id	sid	tid	token	lemma	pos
ejpam-2571	1	1	compile	compile	NOUN
ejpam-2571	1	2	/	/	SYM
ejpam-2571	1	3	output.dvi	output.dvi	NOUN
ejpam-2571	1	4	european	european	ADJ
ejpam-2571	1	5	journal	journal	NOUN
ejpam-2571	1	6	of	of	ADP
ejpam-2571	1	7	pure	pure	ADJ
ejpam-2571	1	8	and	and	CCONJ
ejpam-2571	1	9	applied	apply	VERB
ejpam-2571	1	10	mathematics	mathematic	NOUN
ejpam-2571	1	11	vol	vol	NOUN
ejpam-2571	1	12	.	.	PROPN
ejpam-2571	2	1	9	9	NUM
ejpam-2571	2	2	,	,	PUNCT
ejpam-2571	2	3	no	no	INTJ
ejpam-2571	2	4	.	.	NOUN
ejpam-2571	2	5	1	1	NUM
ejpam-2571	2	6	,	,	PUNCT
ejpam-2571	2	7	2016	2016	NUM
ejpam-2571	2	8	,	,	PUNCT
ejpam-2571	2	9	39	39	NUM
ejpam-2571	2	10	-	-	SYM
ejpam-2571	2	11	47	47	NUM
ejpam-2571	2	12	issn	issn	PROPN
ejpam-2571	2	13	1307	1307	NUM
ejpam-2571	2	14	-	-	SYM
ejpam-2571	2	15	5543	5543	NUM
ejpam-2571	2	16	–	–	PUNCT
ejpam-2571	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2571	2	18	(	(	PUNCT
ejpam-2571	2	19	1−	1−	NUM
ejpam-2571	2	20	2u2)-constacyclic	2u2)-constacyclic	PROPN
ejpam-2571	2	21	codes	code	NOUN
ejpam-2571	2	22	over	over	ADP
ejpam-2571	2	23	fp	fp	NOUN
ejpam-2571	2	24	+	+	NUM
ejpam-2571	2	25	ufp	ufp	NOUN
ejpam-2571	3	1	+	+	CCONJ
ejpam-2571	4	1	u2	u2	PROPN
ejpam-2571	4	2	fp	fp	PROPN
ejpam-2571	4	3	hojjat	hojjat	PROPN
ejpam-2571	4	4	mostafanasab∗and	mostafanasab∗and	PROPN
ejpam-2571	4	5	negin	negin	PROPN
ejpam-2571	4	6	karimi	karimi	PROPN
ejpam-2571	4	7	department	department	PROPN
ejpam-2571	4	8	of	of	ADP
ejpam-2571	4	9	mathematics	mathematic	NOUN
ejpam-2571	4	10	and	and	CCONJ
ejpam-2571	4	11	applications	application	NOUN
ejpam-2571	4	12	,	,	PUNCT
ejpam-2571	4	13	university	university	NOUN
ejpam-2571	4	14	of	of	ADP
ejpam-2571	4	15	mohaghegh	mohaghegh	PROPN
ejpam-2571	4	16	ardabili	ardabili	PROPN
ejpam-2571	4	17	,	,	PUNCT
ejpam-2571	4	18	p.o	p.o	PROPN
ejpam-2571	4	19	.	.	PROPN
ejpam-2571	4	20	box	box	PROPN
ejpam-2571	4	21	179	179	NUM
ejpam-2571	4	22	,	,	PUNCT
ejpam-2571	4	23	ardabil	ardabil	VERB
ejpam-2571	4	24	,	,	PUNCT
ejpam-2571	4	25	iran	iran	PROPN
ejpam-2571	4	26	abstract	abstract	NOUN
ejpam-2571	4	27	.	.	PUNCT
ejpam-2571	5	1	let	let	VERB
ejpam-2571	5	2	fp	fp	NOUN
ejpam-2571	5	3	be	be	AUX
ejpam-2571	5	4	a	a	DET
ejpam-2571	5	5	finite	finite	ADJ
ejpam-2571	5	6	field	field	NOUN
ejpam-2571	5	7	,	,	PUNCT
ejpam-2571	5	8	where	where	SCONJ
ejpam-2571	5	9	p	p	NOUN
ejpam-2571	5	10	is	be	AUX
ejpam-2571	5	11	an	an	DET
ejpam-2571	5	12	odd	odd	ADJ
ejpam-2571	5	13	prime	prime	NOUN
ejpam-2571	5	14	,	,	PUNCT
ejpam-2571	5	15	and	and	CCONJ
ejpam-2571	5	16	let	let	VERB
ejpam-2571	5	17	u	u	PRON
ejpam-2571	5	18	be	be	AUX
ejpam-2571	5	19	an	an	DET
ejpam-2571	5	20	indeterminate	indeterminate	NOUN
ejpam-2571	5	21	.	.	PUNCT
ejpam-2571	6	1	this	this	DET
ejpam-2571	6	2	article	article	NOUN
ejpam-2571	6	3	studies	study	NOUN
ejpam-2571	6	4	(	(	PUNCT
ejpam-2571	6	5	1	1	NUM
ejpam-2571	6	6	−	−	PROPN
ejpam-2571	6	7	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	6	8	codes	code	NOUN
ejpam-2571	6	9	over	over	ADP
ejpam-2571	6	10	the	the	DET
ejpam-2571	6	11	ring	ring	NOUN
ejpam-2571	6	12	fp	fp	X
ejpam-2571	6	13	+	+	NUM
ejpam-2571	6	14	ufp	ufp	NOUN
ejpam-2571	6	15	+	+	CCONJ
ejpam-2571	6	16	u2	u2	PROPN
ejpam-2571	6	17	fp	fp	NOUN
ejpam-2571	6	18	,	,	PUNCT
ejpam-2571	6	19	where	where	SCONJ
ejpam-2571	6	20	u3	u3	NOUN
ejpam-2571	6	21	=	=	PUNCT
ejpam-2571	6	22	u.	u.	NOUN
ejpam-2571	6	23	we	we	PRON
ejpam-2571	6	24	describe	describe	VERB
ejpam-2571	6	25	generator	generator	NOUN
ejpam-2571	6	26	polynomials	polynomial	NOUN
ejpam-2571	6	27	of	of	ADP
ejpam-2571	6	28	this	this	DET
ejpam-2571	6	29	kind	kind	NOUN
ejpam-2571	6	30	of	of	ADP
ejpam-2571	6	31	codes	code	NOUN
ejpam-2571	6	32	and	and	CCONJ
ejpam-2571	6	33	investigate	investigate	VERB
ejpam-2571	6	34	the	the	DET
ejpam-2571	6	35	structural	structural	ADJ
ejpam-2571	6	36	properties	property	NOUN
ejpam-2571	6	37	of	of	ADP
ejpam-2571	6	38	these	these	DET
ejpam-2571	6	39	codes	code	NOUN
ejpam-2571	6	40	by	by	ADP
ejpam-2571	6	41	a	a	DET
ejpam-2571	6	42	decomposition	decomposition	NOUN
ejpam-2571	6	43	theorem	theorem	NOUN
ejpam-2571	6	44	.	.	PROPN
ejpam-2571	6	45	2010	2010	NUM
ejpam-2571	6	46	mathematics	mathematic	NOUN
ejpam-2571	6	47	subject	subject	NOUN
ejpam-2571	6	48	classifications	classification	NOUN
ejpam-2571	6	49	:	:	PUNCT
ejpam-2571	6	50	94b05	94b05	NUM
ejpam-2571	6	51	,	,	PUNCT
ejpam-2571	6	52	94b15	94b15	NUM
ejpam-2571	6	53	,	,	PUNCT
ejpam-2571	6	54	11t71	11t71	NUM
ejpam-2571	6	55	,	,	PUNCT
ejpam-2571	6	56	13m99	13m99	NUM
ejpam-2571	6	57	key	key	ADJ
ejpam-2571	6	58	words	word	NOUN
ejpam-2571	6	59	and	and	CCONJ
ejpam-2571	6	60	phrases	phrase	NOUN
ejpam-2571	6	61	:	:	PUNCT
ejpam-2571	6	62	finite	finite	PROPN
ejpam-2571	6	63	fields	field	NOUN
ejpam-2571	6	64	,	,	PUNCT
ejpam-2571	6	65	cyclic	cyclic	ADJ
ejpam-2571	6	66	codes	code	NOUN
ejpam-2571	6	67	,	,	PUNCT
ejpam-2571	6	68	constacyclic	constacyclic	ADJ
ejpam-2571	6	69	codes	code	NOUN
ejpam-2571	6	70	1	1	NUM
ejpam-2571	6	71	.	.	PUNCT
ejpam-2571	6	72	introduction	introduction	NOUN
ejpam-2571	6	73	error	error	NOUN
ejpam-2571	6	74	-	-	PUNCT
ejpam-2571	6	75	correcting	correct	VERB
ejpam-2571	6	76	codes	code	NOUN
ejpam-2571	6	77	play	play	VERB
ejpam-2571	6	78	important	important	ADJ
ejpam-2571	6	79	roles	role	NOUN
ejpam-2571	6	80	in	in	ADP
ejpam-2571	6	81	applications	application	NOUN
ejpam-2571	6	82	ranging	range	VERB
ejpam-2571	6	83	from	from	ADP
ejpam-2571	6	84	data	datum	NOUN
ejpam-2571	6	85	networking	network	VERB
ejpam-2571	6	86	to	to	ADP
ejpam-2571	6	87	satellite	satellite	NOUN
ejpam-2571	6	88	communication	communication	NOUN
ejpam-2571	6	89	to	to	ADP
ejpam-2571	6	90	compact	compact	ADJ
ejpam-2571	6	91	disks	disk	NOUN
ejpam-2571	6	92	.	.	PUNCT
ejpam-2571	7	1	most	most	ADJ
ejpam-2571	7	2	coding	code	VERB
ejpam-2571	7	3	theory	theory	NOUN
ejpam-2571	7	4	concerns	concern	NOUN
ejpam-2571	7	5	on	on	ADP
ejpam-2571	7	6	linear	linear	ADJ
ejpam-2571	7	7	codes	code	NOUN
ejpam-2571	7	8	since	since	SCONJ
ejpam-2571	7	9	they	they	PRON
ejpam-2571	7	10	have	have	VERB
ejpam-2571	7	11	clear	clear	ADJ
ejpam-2571	7	12	structure	structure	NOUN
ejpam-2571	7	13	that	that	PRON
ejpam-2571	7	14	makes	make	VERB
ejpam-2571	7	15	them	they	PRON
ejpam-2571	7	16	simpler	simple	ADJ
ejpam-2571	7	17	to	to	PART
ejpam-2571	7	18	discover	discover	VERB
ejpam-2571	7	19	,	,	PUNCT
ejpam-2571	7	20	to	to	PART
ejpam-2571	7	21	understand	understand	VERB
ejpam-2571	7	22	and	and	CCONJ
ejpam-2571	7	23	to	to	PART
ejpam-2571	7	24	encode	encode	VERB
ejpam-2571	7	25	and	and	CCONJ
ejpam-2571	7	26	decode	decode	VERB
ejpam-2571	7	27	.	.	PUNCT
ejpam-2571	8	1	codes	code	NOUN
ejpam-2571	8	2	over	over	ADP
ejpam-2571	8	3	finite	finite	ADJ
ejpam-2571	8	4	rings	ring	NOUN
ejpam-2571	8	5	have	have	AUX
ejpam-2571	8	6	been	be	AUX
ejpam-2571	8	7	studied	study	VERB
ejpam-2571	8	8	since	since	SCONJ
ejpam-2571	8	9	the	the	DET
ejpam-2571	8	10	early	early	ADJ
ejpam-2571	8	11	1970s	1970	NOUN
ejpam-2571	8	12	.	.	PUNCT
ejpam-2571	9	1	recently	recently	ADV
ejpam-2571	9	2	codes	code	VERB
ejpam-2571	9	3	over	over	ADP
ejpam-2571	9	4	rings	ring	NOUN
ejpam-2571	9	5	have	have	AUX
ejpam-2571	9	6	generated	generate	VERB
ejpam-2571	9	7	a	a	DET
ejpam-2571	9	8	lot	lot	NOUN
ejpam-2571	9	9	of	of	ADP
ejpam-2571	9	10	interest	interest	NOUN
ejpam-2571	9	11	after	after	ADP
ejpam-2571	9	12	a	a	DET
ejpam-2571	9	13	breakthrough	breakthrough	ADJ
ejpam-2571	9	14	paper	paper	NOUN
ejpam-2571	9	15	by	by	ADP
ejpam-2571	9	16	hammons	hammon	NOUN
ejpam-2571	9	17	et	et	PROPN
ejpam-2571	9	18	al	al	PROPN
ejpam-2571	9	19	.	.	PUNCT
ejpam-2571	10	1	[	[	X
ejpam-2571	10	2	9	9	NUM
ejpam-2571	10	3	]	]	PUNCT
ejpam-2571	10	4	showed	show	VERB
ejpam-2571	10	5	that	that	SCONJ
ejpam-2571	10	6	some	some	DET
ejpam-2571	10	7	well	well	ADV
ejpam-2571	10	8	known	know	VERB
ejpam-2571	10	9	binary	binary	ADJ
ejpam-2571	10	10	non	non	ADJ
ejpam-2571	10	11	-	-	ADJ
ejpam-2571	10	12	linear	linear	ADJ
ejpam-2571	10	13	codes	code	NOUN
ejpam-2571	10	14	are	be	AUX
ejpam-2571	10	15	actually	actually	ADV
ejpam-2571	10	16	images	image	NOUN
ejpam-2571	10	17	of	of	ADP
ejpam-2571	10	18	some	some	DET
ejpam-2571	10	19	linear	linear	ADJ
ejpam-2571	10	20	codes	code	NOUN
ejpam-2571	10	21	over	over	ADP
ejpam-2571	10	22	z4	z4	PROPN
ejpam-2571	10	23	under	under	ADP
ejpam-2571	10	24	the	the	DET
ejpam-2571	10	25	gray	gray	ADJ
ejpam-2571	10	26	map	map	NOUN
ejpam-2571	10	27	.	.	PUNCT
ejpam-2571	11	1	cyclic	cyclic	ADJ
ejpam-2571	11	2	codes	code	NOUN
ejpam-2571	11	3	are	be	AUX
ejpam-2571	11	4	amongst	amongst	ADP
ejpam-2571	11	5	the	the	DET
ejpam-2571	11	6	most	most	ADV
ejpam-2571	11	7	studied	study	VERB
ejpam-2571	11	8	algebraic	algebraic	ADJ
ejpam-2571	11	9	codes	code	NOUN
ejpam-2571	11	10	.	.	PUNCT
ejpam-2571	12	1	their	their	PRON
ejpam-2571	12	2	structure	structure	NOUN
ejpam-2571	12	3	is	be	AUX
ejpam-2571	12	4	well	well	ADV
ejpam-2571	12	5	known	know	VERB
ejpam-2571	12	6	over	over	ADP
ejpam-2571	12	7	finite	finite	ADJ
ejpam-2571	12	8	fields	field	NOUN
ejpam-2571	12	9	[	[	X
ejpam-2571	12	10	13	13	NUM
ejpam-2571	12	11	]	]	PUNCT
ejpam-2571	12	12	.	.	PUNCT
ejpam-2571	13	1	constacyclic	constacyclic	PROPN
ejpam-2571	13	2	codes	code	NOUN
ejpam-2571	13	3	over	over	ADP
ejpam-2571	13	4	finite	finite	ADJ
ejpam-2571	13	5	fields	field	NOUN
ejpam-2571	13	6	form	form	VERB
ejpam-2571	13	7	a	a	DET
ejpam-2571	13	8	remarkable	remarkable	ADJ
ejpam-2571	13	9	class	class	NOUN
ejpam-2571	13	10	of	of	ADP
ejpam-2571	13	11	linear	linear	PROPN
ejpam-2571	13	12	codes	code	NOUN
ejpam-2571	13	13	,	,	PUNCT
ejpam-2571	13	14	as	as	SCONJ
ejpam-2571	13	15	they	they	PRON
ejpam-2571	13	16	include	include	VERB
ejpam-2571	13	17	the	the	DET
ejpam-2571	13	18	important	important	ADJ
ejpam-2571	13	19	family	family	NOUN
ejpam-2571	13	20	of	of	ADP
ejpam-2571	13	21	cyclic	cyclic	ADJ
ejpam-2571	13	22	codes	code	NOUN
ejpam-2571	13	23	.	.	PUNCT
ejpam-2571	14	1	constacyclic	constacyclic	ADJ
ejpam-2571	14	2	codes	code	NOUN
ejpam-2571	14	3	also	also	ADV
ejpam-2571	14	4	have	have	VERB
ejpam-2571	14	5	practical	practical	ADJ
ejpam-2571	14	6	applications	application	NOUN
ejpam-2571	14	7	as	as	SCONJ
ejpam-2571	14	8	they	they	PRON
ejpam-2571	14	9	can	can	AUX
ejpam-2571	14	10	be	be	AUX
ejpam-2571	14	11	efficiently	efficiently	ADV
ejpam-2571	14	12	encoded	encode	VERB
ejpam-2571	14	13	using	use	VERB
ejpam-2571	14	14	simple	simple	ADJ
ejpam-2571	14	15	shift	shift	NOUN
ejpam-2571	14	16	registers	register	NOUN
ejpam-2571	14	17	.	.	PUNCT
ejpam-2571	15	1	they	they	PRON
ejpam-2571	15	2	have	have	VERB
ejpam-2571	15	3	rich	rich	ADJ
ejpam-2571	15	4	algebraic	algebraic	ADJ
ejpam-2571	15	5	structures	structure	NOUN
ejpam-2571	15	6	for	for	ADP
ejpam-2571	15	7	efficient	efficient	ADJ
ejpam-2571	15	8	error	error	NOUN
ejpam-2571	15	9	detection	detection	NOUN
ejpam-2571	15	10	and	and	CCONJ
ejpam-2571	15	11	correction	correction	NOUN
ejpam-2571	15	12	,	,	PUNCT
ejpam-2571	15	13	which	which	PRON
ejpam-2571	15	14	explains	explain	VERB
ejpam-2571	15	15	their	their	PRON
ejpam-2571	15	16	preferred	preferred	ADJ
ejpam-2571	15	17	role	role	NOUN
ejpam-2571	15	18	in	in	ADP
ejpam-2571	15	19	engineering	engineering	NOUN
ejpam-2571	15	20	.	.	PUNCT
ejpam-2571	16	1	in	in	ADP
ejpam-2571	16	2	general	general	ADJ
ejpam-2571	16	3	,	,	PUNCT
ejpam-2571	16	4	due	due	ADP
ejpam-2571	16	5	to	to	ADP
ejpam-2571	16	6	their	their	PRON
ejpam-2571	16	7	rich	rich	ADJ
ejpam-2571	16	8	algebraic	algebraic	ADJ
ejpam-2571	16	9	structure	structure	NOUN
ejpam-2571	16	10	,	,	PUNCT
ejpam-2571	16	11	constacyclic	constacyclic	ADJ
ejpam-2571	16	12	codes	code	NOUN
ejpam-2571	16	13	have	have	AUX
ejpam-2571	16	14	been	be	AUX
ejpam-2571	16	15	studied	study	VERB
ejpam-2571	16	16	over	over	ADP
ejpam-2571	16	17	various	various	ADJ
ejpam-2571	16	18	finite	finite	ADJ
ejpam-2571	16	19	chain	chain	NOUN
ejpam-2571	16	20	rings	ring	NOUN
ejpam-2571	16	21	(	(	PUNCT
ejpam-2571	16	22	see	see	VERB
ejpam-2571	16	23	[	[	X
ejpam-2571	16	24	1	1	NUM
ejpam-2571	16	25	,	,	PUNCT
ejpam-2571	16	26	3–7	3–7	NUM
ejpam-2571	16	27	,	,	PUNCT
ejpam-2571	16	28	14	14	NUM
ejpam-2571	16	29	,	,	PUNCT
ejpam-2571	16	30	15	15	NUM
ejpam-2571	16	31	]	]	NUM
ejpam-2571	16	32	)	)	PUNCT
ejpam-2571	16	33	.	.	PUNCT
ejpam-2571	17	1	in	in	ADP
ejpam-2571	17	2	[	[	X
ejpam-2571	17	3	15	15	NUM
ejpam-2571	17	4	]	]	PUNCT
ejpam-2571	17	5	,	,	PUNCT
ejpam-2571	17	6	zhu	zhu	PROPN
ejpam-2571	17	7	and	and	CCONJ
ejpam-2571	17	8	wang	wang	PROPN
ejpam-2571	17	9	investigated	investigate	VERB
ejpam-2571	17	10	(	(	PUNCT
ejpam-2571	17	11	1−	1−	NUM
ejpam-2571	17	12	2u)-constacyclic	2u)-constacyclic	NUM
ejpam-2571	17	13	codes	code	NOUN
ejpam-2571	17	14	over	over	ADP
ejpam-2571	17	15	fp	fp	PROPN
ejpam-2571	17	16	+	+	NUM
ejpam-2571	17	17	vfp	vfp	PROPN
ejpam-2571	17	18	,	,	PUNCT
ejpam-2571	17	19	where	where	SCONJ
ejpam-2571	17	20	v2	v2	NOUN
ejpam-2571	17	21	=	=	NOUN
ejpam-2571	18	1	v.	v.	CCONJ
ejpam-2571	18	2	in	in	ADP
ejpam-2571	18	3	[	[	X
ejpam-2571	18	4	8	8	NUM
ejpam-2571	18	5	,	,	PUNCT
ejpam-2571	18	6	11	11	NUM
ejpam-2571	18	7	,	,	PUNCT
ejpam-2571	18	8	12	12	NUM
ejpam-2571	18	9	]	]	PUNCT
ejpam-2571	18	10	,	,	PUNCT
ejpam-2571	18	11	some	some	DET
ejpam-2571	18	12	kind	kind	NOUN
ejpam-2571	18	13	of	of	ADP
ejpam-2571	18	14	codes	code	NOUN
ejpam-2571	18	15	over	over	ADP
ejpam-2571	18	16	fp	fp	PRON
ejpam-2571	18	17	+	+	NUM
ejpam-2571	18	18	ufp	ufp	NOUN
ejpam-2571	18	19	+	+	CCONJ
ejpam-2571	18	20	u2	u2	PROPN
ejpam-2571	18	21	fp	fp	NOUN
ejpam-2571	18	22	,	,	PUNCT
ejpam-2571	18	23	where	where	SCONJ
ejpam-2571	18	24	u3	u3	NOUN
ejpam-2571	18	25	=	=	SYM
ejpam-2571	18	26	u	u	PROPN
ejpam-2571	18	27	,	,	PUNCT
ejpam-2571	18	28	have	have	AUX
ejpam-2571	18	29	been	be	AUX
ejpam-2571	18	30	studied	study	VERB
ejpam-2571	18	31	.	.	PUNCT
ejpam-2571	19	1	the	the	DET
ejpam-2571	19	2	present	present	ADJ
ejpam-2571	19	3	paper	paper	NOUN
ejpam-2571	19	4	is	be	AUX
ejpam-2571	19	5	devoted	devote	VERB
ejpam-2571	19	6	to	to	ADP
ejpam-2571	19	7	a	a	DET
ejpam-2571	19	8	class	class	NOUN
ejpam-2571	19	9	of	of	ADP
ejpam-2571	19	10	constacyclic	constacyclic	ADJ
ejpam-2571	19	11	codes	code	NOUN
ejpam-2571	19	12	over	over	ADP
ejpam-2571	19	13	fp	fp	PRON
ejpam-2571	19	14	+	+	NUM
ejpam-2571	19	15	ufp	ufp	NOUN
ejpam-2571	20	1	+	+	CCONJ
ejpam-2571	20	2	u2	u2	PROPN
ejpam-2571	20	3	fp	fp	PROPN
ejpam-2571	20	4	,	,	PUNCT
ejpam-2571	20	5	i.e.	i.e.	X
ejpam-2571	20	6	,	,	PUNCT
ejpam-2571	20	7	(	(	PUNCT
ejpam-2571	20	8	1−	1−	NUM
ejpam-2571	20	9	2u2)-constacyclic	2u2)-constacyclic	PROPN
ejpam-2571	20	10	codes	code	NOUN
ejpam-2571	20	11	over	over	ADP
ejpam-2571	20	12	fp	fp	NOUN
ejpam-2571	20	13	+	+	NUM
ejpam-2571	20	14	ufp	ufp	NOUN
ejpam-2571	20	15	+	+	X
ejpam-2571	20	16	u2	u2	PROPN
ejpam-2571	20	17	fp	fp	PROPN
ejpam-2571	20	18	.	.	PUNCT
ejpam-2571	20	19	∗corresponding	∗corresponde	VERB
ejpam-2571	20	20	author	author	NOUN
ejpam-2571	20	21	.	.	PUNCT
ejpam-2571	21	1	email	email	NOUN
ejpam-2571	21	2	addresses	address	NOUN
ejpam-2571	21	3	:	:	PUNCT
ejpam-2571	21	4	h.mostafanasab@gmail.com	h.mostafanasab@gmail.com	X
ejpam-2571	21	5	(	(	PUNCT
ejpam-2571	21	6	h.	h.	PROPN
ejpam-2571	21	7	mostafanasab	mostafanasab	PROPN
ejpam-2571	21	8	)	)	PUNCT
ejpam-2571	21	9	,	,	PUNCT
ejpam-2571	21	10	neginkarimi8834@gmail.com	neginkarimi8834@gmail.com	X
ejpam-2571	22	1	(	(	PUNCT
ejpam-2571	22	2	n.	n.	PROPN
ejpam-2571	22	3	karimi	karimi	PROPN
ejpam-2571	22	4	)	)	PUNCT
ejpam-2571	22	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2571	23	1	39	39	NUM
ejpam-2571	23	2	c	c	NOUN
ejpam-2571	23	3	©	©	PROPN
ejpam-2571	23	4	2016	2016	NUM
ejpam-2571	23	5	ejpam	ejpam	VERB
ejpam-2571	23	6	all	all	DET
ejpam-2571	23	7	rights	right	NOUN
ejpam-2571	23	8	reserved	reserve	VERB
ejpam-2571	23	9	.	.	PUNCT
ejpam-2571	24	1	h.	h.	PROPN
ejpam-2571	24	2	mostafanasab	mostafanasab	PROPN
ejpam-2571	24	3	,	,	PUNCT
ejpam-2571	24	4	n.	n.	PROPN
ejpam-2571	24	5	karimi	karimi	PROPN
ejpam-2571	24	6	/	/	SYM
ejpam-2571	24	7	eur	eur	PROPN
ejpam-2571	24	8	.	.	PUNCT
ejpam-2571	25	1	j.	j.	PROPN
ejpam-2571	25	2	pure	pure	PROPN
ejpam-2571	25	3	appl	appl	PROPN
ejpam-2571	25	4	.	.	PROPN
ejpam-2571	25	5	math	math	PROPN
ejpam-2571	25	6	,	,	PUNCT
ejpam-2571	25	7	9	9	NUM
ejpam-2571	25	8	(	(	PUNCT
ejpam-2571	25	9	2016	2016	NUM
ejpam-2571	25	10	)	)	PUNCT
ejpam-2571	25	11	,	,	PUNCT
ejpam-2571	25	12	39	39	NUM
ejpam-2571	25	13	-	-	SYM
ejpam-2571	25	14	47	47	NUM
ejpam-2571	25	15	40	40	NUM
ejpam-2571	25	16	let	let	VERB
ejpam-2571	25	17	σ	σ	PROPN
ejpam-2571	25	18	,	,	PUNCT
ejpam-2571	25	19	γ	γ	PROPN
ejpam-2571	25	20	and	and	CCONJ
ejpam-2571	25	21	̺	̺	AUX
ejpam-2571	25	22	be	be	AUX
ejpam-2571	25	23	maps	map	NOUN
ejpam-2571	25	24	from	from	ADP
ejpam-2571	25	25	rn	rn	PROPN
ejpam-2571	25	26	to	to	PART
ejpam-2571	25	27	rn	rn	PROPN
ejpam-2571	25	28	given	give	VERB
ejpam-2571	25	29	by	by	ADP
ejpam-2571	25	30	σ(r0	σ(r0	NOUN
ejpam-2571	25	31	,	,	PUNCT
ejpam-2571	25	32	r1	r1	NOUN
ejpam-2571	25	33	,	,	PUNCT
ejpam-2571	25	34	.	.	PUNCT
ejpam-2571	25	35	.	.	PUNCT
ejpam-2571	26	1	.	.	PUNCT
ejpam-2571	27	1	,	,	PUNCT
ejpam-2571	27	2	rn−1	rn−1	NOUN
ejpam-2571	27	3	)	)	PUNCT
ejpam-2571	27	4	=(	=(	NOUN
ejpam-2571	27	5	rn−1	rn−1	PROPN
ejpam-2571	27	6	,	,	PUNCT
ejpam-2571	27	7	r0	r0	NOUN
ejpam-2571	27	8	,	,	PUNCT
ejpam-2571	27	9	r1	r1	NOUN
ejpam-2571	27	10	,	,	PUNCT
ejpam-2571	27	11	.	.	PUNCT
ejpam-2571	27	12	.	.	PUNCT
ejpam-2571	28	1	.	.	PUNCT
ejpam-2571	29	1	,	,	PUNCT
ejpam-2571	29	2	rn−2	rn−2	PROPN
ejpam-2571	29	3	)	)	PUNCT
ejpam-2571	29	4	,	,	PUNCT
ejpam-2571	29	5	γ(r0	γ(r0	NOUN
ejpam-2571	29	6	,	,	PUNCT
ejpam-2571	29	7	r1	r1	PROPN
ejpam-2571	29	8	,	,	PUNCT
ejpam-2571	29	9	.	.	PUNCT
ejpam-2571	29	10	.	.	PUNCT
ejpam-2571	30	1	.	.	PUNCT
ejpam-2571	31	1	,	,	PUNCT
ejpam-2571	31	2	rn−1	rn−1	NOUN
ejpam-2571	31	3	)	)	PUNCT
ejpam-2571	31	4	=(	=(	NOUN
ejpam-2571	31	5	−rn−1	−rn−1	PROPN
ejpam-2571	31	6	,	,	PUNCT
ejpam-2571	31	7	r0	r0	NOUN
ejpam-2571	31	8	,	,	PUNCT
ejpam-2571	31	9	r1	r1	NOUN
ejpam-2571	31	10	,	,	PUNCT
ejpam-2571	31	11	.	.	PUNCT
ejpam-2571	31	12	.	.	PUNCT
ejpam-2571	32	1	.	.	PUNCT
ejpam-2571	33	1	,	,	PUNCT
ejpam-2571	33	2	rn−2	rn−2	PROPN
ejpam-2571	33	3	)	)	PUNCT
ejpam-2571	33	4	,	,	PUNCT
ejpam-2571	33	5	and	and	CCONJ
ejpam-2571	33	6	̺(r0	̺(r0	PROPN
ejpam-2571	33	7	,	,	PUNCT
ejpam-2571	33	8	r1	r1	NOUN
ejpam-2571	33	9	,	,	PUNCT
ejpam-2571	33	10	.	.	PUNCT
ejpam-2571	33	11	.	.	PUNCT
ejpam-2571	34	1	.	.	PUNCT
ejpam-2571	35	1	,	,	PUNCT
ejpam-2571	35	2	rn−1	rn−1	NOUN
ejpam-2571	35	3	)	)	PUNCT
ejpam-2571	35	4	=(	=(	NOUN
ejpam-2571	35	5	(	(	PUNCT
ejpam-2571	35	6	1−	1−	NUM
ejpam-2571	35	7	2u2)rn−1	2u2)rn−1	NUM
ejpam-2571	35	8	,	,	PUNCT
ejpam-2571	35	9	r0	r0	NOUN
ejpam-2571	35	10	,	,	PUNCT
ejpam-2571	35	11	r1	r1	NOUN
ejpam-2571	35	12	,	,	PUNCT
ejpam-2571	35	13	.	.	PUNCT
ejpam-2571	35	14	.	.	PUNCT
ejpam-2571	36	1	.	.	PUNCT
ejpam-2571	37	1	,	,	PUNCT
ejpam-2571	37	2	rn−2	rn−2	PROPN
ejpam-2571	37	3	)	)	PUNCT
ejpam-2571	37	4	,	,	PUNCT
ejpam-2571	37	5	respectively	respectively	ADV
ejpam-2571	37	6	.	.	PUNCT
ejpam-2571	38	1	letc	letc	PROPN
ejpam-2571	38	2	be	be	AUX
ejpam-2571	38	3	a	a	DET
ejpam-2571	38	4	linear	linear	ADJ
ejpam-2571	38	5	code	code	NOUN
ejpam-2571	38	6	of	of	ADP
ejpam-2571	38	7	lenght	lenght	ADJ
ejpam-2571	38	8	n	n	NOUN
ejpam-2571	38	9	overr	overr	NOUN
ejpam-2571	38	10	.	.	PUNCT
ejpam-2571	39	1	thenc	thenc	NOUN
ejpam-2571	39	2	is	be	AUX
ejpam-2571	39	3	said	say	VERB
ejpam-2571	39	4	to	to	PART
ejpam-2571	39	5	be	be	AUX
ejpam-2571	39	6	cyclic	cyclic	ADJ
ejpam-2571	39	7	ifσ(c	ifσ(c	ADJ
ejpam-2571	39	8	)	)	PUNCT
ejpam-2571	40	1	=	=	SYM
ejpam-2571	40	2	c	c	NOUN
ejpam-2571	40	3	,	,	PUNCT
ejpam-2571	40	4	negacyclic	negacyclic	ADJ
ejpam-2571	40	5	if	if	SCONJ
ejpam-2571	40	6	γ(c	γ(c	PROPN
ejpam-2571	40	7	)	)	PUNCT
ejpam-2571	41	1	=	=	PUNCT
ejpam-2571	41	2	c	c	PROPN
ejpam-2571	41	3	and	and	CCONJ
ejpam-2571	41	4	(	(	PUNCT
ejpam-2571	41	5	1−	1−	NUM
ejpam-2571	41	6	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	41	7	if	if	SCONJ
ejpam-2571	41	8	̺(c	̺(c	NOUN
ejpam-2571	41	9	)	)	PUNCT
ejpam-2571	42	1	=	=	PUNCT
ejpam-2571	42	2	c	c	X
ejpam-2571	42	3	.	.	PUNCT
ejpam-2571	43	1	let	let	VERB
ejpam-2571	43	2	c	c	PRON
ejpam-2571	43	3	be	be	AUX
ejpam-2571	43	4	a	a	DET
ejpam-2571	43	5	code	code	NOUN
ejpam-2571	43	6	of	of	ADP
ejpam-2571	43	7	length	length	NOUN
ejpam-2571	43	8	n	n	CCONJ
ejpam-2571	43	9	over	over	ADP
ejpam-2571	43	10	r	r	NOUN
ejpam-2571	43	11	,	,	PUNCT
ejpam-2571	43	12	and	and	CCONJ
ejpam-2571	43	13	p(c	p(c	PROPN
ejpam-2571	43	14	)	)	PUNCT
ejpam-2571	43	15	be	be	AUX
ejpam-2571	43	16	its	its	PRON
ejpam-2571	43	17	polynomial	polynomial	ADJ
ejpam-2571	43	18	representation	representation	NOUN
ejpam-2571	43	19	,	,	PUNCT
ejpam-2571	43	20	i.e.	i.e.	X
ejpam-2571	43	21	,	,	PUNCT
ejpam-2571	43	22	p(c	p(c	NOUN
ejpam-2571	43	23	)	)	PUNCT
ejpam-2571	44	1	=	=	PUNCT
ejpam-2571	44	2	¦	¦	PROPN
ejpam-2571	44	3	n−1	n−1	PROPN
ejpam-2571	44	4	∑	∑	PUNCT
ejpam-2571	44	5	i=0	i=0	PROPN
ejpam-2571	44	6	ri	ri	X
ejpam-2571	45	1	x	x	PUNCT
ejpam-2571	45	2	i	i	PRON
ejpam-2571	45	3	|(r0	|(r0	VERB
ejpam-2571	45	4	,	,	PUNCT
ejpam-2571	45	5	.	.	PUNCT
ejpam-2571	45	6	.	.	PUNCT
ejpam-2571	46	1	.	.	PUNCT
ejpam-2571	47	1	,	,	PUNCT
ejpam-2571	47	2	rn−1	rn−1	NOUN
ejpam-2571	47	3	)	)	PUNCT
ejpam-2571	47	4	∈	∈	PROPN
ejpam-2571	47	5	c	c	NOUN
ejpam-2571	48	1	©	©	NOUN
ejpam-2571	48	2	.	.	PUNCT
ejpam-2571	49	1	it	it	PRON
ejpam-2571	49	2	is	be	AUX
ejpam-2571	49	3	easy	easy	ADJ
ejpam-2571	49	4	to	to	PART
ejpam-2571	49	5	see	see	VERB
ejpam-2571	49	6	that	that	PRON
ejpam-2571	49	7	:	:	PUNCT
ejpam-2571	49	8	theorem	theorem	NOUN
ejpam-2571	49	9	1	1	NUM
ejpam-2571	49	10	.	.	PUNCT
ejpam-2571	50	1	a	a	DET
ejpam-2571	50	2	code	code	NOUN
ejpam-2571	50	3	c	c	NOUN
ejpam-2571	50	4	of	of	ADP
ejpam-2571	50	5	length	length	NOUN
ejpam-2571	50	6	n	n	PRON
ejpam-2571	50	7	overr	overr	NOUN
ejpam-2571	50	8	is	be	AUX
ejpam-2571	50	9	(	(	PUNCT
ejpam-2571	50	10	1−2u2)-constacyclic	1−2u2)-constacyclic	NUM
ejpam-2571	50	11	if	if	SCONJ
ejpam-2571	50	12	and	and	CCONJ
ejpam-2571	50	13	only	only	ADV
ejpam-2571	50	14	if	if	SCONJ
ejpam-2571	50	15	p(c	p(c	PROPN
ejpam-2571	50	16	)	)	PUNCT
ejpam-2571	50	17	is	be	AUX
ejpam-2571	50	18	an	an	DET
ejpam-2571	50	19	ideal	ideal	NOUN
ejpam-2571	50	20	of	of	ADP
ejpam-2571	50	21	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2571	50	22	−	−	PROPN
ejpam-2571	50	23	(	(	PUNCT
ejpam-2571	50	24	1−	1−	NUM
ejpam-2571	50	25	2u2	2u2	NUM
ejpam-2571	50	26	)	)	PUNCT
ejpam-2571	50	27	〉	〉	NOUN
ejpam-2571	50	28	.	.	PUNCT
ejpam-2571	51	1	let	let	VERB
ejpam-2571	51	2	x	x	PUNCT
ejpam-2571	51	3	=	=	PRON
ejpam-2571	51	4	(	(	PUNCT
ejpam-2571	51	5	x0	x0	PROPN
ejpam-2571	51	6	,	,	PUNCT
ejpam-2571	51	7	x1	x1	PROPN
ejpam-2571	51	8	,	,	PUNCT
ejpam-2571	51	9	.	.	PUNCT
ejpam-2571	51	10	.	.	PUNCT
ejpam-2571	52	1	.	.	PUNCT
ejpam-2571	53	1	,	,	PUNCT
ejpam-2571	53	2	xn−1	xn−1	PROPN
ejpam-2571	53	3	)	)	PUNCT
ejpam-2571	53	4	and	and	CCONJ
ejpam-2571	53	5	y	y	PROPN
ejpam-2571	53	6	=	=	SYM
ejpam-2571	53	7	(	(	PUNCT
ejpam-2571	53	8	y0	y0	NOUN
ejpam-2571	53	9	,	,	PUNCT
ejpam-2571	53	10	y1	y1	NOUN
ejpam-2571	53	11	,	,	PUNCT
ejpam-2571	53	12	.	.	PUNCT
ejpam-2571	53	13	.	.	PUNCT
ejpam-2571	53	14	.	.	PUNCT
ejpam-2571	54	1	,	,	PUNCT
ejpam-2571	54	2	yn−1	yn−1	PROPN
ejpam-2571	54	3	)	)	PUNCT
ejpam-2571	54	4	be	be	VERB
ejpam-2571	54	5	two	two	NUM
ejpam-2571	54	6	elements	element	NOUN
ejpam-2571	54	7	ofrn	ofrn	ADV
ejpam-2571	54	8	.	.	PUNCT
ejpam-2571	55	1	the	the	DET
ejpam-2571	55	2	euclidean	euclidean	ADJ
ejpam-2571	55	3	inner	inner	ADJ
ejpam-2571	55	4	product	product	NOUN
ejpam-2571	55	5	of	of	ADP
ejpam-2571	55	6	x	x	PROPN
ejpam-2571	55	7	and	and	CCONJ
ejpam-2571	55	8	y	y	PROPN
ejpam-2571	55	9	in	in	ADP
ejpam-2571	55	10	rn	rn	PROPN
ejpam-2571	55	11	is	be	AUX
ejpam-2571	55	12	defined	define	VERB
ejpam-2571	55	13	as	as	ADP
ejpam-2571	55	14	x	x	X
ejpam-2571	55	15	·	·	PUNCT
ejpam-2571	55	16	y	y	X
ejpam-2571	55	17	=	=	PUNCT
ejpam-2571	56	1	x0	x0	PROPN
ejpam-2571	56	2	y0	y0	PROPN
ejpam-2571	56	3	+	+	CCONJ
ejpam-2571	56	4	x1	x1	PROPN
ejpam-2571	56	5	y1	y1	NOUN
ejpam-2571	56	6	+	+	X
ejpam-2571	56	7	.	.	PUNCT
ejpam-2571	56	8	.	.	PUNCT
ejpam-2571	57	1	.+	.+	NOUN
ejpam-2571	58	1	xn−1	xn−1	PROPN
ejpam-2571	58	2	yn−1	yn−1	PROPN
ejpam-2571	58	3	,	,	PUNCT
ejpam-2571	58	4	where	where	SCONJ
ejpam-2571	58	5	the	the	DET
ejpam-2571	58	6	operation	operation	NOUN
ejpam-2571	58	7	is	be	AUX
ejpam-2571	58	8	performed	perform	VERB
ejpam-2571	58	9	in	in	ADP
ejpam-2571	58	10	r	r	NOUN
ejpam-2571	58	11	.	.	PUNCT
ejpam-2571	59	1	the	the	DET
ejpam-2571	59	2	dual	dual	ADJ
ejpam-2571	59	3	code	code	NOUN
ejpam-2571	59	4	of	of	ADP
ejpam-2571	59	5	c	c	PROPN
ejpam-2571	59	6	is	be	AUX
ejpam-2571	59	7	defined	define	VERB
ejpam-2571	59	8	as	as	ADP
ejpam-2571	59	9	c⊥	c⊥	X
ejpam-2571	59	10	=	=	PUNCT
ejpam-2571	59	11	{	{	PUNCT
ejpam-2571	59	12	x	x	PUNCT
ejpam-2571	59	13	∈	∈	NOUN
ejpam-2571	59	14	rn|x	rn|x	X
ejpam-2571	59	15	·	·	PUNCT
ejpam-2571	59	16	y	y	X
ejpam-2571	59	17	=	=	PUNCT
ejpam-2571	59	18	0	0	NUM
ejpam-2571	59	19	for	for	ADP
ejpam-2571	59	20	every	every	DET
ejpam-2571	59	21	y	y	PROPN
ejpam-2571	59	22	∈	∈	PROPN
ejpam-2571	59	23	c	c	PROPN
ejpam-2571	59	24	}	}	PUNCT
ejpam-2571	59	25	.	.	PUNCT
ejpam-2571	60	1	we	we	PRON
ejpam-2571	60	2	define	define	VERB
ejpam-2571	60	3	the	the	DET
ejpam-2571	60	4	gray	gray	ADJ
ejpam-2571	60	5	map	map	NOUN
ejpam-2571	60	6	φ	φ	X
ejpam-2571	60	7	:	:	PUNCT
ejpam-2571	60	8	r	r	X
ejpam-2571	60	9	→	→	SYM
ejpam-2571	60	10	f2	f2	X
ejpam-2571	60	11	p	p	NOUN
ejpam-2571	60	12	by	by	ADP
ejpam-2571	60	13	a+	a+	PUNCT
ejpam-2571	60	14	bu+	bu+	NOUN
ejpam-2571	60	15	cu2	cu2	NOUN
ejpam-2571	60	16	7→	7→	NUM
ejpam-2571	60	17	(	(	PUNCT
ejpam-2571	60	18	−c	−c	NOUN
ejpam-2571	60	19	,	,	PUNCT
ejpam-2571	60	20	2a+	2a+	NUM
ejpam-2571	60	21	c	c	NOUN
ejpam-2571	60	22	)	)	PUNCT
ejpam-2571	60	23	.	.	PUNCT
ejpam-2571	61	1	this	this	DET
ejpam-2571	61	2	map	map	NOUN
ejpam-2571	61	3	can	can	AUX
ejpam-2571	61	4	be	be	AUX
ejpam-2571	61	5	extended	extend	VERB
ejpam-2571	61	6	to	to	ADP
ejpam-2571	61	7	rn	rn	PROPN
ejpam-2571	61	8	in	in	ADP
ejpam-2571	61	9	a	a	DET
ejpam-2571	61	10	natural	natural	ADJ
ejpam-2571	61	11	way	way	NOUN
ejpam-2571	61	12	:	:	PUNCT
ejpam-2571	61	13	φ	φ	NUM
ejpam-2571	61	14	:	:	PUNCT
ejpam-2571	61	15	rn→	rn→	PROPN
ejpam-2571	61	16	f2n	f2n	PROPN
ejpam-2571	61	17	p	p	X
ejpam-2571	61	18	(	(	PUNCT
ejpam-2571	61	19	r0	r0	NOUN
ejpam-2571	61	20	,	,	PUNCT
ejpam-2571	61	21	r1	r1	NOUN
ejpam-2571	61	22	,	,	PUNCT
ejpam-2571	61	23	.	.	PUNCT
ejpam-2571	61	24	.	.	PUNCT
ejpam-2571	62	1	.	.	PUNCT
ejpam-2571	63	1	,	,	PUNCT
ejpam-2571	63	2	rn−1	rn−1	NOUN
ejpam-2571	63	3	)	)	PUNCT
ejpam-2571	63	4	7→(−c0,−c1	7→(−c0,−c1	PROPN
ejpam-2571	63	5	,	,	PUNCT
ejpam-2571	63	6	.	.	PUNCT
ejpam-2571	63	7	.	.	PUNCT
ejpam-2571	64	1	.	.	PUNCT
ejpam-2571	65	1	,	,	PUNCT
ejpam-2571	65	2	−cn−1	−cn−1	NUM
ejpam-2571	65	3	,	,	PUNCT
ejpam-2571	65	4	2a0	2a0	NUM
ejpam-2571	66	1	+	+	CCONJ
ejpam-2571	66	2	c0	c0	NOUN
ejpam-2571	66	3	,	,	PUNCT
ejpam-2571	66	4	2a1	2a1	NUM
ejpam-2571	66	5	+	+	CCONJ
ejpam-2571	66	6	c1	c1	NOUN
ejpam-2571	66	7	,	,	PUNCT
ejpam-2571	66	8	.	.	PUNCT
ejpam-2571	66	9	.	.	PUNCT
ejpam-2571	67	1	.	.	PUNCT
ejpam-2571	68	1	,	,	PUNCT
ejpam-2571	68	2	2an−1	2an−1	NUM
ejpam-2571	68	3	+	+	CCONJ
ejpam-2571	68	4	cn−1	cn−1	NOUN
ejpam-2571	68	5	)	)	PUNCT
ejpam-2571	68	6	where	where	SCONJ
ejpam-2571	68	7	ri	ri	PROPN
ejpam-2571	68	8	=	=	NOUN
ejpam-2571	68	9	ai	ai	VERB
ejpam-2571	68	10	+	+	ADJ
ejpam-2571	68	11	biu+	biu+	ADJ
ejpam-2571	68	12	ciu	ciu	NOUN
ejpam-2571	68	13	2	2	NUM
ejpam-2571	68	14	,	,	PUNCT
ejpam-2571	68	15	0≤	0≤	PUNCT
ejpam-2571	69	1	i	i	PRON
ejpam-2571	69	2	≤	≤	ADJ
ejpam-2571	69	3	n−	n−	NOUN
ejpam-2571	69	4	1	1	NUM
ejpam-2571	69	5	.	.	PUNCT
ejpam-2571	70	1	we	we	PRON
ejpam-2571	70	2	denote	denote	VERB
ejpam-2571	70	3	by	by	ADP
ejpam-2571	70	4	η1	η1	NOUN
ejpam-2571	70	5	,	,	PUNCT
ejpam-2571	70	6	η2	η2	NOUN
ejpam-2571	70	7	,	,	PUNCT
ejpam-2571	70	8	η3	η3	NOUN
ejpam-2571	70	9	respectively	respectively	ADV
ejpam-2571	70	10	the	the	DET
ejpam-2571	70	11	following	follow	VERB
ejpam-2571	70	12	elements	element	NOUN
ejpam-2571	70	13	of	of	ADP
ejpam-2571	70	14	r	r	NOUN
ejpam-2571	70	15	:	:	PUNCT
ejpam-2571	70	16	η1	η1	NOUN
ejpam-2571	70	17	=	=	SYM
ejpam-2571	70	18	1−	1−	NUM
ejpam-2571	70	19	u2	u2	NOUN
ejpam-2571	70	20	,	,	PUNCT
ejpam-2571	70	21	η2	η2	ADJ
ejpam-2571	70	22	=	=	SYM
ejpam-2571	70	23	2−1(u+	2−1(u+	NUM
ejpam-2571	70	24	u2	u2	NOUN
ejpam-2571	70	25	)	)	PUNCT
ejpam-2571	70	26	,	,	PUNCT
ejpam-2571	70	27	η3	η3	NOUN
ejpam-2571	70	28	=	=	NOUN
ejpam-2571	70	29	2−1(−u+	2−1(−u+	NUM
ejpam-2571	70	30	u2	u2	NOUN
ejpam-2571	70	31	)	)	PUNCT
ejpam-2571	70	32	.	.	PUNCT
ejpam-2571	71	1	note	note	VERB
ejpam-2571	71	2	that	that	SCONJ
ejpam-2571	71	3	η1	η1	NOUN
ejpam-2571	71	4	,	,	PUNCT
ejpam-2571	71	5	η2	η2	PROPN
ejpam-2571	71	6	and	and	CCONJ
ejpam-2571	71	7	η3	η3	NOUN
ejpam-2571	71	8	are	be	AUX
ejpam-2571	71	9	mutually	mutually	ADV
ejpam-2571	71	10	orthogonal	orthogonal	ADJ
ejpam-2571	71	11	idempotents	idempotent	NOUN
ejpam-2571	71	12	over	over	ADP
ejpam-2571	71	13	r	r	NOUN
ejpam-2571	71	14	and	and	CCONJ
ejpam-2571	71	15	η1	η1	NOUN
ejpam-2571	71	16	+	+	CCONJ
ejpam-2571	71	17	η2	η2	ADJ
ejpam-2571	71	18	+	+	CCONJ
ejpam-2571	71	19	η3	η3	NOUN
ejpam-2571	71	20	=	=	PUNCT
ejpam-2571	72	1	1	1	X
ejpam-2571	72	2	.	.	PUNCT
ejpam-2571	72	3	let	let	VERB
ejpam-2571	72	4	c	c	PRON
ejpam-2571	72	5	be	be	AUX
ejpam-2571	72	6	a	a	DET
ejpam-2571	72	7	linear	linear	ADJ
ejpam-2571	72	8	code	code	NOUN
ejpam-2571	72	9	of	of	ADP
ejpam-2571	72	10	length	length	NOUN
ejpam-2571	72	11	n	n	CCONJ
ejpam-2571	72	12	over	over	ADP
ejpam-2571	72	13	r	r	NOUN
ejpam-2571	72	14	.	.	PUNCT
ejpam-2571	73	1	define	define	VERB
ejpam-2571	73	2	c1	c1	PROPN
ejpam-2571	73	3	=	=	PROPN
ejpam-2571	73	4	{	{	PUNCT
ejpam-2571	73	5	x	x	SYM
ejpam-2571	73	6	∈	∈	PROPN
ejpam-2571	73	7	f	f	NOUN
ejpam-2571	73	8	n	n	PRON
ejpam-2571	73	9	p	p	PROPN
ejpam-2571	74	1	|	|	PROPN
ejpam-2571	74	2	∃y	∃y	PROPN
ejpam-2571	74	3	,	,	PUNCT
ejpam-2571	74	4	z	z	PROPN
ejpam-2571	74	5	∈	∈	PROPN
ejpam-2571	74	6	fn	fn	NOUN
ejpam-2571	74	7	p	p	NOUN
ejpam-2571	74	8	,	,	PUNCT
ejpam-2571	74	9	η1	η1	NOUN
ejpam-2571	74	10	x	x	PUNCT
ejpam-2571	75	1	+	+	ADJ
ejpam-2571	75	2	η2	η2	ADJ
ejpam-2571	75	3	y	y	PROPN
ejpam-2571	75	4	+	+	PROPN
ejpam-2571	75	5	η3z	η3z	VERB
ejpam-2571	75	6	∈	∈	PROPN
ejpam-2571	75	7	c	c	NOUN
ejpam-2571	75	8	}	}	PUNCT
ejpam-2571	75	9	,	,	PUNCT
ejpam-2571	75	10	c2	c2	PROPN
ejpam-2571	75	11	=	=	PRON
ejpam-2571	75	12	{	{	PUNCT
ejpam-2571	75	13	y	y	PROPN
ejpam-2571	75	14	∈	∈	PROPN
ejpam-2571	75	15	f	f	PROPN
ejpam-2571	75	16	n	n	PRON
ejpam-2571	75	17	p	p	NOUN
ejpam-2571	75	18	|	|	ADV
ejpam-2571	75	19	∃x	∃x	PROPN
ejpam-2571	75	20	,	,	PUNCT
ejpam-2571	76	1	z	z	NOUN
ejpam-2571	76	2	∈	∈	PROPN
ejpam-2571	76	3	fn	fn	NOUN
ejpam-2571	76	4	p	p	NOUN
ejpam-2571	76	5	,	,	PUNCT
ejpam-2571	76	6	η1	η1	NOUN
ejpam-2571	76	7	x	x	PUNCT
ejpam-2571	77	1	+	+	ADJ
ejpam-2571	77	2	η2	η2	ADJ
ejpam-2571	77	3	y	y	PROPN
ejpam-2571	77	4	+	+	PROPN
ejpam-2571	77	5	η3z	η3z	VERB
ejpam-2571	77	6	∈	∈	NOUN
ejpam-2571	77	7	c	c	NOUN
ejpam-2571	77	8	}	}	PUNCT
ejpam-2571	77	9	,	,	PUNCT
ejpam-2571	77	10	c3	c3	PROPN
ejpam-2571	77	11	=	=	PRON
ejpam-2571	77	12	{	{	PUNCT
ejpam-2571	77	13	z	z	NOUN
ejpam-2571	77	14	∈	∈	PROPN
ejpam-2571	77	15	f	f	PROPN
ejpam-2571	77	16	n	n	CCONJ
ejpam-2571	77	17	p	p	NOUN
ejpam-2571	77	18	|	|	ADV
ejpam-2571	77	19	∃x	∃x	PROPN
ejpam-2571	77	20	,	,	PUNCT
ejpam-2571	77	21	y	y	PROPN
ejpam-2571	77	22	∈	∈	PROPN
ejpam-2571	77	23	fn	fn	NOUN
ejpam-2571	77	24	p	p	NOUN
ejpam-2571	77	25	,	,	PUNCT
ejpam-2571	77	26	η1	η1	NOUN
ejpam-2571	77	27	x	x	PUNCT
ejpam-2571	77	28	+	+	ADJ
ejpam-2571	77	29	η2	η2	ADJ
ejpam-2571	77	30	y	y	PROPN
ejpam-2571	77	31	+	+	PROPN
ejpam-2571	77	32	η3z	η3z	VERB
ejpam-2571	77	33	∈	∈	NOUN
ejpam-2571	77	34	c	c	NOUN
ejpam-2571	77	35	}	}	PUNCT
ejpam-2571	77	36	.	.	PUNCT
ejpam-2571	78	1	then	then	ADV
ejpam-2571	78	2	c1,c2	c1,c2	PROPN
ejpam-2571	78	3	and	and	CCONJ
ejpam-2571	78	4	c3	c3	PROPN
ejpam-2571	78	5	are	be	AUX
ejpam-2571	78	6	all	all	PRON
ejpam-2571	78	7	linear	linear	ADJ
ejpam-2571	78	8	codes	code	NOUN
ejpam-2571	78	9	of	of	ADP
ejpam-2571	78	10	length	length	NOUN
ejpam-2571	78	11	n	n	PROPN
ejpam-2571	78	12	over	over	ADP
ejpam-2571	78	13	fp	fp	NOUN
ejpam-2571	78	14	.	.	PUNCT
ejpam-2571	79	1	moreover	moreover	ADV
ejpam-2571	79	2	,	,	PUNCT
ejpam-2571	79	3	the	the	DET
ejpam-2571	79	4	code	code	NOUN
ejpam-2571	79	5	c	c	NOUN
ejpam-2571	79	6	of	of	ADP
ejpam-2571	79	7	length	length	NOUN
ejpam-2571	79	8	n	n	CCONJ
ejpam-2571	79	9	over	over	ADP
ejpam-2571	79	10	r	r	NOUN
ejpam-2571	79	11	can	can	AUX
ejpam-2571	79	12	be	be	AUX
ejpam-2571	79	13	uniquely	uniquely	ADV
ejpam-2571	79	14	expressed	express	VERB
ejpam-2571	79	15	as	as	ADP
ejpam-2571	79	16	c	c	NOUN
ejpam-2571	79	17	=	=	PUNCT
ejpam-2571	79	18	η1c1	η1c1	X
ejpam-2571	79	19	⊕η2c2	⊕η2c2	PUNCT
ejpam-2571	79	20	⊕η3c3	⊕η3c3	X
ejpam-2571	79	21	.	.	PUNCT
ejpam-2571	79	22	h.	h.	PROPN
ejpam-2571	79	23	mostafanasab	mostafanasab	PROPN
ejpam-2571	79	24	,	,	PUNCT
ejpam-2571	79	25	n.	n.	PROPN
ejpam-2571	79	26	karimi	karimi	PROPN
ejpam-2571	79	27	/	/	SYM
ejpam-2571	79	28	eur	eur	PROPN
ejpam-2571	79	29	.	.	PUNCT
ejpam-2571	80	1	j.	j.	PROPN
ejpam-2571	80	2	pure	pure	PROPN
ejpam-2571	80	3	appl	appl	PROPN
ejpam-2571	80	4	.	.	PROPN
ejpam-2571	80	5	math	math	PROPN
ejpam-2571	80	6	,	,	PUNCT
ejpam-2571	80	7	9	9	NUM
ejpam-2571	80	8	(	(	PUNCT
ejpam-2571	80	9	2016	2016	NUM
ejpam-2571	80	10	)	)	PUNCT
ejpam-2571	80	11	,	,	PUNCT
ejpam-2571	80	12	39	39	NUM
ejpam-2571	80	13	-	-	SYM
ejpam-2571	80	14	47	47	NUM
ejpam-2571	80	15	41	41	NUM
ejpam-2571	80	16	2	2	NUM
ejpam-2571	80	17	.	.	PUNCT
ejpam-2571	80	18	main	main	ADJ
ejpam-2571	80	19	results	result	NOUN
ejpam-2571	80	20	theorem	theorem	VERB
ejpam-2571	80	21	2	2	X
ejpam-2571	80	22	.	.	PUNCT
ejpam-2571	81	1	let	let	VERB
ejpam-2571	81	2	̺	̺	PART
ejpam-2571	81	3	denote	denote	VERB
ejpam-2571	81	4	the	the	DET
ejpam-2571	81	5	(	(	PUNCT
ejpam-2571	81	6	1−	1−	NUM
ejpam-2571	81	7	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	81	8	shift	shift	NOUN
ejpam-2571	81	9	of	of	ADP
ejpam-2571	81	10	rn	rn	PROPN
ejpam-2571	81	11	and	and	CCONJ
ejpam-2571	81	12	σ	σ	NUM
ejpam-2571	81	13	the	the	DET
ejpam-2571	81	14	cyclic	cyclic	ADJ
ejpam-2571	81	15	shift	shift	NOUN
ejpam-2571	81	16	of	of	ADP
ejpam-2571	81	17	f2n	f2n	PROPN
ejpam-2571	81	18	p	p	NOUN
ejpam-2571	81	19	.	.	PUNCT
ejpam-2571	82	1	if	if	SCONJ
ejpam-2571	82	2	φ	φ	PROPN
ejpam-2571	82	3	is	be	AUX
ejpam-2571	82	4	the	the	DET
ejpam-2571	82	5	gray	gray	ADJ
ejpam-2571	82	6	map	map	NOUN
ejpam-2571	82	7	of	of	ADP
ejpam-2571	82	8	rn	rn	PROPN
ejpam-2571	82	9	into	into	ADP
ejpam-2571	82	10	f2n	f2n	PROPN
ejpam-2571	82	11	p	p	NOUN
ejpam-2571	82	12	,	,	PUNCT
ejpam-2571	82	13	then	then	ADV
ejpam-2571	82	14	φ̺	φ̺	PROPN
ejpam-2571	82	15	=	=	SYM
ejpam-2571	82	16	σφ	σφ	NOUN
ejpam-2571	82	17	.	.	PUNCT
ejpam-2571	83	1	proof	proof	NOUN
ejpam-2571	83	2	.	.	PUNCT
ejpam-2571	84	1	let	let	VERB
ejpam-2571	84	2	r̄	r̄	NOUN
ejpam-2571	84	3	=	=	SYM
ejpam-2571	84	4	(	(	PUNCT
ejpam-2571	84	5	r0	r0	NOUN
ejpam-2571	84	6	,	,	PUNCT
ejpam-2571	84	7	r1	r1	NOUN
ejpam-2571	84	8	,	,	PUNCT
ejpam-2571	84	9	.	.	PUNCT
ejpam-2571	84	10	.	.	PUNCT
ejpam-2571	85	1	.	.	PUNCT
ejpam-2571	86	1	,	,	PUNCT
ejpam-2571	86	2	rn−1	rn−1	NOUN
ejpam-2571	86	3	)	)	PUNCT
ejpam-2571	86	4	∈	∈	PROPN
ejpam-2571	86	5	r	r	NOUN
ejpam-2571	86	6	n	n	NOUN
ejpam-2571	86	7	where	where	SCONJ
ejpam-2571	86	8	ri	ri	PROPN
ejpam-2571	86	9	=	=	NOUN
ejpam-2571	86	10	ai	ai	PROPN
ejpam-2571	86	11	+	+	CCONJ
ejpam-2571	86	12	biu	biu	PROPN
ejpam-2571	86	13	+	+	CCONJ
ejpam-2571	86	14	ciu	ciu	NOUN
ejpam-2571	86	15	2	2	NUM
ejpam-2571	86	16	with	with	ADP
ejpam-2571	86	17	ai	ai	PROPN
ejpam-2571	86	18	,	,	PUNCT
ejpam-2571	86	19	bi	bi	NOUN
ejpam-2571	86	20	,	,	PUNCT
ejpam-2571	86	21	ci	ci	PROPN
ejpam-2571	86	22	∈	∈	PROPN
ejpam-2571	86	23	fp	fp	PROPN
ejpam-2571	86	24	for	for	ADP
ejpam-2571	86	25	0≤	0≤	NUM
ejpam-2571	87	1	i	i	PRON
ejpam-2571	87	2	≤	≤	ADJ
ejpam-2571	87	3	n−	n−	NOUN
ejpam-2571	87	4	1	1	NUM
ejpam-2571	87	5	.	.	PUNCT
ejpam-2571	88	1	taking	take	VERB
ejpam-2571	88	2	(	(	PUNCT
ejpam-2571	88	3	1−	1−	NUM
ejpam-2571	88	4	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	88	5	shift	shift	NOUN
ejpam-2571	88	6	on	on	ADP
ejpam-2571	88	7	r̄	r̄	NOUN
ejpam-2571	88	8	,	,	PUNCT
ejpam-2571	88	9	we	we	PRON
ejpam-2571	88	10	have	have	VERB
ejpam-2571	88	11	̺(r̄	̺(r̄	ADV
ejpam-2571	88	12	)	)	PUNCT
ejpam-2571	88	13	=	=	SYM
ejpam-2571	88	14	�	�	PROPN
ejpam-2571	88	15	(	(	PUNCT
ejpam-2571	88	16	1−	1−	NUM
ejpam-2571	88	17	2u2)rn−1	2u2)rn−1	NUM
ejpam-2571	88	18	,	,	PUNCT
ejpam-2571	88	19	r0	r0	NOUN
ejpam-2571	88	20	,	,	PUNCT
ejpam-2571	88	21	r1	r1	NOUN
ejpam-2571	88	22	,	,	PUNCT
ejpam-2571	88	23	.	.	PUNCT
ejpam-2571	88	24	.	.	PUNCT
ejpam-2571	89	1	.	.	PUNCT
ejpam-2571	90	1	,	,	PUNCT
ejpam-2571	90	2	rn−2	rn−2	PROPN
ejpam-2571	90	3	�	�	PROPN
ejpam-2571	90	4	=	=	SYM
ejpam-2571	90	5	�	�	PROPN
ejpam-2571	90	6	an−1	an−1	ADJ
ejpam-2571	90	7	−	−	PROPN
ejpam-2571	90	8	bn−1u+	bn−1u+	NOUN
ejpam-2571	90	9	(	(	PUNCT
ejpam-2571	90	10	−2an−1	−2an−1	NOUN
ejpam-2571	90	11	−	−	NOUN
ejpam-2571	90	12	cn−1)u	cn−1)u	SYM
ejpam-2571	90	13	2	2	NUM
ejpam-2571	90	14	,	,	PUNCT
ejpam-2571	90	15	a0	a0	PROPN
ejpam-2571	90	16	+	+	CCONJ
ejpam-2571	90	17	b0u+	b0u+	PROPN
ejpam-2571	90	18	c0u2	c0u2	PROPN
ejpam-2571	90	19	,	,	PUNCT
ejpam-2571	90	20	a1	a1	NOUN
ejpam-2571	90	21	+	+	CCONJ
ejpam-2571	90	22	b1u+	b1u+	NOUN
ejpam-2571	90	23	c1u2	c1u2	NOUN
ejpam-2571	90	24	,	,	PUNCT
ejpam-2571	90	25	.	.	PUNCT
ejpam-2571	90	26	.	.	PUNCT
ejpam-2571	91	1	.	.	PUNCT
ejpam-2571	92	1	,	,	PUNCT
ejpam-2571	92	2	an−2	an−2	PROPN
ejpam-2571	92	3	+	+	CCONJ
ejpam-2571	92	4	bn−2u+	bn−2u+	VERB
ejpam-2571	92	5	cn−2u2	cn−2u2	PROPN
ejpam-2571	92	6	�	�	PROPN
ejpam-2571	92	7	.	.	PUNCT
ejpam-2571	93	1	now	now	ADV
ejpam-2571	93	2	,	,	PUNCT
ejpam-2571	93	3	using	use	VERB
ejpam-2571	93	4	the	the	DET
ejpam-2571	93	5	definition	definition	NOUN
ejpam-2571	93	6	of	of	ADP
ejpam-2571	93	7	gray	gray	ADJ
ejpam-2571	93	8	map	map	NOUN
ejpam-2571	93	9	φ	φ	NOUN
ejpam-2571	93	10	,	,	PUNCT
ejpam-2571	93	11	we	we	PRON
ejpam-2571	93	12	can	can	AUX
ejpam-2571	93	13	deduce	deduce	VERB
ejpam-2571	93	14	that	that	DET
ejpam-2571	93	15	φ(̺(r̄	φ(̺(r̄	NOUN
ejpam-2571	93	16	)	)	PUNCT
ejpam-2571	93	17	)	)	PUNCT
ejpam-2571	94	1	=	=	PUNCT
ejpam-2571	94	2	�	�	PROPN
ejpam-2571	94	3	2an−1	2an−1	PROPN
ejpam-2571	94	4	+	+	CCONJ
ejpam-2571	94	5	cn−1,−c0,−c1	cn−1,−c0,−c1	NOUN
ejpam-2571	94	6	,	,	PUNCT
ejpam-2571	94	7	.	.	PUNCT
ejpam-2571	94	8	.	.	PUNCT
ejpam-2571	94	9	.	.	PUNCT
ejpam-2571	95	1	,	,	PUNCT
ejpam-2571	95	2	−cn−2	−cn−2	PROPN
ejpam-2571	95	3	,	,	PUNCT
ejpam-2571	95	4	2an−1	2an−1	NUM
ejpam-2571	95	5	+	+	CCONJ
ejpam-2571	95	6	(	(	PUNCT
ejpam-2571	95	7	−2an−1	−2an−1	PROPN
ejpam-2571	95	8	−	−	PROPN
ejpam-2571	95	9	cn−1	cn−1	PROPN
ejpam-2571	95	10	)	)	PUNCT
ejpam-2571	95	11	,	,	PUNCT
ejpam-2571	95	12	2a0	2a0	NUM
ejpam-2571	96	1	+	+	CCONJ
ejpam-2571	96	2	c0	c0	NOUN
ejpam-2571	96	3	,	,	PUNCT
ejpam-2571	96	4	2a1	2a1	NUM
ejpam-2571	96	5	+	+	CCONJ
ejpam-2571	96	6	c1	c1	NOUN
ejpam-2571	96	7	,	,	PUNCT
ejpam-2571	96	8	.	.	PUNCT
ejpam-2571	96	9	.	.	PUNCT
ejpam-2571	97	1	.	.	PUNCT
ejpam-2571	98	1	,	,	PUNCT
ejpam-2571	98	2	2an−2	2an−2	PROPN
ejpam-2571	98	3	+	+	CCONJ
ejpam-2571	98	4	cn−2	cn−2	PROPN
ejpam-2571	98	5	�	�	PROPN
ejpam-2571	98	6	.	.	PUNCT
ejpam-2571	99	1	on	on	ADP
ejpam-2571	99	2	the	the	DET
ejpam-2571	99	3	other	other	ADJ
ejpam-2571	99	4	hand	hand	NOUN
ejpam-2571	99	5	,	,	PUNCT
ejpam-2571	99	6	σ(φ(r̄	σ(φ(r̄	NOUN
ejpam-2571	99	7	)	)	PUNCT
ejpam-2571	99	8	)	)	PUNCT
ejpam-2571	100	1	=	=	PUNCT
ejpam-2571	100	2	σ(−c0,−c1	σ(−c0,−c1	NOUN
ejpam-2571	100	3	,	,	PUNCT
ejpam-2571	100	4	.	.	PUNCT
ejpam-2571	100	5	.	.	PUNCT
ejpam-2571	100	6	.	.	PUNCT
ejpam-2571	101	1	,	,	PUNCT
ejpam-2571	101	2	−cn−1	−cn−1	NUM
ejpam-2571	101	3	,	,	PUNCT
ejpam-2571	101	4	2a0	2a0	NUM
ejpam-2571	102	1	+	+	CCONJ
ejpam-2571	102	2	c0	c0	NOUN
ejpam-2571	102	3	,	,	PUNCT
ejpam-2571	102	4	2a1	2a1	NUM
ejpam-2571	102	5	+	+	CCONJ
ejpam-2571	102	6	c1	c1	NOUN
ejpam-2571	102	7	,	,	PUNCT
ejpam-2571	102	8	.	.	PUNCT
ejpam-2571	102	9	.	.	PUNCT
ejpam-2571	103	1	.	.	PUNCT
ejpam-2571	104	1	,	,	PUNCT
ejpam-2571	104	2	2an−1	2an−1	NUM
ejpam-2571	104	3	+	+	CCONJ
ejpam-2571	104	4	cn−1	cn−1	ADJ
ejpam-2571	104	5	)	)	PUNCT
ejpam-2571	104	6	=	=	SYM
ejpam-2571	104	7	�	�	PROPN
ejpam-2571	104	8	2an−1	2an−1	PROPN
ejpam-2571	104	9	+	+	CCONJ
ejpam-2571	104	10	cn−1,−c0,−c1	cn−1,−c0,−c1	NOUN
ejpam-2571	104	11	,	,	PUNCT
ejpam-2571	104	12	.	.	PUNCT
ejpam-2571	104	13	.	.	PUNCT
ejpam-2571	104	14	.	.	PUNCT
ejpam-2571	105	1	,	,	PUNCT
ejpam-2571	105	2	−cn−1	−cn−1	NUM
ejpam-2571	105	3	,	,	PUNCT
ejpam-2571	105	4	2a0	2a0	NUM
ejpam-2571	106	1	+	+	CCONJ
ejpam-2571	106	2	c0	c0	NOUN
ejpam-2571	106	3	,	,	PUNCT
ejpam-2571	106	4	2a1	2a1	NUM
ejpam-2571	106	5	+	+	CCONJ
ejpam-2571	106	6	c1	c1	NOUN
ejpam-2571	106	7	,	,	PUNCT
ejpam-2571	106	8	.	.	PUNCT
ejpam-2571	106	9	.	.	PUNCT
ejpam-2571	107	1	.	.	PUNCT
ejpam-2571	108	1	,	,	PUNCT
ejpam-2571	108	2	2an−2	2an−2	PROPN
ejpam-2571	108	3	+	+	CCONJ
ejpam-2571	108	4	cn−2	cn−2	PROPN
ejpam-2571	108	5	�	�	PROPN
ejpam-2571	108	6	.	.	PUNCT
ejpam-2571	109	1	therefore	therefore	ADV
ejpam-2571	109	2	,	,	PUNCT
ejpam-2571	109	3	φ̺	φ̺	PROPN
ejpam-2571	109	4	=	=	PUNCT
ejpam-2571	109	5	σφ	σφ	PROPN
ejpam-2571	109	6	.	.	PUNCT
ejpam-2571	109	7	theorem	theorem	NOUN
ejpam-2571	109	8	3	3	NUM
ejpam-2571	109	9	.	.	PUNCT
ejpam-2571	110	1	the	the	DET
ejpam-2571	110	2	gray	gray	ADJ
ejpam-2571	110	3	image	image	NOUN
ejpam-2571	110	4	of	of	ADP
ejpam-2571	110	5	a	a	DET
ejpam-2571	110	6	(	(	PUNCT
ejpam-2571	110	7	1−	1−	NUM
ejpam-2571	110	8	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	110	9	code	code	NOUN
ejpam-2571	110	10	over	over	ADP
ejpam-2571	110	11	r	r	NOUN
ejpam-2571	110	12	of	of	ADP
ejpam-2571	110	13	lenght	lenght	ADJ
ejpam-2571	110	14	n	n	NOUN
ejpam-2571	110	15	is	be	AUX
ejpam-2571	110	16	a	a	DET
ejpam-2571	110	17	cyclic	cyclic	ADJ
ejpam-2571	110	18	code	code	NOUN
ejpam-2571	110	19	over	over	ADP
ejpam-2571	110	20	fp	fp	PROPN
ejpam-2571	110	21	of	of	ADP
ejpam-2571	110	22	lenght	lenght	ADJ
ejpam-2571	110	23	2n	2n	NUM
ejpam-2571	110	24	.	.	PUNCT
ejpam-2571	111	1	proof	proof	NOUN
ejpam-2571	111	2	.	.	PUNCT
ejpam-2571	112	1	let	let	VERB
ejpam-2571	112	2	c	c	PRON
ejpam-2571	112	3	be	be	AUX
ejpam-2571	112	4	a	a	DET
ejpam-2571	112	5	(	(	PUNCT
ejpam-2571	112	6	1	1	NUM
ejpam-2571	112	7	−	−	PROPN
ejpam-2571	112	8	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	112	9	code	code	NOUN
ejpam-2571	112	10	over	over	ADP
ejpam-2571	112	11	r	r	NOUN
ejpam-2571	112	12	.	.	PUNCT
ejpam-2571	113	1	then	then	ADV
ejpam-2571	113	2	̺(c	̺(c	VERB
ejpam-2571	113	3	)	)	PUNCT
ejpam-2571	114	1	=	=	SYM
ejpam-2571	114	2	c	c	NOUN
ejpam-2571	114	3	,	,	PUNCT
ejpam-2571	114	4	and	and	CCONJ
ejpam-2571	114	5	therefore	therefore	ADV
ejpam-2571	114	6	,	,	PUNCT
ejpam-2571	114	7	(	(	PUNCT
ejpam-2571	114	8	φ̺)(c	φ̺)(c	X
ejpam-2571	114	9	)	)	PUNCT
ejpam-2571	114	10	=	=	SYM
ejpam-2571	114	11	φ(c	φ(c	NOUN
ejpam-2571	114	12	)	)	PUNCT
ejpam-2571	114	13	.	.	PUNCT
ejpam-2571	115	1	it	it	PRON
ejpam-2571	115	2	follows	follow	VERB
ejpam-2571	115	3	from	from	ADP
ejpam-2571	115	4	theorem	theorem	ADJ
ejpam-2571	115	5	2	2	NUM
ejpam-2571	115	6	that	that	DET
ejpam-2571	115	7	σ(φ(c	σ(φ(c	NOUN
ejpam-2571	115	8	)	)	PUNCT
ejpam-2571	115	9	)	)	PUNCT
ejpam-2571	116	1	=	=	SYM
ejpam-2571	116	2	φ(c	φ(c	NOUN
ejpam-2571	116	3	)	)	PUNCT
ejpam-2571	116	4	,	,	PUNCT
ejpam-2571	116	5	which	which	PRON
ejpam-2571	116	6	means	mean	VERB
ejpam-2571	116	7	that	that	SCONJ
ejpam-2571	116	8	φ(c	φ(c	NOUN
ejpam-2571	116	9	)	)	PUNCT
ejpam-2571	116	10	is	be	AUX
ejpam-2571	116	11	a	a	DET
ejpam-2571	116	12	cyclic	cyclic	ADJ
ejpam-2571	116	13	code	code	NOUN
ejpam-2571	116	14	.	.	PUNCT
ejpam-2571	117	1	notice	notice	VERB
ejpam-2571	117	2	that	that	SCONJ
ejpam-2571	117	3	(	(	PUNCT
ejpam-2571	117	4	1−	1−	NUM
ejpam-2571	117	5	2u2)n	2u2)n	NUM
ejpam-2571	117	6	=	=	SYM
ejpam-2571	117	7	1−	1−	NUM
ejpam-2571	117	8	2u2	2u2	NUM
ejpam-2571	117	9	if	if	SCONJ
ejpam-2571	117	10	n	n	PRON
ejpam-2571	117	11	is	be	AUX
ejpam-2571	117	12	odd	odd	ADJ
ejpam-2571	117	13	and	and	CCONJ
ejpam-2571	117	14	(	(	PUNCT
ejpam-2571	117	15	1−	1−	NUM
ejpam-2571	117	16	2u2)n	2u2)n	NUM
ejpam-2571	117	17	=	=	SYM
ejpam-2571	117	18	1	1	NUM
ejpam-2571	117	19	if	if	SCONJ
ejpam-2571	117	20	n	n	PRON
ejpam-2571	117	21	is	be	AUX
ejpam-2571	117	22	even	even	ADV
ejpam-2571	117	23	.	.	PUNCT
ejpam-2571	118	1	proposition	proposition	NOUN
ejpam-2571	118	2	1	1	NUM
ejpam-2571	118	3	.	.	PUNCT
ejpam-2571	119	1	let	let	VERB
ejpam-2571	119	2	c	c	PRON
ejpam-2571	119	3	be	be	AUX
ejpam-2571	119	4	a	a	DET
ejpam-2571	119	5	code	code	NOUN
ejpam-2571	119	6	of	of	ADP
ejpam-2571	119	7	lenght	lenght	ADJ
ejpam-2571	119	8	n	n	NOUN
ejpam-2571	119	9	over	over	ADP
ejpam-2571	119	10	r	r	NOUN
ejpam-2571	119	11	.	.	PUNCT
ejpam-2571	120	1	then	then	ADV
ejpam-2571	120	2	c	c	PROPN
ejpam-2571	120	3	is	be	AUX
ejpam-2571	120	4	a	a	DET
ejpam-2571	120	5	(	(	PUNCT
ejpam-2571	120	6	1−	1−	NUM
ejpam-2571	120	7	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	120	8	code	code	NOUN
ejpam-2571	120	9	if	if	SCONJ
ejpam-2571	120	10	and	and	CCONJ
ejpam-2571	120	11	only	only	ADV
ejpam-2571	120	12	if	if	SCONJ
ejpam-2571	120	13	c	c	PROPN
ejpam-2571	120	14	⊥	⊥	PROPN
ejpam-2571	120	15	is	be	AUX
ejpam-2571	120	16	a	a	DET
ejpam-2571	120	17	(	(	PUNCT
ejpam-2571	120	18	1−	1−	NUM
ejpam-2571	120	19	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	120	20	code	code	NOUN
ejpam-2571	120	21	.	.	PUNCT
ejpam-2571	121	1	proof	proof	NOUN
ejpam-2571	121	2	.	.	PUNCT
ejpam-2571	122	1	the	the	DET
ejpam-2571	122	2	“	"	PUNCT
ejpam-2571	122	3	only	only	ADV
ejpam-2571	122	4	if	if	SCONJ
ejpam-2571	122	5	”	"	PUNCT
ejpam-2571	122	6	part	part	NOUN
ejpam-2571	122	7	follows	follow	VERB
ejpam-2571	122	8	from	from	ADP
ejpam-2571	122	9	proposition	proposition	NOUN
ejpam-2571	122	10	2.4	2.4	NUM
ejpam-2571	122	11	of	of	ADP
ejpam-2571	122	12	[	[	X
ejpam-2571	122	13	6	6	NUM
ejpam-2571	122	14	]	]	PUNCT
ejpam-2571	122	15	.	.	PUNCT
ejpam-2571	123	1	for	for	ADP
ejpam-2571	123	2	the	the	DET
ejpam-2571	123	3	converse	converse	NOUN
ejpam-2571	123	4	,	,	PUNCT
ejpam-2571	123	5	note	note	VERB
ejpam-2571	123	6	the	the	DET
ejpam-2571	123	7	fact	fact	NOUN
ejpam-2571	124	1	that	that	SCONJ
ejpam-2571	124	2	(	(	PUNCT
ejpam-2571	124	3	c	c	NOUN
ejpam-2571	124	4	⊥)⊥	⊥)⊥	NOUN
ejpam-2571	124	5	=	=	SYM
ejpam-2571	124	6	c	c	PROPN
ejpam-2571	124	7	.	.	PUNCT
ejpam-2571	125	1	recall	recall	VERB
ejpam-2571	125	2	that	that	SCONJ
ejpam-2571	125	3	a	a	DET
ejpam-2571	125	4	code	code	NOUN
ejpam-2571	125	5	c	c	NOUN
ejpam-2571	125	6	is	be	AUX
ejpam-2571	125	7	said	say	VERB
ejpam-2571	125	8	to	to	PART
ejpam-2571	125	9	be	be	AUX
ejpam-2571	125	10	self	self	NOUN
ejpam-2571	125	11	-	-	PUNCT
ejpam-2571	125	12	orthogonal	orthogonal	NOUN
ejpam-2571	125	13	provided	provide	VERB
ejpam-2571	125	14	c	c	NOUN
ejpam-2571	125	15	⊆	⊆	NUM
ejpam-2571	125	16	c	c	X
ejpam-2571	125	17	⊥.	⊥.	NUM
ejpam-2571	125	18	proposition	proposition	NOUN
ejpam-2571	125	19	2	2	NUM
ejpam-2571	125	20	.	.	PUNCT
ejpam-2571	126	1	let	let	VERB
ejpam-2571	126	2	c	c	PRON
ejpam-2571	126	3	be	be	AUX
ejpam-2571	126	4	a	a	DET
ejpam-2571	126	5	code	code	NOUN
ejpam-2571	126	6	of	of	ADP
ejpam-2571	126	7	length	length	NOUN
ejpam-2571	126	8	n	n	CCONJ
ejpam-2571	126	9	over	over	ADP
ejpam-2571	126	10	r	r	NOUN
ejpam-2571	126	11	such	such	ADJ
ejpam-2571	127	1	that	that	SCONJ
ejpam-2571	127	2	c	c	PROPN
ejpam-2571	127	3	⊂	⊂	PROPN
ejpam-2571	127	4	�	�	PROPN
ejpam-2571	127	5	fp	fp	PROPN
ejpam-2571	127	6	+	+	PROPN
ejpam-2571	127	7	u2	u2	PROPN
ejpam-2571	127	8	fp	fp	PROPN
ejpam-2571	127	9	�	�	PROPN
ejpam-2571	127	10	n	n	PROPN
ejpam-2571	127	11	.	.	PUNCT
ejpam-2571	128	1	if	if	SCONJ
ejpam-2571	128	2	c	c	PROPN
ejpam-2571	128	3	is	be	AUX
ejpam-2571	128	4	selforthogonal	selforthogonal	ADJ
ejpam-2571	128	5	,	,	PUNCT
ejpam-2571	128	6	then	then	ADV
ejpam-2571	128	7	so	so	ADV
ejpam-2571	128	8	is	be	AUX
ejpam-2571	128	9	φ(c	φ(c	NOUN
ejpam-2571	128	10	)	)	PUNCT
ejpam-2571	128	11	.	.	PUNCT
ejpam-2571	129	1	h.	h.	PROPN
ejpam-2571	129	2	mostafanasab	mostafanasab	PROPN
ejpam-2571	129	3	,	,	PUNCT
ejpam-2571	129	4	n.	n.	PROPN
ejpam-2571	129	5	karimi	karimi	PROPN
ejpam-2571	129	6	/	/	SYM
ejpam-2571	129	7	eur	eur	PROPN
ejpam-2571	129	8	.	.	PUNCT
ejpam-2571	130	1	j.	j.	PROPN
ejpam-2571	130	2	pure	pure	PROPN
ejpam-2571	130	3	appl	appl	PROPN
ejpam-2571	130	4	.	.	PROPN
ejpam-2571	130	5	math	math	PROPN
ejpam-2571	130	6	,	,	PUNCT
ejpam-2571	130	7	9	9	NUM
ejpam-2571	130	8	(	(	PUNCT
ejpam-2571	130	9	2016	2016	NUM
ejpam-2571	130	10	)	)	PUNCT
ejpam-2571	130	11	,	,	PUNCT
ejpam-2571	130	12	39	39	NUM
ejpam-2571	130	13	-	-	SYM
ejpam-2571	130	14	47	47	NUM
ejpam-2571	130	15	42	42	NUM
ejpam-2571	130	16	proof	proof	NOUN
ejpam-2571	130	17	.	.	PUNCT
ejpam-2571	131	1	assume	assume	VERB
ejpam-2571	131	2	that	that	SCONJ
ejpam-2571	131	3	c	c	PROPN
ejpam-2571	131	4	is	be	AUX
ejpam-2571	131	5	self	self	NOUN
ejpam-2571	131	6	-	-	PUNCT
ejpam-2571	131	7	orthogonal	orthogonal	NOUN
ejpam-2571	131	8	.	.	PUNCT
ejpam-2571	132	1	let	let	VERB
ejpam-2571	132	2	r1	r1	PROPN
ejpam-2571	132	3	=	=	SYM
ejpam-2571	132	4	a1	a1	PROPN
ejpam-2571	132	5	+	+	CCONJ
ejpam-2571	132	6	c1u2	c1u2	NOUN
ejpam-2571	132	7	,	,	PUNCT
ejpam-2571	132	8	r2	r2	PROPN
ejpam-2571	132	9	=	=	PROPN
ejpam-2571	132	10	a2	a2	PROPN
ejpam-2571	132	11	+	+	CCONJ
ejpam-2571	132	12	c2u2	c2u2	PROPN
ejpam-2571	132	13	∈	∈	PROPN
ejpam-2571	132	14	c	c	PROPN
ejpam-2571	132	15	,	,	PUNCT
ejpam-2571	132	16	where	where	SCONJ
ejpam-2571	132	17	ai	ai	VERB
ejpam-2571	132	18	,	,	PUNCT
ejpam-2571	132	19	ci	ci	PROPN
ejpam-2571	132	20	∈	∈	PROPN
ejpam-2571	132	21	f	f	PROPN
ejpam-2571	132	22	n	n	PRON
ejpam-2571	132	23	p	p	NOUN
ejpam-2571	132	24	for	for	ADP
ejpam-2571	132	25	i	i	PRON
ejpam-2571	133	1	=	=	NOUN
ejpam-2571	133	2	1,2	1,2	NUM
ejpam-2571	133	3	.	.	PUNCT
ejpam-2571	134	1	now	now	ADV
ejpam-2571	134	2	by	by	ADP
ejpam-2571	134	3	euclidean	euclidean	ADJ
ejpam-2571	134	4	inner	inner	ADJ
ejpam-2571	134	5	product	product	NOUN
ejpam-2571	134	6	of	of	ADP
ejpam-2571	134	7	r1	r1	PROPN
ejpam-2571	134	8	and	and	CCONJ
ejpam-2571	134	9	r2	r2	PROPN
ejpam-2571	134	10	,	,	PUNCT
ejpam-2571	134	11	we	we	PRON
ejpam-2571	134	12	have	have	VERB
ejpam-2571	134	13	r1	r1	NOUN
ejpam-2571	134	14	·	·	PUNCT
ejpam-2571	134	15	r2	r2	PROPN
ejpam-2571	134	16	=(	=(	NOUN
ejpam-2571	134	17	a1	a1	NOUN
ejpam-2571	134	18	+	+	CCONJ
ejpam-2571	134	19	c1u2	c1u2	NOUN
ejpam-2571	134	20	)	)	PUNCT
ejpam-2571	134	21	·	·	PUNCT
ejpam-2571	134	22	(	(	PUNCT
ejpam-2571	134	23	a2	a2	PROPN
ejpam-2571	134	24	+	+	CCONJ
ejpam-2571	134	25	c2u2	c2u2	SYM
ejpam-2571	134	26	)	)	PUNCT
ejpam-2571	134	27	=	=	NOUN
ejpam-2571	134	28	a1a2	a1a2	X
ejpam-2571	134	29	+	+	X
ejpam-2571	135	1	(	(	PUNCT
ejpam-2571	135	2	a1c2	a1c2	INTJ
ejpam-2571	135	3	+	+	NOUN
ejpam-2571	135	4	c1a2	c1a2	NOUN
ejpam-2571	135	5	+	+	CCONJ
ejpam-2571	135	6	c1c2)u	c1c2)u	NOUN
ejpam-2571	135	7	2	2	NUM
ejpam-2571	135	8	.	.	PUNCT
ejpam-2571	136	1	if	if	SCONJ
ejpam-2571	136	2	r1	r1	PROPN
ejpam-2571	136	3	·	·	PUNCT
ejpam-2571	136	4	r2	r2	PROPN
ejpam-2571	136	5	=	=	SYM
ejpam-2571	136	6	0	0	NUM
ejpam-2571	136	7	,	,	PUNCT
ejpam-2571	136	8	then	then	ADV
ejpam-2571	136	9	a1a2	a1a2	ADP
ejpam-2571	136	10	=	=	X
ejpam-2571	136	11	a1c2	a1c2	INTJ
ejpam-2571	136	12	+	+	PUNCT
ejpam-2571	136	13	c1a2	c1a2	ADJ
ejpam-2571	136	14	+	+	ADJ
ejpam-2571	136	15	c1c2	c1c2	NOUN
ejpam-2571	136	16	=	=	NOUN
ejpam-2571	136	17	0	0	X
ejpam-2571	136	18	.	.	PUNCT
ejpam-2571	136	19	therefore	therefore	ADV
ejpam-2571	136	20	φ(r1	φ(r1	ADV
ejpam-2571	136	21	)	)	PUNCT
ejpam-2571	136	22	·	·	PUNCT
ejpam-2571	136	23	φ(r2	φ(r2	NOUN
ejpam-2571	136	24	)	)	PUNCT
ejpam-2571	136	25	=(	=(	NOUN
ejpam-2571	136	26	−c1	−c1	NOUN
ejpam-2571	136	27	,	,	PUNCT
ejpam-2571	136	28	2a1	2a1	NUM
ejpam-2571	136	29	+	+	CCONJ
ejpam-2571	136	30	c1	c1	NOUN
ejpam-2571	136	31	)	)	PUNCT
ejpam-2571	136	32	·	·	PUNCT
ejpam-2571	137	1	(	(	PUNCT
ejpam-2571	137	2	−c2	−c2	NOUN
ejpam-2571	137	3	,	,	PUNCT
ejpam-2571	137	4	2a2	2a2	NUM
ejpam-2571	137	5	+	+	CCONJ
ejpam-2571	137	6	c2	c2	PROPN
ejpam-2571	137	7	)	)	PUNCT
ejpam-2571	138	1	=	=	NOUN
ejpam-2571	138	2	4a1a2	4a1a2	PRON
ejpam-2571	139	1	+	+	NUM
ejpam-2571	139	2	2(c1c2	2(c1c2	NUM
ejpam-2571	140	1	+	+	CCONJ
ejpam-2571	140	2	a1c2	a1c2	PROPN
ejpam-2571	140	3	+	+	CCONJ
ejpam-2571	140	4	c1a2	c1a2	ADJ
ejpam-2571	140	5	)	)	PUNCT
ejpam-2571	140	6	=	=	SYM
ejpam-2571	140	7	0	0	X
ejpam-2571	140	8	.	.	PUNCT
ejpam-2571	140	9	hence	hence	ADV
ejpam-2571	140	10	φ(c	φ(c	NOUN
ejpam-2571	140	11	⊥	⊥	NOUN
ejpam-2571	140	12	)	)	PUNCT
ejpam-2571	140	13	⊆	⊆	NUM
ejpam-2571	140	14	φ(c	φ(c	NOUN
ejpam-2571	140	15	)	)	PUNCT
ejpam-2571	140	16	⊥.	⊥.	PROPN
ejpam-2571	140	17	consequently	consequently	ADV
ejpam-2571	140	18	φ(c	φ(c	NOUN
ejpam-2571	140	19	)	)	PUNCT
ejpam-2571	141	1	⊆	⊆	NUM
ejpam-2571	141	2	φ(c	φ(c	NOUN
ejpam-2571	141	3	)	)	PUNCT
ejpam-2571	141	4	⊥.	⊥.	PROPN
ejpam-2571	141	5	theorem	theorem	VERB
ejpam-2571	141	6	4	4	NUM
ejpam-2571	141	7	.	.	PUNCT
ejpam-2571	142	1	let	let	VERB
ejpam-2571	142	2	c	c	NOUN
ejpam-2571	142	3	=	=	SYM
ejpam-2571	142	4	η1c1⊕η2c2⊕η3c3	η1c1⊕η2c2⊕η3c3	PROPN
ejpam-2571	142	5	be	be	AUX
ejpam-2571	142	6	a	a	DET
ejpam-2571	142	7	code	code	NOUN
ejpam-2571	142	8	of	of	ADP
ejpam-2571	142	9	length	length	NOUN
ejpam-2571	142	10	n	n	NOUN
ejpam-2571	142	11	overr	overr	NOUN
ejpam-2571	142	12	.	.	PUNCT
ejpam-2571	143	1	then	then	ADV
ejpam-2571	143	2	c	c	PROPN
ejpam-2571	143	3	is	be	AUX
ejpam-2571	143	4	a	a	DET
ejpam-2571	143	5	(	(	PUNCT
ejpam-2571	143	6	1−2u2)constacyclic	1−2u2)constacyclic	NUM
ejpam-2571	143	7	code	code	NOUN
ejpam-2571	143	8	of	of	ADP
ejpam-2571	143	9	length	length	NOUN
ejpam-2571	143	10	n	n	CCONJ
ejpam-2571	143	11	over	over	ADP
ejpam-2571	143	12	r	r	NOUN
ejpam-2571	143	13	if	if	SCONJ
ejpam-2571	144	1	and	and	CCONJ
ejpam-2571	144	2	only	only	ADV
ejpam-2571	144	3	if	if	SCONJ
ejpam-2571	144	4	c1	c1	PROPN
ejpam-2571	144	5	is	be	AUX
ejpam-2571	144	6	cyclic	cyclic	ADJ
ejpam-2571	144	7	and	and	CCONJ
ejpam-2571	144	8	c2	c2	PROPN
ejpam-2571	144	9	,	,	PUNCT
ejpam-2571	144	10	c3	c3	PROPN
ejpam-2571	144	11	are	be	AUX
ejpam-2571	144	12	negacyclic	negacyclic	ADJ
ejpam-2571	144	13	codes	code	NOUN
ejpam-2571	144	14	of	of	ADP
ejpam-2571	144	15	length	length	NOUN
ejpam-2571	144	16	n	n	PROPN
ejpam-2571	144	17	over	over	ADP
ejpam-2571	144	18	fp	fp	NOUN
ejpam-2571	144	19	.	.	PUNCT
ejpam-2571	144	20	proof	proof	NOUN
ejpam-2571	144	21	.	.	PUNCT
ejpam-2571	145	1	first	first	ADV
ejpam-2571	145	2	of	of	ADP
ejpam-2571	145	3	all	all	PRON
ejpam-2571	145	4	notice	notice	NOUN
ejpam-2571	145	5	that	that	SCONJ
ejpam-2571	145	6	(	(	PUNCT
ejpam-2571	145	7	1−2u2)η1	1−2u2)η1	PROPN
ejpam-2571	145	8	=	=	SYM
ejpam-2571	145	9	η1	η1	PROPN
ejpam-2571	145	10	,	,	PUNCT
ejpam-2571	145	11	(	(	PUNCT
ejpam-2571	145	12	1−2u2)η2	1−2u2)η2	PROPN
ejpam-2571	145	13	=	=	SYM
ejpam-2571	145	14	−η2	−η2	PROPN
ejpam-2571	145	15	and	and	CCONJ
ejpam-2571	145	16	(	(	PUNCT
ejpam-2571	145	17	1−2u2)η3	1−2u2)η3	PROPN
ejpam-2571	145	18	=	=	PUNCT
ejpam-2571	145	19	−η3	−η3	PROPN
ejpam-2571	145	20	.	.	PUNCT
ejpam-2571	146	1	let	let	VERB
ejpam-2571	146	2	r̄	r̄	NOUN
ejpam-2571	146	3	=	=	SYM
ejpam-2571	146	4	(	(	PUNCT
ejpam-2571	146	5	r0	r0	NOUN
ejpam-2571	146	6	,	,	PUNCT
ejpam-2571	146	7	r1	r1	NOUN
ejpam-2571	146	8	,	,	PUNCT
ejpam-2571	146	9	.	.	PUNCT
ejpam-2571	146	10	.	.	PUNCT
ejpam-2571	147	1	.	.	PUNCT
ejpam-2571	148	1	,	,	PUNCT
ejpam-2571	148	2	rn−1	rn−1	NOUN
ejpam-2571	148	3	)	)	PUNCT
ejpam-2571	148	4	∈	∈	PROPN
ejpam-2571	148	5	c	c	NOUN
ejpam-2571	148	6	.	.	PUNCT
ejpam-2571	149	1	then	then	ADV
ejpam-2571	149	2	ri	ri	PROPN
ejpam-2571	149	3	=	=	PUNCT
ejpam-2571	149	4	η1ai+η2	η1ai+η2	PROPN
ejpam-2571	149	5	bi+η3ci	bi+η3ci	NUM
ejpam-2571	149	6	,	,	PUNCT
ejpam-2571	149	7	where	where	SCONJ
ejpam-2571	149	8	ai	ai	VERB
ejpam-2571	149	9	,	,	PUNCT
ejpam-2571	149	10	bi	bi	NOUN
ejpam-2571	149	11	,	,	PUNCT
ejpam-2571	149	12	ci	ci	PROPN
ejpam-2571	149	13	∈	∈	PROPN
ejpam-2571	149	14	fp	fp	PROPN
ejpam-2571	149	15	,	,	PUNCT
ejpam-2571	149	16	0≤	0≤	NUM
ejpam-2571	150	1	i	i	NOUN
ejpam-2571	150	2	≤	≤	PUNCT
ejpam-2571	150	3	n−1	n−1	PROPN
ejpam-2571	150	4	.	.	PUNCT
ejpam-2571	151	1	let	let	VERB
ejpam-2571	151	2	a	a	DET
ejpam-2571	151	3	=	=	SYM
ejpam-2571	151	4	(	(	PUNCT
ejpam-2571	151	5	a0	a0	PROPN
ejpam-2571	151	6	,	,	PUNCT
ejpam-2571	151	7	a1	a1	NOUN
ejpam-2571	151	8	,	,	PUNCT
ejpam-2571	151	9	.	.	PUNCT
ejpam-2571	151	10	.	.	PUNCT
ejpam-2571	152	1	.	.	PUNCT
ejpam-2571	153	1	,	,	PUNCT
ejpam-2571	153	2	an−1	an−1	ADJ
ejpam-2571	153	3	)	)	PUNCT
ejpam-2571	153	4	,	,	PUNCT
ejpam-2571	153	5	b	b	X
ejpam-2571	153	6	=	=	SYM
ejpam-2571	153	7	(	(	PUNCT
ejpam-2571	153	8	b0	b0	NOUN
ejpam-2571	153	9	,	,	PUNCT
ejpam-2571	153	10	b1	b1	NOUN
ejpam-2571	153	11	,	,	PUNCT
ejpam-2571	153	12	.	.	PUNCT
ejpam-2571	153	13	.	.	PUNCT
ejpam-2571	154	1	.	.	PUNCT
ejpam-2571	155	1	,	,	PUNCT
ejpam-2571	155	2	bn−1	bn−1	X
ejpam-2571	155	3	)	)	PUNCT
ejpam-2571	155	4	and	and	CCONJ
ejpam-2571	155	5	c	c	X
ejpam-2571	155	6	=	=	SYM
ejpam-2571	155	7	(	(	PUNCT
ejpam-2571	155	8	c0	c0	PROPN
ejpam-2571	155	9	,	,	PUNCT
ejpam-2571	155	10	c1	c1	PROPN
ejpam-2571	155	11	,	,	PUNCT
ejpam-2571	155	12	.	.	PUNCT
ejpam-2571	155	13	.	.	PUNCT
ejpam-2571	156	1	.	.	PUNCT
ejpam-2571	157	1	,	,	PUNCT
ejpam-2571	157	2	cn−1	cn−1	PROPN
ejpam-2571	157	3	)	)	PUNCT
ejpam-2571	157	4	.	.	PUNCT
ejpam-2571	158	1	then	then	ADV
ejpam-2571	158	2	a	a	DET
ejpam-2571	158	3	∈	∈	PROPN
ejpam-2571	158	4	c1	c1	NOUN
ejpam-2571	158	5	,	,	PUNCT
ejpam-2571	158	6	b	b	PROPN
ejpam-2571	158	7	∈	∈	PROPN
ejpam-2571	158	8	c2	c2	PROPN
ejpam-2571	158	9	and	and	CCONJ
ejpam-2571	158	10	c	c	PROPN
ejpam-2571	158	11	∈	∈	PROPN
ejpam-2571	158	12	c3	c3	PROPN
ejpam-2571	158	13	.	.	PUNCT
ejpam-2571	158	14	assume	assume	VERB
ejpam-2571	158	15	that	that	SCONJ
ejpam-2571	158	16	c1	c1	PROPN
ejpam-2571	158	17	is	be	AUX
ejpam-2571	158	18	cyclic	cyclic	ADJ
ejpam-2571	158	19	and	and	CCONJ
ejpam-2571	158	20	c2	c2	PROPN
ejpam-2571	158	21	,	,	PUNCT
ejpam-2571	158	22	c3	c3	PROPN
ejpam-2571	158	23	are	be	AUX
ejpam-2571	158	24	negacyclic	negacyclic	ADJ
ejpam-2571	158	25	codes	code	NOUN
ejpam-2571	158	26	.	.	PUNCT
ejpam-2571	159	1	therefore	therefore	ADV
ejpam-2571	159	2	σ(a	σ(a	PROPN
ejpam-2571	159	3	)	)	PUNCT
ejpam-2571	159	4	∈	∈	PROPN
ejpam-2571	159	5	c1	c1	NOUN
ejpam-2571	159	6	,	,	PUNCT
ejpam-2571	159	7	γ(b	γ(b	X
ejpam-2571	159	8	)	)	PUNCT
ejpam-2571	159	9	∈	∈	PROPN
ejpam-2571	159	10	c2	c2	PROPN
ejpam-2571	159	11	and	and	CCONJ
ejpam-2571	159	12	γ(c	γ(c	PROPN
ejpam-2571	159	13	)	)	PUNCT
ejpam-2571	159	14	∈	∈	PROPN
ejpam-2571	159	15	c3	c3	PROPN
ejpam-2571	159	16	.	.	PUNCT
ejpam-2571	160	1	thus	thus	ADV
ejpam-2571	160	2	̺(r̄	̺(r̄	ADV
ejpam-2571	160	3	)	)	PUNCT
ejpam-2571	160	4	=	=	SYM
ejpam-2571	160	5	η1σ(a	η1σ(a	NOUN
ejpam-2571	160	6	)	)	PUNCT
ejpam-2571	161	1	+	+	CCONJ
ejpam-2571	161	2	η2γ(b	η2γ(b	PROPN
ejpam-2571	161	3	)	)	PUNCT
ejpam-2571	162	1	+	+	CCONJ
ejpam-2571	162	2	η3γ(c	η3γ(c	PROPN
ejpam-2571	162	3	)	)	PUNCT
ejpam-2571	162	4	∈	∈	PROPN
ejpam-2571	162	5	c	c	NOUN
ejpam-2571	162	6	.	.	PUNCT
ejpam-2571	163	1	consequently	consequently	ADV
ejpam-2571	163	2	c	c	PROPN
ejpam-2571	163	3	is	be	AUX
ejpam-2571	163	4	a	a	DET
ejpam-2571	163	5	(	(	PUNCT
ejpam-2571	163	6	1	1	NUM
ejpam-2571	163	7	−	−	PROPN
ejpam-2571	163	8	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	163	9	codes	code	NOUN
ejpam-2571	163	10	over	over	ADP
ejpam-2571	163	11	r	r	NOUN
ejpam-2571	163	12	.	.	PUNCT
ejpam-2571	164	1	for	for	ADP
ejpam-2571	164	2	the	the	DET
ejpam-2571	164	3	converse	converse	NOUN
ejpam-2571	164	4	,	,	PUNCT
ejpam-2571	164	5	let	let	VERB
ejpam-2571	164	6	a	a	DET
ejpam-2571	164	7	=	=	SYM
ejpam-2571	164	8	(	(	PUNCT
ejpam-2571	164	9	a0	a0	PROPN
ejpam-2571	164	10	,	,	PUNCT
ejpam-2571	164	11	a1	a1	NOUN
ejpam-2571	164	12	,	,	PUNCT
ejpam-2571	164	13	.	.	PUNCT
ejpam-2571	164	14	.	.	PUNCT
ejpam-2571	165	1	.	.	PUNCT
ejpam-2571	166	1	,	,	PUNCT
ejpam-2571	166	2	an−1	an−1	ADJ
ejpam-2571	166	3	)	)	PUNCT
ejpam-2571	166	4	∈	∈	PROPN
ejpam-2571	166	5	c1	c1	NOUN
ejpam-2571	166	6	,	,	PUNCT
ejpam-2571	166	7	b	b	X
ejpam-2571	167	1	=	=	SYM
ejpam-2571	168	1	(	(	PUNCT
ejpam-2571	169	1	b0	b0	NOUN
ejpam-2571	169	2	,	,	PUNCT
ejpam-2571	169	3	b1	b1	NOUN
ejpam-2571	169	4	,	,	PUNCT
ejpam-2571	169	5	.	.	PUNCT
ejpam-2571	169	6	.	.	PUNCT
ejpam-2571	169	7	.	.	PUNCT
ejpam-2571	170	1	,	,	PUNCT
ejpam-2571	170	2	bn−1	bn−1	X
ejpam-2571	170	3	)	)	PUNCT
ejpam-2571	170	4	∈	∈	PROPN
ejpam-2571	170	5	c2	c2	PROPN
ejpam-2571	170	6	and	and	CCONJ
ejpam-2571	170	7	c	c	NOUN
ejpam-2571	170	8	=	=	SYM
ejpam-2571	170	9	(	(	PUNCT
ejpam-2571	170	10	c0	c0	PROPN
ejpam-2571	170	11	,	,	PUNCT
ejpam-2571	170	12	c1	c1	PROPN
ejpam-2571	170	13	,	,	PUNCT
ejpam-2571	170	14	.	.	PUNCT
ejpam-2571	170	15	.	.	PUNCT
ejpam-2571	171	1	.	.	PUNCT
ejpam-2571	172	1	,	,	PUNCT
ejpam-2571	172	2	cn−1	cn−1	X
ejpam-2571	172	3	)	)	PUNCT
ejpam-2571	172	4	∈	∈	PROPN
ejpam-2571	172	5	c3	c3	PROPN
ejpam-2571	172	6	.	.	PUNCT
ejpam-2571	173	1	set	set	VERB
ejpam-2571	173	2	ri	ri	PROPN
ejpam-2571	173	3	=	=	PUNCT
ejpam-2571	173	4	η1ai	η1ai	PUNCT
ejpam-2571	174	1	+	+	ADJ
ejpam-2571	174	2	η2	η2	ADJ
ejpam-2571	174	3	bi	bi	NOUN
ejpam-2571	174	4	+	+	PROPN
ejpam-2571	174	5	η3ci	η3ci	X
ejpam-2571	174	6	,	,	PUNCT
ejpam-2571	174	7	where	where	SCONJ
ejpam-2571	174	8	0	0	NUM
ejpam-2571	174	9	≤	≤	PUNCT
ejpam-2571	175	1	i	i	PRON
ejpam-2571	175	2	≤	≤	ADJ
ejpam-2571	175	3	n−	n−	NOUN
ejpam-2571	175	4	1	1	NUM
ejpam-2571	175	5	.	.	PUNCT
ejpam-2571	176	1	hence	hence	ADV
ejpam-2571	176	2	r̄	r̄	NOUN
ejpam-2571	176	3	=	=	SYM
ejpam-2571	176	4	(	(	PUNCT
ejpam-2571	176	5	r0	r0	NOUN
ejpam-2571	176	6	,	,	PUNCT
ejpam-2571	176	7	r1	r1	NOUN
ejpam-2571	176	8	,	,	PUNCT
ejpam-2571	176	9	.	.	PUNCT
ejpam-2571	176	10	.	.	PUNCT
ejpam-2571	177	1	.	.	PUNCT
ejpam-2571	178	1	,	,	PUNCT
ejpam-2571	178	2	rn−1	rn−1	NOUN
ejpam-2571	178	3	)	)	PUNCT
ejpam-2571	178	4	∈	∈	PROPN
ejpam-2571	178	5	c	c	NOUN
ejpam-2571	178	6	.	.	PUNCT
ejpam-2571	179	1	therefore	therefore	ADV
ejpam-2571	179	2	̺(r̄	̺(r̄	ADV
ejpam-2571	179	3	)	)	PUNCT
ejpam-2571	179	4	=	=	SYM
ejpam-2571	179	5	η1σ(a	η1σ(a	NOUN
ejpam-2571	179	6	)	)	PUNCT
ejpam-2571	180	1	+	+	VERB
ejpam-2571	180	2	η2γ(b	η2γ(b	X
ejpam-2571	180	3	)	)	PUNCT
ejpam-2571	180	4	+	+	NOUN
ejpam-2571	180	5	η3γ(c	η3γ(c	PROPN
ejpam-2571	180	6	)	)	PUNCT
ejpam-2571	180	7	,	,	PUNCT
ejpam-2571	180	8	̺(r̄	̺(r̄	ADV
ejpam-2571	180	9	)	)	PUNCT
ejpam-2571	180	10	∈	∈	PROPN
ejpam-2571	180	11	c	c	NOUN
ejpam-2571	180	12	which	which	PRON
ejpam-2571	180	13	shows	show	VERB
ejpam-2571	180	14	that	that	SCONJ
ejpam-2571	180	15	σ(a	σ(a	PROPN
ejpam-2571	180	16	)	)	PUNCT
ejpam-2571	180	17	∈	∈	PROPN
ejpam-2571	180	18	c1	c1	NOUN
ejpam-2571	180	19	,	,	PUNCT
ejpam-2571	180	20	γ(b	γ(b	X
ejpam-2571	180	21	)	)	PUNCT
ejpam-2571	180	22	∈	∈	PROPN
ejpam-2571	180	23	c2	c2	PROPN
ejpam-2571	180	24	and	and	CCONJ
ejpam-2571	180	25	γ(c	γ(c	PROPN
ejpam-2571	180	26	)	)	PUNCT
ejpam-2571	180	27	∈	∈	PROPN
ejpam-2571	180	28	c3	c3	NOUN
ejpam-2571	180	29	.	.	PUNCT
ejpam-2571	181	1	so	so	ADV
ejpam-2571	181	2	c1	c1	PROPN
ejpam-2571	181	3	is	be	AUX
ejpam-2571	181	4	cyclic	cyclic	ADJ
ejpam-2571	181	5	and	and	CCONJ
ejpam-2571	181	6	c2	c2	PROPN
ejpam-2571	181	7	,	,	PUNCT
ejpam-2571	181	8	c3	c3	PROPN
ejpam-2571	181	9	are	be	AUX
ejpam-2571	181	10	negacyclic	negacyclic	ADJ
ejpam-2571	181	11	codes	code	NOUN
ejpam-2571	181	12	.	.	PUNCT
ejpam-2571	182	1	theorem	theorem	NOUN
ejpam-2571	182	2	5	5	NUM
ejpam-2571	182	3	.	.	PUNCT
ejpam-2571	183	1	let	let	VERB
ejpam-2571	183	2	c	c	NOUN
ejpam-2571	183	3	=	=	PUNCT
ejpam-2571	184	1	η1c1	η1c1	NOUN
ejpam-2571	184	2	⊕η2c2	⊕η2c2	AUX
ejpam-2571	184	3	⊕η3c3	⊕η3c3	INTJ
ejpam-2571	184	4	be	be	AUX
ejpam-2571	184	5	a	a	DET
ejpam-2571	184	6	(	(	PUNCT
ejpam-2571	184	7	1−	1−	NUM
ejpam-2571	184	8	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	184	9	code	code	NOUN
ejpam-2571	184	10	of	of	ADP
ejpam-2571	184	11	length	length	NOUN
ejpam-2571	184	12	n	n	CCONJ
ejpam-2571	184	13	over	over	ADP
ejpam-2571	184	14	r	r	NOUN
ejpam-2571	184	15	such	such	ADJ
ejpam-2571	184	16	that	that	DET
ejpam-2571	184	17	g1(x	g1(x	NOUN
ejpam-2571	184	18	)	)	PUNCT
ejpam-2571	184	19	,	,	PUNCT
ejpam-2571	184	20	g2(x	g2(x	PROPN
ejpam-2571	184	21	)	)	PUNCT
ejpam-2571	184	22	,	,	PUNCT
ejpam-2571	184	23	g3(x	g3(x	X
ejpam-2571	184	24	)	)	PUNCT
ejpam-2571	184	25	are	be	AUX
ejpam-2571	184	26	the	the	DET
ejpam-2571	184	27	monic	monic	ADJ
ejpam-2571	184	28	generator	generator	NOUN
ejpam-2571	184	29	polynomials	polynomial	NOUN
ejpam-2571	184	30	of	of	ADP
ejpam-2571	184	31	c1	c1	PROPN
ejpam-2571	184	32	,	,	PUNCT
ejpam-2571	184	33	c2	c2	PROPN
ejpam-2571	184	34	,	,	PUNCT
ejpam-2571	184	35	c2	c2	PROPN
ejpam-2571	184	36	,	,	PUNCT
ejpam-2571	184	37	respectively	respectively	ADV
ejpam-2571	184	38	.	.	PUNCT
ejpam-2571	185	1	then	then	ADV
ejpam-2571	185	2	c	c	X
ejpam-2571	185	3	=	=	PUNCT
ejpam-2571	185	4	〈	〈	NOUN
ejpam-2571	185	5	η1	η1	NOUN
ejpam-2571	185	6	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	185	7	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	185	8	g3(x	g3(x	PROPN
ejpam-2571	185	9	)	)	PUNCT
ejpam-2571	185	10	〉	〉	NOUN
ejpam-2571	185	11	and	and	CCONJ
ejpam-2571	185	12	|c	|c	ADJ
ejpam-2571	185	13	|=	|=	NOUN
ejpam-2571	185	14	p3n−	p3n−	NOUN
ejpam-2571	185	15	∑3	∑3	PROPN
ejpam-2571	185	16	i=1	i=1	PROPN
ejpam-2571	185	17	deg(gi	deg(gi	NOUN
ejpam-2571	185	18	)	)	PUNCT
ejpam-2571	185	19	.	.	PUNCT
ejpam-2571	186	1	proof	proof	NOUN
ejpam-2571	186	2	.	.	PUNCT
ejpam-2571	187	1	by	by	ADP
ejpam-2571	187	2	theorem	theorem	NOUN
ejpam-2571	187	3	4	4	NUM
ejpam-2571	187	4	,	,	PUNCT
ejpam-2571	187	5	c1	c1	NOUN
ejpam-2571	187	6	=	=	PUNCT
ejpam-2571	187	7	〈	〈	PROPN
ejpam-2571	187	8	g1(x	g1(x	NOUN
ejpam-2571	187	9	)	)	PUNCT
ejpam-2571	187	10	〉	〉	NOUN
ejpam-2571	187	11	⊆	⊆	NUM
ejpam-2571	187	12	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	187	13	n	n	CCONJ
ejpam-2571	187	14	−	−	PROPN
ejpam-2571	187	15	1〉,c2	1〉,c2	NUM
ejpam-2571	187	16	=	=	SYM
ejpam-2571	187	17	〈	〈	PROPN
ejpam-2571	187	18	g2(x	g2(x	NOUN
ejpam-2571	187	19	)	)	PUNCT
ejpam-2571	187	20	〉	〉	NOUN
ejpam-2571	187	21	⊆	⊆	NUM
ejpam-2571	187	22	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	187	23	n	n	PROPN
ejpam-2571	187	24	+	+	CCONJ
ejpam-2571	187	25	1	1	NUM
ejpam-2571	187	26	〉	〉	NOUN
ejpam-2571	187	27	and	and	CCONJ
ejpam-2571	187	28	c3	c3	NOUN
ejpam-2571	187	29	=	=	PROPN
ejpam-2571	187	30	〈	〈	PROPN
ejpam-2571	187	31	g3(x	g3(x	PROPN
ejpam-2571	187	32	)	)	PUNCT
ejpam-2571	187	33	〉	〉	NOUN
ejpam-2571	187	34	⊆	⊆	NUM
ejpam-2571	187	35	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	187	36	n	n	PROPN
ejpam-2571	187	37	+	+	CCONJ
ejpam-2571	187	38	1	1	NUM
ejpam-2571	187	39	〉	〉	NOUN
ejpam-2571	187	40	.	.	PUNCT
ejpam-2571	188	1	since	since	SCONJ
ejpam-2571	188	2	c	c	NOUN
ejpam-2571	188	3	=	=	PUNCT
ejpam-2571	188	4	η1c1	η1c1	NOUN
ejpam-2571	188	5	⊕η2c2	⊕η2c2	X
ejpam-2571	188	6	⊕η3c3	⊕η3c3	INTJ
ejpam-2571	188	7	,	,	PUNCT
ejpam-2571	188	8	then	then	ADV
ejpam-2571	188	9	c	c	NOUN
ejpam-2571	188	10	=	=	SYM
ejpam-2571	188	11	{	{	PUNCT
ejpam-2571	188	12	c(x)|c(x	c(x)|c(x	NOUN
ejpam-2571	188	13	)	)	PUNCT
ejpam-2571	188	14	=	=	PUNCT
ejpam-2571	188	15	η1	η1	NOUN
ejpam-2571	188	16	f1(x	f1(x	NOUN
ejpam-2571	188	17	)	)	PUNCT
ejpam-2571	188	18	+	+	NOUN
ejpam-2571	188	19	η2	η2	ADJ
ejpam-2571	188	20	f2(x	f2(x	NOUN
ejpam-2571	188	21	)	)	PUNCT
ejpam-2571	188	22	+	+	ADJ
ejpam-2571	188	23	η3	η3	PROPN
ejpam-2571	188	24	f3(x	f3(x	NUM
ejpam-2571	188	25	)	)	PUNCT
ejpam-2571	188	26	,	,	PUNCT
ejpam-2571	188	27	f1(x	f1(x	NOUN
ejpam-2571	188	28	)	)	PUNCT
ejpam-2571	188	29	∈	∈	PROPN
ejpam-2571	188	30	c1	c1	NOUN
ejpam-2571	188	31	,	,	PUNCT
ejpam-2571	188	32	f2(x	f2(x	PROPN
ejpam-2571	188	33	)	)	PUNCT
ejpam-2571	188	34	∈	∈	PROPN
ejpam-2571	188	35	c2	c2	PROPN
ejpam-2571	188	36	and	and	CCONJ
ejpam-2571	188	37	f3(x	f3(x	NUM
ejpam-2571	188	38	)	)	PUNCT
ejpam-2571	188	39	∈	∈	PROPN
ejpam-2571	188	40	c3	c3	NOUN
ejpam-2571	188	41	}	}	PUNCT
ejpam-2571	188	42	.	.	PUNCT
ejpam-2571	189	1	hence	hence	ADV
ejpam-2571	189	2	c	c	NOUN
ejpam-2571	189	3	⊆	⊆	NUM
ejpam-2571	189	4	〈	〈	NOUN
ejpam-2571	189	5	η1	η1	NOUN
ejpam-2571	189	6	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	189	7	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	189	8	g3(x	g3(x	PROPN
ejpam-2571	189	9	)	)	PUNCT
ejpam-2571	189	10	〉	〉	NOUN
ejpam-2571	189	11	⊆	⊆	NUM
ejpam-2571	189	12	rn	rn	PROPN
ejpam-2571	189	13	=	=	PROPN
ejpam-2571	189	14	r[x]/〈x	r[x]/〈x	PROPN
ejpam-2571	189	15	n	n	ADV
ejpam-2571	189	16	−	−	PROPN
ejpam-2571	189	17	(	(	PUNCT
ejpam-2571	189	18	1−	1−	NUM
ejpam-2571	189	19	2u2	2u2	NUM
ejpam-2571	189	20	)	)	PUNCT
ejpam-2571	189	21	〉	〉	NOUN
ejpam-2571	189	22	.	.	PUNCT
ejpam-2571	189	23	suppose	suppose	VERB
ejpam-2571	189	24	that	that	SCONJ
ejpam-2571	189	25	η1	η1	NOUN
ejpam-2571	189	26	g1(x)h1(x	g1(x)h1(x	NOUN
ejpam-2571	189	27	)	)	PUNCT
ejpam-2571	189	28	+	+	CCONJ
ejpam-2571	189	29	η2	η2	ADJ
ejpam-2571	189	30	g2(x)h2(x	g2(x)h2(x	PROPN
ejpam-2571	189	31	)	)	PUNCT
ejpam-2571	189	32	+	+	CCONJ
ejpam-2571	189	33	η3	η3	PROPN
ejpam-2571	189	34	g3(x)h3(x	g3(x)h3(x	PROPN
ejpam-2571	189	35	)	)	PUNCT
ejpam-2571	189	36	∈	∈	PROPN
ejpam-2571	189	37	〈	〈	NOUN
ejpam-2571	189	38	η1	η1	NOUN
ejpam-2571	189	39	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	189	40	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	189	41	g3(x	g3(x	PROPN
ejpam-2571	189	42	)	)	PUNCT
ejpam-2571	189	43	〉	〉	NOUN
ejpam-2571	189	44	,	,	PUNCT
ejpam-2571	189	45	where	where	SCONJ
ejpam-2571	189	46	h1(x),h2(x),h3(x	h1(x),h2(x),h3(x	NOUN
ejpam-2571	189	47	)	)	PUNCT
ejpam-2571	189	48	∈	∈	PROPN
ejpam-2571	189	49	rn	rn	PROPN
ejpam-2571	189	50	.	.	PUNCT
ejpam-2571	189	51	there	there	PRON
ejpam-2571	189	52	exist	exist	VERB
ejpam-2571	189	53	q1(x	q1(x	NOUN
ejpam-2571	189	54	)	)	PUNCT
ejpam-2571	189	55	∈	∈	PROPN
ejpam-2571	189	56	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	189	57	n	n	CCONJ
ejpam-2571	189	58	−	−	PROPN
ejpam-2571	189	59	1〉,q2(x	1〉,q2(x	NUM
ejpam-2571	189	60	)	)	PUNCT
ejpam-2571	189	61	∈	∈	PROPN
ejpam-2571	189	62	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	189	63	n	n	PROPN
ejpam-2571	189	64	+	+	NOUN
ejpam-2571	189	65	1	1	NUM
ejpam-2571	189	66	〉	〉	NOUN
ejpam-2571	189	67	and	and	CCONJ
ejpam-2571	189	68	q3(x	q3(x	NOUN
ejpam-2571	189	69	)	)	PUNCT
ejpam-2571	189	70	∈	∈	PROPN
ejpam-2571	189	71	fp[x]/〈x	fp[x]/〈x	PROPN
ejpam-2571	189	72	n	n	PROPN
ejpam-2571	189	73	+	+	NOUN
ejpam-2571	189	74	1	1	NUM
ejpam-2571	189	75	〉	〉	NOUN
ejpam-2571	189	76	such	such	ADJ
ejpam-2571	189	77	that	that	DET
ejpam-2571	189	78	η1h1(x	η1h1(x	NOUN
ejpam-2571	189	79	)	)	PUNCT
ejpam-2571	189	80	=	=	SYM
ejpam-2571	189	81	η1q1(x	η1q1(x	NOUN
ejpam-2571	189	82	)	)	PUNCT
ejpam-2571	189	83	,	,	PUNCT
ejpam-2571	189	84	η2h2(x	η2h2(x	NOUN
ejpam-2571	189	85	)	)	PUNCT
ejpam-2571	189	86	=	=	SYM
ejpam-2571	189	87	η2q2(x	η2q2(x	NOUN
ejpam-2571	189	88	)	)	PUNCT
ejpam-2571	189	89	and	and	CCONJ
ejpam-2571	189	90	η3h3(x	η3h3(x	NOUN
ejpam-2571	189	91	)	)	PUNCT
ejpam-2571	189	92	=	=	SYM
ejpam-2571	189	93	η3q3(x	η3q3(x	NOUN
ejpam-2571	189	94	)	)	PUNCT
ejpam-2571	189	95	.	.	PUNCT
ejpam-2571	190	1	therefore	therefore	ADV
ejpam-2571	190	2	〈	〈	NOUN
ejpam-2571	190	3	η1	η1	NOUN
ejpam-2571	190	4	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	190	5	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	190	6	g3(x	g3(x	PROPN
ejpam-2571	190	7	)	)	PUNCT
ejpam-2571	190	8	〉	〉	NOUN
ejpam-2571	190	9	⊆	⊆	NUM
ejpam-2571	190	10	c	c	NOUN
ejpam-2571	190	11	.	.	PUNCT
ejpam-2571	191	1	consequently	consequently	ADV
ejpam-2571	191	2	c	c	X
ejpam-2571	191	3	=	=	PUNCT
ejpam-2571	192	1	〈	〈	NOUN
ejpam-2571	192	2	η1	η1	NOUN
ejpam-2571	192	3	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	192	4	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	192	5	g3(x	g3(x	PROPN
ejpam-2571	192	6	)	)	PUNCT
ejpam-2571	192	7	〉	〉	NOUN
ejpam-2571	192	8	.	.	PUNCT
ejpam-2571	193	1	on	on	ADP
ejpam-2571	193	2	the	the	DET
ejpam-2571	193	3	other	other	ADJ
ejpam-2571	193	4	hand	hand	NOUN
ejpam-2571	193	5	|c	|c	VERB
ejpam-2571	193	6	|=	|=	NOUN
ejpam-2571	193	7	|c1|	|c1|	NOUN
ejpam-2571	193	8	·	·	PUNCT
ejpam-2571	193	9	|c2|	|c2|	NOUN
ejpam-2571	193	10	·	·	PUNCT
ejpam-2571	193	11	|c3|=	|c3|=	PROPN
ejpam-2571	193	12	p3n−	p3n−	NOUN
ejpam-2571	193	13	∑3	∑3	PROPN
ejpam-2571	193	14	i=1	i=1	PROPN
ejpam-2571	193	15	deg(gi	deg(gi	NOUN
ejpam-2571	193	16	)	)	PUNCT
ejpam-2571	193	17	.	.	PUNCT
ejpam-2571	194	1	h.	h.	PROPN
ejpam-2571	194	2	mostafanasab	mostafanasab	PROPN
ejpam-2571	194	3	,	,	PUNCT
ejpam-2571	194	4	n.	n.	PROPN
ejpam-2571	194	5	karimi	karimi	PROPN
ejpam-2571	194	6	/	/	SYM
ejpam-2571	194	7	eur	eur	PROPN
ejpam-2571	194	8	.	.	PUNCT
ejpam-2571	195	1	j.	j.	PROPN
ejpam-2571	195	2	pure	pure	PROPN
ejpam-2571	195	3	appl	appl	PROPN
ejpam-2571	195	4	.	.	PROPN
ejpam-2571	195	5	math	math	PROPN
ejpam-2571	195	6	,	,	PUNCT
ejpam-2571	195	7	9	9	NUM
ejpam-2571	195	8	(	(	PUNCT
ejpam-2571	195	9	2016	2016	NUM
ejpam-2571	195	10	)	)	PUNCT
ejpam-2571	195	11	,	,	PUNCT
ejpam-2571	195	12	39	39	NUM
ejpam-2571	195	13	-	-	SYM
ejpam-2571	195	14	47	47	NUM
ejpam-2571	195	15	43	43	NUM
ejpam-2571	195	16	theorem	theorem	NOUN
ejpam-2571	195	17	6	6	NUM
ejpam-2571	195	18	.	.	PUNCT
ejpam-2571	195	19	letc	letc	PROPN
ejpam-2571	195	20	be	be	AUX
ejpam-2571	195	21	a	a	DET
ejpam-2571	195	22	(	(	PUNCT
ejpam-2571	195	23	1−2u2)-constacyclic	1−2u2)-constacyclic	NUM
ejpam-2571	195	24	code	code	NOUN
ejpam-2571	195	25	of	of	ADP
ejpam-2571	195	26	length	length	NOUN
ejpam-2571	195	27	n	n	NOUN
ejpam-2571	195	28	overr	overr	NOUN
ejpam-2571	195	29	.	.	PUNCT
ejpam-2571	196	1	then	then	ADV
ejpam-2571	196	2	there	there	PRON
ejpam-2571	196	3	exists	exist	VERB
ejpam-2571	196	4	a	a	DET
ejpam-2571	196	5	unique	unique	ADJ
ejpam-2571	196	6	polynomial	polynomial	ADJ
ejpam-2571	196	7	g(x	g(x	NOUN
ejpam-2571	196	8	)	)	PUNCT
ejpam-2571	197	1	such	such	ADJ
ejpam-2571	197	2	that	that	SCONJ
ejpam-2571	197	3	c	c	NOUN
ejpam-2571	197	4	=	=	PUNCT
ejpam-2571	197	5	〈	〈	PROPN
ejpam-2571	197	6	g(x	g(x	NOUN
ejpam-2571	197	7	)	)	PUNCT
ejpam-2571	197	8	〉	〉	NOUN
ejpam-2571	197	9	where	where	SCONJ
ejpam-2571	197	10	g(x	g(x	NOUN
ejpam-2571	197	11	)	)	PUNCT
ejpam-2571	197	12	=	=	PUNCT
ejpam-2571	197	13	η1	η1	NOUN
ejpam-2571	197	14	g1(x	g1(x	NOUN
ejpam-2571	197	15	)	)	PUNCT
ejpam-2571	197	16	+	+	ADJ
ejpam-2571	197	17	η2	η2	ADJ
ejpam-2571	197	18	g2(x	g2(x	X
ejpam-2571	197	19	)	)	PUNCT
ejpam-2571	197	20	+	+	PROPN
ejpam-2571	197	21	η3	η3	PROPN
ejpam-2571	197	22	g3(x	g3(x	PROPN
ejpam-2571	197	23	)	)	PUNCT
ejpam-2571	198	1	.	.	PUNCT
ejpam-2571	199	1	proof	proof	NOUN
ejpam-2571	199	2	.	.	PUNCT
ejpam-2571	200	1	suppose	suppose	VERB
ejpam-2571	200	2	that	that	SCONJ
ejpam-2571	200	3	g1(x	g1(x	NOUN
ejpam-2571	200	4	)	)	PUNCT
ejpam-2571	200	5	,	,	PUNCT
ejpam-2571	200	6	g2(x	g2(x	PROPN
ejpam-2571	200	7	)	)	PUNCT
ejpam-2571	200	8	,	,	PUNCT
ejpam-2571	200	9	and	and	CCONJ
ejpam-2571	200	10	g3(x	g3(x	NOUN
ejpam-2571	200	11	)	)	PUNCT
ejpam-2571	200	12	are	be	AUX
ejpam-2571	200	13	the	the	DET
ejpam-2571	200	14	monic	monic	ADJ
ejpam-2571	200	15	generator	generator	NOUN
ejpam-2571	200	16	polynomials	polynomial	NOUN
ejpam-2571	200	17	of	of	ADP
ejpam-2571	200	18	c1	c1	PROPN
ejpam-2571	200	19	,	,	PUNCT
ejpam-2571	200	20	c2	c2	PROPN
ejpam-2571	200	21	,	,	PUNCT
ejpam-2571	200	22	and	and	CCONJ
ejpam-2571	200	23	c3	c3	PROPN
ejpam-2571	200	24	,	,	PUNCT
ejpam-2571	200	25	respectively	respectively	ADV
ejpam-2571	200	26	.	.	PUNCT
ejpam-2571	201	1	by	by	ADP
ejpam-2571	201	2	theorem	theorem	NOUN
ejpam-2571	201	3	5	5	NUM
ejpam-2571	201	4	,	,	PUNCT
ejpam-2571	201	5	we	we	PRON
ejpam-2571	201	6	have	have	VERB
ejpam-2571	201	7	c	c	NOUN
ejpam-2571	201	8	=	=	PUNCT
ejpam-2571	201	9	〈	〈	NOUN
ejpam-2571	201	10	η1	η1	NOUN
ejpam-2571	201	11	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	201	12	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	201	13	g3(x	g3(x	PROPN
ejpam-2571	201	14	)	)	PUNCT
ejpam-2571	201	15	〉	〉	NOUN
ejpam-2571	201	16	.	.	PUNCT
ejpam-2571	202	1	let	let	VERB
ejpam-2571	202	2	g(x	g(x	NOUN
ejpam-2571	202	3	)	)	PUNCT
ejpam-2571	202	4	=	=	PUNCT
ejpam-2571	202	5	η1	η1	NOUN
ejpam-2571	202	6	g1(x	g1(x	NOUN
ejpam-2571	202	7	)	)	PUNCT
ejpam-2571	203	1	+	+	CCONJ
ejpam-2571	203	2	η2	η2	ADJ
ejpam-2571	203	3	g2(x	g2(x	PROPN
ejpam-2571	203	4	)	)	PUNCT
ejpam-2571	203	5	+	+	CCONJ
ejpam-2571	203	6	η3	η3	PROPN
ejpam-2571	203	7	g3(x	g3(x	PROPN
ejpam-2571	203	8	)	)	PUNCT
ejpam-2571	203	9	.	.	PUNCT
ejpam-2571	204	1	clearly	clearly	ADV
ejpam-2571	204	2	,	,	PUNCT
ejpam-2571	204	3	〈	〈	PROPN
ejpam-2571	204	4	g(x	g(x	NOUN
ejpam-2571	204	5	)	)	PUNCT
ejpam-2571	204	6	〉	〉	NOUN
ejpam-2571	204	7	⊆	⊆	NUM
ejpam-2571	204	8	c	c	NOUN
ejpam-2571	204	9	.	.	PUNCT
ejpam-2571	205	1	however	however	ADV
ejpam-2571	205	2	,	,	PUNCT
ejpam-2571	205	3	η1	η1	PROPN
ejpam-2571	205	4	g1(x	g1(x	NOUN
ejpam-2571	205	5	)	)	PUNCT
ejpam-2571	205	6	=	=	SYM
ejpam-2571	205	7	η1	η1	NOUN
ejpam-2571	205	8	g(x	g(x	NOUN
ejpam-2571	205	9	)	)	PUNCT
ejpam-2571	205	10	,	,	PUNCT
ejpam-2571	205	11	η2	η2	PROPN
ejpam-2571	205	12	g2(x	g2(x	X
ejpam-2571	205	13	)	)	PUNCT
ejpam-2571	205	14	=	=	SYM
ejpam-2571	205	15	η2	η2	VERB
ejpam-2571	205	16	g(x	g(x	NOUN
ejpam-2571	205	17	)	)	PUNCT
ejpam-2571	205	18	and	and	CCONJ
ejpam-2571	205	19	η3	η3	PROPN
ejpam-2571	205	20	g3(x	g3(x	PROPN
ejpam-2571	205	21	)	)	PUNCT
ejpam-2571	205	22	=	=	PROPN
ejpam-2571	205	23	η3	η3	PROPN
ejpam-2571	205	24	g(x	g(x	PROPN
ejpam-2571	205	25	)	)	PUNCT
ejpam-2571	205	26	,	,	PUNCT
ejpam-2571	205	27	whence	whence	ADP
ejpam-2571	205	28	c	c	PROPN
ejpam-2571	205	29	⊆	⊆	NUM
ejpam-2571	205	30	〈	〈	PROPN
ejpam-2571	205	31	g(x	g(x	NOUN
ejpam-2571	205	32	)	)	PUNCT
ejpam-2571	205	33	〉	〉	NOUN
ejpam-2571	205	34	.	.	PUNCT
ejpam-2571	206	1	thus	thus	ADV
ejpam-2571	206	2	c	c	X
ejpam-2571	206	3	=	=	PUNCT
ejpam-2571	206	4	〈	〈	PROPN
ejpam-2571	206	5	g(x	g(x	NOUN
ejpam-2571	206	6	)	)	PUNCT
ejpam-2571	206	7	〉	〉	NOUN
ejpam-2571	206	8	.	.	PUNCT
ejpam-2571	207	1	the	the	DET
ejpam-2571	207	2	uniqueness	uniqueness	NOUN
ejpam-2571	207	3	of	of	ADP
ejpam-2571	207	4	g(x	g(x	NOUN
ejpam-2571	207	5	)	)	PUNCT
ejpam-2571	207	6	is	be	AUX
ejpam-2571	207	7	followed	follow	VERB
ejpam-2571	207	8	by	by	ADP
ejpam-2571	207	9	that	that	PRON
ejpam-2571	207	10	of	of	ADP
ejpam-2571	207	11	g1(x	g1(x	NOUN
ejpam-2571	207	12	)	)	PUNCT
ejpam-2571	207	13	,	,	PUNCT
ejpam-2571	207	14	g2(x	g2(x	PROPN
ejpam-2571	207	15	)	)	PUNCT
ejpam-2571	207	16	,	,	PUNCT
ejpam-2571	207	17	and	and	CCONJ
ejpam-2571	207	18	g3(x	g3(x	PROPN
ejpam-2571	207	19	)	)	PUNCT
ejpam-2571	207	20	.	.	PUNCT
ejpam-2571	208	1	lemma	lemma	PROPN
ejpam-2571	208	2	1	1	X
ejpam-2571	208	3	.	.	PUNCT
ejpam-2571	209	1	let	let	VERB
ejpam-2571	209	2	xn	xn	PROPN
ejpam-2571	210	1	−	−	PROPN
ejpam-2571	210	2	(	(	PUNCT
ejpam-2571	210	3	1−	1−	NUM
ejpam-2571	210	4	2u2	2u2	NUM
ejpam-2571	210	5	)	)	PUNCT
ejpam-2571	210	6	=	=	SYM
ejpam-2571	210	7	g(x)h(x	g(x)h(x	X
ejpam-2571	210	8	)	)	PUNCT
ejpam-2571	210	9	in	in	ADP
ejpam-2571	210	10	r[x	r[x	NOUN
ejpam-2571	210	11	]	]	PUNCT
ejpam-2571	210	12	and	and	CCONJ
ejpam-2571	210	13	let	let	VERB
ejpam-2571	210	14	c	c	PRON
ejpam-2571	210	15	be	be	AUX
ejpam-2571	210	16	the	the	DET
ejpam-2571	210	17	(	(	PUNCT
ejpam-2571	210	18	1−	1−	NUM
ejpam-2571	210	19	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	210	20	code	code	NOUN
ejpam-2571	210	21	generated	generate	VERB
ejpam-2571	210	22	by	by	ADP
ejpam-2571	210	23	g(x	g(x	PROPN
ejpam-2571	210	24	)	)	PUNCT
ejpam-2571	210	25	.	.	PUNCT
ejpam-2571	211	1	if	if	SCONJ
ejpam-2571	211	2	f	f	PROPN
ejpam-2571	211	3	(	(	PUNCT
ejpam-2571	211	4	x	x	X
ejpam-2571	211	5	)	)	PUNCT
ejpam-2571	211	6	is	be	AUX
ejpam-2571	211	7	relatively	relatively	ADV
ejpam-2571	211	8	prime	prime	ADJ
ejpam-2571	211	9	with	with	ADP
ejpam-2571	211	10	h(x	h(x	PROPN
ejpam-2571	211	11	)	)	PUNCT
ejpam-2571	211	12	then	then	ADV
ejpam-2571	211	13	c	c	X
ejpam-2571	211	14	=	=	PUNCT
ejpam-2571	211	15	〈	〈	PROPN
ejpam-2571	211	16	g(x	g(x	NOUN
ejpam-2571	211	17	)	)	PUNCT
ejpam-2571	211	18	f	f	NOUN
ejpam-2571	211	19	(	(	PUNCT
ejpam-2571	211	20	x	x	NOUN
ejpam-2571	211	21	)	)	PUNCT
ejpam-2571	211	22	〉	〉	NOUN
ejpam-2571	211	23	.	.	PUNCT
ejpam-2571	212	1	proof	proof	NOUN
ejpam-2571	212	2	.	.	PUNCT
ejpam-2571	213	1	the	the	DET
ejpam-2571	213	2	proof	proof	NOUN
ejpam-2571	213	3	is	be	AUX
ejpam-2571	213	4	similar	similar	ADJ
ejpam-2571	213	5	to	to	ADP
ejpam-2571	213	6	that	that	PRON
ejpam-2571	213	7	of	of	ADP
ejpam-2571	213	8	[	[	X
ejpam-2571	213	9	2	2	NUM
ejpam-2571	213	10	,	,	PUNCT
ejpam-2571	213	11	lemma	lemma	PROPN
ejpam-2571	213	12	2	2	NUM
ejpam-2571	213	13	]	]	PUNCT
ejpam-2571	213	14	.	.	PUNCT
ejpam-2571	214	1	theorem	theorem	ADJ
ejpam-2571	214	2	7	7	NUM
ejpam-2571	214	3	.	.	PUNCT
ejpam-2571	215	1	let	let	VERB
ejpam-2571	215	2	c	c	NOUN
ejpam-2571	215	3	=	=	PUNCT
ejpam-2571	216	1	η1c1	η1c1	NOUN
ejpam-2571	216	2	⊕η2c2	⊕η2c2	AUX
ejpam-2571	216	3	⊕η3c3	⊕η3c3	INTJ
ejpam-2571	216	4	be	be	AUX
ejpam-2571	216	5	a	a	DET
ejpam-2571	216	6	(	(	PUNCT
ejpam-2571	216	7	1−	1−	NUM
ejpam-2571	216	8	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	216	9	code	code	NOUN
ejpam-2571	216	10	of	of	ADP
ejpam-2571	216	11	length	length	NOUN
ejpam-2571	216	12	n	n	CCONJ
ejpam-2571	216	13	over	over	ADP
ejpam-2571	216	14	r	r	NOUN
ejpam-2571	216	15	such	such	ADJ
ejpam-2571	216	16	that	that	DET
ejpam-2571	216	17	g1(x	g1(x	NOUN
ejpam-2571	216	18	)	)	PUNCT
ejpam-2571	216	19	,	,	PUNCT
ejpam-2571	216	20	g2(x	g2(x	PROPN
ejpam-2571	216	21	)	)	PUNCT
ejpam-2571	216	22	,	,	PUNCT
ejpam-2571	216	23	g3(x	g3(x	X
ejpam-2571	216	24	)	)	PUNCT
ejpam-2571	216	25	are	be	AUX
ejpam-2571	216	26	the	the	DET
ejpam-2571	216	27	monic	monic	ADJ
ejpam-2571	216	28	generator	generator	NOUN
ejpam-2571	216	29	polynomials	polynomial	NOUN
ejpam-2571	216	30	of	of	ADP
ejpam-2571	216	31	c1	c1	PROPN
ejpam-2571	216	32	,	,	PUNCT
ejpam-2571	216	33	c2	c2	PROPN
ejpam-2571	216	34	,	,	PUNCT
ejpam-2571	216	35	c2	c2	PROPN
ejpam-2571	216	36	,	,	PUNCT
ejpam-2571	216	37	respectively	respectively	ADV
ejpam-2571	216	38	.	.	PUNCT
ejpam-2571	217	1	suppose	suppose	VERB
ejpam-2571	217	2	that	that	SCONJ
ejpam-2571	217	3	g1(x)h1(x	g1(x)h1(x	NOUN
ejpam-2571	217	4	)	)	PUNCT
ejpam-2571	217	5	=	=	SYM
ejpam-2571	218	1	xn	xn	PROPN
ejpam-2571	219	1	−	−	NUM
ejpam-2571	219	2	1	1	NUM
ejpam-2571	219	3	and	and	CCONJ
ejpam-2571	219	4	g2(x)h2(x	g2(x)h2(x	PROPN
ejpam-2571	219	5	)	)	PUNCT
ejpam-2571	219	6	=	=	PUNCT
ejpam-2571	219	7	g3(x)h3(x	g3(x)h3(x	PROPN
ejpam-2571	219	8	)	)	PUNCT
ejpam-2571	219	9	=	=	SYM
ejpam-2571	219	10	xn	xn	PROPN
ejpam-2571	220	1	+	+	CCONJ
ejpam-2571	220	2	1	1	NUM
ejpam-2571	220	3	and	and	CCONJ
ejpam-2571	220	4	set	set	VERB
ejpam-2571	220	5	g(x	g(x	NOUN
ejpam-2571	220	6	)	)	PUNCT
ejpam-2571	221	1	=	=	PUNCT
ejpam-2571	221	2	η1	η1	NOUN
ejpam-2571	221	3	g1(x	g1(x	NOUN
ejpam-2571	221	4	)	)	PUNCT
ejpam-2571	221	5	+	+	ADJ
ejpam-2571	221	6	η2	η2	ADJ
ejpam-2571	221	7	g2(x	g2(x	X
ejpam-2571	221	8	)	)	PUNCT
ejpam-2571	221	9	+	+	PROPN
ejpam-2571	221	10	η3	η3	PROPN
ejpam-2571	221	11	g3(x	g3(x	PROPN
ejpam-2571	221	12	)	)	PUNCT
ejpam-2571	221	13	,	,	PUNCT
ejpam-2571	221	14	h(x	h(x	PROPN
ejpam-2571	221	15	)	)	PUNCT
ejpam-2571	221	16	=	=	SYM
ejpam-2571	221	17	η1h1(x	η1h1(x	NOUN
ejpam-2571	221	18	)	)	PUNCT
ejpam-2571	222	1	+	+	NOUN
ejpam-2571	222	2	η2h2(x	η2h2(x	X
ejpam-2571	222	3	)	)	PUNCT
ejpam-2571	222	4	+	+	NOUN
ejpam-2571	222	5	η3h3(x	η3h3(x	NOUN
ejpam-2571	222	6	)	)	PUNCT
ejpam-2571	222	7	.	.	PUNCT
ejpam-2571	223	1	then	then	ADV
ejpam-2571	223	2	(	(	PUNCT
ejpam-2571	223	3	i	i	NOUN
ejpam-2571	223	4	)	)	PUNCT
ejpam-2571	223	5	g(x)h(x	g(x)h(x	PROPN
ejpam-2571	223	6	)	)	PUNCT
ejpam-2571	224	1	=	=	SYM
ejpam-2571	224	2	xn	xn	NUM
ejpam-2571	225	1	−	−	PROPN
ejpam-2571	225	2	(	(	PUNCT
ejpam-2571	225	3	1−	1−	NUM
ejpam-2571	225	4	2u2	2u2	NUM
ejpam-2571	225	5	)	)	PUNCT
ejpam-2571	225	6	.	.	PUNCT
ejpam-2571	226	1	(	(	PUNCT
ejpam-2571	226	2	ii	ii	NOUN
ejpam-2571	226	3	)	)	PUNCT
ejpam-2571	226	4	if	if	SCONJ
ejpam-2571	226	5	gc	gc	PROPN
ejpam-2571	226	6	d	d	PROPN
ejpam-2571	226	7	(	(	PUNCT
ejpam-2571	226	8	fi(x),hi(x	fi(x),hi(x	NUM
ejpam-2571	226	9	)	)	PUNCT
ejpam-2571	226	10	)	)	PUNCT
ejpam-2571	227	1	=	=	SYM
ejpam-2571	227	2	1	1	NUM
ejpam-2571	227	3	for	for	ADP
ejpam-2571	227	4	1	1	NUM
ejpam-2571	227	5	≤	≤	NUM
ejpam-2571	227	6	i	i	PRON
ejpam-2571	227	7	≤	≤	NOUN
ejpam-2571	227	8	3	3	NUM
ejpam-2571	227	9	,	,	PUNCT
ejpam-2571	227	10	then	then	ADV
ejpam-2571	227	11	gc	gc	PROPN
ejpam-2571	228	1	d	d	PROPN
ejpam-2571	228	2	(	(	PUNCT
ejpam-2571	228	3	f	f	PROPN
ejpam-2571	228	4	(	(	PUNCT
ejpam-2571	228	5	x),h(x	x),h(x	PROPN
ejpam-2571	228	6	)	)	PUNCT
ejpam-2571	228	7	)	)	PUNCT
ejpam-2571	228	8	=	=	SYM
ejpam-2571	228	9	1	1	NUM
ejpam-2571	228	10	and	and	CCONJ
ejpam-2571	228	11	g(x	g(x	NOUN
ejpam-2571	228	12	)	)	PUNCT
ejpam-2571	229	1	=	=	SYM
ejpam-2571	229	2	g(x	g(x	NOUN
ejpam-2571	229	3	)	)	PUNCT
ejpam-2571	229	4	f	f	NOUN
ejpam-2571	229	5	(	(	PUNCT
ejpam-2571	229	6	x	x	X
ejpam-2571	229	7	)	)	PUNCT
ejpam-2571	229	8	where	where	SCONJ
ejpam-2571	229	9	f	f	PROPN
ejpam-2571	229	10	(	(	PUNCT
ejpam-2571	229	11	x	x	NOUN
ejpam-2571	229	12	)	)	PUNCT
ejpam-2571	229	13	=	=	SYM
ejpam-2571	229	14	η1	η1	NOUN
ejpam-2571	229	15	f1(x	f1(x	NOUN
ejpam-2571	229	16	)	)	PUNCT
ejpam-2571	229	17	+	+	NOUN
ejpam-2571	229	18	η2	η2	ADJ
ejpam-2571	229	19	f2(x	f2(x	NOUN
ejpam-2571	229	20	)	)	PUNCT
ejpam-2571	229	21	+	+	ADJ
ejpam-2571	229	22	η3	η3	PROPN
ejpam-2571	229	23	f3(x	f3(x	NUM
ejpam-2571	229	24	)	)	PUNCT
ejpam-2571	229	25	.	.	PUNCT
ejpam-2571	230	1	proof	proof	NOUN
ejpam-2571	230	2	.	.	PUNCT
ejpam-2571	231	1	(	(	PUNCT
ejpam-2571	231	2	i	i	NOUN
ejpam-2571	231	3	)	)	PUNCT
ejpam-2571	231	4	by	by	ADP
ejpam-2571	231	5	assumptions	assumption	NOUN
ejpam-2571	231	6	we	we	PRON
ejpam-2571	231	7	have	have	VERB
ejpam-2571	231	8	that	that	DET
ejpam-2571	231	9	g(x)h(x	g(x)h(x	NOUN
ejpam-2571	231	10	)	)	PUNCT
ejpam-2571	232	1	=	=	SYM
ejpam-2571	232	2	g(x	g(x	NOUN
ejpam-2571	232	3	)	)	PUNCT
ejpam-2571	232	4	�	�	PROPN
ejpam-2571	232	5	η1h1(x	η1h1(x	NOUN
ejpam-2571	232	6	)	)	PUNCT
ejpam-2571	233	1	+	+	VERB
ejpam-2571	233	2	η2h2(x	η2h2(x	X
ejpam-2571	233	3	)	)	PUNCT
ejpam-2571	233	4	+	+	NOUN
ejpam-2571	233	5	η3h3(x	η3h3(x	NOUN
ejpam-2571	233	6	)	)	PUNCT
ejpam-2571	233	7	�	�	NOUN
ejpam-2571	233	8	=	=	SYM
ejpam-2571	233	9	η1	η1	NOUN
ejpam-2571	233	10	g1(x)h1(x	g1(x)h1(x	NOUN
ejpam-2571	233	11	)	)	PUNCT
ejpam-2571	234	1	+	+	ADJ
ejpam-2571	234	2	η2	η2	ADJ
ejpam-2571	234	3	g2(x)h2(x	g2(x)h2(x	PROPN
ejpam-2571	234	4	)	)	PUNCT
ejpam-2571	234	5	+	+	PROPN
ejpam-2571	234	6	η3	η3	PROPN
ejpam-2571	234	7	g3(x)h3(x	g3(x)h3(x	PROPN
ejpam-2571	234	8	)	)	PUNCT
ejpam-2571	235	1	=	=	NOUN
ejpam-2571	235	2	η1(x	η1(x	NOUN
ejpam-2571	235	3	n	n	CCONJ
ejpam-2571	235	4	−	−	PROPN
ejpam-2571	235	5	1	1	NUM
ejpam-2571	235	6	)	)	PUNCT
ejpam-2571	236	1	+	+	NOUN
ejpam-2571	236	2	η2(x	η2(x	PROPN
ejpam-2571	236	3	n	n	NOUN
ejpam-2571	236	4	+	+	NOUN
ejpam-2571	236	5	1	1	NUM
ejpam-2571	236	6	)	)	PUNCT
ejpam-2571	237	1	+	+	VERB
ejpam-2571	237	2	η3(x	η3(x	PROPN
ejpam-2571	237	3	n	n	NOUN
ejpam-2571	237	4	+	+	NOUN
ejpam-2571	237	5	1	1	NUM
ejpam-2571	237	6	)	)	PUNCT
ejpam-2571	237	7	=(	=(	NOUN
ejpam-2571	237	8	η1	η1	NOUN
ejpam-2571	237	9	+	+	NOUN
ejpam-2571	237	10	η2	η2	ADJ
ejpam-2571	237	11	+	+	ADV
ejpam-2571	237	12	η3)x	η3)x	ADJ
ejpam-2571	237	13	n	n	PRON
ejpam-2571	237	14	−	−	PROPN
ejpam-2571	237	15	(	(	PUNCT
ejpam-2571	237	16	η1	η1	NOUN
ejpam-2571	237	17	−η2	−η2	PROPN
ejpam-2571	237	18	−η3	−η3	PROPN
ejpam-2571	237	19	)	)	PUNCT
ejpam-2571	238	1	=	=	NOUN
ejpam-2571	238	2	xn	xn	NUM
ejpam-2571	238	3	−	−	PROPN
ejpam-2571	238	4	(	(	PUNCT
ejpam-2571	238	5	1−	1−	NUM
ejpam-2571	238	6	2u2	2u2	NUM
ejpam-2571	238	7	)	)	PUNCT
ejpam-2571	238	8	.	.	PUNCT
ejpam-2571	239	1	hence	hence	ADV
ejpam-2571	239	2	,	,	PUNCT
ejpam-2571	239	3	g(x)h(x	g(x)h(x	X
ejpam-2571	239	4	)	)	PUNCT
ejpam-2571	239	5	=	=	SYM
ejpam-2571	240	1	xn	xn	NUM
ejpam-2571	241	1	−	−	PROPN
ejpam-2571	241	2	(	(	PUNCT
ejpam-2571	241	3	1−	1−	NUM
ejpam-2571	241	4	2u2	2u2	NUM
ejpam-2571	241	5	)	)	PUNCT
ejpam-2571	241	6	.	.	PUNCT
ejpam-2571	242	1	(	(	PUNCT
ejpam-2571	242	2	ii	ii	NOUN
ejpam-2571	242	3	)	)	PUNCT
ejpam-2571	242	4	suppose	suppose	VERB
ejpam-2571	242	5	that	that	SCONJ
ejpam-2571	242	6	gc	gc	PROPN
ejpam-2571	242	7	d	d	PROPN
ejpam-2571	242	8	(	(	PUNCT
ejpam-2571	242	9	fi(x),hi(x	fi(x),hi(x	NUM
ejpam-2571	242	10	)	)	PUNCT
ejpam-2571	242	11	)	)	PUNCT
ejpam-2571	242	12	=	=	SYM
ejpam-2571	242	13	1	1	NUM
ejpam-2571	242	14	for	for	ADP
ejpam-2571	242	15	1≤	1≤	NUM
ejpam-2571	242	16	i	i	PRON
ejpam-2571	242	17	≤	≤	ADV
ejpam-2571	242	18	3	3	NUM
ejpam-2571	242	19	and	and	CCONJ
ejpam-2571	242	20	let	let	VERB
ejpam-2571	242	21	f	f	PROPN
ejpam-2571	242	22	(	(	PUNCT
ejpam-2571	242	23	x	x	NOUN
ejpam-2571	242	24	)	)	PUNCT
ejpam-2571	242	25	=	=	NOUN
ejpam-2571	242	26	η1	η1	NOUN
ejpam-2571	242	27	f1(x)+η2	f1(x)+η2	PROPN
ejpam-2571	242	28	f2(x)+η3	f2(x)+η3	PROPN
ejpam-2571	242	29	f3(x	f3(x	PROPN
ejpam-2571	242	30	)	)	PUNCT
ejpam-2571	242	31	.	.	PUNCT
ejpam-2571	243	1	then	then	ADV
ejpam-2571	243	2	for	for	ADP
ejpam-2571	243	3	every	every	DET
ejpam-2571	243	4	1≤	1≤	NUM
ejpam-2571	243	5	i	i	PRON
ejpam-2571	243	6	≤	≤	ADV
ejpam-2571	243	7	3	3	NUM
ejpam-2571	243	8	there	there	ADV
ejpam-2571	243	9	exist	exist	VERB
ejpam-2571	243	10	ai(x	ai(x	NUM
ejpam-2571	243	11	)	)	PUNCT
ejpam-2571	243	12	,	,	PUNCT
ejpam-2571	243	13	bi(x	bi(x	NUM
ejpam-2571	243	14	)	)	PUNCT
ejpam-2571	243	15	∈	∈	PROPN
ejpam-2571	243	16	r[x	r[x	NOUN
ejpam-2571	243	17	]	]	PUNCT
ejpam-2571	243	18	such	such	ADJ
ejpam-2571	243	19	that	that	DET
ejpam-2571	243	20	ai(x	ai(x	NUM
ejpam-2571	243	21	)	)	PUNCT
ejpam-2571	243	22	fi(x	fi(x	NUM
ejpam-2571	243	23	)	)	PUNCT
ejpam-2571	244	1	+	+	CCONJ
ejpam-2571	244	2	bi(x)hi(x	bi(x)hi(x	NOUN
ejpam-2571	244	3	)	)	PUNCT
ejpam-2571	244	4	=	=	SYM
ejpam-2571	244	5	1	1	X
ejpam-2571	244	6	.	.	X
ejpam-2571	244	7	set	set	VERB
ejpam-2571	244	8	a(x	a(x	NOUN
ejpam-2571	244	9	)	)	PUNCT
ejpam-2571	244	10	:	:	PUNCT
ejpam-2571	245	1	=	=	SYM
ejpam-2571	245	2	η1a1(x	η1a1(x	NOUN
ejpam-2571	245	3	)	)	PUNCT
ejpam-2571	245	4	+	+	NOUN
ejpam-2571	245	5	η2a2(x	η2a2(x	NOUN
ejpam-2571	245	6	)	)	PUNCT
ejpam-2571	245	7	+	+	NOUN
ejpam-2571	245	8	η3a3(x	η3a3(x	NOUN
ejpam-2571	245	9	)	)	PUNCT
ejpam-2571	245	10	and	and	CCONJ
ejpam-2571	245	11	b(x	b(x	NOUN
ejpam-2571	245	12	)	)	PUNCT
ejpam-2571	245	13	:	:	PUNCT
ejpam-2571	246	1	=	=	PUNCT
ejpam-2571	246	2	η1	η1	NOUN
ejpam-2571	246	3	b1(x	b1(x	NOUN
ejpam-2571	246	4	)	)	PUNCT
ejpam-2571	246	5	+	+	ADJ
ejpam-2571	246	6	η2	η2	ADJ
ejpam-2571	246	7	b2(x	b2(x	NOUN
ejpam-2571	246	8	)	)	PUNCT
ejpam-2571	246	9	+	+	PROPN
ejpam-2571	246	10	η3	η3	PROPN
ejpam-2571	246	11	b3(x	b3(x	PROPN
ejpam-2571	246	12	)	)	PUNCT
ejpam-2571	246	13	.	.	PUNCT
ejpam-2571	247	1	notice	notice	VERB
ejpam-2571	247	2	that	that	SCONJ
ejpam-2571	247	3	η1	η1	NOUN
ejpam-2571	247	4	+	+	CCONJ
ejpam-2571	247	5	η2	η2	VERB
ejpam-2571	247	6	+	+	NOUN
ejpam-2571	247	7	η3	η3	NOUN
ejpam-2571	247	8	=	=	SYM
ejpam-2571	247	9	1	1	NUM
ejpam-2571	247	10	,	,	PUNCT
ejpam-2571	247	11	η2	η2	PUNCT
ejpam-2571	247	12	i	i	NOUN
ejpam-2571	247	13	=	=	NOUN
ejpam-2571	247	14	1	1	NUM
ejpam-2571	247	15	and	and	CCONJ
ejpam-2571	247	16	ηiη	ηiη	X
ejpam-2571	247	17	j	j	PROPN
ejpam-2571	247	18	=	=	SYM
ejpam-2571	247	19	0	0	PROPN
ejpam-2571	247	20	for	for	ADP
ejpam-2571	247	21	every	every	DET
ejpam-2571	247	22	1≤	1≤	NUM
ejpam-2571	247	23	i	i	PROPN
ejpam-2571	247	24	6=	6=	PROPN
ejpam-2571	247	25	j	j	PROPN
ejpam-2571	247	26	≤	≤	ADV
ejpam-2571	247	27	3	3	NUM
ejpam-2571	247	28	.	.	PUNCT
ejpam-2571	247	29	thus	thus	ADV
ejpam-2571	247	30	a(x	a(x	NOUN
ejpam-2571	247	31	)	)	PUNCT
ejpam-2571	247	32	f	f	NOUN
ejpam-2571	247	33	(	(	PUNCT
ejpam-2571	247	34	x	x	X
ejpam-2571	247	35	)	)	PUNCT
ejpam-2571	247	36	+	+	X
ejpam-2571	247	37	b(x)h(x	b(x)h(x	NOUN
ejpam-2571	247	38	)	)	PUNCT
ejpam-2571	247	39	=	=	SYM
ejpam-2571	247	40	η1[a1(x	η1[a1(x	NOUN
ejpam-2571	247	41	)	)	PUNCT
ejpam-2571	247	42	f1(x	f1(x	NUM
ejpam-2571	247	43	)	)	PUNCT
ejpam-2571	247	44	+	+	NUM
ejpam-2571	247	45	b1(x)h1(x	b1(x)h1(x	NOUN
ejpam-2571	247	46	)	)	PUNCT
ejpam-2571	247	47	]	]	PUNCT
ejpam-2571	248	1	+	+	X
ejpam-2571	248	2	η2[a2(x	η2[a2(x	PROPN
ejpam-2571	248	3	)	)	PUNCT
ejpam-2571	248	4	f2(x	f2(x	NOUN
ejpam-2571	248	5	)	)	PUNCT
ejpam-2571	248	6	+	+	NUM
ejpam-2571	248	7	b2(x)h2(x	b2(x)h2(x	X
ejpam-2571	248	8	)	)	PUNCT
ejpam-2571	248	9	]	]	PUNCT
ejpam-2571	249	1	+	+	PUNCT
ejpam-2571	249	2	η3[a3(x	η3[a3(x	PROPN
ejpam-2571	249	3	)	)	PUNCT
ejpam-2571	249	4	f3(x	f3(x	PROPN
ejpam-2571	249	5	)	)	PUNCT
ejpam-2571	249	6	+	+	NUM
ejpam-2571	249	7	b3(x)h3(x	b3(x)h3(x	PROPN
ejpam-2571	249	8	)	)	PUNCT
ejpam-2571	249	9	]	]	PUNCT
ejpam-2571	249	10	=	=	PUNCT
ejpam-2571	249	11	η1	η1	NOUN
ejpam-2571	249	12	+	+	NOUN
ejpam-2571	249	13	η2	η2	VERB
ejpam-2571	249	14	+	+	NOUN
ejpam-2571	249	15	η3	η3	NOUN
ejpam-2571	249	16	=	=	SYM
ejpam-2571	249	17	1	1	X
ejpam-2571	249	18	.	.	PUNCT
ejpam-2571	250	1	it	it	PRON
ejpam-2571	250	2	follows	follow	VERB
ejpam-2571	250	3	that	that	SCONJ
ejpam-2571	250	4	gc	gc	PROPN
ejpam-2571	250	5	d	d	PROPN
ejpam-2571	250	6	(	(	PUNCT
ejpam-2571	250	7	f	f	PROPN
ejpam-2571	250	8	(	(	PUNCT
ejpam-2571	250	9	x),h(x	x),h(x	PROPN
ejpam-2571	250	10	)	)	PUNCT
ejpam-2571	250	11	)	)	PUNCT
ejpam-2571	251	1	=	=	PUNCT
ejpam-2571	251	2	1	1	X
ejpam-2571	251	3	.	.	PUNCT
ejpam-2571	251	4	now	now	ADV
ejpam-2571	251	5	,	,	PUNCT
ejpam-2571	251	6	by	by	ADP
ejpam-2571	251	7	part	part	NOUN
ejpam-2571	251	8	(	(	PUNCT
ejpam-2571	251	9	i	i	NOUN
ejpam-2571	251	10	)	)	PUNCT
ejpam-2571	251	11	and	and	CCONJ
ejpam-2571	251	12	lemma	lemma	PROPN
ejpam-2571	251	13	1	1	NUM
ejpam-2571	251	14	,	,	PUNCT
ejpam-2571	251	15	c	c	NOUN
ejpam-2571	251	16	=	=	PUNCT
ejpam-2571	251	17	〈	〈	PROPN
ejpam-2571	251	18	g(x	g(x	NOUN
ejpam-2571	251	19	)	)	PUNCT
ejpam-2571	251	20	f	f	NOUN
ejpam-2571	251	21	(	(	PUNCT
ejpam-2571	251	22	x	x	NOUN
ejpam-2571	251	23	)	)	PUNCT
ejpam-2571	251	24	〉	〉	NOUN
ejpam-2571	251	25	.	.	PUNCT
ejpam-2571	252	1	so	so	ADV
ejpam-2571	252	2	,	,	PUNCT
ejpam-2571	252	3	the	the	DET
ejpam-2571	252	4	uniqueness	uniqueness	NOUN
ejpam-2571	252	5	of	of	ADP
ejpam-2571	252	6	g(x	g(x	NOUN
ejpam-2571	252	7	)	)	PUNCT
ejpam-2571	252	8	implies	imply	VERB
ejpam-2571	252	9	that	that	SCONJ
ejpam-2571	252	10	g(x	g(x	NOUN
ejpam-2571	252	11	)	)	PUNCT
ejpam-2571	253	1	=	=	SYM
ejpam-2571	253	2	g(x	g(x	NOUN
ejpam-2571	253	3	)	)	PUNCT
ejpam-2571	253	4	f	f	NOUN
ejpam-2571	253	5	(	(	PUNCT
ejpam-2571	253	6	x	x	NOUN
ejpam-2571	253	7	)	)	PUNCT
ejpam-2571	253	8	.	.	PUNCT
ejpam-2571	254	1	similar	similar	ADJ
ejpam-2571	254	2	to	to	ADP
ejpam-2571	254	3	[	[	X
ejpam-2571	254	4	8	8	NUM
ejpam-2571	254	5	,	,	PUNCT
ejpam-2571	254	6	theorem	theorem	VERB
ejpam-2571	254	7	3	3	NUM
ejpam-2571	254	8	]	]	PUNCT
ejpam-2571	254	9	,	,	PUNCT
ejpam-2571	254	10	we	we	PRON
ejpam-2571	254	11	have	have	VERB
ejpam-2571	254	12	the	the	DET
ejpam-2571	254	13	following	follow	VERB
ejpam-2571	254	14	theorem	theorem	PROPN
ejpam-2571	254	15	.	.	PUNCT
ejpam-2571	255	1	h.	h.	PROPN
ejpam-2571	255	2	mostafanasab	mostafanasab	PROPN
ejpam-2571	255	3	,	,	PUNCT
ejpam-2571	255	4	n.	n.	PROPN
ejpam-2571	255	5	karimi	karimi	PROPN
ejpam-2571	255	6	/	/	SYM
ejpam-2571	255	7	eur	eur	PROPN
ejpam-2571	255	8	.	.	PUNCT
ejpam-2571	256	1	j.	j.	PROPN
ejpam-2571	256	2	pure	pure	PROPN
ejpam-2571	256	3	appl	appl	PROPN
ejpam-2571	256	4	.	.	PROPN
ejpam-2571	256	5	math	math	PROPN
ejpam-2571	256	6	,	,	PUNCT
ejpam-2571	256	7	9	9	NUM
ejpam-2571	256	8	(	(	PUNCT
ejpam-2571	256	9	2016	2016	NUM
ejpam-2571	256	10	)	)	PUNCT
ejpam-2571	256	11	,	,	PUNCT
ejpam-2571	256	12	39	39	NUM
ejpam-2571	256	13	-	-	SYM
ejpam-2571	256	14	47	47	NUM
ejpam-2571	256	15	44	44	NUM
ejpam-2571	256	16	theorem	theorem	NOUN
ejpam-2571	256	17	8	8	NUM
ejpam-2571	256	18	.	.	PUNCT
ejpam-2571	257	1	let	let	VERB
ejpam-2571	257	2	c	c	PRON
ejpam-2571	257	3	be	be	AUX
ejpam-2571	257	4	a	a	DET
ejpam-2571	257	5	(	(	PUNCT
ejpam-2571	257	6	1−	1−	NUM
ejpam-2571	257	7	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	257	8	code	code	NOUN
ejpam-2571	257	9	of	of	ADP
ejpam-2571	257	10	length	length	NOUN
ejpam-2571	257	11	n	n	CCONJ
ejpam-2571	257	12	over	over	ADP
ejpam-2571	257	13	r	r	NOUN
ejpam-2571	257	14	.	.	PUNCT
ejpam-2571	258	1	then	then	ADV
ejpam-2571	258	2	c	c	PROPN
ejpam-2571	258	3	⊥	⊥	NOUN
ejpam-2571	258	4	=	=	PUNCT
ejpam-2571	258	5	η1c	η1c	NUM
ejpam-2571	258	6	⊥	⊥	PROPN
ejpam-2571	258	7	1	1	NUM
ejpam-2571	258	8	⊕η2c	⊕η2c	NOUN
ejpam-2571	258	9	⊥	⊥	ADJ
ejpam-2571	258	10	2	2	NUM
ejpam-2571	258	11	⊕η3c	⊕η3c	NOUN
ejpam-2571	258	12	⊥	⊥	NOUN
ejpam-2571	258	13	3	3	NUM
ejpam-2571	258	14	.	.	PUNCT
ejpam-2571	259	1	as	as	ADP
ejpam-2571	259	2	a	a	DET
ejpam-2571	259	3	consequence	consequence	NOUN
ejpam-2571	259	4	of	of	ADP
ejpam-2571	259	5	the	the	DET
ejpam-2571	259	6	previous	previous	ADJ
ejpam-2571	259	7	theorems	theorem	NOUN
ejpam-2571	259	8	and	and	CCONJ
ejpam-2571	259	9	[	[	X
ejpam-2571	259	10	10	10	NUM
ejpam-2571	259	11	,	,	PUNCT
ejpam-2571	259	12	theorem	theorem	VERB
ejpam-2571	259	13	3.3]we	3.3]we	PRON
ejpam-2571	259	14	have	have	VERB
ejpam-2571	259	15	the	the	DET
ejpam-2571	259	16	next	next	ADJ
ejpam-2571	259	17	result	result	NOUN
ejpam-2571	259	18	.	.	PUNCT
ejpam-2571	260	1	corollary	corollary	ADJ
ejpam-2571	260	2	1	1	NUM
ejpam-2571	260	3	.	.	PUNCT
ejpam-2571	261	1	let	let	VERB
ejpam-2571	261	2	c	c	NOUN
ejpam-2571	261	3	=	=	PUNCT
ejpam-2571	261	4	〈	〈	NOUN
ejpam-2571	261	5	η1	η1	NOUN
ejpam-2571	261	6	g1(x),η2	g1(x),η2	PROPN
ejpam-2571	261	7	g2(x),η3	g2(x),η3	PROPN
ejpam-2571	261	8	g3(x	g3(x	PROPN
ejpam-2571	261	9	)	)	PUNCT
ejpam-2571	261	10	〉	〉	NOUN
ejpam-2571	261	11	be	be	VERB
ejpam-2571	261	12	a	a	DET
ejpam-2571	261	13	(	(	PUNCT
ejpam-2571	261	14	1−	1−	NUM
ejpam-2571	261	15	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	261	16	code	code	NOUN
ejpam-2571	261	17	of	of	ADP
ejpam-2571	261	18	length	length	NOUN
ejpam-2571	261	19	n	n	CCONJ
ejpam-2571	261	20	over	over	ADP
ejpam-2571	261	21	r	r	NOUN
ejpam-2571	261	22	and	and	CCONJ
ejpam-2571	261	23	g1(x	g1(x	NOUN
ejpam-2571	261	24	)	)	PUNCT
ejpam-2571	261	25	,	,	PUNCT
ejpam-2571	261	26	g2(x	g2(x	PROPN
ejpam-2571	261	27	)	)	PUNCT
ejpam-2571	261	28	,	,	PUNCT
ejpam-2571	261	29	g3(x	g3(x	X
ejpam-2571	261	30	)	)	PUNCT
ejpam-2571	261	31	be	be	VERB
ejpam-2571	261	32	the	the	DET
ejpam-2571	261	33	monic	monic	ADJ
ejpam-2571	261	34	generator	generator	NOUN
ejpam-2571	261	35	polynomials	polynomial	NOUN
ejpam-2571	261	36	of	of	ADP
ejpam-2571	261	37	c1	c1	PROPN
ejpam-2571	261	38	,	,	PUNCT
ejpam-2571	261	39	c2	c2	PROPN
ejpam-2571	261	40	,	,	PUNCT
ejpam-2571	261	41	c3	c3	PROPN
ejpam-2571	261	42	,	,	PUNCT
ejpam-2571	261	43	respectively	respectively	ADV
ejpam-2571	261	44	.	.	PUNCT
ejpam-2571	262	1	suppose	suppose	VERB
ejpam-2571	262	2	that	that	SCONJ
ejpam-2571	262	3	g1(x)h1(x	g1(x)h1(x	NOUN
ejpam-2571	262	4	)	)	PUNCT
ejpam-2571	262	5	=	=	SYM
ejpam-2571	263	1	xn	xn	PROPN
ejpam-2571	264	1	−	−	NUM
ejpam-2571	264	2	1	1	NUM
ejpam-2571	264	3	and	and	CCONJ
ejpam-2571	264	4	g2(x)h2(x	g2(x)h2(x	PROPN
ejpam-2571	264	5	)	)	PUNCT
ejpam-2571	264	6	=	=	PUNCT
ejpam-2571	264	7	g3(x)h3(x	g3(x)h3(x	PROPN
ejpam-2571	264	8	)	)	PUNCT
ejpam-2571	264	9	=	=	SYM
ejpam-2571	264	10	xn	xn	PROPN
ejpam-2571	265	1	+	+	CCONJ
ejpam-2571	265	2	1	1	NUM
ejpam-2571	265	3	and	and	CCONJ
ejpam-2571	265	4	let	let	VERB
ejpam-2571	265	5	h(x	h(x	PROPN
ejpam-2571	265	6	)	)	PUNCT
ejpam-2571	265	7	=	=	SYM
ejpam-2571	265	8	η1h1(x	η1h1(x	NOUN
ejpam-2571	265	9	)	)	PUNCT
ejpam-2571	266	1	+	+	NOUN
ejpam-2571	266	2	η2h2(x	η2h2(x	X
ejpam-2571	266	3	)	)	PUNCT
ejpam-2571	266	4	+	+	ADJ
ejpam-2571	266	5	η3h3(x	η3h3(x	NOUN
ejpam-2571	266	6	)	)	PUNCT
ejpam-2571	266	7	.	.	PUNCT
ejpam-2571	267	1	the	the	DET
ejpam-2571	267	2	following	follow	VERB
ejpam-2571	267	3	conditions	condition	NOUN
ejpam-2571	267	4	hold	hold	VERB
ejpam-2571	267	5	:	:	PUNCT
ejpam-2571	267	6	(	(	PUNCT
ejpam-2571	267	7	i	i	NOUN
ejpam-2571	267	8	)	)	PUNCT
ejpam-2571	267	9	c	c	PROPN
ejpam-2571	268	1	⊥	⊥	PROPN
ejpam-2571	268	2	=	=	PUNCT
ejpam-2571	268	3	〈	〈	PROPN
ejpam-2571	268	4	η1h⊥1	η1h⊥1	PROPN
ejpam-2571	268	5	(	(	PUNCT
ejpam-2571	268	6	x),η2h⊥2	x),η2h⊥2	PROPN
ejpam-2571	268	7	(	(	PUNCT
ejpam-2571	268	8	x),η3h⊥3	x),η3h⊥3	X
ejpam-2571	268	9	(	(	PUNCT
ejpam-2571	268	10	x	x	NOUN
ejpam-2571	268	11	)	)	PUNCT
ejpam-2571	268	12	〉	〉	NOUN
ejpam-2571	268	13	and	and	CCONJ
ejpam-2571	268	14	|c	|c	NOUN
ejpam-2571	268	15	⊥|=	⊥|=	PROPN
ejpam-2571	268	16	p	p	NOUN
ejpam-2571	268	17	∑3	∑3	PROPN
ejpam-2571	268	18	i=1	i=1	PROPN
ejpam-2571	268	19	deg(gi	deg(gi	NOUN
ejpam-2571	268	20	)	)	PUNCT
ejpam-2571	268	21	.	.	PUNCT
ejpam-2571	269	1	(	(	PUNCT
ejpam-2571	269	2	ii	ii	NOUN
ejpam-2571	269	3	)	)	PUNCT
ejpam-2571	269	4	c	c	PROPN
ejpam-2571	269	5	⊥	⊥	PROPN
ejpam-2571	269	6	=	=	PUNCT
ejpam-2571	269	7	〈	〈	PROPN
ejpam-2571	269	8	h⊥(x	h⊥(x	PROPN
ejpam-2571	269	9	)	)	PUNCT
ejpam-2571	269	10	〉	〉	NOUN
ejpam-2571	269	11	,	,	PUNCT
ejpam-2571	269	12	h⊥(x	h⊥(x	PROPN
ejpam-2571	269	13	)	)	PUNCT
ejpam-2571	269	14	=	=	SYM
ejpam-2571	270	1	η1h⊥1	η1h⊥1	PROPN
ejpam-2571	270	2	(	(	PUNCT
ejpam-2571	270	3	x	x	X
ejpam-2571	270	4	)	)	PUNCT
ejpam-2571	270	5	+	+	ADJ
ejpam-2571	270	6	η2h⊥2	η2h⊥2	PROPN
ejpam-2571	270	7	(	(	PUNCT
ejpam-2571	270	8	x	x	X
ejpam-2571	270	9	)	)	PUNCT
ejpam-2571	270	10	+	+	NOUN
ejpam-2571	270	11	η3h⊥3	η3h⊥3	PROPN
ejpam-2571	270	12	(	(	PUNCT
ejpam-2571	270	13	x	x	NOUN
ejpam-2571	270	14	)	)	PUNCT
ejpam-2571	270	15	,	,	PUNCT
ejpam-2571	270	16	where	where	SCONJ
ejpam-2571	270	17	for	for	ADP
ejpam-2571	270	18	1	1	NUM
ejpam-2571	270	19	≤	≤	NUM
ejpam-2571	270	20	i	i	PRON
ejpam-2571	270	21	≤	≤	NOUN
ejpam-2571	270	22	3	3	NUM
ejpam-2571	270	23	,	,	PUNCT
ejpam-2571	270	24	h⊥	h⊥	NOUN
ejpam-2571	270	25	i	i	PRON
ejpam-2571	270	26	(	(	PUNCT
ejpam-2571	270	27	x	x	X
ejpam-2571	270	28	)	)	PUNCT
ejpam-2571	270	29	is	be	AUX
ejpam-2571	270	30	the	the	DET
ejpam-2571	270	31	reciprocal	reciprocal	ADJ
ejpam-2571	270	32	polynomial	polynomial	NOUN
ejpam-2571	270	33	of	of	ADP
ejpam-2571	270	34	hi(x	hi(x	PROPN
ejpam-2571	270	35	)	)	PUNCT
ejpam-2571	270	36	,	,	PUNCT
ejpam-2571	270	37	and	and	CCONJ
ejpam-2571	270	38	h⊥(x	h⊥(x	PROPN
ejpam-2571	270	39	)	)	PUNCT
ejpam-2571	270	40	is	be	AUX
ejpam-2571	270	41	the	the	DET
ejpam-2571	270	42	reciprocal	reciprocal	ADJ
ejpam-2571	270	43	polynomial	polynomial	NOUN
ejpam-2571	270	44	of	of	ADP
ejpam-2571	270	45	h(x	h(x	PROPN
ejpam-2571	270	46	)	)	PUNCT
ejpam-2571	270	47	.	.	PUNCT
ejpam-2571	271	1	theorem	theorem	VERB
ejpam-2571	271	2	9	9	NUM
ejpam-2571	271	3	.	.	PUNCT
ejpam-2571	271	4	let	let	VERB
ejpam-2571	271	5	µ	µ	X
ejpam-2571	271	6	:	:	PUNCT
ejpam-2571	271	7	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2571	271	8	−	−	NOUN
ejpam-2571	271	9	1	1	NUM
ejpam-2571	271	10	〉	〉	NOUN
ejpam-2571	271	11	→	→	SYM
ejpam-2571	271	12	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2571	271	13	−	−	PROPN
ejpam-2571	271	14	(	(	PUNCT
ejpam-2571	271	15	1−	1−	NUM
ejpam-2571	271	16	2u2	2u2	NUM
ejpam-2571	271	17	)	)	PUNCT
ejpam-2571	271	18	〉	〉	NOUN
ejpam-2571	271	19	be	be	AUX
ejpam-2571	271	20	defined	define	VERB
ejpam-2571	271	21	as	as	ADP
ejpam-2571	271	22	µ	µ	PROPN
ejpam-2571	271	23	�	�	PROPN
ejpam-2571	271	24	c(x	c(x	NOUN
ejpam-2571	271	25	)	)	PUNCT
ejpam-2571	271	26	�	�	PROPN
ejpam-2571	271	27	=	=	SYM
ejpam-2571	271	28	c	c	PROPN
ejpam-2571	271	29	�	�	PROPN
ejpam-2571	271	30	(	(	PUNCT
ejpam-2571	271	31	1−	1−	NUM
ejpam-2571	271	32	2u2)x	2u2)x	NUM
ejpam-2571	271	33	�	�	NOUN
ejpam-2571	271	34	.	.	PUNCT
ejpam-2571	272	1	if	if	SCONJ
ejpam-2571	272	2	n	n	NOUN
ejpam-2571	272	3	is	be	AUX
ejpam-2571	272	4	odd	odd	ADJ
ejpam-2571	272	5	,	,	PUNCT
ejpam-2571	272	6	then	then	ADV
ejpam-2571	272	7	µ	µ	NOUN
ejpam-2571	272	8	is	be	AUX
ejpam-2571	272	9	a	a	DET
ejpam-2571	272	10	ring	ring	NOUN
ejpam-2571	272	11	isomorphism	isomorphism	NOUN
ejpam-2571	272	12	.	.	PUNCT
ejpam-2571	273	1	proof	proof	NOUN
ejpam-2571	273	2	.	.	PUNCT
ejpam-2571	274	1	suppose	suppose	VERB
ejpam-2571	274	2	that	that	SCONJ
ejpam-2571	274	3	a(x	a(x	NOUN
ejpam-2571	274	4	)	)	PUNCT
ejpam-2571	274	5	≡	≡	PROPN
ejpam-2571	274	6	b(x	b(x	PROPN
ejpam-2571	274	7	)	)	PUNCT
ejpam-2571	274	8	(	(	PUNCT
ejpam-2571	274	9	mod	mod	PROPN
ejpam-2571	274	10	xn	xn	PROPN
ejpam-2571	274	11	−	−	PROPN
ejpam-2571	274	12	1	1	NUM
ejpam-2571	274	13	)	)	PUNCT
ejpam-2571	274	14	.	.	PUNCT
ejpam-2571	275	1	then	then	ADV
ejpam-2571	275	2	there	there	PRON
ejpam-2571	275	3	exists	exist	VERB
ejpam-2571	275	4	h(x	h(x	PROPN
ejpam-2571	275	5	)	)	PUNCT
ejpam-2571	275	6	∈	∈	PROPN
ejpam-2571	275	7	r[x	r[x	NOUN
ejpam-2571	275	8	]	]	PUNCT
ejpam-2571	275	9	such	such	ADJ
ejpam-2571	275	10	that	that	SCONJ
ejpam-2571	275	11	a(x)−	a(x)−	NOUN
ejpam-2571	275	12	b(x	b(x	NOUN
ejpam-2571	275	13	)	)	PUNCT
ejpam-2571	275	14	=	=	SYM
ejpam-2571	275	15	(	(	PUNCT
ejpam-2571	276	1	xn	xn	PROPN
ejpam-2571	276	2	−	−	PROPN
ejpam-2571	276	3	1)h(x	1)h(x	NUM
ejpam-2571	276	4	)	)	PUNCT
ejpam-2571	276	5	.	.	PUNCT
ejpam-2571	277	1	therefore	therefore	ADV
ejpam-2571	277	2	a	a	DET
ejpam-2571	277	3	�	�	PROPN
ejpam-2571	277	4	(	(	PUNCT
ejpam-2571	277	5	1−	1−	NUM
ejpam-2571	277	6	2u2)x	2u2)x	NUM
ejpam-2571	277	7	�	�	PROPN
ejpam-2571	277	8	−	−	PROPN
ejpam-2571	277	9	b	b	PROPN
ejpam-2571	277	10	�	�	PROPN
ejpam-2571	277	11	(	(	PUNCT
ejpam-2571	277	12	1−	1−	NUM
ejpam-2571	277	13	2u2)x	2u2)x	NUM
ejpam-2571	277	14	�	�	PROPN
ejpam-2571	277	15	=	=	SYM
ejpam-2571	277	16	�	�	PROPN
ejpam-2571	277	17	(	(	PUNCT
ejpam-2571	277	18	1−	1−	NUM
ejpam-2571	277	19	2u2)n	2u2)n	NUM
ejpam-2571	277	20	xn	xn	NUM
ejpam-2571	277	21	−	−	PROPN
ejpam-2571	277	22	1	1	NUM
ejpam-2571	277	23	�	�	PROPN
ejpam-2571	277	24	h	h	PROPN
ejpam-2571	277	25	�	�	PROPN
ejpam-2571	277	26	(	(	PUNCT
ejpam-2571	277	27	1−	1−	NUM
ejpam-2571	277	28	2u2)x	2u2)x	NUM
ejpam-2571	277	29	�	�	PROPN
ejpam-2571	277	30	=	=	SYM
ejpam-2571	277	31	�	�	PROPN
ejpam-2571	277	32	(	(	PUNCT
ejpam-2571	277	33	1−	1−	NUM
ejpam-2571	277	34	2u2)xn	2u2)xn	NUM
ejpam-2571	277	35	−	−	NOUN
ejpam-2571	277	36	(	(	PUNCT
ejpam-2571	277	37	1−	1−	NUM
ejpam-2571	277	38	2u2)2	2u2)2	NUM
ejpam-2571	277	39	�	�	PROPN
ejpam-2571	277	40	h	h	PROPN
ejpam-2571	277	41	�	�	PROPN
ejpam-2571	277	42	(	(	PUNCT
ejpam-2571	277	43	1−	1−	NUM
ejpam-2571	277	44	2u2)x	2u2)x	NUM
ejpam-2571	277	45	�	�	PROPN
ejpam-2571	277	46	=(	=(	NOUN
ejpam-2571	277	47	1−	1−	NUM
ejpam-2571	277	48	2u2	2u2	NUM
ejpam-2571	277	49	)	)	PUNCT
ejpam-2571	277	50	�	�	PROPN
ejpam-2571	277	51	xn	xn	PUNCT
ejpam-2571	277	52	−	−	PROPN
ejpam-2571	277	53	(	(	PUNCT
ejpam-2571	277	54	1−	1−	NUM
ejpam-2571	277	55	2u2	2u2	NUM
ejpam-2571	277	56	)	)	PUNCT
ejpam-2571	277	57	�	�	PROPN
ejpam-2571	277	58	h	h	PROPN
ejpam-2571	277	59	�	�	PROPN
ejpam-2571	277	60	(	(	PUNCT
ejpam-2571	277	61	1−	1−	NUM
ejpam-2571	277	62	2u2)x	2u2)x	NUM
ejpam-2571	277	63	�	�	PROPN
ejpam-2571	277	64	,	,	PUNCT
ejpam-2571	277	65	which	which	PRON
ejpam-2571	277	66	means	mean	VERB
ejpam-2571	277	67	if	if	SCONJ
ejpam-2571	277	68	a(x)≡	a(x)≡	PROPN
ejpam-2571	277	69	b(x	b(x	VERB
ejpam-2571	277	70	)	)	PUNCT
ejpam-2571	277	71	(	(	PUNCT
ejpam-2571	277	72	mod	mod	PROPN
ejpam-2571	277	73	xn	xn	PROPN
ejpam-2571	278	1	−	−	PROPN
ejpam-2571	278	2	1	1	NUM
ejpam-2571	278	3	)	)	PUNCT
ejpam-2571	278	4	,	,	PUNCT
ejpam-2571	278	5	then	then	ADV
ejpam-2571	278	6	a	a	DET
ejpam-2571	278	7	�	�	PROPN
ejpam-2571	278	8	(	(	PUNCT
ejpam-2571	278	9	1−	1−	NUM
ejpam-2571	278	10	2u2)x	2u2)x	NUM
ejpam-2571	278	11	�	�	PROPN
ejpam-2571	278	12	≡	≡	PROPN
ejpam-2571	278	13	b	b	PROPN
ejpam-2571	278	14	�	�	PROPN
ejpam-2571	278	15	(	(	PUNCT
ejpam-2571	278	16	1−	1−	NUM
ejpam-2571	278	17	2u2)x	2u2)x	NUM
ejpam-2571	278	18	�	�	PROPN
ejpam-2571	278	19	�	�	PROPN
ejpam-2571	278	20	mod	mod	PROPN
ejpam-2571	278	21	xn	xn	PROPN
ejpam-2571	279	1	−	−	PROPN
ejpam-2571	279	2	(	(	PUNCT
ejpam-2571	279	3	1−	1−	NUM
ejpam-2571	279	4	2u2	2u2	NUM
ejpam-2571	279	5	)	)	PUNCT
ejpam-2571	279	6	�	�	PROPN
ejpam-2571	279	7	.	.	PUNCT
ejpam-2571	280	1	now	now	ADV
ejpam-2571	280	2	,	,	PUNCT
ejpam-2571	280	3	assume	assume	VERB
ejpam-2571	280	4	that	that	SCONJ
ejpam-2571	280	5	a	a	DET
ejpam-2571	280	6	�	�	PROPN
ejpam-2571	280	7	(	(	PUNCT
ejpam-2571	280	8	1	1	NUM
ejpam-2571	280	9	−	−	NUM
ejpam-2571	280	10	2u2)x	2u2)x	NUM
ejpam-2571	280	11	�	�	PROPN
ejpam-2571	280	12	≡	≡	PROPN
ejpam-2571	280	13	b	b	PROPN
ejpam-2571	280	14	�	�	PROPN
ejpam-2571	280	15	(	(	PUNCT
ejpam-2571	280	16	1	1	NUM
ejpam-2571	280	17	−	−	NUM
ejpam-2571	280	18	2u2)x	2u2)x	NUM
ejpam-2571	280	19	�	�	PROPN
ejpam-2571	280	20	�	�	PROPN
ejpam-2571	280	21	mod	mod	PROPN
ejpam-2571	280	22	xn	xn	PROPN
ejpam-2571	281	1	−	−	PROPN
ejpam-2571	281	2	(	(	PUNCT
ejpam-2571	281	3	1	1	NUM
ejpam-2571	281	4	−	−	NUM
ejpam-2571	281	5	2u2	2u2	NUM
ejpam-2571	281	6	)	)	PUNCT
ejpam-2571	281	7	�	�	PROPN
ejpam-2571	281	8	.	.	PUNCT
ejpam-2571	282	1	then	then	ADV
ejpam-2571	282	2	there	there	PRON
ejpam-2571	282	3	exists	exist	VERB
ejpam-2571	282	4	q(x	q(x	NOUN
ejpam-2571	282	5	)	)	PUNCT
ejpam-2571	282	6	∈	∈	PROPN
ejpam-2571	282	7	r[x	r[x	NOUN
ejpam-2571	282	8	]	]	PUNCT
ejpam-2571	282	9	such	such	ADJ
ejpam-2571	282	10	that	that	SCONJ
ejpam-2571	282	11	a	a	DET
ejpam-2571	282	12	�	�	PROPN
ejpam-2571	282	13	(	(	PUNCT
ejpam-2571	282	14	1−	1−	NUM
ejpam-2571	282	15	2u2)x	2u2)x	NUM
ejpam-2571	282	16	�	�	PROPN
ejpam-2571	282	17	−	−	PROPN
ejpam-2571	282	18	b	b	PROPN
ejpam-2571	282	19	�	�	PROPN
ejpam-2571	282	20	(	(	PUNCT
ejpam-2571	282	21	1−	1−	NUM
ejpam-2571	282	22	2u2)x	2u2)x	NUM
ejpam-2571	282	23	�	�	PROPN
ejpam-2571	282	24	=	=	SYM
ejpam-2571	282	25	�	�	PROPN
ejpam-2571	282	26	xn	xn	PROPN
ejpam-2571	282	27	−	−	PROPN
ejpam-2571	282	28	(	(	PUNCT
ejpam-2571	282	29	1−	1−	NUM
ejpam-2571	282	30	2u2	2u2	NUM
ejpam-2571	282	31	)	)	PUNCT
ejpam-2571	282	32	�	�	PROPN
ejpam-2571	282	33	q(x	q(x	PROPN
ejpam-2571	282	34	)	)	PUNCT
ejpam-2571	282	35	.	.	PUNCT
ejpam-2571	283	1	hence	hence	ADV
ejpam-2571	283	2	a(x)−	a(x)−	ADV
ejpam-2571	283	3	b(x	b(x	NOUN
ejpam-2571	283	4	)	)	PUNCT
ejpam-2571	284	1	=	=	SYM
ejpam-2571	284	2	a	a	DET
ejpam-2571	284	3	�	�	PROPN
ejpam-2571	284	4	(	(	PUNCT
ejpam-2571	284	5	1−	1−	NUM
ejpam-2571	284	6	2u2)2	2u2)2	NUM
ejpam-2571	284	7	x	x	SYM
ejpam-2571	284	8	�	�	PROPN
ejpam-2571	284	9	−	−	PROPN
ejpam-2571	284	10	b	b	PROPN
ejpam-2571	284	11	�	�	PROPN
ejpam-2571	284	12	(	(	PUNCT
ejpam-2571	284	13	1−	1−	NUM
ejpam-2571	284	14	2u2)2	2u2)2	NUM
ejpam-2571	284	15	x	x	SYM
ejpam-2571	284	16	�	�	PROPN
ejpam-2571	284	17	=	=	SYM
ejpam-2571	284	18	�	�	PROPN
ejpam-2571	284	19	(	(	PUNCT
ejpam-2571	284	20	1−	1−	NUM
ejpam-2571	284	21	2u2)n	2u2)n	NUM
ejpam-2571	284	22	xn	xn	NUM
ejpam-2571	284	23	−	−	PROPN
ejpam-2571	284	24	(	(	PUNCT
ejpam-2571	284	25	1−	1−	NUM
ejpam-2571	284	26	2u2	2u2	NUM
ejpam-2571	284	27	)	)	PUNCT
ejpam-2571	284	28	�	�	PROPN
ejpam-2571	284	29	q	q	PROPN
ejpam-2571	284	30	�	�	PROPN
ejpam-2571	284	31	(	(	PUNCT
ejpam-2571	284	32	1−	1−	NUM
ejpam-2571	284	33	2u2)x	2u2)x	NUM
ejpam-2571	284	34	�	�	PROPN
ejpam-2571	284	35	=	=	SYM
ejpam-2571	284	36	�	�	PROPN
ejpam-2571	284	37	(	(	PUNCT
ejpam-2571	284	38	1−	1−	NUM
ejpam-2571	284	39	2u2)xn	2u2)xn	NUM
ejpam-2571	284	40	−	−	NOUN
ejpam-2571	284	41	(	(	PUNCT
ejpam-2571	284	42	1−	1−	NUM
ejpam-2571	284	43	2u2	2u2	NUM
ejpam-2571	284	44	)	)	PUNCT
ejpam-2571	284	45	�	�	PROPN
ejpam-2571	284	46	q	q	PROPN
ejpam-2571	284	47	�	�	PROPN
ejpam-2571	284	48	(	(	PUNCT
ejpam-2571	284	49	1−	1−	NUM
ejpam-2571	284	50	2u2)x	2u2)x	NUM
ejpam-2571	284	51	�	�	PROPN
ejpam-2571	284	52	=(	=(	NOUN
ejpam-2571	284	53	1−	1−	NUM
ejpam-2571	284	54	2u2)(xn	2u2)(xn	NUM
ejpam-2571	284	55	−	−	PROPN
ejpam-2571	284	56	1)q	1)q	NUM
ejpam-2571	284	57	�	�	PROPN
ejpam-2571	284	58	(	(	PUNCT
ejpam-2571	284	59	1−	1−	NUM
ejpam-2571	284	60	2u2)x	2u2)x	NUM
ejpam-2571	284	61	�	�	PROPN
ejpam-2571	284	62	,	,	PUNCT
ejpam-2571	284	63	h.	h.	PROPN
ejpam-2571	284	64	mostafanasab	mostafanasab	PROPN
ejpam-2571	284	65	,	,	PUNCT
ejpam-2571	284	66	n.	n.	PROPN
ejpam-2571	284	67	karimi	karimi	PROPN
ejpam-2571	284	68	/	/	SYM
ejpam-2571	284	69	eur	eur	PROPN
ejpam-2571	284	70	.	.	PUNCT
ejpam-2571	285	1	j.	j.	PROPN
ejpam-2571	285	2	pure	pure	PROPN
ejpam-2571	285	3	appl	appl	PROPN
ejpam-2571	285	4	.	.	PROPN
ejpam-2571	285	5	math	math	PROPN
ejpam-2571	285	6	,	,	PUNCT
ejpam-2571	285	7	9	9	NUM
ejpam-2571	285	8	(	(	PUNCT
ejpam-2571	285	9	2016	2016	NUM
ejpam-2571	285	10	)	)	PUNCT
ejpam-2571	285	11	,	,	PUNCT
ejpam-2571	285	12	39	39	NUM
ejpam-2571	285	13	-	-	SYM
ejpam-2571	285	14	47	47	NUM
ejpam-2571	285	15	45	45	NUM
ejpam-2571	285	16	which	which	PRON
ejpam-2571	285	17	means	mean	VERB
ejpam-2571	285	18	if	if	SCONJ
ejpam-2571	285	19	a	a	DET
ejpam-2571	285	20	�	�	PROPN
ejpam-2571	285	21	(	(	PUNCT
ejpam-2571	285	22	1−	1−	NUM
ejpam-2571	285	23	2u2)x	2u2)x	NUM
ejpam-2571	285	24	�	�	PROPN
ejpam-2571	285	25	≡	≡	PROPN
ejpam-2571	285	26	b	b	PROPN
ejpam-2571	285	27	�	�	PROPN
ejpam-2571	285	28	(	(	PUNCT
ejpam-2571	285	29	1−	1−	NUM
ejpam-2571	285	30	2u2)x	2u2)x	NUM
ejpam-2571	285	31	�	�	PROPN
ejpam-2571	285	32	�	�	PROPN
ejpam-2571	285	33	mod	mod	PROPN
ejpam-2571	285	34	xn	xn	PROPN
ejpam-2571	286	1	−	−	PROPN
ejpam-2571	286	2	(	(	PUNCT
ejpam-2571	286	3	1−	1−	NUM
ejpam-2571	286	4	2u2	2u2	NUM
ejpam-2571	286	5	)	)	PUNCT
ejpam-2571	286	6	�	�	PROPN
ejpam-2571	286	7	,	,	PUNCT
ejpam-2571	286	8	then	then	ADV
ejpam-2571	286	9	a(x)≡	a(x)≡	PROPN
ejpam-2571	286	10	b(x	b(x	PROPN
ejpam-2571	286	11	)	)	PUNCT
ejpam-2571	286	12	(	(	PUNCT
ejpam-2571	286	13	mod	mod	PROPN
ejpam-2571	286	14	xn	xn	PROPN
ejpam-2571	287	1	−	−	PROPN
ejpam-2571	287	2	1	1	NUM
ejpam-2571	287	3	)	)	PUNCT
ejpam-2571	287	4	.	.	PUNCT
ejpam-2571	288	1	consequently	consequently	ADV
ejpam-2571	288	2	a(x)≡	a(x)≡	ADP
ejpam-2571	288	3	b(x	b(x	NOUN
ejpam-2571	288	4	)	)	PUNCT
ejpam-2571	288	5	(	(	PUNCT
ejpam-2571	288	6	mod	mod	PROPN
ejpam-2571	288	7	xn	xn	PROPN
ejpam-2571	288	8	−	−	PROPN
ejpam-2571	288	9	1)⇔	1)⇔	NUM
ejpam-2571	289	1	a	a	DET
ejpam-2571	289	2	�	�	PROPN
ejpam-2571	289	3	(	(	PUNCT
ejpam-2571	289	4	1−	1−	NUM
ejpam-2571	289	5	2u2)x	2u2)x	NUM
ejpam-2571	289	6	�	�	PROPN
ejpam-2571	289	7	≡	≡	PROPN
ejpam-2571	289	8	b	b	PROPN
ejpam-2571	289	9	�	�	PROPN
ejpam-2571	289	10	(	(	PUNCT
ejpam-2571	289	11	1−	1−	NUM
ejpam-2571	289	12	2u2)x	2u2)x	NUM
ejpam-2571	289	13	�	�	PROPN
ejpam-2571	289	14	�	�	PROPN
ejpam-2571	289	15	mod	mod	PROPN
ejpam-2571	289	16	xn	xn	PROPN
ejpam-2571	290	1	−	−	PROPN
ejpam-2571	290	2	(	(	PUNCT
ejpam-2571	290	3	1−	1−	NUM
ejpam-2571	290	4	2u2	2u2	NUM
ejpam-2571	290	5	)	)	PUNCT
ejpam-2571	290	6	�	�	PROPN
ejpam-2571	290	7	.	.	PUNCT
ejpam-2571	291	1	note	note	VERB
ejpam-2571	291	2	that	that	SCONJ
ejpam-2571	291	3	one	one	NUM
ejpam-2571	291	4	side	side	NOUN
ejpam-2571	291	5	of	of	ADP
ejpam-2571	291	6	the	the	DET
ejpam-2571	291	7	implication	implication	NOUN
ejpam-2571	291	8	tells	tell	VERB
ejpam-2571	291	9	us	we	PRON
ejpam-2571	291	10	that	that	SCONJ
ejpam-2571	291	11	µ	µ	NOUN
ejpam-2571	291	12	is	be	AUX
ejpam-2571	291	13	well	well	ADV
ejpam-2571	291	14	defined	define	VERB
ejpam-2571	291	15	and	and	CCONJ
ejpam-2571	291	16	the	the	DET
ejpam-2571	291	17	other	other	ADJ
ejpam-2571	291	18	side	side	NOUN
ejpam-2571	291	19	tells	tell	VERB
ejpam-2571	291	20	us	we	PRON
ejpam-2571	291	21	that	that	SCONJ
ejpam-2571	291	22	it	it	PRON
ejpam-2571	291	23	is	be	AUX
ejpam-2571	291	24	injective	injective	ADJ
ejpam-2571	291	25	,	,	PUNCT
ejpam-2571	291	26	but	but	CCONJ
ejpam-2571	291	27	since	since	SCONJ
ejpam-2571	291	28	the	the	DET
ejpam-2571	291	29	rings	ring	NOUN
ejpam-2571	291	30	are	be	AUX
ejpam-2571	291	31	finite	finite	ADJ
ejpam-2571	291	32	this	this	PRON
ejpam-2571	291	33	proves	prove	VERB
ejpam-2571	291	34	that	that	SCONJ
ejpam-2571	291	35	µ	µ	NOUN
ejpam-2571	291	36	is	be	AUX
ejpam-2571	291	37	an	an	DET
ejpam-2571	291	38	isomorphism	isomorphism	NOUN
ejpam-2571	291	39	.	.	PUNCT
ejpam-2571	292	1	corollary	corollary	ADJ
ejpam-2571	292	2	2	2	NUM
ejpam-2571	292	3	.	.	PUNCT
ejpam-2571	293	1	let	let	VERB
ejpam-2571	293	2	n	n	PRON
ejpam-2571	293	3	be	be	AUX
ejpam-2571	293	4	an	an	DET
ejpam-2571	293	5	odd	odd	ADJ
ejpam-2571	293	6	natural	natural	ADJ
ejpam-2571	293	7	number	number	NOUN
ejpam-2571	293	8	.	.	PUNCT
ejpam-2571	294	1	then	then	ADV
ejpam-2571	294	2	i	i	PRON
ejpam-2571	294	3	is	be	AUX
ejpam-2571	294	4	an	an	DET
ejpam-2571	294	5	ideal	ideal	NOUN
ejpam-2571	294	6	of	of	ADP
ejpam-2571	294	7	r[x]/〈xn−1	r[x]/〈xn−1	VERB
ejpam-2571	294	8	〉	〉	NOUN
ejpam-2571	294	9	if	if	SCONJ
ejpam-2571	294	10	and	and	CCONJ
ejpam-2571	294	11	only	only	ADV
ejpam-2571	294	12	if	if	SCONJ
ejpam-2571	294	13	µ(i	µ(i	PROPN
ejpam-2571	294	14	)	)	PUNCT
ejpam-2571	294	15	is	be	AUX
ejpam-2571	294	16	an	an	DET
ejpam-2571	294	17	ideal	ideal	NOUN
ejpam-2571	294	18	of	of	ADP
ejpam-2571	294	19	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2571	294	20	−	−	PROPN
ejpam-2571	294	21	(	(	PUNCT
ejpam-2571	294	22	1−	1−	NUM
ejpam-2571	294	23	2u2	2u2	NUM
ejpam-2571	294	24	)	)	PUNCT
ejpam-2571	294	25	〉	〉	NOUN
ejpam-2571	294	26	.	.	PUNCT
ejpam-2571	294	27	corollary	corollary	ADJ
ejpam-2571	294	28	3	3	NUM
ejpam-2571	294	29	.	.	PUNCT
ejpam-2571	295	1	let	let	VERB
ejpam-2571	295	2	µ	µ	X
ejpam-2571	295	3	be	be	AUX
ejpam-2571	295	4	the	the	DET
ejpam-2571	295	5	permutation	permutation	NOUN
ejpam-2571	295	6	of	of	ADP
ejpam-2571	295	7	rn	rn	PROPN
ejpam-2571	295	8	with	with	ADP
ejpam-2571	295	9	n	n	CCONJ
ejpam-2571	295	10	odd	odd	ADJ
ejpam-2571	295	11	such	such	ADJ
ejpam-2571	295	12	that	that	SCONJ
ejpam-2571	295	13	µ̄(c0	µ̄(c0	PROPN
ejpam-2571	295	14	,	,	PUNCT
ejpam-2571	295	15	c1	c1	PROPN
ejpam-2571	295	16	,	,	PUNCT
ejpam-2571	295	17	.	.	PUNCT
ejpam-2571	295	18	.	.	PUNCT
ejpam-2571	296	1	.	.	PUNCT
ejpam-2571	297	1	,	,	PUNCT
ejpam-2571	297	2	cn−1	cn−1	X
ejpam-2571	297	3	)	)	PUNCT
ejpam-2571	297	4	=	=	SYM
ejpam-2571	297	5	(	(	PUNCT
ejpam-2571	298	1	c0	c0	NOUN
ejpam-2571	298	2	,	,	PUNCT
ejpam-2571	298	3	(	(	PUNCT
ejpam-2571	298	4	1−	1−	NUM
ejpam-2571	298	5	2u2)c1	2u2)c1	NUM
ejpam-2571	298	6	,	,	PUNCT
ejpam-2571	298	7	(	(	PUNCT
ejpam-2571	298	8	1−	1−	NUM
ejpam-2571	298	9	2u2)2c2	2u2)2c2	NUM
ejpam-2571	298	10	,	,	PUNCT
ejpam-2571	298	11	.	.	PUNCT
ejpam-2571	298	12	.	.	PUNCT
ejpam-2571	298	13	.	.	PUNCT
ejpam-2571	299	1	,	,	PUNCT
ejpam-2571	299	2	(	(	PUNCT
ejpam-2571	299	3	1−	1−	NUM
ejpam-2571	299	4	2u2)ici	2u2)ici	NUM
ejpam-2571	299	5	,	,	PUNCT
ejpam-2571	299	6	.	.	PUNCT
ejpam-2571	299	7	.	.	PUNCT
ejpam-2571	299	8	.	.	PUNCT
ejpam-2571	300	1	,	,	PUNCT
ejpam-2571	300	2	(	(	PUNCT
ejpam-2571	300	3	1−	1−	NUM
ejpam-2571	300	4	2u2)n−1cn−1	2u2)n−1cn−1	NUM
ejpam-2571	300	5	)	)	PUNCT
ejpam-2571	300	6	,	,	PUNCT
ejpam-2571	300	7	and	and	CCONJ
ejpam-2571	300	8	d	d	PRON
ejpam-2571	300	9	be	be	AUX
ejpam-2571	300	10	a	a	DET
ejpam-2571	300	11	subset	subset	NOUN
ejpam-2571	300	12	of	of	ADP
ejpam-2571	300	13	rn	rn	PROPN
ejpam-2571	300	14	.	.	PUNCT
ejpam-2571	301	1	then	then	ADV
ejpam-2571	301	2	d	d	PROPN
ejpam-2571	301	3	is	be	AUX
ejpam-2571	301	4	a	a	DET
ejpam-2571	301	5	cyclic	cyclic	ADJ
ejpam-2571	301	6	code	code	NOUN
ejpam-2571	301	7	if	if	SCONJ
ejpam-2571	301	8	and	and	CCONJ
ejpam-2571	301	9	only	only	ADV
ejpam-2571	301	10	if	if	SCONJ
ejpam-2571	301	11	µ̄(d	µ̄(d	NOUN
ejpam-2571	301	12	)	)	PUNCT
ejpam-2571	301	13	is	be	AUX
ejpam-2571	301	14	a	a	DET
ejpam-2571	301	15	(	(	PUNCT
ejpam-2571	301	16	1−	1−	NUM
ejpam-2571	301	17	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	301	18	code	code	NOUN
ejpam-2571	301	19	.	.	PUNCT
ejpam-2571	302	1	definition	definition	NOUN
ejpam-2571	302	2	1	1	NUM
ejpam-2571	302	3	.	.	PUNCT
ejpam-2571	303	1	let	let	VERB
ejpam-2571	303	2	τ	τ	PROPN
ejpam-2571	303	3	be	be	AUX
ejpam-2571	303	4	the	the	DET
ejpam-2571	303	5	following	follow	VERB
ejpam-2571	303	6	permutation	permutation	NOUN
ejpam-2571	303	7	of	of	ADP
ejpam-2571	303	8	{	{	PUNCT
ejpam-2571	303	9	0,1	0,1	NUM
ejpam-2571	303	10	,	,	PUNCT
ejpam-2571	303	11	.	.	PUNCT
ejpam-2571	303	12	.	.	PUNCT
ejpam-2571	304	1	.	.	PUNCT
ejpam-2571	305	1	,	,	PUNCT
ejpam-2571	306	1	2n−	2n−	PROPN
ejpam-2571	306	2	1	1	NUM
ejpam-2571	306	3	}	}	PUNCT
ejpam-2571	306	4	with	with	ADP
ejpam-2571	306	5	n	n	PRON
ejpam-2571	306	6	odd	odd	ADJ
ejpam-2571	306	7	:	:	PUNCT
ejpam-2571	306	8	τ=	τ=	PRON
ejpam-2571	306	9	(	(	PUNCT
ejpam-2571	306	10	1	1	NUM
ejpam-2571	306	11	,	,	PUNCT
ejpam-2571	306	12	n+	n+	X
ejpam-2571	306	13	1)(3	1)(3	NUM
ejpam-2571	306	14	,	,	PUNCT
ejpam-2571	306	15	n+	n+	X
ejpam-2571	306	16	3	3	NUM
ejpam-2571	306	17	)	)	PUNCT
ejpam-2571	306	18	·	·	PUNCT
ejpam-2571	306	19	·	·	PUNCT
ejpam-2571	306	20	·	·	PUNCT
ejpam-2571	306	21	(	(	PUNCT
ejpam-2571	306	22	2i	2i	NOUN
ejpam-2571	306	23	+	+	CCONJ
ejpam-2571	306	24	1	1	NUM
ejpam-2571	306	25	,	,	PUNCT
ejpam-2571	306	26	n+	n+	PRON
ejpam-2571	306	27	2i	2i	NOUN
ejpam-2571	306	28	+	+	CCONJ
ejpam-2571	306	29	1	1	NUM
ejpam-2571	306	30	)	)	PUNCT
ejpam-2571	306	31	·	·	PUNCT
ejpam-2571	306	32	·	·	PUNCT
ejpam-2571	306	33	·	·	PUNCT
ejpam-2571	306	34	(	(	PUNCT
ejpam-2571	306	35	n−	n−	NOUN
ejpam-2571	306	36	2,2n−	2,2n−	NOUN
ejpam-2571	306	37	2	2	NUM
ejpam-2571	306	38	)	)	PUNCT
ejpam-2571	306	39	.	.	PUNCT
ejpam-2571	307	1	the	the	DET
ejpam-2571	307	2	nechaev	nechaev	NOUN
ejpam-2571	307	3	permutation	permutation	NOUN
ejpam-2571	307	4	is	be	AUX
ejpam-2571	307	5	the	the	DET
ejpam-2571	307	6	permutation	permutation	NOUN
ejpam-2571	307	7	π	π	PROPN
ejpam-2571	307	8	of	of	ADP
ejpam-2571	307	9	f2n	f2n	PROPN
ejpam-2571	307	10	p	p	NOUN
ejpam-2571	307	11	defined	define	VERB
ejpam-2571	307	12	by	by	ADP
ejpam-2571	307	13	π(c0	π(c0	NOUN
ejpam-2571	307	14	,	,	PUNCT
ejpam-2571	307	15	c1	c1	PROPN
ejpam-2571	307	16	,	,	PUNCT
ejpam-2571	307	17	.	.	PUNCT
ejpam-2571	307	18	.	.	PUNCT
ejpam-2571	308	1	.	.	PUNCT
ejpam-2571	309	1	,	,	PUNCT
ejpam-2571	309	2	c2n−1	c2n−1	PROPN
ejpam-2571	309	3	)	)	PUNCT
ejpam-2571	309	4	=	=	PRON
ejpam-2571	309	5	(	(	PUNCT
ejpam-2571	309	6	cτ(0	cτ(0	NOUN
ejpam-2571	309	7	)	)	PUNCT
ejpam-2571	309	8	,	,	PUNCT
ejpam-2571	309	9	cτ(1	cτ(1	NOUN
ejpam-2571	309	10	)	)	PUNCT
ejpam-2571	309	11	,	,	PUNCT
ejpam-2571	309	12	.	.	PUNCT
ejpam-2571	309	13	.	.	PUNCT
ejpam-2571	310	1	.	.	PUNCT
ejpam-2571	311	1	,	,	PUNCT
ejpam-2571	311	2	cτ(2n−1	cτ(2n−1	PROPN
ejpam-2571	311	3	)	)	PUNCT
ejpam-2571	311	4	)	)	PUNCT
ejpam-2571	311	5	.	.	PUNCT
ejpam-2571	312	1	proposition	proposition	NOUN
ejpam-2571	312	2	3	3	X
ejpam-2571	312	3	.	.	PUNCT
ejpam-2571	313	1	let	let	VERB
ejpam-2571	313	2	µ	µ	X
ejpam-2571	313	3	be	be	AUX
ejpam-2571	313	4	defined	define	VERB
ejpam-2571	313	5	as	as	ADP
ejpam-2571	313	6	above	above	ADV
ejpam-2571	313	7	.	.	PUNCT
ejpam-2571	314	1	if	if	SCONJ
ejpam-2571	314	2	π	π	PROPN
ejpam-2571	314	3	is	be	AUX
ejpam-2571	314	4	the	the	DET
ejpam-2571	314	5	nechaev	nechaev	NOUN
ejpam-2571	314	6	permutation	permutation	NOUN
ejpam-2571	314	7	and	and	CCONJ
ejpam-2571	314	8	n	n	NOUN
ejpam-2571	314	9	is	be	AUX
ejpam-2571	314	10	odd	odd	ADJ
ejpam-2571	314	11	,	,	PUNCT
ejpam-2571	314	12	then	then	ADV
ejpam-2571	314	13	φµ̄	φµ̄	PROPN
ejpam-2571	314	14	=	=	SYM
ejpam-2571	314	15	πφ	πφ	PROPN
ejpam-2571	314	16	.	.	PUNCT
ejpam-2571	314	17	proof	proof	NOUN
ejpam-2571	314	18	.	.	PUNCT
ejpam-2571	315	1	let	let	VERB
ejpam-2571	315	2	r̄	r̄	NOUN
ejpam-2571	315	3	=	=	SYM
ejpam-2571	315	4	(	(	PUNCT
ejpam-2571	315	5	r0	r0	NOUN
ejpam-2571	315	6	,	,	PUNCT
ejpam-2571	315	7	r1	r1	NOUN
ejpam-2571	315	8	,	,	PUNCT
ejpam-2571	315	9	.	.	PUNCT
ejpam-2571	315	10	.	.	PUNCT
ejpam-2571	316	1	.	.	PUNCT
ejpam-2571	317	1	,	,	PUNCT
ejpam-2571	317	2	ri	ri	PROPN
ejpam-2571	317	3	,	,	PUNCT
ejpam-2571	317	4	.	.	PUNCT
ejpam-2571	317	5	.	.	PUNCT
ejpam-2571	318	1	.	.	PUNCT
ejpam-2571	319	1	,	,	PUNCT
ejpam-2571	319	2	rn−1	rn−1	NOUN
ejpam-2571	319	3	)	)	PUNCT
ejpam-2571	319	4	∈	∈	PROPN
ejpam-2571	319	5	r	r	NOUN
ejpam-2571	319	6	n	n	NOUN
ejpam-2571	319	7	where	where	SCONJ
ejpam-2571	319	8	ri	ri	PROPN
ejpam-2571	319	9	=	=	NOUN
ejpam-2571	319	10	ai	ai	PROPN
ejpam-2571	320	1	+	+	ADJ
ejpam-2571	320	2	biu+	biu+	ADJ
ejpam-2571	320	3	ciu	ciu	NOUN
ejpam-2571	320	4	2	2	NUM
ejpam-2571	320	5	,	,	PUNCT
ejpam-2571	320	6	0≤	0≤	NUM
ejpam-2571	321	1	i	i	NOUN
ejpam-2571	321	2	≤	≤	PUNCT
ejpam-2571	321	3	n−1	n−1	PROPN
ejpam-2571	321	4	.	.	PROPN
ejpam-2571	321	5	from	from	ADP
ejpam-2571	321	6	µ̄(r̄	µ̄(r̄	NOUN
ejpam-2571	321	7	)	)	PUNCT
ejpam-2571	321	8	=	=	SYM
ejpam-2571	321	9	(	(	PUNCT
ejpam-2571	321	10	r0	r0	NOUN
ejpam-2571	321	11	,	,	PUNCT
ejpam-2571	321	12	(	(	PUNCT
ejpam-2571	321	13	1−	1−	NUM
ejpam-2571	321	14	2u2)r1	2u2)r1	NUM
ejpam-2571	321	15	,	,	PUNCT
ejpam-2571	321	16	.	.	PUNCT
ejpam-2571	321	17	.	.	PUNCT
ejpam-2571	321	18	.	.	PUNCT
ejpam-2571	322	1	,	,	PUNCT
ejpam-2571	322	2	(	(	PUNCT
ejpam-2571	322	3	1−	1−	NUM
ejpam-2571	322	4	2u2)i	2u2)i	NUM
ejpam-2571	322	5	ri	ri	NOUN
ejpam-2571	322	6	,	,	PUNCT
ejpam-2571	322	7	.	.	PUNCT
ejpam-2571	322	8	.	.	PUNCT
ejpam-2571	322	9	.	.	PUNCT
ejpam-2571	323	1	,	,	PUNCT
ejpam-2571	323	2	(	(	PUNCT
ejpam-2571	323	3	1−	1−	NUM
ejpam-2571	323	4	2u2)n−1rn−1	2u2)n−1rn−1	NUM
ejpam-2571	323	5	)	)	PUNCT
ejpam-2571	323	6	it	it	PRON
ejpam-2571	323	7	follows	follow	VERB
ejpam-2571	323	8	that	that	SCONJ
ejpam-2571	323	9	(	(	PUNCT
ejpam-2571	323	10	φµ̄)(r̄	φµ̄)(r̄	ADJ
ejpam-2571	323	11	)	)	PUNCT
ejpam-2571	323	12	=(	=(	NOUN
ejpam-2571	323	13	−c0	−c0	PROPN
ejpam-2571	323	14	,	,	PUNCT
ejpam-2571	323	15	2a1	2a1	NUM
ejpam-2571	324	1	+	+	CCONJ
ejpam-2571	324	2	c1,−c2	c1,−c2	NOUN
ejpam-2571	324	3	,	,	PUNCT
ejpam-2571	324	4	2a3	2a3	NUM
ejpam-2571	325	1	+	+	CCONJ
ejpam-2571	325	2	c3	c3	NOUN
ejpam-2571	325	3	,	,	PUNCT
ejpam-2571	325	4	.	.	PUNCT
ejpam-2571	325	5	.	.	PUNCT
ejpam-2571	326	1	.	.	PUNCT
ejpam-2571	327	1	,	,	PUNCT
ejpam-2571	327	2	2an−2	2an−2	PROPN
ejpam-2571	327	3	+	+	CCONJ
ejpam-2571	327	4	cn−2,−cn−1	cn−2,−cn−1	PROPN
ejpam-2571	327	5	,	,	PUNCT
ejpam-2571	327	6	2a0	2a0	NUM
ejpam-2571	327	7	+	+	CCONJ
ejpam-2571	327	8	c0,−c1	c0,−c1	ADJ
ejpam-2571	327	9	,	,	PUNCT
ejpam-2571	327	10	2a2	2a2	NUM
ejpam-2571	327	11	+	+	CCONJ
ejpam-2571	327	12	c2,−c3	c2,−c3	VERB
ejpam-2571	327	13	,	,	PUNCT
ejpam-2571	327	14	.	.	PUNCT
ejpam-2571	327	15	.	.	PUNCT
ejpam-2571	327	16	.	.	PUNCT
ejpam-2571	328	1	,	,	PUNCT
ejpam-2571	328	2	−cn−2	−cn−2	PROPN
ejpam-2571	328	3	,	,	PUNCT
ejpam-2571	328	4	2an−1	2an−1	NUM
ejpam-2571	328	5	+	+	CCONJ
ejpam-2571	328	6	cn−1	cn−1	ADJ
ejpam-2571	328	7	)	)	PUNCT
ejpam-2571	328	8	,	,	PUNCT
ejpam-2571	328	9	is	be	AUX
ejpam-2571	328	10	equal	equal	ADJ
ejpam-2571	328	11	to	to	ADP
ejpam-2571	328	12	(	(	PUNCT
ejpam-2571	328	13	πφ)(r̄	πφ)(r̄	ADJ
ejpam-2571	328	14	)	)	PUNCT
ejpam-2571	328	15	.	.	PUNCT
ejpam-2571	329	1	corollary	corollary	ADJ
ejpam-2571	329	2	4	4	NUM
ejpam-2571	329	3	.	.	PUNCT
ejpam-2571	330	1	let	let	VERB
ejpam-2571	330	2	π	π	PRON
ejpam-2571	330	3	be	be	AUX
ejpam-2571	330	4	the	the	DET
ejpam-2571	330	5	nechaev	nechaev	NOUN
ejpam-2571	330	6	permutation	permutation	NOUN
ejpam-2571	330	7	and	and	CCONJ
ejpam-2571	330	8	n	n	CCONJ
ejpam-2571	330	9	be	be	AUX
ejpam-2571	330	10	odd	odd	ADJ
ejpam-2571	330	11	.	.	PUNCT
ejpam-2571	331	1	if	if	SCONJ
ejpam-2571	331	2	γ	γ	X
ejpam-2571	331	3	is	be	AUX
ejpam-2571	331	4	the	the	DET
ejpam-2571	331	5	gray	gray	ADJ
ejpam-2571	331	6	image	image	NOUN
ejpam-2571	331	7	of	of	ADP
ejpam-2571	331	8	a	a	DET
ejpam-2571	331	9	cyclic	cyclic	ADJ
ejpam-2571	331	10	code	code	NOUN
ejpam-2571	331	11	over	over	ADP
ejpam-2571	331	12	r	r	NOUN
ejpam-2571	331	13	,	,	PUNCT
ejpam-2571	331	14	then	then	ADV
ejpam-2571	331	15	π(γ	π(γ	PROPN
ejpam-2571	331	16	)	)	PUNCT
ejpam-2571	331	17	is	be	AUX
ejpam-2571	331	18	a	a	DET
ejpam-2571	331	19	cyclic	cyclic	ADJ
ejpam-2571	331	20	code	code	NOUN
ejpam-2571	331	21	.	.	PUNCT
ejpam-2571	332	1	proof	proof	NOUN
ejpam-2571	332	2	.	.	PUNCT
ejpam-2571	333	1	let	let	VERB
ejpam-2571	333	2	γ	γ	NOUN
ejpam-2571	333	3	be	be	AUX
ejpam-2571	333	4	such	such	ADJ
ejpam-2571	333	5	that	that	SCONJ
ejpam-2571	333	6	γ	γ	X
ejpam-2571	333	7	=	=	SYM
ejpam-2571	333	8	φ(d	φ(d	PROPN
ejpam-2571	333	9	)	)	PUNCT
ejpam-2571	333	10	where	where	SCONJ
ejpam-2571	333	11	d	d	NOUN
ejpam-2571	333	12	is	be	AUX
ejpam-2571	333	13	a	a	DET
ejpam-2571	333	14	cyclic	cyclic	ADJ
ejpam-2571	333	15	code	code	NOUN
ejpam-2571	333	16	over	over	ADP
ejpam-2571	333	17	r	r	NOUN
ejpam-2571	333	18	.	.	PUNCT
ejpam-2571	334	1	from	from	ADP
ejpam-2571	334	2	proposition	proposition	NOUN
ejpam-2571	334	3	3	3	NUM
ejpam-2571	334	4	,	,	PUNCT
ejpam-2571	334	5	(	(	PUNCT
ejpam-2571	334	6	φµ̄)(d	φµ̄)(d	ADJ
ejpam-2571	334	7	)	)	PUNCT
ejpam-2571	334	8	=	=	SYM
ejpam-2571	334	9	(	(	PUNCT
ejpam-2571	334	10	πφ)(d	πφ)(d	PROPN
ejpam-2571	334	11	)	)	PUNCT
ejpam-2571	334	12	=	=	SYM
ejpam-2571	334	13	π(γ	π(γ	PROPN
ejpam-2571	334	14	)	)	PUNCT
ejpam-2571	334	15	.	.	PUNCT
ejpam-2571	335	1	we	we	PRON
ejpam-2571	335	2	know	know	VERB
ejpam-2571	335	3	from	from	ADP
ejpam-2571	335	4	corollary	corollary	ADJ
ejpam-2571	335	5	3	3	NUM
ejpam-2571	335	6	that	that	SCONJ
ejpam-2571	335	7	µ̄(d	µ̄(d	NOUN
ejpam-2571	335	8	)	)	PUNCT
ejpam-2571	335	9	is	be	AUX
ejpam-2571	335	10	a	a	DET
ejpam-2571	335	11	(	(	PUNCT
ejpam-2571	335	12	1−	1−	NUM
ejpam-2571	335	13	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	335	14	code	code	NOUN
ejpam-2571	335	15	.	.	PUNCT
ejpam-2571	336	1	thus	thus	ADV
ejpam-2571	336	2	(	(	PUNCT
ejpam-2571	336	3	φµ̄)(d	φµ̄)(d	PROPN
ejpam-2571	336	4	)	)	PUNCT
ejpam-2571	336	5	=	=	SYM
ejpam-2571	336	6	π(γ	π(γ	PROPN
ejpam-2571	336	7	)	)	PUNCT
ejpam-2571	336	8	is	be	AUX
ejpam-2571	336	9	a	a	DET
ejpam-2571	336	10	cyclic	cyclic	ADJ
ejpam-2571	336	11	code	code	NOUN
ejpam-2571	336	12	,	,	PUNCT
ejpam-2571	336	13	by	by	ADP
ejpam-2571	336	14	theorem	theorem	NOUN
ejpam-2571	336	15	3	3	NUM
ejpam-2571	336	16	.	.	NOUN
ejpam-2571	336	17	recall	recall	VERB
ejpam-2571	336	18	that	that	SCONJ
ejpam-2571	336	19	two	two	NUM
ejpam-2571	336	20	codes	code	NOUN
ejpam-2571	336	21	c1	c1	PROPN
ejpam-2571	336	22	and	and	CCONJ
ejpam-2571	336	23	c2	c2	PROPN
ejpam-2571	336	24	of	of	ADP
ejpam-2571	336	25	length	length	NOUN
ejpam-2571	337	1	n	n	DET
ejpam-2571	337	2	overr	overr	NOUN
ejpam-2571	337	3	are	be	AUX
ejpam-2571	337	4	said	say	VERB
ejpam-2571	337	5	to	to	PART
ejpam-2571	337	6	be	be	AUX
ejpam-2571	337	7	equivalent	equivalent	ADJ
ejpam-2571	337	8	if	if	SCONJ
ejpam-2571	337	9	there	there	PRON
ejpam-2571	337	10	exists	exist	VERB
ejpam-2571	337	11	a	a	DET
ejpam-2571	337	12	permutation	permutation	NOUN
ejpam-2571	337	13	w	w	ADP
ejpam-2571	337	14	of	of	ADP
ejpam-2571	337	15	{	{	PUNCT
ejpam-2571	337	16	0,1	0,1	NUM
ejpam-2571	337	17	,	,	PUNCT
ejpam-2571	337	18	.	.	PUNCT
ejpam-2571	337	19	.	.	PUNCT
ejpam-2571	337	20	.	.	PUNCT
ejpam-2571	338	1	,	,	PUNCT
ejpam-2571	338	2	n−	n−	NOUN
ejpam-2571	338	3	1	1	NUM
ejpam-2571	338	4	}	}	PUNCT
ejpam-2571	338	5	such	such	ADJ
ejpam-2571	338	6	that	that	SCONJ
ejpam-2571	338	7	c2	c2	PROPN
ejpam-2571	338	8	=	=	SYM
ejpam-2571	338	9	w̄(c1	w̄(c1	PROPN
ejpam-2571	338	10	)	)	PUNCT
ejpam-2571	338	11	where	where	SCONJ
ejpam-2571	338	12	w̄	w̄	NOUN
ejpam-2571	338	13	is	be	AUX
ejpam-2571	338	14	the	the	DET
ejpam-2571	338	15	permutation	permutation	NOUN
ejpam-2571	338	16	of	of	ADP
ejpam-2571	338	17	rn	rn	PROPN
ejpam-2571	338	18	such	such	ADJ
ejpam-2571	338	19	that	that	DET
ejpam-2571	338	20	w̄(c0	w̄(c0	NOUN
ejpam-2571	338	21	,	,	PUNCT
ejpam-2571	338	22	c1	c1	PROPN
ejpam-2571	338	23	,	,	PUNCT
ejpam-2571	338	24	.	.	PUNCT
ejpam-2571	338	25	.	.	PUNCT
ejpam-2571	339	1	.	.	PUNCT
ejpam-2571	340	1	,	,	PUNCT
ejpam-2571	340	2	ci	ci	PROPN
ejpam-2571	340	3	,	,	PUNCT
ejpam-2571	340	4	.	.	PUNCT
ejpam-2571	340	5	.	.	PUNCT
ejpam-2571	341	1	.	.	PUNCT
ejpam-2571	342	1	,	,	PUNCT
ejpam-2571	342	2	cn−1	cn−1	X
ejpam-2571	342	3	)	)	PUNCT
ejpam-2571	342	4	=	=	PUNCT
ejpam-2571	342	5	(	(	PUNCT
ejpam-2571	342	6	cw(0	cw(0	NOUN
ejpam-2571	342	7	)	)	PUNCT
ejpam-2571	342	8	,	,	PUNCT
ejpam-2571	343	1	cw(1	cw(1	NOUN
ejpam-2571	343	2	)	)	PUNCT
ejpam-2571	343	3	,	,	PUNCT
ejpam-2571	343	4	.	.	PUNCT
ejpam-2571	343	5	.	.	PUNCT
ejpam-2571	344	1	.	.	PUNCT
ejpam-2571	345	1	,	,	PUNCT
ejpam-2571	345	2	cw(i	cw(i	NUM
ejpam-2571	345	3	)	)	PUNCT
ejpam-2571	345	4	,	,	PUNCT
ejpam-2571	345	5	.	.	PUNCT
ejpam-2571	346	1	.	.	PUNCT
ejpam-2571	347	1	.	.	PUNCT
ejpam-2571	348	1	,	,	PUNCT
ejpam-2571	348	2	cw(n−1	cw(n−1	PROPN
ejpam-2571	348	3	)	)	PUNCT
ejpam-2571	348	4	)	)	PUNCT
ejpam-2571	348	5	.	.	PUNCT
ejpam-2571	349	1	references	reference	NOUN
ejpam-2571	349	2	46	46	NUM
ejpam-2571	349	3	corollary	corollary	ADJ
ejpam-2571	349	4	5	5	NUM
ejpam-2571	349	5	.	.	PUNCT
ejpam-2571	350	1	the	the	DET
ejpam-2571	350	2	gray	gray	ADJ
ejpam-2571	350	3	image	image	NOUN
ejpam-2571	350	4	of	of	ADP
ejpam-2571	350	5	a	a	DET
ejpam-2571	350	6	cyclic	cyclic	ADJ
ejpam-2571	350	7	code	code	NOUN
ejpam-2571	350	8	over	over	ADP
ejpam-2571	350	9	r	r	NOUN
ejpam-2571	350	10	of	of	ADP
ejpam-2571	350	11	odd	odd	ADJ
ejpam-2571	350	12	length	length	NOUN
ejpam-2571	350	13	is	be	AUX
ejpam-2571	350	14	equivalent	equivalent	ADJ
ejpam-2571	350	15	to	to	ADP
ejpam-2571	350	16	a	a	DET
ejpam-2571	350	17	cyclic	cyclic	ADJ
ejpam-2571	350	18	code	code	NOUN
ejpam-2571	350	19	.	.	PUNCT
ejpam-2571	351	1	example	example	NOUN
ejpam-2571	352	1	1	1	NUM
ejpam-2571	352	2	.	.	X
ejpam-2571	352	3	for	for	ADP
ejpam-2571	352	4	n	n	NOUN
ejpam-2571	352	5	=	=	SYM
ejpam-2571	352	6	7	7	NUM
ejpam-2571	352	7	,	,	PUNCT
ejpam-2571	352	8	x7	x7	NOUN
ejpam-2571	352	9	−	−	PROPN
ejpam-2571	352	10	1	1	NUM
ejpam-2571	352	11	=	=	SYM
ejpam-2571	352	12	(	(	PUNCT
ejpam-2571	352	13	x	x	X
ejpam-2571	352	14	−	−	NOUN
ejpam-2571	352	15	1)(x3	1)(x3	NUM
ejpam-2571	353	1	+	+	NOUN
ejpam-2571	353	2	x	x	SYM
ejpam-2571	354	1	+	+	SYM
ejpam-2571	354	2	1)(x3	1)(x3	NUM
ejpam-2571	354	3	+	+	CCONJ
ejpam-2571	354	4	x2	x2	PROPN
ejpam-2571	355	1	+	+	CCONJ
ejpam-2571	355	2	1	1	X
ejpam-2571	355	3	)	)	PUNCT
ejpam-2571	355	4	in	in	ADP
ejpam-2571	355	5	r[x	r[x	NOUN
ejpam-2571	355	6	]	]	PUNCT
ejpam-2571	355	7	.	.	PUNCT
ejpam-2571	356	1	applying	apply	VERB
ejpam-2571	356	2	the	the	DET
ejpam-2571	356	3	ring	ring	NOUN
ejpam-2571	356	4	isomorphism	isomorphism	PROPN
ejpam-2571	356	5	µ	µ	NUM
ejpam-2571	356	6	,	,	PUNCT
ejpam-2571	356	7	we	we	PRON
ejpam-2571	356	8	have	have	AUX
ejpam-2571	356	9	x7	x7	VERB
ejpam-2571	356	10	−	−	PROPN
ejpam-2571	356	11	(	(	PUNCT
ejpam-2571	356	12	1−	1−	NUM
ejpam-2571	356	13	2u2	2u2	NUM
ejpam-2571	356	14	)	)	PUNCT
ejpam-2571	356	15	=	=	PRON
ejpam-2571	357	1	(	(	PUNCT
ejpam-2571	357	2	x	x	SYM
ejpam-2571	357	3	−	−	PROPN
ejpam-2571	357	4	(	(	PUNCT
ejpam-2571	357	5	1−	1−	NUM
ejpam-2571	357	6	2u2))(x3	2u2))(x3	NUM
ejpam-2571	358	1	+	+	CCONJ
ejpam-2571	358	2	x	x	SYM
ejpam-2571	359	1	+	+	PUNCT
ejpam-2571	359	2	(	(	PUNCT
ejpam-2571	359	3	1−	1−	NUM
ejpam-2571	359	4	2u2))(x3	2u2))(x3	NUM
ejpam-2571	360	1	+	+	CCONJ
ejpam-2571	360	2	(	(	PUNCT
ejpam-2571	360	3	1−	1−	NUM
ejpam-2571	360	4	2u2)x2	2u2)x2	NUM
ejpam-2571	360	5	+	+	CCONJ
ejpam-2571	360	6	(	(	PUNCT
ejpam-2571	360	7	1−	1−	NUM
ejpam-2571	360	8	2u2	2u2	NUM
ejpam-2571	360	9	)	)	PUNCT
ejpam-2571	360	10	)	)	PUNCT
ejpam-2571	360	11	.	.	PUNCT
ejpam-2571	361	1	let	let	VERB
ejpam-2571	361	2	f1	f1	NOUN
ejpam-2571	361	3	=	=	PUNCT
ejpam-2571	361	4	x	x	SYM
ejpam-2571	361	5	−	−	PROPN
ejpam-2571	361	6	(	(	PUNCT
ejpam-2571	361	7	1−	1−	NUM
ejpam-2571	361	8	2u2	2u2	NUM
ejpam-2571	361	9	)	)	PUNCT
ejpam-2571	361	10	and	and	CCONJ
ejpam-2571	361	11	f2	f2	ADV
ejpam-2571	361	12	=	=	PUNCT
ejpam-2571	361	13	x3	x3	PROPN
ejpam-2571	362	1	+	+	CCONJ
ejpam-2571	362	2	x	x	X
ejpam-2571	363	1	+	+	PUNCT
ejpam-2571	363	2	(	(	PUNCT
ejpam-2571	363	3	1−	1−	NUM
ejpam-2571	363	4	2u2	2u2	NUM
ejpam-2571	363	5	)	)	PUNCT
ejpam-2571	363	6	.	.	PUNCT
ejpam-2571	364	1	if	if	SCONJ
ejpam-2571	364	2	c	c	NOUN
ejpam-2571	364	3	=	=	SYM
ejpam-2571	364	4	(	(	PUNCT
ejpam-2571	364	5	f1	f1	NOUN
ejpam-2571	364	6	f2	f2	PROPN
ejpam-2571	364	7	)	)	PUNCT
ejpam-2571	364	8	,	,	PUNCT
ejpam-2571	364	9	then	then	ADV
ejpam-2571	364	10	by	by	ADP
ejpam-2571	364	11	theorem	theorem	NOUN
ejpam-2571	364	12	3	3	NUM
ejpam-2571	364	13	,	,	PUNCT
ejpam-2571	364	14	we	we	PRON
ejpam-2571	364	15	know	know	VERB
ejpam-2571	364	16	that	that	SCONJ
ejpam-2571	364	17	the	the	DET
ejpam-2571	364	18	gray	gray	ADJ
ejpam-2571	364	19	image	image	NOUN
ejpam-2571	364	20	of	of	ADP
ejpam-2571	364	21	the	the	DET
ejpam-2571	364	22	(	(	PUNCT
ejpam-2571	364	23	1−	1−	NUM
ejpam-2571	364	24	2u2)-constacyclic	2u2)-constacyclic	NUM
ejpam-2571	364	25	code	code	NOUN
ejpam-2571	364	26	c	c	NOUN
ejpam-2571	364	27	is	be	AUX
ejpam-2571	364	28	a	a	DET
ejpam-2571	364	29	cyclic	cyclic	ADJ
ejpam-2571	364	30	code	code	NOUN
ejpam-2571	364	31	.	.	PUNCT
ejpam-2571	365	1	references	reference	NOUN
ejpam-2571	365	2	[	[	X
ejpam-2571	365	3	1	1	NUM
ejpam-2571	365	4	]	]	PUNCT
ejpam-2571	365	5	m.	m.	NOUN
ejpam-2571	365	6	c.	c.	PROPN
ejpam-2571	365	7	v.	v.	PROPN
ejpam-2571	365	8	amarra	amarra	PROPN
ejpam-2571	365	9	and	and	CCONJ
ejpam-2571	365	10	f.	f.	PROPN
ejpam-2571	365	11	r.	r.	PROPN
ejpam-2571	365	12	nemenzo	nemenzo	PROPN
ejpam-2571	365	13	.	.	PUNCT
ejpam-2571	366	1	on	on	ADP
ejpam-2571	366	2	(	(	PUNCT
ejpam-2571	366	3	1	1	NUM
ejpam-2571	366	4	−	−	NOUN
ejpam-2571	366	5	u)-cyclic	u)-cyclic	ADJ
ejpam-2571	366	6	codes	code	NOUN
ejpam-2571	366	7	over	over	ADP
ejpam-2571	366	8	fpk	fpk	NOUN
ejpam-2571	366	9	+	+	CCONJ
ejpam-2571	366	10	ufpk	ufpk	NOUN
ejpam-2571	366	11	,	,	PUNCT
ejpam-2571	366	12	applied	apply	VERB
ejpam-2571	366	13	mathematics	mathematics	NOUN
ejpam-2571	366	14	letters	letter	NOUN
ejpam-2571	366	15	,	,	PUNCT
ejpam-2571	366	16	21	21	NUM
ejpam-2571	366	17	,	,	PUNCT
ejpam-2571	366	18	1129–1133	1129–1133	NUM
ejpam-2571	366	19	.	.	PUNCT
ejpam-2571	366	20	2008	2008	NUM
ejpam-2571	366	21	.	.	PUNCT
ejpam-2571	367	1	[	[	X
ejpam-2571	367	2	2	2	NUM
ejpam-2571	367	3	]	]	X
ejpam-2571	367	4	n.	n.	NOUN
ejpam-2571	367	5	aydin	aydin	PROPN
ejpam-2571	367	6	,	,	PUNCT
ejpam-2571	367	7	s.	s.	PROPN
ejpam-2571	367	8	karadeniz	karadeniz	PROPN
ejpam-2571	367	9	,	,	PUNCT
ejpam-2571	367	10	and	and	CCONJ
ejpam-2571	367	11	b.	b.	PROPN
ejpam-2571	367	12	yildiz	yildiz	PROPN
ejpam-2571	367	13	.	.	PUNCT
ejpam-2571	368	1	some	some	DET
ejpam-2571	368	2	new	new	ADJ
ejpam-2571	368	3	binary	binary	ADJ
ejpam-2571	368	4	quasi	quasi	ADJ
ejpam-2571	368	5	-	-	ADJ
ejpam-2571	368	6	cyclic	cyclic	ADJ
ejpam-2571	368	7	codes	code	NOUN
ejpam-2571	368	8	from	from	ADP
ejpam-2571	368	9	codes	code	NOUN
ejpam-2571	368	10	over	over	ADP
ejpam-2571	368	11	the	the	DET
ejpam-2571	368	12	ring	ring	NOUN
ejpam-2571	368	13	f2	f2	PROPN
ejpam-2571	368	14	+	+	CCONJ
ejpam-2571	368	15	uf2	uf2	NOUN
ejpam-2571	368	16	+	+	CCONJ
ejpam-2571	368	17	vf2	vf2	NOUN
ejpam-2571	368	18	+	+	CCONJ
ejpam-2571	368	19	uvf2	uvf2	PROPN
ejpam-2571	368	20	,	,	PUNCT
ejpam-2571	368	21	applicable	applicable	ADJ
ejpam-2571	368	22	algebra	algebra	NOUN
ejpam-2571	368	23	in	in	ADP
ejpam-2571	368	24	engineering	engineering	NOUN
ejpam-2571	368	25	,	,	PUNCT
ejpam-2571	368	26	communication	communication	NOUN
ejpam-2571	368	27	and	and	CCONJ
ejpam-2571	368	28	computing	computing	NOUN
ejpam-2571	368	29	,	,	PUNCT
ejpam-2571	368	30	24	24	NUM
ejpam-2571	368	31	,	,	PUNCT
ejpam-2571	368	32	355–367	355–367	NUM
ejpam-2571	368	33	.	.	NOUN
ejpam-2571	368	34	2013	2013	NUM
ejpam-2571	368	35	.	.	PUNCT
ejpam-2571	369	1	[	[	X
ejpam-2571	369	2	3	3	NUM
ejpam-2571	369	3	]	]	PUNCT
ejpam-2571	369	4	a.	a.	NOUN
ejpam-2571	369	5	bonnecaze	bonnecaze	NOUN
ejpam-2571	369	6	and	and	CCONJ
ejpam-2571	369	7	p.	p.	PROPN
ejpam-2571	369	8	udaya	udaya	PROPN
ejpam-2571	369	9	.	.	PUNCT
ejpam-2571	370	1	cyclic	cyclic	ADJ
ejpam-2571	370	2	codes	code	NOUN
ejpam-2571	370	3	and	and	CCONJ
ejpam-2571	370	4	self	self	NOUN
ejpam-2571	370	5	-	-	PUNCT
ejpam-2571	370	6	dual	dual	ADJ
ejpam-2571	370	7	codes	code	NOUN
ejpam-2571	370	8	over	over	ADP
ejpam-2571	370	9	f2	f2	PROPN
ejpam-2571	370	10	+	+	CCONJ
ejpam-2571	370	11	uf2	uf2	NOUN
ejpam-2571	370	12	,	,	PUNCT
ejpam-2571	370	13	ieee	ieee	NOUN
ejpam-2571	370	14	transactions	transaction	NOUN
ejpam-2571	370	15	on	on	ADP
ejpam-2571	370	16	information	information	NOUN
ejpam-2571	370	17	theory	theory	NOUN
ejpam-2571	370	18	,	,	PUNCT
ejpam-2571	370	19	45	45	NUM
ejpam-2571	370	20	,	,	PUNCT
ejpam-2571	370	21	1250–1255	1250–1255	NUM
ejpam-2571	370	22	.	.	NOUN
ejpam-2571	370	23	1999	1999	NUM
ejpam-2571	370	24	.	.	PUNCT
ejpam-2571	371	1	[	[	X
ejpam-2571	371	2	4	4	X
ejpam-2571	371	3	]	]	PUNCT
ejpam-2571	371	4	h.	h.	PROPN
ejpam-2571	371	5	q.	q.	PROPN
ejpam-2571	371	6	dinh	dinh	PROPN
ejpam-2571	371	7	.	.	PUNCT
ejpam-2571	372	1	constacyclic	constacyclic	ADJ
ejpam-2571	372	2	codes	code	NOUN
ejpam-2571	372	3	of	of	ADP
ejpam-2571	372	4	length	length	NOUN
ejpam-2571	372	5	2s	2s	NUM
ejpam-2571	372	6	over	over	ADP
ejpam-2571	372	7	galois	galois	PROPN
ejpam-2571	372	8	extension	extension	NOUN
ejpam-2571	372	9	rings	ring	NOUN
ejpam-2571	372	10	of	of	ADP
ejpam-2571	372	11	f2	f2	PROPN
ejpam-2571	372	12	+	+	CCONJ
ejpam-2571	372	13	uf2	uf2	NOUN
ejpam-2571	372	14	,	,	PUNCT
ejpam-2571	372	15	ieee	ieee	NOUN
ejpam-2571	372	16	transactions	transaction	NOUN
ejpam-2571	372	17	on	on	ADP
ejpam-2571	372	18	information	information	NOUN
ejpam-2571	372	19	theory	theory	NOUN
ejpam-2571	372	20	,	,	PUNCT
ejpam-2571	372	21	55	55	NUM
ejpam-2571	372	22	,	,	PUNCT
ejpam-2571	372	23	1730–1740	1730–1740	NUM
ejpam-2571	372	24	.	.	PUNCT
ejpam-2571	372	25	2009	2009	NUM
ejpam-2571	372	26	.	.	PUNCT
ejpam-2571	373	1	[	[	X
ejpam-2571	373	2	5	5	X
ejpam-2571	373	3	]	]	PUNCT
ejpam-2571	373	4	h.	h.	PROPN
ejpam-2571	373	5	q.	q.	PROPN
ejpam-2571	373	6	dinh	dinh	PROPN
ejpam-2571	373	7	.	.	PUNCT
ejpam-2571	374	1	negacyclic	negacyclic	ADJ
ejpam-2571	374	2	codes	code	NOUN
ejpam-2571	374	3	of	of	ADP
ejpam-2571	374	4	length	length	NOUN
ejpam-2571	374	5	2s	2s	NUM
ejpam-2571	374	6	over	over	ADP
ejpam-2571	374	7	galois	galois	PROPN
ejpam-2571	374	8	rings	ring	NOUN
ejpam-2571	374	9	,	,	PUNCT
ejpam-2571	374	10	ieee	ieee	NOUN
ejpam-2571	374	11	transactions	transaction	NOUN
ejpam-2571	374	12	on	on	ADP
ejpam-2571	374	13	information	information	NOUN
ejpam-2571	374	14	theory	theory	NOUN
ejpam-2571	374	15	,	,	PUNCT
ejpam-2571	374	16	51	51	NUM
ejpam-2571	374	17	,	,	PUNCT
ejpam-2571	374	18	4252–4262	4252–4262	NUM
ejpam-2571	374	19	.	.	PUNCT
ejpam-2571	374	20	2005	2005	NUM
ejpam-2571	374	21	.	.	PUNCT
ejpam-2571	375	1	[	[	X
ejpam-2571	375	2	6	6	NUM
ejpam-2571	375	3	]	]	PUNCT
ejpam-2571	375	4	h.	h.	PROPN
ejpam-2571	375	5	q.	q.	PROPN
ejpam-2571	375	6	dinh	dinh	PROPN
ejpam-2571	375	7	.	.	PUNCT
ejpam-2571	376	1	constacyclic	constacyclic	ADJ
ejpam-2571	376	2	codes	code	NOUN
ejpam-2571	376	3	of	of	ADP
ejpam-2571	376	4	length	length	NOUN
ejpam-2571	376	5	ps	ps	PROPN
ejpam-2571	376	6	over	over	ADP
ejpam-2571	376	7	fpm	fpm	NOUN
ejpam-2571	376	8	+	+	CCONJ
ejpam-2571	376	9	ufpm	ufpm	ADJ
ejpam-2571	376	10	,	,	PUNCT
ejpam-2571	376	11	journal	journal	NOUN
ejpam-2571	376	12	of	of	ADP
ejpam-2571	376	13	algebra	algebra	PROPN
ejpam-2571	376	14	,	,	PUNCT
ejpam-2571	376	15	324	324	NUM
ejpam-2571	376	16	,	,	PUNCT
ejpam-2571	376	17	940–950	940–950	NUM
ejpam-2571	376	18	.	.	PUNCT
ejpam-2571	376	19	2010	2010	NUM
ejpam-2571	376	20	.	.	PUNCT
ejpam-2571	377	1	[	[	X
ejpam-2571	377	2	7	7	X
ejpam-2571	377	3	]	]	PUNCT
ejpam-2571	377	4	h.	h.	PROPN
ejpam-2571	377	5	q.	q.	PROPN
ejpam-2571	377	6	dinh	dinh	PROPN
ejpam-2571	377	7	and	and	CCONJ
ejpam-2571	377	8	s.	s.	PROPN
ejpam-2571	377	9	r.	r.	PROPN
ejpam-2571	377	10	lópez	lópez	PROPN
ejpam-2571	377	11	-	-	PUNCT
ejpam-2571	377	12	permouth	permouth	NOUN
ejpam-2571	377	13	.	.	PUNCT
ejpam-2571	378	1	cyclic	cyclic	ADJ
ejpam-2571	378	2	and	and	CCONJ
ejpam-2571	378	3	negacyclic	negacyclic	ADJ
ejpam-2571	378	4	codes	code	NOUN
ejpam-2571	378	5	over	over	ADP
ejpam-2571	378	6	finite	finite	ADJ
ejpam-2571	378	7	chain	chain	NOUN
ejpam-2571	378	8	rings	ring	NOUN
ejpam-2571	378	9	,	,	PUNCT
ejpam-2571	378	10	ieee	ieee	NOUN
ejpam-2571	378	11	transactions	transaction	NOUN
ejpam-2571	378	12	on	on	ADP
ejpam-2571	378	13	information	information	NOUN
ejpam-2571	378	14	theory	theory	NOUN
ejpam-2571	378	15	,	,	PUNCT
ejpam-2571	378	16	50	50	NUM
ejpam-2571	378	17	,	,	PUNCT
ejpam-2571	378	18	1728–1744	1728–1744	NUM
ejpam-2571	378	19	.	.	PUNCT
ejpam-2571	379	1	2004	2004	NUM
ejpam-2571	379	2	.	.	PUNCT
ejpam-2571	380	1	[	[	X
ejpam-2571	380	2	8	8	X
ejpam-2571	380	3	]	]	PUNCT
ejpam-2571	380	4	j.	j.	PROPN
ejpam-2571	380	5	gao	gao	PROPN
ejpam-2571	380	6	.	.	PUNCT
ejpam-2571	381	1	some	some	DET
ejpam-2571	381	2	results	result	NOUN
ejpam-2571	381	3	on	on	ADP
ejpam-2571	381	4	linear	linear	ADJ
ejpam-2571	381	5	codes	code	NOUN
ejpam-2571	381	6	over	over	ADP
ejpam-2571	381	7	fp+ufp+u2	fp+ufp+u2	PROPN
ejpam-2571	381	8	fp	fp	PROPN
ejpam-2571	381	9	,	,	PUNCT
ejpam-2571	381	10	journal	journal	NOUN
ejpam-2571	381	11	of	of	ADP
ejpam-2571	381	12	applied	apply	VERB
ejpam-2571	381	13	mathematics	mathematic	NOUN
ejpam-2571	381	14	and	and	CCONJ
ejpam-2571	381	15	computing	computing	NOUN
ejpam-2571	381	16	,	,	PUNCT
ejpam-2571	381	17	47	47	NUM
ejpam-2571	381	18	,	,	PUNCT
ejpam-2571	381	19	473–485	473–485	NUM
ejpam-2571	381	20	,	,	PUNCT
ejpam-2571	381	21	2015	2015	NUM
ejpam-2571	381	22	.	.	PUNCT
ejpam-2571	382	1	[	[	X
ejpam-2571	382	2	9	9	NUM
ejpam-2571	382	3	]	]	PUNCT
ejpam-2571	382	4	a.	a.	NOUN
ejpam-2571	382	5	hammons	hammon	NOUN
ejpam-2571	382	6	,	,	PUNCT
ejpam-2571	382	7	p.	p.	NOUN
ejpam-2571	382	8	v.	v.	PROPN
ejpam-2571	382	9	kumar	kumar	PROPN
ejpam-2571	382	10	,	,	PUNCT
ejpam-2571	382	11	a.	a.	PROPN
ejpam-2571	382	12	r.	r.	PROPN
ejpam-2571	382	13	calderbank	calderbank	PROPN
ejpam-2571	382	14	,	,	PUNCT
ejpam-2571	382	15	n.	n.	PROPN
ejpam-2571	382	16	j.	j.	PROPN
ejpam-2571	382	17	a.	a.	PROPN
ejpam-2571	382	18	slone	slone	PROPN
ejpam-2571	382	19	,	,	PUNCT
ejpam-2571	382	20	and	and	CCONJ
ejpam-2571	382	21	p.	p.	PROPN
ejpam-2571	382	22	sole	sole	NOUN
ejpam-2571	382	23	.	.	PUNCT
ejpam-2571	383	1	the	the	DET
ejpam-2571	383	2	z4	z4	PROPN
ejpam-2571	383	3	linearity	linearity	PROPN
ejpam-2571	383	4	of	of	ADP
ejpam-2571	383	5	kerdock	kerdock	NOUN
ejpam-2571	383	6	,	,	PUNCT
ejpam-2571	383	7	preparata	preparata	NOUN
ejpam-2571	383	8	,	,	PUNCT
ejpam-2571	383	9	goethals	goethal	NOUN
ejpam-2571	383	10	and	and	CCONJ
ejpam-2571	383	11	related	related	ADJ
ejpam-2571	383	12	codes	code	NOUN
ejpam-2571	383	13	,	,	PUNCT
ejpam-2571	383	14	ieee	ieee	NOUN
ejpam-2571	383	15	transactions	transaction	NOUN
ejpam-2571	383	16	on	on	ADP
ejpam-2571	383	17	information	information	NOUN
ejpam-2571	383	18	theory	theory	NOUN
ejpam-2571	383	19	,	,	PUNCT
ejpam-2571	383	20	40(4	40(4	NUM
ejpam-2571	383	21	)	)	PUNCT
ejpam-2571	383	22	,	,	PUNCT
ejpam-2571	383	23	301–319	301–319	NUM
ejpam-2571	383	24	.	.	NOUN
ejpam-2571	383	25	1994	1994	NUM
ejpam-2571	383	26	.	.	PUNCT
ejpam-2571	384	1	[	[	X
ejpam-2571	384	2	10	10	NUM
ejpam-2571	384	3	]	]	X
ejpam-2571	384	4	s.	s.	PROPN
ejpam-2571	384	5	jitman	jitman	PROPN
ejpam-2571	384	6	,	,	PUNCT
ejpam-2571	384	7	s.	s.	PROPN
ejpam-2571	384	8	ling	ling	PROPN
ejpam-2571	384	9	,	,	PUNCT
ejpam-2571	384	10	and	and	CCONJ
ejpam-2571	384	11	p.	p.	NOUN
ejpam-2571	384	12	udomkavanich	udomkavanich	PROPN
ejpam-2571	384	13	.	.	PUNCT
ejpam-2571	385	1	skew	skew	ADJ
ejpam-2571	385	2	constacyclic	constacyclic	ADJ
ejpam-2571	385	3	codes	code	NOUN
ejpam-2571	385	4	over	over	ADP
ejpam-2571	385	5	finite	finite	ADJ
ejpam-2571	385	6	chain	chain	NOUN
ejpam-2571	385	7	rings	ring	NOUN
ejpam-2571	385	8	,	,	PUNCT
ejpam-2571	385	9	advances	advance	NOUN
ejpam-2571	385	10	in	in	ADP
ejpam-2571	385	11	mathematics	mathematic	NOUN
ejpam-2571	385	12	of	of	ADP
ejpam-2571	385	13	communications	communication	NOUN
ejpam-2571	385	14	,	,	PUNCT
ejpam-2571	385	15	6(1	6(1	NUM
ejpam-2571	385	16	)	)	PUNCT
ejpam-2571	385	17	,	,	PUNCT
ejpam-2571	386	1	39–63	39–63	NUM
ejpam-2571	386	2	.	.	NOUN
ejpam-2571	386	3	2012	2012	NUM
ejpam-2571	386	4	.	.	PUNCT
ejpam-2571	387	1	[	[	X
ejpam-2571	387	2	11	11	NUM
ejpam-2571	387	3	]	]	PUNCT
ejpam-2571	387	4	a.	a.	PROPN
ejpam-2571	387	5	kaya	kaya	PROPN
ejpam-2571	387	6	,	,	PUNCT
ejpam-2571	387	7	b.	b.	PROPN
ejpam-2571	387	8	yildiz	yildiz	PROPN
ejpam-2571	387	9	,	,	PUNCT
ejpam-2571	387	10	and	and	CCONJ
ejpam-2571	387	11	i.	i.	PROPN
ejpam-2571	387	12	siap	siap	PROPN
ejpam-2571	387	13	.	.	PUNCT
ejpam-2571	388	1	new	new	ADJ
ejpam-2571	388	2	extremal	extremal	ADJ
ejpam-2571	388	3	binary	binary	NOUN
ejpam-2571	388	4	self	self	NOUN
ejpam-2571	388	5	-	-	PUNCT
ejpam-2571	388	6	dual	dual	ADJ
ejpam-2571	388	7	codes	code	NOUN
ejpam-2571	388	8	of	of	ADP
ejpam-2571	388	9	length	length	NOUN
ejpam-2571	388	10	68	68	NUM
ejpam-2571	388	11	from	from	ADP
ejpam-2571	388	12	quadratic	quadratic	ADJ
ejpam-2571	388	13	residue	residue	NOUN
ejpam-2571	388	14	codes	code	NOUN
ejpam-2571	388	15	over	over	ADP
ejpam-2571	388	16	fp	fp	PRON
ejpam-2571	388	17	+	+	NUM
ejpam-2571	388	18	ufp	ufp	NOUN
ejpam-2571	388	19	+	+	CCONJ
ejpam-2571	388	20	u2	u2	PROPN
ejpam-2571	388	21	fp	fp	PROPN
ejpam-2571	388	22	,	,	PUNCT
ejpam-2571	388	23	finite	finite	ADJ
ejpam-2571	388	24	fields	field	NOUN
ejpam-2571	388	25	and	and	CCONJ
ejpam-2571	388	26	their	their	PRON
ejpam-2571	388	27	applications	application	NOUN
ejpam-2571	388	28	,	,	PUNCT
ejpam-2571	388	29	29	29	NUM
ejpam-2571	388	30	,	,	PUNCT
ejpam-2571	388	31	160–177	160–177	NUM
ejpam-2571	388	32	.	.	NOUN
ejpam-2571	388	33	2014	2014	NUM
ejpam-2571	388	34	.	.	PUNCT
ejpam-2571	389	1	references	reference	NOUN
ejpam-2571	389	2	47	47	NUM
ejpam-2571	390	1	[	[	X
ejpam-2571	390	2	12	12	NUM
ejpam-2571	390	3	]	]	X
ejpam-2571	390	4	y.	y.	PROPN
ejpam-2571	390	5	liu	liu	PROPN
ejpam-2571	390	6	,	,	PUNCT
ejpam-2571	390	7	m.	m.	PROPN
ejpam-2571	390	8	shi	shi	PROPN
ejpam-2571	390	9	,	,	PUNCT
ejpam-2571	390	10	and	and	CCONJ
ejpam-2571	390	11	p.	p.	PROPN
ejpam-2571	390	12	sole	sole	NOUN
ejpam-2571	390	13	.	.	PUNCT
ejpam-2571	391	1	quadratic	quadratic	ADJ
ejpam-2571	391	2	residue	residue	NOUN
ejpam-2571	391	3	codes	code	NOUN
ejpam-2571	391	4	over	over	ADP
ejpam-2571	391	5	fp	fp	PROPN
ejpam-2571	391	6	+	+	NUM
ejpam-2571	391	7	vfp	vfp	NOUN
ejpam-2571	391	8	+	+	CCONJ
ejpam-2571	391	9	v2	v2	PROPN
ejpam-2571	391	10	fp	fp	NOUN
ejpam-2571	391	11	,	,	PUNCT
ejpam-2571	391	12	arithmetic	arithmetic	NOUN
ejpam-2571	391	13	of	of	ADP
ejpam-2571	391	14	finite	finite	ADJ
ejpam-2571	391	15	fields	field	NOUN
ejpam-2571	391	16	:	:	PUNCT
ejpam-2571	391	17	lecture	lecture	NOUN
ejpam-2571	391	18	notes	note	NOUN
ejpam-2571	391	19	in	in	ADP
ejpam-2571	391	20	computer	computer	NOUN
ejpam-2571	391	21	science	science	NOUN
ejpam-2571	391	22	,	,	PUNCT
ejpam-2571	391	23	9061	9061	NUM
ejpam-2571	391	24	,	,	PUNCT
ejpam-2571	391	25	204	204	NUM
ejpam-2571	391	26	-	-	SYM
ejpam-2571	391	27	201	201	NUM
ejpam-2571	391	28	.	.	PUNCT
ejpam-2571	391	29	2015	2015	NUM
ejpam-2571	391	30	.	.	PUNCT
ejpam-2571	392	1	[	[	X
ejpam-2571	392	2	13	13	NUM
ejpam-2571	392	3	]	]	X
ejpam-2571	392	4	f.	f.	PROPN
ejpam-2571	392	5	j.	j.	PROPN
ejpam-2571	392	6	macwilliams	macwilliams	PROPN
ejpam-2571	392	7	and	and	CCONJ
ejpam-2571	392	8	n.	n.	PROPN
ejpam-2571	392	9	j.	j.	PROPN
ejpam-2571	392	10	a.	a.	PROPN
ejpam-2571	392	11	sloane	sloane	PROPN
ejpam-2571	392	12	.	.	PUNCT
ejpam-2571	393	1	the	the	DET
ejpam-2571	393	2	theory	theory	NOUN
ejpam-2571	393	3	of	of	ADP
ejpam-2571	393	4	error	error	NOUN
ejpam-2571	393	5	correcting	correct	VERB
ejpam-2571	393	6	codes	code	NOUN
ejpam-2571	393	7	,	,	PUNCT
ejpam-2571	393	8	north	north	NOUN
ejpam-2571	393	9	holland	holland	PROPN
ejpam-2571	393	10	,	,	PUNCT
ejpam-2571	393	11	1977	1977	NUM
ejpam-2571	393	12	.	.	PUNCT
ejpam-2571	394	1	[	[	X
ejpam-2571	394	2	14	14	NUM
ejpam-2571	394	3	]	]	PUNCT
ejpam-2571	394	4	j.	j.	PROPN
ejpam-2571	394	5	f.	f.	PROPN
ejpam-2571	394	6	qian	qian	PROPN
ejpam-2571	394	7	,	,	PUNCT
ejpam-2571	394	8	l.	l.	PROPN
ejpam-2571	394	9	n.	n.	PROPN
ejpam-2571	394	10	zhang	zhang	PROPN
ejpam-2571	394	11	,	,	PUNCT
ejpam-2571	394	12	and	and	CCONJ
ejpam-2571	394	13	s.	s.	PROPN
ejpam-2571	394	14	x.	x.	PROPN
ejpam-2571	394	15	zhu	zhu	PROPN
ejpam-2571	394	16	.	.	PUNCT
ejpam-2571	395	1	(	(	PUNCT
ejpam-2571	395	2	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2571	395	3	and	and	CCONJ
ejpam-2571	395	4	cyclic	cyclic	ADJ
ejpam-2571	395	5	codes	code	NOUN
ejpam-2571	395	6	over	over	ADP
ejpam-2571	395	7	the	the	DET
ejpam-2571	395	8	ring	ring	NOUN
ejpam-2571	395	9	f2+uf2	f2+uf2	NOUN
ejpam-2571	395	10	,	,	PUNCT
ejpam-2571	395	11	applied	apply	VERB
ejpam-2571	395	12	mathematics	mathematic	NOUN
ejpam-2571	395	13	letters	letter	NOUN
ejpam-2571	395	14	,	,	PUNCT
ejpam-2571	395	15	19	19	NUM
ejpam-2571	395	16	,	,	PUNCT
ejpam-2571	395	17	820–823	820–823	NUM
ejpam-2571	395	18	.	.	NOUN
ejpam-2571	395	19	2006	2006	NUM
ejpam-2571	395	20	.	.	PUNCT
ejpam-2571	396	1	[	[	X
ejpam-2571	396	2	15	15	NUM
ejpam-2571	396	3	]	]	X
ejpam-2571	396	4	sh	sh	PROPN
ejpam-2571	396	5	.	.	PROPN
ejpam-2571	396	6	zhu	zhu	PROPN
ejpam-2571	396	7	and	and	CCONJ
ejpam-2571	396	8	l.	l.	PROPN
ejpam-2571	396	9	wang	wang	PROPN
ejpam-2571	396	10	.	.	PUNCT
ejpam-2571	397	1	a	a	DET
ejpam-2571	397	2	class	class	NOUN
ejpam-2571	397	3	of	of	ADP
ejpam-2571	397	4	constacyclic	constacyclic	ADJ
ejpam-2571	397	5	codes	code	NOUN
ejpam-2571	397	6	over	over	ADP
ejpam-2571	397	7	fp+vfp	fp+vfp	PROPN
ejpam-2571	397	8	and	and	CCONJ
ejpam-2571	397	9	its	its	PRON
ejpam-2571	397	10	gray	gray	ADJ
ejpam-2571	397	11	image	image	NOUN
ejpam-2571	397	12	,	,	PUNCT
ejpam-2571	397	13	discrete	discrete	ADJ
ejpam-2571	397	14	mathematics	mathematic	NOUN
ejpam-2571	397	15	,	,	PUNCT
ejpam-2571	397	16	311	311	NUM
ejpam-2571	397	17	,	,	PUNCT
ejpam-2571	397	18	2677–2682	2677–2682	NOUN
ejpam-2571	397	19	.	.	PUNCT
ejpam-2571	397	20	2011	2011	NUM
ejpam-2571	397	21	.	.	PUNCT