	28	vfq	vfq	NOUN
ejpam-2245	20	29	which	which	PRON
ejpam-2245	20	30	is	be	AUX
ejpam-2245	20	31	isomorphic	isomorphic	ADJ
ejpam-2245	20	32	to	to	ADP
ejpam-2245	20	33	fq	fq	PROPN
ejpam-2245	20	34	×	×	PROPN
ejpam-2245	20	35	fq	fq	PROPN
ejpam-2245	20	36	for	for	ADP
ejpam-2245	20	37	q	q	DET
ejpam-2245	20	38	a	a	DET
ejpam-2245	20	39	prime	prime	ADJ
ejpam-2245	20	40	∗corresponding	∗corresponde	VERB
ejpam-2245	20	41	author	author	NOUN
ejpam-2245	20	42	.	.	PUNCT
ejpam-2245	21	1	email	email	NOUN
ejpam-2245	21	2	addresses	address	NOUN
ejpam-2245	21	3	:	:	PUNCT
ejpam-2245	21	4	abatoul@usthb.dz	abatoul@usthb.dz	PROPN
ejpam-2245	21	5	(	(	PUNCT
ejpam-2245	21	6	a.	a.	NOUN
ejpam-2245	21	7	batoul	batoul	PROPN
ejpam-2245	21	8	)	)	PUNCT
ejpam-2245	21	9	,	,	PUNCT
ejpam-2245	21	10	kguenda@usthb.dz	kguenda@usthb.dz	PROPN
ejpam-2245	22	1	(	(	PUNCT
ejpam-2245	22	2	k.	k.	PROPN
ejpam-2245	22	3	guenda),akaya@fatih.edu.tr	guenda),akaya@fatih.edu.tr	PROPN
ejpam-2245	22	4	(	(	PUNCT
ejpam-2245	22	5	a.	a.	PROPN
ejpam-2245	22	6	kaya	kaya	PROPN
ejpam-2245	22	7	)	)	PUNCT
ejpam-2245	22	8	,	,	PUNCT
ejpam-2245	22	9	byildiz@fatih.edu.tr	byildiz@fatih.edu.tr	PROPN
ejpam-2245	22	10	(	(	PUNCT
ejpam-2245	22	11	b.	b.	PROPN
ejpam-2245	22	12	yildiz	yildiz	PROPN
ejpam-2245	22	13	)	)	PUNCT
ejpam-2245	22	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2245	23	1	64	64	NUM
ejpam-2245	23	2	c	c	NOUN
ejpam-2245	23	3	©	©	PROPN
ejpam-2245	23	4	2015	2015	NUM
ejpam-2245	23	5	ejpam	ejpam	NOUN
ejpam-2245	23	6	all	all	DET
ejpam-2245	23	7	rights	right	NOUN
ejpam-2245	23	8	reserved	reserve	VERB
ejpam-2245	23	9	.	.	PUNCT
ejpam-2245	24	1	a.	a.	PROPN
ejpam-2245	24	2	batoul	batoul	PROPN
ejpam-2245	24	3	,	,	PUNCT
ejpam-2245	24	4	k.	k.	PROPN
ejpam-2245	24	5	guenda	guenda	PROPN
ejpam-2245	24	6	,	,	PUNCT
ejpam-2245	24	7	a.	a.	PROPN
ejpam-2245	24	8	kaya	kaya	PROPN
ejpam-2245	24	9	,	,	PUNCT
ejpam-2245	24	10	b.	b.	PROPN
ejpam-2245	24	11	yildiz	yildiz	PROPN
ejpam-2245	24	12	/	/	SYM
ejpam-2245	24	13	eur	eur	PROPN
ejpam-2245	24	14	.	.	PUNCT
ejpam-2245	25	1	j.	j.	PROPN
ejpam-2245	25	2	pure	pure	PROPN
ejpam-2245	25	3	appl	appl	PROPN
ejpam-2245	25	4	.	.	PROPN
ejpam-2245	25	5	math	math	PROPN
ejpam-2245	25	6	,	,	PUNCT
ejpam-2245	25	7	8	8	NUM
ejpam-2245	25	8	(	(	PUNCT
ejpam-2245	25	9	2015	2015	NUM
ejpam-2245	25	10	)	)	PUNCT
ejpam-2245	25	11	,	,	PUNCT
ejpam-2245	25	12	64	64	NUM
ejpam-2245	25	13	-	-	SYM
ejpam-2245	25	14	80	80	NUM
ejpam-2245	25	15	65	65	NUM
ejpam-2245	25	16	power	power	NOUN
ejpam-2245	25	17	.	.	PUNCT
ejpam-2245	26	1	we	we	PRON
ejpam-2245	26	2	first	first	ADV
ejpam-2245	26	3	give	give	VERB
ejpam-2245	26	4	some	some	DET
ejpam-2245	26	5	preliminaries	preliminary	NOUN
ejpam-2245	26	6	about	about	ADP
ejpam-2245	26	7	the	the	DET
ejpam-2245	26	8	ring	ring	NOUN
ejpam-2245	26	9	r	r	NOUN
ejpam-2245	26	10	=	=	SYM
ejpam-2245	26	11	fq	fq	PROPN
ejpam-2245	26	12	+	+	CCONJ
ejpam-2245	26	13	vfq	vfq	NOUN
ejpam-2245	26	14	and	and	CCONJ
ejpam-2245	26	15	linear	linear	ADJ
ejpam-2245	26	16	codes	code	NOUN
ejpam-2245	26	17	over	over	ADP
ejpam-2245	26	18	r.	r.	PROPN
ejpam-2245	26	19	then	then	ADV
ejpam-2245	26	20	we	we	PRON
ejpam-2245	26	21	introduce	introduce	VERB
ejpam-2245	26	22	a	a	DET
ejpam-2245	26	23	weight	weight	NOUN
ejpam-2245	26	24	and	and	CCONJ
ejpam-2245	26	25	an	an	DET
ejpam-2245	26	26	associated	associated	ADJ
ejpam-2245	26	27	gray	gray	ADJ
ejpam-2245	26	28	map	map	NOUN
ejpam-2245	26	29	.	.	PUNCT
ejpam-2245	27	1	thus	thus	ADV
ejpam-2245	27	2	we	we	PRON
ejpam-2245	27	3	characterize	characterize	VERB
ejpam-2245	27	4	duadic	duadic	ADJ
ejpam-2245	27	5	codes	code	NOUN
ejpam-2245	27	6	and	and	CCONJ
ejpam-2245	27	7	isodual	isodual	ADJ
ejpam-2245	27	8	cyclic	cyclic	ADJ
ejpam-2245	27	9	codes	code	NOUN
ejpam-2245	27	10	over	over	ADP
ejpam-2245	27	11	the	the	DET
ejpam-2245	27	12	ring	ring	NOUN
ejpam-2245	27	13	and	and	CCONJ
ejpam-2245	27	14	tabulate	tabulate	VERB
ejpam-2245	27	15	some	some	DET
ejpam-2245	27	16	good	good	ADJ
ejpam-2245	27	17	codes	code	NOUN
ejpam-2245	27	18	obtained	obtain	VERB
ejpam-2245	27	19	from	from	ADP
ejpam-2245	27	20	isodual	isodual	ADJ
ejpam-2245	27	21	cyclic	cyclic	ADJ
ejpam-2245	27	22	codes	code	NOUN
ejpam-2245	27	23	.	.	PUNCT
ejpam-2245	28	1	we	we	PRON
ejpam-2245	28	2	finish	finish	VERB
ejpam-2245	28	3	by	by	ADP
ejpam-2245	28	4	giving	give	VERB
ejpam-2245	28	5	several	several	ADJ
ejpam-2245	28	6	constructions	construction	NOUN
ejpam-2245	28	7	of	of	ADP
ejpam-2245	28	8	formally	formally	ADV
ejpam-2245	28	9	self	self	NOUN
ejpam-2245	28	10	-	-	PUNCT
ejpam-2245	28	11	dual	dual	ADJ
ejpam-2245	28	12	codes	code	NOUN
ejpam-2245	28	13	together	together	ADV
ejpam-2245	28	14	with	with	ADP
ejpam-2245	28	15	many	many	ADJ
ejpam-2245	28	16	examples	example	NOUN
ejpam-2245	28	17	of	of	ADP
ejpam-2245	28	18	good	good	ADJ
ejpam-2245	28	19	formally	formally	ADV
ejpam-2245	28	20	self	self	NOUN
ejpam-2245	28	21	-	-	PUNCT
ejpam-2245	28	22	dual	dual	ADJ
ejpam-2245	28	23	codes	code	NOUN
ejpam-2245	28	24	obtained	obtain	VERB
ejpam-2245	28	25	as	as	ADP
ejpam-2245	28	26	gray	gray	ADJ
ejpam-2245	28	27	images	image	NOUN
ejpam-2245	28	28	.	.	PUNCT
ejpam-2245	29	1	2	2	X
ejpam-2245	29	2	.	.	X
ejpam-2245	29	3	preliminaries	preliminary	NOUN
ejpam-2245	29	4	in	in	ADP
ejpam-2245	29	5	this	this	DET
ejpam-2245	29	6	section	section	NOUN
ejpam-2245	29	7	,	,	PUNCT
ejpam-2245	29	8	we	we	PRON
ejpam-2245	29	9	introduce	introduce	VERB
ejpam-2245	29	10	some	some	DET
ejpam-2245	29	11	basic	basic	ADJ
ejpam-2245	29	12	results	result	NOUN
ejpam-2245	29	13	on	on	ADP
ejpam-2245	29	14	linear	linear	ADJ
ejpam-2245	29	15	codes	code	NOUN
ejpam-2245	29	16	over	over	ADP
ejpam-2245	29	17	the	the	DET
ejpam-2245	29	18	ring	ring	NOUN
ejpam-2245	29	19	r=	r=	ADJ
ejpam-2245	29	20	fq+	fq+	PROPN
ejpam-2245	29	21	vfq	vfq	NOUN
ejpam-2245	29	22	,	,	PUNCT
ejpam-2245	29	23	q	q	DET
ejpam-2245	29	24	a	a	DET
ejpam-2245	29	25	prime	prime	ADJ
ejpam-2245	29	26	power	power	NOUN
ejpam-2245	29	27	,	,	PUNCT
ejpam-2245	29	28	where	where	SCONJ
ejpam-2245	29	29	v2	v2	NOUN
ejpam-2245	29	30	=	=	PUNCT
ejpam-2245	29	31	v.	v.	CCONJ
ejpam-2245	29	32	let	let	VERB
ejpam-2245	29	33	fq	fq	PRON
ejpam-2245	29	34	be	be	AUX
ejpam-2245	29	35	the	the	DET
ejpam-2245	29	36	finite	finite	ADJ
ejpam-2245	29	37	field	field	NOUN
ejpam-2245	29	38	of	of	ADP
ejpam-2245	29	39	order	order	NOUN
ejpam-2245	29	40	q	q	NOUN
ejpam-2245	29	41	and	and	CCONJ
ejpam-2245	29	42	f∗q	f∗q	NOUN
ejpam-2245	29	43	the	the	DET
ejpam-2245	29	44	multiplicative	multiplicative	ADJ
ejpam-2245	29	45	group	group	NOUN
ejpam-2245	29	46	of	of	ADP
ejpam-2245	29	47	fq	fq	PROPN
ejpam-2245	29	48	.	.	PUNCT
ejpam-2245	30	1	it	it	PRON
ejpam-2245	30	2	is	be	AUX
ejpam-2245	30	3	known	know	VERB
ejpam-2245	30	4	that	that	SCONJ
ejpam-2245	30	5	fq[x]/〈x	fq[x]/〈x	PROPN
ejpam-2245	30	6	n	n	CCONJ
ejpam-2245	30	7	−	−	PROPN
ejpam-2245	30	8	1	1	NUM
ejpam-2245	30	9	〉	〉	NOUN
ejpam-2245	30	10	is	be	AUX
ejpam-2245	30	11	a	a	DET
ejpam-2245	30	12	principal	principal	ADJ
ejpam-2245	30	13	ideal	ideal	ADJ
ejpam-2245	30	14	ring	ring	NOUN
ejpam-2245	30	15	.	.	PUNCT
ejpam-2245	31	1	we	we	PRON
ejpam-2245	31	2	adopt	adopt	VERB
ejpam-2245	31	3	the	the	DET
ejpam-2245	31	4	notation	notation	NOUN
ejpam-2245	31	5	〈	〈	NOUN
ejpam-2245	31	6	g(x	g(x	NOUN
ejpam-2245	31	7	)	)	PUNCT
ejpam-2245	31	8	〉	〉	NOUN
ejpam-2245	31	9	to	to	PART
ejpam-2245	31	10	denote	denote	VERB
ejpam-2245	31	11	the	the	DET
ejpam-2245	31	12	ideal	ideal	NOUN
ejpam-2245	31	13	in	in	ADP
ejpam-2245	31	14	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2245	31	15	n−1	n−1	PROPN
ejpam-2245	31	16	〉	〉	NOUN
ejpam-2245	31	17	generated	generate	VERB
ejpam-2245	31	18	by	by	ADP
ejpam-2245	31	19	g(x)with	g(x)with	VERB
ejpam-2245	31	20	g(x	g(x	NOUN
ejpam-2245	31	21	)	)	PUNCT
ejpam-2245	31	22	being	be	AUX
ejpam-2245	31	23	a	a	DET
ejpam-2245	31	24	monic	monic	ADJ
ejpam-2245	31	25	divisor	divisor	NOUN
ejpam-2245	31	26	of	of	ADP
ejpam-2245	31	27	xn	xn	PROPN
ejpam-2245	32	1	−	−	PROPN
ejpam-2245	32	2	1	1	NUM
ejpam-2245	32	3	,	,	PUNCT
ejpam-2245	32	4	in	in	ADP
ejpam-2245	32	5	this	this	DET
ejpam-2245	32	6	case	case	NOUN
ejpam-2245	32	7	g(x	g(x	NOUN
ejpam-2245	32	8	)	)	PUNCT
ejpam-2245	32	9	is	be	AUX
ejpam-2245	32	10	called	call	VERB
ejpam-2245	32	11	a	a	DET
ejpam-2245	32	12	generator	generator	NOUN
ejpam-2245	32	13	polynomial	polynomial	ADJ
ejpam-2245	32	14	.	.	PUNCT
ejpam-2245	33	1	throughout	throughout	ADP
ejpam-2245	33	2	this	this	DET
ejpam-2245	33	3	paper	paper	NOUN
ejpam-2245	33	4	,	,	PUNCT
ejpam-2245	33	5	we	we	PRON
ejpam-2245	33	6	let	let	VERB
ejpam-2245	33	7	r	r	NOUN
ejpam-2245	33	8	denote	denote	VERB
ejpam-2245	33	9	the	the	DET
ejpam-2245	33	10	commutative	commutative	ADJ
ejpam-2245	33	11	ring	ring	NOUN
ejpam-2245	33	12	fq	fq	PROPN
ejpam-2245	33	13	+	+	CCONJ
ejpam-2245	33	14	vfq	vfq	X
ejpam-2245	33	15	=	=	SYM
ejpam-2245	33	16	{	{	PUNCT
ejpam-2245	33	17	a+	a+	PUNCT
ejpam-2245	33	18	vb	vb	NOUN
ejpam-2245	33	19	|	|	ADV
ejpam-2245	33	20	a	a	PRON
ejpam-2245	33	21	,	,	PUNCT
ejpam-2245	33	22	b	b	PROPN
ejpam-2245	33	23	∈	∈	PROPN
ejpam-2245	33	24	fq	fq	PROPN
ejpam-2245	33	25	}	}	PUNCT
ejpam-2245	33	26	with	with	ADP
ejpam-2245	33	27	v2	v2	PROPN
ejpam-2245	33	28	=	=	PUNCT
ejpam-2245	34	1	v.	v.	CCONJ
ejpam-2245	34	2	it	it	PRON
ejpam-2245	34	3	turns	turn	VERB
ejpam-2245	34	4	out	out	ADP
ejpam-2245	34	5	r	r	NOUN
ejpam-2245	34	6	is	be	AUX
ejpam-2245	34	7	a	a	DET
ejpam-2245	34	8	principal	principal	ADJ
ejpam-2245	34	9	ideal	ideal	ADJ
ejpam-2245	34	10	ring	ring	NOUN
ejpam-2245	34	11	and	and	CCONJ
ejpam-2245	34	12	has	have	VERB
ejpam-2245	34	13	only	only	ADV
ejpam-2245	34	14	two	two	NUM
ejpam-2245	34	15	non	non	ADJ
ejpam-2245	34	16	-	-	ADJ
ejpam-2245	34	17	trivial	trivial	ADJ
ejpam-2245	34	18	ideals	ideal	NOUN
ejpam-2245	34	19	,	,	PUNCT
ejpam-2245	34	20	namely	namely	ADV
ejpam-2245	34	21	,	,	PUNCT
ejpam-2245	34	22	〈	〈	ADJ
ejpam-2245	34	23	v〉=	v〉=	NOUN
ejpam-2245	34	24	{	{	PUNCT
ejpam-2245	34	25	av	av	PROPN
ejpam-2245	34	26	|	|	ADV
ejpam-2245	34	27	a	a	DET
ejpam-2245	34	28	∈	∈	PROPN
ejpam-2245	34	29	fq	fq	NOUN
ejpam-2245	34	30	}	}	PUNCT
ejpam-2245	34	31	and	and	CCONJ
ejpam-2245	34	32	〈	〈	PROPN
ejpam-2245	34	33	1−	1−	NUM
ejpam-2245	34	34	v〉=	v〉=	NOUN
ejpam-2245	34	35	{	{	PUNCT
ejpam-2245	34	36	b(1−	b(1−	PROPN
ejpam-2245	34	37	v	v	NOUN
ejpam-2245	34	38	)	)	PUNCT
ejpam-2245	35	1	|	|	ADV
ejpam-2245	35	2	b	b	X
ejpam-2245	35	3	∈	∈	PROPN
ejpam-2245	35	4	fq	fq	PROPN
ejpam-2245	35	5	}	}	PUNCT
ejpam-2245	35	6	.	.	PUNCT
ejpam-2245	36	1	we	we	PRON
ejpam-2245	36	2	can	can	AUX
ejpam-2245	36	3	easily	easily	ADV
ejpam-2245	36	4	prove	prove	VERB
ejpam-2245	36	5	that	that	SCONJ
ejpam-2245	36	6	〈	〈	PROPN
ejpam-2245	36	7	v	v	NUM
ejpam-2245	36	8	〉	〉	NOUN
ejpam-2245	36	9	and	and	CCONJ
ejpam-2245	36	10	〈	〈	PROPN
ejpam-2245	36	11	1−	1−	NUM
ejpam-2245	36	12	v	v	NOUN
ejpam-2245	36	13	〉	〉	NOUN
ejpam-2245	36	14	are	be	AUX
ejpam-2245	36	15	maximal	maximal	ADJ
ejpam-2245	36	16	ideals	ideal	NOUN
ejpam-2245	36	17	in	in	ADP
ejpam-2245	36	18	r	r	NOUN
ejpam-2245	36	19	,	,	PUNCT
ejpam-2245	36	20	hence	hence	ADV
ejpam-2245	36	21	r	r	NOUN
ejpam-2245	36	22	is	be	AUX
ejpam-2245	36	23	not	not	PART
ejpam-2245	36	24	a	a	DET
ejpam-2245	36	25	chain	chain	NOUN
ejpam-2245	36	26	ring	ring	NOUN
ejpam-2245	36	27	.	.	PUNCT
ejpam-2245	37	1	let	let	VERB
ejpam-2245	37	2	rn	rn	PART
ejpam-2245	37	3	be	be	AUX
ejpam-2245	37	4	the	the	DET
ejpam-2245	37	5	r	r	NOUN
ejpam-2245	37	6	-	-	PUNCT
ejpam-2245	37	7	module	module	NOUN
ejpam-2245	37	8	of	of	ADP
ejpam-2245	37	9	n	n	CCONJ
ejpam-2245	37	10	-	-	PUNCT
ejpam-2245	37	11	tuples	tuple	NOUN
ejpam-2245	37	12	over	over	ADP
ejpam-2245	37	13	r.	r.	PROPN
ejpam-2245	37	14	a	a	DET
ejpam-2245	37	15	linear	linear	PROPN
ejpam-2245	37	16	code	code	NOUN
ejpam-2245	37	17	c	c	NOUN
ejpam-2245	37	18	over	over	ADP
ejpam-2245	37	19	r	r	NOUN
ejpam-2245	37	20	of	of	ADP
ejpam-2245	37	21	length	length	NOUN
ejpam-2245	37	22	n	n	CCONJ
ejpam-2245	37	23	over	over	ADP
ejpam-2245	37	24	r	r	NOUN
ejpam-2245	37	25	is	be	AUX
ejpam-2245	37	26	an	an	DET
ejpam-2245	37	27	r	r	NOUN
ejpam-2245	37	28	-	-	PUNCT
ejpam-2245	37	29	submodule	submodule	NOUN
ejpam-2245	37	30	of	of	ADP
ejpam-2245	37	31	rn	rn	PROPN
ejpam-2245	37	32	.	.	PROPN
ejpam-2245	38	1	for	for	ADP
ejpam-2245	38	2	any	any	DET
ejpam-2245	38	3	linear	linear	PROPN
ejpam-2245	38	4	code	code	NOUN
ejpam-2245	38	5	c	c	NOUN
ejpam-2245	38	6	of	of	ADP
ejpam-2245	38	7	length	length	NOUN
ejpam-2245	38	8	n	n	CCONJ
ejpam-2245	38	9	over	over	ADP
ejpam-2245	38	10	r	r	NOUN
ejpam-2245	38	11	the	the	DET
ejpam-2245	38	12	dual	dual	ADJ
ejpam-2245	38	13	c⊥	c⊥	NOUN
ejpam-2245	38	14	is	be	AUX
ejpam-2245	38	15	defined	define	VERB
ejpam-2245	38	16	as	as	ADP
ejpam-2245	38	17	c⊥	c⊥	X
ejpam-2245	38	18	=	=	X
ejpam-2245	38	19	{	{	PUNCT
ejpam-2245	38	20	u	u	NOUN
ejpam-2245	38	21	∈	∈	PROPN
ejpam-2245	38	22	rn	rn	PROPN
ejpam-2245	38	23	|u	|u	PROPN
ejpam-2245	38	24	·	·	SYM
ejpam-2245	38	25	w=	w=	NOUN
ejpam-2245	38	26	0	0	NUM
ejpam-2245	38	27	,	,	PUNCT
ejpam-2245	38	28	∀w	∀w	X
ejpam-2245	38	29	∈	∈	PROPN
ejpam-2245	38	30	c	c	NOUN
ejpam-2245	38	31	}	}	PUNCT
ejpam-2245	38	32	where	where	SCONJ
ejpam-2245	38	33	u	u	NOUN
ejpam-2245	38	34	·	·	PUNCT
ejpam-2245	38	35	w	w	PROPN
ejpam-2245	38	36	denotes	denote	VERB
ejpam-2245	38	37	the	the	DET
ejpam-2245	38	38	standard	standard	ADJ
ejpam-2245	38	39	euclidean	euclidean	ADJ
ejpam-2245	38	40	inner	inner	ADJ
ejpam-2245	38	41	product	product	NOUN
ejpam-2245	38	42	of	of	ADP
ejpam-2245	38	43	u	u	PROPN
ejpam-2245	38	44	and	and	CCONJ
ejpam-2245	38	45	w	w	PROPN
ejpam-2245	38	46	in	in	ADP
ejpam-2245	38	47	rn	rn	PROPN
ejpam-2245	38	48	.	.	PROPN
ejpam-2245	38	49	note	note	VERB
ejpam-2245	38	50	that	that	SCONJ
ejpam-2245	38	51	c⊥	c⊥	PROPN
ejpam-2245	38	52	is	be	AUX
ejpam-2245	38	53	linear	linear	ADJ
ejpam-2245	38	54	whether	whether	SCONJ
ejpam-2245	38	55	or	or	CCONJ
ejpam-2245	38	56	not	not	PART
ejpam-2245	38	57	c	c	NOUN
ejpam-2245	38	58	is	be	AUX
ejpam-2245	38	59	linear	linear	ADJ
ejpam-2245	38	60	.	.	PUNCT
ejpam-2245	39	1	the	the	DET
ejpam-2245	39	2	gray	gray	ADJ
ejpam-2245	39	3	map	map	NOUN
ejpam-2245	39	4	ψ	ψ	VERB
ejpam-2245	39	5	from	from	ADP
ejpam-2245	39	6	r	r	NOUN
ejpam-2245	39	7	to	to	ADP
ejpam-2245	39	8	fq⊕fq	fq⊕fq	PROPN
ejpam-2245	39	9	given	give	VERB
ejpam-2245	39	10	by	by	ADP
ejpam-2245	39	11	ψ(c	ψ(c	NOUN
ejpam-2245	39	12	)	)	PUNCT
ejpam-2245	39	13	=	=	PUNCT
ejpam-2245	39	14	(	(	PUNCT
ejpam-2245	39	15	a	a	PRON
ejpam-2245	39	16	,	,	PUNCT
ejpam-2245	39	17	a+	a+	PRON
ejpam-2245	39	18	b	b	X
ejpam-2245	39	19	)	)	PUNCT
ejpam-2245	39	20	,	,	PUNCT
ejpam-2245	39	21	is	be	AUX
ejpam-2245	39	22	a	a	DET
ejpam-2245	39	23	ring	ring	NOUN
ejpam-2245	39	24	isomorphism	isomorphism	NOUN
ejpam-2245	39	25	,	,	PUNCT
ejpam-2245	39	26	which	which	PRON
ejpam-2245	39	27	means	mean	VERB
ejpam-2245	39	28	that	that	SCONJ
ejpam-2245	39	29	r	r	NOUN
ejpam-2245	39	30	is	be	AUX
ejpam-2245	39	31	isomorphic	isomorphic	ADJ
ejpam-2245	39	32	to	to	ADP
ejpam-2245	39	33	the	the	DET
ejpam-2245	39	34	ring	ring	NOUN
ejpam-2245	39	35	fq	fq	PROPN
ejpam-2245	39	36	⊕	⊕	PROPN
ejpam-2245	39	37	fq	fq	PROPN
ejpam-2245	39	38	therefore	therefore	ADV
ejpam-2245	39	39	r	r	NOUN
ejpam-2245	39	40	is	be	AUX
ejpam-2245	39	41	a	a	DET
ejpam-2245	39	42	finite	finite	ADJ
ejpam-2245	39	43	frobenius	frobenius	NOUN
ejpam-2245	39	44	ring	ring	NOUN
ejpam-2245	39	45	.	.	PUNCT
ejpam-2245	40	1	for	for	ADP
ejpam-2245	40	2	the	the	DET
ejpam-2245	40	3	case	case	NOUN
ejpam-2245	40	4	where	where	SCONJ
ejpam-2245	40	5	q	q	NOUN
ejpam-2245	40	6	is	be	AUX
ejpam-2245	40	7	a	a	DET
ejpam-2245	40	8	prime	prime	NOUN
ejpam-2245	40	9	the	the	DET
ejpam-2245	40	10	linear	linear	ADJ
ejpam-2245	40	11	and	and	CCONJ
ejpam-2245	40	12	duality	duality	NOUN
ejpam-2245	40	13	preserving	preserve	VERB
ejpam-2245	40	14	gray	gray	ADJ
ejpam-2245	40	15	map	map	NOUN
ejpam-2245	40	16	ψ	ψ	X
ejpam-2245	40	17	(	(	PUNCT
ejpam-2245	40	18	a+	a+	X
ejpam-2245	40	19	bv	bv	PROPN
ejpam-2245	40	20	)	)	PUNCT
ejpam-2245	40	21	=	=	NOUN
ejpam-2245	40	22	(	(	PUNCT
ejpam-2245	40	23	−b	−b	ADJ
ejpam-2245	40	24	,	,	PUNCT
ejpam-2245	40	25	2a+	2a+	NUM
ejpam-2245	40	26	b	b	X
ejpam-2245	40	27	)	)	PUNCT
ejpam-2245	40	28	from	from	ADP
ejpam-2245	40	29	[	[	X
ejpam-2245	40	30	16	16	NUM
ejpam-2245	40	31	]	]	PUNCT
ejpam-2245	40	32	is	be	AUX
ejpam-2245	40	33	used	use	VERB
ejpam-2245	40	34	for	for	ADP
ejpam-2245	40	35	computational	computational	ADJ
ejpam-2245	40	36	results	result	NOUN
ejpam-2245	40	37	in	in	ADP
ejpam-2245	40	38	tables	table	NOUN
ejpam-2245	40	39	1	1	NUM
ejpam-2245	40	40	,	,	PUNCT
ejpam-2245	40	41	2	2	NUM
ejpam-2245	40	42	and	and	CCONJ
ejpam-2245	40	43	3	3	NUM
ejpam-2245	40	44	.	.	PUNCT
ejpam-2245	41	1	if	if	SCONJ
ejpam-2245	41	2	c	c	PROPN
ejpam-2245	41	3	is	be	AUX
ejpam-2245	41	4	linear	linear	ADJ
ejpam-2245	41	5	then	then	ADV
ejpam-2245	41	6	|c	|c	VERB
ejpam-2245	41	7	||c⊥|	||c⊥|	ADJ
ejpam-2245	41	8	=	=	SYM
ejpam-2245	41	9	|r|n	|r|n	PRON
ejpam-2245	41	10	see	see	VERB
ejpam-2245	41	11	[	[	X
ejpam-2245	41	12	15	15	NUM
ejpam-2245	41	13	]	]	PUNCT
ejpam-2245	41	14	.	.	PUNCT
ejpam-2245	42	1	a	a	DET
ejpam-2245	42	2	linear	linear	PROPN
ejpam-2245	42	3	code	code	NOUN
ejpam-2245	42	4	c	c	NOUN
ejpam-2245	42	5	over	over	ADP
ejpam-2245	42	6	r	r	NOUN
ejpam-2245	42	7	is	be	AUX
ejpam-2245	42	8	said	say	VERB
ejpam-2245	42	9	to	to	PART
ejpam-2245	42	10	be	be	AUX
ejpam-2245	42	11	cyclic	cyclic	ADJ
ejpam-2245	42	12	if	if	SCONJ
ejpam-2245	42	13	it	it	PRON
ejpam-2245	42	14	satisfies	satisfy	VERB
ejpam-2245	42	15	(	(	PUNCT
ejpam-2245	42	16	cn−1	cn−1	PROPN
ejpam-2245	42	17	,	,	PUNCT
ejpam-2245	42	18	c0	c0	NOUN
ejpam-2245	42	19	,	,	PUNCT
ejpam-2245	42	20	.	.	PUNCT
ejpam-2245	42	21	.	.	PUNCT
ejpam-2245	43	1	.	.	PUNCT
ejpam-2245	44	1	,	,	PUNCT
ejpam-2245	44	2	cn−2	cn−2	PROPN
ejpam-2245	44	3	)	)	PUNCT
ejpam-2245	44	4	∈	∈	PROPN
ejpam-2245	44	5	c	c	NOUN
ejpam-2245	44	6	,	,	PUNCT
ejpam-2245	44	7	whenever	whenever	SCONJ
ejpam-2245	44	8	(	(	PUNCT
ejpam-2245	44	9	c0	c0	NOUN
ejpam-2245	44	10	,	,	PUNCT
ejpam-2245	44	11	c1	c1	PROPN
ejpam-2245	44	12	,	,	PUNCT
ejpam-2245	44	13	.	.	PUNCT
ejpam-2245	44	14	.	.	PUNCT
ejpam-2245	44	15	.	.	PUNCT
ejpam-2245	45	1	,	,	PUNCT
ejpam-2245	45	2	cn−1	cn−1	X
ejpam-2245	45	3	)	)	PUNCT
ejpam-2245	45	4	∈	∈	PROPN
ejpam-2245	45	5	c	c	NOUN
ejpam-2245	45	6	.	.	PUNCT
ejpam-2245	46	1	it	it	PRON
ejpam-2245	46	2	is	be	AUX
ejpam-2245	46	3	well	well	ADV
ejpam-2245	46	4	known	know	VERB
ejpam-2245	46	5	that	that	SCONJ
ejpam-2245	46	6	cyclic	cyclic	ADJ
ejpam-2245	46	7	codes	code	NOUN
ejpam-2245	46	8	of	of	ADP
ejpam-2245	46	9	length	length	NOUN
ejpam-2245	46	10	n	n	CCONJ
ejpam-2245	46	11	over	over	ADP
ejpam-2245	46	12	r	r	NOUN
ejpam-2245	46	13	can	can	AUX
ejpam-2245	46	14	be	be	AUX
ejpam-2245	46	15	identified	identify	VERB
ejpam-2245	46	16	with	with	ADP
ejpam-2245	46	17	an	an	DET
ejpam-2245	46	18	ideal	ideal	NOUN
ejpam-2245	46	19	in	in	ADP
ejpam-2245	46	20	the	the	DET
ejpam-2245	46	21	quotient	quotient	NOUN
ejpam-2245	46	22	ring	ring	NOUN
ejpam-2245	46	23	r[x]/〈xn	r[x]/〈xn	PROPN
ejpam-2245	46	24	−	−	NOUN
ejpam-2245	46	25	1	1	NUM
ejpam-2245	46	26	〉	〉	NOUN
ejpam-2245	46	27	via	via	ADP
ejpam-2245	46	28	the	the	DET
ejpam-2245	46	29	r	r	NOUN
ejpam-2245	46	30	-	-	PUNCT
ejpam-2245	46	31	module	module	NOUN
ejpam-2245	46	32	isomorphism	isomorphism	NOUN
ejpam-2245	46	33	as	as	SCONJ
ejpam-2245	46	34	follows	follow	VERB
ejpam-2245	46	35	:	:	PUNCT
ejpam-2245	47	1	rn	rn	ADV
ejpam-2245	47	2	−→	−→	NOUN
ejpam-2245	47	3	r[x]/〈xn	r[x]/〈xn	PROPN
ejpam-2245	47	4	−	−	NOUN
ejpam-2245	47	5	1	1	NUM
ejpam-2245	47	6	〉	〉	NOUN
ejpam-2245	47	7	(	(	PUNCT
ejpam-2245	47	8	c0	c0	NOUN
ejpam-2245	47	9	,	,	PUNCT
ejpam-2245	47	10	c1	c1	PROPN
ejpam-2245	47	11	,	,	PUNCT
ejpam-2245	47	12	.	.	PUNCT
ejpam-2245	47	13	.	.	PUNCT
ejpam-2245	47	14	.	.	PUNCT
ejpam-2245	48	1	,	,	PUNCT
ejpam-2245	48	2	cn−1	cn−1	NOUN
ejpam-2245	48	3	)	)	PUNCT
ejpam-2245	48	4	7→	7→	NUM
ejpam-2245	48	5	c0	c0	NOUN
ejpam-2245	48	6	+	+	CCONJ
ejpam-2245	48	7	c1	c1	PROPN
ejpam-2245	48	8	x	x	PUNCT
ejpam-2245	49	1	+	+	CCONJ
ejpam-2245	49	2	.	.	PUNCT
ejpam-2245	49	3	.	.	PUNCT
ejpam-2245	50	1	.+	.+	NOUN
ejpam-2245	50	2	cn−1	cn−1	PROPN
ejpam-2245	50	3	xn−1	xn−1	PROPN
ejpam-2245	50	4	.	.	PUNCT
ejpam-2245	51	1	(	(	PUNCT
ejpam-2245	51	2	1	1	X
ejpam-2245	51	3	)	)	PUNCT
ejpam-2245	51	4	let	let	VERB
ejpam-2245	51	5	a	a	DET
ejpam-2245	51	6	,	,	PUNCT
ejpam-2245	51	7	b	b	NOUN
ejpam-2245	51	8	be	be	AUX
ejpam-2245	51	9	codes	code	NOUN
ejpam-2245	51	10	over	over	ADP
ejpam-2245	51	11	r.	r.	PROPN
ejpam-2245	51	12	we	we	PRON
ejpam-2245	51	13	denote	denote	VERB
ejpam-2245	51	14	a⊕	a⊕	PROPN
ejpam-2245	51	15	b	b	PROPN
ejpam-2245	51	16	=	=	PRON
ejpam-2245	51	17	{	{	PUNCT
ejpam-2245	51	18	a+	a+	NOUN
ejpam-2245	51	19	b	b	NOUN
ejpam-2245	52	1	|	|	ADV
ejpam-2245	52	2	a	a	DET
ejpam-2245	52	3	∈	∈	PROPN
ejpam-2245	52	4	a	a	PRON
ejpam-2245	52	5	,	,	PUNCT
ejpam-2245	52	6	b	b	PROPN
ejpam-2245	52	7	∈	∈	PROPN
ejpam-2245	52	8	b	b	NOUN
ejpam-2245	52	9	}	}	PUNCT
ejpam-2245	52	10	.	.	PUNCT
ejpam-2245	53	1	a.	a.	PROPN
ejpam-2245	53	2	batoul	batoul	PROPN
ejpam-2245	53	3	,	,	PUNCT
ejpam-2245	53	4	k.	k.	PROPN
ejpam-2245	53	5	guenda	guenda	PROPN
ejpam-2245	53	6	,	,	PUNCT
ejpam-2245	53	7	a.	a.	PROPN
ejpam-2245	53	8	kaya	kaya	PROPN
ejpam-2245	53	9	,	,	PUNCT
ejpam-2245	53	10	b.	b.	PROPN
ejpam-2245	53	11	yildiz	yildiz	PROPN
ejpam-2245	53	12	/	/	SYM
ejpam-2245	53	13	eur	eur	PROPN
ejpam-2245	53	14	.	.	PUNCT
ejpam-2245	54	1	j.	j.	PROPN
ejpam-2245	54	2	pure	pure	PROPN
ejpam-2245	54	3	appl	appl	PROPN
ejpam-2245	54	4	.	.	PROPN
ejpam-2245	54	5	math	math	PROPN
ejpam-2245	54	6	,	,	PUNCT
ejpam-2245	54	7	8	8	NUM
ejpam-2245	54	8	(	(	PUNCT
ejpam-2245	54	9	2015	2015	NUM
ejpam-2245	54	10	)	)	PUNCT
ejpam-2245	54	11	,	,	PUNCT
ejpam-2245	54	12	64	64	NUM
ejpam-2245	54	13	-	-	SYM
ejpam-2245	54	14	80	80	NUM
ejpam-2245	54	15	66	66	NUM
ejpam-2245	54	16	note	note	NOUN
ejpam-2245	54	17	that	that	SCONJ
ejpam-2245	54	18	any	any	DET
ejpam-2245	54	19	element	element	NOUN
ejpam-2245	54	20	c	c	PROPN
ejpam-2245	54	21	of	of	ADP
ejpam-2245	54	22	rn	rn	PROPN
ejpam-2245	54	23	can	can	AUX
ejpam-2245	54	24	be	be	AUX
ejpam-2245	54	25	expressed	express	VERB
ejpam-2245	54	26	as	as	ADP
ejpam-2245	54	27	av	av	PROPN
ejpam-2245	54	28	+	+	CCONJ
ejpam-2245	54	29	b(1−	b(1−	PROPN
ejpam-2245	54	30	v	v	NOUN
ejpam-2245	54	31	)	)	PUNCT
ejpam-2245	54	32	where	where	SCONJ
ejpam-2245	54	33	a	a	PRON
ejpam-2245	54	34	,	,	PUNCT
ejpam-2245	54	35	b	b	PROPN
ejpam-2245	54	36	∈	∈	PROPN
ejpam-2245	54	37	fn	fn	NOUN
ejpam-2245	54	38	q	q	NOUN
ejpam-2245	54	39	.	.	PUNCT
ejpam-2245	55	1	let	let	VERB
ejpam-2245	55	2	c	c	PRON
ejpam-2245	55	3	be	be	AUX
ejpam-2245	55	4	a	a	DET
ejpam-2245	55	5	linear	linear	ADJ
ejpam-2245	55	6	code	code	NOUN
ejpam-2245	55	7	of	of	ADP
ejpam-2245	55	8	length	length	NOUN
ejpam-2245	55	9	n	n	PROPN
ejpam-2245	55	10	over	over	ADP
ejpam-2245	55	11	r.	r.	PROPN
ejpam-2245	55	12	define	define	PROPN
ejpam-2245	55	13	c1	c1	PROPN
ejpam-2245	55	14	=	=	PUNCT
ejpam-2245	55	15	{	{	PUNCT
ejpam-2245	55	16	a	a	DET
ejpam-2245	55	17	∈	∈	X
ejpam-2245	55	18	f	f	NOUN
ejpam-2245	55	19	n	n	CCONJ
ejpam-2245	55	20	p	p	PROPN
ejpam-2245	55	21	|	|	ADV
ejpam-2245	55	22	va+	va+	PROPN
ejpam-2245	55	23	(	(	PUNCT
ejpam-2245	55	24	1−	1−	NUM
ejpam-2245	55	25	v)b	v)b	NOUN
ejpam-2245	55	26	∈	∈	PROPN
ejpam-2245	55	27	c	c	NOUN
ejpam-2245	55	28	for	for	ADP
ejpam-2245	55	29	some	some	DET
ejpam-2245	55	30	b	b	NOUN
ejpam-2245	55	31	∈	∈	NOUN
ejpam-2245	55	32	fn	fn	NOUN
ejpam-2245	55	33	q	q	NOUN
ejpam-2245	55	34	}	}	PUNCT
ejpam-2245	55	35	and	and	CCONJ
ejpam-2245	55	36	c2	c2	PROPN
ejpam-2245	55	37	=	=	PUNCT
ejpam-2245	55	38	{	{	PUNCT
ejpam-2245	55	39	b	b	PROPN
ejpam-2245	55	40	∈	∈	PROPN
ejpam-2245	55	41	f	f	PROPN
ejpam-2245	55	42	n	n	PRON
ejpam-2245	55	43	p	p	PROPN
ejpam-2245	55	44	|	|	ADV
ejpam-2245	55	45	va+	va+	PROPN
ejpam-2245	55	46	(	(	PUNCT
ejpam-2245	55	47	1−	1−	NUM
ejpam-2245	55	48	v)b	v)b	NOUN
ejpam-2245	55	49	∈	∈	PROPN
ejpam-2245	55	50	c	c	NOUN
ejpam-2245	55	51	for	for	ADP
ejpam-2245	55	52	some	some	DET
ejpam-2245	55	53	a	a	DET
ejpam-2245	55	54	∈	∈	NOUN
ejpam-2245	55	55	fn	fn	NOUN
ejpam-2245	55	56	q	q	NOUN
ejpam-2245	55	57	}	}	PUNCT
ejpam-2245	55	58	.	.	PUNCT
ejpam-2245	56	1	obviously	obviously	ADV
ejpam-2245	56	2	c1	c1	PROPN
ejpam-2245	56	3	and	and	CCONJ
ejpam-2245	56	4	c2	c2	PROPN
ejpam-2245	56	5	are	be	AUX
ejpam-2245	56	6	linear	linear	PROPN
ejpam-2245	56	7	codes	code	NOUN
ejpam-2245	56	8	over	over	ADP
ejpam-2245	56	9	fq	fq	PROPN
ejpam-2245	56	10	.	.	PROPN
ejpam-2245	56	11	by	by	ADP
ejpam-2245	56	12	the	the	DET
ejpam-2245	56	13	definition	definition	NOUN
ejpam-2245	56	14	of	of	ADP
ejpam-2245	56	15	c1	c1	PROPN
ejpam-2245	56	16	and	and	CCONJ
ejpam-2245	56	17	c2	c2	PROPN
ejpam-2245	56	18	we	we	PRON
ejpam-2245	56	19	have	have	VERB
ejpam-2245	56	20	that	that	PRON
ejpam-2245	56	21	c	c	PROPN
ejpam-2245	56	22	can	can	AUX
ejpam-2245	56	23	be	be	AUX
ejpam-2245	56	24	uniquely	uniquely	ADV
ejpam-2245	56	25	expressed	express	VERB
ejpam-2245	56	26	as	as	ADP
ejpam-2245	56	27	c	c	X
ejpam-2245	56	28	=	=	PUNCT
ejpam-2245	56	29	vc1	vc1	PROPN
ejpam-2245	56	30	⊕	⊕	PROPN
ejpam-2245	56	31	(	(	PUNCT
ejpam-2245	56	32	1−	1−	NUM
ejpam-2245	56	33	v)c2	v)c2	PROPN
ejpam-2245	56	34	.	.	PUNCT
ejpam-2245	57	1	so	so	ADV
ejpam-2245	57	2	c1	c1	PROPN
ejpam-2245	57	3	and	and	CCONJ
ejpam-2245	57	4	c2	c2	PROPN
ejpam-2245	57	5	are	be	AUX
ejpam-2245	57	6	unique	unique	ADJ
ejpam-2245	57	7	.	.	PUNCT
ejpam-2245	58	1	we	we	PRON
ejpam-2245	58	2	observe	observe	VERB
ejpam-2245	58	3	that	that	SCONJ
ejpam-2245	58	4	in	in	ADP
ejpam-2245	58	5	that	that	DET
ejpam-2245	58	6	case	case	NOUN
ejpam-2245	58	7	we	we	PRON
ejpam-2245	58	8	have	have	VERB
ejpam-2245	58	9	|c	|c	VERB
ejpam-2245	58	10	|=	|=	NOUN
ejpam-2245	58	11	|c1||c2|	|c1||c2|	NOUN
ejpam-2245	58	12	.	.	PUNCT
ejpam-2245	59	1	the	the	DET
ejpam-2245	59	2	extended	extended	ADJ
ejpam-2245	59	3	code	code	NOUN
ejpam-2245	59	4	of	of	ADP
ejpam-2245	59	5	a	a	DET
ejpam-2245	59	6	code	code	NOUN
ejpam-2245	59	7	c	c	NOUN
ejpam-2245	59	8	over	over	ADP
ejpam-2245	59	9	fq	fq	PROPN
ejpam-2245	59	10	+	+	CCONJ
ejpam-2245	59	11	vfq	vfq	NOUN
ejpam-2245	59	12	will	will	AUX
ejpam-2245	59	13	be	be	AUX
ejpam-2245	59	14	denoted	denote	VERB
ejpam-2245	59	15	by	by	ADP
ejpam-2245	59	16	ec	ec	PROPN
ejpam-2245	59	17	,	,	PUNCT
ejpam-2245	59	18	which	which	PRON
ejpam-2245	59	19	is	be	AUX
ejpam-2245	59	20	the	the	DET
ejpam-2245	59	21	code	code	NOUN
ejpam-2245	59	22	obtained	obtain	VERB
ejpam-2245	59	23	by	by	ADP
ejpam-2245	59	24	adding	add	VERB
ejpam-2245	59	25	a	a	DET
ejpam-2245	59	26	specific	specific	ADJ
ejpam-2245	59	27	column	column	NOUN
ejpam-2245	59	28	to	to	ADP
ejpam-2245	59	29	the	the	DET
ejpam-2245	59	30	generator	generator	NOUN
ejpam-2245	59	31	matrix	matrix	NOUN
ejpam-2245	59	32	of	of	ADP
ejpam-2245	59	33	c	c	PROPN
ejpam-2245	59	34	.	.	PUNCT
ejpam-2245	60	1	lemma	lemma	PROPN
ejpam-2245	60	2	1	1	X
ejpam-2245	60	3	.	.	PUNCT
ejpam-2245	61	1	let	let	VERB
ejpam-2245	61	2	r∗	r∗	PROPN
ejpam-2245	61	3	denote	denote	VERB
ejpam-2245	61	4	the	the	DET
ejpam-2245	61	5	group	group	NOUN
ejpam-2245	61	6	of	of	ADP
ejpam-2245	61	7	units	unit	NOUN
ejpam-2245	61	8	of	of	ADP
ejpam-2245	61	9	r	r	NOUN
ejpam-2245	61	10	then	then	ADV
ejpam-2245	61	11	r∗	r∗	VERB
ejpam-2245	61	12	=	=	PUNCT
ejpam-2245	61	13	vf∗q	vf∗q	PROPN
ejpam-2245	61	14	⊕	⊕	PROPN
ejpam-2245	61	15	(	(	PUNCT
ejpam-2245	61	16	1−	1−	NUM
ejpam-2245	61	17	v)f∗q	v)f∗q	NOUN
ejpam-2245	61	18	.	.	PUNCT
ejpam-2245	62	1	proof	proof	NOUN
ejpam-2245	62	2	.	.	PUNCT
ejpam-2245	63	1	since	since	SCONJ
ejpam-2245	63	2	r	r	NOUN
ejpam-2245	63	3	decomposes	decompose	NOUN
ejpam-2245	63	4	as	as	ADP
ejpam-2245	63	5	a	a	DET
ejpam-2245	63	6	direct	direct	ADJ
ejpam-2245	63	7	sum	sum	NOUN
ejpam-2245	63	8	r	r	NOUN
ejpam-2245	63	9	=	=	SYM
ejpam-2245	63	10	vfq	vfq	NOUN
ejpam-2245	63	11	⊕	⊕	PROPN
ejpam-2245	63	12	(	(	PUNCT
ejpam-2245	63	13	1	1	NUM
ejpam-2245	63	14	−	−	PROPN
ejpam-2245	63	15	v)fq	v)fq	PROPN
ejpam-2245	63	16	.	.	PUNCT
ejpam-2245	64	1	then	then	ADV
ejpam-2245	64	2	r∗	r∗	VERB
ejpam-2245	64	3	decomposes	decompose	VERB
ejpam-2245	64	4	naturally	naturally	ADV
ejpam-2245	64	5	as	as	ADP
ejpam-2245	64	6	a	a	DET
ejpam-2245	64	7	direct	direct	ADJ
ejpam-2245	64	8	product	product	NOUN
ejpam-2245	64	9	of	of	ADP
ejpam-2245	64	10	groups	group	NOUN
ejpam-2245	64	11	;	;	PUNCT
ejpam-2245	64	12	r∗	r∗	PROPN
ejpam-2245	64	13	=	=	SYM
ejpam-2245	64	14	vf∗q	vf∗q	PROPN
ejpam-2245	64	15	⊕	⊕	PROPN
ejpam-2245	64	16	(	(	PUNCT
ejpam-2245	64	17	1−	1−	NUM
ejpam-2245	64	18	v)f∗q	v)f∗q	NOUN
ejpam-2245	64	19	.	.	PUNCT
ejpam-2245	65	1	so	so	ADV
ejpam-2245	65	2	if	if	SCONJ
ejpam-2245	65	3	λ	λ	PROPN
ejpam-2245	65	4	∈	∈	PROPN
ejpam-2245	65	5	r∗	r∗	PROPN
ejpam-2245	65	6	,	,	PUNCT
ejpam-2245	65	7	then	then	ADV
ejpam-2245	65	8	λ	λ	X
ejpam-2245	65	9	=	=	PRON
ejpam-2245	65	10	λ1v	λ1v	X
ejpam-2245	66	1	+	+	CCONJ
ejpam-2245	66	2	(	(	PUNCT
ejpam-2245	66	3	1−	1−	NUM
ejpam-2245	66	4	v)λ2	v)λ2	PROPN
ejpam-2245	66	5	where	where	SCONJ
ejpam-2245	66	6	each	each	PRON
ejpam-2245	66	7	λi	λi	ADP
ejpam-2245	66	8	∈	∈	PROPN
ejpam-2245	66	9	f	f	PROPN
ejpam-2245	66	10	∗	∗	X
ejpam-2245	66	11	q	q	PROPN
ejpam-2245	66	12	,	,	PUNCT
ejpam-2245	66	13	for	for	ADP
ejpam-2245	66	14	1≤	1≤	NUM
ejpam-2245	66	15	i	i	PRON
ejpam-2245	66	16	≤	≤	ADJ
ejpam-2245	66	17	2	2	NUM
ejpam-2245	66	18	.	.	PUNCT
ejpam-2245	67	1	a	a	DET
ejpam-2245	67	2	monomial	monomial	ADJ
ejpam-2245	67	3	linear	linear	ADJ
ejpam-2245	67	4	transformation	transformation	NOUN
ejpam-2245	67	5	of	of	ADP
ejpam-2245	67	6	rn	rn	PROPN
ejpam-2245	67	7	is	be	AUX
ejpam-2245	67	8	an	an	DET
ejpam-2245	67	9	r	r	NOUN
ejpam-2245	67	10	-	-	PUNCT
ejpam-2245	67	11	linear	linear	NOUN
ejpam-2245	67	12	transformation	transformation	NOUN
ejpam-2245	67	13	τ	τ	PUNCT
ejpam-2245	67	14	such	such	ADJ
ejpam-2245	67	15	that	that	SCONJ
ejpam-2245	67	16	there	there	PRON
ejpam-2245	67	17	exist	exist	VERB
ejpam-2245	67	18	scalars	scalar	NOUN
ejpam-2245	67	19	λ1	λ1	ADJ
ejpam-2245	67	20	,	,	PUNCT
ejpam-2245	67	21	.	.	PUNCT
ejpam-2245	67	22	.	.	PUNCT
ejpam-2245	68	1	.	.	PUNCT
ejpam-2245	69	1	,	,	PUNCT
ejpam-2245	69	2	λn	λn	NOUN
ejpam-2245	69	3	in	in	ADP
ejpam-2245	69	4	r∗	r∗	PROPN
ejpam-2245	69	5	and	and	CCONJ
ejpam-2245	69	6	a	a	DET
ejpam-2245	69	7	permutation	permutation	NOUN
ejpam-2245	69	8	σ	σ	X
ejpam-2245	69	9	∈	∈	PROPN
ejpam-2245	69	10	sn	sn	PROPN
ejpam-2245	69	11	,	,	PUNCT
ejpam-2245	69	12	the	the	DET
ejpam-2245	69	13	group	group	NOUN
ejpam-2245	69	14	of	of	ADP
ejpam-2245	69	15	permutations	permutation	NOUN
ejpam-2245	69	16	of	of	ADP
ejpam-2245	69	17	the	the	DET
ejpam-2245	69	18	set	set	NOUN
ejpam-2245	69	19	{	{	PUNCT
ejpam-2245	69	20	1,2	1,2	NUM
ejpam-2245	69	21	,	,	PUNCT
ejpam-2245	69	22	.	.	PUNCT
ejpam-2245	69	23	.	.	PUNCT
ejpam-2245	70	1	.	.	PUNCT
ejpam-2245	71	1	,	,	PUNCT
ejpam-2245	71	2	n	n	CCONJ
ejpam-2245	71	3	}	}	PUNCT
ejpam-2245	71	4	,	,	PUNCT
ejpam-2245	71	5	such	such	ADJ
ejpam-2245	71	6	that	that	SCONJ
ejpam-2245	71	7	,	,	PUNCT
ejpam-2245	71	8	for	for	ADP
ejpam-2245	71	9	all	all	PRON
ejpam-2245	71	10	(	(	PUNCT
ejpam-2245	71	11	x1	x1	PROPN
ejpam-2245	71	12	,	,	PUNCT
ejpam-2245	71	13	x2	x2	PROPN
ejpam-2245	71	14	,	,	PUNCT
ejpam-2245	71	15	.	.	PUNCT
ejpam-2245	71	16	.	.	PUNCT
ejpam-2245	72	1	.	.	PUNCT
ejpam-2245	73	1	,	,	PUNCT
ejpam-2245	73	2	xn	xn	X
ejpam-2245	73	3	)	)	PUNCT
ejpam-2245	73	4	∈	∈	PROPN
ejpam-2245	73	5	rn	rn	PROPN
ejpam-2245	73	6	,	,	PUNCT
ejpam-2245	73	7	we	we	PRON
ejpam-2245	73	8	have	have	VERB
ejpam-2245	73	9	τ(x1	τ(x1	NUM
ejpam-2245	73	10	,	,	PUNCT
ejpam-2245	73	11	.	.	PUNCT
ejpam-2245	73	12	.	.	PUNCT
ejpam-2245	74	1	.	.	PUNCT
ejpam-2245	75	1	,	,	PUNCT
ejpam-2245	75	2	xn	xn	X
ejpam-2245	75	3	)	)	PUNCT
ejpam-2245	76	1	=	=	PRON
ejpam-2245	76	2	(	(	PUNCT
ejpam-2245	76	3	λ1	λ1	PROPN
ejpam-2245	76	4	xσ(1),λ2	xσ(1),λ2	PROPN
ejpam-2245	76	5	xσ(2	xσ(2	PROPN
ejpam-2245	76	6	)	)	PUNCT
ejpam-2245	76	7	,	,	PUNCT
ejpam-2245	76	8	.	.	PUNCT
ejpam-2245	76	9	.	.	PUNCT
ejpam-2245	76	10	.	.	PUNCT
ejpam-2245	77	1	,	,	PUNCT
ejpam-2245	77	2	λn	λn	NOUN
ejpam-2245	77	3	xσ(n	xσ(n	NUM
ejpam-2245	77	4	)	)	PUNCT
ejpam-2245	77	5	)	)	PUNCT
ejpam-2245	77	6	.	.	PUNCT
ejpam-2245	78	1	two	two	NUM
ejpam-2245	78	2	linear	linear	ADJ
ejpam-2245	78	3	codes	code	NOUN
ejpam-2245	78	4	c	c	PROPN
ejpam-2245	78	5	and	and	CCONJ
ejpam-2245	78	6	c	c	NOUN
ejpam-2245	78	7	′	′	NOUN
ejpam-2245	78	8	of	of	ADP
ejpam-2245	78	9	length	length	NOUN
ejpam-2245	78	10	n	n	NUM
ejpam-2245	78	11	are	be	AUX
ejpam-2245	78	12	called	call	VERB
ejpam-2245	78	13	monomially	monomially	ADV
ejpam-2245	78	14	equivalent	equivalent	ADJ
ejpam-2245	78	15	if	if	SCONJ
ejpam-2245	78	16	there	there	PRON
ejpam-2245	78	17	exists	exist	VERB
ejpam-2245	78	18	a	a	DET
ejpam-2245	78	19	monomial	monomial	ADJ
ejpam-2245	78	20	transformation	transformation	NOUN
ejpam-2245	78	21	of	of	ADP
ejpam-2245	78	22	rn	rn	PROPN
ejpam-2245	79	1	such	such	ADJ
ejpam-2245	79	2	that	that	SCONJ
ejpam-2245	79	3	τ(c	τ(c	PROPN
ejpam-2245	79	4	)	)	PUNCT
ejpam-2245	79	5	=	=	PUNCT
ejpam-2245	79	6	c	c	NOUN
ejpam-2245	79	7	′.	′.	NOUN
ejpam-2245	79	8	an	an	DET
ejpam-2245	79	9	isodual	isodual	ADJ
ejpam-2245	79	10	code	code	NOUN
ejpam-2245	79	11	is	be	AUX
ejpam-2245	79	12	a	a	DET
ejpam-2245	79	13	linear	linear	ADJ
ejpam-2245	79	14	code	code	NOUN
ejpam-2245	79	15	which	which	PRON
ejpam-2245	79	16	is	be	AUX
ejpam-2245	79	17	equivalent	equivalent	ADJ
ejpam-2245	79	18	to	to	ADP
ejpam-2245	79	19	its	its	PRON
ejpam-2245	79	20	dual	dual	NOUN
ejpam-2245	79	21	.	.	PUNCT
ejpam-2245	80	1	the	the	DET
ejpam-2245	80	2	class	class	NOUN
ejpam-2245	80	3	of	of	ADP
ejpam-2245	80	4	isodual	isodual	ADJ
ejpam-2245	80	5	codes	code	NOUN
ejpam-2245	80	6	is	be	AUX
ejpam-2245	80	7	important	important	ADJ
ejpam-2245	80	8	in	in	ADP
ejpam-2245	80	9	coding	code	VERB
ejpam-2245	80	10	theory	theory	NOUN
ejpam-2245	80	11	,	,	PUNCT
ejpam-2245	80	12	in	in	ADP
ejpam-2245	80	13	particular	particular	ADJ
ejpam-2245	80	14	because	because	SCONJ
ejpam-2245	80	15	it	it	PRON
ejpam-2245	80	16	contains	contain	VERB
ejpam-2245	80	17	the	the	DET
ejpam-2245	80	18	self	self	NOUN
ejpam-2245	80	19	-	-	PUNCT
ejpam-2245	80	20	dual	dual	ADJ
ejpam-2245	80	21	codes	code	NOUN
ejpam-2245	80	22	as	as	ADP
ejpam-2245	80	23	a	a	DET
ejpam-2245	80	24	subclass	subclass	NOUN
ejpam-2245	80	25	.	.	PUNCT
ejpam-2245	81	1	in	in	ADP
ejpam-2245	81	2	addition	addition	NOUN
ejpam-2245	81	3	,	,	PUNCT
ejpam-2245	81	4	isodual	isodual	ADJ
ejpam-2245	81	5	codes	code	NOUN
ejpam-2245	81	6	are	be	AUX
ejpam-2245	81	7	contained	contain	VERB
ejpam-2245	81	8	in	in	ADP
ejpam-2245	81	9	the	the	DET
ejpam-2245	81	10	larger	large	ADJ
ejpam-2245	81	11	class	class	NOUN
ejpam-2245	81	12	of	of	ADP
ejpam-2245	81	13	formally	formally	ADV
ejpam-2245	81	14	self	self	NOUN
ejpam-2245	81	15	-	-	PUNCT
ejpam-2245	81	16	dual	dual	ADJ
ejpam-2245	81	17	codes	code	NOUN
ejpam-2245	81	18	,	,	PUNCT
ejpam-2245	81	19	and	and	CCONJ
ejpam-2245	81	20	they	they	PRON
ejpam-2245	81	21	are	be	AUX
ejpam-2245	81	22	related	relate	VERB
ejpam-2245	81	23	to	to	ADP
ejpam-2245	81	24	isodual	isodual	ADJ
ejpam-2245	81	25	lattices	lattice	NOUN
ejpam-2245	81	26	[	[	X
ejpam-2245	81	27	1	1	NUM
ejpam-2245	81	28	]	]	PUNCT
ejpam-2245	81	29	.	.	PUNCT
ejpam-2245	82	1	in	in	ADP
ejpam-2245	82	2	this	this	DET
ejpam-2245	82	3	work	work	NOUN
ejpam-2245	82	4	,	,	PUNCT
ejpam-2245	82	5	by	by	ADP
ejpam-2245	82	6	the	the	DET
ejpam-2245	82	7	equivalence	equivalence	NOUN
ejpam-2245	82	8	of	of	ADP
ejpam-2245	82	9	two	two	NUM
ejpam-2245	82	10	codes	code	NOUN
ejpam-2245	82	11	we	we	PRON
ejpam-2245	82	12	will	will	AUX
ejpam-2245	82	13	mean	mean	VERB
ejpam-2245	82	14	the	the	DET
ejpam-2245	82	15	monomoial	monomoial	ADJ
ejpam-2245	82	16	equivalence	equivalence	NOUN
ejpam-2245	82	17	.	.	PUNCT
ejpam-2245	83	1	hence	hence	ADV
ejpam-2245	83	2	in	in	ADP
ejpam-2245	83	3	our	our	PRON
ejpam-2245	83	4	context	context	NOUN
ejpam-2245	83	5	an	an	DET
ejpam-2245	83	6	isodual	isodual	ADJ
ejpam-2245	83	7	code	code	NOUN
ejpam-2245	83	8	is	be	AUX
ejpam-2245	83	9	a	a	DET
ejpam-2245	83	10	linear	linear	ADJ
ejpam-2245	83	11	code	code	NOUN
ejpam-2245	83	12	which	which	PRON
ejpam-2245	83	13	is	be	AUX
ejpam-2245	83	14	monomially	monomially	ADV
ejpam-2245	83	15	equivalent	equivalent	ADJ
ejpam-2245	83	16	to	to	ADP
ejpam-2245	83	17	its	its	PRON
ejpam-2245	83	18	dual	dual	ADJ
ejpam-2245	83	19	.	.	PUNCT
ejpam-2245	84	1	3	3	X
ejpam-2245	84	2	.	.	X
ejpam-2245	84	3	cyclic	cyclic	ADJ
ejpam-2245	84	4	codes	code	NOUN
ejpam-2245	84	5	over	over	ADP
ejpam-2245	84	6	r=	r=	ADJ
ejpam-2245	84	7	fq	fq	NOUN
ejpam-2245	84	8	+	+	CCONJ
ejpam-2245	84	9	vfq	vfq	NOUN
ejpam-2245	84	10	in	in	ADP
ejpam-2245	84	11	this	this	DET
ejpam-2245	84	12	section	section	NOUN
ejpam-2245	84	13	,	,	PUNCT
ejpam-2245	84	14	we	we	PRON
ejpam-2245	84	15	let	let	VERB
ejpam-2245	84	16	rn	rn	PROPN
ejpam-2245	84	17	=	=	PRON
ejpam-2245	84	18	r[x]|〈xn	r[x]|〈xn	ADJ
ejpam-2245	84	19	−	−	PROPN
ejpam-2245	84	20	1	1	NUM
ejpam-2245	84	21	〉	〉	NOUN
ejpam-2245	84	22	.	.	PUNCT
ejpam-2245	85	1	as	as	ADP
ejpam-2245	85	2	usual	usual	ADJ
ejpam-2245	85	3	we	we	PRON
ejpam-2245	85	4	identify	identify	VERB
ejpam-2245	85	5	rn	rn	ADV
ejpam-2245	85	6	by	by	ADP
ejpam-2245	85	7	the	the	DET
ejpam-2245	85	8	set	set	NOUN
ejpam-2245	85	9	of	of	ADP
ejpam-2245	85	10	all	all	DET
ejpam-2245	85	11	polynomials	polynomial	NOUN
ejpam-2245	85	12	over	over	ADP
ejpam-2245	85	13	r	r	NOUN
ejpam-2245	85	14	of	of	ADP
ejpam-2245	85	15	degree	degree	NOUN
ejpam-2245	85	16	less	less	ADJ
ejpam-2245	85	17	than	than	SCONJ
ejpam-2245	85	18	n.	n.	VERB
ejpam-2245	85	19	the	the	DET
ejpam-2245	85	20	following	follow	VERB
ejpam-2245	85	21	results	result	NOUN
ejpam-2245	85	22	are	be	AUX
ejpam-2245	85	23	quite	quite	ADV
ejpam-2245	85	24	analogous	analogous	ADJ
ejpam-2245	85	25	to	to	ADP
ejpam-2245	85	26	the	the	DET
ejpam-2245	85	27	ones	one	NOUN
ejpam-2245	85	28	obtained	obtain	VERB
ejpam-2245	85	29	in	in	ADP
ejpam-2245	85	30	[	[	X
ejpam-2245	85	31	16	16	NUM
ejpam-2245	85	32	]	]	PUNCT
ejpam-2245	85	33	for	for	ADP
ejpam-2245	85	34	the	the	DET
ejpam-2245	85	35	ring	ring	NOUN
ejpam-2245	85	36	f2	f2	PROPN
ejpam-2245	85	37	+	+	CCONJ
ejpam-2245	85	38	vf2	vf2	ADJ
ejpam-2245	85	39	,	,	PUNCT
ejpam-2245	85	40	and	and	CCONJ
ejpam-2245	85	41	thus	thus	ADV
ejpam-2245	85	42	the	the	DET
ejpam-2245	85	43	proofs	proof	NOUN
ejpam-2245	85	44	being	be	AUX
ejpam-2245	85	45	the	the	DET
ejpam-2245	85	46	same	same	ADJ
ejpam-2245	85	47	,	,	PUNCT
ejpam-2245	85	48	will	will	AUX
ejpam-2245	85	49	be	be	AUX
ejpam-2245	85	50	omitted	omit	VERB
ejpam-2245	85	51	here	here	ADV
ejpam-2245	85	52	:	:	PUNCT
ejpam-2245	85	53	theorem	theorem	NOUN
ejpam-2245	85	54	1	1	NUM
ejpam-2245	85	55	.	.	PUNCT
ejpam-2245	86	1	let	let	VERB
ejpam-2245	86	2	c	c	NOUN
ejpam-2245	86	3	=	=	PUNCT
ejpam-2245	86	4	vc1	vc1	PROPN
ejpam-2245	86	5	⊕	⊕	PROPN
ejpam-2245	86	6	(	(	PUNCT
ejpam-2245	86	7	1−	1−	NUM
ejpam-2245	86	8	v)c2	v)c2	PROPN
ejpam-2245	86	9	be	be	AUX
ejpam-2245	86	10	a	a	DET
ejpam-2245	86	11	linear	linear	ADJ
ejpam-2245	86	12	cyclic	cyclic	ADJ
ejpam-2245	86	13	code	code	NOUN
ejpam-2245	86	14	of	of	ADP
ejpam-2245	86	15	length	length	NOUN
ejpam-2245	86	16	n	n	PROPN
ejpam-2245	86	17	over	over	ADP
ejpam-2245	86	18	r.	r.	PROPN
ejpam-2245	86	19	then	then	ADV
ejpam-2245	86	20	c	c	PROPN
ejpam-2245	86	21	is	be	AUX
ejpam-2245	86	22	cyclic	cyclic	ADJ
ejpam-2245	86	23	code	code	NOUN
ejpam-2245	86	24	of	of	ADP
ejpam-2245	86	25	length	length	NOUN
ejpam-2245	86	26	n	n	CCONJ
ejpam-2245	86	27	over	over	ADP
ejpam-2245	86	28	r	r	NOUN
ejpam-2245	86	29	if	if	SCONJ
ejpam-2245	87	1	and	and	CCONJ
ejpam-2245	87	2	only	only	ADV
ejpam-2245	87	3	if	if	SCONJ
ejpam-2245	87	4	c1	c1	PROPN
ejpam-2245	87	5	and	and	CCONJ
ejpam-2245	87	6	c2	c2	PROPN
ejpam-2245	87	7	are	be	AUX
ejpam-2245	87	8	cyclic	cyclic	ADJ
ejpam-2245	87	9	codes	code	NOUN
ejpam-2245	87	10	of	of	ADP
ejpam-2245	87	11	length	length	NOUN
ejpam-2245	87	12	n	n	PROPN
ejpam-2245	87	13	over	over	ADP
ejpam-2245	87	14	fq	fq	PROPN
ejpam-2245	87	15	.	.	PUNCT
ejpam-2245	88	1	the	the	DET
ejpam-2245	88	2	following	follow	VERB
ejpam-2245	88	3	theorem	theorem	NOUN
ejpam-2245	88	4	tells	tell	VERB
ejpam-2245	88	5	us	we	PRON
ejpam-2245	88	6	that	that	SCONJ
ejpam-2245	88	7	c	c	PROPN
ejpam-2245	88	8	is	be	AUX
ejpam-2245	88	9	also	also	ADV
ejpam-2245	88	10	principally	principally	ADV
ejpam-2245	88	11	generated	generate	VERB
ejpam-2245	88	12	in	in	ADP
ejpam-2245	88	13	that	that	DET
ejpam-2245	88	14	case	case	NOUN
ejpam-2245	88	15	:	:	PUNCT
ejpam-2245	88	16	a.	a.	PROPN
ejpam-2245	88	17	batoul	batoul	PROPN
ejpam-2245	88	18	,	,	PUNCT
ejpam-2245	88	19	k.	k.	PROPN
ejpam-2245	88	20	guenda	guenda	PROPN
ejpam-2245	88	21	,	,	PUNCT
ejpam-2245	88	22	a.	a.	PROPN
ejpam-2245	88	23	kaya	kaya	PROPN
ejpam-2245	88	24	,	,	PUNCT
ejpam-2245	88	25	b.	b.	PROPN
ejpam-2245	88	26	yildiz	yildiz	PROPN
ejpam-2245	88	27	/	/	SYM
ejpam-2245	88	28	eur	eur	PROPN
ejpam-2245	88	29	.	.	PUNCT
ejpam-2245	89	1	j.	j.	PROPN
ejpam-2245	89	2	pure	pure	PROPN
ejpam-2245	89	3	appl	appl	PROPN
ejpam-2245	89	4	.	.	PROPN
ejpam-2245	89	5	math	math	PROPN
ejpam-2245	89	6	,	,	PUNCT
ejpam-2245	89	7	8	8	NUM
ejpam-2245	89	8	(	(	PUNCT
ejpam-2245	89	9	2015	2015	NUM
ejpam-2245	89	10	)	)	PUNCT
ejpam-2245	89	11	,	,	PUNCT
ejpam-2245	89	12	64	64	NUM
ejpam-2245	89	13	-	-	SYM
ejpam-2245	89	14	80	80	NUM
ejpam-2245	89	15	67	67	NUM
ejpam-2245	89	16	theorem	theorem	NOUN
ejpam-2245	89	17	2	2	NUM
ejpam-2245	89	18	.	.	PUNCT
ejpam-2245	90	1	let	let	AUX
ejpam-2245	90	2	c	c	NOUN
ejpam-2245	90	3	=	=	PUNCT
ejpam-2245	90	4	vc1	vc1	PROPN
ejpam-2245	90	5	⊕	⊕	PROPN
ejpam-2245	90	6	(	(	PUNCT
ejpam-2245	90	7	1−	1−	NUM
ejpam-2245	90	8	v)c2	v)c2	PROPN
ejpam-2245	90	9	be	be	AUX
ejpam-2245	90	10	a	a	DET
ejpam-2245	90	11	cyclic	cyclic	ADJ
ejpam-2245	90	12	code	code	NOUN
ejpam-2245	90	13	of	of	ADP
ejpam-2245	90	14	length	length	NOUN
ejpam-2245	90	15	n	n	PROPN
ejpam-2245	90	16	over	over	ADP
ejpam-2245	90	17	r.	r.	PROPN
ejpam-2245	90	18	there	there	PRON
ejpam-2245	90	19	exist	exist	VERB
ejpam-2245	90	20	a	a	DET
ejpam-2245	90	21	unique	unique	ADJ
ejpam-2245	90	22	polynomial	polynomial	ADJ
ejpam-2245	90	23	f	f	NOUN
ejpam-2245	90	24	(	(	PUNCT
ejpam-2245	90	25	x	x	X
ejpam-2245	90	26	)	)	PUNCT
ejpam-2245	90	27	such	such	ADJ
ejpam-2245	90	28	that	that	SCONJ
ejpam-2245	90	29	c	c	NOUN
ejpam-2245	90	30	=	=	PUNCT
ejpam-2245	90	31	〈	〈	PROPN
ejpam-2245	90	32	f	f	X
ejpam-2245	90	33	(	(	PUNCT
ejpam-2245	90	34	x	x	NOUN
ejpam-2245	90	35	)	)	PUNCT
ejpam-2245	90	36	〉	〉	NOUN
ejpam-2245	90	37	,	,	PUNCT
ejpam-2245	90	38	where	where	SCONJ
ejpam-2245	90	39	f	f	PROPN
ejpam-2245	90	40	(	(	PUNCT
ejpam-2245	90	41	x	x	X
ejpam-2245	90	42	)	)	PUNCT
ejpam-2245	90	43	=	=	SYM
ejpam-2245	90	44	v	v	ADP
ejpam-2245	90	45	f1(x	f1(x	NOUN
ejpam-2245	90	46	)	)	PUNCT
ejpam-2245	91	1	+	+	CCONJ
ejpam-2245	91	2	(	(	PUNCT
ejpam-2245	91	3	1−	1−	NUM
ejpam-2245	91	4	v	v	NOUN
ejpam-2245	91	5	)	)	PUNCT
ejpam-2245	91	6	f2(x	f2(x	NOUN
ejpam-2245	91	7	)	)	PUNCT
ejpam-2245	91	8	corollary	corollary	ADJ
ejpam-2245	92	1	1	1	NUM
ejpam-2245	92	2	.	.	PUNCT
ejpam-2245	93	1	let	let	VERB
ejpam-2245	93	2	c	c	NOUN
ejpam-2245	93	3	=	=	VERB
ejpam-2245	93	4	vc1⊕	vc1⊕	X
ejpam-2245	93	5	(	(	PUNCT
ejpam-2245	93	6	1−	1−	NUM
ejpam-2245	93	7	v)c2	v)c2	PROPN
ejpam-2245	93	8	be	be	AUX
ejpam-2245	93	9	a	a	DET
ejpam-2245	93	10	cyclic	cyclic	ADJ
ejpam-2245	93	11	code	code	NOUN
ejpam-2245	93	12	of	of	ADP
ejpam-2245	93	13	length	length	NOUN
ejpam-2245	93	14	n	n	CCONJ
ejpam-2245	93	15	over	over	ADP
ejpam-2245	93	16	r	r	NOUN
ejpam-2245	93	17	and	and	CCONJ
ejpam-2245	93	18	f1(x	f1(x	NUM
ejpam-2245	93	19	)	)	PUNCT
ejpam-2245	93	20	,	,	PUNCT
ejpam-2245	93	21	f2(x	f2(x	X
ejpam-2245	93	22	)	)	PUNCT
ejpam-2245	93	23	are	be	AUX
ejpam-2245	93	24	the	the	DET
ejpam-2245	93	25	generator	generator	NOUN
ejpam-2245	93	26	polynomials	polynomial	NOUN
ejpam-2245	93	27	of	of	ADP
ejpam-2245	93	28	c1	c1	PROPN
ejpam-2245	93	29	and	and	CCONJ
ejpam-2245	93	30	c2	c2	PROPN
ejpam-2245	93	31	respectively	respectively	ADV
ejpam-2245	93	32	.	.	PUNCT
ejpam-2245	94	1	then	then	ADV
ejpam-2245	94	2	|c	|c	VERB
ejpam-2245	94	3	|=	|=	NOUN
ejpam-2245	94	4	q2n−deg	q2n−deg	NOUN
ejpam-2245	94	5	(	(	PUNCT
ejpam-2245	94	6	f1(x))−deg	f1(x))−deg	ADJ
ejpam-2245	94	7	(	(	PUNCT
ejpam-2245	94	8	f2(x	f2(x	NOUN
ejpam-2245	94	9	)	)	PUNCT
ejpam-2245	94	10	)	)	PUNCT
ejpam-2245	94	11	.	.	PUNCT
ejpam-2245	95	1	for	for	ADP
ejpam-2245	95	2	the	the	DET
ejpam-2245	95	3	proof	proof	NOUN
ejpam-2245	95	4	of	of	ADP
ejpam-2245	95	5	the	the	DET
ejpam-2245	95	6	following	follow	VERB
ejpam-2245	95	7	theorem	theorem	NOUN
ejpam-2245	95	8	we	we	PRON
ejpam-2245	95	9	introduce	introduce	VERB
ejpam-2245	95	10	some	some	DET
ejpam-2245	95	11	notations	notation	NOUN
ejpam-2245	95	12	.	.	PUNCT
ejpam-2245	96	1	since	since	SCONJ
ejpam-2245	96	2	the	the	DET
ejpam-2245	96	3	ring	ring	NOUN
ejpam-2245	96	4	r	r	NOUN
ejpam-2245	96	5	has	have	VERB
ejpam-2245	96	6	two	two	NUM
ejpam-2245	96	7	maximal	maximal	ADJ
ejpam-2245	96	8	ideals	ideal	NOUN
ejpam-2245	96	9	〈	〈	PROPN
ejpam-2245	96	10	v	v	NOUN
ejpam-2245	96	11	〉	〉	NOUN
ejpam-2245	96	12	and	and	CCONJ
ejpam-2245	96	13	〈	〈	PROPN
ejpam-2245	96	14	1−	1−	NUM
ejpam-2245	96	15	v	v	NOUN
ejpam-2245	96	16	〉	〉	NOUN
ejpam-2245	96	17	with	with	ADP
ejpam-2245	96	18	the	the	DET
ejpam-2245	96	19	same	same	ADJ
ejpam-2245	96	20	residue	residue	NOUN
ejpam-2245	96	21	field	field	NOUN
ejpam-2245	96	22	fp	fp	NOUN
ejpam-2245	96	23	thus	thus	ADV
ejpam-2245	96	24	we	we	PRON
ejpam-2245	96	25	have	have	VERB
ejpam-2245	96	26	two	two	NUM
ejpam-2245	96	27	canonical	canonical	ADJ
ejpam-2245	96	28	projections	projection	NOUN
ejpam-2245	96	29	defined	define	VERB
ejpam-2245	96	30	as	as	SCONJ
ejpam-2245	96	31	follows	follow	VERB
ejpam-2245	96	32	:	:	PUNCT
ejpam-2245	96	33	ψ1	ψ1	ADJ
ejpam-2245	96	34	:	:	PUNCT
ejpam-2245	96	35	r=	r=	ADJ
ejpam-2245	96	36	fq	fq	NOUN
ejpam-2245	96	37	+	+	CCONJ
ejpam-2245	96	38	vfq	vfq	NOUN
ejpam-2245	96	39	−→	−→	ADJ
ejpam-2245	96	40	fq	fq	PROPN
ejpam-2245	96	41	va+	va+	PROPN
ejpam-2245	96	42	(	(	PUNCT
ejpam-2245	96	43	1−	1−	NUM
ejpam-2245	96	44	v)b	v)b	NOUN
ejpam-2245	96	45	7−→ψ1(va+	7−→ψ1(va+	X
ejpam-2245	96	46	(	(	PUNCT
ejpam-2245	96	47	1−	1−	NUM
ejpam-2245	96	48	v)b	v)b	NOUN
ejpam-2245	96	49	)	)	PUNCT
ejpam-2245	96	50	=	=	SYM
ejpam-2245	96	51	a	a	PRON
ejpam-2245	96	52	and	and	CCONJ
ejpam-2245	96	53	ψ2	ψ2	NOUN
ejpam-2245	96	54	:	:	PUNCT
ejpam-2245	96	55	r=	r=	ADJ
ejpam-2245	96	56	fq	fq	NOUN
ejpam-2245	96	57	+	+	CCONJ
ejpam-2245	96	58	vfq	vfq	NOUN
ejpam-2245	96	59	−→	−→	ADJ
ejpam-2245	96	60	fq	fq	PROPN
ejpam-2245	96	61	va+	va+	PROPN
ejpam-2245	96	62	(	(	PUNCT
ejpam-2245	96	63	1−	1−	NUM
ejpam-2245	96	64	v)b	v)b	NOUN
ejpam-2245	96	65	7−→ψ2(va+	7−→ψ2(va+	NUM
ejpam-2245	96	66	(	(	PUNCT
ejpam-2245	96	67	1−	1−	NUM
ejpam-2245	96	68	v)b	v)b	NOUN
ejpam-2245	96	69	)	)	PUNCT
ejpam-2245	96	70	=	=	SYM
ejpam-2245	96	71	b.	b.	PROPN
ejpam-2245	96	72	denote	denote	VERB
ejpam-2245	96	73	by	by	ADP
ejpam-2245	96	74	ψ1(u	ψ1(u	NOUN
ejpam-2245	96	75	)	)	PUNCT
ejpam-2245	96	76	and	and	CCONJ
ejpam-2245	96	77	ψ2(u	ψ2(u	NOUN
ejpam-2245	96	78	)	)	PUNCT
ejpam-2245	96	79	the	the	DET
ejpam-2245	96	80	images	image	NOUN
ejpam-2245	96	81	of	of	ADP
ejpam-2245	96	82	an	an	DET
ejpam-2245	96	83	element	element	NOUN
ejpam-2245	96	84	u	u	PROPN
ejpam-2245	96	85	∈	∈	PROPN
ejpam-2245	96	86	r.	r.	NOUN
ejpam-2245	96	87	these	these	DET
ejpam-2245	96	88	two	two	NUM
ejpam-2245	96	89	projections	projection	NOUN
ejpam-2245	96	90	can	can	AUX
ejpam-2245	96	91	be	be	AUX
ejpam-2245	96	92	extended	extend	VERB
ejpam-2245	96	93	naturally	naturally	ADV
ejpam-2245	96	94	from	from	ADP
ejpam-2245	96	95	rn	rn	PROPN
ejpam-2245	96	96	to	to	ADP
ejpam-2245	96	97	fn	fn	PROPN
ejpam-2245	96	98	q	q	NOUN
ejpam-2245	96	99	and	and	CCONJ
ejpam-2245	96	100	from	from	ADP
ejpam-2245	96	101	r[x	r[x	NOUN
ejpam-2245	96	102	]	]	PUNCT
ejpam-2245	96	103	to	to	PART
ejpam-2245	96	104	fq[x	fq[x	VERB
ejpam-2245	96	105	]	]	PUNCT
ejpam-2245	96	106	.	.	PUNCT
ejpam-2245	97	1	let	let	VERB
ejpam-2245	97	2	f	f	PROPN
ejpam-2245	97	3	(	(	PUNCT
ejpam-2245	97	4	x	x	X
ejpam-2245	97	5	)	)	PUNCT
ejpam-2245	97	6	=	=	SYM
ejpam-2245	97	7	a0	a0	PROPN
ejpam-2245	97	8	+	+	CCONJ
ejpam-2245	97	9	a1	a1	NOUN
ejpam-2245	97	10	x	x	SYM
ejpam-2245	97	11	+	+	NUM
ejpam-2245	97	12	a2	a2	PROPN
ejpam-2245	97	13	x2	x2	PROPN
ejpam-2245	98	1	+	+	CCONJ
ejpam-2245	98	2	·	·	PUNCT
ejpam-2245	98	3	·	·	PUNCT
ejpam-2245	98	4	·	·	PUNCT
ejpam-2245	98	5	+	+	CCONJ
ejpam-2245	98	6	an−1	an−1	PROPN
ejpam-2245	98	7	xn−1	xn−1	PROPN
ejpam-2245	98	8	where	where	SCONJ
ejpam-2245	98	9	ai	ai	VERB
ejpam-2245	98	10	∈	∈	PROPN
ejpam-2245	98	11	r	r	NOUN
ejpam-2245	98	12	,	,	PUNCT
ejpam-2245	98	13	0≤	0≤	PUNCT
ejpam-2245	99	1	i	i	PRON
ejpam-2245	99	2	≤	≤	ADJ
ejpam-2245	99	3	n−	n−	NOUN
ejpam-2245	99	4	1	1	NUM
ejpam-2245	99	5	,	,	PUNCT
ejpam-2245	99	6	and	and	CCONJ
ejpam-2245	99	7	we	we	PRON
ejpam-2245	99	8	denote	denote	VERB
ejpam-2245	99	9	ψ1	ψ1	NOUN
ejpam-2245	99	10	(	(	PUNCT
ejpam-2245	99	11	f	f	PROPN
ejpam-2245	99	12	(	(	PUNCT
ejpam-2245	99	13	x	x	NOUN
ejpam-2245	99	14	)	)	PUNCT
ejpam-2245	99	15	)	)	PUNCT
ejpam-2245	100	1	=	=	NOUN
ejpam-2245	100	2	ψ1(a0	ψ1(a0	X
ejpam-2245	100	3	)	)	PUNCT
ejpam-2245	101	1	+	+	PUNCT
ejpam-2245	101	2	ψ1(a1)x	ψ1(a1)x	NUM
ejpam-2245	101	3	+	+	ADJ
ejpam-2245	101	4	ψ1(a2)x	ψ1(a2)x	NOUN
ejpam-2245	101	5	2	2	NUM
ejpam-2245	101	6	+	+	CCONJ
ejpam-2245	101	7	.	.	PUNCT
ejpam-2245	101	8	.	.	PUNCT
ejpam-2245	102	1	.+ψ1(an−1)x	.+ψ1(an−1)x	PUNCT
ejpam-2245	103	1	n−1	n−1	NUM
ejpam-2245	103	2	ψ2	ψ2	NOUN
ejpam-2245	103	3	(	(	PUNCT
ejpam-2245	103	4	f	f	X
ejpam-2245	103	5	(	(	PUNCT
ejpam-2245	103	6	x	x	NOUN
ejpam-2245	103	7	)	)	PUNCT
ejpam-2245	103	8	)	)	PUNCT
ejpam-2245	104	1	=	=	SYM
ejpam-2245	104	2	ψ2(a0	ψ2(a0	X
ejpam-2245	104	3	)	)	PUNCT
ejpam-2245	105	1	+	+	ADJ
ejpam-2245	105	2	ψ2(a1)x	ψ2(a1)x	X
ejpam-2245	105	3	+	+	ADJ
ejpam-2245	105	4	ψ2(a2)x	ψ2(a2)x	NOUN
ejpam-2245	105	5	2	2	NUM
ejpam-2245	105	6	+	+	CCONJ
ejpam-2245	105	7	.	.	PUNCT
ejpam-2245	105	8	.	.	PUNCT
ejpam-2245	106	1	.+ψ2(an−1)x	.+ψ2(an−1)x	PUNCT
ejpam-2245	107	1	n−1	n−1	INTJ
ejpam-2245	107	2	.	.	PUNCT
ejpam-2245	108	1	hence	hence	ADV
ejpam-2245	108	2	f	f	PROPN
ejpam-2245	108	3	(	(	PUNCT
ejpam-2245	108	4	x	x	X
ejpam-2245	108	5	)	)	PUNCT
ejpam-2245	108	6	has	have	VERB
ejpam-2245	108	7	a	a	DET
ejpam-2245	108	8	unique	unique	ADJ
ejpam-2245	108	9	expression	expression	NOUN
ejpam-2245	108	10	as	as	ADP
ejpam-2245	108	11	f	f	PROPN
ejpam-2245	108	12	(	(	PUNCT
ejpam-2245	108	13	x	x	NOUN
ejpam-2245	108	14	)	)	PUNCT
ejpam-2245	108	15	=	=	SYM
ejpam-2245	108	16	vψ1	vψ1	NOUN
ejpam-2245	108	17	(	(	PUNCT
ejpam-2245	108	18	f	f	PROPN
ejpam-2245	108	19	(	(	PUNCT
ejpam-2245	108	20	x	x	NOUN
ejpam-2245	108	21	)	)	PUNCT
ejpam-2245	108	22	)	)	PUNCT
ejpam-2245	109	1	+	+	CCONJ
ejpam-2245	109	2	(	(	PUNCT
ejpam-2245	109	3	1−	1−	NUM
ejpam-2245	109	4	v)ψ2	v)ψ2	PROPN
ejpam-2245	109	5	(	(	PUNCT
ejpam-2245	109	6	f	f	PROPN
ejpam-2245	109	7	(	(	PUNCT
ejpam-2245	109	8	x	x	NOUN
ejpam-2245	109	9	)	)	PUNCT
ejpam-2245	109	10	)	)	PUNCT
ejpam-2245	109	11	.	.	PUNCT
ejpam-2245	110	1	theorem	theorem	NOUN
ejpam-2245	110	2	3	3	X
ejpam-2245	110	3	.	.	PUNCT
ejpam-2245	111	1	let	let	VERB
ejpam-2245	111	2	c	c	NOUN
ejpam-2245	111	3	=	=	PUNCT
ejpam-2245	111	4	vc1	vc1	PROPN
ejpam-2245	111	5	⊕	⊕	PROPN
ejpam-2245	111	6	(	(	PUNCT
ejpam-2245	111	7	1−	1−	NUM
ejpam-2245	111	8	v)c2	v)c2	PROPN
ejpam-2245	111	9	be	be	AUX
ejpam-2245	111	10	a	a	DET
ejpam-2245	111	11	cyclic	cyclic	ADJ
ejpam-2245	111	12	code	code	NOUN
ejpam-2245	111	13	of	of	ADP
ejpam-2245	111	14	length	length	NOUN
ejpam-2245	111	15	n	n	CCONJ
ejpam-2245	111	16	over	over	ADP
ejpam-2245	111	17	r	r	NOUN
ejpam-2245	111	18	,	,	PUNCT
ejpam-2245	111	19	then	then	ADV
ejpam-2245	111	20	its	its	PRON
ejpam-2245	111	21	dual	dual	ADJ
ejpam-2245	111	22	code	code	NOUN
ejpam-2245	111	23	c⊥	c⊥	NOUN
ejpam-2245	111	24	is	be	AUX
ejpam-2245	111	25	also	also	ADV
ejpam-2245	111	26	cyclic	cyclic	ADJ
ejpam-2245	112	1	and	and	CCONJ
ejpam-2245	112	2	moreover	moreover	ADV
ejpam-2245	112	3	we	we	PRON
ejpam-2245	112	4	have	have	AUX
ejpam-2245	112	5	c⊥	c⊥	X
ejpam-2245	112	6	=	=	SYM
ejpam-2245	112	7	vc⊥1	vc⊥1	NUM
ejpam-2245	112	8	⊕	⊕	PROPN
ejpam-2245	112	9	(	(	PUNCT
ejpam-2245	112	10	1−	1−	NUM
ejpam-2245	112	11	v)c⊥2	v)c⊥2	NOUN
ejpam-2245	112	12	.	.	PUNCT
ejpam-2245	113	1	proof	proof	NOUN
ejpam-2245	113	2	.	.	PUNCT
ejpam-2245	114	1	let	let	VERB
ejpam-2245	114	2	c	c	NOUN
ejpam-2245	114	3	=	=	PUNCT
ejpam-2245	114	4	vc1	vc1	PROPN
ejpam-2245	114	5	⊕	⊕	PROPN
ejpam-2245	114	6	(	(	PUNCT
ejpam-2245	114	7	1−	1−	NUM
ejpam-2245	114	8	v)c2	v)c2	PROPN
ejpam-2245	115	1	so	so	ADV
ejpam-2245	115	2	ψ1(c	ψ1(c	PROPN
ejpam-2245	115	3	)	)	PUNCT
ejpam-2245	115	4	=	=	SYM
ejpam-2245	115	5	c1	c1	PROPN
ejpam-2245	115	6	and	and	CCONJ
ejpam-2245	115	7	ψ2(c	ψ2(c	PROPN
ejpam-2245	115	8	)	)	PUNCT
ejpam-2245	116	1	=	=	SYM
ejpam-2245	116	2	c2	c2	PROPN
ejpam-2245	116	3	are	be	AUX
ejpam-2245	116	4	cyclic	cyclic	ADJ
ejpam-2245	116	5	codes	code	NOUN
ejpam-2245	116	6	over	over	ADP
ejpam-2245	116	7	fq	fq	PROPN
ejpam-2245	116	8	then	then	ADV
ejpam-2245	116	9	c⊥1	c⊥1	VERB
ejpam-2245	116	10	and	and	CCONJ
ejpam-2245	116	11	c⊥2	c⊥2	NOUN
ejpam-2245	116	12	are	be	AUX
ejpam-2245	116	13	also	also	ADV
ejpam-2245	116	14	cyclic	cyclic	ADJ
ejpam-2245	116	15	codes	code	NOUN
ejpam-2245	116	16	.	.	PUNCT
ejpam-2245	117	1	let	let	VERB
ejpam-2245	117	2	d	d	NOUN
ejpam-2245	117	3	=	=	SYM
ejpam-2245	117	4	vc⊥1	vc⊥1	NUM
ejpam-2245	117	5	⊕	⊕	PROPN
ejpam-2245	117	6	(	(	PUNCT
ejpam-2245	117	7	1−	1−	NUM
ejpam-2245	117	8	v)c⊥2	v)c⊥2	NOUN
ejpam-2245	117	9	so	so	ADV
ejpam-2245	117	10	by	by	ADP
ejpam-2245	117	11	theorem	theorem	NOUN
ejpam-2245	117	12	1	1	NUM
ejpam-2245	117	13	d	d	NOUN
ejpam-2245	117	14	is	be	AUX
ejpam-2245	117	15	a	a	DET
ejpam-2245	117	16	cyclic	cyclic	ADJ
ejpam-2245	117	17	code	code	NOUN
ejpam-2245	117	18	of	of	ADP
ejpam-2245	117	19	length	length	NOUN
ejpam-2245	117	20	n	n	CCONJ
ejpam-2245	117	21	over	over	ADP
ejpam-2245	117	22	r	r	NOUN
ejpam-2245	117	23	we	we	PRON
ejpam-2245	117	24	can	can	AUX
ejpam-2245	117	25	prove	prove	VERB
ejpam-2245	117	26	that	that	PRON
ejpam-2245	117	27	c⊥	c⊥	PROPN
ejpam-2245	117	28	=	=	SYM
ejpam-2245	117	29	d.	d.	PROPN
ejpam-2245	117	30	corollary	corollary	NOUN
ejpam-2245	117	31	2	2	PROPN
ejpam-2245	117	32	.	.	PUNCT
ejpam-2245	118	1	let	let	VERB
ejpam-2245	118	2	c	c	NOUN
ejpam-2245	118	3	=	=	PUNCT
ejpam-2245	118	4	〈	〈	PROPN
ejpam-2245	118	5	v	v	NOUN
ejpam-2245	118	6	f1(x	f1(x	NOUN
ejpam-2245	118	7	)	)	PUNCT
ejpam-2245	118	8	,	,	PUNCT
ejpam-2245	118	9	(	(	PUNCT
ejpam-2245	118	10	1−	1−	NUM
ejpam-2245	118	11	v	v	NOUN
ejpam-2245	118	12	)	)	PUNCT
ejpam-2245	118	13	f2(x	f2(x	NOUN
ejpam-2245	118	14	)	)	PUNCT
ejpam-2245	118	15	〉	〉	NOUN
ejpam-2245	118	16	be	be	VERB
ejpam-2245	118	17	a	a	DET
ejpam-2245	118	18	cyclic	cyclic	ADJ
ejpam-2245	118	19	code	code	NOUN
ejpam-2245	118	20	of	of	ADP
ejpam-2245	118	21	length	length	NOUN
ejpam-2245	118	22	n	n	CCONJ
ejpam-2245	118	23	over	over	ADP
ejpam-2245	118	24	r	r	NOUN
ejpam-2245	118	25	,	,	PUNCT
ejpam-2245	118	26	with	with	ADP
ejpam-2245	118	27	f1(x	f1(x	NOUN
ejpam-2245	118	28	)	)	PUNCT
ejpam-2245	118	29	and	and	CCONJ
ejpam-2245	118	30	f2(x	f2(x	NUM
ejpam-2245	118	31	)	)	PUNCT
ejpam-2245	118	32	as	as	ADP
ejpam-2245	118	33	the	the	DET
ejpam-2245	118	34	generator	generator	NOUN
ejpam-2245	118	35	polynomials	polynomial	NOUN
ejpam-2245	118	36	of	of	ADP
ejpam-2245	118	37	c1	c1	PROPN
ejpam-2245	118	38	and	and	CCONJ
ejpam-2245	118	39	c2	c2	PROPN
ejpam-2245	118	40	respectively	respectively	ADV
ejpam-2245	118	41	such	such	ADJ
ejpam-2245	118	42	that	that	SCONJ
ejpam-2245	118	43	xn	xn	PROPN
ejpam-2245	119	1	−	−	NUM
ejpam-2245	119	2	1=	1=	NUM
ejpam-2245	119	3	f1(x)h1(x	f1(x)h1(x	NOUN
ejpam-2245	119	4	)	)	PUNCT
ejpam-2245	119	5	and	and	CCONJ
ejpam-2245	119	6	xn	xn	NUM
ejpam-2245	120	1	−	−	PROPN
ejpam-2245	120	2	1=	1=	X
ejpam-2245	120	3	f2(x)h2(x	f2(x)h2(x	X
ejpam-2245	120	4	)	)	PUNCT
ejpam-2245	120	5	.	.	PUNCT
ejpam-2245	121	1	then	then	ADV
ejpam-2245	121	2	(	(	PUNCT
ejpam-2245	121	3	i	i	NOUN
ejpam-2245	121	4	)	)	PUNCT
ejpam-2245	121	5	c⊥	c⊥	PROPN
ejpam-2245	121	6	=	=	PUNCT
ejpam-2245	121	7	〈	〈	NOUN
ejpam-2245	121	8	vh∗1(x	vh∗1(x	NOUN
ejpam-2245	121	9	)	)	PUNCT
ejpam-2245	121	10	,	,	PUNCT
ejpam-2245	121	11	(	(	PUNCT
ejpam-2245	121	12	1−	1−	NUM
ejpam-2245	121	13	v)h∗2(x	v)h∗2(x	ADJ
ejpam-2245	121	14	)	)	PUNCT
ejpam-2245	121	15	〉	〉	NOUN
ejpam-2245	121	16	and	and	CCONJ
ejpam-2245	121	17	|c⊥|=	|c⊥|=	ADJ
ejpam-2245	121	18	qdeg	qdeg	NOUN
ejpam-2245	121	19	(	(	PUNCT
ejpam-2245	121	20	f1(x)+deg	f1(x)+deg	NOUN
ejpam-2245	121	21	(	(	PUNCT
ejpam-2245	121	22	f2(x	f2(x	PROPN
ejpam-2245	121	23	)	)	PUNCT
ejpam-2245	121	24	)	)	PUNCT
ejpam-2245	121	25	)	)	PUNCT
ejpam-2245	121	26	,	,	PUNCT
ejpam-2245	121	27	(	(	PUNCT
ejpam-2245	121	28	ii	ii	NOUN
ejpam-2245	121	29	)	)	PUNCT
ejpam-2245	121	30	c⊥	c⊥	PROPN
ejpam-2245	122	1	=	=	PUNCT
ejpam-2245	122	2	〈	〈	PROPN
ejpam-2245	122	3	h(x	h(x	PROPN
ejpam-2245	122	4	)	)	PUNCT
ejpam-2245	122	5	〉	〉	NOUN
ejpam-2245	122	6	where	where	SCONJ
ejpam-2245	122	7	h(x	h(x	PROPN
ejpam-2245	122	8	)	)	PUNCT
ejpam-2245	122	9	=	=	PUNCT
ejpam-2245	122	10	vh∗1(x	vh∗1(x	NOUN
ejpam-2245	122	11	)	)	PUNCT
ejpam-2245	123	1	+	+	CCONJ
ejpam-2245	123	2	(	(	PUNCT
ejpam-2245	123	3	1−	1−	NUM
ejpam-2245	123	4	v)h∗2(x	v)h∗2(x	X
ejpam-2245	123	5	)	)	PUNCT
ejpam-2245	123	6	.	.	PUNCT
ejpam-2245	124	1	the	the	DET
ejpam-2245	124	2	following	follow	VERB
ejpam-2245	124	3	lemma	lemma	PROPN
ejpam-2245	124	4	is	be	AUX
ejpam-2245	124	5	a	a	DET
ejpam-2245	124	6	well	well	ADV
ejpam-2245	124	7	known	know	VERB
ejpam-2245	124	8	result	result	NOUN
ejpam-2245	124	9	,	,	PUNCT
ejpam-2245	124	10	for	for	ADP
ejpam-2245	124	11	its	its	PRON
ejpam-2245	124	12	proof	proof	NOUN
ejpam-2245	124	13	see	see	VERB
ejpam-2245	124	14	for	for	ADP
ejpam-2245	124	15	example	example	NOUN
ejpam-2245	124	16	[	[	X
ejpam-2245	124	17	5	5	NUM
ejpam-2245	124	18	]	]	PUNCT
ejpam-2245	124	19	.	.	PUNCT
ejpam-2245	125	1	a.	a.	PROPN
ejpam-2245	125	2	batoul	batoul	PROPN
ejpam-2245	125	3	,	,	PUNCT
ejpam-2245	125	4	k.	k.	PROPN
ejpam-2245	125	5	guenda	guenda	PROPN
ejpam-2245	125	6	,	,	PUNCT
ejpam-2245	125	7	a.	a.	PROPN
ejpam-2245	125	8	kaya	kaya	PROPN
ejpam-2245	125	9	,	,	PUNCT
ejpam-2245	125	10	b.	b.	PROPN
ejpam-2245	125	11	yildiz	yildiz	PROPN
ejpam-2245	125	12	/	/	SYM
ejpam-2245	125	13	eur	eur	PROPN
ejpam-2245	125	14	.	.	PUNCT
ejpam-2245	126	1	j.	j.	PROPN
ejpam-2245	126	2	pure	pure	PROPN
ejpam-2245	126	3	appl	appl	PROPN
ejpam-2245	126	4	.	.	PROPN
ejpam-2245	126	5	math	math	PROPN
ejpam-2245	126	6	,	,	PUNCT
ejpam-2245	126	7	8	8	NUM
ejpam-2245	126	8	(	(	PUNCT
ejpam-2245	126	9	2015	2015	NUM
ejpam-2245	126	10	)	)	PUNCT
ejpam-2245	126	11	,	,	PUNCT
ejpam-2245	126	12	64	64	NUM
ejpam-2245	126	13	-	-	SYM
ejpam-2245	126	14	80	80	NUM
ejpam-2245	126	15	68	68	NUM
ejpam-2245	126	16	lemma	lemma	PROPN
ejpam-2245	126	17	2	2	NUM
ejpam-2245	126	18	.	.	PUNCT
ejpam-2245	126	19	a	a	DET
ejpam-2245	126	20	linear	linear	ADJ
ejpam-2245	126	21	cyclic	cyclic	ADJ
ejpam-2245	126	22	code	code	NOUN
ejpam-2245	126	23	over	over	ADP
ejpam-2245	126	24	fq	fq	PROPN
ejpam-2245	126	25	with	with	ADP
ejpam-2245	126	26	generator	generator	PROPN
ejpam-2245	126	27	polynomial	polynomial	PROPN
ejpam-2245	126	28	f	f	PROPN
ejpam-2245	126	29	(	(	PUNCT
ejpam-2245	126	30	x	x	X
ejpam-2245	126	31	)	)	PUNCT
ejpam-2245	126	32	is	be	AUX
ejpam-2245	126	33	self	self	NOUN
ejpam-2245	126	34	-	-	PUNCT
ejpam-2245	126	35	orthogonal	orthogonal	ADJ
ejpam-2245	126	36	if	if	SCONJ
ejpam-2245	126	37	and	and	CCONJ
ejpam-2245	126	38	only	only	ADV
ejpam-2245	126	39	if	if	SCONJ
ejpam-2245	126	40	h(x)h∗(x	h(x)h∗(x	NOUN
ejpam-2245	126	41	)	)	PUNCT
ejpam-2245	127	1	|	|	ADV
ejpam-2245	127	2	(	(	PUNCT
ejpam-2245	127	3	xn−1	xn−1	PROPN
ejpam-2245	127	4	)	)	PUNCT
ejpam-2245	127	5	,	,	PUNCT
ejpam-2245	127	6	where	where	SCONJ
ejpam-2245	127	7	h∗(x	h∗(x	ADP
ejpam-2245	127	8	)	)	PUNCT
ejpam-2245	127	9	=	=	SYM
ejpam-2245	127	10	xdeg(h(x))h(x−1	xdeg(h(x))h(x−1	X
ejpam-2245	127	11	)	)	PUNCT
ejpam-2245	128	1	is	be	AUX
ejpam-2245	128	2	the	the	DET
ejpam-2245	128	3	reciprocal	reciprocal	ADJ
ejpam-2245	128	4	polynomial	polynomial	NOUN
ejpam-2245	128	5	of	of	ADP
ejpam-2245	128	6	h(x	h(x	PROPN
ejpam-2245	128	7	)	)	PUNCT
ejpam-2245	128	8	with	with	ADP
ejpam-2245	128	9	h(x	h(x	PROPN
ejpam-2245	128	10	)	)	PUNCT
ejpam-2245	128	11	=	=	PUNCT
ejpam-2245	129	1	(	(	PUNCT
ejpam-2245	129	2	xn	xn	NUM
ejpam-2245	129	3	−	−	PROPN
ejpam-2245	129	4	1)/	1)/	NUM
ejpam-2245	129	5	f	f	X
ejpam-2245	129	6	(	(	PUNCT
ejpam-2245	129	7	x	x	NOUN
ejpam-2245	129	8	)	)	PUNCT
ejpam-2245	129	9	.	.	PUNCT
ejpam-2245	130	1	the	the	DET
ejpam-2245	130	2	following	following	NOUN
ejpam-2245	130	3	follows	follow	VERB
ejpam-2245	130	4	easily	easily	ADV
ejpam-2245	130	5	from	from	ADP
ejpam-2245	130	6	the	the	DET
ejpam-2245	130	7	previous	previous	ADJ
ejpam-2245	130	8	lemma	lemma	PROPN
ejpam-2245	130	9	:	:	PUNCT
ejpam-2245	130	10	theorem	theorem	ADJ
ejpam-2245	130	11	4	4	NUM
ejpam-2245	130	12	.	.	PUNCT
ejpam-2245	130	13	suppose	suppose	VERB
ejpam-2245	130	14	c	c	NOUN
ejpam-2245	130	15	=	=	SYM
ejpam-2245	130	16	〈	〈	PROPN
ejpam-2245	130	17	f	f	X
ejpam-2245	130	18	(	(	PUNCT
ejpam-2245	130	19	x	x	NOUN
ejpam-2245	130	20	)	)	PUNCT
ejpam-2245	130	21	〉	〉	NOUN
ejpam-2245	130	22	is	be	AUX
ejpam-2245	130	23	cyclic	cyclic	ADJ
ejpam-2245	130	24	code	code	NOUN
ejpam-2245	130	25	over	over	ADP
ejpam-2245	130	26	r	r	NOUN
ejpam-2245	130	27	,	,	PUNCT
ejpam-2245	130	28	where	where	SCONJ
ejpam-2245	130	29	f	f	PROPN
ejpam-2245	130	30	(	(	PUNCT
ejpam-2245	130	31	x	x	X
ejpam-2245	130	32	)	)	PUNCT
ejpam-2245	130	33	=	=	SYM
ejpam-2245	130	34	v	v	ADP
ejpam-2245	130	35	f1(x)+(1−	f1(x)+(1−	PROPN
ejpam-2245	130	36	v	v	NOUN
ejpam-2245	130	37	)	)	PUNCT
ejpam-2245	130	38	f2(x	f2(x	NOUN
ejpam-2245	130	39	)	)	PUNCT
ejpam-2245	130	40	,	,	PUNCT
ejpam-2245	130	41	then	then	ADV
ejpam-2245	130	42	c	c	PROPN
ejpam-2245	130	43	⊂	⊂	PROPN
ejpam-2245	130	44	c⊥	c⊥	VERB
ejpam-2245	131	1	if	if	SCONJ
ejpam-2245	131	2	and	and	CCONJ
ejpam-2245	131	3	only	only	ADV
ejpam-2245	131	4	if	if	SCONJ
ejpam-2245	131	5	c1	c1	PROPN
ejpam-2245	131	6	⊂	⊂	PROPN
ejpam-2245	131	7	c⊥1	c⊥1	VERB
ejpam-2245	131	8	and	and	CCONJ
ejpam-2245	131	9	c2	c2	PROPN
ejpam-2245	131	10	⊂	⊂	PROPN
ejpam-2245	131	11	c⊥2	c⊥2	X
ejpam-2245	131	12	,	,	PUNCT
ejpam-2245	131	13	where	where	SCONJ
ejpam-2245	131	14	c1	c1	NOUN
ejpam-2245	131	15	=	=	PROPN
ejpam-2245	131	16	〈	〈	PROPN
ejpam-2245	131	17	f1(x	f1(x	NOUN
ejpam-2245	131	18	)	)	PUNCT
ejpam-2245	131	19	〉	〉	NOUN
ejpam-2245	131	20	and	and	CCONJ
ejpam-2245	131	21	c2	c2	PROPN
ejpam-2245	131	22	=	=	SYM
ejpam-2245	131	23	〈	〈	PROPN
ejpam-2245	131	24	f2(x	f2(x	NOUN
ejpam-2245	131	25	)	)	PUNCT
ejpam-2245	131	26	〉	〉	NOUN
ejpam-2245	131	27	.	.	PUNCT
ejpam-2245	131	28	corollary	corollary	ADJ
ejpam-2245	131	29	3	3	PROPN
ejpam-2245	131	30	.	.	PUNCT
ejpam-2245	131	31	suppose	suppose	VERB
ejpam-2245	131	32	c	c	NOUN
ejpam-2245	131	33	=	=	PUNCT
ejpam-2245	131	34	vc1	vc1	PROPN
ejpam-2245	131	35	⊕	⊕	PROPN
ejpam-2245	131	36	(	(	PUNCT
ejpam-2245	131	37	1−	1−	NUM
ejpam-2245	131	38	v)c2	v)c2	PROPN
ejpam-2245	131	39	is	be	AUX
ejpam-2245	131	40	a	a	DET
ejpam-2245	131	41	cyclic	cyclic	ADJ
ejpam-2245	131	42	code	code	NOUN
ejpam-2245	131	43	of	of	ADP
ejpam-2245	131	44	arbitrary	arbitrary	ADJ
ejpam-2245	131	45	length	length	NOUN
ejpam-2245	131	46	n	n	CCONJ
ejpam-2245	131	47	over	over	ADP
ejpam-2245	131	48	r	r	NOUN
ejpam-2245	131	49	then	then	ADV
ejpam-2245	131	50	c	c	PROPN
ejpam-2245	131	51	⊂	⊂	PROPN
ejpam-2245	131	52	c⊥	c⊥	VERB
ejpam-2245	132	1	if	if	SCONJ
ejpam-2245	132	2	and	and	CCONJ
ejpam-2245	132	3	only	only	ADV
ejpam-2245	132	4	if	if	SCONJ
ejpam-2245	132	5	c1	c1	PROPN
ejpam-2245	132	6	⊂	⊂	PROPN
ejpam-2245	132	7	c⊥1	c⊥1	VERB
ejpam-2245	132	8	and	and	CCONJ
ejpam-2245	132	9	c2	c2	PROPN
ejpam-2245	132	10	⊂	⊂	PRON
ejpam-2245	132	11	c⊥2	c⊥2	PROPN
ejpam-2245	132	12	.	.	PUNCT
ejpam-2245	133	1	lemma	lemma	PROPN
ejpam-2245	133	2	3	3	X
ejpam-2245	133	3	.	.	PUNCT
ejpam-2245	134	1	let	let	VERB
ejpam-2245	134	2	c1	c1	PROPN
ejpam-2245	134	3	and	and	CCONJ
ejpam-2245	134	4	c2	c2	PROPN
ejpam-2245	134	5	be	be	VERB
ejpam-2245	134	6	two	two	NUM
ejpam-2245	134	7	linear	linear	ADJ
ejpam-2245	134	8	codes	code	NOUN
ejpam-2245	134	9	of	of	ADP
ejpam-2245	134	10	length	length	NOUN
ejpam-2245	134	11	n	n	PROPN
ejpam-2245	134	12	over	over	ADP
ejpam-2245	134	13	fq	fq	PROPN
ejpam-2245	134	14	and	and	CCONJ
ejpam-2245	134	15	c	c	NOUN
ejpam-2245	134	16	=	=	PUNCT
ejpam-2245	134	17	vc1	vc1	PROPN
ejpam-2245	134	18	⊕	⊕	PROPN
ejpam-2245	134	19	(	(	PUNCT
ejpam-2245	134	20	1−	1−	NUM
ejpam-2245	134	21	v)c2	v)c2	PROPN
ejpam-2245	134	22	=	=	PRON
ejpam-2245	134	23	{	{	PUNCT
ejpam-2245	134	24	(	(	PUNCT
ejpam-2245	134	25	vc1	vc1	PROPN
ejpam-2245	134	26	+	+	CCONJ
ejpam-2245	134	27	(	(	PUNCT
ejpam-2245	134	28	1−	1−	NUM
ejpam-2245	134	29	v)c2	v)c2	PROPN
ejpam-2245	134	30	)	)	PUNCT
ejpam-2245	134	31	,	,	PUNCT
ejpam-2245	134	32	c1	c1	PROPN
ejpam-2245	134	33	∈	∈	PROPN
ejpam-2245	134	34	c1	c1	PROPN
ejpam-2245	134	35	,	,	PUNCT
ejpam-2245	134	36	c2	c2	PROPN
ejpam-2245	134	37	∈	∈	PROPN
ejpam-2245	134	38	c2	c2	PROPN
ejpam-2245	134	39	}	}	PUNCT
ejpam-2245	134	40	.	.	PUNCT
ejpam-2245	135	1	we	we	PRON
ejpam-2245	135	2	have	have	VERB
ejpam-2245	135	3	c⊥	c⊥	X
ejpam-2245	135	4	=	=	SYM
ejpam-2245	135	5	vc⊥1	vc⊥1	NUM
ejpam-2245	135	6	⊕	⊕	PROPN
ejpam-2245	135	7	(	(	PUNCT
ejpam-2245	135	8	1−	1−	NUM
ejpam-2245	135	9	v)c⊥2	v)c⊥2	NOUN
ejpam-2245	135	10	=	=	SYM
ejpam-2245	135	11	{	{	PUNCT
ejpam-2245	135	12	(	(	PUNCT
ejpam-2245	135	13	vc1	vc1	PROPN
ejpam-2245	135	14	+	+	CCONJ
ejpam-2245	135	15	(	(	PUNCT
ejpam-2245	135	16	1−	1−	NUM
ejpam-2245	135	17	v)c2	v)c2	PROPN
ejpam-2245	135	18	)	)	PUNCT
ejpam-2245	135	19	,	,	PUNCT
ejpam-2245	135	20	c1	c1	PROPN
ejpam-2245	135	21	∈	∈	PROPN
ejpam-2245	135	22	c⊥1	c⊥1	VERB
ejpam-2245	135	23	,	,	PUNCT
ejpam-2245	135	24	c2	c2	PROPN
ejpam-2245	135	25	∈	∈	PROPN
ejpam-2245	135	26	c⊥2	c⊥2	PUNCT
ejpam-2245	135	27	}	}	PUNCT
ejpam-2245	135	28	c	c	NOUN
ejpam-2245	135	29	is	be	AUX
ejpam-2245	135	30	self	self	NOUN
ejpam-2245	135	31	-	-	PUNCT
ejpam-2245	135	32	dual	dual	ADJ
ejpam-2245	135	33	if	if	SCONJ
ejpam-2245	135	34	and	and	CCONJ
ejpam-2245	135	35	only	only	ADV
ejpam-2245	135	36	if	if	SCONJ
ejpam-2245	135	37	c1	c1	PROPN
ejpam-2245	135	38	and	and	CCONJ
ejpam-2245	135	39	c2	c2	PROPN
ejpam-2245	135	40	are	be	AUX
ejpam-2245	135	41	self	self	NOUN
ejpam-2245	135	42	-	-	PUNCT
ejpam-2245	135	43	dual	dual	ADJ
ejpam-2245	135	44	.	.	PUNCT
ejpam-2245	136	1	proposition	proposition	NOUN
ejpam-2245	136	2	1	1	NUM
ejpam-2245	136	3	.	.	PUNCT
ejpam-2245	137	1	let	let	VERB
ejpam-2245	137	2	c1	c1	PROPN
ejpam-2245	137	3	,	,	PUNCT
ejpam-2245	137	4	c2	c2	PROPN
ejpam-2245	137	5	,	,	PUNCT
ejpam-2245	137	6	c	c	NOUN
ejpam-2245	137	7	′1	′1	X
ejpam-2245	137	8	and	and	CCONJ
ejpam-2245	137	9	c	c	PROPN
ejpam-2245	137	10	′2	′2	X
ejpam-2245	137	11	be	be	AUX
ejpam-2245	137	12	four	four	NUM
ejpam-2245	137	13	linear	linear	ADJ
ejpam-2245	137	14	codes	code	NOUN
ejpam-2245	137	15	of	of	ADP
ejpam-2245	137	16	length	length	NOUN
ejpam-2245	137	17	n	n	PROPN
ejpam-2245	137	18	over	over	ADP
ejpam-2245	137	19	fq	fq	PROPN
ejpam-2245	137	20	.	.	PUNCT
ejpam-2245	138	1	then	then	ADV
ejpam-2245	138	2	c	c	X
ejpam-2245	138	3	=	=	PUNCT
ejpam-2245	138	4	vc1	vc1	PROPN
ejpam-2245	138	5	⊕	⊕	PROPN
ejpam-2245	138	6	(	(	PUNCT
ejpam-2245	138	7	1−	1−	NUM
ejpam-2245	138	8	v)c2	v)c2	PROPN
ejpam-2245	138	9	=	=	PRON
ejpam-2245	138	10	{	{	PUNCT
ejpam-2245	138	11	(	(	PUNCT
ejpam-2245	138	12	vc1	vc1	PROPN
ejpam-2245	138	13	+	+	CCONJ
ejpam-2245	138	14	(	(	PUNCT
ejpam-2245	138	15	1−	1−	NUM
ejpam-2245	138	16	v)c2	v)c2	PROPN
ejpam-2245	138	17	)	)	PUNCT
ejpam-2245	138	18	,	,	PUNCT
ejpam-2245	138	19	c1	c1	PROPN
ejpam-2245	138	20	∈	∈	PROPN
ejpam-2245	138	21	c1	c1	PROPN
ejpam-2245	138	22	,	,	PUNCT
ejpam-2245	138	23	c2	c2	PROPN
ejpam-2245	138	24	∈	∈	PROPN
ejpam-2245	138	25	c2	c2	PROPN
ejpam-2245	138	26	}	}	PUNCT
ejpam-2245	138	27	is	be	AUX
ejpam-2245	138	28	equivalent	equivalent	ADJ
ejpam-2245	138	29	to	to	ADP
ejpam-2245	138	30	c	c	NOUN
ejpam-2245	138	31	′	′	NUM
ejpam-2245	139	1	=	=	SYM
ejpam-2245	139	2	vc	vc	PROPN
ejpam-2245	139	3	′1	′1	PROPN
ejpam-2245	139	4	⊕	⊕	PROPN
ejpam-2245	139	5	(	(	PUNCT
ejpam-2245	139	6	1−	1−	NUM
ejpam-2245	139	7	v)c	v)c	SYM
ejpam-2245	139	8	′2	′2	X
ejpam-2245	139	9	=	=	SYM
ejpam-2245	139	10	{	{	PUNCT
ejpam-2245	139	11	(	(	PUNCT
ejpam-2245	139	12	vc′1	vc′1	VERB
ejpam-2245	139	13	+	+	CCONJ
ejpam-2245	139	14	(	(	PUNCT
ejpam-2245	139	15	1−	1−	NUM
ejpam-2245	139	16	v)c′2	v)c′2	NOUN
ejpam-2245	139	17	)	)	PUNCT
ejpam-2245	139	18	,	,	PUNCT
ejpam-2245	139	19	c′1	c′1	VERB
ejpam-2245	139	20	∈	∈	PROPN
ejpam-2245	139	21	c	c	NOUN
ejpam-2245	139	22	′1	′1	NOUN
ejpam-2245	139	23	,	,	PUNCT
ejpam-2245	139	24	c′2	c′2	VERB
ejpam-2245	139	25	∈	∈	PROPN
ejpam-2245	139	26	c	c	X
ejpam-2245	139	27	′2	′2	NOUN
ejpam-2245	139	28	}	}	PUNCT
ejpam-2245	139	29	over	over	ADP
ejpam-2245	139	30	r	r	NOUN
ejpam-2245	139	31	if	if	SCONJ
ejpam-2245	139	32	and	and	CCONJ
ejpam-2245	139	33	only	only	ADV
ejpam-2245	139	34	if	if	SCONJ
ejpam-2245	139	35	c1	c1	PROPN
ejpam-2245	139	36	and	and	CCONJ
ejpam-2245	139	37	c2	c2	PROPN
ejpam-2245	139	38	are	be	AUX
ejpam-2245	139	39	equivalent	equivalent	ADJ
ejpam-2245	139	40	respectively	respectively	ADV
ejpam-2245	139	41	to	to	ADP
ejpam-2245	139	42	c	c	NOUN
ejpam-2245	139	43	′1	′1	X
ejpam-2245	139	44	and	and	CCONJ
ejpam-2245	139	45	c	c	NOUN
ejpam-2245	139	46	′2	′2	X
ejpam-2245	139	47	.	.	PUNCT
ejpam-2245	140	1	proof	proof	NOUN
ejpam-2245	140	2	.	.	PUNCT
ejpam-2245	141	1	let	let	VERB
ejpam-2245	141	2	τ1	τ1	NOUN
ejpam-2245	141	3	and	and	CCONJ
ejpam-2245	141	4	τ2	τ2	VERB
ejpam-2245	141	5	two	two	NUM
ejpam-2245	141	6	monomial	monomial	ADJ
ejpam-2245	141	7	permutations	permutation	NOUN
ejpam-2245	141	8	such	such	ADJ
ejpam-2245	141	9	that	that	SCONJ
ejpam-2245	141	10	τ1(c1	τ1(c1	NUM
ejpam-2245	141	11	)	)	PUNCT
ejpam-2245	141	12	=	=	SYM
ejpam-2245	141	13	c	c	NOUN
ejpam-2245	141	14	′1	′1	NOUN
ejpam-2245	141	15	and	and	CCONJ
ejpam-2245	141	16	τ2(c2	τ2(c2	NOUN
ejpam-2245	141	17	)	)	PUNCT
ejpam-2245	141	18	=	=	SYM
ejpam-2245	141	19	c	c	NOUN
ejpam-2245	141	20	′2	′2	X
ejpam-2245	141	21	.	.	PUNCT
ejpam-2245	142	1	define	define	VERB
ejpam-2245	142	2	the	the	DET
ejpam-2245	142	3	map	map	NOUN
ejpam-2245	142	4	τ	τ	X
ejpam-2245	142	5	:	:	PUNCT
ejpam-2245	142	6	rn	rn	PROPN
ejpam-2245	142	7	−→	−→	PROPN
ejpam-2245	142	8	rn	rn	PROPN
ejpam-2245	142	9	va+	va+	PROPN
ejpam-2245	142	10	(	(	PUNCT
ejpam-2245	142	11	1−	1−	NUM
ejpam-2245	142	12	v)b	v)b	NOUN
ejpam-2245	142	13	7−→	7−→	NOUN
ejpam-2245	142	14	vτ1(a	vτ1(a	NOUN
ejpam-2245	142	15	)	)	PUNCT
ejpam-2245	143	1	+	+	CCONJ
ejpam-2245	143	2	(	(	PUNCT
ejpam-2245	143	3	1−	1−	NUM
ejpam-2245	143	4	v)τ2(b	v)τ2(b	NUM
ejpam-2245	143	5	)	)	PUNCT
ejpam-2245	143	6	)	)	PUNCT
ejpam-2245	144	1	we	we	PRON
ejpam-2245	144	2	have	have	VERB
ejpam-2245	144	3	τ(c	τ(c	PROPN
ejpam-2245	144	4	)	)	PUNCT
ejpam-2245	145	1	=	=	SYM
ejpam-2245	145	2	vτ(c)⊕	vτ(c)⊕	PROPN
ejpam-2245	145	3	(	(	PUNCT
ejpam-2245	145	4	1−	1−	NUM
ejpam-2245	145	5	v)τ(c	v)τ(c	NOUN
ejpam-2245	145	6	)	)	PUNCT
ejpam-2245	146	1	=	=	SYM
ejpam-2245	146	2	vτ1(c1)⊕	vτ1(c1)⊕	NOUN
ejpam-2245	146	3	(	(	PUNCT
ejpam-2245	146	4	1−	1−	NUM
ejpam-2245	146	5	v)τ2(c2	v)τ2(c2	NOUN
ejpam-2245	146	6	)	)	PUNCT
ejpam-2245	146	7	=	=	SYM
ejpam-2245	146	8	vc	vc	PROPN
ejpam-2245	146	9	′1	′1	PROPN
ejpam-2245	146	10	⊕	⊕	PROPN
ejpam-2245	146	11	(	(	PUNCT
ejpam-2245	146	12	1−	1−	NUM
ejpam-2245	146	13	v)c	v)c	SYM
ejpam-2245	146	14	′2	′2	X
ejpam-2245	146	15	=	=	SYM
ejpam-2245	146	16	c	c	NOUN
ejpam-2245	146	17	′.	′.	NOUN
ejpam-2245	146	18	conversely	conversely	ADV
ejpam-2245	146	19	,	,	PUNCT
ejpam-2245	146	20	let	let	VERB
ejpam-2245	146	21	τ	τ	PRON
ejpam-2245	146	22	be	be	AUX
ejpam-2245	146	23	a	a	DET
ejpam-2245	146	24	monomial	monomial	ADJ
ejpam-2245	146	25	permutation	permutation	NOUN
ejpam-2245	146	26	such	such	ADJ
ejpam-2245	146	27	that	that	SCONJ
ejpam-2245	146	28	τ(c	τ(c	PROPN
ejpam-2245	146	29	)	)	PUNCT
ejpam-2245	147	1	=	=	PUNCT
ejpam-2245	147	2	c	c	NOUN
ejpam-2245	147	3	′	′	NOUN
ejpam-2245	147	4	,	,	PUNCT
ejpam-2245	147	5	since	since	SCONJ
ejpam-2245	147	6	fq	fq	PROPN
ejpam-2245	147	7	⊂	⊂	PROPN
ejpam-2245	147	8	fq+	fq+	PROPN
ejpam-2245	147	9	vfq	vfq	NOUN
ejpam-2245	147	10	,	,	PUNCT
ejpam-2245	147	11	we	we	PRON
ejpam-2245	147	12	can	can	AUX
ejpam-2245	147	13	take	take	VERB
ejpam-2245	147	14	the	the	DET
ejpam-2245	147	15	restriction	restriction	NOUN
ejpam-2245	147	16	of	of	ADP
ejpam-2245	147	17	τ	τ	PROPN
ejpam-2245	147	18	over	over	ADP
ejpam-2245	147	19	fq	fq	PROPN
ejpam-2245	147	20	.	.	PROPN
ejpam-2245	148	1	then	then	ADV
ejpam-2245	148	2	define	define	VERB
ejpam-2245	148	3	τi	τi	ADP
ejpam-2245	148	4	=	=	VERB
ejpam-2245	148	5	ψi	ψi	ADP
ejpam-2245	148	6	◦	◦	NOUN
ejpam-2245	148	7	τ	τ	PROPN
ejpam-2245	148	8	,	,	PUNCT
ejpam-2245	148	9	1≤	1≤	NUM
ejpam-2245	148	10	i	i	NOUN
ejpam-2245	148	11	≤	≤	ADV
ejpam-2245	148	12	2	2	NUM
ejpam-2245	148	13	thus	thus	ADV
ejpam-2245	148	14	c	c	NOUN
ejpam-2245	149	1	′	′	NUM
ejpam-2245	149	2	=	=	SYM
ejpam-2245	149	3	vc	vc	PROPN
ejpam-2245	149	4	′1	′1	PROPN
ejpam-2245	149	5	⊕	⊕	PROPN
ejpam-2245	149	6	(	(	PUNCT
ejpam-2245	149	7	1	1	NUM
ejpam-2245	149	8	−	−	NOUN
ejpam-2245	149	9	v)c	v)c	SYM
ejpam-2245	149	10	′2	′2	X
ejpam-2245	149	11	=	=	SYM
ejpam-2245	149	12	τ(c	τ(c	PROPN
ejpam-2245	149	13	)	)	PUNCT
ejpam-2245	149	14	=	=	PUNCT
ejpam-2245	150	1	τ(vc1	τ(vc1	PUNCT
ejpam-2245	150	2	⊕	⊕	NOUN
ejpam-2245	150	3	(	(	PUNCT
ejpam-2245	150	4	1	1	NUM
ejpam-2245	150	5	−	−	PROPN
ejpam-2245	150	6	v)c2	v)c2	PROPN
ejpam-2245	150	7	)	)	PUNCT
ejpam-2245	151	1	=	=	PRON
ejpam-2245	151	2	vψ1	vψ1	NOUN
ejpam-2245	151	3	◦	◦	NOUN
ejpam-2245	151	4	τ(c	τ(c	NOUN
ejpam-2245	151	5	)	)	PUNCT
ejpam-2245	151	6	⊕	⊕	PROPN
ejpam-2245	151	7	(	(	PUNCT
ejpam-2245	151	8	1	1	NUM
ejpam-2245	151	9	−	−	PROPN
ejpam-2245	151	10	v)ψ2	v)ψ2	PROPN
ejpam-2245	151	11	◦	◦	NOUN
ejpam-2245	151	12	τ(c	τ(c	PROPN
ejpam-2245	151	13	)	)	PUNCT
ejpam-2245	152	1	=	=	PRON
ejpam-2245	152	2	vψ1	vψ1	NOUN
ejpam-2245	152	3	◦	◦	NOUN
ejpam-2245	152	4	τ(c1	τ(c1	PUNCT
ejpam-2245	152	5	)	)	PUNCT
ejpam-2245	152	6	⊕	⊕	PROPN
ejpam-2245	152	7	(	(	PUNCT
ejpam-2245	152	8	1	1	NUM
ejpam-2245	152	9	−	−	PROPN
ejpam-2245	152	10	v)ψ2	v)ψ2	PROPN
ejpam-2245	152	11	◦	◦	NOUN
ejpam-2245	152	12	τ(c2	τ(c2	NOUN
ejpam-2245	152	13	)	)	PUNCT
ejpam-2245	152	14	.	.	PUNCT
ejpam-2245	153	1	since	since	SCONJ
ejpam-2245	153	2	c	c	PROPN
ejpam-2245	153	3	′1	′1	PROPN
ejpam-2245	153	4	and	and	CCONJ
ejpam-2245	153	5	c	c	PROPN
ejpam-2245	153	6	′2	′2	NOUN
ejpam-2245	153	7	are	be	AUX
ejpam-2245	153	8	unique	unique	ADJ
ejpam-2245	153	9	then	then	ADV
ejpam-2245	153	10	ψ1	ψ1	ADJ
ejpam-2245	153	11	◦	◦	NOUN
ejpam-2245	153	12	τ(c1	τ(c1	PUNCT
ejpam-2245	153	13	)	)	PUNCT
ejpam-2245	154	1	=	=	SYM
ejpam-2245	154	2	c	c	NOUN
ejpam-2245	154	3	′1	′1	NOUN
ejpam-2245	154	4	and	and	CCONJ
ejpam-2245	154	5	ψ2	ψ2	NOUN
ejpam-2245	154	6	◦	◦	VERB
ejpam-2245	154	7	τ(c2	τ(c2	NOUN
ejpam-2245	154	8	)	)	PUNCT
ejpam-2245	154	9	=	=	SYM
ejpam-2245	154	10	c	c	NOUN
ejpam-2245	154	11	′2	′2	X
ejpam-2245	154	12	.	.	PUNCT
ejpam-2245	154	13	a.	a.	PROPN
ejpam-2245	154	14	batoul	batoul	PROPN
ejpam-2245	154	15	,	,	PUNCT
ejpam-2245	154	16	k.	k.	PROPN
ejpam-2245	154	17	guenda	guenda	PROPN
ejpam-2245	154	18	,	,	PUNCT
ejpam-2245	154	19	a.	a.	PROPN
ejpam-2245	154	20	kaya	kaya	PROPN
ejpam-2245	154	21	,	,	PUNCT
ejpam-2245	154	22	b.	b.	PROPN
ejpam-2245	154	23	yildiz	yildiz	PROPN
ejpam-2245	154	24	/	/	SYM
ejpam-2245	154	25	eur	eur	PROPN
ejpam-2245	154	26	.	.	PUNCT
ejpam-2245	155	1	j.	j.	PROPN
ejpam-2245	155	2	pure	pure	PROPN
ejpam-2245	155	3	appl	appl	PROPN
ejpam-2245	155	4	.	.	PROPN
ejpam-2245	155	5	math	math	PROPN
ejpam-2245	155	6	,	,	PUNCT
ejpam-2245	155	7	8	8	NUM
ejpam-2245	155	8	(	(	PUNCT
ejpam-2245	155	9	2015	2015	NUM
ejpam-2245	155	10	)	)	PUNCT
ejpam-2245	155	11	,	,	PUNCT
ejpam-2245	155	12	64	64	NUM
ejpam-2245	155	13	-	-	SYM
ejpam-2245	155	14	80	80	NUM
ejpam-2245	155	15	69	69	NUM
ejpam-2245	155	16	4	4	NUM
ejpam-2245	155	17	.	.	PUNCT
ejpam-2245	156	1	duadic	duadic	ADJ
ejpam-2245	156	2	codes	code	NOUN
ejpam-2245	156	3	over	over	ADP
ejpam-2245	156	4	r=	r=	ADJ
ejpam-2245	156	5	fq	fq	NOUN
ejpam-2245	156	6	+	+	CCONJ
ejpam-2245	156	7	vfq	vfq	NOUN
ejpam-2245	156	8	before	before	ADP
ejpam-2245	156	9	giving	give	VERB
ejpam-2245	156	10	our	our	PRON
ejpam-2245	156	11	constructions	construction	NOUN
ejpam-2245	156	12	of	of	ADP
ejpam-2245	156	13	duadic	duadic	ADJ
ejpam-2245	156	14	codes	code	NOUN
ejpam-2245	156	15	over	over	ADP
ejpam-2245	156	16	fq+vfq	fq+vfq	PROPN
ejpam-2245	156	17	,	,	PUNCT
ejpam-2245	156	18	we	we	PRON
ejpam-2245	156	19	recall	recall	VERB
ejpam-2245	156	20	some	some	DET
ejpam-2245	156	21	results	result	NOUN
ejpam-2245	156	22	about	about	ADP
ejpam-2245	156	23	duadic	duadic	ADJ
ejpam-2245	156	24	codes	code	NOUN
ejpam-2245	156	25	over	over	ADP
ejpam-2245	156	26	finite	finite	ADJ
ejpam-2245	156	27	fields	field	NOUN
ejpam-2245	156	28	which	which	PRON
ejpam-2245	156	29	we	we	PRON
ejpam-2245	156	30	will	will	AUX
ejpam-2245	156	31	use	use	VERB
ejpam-2245	156	32	thereafter	thereafter	ADV
ejpam-2245	156	33	.	.	PUNCT
ejpam-2245	157	1	4.1	4.1	NUM
ejpam-2245	157	2	.	.	PUNCT
ejpam-2245	158	1	duadic	duadic	ADJ
ejpam-2245	158	2	codes	code	NOUN
ejpam-2245	158	3	over	over	ADP
ejpam-2245	158	4	finite	finite	ADJ
ejpam-2245	158	5	fields	field	NOUN
ejpam-2245	158	6	it	it	PRON
ejpam-2245	158	7	is	be	AUX
ejpam-2245	158	8	well	well	ADV
ejpam-2245	158	9	known	know	VERB
ejpam-2245	158	10	that	that	SCONJ
ejpam-2245	158	11	every	every	DET
ejpam-2245	158	12	cyclic	cyclic	ADJ
ejpam-2245	158	13	code	code	NOUN
ejpam-2245	158	14	over	over	ADP
ejpam-2245	158	15	fq	fq	PROPN
ejpam-2245	158	16	has	have	VERB
ejpam-2245	158	17	a	a	DET
ejpam-2245	158	18	polynomial	polynomial	NOUN
ejpam-2245	158	19	that	that	PRON
ejpam-2245	158	20	generates	generate	VERB
ejpam-2245	158	21	it	it	PRON
ejpam-2245	158	22	as	as	ADP
ejpam-2245	158	23	an	an	DET
ejpam-2245	158	24	ideal	ideal	NOUN
ejpam-2245	158	25	in	in	ADP
ejpam-2245	158	26	the	the	DET
ejpam-2245	158	27	finite	finite	NOUN
ejpam-2245	158	28	ring	ring	NOUN
ejpam-2245	158	29	fq[x]/(x	fq[x]/(x	NOUN
ejpam-2245	158	30	n−1	n−1	PROPN
ejpam-2245	158	31	)	)	PUNCT
ejpam-2245	158	32	.	.	PUNCT
ejpam-2245	159	1	in	in	ADP
ejpam-2245	159	2	general	general	ADJ
ejpam-2245	159	3	there	there	PRON
ejpam-2245	159	4	are	be	VERB
ejpam-2245	159	5	many	many	ADJ
ejpam-2245	159	6	generators	generator	NOUN
ejpam-2245	159	7	for	for	ADP
ejpam-2245	159	8	a	a	DET
ejpam-2245	159	9	given	give	VERB
ejpam-2245	159	10	cyclic	cyclic	ADJ
ejpam-2245	159	11	code	code	NOUN
ejpam-2245	159	12	.	.	PUNCT
ejpam-2245	160	1	however	however	ADV
ejpam-2245	160	2	,	,	PUNCT
ejpam-2245	160	3	if	if	SCONJ
ejpam-2245	160	4	we	we	PRON
ejpam-2245	160	5	consider	consider	VERB
ejpam-2245	160	6	the	the	DET
ejpam-2245	160	7	monic	monic	ADJ
ejpam-2245	160	8	generator	generator	NOUN
ejpam-2245	160	9	of	of	ADP
ejpam-2245	160	10	least	least	ADJ
ejpam-2245	160	11	degree	degree	NOUN
ejpam-2245	160	12	then	then	ADV
ejpam-2245	160	13	it	it	PRON
ejpam-2245	160	14	is	be	AUX
ejpam-2245	160	15	unique	unique	ADJ
ejpam-2245	160	16	.	.	PUNCT
ejpam-2245	161	1	such	such	DET
ejpam-2245	161	2	a	a	DET
ejpam-2245	161	3	polynomial	polynomial	NOUN
ejpam-2245	161	4	is	be	AUX
ejpam-2245	161	5	called	call	VERB
ejpam-2245	161	6	the	the	DET
ejpam-2245	161	7	generator	generator	NOUN
ejpam-2245	161	8	of	of	ADP
ejpam-2245	161	9	the	the	DET
ejpam-2245	161	10	code	code	NOUN
ejpam-2245	161	11	and	and	CCONJ
ejpam-2245	161	12	naturally	naturally	ADV
ejpam-2245	161	13	it	it	PRON
ejpam-2245	161	14	has	have	VERB
ejpam-2245	161	15	to	to	PART
ejpam-2245	161	16	be	be	AUX
ejpam-2245	161	17	a	a	DET
ejpam-2245	161	18	divisor	divisor	NOUN
ejpam-2245	161	19	of	of	ADP
ejpam-2245	161	20	xn	xn	PROPN
ejpam-2245	162	1	−	−	PROPN
ejpam-2245	162	2	1	1	X
ejpam-2245	162	3	.	.	PUNCT
ejpam-2245	163	1	therefore	therefore	ADV
ejpam-2245	163	2	,	,	PUNCT
ejpam-2245	163	3	there	there	PRON
ejpam-2245	163	4	is	be	VERB
ejpam-2245	163	5	one	one	NUM
ejpam-2245	163	6	-	-	PUNCT
ejpam-2245	163	7	to	to	ADP
ejpam-2245	163	8	-	-	PUNCT
ejpam-2245	163	9	one	one	NUM
ejpam-2245	163	10	correspondence	correspondence	NOUN
ejpam-2245	163	11	between	between	ADP
ejpam-2245	163	12	cyclic	cyclic	ADJ
ejpam-2245	163	13	codes	code	NOUN
ejpam-2245	163	14	of	of	ADP
ejpam-2245	163	15	length	length	NOUN
ejpam-2245	163	16	n	n	PROPN
ejpam-2245	163	17	over	over	ADP
ejpam-2245	163	18	fq	fq	PROPN
ejpam-2245	163	19	,	,	PUNCT
ejpam-2245	163	20	and	and	CCONJ
ejpam-2245	163	21	divisors	divisor	NOUN
ejpam-2245	163	22	of	of	ADP
ejpam-2245	163	23	xn	xn	PROPN
ejpam-2245	163	24	−	−	PROPN
ejpam-2245	164	1	1	1	X
ejpam-2245	164	2	.	.	PUNCT
ejpam-2245	164	3	let	let	VERB
ejpam-2245	164	4	a	a	DET
ejpam-2245	164	5	be	be	AUX
ejpam-2245	164	6	an	an	DET
ejpam-2245	164	7	integer	integer	NOUN
ejpam-2245	164	8	such	such	ADJ
ejpam-2245	164	9	that	that	SCONJ
ejpam-2245	164	10	(	(	PUNCT
ejpam-2245	164	11	a	a	PRON
ejpam-2245	164	12	,	,	PUNCT
ejpam-2245	164	13	n	n	CCONJ
ejpam-2245	164	14	)	)	PUNCT
ejpam-2245	164	15	=	=	SYM
ejpam-2245	165	1	1	1	X
ejpam-2245	165	2	.	.	PUNCT
ejpam-2245	166	1	the	the	DET
ejpam-2245	166	2	function	function	NOUN
ejpam-2245	166	3	µa	µa	ADP
ejpam-2245	166	4	defined	define	VERB
ejpam-2245	166	5	on	on	ADP
ejpam-2245	166	6	zn	zn	X
ejpam-2245	166	7	=	=	SYM
ejpam-2245	166	8	{	{	PUNCT
ejpam-2245	166	9	0,1	0,1	NUM
ejpam-2245	166	10	,	,	PUNCT
ejpam-2245	166	11	.	.	PUNCT
ejpam-2245	166	12	.	.	PUNCT
ejpam-2245	166	13	.	.	PUNCT
ejpam-2245	167	1	,	,	PUNCT
ejpam-2245	167	2	n−	n−	NOUN
ejpam-2245	167	3	1	1	NUM
ejpam-2245	167	4	}	}	PUNCT
ejpam-2245	167	5	by	by	ADP
ejpam-2245	167	6	µa(i	µa(i	NOUN
ejpam-2245	167	7	)	)	PUNCT
ejpam-2245	167	8	≡	≡	PROPN
ejpam-2245	167	9	ia	ia	PROPN
ejpam-2245	167	10	(	(	PUNCT
ejpam-2245	167	11	mod	mod	PROPN
ejpam-2245	167	12	n	n	CCONJ
ejpam-2245	167	13	)	)	PUNCT
ejpam-2245	167	14	is	be	AUX
ejpam-2245	167	15	a	a	DET
ejpam-2245	167	16	permutation	permutation	NOUN
ejpam-2245	167	17	of	of	ADP
ejpam-2245	167	18	the	the	DET
ejpam-2245	167	19	coordinate	coordinate	NOUN
ejpam-2245	167	20	positions	position	NOUN
ejpam-2245	167	21	{	{	PUNCT
ejpam-2245	167	22	0,1,2	0,1,2	NOUN
ejpam-2245	167	23	,	,	PUNCT
ejpam-2245	167	24	.	.	PUNCT
ejpam-2245	167	25	.	.	PUNCT
ejpam-2245	168	1	.	.	PUNCT
ejpam-2245	169	1	,	,	PUNCT
ejpam-2245	169	2	n	n	CCONJ
ejpam-2245	169	3	−	−	PROPN
ejpam-2245	169	4	1	1	NUM
ejpam-2245	169	5	}	}	PUNCT
ejpam-2245	169	6	and	and	CCONJ
ejpam-2245	169	7	is	be	AUX
ejpam-2245	169	8	called	call	VERB
ejpam-2245	169	9	a	a	DET
ejpam-2245	169	10	multiplier	multipli	ADJ
ejpam-2245	169	11	.	.	PUNCT
ejpam-2245	170	1	multipliers	multiplier	NOUN
ejpam-2245	170	2	also	also	ADV
ejpam-2245	170	3	act	act	VERB
ejpam-2245	170	4	on	on	ADP
ejpam-2245	170	5	polynomials	polynomial	NOUN
ejpam-2245	170	6	and	and	CCONJ
ejpam-2245	170	7	this	this	PRON
ejpam-2245	170	8	gives	give	VERB
ejpam-2245	170	9	the	the	DET
ejpam-2245	170	10	following	follow	VERB
ejpam-2245	170	11	ring	ring	NOUN
ejpam-2245	170	12	automorphism	automorphism	NOUN
ejpam-2245	170	13	µa	µa	NOUN
ejpam-2245	170	14	:	:	PUNCT
ejpam-2245	170	15	fq[x]/(x	fq[x]/(x	VERB
ejpam-2245	170	16	n	n	PRON
ejpam-2245	170	17	−	−	NUM
ejpam-2245	170	18	1	1	X
ejpam-2245	170	19	)	)	PUNCT
ejpam-2245	170	20	−→	−→	NOUN
ejpam-2245	170	21	fq[x]/(x	fq[x]/(x	PUNCT
ejpam-2245	170	22	n	n	CCONJ
ejpam-2245	170	23	−	−	PROPN
ejpam-2245	170	24	1	1	X
ejpam-2245	170	25	)	)	PUNCT
ejpam-2245	170	26	f	f	NOUN
ejpam-2245	170	27	(	(	PUNCT
ejpam-2245	170	28	x	x	NOUN
ejpam-2245	170	29	)	)	PUNCT
ejpam-2245	170	30	7→	7→	NUM
ejpam-2245	170	31	µa	µa	NOUN
ejpam-2245	170	32	(	(	PUNCT
ejpam-2245	170	33	f	f	PROPN
ejpam-2245	170	34	(	(	PUNCT
ejpam-2245	170	35	x	x	NOUN
ejpam-2245	170	36	)	)	PUNCT
ejpam-2245	170	37	)	)	PUNCT
ejpam-2245	171	1	=	=	SYM
ejpam-2245	171	2	f	f	PROPN
ejpam-2245	171	3	(	(	PUNCT
ejpam-2245	171	4	xa	xa	PROPN
ejpam-2245	171	5	)	)	PUNCT
ejpam-2245	171	6	.	.	PUNCT
ejpam-2245	172	1	(	(	PUNCT
ejpam-2245	172	2	2	2	X
ejpam-2245	172	3	)	)	PUNCT
ejpam-2245	172	4	suppose	suppose	VERB
ejpam-2245	172	5	that	that	SCONJ
ejpam-2245	172	6	f	f	PROPN
ejpam-2245	172	7	(	(	PUNCT
ejpam-2245	172	8	x	x	X
ejpam-2245	172	9	)	)	PUNCT
ejpam-2245	172	10	=	=	SYM
ejpam-2245	172	11	a0	a0	PROPN
ejpam-2245	172	12	+	+	CCONJ
ejpam-2245	172	13	a1	a1	NOUN
ejpam-2245	172	14	x	x	X
ejpam-2245	172	15	+	+	CCONJ
ejpam-2245	172	16	.	.	PUNCT
ejpam-2245	172	17	.	.	PUNCT
ejpam-2245	173	1	.+	.+	NOUN
ejpam-2245	173	2	ar	ar	NOUN
ejpam-2245	173	3	x	x	PUNCT
ejpam-2245	173	4	r	r	NOUN
ejpam-2245	173	5	is	be	AUX
ejpam-2245	173	6	a	a	DET
ejpam-2245	173	7	polynomial	polynomial	NOUN
ejpam-2245	173	8	of	of	ADP
ejpam-2245	173	9	degree	degree	NOUN
ejpam-2245	173	10	r	r	NOUN
ejpam-2245	173	11	with	with	ADP
ejpam-2245	173	12	f	f	PROPN
ejpam-2245	173	13	(	(	PUNCT
ejpam-2245	173	14	0	0	NUM
ejpam-2245	173	15	)	)	PUNCT
ejpam-2245	173	16	=	=	SYM
ejpam-2245	173	17	a0	a0	PROPN
ejpam-2245	173	18	6=	6=	ADP
ejpam-2245	173	19	0	0	PROPN
ejpam-2245	173	20	.	.	PUNCT
ejpam-2245	174	1	then	then	ADV
ejpam-2245	174	2	the	the	DET
ejpam-2245	174	3	monic	monic	ADJ
ejpam-2245	174	4	reciprocal	reciprocal	ADJ
ejpam-2245	174	5	polynomial	polynomial	NOUN
ejpam-2245	174	6	of	of	ADP
ejpam-2245	174	7	f	f	PROPN
ejpam-2245	174	8	(	(	PUNCT
ejpam-2245	174	9	x	x	X
ejpam-2245	174	10	)	)	PUNCT
ejpam-2245	174	11	is	be	AUX
ejpam-2245	174	12	f	f	PROPN
ejpam-2245	174	13	∗(x	∗(x	PROPN
ejpam-2245	174	14	)	)	PUNCT
ejpam-2245	175	1	=	=	SYM
ejpam-2245	175	2	f	f	PROPN
ejpam-2245	175	3	(	(	PUNCT
ejpam-2245	175	4	0)−1	0)−1	NUM
ejpam-2245	175	5	x	x	SYM
ejpam-2245	175	6	r	r	NOUN
ejpam-2245	175	7	f	f	X
ejpam-2245	175	8	(	(	PUNCT
ejpam-2245	175	9	x−1	x−1	PROPN
ejpam-2245	175	10	)	)	PUNCT
ejpam-2245	175	11	=	=	SYM
ejpam-2245	176	1	f	f	PROPN
ejpam-2245	176	2	(	(	PUNCT
ejpam-2245	176	3	0)−1	0)−1	NUM
ejpam-2245	176	4	x	x	SYM
ejpam-2245	176	5	r(µ−1	r(µ−1	PROPN
ejpam-2245	176	6	(	(	PUNCT
ejpam-2245	176	7	f	f	PROPN
ejpam-2245	176	8	(	(	PUNCT
ejpam-2245	176	9	x	x	NOUN
ejpam-2245	176	10	)	)	PUNCT
ejpam-2245	176	11	)	)	PUNCT
ejpam-2245	176	12	)	)	PUNCT
ejpam-2245	177	1	=	=	SYM
ejpam-2245	177	2	a−1	a−1	PROPN
ejpam-2245	177	3	0	0	NUM
ejpam-2245	177	4	(	(	PUNCT
ejpam-2245	177	5	ar	ar	NOUN
ejpam-2245	177	6	+	+	NOUN
ejpam-2245	177	7	ar−1	ar−1	PROPN
ejpam-2245	177	8	x	x	X
ejpam-2245	177	9	+	+	CCONJ
ejpam-2245	177	10	.	.	PUNCT
ejpam-2245	177	11	.	.	PUNCT
ejpam-2245	178	1	.+	.+	NOUN
ejpam-2245	178	2	a0	a0	NOUN
ejpam-2245	178	3	x	x	SYM
ejpam-2245	178	4	r	r	NOUN
ejpam-2245	178	5	)	)	PUNCT
ejpam-2245	178	6	.	.	PUNCT
ejpam-2245	179	1	if	if	SCONJ
ejpam-2245	179	2	a	a	DET
ejpam-2245	179	3	polynomial	polynomial	NOUN
ejpam-2245	179	4	is	be	AUX
ejpam-2245	179	5	equal	equal	ADJ
ejpam-2245	179	6	to	to	ADP
ejpam-2245	179	7	its	its	PRON
ejpam-2245	179	8	reciprocal	reciprocal	ADJ
ejpam-2245	179	9	polynomial	polynomial	NOUN
ejpam-2245	179	10	,	,	PUNCT
ejpam-2245	179	11	then	then	ADV
ejpam-2245	179	12	it	it	PRON
ejpam-2245	179	13	is	be	AUX
ejpam-2245	179	14	called	call	VERB
ejpam-2245	179	15	a	a	DET
ejpam-2245	179	16	self	self	NOUN
ejpam-2245	179	17	-	-	PUNCT
ejpam-2245	179	18	reciprocal	reciprocal	ADJ
ejpam-2245	179	19	polynomial	polynomial	NOUN
ejpam-2245	179	20	over	over	ADP
ejpam-2245	179	21	fq	fq	PROPN
ejpam-2245	179	22	.	.	PUNCT
ejpam-2245	180	1	if	if	SCONJ
ejpam-2245	180	2	g(x	g(x	NOUN
ejpam-2245	180	3	)	)	PUNCT
ejpam-2245	180	4	is	be	AUX
ejpam-2245	180	5	a	a	DET
ejpam-2245	180	6	generator	generator	NOUN
ejpam-2245	180	7	polynomial	polynomial	NOUN
ejpam-2245	180	8	of	of	ADP
ejpam-2245	180	9	a	a	DET
ejpam-2245	180	10	cyclic	cyclic	ADJ
ejpam-2245	180	11	code	code	NOUN
ejpam-2245	180	12	c	c	NOUN
ejpam-2245	180	13	of	of	ADP
ejpam-2245	180	14	length	length	NOUN
ejpam-2245	180	15	n	n	PROPN
ejpam-2245	180	16	over	over	ADP
ejpam-2245	180	17	fq	fq	PROPN
ejpam-2245	180	18	,	,	PUNCT
ejpam-2245	180	19	then	then	ADV
ejpam-2245	180	20	the	the	DET
ejpam-2245	180	21	dual	dual	ADJ
ejpam-2245	180	22	code	code	NOUN
ejpam-2245	180	23	c⊥	c⊥	NOUN
ejpam-2245	180	24	of	of	ADP
ejpam-2245	180	25	c	c	PROPN
ejpam-2245	180	26	is	be	AUX
ejpam-2245	180	27	the	the	DET
ejpam-2245	180	28	cyclic	cyclic	PROPN
ejpam-2245	180	29	code	code	NOUN
ejpam-2245	180	30	whose	whose	DET
ejpam-2245	180	31	generator	generator	NOUN
ejpam-2245	180	32	polynomial	polynomial	NOUN
ejpam-2245	180	33	is	be	AUX
ejpam-2245	180	34	h∗(x	h∗(x	NOUN
ejpam-2245	180	35	)	)	PUNCT
ejpam-2245	180	36	where	where	SCONJ
ejpam-2245	180	37	h∗(x	h∗(x	NOUN
ejpam-2245	180	38	)	)	PUNCT
ejpam-2245	180	39	is	be	AUX
ejpam-2245	180	40	the	the	DET
ejpam-2245	180	41	monic	monic	ADJ
ejpam-2245	180	42	reciprocal	reciprocal	ADJ
ejpam-2245	180	43	polynomial	polynomial	NOUN
ejpam-2245	180	44	of	of	ADP
ejpam-2245	180	45	h(x	h(x	PROPN
ejpam-2245	180	46	)	)	PUNCT
ejpam-2245	180	47	=	=	PUNCT
ejpam-2245	181	1	(	(	PUNCT
ejpam-2245	181	2	xn	xn	PROPN
ejpam-2245	181	3	−	−	NOUN
ejpam-2245	182	1	1)/g(x	1)/g(x	NUM
ejpam-2245	182	2	)	)	PUNCT
ejpam-2245	182	3	.	.	PUNCT
ejpam-2245	183	1	thus	thus	ADV
ejpam-2245	183	2	the	the	DET
ejpam-2245	183	3	cyclic	cyclic	PROPN
ejpam-2245	183	4	code	code	NOUN
ejpam-2245	183	5	c	c	PROPN
ejpam-2245	183	6	is	be	AUX
ejpam-2245	183	7	self	self	NOUN
ejpam-2245	183	8	-	-	PUNCT
ejpam-2245	183	9	dual	dual	ADJ
ejpam-2245	183	10	if	if	SCONJ
ejpam-2245	183	11	and	and	CCONJ
ejpam-2245	183	12	only	only	ADV
ejpam-2245	183	13	if	if	SCONJ
ejpam-2245	183	14	g(x	g(x	NOUN
ejpam-2245	183	15	)	)	PUNCT
ejpam-2245	183	16	=	=	SYM
ejpam-2245	183	17	h∗(x	h∗(x	NOUN
ejpam-2245	183	18	)	)	PUNCT
ejpam-2245	183	19	.	.	PUNCT
ejpam-2245	184	1	let	let	VERB
ejpam-2245	184	2	s1	s1	NOUN
ejpam-2245	184	3	and	and	CCONJ
ejpam-2245	184	4	s2	s2	PROPN
ejpam-2245	184	5	be	be	VERB
ejpam-2245	184	6	unions	union	NOUN
ejpam-2245	184	7	of	of	ADP
ejpam-2245	184	8	q	q	ADJ
ejpam-2245	184	9	-	-	PUNCT
ejpam-2245	184	10	cyclotomic	cyclotomic	ADJ
ejpam-2245	184	11	cosets	coset	NOUN
ejpam-2245	184	12	modulo	modulo	VERB
ejpam-2245	184	13	m	m	VERB
ejpam-2245	184	14	such	such	ADJ
ejpam-2245	184	15	that	that	SCONJ
ejpam-2245	184	16	s1	s1	PROPN
ejpam-2245	184	17	∩	∩	ADJ
ejpam-2245	184	18	s2	s2	NOUN
ejpam-2245	184	19	=	=	PUNCT
ejpam-2245	184	20	;	;	PUNCT
ejpam-2245	184	21	,	,	PUNCT
ejpam-2245	184	22	s1∪s2	s1∪s2	X
ejpam-2245	184	23	=	=	SYM
ejpam-2245	184	24	zm\{0	zm\{0	ADJ
ejpam-2245	184	25	}	}	PUNCT
ejpam-2245	184	26	and	and	CCONJ
ejpam-2245	184	27	µasi	µasi	NOUN
ejpam-2245	184	28	mod	mod	PROPN
ejpam-2245	184	29	m=	m=	X
ejpam-2245	184	30	s(i+1	s(i+1	NOUN
ejpam-2245	184	31	)	)	PUNCT
ejpam-2245	184	32	mod	mod	PROPN
ejpam-2245	185	1	2	2	X
ejpam-2245	185	2	.	.	PUNCT
ejpam-2245	185	3	then	then	ADV
ejpam-2245	185	4	the	the	DET
ejpam-2245	185	5	triple	triple	ADJ
ejpam-2245	185	6	µa	µa	NOUN
ejpam-2245	185	7	,	,	PUNCT
ejpam-2245	185	8	s1,s2	s1,s2	PROPN
ejpam-2245	185	9	is	be	AUX
ejpam-2245	185	10	called	call	VERB
ejpam-2245	185	11	a	a	DET
ejpam-2245	185	12	splitting	splitting	NOUN
ejpam-2245	185	13	modulo	modulo	NOUN
ejpam-2245	185	14	m.	m.	NOUN
ejpam-2245	185	15	the	the	DET
ejpam-2245	185	16	odd	odd	ADV
ejpam-2245	185	17	-	-	PUNCT
ejpam-2245	185	18	like	like	ADJ
ejpam-2245	185	19	duadic	duadic	ADJ
ejpam-2245	185	20	codes	code	NOUN
ejpam-2245	185	21	d1	d1	PROPN
ejpam-2245	185	22	and	and	CCONJ
ejpam-2245	185	23	d2	d2	PROPN
ejpam-2245	185	24	are	be	AUX
ejpam-2245	185	25	the	the	DET
ejpam-2245	185	26	cyclic	cyclic	ADJ
ejpam-2245	185	27	codes	code	NOUN
ejpam-2245	185	28	over	over	ADP
ejpam-2245	185	29	fq	fq	PROPN
ejpam-2245	185	30	with	with	ADP
ejpam-2245	185	31	defining	define	VERB
ejpam-2245	185	32	sets	set	NOUN
ejpam-2245	185	33	s1	s1	NOUN
ejpam-2245	185	34	and	and	CCONJ
ejpam-2245	185	35	s2	s2	PROPN
ejpam-2245	185	36	and	and	CCONJ
ejpam-2245	185	37	generator	generator	NOUN
ejpam-2245	185	38	polynomials	polynomial	NOUN
ejpam-2245	185	39	f1(x	f1(x	NOUN
ejpam-2245	185	40	)	)	PUNCT
ejpam-2245	185	41	=	=	SYM
ejpam-2245	185	42	πi∈s1	πi∈s1	PROPN
ejpam-2245	186	1	(	(	PUNCT
ejpam-2245	186	2	x	x	X
ejpam-2245	186	3	−	−	PUNCT
ejpam-2245	186	4	αi	αi	NOUN
ejpam-2245	186	5	)	)	PUNCT
ejpam-2245	186	6	and	and	CCONJ
ejpam-2245	186	7	f2(x	f2(x	NUM
ejpam-2245	186	8	)	)	PUNCT
ejpam-2245	187	1	=	=	PRON
ejpam-2245	187	2	πi∈s2	πi∈s2	X
ejpam-2245	187	3	(	(	PUNCT
ejpam-2245	187	4	x	x	X
ejpam-2245	187	5	−	−	NOUN
ejpam-2245	187	6	αi	αi	NOUN
ejpam-2245	187	7	)	)	PUNCT
ejpam-2245	187	8	,	,	PUNCT
ejpam-2245	187	9	respectively	respectively	ADV
ejpam-2245	187	10	.	.	PUNCT
ejpam-2245	188	1	the	the	DET
ejpam-2245	188	2	even	even	ADV
ejpam-2245	188	3	-	-	PUNCT
ejpam-2245	188	4	like	like	ADJ
ejpam-2245	188	5	duadic	duadic	ADJ
ejpam-2245	188	6	codes	code	NOUN
ejpam-2245	188	7	c1	c1	PROPN
ejpam-2245	188	8	and	and	CCONJ
ejpam-2245	188	9	c2	c2	PROPN
ejpam-2245	188	10	are	be	AUX
ejpam-2245	188	11	the	the	DET
ejpam-2245	188	12	cyclic	cyclic	ADJ
ejpam-2245	188	13	codes	code	NOUN
ejpam-2245	188	14	over	over	ADP
ejpam-2245	188	15	fq	fq	PROPN
ejpam-2245	188	16	with	with	ADP
ejpam-2245	188	17	defining	define	VERB
ejpam-2245	188	18	sets	set	NOUN
ejpam-2245	188	19	{	{	PUNCT
ejpam-2245	188	20	0	0	NUM
ejpam-2245	188	21	}	}	PUNCT
ejpam-2245	188	22	∪	∪	NOUN
ejpam-2245	188	23	s1	s1	NOUN
ejpam-2245	188	24	and	and	CCONJ
ejpam-2245	188	25	{	{	PUNCT
ejpam-2245	188	26	0	0	NUM
ejpam-2245	188	27	}	}	PUNCT
ejpam-2245	188	28	∪	∪	ADJ
ejpam-2245	188	29	s2	s2	PROPN
ejpam-2245	188	30	,	,	PUNCT
ejpam-2245	188	31	respectively	respectively	ADV
ejpam-2245	188	32	.	.	PUNCT
ejpam-2245	189	1	for	for	ADP
ejpam-2245	189	2	the	the	DET
ejpam-2245	189	3	remainder	remainder	NOUN
ejpam-2245	189	4	of	of	ADP
ejpam-2245	189	5	the	the	DET
ejpam-2245	189	6	paper	paper	NOUN
ejpam-2245	189	7	,	,	PUNCT
ejpam-2245	189	8	the	the	DET
ejpam-2245	189	9	notation	notation	NOUN
ejpam-2245	189	10	q	q	NOUN
ejpam-2245	189	11	=	=	SYM
ejpam-2245	189	12	�	�	PROPN
ejpam-2245	189	13	mod	mod	NOUN
ejpam-2245	189	14	m	m	PROPN
ejpam-2245	189	15	means	mean	VERB
ejpam-2245	189	16	that	that	SCONJ
ejpam-2245	189	17	q	q	NOUN
ejpam-2245	189	18	is	be	AUX
ejpam-2245	189	19	a	a	DET
ejpam-2245	189	20	quadratic	quadratic	ADJ
ejpam-2245	189	21	residue	residue	NOUN
ejpam-2245	189	22	modulo	modulo	NOUN
ejpam-2245	189	23	m.	m.	NOUN
ejpam-2245	189	24	for	for	ADP
ejpam-2245	189	25	a	a	DET
ejpam-2245	189	26	prime	prime	ADJ
ejpam-2245	189	27	power	power	NOUN
ejpam-2245	189	28	q	q	NOUN
ejpam-2245	189	29	and	and	CCONJ
ejpam-2245	189	30	integer	integer	PROPN
ejpam-2245	189	31	m	m	VERB
ejpam-2245	189	32	such	such	ADJ
ejpam-2245	189	33	that	that	SCONJ
ejpam-2245	189	34	gcd(q	gcd(q	PROPN
ejpam-2245	189	35	,	,	PUNCT
ejpam-2245	189	36	m	m	PROPN
ejpam-2245	189	37	)	)	PUNCT
ejpam-2245	189	38	=	=	SYM
ejpam-2245	189	39	1	1	NUM
ejpam-2245	189	40	,	,	PUNCT
ejpam-2245	189	41	we	we	PRON
ejpam-2245	189	42	denote	denote	VERB
ejpam-2245	189	43	by	by	ADP
ejpam-2245	189	44	ordm(q	ordm(q	PROPN
ejpam-2245	189	45	)	)	PUNCT
ejpam-2245	189	46	the	the	DET
ejpam-2245	189	47	multiplicative	multiplicative	ADJ
ejpam-2245	189	48	order	order	NOUN
ejpam-2245	189	49	of	of	ADP
ejpam-2245	189	50	q	q	NOUN
ejpam-2245	189	51	modulo	modulo	ADJ
ejpam-2245	189	52	m.	m.	NOUN
ejpam-2245	189	53	this	this	PRON
ejpam-2245	189	54	is	be	AUX
ejpam-2245	189	55	the	the	DET
ejpam-2245	189	56	smallest	small	ADJ
ejpam-2245	189	57	integer	integer	NOUN
ejpam-2245	189	58	l	l	NOUN
ejpam-2245	190	1	such	such	ADJ
ejpam-2245	190	2	that	that	PRON
ejpam-2245	190	3	ql	ql	CCONJ
ejpam-2245	190	4	≡	≡	PROPN
ejpam-2245	190	5	1	1	NUM
ejpam-2245	190	6	(	(	PUNCT
ejpam-2245	190	7	mod	mod	PROPN
ejpam-2245	190	8	m	m	PROPN
ejpam-2245	190	9	)	)	PUNCT
ejpam-2245	190	10	.	.	PUNCT
ejpam-2245	191	1	in	in	ADP
ejpam-2245	191	2	the	the	DET
ejpam-2245	191	3	following	following	NOUN
ejpam-2245	191	4	we	we	PRON
ejpam-2245	191	5	give	give	VERB
ejpam-2245	191	6	necessary	necessary	ADJ
ejpam-2245	191	7	and	and	CCONJ
ejpam-2245	191	8	sufficient	sufficient	ADJ
ejpam-2245	191	9	conditions	condition	NOUN
ejpam-2245	191	10	for	for	ADP
ejpam-2245	191	11	the	the	DET
ejpam-2245	191	12	existence	existence	NOUN
ejpam-2245	191	13	of	of	ADP
ejpam-2245	191	14	duadic	duadic	ADJ
ejpam-2245	191	15	codes	code	NOUN
ejpam-2245	191	16	.	.	PUNCT
ejpam-2245	192	1	theorem	theorem	NOUN
ejpam-2245	192	2	5	5	NUM
ejpam-2245	192	3	.	.	PUNCT
ejpam-2245	193	1	[	[	X
ejpam-2245	193	2	14	14	NUM
ejpam-2245	193	3	]	]	X
ejpam-2245	193	4	duadic	duadic	ADJ
ejpam-2245	193	5	codes	code	NOUN
ejpam-2245	193	6	of	of	ADP
ejpam-2245	193	7	length	length	NOUN
ejpam-2245	193	8	m	m	VERB
ejpam-2245	193	9	over	over	ADP
ejpam-2245	193	10	fq	fq	PROPN
ejpam-2245	193	11	exist	exist	VERB
ejpam-2245	193	12	if	if	SCONJ
ejpam-2245	193	13	and	and	CCONJ
ejpam-2245	193	14	only	only	ADV
ejpam-2245	193	15	if	if	SCONJ
ejpam-2245	193	16	q	q	ADJ
ejpam-2245	193	17	=	=	SYM
ejpam-2245	193	18	�	�	PROPN
ejpam-2245	193	19	mod	mod	PROPN
ejpam-2245	193	20	m	m	PROPN
ejpam-2245	193	21	,	,	PUNCT
ejpam-2245	193	22	i.e	i.e	X
ejpam-2245	193	23	,	,	PUNCT
ejpam-2245	193	24	if	if	SCONJ
ejpam-2245	193	25	m	m	VERB
ejpam-2245	193	26	=	=	SYM
ejpam-2245	193	27	p	p	NOUN
ejpam-2245	193	28	s1	s1	NOUN
ejpam-2245	193	29	1	1	NUM
ejpam-2245	193	30	p	p	PROPN
ejpam-2245	193	31	s2	s2	NOUN
ejpam-2245	193	32	2	2	NUM
ejpam-2245	193	33	.	.	PUNCT
ejpam-2245	193	34	.	.	PUNCT
ejpam-2245	193	35	.	.	PUNCT
ejpam-2245	194	1	p	p	NOUN
ejpam-2245	194	2	sk	sk	PROPN
ejpam-2245	194	3	k	k	PROPN
ejpam-2245	194	4	is	be	AUX
ejpam-2245	194	5	the	the	DET
ejpam-2245	194	6	prime	prime	ADJ
ejpam-2245	194	7	factorization	factorization	NOUN
ejpam-2245	194	8	of	of	ADP
ejpam-2245	194	9	the	the	DET
ejpam-2245	194	10	odd	odd	ADJ
ejpam-2245	194	11	integer	integer	NOUN
ejpam-2245	194	12	m	m	ADP
ejpam-2245	194	13	where	where	SCONJ
ejpam-2245	194	14	each	each	DET
ejpam-2245	194	15	si	si	X
ejpam-2245	194	16	>	>	X
ejpam-2245	194	17	0	0	NUM
ejpam-2245	194	18	,	,	PUNCT
ejpam-2245	194	19	then	then	ADV
ejpam-2245	194	20	duadic	duadic	ADJ
ejpam-2245	194	21	codes	code	NOUN
ejpam-2245	194	22	of	of	ADP
ejpam-2245	194	23	length	length	NOUN
ejpam-2245	194	24	m	m	VERB
ejpam-2245	194	25	over	over	ADP
ejpam-2245	194	26	fq	fq	PROPN
ejpam-2245	194	27	exist	exist	VERB
ejpam-2245	194	28	if	if	SCONJ
ejpam-2245	194	29	and	and	CCONJ
ejpam-2245	195	1	only	only	ADV
ejpam-2245	195	2	if	if	SCONJ
ejpam-2245	195	3	q	q	ADJ
ejpam-2245	195	4	=	=	SYM
ejpam-2245	195	5	�	�	PROPN
ejpam-2245	195	6	mod	mod	NOUN
ejpam-2245	195	7	pi	pi	NOUN
ejpam-2245	195	8	i	i	NOUN
ejpam-2245	195	9	=	=	NOUN
ejpam-2245	195	10	1,2	1,2	NUM
ejpam-2245	195	11	,	,	PUNCT
ejpam-2245	195	12	.	.	PUNCT
ejpam-2245	195	13	.	.	PUNCT
ejpam-2245	196	1	.	.	PUNCT
ejpam-2245	197	1	,	,	PUNCT
ejpam-2245	197	2	k.	k.	PROPN
ejpam-2245	197	3	a.	a.	PROPN
ejpam-2245	197	4	batoul	batoul	PROPN
ejpam-2245	197	5	,	,	PUNCT
ejpam-2245	197	6	k.	k.	PROPN
ejpam-2245	197	7	guenda	guenda	PROPN
ejpam-2245	197	8	,	,	PUNCT
ejpam-2245	197	9	a.	a.	PROPN
ejpam-2245	197	10	kaya	kaya	PROPN
ejpam-2245	197	11	,	,	PUNCT
ejpam-2245	197	12	b.	b.	PROPN
ejpam-2245	197	13	yildiz	yildiz	PROPN
ejpam-2245	197	14	/	/	SYM
ejpam-2245	197	15	eur	eur	PROPN
ejpam-2245	197	16	.	.	PUNCT
ejpam-2245	198	1	j.	j.	PROPN
ejpam-2245	198	2	pure	pure	PROPN
ejpam-2245	198	3	appl	appl	PROPN
ejpam-2245	198	4	.	.	PROPN
ejpam-2245	198	5	math	math	PROPN
ejpam-2245	198	6	,	,	PUNCT
ejpam-2245	198	7	8	8	NUM
ejpam-2245	198	8	(	(	PUNCT
ejpam-2245	198	9	2015	2015	NUM
ejpam-2245	198	10	)	)	PUNCT
ejpam-2245	198	11	,	,	PUNCT
ejpam-2245	198	12	64	64	NUM
ejpam-2245	198	13	-	-	SYM
ejpam-2245	198	14	80	80	NUM
ejpam-2245	198	15	70	70	NUM
ejpam-2245	198	16	remark	remark	NOUN
ejpam-2245	198	17	1	1	NUM
ejpam-2245	198	18	.	.	PUNCT
ejpam-2245	199	1	in	in	ADP
ejpam-2245	199	2	general	general	ADJ
ejpam-2245	199	3	the	the	DET
ejpam-2245	199	4	same	same	ADJ
ejpam-2245	199	5	splitting	splitting	NOUN
ejpam-2245	199	6	modulo	modulo	VERB
ejpam-2245	199	7	an	an	DET
ejpam-2245	199	8	odd	odd	ADJ
ejpam-2245	199	9	integer	integer	NOUN
ejpam-2245	199	10	m	m	VERB
ejpam-2245	199	11	can	can	AUX
ejpam-2245	199	12	be	be	AUX
ejpam-2245	199	13	given	give	VERB
ejpam-2245	199	14	by	by	ADP
ejpam-2245	199	15	different	different	ADJ
ejpam-2245	199	16	multipliers	multiplier	NOUN
ejpam-2245	199	17	.	.	PUNCT
ejpam-2245	200	1	for	for	SCONJ
ejpam-2245	200	2	more	more	ADJ
ejpam-2245	200	3	details	detail	NOUN
ejpam-2245	200	4	see	see	VERB
ejpam-2245	200	5	[	[	X
ejpam-2245	200	6	5	5	NUM
ejpam-2245	200	7	,	,	PUNCT
ejpam-2245	200	8	page	page	NOUN
ejpam-2245	200	9	214	214	NUM
ejpam-2245	200	10	]	]	PUNCT
ejpam-2245	200	11	.	.	PUNCT
ejpam-2245	201	1	when	when	SCONJ
ejpam-2245	201	2	we	we	PRON
ejpam-2245	201	3	consider	consider	VERB
ejpam-2245	201	4	the	the	DET
ejpam-2245	201	5	multiplier	multipli	ADJ
ejpam-2245	201	6	µ−1	µ−1	PROPN
ejpam-2245	201	7	,	,	PUNCT
ejpam-2245	201	8	we	we	PRON
ejpam-2245	201	9	mean	mean	VERB
ejpam-2245	201	10	any	any	DET
ejpam-2245	201	11	multiplier	multipli	ADJ
ejpam-2245	201	12	which	which	PRON
ejpam-2245	201	13	gives	give	VERB
ejpam-2245	201	14	the	the	DET
ejpam-2245	201	15	same	same	ADJ
ejpam-2245	201	16	splitting	splitting	NOUN
ejpam-2245	201	17	as	as	ADP
ejpam-2245	201	18	the	the	DET
ejpam-2245	201	19	multiplier	multipli	ADJ
ejpam-2245	201	20	µ−1	µ−1	PROPN
ejpam-2245	201	21	.	.	PUNCT
ejpam-2245	202	1	the	the	DET
ejpam-2245	202	2	multiplier	multipli	ADJ
ejpam-2245	202	3	µ−1	µ−1	PROPN
ejpam-2245	202	4	plays	play	VERB
ejpam-2245	202	5	a	a	DET
ejpam-2245	202	6	special	special	ADJ
ejpam-2245	202	7	role	role	NOUN
ejpam-2245	202	8	in	in	ADP
ejpam-2245	202	9	determining	determine	VERB
ejpam-2245	202	10	the	the	DET
ejpam-2245	202	11	duals	dual	NOUN
ejpam-2245	202	12	of	of	ADP
ejpam-2245	202	13	duadic	duadic	ADJ
ejpam-2245	202	14	codes	code	NOUN
ejpam-2245	202	15	just	just	ADV
ejpam-2245	202	16	as	as	SCONJ
ejpam-2245	202	17	it	it	PRON
ejpam-2245	202	18	does	do	AUX
ejpam-2245	202	19	for	for	ADP
ejpam-2245	202	20	duals	dual	NOUN
ejpam-2245	202	21	in	in	ADP
ejpam-2245	202	22	general	general	ADJ
ejpam-2245	202	23	cyclic	cyclic	ADJ
ejpam-2245	202	24	codes	code	NOUN
ejpam-2245	202	25	.	.	PUNCT
ejpam-2245	203	1	in	in	ADP
ejpam-2245	203	2	the	the	DET
ejpam-2245	203	3	following	following	NOUN
ejpam-2245	203	4	we	we	PRON
ejpam-2245	203	5	give	give	VERB
ejpam-2245	203	6	some	some	DET
ejpam-2245	203	7	important	important	ADJ
ejpam-2245	203	8	result	result	NOUN
ejpam-2245	203	9	which	which	PRON
ejpam-2245	203	10	concerns	concern	VERB
ejpam-2245	203	11	the	the	DET
ejpam-2245	203	12	multiplier	multipli	ADJ
ejpam-2245	203	13	µ−1	µ−1	PROPN
ejpam-2245	203	14	.	.	PUNCT
ejpam-2245	204	1	theorem	theorem	VERB
ejpam-2245	204	2	6	6	NUM
ejpam-2245	204	3	.	.	PUNCT
ejpam-2245	205	1	[	[	X
ejpam-2245	205	2	5	5	NUM
ejpam-2245	205	3	,	,	PUNCT
ejpam-2245	205	4	theorem	theorem	VERB
ejpam-2245	205	5	6.4.2	6.4.2	NUM
ejpam-2245	205	6	]	]	X
ejpam-2245	205	7	if	if	SCONJ
ejpam-2245	205	8	c1	c1	PROPN
ejpam-2245	205	9	and	and	CCONJ
ejpam-2245	205	10	c2	c2	PROPN
ejpam-2245	205	11	are	be	AUX
ejpam-2245	205	12	a	a	DET
ejpam-2245	205	13	pair	pair	NOUN
ejpam-2245	205	14	of	of	ADP
ejpam-2245	205	15	even	even	ADV
ejpam-2245	205	16	-	-	PUNCT
ejpam-2245	205	17	like	like	ADJ
ejpam-2245	205	18	duadic	duadic	ADJ
ejpam-2245	205	19	codes	code	NOUN
ejpam-2245	205	20	over	over	ADP
ejpam-2245	205	21	fq	fq	PROPN
ejpam-2245	205	22	,	,	PUNCT
ejpam-2245	205	23	with	with	ADP
ejpam-2245	205	24	d1	d1	PROPN
ejpam-2245	205	25	and	and	CCONJ
ejpam-2245	205	26	d2	d2	VERB
ejpam-2245	205	27	the	the	DET
ejpam-2245	205	28	associated	associated	ADJ
ejpam-2245	205	29	pair	pair	NOUN
ejpam-2245	205	30	of	of	ADP
ejpam-2245	205	31	duadic	duadic	ADJ
ejpam-2245	205	32	codes	code	NOUN
ejpam-2245	205	33	,	,	PUNCT
ejpam-2245	205	34	the	the	DET
ejpam-2245	205	35	following	follow	VERB
ejpam-2245	205	36	are	be	AUX
ejpam-2245	205	37	equivalent	equivalent	ADJ
ejpam-2245	205	38	:	:	PUNCT
ejpam-2245	205	39	(	(	PUNCT
ejpam-2245	205	40	i	i	NOUN
ejpam-2245	205	41	)	)	PUNCT
ejpam-2245	205	42	c⊥1	c⊥1	VERB
ejpam-2245	205	43	=	=	SYM
ejpam-2245	205	44	d1	d1	PROPN
ejpam-2245	205	45	(	(	PUNCT
ejpam-2245	205	46	ii	ii	NOUN
ejpam-2245	205	47	)	)	PUNCT
ejpam-2245	205	48	c⊥2	c⊥2	PROPN
ejpam-2245	205	49	=	=	SYM
ejpam-2245	205	50	d2	d2	PROPN
ejpam-2245	205	51	(	(	PUNCT
ejpam-2245	205	52	iii	iii	NOUN
ejpam-2245	205	53	)	)	PUNCT
ejpam-2245	205	54	µ−1(c1	µ−1(c1	NUM
ejpam-2245	205	55	)	)	PUNCT
ejpam-2245	206	1	=	=	SYM
ejpam-2245	206	2	c2	c2	PROPN
ejpam-2245	206	3	(	(	PUNCT
ejpam-2245	206	4	iv	iv	X
ejpam-2245	206	5	)	)	PUNCT
ejpam-2245	206	6	µ−1(c2	µ−1(c2	NOUN
ejpam-2245	206	7	)	)	PUNCT
ejpam-2245	206	8	=	=	SYM
ejpam-2245	206	9	c1	c1	PROPN
ejpam-2245	206	10	.	.	PUNCT
ejpam-2245	207	1	theorem	theorem	VERB
ejpam-2245	207	2	7	7	NUM
ejpam-2245	207	3	.	.	PUNCT
ejpam-2245	208	1	[	[	X
ejpam-2245	208	2	5	5	NUM
ejpam-2245	208	3	,	,	PUNCT
ejpam-2245	208	4	theorem	theorem	VERB
ejpam-2245	208	5	6.4.3	6.4.3	NOUN
ejpam-2245	208	6	]	]	PUNCT
ejpam-2245	208	7	if	if	SCONJ
ejpam-2245	208	8	c1	c1	PROPN
ejpam-2245	208	9	and	and	CCONJ
ejpam-2245	208	10	c2	c2	PROPN
ejpam-2245	208	11	are	be	AUX
ejpam-2245	208	12	a	a	DET
ejpam-2245	208	13	pair	pair	NOUN
ejpam-2245	208	14	of	of	ADP
ejpam-2245	208	15	even	even	ADV
ejpam-2245	208	16	-	-	PUNCT
ejpam-2245	208	17	like	like	ADJ
ejpam-2245	208	18	duadic	duadic	ADJ
ejpam-2245	208	19	codes	code	NOUN
ejpam-2245	208	20	over	over	ADP
ejpam-2245	208	21	fq	fq	PROPN
ejpam-2245	208	22	,	,	PUNCT
ejpam-2245	208	23	with	with	ADP
ejpam-2245	208	24	d1	d1	PROPN
ejpam-2245	208	25	and	and	CCONJ
ejpam-2245	208	26	d2	d2	VERB
ejpam-2245	208	27	the	the	DET
ejpam-2245	208	28	associated	associated	ADJ
ejpam-2245	208	29	pair	pair	NOUN
ejpam-2245	208	30	of	of	ADP
ejpam-2245	208	31	duadic	duadic	ADJ
ejpam-2245	208	32	codes	code	NOUN
ejpam-2245	208	33	.	.	PUNCT
ejpam-2245	209	1	then	then	ADV
ejpam-2245	209	2	the	the	DET
ejpam-2245	209	3	following	follow	VERB
ejpam-2245	209	4	are	be	AUX
ejpam-2245	209	5	equivalent	equivalent	ADJ
ejpam-2245	209	6	:	:	PUNCT
ejpam-2245	209	7	(	(	PUNCT
ejpam-2245	209	8	i	i	NOUN
ejpam-2245	209	9	)	)	PUNCT
ejpam-2245	209	10	c⊥1	c⊥1	VERB
ejpam-2245	209	11	=	=	SYM
ejpam-2245	209	12	d2	d2	PROPN
ejpam-2245	209	13	(	(	PUNCT
ejpam-2245	209	14	ii	ii	NOUN
ejpam-2245	209	15	)	)	PUNCT
ejpam-2245	209	16	c⊥2	c⊥2	PUNCT
ejpam-2245	209	17	=	=	SYM
ejpam-2245	209	18	d1	d1	PROPN
ejpam-2245	209	19	(	(	PUNCT
ejpam-2245	209	20	iii	iii	NOUN
ejpam-2245	209	21	)	)	PUNCT
ejpam-2245	209	22	µ−1(c1	µ−1(c1	NUM
ejpam-2245	209	23	)	)	PUNCT
ejpam-2245	209	24	=	=	SYM
ejpam-2245	209	25	c1	c1	PROPN
ejpam-2245	209	26	(	(	PUNCT
ejpam-2245	209	27	iv	iv	X
ejpam-2245	209	28	)	)	PUNCT
ejpam-2245	209	29	µ−1(c2	µ−1(c2	NOUN
ejpam-2245	209	30	)	)	PUNCT
ejpam-2245	209	31	=	=	SYM
ejpam-2245	209	32	c2	c2	PROPN
ejpam-2245	209	33	.	.	PUNCT
ejpam-2245	210	1	in	in	ADP
ejpam-2245	210	2	the	the	DET
ejpam-2245	210	3	following	following	NOUN
ejpam-2245	210	4	we	we	PRON
ejpam-2245	210	5	investigate	investigate	VERB
ejpam-2245	210	6	when	when	SCONJ
ejpam-2245	210	7	a	a	DET
ejpam-2245	210	8	splitting	splitting	NOUN
ejpam-2245	210	9	modulo	modulo	VERB
ejpam-2245	210	10	an	an	DET
ejpam-2245	210	11	odd	odd	ADJ
ejpam-2245	210	12	integer	integer	NOUN
ejpam-2245	210	13	m	m	AUX
ejpam-2245	210	14	is	be	AUX
ejpam-2245	210	15	given	give	VERB
ejpam-2245	210	16	by	by	ADP
ejpam-2245	210	17	the	the	DET
ejpam-2245	210	18	multiplier	multipli	ADJ
ejpam-2245	210	19	µ−1	µ−1	PROPN
ejpam-2245	210	20	and	and	CCONJ
ejpam-2245	210	21	when	when	SCONJ
ejpam-2245	210	22	it	it	PRON
ejpam-2245	210	23	is	be	AUX
ejpam-2245	210	24	left	leave	VERB
ejpam-2245	210	25	invariant	invariant	ADJ
ejpam-2245	210	26	by	by	ADP
ejpam-2245	210	27	it	it	PRON
ejpam-2245	210	28	.	.	PUNCT
ejpam-2245	211	1	theorem	theorem	ADJ
ejpam-2245	211	2	8	8	NUM
ejpam-2245	211	3	.	.	PUNCT
ejpam-2245	212	1	[	[	X
ejpam-2245	212	2	14	14	NUM
ejpam-2245	212	3	]	]	PUNCT
ejpam-2245	212	4	let	let	VERB
ejpam-2245	212	5	fq	fq	PRON
ejpam-2245	212	6	be	be	AUX
ejpam-2245	212	7	a	a	DET
ejpam-2245	212	8	finite	finite	ADJ
ejpam-2245	212	9	field	field	NOUN
ejpam-2245	212	10	and	and	CCONJ
ejpam-2245	212	11	m	m	NOUN
ejpam-2245	212	12	=	=	SYM
ejpam-2245	212	13	p	p	NOUN
ejpam-2245	212	14	s1	s1	NOUN
ejpam-2245	212	15	1	1	NUM
ejpam-2245	212	16	p	p	PROPN
ejpam-2245	212	17	s2	s2	NOUN
ejpam-2245	212	18	2	2	NUM
ejpam-2245	212	19	.	.	PUNCT
ejpam-2245	212	20	.	.	PUNCT
ejpam-2245	212	21	.	.	PUNCT
ejpam-2245	213	1	p	p	NOUN
ejpam-2245	214	1	sk	sk	PRON
ejpam-2245	214	2	k	k	X
ejpam-2245	214	3	be	be	AUX
ejpam-2245	214	4	a	a	DET
ejpam-2245	214	5	prime	prime	ADJ
ejpam-2245	214	6	factorization	factorization	NOUN
ejpam-2245	214	7	of	of	ADP
ejpam-2245	214	8	the	the	DET
ejpam-2245	214	9	odd	odd	ADJ
ejpam-2245	214	10	integer	integer	NOUN
ejpam-2245	214	11	m	m	PROPN
ejpam-2245	214	12	,	,	PUNCT
ejpam-2245	214	13	such	such	ADJ
ejpam-2245	214	14	that	that	DET
ejpam-2245	214	15	q	q	PROPN
ejpam-2245	214	16	≡	≡	PROPN
ejpam-2245	214	17	�	�	PROPN
ejpam-2245	214	18	mod	mod	PROPN
ejpam-2245	214	19	m.	m.	NOUN
ejpam-2245	214	20	(	(	PUNCT
ejpam-2245	214	21	i	i	NOUN
ejpam-2245	214	22	)	)	PUNCT
ejpam-2245	215	1	if	if	SCONJ
ejpam-2245	215	2	pi	pi	PROPN
ejpam-2245	215	3	≡	≡	PROPN
ejpam-2245	215	4	−1	−1	NOUN
ejpam-2245	215	5	mod	mod	NOUN
ejpam-2245	215	6	4	4	NUM
ejpam-2245	215	7	,	,	PUNCT
ejpam-2245	215	8	i	i	PRON
ejpam-2245	215	9	=	=	NOUN
ejpam-2245	215	10	1,2	1,2	NUM
ejpam-2245	215	11	,	,	PUNCT
ejpam-2245	215	12	.	.	PUNCT
ejpam-2245	215	13	.	.	PUNCT
ejpam-2245	216	1	.	.	PUNCT
ejpam-2245	217	1	,	,	PUNCT
ejpam-2245	217	2	k	k	PROPN
ejpam-2245	217	3	then	then	ADV
ejpam-2245	217	4	all	all	DET
ejpam-2245	217	5	splittings	splitting	NOUN
ejpam-2245	217	6	modm	modm	NOUN
ejpam-2245	217	7	are	be	AUX
ejpam-2245	217	8	given	give	VERB
ejpam-2245	217	9	by	by	ADP
ejpam-2245	217	10	µ−1	µ−1	PROPN
ejpam-2245	217	11	,	,	PUNCT
ejpam-2245	217	12	(	(	PUNCT
ejpam-2245	217	13	ii	ii	NOUN
ejpam-2245	217	14	)	)	PUNCT
ejpam-2245	217	15	if	if	SCONJ
ejpam-2245	217	16	at	at	ADV
ejpam-2245	217	17	least	least	ADV
ejpam-2245	217	18	one	one	NUM
ejpam-2245	217	19	pi	pi	NOUN
ejpam-2245	217	20	≡	≡	PROPN
ejpam-2245	217	21	1	1	NUM
ejpam-2245	217	22	mod	mod	NOUN
ejpam-2245	217	23	4	4	NUM
ejpam-2245	217	24	,	,	PUNCT
ejpam-2245	217	25	i	i	PRON
ejpam-2245	217	26	∈	∈	PROPN
ejpam-2245	217	27	{	{	PUNCT
ejpam-2245	217	28	1,2	1,2	NUM
ejpam-2245	217	29	,	,	PUNCT
ejpam-2245	217	30	.	.	PUNCT
ejpam-2245	217	31	.	.	PUNCT
ejpam-2245	217	32	.	.	PUNCT
ejpam-2245	218	1	,	,	PUNCT
ejpam-2245	218	2	k	k	X
ejpam-2245	218	3	}	}	PUNCT
ejpam-2245	218	4	,	,	PUNCT
ejpam-2245	218	5	then	then	ADV
ejpam-2245	218	6	there	there	PRON
ejpam-2245	218	7	is	be	VERB
ejpam-2245	218	8	a	a	DET
ejpam-2245	218	9	splitting	splitting	NOUN
ejpam-2245	218	10	modm	modm	NOUN
ejpam-2245	218	11	which	which	PRON
ejpam-2245	218	12	is	be	AUX
ejpam-2245	218	13	not	not	PART
ejpam-2245	218	14	given	give	VERB
ejpam-2245	218	15	by	by	ADP
ejpam-2245	218	16	µ−1	µ−1	PROPN
ejpam-2245	218	17	.	.	PUNCT
ejpam-2245	219	1	the	the	DET
ejpam-2245	219	2	following	follow	VERB
ejpam-2245	219	3	theorem	theorem	NOUN
ejpam-2245	219	4	gives	give	VERB
ejpam-2245	219	5	us	we	PRON
ejpam-2245	219	6	the	the	DET
ejpam-2245	219	7	relation	relation	NOUN
ejpam-2245	219	8	between	between	ADP
ejpam-2245	219	9	the	the	DET
ejpam-2245	219	10	generators	generator	NOUN
ejpam-2245	219	11	and	and	CCONJ
ejpam-2245	219	12	the	the	DET
ejpam-2245	219	13	splitting	splitting	NOUN
ejpam-2245	219	14	:	:	PUNCT
ejpam-2245	219	15	proposition	proposition	NOUN
ejpam-2245	219	16	2	2	NUM
ejpam-2245	219	17	.	.	PUNCT
ejpam-2245	220	1	[	[	X
ejpam-2245	220	2	2	2	NUM
ejpam-2245	220	3	,	,	PUNCT
ejpam-2245	220	4	proposition	proposition	NOUN
ejpam-2245	220	5	4.4	4.4	NUM
ejpam-2245	220	6	]	]	PUNCT
ejpam-2245	220	7	let	let	VERB
ejpam-2245	220	8	fq	fq	PRON
ejpam-2245	220	9	be	be	AUX
ejpam-2245	220	10	a	a	DET
ejpam-2245	220	11	finite	finite	ADJ
ejpam-2245	220	12	field	field	NOUN
ejpam-2245	220	13	and	and	CCONJ
ejpam-2245	220	14	m	m	PRON
ejpam-2245	220	15	a	a	DET
ejpam-2245	220	16	positive	positive	ADJ
ejpam-2245	220	17	odd	odd	ADJ
ejpam-2245	220	18	integer	integer	NOUN
ejpam-2245	220	19	such	such	ADJ
ejpam-2245	220	20	that	that	PRON
ejpam-2245	220	21	(	(	PUNCT
ejpam-2245	220	22	m	m	NOUN
ejpam-2245	220	23	,	,	PUNCT
ejpam-2245	220	24	q	q	NOUN
ejpam-2245	220	25	)	)	PUNCT
ejpam-2245	220	26	=	=	SYM
ejpam-2245	220	27	1	1	NUM
ejpam-2245	220	28	and	and	CCONJ
ejpam-2245	220	29	q	q	ADJ
ejpam-2245	220	30	=	=	PUNCT
ejpam-2245	220	31	�	�	PROPN
ejpam-2245	220	32	mod	mod	PROPN
ejpam-2245	220	33	m.	m.	NOUN
ejpam-2245	220	34	thus	thus	ADV
ejpam-2245	220	35	there	there	PRON
ejpam-2245	220	36	exists	exist	VERB
ejpam-2245	220	37	a	a	DET
ejpam-2245	220	38	pair	pair	NOUN
ejpam-2245	220	39	of	of	ADP
ejpam-2245	220	40	odd	odd	ADV
ejpam-2245	220	41	-	-	PUNCT
ejpam-2245	220	42	like	like	ADJ
ejpam-2245	220	43	duadic	duadic	ADJ
ejpam-2245	220	44	codes	code	NOUN
ejpam-2245	220	45	over	over	ADP
ejpam-2245	220	46	fq	fq	PROPN
ejpam-2245	220	47	,	,	PUNCT
ejpam-2245	220	48	d1	d1	PROPN
ejpam-2245	220	49	and	and	CCONJ
ejpam-2245	220	50	d2	d2	PROPN
ejpam-2245	220	51	generated	generate	VERB
ejpam-2245	220	52	respectively	respectively	ADV
ejpam-2245	220	53	by	by	ADP
ejpam-2245	220	54	f1(x	f1(x	PROPN
ejpam-2245	220	55	)	)	PUNCT
ejpam-2245	220	56	and	and	CCONJ
ejpam-2245	220	57	f2(x	f2(x	NUM
ejpam-2245	220	58	)	)	PUNCT
ejpam-2245	221	1	such	such	ADJ
ejpam-2245	221	2	that	that	PRON
ejpam-2245	221	3	xm	xm	PROPN
ejpam-2245	222	1	−	−	NOUN
ejpam-2245	223	1	1	1	NUM
ejpam-2245	224	1	=	=	SYM
ejpam-2245	225	1	(	(	PUNCT
ejpam-2245	225	2	x	x	SYM
ejpam-2245	225	3	−	−	NOUN
ejpam-2245	225	4	1	1	NUM
ejpam-2245	225	5	)	)	PUNCT
ejpam-2245	225	6	f1(x	f1(x	NUM
ejpam-2245	225	7	)	)	PUNCT
ejpam-2245	225	8	f2(x	f2(x	NOUN
ejpam-2245	225	9	)	)	PUNCT
ejpam-2245	225	10	.	.	PUNCT
ejpam-2245	226	1	then	then	ADV
ejpam-2245	226	2	the	the	DET
ejpam-2245	226	3	following	follow	VERB
ejpam-2245	226	4	holds	hold	VERB
ejpam-2245	226	5	.	.	PUNCT
ejpam-2245	227	1	(	(	PUNCT
ejpam-2245	227	2	i	i	NOUN
ejpam-2245	227	3	)	)	PUNCT
ejpam-2245	227	4	if	if	SCONJ
ejpam-2245	227	5	the	the	DET
ejpam-2245	227	6	splitting	splitting	NOUN
ejpam-2245	227	7	modulo	modulo	NOUN
ejpam-2245	227	8	m	m	VERB
ejpam-2245	227	9	is	be	AUX
ejpam-2245	227	10	given	give	VERB
ejpam-2245	227	11	by	by	ADP
ejpam-2245	227	12	µ−1	µ−1	PROPN
ejpam-2245	227	13	then	then	ADV
ejpam-2245	227	14	f	f	PROPN
ejpam-2245	227	15	∗1	∗1	PROPN
ejpam-2245	227	16	(	(	PUNCT
ejpam-2245	227	17	x	x	X
ejpam-2245	227	18	)	)	PUNCT
ejpam-2245	227	19	=	=	SYM
ejpam-2245	227	20	f2(x	f2(x	PROPN
ejpam-2245	227	21	)	)	PUNCT
ejpam-2245	227	22	and	and	CCONJ
ejpam-2245	227	23	f	f	PROPN
ejpam-2245	227	24	∗2	∗2	PROPN
ejpam-2245	227	25	(	(	PUNCT
ejpam-2245	227	26	x	x	X
ejpam-2245	227	27	)	)	PUNCT
ejpam-2245	227	28	=	=	SYM
ejpam-2245	227	29	f1(x	f1(x	PROPN
ejpam-2245	227	30	)	)	PUNCT
ejpam-2245	227	31	.	.	PUNCT
ejpam-2245	228	1	a.	a.	PROPN
ejpam-2245	228	2	batoul	batoul	PROPN
ejpam-2245	228	3	,	,	PUNCT
ejpam-2245	228	4	k.	k.	PROPN
ejpam-2245	228	5	guenda	guenda	PROPN
ejpam-2245	228	6	,	,	PUNCT
ejpam-2245	228	7	a.	a.	PROPN
ejpam-2245	228	8	kaya	kaya	PROPN
ejpam-2245	228	9	,	,	PUNCT
ejpam-2245	228	10	b.	b.	PROPN
ejpam-2245	228	11	yildiz	yildiz	PROPN
ejpam-2245	228	12	/	/	SYM
ejpam-2245	228	13	eur	eur	PROPN
ejpam-2245	228	14	.	.	PUNCT
ejpam-2245	229	1	j.	j.	PROPN
ejpam-2245	229	2	pure	pure	PROPN
ejpam-2245	229	3	appl	appl	PROPN
ejpam-2245	229	4	.	.	PROPN
ejpam-2245	229	5	math	math	PROPN
ejpam-2245	229	6	,	,	PUNCT
ejpam-2245	229	7	8	8	NUM
ejpam-2245	229	8	(	(	PUNCT
ejpam-2245	229	9	2015	2015	NUM
ejpam-2245	229	10	)	)	PUNCT
ejpam-2245	229	11	,	,	PUNCT
ejpam-2245	229	12	64	64	NUM
ejpam-2245	229	13	-	-	SYM
ejpam-2245	229	14	80	80	NUM
ejpam-2245	229	15	71	71	NUM
ejpam-2245	229	16	(	(	PUNCT
ejpam-2245	229	17	ii	ii	NOUN
ejpam-2245	229	18	)	)	PUNCT
ejpam-2245	229	19	if	if	SCONJ
ejpam-2245	229	20	the	the	DET
ejpam-2245	229	21	splitting	splitting	NOUN
ejpam-2245	229	22	modulo	modulo	VERB
ejpam-2245	229	23	m	m	VERB
ejpam-2245	229	24	is	be	AUX
ejpam-2245	229	25	not	not	PART
ejpam-2245	229	26	given	give	VERB
ejpam-2245	229	27	by	by	ADP
ejpam-2245	229	28	µ−1	µ−1	PROPN
ejpam-2245	229	29	then	then	ADV
ejpam-2245	229	30	f	f	PROPN
ejpam-2245	229	31	∗1	∗1	PROPN
ejpam-2245	229	32	(	(	PUNCT
ejpam-2245	229	33	x	x	X
ejpam-2245	229	34	)	)	PUNCT
ejpam-2245	229	35	=	=	SYM
ejpam-2245	229	36	f1(x	f1(x	PROPN
ejpam-2245	229	37	)	)	PUNCT
ejpam-2245	229	38	and	and	CCONJ
ejpam-2245	229	39	f	f	PROPN
ejpam-2245	229	40	∗2	∗2	PROPN
ejpam-2245	229	41	(	(	PUNCT
ejpam-2245	229	42	x	x	X
ejpam-2245	229	43	)	)	PUNCT
ejpam-2245	229	44	=	=	SYM
ejpam-2245	229	45	f2(x	f2(x	PROPN
ejpam-2245	229	46	)	)	PUNCT
ejpam-2245	229	47	.	.	PUNCT
ejpam-2245	230	1	remark	remark	NOUN
ejpam-2245	230	2	2	2	NUM
ejpam-2245	230	3	.	.	PUNCT
ejpam-2245	231	1	so	so	ADV
ejpam-2245	231	2	with	with	ADP
ejpam-2245	231	3	the	the	DET
ejpam-2245	231	4	assumption	assumption	NOUN
ejpam-2245	231	5	of	of	ADP
ejpam-2245	231	6	proposition	proposition	NOUN
ejpam-2245	231	7	2	2	NUM
ejpam-2245	231	8	,	,	PUNCT
ejpam-2245	231	9	we	we	PRON
ejpam-2245	231	10	have	have	AUX
ejpam-2245	231	11	that	that	PRON
ejpam-2245	231	12	either	either	PRON
ejpam-2245	231	13	f1(x	f1(x	PROPN
ejpam-2245	231	14	)	)	PUNCT
ejpam-2245	231	15	and	and	CCONJ
ejpam-2245	231	16	f2(x	f2(x	NUM
ejpam-2245	231	17	)	)	PUNCT
ejpam-2245	231	18	are	be	AUX
ejpam-2245	231	19	self	self	NOUN
ejpam-2245	231	20	-	-	PUNCT
ejpam-2245	231	21	reciprocal	reciprocal	ADJ
ejpam-2245	231	22	polynomials	polynomial	NOUN
ejpam-2245	231	23	or	or	CCONJ
ejpam-2245	231	24	one	one	NUM
ejpam-2245	231	25	is	be	AUX
ejpam-2245	231	26	the	the	DET
ejpam-2245	231	27	reciprocal	reciprocal	NOUN
ejpam-2245	231	28	of	of	ADP
ejpam-2245	231	29	the	the	DET
ejpam-2245	231	30	other	other	ADJ
ejpam-2245	231	31	.	.	PUNCT
ejpam-2245	232	1	proposition	proposition	NOUN
ejpam-2245	232	2	3	3	NUM
ejpam-2245	232	3	.	.	PUNCT
ejpam-2245	233	1	[	[	X
ejpam-2245	233	2	2	2	NUM
ejpam-2245	233	3	,	,	PUNCT
ejpam-2245	233	4	proposition	proposition	NOUN
ejpam-2245	233	5	4.8	4.8	NUM
ejpam-2245	233	6	]	]	PUNCT
ejpam-2245	233	7	let	let	VERB
ejpam-2245	233	8	q	q	PART
ejpam-2245	233	9	be	be	AUX
ejpam-2245	233	10	a	a	DET
ejpam-2245	233	11	prime	prime	ADJ
ejpam-2245	233	12	power	power	NOUN
ejpam-2245	233	13	and	and	CCONJ
ejpam-2245	233	14	m	m	VERB
ejpam-2245	233	15	an	an	DET
ejpam-2245	233	16	odd	odd	ADJ
ejpam-2245	233	17	integer	integer	NOUN
ejpam-2245	233	18	.	.	PUNCT
ejpam-2245	234	1	then	then	ADV
ejpam-2245	234	2	ordm(q	ordm(q	VERB
ejpam-2245	234	3	)	)	PUNCT
ejpam-2245	234	4	is	be	AUX
ejpam-2245	234	5	odd	odd	ADJ
ejpam-2245	234	6	if	if	SCONJ
ejpam-2245	234	7	and	and	CCONJ
ejpam-2245	234	8	only	only	ADV
ejpam-2245	234	9	if	if	SCONJ
ejpam-2245	234	10	there	there	PRON
ejpam-2245	234	11	exists	exist	VERB
ejpam-2245	234	12	a	a	DET
ejpam-2245	234	13	pair	pair	NOUN
ejpam-2245	234	14	of	of	ADP
ejpam-2245	234	15	odd	odd	ADJ
ejpam-2245	234	16	like	like	ADP
ejpam-2245	234	17	duadic	duadic	ADJ
ejpam-2245	234	18	codes	code	NOUN
ejpam-2245	234	19	d1	d1	NOUN
ejpam-2245	234	20	=	=	PUNCT
ejpam-2245	234	21	〈	〈	PROPN
ejpam-2245	234	22	g1(x	g1(x	NOUN
ejpam-2245	234	23	)	)	PUNCT
ejpam-2245	234	24	〉	〉	NOUN
ejpam-2245	234	25	and	and	CCONJ
ejpam-2245	234	26	d2	d2	PROPN
ejpam-2245	234	27	=	=	SYM
ejpam-2245	234	28	〈	〈	PROPN
ejpam-2245	234	29	g2(x	g2(x	PROPN
ejpam-2245	234	30	)	)	PUNCT
ejpam-2245	234	31	〉	〉	NOUN
ejpam-2245	234	32	given	give	VERB
ejpam-2245	234	33	by	by	ADP
ejpam-2245	234	34	the	the	DET
ejpam-2245	234	35	the	the	DET
ejpam-2245	234	36	multiplier	multipli	ADJ
ejpam-2245	234	37	µ−1	µ−1	PROPN
ejpam-2245	234	38	and	and	CCONJ
ejpam-2245	234	39	such	such	ADJ
ejpam-2245	234	40	that	that	DET
ejpam-2245	234	41	g∗1(x	g∗1(x	NOUN
ejpam-2245	234	42	)	)	PUNCT
ejpam-2245	234	43	=	=	SYM
ejpam-2245	234	44	g2(x	g2(x	PROPN
ejpam-2245	234	45	)	)	PUNCT
ejpam-2245	234	46	.	.	PUNCT
ejpam-2245	235	1	let	let	VERB
ejpam-2245	235	2	q	q	PRON
ejpam-2245	235	3	be	be	AUX
ejpam-2245	235	4	a	a	DET
ejpam-2245	235	5	prime	prime	ADJ
ejpam-2245	235	6	power	power	NOUN
ejpam-2245	235	7	and	and	CCONJ
ejpam-2245	235	8	m	m	VERB
ejpam-2245	235	9	an	an	DET
ejpam-2245	235	10	odd	odd	ADJ
ejpam-2245	235	11	integer	integer	NOUN
ejpam-2245	235	12	such	such	DET
ejpam-2245	235	13	that	that	DET
ejpam-2245	235	14	q	q	PROPN
ejpam-2245	235	15	≡	≡	PROPN
ejpam-2245	235	16	�	�	PROPN
ejpam-2245	235	17	mod	mod	PROPN
ejpam-2245	235	18	m.	m.	NOUN
ejpam-2245	235	19	let	let	VERB
ejpam-2245	235	20	f1(x	f1(x	VERB
ejpam-2245	235	21	)	)	PUNCT
ejpam-2245	235	22	and	and	CCONJ
ejpam-2245	235	23	f2(x	f2(x	NUM
ejpam-2245	235	24	)	)	PUNCT
ejpam-2245	235	25	be	be	VERB
ejpam-2245	235	26	the	the	DET
ejpam-2245	235	27	generators	generator	NOUN
ejpam-2245	235	28	polynomials	polynomial	NOUN
ejpam-2245	235	29	of	of	ADP
ejpam-2245	235	30	[	[	X
ejpam-2245	235	31	m	m	X
ejpam-2245	235	32	,	,	PUNCT
ejpam-2245	235	33	m+1	m+1	NUM
ejpam-2245	235	34	2	2	NUM
ejpam-2245	235	35	]	]	PUNCT
ejpam-2245	235	36	odd	odd	ADJ
ejpam-2245	235	37	-	-	PUNCT
ejpam-2245	235	38	like	like	ADJ
ejpam-2245	235	39	duadic	duadic	ADJ
ejpam-2245	235	40	codes	code	NOUN
ejpam-2245	235	41	over	over	ADP
ejpam-2245	235	42	fq	fq	PROPN
ejpam-2245	235	43	,	,	PUNCT
ejpam-2245	235	44	and	and	CCONJ
ejpam-2245	235	45	(	(	PUNCT
ejpam-2245	235	46	x	x	X
ejpam-2245	235	47	−	−	NOUN
ejpam-2245	235	48	1	1	NUM
ejpam-2245	235	49	)	)	PUNCT
ejpam-2245	235	50	f1(x	f1(x	NUM
ejpam-2245	235	51	)	)	PUNCT
ejpam-2245	235	52	and	and	CCONJ
ejpam-2245	235	53	(	(	PUNCT
ejpam-2245	235	54	x	x	X
ejpam-2245	235	55	−	−	PROPN
ejpam-2245	235	56	1	1	NUM
ejpam-2245	235	57	)	)	PUNCT
ejpam-2245	235	58	f2(x	f2(x	PROPN
ejpam-2245	235	59	)	)	PUNCT
ejpam-2245	235	60	be	be	VERB
ejpam-2245	235	61	the	the	DET
ejpam-2245	235	62	generators	generator	NOUN
ejpam-2245	235	63	polynomials	polynomial	NOUN
ejpam-2245	235	64	of	of	ADP
ejpam-2245	235	65	[	[	X
ejpam-2245	235	66	m	m	X
ejpam-2245	235	67	,	,	PUNCT
ejpam-2245	235	68	m−1	m−1	PROPN
ejpam-2245	235	69	2	2	NUM
ejpam-2245	235	70	]	]	PUNCT
ejpam-2245	235	71	even	even	ADV
ejpam-2245	235	72	-	-	PUNCT
ejpam-2245	235	73	like	like	ADJ
ejpam-2245	235	74	duadic	duadic	ADJ
ejpam-2245	235	75	codes	code	NOUN
ejpam-2245	235	76	over	over	ADP
ejpam-2245	235	77	fq	fq	PROPN
ejpam-2245	235	78	.	.	PROPN
ejpam-2245	235	79	definition	definition	NOUN
ejpam-2245	235	80	1	1	NUM
ejpam-2245	235	81	.	.	PUNCT
ejpam-2245	236	1	let	let	VERB
ejpam-2245	236	2	d1	d1	PROPN
ejpam-2245	236	3	=	=	PUNCT
ejpam-2245	237	1	〈	〈	PROPN
ejpam-2245	237	2	v	v	NOUN
ejpam-2245	237	3	f1(x	f1(x	NOUN
ejpam-2245	237	4	)	)	PUNCT
ejpam-2245	237	5	,	,	PUNCT
ejpam-2245	237	6	(	(	PUNCT
ejpam-2245	237	7	1−	1−	NUM
ejpam-2245	237	8	v	v	NOUN
ejpam-2245	237	9	)	)	PUNCT
ejpam-2245	237	10	f2(x	f2(x	NOUN
ejpam-2245	237	11	)	)	PUNCT
ejpam-2245	237	12	〉	〉	NOUN
ejpam-2245	237	13	and	and	CCONJ
ejpam-2245	237	14	d2	d2	PROPN
ejpam-2245	237	15	=	=	SYM
ejpam-2245	237	16	〈	〈	PROPN
ejpam-2245	237	17	v	v	NOUN
ejpam-2245	237	18	f2(x	f2(x	NOUN
ejpam-2245	237	19	)	)	PUNCT
ejpam-2245	237	20	,	,	PUNCT
ejpam-2245	237	21	(	(	PUNCT
ejpam-2245	237	22	1−	1−	NUM
ejpam-2245	237	23	v	v	NOUN
ejpam-2245	237	24	)	)	PUNCT
ejpam-2245	237	25	f1(x	f1(x	NOUN
ejpam-2245	237	26	)	)	PUNCT
ejpam-2245	237	27	〉	〉	NOUN
ejpam-2245	237	28	and	and	CCONJ
ejpam-2245	237	29	c1	c1	NOUN
ejpam-2245	237	30	=	=	PROPN
ejpam-2245	238	1	〈	〈	PROPN
ejpam-2245	238	2	v(x	v(x	PROPN
ejpam-2245	238	3	−1	−1	NOUN
ejpam-2245	238	4	)	)	PUNCT
ejpam-2245	238	5	f1(x	f1(x	NUM
ejpam-2245	238	6	)	)	PUNCT
ejpam-2245	238	7	,	,	PUNCT
ejpam-2245	238	8	(	(	PUNCT
ejpam-2245	238	9	1−	1−	NUM
ejpam-2245	238	10	v)(x	v)(x	X
ejpam-2245	238	11	−1	−1	NOUN
ejpam-2245	238	12	)	)	PUNCT
ejpam-2245	238	13	f2(x	f2(x	NOUN
ejpam-2245	238	14	)	)	PUNCT
ejpam-2245	238	15	〉	〉	NOUN
ejpam-2245	238	16	and	and	CCONJ
ejpam-2245	238	17	c2	c2	PROPN
ejpam-2245	238	18	=	=	PUNCT
ejpam-2245	238	19	〈	〈	PROPN
ejpam-2245	238	20	v(x	v(x	NOUN
ejpam-2245	238	21	−1	−1	NOUN
ejpam-2245	238	22	)	)	PUNCT
ejpam-2245	238	23	f2(x	f2(x	NOUN
ejpam-2245	238	24	)	)	PUNCT
ejpam-2245	238	25	,	,	PUNCT
ejpam-2245	238	26	(	(	PUNCT
ejpam-2245	238	27	1−	1−	NUM
ejpam-2245	238	28	v)(x	v)(x	X
ejpam-2245	238	29	−1	−1	NOUN
ejpam-2245	238	30	)	)	PUNCT
ejpam-2245	238	31	f1(x	f1(x	NOUN
ejpam-2245	238	32	)	)	PUNCT
ejpam-2245	238	33	〉	〉	NOUN
ejpam-2245	238	34	.	.	PUNCT
ejpam-2245	239	1	these	these	DET
ejpam-2245	239	2	four	four	NUM
ejpam-2245	239	3	codes	code	NOUN
ejpam-2245	239	4	are	be	AUX
ejpam-2245	239	5	called	call	VERB
ejpam-2245	239	6	duadic	duadic	ADJ
ejpam-2245	239	7	codes	code	NOUN
ejpam-2245	239	8	over	over	ADP
ejpam-2245	239	9	r=	r=	ADJ
ejpam-2245	239	10	of	of	ADP
ejpam-2245	239	11	length	length	NOUN
ejpam-2245	239	12	m.	m.	NOUN
ejpam-2245	239	13	in	in	ADP
ejpam-2245	239	14	the	the	DET
ejpam-2245	239	15	following	following	NOUN
ejpam-2245	239	16	we	we	PRON
ejpam-2245	239	17	give	give	VERB
ejpam-2245	239	18	some	some	DET
ejpam-2245	239	19	properties	property	NOUN
ejpam-2245	239	20	of	of	ADP
ejpam-2245	239	21	duadic	duadic	ADJ
ejpam-2245	239	22	codes	code	NOUN
ejpam-2245	239	23	over	over	ADP
ejpam-2245	239	24	r.	r.	PROPN
ejpam-2245	239	25	as	as	ADP
ejpam-2245	239	26	in	in	ADP
ejpam-2245	239	27	the	the	DET
ejpam-2245	239	28	case	case	NOUN
ejpam-2245	239	29	of	of	ADP
ejpam-2245	239	30	duadic	duadic	ADJ
ejpam-2245	239	31	codes	code	NOUN
ejpam-2245	239	32	over	over	ADP
ejpam-2245	239	33	finite	finite	ADJ
ejpam-2245	239	34	fields	field	NOUN
ejpam-2245	239	35	,	,	PUNCT
ejpam-2245	239	36	the	the	DET
ejpam-2245	239	37	properties	property	NOUN
ejpam-2245	239	38	of	of	ADP
ejpam-2245	239	39	duadic	duadic	ADJ
ejpam-2245	239	40	codes	code	NOUN
ejpam-2245	239	41	over	over	ADP
ejpam-2245	239	42	r	r	NOUN
ejpam-2245	239	43	differ	differ	VERB
ejpam-2245	239	44	for	for	ADP
ejpam-2245	239	45	the	the	DET
ejpam-2245	239	46	cases	case	NOUN
ejpam-2245	239	47	when	when	SCONJ
ejpam-2245	239	48	the	the	DET
ejpam-2245	239	49	splitting	splitting	NOUN
ejpam-2245	239	50	is	be	AUX
ejpam-2245	239	51	given	give	VERB
ejpam-2245	239	52	by	by	ADP
ejpam-2245	239	53	µ−1	µ−1	PROPN
ejpam-2245	239	54	or	or	CCONJ
ejpam-2245	239	55	not	not	PART
ejpam-2245	239	56	(	(	PUNCT
ejpam-2245	239	57	i.e.	i.e.	X
ejpam-2245	239	58	,	,	PUNCT
ejpam-2245	239	59	the	the	DET
ejpam-2245	239	60	polynomials	polynomial	NOUN
ejpam-2245	239	61	f1(x	f1(x	VERB
ejpam-2245	239	62	)	)	PUNCT
ejpam-2245	239	63	and	and	CCONJ
ejpam-2245	239	64	f2(x	f2(x	NUM
ejpam-2245	239	65	)	)	PUNCT
ejpam-2245	239	66	are	be	AUX
ejpam-2245	239	67	self	self	NOUN
ejpam-2245	239	68	-	-	PUNCT
ejpam-2245	239	69	reciprocal	reciprocal	ADJ
ejpam-2245	239	70	or	or	CCONJ
ejpam-2245	239	71	reciprocals	reciprocal	NOUN
ejpam-2245	239	72	of	of	ADP
ejpam-2245	239	73	each	each	DET
ejpam-2245	239	74	other	other	ADJ
ejpam-2245	239	75	.	.	PUNCT
ejpam-2245	239	76	)	)	PUNCT
ejpam-2245	240	1	proposition	proposition	NOUN
ejpam-2245	240	2	4	4	NUM
ejpam-2245	240	3	.	.	PUNCT
ejpam-2245	240	4	with	with	ADP
ejpam-2245	240	5	the	the	DET
ejpam-2245	240	6	same	same	ADJ
ejpam-2245	240	7	assumptions	assumption	NOUN
ejpam-2245	240	8	as	as	ADP
ejpam-2245	240	9	for	for	ADP
ejpam-2245	240	10	definition	definition	NOUN
ejpam-2245	240	11	1	1	NUM
ejpam-2245	240	12	,	,	PUNCT
ejpam-2245	240	13	the	the	DET
ejpam-2245	240	14	following	follow	VERB
ejpam-2245	240	15	hold	hold	NOUN
ejpam-2245	240	16	:	:	PUNCT
ejpam-2245	240	17	(	(	PUNCT
ejpam-2245	240	18	i	i	NOUN
ejpam-2245	240	19	)	)	PUNCT
ejpam-2245	240	20	|d1|=	|d1|=	PROPN
ejpam-2245	240	21	qm+1	qm+1	PROPN
ejpam-2245	240	22	=	=	SYM
ejpam-2245	240	23	|d2|	|d2|	PROPN
ejpam-2245	240	24	,	,	PUNCT
ejpam-2245	240	25	(	(	PUNCT
ejpam-2245	240	26	ii	ii	NOUN
ejpam-2245	240	27	)	)	PUNCT
ejpam-2245	240	28	|c1|=	|c1|=	PROPN
ejpam-2245	240	29	qm−1	qm−1	NOUN
ejpam-2245	240	30	=	=	PUNCT
ejpam-2245	240	31	|c2|	|c2|	NOUN
ejpam-2245	240	32	.	.	PUNCT
ejpam-2245	241	1	proof	proof	NOUN
ejpam-2245	241	2	.	.	PUNCT
ejpam-2245	242	1	for	for	ADP
ejpam-2245	242	2	the	the	DET
ejpam-2245	242	3	(	(	PUNCT
ejpam-2245	242	4	i	i	NOUN
ejpam-2245	242	5	)	)	PUNCT
ejpam-2245	242	6	part	part	NOUN
ejpam-2245	242	7	,	,	PUNCT
ejpam-2245	242	8	we	we	PRON
ejpam-2245	242	9	know	know	VERB
ejpam-2245	242	10	that	that	DET
ejpam-2245	242	11	|d2|	|d2|	NOUN
ejpam-2245	242	12	=	=	NUM
ejpam-2245	243	1	|d1|	|d1|	NOUN
ejpam-2245	243	2	=	=	SYM
ejpam-2245	243	3	|	|	ADP
ejpam-2245	243	4	〈	〈	PROPN
ejpam-2245	243	5	f1(x)〉||	f1(x)〉||	NOUN
ejpam-2245	243	6	〈	〈	PROPN
ejpam-2245	243	7	f2(x)〉|	f2(x)〉|	PROPN
ejpam-2245	243	8	.	.	PUNCT
ejpam-2245	244	1	hence	hence	ADV
ejpam-2245	244	2	the	the	DET
ejpam-2245	244	3	result	result	NOUN
ejpam-2245	244	4	follows	follow	VERB
ejpam-2245	244	5	.	.	PUNCT
ejpam-2245	245	1	for	for	ADP
ejpam-2245	245	2	the	the	DET
ejpam-2245	245	3	(	(	PUNCT
ejpam-2245	245	4	ii	ii	NOUN
ejpam-2245	245	5	)	)	PUNCT
ejpam-2245	245	6	part	part	NOUN
ejpam-2245	245	7	;	;	PUNCT
ejpam-2245	245	8	we	we	PRON
ejpam-2245	245	9	know	know	VERB
ejpam-2245	245	10	that	that	SCONJ
ejpam-2245	245	11	|c2|=	|c2|=	PROPN
ejpam-2245	245	12	|c1|=	|c1|=	PROPN
ejpam-2245	245	13	|〈(x	|〈(x	PROPN
ejpam-2245	245	14	−	−	PROPN
ejpam-2245	245	15	1	1	NUM
ejpam-2245	245	16	)	)	PUNCT
ejpam-2245	245	17	f1(x)〉||〈(x	f1(x)〉||〈(x	PROPN
ejpam-2245	245	18	−	−	PROPN
ejpam-2245	245	19	1	1	NUM
ejpam-2245	245	20	)	)	PUNCT
ejpam-2245	245	21	f2(x)〉|=	f2(x)〉|=	NOUN
ejpam-2245	245	22	q	q	PROPN
ejpam-2245	245	23	m−1	m−1	PROPN
ejpam-2245	245	24	2	2	NUM
ejpam-2245	245	25	q	q	NOUN
ejpam-2245	245	26	m−1	m−1	PROPN
ejpam-2245	245	27	2	2	NUM
ejpam-2245	245	28	=	=	SYM
ejpam-2245	245	29	qm−1	qm−1	NOUN
ejpam-2245	245	30	.	.	PUNCT
ejpam-2245	246	1	proposition	proposition	NOUN
ejpam-2245	246	2	5	5	NUM
ejpam-2245	246	3	.	.	PUNCT
ejpam-2245	246	4	with	with	ADP
ejpam-2245	246	5	the	the	DET
ejpam-2245	246	6	same	same	ADJ
ejpam-2245	246	7	assumptions	assumption	NOUN
ejpam-2245	246	8	as	as	ADP
ejpam-2245	246	9	for	for	ADP
ejpam-2245	246	10	definition	definition	NOUN
ejpam-2245	246	11	1	1	NUM
ejpam-2245	246	12	,	,	PUNCT
ejpam-2245	246	13	we	we	PRON
ejpam-2245	246	14	obtain	obtain	VERB
ejpam-2245	246	15	that	that	PRON
ejpam-2245	246	16	:	:	PUNCT
ejpam-2245	246	17	d1	d1	PROPN
ejpam-2245	246	18	and	and	CCONJ
ejpam-2245	246	19	c1	c1	PROPN
ejpam-2245	246	20	are	be	AUX
ejpam-2245	246	21	equivalent	equivalent	ADJ
ejpam-2245	246	22	to	to	AUX
ejpam-2245	246	23	d2	d2	VERB
ejpam-2245	246	24	and	and	CCONJ
ejpam-2245	246	25	c2	c2	PROPN
ejpam-2245	246	26	respectively	respectively	ADV
ejpam-2245	246	27	.	.	PUNCT
ejpam-2245	247	1	proof	proof	NOUN
ejpam-2245	247	2	.	.	PUNCT
ejpam-2245	248	1	let	let	VERB
ejpam-2245	248	2	d1	d1	PROPN
ejpam-2245	248	3	=	=	PUNCT
ejpam-2245	249	1	〈	〈	PROPN
ejpam-2245	249	2	v	v	NOUN
ejpam-2245	249	3	f1(x	f1(x	NOUN
ejpam-2245	249	4	)	)	PUNCT
ejpam-2245	249	5	,	,	PUNCT
ejpam-2245	249	6	(	(	PUNCT
ejpam-2245	249	7	1−	1−	NUM
ejpam-2245	249	8	v	v	NOUN
ejpam-2245	249	9	)	)	PUNCT
ejpam-2245	249	10	f2(x	f2(x	NOUN
ejpam-2245	249	11	)	)	PUNCT
ejpam-2245	249	12	〉	〉	NOUN
ejpam-2245	249	13	and	and	CCONJ
ejpam-2245	249	14	d2	d2	PROPN
ejpam-2245	249	15	=	=	SYM
ejpam-2245	249	16	〈	〈	PROPN
ejpam-2245	249	17	v	v	NOUN
ejpam-2245	249	18	f2(x	f2(x	NOUN
ejpam-2245	249	19	)	)	PUNCT
ejpam-2245	249	20	,	,	PUNCT
ejpam-2245	249	21	(	(	PUNCT
ejpam-2245	249	22	1−	1−	NUM
ejpam-2245	249	23	v	v	NOUN
ejpam-2245	249	24	)	)	PUNCT
ejpam-2245	249	25	f1(x	f1(x	NOUN
ejpam-2245	249	26	)	)	PUNCT
ejpam-2245	249	27	〉	〉	NOUN
ejpam-2245	249	28	and	and	CCONJ
ejpam-2245	249	29	c1	c1	NOUN
ejpam-2245	249	30	=	=	PROPN
ejpam-2245	250	1	〈	〈	PROPN
ejpam-2245	250	2	v(x	v(x	PROPN
ejpam-2245	250	3	−1	−1	NOUN
ejpam-2245	250	4	)	)	PUNCT
ejpam-2245	250	5	f1(x	f1(x	NUM
ejpam-2245	250	6	)	)	PUNCT
ejpam-2245	250	7	,	,	PUNCT
ejpam-2245	250	8	(	(	PUNCT
ejpam-2245	250	9	1−	1−	NUM
ejpam-2245	250	10	v)(x	v)(x	X
ejpam-2245	250	11	−1	−1	NOUN
ejpam-2245	250	12	)	)	PUNCT
ejpam-2245	250	13	f2(x	f2(x	NOUN
ejpam-2245	250	14	)	)	PUNCT
ejpam-2245	250	15	〉	〉	NOUN
ejpam-2245	250	16	and	and	CCONJ
ejpam-2245	250	17	c2	c2	PROPN
ejpam-2245	250	18	=	=	PUNCT
ejpam-2245	250	19	〈	〈	PROPN
ejpam-2245	250	20	v(x	v(x	NOUN
ejpam-2245	250	21	−1	−1	NOUN
ejpam-2245	250	22	)	)	PUNCT
ejpam-2245	250	23	f2(x	f2(x	NOUN
ejpam-2245	250	24	)	)	PUNCT
ejpam-2245	250	25	,	,	PUNCT
ejpam-2245	250	26	(	(	PUNCT
ejpam-2245	250	27	1−	1−	NUM
ejpam-2245	250	28	v)(x	v)(x	X
ejpam-2245	250	29	−1	−1	NOUN
ejpam-2245	250	30	)	)	PUNCT
ejpam-2245	250	31	f1(x	f1(x	NOUN
ejpam-2245	250	32	)	)	PUNCT
ejpam-2245	250	33	〉	〉	NOUN
ejpam-2245	250	34	.	.	PUNCT
ejpam-2245	251	1	since	since	SCONJ
ejpam-2245	251	2	〈	〈	PROPN
ejpam-2245	251	3	f1(x	f1(x	NOUN
ejpam-2245	251	4	)	)	PUNCT
ejpam-2245	251	5	〉	〉	NOUN
ejpam-2245	251	6	is	be	AUX
ejpam-2245	251	7	equivalent	equivalent	ADJ
ejpam-2245	251	8	by	by	ADP
ejpam-2245	251	9	multiplier	multipli	ADJ
ejpam-2245	251	10	to	to	PART
ejpam-2245	251	11	〈	〈	PROPN
ejpam-2245	251	12	f2(x	f2(x	NOUN
ejpam-2245	251	13	)	)	PUNCT
ejpam-2245	251	14	〉	〉	NOUN
ejpam-2245	251	15	and	and	CCONJ
ejpam-2245	251	16	〈	〈	PROPN
ejpam-2245	251	17	(	(	PUNCT
ejpam-2245	251	18	x	x	NOUN
ejpam-2245	251	19	−	−	PROPN
ejpam-2245	251	20	1	1	NUM
ejpam-2245	251	21	)	)	PUNCT
ejpam-2245	251	22	f1(x	f1(x	NOUN
ejpam-2245	251	23	)	)	PUNCT
ejpam-2245	251	24	〉	〉	NOUN
ejpam-2245	251	25	is	be	AUX
ejpam-2245	251	26	equivalent	equivalent	ADJ
ejpam-2245	251	27	by	by	ADP
ejpam-2245	251	28	multiplier	multipli	ADJ
ejpam-2245	251	29	to	to	ADP
ejpam-2245	251	30	〈	〈	PROPN
ejpam-2245	251	31	(	(	PUNCT
ejpam-2245	251	32	x	x	NOUN
ejpam-2245	251	33	−	−	PROPN
ejpam-2245	251	34	1	1	NUM
ejpam-2245	251	35	)	)	PUNCT
ejpam-2245	251	36	f2(x	f2(x	NOUN
ejpam-2245	251	37	)	)	PUNCT
ejpam-2245	251	38	〉	〉	NOUN
ejpam-2245	251	39	.	.	PUNCT
ejpam-2245	252	1	by	by	ADP
ejpam-2245	252	2	proposition	proposition	NOUN
ejpam-2245	252	3	1	1	NUM
ejpam-2245	252	4	we	we	PRON
ejpam-2245	252	5	have	have	VERB
ejpam-2245	252	6	the	the	DET
ejpam-2245	252	7	result	result	NOUN
ejpam-2245	252	8	.	.	PUNCT
ejpam-2245	253	1	proposition	proposition	NOUN
ejpam-2245	253	2	6	6	NUM
ejpam-2245	253	3	.	.	PUNCT
ejpam-2245	253	4	with	with	ADP
ejpam-2245	253	5	the	the	DET
ejpam-2245	253	6	assumption	assumption	NOUN
ejpam-2245	253	7	of	of	ADP
ejpam-2245	253	8	definition	definition	NOUN
ejpam-2245	253	9	1	1	NUM
ejpam-2245	253	10	the	the	DET
ejpam-2245	253	11	following	follow	VERB
ejpam-2245	253	12	holds	hold	VERB
ejpam-2245	253	13	(	(	PUNCT
ejpam-2245	253	14	i	i	NOUN
ejpam-2245	253	15	)	)	PUNCT
ejpam-2245	253	16	if	if	SCONJ
ejpam-2245	253	17	the	the	DET
ejpam-2245	253	18	splitting	splitting	NOUN
ejpam-2245	253	19	is	be	AUX
ejpam-2245	253	20	given	give	VERB
ejpam-2245	253	21	by	by	ADP
ejpam-2245	253	22	µ−1	µ−1	PROPN
ejpam-2245	253	23	then	then	ADV
ejpam-2245	253	24	c1	c1	PROPN
ejpam-2245	253	25	and	and	CCONJ
ejpam-2245	253	26	c2	c2	PROPN
ejpam-2245	253	27	are	be	AUX
ejpam-2245	253	28	self	self	NOUN
ejpam-2245	253	29	-	-	PUNCT
ejpam-2245	253	30	orthogonal	orthogonal	ADJ
ejpam-2245	253	31	and	and	CCONJ
ejpam-2245	253	32	d⊥1	d⊥1	PUNCT
ejpam-2245	253	33	=	=	PROPN
ejpam-2245	253	34	c1	c1	PROPN
ejpam-2245	253	35	,	,	PUNCT
ejpam-2245	253	36	d⊥2	d⊥2	PROPN
ejpam-2245	253	37	=	=	SYM
ejpam-2245	253	38	c2	c2	PROPN
ejpam-2245	253	39	,	,	PUNCT
ejpam-2245	253	40	a.	a.	PROPN
ejpam-2245	253	41	batoul	batoul	PROPN
ejpam-2245	253	42	,	,	PUNCT
ejpam-2245	253	43	k.	k.	PROPN
ejpam-2245	253	44	guenda	guenda	PROPN
ejpam-2245	253	45	,	,	PUNCT
ejpam-2245	253	46	a.	a.	PROPN
ejpam-2245	253	47	kaya	kaya	PROPN
ejpam-2245	253	48	,	,	PUNCT
ejpam-2245	253	49	b.	b.	PROPN
ejpam-2245	253	50	yildiz	yildiz	PROPN
ejpam-2245	253	51	/	/	SYM
ejpam-2245	253	52	eur	eur	PROPN
ejpam-2245	253	53	.	.	PUNCT
ejpam-2245	254	1	j.	j.	PROPN
ejpam-2245	254	2	pure	pure	PROPN
ejpam-2245	254	3	appl	appl	PROPN
ejpam-2245	254	4	.	.	PROPN
ejpam-2245	254	5	math	math	PROPN
ejpam-2245	254	6	,	,	PUNCT
ejpam-2245	254	7	8	8	NUM
ejpam-2245	254	8	(	(	PUNCT
ejpam-2245	254	9	2015	2015	NUM
ejpam-2245	254	10	)	)	PUNCT
ejpam-2245	254	11	,	,	PUNCT
ejpam-2245	254	12	64	64	NUM
ejpam-2245	254	13	-	-	SYM
ejpam-2245	254	14	80	80	NUM
ejpam-2245	254	15	72	72	NUM
ejpam-2245	254	16	(	(	PUNCT
ejpam-2245	254	17	ii	ii	NOUN
ejpam-2245	254	18	)	)	PUNCT
ejpam-2245	254	19	if	if	SCONJ
ejpam-2245	254	20	the	the	DET
ejpam-2245	254	21	splitting	splitting	NOUN
ejpam-2245	254	22	is	be	AUX
ejpam-2245	254	23	not	not	PART
ejpam-2245	254	24	given	give	VERB
ejpam-2245	254	25	by	by	ADP
ejpam-2245	254	26	µ−1	µ−1	PROPN
ejpam-2245	254	27	then	then	ADV
ejpam-2245	254	28	d⊥1	d⊥1	PUNCT
ejpam-2245	254	29	=	=	PROPN
ejpam-2245	254	30	c2	c2	PROPN
ejpam-2245	254	31	,	,	PUNCT
ejpam-2245	254	32	d⊥2	d⊥2	PUNCT
ejpam-2245	254	33	=	=	SYM
ejpam-2245	254	34	c1	c1	NOUN
ejpam-2245	254	35	.	.	PUNCT
ejpam-2245	255	1	proof	proof	NOUN
ejpam-2245	255	2	.	.	PUNCT
ejpam-2245	256	1	the	the	DET
ejpam-2245	256	2	proof	proof	NOUN
ejpam-2245	256	3	follows	follow	VERB
ejpam-2245	256	4	easily	easily	ADV
ejpam-2245	256	5	from	from	ADP
ejpam-2245	256	6	proposition	proposition	NOUN
ejpam-2245	256	7	2	2	NUM
ejpam-2245	256	8	.	.	PUNCT
ejpam-2245	257	1	lemma	lemma	PROPN
ejpam-2245	257	2	4	4	NUM
ejpam-2245	257	3	.	.	PUNCT
ejpam-2245	258	1	[	[	X
ejpam-2245	258	2	5	5	NUM
ejpam-2245	258	3	,	,	PUNCT
ejpam-2245	258	4	theorem	theorem	VERB
ejpam-2245	258	5	6.4.12	6.4.12	NOUN
ejpam-2245	258	6	]	]	X
ejpam-2245	258	7	let	let	VERB
ejpam-2245	258	8	〈	〈	PRON
ejpam-2245	258	9	f1(x	f1(x	NOUN
ejpam-2245	258	10	)	)	PUNCT
ejpam-2245	258	11	〉	〉	NOUN
ejpam-2245	258	12	and	and	CCONJ
ejpam-2245	258	13	〈	〈	PROPN
ejpam-2245	258	14	f2(x	f2(x	NOUN
ejpam-2245	258	15	)	)	PUNCT
ejpam-2245	258	16	〉	〉	NOUN
ejpam-2245	258	17	be	be	VERB
ejpam-2245	258	18	a	a	DET
ejpam-2245	258	19	pair	pair	NOUN
ejpam-2245	258	20	of	of	ADP
ejpam-2245	258	21	odd	odd	ADV
ejpam-2245	258	22	-	-	PUNCT
ejpam-2245	258	23	like	like	ADJ
ejpam-2245	258	24	duadic	duadic	ADJ
ejpam-2245	258	25	codes	code	NOUN
ejpam-2245	258	26	of	of	ADP
ejpam-2245	258	27	length	length	NOUN
ejpam-2245	258	28	m	m	PROPN
ejpam-2245	258	29	over	over	ADP
ejpam-2245	258	30	fq	fq	PROPN
ejpam-2245	258	31	.	.	PROPN
ejpam-2245	259	1	assume	assume	VERB
ejpam-2245	259	2	that	that	SCONJ
ejpam-2245	259	3	1+α2m=	1+α2m=	NUM
ejpam-2245	259	4	0	0	NUM
ejpam-2245	259	5	(	(	PUNCT
ejpam-2245	259	6	3	3	X
ejpam-2245	259	7	)	)	PUNCT
ejpam-2245	259	8	has	have	VERB
ejpam-2245	259	9	a	a	DET
ejpam-2245	259	10	solution	solution	NOUN
ejpam-2245	259	11	in	in	ADP
ejpam-2245	259	12	fq	fq	PROPN
ejpam-2245	259	13	.	.	PUNCT
ejpam-2245	260	1	then	then	ADV
ejpam-2245	260	2	(	(	PUNCT
ejpam-2245	260	3	i	i	NOUN
ejpam-2245	260	4	)	)	PUNCT
ejpam-2245	260	5	if	if	SCONJ
ejpam-2245	260	6	µ−1	µ−1	PROPN
ejpam-2245	260	7	gives	give	VERB
ejpam-2245	260	8	the	the	DET
ejpam-2245	260	9	splitting	splitting	NOUN
ejpam-2245	260	10	from	from	ADP
ejpam-2245	260	11	〈	〈	PROPN
ejpam-2245	260	12	f1(x	f1(x	NOUN
ejpam-2245	260	13	)	)	PUNCT
ejpam-2245	260	14	〉	〉	NOUN
ejpam-2245	260	15	to	to	ADP
ejpam-2245	260	16	〈	〈	PROPN
ejpam-2245	260	17	f2(x	f2(x	NOUN
ejpam-2245	260	18	)	)	PUNCT
ejpam-2245	260	19	〉	〉	NOUN
ejpam-2245	260	20	thenä	thenä	NOUN
ejpam-2245	260	21	〈	〈	PROPN
ejpam-2245	260	22	f1(x	f1(x	NOUN
ejpam-2245	260	23	)	)	PUNCT
ejpam-2245	260	24	〉	〉	NOUN
ejpam-2245	260	25	andä	andä	VERB
ejpam-2245	260	26	〈	〈	PRON
ejpam-2245	260	27	f1(x	f1(x	NOUN
ejpam-2245	260	28	)	)	PUNCT
ejpam-2245	260	29	〉	〉	NOUN
ejpam-2245	260	30	are	be	AUX
ejpam-2245	260	31	self	self	NOUN
ejpam-2245	260	32	-	-	PUNCT
ejpam-2245	260	33	dual	dual	ADJ
ejpam-2245	260	34	,	,	PUNCT
ejpam-2245	260	35	(	(	PUNCT
ejpam-2245	260	36	ii	ii	NOUN
ejpam-2245	260	37	)	)	PUNCT
ejpam-2245	260	38	if	if	SCONJ
ejpam-2245	260	39	the	the	DET
ejpam-2245	260	40	splitting	splitting	NOUN
ejpam-2245	260	41	from	from	ADP
ejpam-2245	260	42	〈	〈	PROPN
ejpam-2245	260	43	f1(x	f1(x	NOUN
ejpam-2245	260	44	)	)	PUNCT
ejpam-2245	260	45	〉	〉	NOUN
ejpam-2245	260	46	to	to	ADP
ejpam-2245	260	47	〈	〈	PROPN
ejpam-2245	260	48	f2(x	f2(x	NOUN
ejpam-2245	260	49	)	)	PUNCT
ejpam-2245	260	50	〉	〉	NOUN
ejpam-2245	260	51	is	be	AUX
ejpam-2245	260	52	not	not	PART
ejpam-2245	260	53	given	give	VERB
ejpam-2245	260	54	by	by	ADP
ejpam-2245	260	55	µ−1	µ−1	PROPN
ejpam-2245	260	56	thenä	thenä	NOUN
ejpam-2245	260	57	〈	〈	PROPN
ejpam-2245	260	58	f1(x	f1(x	NOUN
ejpam-2245	260	59	)	)	PUNCT
ejpam-2245	260	60	〉	〉	NOUN
ejpam-2245	260	61	andä	andä	VERB
ejpam-2245	260	62	〈	〈	PRON
ejpam-2245	260	63	f1(x	f1(x	NOUN
ejpam-2245	260	64	)	)	PUNCT
ejpam-2245	260	65	〉	〉	NOUN
ejpam-2245	260	66	are	be	AUX
ejpam-2245	260	67	duals	dual	NOUN
ejpam-2245	260	68	of	of	ADP
ejpam-2245	260	69	each	each	DET
ejpam-2245	260	70	other	other	ADJ
ejpam-2245	260	71	.	.	PUNCT
ejpam-2245	261	1	hereã	hereã	PROPN
ejpam-2245	261	2	〈	〈	PROPN
ejpam-2245	261	3	fi(x)〉=	fi(x)〉=	PROPN
ejpam-2245	261	4	{	{	PUNCT
ejpam-2245	261	5	ec|c	ec|c	PROPN
ejpam-2245	261	6	∈	∈	PROPN
ejpam-2245	261	7	〈	〈	PROPN
ejpam-2245	262	1	fi(x)〉for1≤	fi(x)〉for1≤	PROPN
ejpam-2245	262	2	i	i	NOUN
ejpam-2245	262	3	≤	≤	VERB
ejpam-2245	262	4	2andec	2andec	NUM
ejpam-2245	262	5	=	=	SYM
ejpam-2245	262	6	c0	c0	PROPN
ejpam-2245	262	7	.	.	PUNCT
ejpam-2245	262	8	.	.	PUNCT
ejpam-2245	262	9	.	.	PUNCT
ejpam-2245	263	1	cm−1c∞with	cm−1c∞with	PROPN
ejpam-2245	264	1	c∞	c∞	PROPN
ejpam-2245	265	1	=	=	SYM
ejpam-2245	265	2	−ας	−ας	NOUN
ejpam-2245	265	3	m−1	m−1	PROPN
ejpam-2245	265	4	i=0	i=0	PROPN
ejpam-2245	265	5	ci	ci	PROPN
ejpam-2245	265	6	}	}	PUNCT
ejpam-2245	265	7	.	.	PUNCT
ejpam-2245	266	1	theorem	theorem	NOUN
ejpam-2245	266	2	9	9	NUM
ejpam-2245	266	3	.	.	PUNCT
ejpam-2245	267	1	let	let	VERB
ejpam-2245	267	2	d1	d1	PROPN
ejpam-2245	267	3	=	=	PUNCT
ejpam-2245	268	1	〈	〈	PROPN
ejpam-2245	268	2	v	v	NOUN
ejpam-2245	268	3	f1(x	f1(x	NOUN
ejpam-2245	268	4	)	)	PUNCT
ejpam-2245	268	5	,	,	PUNCT
ejpam-2245	268	6	(	(	PUNCT
ejpam-2245	268	7	1−	1−	NUM
ejpam-2245	268	8	v	v	NOUN
ejpam-2245	268	9	)	)	PUNCT
ejpam-2245	268	10	f2(x	f2(x	NOUN
ejpam-2245	268	11	)	)	PUNCT
ejpam-2245	268	12	〉	〉	NOUN
ejpam-2245	268	13	and	and	CCONJ
ejpam-2245	268	14	d2	d2	PROPN
ejpam-2245	268	15	=	=	SYM
ejpam-2245	268	16	〈	〈	PROPN
ejpam-2245	268	17	v	v	NOUN
ejpam-2245	268	18	f2(x	f2(x	NOUN
ejpam-2245	268	19	)	)	PUNCT
ejpam-2245	268	20	,	,	PUNCT
ejpam-2245	268	21	(	(	PUNCT
ejpam-2245	268	22	1−	1−	NUM
ejpam-2245	268	23	v	v	NOUN
ejpam-2245	268	24	)	)	PUNCT
ejpam-2245	268	25	f1(x	f1(x	NOUN
ejpam-2245	268	26	)	)	PUNCT
ejpam-2245	268	27	〉	〉	NOUN
ejpam-2245	268	28	a	a	DET
ejpam-2245	268	29	pair	pair	NOUN
ejpam-2245	268	30	of	of	ADP
ejpam-2245	268	31	odd	odd	ADV
ejpam-2245	268	32	-	-	PUNCT
ejpam-2245	268	33	like	like	ADJ
ejpam-2245	268	34	duadic	duadic	ADJ
ejpam-2245	268	35	codes	code	NOUN
ejpam-2245	268	36	over	over	ADP
ejpam-2245	268	37	r	r	NOUN
ejpam-2245	268	38	as	as	SCONJ
ejpam-2245	268	39	given	give	VERB
ejpam-2245	268	40	in	in	ADP
ejpam-2245	268	41	definition	definition	NOUN
ejpam-2245	268	42	1	1	NUM
ejpam-2245	268	43	.	.	PUNCT
ejpam-2245	268	44	assume	assume	VERB
ejpam-2245	268	45	that	that	SCONJ
ejpam-2245	268	46	1+α2m=	1+α2m=	NUM
ejpam-2245	268	47	0	0	NUM
ejpam-2245	268	48	(	(	PUNCT
ejpam-2245	268	49	4	4	X
ejpam-2245	268	50	)	)	PUNCT
ejpam-2245	268	51	has	have	VERB
ejpam-2245	268	52	a	a	DET
ejpam-2245	268	53	solution	solution	NOUN
ejpam-2245	268	54	in	in	ADP
ejpam-2245	268	55	fq	fq	PROPN
ejpam-2245	268	56	.	.	PUNCT
ejpam-2245	269	1	then	then	ADV
ejpam-2245	269	2	(	(	PUNCT
ejpam-2245	269	3	i	i	NOUN
ejpam-2245	269	4	)	)	PUNCT
ejpam-2245	269	5	if	if	SCONJ
ejpam-2245	269	6	the	the	DET
ejpam-2245	269	7	splitting	splitting	NOUN
ejpam-2245	269	8	is	be	AUX
ejpam-2245	269	9	given	give	VERB
ejpam-2245	269	10	by	by	ADP
ejpam-2245	269	11	µ−1	µ−1	PROPN
ejpam-2245	269	12	,	,	PUNCT
ejpam-2245	269	13	then	then	ADV
ejpam-2245	269	14	fd1	fd1	NOUN
ejpam-2245	269	15	=	=	SYM
ejpam-2245	269	16	vä	vä	PROPN
ejpam-2245	269	17	〈	〈	PROPN
ejpam-2245	269	18	f1(x	f1(x	NOUN
ejpam-2245	269	19	)	)	PUNCT
ejpam-2245	269	20	〉	〉	NOUN
ejpam-2245	269	21	⊕	⊕	PROPN
ejpam-2245	269	22	(	(	PUNCT
ejpam-2245	269	23	1−	1−	NUM
ejpam-2245	269	24	v)ä	v)ä	ADJ
ejpam-2245	269	25	〈	〈	PROPN
ejpam-2245	269	26	f2(x	f2(x	NOUN
ejpam-2245	269	27	)	)	PUNCT
ejpam-2245	269	28	〉	〉	NOUN
ejpam-2245	269	29	and	and	CCONJ
ejpam-2245	269	30	fd2	fd2	PROPN
ejpam-2245	269	31	=	=	SYM
ejpam-2245	269	32	vä	vä	PROPN
ejpam-2245	269	33	〈	〈	PROPN
ejpam-2245	269	34	f2(x	f2(x	NOUN
ejpam-2245	269	35	)	)	PUNCT
ejpam-2245	269	36	〉	〉	NOUN
ejpam-2245	269	37	⊕	⊕	PROPN
ejpam-2245	269	38	(	(	PUNCT
ejpam-2245	269	39	1−	1−	NUM
ejpam-2245	269	40	v)ä	v)ä	ADJ
ejpam-2245	269	41	〈	〈	NOUN
ejpam-2245	269	42	f1(x	f1(x	NOUN
ejpam-2245	269	43	)	)	PUNCT
ejpam-2245	269	44	〉	〉	NOUN
ejpam-2245	269	45	are	be	AUX
ejpam-2245	269	46	self	self	NOUN
ejpam-2245	269	47	-	-	PUNCT
ejpam-2245	269	48	dual	dual	ADJ
ejpam-2245	269	49	over	over	ADP
ejpam-2245	269	50	r	r	NOUN
ejpam-2245	269	51	,	,	PUNCT
ejpam-2245	269	52	(	(	PUNCT
ejpam-2245	269	53	ii	ii	NOUN
ejpam-2245	269	54	)	)	PUNCT
ejpam-2245	269	55	if	if	SCONJ
ejpam-2245	269	56	the	the	DET
ejpam-2245	269	57	splitting	splitting	NOUN
ejpam-2245	269	58	is	be	AUX
ejpam-2245	269	59	not	not	PART
ejpam-2245	269	60	given	give	VERB
ejpam-2245	269	61	by	by	ADP
ejpam-2245	269	62	µ−1	µ−1	PROPN
ejpam-2245	269	63	,	,	PUNCT
ejpam-2245	269	64	then	then	ADV
ejpam-2245	269	65	fd1	fd1	NOUN
ejpam-2245	269	66	=	=	SYM
ejpam-2245	269	67	vä	vä	PROPN
ejpam-2245	269	68	〈	〈	PROPN
ejpam-2245	269	69	f1(x	f1(x	NOUN
ejpam-2245	269	70	)	)	PUNCT
ejpam-2245	269	71	〉	〉	NOUN
ejpam-2245	269	72	⊕	⊕	PROPN
ejpam-2245	269	73	(	(	PUNCT
ejpam-2245	269	74	1−	1−	NUM
ejpam-2245	269	75	v)ä	v)ä	ADJ
ejpam-2245	269	76	〈	〈	PROPN
ejpam-2245	269	77	f2(x	f2(x	NOUN
ejpam-2245	269	78	)	)	PUNCT
ejpam-2245	269	79	〉	〉	NOUN
ejpam-2245	269	80	and	and	CCONJ
ejpam-2245	269	81	fd2	fd2	PROPN
ejpam-2245	269	82	=	=	SYM
ejpam-2245	269	83	vä	vä	PROPN
ejpam-2245	269	84	〈	〈	PROPN
ejpam-2245	269	85	f2(x	f2(x	NOUN
ejpam-2245	269	86	)	)	PUNCT
ejpam-2245	269	87	〉	〉	NOUN
ejpam-2245	269	88	⊕	⊕	PROPN
ejpam-2245	269	89	(	(	PUNCT
ejpam-2245	269	90	1−	1−	NUM
ejpam-2245	269	91	v)ä	v)ä	ADJ
ejpam-2245	269	92	〈	〈	NOUN
ejpam-2245	269	93	f1(x	f1(x	NOUN
ejpam-2245	269	94	)	)	PUNCT
ejpam-2245	269	95	〉	〉	NOUN
ejpam-2245	269	96	are	be	AUX
ejpam-2245	269	97	isodual	isodual	ADJ
ejpam-2245	269	98	over	over	ADP
ejpam-2245	269	99	r.	r.	NOUN
ejpam-2245	269	100	proof	proof	NOUN
ejpam-2245	269	101	.	.	PUNCT
ejpam-2245	270	1	for	for	ADP
ejpam-2245	270	2	part	part	NOUN
ejpam-2245	270	3	(	(	PUNCT
ejpam-2245	270	4	i	i	NOUN
ejpam-2245	270	5	)	)	PUNCT
ejpam-2245	270	6	we	we	PRON
ejpam-2245	270	7	observe	observe	VERB
ejpam-2245	270	8	that	that	SCONJ
ejpam-2245	270	9	since	since	SCONJ
ejpam-2245	270	10	edi	edi	PROPN
ejpam-2245	270	11	⊥	⊥	PROPN
ejpam-2245	270	12	=	=	SYM
ejpam-2245	270	13	vã	vã	PROPN
ejpam-2245	270	14	〈	〈	PROPN
ejpam-2245	270	15	fi(x	fi(x	NUM
ejpam-2245	270	16	)	)	PUNCT
ejpam-2245	270	17	〉	〉	NOUN
ejpam-2245	270	18	⊥	⊥	PROPN
ejpam-2245	270	19	⊕	⊕	PROPN
ejpam-2245	270	20	(	(	PUNCT
ejpam-2245	270	21	1−	1−	NUM
ejpam-2245	270	22	v)ã	v)ã	NUM
ejpam-2245	270	23	〈	〈	PROPN
ejpam-2245	270	24	f	f	PROPN
ejpam-2245	270	25	j(x	j(x	PROPN
ejpam-2245	270	26	)	)	PUNCT
ejpam-2245	270	27	〉	〉	NOUN
ejpam-2245	270	28	⊥	⊥	PROPN
ejpam-2245	270	29	for	for	ADP
ejpam-2245	270	30	1≤	1≤	NUM
ejpam-2245	270	31	i	i	PROPN
ejpam-2245	270	32	,	,	PUNCT
ejpam-2245	270	33	j	j	PROPN
ejpam-2245	270	34	≤	≤	PROPN
ejpam-2245	270	35	2	2	NUM
ejpam-2245	270	36	,	,	PUNCT
ejpam-2245	270	37	i	i	PROPN
ejpam-2245	270	38	6=	6=	PROPN
ejpam-2245	270	39	j	j	PROPN
ejpam-2245	270	40	,	,	PUNCT
ejpam-2245	270	41	the	the	DET
ejpam-2245	270	42	result	result	NOUN
ejpam-2245	270	43	follows	follow	VERB
ejpam-2245	270	44	by	by	ADP
ejpam-2245	270	45	lemma	lemma	PROPN
ejpam-2245	270	46	4	4	NUM
ejpam-2245	270	47	.	.	PUNCT
ejpam-2245	271	1	the	the	DET
ejpam-2245	271	2	result	result	NOUN
ejpam-2245	271	3	in	in	ADP
ejpam-2245	271	4	part	part	NOUN
ejpam-2245	271	5	(	(	PUNCT
ejpam-2245	271	6	ii	ii	NOUN
ejpam-2245	271	7	)	)	PUNCT
ejpam-2245	271	8	follows	follow	VERB
ejpam-2245	271	9	from	from	ADP
ejpam-2245	271	10	lemma	lemma	PROPN
ejpam-2245	271	11	4	4	NUM
ejpam-2245	271	12	and	and	CCONJ
ejpam-2245	271	13	proposition	proposition	NOUN
ejpam-2245	271	14	1	1	NUM
ejpam-2245	271	15	.	.	PUNCT
ejpam-2245	271	16	example	example	NOUN
ejpam-2245	272	1	1	1	NUM
ejpam-2245	272	2	.	.	PUNCT
ejpam-2245	273	1	over	over	ADP
ejpam-2245	273	2	f5	f5	NOUN
ejpam-2245	273	3	we	we	PRON
ejpam-2245	273	4	have	have	VERB
ejpam-2245	273	5	x11	x11	NOUN
ejpam-2245	273	6	−	−	NOUN
ejpam-2245	273	7	1=	1=	X
ejpam-2245	273	8	(	(	PUNCT
ejpam-2245	273	9	x	x	SYM
ejpam-2245	274	1	+	+	NUM
ejpam-2245	274	2	4)(x5	4)(x5	NUM
ejpam-2245	275	1	+	+	CCONJ
ejpam-2245	275	2	x4	x4	PROPN
ejpam-2245	275	3	+	+	NUM
ejpam-2245	275	4	4x3	4x3	NUM
ejpam-2245	275	5	+	+	CCONJ
ejpam-2245	275	6	4x2	4x2	NUM
ejpam-2245	276	1	+	+	CCONJ
ejpam-2245	276	2	3x	3x	NUM
ejpam-2245	276	3	+	+	CCONJ
ejpam-2245	276	4	1)(x5	1)(x5	NUM
ejpam-2245	276	5	+	+	SYM
ejpam-2245	276	6	4x4	4x4	NUM
ejpam-2245	277	1	+	+	NUM
ejpam-2245	277	2	4x3	4x3	NUM
ejpam-2245	277	3	+	+	CCONJ
ejpam-2245	277	4	x2	x2	PROPN
ejpam-2245	278	1	+	+	CCONJ
ejpam-2245	278	2	3x	3x	NUM
ejpam-2245	278	3	+	+	NOUN
ejpam-2245	278	4	4	4	NUM
ejpam-2245	278	5	)	)	PUNCT
ejpam-2245	278	6	.	.	PUNCT
ejpam-2245	279	1	since	since	SCONJ
ejpam-2245	279	2	11≡	11≡	NUM
ejpam-2245	279	3	−1	−1	NOUN
ejpam-2245	279	4	mod	mod	ADJ
ejpam-2245	279	5	4	4	NUM
ejpam-2245	279	6	,	,	PUNCT
ejpam-2245	279	7	then	then	ADV
ejpam-2245	279	8	by	by	ADP
ejpam-2245	279	9	theorem	theorem	NOUN
ejpam-2245	279	10	8	8	NUM
ejpam-2245	279	11	there	there	PRON
ejpam-2245	279	12	exists	exist	VERB
ejpam-2245	279	13	one	one	NUM
ejpam-2245	279	14	splitting	splitting	NOUN
ejpam-2245	279	15	given	give	VERB
ejpam-2245	279	16	by	by	ADP
ejpam-2245	279	17	µ−1	µ−1	PROPN
ejpam-2245	279	18	.	.	PUNCT
ejpam-2245	280	1	the	the	DET
ejpam-2245	280	2	solutions	solution	NOUN
ejpam-2245	280	3	of	of	ADP
ejpam-2245	280	4	(	(	PUNCT
ejpam-2245	280	5	4	4	NUM
ejpam-2245	280	6	)	)	PUNCT
ejpam-2245	280	7	are	be	AUX
ejpam-2245	280	8	α=	α=	NOUN
ejpam-2245	280	9	±2	±2	NOUN
ejpam-2245	280	10	.	.	PUNCT
ejpam-2245	281	1	so	so	ADV
ejpam-2245	281	2	fd1	fd1	NOUN
ejpam-2245	281	3	=	=	NOUN
ejpam-2245	281	4	v	v	X
ejpam-2245	281	5	å〈(x5	å〈(x5	ADJ
ejpam-2245	281	6	+	+	CCONJ
ejpam-2245	281	7	x4	x4	PROPN
ejpam-2245	281	8	+	+	NUM
ejpam-2245	281	9	4x3	4x3	NUM
ejpam-2245	281	10	+	+	CCONJ
ejpam-2245	281	11	4x2	4x2	NUM
ejpam-2245	282	1	+	+	CCONJ
ejpam-2245	282	2	3x	3x	NUM
ejpam-2245	282	3	+	+	CCONJ
ejpam-2245	282	4	1	1	X
ejpam-2245	282	5	)	)	PUNCT
ejpam-2245	282	6	〉	〉	NOUN
ejpam-2245	282	7	⊕	⊕	PROPN
ejpam-2245	282	8	(	(	PUNCT
ejpam-2245	282	9	1−	1−	NUM
ejpam-2245	282	10	v	v	NOUN
ejpam-2245	282	11	)	)	PUNCT
ejpam-2245	282	12	å〈(x5	å〈(x5	VERB
ejpam-2245	282	13	+	+	CCONJ
ejpam-2245	283	1	4x4	4x4	NUM
ejpam-2245	284	1	+	+	NUM
ejpam-2245	284	2	4x3	4x3	NUM
ejpam-2245	284	3	+	+	CCONJ
ejpam-2245	284	4	x2	x2	PROPN
ejpam-2245	285	1	+	+	CCONJ
ejpam-2245	285	2	3x	3x	NUM
ejpam-2245	285	3	+	+	CCONJ
ejpam-2245	285	4	4	4	X
ejpam-2245	285	5	)	)	PUNCT
ejpam-2245	285	6	〉	〉	NOUN
ejpam-2245	285	7	fd2	fd2	NOUN
ejpam-2245	286	1	=	=	NOUN
ejpam-2245	286	2	v	v	X
ejpam-2245	286	3	å〈(x5	å〈(x5	VERB
ejpam-2245	286	4	+	+	CCONJ
ejpam-2245	286	5	4x4	4x4	NUM
ejpam-2245	286	6	+	+	NUM
ejpam-2245	286	7	4x3	4x3	NUM
ejpam-2245	287	1	+	+	CCONJ
ejpam-2245	287	2	x2	x2	PROPN
ejpam-2245	288	1	+	+	CCONJ
ejpam-2245	288	2	3x	3x	NUM
ejpam-2245	288	3	+	+	CCONJ
ejpam-2245	288	4	4	4	X
ejpam-2245	288	5	)	)	PUNCT
ejpam-2245	288	6	〉	〉	NOUN
ejpam-2245	288	7	⊕	⊕	PROPN
ejpam-2245	288	8	(	(	PUNCT
ejpam-2245	288	9	1−	1−	NUM
ejpam-2245	288	10	v	v	NOUN
ejpam-2245	288	11	)	)	PUNCT
ejpam-2245	288	12	å〈(x5	å〈(x5	VERB
ejpam-2245	288	13	+	+	CCONJ
ejpam-2245	288	14	x4	x4	PROPN
ejpam-2245	288	15	+	+	NUM
ejpam-2245	288	16	4x3	4x3	NUM
ejpam-2245	288	17	+	+	CCONJ
ejpam-2245	288	18	4x2	4x2	NUM
ejpam-2245	289	1	+	+	CCONJ
ejpam-2245	289	2	3x	3x	NUM
ejpam-2245	289	3	+	+	CCONJ
ejpam-2245	289	4	1	1	X
ejpam-2245	289	5	)	)	PUNCT
ejpam-2245	289	6	〉	〉	NOUN
ejpam-2245	289	7	are	be	AUX
ejpam-2245	289	8	self	self	NOUN
ejpam-2245	289	9	-	-	PUNCT
ejpam-2245	289	10	dual	dual	ADJ
ejpam-2245	289	11	codes	code	NOUN
ejpam-2245	289	12	of	of	ADP
ejpam-2245	289	13	length	length	NOUN
ejpam-2245	289	14	12	12	NUM
ejpam-2245	289	15	over	over	ADP
ejpam-2245	289	16	r=	r=	ADJ
ejpam-2245	289	17	f5	f5	NOUN
ejpam-2245	289	18	+	+	CCONJ
ejpam-2245	289	19	vf5	vf5	NOUN
ejpam-2245	289	20	.	.	PUNCT
ejpam-2245	290	1	a.	a.	PROPN
ejpam-2245	290	2	batoul	batoul	PROPN
ejpam-2245	290	3	,	,	PUNCT
ejpam-2245	290	4	k.	k.	PROPN
ejpam-2245	290	5	guenda	guenda	PROPN
ejpam-2245	290	6	,	,	PUNCT
ejpam-2245	290	7	a.	a.	PROPN
ejpam-2245	290	8	kaya	kaya	PROPN
ejpam-2245	290	9	,	,	PUNCT
ejpam-2245	290	10	b.	b.	PROPN
ejpam-2245	290	11	yildiz	yildiz	PROPN
ejpam-2245	290	12	/	/	SYM
ejpam-2245	290	13	eur	eur	PROPN
ejpam-2245	290	14	.	.	PUNCT
ejpam-2245	291	1	j.	j.	PROPN
ejpam-2245	291	2	pure	pure	PROPN
ejpam-2245	291	3	appl	appl	PROPN
ejpam-2245	291	4	.	.	PROPN
ejpam-2245	291	5	math	math	PROPN
ejpam-2245	291	6	,	,	PUNCT
ejpam-2245	291	7	8	8	NUM
ejpam-2245	291	8	(	(	PUNCT
ejpam-2245	291	9	2015	2015	NUM
ejpam-2245	291	10	)	)	PUNCT
ejpam-2245	291	11	,	,	PUNCT
ejpam-2245	291	12	64	64	NUM
ejpam-2245	291	13	-	-	SYM
ejpam-2245	291	14	80	80	NUM
ejpam-2245	291	15	73	73	NUM
ejpam-2245	291	16	example	example	NOUN
ejpam-2245	291	17	2	2	NUM
ejpam-2245	291	18	.	.	PUNCT
ejpam-2245	292	1	over	over	ADP
ejpam-2245	292	2	f5	f5	NOUN
ejpam-2245	292	3	we	we	PRON
ejpam-2245	292	4	have	have	VERB
ejpam-2245	292	5	x29	x29	NOUN
ejpam-2245	292	6	−	−	NOUN
ejpam-2245	292	7	1=(x	1=(x	PROPN
ejpam-2245	293	1	+	+	CCONJ
ejpam-2245	293	2	28)(x14	28)(x14	NUM
ejpam-2245	293	3	+	+	CCONJ
ejpam-2245	293	4	2x13	2x13	NUM
ejpam-2245	293	5	+	+	NUM
ejpam-2245	293	6	4x12	4x12	NUM
ejpam-2245	294	1	+	+	NUM
ejpam-2245	294	2	4x10	4x10	NUM
ejpam-2245	294	3	+	+	SYM
ejpam-2245	294	4	4x9	4x9	NUM
ejpam-2245	295	1	+	+	SYM
ejpam-2245	295	2	3x8	3x8	NUM
ejpam-2245	295	3	+	+	CCONJ
ejpam-2245	295	4	x7	x7	NOUN
ejpam-2245	296	1	+	+	NOUN
ejpam-2245	296	2	3x6	3x6	NUM
ejpam-2245	296	3	+	+	CCONJ
ejpam-2245	296	4	4x5	4x5	NUM
ejpam-2245	297	1	+	+	NUM
ejpam-2245	297	2	4x4	4x4	NUM
ejpam-2245	298	1	+	+	NUM
ejpam-2245	298	2	4x2	4x2	NUM
ejpam-2245	299	1	+	+	CCONJ
ejpam-2245	299	2	2x	2x	NUM
ejpam-2245	299	3	+	+	CCONJ
ejpam-2245	299	4	1	1	X
ejpam-2245	299	5	)	)	PUNCT
ejpam-2245	299	6	×	×	NOUN
ejpam-2245	299	7	(	(	PUNCT
ejpam-2245	299	8	x14	x14	PROPN
ejpam-2245	299	9	+	+	NUM
ejpam-2245	299	10	4x13	4x13	NUM
ejpam-2245	300	1	+	+	CCONJ
ejpam-2245	300	2	4x12	4x12	NUM
ejpam-2245	301	1	+	+	NUM
ejpam-2245	301	2	2x11	2x11	NUM
ejpam-2245	302	1	+	+	CCONJ
ejpam-2245	302	2	2x10	2x10	NUM
ejpam-2245	302	3	+	+	CCONJ
ejpam-2245	302	4	4x9	4x9	NUM
ejpam-2245	303	1	+	+	CCONJ
ejpam-2245	303	2	3x7	3x7	NUM
ejpam-2245	303	3	+	+	NUM
ejpam-2245	303	4	4x5	4x5	NUM
ejpam-2245	304	1	+	+	CCONJ
ejpam-2245	304	2	2x4	2x4	NUM
ejpam-2245	304	3	+	+	CCONJ
ejpam-2245	304	4	2x3	2x3	NUM
ejpam-2245	305	1	+	+	NUM
ejpam-2245	305	2	4x2	4x2	NUM
ejpam-2245	306	1	+	+	CCONJ
ejpam-2245	306	2	4x	4x	NUM
ejpam-2245	306	3	+	+	NOUN
ejpam-2245	306	4	1	1	NUM
ejpam-2245	306	5	)	)	PUNCT
ejpam-2245	306	6	.	.	PUNCT
ejpam-2245	307	1	let	let	VERB
ejpam-2245	307	2	f1(x	f1(x	VERB
ejpam-2245	307	3	)	)	PUNCT
ejpam-2245	308	1	=	=	NOUN
ejpam-2245	308	2	x14	x14	PROPN
ejpam-2245	308	3	+	+	CCONJ
ejpam-2245	308	4	2x13	2x13	NUM
ejpam-2245	308	5	+	+	NUM
ejpam-2245	308	6	4x12	4x12	NUM
ejpam-2245	308	7	+	+	NUM
ejpam-2245	308	8	4x10	4x10	NUM
ejpam-2245	308	9	+	+	SYM
ejpam-2245	308	10	4x9	4x9	NUM
ejpam-2245	308	11	+	+	SYM
ejpam-2245	308	12	3x8	3x8	NUM
ejpam-2245	308	13	+	+	CCONJ
ejpam-2245	308	14	x7	x7	NOUN
ejpam-2245	309	1	+	+	NOUN
ejpam-2245	309	2	3x6	3x6	NUM
ejpam-2245	309	3	+	+	CCONJ
ejpam-2245	309	4	4x5	4x5	NUM
ejpam-2245	310	1	+	+	NUM
ejpam-2245	310	2	4x4	4x4	NUM
ejpam-2245	311	1	+	+	NUM
ejpam-2245	311	2	4x2	4x2	NUM
ejpam-2245	312	1	+	+	CCONJ
ejpam-2245	312	2	2x	2x	NUM
ejpam-2245	312	3	+	+	CCONJ
ejpam-2245	312	4	1	1	NUM
ejpam-2245	312	5	f2(x	f2(x	NOUN
ejpam-2245	312	6	)	)	PUNCT
ejpam-2245	312	7	=	=	NOUN
ejpam-2245	312	8	x14	x14	PROPN
ejpam-2245	312	9	+	+	NUM
ejpam-2245	312	10	4x13	4x13	NUM
ejpam-2245	312	11	+	+	CCONJ
ejpam-2245	312	12	4x12	4x12	NUM
ejpam-2245	313	1	+	+	NUM
ejpam-2245	313	2	2x11	2x11	NUM
ejpam-2245	314	1	+	+	CCONJ
ejpam-2245	314	2	2x10	2x10	NUM
ejpam-2245	314	3	+	+	CCONJ
ejpam-2245	314	4	4x9	4x9	NUM
ejpam-2245	315	1	+	+	CCONJ
ejpam-2245	315	2	3x7	3x7	NUM
ejpam-2245	315	3	+	+	NUM
ejpam-2245	315	4	4x5	4x5	NUM
ejpam-2245	316	1	+	+	CCONJ
ejpam-2245	316	2	2x4	2x4	NUM
ejpam-2245	316	3	+	+	CCONJ
ejpam-2245	316	4	2x3	2x3	NUM
ejpam-2245	317	1	+	+	NUM
ejpam-2245	317	2	4x2	4x2	NUM
ejpam-2245	318	1	+	+	CCONJ
ejpam-2245	318	2	4x	4x	NUM
ejpam-2245	318	3	+	+	NOUN
ejpam-2245	318	4	1	1	X
ejpam-2245	318	5	.	.	PUNCT
ejpam-2245	319	1	since	since	SCONJ
ejpam-2245	319	2	19	19	NUM
ejpam-2245	319	3	≡	≡	PROPN
ejpam-2245	319	4	1	1	NUM
ejpam-2245	319	5	mod	mod	NOUN
ejpam-2245	319	6	4	4	NUM
ejpam-2245	319	7	,	,	PUNCT
ejpam-2245	319	8	then	then	ADV
ejpam-2245	319	9	by	by	ADP
ejpam-2245	319	10	theorem	theorem	NOUN
ejpam-2245	319	11	8	8	NUM
ejpam-2245	319	12	there	there	PRON
ejpam-2245	319	13	exists	exist	VERB
ejpam-2245	319	14	a	a	DET
ejpam-2245	319	15	splitting	splitting	NOUN
ejpam-2245	319	16	witch	witch	NOUN
ejpam-2245	319	17	is	be	AUX
ejpam-2245	319	18	not	not	PART
ejpam-2245	319	19	given	give	VERB
ejpam-2245	319	20	by	by	ADP
ejpam-2245	319	21	µ−1	µ−1	PROPN
ejpam-2245	319	22	.	.	PUNCT
ejpam-2245	320	1	the	the	DET
ejpam-2245	320	2	solution	solution	NOUN
ejpam-2245	320	3	of	of	ADP
ejpam-2245	320	4	(	(	PUNCT
ejpam-2245	320	5	4	4	NUM
ejpam-2245	320	6	)	)	PUNCT
ejpam-2245	320	7	are	be	AUX
ejpam-2245	320	8	α=	α=	NOUN
ejpam-2245	320	9	±2	±2	NOUN
ejpam-2245	320	10	.	.	PUNCT
ejpam-2245	320	11	sofd1	sofd1	PUNCT
ejpam-2245	321	1	=	=	PRON
ejpam-2245	321	2	vä	vä	ADP
ejpam-2245	321	3	〈	〈	PROPN
ejpam-2245	321	4	f1(x)〉⊕(1−v)ä	f1(x)〉⊕(1−v)ä	ADJ
ejpam-2245	321	5	〈	〈	PROPN
ejpam-2245	321	6	f2(x	f2(x	NOUN
ejpam-2245	321	7	)	)	PUNCT
ejpam-2245	321	8	〉	〉	NOUN
ejpam-2245	321	9	andfd2	andfd2	NOUN
ejpam-2245	321	10	=	=	PUNCT
ejpam-2245	321	11	vä	vä	ADP
ejpam-2245	321	12	〈	〈	PROPN
ejpam-2245	321	13	f2(x)〉⊕(1−v)ä	f2(x)〉⊕(1−v)ä	ADJ
ejpam-2245	321	14	〈	〈	ADJ
ejpam-2245	321	15	f1(x	f1(x	NUM
ejpam-2245	321	16	)	)	PUNCT
ejpam-2245	321	17	〉	〉	NOUN
ejpam-2245	321	18	are	be	AUX
ejpam-2245	321	19	isodual	isodual	ADJ
ejpam-2245	321	20	codes	code	NOUN
ejpam-2245	321	21	of	of	ADP
ejpam-2245	321	22	length	length	NOUN
ejpam-2245	321	23	30	30	NUM
ejpam-2245	321	24	over	over	ADP
ejpam-2245	321	25	r=	r=	ADJ
ejpam-2245	321	26	f5	f5	NOUN
ejpam-2245	321	27	+	+	CCONJ
ejpam-2245	321	28	vf5	vf5	NOUN
ejpam-2245	321	29	.	.	PUNCT
ejpam-2245	322	1	5	5	X
ejpam-2245	322	2	.	.	X
ejpam-2245	322	3	the	the	DET
ejpam-2245	322	4	existence	existence	NOUN
ejpam-2245	322	5	of	of	ADP
ejpam-2245	322	6	cyclic	cyclic	ADJ
ejpam-2245	322	7	isodual	isodual	ADJ
ejpam-2245	322	8	codes	code	NOUN
ejpam-2245	322	9	over	over	ADP
ejpam-2245	322	10	r	r	NOUN
ejpam-2245	322	11	we	we	PRON
ejpam-2245	322	12	have	have	AUX
ejpam-2245	322	13	seen	see	VERB
ejpam-2245	322	14	in	in	ADP
ejpam-2245	322	15	section	section	NOUN
ejpam-2245	322	16	3	3	NUM
ejpam-2245	322	17	that	that	SCONJ
ejpam-2245	322	18	the	the	DET
ejpam-2245	322	19	existence	existence	NOUN
ejpam-2245	322	20	of	of	ADP
ejpam-2245	322	21	cyclic	cyclic	ADJ
ejpam-2245	322	22	self	self	NOUN
ejpam-2245	322	23	-	-	PUNCT
ejpam-2245	322	24	dual	dual	ADJ
ejpam-2245	322	25	codes	code	NOUN
ejpam-2245	322	26	over	over	ADP
ejpam-2245	322	27	r	r	NOUN
ejpam-2245	322	28	depends	depend	VERB
ejpam-2245	322	29	on	on	ADP
ejpam-2245	322	30	the	the	DET
ejpam-2245	322	31	existence	existence	NOUN
ejpam-2245	322	32	of	of	ADP
ejpam-2245	322	33	cyclic	cyclic	ADJ
ejpam-2245	322	34	self	self	NOUN
ejpam-2245	322	35	-	-	PUNCT
ejpam-2245	322	36	dual	dual	ADJ
ejpam-2245	322	37	codes	code	NOUN
ejpam-2245	322	38	over	over	ADP
ejpam-2245	322	39	fq	fq	PROPN
ejpam-2245	322	40	.	.	PUNCT
ejpam-2245	323	1	but	but	CCONJ
ejpam-2245	323	2	by	by	ADP
ejpam-2245	323	3	[	[	X
ejpam-2245	323	4	6	6	NUM
ejpam-2245	323	5	]	]	PUNCT
ejpam-2245	323	6	these	these	DET
ejpam-2245	323	7	latter	latter	ADJ
ejpam-2245	323	8	codes	code	NOUN
ejpam-2245	323	9	do	do	AUX
ejpam-2245	323	10	not	not	PART
ejpam-2245	323	11	exist	exist	VERB
ejpam-2245	323	12	when	when	SCONJ
ejpam-2245	323	13	q	q	NOUN
ejpam-2245	323	14	is	be	AUX
ejpam-2245	323	15	odd	odd	ADJ
ejpam-2245	323	16	.	.	PUNCT
ejpam-2245	324	1	this	this	PRON
ejpam-2245	324	2	shows	show	VERB
ejpam-2245	324	3	that	that	SCONJ
ejpam-2245	324	4	if	if	SCONJ
ejpam-2245	324	5	q	q	NOUN
ejpam-2245	324	6	is	be	AUX
ejpam-2245	324	7	odd	odd	ADJ
ejpam-2245	324	8	,	,	PUNCT
ejpam-2245	324	9	then	then	ADV
ejpam-2245	324	10	there	there	PRON
ejpam-2245	324	11	are	be	VERB
ejpam-2245	324	12	no	no	DET
ejpam-2245	324	13	cyclic	cyclic	ADJ
ejpam-2245	324	14	self	self	NOUN
ejpam-2245	324	15	-	-	PUNCT
ejpam-2245	324	16	dual	dual	ADJ
ejpam-2245	324	17	codes	code	NOUN
ejpam-2245	324	18	over	over	ADP
ejpam-2245	324	19	r.	r.	NOUN
ejpam-2245	324	20	for	for	ADP
ejpam-2245	324	21	that	that	PRON
ejpam-2245	324	22	in	in	ADP
ejpam-2245	324	23	this	this	DET
ejpam-2245	324	24	section	section	NOUN
ejpam-2245	324	25	,	,	PUNCT
ejpam-2245	324	26	conditions	condition	NOUN
ejpam-2245	324	27	are	be	AUX
ejpam-2245	324	28	given	give	VERB
ejpam-2245	324	29	on	on	ADP
ejpam-2245	324	30	the	the	DET
ejpam-2245	324	31	existence	existence	NOUN
ejpam-2245	324	32	of	of	ADP
ejpam-2245	324	33	cyclic	cyclic	ADJ
ejpam-2245	324	34	isodual	isodual	ADJ
ejpam-2245	324	35	codes	code	NOUN
ejpam-2245	324	36	over	over	ADP
ejpam-2245	324	37	r.	r.	PROPN
ejpam-2245	324	38	in	in	ADP
ejpam-2245	324	39	the	the	DET
ejpam-2245	324	40	following	following	NOUN
ejpam-2245	324	41	we	we	PRON
ejpam-2245	324	42	give	give	VERB
ejpam-2245	324	43	some	some	DET
ejpam-2245	324	44	explicit	explicit	ADJ
ejpam-2245	324	45	constructions	construction	NOUN
ejpam-2245	324	46	of	of	ADP
ejpam-2245	324	47	monomial	monomial	ADJ
ejpam-2245	324	48	isodual	isodual	ADJ
ejpam-2245	324	49	cyclic	cyclic	NOUN
ejpam-2245	324	50	codes	code	NOUN
ejpam-2245	324	51	over	over	ADP
ejpam-2245	324	52	r.	r.	PROPN
ejpam-2245	324	53	the	the	DET
ejpam-2245	324	54	following	follow	VERB
ejpam-2245	324	55	proposition	proposition	NOUN
ejpam-2245	324	56	will	will	AUX
ejpam-2245	324	57	be	be	AUX
ejpam-2245	324	58	useful	useful	ADJ
ejpam-2245	324	59	later	later	ADV
ejpam-2245	324	60	.	.	PUNCT
ejpam-2245	325	1	proposition	proposition	NOUN
ejpam-2245	325	2	7	7	NUM
ejpam-2245	325	3	.	.	PUNCT
ejpam-2245	326	1	let	let	VERB
ejpam-2245	326	2	c1	c1	PROPN
ejpam-2245	326	3	and	and	CCONJ
ejpam-2245	326	4	c2	c2	PROPN
ejpam-2245	326	5	be	be	VERB
ejpam-2245	326	6	two	two	NUM
ejpam-2245	326	7	linear	linear	ADJ
ejpam-2245	326	8	codes	code	NOUN
ejpam-2245	326	9	of	of	ADP
ejpam-2245	326	10	length	length	NOUN
ejpam-2245	326	11	n	n	PROPN
ejpam-2245	326	12	over	over	ADP
ejpam-2245	326	13	fq	fq	PROPN
ejpam-2245	326	14	.	.	PROPN
ejpam-2245	327	1	then	then	ADV
ejpam-2245	327	2	c1	c1	PROPN
ejpam-2245	327	3	and	and	CCONJ
ejpam-2245	327	4	c2	c2	PROPN
ejpam-2245	327	5	are	be	AUX
ejpam-2245	327	6	isodual	isodual	ADJ
ejpam-2245	327	7	codes	code	NOUN
ejpam-2245	327	8	if	if	SCONJ
ejpam-2245	327	9	and	and	CCONJ
ejpam-2245	327	10	only	only	ADV
ejpam-2245	327	11	if	if	SCONJ
ejpam-2245	327	12	c	c	NOUN
ejpam-2245	327	13	=	=	PUNCT
ejpam-2245	327	14	vc1	vc1	PROPN
ejpam-2245	327	15	⊕	⊕	PROPN
ejpam-2245	327	16	(	(	PUNCT
ejpam-2245	327	17	1−	1−	NUM
ejpam-2245	327	18	v)c2	v)c2	PROPN
ejpam-2245	327	19	=	=	PRON
ejpam-2245	327	20	{	{	PUNCT
ejpam-2245	327	21	(	(	PUNCT
ejpam-2245	327	22	vc1	vc1	PROPN
ejpam-2245	327	23	+	+	CCONJ
ejpam-2245	327	24	(	(	PUNCT
ejpam-2245	327	25	1−	1−	NUM
ejpam-2245	327	26	v)c2	v)c2	PROPN
ejpam-2245	327	27	)	)	PUNCT
ejpam-2245	327	28	,	,	PUNCT
ejpam-2245	327	29	c1	c1	PROPN
ejpam-2245	327	30	∈	∈	PROPN
ejpam-2245	327	31	c1	c1	PROPN
ejpam-2245	327	32	,	,	PUNCT
ejpam-2245	327	33	c2	c2	PROPN
ejpam-2245	327	34	∈	∈	PROPN
ejpam-2245	327	35	c2	c2	PROPN
ejpam-2245	327	36	}	}	PUNCT
ejpam-2245	327	37	is	be	AUX
ejpam-2245	327	38	an	an	DET
ejpam-2245	327	39	isodual	isodual	ADJ
ejpam-2245	327	40	code	code	NOUN
ejpam-2245	327	41	of	of	ADP
ejpam-2245	327	42	length	length	NOUN
ejpam-2245	327	43	n	n	PROPN
ejpam-2245	327	44	over	over	ADP
ejpam-2245	327	45	r.	r.	PROPN
ejpam-2245	327	46	proof	proof	NOUN
ejpam-2245	327	47	.	.	PUNCT
ejpam-2245	328	1	the	the	DET
ejpam-2245	328	2	proof	proof	NOUN
ejpam-2245	328	3	is	be	AUX
ejpam-2245	328	4	the	the	DET
ejpam-2245	328	5	same	same	ADJ
ejpam-2245	328	6	as	as	ADP
ejpam-2245	328	7	for	for	ADP
ejpam-2245	328	8	proposition	proposition	NOUN
ejpam-2245	328	9	1	1	NUM
ejpam-2245	328	10	.	.	PUNCT
ejpam-2245	329	1	in	in	ADP
ejpam-2245	329	2	[	[	X
ejpam-2245	329	3	2	2	X
ejpam-2245	329	4	]	]	PUNCT
ejpam-2245	329	5	we	we	PRON
ejpam-2245	329	6	gave	give	VERB
ejpam-2245	329	7	several	several	ADJ
ejpam-2245	329	8	constructions	construction	NOUN
ejpam-2245	329	9	of	of	ADP
ejpam-2245	329	10	isodual	isodual	ADJ
ejpam-2245	329	11	cyclic	cyclic	ADJ
ejpam-2245	329	12	codes	code	NOUN
ejpam-2245	329	13	over	over	ADP
ejpam-2245	329	14	finite	finite	ADJ
ejpam-2245	329	15	fields	field	NOUN
ejpam-2245	329	16	.	.	PUNCT
ejpam-2245	330	1	in	in	ADP
ejpam-2245	330	2	the	the	DET
ejpam-2245	330	3	next	next	ADJ
ejpam-2245	330	4	examples	example	NOUN
ejpam-2245	330	5	using	use	VERB
ejpam-2245	330	6	proposition	proposition	NOUN
ejpam-2245	330	7	7	7	NUM
ejpam-2245	330	8	,	,	PUNCT
ejpam-2245	330	9	the	the	DET
ejpam-2245	330	10	construction	construction	NOUN
ejpam-2245	330	11	of	of	ADP
ejpam-2245	330	12	new	new	ADJ
ejpam-2245	330	13	cyclic	cyclic	ADJ
ejpam-2245	330	14	codes	code	NOUN
ejpam-2245	330	15	over	over	ADP
ejpam-2245	330	16	r	r	NOUN
ejpam-2245	330	17	are	be	AUX
ejpam-2245	330	18	given	give	VERB
ejpam-2245	330	19	.	.	PUNCT
ejpam-2245	330	20	example	example	NOUN
ejpam-2245	330	21	3	3	NUM
ejpam-2245	330	22	.	.	PUNCT
ejpam-2245	330	23	over	over	ADP
ejpam-2245	330	24	f3	f3	PROPN
ejpam-2245	330	25	we	we	PRON
ejpam-2245	330	26	have	have	AUX
ejpam-2245	330	27	x7	x7	VERB
ejpam-2245	330	28	−	−	PRON
ejpam-2245	330	29	1=	1=	NUM
ejpam-2245	330	30	(	(	PUNCT
ejpam-2245	330	31	x	x	SYM
ejpam-2245	331	1	+	+	NUM
ejpam-2245	331	2	2)(x6	2)(x6	NUM
ejpam-2245	331	3	+	+	NUM
ejpam-2245	331	4	x5	x5	NOUN
ejpam-2245	331	5	+	+	CCONJ
ejpam-2245	331	6	x4	x4	PROPN
ejpam-2245	332	1	+	+	CCONJ
ejpam-2245	332	2	x3	x3	ADJ
ejpam-2245	332	3	+	+	CCONJ
ejpam-2245	332	4	x2	x2	PROPN
ejpam-2245	333	1	+	+	CCONJ
ejpam-2245	333	2	x	x	SYM
ejpam-2245	333	3	+	+	ADJ
ejpam-2245	333	4	1	1	NUM
ejpam-2245	333	5	)	)	PUNCT
ejpam-2245	333	6	.	.	PUNCT
ejpam-2245	334	1	then	then	ADV
ejpam-2245	334	2	x14	x14	PROPN
ejpam-2245	335	1	−	−	PROPN
ejpam-2245	335	2	1=	1=	X
ejpam-2245	335	3	(	(	PUNCT
ejpam-2245	335	4	x	x	SYM
ejpam-2245	335	5	+	+	NUM
ejpam-2245	335	6	2)(x6	2)(x6	NUM
ejpam-2245	335	7	+	+	NUM
ejpam-2245	335	8	x5	x5	NOUN
ejpam-2245	335	9	+	+	CCONJ
ejpam-2245	335	10	x4	x4	PROPN
ejpam-2245	335	11	+	+	CCONJ
ejpam-2245	335	12	x3	x3	ADJ
ejpam-2245	335	13	+	+	CCONJ
ejpam-2245	335	14	x2	x2	PROPN
ejpam-2245	336	1	+	+	CCONJ
ejpam-2245	336	2	x	x	SYM
ejpam-2245	336	3	+	+	CCONJ
ejpam-2245	336	4	1)(x	1)(x	NUM
ejpam-2245	336	5	+	+	SYM
ejpam-2245	336	6	1)(x6	1)(x6	NUM
ejpam-2245	336	7	−	−	PROPN
ejpam-2245	336	8	x5	x5	NOUN
ejpam-2245	336	9	+	+	CCONJ
ejpam-2245	336	10	x4	x4	PROPN
ejpam-2245	336	11	−	−	NOUN
ejpam-2245	337	1	x3	x3	PROPN
ejpam-2245	338	1	+	+	CCONJ
ejpam-2245	338	2	x2	x2	INTJ
ejpam-2245	338	3	−	−	PROPN
ejpam-2245	339	1	x	x	SYM
ejpam-2245	340	1	+	+	NOUN
ejpam-2245	340	2	1	1	NUM
ejpam-2245	340	3	)	)	PUNCT
ejpam-2245	340	4	,	,	PUNCT
ejpam-2245	340	5	and	and	CCONJ
ejpam-2245	340	6	the	the	DET
ejpam-2245	340	7	cyclic	cyclic	PROPN
ejpam-2245	340	8	codes	code	NOUN
ejpam-2245	340	9	c1	c1	PROPN
ejpam-2245	340	10	and	and	CCONJ
ejpam-2245	340	11	c2	c2	PROPN
ejpam-2245	340	12	generated	generate	VERB
ejpam-2245	340	13	respectively	respectively	ADV
ejpam-2245	340	14	by	by	ADP
ejpam-2245	340	15	(	(	PUNCT
ejpam-2245	340	16	x	x	SYM
ejpam-2245	340	17	+	+	PRON
ejpam-2245	340	18	2)(x6	2)(x6	NUM
ejpam-2245	340	19	−	−	PROPN
ejpam-2245	340	20	x5	x5	NOUN
ejpam-2245	340	21	+	+	CCONJ
ejpam-2245	340	22	x4	x4	PROPN
ejpam-2245	340	23	−	−	NOUN
ejpam-2245	341	1	x3	x3	PROPN
ejpam-2245	342	1	+	+	CCONJ
ejpam-2245	342	2	x2	x2	INTJ
ejpam-2245	342	3	−	−	PROPN
ejpam-2245	343	1	x	x	SYM
ejpam-2245	344	1	+	+	NOUN
ejpam-2245	344	2	1	1	NUM
ejpam-2245	344	3	)	)	PUNCT
ejpam-2245	344	4	and	and	CCONJ
ejpam-2245	344	5	(	(	PUNCT
ejpam-2245	344	6	x	x	X
ejpam-2245	344	7	+	+	NUM
ejpam-2245	344	8	1)(x6	1)(x6	NUM
ejpam-2245	344	9	+	+	NUM
ejpam-2245	344	10	x5	x5	NOUN
ejpam-2245	344	11	+	+	CCONJ
ejpam-2245	344	12	x4	x4	PROPN
ejpam-2245	344	13	+	+	CCONJ
ejpam-2245	344	14	x3	x3	ADJ
ejpam-2245	345	1	+	+	CCONJ
ejpam-2245	345	2	x2	x2	PROPN
ejpam-2245	346	1	+	+	CCONJ
ejpam-2245	346	2	x	x	SYM
ejpam-2245	346	3	+	+	NOUN
ejpam-2245	346	4	1	1	NUM
ejpam-2245	346	5	)	)	PUNCT
ejpam-2245	346	6	are	be	AUX
ejpam-2245	346	7	isodual	isodual	ADJ
ejpam-2245	346	8	.	.	PUNCT
ejpam-2245	347	1	so	so	ADV
ejpam-2245	347	2	the	the	DET
ejpam-2245	347	3	cyclic	cyclic	PROPN
ejpam-2245	347	4	code	code	NOUN
ejpam-2245	347	5	generated	generate	VERB
ejpam-2245	347	6	by	by	ADP
ejpam-2245	347	7	v(x	v(x	PROPN
ejpam-2245	347	8	+	+	CCONJ
ejpam-2245	347	9	2)(x6	2)(x6	NUM
ejpam-2245	347	10	−	−	PROPN
ejpam-2245	347	11	x5	x5	NOUN
ejpam-2245	347	12	+	+	CCONJ
ejpam-2245	347	13	x4	x4	PROPN
ejpam-2245	347	14	−	−	NOUN
ejpam-2245	348	1	x3	x3	PROPN
ejpam-2245	349	1	+	+	CCONJ
ejpam-2245	349	2	x2	x2	INTJ
ejpam-2245	349	3	−	−	PROPN
ejpam-2245	350	1	x	x	SYM
ejpam-2245	351	1	+	+	NOUN
ejpam-2245	351	2	1	1	NUM
ejpam-2245	351	3	)	)	PUNCT
ejpam-2245	351	4	+	+	CCONJ
ejpam-2245	351	5	(	(	PUNCT
ejpam-2245	351	6	1−	1−	NUM
ejpam-2245	351	7	v)(x	v)(x	X
ejpam-2245	351	8	+	+	CCONJ
ejpam-2245	351	9	1)(x6	1)(x6	NUM
ejpam-2245	351	10	+	+	NUM
ejpam-2245	351	11	x5	x5	NOUN
ejpam-2245	351	12	+	+	CCONJ
ejpam-2245	351	13	x4	x4	PROPN
ejpam-2245	352	1	+	+	CCONJ
ejpam-2245	352	2	x3	x3	ADJ
ejpam-2245	352	3	+	+	CCONJ
ejpam-2245	352	4	x2	x2	PROPN
ejpam-2245	353	1	+	+	CCONJ
ejpam-2245	353	2	x	x	SYM
ejpam-2245	353	3	+	+	NOUN
ejpam-2245	353	4	1	1	NUM
ejpam-2245	353	5	)	)	PUNCT
ejpam-2245	353	6	is	be	AUX
ejpam-2245	353	7	an	an	DET
ejpam-2245	353	8	isodual	isodual	ADJ
ejpam-2245	353	9	code	code	NOUN
ejpam-2245	353	10	over	over	ADP
ejpam-2245	353	11	f3	f3	PROPN
ejpam-2245	353	12	+	+	CCONJ
ejpam-2245	353	13	vf3	vf3	NOUN
ejpam-2245	353	14	with	with	ADP
ejpam-2245	353	15	minimum	minimum	ADJ
ejpam-2245	353	16	lee	lee	PROPN
ejpam-2245	353	17	weight	weight	PROPN
ejpam-2245	353	18	4	4	NUM
ejpam-2245	353	19	.	.	PUNCT
ejpam-2245	353	20	a.	a.	PROPN
ejpam-2245	353	21	batoul	batoul	PROPN
ejpam-2245	353	22	,	,	PUNCT
ejpam-2245	353	23	k.	k.	PROPN
ejpam-2245	353	24	guenda	guenda	PROPN
ejpam-2245	353	25	,	,	PUNCT
ejpam-2245	353	26	a.	a.	PROPN
ejpam-2245	353	27	kaya	kaya	PROPN
ejpam-2245	353	28	,	,	PUNCT
ejpam-2245	353	29	b.	b.	PROPN
ejpam-2245	353	30	yildiz	yildiz	PROPN
ejpam-2245	353	31	/	/	SYM
ejpam-2245	353	32	eur	eur	PROPN
ejpam-2245	353	33	.	.	PUNCT
ejpam-2245	354	1	j.	j.	PROPN
ejpam-2245	354	2	pure	pure	PROPN
ejpam-2245	354	3	appl	appl	PROPN
ejpam-2245	354	4	.	.	PROPN
ejpam-2245	354	5	math	math	PROPN
ejpam-2245	354	6	,	,	PUNCT
ejpam-2245	354	7	8	8	NUM
ejpam-2245	354	8	(	(	PUNCT
ejpam-2245	354	9	2015	2015	NUM
ejpam-2245	354	10	)	)	PUNCT
ejpam-2245	354	11	,	,	PUNCT
ejpam-2245	354	12	64	64	NUM
ejpam-2245	354	13	-	-	SYM
ejpam-2245	354	14	80	80	NUM
ejpam-2245	354	15	74	74	NUM
ejpam-2245	354	16	example	example	NOUN
ejpam-2245	354	17	4	4	NUM
ejpam-2245	354	18	.	.	X
ejpam-2245	355	1	for	for	ADP
ejpam-2245	355	2	q	q	NOUN
ejpam-2245	355	3	=	=	SYM
ejpam-2245	355	4	7	7	NUM
ejpam-2245	355	5	and	and	CCONJ
ejpam-2245	355	6	m	m	VERB
ejpam-2245	355	7	=	=	ADJ
ejpam-2245	355	8	9	9	NUM
ejpam-2245	355	9	,	,	PUNCT
ejpam-2245	355	10	7	7	NUM
ejpam-2245	355	11	≡	≡	PROPN
ejpam-2245	355	12	1	1	NUM
ejpam-2245	355	13	mod	mod	NOUN
ejpam-2245	355	14	3	3	NUM
ejpam-2245	355	15	,	,	PUNCT
ejpam-2245	355	16	so	so	SCONJ
ejpam-2245	355	17	there	there	PRON
ejpam-2245	355	18	exist	exist	VERB
ejpam-2245	355	19	duadic	duadic	ADJ
ejpam-2245	355	20	codes	code	NOUN
ejpam-2245	355	21	generated	generate	VERB
ejpam-2245	355	22	by	by	ADP
ejpam-2245	355	23	fi	fi	NOUN
ejpam-2245	355	24	,	,	PUNCT
ejpam-2245	355	25	1≤	1≤	NUM
ejpam-2245	355	26	i	i	X
ejpam-2245	355	27	≤	≤	ADV
ejpam-2245	355	28	2	2	NUM
ejpam-2245	355	29	.	.	PUNCT
ejpam-2245	356	1	since	since	SCONJ
ejpam-2245	356	2	3≡	3≡	NUM
ejpam-2245	356	3	−1	−1	ADV
ejpam-2245	356	4	mod	mod	ADJ
ejpam-2245	356	5	4	4	NUM
ejpam-2245	356	6	,	,	PUNCT
ejpam-2245	356	7	by	by	ADP
ejpam-2245	356	8	theorem	theorem	NOUN
ejpam-2245	356	9	8	8	NUM
ejpam-2245	356	10	all	all	DET
ejpam-2245	356	11	splittings	splitting	NOUN
ejpam-2245	356	12	are	be	AUX
ejpam-2245	356	13	given	give	VERB
ejpam-2245	356	14	by	by	ADP
ejpam-2245	356	15	µ−1	µ−1	PROPN
ejpam-2245	356	16	,	,	PUNCT
ejpam-2245	356	17	and	and	CCONJ
ejpam-2245	356	18	we	we	PRON
ejpam-2245	356	19	have	have	VERB
ejpam-2245	356	20	(	(	PUNCT
ejpam-2245	356	21	x9	x9	NOUN
ejpam-2245	356	22	−	−	PROPN
ejpam-2245	356	23	1	1	NUM
ejpam-2245	356	24	)	)	PUNCT
ejpam-2245	356	25	=	=	SYM
ejpam-2245	357	1	(	(	PUNCT
ejpam-2245	357	2	x	x	SYM
ejpam-2245	357	3	−	−	PROPN
ejpam-2245	357	4	1)(x	1)(x	NUM
ejpam-2245	357	5	+	+	SYM
ejpam-2245	357	6	3)(x	3)(x	NUM
ejpam-2245	357	7	+	+	NUM
ejpam-2245	357	8	5)(x3	5)(x3	NUM
ejpam-2245	357	9	+	+	CCONJ
ejpam-2245	357	10	3)(x3	3)(x3	NUM
ejpam-2245	357	11	+	+	CCONJ
ejpam-2245	357	12	5	5	NUM
ejpam-2245	357	13	)	)	PUNCT
ejpam-2245	357	14	,	,	PUNCT
ejpam-2245	357	15	so	so	SCONJ
ejpam-2245	357	16	that	that	DET
ejpam-2245	357	17	f1(x	f1(x	NOUN
ejpam-2245	357	18	)	)	PUNCT
ejpam-2245	357	19	=	=	SYM
ejpam-2245	357	20	(	(	PUNCT
ejpam-2245	357	21	x	x	X
ejpam-2245	357	22	+	+	PUNCT
ejpam-2245	357	23	3)(x3	3)(x3	NUM
ejpam-2245	357	24	+	+	CCONJ
ejpam-2245	357	25	3	3	NUM
ejpam-2245	357	26	)	)	PUNCT
ejpam-2245	357	27	and	and	CCONJ
ejpam-2245	357	28	f2(x	f2(x	NUM
ejpam-2245	357	29	)	)	PUNCT
ejpam-2245	357	30	=	=	NOUN
ejpam-2245	357	31	(	(	PUNCT
ejpam-2245	357	32	x	x	SYM
ejpam-2245	358	1	+	+	PUNCT
ejpam-2245	358	2	5)(x3	5)(x3	NUM
ejpam-2245	358	3	+	+	CCONJ
ejpam-2245	358	4	5	5	NUM
ejpam-2245	358	5	)	)	PUNCT
ejpam-2245	358	6	.	.	PUNCT
ejpam-2245	359	1	thus	thus	ADV
ejpam-2245	359	2	(	(	PUNCT
ejpam-2245	359	3	x9	x9	NOUN
ejpam-2245	359	4	−	−	PROPN
ejpam-2245	359	5	1	1	NUM
ejpam-2245	359	6	)	)	PUNCT
ejpam-2245	359	7	=	=	SYM
ejpam-2245	359	8	(	(	PUNCT
ejpam-2245	359	9	x	x	SYM
ejpam-2245	359	10	−	−	NOUN
ejpam-2245	359	11	1	1	NUM
ejpam-2245	359	12	)	)	PUNCT
ejpam-2245	359	13	f1(x	f1(x	NUM
ejpam-2245	359	14	)	)	PUNCT
ejpam-2245	359	15	f2(x	f2(x	NOUN
ejpam-2245	359	16	)	)	PUNCT
ejpam-2245	359	17	=	=	SYM
ejpam-2245	359	18	(	(	PUNCT
ejpam-2245	359	19	x	x	SYM
ejpam-2245	359	20	−	−	NOUN
ejpam-2245	359	21	1	1	NUM
ejpam-2245	359	22	)	)	PUNCT
ejpam-2245	359	23	f1(x	f1(x	NUM
ejpam-2245	359	24	)	)	PUNCT
ejpam-2245	359	25	f	f	PROPN
ejpam-2245	359	26	∗	∗	NOUN
ejpam-2245	359	27	1	1	NUM
ejpam-2245	359	28	(	(	PUNCT
ejpam-2245	359	29	x	x	NOUN
ejpam-2245	359	30	)	)	PUNCT
ejpam-2245	359	31	,	,	PUNCT
ejpam-2245	359	32	and	and	CCONJ
ejpam-2245	359	33	the	the	DET
ejpam-2245	359	34	cyclic	cyclic	ADJ
ejpam-2245	359	35	codes	code	NOUN
ejpam-2245	359	36	of	of	ADP
ejpam-2245	359	37	length	length	NOUN
ejpam-2245	359	38	18	18	NUM
ejpam-2245	359	39	over	over	ADP
ejpam-2245	359	40	f7	f7	PROPN
ejpam-2245	359	41	generated	generate	VERB
ejpam-2245	359	42	by	by	ADP
ejpam-2245	359	43	(	(	PUNCT
ejpam-2245	359	44	x−1	x−1	PROPN
ejpam-2245	359	45	)	)	PUNCT
ejpam-2245	359	46	fi(x	fi(x	NUM
ejpam-2245	359	47	)	)	PUNCT
ejpam-2245	359	48	fi(−x	fi(−x	PROPN
ejpam-2245	359	49	)	)	PUNCT
ejpam-2245	359	50	and	and	CCONJ
ejpam-2245	359	51	(	(	PUNCT
ejpam-2245	359	52	x−1	x−1	PROPN
ejpam-2245	359	53	)	)	PUNCT
ejpam-2245	359	54	f	f	PROPN
ejpam-2245	359	55	j(x	j(x	PROPN
ejpam-2245	359	56	)	)	PUNCT
ejpam-2245	359	57	f	f	PROPN
ejpam-2245	359	58	j(−x	j(−x	PROPN
ejpam-2245	359	59	)	)	PUNCT
ejpam-2245	359	60	are	be	AUX
ejpam-2245	359	61	isodual	isodual	ADJ
ejpam-2245	359	62	over	over	ADP
ejpam-2245	359	63	f7	f7	PROPN
ejpam-2245	359	64	.	.	PUNCT
ejpam-2245	360	1	so	so	ADV
ejpam-2245	360	2	the	the	DET
ejpam-2245	360	3	cyclic	cyclic	ADJ
ejpam-2245	360	4	codes	code	NOUN
ejpam-2245	360	5	generated	generate	VERB
ejpam-2245	360	6	by	by	ADP
ejpam-2245	360	7	v(x	v(x	NOUN
ejpam-2245	360	8	−	−	ADP
ejpam-2245	360	9	1	1	NUM
ejpam-2245	360	10	)	)	PUNCT
ejpam-2245	360	11	fi(x	fi(x	NUM
ejpam-2245	360	12	)	)	PUNCT
ejpam-2245	360	13	fi(−x	fi(−x	PROPN
ejpam-2245	360	14	)	)	PUNCT
ejpam-2245	361	1	+	+	CCONJ
ejpam-2245	361	2	(	(	PUNCT
ejpam-2245	361	3	1−	1−	NUM
ejpam-2245	361	4	v)(x	v)(x	NOUN
ejpam-2245	362	1	−	−	ADP
ejpam-2245	362	2	1	1	X
ejpam-2245	362	3	)	)	PUNCT
ejpam-2245	362	4	f	f	PROPN
ejpam-2245	362	5	j(x	j(x	PROPN
ejpam-2245	362	6	)	)	PUNCT
ejpam-2245	362	7	f	f	PROPN
ejpam-2245	362	8	j(−x	j(−x	PROPN
ejpam-2245	362	9	)	)	PUNCT
ejpam-2245	362	10	is	be	AUX
ejpam-2245	362	11	an	an	DET
ejpam-2245	362	12	isodual	isodual	ADJ
ejpam-2245	362	13	code	code	NOUN
ejpam-2245	362	14	over	over	ADP
ejpam-2245	362	15	f7	f7	PROPN
ejpam-2245	362	16	+	+	CCONJ
ejpam-2245	362	17	vf7	vf7	NOUN
ejpam-2245	362	18	with	with	ADP
ejpam-2245	362	19	minimum	minimum	PROPN
ejpam-2245	362	20	lee	lee	PROPN
ejpam-2245	362	21	weight	weight	PROPN
ejpam-2245	362	22	5	5	NUM
ejpam-2245	362	23	.	.	PUNCT
ejpam-2245	363	1	we	we	PRON
ejpam-2245	363	2	complete	complete	VERB
ejpam-2245	363	3	this	this	DET
ejpam-2245	363	4	section	section	NOUN
ejpam-2245	363	5	by	by	ADP
ejpam-2245	363	6	giving	give	VERB
ejpam-2245	363	7	some	some	PRON
ejpam-2245	363	8	more	more	ADJ
ejpam-2245	363	9	examples	example	NOUN
ejpam-2245	363	10	in	in	ADP
ejpam-2245	363	11	table	table	NOUN
ejpam-2245	363	12	1	1	NUM
ejpam-2245	363	13	where	where	SCONJ
ejpam-2245	363	14	c	c	NOUN
ejpam-2245	363	15	is	be	AUX
ejpam-2245	363	16	an	an	DET
ejpam-2245	363	17	isodual	isodual	ADJ
ejpam-2245	363	18	cyclic	cyclic	ADJ
ejpam-2245	363	19	code	code	NOUN
ejpam-2245	363	20	of	of	ADP
ejpam-2245	363	21	length	length	NOUN
ejpam-2245	363	22	2n	2n	NUM
ejpam-2245	363	23	over	over	ADP
ejpam-2245	363	24	fp	fp	PROPN
ejpam-2245	363	25	+	+	NUM
ejpam-2245	363	26	vfp	vfp	PROPN
ejpam-2245	363	27	with	with	ADP
ejpam-2245	363	28	generator	generator	NOUN
ejpam-2245	363	29	polynomial	polynomial	PROPN
ejpam-2245	363	30	g	g	PROPN
ejpam-2245	363	31	(	(	PUNCT
ejpam-2245	363	32	x	x	NOUN
ejpam-2245	363	33	)	)	PUNCT
ejpam-2245	364	1	=	=	NOUN
ejpam-2245	364	2	v(x	v(x	NOUN
ejpam-2245	364	3	−	−	ADP
ejpam-2245	364	4	1	1	NUM
ejpam-2245	364	5	)	)	PUNCT
ejpam-2245	364	6	f1	f1	NOUN
ejpam-2245	364	7	(	(	PUNCT
ejpam-2245	364	8	x	x	NOUN
ejpam-2245	364	9	)	)	PUNCT
ejpam-2245	364	10	f1	f1	NOUN
ejpam-2245	364	11	(	(	PUNCT
ejpam-2245	364	12	−x	−x	NOUN
ejpam-2245	364	13	)	)	PUNCT
ejpam-2245	364	14	+	+	CCONJ
ejpam-2245	364	15	(	(	PUNCT
ejpam-2245	364	16	1−	1−	NUM
ejpam-2245	364	17	v)(x	v)(x	NOUN
ejpam-2245	364	18	+	+	CCONJ
ejpam-2245	364	19	1	1	X
ejpam-2245	364	20	)	)	PUNCT
ejpam-2245	364	21	f2	f2	PROPN
ejpam-2245	364	22	(	(	PUNCT
ejpam-2245	364	23	x	x	X
ejpam-2245	364	24	)	)	PUNCT
ejpam-2245	364	25	f2	f2	PROPN
ejpam-2245	364	26	(	(	PUNCT
ejpam-2245	364	27	−x	−x	NOUN
ejpam-2245	364	28	)	)	PUNCT
ejpam-2245	364	29	and	and	CCONJ
ejpam-2245	364	30	a	a	DET
ejpam-2245	364	31	polynomial	polynomial	ADJ
ejpam-2245	364	32	f	f	NOUN
ejpam-2245	364	33	(	(	PUNCT
ejpam-2245	364	34	x	x	NOUN
ejpam-2245	364	35	)	)	PUNCT
ejpam-2245	364	36	=	=	SYM
ejpam-2245	364	37	a0	a0	PROPN
ejpam-2245	364	38	+	+	CCONJ
ejpam-2245	364	39	a1	a1	NOUN
ejpam-2245	364	40	x	x	X
ejpam-2245	364	41	+	+	CCONJ
ejpam-2245	364	42	.	.	PUNCT
ejpam-2245	364	43	.	.	PUNCT
ejpam-2245	365	1	.+	.+	NOUN
ejpam-2245	365	2	am	be	AUX
ejpam-2245	365	3	xm	xm	PROPN
ejpam-2245	365	4	is	be	AUX
ejpam-2245	365	5	abbreviated	abbreviate	VERB
ejpam-2245	365	6	as	as	ADP
ejpam-2245	365	7	a0a1	a0a1	X
ejpam-2245	365	8	.	.	PUNCT
ejpam-2245	365	9	.	.	PUNCT
ejpam-2245	365	10	.	.	PUNCT
ejpam-2245	366	1	am	be	AUX
ejpam-2245	366	2	.	.	PUNCT
ejpam-2245	367	1	table	table	NOUN
ejpam-2245	367	2	1	1	NUM
ejpam-2245	367	3	:	:	PUNCT
ejpam-2245	367	4	isodual	isodual	ADJ
ejpam-2245	367	5	cyclic	cyclic	ADJ
ejpam-2245	367	6	codes	code	NOUN
ejpam-2245	367	7	of	of	ADP
ejpam-2245	367	8	length	length	NOUN
ejpam-2245	367	9	2n	2n	NUM
ejpam-2245	367	10	over	over	ADP
ejpam-2245	367	11	fp	fp	PROPN
ejpam-2245	367	12	+	+	NUM
ejpam-2245	367	13	vfp	vfp	PROPN
ejpam-2245	367	14	n	n	CCONJ
ejpam-2245	367	15	p	p	PROPN
ejpam-2245	367	16	f1	f1	NOUN
ejpam-2245	367	17	f2	f2	PROPN
ejpam-2245	367	18	ϕ	ϕ	PROPN
ejpam-2245	367	19	(	(	PUNCT
ejpam-2245	367	20	c	c	NOUN
ejpam-2245	367	21	)	)	PUNCT
ejpam-2245	367	22	11	11	NUM
ejpam-2245	367	23	3	3	NUM
ejpam-2245	367	24	221201	221201	NUM
ejpam-2245	367	25	201211	201211	NUM
ejpam-2245	368	1	[	[	X
ejpam-2245	368	2	44,22,9]3	44,22,9]3	NUM
ejpam-2245	368	3	23	23	NUM
ejpam-2245	368	4	3	3	NUM
ejpam-2245	368	5	222110202001	222110202001	NUM
ejpam-2245	368	6	200101022111	200101022111	NUM
ejpam-2245	368	7	[	[	X
ejpam-2245	368	8	92,46,15]3	92,46,15]3	NUM
ejpam-2245	368	9	11	11	NUM
ejpam-2245	368	10	5	5	NUM
ejpam-2245	368	11	411421	411421	NUM
ejpam-2245	368	12	431441	431441	NUM
ejpam-2245	368	13	[	[	X
ejpam-2245	368	14	44,22,9]5	44,22,9]5	NUM
ejpam-2245	368	15	19	19	NUM
ejpam-2245	368	16	5	5	NUM
ejpam-2245	368	17	4424222301	4424222301	NUM
ejpam-2245	368	18	4023331321	4023331321	NUM
ejpam-2245	369	1	[	[	X
ejpam-2245	369	2	76,38,13]5	76,38,13]5	NUM
ejpam-2245	369	3	5.1	5.1	NUM
ejpam-2245	369	4	.	.	PUNCT
ejpam-2245	370	1	construction	construction	NOUN
ejpam-2245	370	2	of	of	ADP
ejpam-2245	370	3	self	self	NOUN
ejpam-2245	370	4	-	-	PUNCT
ejpam-2245	370	5	dual	dual	ADJ
ejpam-2245	370	6	and	and	CCONJ
ejpam-2245	370	7	isodual	isodual	ADJ
ejpam-2245	370	8	codes	code	NOUN
ejpam-2245	370	9	over	over	ADP
ejpam-2245	370	10	f2r	f2r	PROPN
ejpam-2245	370	11	+	+	CCONJ
ejpam-2245	370	12	vf2r	vf2r	NOUN
ejpam-2245	370	13	theorem	theorem	NOUN
ejpam-2245	370	14	10	10	NUM
ejpam-2245	370	15	.	.	PUNCT
ejpam-2245	371	1	[	[	X
ejpam-2245	371	2	2	2	NUM
ejpam-2245	371	3	,	,	PUNCT
ejpam-2245	371	4	theorem	theorem	VERB
ejpam-2245	371	5	4.16	4.16	NUM
ejpam-2245	371	6	]	]	PUNCT
ejpam-2245	371	7	let	let	VERB
ejpam-2245	371	8	n=	n=	ADJ
ejpam-2245	371	9	2	2	NUM
ejpam-2245	371	10	am	am	NOUN
ejpam-2245	371	11	with	with	ADP
ejpam-2245	371	12	m	m	NOUN
ejpam-2245	371	13	an	an	DET
ejpam-2245	371	14	odd	odd	ADJ
ejpam-2245	371	15	integer	integer	NOUN
ejpam-2245	371	16	such	such	ADJ
ejpam-2245	371	17	that	that	PRON
ejpam-2245	371	18	and	and	CCONJ
ejpam-2245	371	19	di	di	NOUN
ejpam-2245	371	20	=	=	NOUN
ejpam-2245	371	21	〈	〈	PROPN
ejpam-2245	371	22	fi(x	fi(x	NUM
ejpam-2245	371	23	)	)	PUNCT
ejpam-2245	371	24	〉	〉	NOUN
ejpam-2245	371	25	,	,	PUNCT
ejpam-2245	371	26	1≤	1≤	NUM
ejpam-2245	371	27	i	i	NOUN
ejpam-2245	371	28	≤	≤	ADV
ejpam-2245	371	29	2	2	NUM
ejpam-2245	371	30	be	be	AUX
ejpam-2245	371	31	duadic	duadic	ADJ
ejpam-2245	371	32	codes	code	NOUN
ejpam-2245	371	33	over	over	ADP
ejpam-2245	371	34	f2r	f2r	PROPN
ejpam-2245	371	35	.	.	PUNCT
ejpam-2245	372	1	then	then	ADV
ejpam-2245	372	2	for	for	ADP
ejpam-2245	372	3	1≤	1≤	NUM
ejpam-2245	372	4	i	i	PRON
ejpam-2245	372	5	≤	≤	ADV
ejpam-2245	372	6	2	2	NUM
ejpam-2245	372	7	,	,	PUNCT
ejpam-2245	372	8	the	the	DET
ejpam-2245	372	9	cyclic	cyclic	ADJ
ejpam-2245	372	10	codes	code	NOUN
ejpam-2245	372	11	generated	generate	VERB
ejpam-2245	372	12	by	by	ADP
ejpam-2245	372	13	fi(x	fi(x	NUM
ejpam-2245	372	14	)	)	PUNCT
ejpam-2245	373	1	=	=	PRON
ejpam-2245	374	1	(	(	PUNCT
ejpam-2245	374	2	x	x	X
ejpam-2245	374	3	−	−	PROPN
ejpam-2245	374	4	1)2	1)2	NUM
ejpam-2245	374	5	a−1	a−1	PROPN
ejpam-2245	374	6	f	f	PROPN
ejpam-2245	374	7	2a	2a	NUM
ejpam-2245	374	8	i	i	PRON
ejpam-2245	374	9	(	(	PUNCT
ejpam-2245	374	10	x	x	NOUN
ejpam-2245	374	11	)	)	PUNCT
ejpam-2245	374	12	,	,	PUNCT
ejpam-2245	374	13	are	be	AUX
ejpam-2245	374	14	self	self	NOUN
ejpam-2245	374	15	-	-	PUNCT
ejpam-2245	374	16	dual	dual	ADJ
ejpam-2245	374	17	or	or	CCONJ
ejpam-2245	374	18	isodual	isodual	ADJ
ejpam-2245	374	19	.	.	PUNCT
ejpam-2245	375	1	theorem	theorem	NOUN
ejpam-2245	375	2	11	11	NUM
ejpam-2245	375	3	.	.	PUNCT
ejpam-2245	376	1	let	let	VERB
ejpam-2245	376	2	n	n	NOUN
ejpam-2245	376	3	=	=	SYM
ejpam-2245	376	4	2	2	NUM
ejpam-2245	376	5	am	am	NOUN
ejpam-2245	376	6	with	with	ADP
ejpam-2245	376	7	m	m	NOUN
ejpam-2245	376	8	an	an	DET
ejpam-2245	376	9	odd	odd	ADJ
ejpam-2245	376	10	integer	integer	NOUN
ejpam-2245	376	11	such	such	ADJ
ejpam-2245	376	12	that	that	PRON
ejpam-2245	376	13	and	and	CCONJ
ejpam-2245	376	14	di	di	NOUN
ejpam-2245	376	15	=	=	NOUN
ejpam-2245	376	16	〈	〈	PROPN
ejpam-2245	376	17	fi(x	fi(x	NUM
ejpam-2245	376	18	)	)	PUNCT
ejpam-2245	376	19	〉	〉	NOUN
ejpam-2245	376	20	,	,	PUNCT
ejpam-2245	376	21	1	1	NUM
ejpam-2245	376	22	≤	≤	NUM
ejpam-2245	376	23	i	i	PRON
ejpam-2245	376	24	≤	≤	NOUN
ejpam-2245	376	25	2	2	NUM
ejpam-2245	376	26	be	be	AUX
ejpam-2245	376	27	duadic	duadic	ADJ
ejpam-2245	376	28	codes	code	NOUN
ejpam-2245	376	29	over	over	ADP
ejpam-2245	376	30	f2r	f2r	PROPN
ejpam-2245	376	31	.	.	PUNCT
ejpam-2245	377	1	then	then	ADV
ejpam-2245	377	2	for	for	ADP
ejpam-2245	377	3	1≤	1≤	NUM
ejpam-2245	377	4	i	i	PRON
ejpam-2245	377	5	≤	≤	ADV
ejpam-2245	377	6	2	2	NUM
ejpam-2245	377	7	,	,	PUNCT
ejpam-2245	377	8	the	the	DET
ejpam-2245	377	9	cyclic	cyclic	ADJ
ejpam-2245	377	10	codes	code	NOUN
ejpam-2245	377	11	over	over	ADP
ejpam-2245	377	12	f2r	f2r	PROPN
ejpam-2245	377	13	+	+	CCONJ
ejpam-2245	377	14	vf2r	vf2r	NOUN
ejpam-2245	377	15	generated	generate	VERB
ejpam-2245	377	16	by	by	ADP
ejpam-2245	377	17	f	f	PROPN
ejpam-2245	377	18	(	(	PUNCT
ejpam-2245	377	19	x	x	X
ejpam-2245	377	20	)	)	PUNCT
ejpam-2245	378	1	=	=	NOUN
ejpam-2245	378	2	v(x	v(x	NOUN
ejpam-2245	378	3	−	−	PROPN
ejpam-2245	378	4	1)2	1)2	NUM
ejpam-2245	378	5	a−1	a−1	PROPN
ejpam-2245	378	6	f	f	PROPN
ejpam-2245	378	7	2a	2a	NUM
ejpam-2245	379	1	i	i	PRON
ejpam-2245	379	2	(	(	PUNCT
ejpam-2245	379	3	x	x	X
ejpam-2245	379	4	)	)	PUNCT
ejpam-2245	379	5	+	+	CCONJ
ejpam-2245	379	6	(	(	PUNCT
ejpam-2245	379	7	1−	1−	NUM
ejpam-2245	379	8	v)(x	v)(x	NOUN
ejpam-2245	379	9	−	−	PROPN
ejpam-2245	379	10	1)2	1)2	NUM
ejpam-2245	379	11	a−1	a−1	PROPN
ejpam-2245	379	12	f	f	PROPN
ejpam-2245	379	13	2a	2a	NUM
ejpam-2245	379	14	j	j	PROPN
ejpam-2245	379	15	(	(	PUNCT
ejpam-2245	379	16	x	x	NOUN
ejpam-2245	379	17	)	)	PUNCT
ejpam-2245	379	18	,	,	PUNCT
ejpam-2245	379	19	are	be	AUX
ejpam-2245	379	20	self	self	NOUN
ejpam-2245	379	21	-	-	PUNCT
ejpam-2245	379	22	dual	dual	ADJ
ejpam-2245	379	23	or	or	CCONJ
ejpam-2245	379	24	isodual	isodual	ADJ
ejpam-2245	379	25	.	.	PUNCT
ejpam-2245	380	1	a.	a.	PROPN
ejpam-2245	380	2	batoul	batoul	PROPN
ejpam-2245	380	3	,	,	PUNCT
ejpam-2245	380	4	k.	k.	PROPN
ejpam-2245	380	5	guenda	guenda	PROPN
ejpam-2245	380	6	,	,	PUNCT
ejpam-2245	380	7	a.	a.	PROPN
ejpam-2245	380	8	kaya	kaya	PROPN
ejpam-2245	380	9	,	,	PUNCT
ejpam-2245	380	10	b.	b.	PROPN
ejpam-2245	380	11	yildiz	yildiz	PROPN
ejpam-2245	380	12	/	/	SYM
ejpam-2245	380	13	eur	eur	PROPN
ejpam-2245	380	14	.	.	PUNCT
ejpam-2245	381	1	j.	j.	PROPN
ejpam-2245	381	2	pure	pure	PROPN
ejpam-2245	381	3	appl	appl	PROPN
ejpam-2245	381	4	.	.	PROPN
ejpam-2245	381	5	math	math	PROPN
ejpam-2245	381	6	,	,	PUNCT
ejpam-2245	381	7	8	8	NUM
ejpam-2245	381	8	(	(	PUNCT
ejpam-2245	381	9	2015	2015	NUM
ejpam-2245	381	10	)	)	PUNCT
ejpam-2245	381	11	,	,	PUNCT
ejpam-2245	381	12	64	64	NUM
ejpam-2245	381	13	-	-	SYM
ejpam-2245	381	14	80	80	NUM
ejpam-2245	381	15	75	75	NUM
ejpam-2245	381	16	proof	proof	NOUN
ejpam-2245	381	17	.	.	PUNCT
ejpam-2245	382	1	if	if	SCONJ
ejpam-2245	382	2	the	the	DET
ejpam-2245	382	3	splitting	splitting	NOUN
ejpam-2245	382	4	is	be	AUX
ejpam-2245	382	5	given	give	VERB
ejpam-2245	382	6	by	by	ADP
ejpam-2245	382	7	µ−1	µ−1	PROPN
ejpam-2245	382	8	then	then	ADV
ejpam-2245	382	9	the	the	DET
ejpam-2245	382	10	cyclic	cyclic	ADJ
ejpam-2245	382	11	codes	code	NOUN
ejpam-2245	382	12	generated	generate	VERB
ejpam-2245	382	13	respectively	respectively	ADV
ejpam-2245	382	14	by	by	ADP
ejpam-2245	382	15	(	(	PUNCT
ejpam-2245	382	16	x	x	SYM
ejpam-2245	382	17	−	−	PROPN
ejpam-2245	382	18	1)2	1)2	NUM
ejpam-2245	382	19	a−1	a−1	PROPN
ejpam-2245	382	20	f	f	PROPN
ejpam-2245	382	21	2a	2a	NUM
ejpam-2245	382	22	1	1	NUM
ejpam-2245	382	23	(	(	PUNCT
ejpam-2245	382	24	x	x	NOUN
ejpam-2245	382	25	)	)	PUNCT
ejpam-2245	382	26	and	and	CCONJ
ejpam-2245	382	27	(	(	PUNCT
ejpam-2245	382	28	x	x	SYM
ejpam-2245	382	29	−	−	PROPN
ejpam-2245	382	30	1)2	1)2	NUM
ejpam-2245	382	31	a−1	a−1	PROPN
ejpam-2245	382	32	f	f	PROPN
ejpam-2245	382	33	2a	2a	NUM
ejpam-2245	382	34	2	2	NUM
ejpam-2245	382	35	(	(	PUNCT
ejpam-2245	382	36	x	x	X
ejpam-2245	382	37	)	)	PUNCT
ejpam-2245	382	38	are	be	AUX
ejpam-2245	382	39	self	self	NOUN
ejpam-2245	382	40	-	-	PUNCT
ejpam-2245	382	41	dual	dual	ADJ
ejpam-2245	382	42	over	over	ADP
ejpam-2245	382	43	f2r	f2r	PROPN
ejpam-2245	382	44	thus	thus	ADV
ejpam-2245	382	45	f	f	X
ejpam-2245	382	46	(	(	PUNCT
ejpam-2245	382	47	x	x	X
ejpam-2245	382	48	)	)	PUNCT
ejpam-2245	382	49	generate	generate	VERB
ejpam-2245	382	50	a	a	DET
ejpam-2245	382	51	self	self	NOUN
ejpam-2245	382	52	-	-	PUNCT
ejpam-2245	382	53	dual	dual	ADJ
ejpam-2245	382	54	cyclic	cyclic	ADJ
ejpam-2245	382	55	code	code	NOUN
ejpam-2245	382	56	over	over	ADP
ejpam-2245	382	57	f2r	f2r	PROPN
ejpam-2245	383	1	+	+	CCONJ
ejpam-2245	383	2	vf2r	vf2r	NOUN
ejpam-2245	383	3	.	.	PUNCT
ejpam-2245	384	1	if	if	SCONJ
ejpam-2245	384	2	the	the	DET
ejpam-2245	384	3	splitting	splitting	NOUN
ejpam-2245	384	4	is	be	AUX
ejpam-2245	384	5	not	not	PART
ejpam-2245	384	6	given	give	VERB
ejpam-2245	384	7	by	by	ADP
ejpam-2245	384	8	µ−1	µ−1	PROPN
ejpam-2245	384	9	then	then	ADV
ejpam-2245	384	10	the	the	DET
ejpam-2245	384	11	cyclic	cyclic	ADJ
ejpam-2245	384	12	codes	code	NOUN
ejpam-2245	384	13	generated	generate	VERB
ejpam-2245	384	14	respectively	respectively	ADV
ejpam-2245	384	15	by	by	ADP
ejpam-2245	384	16	(	(	PUNCT
ejpam-2245	384	17	x	x	SYM
ejpam-2245	384	18	−	−	PROPN
ejpam-2245	384	19	1)2	1)2	NUM
ejpam-2245	384	20	a−1	a−1	PROPN
ejpam-2245	384	21	f	f	PROPN
ejpam-2245	384	22	2a	2a	NUM
ejpam-2245	384	23	1	1	NUM
ejpam-2245	384	24	(	(	PUNCT
ejpam-2245	384	25	x	x	NOUN
ejpam-2245	384	26	)	)	PUNCT
ejpam-2245	384	27	and	and	CCONJ
ejpam-2245	384	28	(	(	PUNCT
ejpam-2245	384	29	x	x	SYM
ejpam-2245	384	30	−	−	PROPN
ejpam-2245	384	31	1)2	1)2	NUM
ejpam-2245	384	32	a−1	a−1	PROPN
ejpam-2245	384	33	f	f	PROPN
ejpam-2245	384	34	2a	2a	NUM
ejpam-2245	384	35	2	2	NUM
ejpam-2245	384	36	(	(	PUNCT
ejpam-2245	384	37	x	x	X
ejpam-2245	384	38	)	)	PUNCT
ejpam-2245	384	39	are	be	AUX
ejpam-2245	384	40	isodual	isodual	ADJ
ejpam-2245	384	41	over	over	ADP
ejpam-2245	384	42	f2r	f2r	PROPN
ejpam-2245	384	43	thus	thus	ADV
ejpam-2245	384	44	f	f	PROPN
ejpam-2245	384	45	(	(	PUNCT
ejpam-2245	384	46	x	x	X
ejpam-2245	384	47	)	)	PUNCT
ejpam-2245	384	48	generate	generate	VERB
ejpam-2245	384	49	an	an	DET
ejpam-2245	384	50	isodual	isodual	ADJ
ejpam-2245	384	51	cyclic	cyclic	ADJ
ejpam-2245	384	52	code	code	NOUN
ejpam-2245	384	53	over	over	ADP
ejpam-2245	384	54	f2r	f2r	PROPN
ejpam-2245	384	55	+	+	CCONJ
ejpam-2245	384	56	vf2r	vf2r	NOUN
ejpam-2245	384	57	.	.	PUNCT
ejpam-2245	384	58	example	example	NOUN
ejpam-2245	385	1	5	5	NUM
ejpam-2245	385	2	.	.	PUNCT
ejpam-2245	385	3	let	let	VERB
ejpam-2245	385	4	n	n	NOUN
ejpam-2245	385	5	=	=	SYM
ejpam-2245	385	6	34	34	NUM
ejpam-2245	385	7	and	and	CCONJ
ejpam-2245	385	8	q	q	NOUN
ejpam-2245	385	9	=	=	NOUN
ejpam-2245	385	10	2	2	NUM
ejpam-2245	385	11	,	,	PUNCT
ejpam-2245	385	12	so	so	SCONJ
ejpam-2245	385	13	that	that	SCONJ
ejpam-2245	385	14	m	m	VERB
ejpam-2245	385	15	=	=	SYM
ejpam-2245	385	16	17	17	NUM
ejpam-2245	385	17	and	and	CCONJ
ejpam-2245	385	18	17	17	NUM
ejpam-2245	385	19	≡	≡	PROPN
ejpam-2245	385	20	1	1	NUM
ejpam-2245	385	21	mod	mod	ADJ
ejpam-2245	385	22	8	8	NUM
ejpam-2245	385	23	.	.	PUNCT
ejpam-2245	386	1	then	then	ADV
ejpam-2245	386	2	duadic	duadic	ADJ
ejpam-2245	386	3	codes	code	NOUN
ejpam-2245	386	4	of	of	ADP
ejpam-2245	386	5	length	length	NOUN
ejpam-2245	386	6	17	17	NUM
ejpam-2245	386	7	over	over	ADP
ejpam-2245	386	8	f2	f2	PROPN
ejpam-2245	386	9	exist	exist	VERB
ejpam-2245	386	10	.	.	PUNCT
ejpam-2245	387	1	the	the	DET
ejpam-2245	387	2	factorization	factorization	NOUN
ejpam-2245	387	3	of	of	ADP
ejpam-2245	387	4	x34	x34	NOUN
ejpam-2245	387	5	−	−	NOUN
ejpam-2245	387	6	1	1	NUM
ejpam-2245	387	7	over	over	ADP
ejpam-2245	387	8	f2	f2	PROPN
ejpam-2245	387	9	is	be	AUX
ejpam-2245	387	10	(	(	PUNCT
ejpam-2245	387	11	x	x	SYM
ejpam-2245	387	12	−	−	PROPN
ejpam-2245	387	13	1)2(x8	1)2(x8	NUM
ejpam-2245	387	14	+	+	NUM
ejpam-2245	387	15	x5	x5	NOUN
ejpam-2245	387	16	+	+	CCONJ
ejpam-2245	387	17	x4	x4	PROPN
ejpam-2245	388	1	+	+	CCONJ
ejpam-2245	388	2	x3	x3	ADJ
ejpam-2245	388	3	+	+	CCONJ
ejpam-2245	388	4	1)2(x8	1)2(x8	NUM
ejpam-2245	389	1	+	+	CCONJ
ejpam-2245	389	2	x7	x7	NOUN
ejpam-2245	389	3	+	+	CCONJ
ejpam-2245	389	4	x6	x6	PROPN
ejpam-2245	389	5	+	+	CCONJ
ejpam-2245	389	6	x4	x4	PROPN
ejpam-2245	390	1	+	+	CCONJ
ejpam-2245	390	2	x2	x2	PROPN
ejpam-2245	391	1	+	+	CCONJ
ejpam-2245	391	2	x	x	PUNCT
ejpam-2245	391	3	+	+	X
ejpam-2245	391	4	1)2	1)2	NUM
ejpam-2245	391	5	.	.	PUNCT
ejpam-2245	392	1	since	since	SCONJ
ejpam-2245	392	2	17≡	17≡	NUM
ejpam-2245	392	3	1	1	NUM
ejpam-2245	392	4	(	(	PUNCT
ejpam-2245	392	5	mod	mod	NOUN
ejpam-2245	392	6	4	4	NUM
ejpam-2245	392	7	)	)	PUNCT
ejpam-2245	392	8	,	,	PUNCT
ejpam-2245	392	9	x8	x8	PROPN
ejpam-2245	392	10	+	+	CCONJ
ejpam-2245	392	11	x5	x5	PROPN
ejpam-2245	392	12	+	+	CCONJ
ejpam-2245	392	13	x4	x4	PROPN
ejpam-2245	393	1	+	+	CCONJ
ejpam-2245	393	2	x3	x3	ADJ
ejpam-2245	393	3	+	+	CCONJ
ejpam-2245	393	4	1	1	NUM
ejpam-2245	393	5	is	be	AUX
ejpam-2245	393	6	not	not	PART
ejpam-2245	393	7	the	the	DET
ejpam-2245	393	8	reciprocal	reciprocal	ADJ
ejpam-2245	393	9	polynomial	polynomial	NOUN
ejpam-2245	393	10	of	of	ADP
ejpam-2245	393	11	x8	x8	PROPN
ejpam-2245	393	12	+	+	CCONJ
ejpam-2245	393	13	x7	x7	NOUN
ejpam-2245	393	14	+	+	CCONJ
ejpam-2245	393	15	x6	x6	PROPN
ejpam-2245	393	16	+	+	CCONJ
ejpam-2245	393	17	x4	x4	PROPN
ejpam-2245	394	1	+	+	CCONJ
ejpam-2245	394	2	x2	x2	PROPN
ejpam-2245	395	1	+	+	CCONJ
ejpam-2245	395	2	x	x	SYM
ejpam-2245	395	3	+	+	NUM
ejpam-2245	395	4	1	1	NUM
ejpam-2245	395	5	,	,	PUNCT
ejpam-2245	395	6	thus	thus	ADV
ejpam-2245	395	7	c1	c1	NOUN
ejpam-2245	395	8	=	=	SYM
ejpam-2245	395	9	〈	〈	PROPN
ejpam-2245	395	10	(	(	PUNCT
ejpam-2245	395	11	x	x	NOUN
ejpam-2245	395	12	−	−	NUM
ejpam-2245	395	13	1)(x8	1)(x8	NOUN
ejpam-2245	396	1	+	+	NUM
ejpam-2245	396	2	x7	x7	NOUN
ejpam-2245	396	3	+	+	CCONJ
ejpam-2245	396	4	x6	x6	PROPN
ejpam-2245	396	5	+	+	CCONJ
ejpam-2245	396	6	x4	x4	PROPN
ejpam-2245	397	1	+	+	CCONJ
ejpam-2245	397	2	x2	x2	PROPN
ejpam-2245	398	1	+	+	CCONJ
ejpam-2245	398	2	x	x	SYM
ejpam-2245	398	3	+	+	ADJ
ejpam-2245	398	4	1	1	NUM
ejpam-2245	398	5	)	)	PUNCT
ejpam-2245	398	6	〉	〉	NOUN
ejpam-2245	398	7	,	,	PUNCT
ejpam-2245	398	8	and	and	CCONJ
ejpam-2245	398	9	c2	c2	PROPN
ejpam-2245	398	10	=	=	SYM
ejpam-2245	398	11	〈	〈	PROPN
ejpam-2245	398	12	(	(	PUNCT
ejpam-2245	398	13	x	x	NOUN
ejpam-2245	398	14	−	−	NUM
ejpam-2245	398	15	1)(x8	1)(x8	NUM
ejpam-2245	398	16	+	+	NUM
ejpam-2245	398	17	x5	x5	NOUN
ejpam-2245	398	18	+	+	CCONJ
ejpam-2245	398	19	x4	x4	PROPN
ejpam-2245	399	1	+	+	CCONJ
ejpam-2245	399	2	x3	x3	ADJ
ejpam-2245	399	3	+	+	CCONJ
ejpam-2245	399	4	1	1	X
ejpam-2245	399	5	)	)	PUNCT
ejpam-2245	399	6	〉	〉	NOUN
ejpam-2245	399	7	,	,	PUNCT
ejpam-2245	399	8	are	be	AUX
ejpam-2245	399	9	isodual	isodual	ADJ
ejpam-2245	399	10	cyclic	cyclic	ADJ
ejpam-2245	399	11	codes	code	NOUN
ejpam-2245	399	12	of	of	ADP
ejpam-2245	399	13	length	length	NOUN
ejpam-2245	399	14	34	34	NUM
ejpam-2245	399	15	over	over	ADP
ejpam-2245	399	16	f2	f2	PROPN
ejpam-2245	399	17	.	.	PUNCT
ejpam-2245	400	1	while	while	SCONJ
ejpam-2245	400	2	the	the	DET
ejpam-2245	400	3	cyclic	cyclic	PROPN
ejpam-2245	400	4	code	code	NOUN
ejpam-2245	400	5	c	c	NOUN
ejpam-2245	400	6	=	=	SYM
ejpam-2245	401	1	vc1+(1−	vc1+(1−	NOUN
ejpam-2245	401	2	v)c2	v)c2	PROPN
ejpam-2245	401	3	is	be	AUX
ejpam-2245	401	4	isodual	isodual	ADJ
ejpam-2245	401	5	over	over	ADP
ejpam-2245	401	6	f2	f2	PROPN
ejpam-2245	401	7	+	+	CCONJ
ejpam-2245	401	8	vf2	vf2	ADJ
ejpam-2245	401	9	.	.	PUNCT
ejpam-2245	401	10	example	example	NOUN
ejpam-2245	402	1	6	6	NUM
ejpam-2245	402	2	.	.	X
ejpam-2245	403	1	for	for	ADP
ejpam-2245	403	2	n=	n=	ADJ
ejpam-2245	403	3	14	14	NUM
ejpam-2245	403	4	,	,	PUNCT
ejpam-2245	403	5	x14−1=	x14−1=	PROPN
ejpam-2245	403	6	(	(	PUNCT
ejpam-2245	403	7	x−1)2(x3+x+1)2(x3+x2	x−1)2(x3+x+1)2(x3+x2	PROPN
ejpam-2245	403	8	+	+	PROPN
ejpam-2245	403	9	1)2	1)2	NUM
ejpam-2245	403	10	,	,	PUNCT
ejpam-2245	403	11	over	over	ADP
ejpam-2245	403	12	f2	f2	PROPN
ejpam-2245	403	13	.	.	PUNCT
ejpam-2245	404	1	since	since	SCONJ
ejpam-2245	404	2	ord7(2	ord7(2	PRON
ejpam-2245	404	3	)	)	PUNCT
ejpam-2245	404	4	=	=	SYM
ejpam-2245	404	5	3	3	NUM
ejpam-2245	404	6	is	be	AUX
ejpam-2245	404	7	odd	odd	ADJ
ejpam-2245	404	8	,	,	PUNCT
ejpam-2245	404	9	x3	x3	VERB
ejpam-2245	404	10	+	+	CCONJ
ejpam-2245	404	11	x	x	SYM
ejpam-2245	405	1	+	+	NUM
ejpam-2245	405	2	1	1	NUM
ejpam-2245	405	3	is	be	AUX
ejpam-2245	405	4	the	the	DET
ejpam-2245	405	5	reciprocal	reciprocal	ADJ
ejpam-2245	405	6	polynomial	polynomial	NOUN
ejpam-2245	405	7	of	of	ADP
ejpam-2245	405	8	x3	x3	PROPN
ejpam-2245	405	9	+	+	CCONJ
ejpam-2245	405	10	x2	x2	PROPN
ejpam-2245	406	1	+	+	NOUN
ejpam-2245	406	2	1	1	X
ejpam-2245	406	3	.	.	X
ejpam-2245	406	4	then	then	ADV
ejpam-2245	406	5	c1	c1	PROPN
ejpam-2245	406	6	=	=	PROPN
ejpam-2245	406	7	〈	〈	PROPN
ejpam-2245	406	8	(	(	PUNCT
ejpam-2245	406	9	x	x	X
ejpam-2245	406	10	−	−	NOUN
ejpam-2245	406	11	1)(x3	1)(x3	NUM
ejpam-2245	407	1	+	+	SYM
ejpam-2245	407	2	x	x	SYM
ejpam-2245	407	3	+	+	ADJ
ejpam-2245	407	4	1	1	NUM
ejpam-2245	407	5	)	)	PUNCT
ejpam-2245	407	6	〉	〉	NOUN
ejpam-2245	407	7	,	,	PUNCT
ejpam-2245	407	8	and	and	CCONJ
ejpam-2245	407	9	c2	c2	PROPN
ejpam-2245	407	10	=	=	SYM
ejpam-2245	407	11	〈	〈	PROPN
ejpam-2245	407	12	(	(	PUNCT
ejpam-2245	407	13	x	x	X
ejpam-2245	407	14	−	−	NOUN
ejpam-2245	407	15	1)(x3	1)(x3	NUM
ejpam-2245	408	1	+	+	CCONJ
ejpam-2245	408	2	x2	x2	PROPN
ejpam-2245	409	1	+	+	CCONJ
ejpam-2245	409	2	1	1	X
ejpam-2245	409	3	)	)	PUNCT
ejpam-2245	409	4	〉	〉	NOUN
ejpam-2245	409	5	,	,	PUNCT
ejpam-2245	409	6	are	be	AUX
ejpam-2245	409	7	self	self	NOUN
ejpam-2245	409	8	-	-	PUNCT
ejpam-2245	409	9	dual	dual	ADJ
ejpam-2245	409	10	cyclic	cyclic	ADJ
ejpam-2245	409	11	codes	code	NOUN
ejpam-2245	409	12	of	of	ADP
ejpam-2245	409	13	length	length	NOUN
ejpam-2245	409	14	14	14	NUM
ejpam-2245	409	15	over	over	ADP
ejpam-2245	409	16	f2	f2	PROPN
ejpam-2245	409	17	.	.	PUNCT
ejpam-2245	410	1	and	and	CCONJ
ejpam-2245	410	2	the	the	DET
ejpam-2245	410	3	cyclic	cyclic	PROPN
ejpam-2245	410	4	code	code	NOUN
ejpam-2245	410	5	c	c	NOUN
ejpam-2245	410	6	=	=	PUNCT
ejpam-2245	411	1	vc1+(1−	vc1+(1−	NOUN
ejpam-2245	411	2	v)c1	v)c1	PROPN
ejpam-2245	411	3	is	be	AUX
ejpam-2245	411	4	self	self	NOUN
ejpam-2245	411	5	-	-	PUNCT
ejpam-2245	411	6	dual	dual	ADJ
ejpam-2245	411	7	over	over	ADP
ejpam-2245	411	8	f2	f2	PROPN
ejpam-2245	411	9	+	+	CCONJ
ejpam-2245	411	10	vf2	vf2	ADJ
ejpam-2245	411	11	.	.	PUNCT
ejpam-2245	412	1	5.1.1	5.1.1	X
ejpam-2245	412	2	.	.	PUNCT
ejpam-2245	413	1	construction	construction	NOUN
ejpam-2245	413	2	of	of	ADP
ejpam-2245	413	3	self	self	NOUN
ejpam-2245	413	4	-	-	PUNCT
ejpam-2245	413	5	dual	dual	ADJ
ejpam-2245	413	6	and	and	CCONJ
ejpam-2245	413	7	isodual	isodual	ADJ
ejpam-2245	413	8	codes	code	NOUN
ejpam-2245	413	9	over	over	ADP
ejpam-2245	413	10	f2	f2	PROPN
ejpam-2245	413	11	+	+	CCONJ
ejpam-2245	413	12	vf2	vf2	INTJ
ejpam-2245	413	13	let	let	VERB
ejpam-2245	413	14	x	x	PUNCT
ejpam-2245	413	15	=	=	SYM
ejpam-2245	413	16	(	(	PUNCT
ejpam-2245	413	17	x1	x1	PROPN
ejpam-2245	413	18	,	,	PUNCT
ejpam-2245	413	19	x2	x2	PROPN
ejpam-2245	413	20	,	,	PUNCT
ejpam-2245	413	21	.	.	PUNCT
ejpam-2245	413	22	.	.	PUNCT
ejpam-2245	414	1	.	.	PUNCT
ejpam-2245	415	1	,	,	PUNCT
ejpam-2245	415	2	xn	xn	X
ejpam-2245	415	3	)	)	PUNCT
ejpam-2245	415	4	and	and	CCONJ
ejpam-2245	415	5	y	y	PROPN
ejpam-2245	415	6	=	=	SYM
ejpam-2245	415	7	(	(	PUNCT
ejpam-2245	415	8	y1	y1	PROPN
ejpam-2245	415	9	,	,	PUNCT
ejpam-2245	415	10	y2	y2	PROPN
ejpam-2245	415	11	,	,	PUNCT
ejpam-2245	415	12	.	.	PUNCT
ejpam-2245	415	13	.	.	PUNCT
ejpam-2245	415	14	.	.	PUNCT
ejpam-2245	416	1	,	,	PUNCT
ejpam-2245	416	2	yn	yn	PROPN
ejpam-2245	416	3	)	)	PUNCT
ejpam-2245	416	4	be	be	VERB
ejpam-2245	416	5	two	two	NUM
ejpam-2245	416	6	elements	element	NOUN
ejpam-2245	416	7	of	of	ADP
ejpam-2245	416	8	(	(	PUNCT
ejpam-2245	416	9	f2+vf2	f2+vf2	NOUN
ejpam-2245	416	10	)	)	PUNCT
ejpam-2245	416	11	n.	n.	NOUN
ejpam-2245	416	12	the	the	DET
ejpam-2245	416	13	hermitian	hermitian	ADJ
ejpam-2245	416	14	inner	inner	ADJ
ejpam-2245	416	15	product	product	NOUN
ejpam-2245	416	16	is	be	AUX
ejpam-2245	416	17	defined	define	VERB
ejpam-2245	416	18	as	as	ADP
ejpam-2245	416	19	〈	〈	NOUN
ejpam-2245	416	20	x	x	X
ejpam-2245	416	21	,	,	PUNCT
ejpam-2245	416	22	y〉h	y〉h	ADP
ejpam-2245	416	23	=	=	PUNCT
ejpam-2245	416	24	∑	∑	PUNCT
ejpam-2245	416	25	x	x	PUNCT
ejpam-2245	416	26	i	i	PRON
ejpam-2245	416	27	yi	yi	INTJ
ejpam-2245	416	28	where	where	SCONJ
ejpam-2245	416	29	0=	0=	NOUN
ejpam-2245	416	30	0	0	NUM
ejpam-2245	416	31	,	,	PUNCT
ejpam-2245	416	32	1=	1=	X
ejpam-2245	416	33	1	1	NUM
ejpam-2245	416	34	,	,	PUNCT
ejpam-2245	416	35	v	v	NOUN
ejpam-2245	416	36	=	=	SYM
ejpam-2245	416	37	1	1	NUM
ejpam-2245	416	38	+	+	NUM
ejpam-2245	416	39	v	v	NUM
ejpam-2245	416	40	and	and	CCONJ
ejpam-2245	416	41	1	1	NUM
ejpam-2245	416	42	+	+	NUM
ejpam-2245	416	43	v	v	NOUN
ejpam-2245	416	44	=	=	SYM
ejpam-2245	416	45	v.	v.	ADP
ejpam-2245	416	46	the	the	DET
ejpam-2245	416	47	dual	dual	ADJ
ejpam-2245	416	48	c⊥h	c⊥h	NOUN
ejpam-2245	416	49	with	with	ADP
ejpam-2245	416	50	respect	respect	NOUN
ejpam-2245	416	51	to	to	ADP
ejpam-2245	416	52	the	the	DET
ejpam-2245	416	53	hermitian	hermitian	ADJ
ejpam-2245	416	54	inner	inner	ADJ
ejpam-2245	416	55	product	product	NOUN
ejpam-2245	416	56	of	of	ADP
ejpam-2245	416	57	c	c	PROPN
ejpam-2245	416	58	is	be	AUX
ejpam-2245	416	59	defined	define	VERB
ejpam-2245	416	60	as	as	ADP
ejpam-2245	416	61	c⊥h	c⊥h	PROPN
ejpam-2245	416	62	=	=	PUNCT
ejpam-2245	416	63	{	{	PUNCT
ejpam-2245	416	64	x	x	SYM
ejpam-2245	416	65	∈	∈	PROPN
ejpam-2245	416	66	(	(	PUNCT
ejpam-2245	416	67	f2r	f2r	PROPN
ejpam-2245	416	68	+	+	CCONJ
ejpam-2245	416	69	vf2r	vf2r	NOUN
ejpam-2245	416	70	)	)	PUNCT
ejpam-2245	417	1	|	|	ADV
ejpam-2245	417	2	〈	〈	NOUN
ejpam-2245	417	3	x	x	X
ejpam-2245	417	4	,	,	PUNCT
ejpam-2245	417	5	y〉h	y〉h	ADP
ejpam-2245	417	6	=	=	NOUN
ejpam-2245	417	7	0	0	NUM
ejpam-2245	417	8	for	for	ADP
ejpam-2245	417	9	all	all	DET
ejpam-2245	417	10	y	y	PROPN
ejpam-2245	417	11	∈	∈	PROPN
ejpam-2245	417	12	c	c	AUX
ejpam-2245	417	13	}	}	PUNCT
ejpam-2245	417	14	c	c	NOUN
ejpam-2245	417	15	is	be	AUX
ejpam-2245	417	16	hermitian	hermitian	ADJ
ejpam-2245	417	17	self	self	NOUN
ejpam-2245	417	18	-	-	PUNCT
ejpam-2245	417	19	dual	dual	ADJ
ejpam-2245	417	20	if	if	SCONJ
ejpam-2245	417	21	c	c	NOUN
ejpam-2245	417	22	=	=	SYM
ejpam-2245	417	23	c⊥h	c⊥h	PROPN
ejpam-2245	417	24	.	.	PUNCT
ejpam-2245	418	1	proposition	proposition	NOUN
ejpam-2245	418	2	8	8	NUM
ejpam-2245	418	3	.	.	PUNCT
ejpam-2245	419	1	[	[	X
ejpam-2245	419	2	1	1	X
ejpam-2245	419	3	]	]	X
ejpam-2245	419	4	if	if	SCONJ
ejpam-2245	419	5	c	c	NOUN
ejpam-2245	419	6	=	=	SYM
ejpam-2245	419	7	(	(	PUNCT
ejpam-2245	419	8	1	1	NUM
ejpam-2245	419	9	+	+	NUM
ejpam-2245	419	10	v)c1	v)c1	PROPN
ejpam-2245	419	11	⊕	⊕	PROPN
ejpam-2245	419	12	vc2	vc2	PROPN
ejpam-2245	420	1	then	then	ADV
ejpam-2245	420	2	c	c	PROPN
ejpam-2245	420	3	is	be	AUX
ejpam-2245	420	4	euclidean	euclidean	ADJ
ejpam-2245	420	5	self	self	NOUN
ejpam-2245	420	6	-	-	PUNCT
ejpam-2245	420	7	dual	dual	ADJ
ejpam-2245	420	8	if	if	SCONJ
ejpam-2245	421	1	and	and	CCONJ
ejpam-2245	421	2	only	only	ADV
ejpam-2245	421	3	if	if	SCONJ
ejpam-2245	421	4	c1	c1	PROPN
ejpam-2245	421	5	and	and	CCONJ
ejpam-2245	421	6	c2	c2	PROPN
ejpam-2245	421	7	are	be	AUX
ejpam-2245	421	8	binary	binary	ADJ
ejpam-2245	421	9	self	self	NOUN
ejpam-2245	421	10	-	-	PUNCT
ejpam-2245	421	11	dual	dual	ADJ
ejpam-2245	421	12	codes	code	NOUN
ejpam-2245	421	13	.	.	PUNCT
ejpam-2245	422	1	c	c	X
ejpam-2245	422	2	=	=	PUNCT
ejpam-2245	422	3	(	(	PUNCT
ejpam-2245	422	4	1	1	NUM
ejpam-2245	422	5	+	+	NUM
ejpam-2245	422	6	v)c1	v)c1	PROPN
ejpam-2245	422	7	⊕	⊕	PROPN
ejpam-2245	422	8	vc2	vc2	PROPN
ejpam-2245	422	9	is	be	AUX
ejpam-2245	422	10	euclidean	euclidean	ADJ
ejpam-2245	422	11	type	type	NOUN
ejpam-2245	422	12	iv	iv	NUM
ejpam-2245	422	13	self	self	NOUN
ejpam-2245	422	14	-	-	PUNCT
ejpam-2245	422	15	dual	dual	ADJ
ejpam-2245	422	16	if	if	SCONJ
ejpam-2245	423	1	and	and	CCONJ
ejpam-2245	423	2	only	only	ADV
ejpam-2245	423	3	if	if	SCONJ
ejpam-2245	423	4	c1	c1	PROPN
ejpam-2245	423	5	=	=	PROPN
ejpam-2245	423	6	c2	c2	PROPN
ejpam-2245	423	7	.	.	PUNCT
ejpam-2245	423	8	a.	a.	PROPN
ejpam-2245	423	9	batoul	batoul	PROPN
ejpam-2245	423	10	,	,	PUNCT
ejpam-2245	423	11	k.	k.	PROPN
ejpam-2245	423	12	guenda	guenda	PROPN
ejpam-2245	423	13	,	,	PUNCT
ejpam-2245	423	14	a.	a.	PROPN
ejpam-2245	423	15	kaya	kaya	PROPN
ejpam-2245	423	16	,	,	PUNCT
ejpam-2245	423	17	b.	b.	PROPN
ejpam-2245	423	18	yildiz	yildiz	PROPN
ejpam-2245	423	19	/	/	SYM
ejpam-2245	423	20	eur	eur	PROPN
ejpam-2245	423	21	.	.	PUNCT
ejpam-2245	424	1	j.	j.	PROPN
ejpam-2245	424	2	pure	pure	PROPN
ejpam-2245	424	3	appl	appl	PROPN
ejpam-2245	424	4	.	.	PROPN
ejpam-2245	424	5	math	math	PROPN
ejpam-2245	424	6	,	,	PUNCT
ejpam-2245	424	7	8	8	NUM
ejpam-2245	424	8	(	(	PUNCT
ejpam-2245	424	9	2015	2015	NUM
ejpam-2245	424	10	)	)	PUNCT
ejpam-2245	424	11	,	,	PUNCT
ejpam-2245	424	12	64	64	NUM
ejpam-2245	424	13	-	-	SYM
ejpam-2245	424	14	80	80	NUM
ejpam-2245	424	15	76	76	NUM
ejpam-2245	424	16	proposition	proposition	NOUN
ejpam-2245	424	17	9	9	NUM
ejpam-2245	424	18	.	.	PUNCT
ejpam-2245	425	1	[	[	X
ejpam-2245	425	2	1	1	X
ejpam-2245	425	3	]	]	X
ejpam-2245	425	4	if	if	SCONJ
ejpam-2245	425	5	c	c	NOUN
ejpam-2245	425	6	=	=	SYM
ejpam-2245	425	7	(	(	PUNCT
ejpam-2245	425	8	1	1	NUM
ejpam-2245	425	9	+	+	NUM
ejpam-2245	425	10	v)c1	v)c1	PROPN
ejpam-2245	425	11	⊕	⊕	PROPN
ejpam-2245	425	12	vc2	vc2	PROPN
ejpam-2245	426	1	then	then	ADV
ejpam-2245	426	2	c	c	PROPN
ejpam-2245	426	3	is	be	AUX
ejpam-2245	426	4	hermitian	hermitian	ADJ
ejpam-2245	426	5	self	self	NOUN
ejpam-2245	426	6	-	-	PUNCT
ejpam-2245	426	7	dual	dual	ADJ
ejpam-2245	426	8	if	if	SCONJ
ejpam-2245	427	1	and	and	CCONJ
ejpam-2245	427	2	only	only	ADV
ejpam-2245	427	3	if	if	SCONJ
ejpam-2245	427	4	c1	c1	PROPN
ejpam-2245	427	5	=	=	PUNCT
ejpam-2245	427	6	c⊥2	c⊥2	X
ejpam-2245	427	7	.	.	PUNCT
ejpam-2245	428	1	c	c	X
ejpam-2245	428	2	=	=	PUNCT
ejpam-2245	428	3	(	(	PUNCT
ejpam-2245	428	4	1	1	NUM
ejpam-2245	428	5	+	+	NUM
ejpam-2245	428	6	v)c1	v)c1	PROPN
ejpam-2245	428	7	⊕	⊕	PROPN
ejpam-2245	428	8	vc2	vc2	PROPN
ejpam-2245	428	9	is	be	AUX
ejpam-2245	428	10	hermitian	hermitian	ADJ
ejpam-2245	428	11	type	type	NOUN
ejpam-2245	428	12	iv	iv	NUM
ejpam-2245	428	13	self	self	NOUN
ejpam-2245	428	14	-	-	PUNCT
ejpam-2245	428	15	dual	dual	ADJ
ejpam-2245	428	16	if	if	SCONJ
ejpam-2245	429	1	and	and	CCONJ
ejpam-2245	429	2	only	only	ADV
ejpam-2245	429	3	if	if	SCONJ
ejpam-2245	429	4	c1	c1	PROPN
ejpam-2245	429	5	and	and	CCONJ
ejpam-2245	429	6	c⊥1	c⊥1	NOUN
ejpam-2245	429	7	are	be	AUX
ejpam-2245	429	8	even	even	ADV
ejpam-2245	429	9	codes	code	NOUN
ejpam-2245	429	10	.	.	PUNCT
ejpam-2245	430	1	theorem	theorem	NOUN
ejpam-2245	430	2	12	12	NUM
ejpam-2245	430	3	.	.	PUNCT
ejpam-2245	431	1	let	let	VERB
ejpam-2245	431	2	n	n	NOUN
ejpam-2245	431	3	=	=	SYM
ejpam-2245	431	4	2	2	NUM
ejpam-2245	431	5	am	am	NOUN
ejpam-2245	431	6	with	with	ADP
ejpam-2245	431	7	m	m	NOUN
ejpam-2245	431	8	an	an	DET
ejpam-2245	431	9	odd	odd	ADJ
ejpam-2245	431	10	integer	integer	NOUN
ejpam-2245	431	11	such	such	ADJ
ejpam-2245	431	12	that	that	PRON
ejpam-2245	431	13	and	and	CCONJ
ejpam-2245	431	14	di	di	NOUN
ejpam-2245	431	15	=	=	NOUN
ejpam-2245	431	16	〈	〈	PROPN
ejpam-2245	431	17	fi(x	fi(x	NUM
ejpam-2245	431	18	)	)	PUNCT
ejpam-2245	431	19	〉	〉	NOUN
ejpam-2245	431	20	,	,	PUNCT
ejpam-2245	431	21	1	1	NUM
ejpam-2245	431	22	≤	≤	NUM
ejpam-2245	431	23	i	i	PRON
ejpam-2245	431	24	≤	≤	NOUN
ejpam-2245	431	25	2	2	NUM
ejpam-2245	431	26	be	be	AUX
ejpam-2245	431	27	duadic	duadic	ADJ
ejpam-2245	431	28	codes	code	NOUN
ejpam-2245	431	29	over	over	ADP
ejpam-2245	431	30	f2	f2	PROPN
ejpam-2245	431	31	.	.	PUNCT
ejpam-2245	432	1	then	then	ADV
ejpam-2245	432	2	for	for	ADP
ejpam-2245	432	3	1≤	1≤	NUM
ejpam-2245	432	4	i	i	PRON
ejpam-2245	432	5	≤	≤	ADV
ejpam-2245	432	6	2	2	NUM
ejpam-2245	432	7	,	,	PUNCT
ejpam-2245	432	8	the	the	DET
ejpam-2245	432	9	cyclic	cyclic	ADJ
ejpam-2245	432	10	codes	code	NOUN
ejpam-2245	432	11	over	over	ADP
ejpam-2245	432	12	r2	r2	PROPN
ejpam-2245	432	13	=	=	SYM
ejpam-2245	433	1	f2	f2	PROPN
ejpam-2245	433	2	+	+	CCONJ
ejpam-2245	433	3	vf2	vf2	NOUN
ejpam-2245	433	4	generated	generate	VERB
ejpam-2245	433	5	by	by	ADP
ejpam-2245	433	6	f	f	PROPN
ejpam-2245	433	7	(	(	PUNCT
ejpam-2245	433	8	x	x	X
ejpam-2245	433	9	)	)	PUNCT
ejpam-2245	433	10	=	=	NOUN
ejpam-2245	434	1	v(x	v(x	NOUN
ejpam-2245	434	2	−	−	PROPN
ejpam-2245	434	3	1)2	1)2	NUM
ejpam-2245	434	4	a−1	a−1	PROPN
ejpam-2245	434	5	f	f	PROPN
ejpam-2245	434	6	2a	2a	NUM
ejpam-2245	435	1	i	i	PRON
ejpam-2245	435	2	(	(	PUNCT
ejpam-2245	435	3	x	x	X
ejpam-2245	435	4	)	)	PUNCT
ejpam-2245	435	5	+	+	CCONJ
ejpam-2245	435	6	(	(	PUNCT
ejpam-2245	435	7	1−	1−	NUM
ejpam-2245	435	8	v)(x	v)(x	NOUN
ejpam-2245	435	9	−	−	PROPN
ejpam-2245	435	10	1)2	1)2	NUM
ejpam-2245	435	11	a−1	a−1	PROPN
ejpam-2245	435	12	f	f	PROPN
ejpam-2245	435	13	2a	2a	NUM
ejpam-2245	435	14	j	j	PROPN
ejpam-2245	435	15	(	(	PUNCT
ejpam-2245	435	16	x	x	NOUN
ejpam-2245	435	17	)	)	PUNCT
ejpam-2245	435	18	,	,	PUNCT
ejpam-2245	435	19	are	be	AUX
ejpam-2245	435	20	euclidean	euclidean	ADJ
ejpam-2245	435	21	self	self	NOUN
ejpam-2245	435	22	-	-	PUNCT
ejpam-2245	435	23	dual	dual	ADJ
ejpam-2245	435	24	or	or	CCONJ
ejpam-2245	435	25	hermitian	hermitian	ADJ
ejpam-2245	435	26	self	self	NOUN
ejpam-2245	435	27	-	-	PUNCT
ejpam-2245	435	28	dual	dual	ADJ
ejpam-2245	435	29	codes	code	NOUN
ejpam-2245	435	30	.	.	PUNCT
ejpam-2245	436	1	proof	proof	NOUN
ejpam-2245	436	2	.	.	PUNCT
ejpam-2245	437	1	if	if	SCONJ
ejpam-2245	437	2	the	the	DET
ejpam-2245	437	3	splitting	splitting	NOUN
ejpam-2245	437	4	is	be	AUX
ejpam-2245	437	5	given	give	VERB
ejpam-2245	437	6	by	by	ADP
ejpam-2245	437	7	µ−1	µ−1	PROPN
ejpam-2245	437	8	then	then	ADV
ejpam-2245	437	9	the	the	DET
ejpam-2245	437	10	cyclic	cyclic	ADJ
ejpam-2245	437	11	codes	code	NOUN
ejpam-2245	437	12	generated	generate	VERB
ejpam-2245	437	13	respectively	respectively	ADV
ejpam-2245	437	14	by	by	ADP
ejpam-2245	437	15	(	(	PUNCT
ejpam-2245	437	16	x−1)2	x−1)2	PROPN
ejpam-2245	437	17	a−1	a−1	PROPN
ejpam-2245	437	18	f	f	PROPN
ejpam-2245	437	19	2a	2a	NUM
ejpam-2245	437	20	1	1	NUM
ejpam-2245	437	21	(	(	PUNCT
ejpam-2245	437	22	x	x	NOUN
ejpam-2245	437	23	)	)	PUNCT
ejpam-2245	437	24	and	and	CCONJ
ejpam-2245	437	25	(	(	PUNCT
ejpam-2245	437	26	x−1)2	x−1)2	PROPN
ejpam-2245	437	27	a−1	a−1	PROPN
ejpam-2245	437	28	f	f	PROPN
ejpam-2245	437	29	2a	2a	NUM
ejpam-2245	437	30	2	2	NUM
ejpam-2245	437	31	(	(	PUNCT
ejpam-2245	437	32	x	x	X
ejpam-2245	437	33	)	)	PUNCT
ejpam-2245	437	34	are	be	AUX
ejpam-2245	437	35	self	self	NOUN
ejpam-2245	437	36	-	-	PUNCT
ejpam-2245	437	37	dual	dual	ADJ
ejpam-2245	437	38	over	over	ADP
ejpam-2245	437	39	f2	f2	PROPN
ejpam-2245	437	40	.	.	PUNCT
ejpam-2245	438	1	thus	thus	ADV
ejpam-2245	438	2	f	f	X
ejpam-2245	438	3	(	(	PUNCT
ejpam-2245	438	4	x	x	X
ejpam-2245	438	5	)	)	PUNCT
ejpam-2245	438	6	generates	generate	VERB
ejpam-2245	438	7	a	a	DET
ejpam-2245	438	8	euclidean	euclidean	ADJ
ejpam-2245	438	9	self	self	NOUN
ejpam-2245	438	10	-	-	PUNCT
ejpam-2245	438	11	dual	dual	ADJ
ejpam-2245	438	12	cyclic	cyclic	ADJ
ejpam-2245	438	13	code	code	NOUN
ejpam-2245	438	14	over	over	ADP
ejpam-2245	438	15	f2	f2	PROPN
ejpam-2245	438	16	+	+	CCONJ
ejpam-2245	438	17	vf2	vf2	ADJ
ejpam-2245	438	18	.	.	PUNCT
ejpam-2245	439	1	if	if	SCONJ
ejpam-2245	439	2	the	the	DET
ejpam-2245	439	3	splitting	splitting	NOUN
ejpam-2245	439	4	is	be	AUX
ejpam-2245	439	5	not	not	PART
ejpam-2245	439	6	given	give	VERB
ejpam-2245	439	7	by	by	ADP
ejpam-2245	439	8	µ−1then	µ−1then	NOUN
ejpam-2245	439	9	the	the	DET
ejpam-2245	439	10	cyclic	cyclic	ADJ
ejpam-2245	439	11	codes	code	NOUN
ejpam-2245	439	12	generated	generate	VERB
ejpam-2245	439	13	respectively	respectively	ADV
ejpam-2245	439	14	by	by	ADP
ejpam-2245	439	15	(	(	PUNCT
ejpam-2245	439	16	x	x	X
ejpam-2245	439	17	−1)2	−1)2	PROPN
ejpam-2245	439	18	a−1	a−1	PROPN
ejpam-2245	439	19	f	f	PROPN
ejpam-2245	439	20	2a	2a	NUM
ejpam-2245	439	21	1	1	NUM
ejpam-2245	439	22	(	(	PUNCT
ejpam-2245	439	23	x	x	NOUN
ejpam-2245	439	24	)	)	PUNCT
ejpam-2245	439	25	and	and	CCONJ
ejpam-2245	439	26	(	(	PUNCT
ejpam-2245	439	27	x	x	X
ejpam-2245	439	28	−1)2	−1)2	PROPN
ejpam-2245	439	29	a−1	a−1	PROPN
ejpam-2245	439	30	f	f	PROPN
ejpam-2245	439	31	2a	2a	NUM
ejpam-2245	439	32	2	2	NUM
ejpam-2245	439	33	(	(	PUNCT
ejpam-2245	439	34	x	x	X
ejpam-2245	439	35	)	)	PUNCT
ejpam-2245	439	36	are	be	AUX
ejpam-2245	439	37	dual	dual	ADJ
ejpam-2245	439	38	of	of	ADP
ejpam-2245	439	39	each	each	DET
ejpam-2245	439	40	other	other	ADJ
ejpam-2245	439	41	over	over	ADP
ejpam-2245	439	42	fq	fq	PROPN
ejpam-2245	439	43	.	.	PROPN
ejpam-2245	439	44	then	then	ADV
ejpam-2245	439	45	by	by	ADP
ejpam-2245	439	46	proposition	proposition	NOUN
ejpam-2245	439	47	8	8	NUM
ejpam-2245	439	48	f	f	NOUN
ejpam-2245	439	49	(	(	PUNCT
ejpam-2245	439	50	x	x	NOUN
ejpam-2245	439	51	)	)	PUNCT
ejpam-2245	439	52	generates	generate	VERB
ejpam-2245	439	53	a	a	DET
ejpam-2245	439	54	hermitian	hermitian	ADJ
ejpam-2245	439	55	self	self	NOUN
ejpam-2245	439	56	-	-	PUNCT
ejpam-2245	439	57	dual	dual	ADJ
ejpam-2245	439	58	cyclic	cyclic	ADJ
ejpam-2245	439	59	code	code	NOUN
ejpam-2245	439	60	over	over	ADP
ejpam-2245	439	61	f2	f2	PROPN
ejpam-2245	439	62	+	+	CCONJ
ejpam-2245	439	63	vf2	vf2	ADJ
ejpam-2245	439	64	.	.	PUNCT
ejpam-2245	440	1	6	6	X
ejpam-2245	440	2	.	.	X
ejpam-2245	440	3	formally	formally	ADV
ejpam-2245	440	4	self	self	NOUN
ejpam-2245	440	5	-	-	PUNCT
ejpam-2245	440	6	dual	dual	ADJ
ejpam-2245	440	7	codes	code	NOUN
ejpam-2245	440	8	over	over	ADP
ejpam-2245	440	9	r	r	NOUN
ejpam-2245	440	10	formally	formally	ADV
ejpam-2245	440	11	self	self	NOUN
ejpam-2245	440	12	-	-	PUNCT
ejpam-2245	440	13	dual	dual	ADJ
ejpam-2245	440	14	codes	code	NOUN
ejpam-2245	440	15	are	be	AUX
ejpam-2245	440	16	an	an	DET
ejpam-2245	440	17	interesting	interesting	ADJ
ejpam-2245	440	18	family	family	NOUN
ejpam-2245	440	19	of	of	ADP
ejpam-2245	440	20	codes	code	NOUN
ejpam-2245	440	21	.	.	PUNCT
ejpam-2245	441	1	especially	especially	ADV
ejpam-2245	441	2	the	the	DET
ejpam-2245	441	3	binary	binary	NOUN
ejpam-2245	441	4	near	near	ADP
ejpam-2245	441	5	extremal	extremal	ADJ
ejpam-2245	441	6	formally	formally	ADV
ejpam-2245	441	7	self	self	NOUN
ejpam-2245	441	8	-	-	PUNCT
ejpam-2245	441	9	dual	dual	ADJ
ejpam-2245	441	10	(	(	PUNCT
ejpam-2245	441	11	f.s.d	f.s.d	ADJ
ejpam-2245	441	12	.	.	PUNCT
ejpam-2245	441	13	)	)	PUNCT
ejpam-2245	441	14	codes	code	NOUN
ejpam-2245	441	15	have	have	AUX
ejpam-2245	441	16	been	be	AUX
ejpam-2245	441	17	studied	study	VERB
ejpam-2245	441	18	extensively	extensively	ADV
ejpam-2245	441	19	.	.	PUNCT
ejpam-2245	442	1	for	for	ADP
ejpam-2245	442	2	more	more	ADJ
ejpam-2245	442	3	detail	detail	NOUN
ejpam-2245	442	4	we	we	PRON
ejpam-2245	442	5	refer	refer	VERB
ejpam-2245	442	6	the	the	DET
ejpam-2245	442	7	reader	reader	NOUN
ejpam-2245	442	8	to	to	ADP
ejpam-2245	442	9	[	[	X
ejpam-2245	442	10	4	4	NUM
ejpam-2245	442	11	,	,	PUNCT
ejpam-2245	442	12	7	7	NUM
ejpam-2245	442	13	,	,	PUNCT
ejpam-2245	442	14	8	8	NUM
ejpam-2245	442	15	]	]	PUNCT
ejpam-2245	442	16	and	and	CCONJ
ejpam-2245	442	17	the	the	DET
ejpam-2245	442	18	references	reference	NOUN
ejpam-2245	442	19	therein	therein	ADV
ejpam-2245	442	20	.	.	PUNCT
ejpam-2245	443	1	recently	recently	ADV
ejpam-2245	443	2	,	,	PUNCT
ejpam-2245	443	3	karadeniz	karadeniz	PROPN
ejpam-2245	443	4	et	et	PROPN
ejpam-2245	443	5	al	al	PROPN
ejpam-2245	443	6	.	.	PROPN
ejpam-2245	443	7	gave	give	VERB
ejpam-2245	443	8	constructions	construction	NOUN
ejpam-2245	443	9	for	for	ADP
ejpam-2245	443	10	f.s.d	f.s.d	ADJ
ejpam-2245	443	11	.	.	PUNCT
ejpam-2245	444	1	codes	code	NOUN
ejpam-2245	444	2	by	by	ADP
ejpam-2245	444	3	using	use	VERB
ejpam-2245	444	4	circulant	circulant	ADJ
ejpam-2245	444	5	matrices	matrix	NOUN
ejpam-2245	444	6	in	in	ADP
ejpam-2245	444	7	[	[	X
ejpam-2245	444	8	7	7	NUM
ejpam-2245	444	9	]	]	PUNCT
ejpam-2245	444	10	.	.	PUNCT
ejpam-2245	445	1	by	by	ADP
ejpam-2245	445	2	using	use	VERB
ejpam-2245	445	3	the	the	DET
ejpam-2245	445	4	constructions	construction	NOUN
ejpam-2245	445	5	over	over	ADP
ejpam-2245	445	6	a	a	DET
ejpam-2245	445	7	family	family	NOUN
ejpam-2245	445	8	of	of	ADP
ejpam-2245	445	9	binary	binary	PROPN
ejpam-2245	445	10	rings	ring	NOUN
ejpam-2245	445	11	;	;	PUNCT
ejpam-2245	445	12	rk	rk	VERB
ejpam-2245	445	13	they	they	PRON
ejpam-2245	445	14	were	be	AUX
ejpam-2245	445	15	able	able	ADJ
ejpam-2245	445	16	to	to	PART
ejpam-2245	445	17	obtain	obtain	VERB
ejpam-2245	445	18	f.s.d	f.s.d	NOUN
ejpam-2245	445	19	.	.	PUNCT
ejpam-2245	446	1	codes	code	NOUN
ejpam-2245	446	2	such	such	ADJ
ejpam-2245	446	3	as	as	ADP
ejpam-2245	446	4	[	[	X
ejpam-2245	446	5	72,36,14]2	72,36,14]2	NUM
ejpam-2245	446	6	,	,	PUNCT
ejpam-2245	446	7	[	[	X
ejpam-2245	446	8	72,36,13]2	72,36,13]2	NUM
ejpam-2245	446	9	and	and	CCONJ
ejpam-2245	446	10	[	[	X
ejpam-2245	446	11	44,22,10]2	44,22,10]2	NUM
ejpam-2245	446	12	which	which	PRON
ejpam-2245	446	13	have	have	VERB
ejpam-2245	446	14	better	well	ADJ
ejpam-2245	446	15	distances	distance	NOUN
ejpam-2245	446	16	than	than	ADP
ejpam-2245	446	17	the	the	DET
ejpam-2245	446	18	best	well	ADV
ejpam-2245	446	19	known	know	VERB
ejpam-2245	446	20	self	self	NOUN
ejpam-2245	446	21	-	-	PUNCT
ejpam-2245	446	22	dual	dual	ADJ
ejpam-2245	446	23	codes	code	NOUN
ejpam-2245	446	24	of	of	ADP
ejpam-2245	446	25	the	the	DET
ejpam-2245	446	26	corresponding	corresponding	ADJ
ejpam-2245	446	27	lengths	length	NOUN
ejpam-2245	446	28	.	.	PUNCT
ejpam-2245	447	1	in	in	ADP
ejpam-2245	447	2	this	this	DET
ejpam-2245	447	3	section	section	NOUN
ejpam-2245	447	4	,	,	PUNCT
ejpam-2245	447	5	we	we	PRON
ejpam-2245	447	6	generalize	generalize	VERB
ejpam-2245	447	7	two	two	NUM
ejpam-2245	447	8	of	of	ADP
ejpam-2245	447	9	their	their	PRON
ejpam-2245	447	10	constructions	construction	NOUN
ejpam-2245	447	11	which	which	PRON
ejpam-2245	447	12	lead	lead	VERB
ejpam-2245	447	13	to	to	ADP
ejpam-2245	447	14	the	the	DET
ejpam-2245	447	15	good	good	ADJ
ejpam-2245	447	16	computational	computational	ADJ
ejpam-2245	447	17	results	result	NOUN
ejpam-2245	447	18	mentioned	mention	VERB
ejpam-2245	447	19	above	above	ADV
ejpam-2245	447	20	.	.	PUNCT
ejpam-2245	448	1	instead	instead	ADV
ejpam-2245	448	2	of	of	ADP
ejpam-2245	448	3	circulant	circulant	ADJ
ejpam-2245	448	4	matrices	matrix	NOUN
ejpam-2245	448	5	we	we	PRON
ejpam-2245	448	6	use	use	VERB
ejpam-2245	448	7	λ	λ	ADJ
ejpam-2245	448	8	-	-	ADJ
ejpam-2245	448	9	circulant	circulant	ADJ
ejpam-2245	448	10	matrices	matrix	NOUN
ejpam-2245	448	11	and	and	CCONJ
ejpam-2245	448	12	state	state	NOUN
ejpam-2245	448	13	that	that	DET
ejpam-2245	448	14	double	double	ADJ
ejpam-2245	448	15	λ	λ	NOUN
ejpam-2245	448	16	-	-	NOUN
ejpam-2245	448	17	circulant	circulant	ADJ
ejpam-2245	448	18	and	and	CCONJ
ejpam-2245	448	19	bordered	border	VERB
ejpam-2245	448	20	double	double	ADJ
ejpam-2245	448	21	λ	λ	NOUN
ejpam-2245	448	22	-	-	ADJ
ejpam-2245	448	23	circulant	circulant	ADJ
ejpam-2245	448	24	codes	code	NOUN
ejpam-2245	448	25	generates	generate	VERB
ejpam-2245	448	26	f.s.d	f.s.d	ADJ
ejpam-2245	448	27	.	.	PUNCT
ejpam-2245	449	1	codes	code	NOUN
ejpam-2245	449	2	over	over	ADP
ejpam-2245	449	3	the	the	DET
ejpam-2245	449	4	rings	ring	NOUN
ejpam-2245	449	5	which	which	PRON
ejpam-2245	449	6	satisfy	satisfy	VERB
ejpam-2245	449	7	wt	wt	PROPN
ejpam-2245	449	8	(	(	PUNCT
ejpam-2245	449	9	a	a	NOUN
ejpam-2245	449	10	)	)	PUNCT
ejpam-2245	449	11	=	=	NOUN
ejpam-2245	449	12	wt	wt	PROPN
ejpam-2245	449	13	(	(	PUNCT
ejpam-2245	449	14	−a	−a	NOUN
ejpam-2245	449	15	)	)	PUNCT
ejpam-2245	449	16	for	for	ADP
ejpam-2245	449	17	any	any	DET
ejpam-2245	449	18	element	element	NOUN
ejpam-2245	449	19	a	a	PRON
ejpam-2245	449	20	of	of	ADP
ejpam-2245	449	21	the	the	DET
ejpam-2245	449	22	ring	ring	NOUN
ejpam-2245	449	23	.	.	PUNCT
ejpam-2245	450	1	we	we	PRON
ejpam-2245	450	2	were	be	AUX
ejpam-2245	450	3	able	able	ADJ
ejpam-2245	450	4	to	to	PART
ejpam-2245	450	5	obtain	obtain	VERB
ejpam-2245	450	6	f.s.d	f.s.d	NOUN
ejpam-2245	450	7	.	.	PUNCT
ejpam-2245	451	1	codes	code	NOUN
ejpam-2245	451	2	with	with	ADP
ejpam-2245	451	3	parameters	parameter	NOUN
ejpam-2245	451	4	[	[	X
ejpam-2245	451	5	32,16,11]5	32,16,11]5	NUM
ejpam-2245	451	6	,	,	PUNCT
ejpam-2245	451	7	[	[	X
ejpam-2245	451	8	32,16,10]3	32,16,10]3	NUM
ejpam-2245	451	9	,	,	PUNCT
ejpam-2245	451	10	[	[	X
ejpam-2245	451	11	20,10,7]3	20,10,7]3	NUM
ejpam-2245	451	12	,	,	PUNCT
ejpam-2245	451	13	[	[	X
ejpam-2245	451	14	8,4,4]3	8,4,4]3	X
ejpam-2245	451	15	and	and	CCONJ
ejpam-2245	451	16	many	many	ADJ
ejpam-2245	451	17	examples	example	NOUN
ejpam-2245	451	18	with	with	ADP
ejpam-2245	451	19	the	the	DET
ejpam-2245	451	20	distance	distance	NOUN
ejpam-2245	451	21	of	of	ADP
ejpam-2245	451	22	the	the	DET
ejpam-2245	451	23	best	well	ADV
ejpam-2245	451	24	known	know	VERB
ejpam-2245	451	25	linear	linear	PROPN
ejpam-2245	451	26	code	code	NOUN
ejpam-2245	451	27	of	of	ADP
ejpam-2245	451	28	the	the	DET
ejpam-2245	451	29	same	same	ADJ
ejpam-2245	451	30	parameters	parameter	NOUN
ejpam-2245	451	31	.	.	PUNCT
ejpam-2245	452	1	the	the	DET
ejpam-2245	452	2	results	result	NOUN
ejpam-2245	452	3	are	be	AUX
ejpam-2245	452	4	tabulated	tabulate	VERB
ejpam-2245	452	5	in	in	ADP
ejpam-2245	452	6	tables	table	NOUN
ejpam-2245	452	7	2	2	NUM
ejpam-2245	452	8	and	and	CCONJ
ejpam-2245	452	9	3	3	NUM
ejpam-2245	452	10	.	.	PUNCT
ejpam-2245	452	11	an	an	DET
ejpam-2245	452	12	n×	n×	PROPN
ejpam-2245	452	13	n	n	CCONJ
ejpam-2245	452	14	square	square	ADJ
ejpam-2245	452	15	matrix	matrix	NOUN
ejpam-2245	452	16	m	m	VERB
ejpam-2245	452	17	is	be	AUX
ejpam-2245	452	18	called	call	VERB
ejpam-2245	452	19	λ	λ	NOUN
ejpam-2245	452	20	-	-	NOUN
ejpam-2245	452	21	circulant	circulant	ADJ
ejpam-2245	452	22	if	if	SCONJ
ejpam-2245	452	23	it	it	PRON
ejpam-2245	452	24	is	be	AUX
ejpam-2245	452	25	in	in	ADP
ejpam-2245	452	26	the	the	DET
ejpam-2245	452	27	following	follow	VERB
ejpam-2245	452	28	form	form	NOUN
ejpam-2245	452	29	;	;	PUNCT
ejpam-2245	452	30	m	m	VERB
ejpam-2245	452	31	=	=	VERB
ejpam-2245	452	32			PROPN
ejpam-2245	452	33			PROPN
ejpam-2245	452	34	a1	a1	NOUN
ejpam-2245	452	35	a2	a2	PROPN
ejpam-2245	452	36	a3	a3	NOUN
ejpam-2245	452	37	·	·	PUNCT
ejpam-2245	452	38	·	·	PUNCT
ejpam-2245	452	39	·	·	PUNCT
ejpam-2245	452	40	an	an	DET
ejpam-2245	452	41	λan	λan	NOUN
ejpam-2245	452	42	a1	a1	NOUN
ejpam-2245	452	43	a2	a2	PROPN
ejpam-2245	452	44	·	·	PUNCT
ejpam-2245	452	45	·	·	PUNCT
ejpam-2245	452	46	·	·	PUNCT
ejpam-2245	452	47	an−1	an−1	ADJ
ejpam-2245	452	48	λan−1	λan−1	PROPN
ejpam-2245	452	49	λan	λan	NOUN
ejpam-2245	452	50	a1	a1	NOUN
ejpam-2245	452	51	·	·	PUNCT
ejpam-2245	452	52	·	·	PUNCT
ejpam-2245	452	53	·	·	PUNCT
ejpam-2245	453	1	an−2	an−2	PROPN
ejpam-2245	453	2	...	...	PUNCT
ejpam-2245	453	3	...	...	PUNCT
ejpam-2245	453	4	...	...	PUNCT
ejpam-2245	453	5	.	.	PUNCT
ejpam-2245	453	6	.	.	PUNCT
ejpam-2245	453	7	.	.	PUNCT
ejpam-2245	454	1	...	...	PUNCT
ejpam-2245	455	1	λa2	λa2	NOUN
ejpam-2245	455	2	λa3	λa3	VERB
ejpam-2245	455	3	λa4	λa4	X
ejpam-2245	455	4	·	·	PUNCT
ejpam-2245	455	5	·	·	PUNCT
ejpam-2245	455	6	·	·	PUNCT
ejpam-2245	455	7	a1	a1	NOUN
ejpam-2245	455	8			NOUN
ejpam-2245	456	1			NOUN
ejpam-2245	456	2	.	.	PUNCT
ejpam-2245	457	1	for	for	ADP
ejpam-2245	457	2	λ	λ	NOUN
ejpam-2245	457	3	=	=	SYM
ejpam-2245	457	4	1	1	NUM
ejpam-2245	457	5	the	the	DET
ejpam-2245	457	6	matrix	matrix	NOUN
ejpam-2245	457	7	is	be	AUX
ejpam-2245	457	8	circulant	circulant	ADJ
ejpam-2245	457	9	and	and	CCONJ
ejpam-2245	457	10	there	there	PRON
ejpam-2245	457	11	is	be	VERB
ejpam-2245	457	12	a	a	DET
ejpam-2245	457	13	vast	vast	ADJ
ejpam-2245	457	14	literature	literature	NOUN
ejpam-2245	457	15	on	on	ADP
ejpam-2245	457	16	double	double	ADJ
ejpam-2245	457	17	circulant	circulant	NOUN
ejpam-2245	457	18	and	and	CCONJ
ejpam-2245	457	19	bordered	border	VERB
ejpam-2245	457	20	double	double	ADJ
ejpam-2245	457	21	circulant	circulant	NOUN
ejpam-2245	457	22	self	self	NOUN
ejpam-2245	457	23	-	-	PUNCT
ejpam-2245	457	24	dual	dual	ADJ
ejpam-2245	457	25	codes	code	NOUN
ejpam-2245	457	26	.	.	PUNCT
ejpam-2245	458	1	in	in	ADP
ejpam-2245	458	2	the	the	DET
ejpam-2245	458	3	sequel	sequel	NOUN
ejpam-2245	458	4	,	,	PUNCT
ejpam-2245	458	5	let	let	VERB
ejpam-2245	458	6	s	s	PRON
ejpam-2245	458	7	to	to	PART
ejpam-2245	458	8	be	be	AUX
ejpam-2245	458	9	a	a	DET
ejpam-2245	458	10	commutative	commutative	ADJ
ejpam-2245	458	11	ring	ring	NOUN
ejpam-2245	458	12	with	with	ADP
ejpam-2245	458	13	identity	identity	NOUN
ejpam-2245	458	14	and	and	CCONJ
ejpam-2245	458	15	the	the	DET
ejpam-2245	458	16	weight	weight	NOUN
ejpam-2245	458	17	used	use	VERB
ejpam-2245	458	18	satisfies	satisfie	NOUN
ejpam-2245	458	19	wt	wt	INTJ
ejpam-2245	458	20	(	(	PUNCT
ejpam-2245	458	21	a	a	NOUN
ejpam-2245	458	22	)	)	PUNCT
ejpam-2245	458	23	=	=	NOUN
ejpam-2245	458	24	wt	wt	PROPN
ejpam-2245	458	25	(	(	PUNCT
ejpam-2245	458	26	−a	−a	NOUN
ejpam-2245	458	27	)	)	PUNCT
ejpam-2245	458	28	for	for	ADP
ejpam-2245	458	29	any	any	DET
ejpam-2245	458	30	element	element	NOUN
ejpam-2245	458	31	a	a	DET
ejpam-2245	458	32	∈	∈	PROPN
ejpam-2245	458	33	r.	r.	NOUN
ejpam-2245	458	34	the	the	DET
ejpam-2245	458	35	constructions	construction	NOUN
ejpam-2245	458	36	are	be	AUX
ejpam-2245	458	37	given	give	VERB
ejpam-2245	458	38	in	in	ADP
ejpam-2245	458	39	the	the	DET
ejpam-2245	458	40	following	follow	VERB
ejpam-2245	458	41	theorems	theorem	NOUN
ejpam-2245	458	42	.	.	PUNCT
ejpam-2245	458	43	a.	a.	PROPN
ejpam-2245	458	44	batoul	batoul	PROPN
ejpam-2245	458	45	,	,	PUNCT
ejpam-2245	458	46	k.	k.	PROPN
ejpam-2245	458	47	guenda	guenda	PROPN
ejpam-2245	458	48	,	,	PUNCT
ejpam-2245	458	49	a.	a.	PROPN
ejpam-2245	458	50	kaya	kaya	PROPN
ejpam-2245	458	51	,	,	PUNCT
ejpam-2245	458	52	b.	b.	PROPN
ejpam-2245	458	53	yildiz	yildiz	PROPN
ejpam-2245	458	54	/	/	SYM
ejpam-2245	458	55	eur	eur	PROPN
ejpam-2245	458	56	.	.	PUNCT
ejpam-2245	459	1	j.	j.	PROPN
ejpam-2245	459	2	pure	pure	PROPN
ejpam-2245	459	3	appl	appl	PROPN
ejpam-2245	459	4	.	.	PROPN
ejpam-2245	459	5	math	math	PROPN
ejpam-2245	459	6	,	,	PUNCT
ejpam-2245	459	7	8	8	NUM
ejpam-2245	459	8	(	(	PUNCT
ejpam-2245	459	9	2015	2015	NUM
ejpam-2245	459	10	)	)	PUNCT
ejpam-2245	459	11	,	,	PUNCT
ejpam-2245	459	12	64	64	NUM
ejpam-2245	459	13	-	-	SYM
ejpam-2245	459	14	80	80	NUM
ejpam-2245	459	15	77	77	NUM
ejpam-2245	459	16	theorem	theorem	VERB
ejpam-2245	459	17	13	13	NUM
ejpam-2245	459	18	.	.	PUNCT
ejpam-2245	460	1	[	[	X
ejpam-2245	460	2	construction	construction	NOUN
ejpam-2245	460	3	a	a	X
ejpam-2245	460	4	]	]	X
ejpam-2245	460	5	let	let	AUX
ejpam-2245	460	6	m	m	PRON
ejpam-2245	460	7	be	be	AUX
ejpam-2245	460	8	an	an	DET
ejpam-2245	460	9	n×	n×	PROPN
ejpam-2245	460	10	n	n	ADV
ejpam-2245	460	11	λ	λ	ADJ
ejpam-2245	460	12	-	-	ADJ
ejpam-2245	460	13	circulant	circulant	ADJ
ejpam-2245	460	14	matrix	matrix	NOUN
ejpam-2245	460	15	then	then	ADV
ejpam-2245	460	16	the	the	DET
ejpam-2245	460	17	code	code	NOUN
ejpam-2245	460	18	generated	generate	VERB
ejpam-2245	460	19	by	by	ADP
ejpam-2245	460	20	g	g	PROPN
ejpam-2245	460	21	=	=	SYM
ejpam-2245	460	22	�	�	PROPN
ejpam-2245	460	23	in	in	ADP
ejpam-2245	460	24	m	m	PROPN
ejpam-2245	460	25	�	�	PROPN
ejpam-2245	460	26	is	be	AUX
ejpam-2245	460	27	a	a	DET
ejpam-2245	460	28	formally	formally	ADV
ejpam-2245	460	29	self	self	NOUN
ejpam-2245	460	30	-	-	PUNCT
ejpam-2245	460	31	dual	dual	ADJ
ejpam-2245	460	32	code	code	NOUN
ejpam-2245	460	33	over	over	ADP
ejpam-2245	460	34	r.	r.	PROPN
ejpam-2245	460	35	proof	proof	NOUN
ejpam-2245	460	36	.	.	PUNCT
ejpam-2245	461	1	let	let	VERB
ejpam-2245	461	2	c	c	PRON
ejpam-2245	461	3	be	be	AUX
ejpam-2245	461	4	the	the	DET
ejpam-2245	461	5	code	code	NOUN
ejpam-2245	461	6	generated	generate	VERB
ejpam-2245	461	7	by	by	ADP
ejpam-2245	461	8	g	g	PROPN
ejpam-2245	461	9	and	and	CCONJ
ejpam-2245	461	10	c	c	PROPN
ejpam-2245	461	11	′	′	NUM
ejpam-2245	461	12	be	be	AUX
ejpam-2245	461	13	the	the	DET
ejpam-2245	461	14	code	code	NOUN
ejpam-2245	461	15	generated	generate	VERB
ejpam-2245	461	16	by	by	ADP
ejpam-2245	461	17	g′	g′	NOUN
ejpam-2245	461	18	=	=	SYM
ejpam-2245	461	19	�	�	PROPN
ejpam-2245	461	20	m	m	PROPN
ejpam-2245	461	21	t	t	PROPN
ejpam-2245	461	22	−in	−in	PROPN
ejpam-2245	461	23	�	�	PROPN
ejpam-2245	461	24	.	.	PUNCT
ejpam-2245	462	1	it	it	PRON
ejpam-2245	462	2	is	be	AUX
ejpam-2245	462	3	easily	easily	ADV
ejpam-2245	462	4	observed	observe	VERB
ejpam-2245	462	5	that	that	SCONJ
ejpam-2245	462	6	the	the	DET
ejpam-2245	462	7	codes	code	NOUN
ejpam-2245	462	8	c	c	PROPN
ejpam-2245	462	9	and	and	CCONJ
ejpam-2245	462	10	c	c	PROPN
ejpam-2245	462	11	′	′	NOUN
ejpam-2245	462	12	are	be	AUX
ejpam-2245	462	13	orthogonal	orthogonal	ADJ
ejpam-2245	462	14	to	to	ADP
ejpam-2245	462	15	each	each	DET
ejpam-2245	462	16	other	other	ADJ
ejpam-2245	462	17	.	.	PUNCT
ejpam-2245	463	1	since	since	SCONJ
ejpam-2245	463	2	they	they	PRON
ejpam-2245	463	3	both	both	PRON
ejpam-2245	463	4	have	have	VERB
ejpam-2245	463	5	free	free	ADJ
ejpam-2245	463	6	rank	rank	NOUN
ejpam-2245	463	7	n	n	PROPN
ejpam-2245	463	8	and	and	CCONJ
ejpam-2245	463	9	length	length	NOUN
ejpam-2245	463	10	2n	2n	NUM
ejpam-2245	463	11	we	we	PRON
ejpam-2245	463	12	have	have	AUX
ejpam-2245	463	13	c⊥	c⊥	X
ejpam-2245	463	14	=	=	SYM
ejpam-2245	463	15	c	c	NOUN
ejpam-2245	463	16	′.	′.	NOUN
ejpam-2245	463	17	let	let	VERB
ejpam-2245	463	18	c	c	X
ejpam-2245	463	19	′′	′′	PROPN
ejpam-2245	463	20	be	be	AUX
ejpam-2245	463	21	the	the	DET
ejpam-2245	463	22	code	code	NOUN
ejpam-2245	463	23	generated	generate	VERB
ejpam-2245	463	24	by	by	ADP
ejpam-2245	463	25	g′′	g′′	PROPN
ejpam-2245	463	26	=	=	SYM
ejpam-2245	463	27	�	�	PROPN
ejpam-2245	463	28	m	m	PROPN
ejpam-2245	463	29	t	t	PROPN
ejpam-2245	463	30	in	in	ADP
ejpam-2245	463	31	�	�	PROPN
ejpam-2245	463	32	.	.	PUNCT
ejpam-2245	464	1	since	since	SCONJ
ejpam-2245	464	2	wt	wt	PROPN
ejpam-2245	464	3	(	(	PUNCT
ejpam-2245	464	4	a	a	NOUN
ejpam-2245	464	5	)	)	PUNCT
ejpam-2245	464	6	=	=	NOUN
ejpam-2245	464	7	wt	wt	PROPN
ejpam-2245	464	8	(	(	PUNCT
ejpam-2245	464	9	−a	−a	NOUN
ejpam-2245	464	10	)	)	PUNCT
ejpam-2245	464	11	for	for	ADP
ejpam-2245	464	12	any	any	DET
ejpam-2245	464	13	a	a	PRON
ejpam-2245	464	14	in	in	ADP
ejpam-2245	464	15	r	r	NOUN
ejpam-2245	464	16	the	the	DET
ejpam-2245	464	17	codes	code	NOUN
ejpam-2245	464	18	c	c	NOUN
ejpam-2245	464	19	′	′	NOUN
ejpam-2245	464	20	and	and	CCONJ
ejpam-2245	464	21	c	c	X
ejpam-2245	464	22	′′	′′	PROPN
ejpam-2245	464	23	have	have	VERB
ejpam-2245	464	24	the	the	DET
ejpam-2245	464	25	same	same	ADJ
ejpam-2245	464	26	weight	weight	NOUN
ejpam-2245	464	27	enumerator	enumerator	NOUN
ejpam-2245	464	28	.	.	PUNCT
ejpam-2245	465	1	in	in	ADP
ejpam-2245	465	2	order	order	NOUN
ejpam-2245	465	3	to	to	PART
ejpam-2245	465	4	conclude	conclude	VERB
ejpam-2245	465	5	that	that	SCONJ
ejpam-2245	465	6	c	c	PROPN
ejpam-2245	465	7	is	be	AUX
ejpam-2245	465	8	formally	formally	ADV
ejpam-2245	465	9	self	self	NOUN
ejpam-2245	465	10	-	-	PUNCT
ejpam-2245	465	11	dual	dual	ADJ
ejpam-2245	465	12	it	it	PRON
ejpam-2245	465	13	is	be	AUX
ejpam-2245	465	14	enough	enough	ADJ
ejpam-2245	465	15	to	to	PART
ejpam-2245	465	16	show	show	VERB
ejpam-2245	465	17	that	that	SCONJ
ejpam-2245	465	18	c	c	VERB
ejpam-2245	465	19	′′	′′	PROPN
ejpam-2245	465	20	is	be	AUX
ejpam-2245	465	21	equivalent	equivalent	ADJ
ejpam-2245	465	22	to	to	ADP
ejpam-2245	465	23	c	c	PROPN
ejpam-2245	465	24	.	.	PUNCT
ejpam-2245	466	1	let	let	VERB
ejpam-2245	466	2	σ	σ	NOUN
ejpam-2245	466	3	be	be	AUX
ejpam-2245	466	4	the	the	DET
ejpam-2245	466	5	permutation	permutation	NOUN
ejpam-2245	466	6	σ	σ	NOUN
ejpam-2245	466	7	=	=	SYM
ejpam-2245	466	8	(	(	PUNCT
ejpam-2245	466	9	1	1	NUM
ejpam-2245	466	10	,	,	PUNCT
ejpam-2245	466	11	n	n	CCONJ
ejpam-2245	466	12	)	)	PUNCT
ejpam-2245	466	13	(	(	PUNCT
ejpam-2245	466	14	2	2	NUM
ejpam-2245	466	15	,	,	PUNCT
ejpam-2245	466	16	n−	n−	NOUN
ejpam-2245	466	17	1	1	NUM
ejpam-2245	466	18	)	)	PUNCT
ejpam-2245	466	19	.	.	PUNCT
ejpam-2245	466	20	.	.	PUNCT
ejpam-2245	467	1	.	.	PUNCT
ejpam-2245	468	1	(	(	PUNCT
ejpam-2245	468	2	k−	k−	NOUN
ejpam-2245	468	3	1	1	NUM
ejpam-2245	468	4	,	,	PUNCT
ejpam-2245	468	5	n−	n−	NOUN
ejpam-2245	468	6	k+	k+	NOUN
ejpam-2245	468	7	2	2	NUM
ejpam-2245	468	8	)	)	PUNCT
ejpam-2245	468	9	(	(	PUNCT
ejpam-2245	468	10	k	k	X
ejpam-2245	468	11	,	,	PUNCT
ejpam-2245	468	12	n−	n−	NOUN
ejpam-2245	468	13	k+	k+	NOUN
ejpam-2245	468	14	1	1	NUM
ejpam-2245	468	15	)	)	PUNCT
ejpam-2245	468	16	where	where	SCONJ
ejpam-2245	468	17	k	k	NOUN
ejpam-2245	468	18	=	=	SYM
ejpam-2245	468	19	⌊n/2⌋	⌊n/2⌋	X
ejpam-2245	468	20	and	and	CCONJ
ejpam-2245	468	21	m	m	PROPN
ejpam-2245	468	22	′	′	NUM
ejpam-2245	468	23	be	be	VERB
ejpam-2245	468	24	the	the	DET
ejpam-2245	468	25	matrix	matrix	NOUN
ejpam-2245	468	26	obtained	obtain	VERB
ejpam-2245	468	27	by	by	ADP
ejpam-2245	468	28	applying	apply	VERB
ejpam-2245	468	29	σ	σ	NOUN
ejpam-2245	468	30	on	on	ADP
ejpam-2245	468	31	rows	row	NOUN
ejpam-2245	468	32	of	of	ADP
ejpam-2245	468	33	m	m	PRON
ejpam-2245	468	34	and	and	CCONJ
ejpam-2245	468	35	let	let	VERB
ejpam-2245	468	36	m	m	PRON
ejpam-2245	468	37	′′	′′	PROPN
ejpam-2245	468	38	be	be	AUX
ejpam-2245	468	39	the	the	DET
ejpam-2245	468	40	matrix	matrix	NOUN
ejpam-2245	468	41	obtained	obtain	VERB
ejpam-2245	468	42	by	by	ADP
ejpam-2245	468	43	applying	apply	VERB
ejpam-2245	468	44	σ	σ	NOUN
ejpam-2245	468	45	on	on	ADP
ejpam-2245	468	46	columns	column	NOUN
ejpam-2245	468	47	of	of	ADP
ejpam-2245	468	48	m	m	PROPN
ejpam-2245	468	49	′.	′.	NOUN
ejpam-2245	468	50	we	we	PRON
ejpam-2245	468	51	observe	observe	VERB
ejpam-2245	468	52	that	that	SCONJ
ejpam-2245	468	53	m	m	VERB
ejpam-2245	468	54	′′	′′	NOUN
ejpam-2245	468	55	=	=	PROPN
ejpam-2245	468	56	m	m	PROPN
ejpam-2245	468	57	t	t	NOUN
ejpam-2245	468	58	.	.	PUNCT
ejpam-2245	469	1	hence	hence	ADV
ejpam-2245	469	2	,	,	PUNCT
ejpam-2245	469	3	m	m	VERB
ejpam-2245	469	4	and	and	CCONJ
ejpam-2245	469	5	m	m	PROPN
ejpam-2245	469	6	t	t	NOUN
ejpam-2245	469	7	are	be	AUX
ejpam-2245	469	8	equivalent	equivalent	ADJ
ejpam-2245	469	9	.	.	PUNCT
ejpam-2245	470	1	similarly	similarly	ADV
ejpam-2245	470	2	,	,	PUNCT
ejpam-2245	470	3	by	by	ADP
ejpam-2245	470	4	applying	apply	VERB
ejpam-2245	470	5	necessary	necessary	ADJ
ejpam-2245	470	6	column	column	NOUN
ejpam-2245	470	7	permutation	permutation	NOUN
ejpam-2245	470	8	we	we	PRON
ejpam-2245	470	9	observe	observe	VERB
ejpam-2245	470	10	g	g	PROPN
ejpam-2245	470	11	and	and	CCONJ
ejpam-2245	470	12	g′′	g′′	PROPN
ejpam-2245	470	13	are	be	AUX
ejpam-2245	470	14	equivalent	equivalent	ADJ
ejpam-2245	470	15	.	.	PUNCT
ejpam-2245	471	1	so	so	ADV
ejpam-2245	471	2	,	,	PUNCT
ejpam-2245	471	3	c	c	PROPN
ejpam-2245	471	4	and	and	CCONJ
ejpam-2245	471	5	c	c	X
ejpam-2245	471	6	′′	′′	PROPN
ejpam-2245	471	7	are	be	AUX
ejpam-2245	471	8	equivalent	equivalent	ADJ
ejpam-2245	471	9	and	and	CCONJ
ejpam-2245	471	10	therefore	therefore	ADV
ejpam-2245	471	11	c	c	PROPN
ejpam-2245	471	12	is	be	AUX
ejpam-2245	471	13	formally	formally	ADV
ejpam-2245	471	14	self	self	NOUN
ejpam-2245	471	15	-	-	PUNCT
ejpam-2245	471	16	dual	dual	ADJ
ejpam-2245	471	17	.	.	PUNCT
ejpam-2245	472	1	theorem	theorem	VERB
ejpam-2245	472	2	14	14	NUM
ejpam-2245	472	3	(	(	PUNCT
ejpam-2245	472	4	construction	construction	NOUN
ejpam-2245	472	5	b	b	NOUN
ejpam-2245	472	6	)	)	PUNCT
ejpam-2245	472	7	.	.	PUNCT
ejpam-2245	473	1	let	let	VERB
ejpam-2245	473	2	m	m	PRON
ejpam-2245	473	3	be	be	AUX
ejpam-2245	473	4	an	an	DET
ejpam-2245	473	5	n×n	n×n	PROPN
ejpam-2245	473	6	λ	λ	NOUN
ejpam-2245	473	7	-	-	ADJ
ejpam-2245	473	8	circulant	circulant	ADJ
ejpam-2245	473	9	matrix	matrix	NOUN
ejpam-2245	473	10	then	then	ADV
ejpam-2245	473	11	the	the	DET
ejpam-2245	473	12	code	code	NOUN
ejpam-2245	473	13	generated	generate	VERB
ejpam-2245	473	14	by	by	ADP
ejpam-2245	473	15	g∗	g∗	PROPN
ejpam-2245	473	16	=	=	SYM
ejpam-2245	473	17			PROPN
ejpam-2245	473	18			NOUN
ejpam-2245	473	19	in+1	in+1	VERB
ejpam-2245	473	20	α	α	PROPN
ejpam-2245	473	21	β	β	X
ejpam-2245	473	22	·	·	PUNCT
ejpam-2245	473	23	·	·	PUNCT
ejpam-2245	473	24	·	·	PUNCT
ejpam-2245	473	25	β	β	X
ejpam-2245	473	26	β	β	X
ejpam-2245	473	27	...	...	PUNCT
ejpam-2245	474	1	m	m	AUX
ejpam-2245	474	2	β	β	X
ejpam-2245	474	3			PROPN
ejpam-2245	474	4			NOUN
ejpam-2245	474	5	is	be	AUX
ejpam-2245	474	6	a	a	DET
ejpam-2245	474	7	formally	formally	ADV
ejpam-2245	474	8	self	self	NOUN
ejpam-2245	474	9	-	-	PUNCT
ejpam-2245	474	10	dual	dual	ADJ
ejpam-2245	474	11	code	code	NOUN
ejpam-2245	474	12	over	over	ADP
ejpam-2245	474	13	r.	r.	PROPN
ejpam-2245	474	14	proof	proof	NOUN
ejpam-2245	474	15	.	.	PUNCT
ejpam-2245	475	1	the	the	DET
ejpam-2245	475	2	proof	proof	NOUN
ejpam-2245	475	3	is	be	AUX
ejpam-2245	475	4	analogous	analogous	ADJ
ejpam-2245	475	5	to	to	ADP
ejpam-2245	475	6	that	that	PRON
ejpam-2245	475	7	of	of	ADP
ejpam-2245	475	8	the	the	DET
ejpam-2245	475	9	theorem	theorem	NOUN
ejpam-2245	475	10	13	13	NUM
ejpam-2245	475	11	and	and	CCONJ
ejpam-2245	475	12	therefore	therefore	ADV
ejpam-2245	475	13	is	be	AUX
ejpam-2245	475	14	skipped	skip	VERB
ejpam-2245	475	15	.	.	PUNCT
ejpam-2245	476	1	remark	remark	NOUN
ejpam-2245	476	2	3	3	NUM
ejpam-2245	476	3	.	.	PUNCT
ejpam-2245	476	4	note	note	VERB
ejpam-2245	476	5	that	that	SCONJ
ejpam-2245	476	6	if	if	SCONJ
ejpam-2245	476	7	r	r	NOUN
ejpam-2245	476	8	is	be	AUX
ejpam-2245	476	9	a	a	DET
ejpam-2245	476	10	ring	ring	NOUN
ejpam-2245	476	11	of	of	ADP
ejpam-2245	476	12	characteristic	characteristic	ADJ
ejpam-2245	476	13	2	2	NUM
ejpam-2245	476	14	then	then	ADV
ejpam-2245	476	15	the	the	DET
ejpam-2245	476	16	constructions	construction	NOUN
ejpam-2245	476	17	give	give	VERB
ejpam-2245	476	18	isodual	isodual	ADJ
ejpam-2245	476	19	codes	code	NOUN
ejpam-2245	476	20	.	.	PUNCT
ejpam-2245	477	1	example	example	NOUN
ejpam-2245	478	1	7	7	NUM
ejpam-2245	478	2	.	.	PUNCT
ejpam-2245	479	1	let	let	VERB
ejpam-2245	479	2	s	s	NOUN
ejpam-2245	479	3	=	=	VERB
ejpam-2245	479	4	f3	f3	PROPN
ejpam-2245	479	5	+	+	CCONJ
ejpam-2245	479	6	vf3	vf3	PROPN
ejpam-2245	479	7	and	and	CCONJ
ejpam-2245	479	8	λ	λ	X
ejpam-2245	479	9	=	=	NOUN
ejpam-2245	480	1	1	1	NUM
ejpam-2245	480	2	+	+	NUM
ejpam-2245	480	3	v	v	NOUN
ejpam-2245	480	4	and	and	CCONJ
ejpam-2245	480	5	n	n	CCONJ
ejpam-2245	480	6	=	=	SYM
ejpam-2245	480	7	5	5	NUM
ejpam-2245	480	8	and	and	CCONJ
ejpam-2245	480	9	m	m	VERB
ejpam-2245	480	10	be	be	AUX
ejpam-2245	480	11	the	the	DET
ejpam-2245	480	12	following	follow	VERB
ejpam-2245	480	13	λ	λ	ADJ
ejpam-2245	480	14	-	-	ADJ
ejpam-2245	480	15	circulant	circulant	ADJ
ejpam-2245	480	16	matrix	matrix	NOUN
ejpam-2245	480	17	m	m	NOUN
ejpam-2245	480	18	=	=	NOUN
ejpam-2245	480	19			NOUN
ejpam-2245	480	20			NOUN
ejpam-2245	480	21	0	0	NUM
ejpam-2245	480	22	1	1	NUM
ejpam-2245	481	1	+	+	NUM
ejpam-2245	481	2	2v	2v	PROPN
ejpam-2245	481	3	2v	2v	PROPN
ejpam-2245	481	4	2	2	NUM
ejpam-2245	481	5	2	2	NUM
ejpam-2245	481	6	2	2	NUM
ejpam-2245	481	7	+	+	NUM
ejpam-2245	481	8	2v	2v	NUM
ejpam-2245	481	9	0	0	SYM
ejpam-2245	481	10	1	1	NUM
ejpam-2245	481	11	+	+	NUM
ejpam-2245	481	12	2v	2v	PROPN
ejpam-2245	481	13	2v	2v	PROPN
ejpam-2245	481	14	2	2	NUM
ejpam-2245	481	15	2	2	NUM
ejpam-2245	481	16	+	+	NUM
ejpam-2245	481	17	2v	2v	NUM
ejpam-2245	481	18	2	2	NUM
ejpam-2245	481	19	+	+	NUM
ejpam-2245	481	20	2v	2v	NUM
ejpam-2245	481	21	0	0	SYM
ejpam-2245	481	22	1	1	NUM
ejpam-2245	481	23	+	+	NUM
ejpam-2245	481	24	2v	2v	PROPN
ejpam-2245	481	25	2v	2v	PROPN
ejpam-2245	481	26	v	v	ADP
ejpam-2245	481	27	2	2	NUM
ejpam-2245	481	28	+	+	NUM
ejpam-2245	481	29	2v	2v	NUM
ejpam-2245	481	30	2	2	NUM
ejpam-2245	481	31	+	+	NUM
ejpam-2245	481	32	2v	2v	NUM
ejpam-2245	481	33	0	0	SYM
ejpam-2245	481	34	1	1	NUM
ejpam-2245	481	35	+	+	NUM
ejpam-2245	481	36	2v	2v	NUM
ejpam-2245	481	37	1	1	NUM
ejpam-2245	481	38	+	+	NUM
ejpam-2245	481	39	2v	2v	PROPN
ejpam-2245	481	40	v	v	ADP
ejpam-2245	481	41	2	2	NUM
ejpam-2245	481	42	+	+	NUM
ejpam-2245	481	43	2v	2v	NUM
ejpam-2245	481	44	2	2	NUM
ejpam-2245	481	45	+	+	NUM
ejpam-2245	481	46	2v	2v	NUM
ejpam-2245	481	47	0	0	PUNCT
ejpam-2245	481	48			PUNCT
ejpam-2245	482	1			NOUN
ejpam-2245	482	2	then	then	ADV
ejpam-2245	482	3	g	g	PROPN
ejpam-2245	482	4	=	=	PROPN
ejpam-2245	482	5	�	�	PROPN
ejpam-2245	482	6	i5	i5	PROPN
ejpam-2245	482	7	m	m	PROPN
ejpam-2245	482	8	�	�	PROPN
ejpam-2245	482	9	generates	generate	VERB
ejpam-2245	482	10	a	a	DET
ejpam-2245	482	11	formally	formally	ADV
ejpam-2245	482	12	self	self	NOUN
ejpam-2245	482	13	-	-	PUNCT
ejpam-2245	482	14	dual	dual	ADJ
ejpam-2245	482	15	code	code	NOUN
ejpam-2245	482	16	of	of	ADP
ejpam-2245	482	17	length	length	NOUN
ejpam-2245	482	18	10	10	NUM
ejpam-2245	482	19	over	over	ADP
ejpam-2245	482	20	f3	f3	PROPN
ejpam-2245	482	21	+	+	CCONJ
ejpam-2245	482	22	vf3	vf3	PROPN
ejpam-2245	482	23	and	and	CCONJ
ejpam-2245	482	24	the	the	DET
ejpam-2245	482	25	gray	gray	ADJ
ejpam-2245	482	26	image	image	NOUN
ejpam-2245	482	27	of	of	ADP
ejpam-2245	482	28	the	the	DET
ejpam-2245	482	29	code	code	NOUN
ejpam-2245	482	30	is	be	AUX
ejpam-2245	482	31	a	a	DET
ejpam-2245	482	32	[	[	X
ejpam-2245	482	33	20,10,7]3	20,10,7]3	NUM
ejpam-2245	482	34	f.s.d	f.s.d	NOUN
ejpam-2245	482	35	.	.	PUNCT
ejpam-2245	483	1	code	code	NOUN
ejpam-2245	483	2	which	which	PRON
ejpam-2245	483	3	has	have	VERB
ejpam-2245	483	4	a	a	DET
ejpam-2245	483	5	better	well	ADJ
ejpam-2245	483	6	distance	distance	NOUN
ejpam-2245	483	7	than	than	ADP
ejpam-2245	483	8	the	the	DET
ejpam-2245	483	9	best	good	ADJ
ejpam-2245	483	10	possible	possible	ADJ
ejpam-2245	483	11	self	self	NOUN
ejpam-2245	483	12	-	-	PUNCT
ejpam-2245	483	13	dual	dual	ADJ
ejpam-2245	483	14	code	code	NOUN
ejpam-2245	483	15	and	and	CCONJ
ejpam-2245	483	16	also	also	ADV
ejpam-2245	483	17	optimal	optimal	ADJ
ejpam-2245	483	18	as	as	ADP
ejpam-2245	483	19	a	a	DET
ejpam-2245	483	20	linear	linear	PROPN
ejpam-2245	483	21	code	code	NOUN
ejpam-2245	483	22	.	.	PUNCT
ejpam-2245	484	1	the	the	DET
ejpam-2245	484	2	code	code	NOUN
ejpam-2245	484	3	has	have	VERB
ejpam-2245	484	4	partial	partial	ADJ
ejpam-2245	484	5	lee	lee	PROPN
ejpam-2245	484	6	weight	weight	NOUN
ejpam-2245	484	7	distribution	distribution	NOUN
ejpam-2245	484	8	1	1	NUM
ejpam-2245	484	9	+	+	NUM
ejpam-2245	484	10	240z7	240z7	NUM
ejpam-2245	484	11	+	+	CCONJ
ejpam-2245	484	12	780z8	780z8	NUM
ejpam-2245	484	13	+	+	CCONJ
ejpam-2245	484	14	.	.	PUNCT
ejpam-2245	484	15	.	.	PUNCT
ejpam-2245	485	1	.	.	PUNCT
ejpam-2245	486	1	and	and	CCONJ
ejpam-2245	486	2	an	an	DET
ejpam-2245	486	3	automorphism	automorphism	NOUN
ejpam-2245	486	4	group	group	NOUN
ejpam-2245	486	5	of	of	ADP
ejpam-2245	486	6	order	order	NOUN
ejpam-2245	486	7	40	40	NUM
ejpam-2245	486	8	.	.	PUNCT
ejpam-2245	487	1	the	the	DET
ejpam-2245	487	2	computational	computational	ADJ
ejpam-2245	487	3	results	result	NOUN
ejpam-2245	487	4	for	for	ADP
ejpam-2245	487	5	constructions	construction	NOUN
ejpam-2245	487	6	a	a	PRON
ejpam-2245	487	7	and	and	CCONJ
ejpam-2245	487	8	b	b	NOUN
ejpam-2245	487	9	are	be	AUX
ejpam-2245	487	10	given	give	VERB
ejpam-2245	487	11	in	in	ADP
ejpam-2245	487	12	tables	table	NOUN
ejpam-2245	487	13	2	2	NUM
ejpam-2245	487	14	and	and	CCONJ
ejpam-2245	487	15	3	3	NUM
ejpam-2245	487	16	where	where	SCONJ
ejpam-2245	487	17	in	in	ADP
ejpam-2245	487	18	order	order	NOUN
ejpam-2245	487	19	to	to	PART
ejpam-2245	487	20	save	save	VERB
ejpam-2245	487	21	space	space	NOUN
ejpam-2245	487	22	the	the	DET
ejpam-2245	487	23	element	element	NOUN
ejpam-2245	487	24	x	x	PUNCT
ejpam-2245	488	1	+	+	CCONJ
ejpam-2245	488	2	yv	yv	PROPN
ejpam-2245	488	3	is	be	AUX
ejpam-2245	488	4	abbreviated	abbreviate	VERB
ejpam-2245	488	5	as	as	ADP
ejpam-2245	488	6	x	x	PROPN
ejpam-2245	488	7	y	y	PROPN
ejpam-2245	488	8	,	,	PUNCT
ejpam-2245	488	9	the	the	DET
ejpam-2245	488	10	elements	element	NOUN
ejpam-2245	488	11	for	for	ADP
ejpam-2245	488	12	the	the	DET
ejpam-2245	488	13	first	first	ADJ
ejpam-2245	488	14	row	row	NOUN
ejpam-2245	488	15	a.	a.	PROPN
ejpam-2245	488	16	batoul	batoul	PROPN
ejpam-2245	488	17	,	,	PUNCT
ejpam-2245	488	18	k.	k.	PROPN
ejpam-2245	488	19	guenda	guenda	PROPN
ejpam-2245	488	20	,	,	PUNCT
ejpam-2245	488	21	a.	a.	PROPN
ejpam-2245	488	22	kaya	kaya	PROPN
ejpam-2245	488	23	,	,	PUNCT
ejpam-2245	488	24	b.	b.	PROPN
ejpam-2245	488	25	yildiz	yildiz	PROPN
ejpam-2245	488	26	/	/	SYM
ejpam-2245	488	27	eur	eur	PROPN
ejpam-2245	488	28	.	.	PUNCT
ejpam-2245	489	1	j.	j.	PROPN
ejpam-2245	489	2	pure	pure	PROPN
ejpam-2245	489	3	appl	appl	PROPN
ejpam-2245	489	4	.	.	PROPN
ejpam-2245	489	5	math	math	PROPN
ejpam-2245	489	6	,	,	PUNCT
ejpam-2245	489	7	8	8	NUM
ejpam-2245	489	8	(	(	PUNCT
ejpam-2245	489	9	2015	2015	NUM
ejpam-2245	489	10	)	)	PUNCT
ejpam-2245	489	11	,	,	PUNCT
ejpam-2245	489	12	64	64	NUM
ejpam-2245	489	13	-	-	SYM
ejpam-2245	489	14	80	80	NUM
ejpam-2245	489	15	78	78	NUM
ejpam-2245	489	16	of	of	ADP
ejpam-2245	489	17	m	m	NOUN
ejpam-2245	489	18	are	be	AUX
ejpam-2245	489	19	separated	separate	VERB
ejpam-2245	489	20	by	by	ADP
ejpam-2245	489	21	|	|	ADV
ejpam-2245	489	22	and	and	CCONJ
ejpam-2245	489	23	ad	ad	NOUN
ejpam-2245	489	24	denotes	denote	VERB
ejpam-2245	489	25	the	the	DET
ejpam-2245	489	26	number	number	NOUN
ejpam-2245	489	27	of	of	ADP
ejpam-2245	489	28	codewords	codeword	NOUN
ejpam-2245	489	29	with	with	ADP
ejpam-2245	489	30	minimum	minimum	ADJ
ejpam-2245	489	31	weight	weight	NOUN
ejpam-2245	489	32	.	.	PUNCT
ejpam-2245	490	1	we	we	PRON
ejpam-2245	490	2	use	use	VERB
ejpam-2245	490	3	∗	∗	NOUN
ejpam-2245	490	4	to	to	PART
ejpam-2245	490	5	indicate	indicate	VERB
ejpam-2245	490	6	that	that	SCONJ
ejpam-2245	490	7	the	the	DET
ejpam-2245	490	8	code	code	NOUN
ejpam-2245	490	9	is	be	AUX
ejpam-2245	490	10	optimal	optimal	ADJ
ejpam-2245	490	11	as	as	ADP
ejpam-2245	490	12	a	a	DET
ejpam-2245	490	13	linear	linear	ADJ
ejpam-2245	490	14	code	code	NOUN
ejpam-2245	490	15	and	and	CCONJ
ejpam-2245	490	16	similarly	similarly	ADV
ejpam-2245	490	17	b	b	PROPN
ejpam-2245	490	18	indicates	indicate	VERB
ejpam-2245	490	19	that	that	SCONJ
ejpam-2245	490	20	the	the	DET
ejpam-2245	490	21	code	code	NOUN
ejpam-2245	490	22	has	have	VERB
ejpam-2245	490	23	the	the	DET
ejpam-2245	490	24	best	well	ADV
ejpam-2245	490	25	known	know	VERB
ejpam-2245	490	26	distance	distance	NOUN
ejpam-2245	490	27	among	among	ADP
ejpam-2245	490	28	the	the	DET
ejpam-2245	490	29	linear	linear	ADJ
ejpam-2245	490	30	codes	code	NOUN
ejpam-2245	490	31	of	of	ADP
ejpam-2245	490	32	these	these	DET
ejpam-2245	490	33	parameters	parameter	NOUN
ejpam-2245	490	34	,	,	PUNCT
ejpam-2245	490	35	according	accord	VERB
ejpam-2245	490	36	to	to	ADP
ejpam-2245	490	37	the	the	DET
ejpam-2245	490	38	online	online	ADJ
ejpam-2245	490	39	database	database	NOUN
ejpam-2245	490	40	in	in	ADP
ejpam-2245	490	41	[	[	X
ejpam-2245	490	42	3	3	NUM
ejpam-2245	490	43	]	]	PUNCT
ejpam-2245	490	44	.	.	PUNCT
ejpam-2245	491	1	remark	remark	PROPN
ejpam-2245	491	2	4	4	NUM
ejpam-2245	491	3	.	.	PUNCT
ejpam-2245	491	4	note	note	VERB
ejpam-2245	491	5	that	that	SCONJ
ejpam-2245	491	6	the	the	DET
ejpam-2245	491	7	codes	code	NOUN
ejpam-2245	491	8	with	with	ADP
ejpam-2245	491	9	parameters	parameter	NOUN
ejpam-2245	491	10	[	[	X
ejpam-2245	491	11	32,16,11]5	32,16,11]5	NUM
ejpam-2245	491	12	,	,	PUNCT
ejpam-2245	491	13	[	[	X
ejpam-2245	491	14	32,16,10]3	32,16,10]3	NUM
ejpam-2245	491	15	and	and	CCONJ
ejpam-2245	491	16	[	[	X
ejpam-2245	491	17	20,10,7]3	20,10,7]3	NUM
ejpam-2245	491	18	in	in	ADP
ejpam-2245	491	19	tables	table	NOUN
ejpam-2245	491	20	2	2	NUM
ejpam-2245	491	21	and	and	CCONJ
ejpam-2245	491	22	3	3	NUM
ejpam-2245	491	23	have	have	VERB
ejpam-2245	491	24	better	well	ADJ
ejpam-2245	491	25	minimum	minimum	ADJ
ejpam-2245	491	26	distances	distance	NOUN
ejpam-2245	491	27	than	than	ADP
ejpam-2245	491	28	the	the	DET
ejpam-2245	491	29	best	well	ADV
ejpam-2245	491	30	known	know	VERB
ejpam-2245	491	31	self	self	NOUN
ejpam-2245	491	32	-	-	PUNCT
ejpam-2245	491	33	dual	dual	ADJ
ejpam-2245	491	34	codes	code	NOUN
ejpam-2245	491	35	for	for	ADP
ejpam-2245	491	36	these	these	DET
ejpam-2245	491	37	parameters	parameter	NOUN
ejpam-2245	491	38	.	.	PUNCT
ejpam-2245	492	1	table	table	NOUN
ejpam-2245	492	2	2	2	NUM
ejpam-2245	492	3	:	:	PUNCT
ejpam-2245	492	4	good	good	ADJ
ejpam-2245	492	5	formally	formally	ADV
ejpam-2245	492	6	self	self	NOUN
ejpam-2245	492	7	-	-	PUNCT
ejpam-2245	492	8	dual	dual	ADJ
ejpam-2245	492	9	codes	code	NOUN
ejpam-2245	492	10	by	by	ADP
ejpam-2245	492	11	construction	construction	NOUN
ejpam-2245	492	12	a	a	DET
ejpam-2245	492	13	p	p	NOUN
ejpam-2245	492	14	n	n	ADP
ejpam-2245	492	15	λ	λ	PROPN
ejpam-2245	492	16	first	first	ADJ
ejpam-2245	492	17	row	row	NOUN
ejpam-2245	492	18	of	of	ADP
ejpam-2245	492	19	m	m	PROPN
ejpam-2245	492	20	ϕ	ϕ	NOUN
ejpam-2245	492	21	(	(	PUNCT
ejpam-2245	492	22	c	c	NOUN
ejpam-2245	492	23	)	)	PUNCT
ejpam-2245	492	24	|aut|	|aut|	NOUN
ejpam-2245	492	25	ad	ad	NOUN
ejpam-2245	492	26	3	3	NUM
ejpam-2245	492	27	5	5	NUM
ejpam-2245	492	28	1	1	NUM
ejpam-2245	492	29	(	(	PUNCT
ejpam-2245	492	30	22|10|20|01|21	22|10|20|01|21	NUM
ejpam-2245	492	31	)	)	PUNCT
ejpam-2245	493	1	[	[	X
ejpam-2245	493	2	20,10,7]∗3	20,10,7]∗3	NUM
ejpam-2245	493	3	20	20	NUM
ejpam-2245	493	4	200	200	NUM
ejpam-2245	493	5	3	3	NUM
ejpam-2245	493	6	7	7	NUM
ejpam-2245	493	7	1−	1−	NUM
ejpam-2245	493	8	2v	2v	X
ejpam-2245	493	9	(	(	PUNCT
ejpam-2245	493	10	21|01|02|11|11|10|10	21|01|02|11|11|10|10	NUM
ejpam-2245	493	11	)	)	PUNCT
ejpam-2245	494	1	[	[	X
ejpam-2245	494	2	28,14,9]b3	28,14,9]b3	NUM
ejpam-2245	494	3	28	28	NUM
ejpam-2245	494	4	924	924	NUM
ejpam-2245	494	5	3	3	NUM
ejpam-2245	494	6	8	8	NUM
ejpam-2245	494	7	1−	1−	NUM
ejpam-2245	494	8	2v	2v	PROPN
ejpam-2245	494	9	(	(	PUNCT
ejpam-2245	494	10	22|01|02|22|21|12|01|01	22|01|02|22|21|12|01|01	NUM
ejpam-2245	494	11	)	)	PUNCT
ejpam-2245	495	1	[	[	X
ejpam-2245	495	2	32,16,10]b3	32,16,10]b3	NUM
ejpam-2245	495	3	64	64	NUM
ejpam-2245	495	4	2208	2208	NUM
ejpam-2245	495	5	3	3	NUM
ejpam-2245	495	6	11	11	NUM
ejpam-2245	495	7	1	1	NUM
ejpam-2245	495	8	(	(	PUNCT
ejpam-2245	495	9	11|11|21|02|01|20|22|12|22|12|10	11|11|21|02|01|20|22|12|22|12|10	NUM
ejpam-2245	495	10	)	)	PUNCT
ejpam-2245	496	1	[	[	X
ejpam-2245	496	2	44,22,11]3	44,22,11]3	NUM
ejpam-2245	496	3	44	44	NUM
ejpam-2245	496	4	2948	2948	NUM
ejpam-2245	496	5	5	5	NUM
ejpam-2245	496	6	5	5	NUM
ejpam-2245	496	7	1−	1−	NUM
ejpam-2245	496	8	2v	2v	PROPN
ejpam-2245	496	9	(	(	PUNCT
ejpam-2245	496	10	03|14|33|42|34	03|14|33|42|34	PROPN
ejpam-2245	496	11	)	)	PUNCT
ejpam-2245	497	1	[	[	X
ejpam-2245	497	2	20,10,8]∗5	20,10,8]∗5	NOUN
ejpam-2245	497	3	40	40	NUM
ejpam-2245	497	4	1000	1000	NUM
ejpam-2245	497	5	5	5	NUM
ejpam-2245	497	6	6	6	NUM
ejpam-2245	497	7	1−	1−	NUM
ejpam-2245	497	8	2v	2v	PROPN
ejpam-2245	497	9	(	(	PUNCT
ejpam-2245	497	10	23|32|01|31|11|21	23|32|01|31|11|21	NUM
ejpam-2245	497	11	)	)	PUNCT
ejpam-2245	498	1	[	[	X
ejpam-2245	498	2	24,12,9]b5	24,12,9]b5	NUM
ejpam-2245	498	3	48	48	NUM
ejpam-2245	498	4	1536	1536	NUM
ejpam-2245	498	5	5	5	NUM
ejpam-2245	498	6	7	7	NUM
ejpam-2245	498	7	1−	1−	NUM
ejpam-2245	498	8	2v	2v	X
ejpam-2245	498	9	(	(	PUNCT
ejpam-2245	498	10	44|31|20|11|23|21|32	44|31|20|11|23|21|32	NUM
ejpam-2245	498	11	)	)	PUNCT
ejpam-2245	499	1	[	[	X
ejpam-2245	499	2	28,14,10]5	28,14,10]5	NUM
ejpam-2245	499	3	56	56	NUM
ejpam-2245	499	4	1876	1876	NUM
ejpam-2245	499	5	5	5	NUM
ejpam-2245	499	6	8	8	NUM
ejpam-2245	499	7	1−	1−	NUM
ejpam-2245	499	8	2v	2v	PROPN
ejpam-2245	499	9	(	(	PUNCT
ejpam-2245	499	10	42|00|42|11|22|30|11|14	42|00|42|11|22|30|11|14	NOUN
ejpam-2245	499	11	)	)	PUNCT
ejpam-2245	500	1	[	[	X
ejpam-2245	500	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	500	3	64	64	NUM
ejpam-2245	500	4	3136	3136	NUM
ejpam-2245	500	5	5	5	NUM
ejpam-2245	500	6	8	8	NUM
ejpam-2245	500	7	1−	1−	NUM
ejpam-2245	500	8	2v	2v	PROPN
ejpam-2245	500	9	(	(	PUNCT
ejpam-2245	500	10	00|22|42|10|44|31|10|32	00|22|42|10|44|31|10|32	NOUN
ejpam-2245	500	11	)	)	PUNCT
ejpam-2245	501	1	[	[	X
ejpam-2245	501	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	501	3	64	64	NUM
ejpam-2245	501	4	3584	3584	NUM
ejpam-2245	501	5	5	5	NUM
ejpam-2245	501	6	8	8	NUM
ejpam-2245	501	7	1−	1−	NUM
ejpam-2245	501	8	2v	2v	PROPN
ejpam-2245	501	9	(	(	PUNCT
ejpam-2245	501	10	01|02|10|32|30|31|12|34	01|02|10|32|30|31|12|34	PROPN
ejpam-2245	501	11	)	)	PUNCT
ejpam-2245	502	1	[	[	X
ejpam-2245	502	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	502	3	64	64	NUM
ejpam-2245	502	4	3776	3776	NUM
ejpam-2245	502	5	5	5	NUM
ejpam-2245	502	6	8	8	NUM
ejpam-2245	502	7	1	1	NUM
ejpam-2245	502	8	(	(	PUNCT
ejpam-2245	502	9	32|13|12|20|11|12|23|32	32|13|12|20|11|12|23|32	NUM
ejpam-2245	502	10	)	)	PUNCT
ejpam-2245	503	1	[	[	X
ejpam-2245	503	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	503	3	64	64	NUM
ejpam-2245	503	4	3328	3328	NUM
ejpam-2245	503	5	5	5	NUM
ejpam-2245	503	6	8	8	NUM
ejpam-2245	503	7	1	1	NUM
ejpam-2245	503	8	(	(	PUNCT
ejpam-2245	503	9	34|03|33|40|12|21|00|02	34|03|33|40|12|21|00|02	NUM
ejpam-2245	503	10	)	)	PUNCT
ejpam-2245	504	1	[	[	X
ejpam-2245	504	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	504	3	64	64	NUM
ejpam-2245	504	4	3264	3264	NUM
ejpam-2245	504	5	5	5	NUM
ejpam-2245	504	6	9	9	NUM
ejpam-2245	504	7	1−	1−	NUM
ejpam-2245	504	8	2v	2v	NUM
ejpam-2245	504	9	(	(	PUNCT
ejpam-2245	504	10	11|30|32|42|23|43|40|10|04	11|30|32|42|23|43|40|10|04	NUM
ejpam-2245	504	11	)	)	PUNCT
ejpam-2245	505	1	[	[	X
ejpam-2245	505	2	36,18,12]b5	36,18,12]b5	NUM
ejpam-2245	505	3	72	72	NUM
ejpam-2245	505	4	4788	4788	NUM
ejpam-2245	505	5	5	5	NUM
ejpam-2245	505	6	11	11	NUM
ejpam-2245	505	7	1−	1−	NUM
ejpam-2245	505	8	2v	2v	PROPN
ejpam-2245	505	9	(	(	PUNCT
ejpam-2245	505	10	13|32|43|12|23|23|34|13|43|30|43	13|32|43|12|23|23|34|13|43|30|43	NUM
ejpam-2245	505	11	)	)	PUNCT
ejpam-2245	506	1	[	[	X
ejpam-2245	506	2	44,22,13]b5	44,22,13]b5	NUM
ejpam-2245	506	3	88	88	NUM
ejpam-2245	506	4	1056	1056	NUM
ejpam-2245	506	5	5	5	NUM
ejpam-2245	506	6	12	12	NUM
ejpam-2245	506	7	1−	1−	NUM
ejpam-2245	506	8	2v	2v	PROPN
ejpam-2245	506	9	(	(	PUNCT
ejpam-2245	506	10	11|00|23|22|44|32|43|23|31|03|00|42	11|00|23|22|44|32|43|23|31|03|00|42	NUM
ejpam-2245	506	11	)	)	PUNCT
ejpam-2245	507	1	[	[	X
ejpam-2245	507	2	48,24,14]5	48,24,14]5	NUM
ejpam-2245	507	3	96	96	NUM
ejpam-2245	507	4	1632	1632	NUM
ejpam-2245	507	5	5	5	NUM
ejpam-2245	507	6	13	13	NUM
ejpam-2245	507	7	1−	1−	NUM
ejpam-2245	507	8	2v	2v	PROPN
ejpam-2245	507	9	(	(	PUNCT
ejpam-2245	507	10	02|13|33|03|24|02|24|42|14|30|04|43|24	02|13|33|03|24|02|24|42|14|30|04|43|24	PROPN
ejpam-2245	507	11	)	)	PUNCT
ejpam-2245	508	1	[	[	X
ejpam-2245	508	2	52,26,15]b5	52,26,15]b5	NOUN
ejpam-2245	508	3	104	104	NUM
ejpam-2245	508	4	3328	3328	NUM
ejpam-2245	508	5	5	5	NUM
ejpam-2245	509	1	13	13	NUM
ejpam-2245	509	2	1	1	NUM
ejpam-2245	509	3	+	+	NUM
ejpam-2245	509	4	v	v	PROPN
ejpam-2245	509	5	(	(	PUNCT
ejpam-2245	509	6	40|03|24|02|43|32|34|13|13|33|34|42|04	40|03|24|02|43|32|34|13|13|33|34|42|04	NOUN
ejpam-2245	509	7	)	)	PUNCT
ejpam-2245	510	1	[	[	X
ejpam-2245	510	2	52,26,15]b5	52,26,15]b5	NOUN
ejpam-2245	510	3	104	104	NUM
ejpam-2245	510	4	2912	2912	NUM
ejpam-2245	510	5	5	5	NUM
ejpam-2245	510	6	13	13	NUM
ejpam-2245	510	7	1	1	NUM
ejpam-2245	510	8	+	+	NUM
ejpam-2245	510	9	v	v	NOUN
ejpam-2245	510	10	(	(	PUNCT
ejpam-2245	510	11	12|40|00|13|32|31|11|44|03|42|03|03|24	12|40|00|13|32|31|11|44|03|42|03|03|24	PROPN
ejpam-2245	510	12	)	)	PUNCT
ejpam-2245	511	1	[	[	X
ejpam-2245	511	2	52,26,15]b5	52,26,15]b5	NOUN
ejpam-2245	511	3	104	104	NUM
ejpam-2245	511	4	3224	3224	NUM
ejpam-2245	511	5	7	7	NUM
ejpam-2245	511	6	6	6	NUM
ejpam-2245	511	7	1−	1−	NUM
ejpam-2245	511	8	2v	2v	PROPN
ejpam-2245	511	9	(	(	PUNCT
ejpam-2245	511	10	60|31|24|64|55|50	60|31|24|64|55|50	NOUN
ejpam-2245	511	11	)	)	PUNCT
ejpam-2245	512	1	[	[	X
ejpam-2245	512	2	24,12,9]7	24,12,9]7	NUM
ejpam-2245	512	3	72	72	NUM
ejpam-2245	512	4	504	504	NUM
ejpam-2245	512	5	7	7	NUM
ejpam-2245	512	6	7	7	NUM
ejpam-2245	512	7	1−	1−	NUM
ejpam-2245	512	8	2v	2v	X
ejpam-2245	512	9	(	(	PUNCT
ejpam-2245	512	10	52|04|03|26|15|56|62	52|04|03|26|15|56|62	NUM
ejpam-2245	512	11	)	)	PUNCT
ejpam-2245	513	1	[	[	X
ejpam-2245	513	2	28,14,10]7	28,14,10]7	NUM
ejpam-2245	513	3	84	84	NUM
ejpam-2245	513	4	168	168	NUM
ejpam-2245	513	5	7	7	NUM
ejpam-2245	513	6	9	9	NUM
ejpam-2245	513	7	1	1	NUM
ejpam-2245	513	8	(	(	PUNCT
ejpam-2245	513	9	03|00|33|02|15|53|65|50|06	03|00|33|02|15|53|65|50|06	NOUN
ejpam-2245	513	10	)	)	PUNCT
ejpam-2245	514	1	[	[	X
ejpam-2245	514	2	36,18,12]7	36,18,12]7	NUM
ejpam-2245	514	3	108	108	NUM
ejpam-2245	514	4	1458	1458	NUM
ejpam-2245	514	5	7	7	NUM
ejpam-2245	514	6	10	10	NUM
ejpam-2245	514	7	1−	1−	NUM
ejpam-2245	514	8	2v	2v	PROPN
ejpam-2245	514	9	(	(	PUNCT
ejpam-2245	514	10	03|15|32|34|06|51|44|10|63|54	03|15|32|34|06|51|44|10|63|54	NOUN
ejpam-2245	514	11	)	)	PUNCT
ejpam-2245	515	1	[	[	X
ejpam-2245	515	2	40,20,13]7	40,20,13]7	NUM
ejpam-2245	515	3	120	120	NUM
ejpam-2245	515	4	1920	1920	NUM
ejpam-2245	515	5	7	7	NUM
ejpam-2245	515	6	11	11	NUM
ejpam-2245	515	7	1−	1−	NUM
ejpam-2245	515	8	2v	2v	PROPN
ejpam-2245	515	9	(	(	PUNCT
ejpam-2245	515	10	43|63|22|11|61|26|06|60|25|14|26	43|63|22|11|61|26|06|60|25|14|26	NUM
ejpam-2245	515	11	)	)	PUNCT
ejpam-2245	516	1	[	[	X
ejpam-2245	516	2	44,22,14]7	44,22,14]7	NUM
ejpam-2245	516	3	132	132	NUM
ejpam-2245	516	4	924	924	NUM
ejpam-2245	516	5	references	reference	NOUN
ejpam-2245	516	6	79	79	NUM
ejpam-2245	516	7	table	table	NOUN
ejpam-2245	516	8	3	3	NUM
ejpam-2245	516	9	:	:	PUNCT
ejpam-2245	516	10	good	good	ADJ
ejpam-2245	516	11	formally	formally	ADV
ejpam-2245	516	12	self	self	NOUN
ejpam-2245	516	13	-	-	PUNCT
ejpam-2245	516	14	dual	dual	ADJ
ejpam-2245	516	15	codes	code	NOUN
ejpam-2245	516	16	by	by	ADP
ejpam-2245	516	17	construction	construction	NOUN
ejpam-2245	516	18	b	b	PROPN
ejpam-2245	516	19	p	p	NOUN
ejpam-2245	516	20	n	n	ADP
ejpam-2245	516	21	λ	λ	PROPN
ejpam-2245	516	22	first	first	ADJ
ejpam-2245	516	23	row	row	NOUN
ejpam-2245	516	24	of	of	ADP
ejpam-2245	516	25	m	m	PROPN
ejpam-2245	516	26	α	α	NOUN
ejpam-2245	516	27	|	|	ADV
ejpam-2245	516	28	β	β	X
ejpam-2245	516	29	ϕ	ϕ	X
ejpam-2245	516	30	(	(	PUNCT
ejpam-2245	516	31	c	c	NOUN
ejpam-2245	516	32	)	)	PUNCT
ejpam-2245	516	33	|aut|	|aut|	NOUN
ejpam-2245	516	34	ad	ad	NOUN
ejpam-2245	516	35	3	3	NUM
ejpam-2245	516	36	4	4	NUM
ejpam-2245	516	37	1	1	NUM
ejpam-2245	516	38	+	+	NUM
ejpam-2245	516	39	v	v	NUM
ejpam-2245	516	40	(	(	PUNCT
ejpam-2245	516	41	11|12|00|02	11|12|00|02	NUM
ejpam-2245	516	42	)	)	PUNCT
ejpam-2245	516	43	11|11	11|11	NOUN
ejpam-2245	517	1	[	[	X
ejpam-2245	517	2	20,10,6]3	20,10,6]3	NUM
ejpam-2245	517	3	4	4	NUM
ejpam-2245	517	4	48	48	NUM
ejpam-2245	517	5	3	3	NUM
ejpam-2245	517	6	5	5	NUM
ejpam-2245	517	7	1	1	NUM
ejpam-2245	517	8	(	(	PUNCT
ejpam-2245	517	9	02|02|20|12|20	02|02|20|12|20	PROPN
ejpam-2245	517	10	)	)	PUNCT
ejpam-2245	517	11	12|20	12|20	NOUN
ejpam-2245	518	1	[	[	X
ejpam-2245	518	2	24,12,8]3	24,12,8]3	NUM
ejpam-2245	518	3	40	40	NUM
ejpam-2245	518	4	458	458	NUM
ejpam-2245	518	5	3	3	NUM
ejpam-2245	518	6	6	6	NUM
ejpam-2245	518	7	1	1	NUM
ejpam-2245	518	8	+	+	NUM
ejpam-2245	518	9	v	v	PROPN
ejpam-2245	518	10	(	(	PUNCT
ejpam-2245	518	11	00|21|21|22|10|00	00|21|21|22|10|00	NOUN
ejpam-2245	518	12	)	)	PUNCT
ejpam-2245	518	13	22|22	22|22	NOUN
ejpam-2245	519	1	[	[	X
ejpam-2245	519	2	28,14,8]3	28,14,8]3	NUM
ejpam-2245	519	3	4	4	NUM
ejpam-2245	519	4	210	210	NUM
ejpam-2245	519	5	3	3	NUM
ejpam-2245	519	6	7	7	NUM
ejpam-2245	519	7	1	1	NUM
ejpam-2245	519	8	(	(	PUNCT
ejpam-2245	519	9	02|01|22|22|00|12|00	02|01|22|22|00|12|00	NUM
ejpam-2245	519	10	)	)	PUNCT
ejpam-2245	519	11	11|22	11|22	PROPN
ejpam-2245	520	1	[	[	X
ejpam-2245	520	2	32,16,9]3	32,16,9]3	NUM
ejpam-2245	520	3	28	28	NUM
ejpam-2245	520	4	340	340	NUM
ejpam-2245	520	5	3	3	NUM
ejpam-2245	520	6	9	9	NUM
ejpam-2245	520	7	1	1	NUM
ejpam-2245	520	8	(	(	PUNCT
ejpam-2245	520	9	02|21|20|02|10|10|20|12|12	02|21|20|02|10|10|20|12|12	PROPN
ejpam-2245	520	10	)	)	PUNCT
ejpam-2245	520	11	20|10	20|10	NOUN
ejpam-2245	521	1	[	[	X
ejpam-2245	521	2	40,20,11]3	40,20,11]3	NUM
ejpam-2245	521	3	36	36	NUM
ejpam-2245	521	4	1232	1232	NUM
ejpam-2245	521	5	3	3	NUM
ejpam-2245	521	6	10	10	NUM
ejpam-2245	521	7	1	1	NUM
ejpam-2245	521	8	(	(	PUNCT
ejpam-2245	521	9	00|01|11|01|00|20|22|11|12|22	00|01|11|01|00|20|22|11|12|22	NOUN
ejpam-2245	521	10	)	)	PUNCT
ejpam-2245	521	11	02|22	02|22	NOUN
ejpam-2245	522	1	[	[	X
ejpam-2245	522	2	44,22,11]3	44,22,11]3	NUM
ejpam-2245	522	3	40	40	NUM
ejpam-2245	522	4	280	280	NUM
ejpam-2245	522	5	5	5	NUM
ejpam-2245	522	6	4	4	NUM
ejpam-2245	522	7	1	1	NUM
ejpam-2245	522	8	+	+	NUM
ejpam-2245	522	9	v	v	PROPN
ejpam-2245	522	10	(	(	PUNCT
ejpam-2245	522	11	01|11|10|20	01|11|10|20	NOUN
ejpam-2245	522	12	)	)	PUNCT
ejpam-2245	522	13	11|22	11|22	PROPN
ejpam-2245	523	1	[	[	X
ejpam-2245	523	2	20,10,7]5	20,10,7]5	NUM
ejpam-2245	523	3	8	8	NUM
ejpam-2245	523	4	112	112	NUM
ejpam-2245	523	5	5	5	NUM
ejpam-2245	523	6	5	5	NUM
ejpam-2245	523	7	1	1	NUM
ejpam-2245	523	8	(	(	PUNCT
ejpam-2245	523	9	12|10|00|10|22	12|10|00|10|22	NUM
ejpam-2245	523	10	)	)	PUNCT
ejpam-2245	523	11	20|11	20|11	NOUN
ejpam-2245	524	1	[	[	X
ejpam-2245	524	2	24,12,9]5	24,12,9]5	NUM
ejpam-2245	524	3	40	40	NUM
ejpam-2245	524	4	1696	1696	NUM
ejpam-2245	524	5	5	5	NUM
ejpam-2245	524	6	6	6	NUM
ejpam-2245	524	7	1	1	NUM
ejpam-2245	524	8	(	(	PUNCT
ejpam-2245	524	9	00|20|12|22|10|11	00|20|12|22|10|11	PROPN
ejpam-2245	524	10	)	)	PUNCT
ejpam-2245	524	11	20|11	20|11	NOUN
ejpam-2245	525	1	[	[	X
ejpam-2245	525	2	28,14,10]5	28,14,10]5	NUM
ejpam-2245	525	3	48	48	NUM
ejpam-2245	525	4	1632	1632	NUM
ejpam-2245	525	5	5	5	NUM
ejpam-2245	525	6	7	7	NUM
ejpam-2245	525	7	1	1	NUM
ejpam-2245	525	8	(	(	PUNCT
ejpam-2245	525	9	21|01|11|22|11|20|20	21|01|11|22|11|20|20	NUM
ejpam-2245	525	10	)	)	PUNCT
ejpam-2245	525	11	01|11	01|11	NOUN
ejpam-2245	526	1	[	[	X
ejpam-2245	526	2	32,16,11]b5	32,16,11]b5	NUM
ejpam-2245	526	3	56	56	NUM
ejpam-2245	526	4	3152	3152	NUM
ejpam-2245	526	5	5	5	NUM
ejpam-2245	526	6	8	8	NUM
ejpam-2245	526	7	1−	1−	NUM
ejpam-2245	526	8	2v	2v	PROPN
ejpam-2245	526	9	(	(	PUNCT
ejpam-2245	526	10	01|10|01|21|00|00|22	01|10|01|21|00|00|22	PROPN
ejpam-2245	526	11	)	)	PUNCT
ejpam-2245	526	12	12|20	12|20	NOUN
ejpam-2245	527	1	[	[	X
ejpam-2245	527	2	36,18,11]5	36,18,11]5	NUM
ejpam-2245	527	3	8	8	NUM
ejpam-2245	527	4	456	456	NUM
ejpam-2245	527	5	5	5	NUM
ejpam-2245	527	6	10	10	NUM
ejpam-2245	527	7	1	1	NUM
ejpam-2245	527	8	+	+	NUM
ejpam-2245	527	9	v	v	PROPN
ejpam-2245	527	10	(	(	PUNCT
ejpam-2245	527	11	14|22|14|14|44|13|34|33|43|14	14|22|14|14|44|13|34|33|43|14	NUM
ejpam-2245	527	12	)	)	PUNCT
ejpam-2245	527	13	34|30	34|30	NOUN
ejpam-2245	527	14	[	[	X
ejpam-2245	527	15	44,22,12]5	44,22,12]5	NUM
ejpam-2245	527	16	8	8	NUM
ejpam-2245	527	17	144	144	NUM
ejpam-2245	527	18	5	5	NUM
ejpam-2245	527	19	11	11	NUM
ejpam-2245	527	20	1−	1−	NUM
ejpam-2245	527	21	2v	2v	PROPN
ejpam-2245	527	22	(	(	PUNCT
ejpam-2245	527	23	13|20|24|40|01|44|00|14|12|04|00	13|20|24|40|01|44|00|14|12|04|00	NUM
ejpam-2245	527	24	)	)	PUNCT
ejpam-2245	527	25	33|31	33|31	NOUN
ejpam-2245	528	1	[	[	PUNCT
ejpam-2245	528	2	48,24,13]5	48,24,13]5	NUM
ejpam-2245	528	3	3	3	NUM
ejpam-2245	528	4	232	232	NUM
ejpam-2245	528	5	5	5	NUM
ejpam-2245	528	6	12	12	NUM
ejpam-2245	528	7	1−	1−	NUM
ejpam-2245	528	8	2v	2v	PROPN
ejpam-2245	528	9	(	(	PUNCT
ejpam-2245	528	10	14|40|32|23|01|22|22|31|13|33|34|30	14|40|32|23|01|22|22|31|13|33|34|30	PROPN
ejpam-2245	528	11	)	)	PUNCT
ejpam-2245	528	12	24|31	24|31	NOUN
ejpam-2245	529	1	[	[	X
ejpam-2245	529	2	52,26,14]5	52,26,14]5	NUM
ejpam-2245	529	3	8	8	NUM
ejpam-2245	529	4	320	320	NUM
ejpam-2245	529	5	7	7	NUM
ejpam-2245	529	6	5	5	NUM
ejpam-2245	529	7	1−	1−	NUM
ejpam-2245	529	8	2v	2v	X
ejpam-2245	529	9	(	(	PUNCT
ejpam-2245	529	10	06|65|35|21|62	06|65|35|21|62	PROPN
ejpam-2245	529	11	)	)	PUNCT
ejpam-2245	529	12	24|21	24|21	NOUN
ejpam-2245	530	1	[	[	X
ejpam-2245	530	2	24,12,9]7	24,12,9]7	NUM
ejpam-2245	530	3	12	12	NUM
ejpam-2245	530	4	900	900	NUM
ejpam-2245	530	5	7	7	NUM
ejpam-2245	530	6	6	6	NUM
ejpam-2245	530	7	1−	1−	NUM
ejpam-2245	530	8	2v	2v	X
ejpam-2245	530	9	(	(	PUNCT
ejpam-2245	530	10	44|06|60|03|45|54	44|06|60|03|45|54	NUM
ejpam-2245	530	11	)	)	PUNCT
ejpam-2245	530	12	35|53	35|53	NOUN
ejpam-2245	531	1	[	[	X
ejpam-2245	531	2	28,14,10]7	28,14,10]7	NUM
ejpam-2245	531	3	12	12	NUM
ejpam-2245	531	4	1110	1110	NUM
ejpam-2245	531	5	7	7	NUM
ejpam-2245	531	6	8	8	NUM
ejpam-2245	531	7	1	1	NUM
ejpam-2245	531	8	(	(	PUNCT
ejpam-2245	531	9	06|54|16|05|36|63|01|35	06|54|16|05|36|63|01|35	PROPN
ejpam-2245	531	10	)	)	PUNCT
ejpam-2245	531	11	16|44	16|44	NUM
ejpam-2245	532	1	[	[	X
ejpam-2245	532	2	36,18,12]7	36,18,12]7	NUM
ejpam-2245	532	3	96	96	NUM
ejpam-2245	532	4	1320	1320	NUM
ejpam-2245	532	5	7	7	NUM
ejpam-2245	532	6	8	8	NUM
ejpam-2245	532	7	1−	1−	NUM
ejpam-2245	532	8	2v	2v	PROPN
ejpam-2245	532	9	(	(	PUNCT
ejpam-2245	532	10	53|51|60|45|32|30|53|61	53|51|60|45|32|30|53|61	NUM
ejpam-2245	532	11	)	)	PUNCT
ejpam-2245	532	12	42|45	42|45	NOUN
ejpam-2245	532	13	[	[	X
ejpam-2245	532	14	36,18,12]7	36,18,12]7	NUM
ejpam-2245	532	15	96	96	NUM
ejpam-2245	532	16	1536	1536	NUM
ejpam-2245	532	17	acknowledgements	acknowledgement	NOUN
ejpam-2245	532	18	the	the	DET
ejpam-2245	532	19	authors	author	NOUN
ejpam-2245	532	20	wish	wish	VERB
ejpam-2245	532	21	to	to	PART
ejpam-2245	532	22	thank	thank	VERB
ejpam-2245	532	23	the	the	DET
ejpam-2245	532	24	anonymous	anonymous	ADJ
ejpam-2245	532	25	referees	referee	NOUN
ejpam-2245	532	26	for	for	ADP
ejpam-2245	532	27	their	their	PRON
ejpam-2245	532	28	useful	useful	ADJ
ejpam-2245	532	29	comments	comment	NOUN
ejpam-2245	532	30	and	and	CCONJ
ejpam-2245	532	31	suggestions	suggestion	NOUN
ejpam-2245	532	32	.	.	PUNCT
ejpam-2245	533	1	references	reference	NOUN
ejpam-2245	533	2	[	[	X
ejpam-2245	533	3	1	1	NUM
ejpam-2245	533	4	]	]	PUNCT
ejpam-2245	533	5	c.	c.	PROPN
ejpam-2245	533	6	bachoc	bachoc	PROPN
ejpam-2245	533	7	.	.	PUNCT
ejpam-2245	534	1	application	application	NOUN
ejpam-2245	534	2	of	of	ADP
ejpam-2245	534	3	coding	code	VERB
ejpam-2245	534	4	theory	theory	NOUN
ejpam-2245	534	5	to	to	ADP
ejpam-2245	534	6	the	the	DET
ejpam-2245	534	7	construction	construction	NOUN
ejpam-2245	534	8	of	of	ADP
ejpam-2245	534	9	modular	modular	ADJ
ejpam-2245	534	10	lattices	lattice	NOUN
ejpam-2245	534	11	,	,	PUNCT
ejpam-2245	534	12	journal	journal	NOUN
ejpam-2245	534	13	of	of	ADP
ejpam-2245	534	14	combinatorial	combinatorial	ADJ
ejpam-2245	534	15	theory	theory	NOUN
ejpam-2245	534	16	series	series	NOUN
ejpam-2245	534	17	:	:	PUNCT
ejpam-2245	534	18	a	a	PRON
ejpam-2245	534	19	,	,	PUNCT
ejpam-2245	534	20	78	78	NUM
ejpam-2245	534	21	,	,	PUNCT
ejpam-2245	534	22	92–119	92–119	NUM
ejpam-2245	534	23	.	.	NOUN
ejpam-2245	534	24	1997	1997	NUM
ejpam-2245	534	25	.	.	PUNCT
ejpam-2245	535	1	[	[	X
ejpam-2245	535	2	2	2	NUM
ejpam-2245	535	3	]	]	PUNCT
ejpam-2245	535	4	a.	a.	NOUN
ejpam-2245	535	5	batoul	batoul	PROPN
ejpam-2245	535	6	,	,	PUNCT
ejpam-2245	535	7	k.	k.	PROPN
ejpam-2245	535	8	guenda	guenda	PROPN
ejpam-2245	535	9	and	and	CCONJ
ejpam-2245	535	10	t.a	t.a	PROPN
ejpam-2245	535	11	.	.	PROPN
ejpam-2245	535	12	gulliver	gulliver	PROPN
ejpam-2245	535	13	.	.	PUNCT
ejpam-2245	536	1	on	on	ADP
ejpam-2245	536	2	isodual	isodual	ADJ
ejpam-2245	536	3	cyclic	cyclic	ADJ
ejpam-2245	536	4	codes	code	NOUN
ejpam-2245	536	5	over	over	ADP
ejpam-2245	536	6	finite	finite	ADJ
ejpam-2245	536	7	fields	field	NOUN
ejpam-2245	536	8	and	and	CCONJ
ejpam-2245	536	9	finite	finite	ADJ
ejpam-2245	536	10	chain	chain	NOUN
ejpam-2245	536	11	rings	ring	NOUN
ejpam-2245	536	12	:	:	PUNCT
ejpam-2245	536	13	monomial	monomial	ADJ
ejpam-2245	536	14	equivalence	equivalence	NOUN
ejpam-2245	536	15	,	,	PUNCT
ejpam-2245	536	16	arxiv:1303.1870v1	arxiv:1303.1870v1	NOUN
ejpam-2245	536	17	,	,	PUNCT
ejpam-2245	536	18	2013	2013	NUM
ejpam-2245	536	19	.	.	PUNCT
ejpam-2245	537	1	[	[	X
ejpam-2245	537	2	3	3	NUM
ejpam-2245	537	3	]	]	PUNCT
ejpam-2245	537	4	m.	m.	NOUN
ejpam-2245	537	5	grassl	grassl	VERB
ejpam-2245	537	6	.	.	PUNCT
ejpam-2245	538	1	bounds	bound	NOUN
ejpam-2245	538	2	on	on	ADP
ejpam-2245	538	3	the	the	DET
ejpam-2245	538	4	minimum	minimum	ADJ
ejpam-2245	538	5	distance	distance	NOUN
ejpam-2245	538	6	of	of	ADP
ejpam-2245	538	7	linear	linear	ADJ
ejpam-2245	538	8	and	and	CCONJ
ejpam-2245	538	9	quantum	quantum	NOUN
ejpam-2245	538	10	codes	code	NOUN
ejpam-2245	538	11	,	,	PUNCT
ejpam-2245	538	12	online	online	ADV
ejpam-2245	538	13	available	available	ADJ
ejpam-2245	538	14	at	at	ADP
ejpam-2245	538	15	:	:	PUNCT
ejpam-2245	538	16	www.codetables.de	www.codetables.de	PROPN
ejpam-2245	538	17	(	(	PUNCT
ejpam-2245	538	18	accessed	access	VERB
ejpam-2245	538	19	on	on	ADP
ejpam-2245	538	20	29.04.2014	29.04.2014	NUM
ejpam-2245	538	21	)	)	PUNCT
ejpam-2245	538	22	.	.	PUNCT
ejpam-2245	539	1	[	[	X
ejpam-2245	539	2	4	4	X
ejpam-2245	539	3	]	]	PUNCT
ejpam-2245	539	4	s.	s.	PROPN
ejpam-2245	539	5	han	han	PROPN
ejpam-2245	539	6	and	and	CCONJ
ejpam-2245	539	7	j	j	PROPN
ejpam-2245	539	8	-	-	PUNCT
ejpam-2245	539	9	l.	l.	PROPN
ejpam-2245	539	10	kim	kim	PROPN
ejpam-2245	539	11	.	.	PUNCT
ejpam-2245	540	1	the	the	DET
ejpam-2245	540	2	non	non	NOUN
ejpam-2245	540	3	-	-	NOUN
ejpam-2245	540	4	existence	existence	NOUN
ejpam-2245	540	5	of	of	ADP
ejpam-2245	540	6	near	near	ADJ
ejpam-2245	540	7	extremal	extremal	ADJ
ejpam-2245	540	8	formally	formally	ADV
ejpam-2245	540	9	self	self	NOUN
ejpam-2245	540	10	-	-	PUNCT
ejpam-2245	540	11	dual	dual	ADJ
ejpam-2245	540	12	codes	code	NOUN
ejpam-2245	540	13	,	,	PUNCT
ejpam-2245	540	14	designs	design	NOUN
ejpam-2245	540	15	,	,	PUNCT
ejpam-2245	540	16	codes	code	NOUN
ejpam-2245	540	17	and	and	CCONJ
ejpam-2245	540	18	cryptography	cryptography	NOUN
ejpam-2245	540	19	,	,	PUNCT
ejpam-2245	540	20	51	51	NUM
ejpam-2245	540	21	,	,	PUNCT
ejpam-2245	540	22	69	69	NUM
ejpam-2245	540	23	-	-	SYM
ejpam-2245	540	24	77	77	NUM
ejpam-2245	540	25	.	.	PUNCT
ejpam-2245	540	26	2009	2009	NUM
ejpam-2245	540	27	.	.	PUNCT
ejpam-2245	541	1	[	[	X
ejpam-2245	541	2	5	5	X
ejpam-2245	541	3	]	]	PUNCT
ejpam-2245	541	4	w.	w.	PROPN
ejpam-2245	541	5	c.	c.	PROPN
ejpam-2245	541	6	huffman	huffman	PROPN
ejpam-2245	541	7	and	and	CCONJ
ejpam-2245	541	8	v.	v.	ADP
ejpam-2245	541	9	pless	pless	PROPN
ejpam-2245	541	10	.	.	PUNCT
ejpam-2245	542	1	fundamentals	fundamental	NOUN
ejpam-2245	542	2	of	of	ADP
ejpam-2245	542	3	error	error	NOUN
ejpam-2245	542	4	-	-	PUNCT
ejpam-2245	542	5	correcting	correct	VERB
ejpam-2245	542	6	codes	code	NOUN
ejpam-2245	542	7	,	,	PUNCT
ejpam-2245	542	8	cambridge	cambridge	PROPN
ejpam-2245	542	9	university	university	PROPN
ejpam-2245	542	10	press	press	NOUN
ejpam-2245	542	11	,	,	PUNCT
ejpam-2245	542	12	new	new	PROPN
ejpam-2245	542	13	york	york	PROPN
ejpam-2245	542	14	,	,	PUNCT
ejpam-2245	542	15	ny	ny	PROPN
ejpam-2245	542	16	,	,	PUNCT
ejpam-2245	542	17	2003	2003	NUM
ejpam-2245	542	18	.	.	PUNCT
ejpam-2245	543	1	[	[	X
ejpam-2245	543	2	6	6	NUM
ejpam-2245	543	3	]	]	X
ejpam-2245	543	4	y.	y.	PROPN
ejpam-2245	543	5	jia	jia	PROPN
ejpam-2245	543	6	,	,	PUNCT
ejpam-2245	543	7	s.	s.	PROPN
ejpam-2245	543	8	ling	ling	PROPN
ejpam-2245	543	9	and	and	CCONJ
ejpam-2245	543	10	c.	c.	PROPN
ejpam-2245	543	11	xing	xing	PROPN
ejpam-2245	543	12	.	.	PUNCT
ejpam-2245	544	1	on	on	ADP
ejpam-2245	544	2	self	self	NOUN
ejpam-2245	544	3	-	-	PUNCT
ejpam-2245	544	4	dual	dual	ADJ
ejpam-2245	544	5	cyclic	cyclic	ADJ
ejpam-2245	544	6	codes	code	NOUN
ejpam-2245	544	7	over	over	ADP
ejpam-2245	544	8	finite	finite	ADJ
ejpam-2245	544	9	fields	field	NOUN
ejpam-2245	544	10	,	,	PUNCT
ejpam-2245	544	11	ieee	ieee	NOUN
ejpam-2245	544	12	transactions	transaction	NOUN
ejpam-2245	544	13	on	on	ADP
ejpam-2245	544	14	information	information	NOUN
ejpam-2245	544	15	theory	theory	NOUN
ejpam-2245	544	16	,	,	PUNCT
ejpam-2245	544	17	57(4	57(4	NUM
ejpam-2245	544	18	)	)	PUNCT
ejpam-2245	544	19	,	,	PUNCT
ejpam-2245	544	20	2243–2251	2243–2251	NUM
ejpam-2245	544	21	.	.	PUNCT
ejpam-2245	545	1	2011	2011	NUM
ejpam-2245	545	2	.	.	PUNCT
ejpam-2245	546	1	references	reference	NOUN
ejpam-2245	546	2	80	80	NUM
ejpam-2245	546	3	[	[	X
ejpam-2245	546	4	7	7	NUM
ejpam-2245	546	5	]	]	X
ejpam-2245	546	6	s.	s.	PROPN
ejpam-2245	546	7	karadeniz	karadeniz	PROPN
ejpam-2245	546	8	,	,	PUNCT
ejpam-2245	546	9	s.	s.	PROPN
ejpam-2245	546	10	t.	t.	PROPN
ejpam-2245	546	11	dougherty	dougherty	PROPN
ejpam-2245	546	12	and	and	CCONJ
ejpam-2245	546	13	b.	b.	PROPN
ejpam-2245	546	14	yildiz	yildiz	PROPN
ejpam-2245	546	15	.	.	PUNCT
ejpam-2245	547	1	constructing	construct	VERB
ejpam-2245	547	2	formally	formally	ADV
ejpam-2245	547	3	self	self	NOUN
ejpam-2245	547	4	-	-	PUNCT
ejpam-2245	547	5	dual	dual	ADJ
ejpam-2245	547	6	codes	code	NOUN
ejpam-2245	547	7	over	over	ADP
ejpam-2245	547	8	rk	rk	NOUN
ejpam-2245	547	9	,	,	PUNCT
ejpam-2245	547	10	discrete	discrete	ADJ
ejpam-2245	547	11	applied	apply	VERB
ejpam-2245	547	12	mathematics	mathematic	NOUN
ejpam-2245	547	13	,	,	PUNCT
ejpam-2245	547	14	167(1	167(1	NUM
ejpam-2245	547	15	)	)	PUNCT
ejpam-2245	547	16	,	,	PUNCT
ejpam-2245	547	17	188	188	NUM
ejpam-2245	547	18	-	-	SYM
ejpam-2245	547	19	196	196	NUM
ejpam-2245	547	20	.	.	PUNCT
ejpam-2245	547	21	2014	2014	NUM
ejpam-2245	547	22	.	.	PUNCT
ejpam-2245	548	1	[	[	X
ejpam-2245	548	2	8	8	NUM
ejpam-2245	548	3	]	]	X
ejpam-2245	548	4	j	j	PROPN
ejpam-2245	548	5	-	-	PUNCT
ejpam-2245	548	6	l.	l.	PROPN
ejpam-2245	548	7	kim	kim	PROPN
ejpam-2245	548	8	,	,	PUNCT
ejpam-2245	548	9	v.	v.	PROPN
ejpam-2245	548	10	pless	pless	PROPN
ejpam-2245	548	11	.	.	PUNCT
ejpam-2245	549	1	a	a	DET
ejpam-2245	549	2	note	note	NOUN
ejpam-2245	549	3	on	on	ADP
ejpam-2245	549	4	formally	formally	ADV
ejpam-2245	549	5	self	self	NOUN
ejpam-2245	549	6	-	-	PUNCT
ejpam-2245	549	7	dual	dual	ADJ
ejpam-2245	549	8	even	even	ADV
ejpam-2245	549	9	codes	code	NOUN
ejpam-2245	549	10	of	of	ADP
ejpam-2245	549	11	length	length	NOUN
ejpam-2245	549	12	divisible	divisible	ADJ
ejpam-2245	549	13	by	by	ADP
ejpam-2245	549	14	8	8	NUM
ejpam-2245	549	15	,	,	PUNCT
ejpam-2245	549	16	finite	finite	ADJ
ejpam-2245	549	17	fields	field	NOUN
ejpam-2245	549	18	and	and	CCONJ
ejpam-2245	549	19	applications	application	NOUN
ejpam-2245	549	20	,	,	PUNCT
ejpam-2245	549	21	13(2	13(2	NOUN
ejpam-2245	549	22	)	)	PUNCT
ejpam-2245	549	23	,	,	PUNCT
ejpam-2245	549	24	224–229	224–229	NUM
ejpam-2245	549	25	.	.	PUNCT
ejpam-2245	549	26	2007	2007	NUM
ejpam-2245	549	27	.	.	PUNCT
ejpam-2245	550	1	[	[	X
ejpam-2245	550	2	9	9	NUM
ejpam-2245	550	3	]	]	PUNCT
ejpam-2245	550	4	p.	p.	NOUN
ejpam-2245	550	5	langevin	langevin	PROPN
ejpam-2245	550	6	.	.	PUNCT
ejpam-2245	551	1	duadic	duadic	ADJ
ejpam-2245	551	2	z4	z4	NOUN
ejpam-2245	551	3	-	-	PUNCT
ejpam-2245	551	4	codes	code	NOUN
ejpam-2245	551	5	,	,	PUNCT
ejpam-2245	551	6	finite	finite	ADJ
ejpam-2245	551	7	fields	field	NOUN
ejpam-2245	551	8	and	and	CCONJ
ejpam-2245	551	9	applications	application	NOUN
ejpam-2245	551	10	,	,	PUNCT
ejpam-2245	551	11	6	6	NUM
ejpam-2245	551	12	,	,	PUNCT
ejpam-2245	551	13	309–326	309–326	NUM
ejpam-2245	551	14	.	.	PUNCT
ejpam-2245	551	15	2000	2000	NUM
ejpam-2245	551	16	.	.	PUNCT
ejpam-2245	552	1	[	[	X
ejpam-2245	552	2	10	10	NUM
ejpam-2245	552	3	]	]	X
ejpam-2245	552	4	j	j	PROPN
ejpam-2245	552	5	s.	s.	PROPN
ejpam-2245	552	6	leon	leon	PROPN
ejpam-2245	552	7	,	,	PUNCT
ejpam-2245	552	8	j.	j.	PROPN
ejpam-2245	552	9	m.	m.	PROPN
ejpam-2245	552	10	masley	masley	PROPN
ejpam-2245	552	11	and	and	CCONJ
ejpam-2245	552	12	v.	v.	ADP
ejpam-2245	552	13	pless	pless	PROPN
ejpam-2245	552	14	.	.	PUNCT
ejpam-2245	553	1	duadic	duadic	ADJ
ejpam-2245	553	2	codes	code	NOUN
ejpam-2245	553	3	,	,	PUNCT
ejpam-2245	553	4	ieee	ieee	NOUN
ejpam-2245	553	5	transactions	transaction	NOUN
ejpam-2245	553	6	on	on	ADP
ejpam-2245	553	7	information	information	NOUN
ejpam-2245	553	8	theory	theory	NOUN
ejpam-2245	553	9	,	,	PUNCT
ejpam-2245	553	10	30	30	NUM
ejpam-2245	553	11	,	,	PUNCT
ejpam-2245	553	12	709–714	709–714	NUM
ejpam-2245	553	13	.	.	NOUN
ejpam-2245	553	14	1984	1984	NUM
ejpam-2245	553	15	.	.	PUNCT
ejpam-2245	554	1	[	[	X
ejpam-2245	554	2	11	11	NUM
ejpam-2245	554	3	]	]	PUNCT
ejpam-2245	554	4	s.	s.	PROPN
ejpam-2245	554	5	ling	ling	PROPN
ejpam-2245	554	6	and	and	CCONJ
ejpam-2245	554	7	p.	p.	PROPN
ejpam-2245	554	8	solé	solé	NOUN
ejpam-2245	554	9	.	.	PUNCT
ejpam-2245	555	1	duadic	duadic	ADJ
ejpam-2245	555	2	codes	code	NOUN
ejpam-2245	555	3	over	over	ADP
ejpam-2245	555	4	f2+uf2	f2+uf2	NOUN
ejpam-2245	555	5	,	,	PUNCT
ejpam-2245	555	6	applicable	applicable	ADJ
ejpam-2245	555	7	algebra	algebra	NOUN
ejpam-2245	555	8	in	in	ADP
ejpam-2245	555	9	engineering	engineering	NOUN
ejpam-2245	555	10	,	,	PUNCT
ejpam-2245	555	11	communication	communication	NOUN
ejpam-2245	555	12	and	and	CCONJ
ejpam-2245	555	13	computing	computing	NOUN
ejpam-2245	555	14	,	,	PUNCT
ejpam-2245	555	15	12(5	12(5	NUM
ejpam-2245	555	16	)	)	PUNCT
ejpam-2245	555	17	,	,	PUNCT
ejpam-2245	555	18	365–379	365–379	NUM
ejpam-2245	555	19	.	.	PUNCT
ejpam-2245	555	20	2001	2001	NUM
ejpam-2245	555	21	.	.	PUNCT
ejpam-2245	556	1	[	[	X
ejpam-2245	556	2	12	12	NUM
ejpam-2245	556	3	]	]	PUNCT
ejpam-2245	556	4	j.	j.	PROPN
ejpam-2245	556	5	j.	j.	PROPN
ejpam-2245	556	6	rushanan	rushanan	PROPN
ejpam-2245	556	7	.	.	PUNCT
ejpam-2245	557	1	duadic	duadic	ADJ
ejpam-2245	557	2	codes	code	NOUN
ejpam-2245	557	3	and	and	CCONJ
ejpam-2245	557	4	difference	difference	NOUN
ejpam-2245	557	5	sets	set	NOUN
ejpam-2245	557	6	,	,	PUNCT
ejpam-2245	557	7	journal	journal	NOUN
ejpam-2245	557	8	of	of	ADP
ejpam-2245	557	9	combinatorial	combinatorial	ADJ
ejpam-2245	557	10	theory	theory	NOUN
ejpam-2245	557	11	series	series	NOUN
ejpam-2245	557	12	:	:	PUNCT
ejpam-2245	557	13	a	a	PRON
ejpam-2245	557	14	,	,	PUNCT
ejpam-2245	557	15	57	57	NUM
ejpam-2245	557	16	,	,	PUNCT
ejpam-2245	557	17	254–261	254–261	NUM
ejpam-2245	557	18	.	.	NOUN
ejpam-2245	557	19	1991	1991	NUM
ejpam-2245	557	20	[	[	X
ejpam-2245	557	21	13	13	NUM
ejpam-2245	557	22	]	]	X
ejpam-2245	557	23	n.	n.	PROPN
ejpam-2245	557	24	j.	j.	PROPN
ejpam-2245	557	25	a.	a.	PROPN
ejpam-2245	557	26	sloane	sloane	PROPN
ejpam-2245	557	27	and	and	CCONJ
ejpam-2245	557	28	j.	j.	PROPN
ejpam-2245	557	29	g.	g.	PROPN
ejpam-2245	557	30	thompson	thompson	PROPN
ejpam-2245	557	31	.	.	PUNCT
ejpam-2245	558	1	cyclic	cyclic	ADJ
ejpam-2245	558	2	self	self	NOUN
ejpam-2245	558	3	-	-	PUNCT
ejpam-2245	558	4	dual	dual	ADJ
ejpam-2245	558	5	codes	code	NOUN
ejpam-2245	558	6	,	,	PUNCT
ejpam-2245	558	7	ieee	ieee	NOUN
ejpam-2245	558	8	transactions	transaction	NOUN
ejpam-2245	558	9	on	on	ADP
ejpam-2245	558	10	information	information	NOUN
ejpam-2245	558	11	theory	theory	NOUN
ejpam-2245	558	12	,	,	PUNCT
ejpam-2245	558	13	29	29	NUM
ejpam-2245	558	14	,	,	PUNCT
ejpam-2245	558	15	364–366	364–366	NUM
ejpam-2245	558	16	.	.	PUNCT
ejpam-2245	558	17	1983	1983	NUM
ejpam-2245	558	18	.	.	PUNCT
ejpam-2245	559	1	[	[	X
ejpam-2245	559	2	14	14	NUM
ejpam-2245	559	3	]	]	PUNCT
ejpam-2245	559	4	m.	m.	NOUN
ejpam-2245	559	5	h.	h.	PROPN
ejpam-2245	559	6	m.	m.	PROPN
ejpam-2245	559	7	smid	smid	PROPN
ejpam-2245	559	8	.	.	PROPN
ejpam-2245	559	9	duadic	duadic	ADJ
ejpam-2245	559	10	codes	code	NOUN
ejpam-2245	559	11	,	,	PUNCT
ejpam-2245	559	12	ieee	ieee	NOUN
ejpam-2245	559	13	transactions	transaction	NOUN
ejpam-2245	559	14	on	on	ADP
ejpam-2245	559	15	information	information	NOUN
ejpam-2245	559	16	theory	theory	NOUN
ejpam-2245	559	17	,	,	PUNCT
ejpam-2245	559	18	33(3	33(3	NOUN
ejpam-2245	559	19	)	)	PUNCT
ejpam-2245	559	20	,	,	PUNCT
ejpam-2245	559	21	432–433	432–433	NUM
ejpam-2245	559	22	.	.	PUNCT
ejpam-2245	559	23	1987	1987	NUM
ejpam-2245	559	24	.	.	PUNCT
ejpam-2245	560	1	[	[	X
ejpam-2245	560	2	15	15	NUM
ejpam-2245	560	3	]	]	X
ejpam-2245	560	4	j.	j.	PROPN
ejpam-2245	560	5	wood	wood	PROPN
ejpam-2245	560	6	.	.	PUNCT
ejpam-2245	561	1	duality	duality	NOUN
ejpam-2245	561	2	for	for	ADP
ejpam-2245	561	3	modules	module	NOUN
ejpam-2245	561	4	over	over	ADP
ejpam-2245	561	5	finite	finite	ADJ
ejpam-2245	561	6	rings	ring	NOUN
ejpam-2245	561	7	and	and	CCONJ
ejpam-2245	561	8	applications	application	NOUN
ejpam-2245	561	9	to	to	ADP
ejpam-2245	561	10	coding	code	VERB
ejpam-2245	561	11	theory	theory	NOUN
ejpam-2245	561	12	,	,	PUNCT
ejpam-2245	561	13	american	american	ADJ
ejpam-2245	561	14	journal	journal	PROPN
ejpam-2245	561	15	of	of	ADP
ejpam-2245	561	16	mathematics	mathematic	NOUN
ejpam-2245	561	17	,	,	PUNCT
ejpam-2245	561	18	121	121	NUM
ejpam-2245	561	19	,	,	PUNCT
ejpam-2245	561	20	555–575	555–575	NUM
ejpam-2245	561	21	.	.	PUNCT
ejpam-2245	561	22	1999	1999	NUM
ejpam-2245	561	23	.	.	PUNCT
ejpam-2245	562	1	[	[	X
ejpam-2245	562	2	16	16	NUM
ejpam-2245	562	3	]	]	PUNCT
ejpam-2245	562	4	s.	s.	PROPN
ejpam-2245	562	5	x.	x.	PROPN
ejpam-2245	562	6	zhu	zhu	PROPN
ejpam-2245	562	7	and	and	CCONJ
ejpam-2245	562	8	l.	l.	PROPN
ejpam-2245	562	9	wang	wang	PROPN
ejpam-2245	562	10	.	.	PUNCT
ejpam-2245	563	1	a	a	DET
ejpam-2245	563	2	class	class	NOUN
ejpam-2245	563	3	of	of	ADP
ejpam-2245	563	4	constacyclic	constacyclic	ADJ
ejpam-2245	563	5	codes	code	NOUN
ejpam-2245	563	6	over	over	ADP
ejpam-2245	563	7	fp	fp	PROPN
ejpam-2245	563	8	+	+	NUM
ejpam-2245	563	9	vfp	vfp	PROPN
ejpam-2245	563	10	and	and	CCONJ
ejpam-2245	563	11	its	its	PRON
ejpam-2245	563	12	gray	gray	ADJ
ejpam-2245	563	13	image	image	NOUN
ejpam-2245	563	14	,	,	PUNCT
ejpam-2245	563	15	discrete	discrete	ADJ
ejpam-2245	563	16	mathematics	mathematic	NOUN
ejpam-2245	563	17	,	,	PUNCT
ejpam-2245	563	18	311	311	NUM
ejpam-2245	563	19	,	,	PUNCT
ejpam-2245	563	20	2677–2682	2677–2682	NOUN
ejpam-2245	563	21	.	.	PUNCT
ejpam-2245	563	22	2011	2011	NUM
ejpam-2245	563	23	.	.	PUNCT
ejpam-2245	564	1	[	[	X
ejpam-2245	564	2	17	17	NUM
ejpam-2245	564	3	]	]	PUNCT
ejpam-2245	564	4	s.	s.	PROPN
ejpam-2245	564	5	x.	x.	PROPN
ejpam-2245	564	6	zhu	zhu	PROPN
ejpam-2245	564	7	,	,	PUNCT
ejpam-2245	564	8	y.	y.	PROPN
ejpam-2245	564	9	wang	wang	PROPN
ejpam-2245	564	10	and	and	CCONJ
ejpam-2245	564	11	m.	m.	PROPN
ejpam-2245	564	12	j.	j.	PROPN
ejpam-2245	564	13	shi	shi	PROPN
ejpam-2245	564	14	.	.	PUNCT
ejpam-2245	565	1	some	some	DET
ejpam-2245	565	2	results	result	NOUN
ejpam-2245	565	3	on	on	ADP
ejpam-2245	565	4	cyclic	cyclic	ADJ
ejpam-2245	565	5	codes	code	NOUN
ejpam-2245	565	6	over	over	ADP
ejpam-2245	565	7	f2	f2	PROPN
ejpam-2245	565	8	+	+	CCONJ
ejpam-2245	565	9	vf2	vf2	ADJ
ejpam-2245	565	10	,	,	PUNCT
ejpam-2245	565	11	ieee	ieee	NOUN
ejpam-2245	565	12	transactions	transaction	NOUN
ejpam-2245	565	13	on	on	ADP
ejpam-2245	565	14	information	information	NOUN
ejpam-2245	565	15	theory	theory	NOUN
ejpam-2245	565	16	,	,	PUNCT
ejpam-2245	565	17	56(4	56(4	NOUN
ejpam-2245	565	18	)	)	PUNCT
ejpam-2245	565	19	,	,	PUNCT
ejpam-2245	565	20	1680–1684	1680–1684	NUM
ejpam-2245	565	21	.	.	PUNCT
ejpam-2245	565	22	2010	2010	NUM
ejpam-2245	565	23	.	.	PUNCT