id	sid	tid	token	lemma	pos
ejpam-2537	1	1	compile	compile	NOUN
ejpam-2537	1	2	/	/	SYM
ejpam-2537	1	3	output.dvi	output.dvi	NOUN
ejpam-2537	1	4	european	european	ADJ
ejpam-2537	1	5	journal	journal	NOUN
ejpam-2537	1	6	of	of	ADP
ejpam-2537	1	7	pure	pure	ADJ
ejpam-2537	1	8	and	and	CCONJ
ejpam-2537	1	9	applied	apply	VERB
ejpam-2537	1	10	mathematics	mathematic	NOUN
ejpam-2537	1	11	vol	vol	NOUN
ejpam-2537	1	12	.	.	PROPN
ejpam-2537	2	1	9	9	NUM
ejpam-2537	2	2	,	,	PUNCT
ejpam-2537	2	3	no	no	INTJ
ejpam-2537	2	4	.	.	NOUN
ejpam-2537	2	5	3	3	NUM
ejpam-2537	2	6	,	,	PUNCT
ejpam-2537	2	7	2016	2016	NUM
ejpam-2537	2	8	,	,	PUNCT
ejpam-2537	2	9	305	305	NUM
ejpam-2537	2	10	-	-	SYM
ejpam-2537	2	11	313	313	NUM
ejpam-2537	2	12	issn	issn	PROPN
ejpam-2537	2	13	1307	1307	NUM
ejpam-2537	2	14	-	-	SYM
ejpam-2537	2	15	5543	5543	NUM
ejpam-2537	2	16	–	–	PUNCT
ejpam-2537	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2537	2	18	on	on	ADP
ejpam-2537	2	19	(	(	PUNCT
ejpam-2537	2	20	1	1	NUM
ejpam-2537	2	21	+	+	CCONJ
ejpam-2537	2	22	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	2	23	and	and	CCONJ
ejpam-2537	2	24	cyclic	cyclic	ADJ
ejpam-2537	2	25	codes	code	NOUN
ejpam-2537	2	26	over	over	ADP
ejpam-2537	2	27	f2	f2	PROPN
ejpam-2537	2	28	+	+	CCONJ
ejpam-2537	2	29	uf2	uf2	NOUN
ejpam-2537	2	30	+	+	CCONJ
ejpam-2537	2	31	vf2	vf2	NOUN
ejpam-2537	2	32	abdullah	abdullah	PROPN
ejpam-2537	2	33	dertli1,∗	dertli1,∗	PROPN
ejpam-2537	2	34	,	,	PUNCT
ejpam-2537	2	35	yasemin	yasemin	PROPN
ejpam-2537	2	36	cengellenmis2	cengellenmis2	PROPN
ejpam-2537	2	37	1	1	NUM
ejpam-2537	2	38	department	department	NOUN
ejpam-2537	2	39	of	of	ADP
ejpam-2537	2	40	mathematics	mathematic	NOUN
ejpam-2537	2	41	,	,	PUNCT
ejpam-2537	2	42	faculty	faculty	NOUN
ejpam-2537	2	43	of	of	ADP
ejpam-2537	2	44	science	science	NOUN
ejpam-2537	2	45	and	and	CCONJ
ejpam-2537	2	46	arts	art	NOUN
ejpam-2537	2	47	,	,	PUNCT
ejpam-2537	2	48	ondokuz	ondokuz	PROPN
ejpam-2537	2	49	mayıs	mayıs	PROPN
ejpam-2537	2	50	university	university	PROPN
ejpam-2537	2	51	,	,	PUNCT
ejpam-2537	2	52	samsun	samsun	PROPN
ejpam-2537	2	53	,	,	PUNCT
ejpam-2537	2	54	turkey	turkey	PROPN
ejpam-2537	2	55	2	2	NUM
ejpam-2537	2	56	department	department	NOUN
ejpam-2537	2	57	of	of	ADP
ejpam-2537	2	58	mathematics	mathematic	NOUN
ejpam-2537	2	59	,	,	PUNCT
ejpam-2537	2	60	faculty	faculty	NOUN
ejpam-2537	2	61	of	of	ADP
ejpam-2537	2	62	science	science	NOUN
ejpam-2537	2	63	and	and	CCONJ
ejpam-2537	2	64	arts	art	NOUN
ejpam-2537	2	65	,	,	PUNCT
ejpam-2537	2	66	trakya	trakya	PROPN
ejpam-2537	2	67	university	university	NOUN
ejpam-2537	2	68	,	,	PUNCT
ejpam-2537	2	69	edirne	edirne	PROPN
ejpam-2537	2	70	,	,	PUNCT
ejpam-2537	2	71	turkey	turkey	NOUN
ejpam-2537	2	72	abstract	abstract	NOUN
ejpam-2537	2	73	.	.	PUNCT
ejpam-2537	3	1	it	it	PRON
ejpam-2537	3	2	is	be	AUX
ejpam-2537	3	3	studied	study	VERB
ejpam-2537	3	4	codes	code	NOUN
ejpam-2537	3	5	over	over	ADP
ejpam-2537	3	6	the	the	DET
ejpam-2537	3	7	ring	ring	NOUN
ejpam-2537	3	8	r=	r=	ADJ
ejpam-2537	3	9	f2+uf2+vf2	f2+uf2+vf2	PROPN
ejpam-2537	3	10	,	,	PUNCT
ejpam-2537	3	11	u2	u2	PROPN
ejpam-2537	3	12	=	=	SYM
ejpam-2537	3	13	0	0	NUM
ejpam-2537	3	14	,	,	PUNCT
ejpam-2537	3	15	v2	v2	PROPN
ejpam-2537	3	16	=	=	SYM
ejpam-2537	3	17	v	v	NOUN
ejpam-2537	3	18	,	,	PUNCT
ejpam-2537	3	19	uv	uv	NOUN
ejpam-2537	3	20	=	=	NOUN
ejpam-2537	3	21	vu=	vu=	NOUN
ejpam-2537	3	22	0	0	NUM
ejpam-2537	3	23	which	which	PRON
ejpam-2537	3	24	contains	contain	VERB
ejpam-2537	3	25	the	the	DET
ejpam-2537	3	26	two	two	NUM
ejpam-2537	3	27	ring	ring	NOUN
ejpam-2537	3	28	f2+uf2,u2	f2+uf2,u2	PUNCT
ejpam-2537	3	29	=	=	SYM
ejpam-2537	3	30	0	0	NUM
ejpam-2537	3	31	and	and	CCONJ
ejpam-2537	3	32	f2	f2	PROPN
ejpam-2537	3	33	+	+	CCONJ
ejpam-2537	3	34	vf2	vf2	ADJ
ejpam-2537	3	35	,	,	PUNCT
ejpam-2537	3	36	v2	v2	PROPN
ejpam-2537	3	37	=	=	NOUN
ejpam-2537	4	1	v.	v.	CCONJ
ejpam-2537	4	2	it	it	PRON
ejpam-2537	4	3	is	be	AUX
ejpam-2537	4	4	introduced	introduce	VERB
ejpam-2537	4	5	(	(	PUNCT
ejpam-2537	4	6	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	4	7	codes	code	NOUN
ejpam-2537	4	8	and	and	CCONJ
ejpam-2537	4	9	cyclic	cyclic	ADJ
ejpam-2537	4	10	codes	code	NOUN
ejpam-2537	4	11	over	over	ADP
ejpam-2537	4	12	f2+uf2	f2+uf2	NOUN
ejpam-2537	4	13	+	+	NOUN
ejpam-2537	4	14	vf2	vf2	ADJ
ejpam-2537	4	15	.	.	PUNCT
ejpam-2537	5	1	it	it	PRON
ejpam-2537	5	2	is	be	AUX
ejpam-2537	5	3	characterized	characterize	VERB
ejpam-2537	5	4	codes	code	NOUN
ejpam-2537	5	5	over	over	ADP
ejpam-2537	5	6	f2	f2	PROPN
ejpam-2537	5	7	+	+	CCONJ
ejpam-2537	5	8	vf2	vf2	NOUN
ejpam-2537	5	9	which	which	PRON
ejpam-2537	5	10	are	be	AUX
ejpam-2537	5	11	the	the	DET
ejpam-2537	5	12	images	image	NOUN
ejpam-2537	5	13	of	of	ADP
ejpam-2537	5	14	(	(	PUNCT
ejpam-2537	5	15	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	5	16	codes	code	NOUN
ejpam-2537	5	17	and	and	CCONJ
ejpam-2537	5	18	cyclic	cyclic	ADJ
ejpam-2537	5	19	codes	code	NOUN
ejpam-2537	5	20	over	over	ADP
ejpam-2537	5	21	f2	f2	PROPN
ejpam-2537	5	22	+	+	CCONJ
ejpam-2537	5	23	uf2	uf2	NOUN
ejpam-2537	5	24	+	+	CCONJ
ejpam-2537	5	25	vf2	vf2	ADJ
ejpam-2537	5	26	.	.	PUNCT
ejpam-2537	6	1	it	it	PRON
ejpam-2537	6	2	is	be	AUX
ejpam-2537	6	3	obtained	obtain	VERB
ejpam-2537	6	4	a	a	DET
ejpam-2537	6	5	representation	representation	NOUN
ejpam-2537	6	6	of	of	ADP
ejpam-2537	6	7	a	a	DET
ejpam-2537	6	8	linear	linear	ADJ
ejpam-2537	6	9	code	code	NOUN
ejpam-2537	6	10	of	of	ADP
ejpam-2537	6	11	length	length	NOUN
ejpam-2537	6	12	n	n	CCONJ
ejpam-2537	6	13	over	over	ADP
ejpam-2537	6	14	r	r	NOUN
ejpam-2537	6	15	by	by	ADP
ejpam-2537	6	16	means	mean	NOUN
ejpam-2537	6	17	of	of	ADP
ejpam-2537	6	18	c1	c1	PROPN
ejpam-2537	6	19	and	and	CCONJ
ejpam-2537	6	20	c2	c2	PROPN
ejpam-2537	6	21	which	which	PRON
ejpam-2537	6	22	are	be	AUX
ejpam-2537	6	23	linear	linear	NOUN
ejpam-2537	6	24	codes	code	NOUN
ejpam-2537	6	25	of	of	ADP
ejpam-2537	6	26	length	length	NOUN
ejpam-2537	6	27	n	n	NOUN
ejpam-2537	6	28	over	over	ADP
ejpam-2537	6	29	f2	f2	PROPN
ejpam-2537	6	30	+	+	CCONJ
ejpam-2537	6	31	uf2	uf2	NOUN
ejpam-2537	6	32	.	.	PUNCT
ejpam-2537	7	1	it	it	PRON
ejpam-2537	7	2	is	be	AUX
ejpam-2537	7	3	also	also	ADV
ejpam-2537	7	4	characterized	characterize	VERB
ejpam-2537	7	5	codes	code	NOUN
ejpam-2537	7	6	over	over	ADP
ejpam-2537	7	7	f2	f2	PROPN
ejpam-2537	7	8	which	which	PRON
ejpam-2537	7	9	are	be	AUX
ejpam-2537	7	10	the	the	DET
ejpam-2537	7	11	gray	gray	ADJ
ejpam-2537	7	12	images	image	NOUN
ejpam-2537	7	13	of	of	ADP
ejpam-2537	7	14	(	(	PUNCT
ejpam-2537	7	15	1	1	NUM
ejpam-2537	7	16	+	+	NUM
ejpam-2537	7	17	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	7	18	codes	code	NOUN
ejpam-2537	7	19	or	or	CCONJ
ejpam-2537	7	20	cyclic	cyclic	ADJ
ejpam-2537	7	21	codes	code	NOUN
ejpam-2537	7	22	over	over	ADP
ejpam-2537	7	23	f2	f2	PROPN
ejpam-2537	7	24	+	+	CCONJ
ejpam-2537	7	25	uf2	uf2	NOUN
ejpam-2537	7	26	+	+	CCONJ
ejpam-2537	7	27	vf2	vf2	ADJ
ejpam-2537	7	28	.	.	PUNCT
ejpam-2537	8	1	2010	2010	NUM
ejpam-2537	8	2	mathematics	mathematic	NOUN
ejpam-2537	8	3	subject	subject	NOUN
ejpam-2537	8	4	classifications	classification	NOUN
ejpam-2537	8	5	:	:	PUNCT
ejpam-2537	8	6	94b05	94b05	NUM
ejpam-2537	8	7	,	,	PUNCT
ejpam-2537	8	8	94b15	94b15	NUM
ejpam-2537	8	9	,	,	PUNCT
ejpam-2537	8	10	94b60	94b60	NUM
ejpam-2537	8	11	.	.	PUNCT
ejpam-2537	9	1	key	key	ADJ
ejpam-2537	9	2	words	word	NOUN
ejpam-2537	9	3	and	and	CCONJ
ejpam-2537	9	4	phrases	phrase	NOUN
ejpam-2537	9	5	:	:	PUNCT
ejpam-2537	9	6	gray	gray	ADJ
ejpam-2537	9	7	map	map	NOUN
ejpam-2537	9	8	,	,	PUNCT
ejpam-2537	9	9	cyclic	cyclic	ADJ
ejpam-2537	9	10	codes	code	NOUN
ejpam-2537	9	11	,	,	PUNCT
ejpam-2537	9	12	quasi	quasi	ADJ
ejpam-2537	9	13	-	-	ADJ
ejpam-2537	9	14	cyclic	cyclic	ADJ
ejpam-2537	9	15	code	code	NOUN
ejpam-2537	9	16	.	.	PUNCT
ejpam-2537	10	1	1	1	X
ejpam-2537	10	2	.	.	X
ejpam-2537	10	3	introduction	introduction	NOUN
ejpam-2537	10	4	it	it	PRON
ejpam-2537	10	5	was	be	AUX
ejpam-2537	10	6	introduced	introduce	VERB
ejpam-2537	10	7	linear	linear	ADJ
ejpam-2537	10	8	(	(	PUNCT
ejpam-2537	10	9	1	1	NUM
ejpam-2537	10	10	+	+	NUM
ejpam-2537	10	11	u	u	NOUN
ejpam-2537	10	12	)	)	PUNCT
ejpam-2537	10	13	constacyclic	constacyclic	ADJ
ejpam-2537	10	14	codes	code	NOUN
ejpam-2537	10	15	and	and	CCONJ
ejpam-2537	10	16	cyclic	cyclic	ADJ
ejpam-2537	10	17	codes	code	NOUN
ejpam-2537	10	18	over	over	ADP
ejpam-2537	10	19	f2	f2	PROPN
ejpam-2537	10	20	+	+	CCONJ
ejpam-2537	10	21	uf2	uf2	NOUN
ejpam-2537	10	22	and	and	CCONJ
ejpam-2537	10	23	characterized	characterize	VERB
ejpam-2537	10	24	codes	code	NOUN
ejpam-2537	10	25	over	over	ADP
ejpam-2537	10	26	f2	f2	PROPN
ejpam-2537	10	27	which	which	PRON
ejpam-2537	10	28	are	be	AUX
ejpam-2537	10	29	the	the	DET
ejpam-2537	10	30	gray	gray	ADJ
ejpam-2537	10	31	images	image	NOUN
ejpam-2537	10	32	of	of	ADP
ejpam-2537	10	33	(	(	PUNCT
ejpam-2537	10	34	1	1	NUM
ejpam-2537	10	35	+	+	NUM
ejpam-2537	10	36	u	u	NOUN
ejpam-2537	10	37	)	)	PUNCT
ejpam-2537	10	38	constacyclic	constacyclic	ADJ
ejpam-2537	10	39	codes	code	NOUN
ejpam-2537	10	40	or	or	CCONJ
ejpam-2537	10	41	cyclic	cyclic	ADJ
ejpam-2537	10	42	codes	code	NOUN
ejpam-2537	10	43	over	over	ADP
ejpam-2537	10	44	f2+uf2	f2+uf2	NOUN
ejpam-2537	10	45	,	,	PUNCT
ejpam-2537	10	46	in	in	ADP
ejpam-2537	10	47	[	[	PUNCT
ejpam-2537	10	48	6	6	NUM
ejpam-2537	10	49	]	]	PUNCT
ejpam-2537	10	50	.	.	PUNCT
ejpam-2537	11	1	in	in	ADP
ejpam-2537	11	2	[	[	X
ejpam-2537	11	3	1	1	NUM
ejpam-2537	11	4	]	]	PUNCT
ejpam-2537	11	5	,	,	PUNCT
ejpam-2537	11	6	they	they	PRON
ejpam-2537	11	7	extended	extend	VERB
ejpam-2537	11	8	the	the	DET
ejpam-2537	11	9	result	result	NOUN
ejpam-2537	11	10	of	of	ADP
ejpam-2537	11	11	[	[	X
ejpam-2537	11	12	6	6	NUM
ejpam-2537	11	13	]	]	PUNCT
ejpam-2537	11	14	to	to	ADP
ejpam-2537	11	15	codes	code	NOUN
ejpam-2537	11	16	over	over	ADP
ejpam-2537	11	17	the	the	DET
ejpam-2537	11	18	commutative	commutative	ADJ
ejpam-2537	11	19	ring	ring	NOUN
ejpam-2537	11	20	fpk	fpk	NOUN
ejpam-2537	11	21	+	+	CCONJ
ejpam-2537	11	22	ufpk	ufpk	NOUN
ejpam-2537	11	23	where	where	SCONJ
ejpam-2537	11	24	p	p	NOUN
ejpam-2537	11	25	is	be	AUX
ejpam-2537	11	26	a	a	DET
ejpam-2537	11	27	prime	prime	NOUN
ejpam-2537	11	28	,	,	PUNCT
ejpam-2537	11	29	k	k	PROPN
ejpam-2537	11	30	∈	∈	PROPN
ejpam-2537	11	31	n	n	NOUN
ejpam-2537	11	32	and	and	CCONJ
ejpam-2537	11	33	u2	u2	PROPN
ejpam-2537	11	34	=	=	NOUN
ejpam-2537	11	35	0	0	NUM
ejpam-2537	11	36	.	.	PUNCT
ejpam-2537	12	1	in	in	ADP
ejpam-2537	12	2	[	[	X
ejpam-2537	12	3	5	5	NUM
ejpam-2537	12	4	]	]	PUNCT
ejpam-2537	12	5	,	,	PUNCT
ejpam-2537	12	6	it	it	PRON
ejpam-2537	12	7	was	be	AUX
ejpam-2537	12	8	introduced	introduce	VERB
ejpam-2537	12	9	(	(	PUNCT
ejpam-2537	12	10	1−u2)-cyclic	1−u2)-cyclic	ADJ
ejpam-2537	12	11	codes	code	NOUN
ejpam-2537	12	12	over	over	ADP
ejpam-2537	12	13	f2+uf2+u2f2	f2+uf2+u2f2	PROPN
ejpam-2537	12	14	and	and	CCONJ
ejpam-2537	12	15	characterized	characterize	VERB
ejpam-2537	12	16	codes	code	NOUN
ejpam-2537	12	17	over	over	ADP
ejpam-2537	12	18	f2	f2	PROPN
ejpam-2537	12	19	which	which	PRON
ejpam-2537	12	20	are	be	AUX
ejpam-2537	12	21	the	the	DET
ejpam-2537	12	22	gray	gray	ADJ
ejpam-2537	12	23	images	image	NOUN
ejpam-2537	12	24	of	of	ADP
ejpam-2537	12	25	(	(	PUNCT
ejpam-2537	12	26	1−u2)-cyclic	1−u2)-cyclic	ADJ
ejpam-2537	12	27	codes	code	NOUN
ejpam-2537	12	28	or	or	CCONJ
ejpam-2537	12	29	cyclic	cyclic	ADJ
ejpam-2537	12	30	codes	code	NOUN
ejpam-2537	12	31	over	over	ADP
ejpam-2537	12	32	f2+uf2+u2f2	f2+uf2+u2f2	PROPN
ejpam-2537	12	33	.	.	PUNCT
ejpam-2537	13	1	in	in	ADP
ejpam-2537	13	2	[	[	X
ejpam-2537	13	3	2	2	NUM
ejpam-2537	13	4	]	]	PUNCT
ejpam-2537	13	5	,	,	PUNCT
ejpam-2537	13	6	it	it	PRON
ejpam-2537	13	7	was	be	AUX
ejpam-2537	13	8	defined	define	VERB
ejpam-2537	13	9	a	a	DET
ejpam-2537	13	10	distance	distance	NOUN
ejpam-2537	13	11	preserving	preserve	VERB
ejpam-2537	13	12	map	map	NOUN
ejpam-2537	13	13	from	from	ADP
ejpam-2537	13	14	f2+uf2+u2f2+u3f2	f2+uf2+u2f2+u3f2	PROPN
ejpam-2537	13	15	+	+	CCONJ
ejpam-2537	13	16	.	.	PUNCT
ejpam-2537	13	17	.	.	PUNCT
ejpam-2537	14	1	.+umf2	.+umf2	PROPN
ejpam-2537	14	2	to	to	ADP
ejpam-2537	14	3	f2	f2	PROPN
ejpam-2537	14	4	and	and	CCONJ
ejpam-2537	14	5	characterized	characterize	VERB
ejpam-2537	14	6	codes	code	NOUN
ejpam-2537	14	7	over	over	ADP
ejpam-2537	14	8	f2	f2	PROPN
ejpam-2537	14	9	which	which	PRON
ejpam-2537	14	10	are	be	AUX
ejpam-2537	14	11	the	the	DET
ejpam-2537	14	12	gray	gray	ADJ
ejpam-2537	14	13	images	image	NOUN
ejpam-2537	14	14	of	of	ADP
ejpam-2537	14	15	(	(	PUNCT
ejpam-2537	14	16	1−um)-cyclic	1−um)-cyclic	NUM
ejpam-2537	14	17	codes	code	NOUN
ejpam-2537	14	18	or	or	CCONJ
ejpam-2537	14	19	cyclic	cyclic	ADJ
ejpam-2537	14	20	codes	code	NOUN
ejpam-2537	14	21	over	over	ADP
ejpam-2537	14	22	f2+uf2+u2f2+u3f2	f2+uf2+u2f2+u3f2	PROPN
ejpam-2537	14	23	+	+	SYM
ejpam-2537	14	24	.	.	PUNCT
ejpam-2537	14	25	.	.	PUNCT
ejpam-2537	15	1	.+umf2	.+umf2	PROPN
ejpam-2537	15	2	.	.	PUNCT
ejpam-2537	16	1	in	in	ADP
ejpam-2537	16	2	[	[	X
ejpam-2537	16	3	8	8	NUM
ejpam-2537	16	4	]	]	PUNCT
ejpam-2537	16	5	,	,	PUNCT
ejpam-2537	16	6	udomkavanich	udomkavanich	NOUN
ejpam-2537	16	7	and	and	CCONJ
ejpam-2537	16	8	jitman	jitman	NOUN
ejpam-2537	16	9	generalized	generalize	VERB
ejpam-2537	16	10	these	these	DET
ejpam-2537	16	11	results	result	NOUN
ejpam-2537	16	12	to	to	ADP
ejpam-2537	16	13	the	the	DET
ejpam-2537	16	14	ring	ring	NOUN
ejpam-2537	16	15	fpk	fpk	NOUN
ejpam-2537	16	16	+	+	CCONJ
ejpam-2537	16	17	ufpk	ufpk	X
ejpam-2537	16	18	+	+	X
ejpam-2537	16	19	.	.	PUNCT
ejpam-2537	16	20	.	.	PUNCT
ejpam-2537	17	1	.+umfpk	.+umfpk	PUNCT
ejpam-2537	17	2	.	.	PUNCT
ejpam-2537	18	1	the	the	DET
ejpam-2537	18	2	gray	gray	ADJ
ejpam-2537	18	3	images	image	NOUN
ejpam-2537	18	4	of	of	ADP
ejpam-2537	18	5	(	(	PUNCT
ejpam-2537	18	6	1−um)-constacyclic	1−um)-constacyclic	NUM
ejpam-2537	18	7	and	and	CCONJ
ejpam-2537	18	8	cyclic	cyclic	ADJ
ejpam-2537	18	9	codes	code	NOUN
ejpam-2537	18	10	over	over	ADP
ejpam-2537	18	11	fpk	fpk	NOUN
ejpam-2537	18	12	+	+	CCONJ
ejpam-2537	18	13	ufpk	ufpk	NOUN
ejpam-2537	18	14	+	+	X
ejpam-2537	18	15	.	.	PUNCT
ejpam-2537	18	16	.	.	PUNCT
ejpam-2537	19	1	.+	.+	NOUN
ejpam-2537	19	2	umf	umf	PROPN
ejpam-2537	20	1	k	k	PROPN
ejpam-2537	20	2	p	p	PROPN
ejpam-2537	20	3	were	be	AUX
ejpam-2537	20	4	studied	study	VERB
ejpam-2537	20	5	in	in	ADP
ejpam-2537	20	6	the	the	DET
ejpam-2537	20	7	mentioned	mention	VERB
ejpam-2537	20	8	paper	paper	NOUN
ejpam-2537	20	9	.	.	PUNCT
ejpam-2537	21	1	in	in	ADP
ejpam-2537	21	2	[	[	X
ejpam-2537	21	3	4	4	NUM
ejpam-2537	21	4	]	]	PUNCT
ejpam-2537	21	5	,	,	PUNCT
ejpam-2537	21	6	(	(	PUNCT
ejpam-2537	21	7	1	1	NUM
ejpam-2537	21	8	+	+	NOUN
ejpam-2537	21	9	v)-constacyclic	v)-constacyclic	ADJ
ejpam-2537	21	10	codes	code	NOUN
ejpam-2537	21	11	over	over	ADP
ejpam-2537	21	12	r2	r2	PROPN
ejpam-2537	21	13	=	=	SYM
ejpam-2537	21	14	f2+uf2	f2+uf2	NOUN
ejpam-2537	21	15	+	+	NOUN
ejpam-2537	21	16	vf2+uvf2,u2	vf2+uvf2,u2	X
ejpam-2537	21	17	=	=	SYM
ejpam-2537	21	18	v2	v2	PROPN
ejpam-2537	21	19	=	=	SYM
ejpam-2537	21	20	0,uv−	0,uv−	PROPN
ejpam-2537	21	21	vu=	vu=	NOUN
ejpam-2537	21	22	0	0	NUM
ejpam-2537	21	23	were	be	AUX
ejpam-2537	21	24	studied	study	VERB
ejpam-2537	21	25	.	.	PUNCT
ejpam-2537	22	1	(	(	PUNCT
ejpam-2537	22	2	1	1	NUM
ejpam-2537	22	3	+	+	NOUN
ejpam-2537	22	4	v)-constacyclic	v)-constacyclic	ADJ
ejpam-2537	22	5	codes	code	NOUN
ejpam-2537	22	6	over	over	ADP
ejpam-2537	22	7	r2	r2	PROPN
ejpam-2537	22	8	of	of	ADP
ejpam-2537	22	9	odd	odd	ADJ
ejpam-2537	22	10	length	length	NOUN
ejpam-2537	22	11	were	be	AUX
ejpam-2537	22	12	characterized	characterize	VERB
ejpam-2537	22	13	with	with	ADP
ejpam-2537	22	14	help	help	NOUN
ejpam-2537	22	15	of	of	ADP
ejpam-2537	22	16	cyclic	cyclic	ADJ
ejpam-2537	22	17	codes	code	NOUN
ejpam-2537	22	18	over	over	ADP
ejpam-2537	22	19	r2	r2	NOUN
ejpam-2537	22	20	.	.	PUNCT
ejpam-2537	23	1	∗corresponding	∗corresponde	VERB
ejpam-2537	23	2	author	author	NOUN
ejpam-2537	23	3	.	.	PUNCT
ejpam-2537	24	1	email	email	NOUN
ejpam-2537	24	2	addresses	address	NOUN
ejpam-2537	24	3	:	:	PUNCT
ejpam-2537	24	4	abdullah.dertli@gmail.com	abdullah.dertli@gmail.com	NOUN
ejpam-2537	24	5	(	(	PUNCT
ejpam-2537	24	6	a.	a.	NOUN
ejpam-2537	24	7	dertli	dertli	PROPN
ejpam-2537	24	8	)	)	PUNCT
ejpam-2537	24	9	,	,	PUNCT
ejpam-2537	24	10	ycengellenmis@yahoo.com	ycengellenmis@yahoo.com	X
ejpam-2537	24	11	(	(	PUNCT
ejpam-2537	24	12	y.	y.	PROPN
ejpam-2537	24	13	cengellenmis	cengellenmis	PROPN
ejpam-2537	24	14	)	)	PUNCT
ejpam-2537	24	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2537	25	1	305	305	NUM
ejpam-2537	25	2	c	c	X
ejpam-2537	25	3	©	©	PROPN
ejpam-2537	25	4	2016	2016	NUM
ejpam-2537	25	5	ejpam	ejpam	VERB
ejpam-2537	25	6	all	all	DET
ejpam-2537	25	7	rights	right	NOUN
ejpam-2537	25	8	reserved	reserve	VERB
ejpam-2537	25	9	.	.	PUNCT
ejpam-2537	26	1	a.	a.	PROPN
ejpam-2537	26	2	dertli	dertli	PROPN
ejpam-2537	26	3	,	,	PUNCT
ejpam-2537	26	4	y.	y.	PROPN
ejpam-2537	26	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	26	6	/	/	SYM
ejpam-2537	26	7	eur	eur	PROPN
ejpam-2537	26	8	.	.	PUNCT
ejpam-2537	27	1	j.	j.	PROPN
ejpam-2537	27	2	pure	pure	PROPN
ejpam-2537	27	3	appl	appl	PROPN
ejpam-2537	27	4	.	.	PROPN
ejpam-2537	27	5	math	math	PROPN
ejpam-2537	27	6	,	,	PUNCT
ejpam-2537	27	7	9	9	NUM
ejpam-2537	27	8	(	(	PUNCT
ejpam-2537	27	9	2016	2016	NUM
ejpam-2537	27	10	)	)	PUNCT
ejpam-2537	27	11	,	,	PUNCT
ejpam-2537	27	12	305	305	NUM
ejpam-2537	27	13	-	-	SYM
ejpam-2537	27	14	313	313	NUM
ejpam-2537	27	15	306	306	NUM
ejpam-2537	27	16	in	in	ADP
ejpam-2537	27	17	[	[	X
ejpam-2537	27	18	3	3	NUM
ejpam-2537	27	19	]	]	PUNCT
ejpam-2537	27	20	,	,	PUNCT
ejpam-2537	27	21	it	it	PRON
ejpam-2537	27	22	is	be	AUX
ejpam-2537	27	23	studied	study	VERB
ejpam-2537	27	24	(	(	PUNCT
ejpam-2537	27	25	1	1	NUM
ejpam-2537	27	26	+	+	NUM
ejpam-2537	27	27	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	27	28	codes	code	NOUN
ejpam-2537	27	29	over	over	ADP
ejpam-2537	27	30	a	a	DET
ejpam-2537	27	31	finite	finite	ADJ
ejpam-2537	27	32	commutative	commutative	ADJ
ejpam-2537	27	33	ring	ring	NOUN
ejpam-2537	27	34	f2+uf2	f2+uf2	NOUN
ejpam-2537	27	35	+	+	NOUN
ejpam-2537	27	36	vf2+uvf2,u2	vf2+uvf2,u2	X
ejpam-2537	27	37	=	=	SYM
ejpam-2537	27	38	0	0	NUM
ejpam-2537	27	39	,	,	PUNCT
ejpam-2537	27	40	v2	v2	PROPN
ejpam-2537	27	41	=	=	SYM
ejpam-2537	27	42	0,uv−	0,uv−	PROPN
ejpam-2537	27	43	vu=	vu=	NOUN
ejpam-2537	27	44	0	0	NUM
ejpam-2537	27	45	.	.	PUNCT
ejpam-2537	28	1	a	a	DET
ejpam-2537	28	2	set	set	NOUN
ejpam-2537	28	3	of	of	ADP
ejpam-2537	28	4	generator	generator	NOUN
ejpam-2537	28	5	of	of	ADP
ejpam-2537	28	6	such	such	ADJ
ejpam-2537	28	7	constacyclic	constacyclic	ADJ
ejpam-2537	28	8	codes	code	NOUN
ejpam-2537	28	9	for	for	ADP
ejpam-2537	28	10	an	an	DET
ejpam-2537	28	11	arbitrary	arbitrary	ADJ
ejpam-2537	28	12	length	length	NOUN
ejpam-2537	28	13	was	be	AUX
ejpam-2537	28	14	determined	determine	VERB
ejpam-2537	28	15	.	.	PUNCT
ejpam-2537	29	1	in	in	ADP
ejpam-2537	29	2	[	[	X
ejpam-2537	29	3	7	7	NUM
ejpam-2537	29	4	]	]	PUNCT
ejpam-2537	29	5	,	,	PUNCT
ejpam-2537	29	6	they	they	PRON
ejpam-2537	29	7	studied	study	VERB
ejpam-2537	29	8	linear	linear	NOUN
ejpam-2537	29	9	codes	code	NOUN
ejpam-2537	29	10	over	over	ADP
ejpam-2537	29	11	a	a	DET
ejpam-2537	29	12	new	new	ADJ
ejpam-2537	29	13	ring	ring	NOUN
ejpam-2537	29	14	s	s	PART
ejpam-2537	29	15	=	=	X
ejpam-2537	29	16	f2	f2	PROPN
ejpam-2537	29	17	+	+	CCONJ
ejpam-2537	29	18	uf2	uf2	NOUN
ejpam-2537	29	19	+	+	CCONJ
ejpam-2537	29	20	vf2	vf2	NOUN
ejpam-2537	30	1	+	+	CCONJ
ejpam-2537	30	2	uvf2,u2	uvf2,u2	PROPN
ejpam-2537	30	3	=	=	SYM
ejpam-2537	30	4	0	0	NUM
ejpam-2537	30	5	,	,	PUNCT
ejpam-2537	30	6	v2	v2	PROPN
ejpam-2537	30	7	=	=	SYM
ejpam-2537	30	8	v	v	NOUN
ejpam-2537	30	9	,	,	PUNCT
ejpam-2537	30	10	uv	uv	NOUN
ejpam-2537	30	11	=	=	SYM
ejpam-2537	30	12	vu	vu	X
ejpam-2537	30	13	.	.	PUNCT
ejpam-2537	31	1	it	it	PRON
ejpam-2537	31	2	is	be	AUX
ejpam-2537	31	3	obtained	obtain	VERB
ejpam-2537	31	4	macwilliams	macwilliam	NOUN
ejpam-2537	31	5	identities	identity	NOUN
ejpam-2537	31	6	for	for	ADP
ejpam-2537	31	7	lee	lee	PROPN
ejpam-2537	31	8	weight	weight	NOUN
ejpam-2537	31	9	enumerator	enumerator	NOUN
ejpam-2537	31	10	of	of	ADP
ejpam-2537	31	11	linear	linear	PROPN
ejpam-2537	31	12	codes	code	NOUN
ejpam-2537	31	13	over	over	ADP
ejpam-2537	31	14	this	this	DET
ejpam-2537	31	15	ring	ring	NOUN
ejpam-2537	31	16	using	use	VERB
ejpam-2537	31	17	a	a	DET
ejpam-2537	31	18	gray	gray	ADJ
ejpam-2537	31	19	map	map	NOUN
ejpam-2537	31	20	from	from	ADP
ejpam-2537	31	21	sn	sn	PROPN
ejpam-2537	31	22	to	to	ADP
ejpam-2537	31	23	(	(	PUNCT
ejpam-2537	31	24	f2+uf2	f2+uf2	NOUN
ejpam-2537	31	25	)	)	PUNCT
ejpam-2537	31	26	n.	n.	NOUN
ejpam-2537	31	27	moreover	moreover	ADV
ejpam-2537	31	28	,	,	PUNCT
ejpam-2537	31	29	they	they	PRON
ejpam-2537	31	30	studied	study	VERB
ejpam-2537	31	31	self	self	NOUN
ejpam-2537	31	32	dual	dual	ADJ
ejpam-2537	31	33	and	and	CCONJ
ejpam-2537	31	34	cyclic	cyclic	ADJ
ejpam-2537	31	35	codes	code	NOUN
ejpam-2537	31	36	over	over	ADP
ejpam-2537	31	37	s.	s.	PROPN
ejpam-2537	31	38	liu	liu	PROPN
ejpam-2537	31	39	xiusheng	xiusheng	PROPN
ejpam-2537	31	40	and	and	CCONJ
ejpam-2537	31	41	liu	liu	PROPN
ejpam-2537	31	42	hualu	hualu	PROPN
ejpam-2537	31	43	gave	give	VERB
ejpam-2537	31	44	rise	rise	NOUN
ejpam-2537	31	45	to	to	ADP
ejpam-2537	31	46	a	a	DET
ejpam-2537	31	47	new	new	ADJ
ejpam-2537	31	48	ring	ring	NOUN
ejpam-2537	31	49	r	r	NOUN
ejpam-2537	31	50	=	=	SYM
ejpam-2537	31	51	f2	f2	PROPN
ejpam-2537	31	52	+	+	CCONJ
ejpam-2537	31	53	uf2	uf2	NOUN
ejpam-2537	31	54	+	+	CCONJ
ejpam-2537	31	55	vf2,u2	vf2,u2	NOUN
ejpam-2537	31	56	=	=	SYM
ejpam-2537	31	57	0	0	NUM
ejpam-2537	31	58	,	,	PUNCT
ejpam-2537	31	59	v2	v2	PROPN
ejpam-2537	31	60	=	=	SYM
ejpam-2537	31	61	v	v	NOUN
ejpam-2537	31	62	,	,	PUNCT
ejpam-2537	31	63	uv	uv	NOUN
ejpam-2537	31	64	=	=	SYM
ejpam-2537	31	65	vu	vu	X
ejpam-2537	32	1	=	=	NOUN
ejpam-2537	32	2	0	0	NUM
ejpam-2537	32	3	in	in	ADP
ejpam-2537	32	4	[	[	X
ejpam-2537	32	5	9	9	NUM
ejpam-2537	32	6	]	]	PUNCT
ejpam-2537	32	7	.	.	PUNCT
ejpam-2537	33	1	it	it	PRON
ejpam-2537	33	2	is	be	AUX
ejpam-2537	33	3	frobenius	frobenius	ADJ
ejpam-2537	33	4	ring	ring	NOUN
ejpam-2537	33	5	.	.	PUNCT
ejpam-2537	34	1	they	they	PRON
ejpam-2537	34	2	defined	define	VERB
ejpam-2537	34	3	a	a	DET
ejpam-2537	34	4	gray	gray	ADJ
ejpam-2537	34	5	map	map	NOUN
ejpam-2537	34	6	.	.	PUNCT
ejpam-2537	35	1	the	the	DET
ejpam-2537	35	2	macwilliams	macwilliams	PROPN
ejpam-2537	35	3	identity	identity	NOUN
ejpam-2537	35	4	over	over	ADP
ejpam-2537	35	5	f2	f2	PROPN
ejpam-2537	35	6	and	and	CCONJ
ejpam-2537	35	7	the	the	DET
ejpam-2537	35	8	macwilliams	macwilliam	NOUN
ejpam-2537	35	9	identities	identity	NOUN
ejpam-2537	35	10	for	for	ADP
ejpam-2537	35	11	the	the	DET
ejpam-2537	35	12	lee	lee	PROPN
ejpam-2537	35	13	weight	weight	NOUN
ejpam-2537	35	14	enumerators	enumerator	NOUN
ejpam-2537	35	15	of	of	ADP
ejpam-2537	35	16	linear	linear	PROPN
ejpam-2537	35	17	codes	code	NOUN
ejpam-2537	35	18	over	over	ADP
ejpam-2537	35	19	the	the	DET
ejpam-2537	35	20	ring	ring	NOUN
ejpam-2537	35	21	f2	f2	PROPN
ejpam-2537	35	22	+	+	CCONJ
ejpam-2537	35	23	uf2	uf2	NOUN
ejpam-2537	35	24	+	+	CCONJ
ejpam-2537	35	25	vf2	vf2	NOUN
ejpam-2537	35	26	were	be	AUX
ejpam-2537	35	27	given	give	VERB
ejpam-2537	35	28	.	.	PUNCT
ejpam-2537	36	1	moreover	moreover	ADV
ejpam-2537	36	2	,	,	PUNCT
ejpam-2537	36	3	they	they	PRON
ejpam-2537	36	4	gave	give	VERB
ejpam-2537	36	5	some	some	DET
ejpam-2537	36	6	examples	example	NOUN
ejpam-2537	36	7	.	.	PUNCT
ejpam-2537	37	1	in	in	ADP
ejpam-2537	37	2	this	this	DET
ejpam-2537	37	3	paper	paper	NOUN
ejpam-2537	37	4	,	,	PUNCT
ejpam-2537	37	5	it	it	PRON
ejpam-2537	37	6	is	be	AUX
ejpam-2537	37	7	given	give	VERB
ejpam-2537	37	8	some	some	DET
ejpam-2537	37	9	definitions	definition	NOUN
ejpam-2537	37	10	in	in	ADP
ejpam-2537	37	11	section	section	NOUN
ejpam-2537	37	12	2	2	NUM
ejpam-2537	37	13	.	.	PUNCT
ejpam-2537	38	1	it	it	PRON
ejpam-2537	38	2	is	be	AUX
ejpam-2537	38	3	seen	see	VERB
ejpam-2537	38	4	that	that	SCONJ
ejpam-2537	38	5	the	the	DET
ejpam-2537	38	6	image	image	NOUN
ejpam-2537	38	7	of	of	ADP
ejpam-2537	38	8	a	a	DET
ejpam-2537	38	9	(	(	PUNCT
ejpam-2537	38	10	1+u)cyclic	1+u)cyclic	ADJ
ejpam-2537	38	11	code	code	NOUN
ejpam-2537	38	12	of	of	ADP
ejpam-2537	38	13	length	length	NOUN
ejpam-2537	38	14	n	n	CCONJ
ejpam-2537	38	15	over	over	ADP
ejpam-2537	38	16	r	r	NOUN
ejpam-2537	38	17	under	under	ADP
ejpam-2537	38	18	the	the	DET
ejpam-2537	38	19	map	map	NOUN
ejpam-2537	38	20	φ1,1	φ1,1	NOUN
ejpam-2537	38	21	is	be	AUX
ejpam-2537	38	22	a	a	DET
ejpam-2537	38	23	distance	distance	NOUN
ejpam-2537	38	24	invariant	invariant	ADJ
ejpam-2537	38	25	cyclic	cyclic	ADJ
ejpam-2537	38	26	code	code	NOUN
ejpam-2537	38	27	of	of	ADP
ejpam-2537	38	28	length	length	NOUN
ejpam-2537	38	29	2n	2n	NUM
ejpam-2537	38	30	over	over	ADP
ejpam-2537	38	31	f2	f2	PROPN
ejpam-2537	38	32	+	+	CCONJ
ejpam-2537	38	33	vf2	vf2	ADJ
ejpam-2537	38	34	.	.	PUNCT
ejpam-2537	39	1	it	it	PRON
ejpam-2537	39	2	is	be	AUX
ejpam-2537	39	3	shown	show	VERB
ejpam-2537	39	4	that	that	SCONJ
ejpam-2537	39	5	if	if	SCONJ
ejpam-2537	39	6	n	n	NOUN
ejpam-2537	39	7	is	be	AUX
ejpam-2537	39	8	odd	odd	ADJ
ejpam-2537	39	9	,	,	PUNCT
ejpam-2537	39	10	then	then	ADV
ejpam-2537	39	11	the	the	DET
ejpam-2537	39	12	image	image	NOUN
ejpam-2537	39	13	of	of	ADP
ejpam-2537	39	14	a	a	DET
ejpam-2537	39	15	cyclic	cyclic	ADJ
ejpam-2537	39	16	code	code	NOUN
ejpam-2537	39	17	of	of	ADP
ejpam-2537	39	18	length	length	NOUN
ejpam-2537	39	19	n	n	CCONJ
ejpam-2537	39	20	over	over	ADP
ejpam-2537	39	21	r	r	NOUN
ejpam-2537	39	22	under	under	ADP
ejpam-2537	39	23	the	the	DET
ejpam-2537	39	24	map	map	NOUN
ejpam-2537	39	25	φ1,1	φ1,1	NOUN
ejpam-2537	39	26	is	be	AUX
ejpam-2537	39	27	a	a	DET
ejpam-2537	39	28	permutation	permutation	NOUN
ejpam-2537	39	29	equivalent	equivalent	ADJ
ejpam-2537	39	30	to	to	ADP
ejpam-2537	39	31	cyclic	cyclic	PROPN
ejpam-2537	39	32	code	code	NOUN
ejpam-2537	39	33	of	of	ADP
ejpam-2537	39	34	length	length	NOUN
ejpam-2537	39	35	2n	2n	NUM
ejpam-2537	39	36	over	over	ADP
ejpam-2537	39	37	f2	f2	PROPN
ejpam-2537	39	38	+	+	CCONJ
ejpam-2537	39	39	vf2	vf2	ADJ
ejpam-2537	39	40	.	.	PUNCT
ejpam-2537	40	1	in	in	ADP
ejpam-2537	40	2	section	section	NOUN
ejpam-2537	40	3	3	3	NUM
ejpam-2537	40	4	,	,	PUNCT
ejpam-2537	40	5	it	it	PRON
ejpam-2537	40	6	is	be	AUX
ejpam-2537	40	7	given	give	VERB
ejpam-2537	40	8	a	a	DET
ejpam-2537	40	9	representation	representation	NOUN
ejpam-2537	40	10	of	of	ADP
ejpam-2537	40	11	a	a	DET
ejpam-2537	40	12	linear	linear	ADJ
ejpam-2537	40	13	code	code	NOUN
ejpam-2537	40	14	of	of	ADP
ejpam-2537	40	15	length	length	NOUN
ejpam-2537	40	16	n	n	CCONJ
ejpam-2537	40	17	over	over	ADP
ejpam-2537	40	18	r	r	NOUN
ejpam-2537	40	19	by	by	ADP
ejpam-2537	40	20	means	mean	NOUN
ejpam-2537	40	21	of	of	ADP
ejpam-2537	40	22	c1	c1	PROPN
ejpam-2537	40	23	and	and	CCONJ
ejpam-2537	40	24	c2	c2	PROPN
ejpam-2537	40	25	which	which	PRON
ejpam-2537	40	26	are	be	AUX
ejpam-2537	40	27	linear	linear	NOUN
ejpam-2537	40	28	codes	code	NOUN
ejpam-2537	40	29	of	of	ADP
ejpam-2537	40	30	length	length	NOUN
ejpam-2537	40	31	n	n	NOUN
ejpam-2537	40	32	over	over	ADP
ejpam-2537	40	33	f2+uf2	f2+uf2	NOUN
ejpam-2537	40	34	.	.	PUNCT
ejpam-2537	41	1	in	in	ADP
ejpam-2537	41	2	section	section	NOUN
ejpam-2537	41	3	4	4	NUM
ejpam-2537	41	4	,	,	PUNCT
ejpam-2537	41	5	it	it	PRON
ejpam-2537	41	6	is	be	AUX
ejpam-2537	41	7	characterized	characterize	VERB
ejpam-2537	41	8	codes	code	NOUN
ejpam-2537	41	9	over	over	ADP
ejpam-2537	41	10	f2	f2	PROPN
ejpam-2537	41	11	which	which	PRON
ejpam-2537	41	12	are	be	AUX
ejpam-2537	41	13	the	the	DET
ejpam-2537	41	14	gray	gray	ADJ
ejpam-2537	41	15	images	image	NOUN
ejpam-2537	41	16	of	of	ADP
ejpam-2537	41	17	(	(	PUNCT
ejpam-2537	41	18	1	1	NUM
ejpam-2537	41	19	+	+	NUM
ejpam-2537	41	20	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	41	21	codes	code	NOUN
ejpam-2537	41	22	or	or	CCONJ
ejpam-2537	41	23	cyclic	cyclic	ADJ
ejpam-2537	41	24	codes	code	NOUN
ejpam-2537	41	25	over	over	ADP
ejpam-2537	41	26	f2	f2	PROPN
ejpam-2537	41	27	+	+	CCONJ
ejpam-2537	41	28	uf2	uf2	NOUN
ejpam-2537	41	29	+	+	CCONJ
ejpam-2537	41	30	vf2	vf2	ADJ
ejpam-2537	41	31	.	.	PUNCT
ejpam-2537	42	1	it	it	PRON
ejpam-2537	42	2	is	be	AUX
ejpam-2537	42	3	proved	prove	VERB
ejpam-2537	42	4	that	that	SCONJ
ejpam-2537	42	5	the	the	DET
ejpam-2537	42	6	gray	gray	ADJ
ejpam-2537	42	7	image	image	NOUN
ejpam-2537	42	8	of	of	ADP
ejpam-2537	42	9	a	a	DET
ejpam-2537	42	10	linear	linear	NOUN
ejpam-2537	42	11	(	(	PUNCT
ejpam-2537	42	12	1	1	NUM
ejpam-2537	42	13	+	+	NUM
ejpam-2537	42	14	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	42	15	code	code	NOUN
ejpam-2537	42	16	over	over	ADP
ejpam-2537	42	17	f2	f2	PROPN
ejpam-2537	42	18	+	+	CCONJ
ejpam-2537	42	19	uf2	uf2	NOUN
ejpam-2537	42	20	+	+	CCONJ
ejpam-2537	42	21	vf2	vf2	NOUN
ejpam-2537	42	22	of	of	ADP
ejpam-2537	42	23	length	length	NOUN
ejpam-2537	42	24	n	n	PROPN
ejpam-2537	42	25	is	be	AUX
ejpam-2537	42	26	a	a	DET
ejpam-2537	42	27	binary	binary	ADJ
ejpam-2537	42	28	permutation	permutation	NOUN
ejpam-2537	42	29	equivalent	equivalent	ADJ
ejpam-2537	42	30	to	to	ADP
ejpam-2537	42	31	quasi	quasi	ADJ
ejpam-2537	42	32	-	-	ADJ
ejpam-2537	42	33	cyclic	cyclic	ADJ
ejpam-2537	42	34	codes	code	NOUN
ejpam-2537	42	35	of	of	ADP
ejpam-2537	42	36	index	index	NOUN
ejpam-2537	42	37	3	3	NUM
ejpam-2537	42	38	and	and	CCONJ
ejpam-2537	42	39	length	length	NOUN
ejpam-2537	42	40	3n	3n	NUM
ejpam-2537	42	41	over	over	ADP
ejpam-2537	42	42	f2	f2	PROPN
ejpam-2537	42	43	.	.	PUNCT
ejpam-2537	43	1	it	it	PRON
ejpam-2537	43	2	is	be	AUX
ejpam-2537	43	3	also	also	ADV
ejpam-2537	43	4	proved	prove	VERB
ejpam-2537	43	5	that	that	SCONJ
ejpam-2537	43	6	if	if	SCONJ
ejpam-2537	43	7	n	n	NOUN
ejpam-2537	43	8	is	be	AUX
ejpam-2537	43	9	odd	odd	ADJ
ejpam-2537	43	10	,	,	PUNCT
ejpam-2537	43	11	then	then	ADV
ejpam-2537	43	12	every	every	DET
ejpam-2537	43	13	code	code	NOUN
ejpam-2537	43	14	over	over	ADP
ejpam-2537	43	15	f2	f2	PROPN
ejpam-2537	43	16	which	which	PRON
ejpam-2537	43	17	is	be	AUX
ejpam-2537	43	18	the	the	DET
ejpam-2537	43	19	gray	gray	ADJ
ejpam-2537	43	20	image	image	NOUN
ejpam-2537	43	21	of	of	ADP
ejpam-2537	43	22	a	a	DET
ejpam-2537	43	23	linear	linear	ADJ
ejpam-2537	43	24	cyclic	cyclic	ADJ
ejpam-2537	43	25	code	code	NOUN
ejpam-2537	43	26	of	of	ADP
ejpam-2537	43	27	length	length	NOUN
ejpam-2537	43	28	n	n	PROPN
ejpam-2537	43	29	over	over	ADP
ejpam-2537	43	30	f2	f2	PROPN
ejpam-2537	43	31	+	+	CCONJ
ejpam-2537	43	32	uf2	uf2	NOUN
ejpam-2537	43	33	+	+	CCONJ
ejpam-2537	43	34	vf2	vf2	NOUN
ejpam-2537	43	35	is	be	AUX
ejpam-2537	43	36	permutation	permutation	NOUN
ejpam-2537	43	37	equivalent	equivalent	ADJ
ejpam-2537	43	38	to	to	ADP
ejpam-2537	43	39	a	a	DET
ejpam-2537	43	40	quasi	quasi	ADJ
ejpam-2537	43	41	-	-	ADJ
ejpam-2537	43	42	cyclic	cyclic	ADJ
ejpam-2537	43	43	code	code	NOUN
ejpam-2537	43	44	of	of	ADP
ejpam-2537	43	45	index	index	NOUN
ejpam-2537	43	46	3	3	NUM
ejpam-2537	43	47	.	.	NOUN
ejpam-2537	43	48	2	2	NUM
ejpam-2537	43	49	.	.	NUM
ejpam-2537	43	50	preliminaries	preliminary	NOUN
ejpam-2537	43	51	in	in	ADP
ejpam-2537	43	52	[	[	X
ejpam-2537	43	53	9	9	NUM
ejpam-2537	43	54	]	]	PUNCT
ejpam-2537	43	55	,	,	PUNCT
ejpam-2537	43	56	the	the	DET
ejpam-2537	43	57	commutative	commutative	ADJ
ejpam-2537	43	58	ring	ring	NOUN
ejpam-2537	43	59	r	r	NOUN
ejpam-2537	43	60	=	=	SYM
ejpam-2537	43	61	f2	f2	PROPN
ejpam-2537	43	62	+	+	CCONJ
ejpam-2537	43	63	uf2	uf2	NOUN
ejpam-2537	43	64	+	+	CCONJ
ejpam-2537	43	65	vf2,u2	vf2,u2	NOUN
ejpam-2537	43	66	=	=	SYM
ejpam-2537	43	67	0	0	NUM
ejpam-2537	43	68	,	,	PUNCT
ejpam-2537	43	69	v2	v2	PROPN
ejpam-2537	43	70	=	=	SYM
ejpam-2537	43	71	v	v	NOUN
ejpam-2537	43	72	,	,	PUNCT
ejpam-2537	44	1	uv	uv	NOUN
ejpam-2537	44	2	=	=	SYM
ejpam-2537	44	3	vu	vu	NOUN
ejpam-2537	44	4	=	=	SYM
ejpam-2537	44	5	0	0	NUM
ejpam-2537	44	6	is	be	AUX
ejpam-2537	44	7	given	give	VERB
ejpam-2537	44	8	.	.	PUNCT
ejpam-2537	45	1	then	then	ADV
ejpam-2537	45	2	r	r	NOUN
ejpam-2537	45	3	is	be	AUX
ejpam-2537	45	4	a	a	DET
ejpam-2537	45	5	finite	finite	NOUN
ejpam-2537	45	6	,	,	PUNCT
ejpam-2537	45	7	principal	principal	ADJ
ejpam-2537	45	8	ideal	ideal	ADJ
ejpam-2537	45	9	and	and	CCONJ
ejpam-2537	45	10	semilocal	semilocal	ADJ
ejpam-2537	45	11	ring	ring	NOUN
ejpam-2537	45	12	with	with	ADP
ejpam-2537	45	13	two	two	NUM
ejpam-2537	45	14	maximal	maximal	ADJ
ejpam-2537	45	15	ideals	ideal	NOUN
ejpam-2537	45	16	iu+v	iu+v	NOUN
ejpam-2537	45	17	and	and	CCONJ
ejpam-2537	45	18	i1+v	i1+v	NOUN
ejpam-2537	45	19	.	.	PUNCT
ejpam-2537	46	1	the	the	DET
ejpam-2537	46	2	quotient	quotient	NOUN
ejpam-2537	46	3	rings	ring	NOUN
ejpam-2537	46	4	r	r	NOUN
ejpam-2537	46	5	/	/	SYM
ejpam-2537	46	6	iu+v	iu+v	NOUN
ejpam-2537	46	7	and	and	CCONJ
ejpam-2537	46	8	r	r	X
ejpam-2537	46	9	/	/	SYM
ejpam-2537	46	10	i1+v	i1+v	NOUN
ejpam-2537	46	11	are	be	AUX
ejpam-2537	46	12	isomorphic	isomorphic	ADJ
ejpam-2537	46	13	to	to	ADP
ejpam-2537	46	14	f2	f2	PROPN
ejpam-2537	46	15	.	.	PUNCT
ejpam-2537	47	1	a	a	DET
ejpam-2537	47	2	direct	direct	ADJ
ejpam-2537	47	3	decomposition	decomposition	NOUN
ejpam-2537	47	4	of	of	ADP
ejpam-2537	47	5	r	r	NOUN
ejpam-2537	47	6	is	be	AUX
ejpam-2537	47	7	r=	r=	ADJ
ejpam-2537	47	8	iv	iv	NUM
ejpam-2537	47	9	⊕	⊕	PROPN
ejpam-2537	47	10	i1+v	i1+v	NOUN
ejpam-2537	47	11	.	.	PUNCT
ejpam-2537	48	1	the	the	DET
ejpam-2537	48	2	set	set	NOUN
ejpam-2537	48	3	of	of	ADP
ejpam-2537	48	4	units	unit	NOUN
ejpam-2537	48	5	of	of	ADP
ejpam-2537	48	6	r	r	NOUN
ejpam-2537	48	7	is	be	AUX
ejpam-2537	48	8	r∗	r∗	ADJ
ejpam-2537	48	9	=	=	PUNCT
ejpam-2537	48	10	{	{	PUNCT
ejpam-2537	48	11	1,1	1,1	NUM
ejpam-2537	48	12	+	+	NUM
ejpam-2537	48	13	u	u	NOUN
ejpam-2537	48	14	}	}	PUNCT
ejpam-2537	48	15	.	.	PUNCT
ejpam-2537	49	1	let	let	AUX
ejpam-2537	49	2	the	the	DET
ejpam-2537	49	3	c	c	NOUN
ejpam-2537	49	4	be	be	AUX
ejpam-2537	49	5	a	a	DET
ejpam-2537	49	6	code	code	NOUN
ejpam-2537	49	7	of	of	ADP
ejpam-2537	49	8	length	length	NOUN
ejpam-2537	49	9	n	n	CCONJ
ejpam-2537	49	10	over	over	ADP
ejpam-2537	49	11	r	r	NOUN
ejpam-2537	49	12	and	and	CCONJ
ejpam-2537	49	13	p(c	p(c	NOUN
ejpam-2537	49	14	)	)	PUNCT
ejpam-2537	49	15	be	be	VERB
ejpam-2537	49	16	its	its	PRON
ejpam-2537	49	17	polynomial	polynomial	ADJ
ejpam-2537	49	18	representation	representation	NOUN
ejpam-2537	49	19	,	,	PUNCT
ejpam-2537	49	20	i.e	i.e	PRON
ejpam-2537	49	21	,	,	PUNCT
ejpam-2537	49	22	p(c	p(c	NOUN
ejpam-2537	49	23	)	)	PUNCT
ejpam-2537	50	1	=	=	PRON
ejpam-2537	50	2	{	{	PUNCT
ejpam-2537	50	3	∑n−1	∑n−1	ADP
ejpam-2537	50	4	i=0	i=0	PROPN
ejpam-2537	50	5	ri	ri	PROPN
ejpam-2537	51	1	x	x	PUNCT
ejpam-2537	51	2	i	i	PRON
ejpam-2537	51	3	|(r0	|(r0	VERB
ejpam-2537	51	4	,	,	PUNCT
ejpam-2537	51	5	.	.	PUNCT
ejpam-2537	51	6	.	.	PUNCT
ejpam-2537	52	1	.	.	PUNCT
ejpam-2537	53	1	,	,	PUNCT
ejpam-2537	53	2	rn−1	rn−1	NOUN
ejpam-2537	53	3	)	)	PUNCT
ejpam-2537	53	4	∈	∈	PROPN
ejpam-2537	53	5	c	c	AUX
ejpam-2537	53	6	}	}	PUNCT
ejpam-2537	53	7	let	let	VERB
ejpam-2537	53	8	σ	σ	NOUN
ejpam-2537	53	9	and	and	CCONJ
ejpam-2537	53	10	ν	ν	PROPN
ejpam-2537	53	11	be	be	AUX
ejpam-2537	53	12	maps	map	NOUN
ejpam-2537	53	13	from	from	ADP
ejpam-2537	53	14	rn	rn	PROPN
ejpam-2537	53	15	to	to	PART
ejpam-2537	53	16	rn	rn	PROPN
ejpam-2537	53	17	given	give	VERB
ejpam-2537	53	18	by	by	ADP
ejpam-2537	53	19	σ(r0	σ(r0	NOUN
ejpam-2537	53	20	,	,	PUNCT
ejpam-2537	53	21	.	.	PUNCT
ejpam-2537	53	22	.	.	PUNCT
ejpam-2537	54	1	.	.	PUNCT
ejpam-2537	55	1	,	,	PUNCT
ejpam-2537	55	2	rn−1	rn−1	NOUN
ejpam-2537	55	3	)	)	PUNCT
ejpam-2537	55	4	=	=	SYM
ejpam-2537	55	5	(	(	PUNCT
ejpam-2537	55	6	rn−1	rn−1	PROPN
ejpam-2537	55	7	,	,	PUNCT
ejpam-2537	55	8	r0	r0	NOUN
ejpam-2537	55	9	,	,	PUNCT
ejpam-2537	55	10	.	.	PUNCT
ejpam-2537	55	11	.	.	PUNCT
ejpam-2537	56	1	.	.	PUNCT
ejpam-2537	57	1	,	,	PUNCT
ejpam-2537	57	2	rn−2	rn−2	PROPN
ejpam-2537	57	3	)	)	PUNCT
ejpam-2537	57	4	and	and	CCONJ
ejpam-2537	57	5	ν(r0	ν(r0	NOUN
ejpam-2537	57	6	,	,	PUNCT
ejpam-2537	57	7	.	.	PUNCT
ejpam-2537	57	8	.	.	PUNCT
ejpam-2537	58	1	.	.	PUNCT
ejpam-2537	59	1	,	,	PUNCT
ejpam-2537	59	2	rn−1	rn−1	NOUN
ejpam-2537	59	3	)	)	PUNCT
ejpam-2537	59	4	=	=	SYM
ejpam-2537	60	1	(	(	PUNCT
ejpam-2537	60	2	(	(	PUNCT
ejpam-2537	60	3	1	1	NUM
ejpam-2537	60	4	+	+	NUM
ejpam-2537	60	5	u)rn−1	u)rn−1	ADJ
ejpam-2537	60	6	,	,	PUNCT
ejpam-2537	60	7	r0	r0	NOUN
ejpam-2537	60	8	,	,	PUNCT
ejpam-2537	60	9	.	.	PUNCT
ejpam-2537	60	10	.	.	PUNCT
ejpam-2537	61	1	.	.	PUNCT
ejpam-2537	62	1	,	,	PUNCT
ejpam-2537	62	2	rn−2	rn−2	PROPN
ejpam-2537	62	3	)	)	PUNCT
ejpam-2537	62	4	then	then	ADV
ejpam-2537	62	5	c	c	PROPN
ejpam-2537	62	6	is	be	AUX
ejpam-2537	62	7	said	say	VERB
ejpam-2537	62	8	to	to	PART
ejpam-2537	62	9	be	be	AUX
ejpam-2537	62	10	cyclic	cyclic	ADJ
ejpam-2537	62	11	if	if	SCONJ
ejpam-2537	62	12	σ(c	σ(c	PROPN
ejpam-2537	62	13	)	)	PUNCT
ejpam-2537	63	1	=	=	SYM
ejpam-2537	63	2	c	c	NOUN
ejpam-2537	63	3	and	and	CCONJ
ejpam-2537	63	4	(	(	PUNCT
ejpam-2537	63	5	1	1	NUM
ejpam-2537	63	6	+	+	CCONJ
ejpam-2537	63	7	u)−	u)−	PROPN
ejpam-2537	63	8	cyclic	cyclic	NOUN
ejpam-2537	63	9	if	if	SCONJ
ejpam-2537	63	10	ν(c	ν(c	NOUN
ejpam-2537	63	11	)	)	PUNCT
ejpam-2537	64	1	=	=	PUNCT
ejpam-2537	64	2	c	c	X
ejpam-2537	64	3	.	.	PUNCT
ejpam-2537	65	1	a	a	DET
ejpam-2537	65	2	code	code	NOUN
ejpam-2537	65	3	c	c	NOUN
ejpam-2537	65	4	of	of	ADP
ejpam-2537	65	5	length	length	NOUN
ejpam-2537	65	6	n	n	CCONJ
ejpam-2537	65	7	over	over	ADP
ejpam-2537	65	8	r	r	NOUN
ejpam-2537	65	9	is	be	AUX
ejpam-2537	65	10	cyclic	cyclic	ADJ
ejpam-2537	65	11	if	if	SCONJ
ejpam-2537	65	12	and	and	CCONJ
ejpam-2537	65	13	only	only	ADV
ejpam-2537	65	14	if	if	SCONJ
ejpam-2537	65	15	p(c	p(c	NOUN
ejpam-2537	65	16	)	)	PUNCT
ejpam-2537	65	17	is	be	AUX
ejpam-2537	65	18	an	an	DET
ejpam-2537	65	19	ideal	ideal	NOUN
ejpam-2537	65	20	of	of	ADP
ejpam-2537	65	21	r[x]/〈xn−1	r[x]/〈xn−1	PROPN
ejpam-2537	65	22	〉	〉	NOUN
ejpam-2537	65	23	.	.	PUNCT
ejpam-2537	66	1	a	a	DET
ejpam-2537	66	2	code	code	NOUN
ejpam-2537	66	3	c	c	NOUN
ejpam-2537	66	4	of	of	ADP
ejpam-2537	66	5	length	length	NOUN
ejpam-2537	66	6	n	n	CCONJ
ejpam-2537	66	7	over	over	ADP
ejpam-2537	66	8	r	r	NOUN
ejpam-2537	66	9	is	be	AUX
ejpam-2537	66	10	(	(	PUNCT
ejpam-2537	66	11	1	1	NUM
ejpam-2537	66	12	+	+	CCONJ
ejpam-2537	66	13	u)−	u)−	PROPN
ejpam-2537	66	14	cyclic	cyclic	NOUN
ejpam-2537	66	15	if	if	SCONJ
ejpam-2537	66	16	and	and	CCONJ
ejpam-2537	66	17	only	only	ADV
ejpam-2537	66	18	if	if	SCONJ
ejpam-2537	66	19	p(c	p(c	NOUN
ejpam-2537	66	20	)	)	PUNCT
ejpam-2537	66	21	is	be	AUX
ejpam-2537	66	22	an	an	DET
ejpam-2537	66	23	ideal	ideal	NOUN
ejpam-2537	66	24	of	of	ADP
ejpam-2537	66	25	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2537	66	26	−	−	PROPN
ejpam-2537	66	27	(	(	PUNCT
ejpam-2537	66	28	1	1	NUM
ejpam-2537	66	29	+	+	NUM
ejpam-2537	66	30	u	u	NOUN
ejpam-2537	66	31	)	)	PUNCT
ejpam-2537	66	32	〉	〉	NOUN
ejpam-2537	66	33	.	.	PUNCT
ejpam-2537	67	1	let	let	VERB
ejpam-2537	67	2	a	a	DET
ejpam-2537	67	3	∈	∈	NOUN
ejpam-2537	67	4	f3n	f3n	PROPN
ejpam-2537	67	5	2	2	NUM
ejpam-2537	67	6	with	with	ADP
ejpam-2537	67	7	a	a	DET
ejpam-2537	67	8	=	=	SYM
ejpam-2537	67	9	(	(	PUNCT
ejpam-2537	67	10	a0	a0	PROPN
ejpam-2537	67	11	,	,	PUNCT
ejpam-2537	67	12	a1	a1	NOUN
ejpam-2537	67	13	,	,	PUNCT
ejpam-2537	67	14	.	.	PUNCT
ejpam-2537	67	15	.	.	PUNCT
ejpam-2537	68	1	.	.	PUNCT
ejpam-2537	69	1	,	,	PUNCT
ejpam-2537	69	2	a3n−1	a3n−1	PROPN
ejpam-2537	69	3	)	)	PUNCT
ejpam-2537	69	4	=	=	PUNCT
ejpam-2537	69	5	(	(	PUNCT
ejpam-2537	69	6	a	a	PRON
ejpam-2537	69	7	(	(	PUNCT
ejpam-2537	69	8	0)|a(1)|a(2	0)|a(1)|a(2	NUM
ejpam-2537	69	9	)	)	PUNCT
ejpam-2537	69	10	)	)	PUNCT
ejpam-2537	69	11	,	,	PUNCT
ejpam-2537	69	12	a(i	a(i	VERB
ejpam-2537	69	13	)	)	PUNCT
ejpam-2537	70	1	∈	∈	PROPN
ejpam-2537	70	2	f	f	PROPN
ejpam-2537	70	3	n	n	PRON
ejpam-2537	70	4	2	2	NUM
ejpam-2537	70	5	for	for	ADP
ejpam-2537	70	6	all	all	PRON
ejpam-2537	70	7	i	i	PRON
ejpam-2537	71	1	=	=	NOUN
ejpam-2537	71	2	0,1,2	0,1,2	X
ejpam-2537	71	3	.	.	PUNCT
ejpam-2537	71	4	let	let	VERB
ejpam-2537	71	5	σ⊗3	σ⊗3	NOUN
ejpam-2537	71	6	be	be	AUX
ejpam-2537	71	7	the	the	DET
ejpam-2537	71	8	map	map	NOUN
ejpam-2537	71	9	from	from	ADP
ejpam-2537	71	10	f3n	f3n	PROPN
ejpam-2537	71	11	2	2	NUM
ejpam-2537	71	12	to	to	ADP
ejpam-2537	71	13	f3n	f3n	PROPN
ejpam-2537	71	14	2	2	NUM
ejpam-2537	71	15	given	give	VERB
ejpam-2537	71	16	by	by	ADP
ejpam-2537	71	17	σ⊗3(a	σ⊗3(a	ADJ
ejpam-2537	71	18	)	)	PUNCT
ejpam-2537	72	1	=	=	SYM
ejpam-2537	72	2	(	(	PUNCT
ejpam-2537	72	3	σ̃(a(0))|σ̃(a(1))|σ̃(a(2	σ̃(a(0))|σ̃(a(1))|σ̃(a(2	NOUN
ejpam-2537	72	4	)	)	PUNCT
ejpam-2537	72	5	)	)	PUNCT
ejpam-2537	72	6	)	)	PUNCT
ejpam-2537	72	7	where	where	SCONJ
ejpam-2537	72	8	σ̃	σ̃	PROPN
ejpam-2537	72	9	is	be	AUX
ejpam-2537	72	10	the	the	DET
ejpam-2537	72	11	a.	a.	NOUN
ejpam-2537	72	12	dertli	dertli	PROPN
ejpam-2537	72	13	,	,	PUNCT
ejpam-2537	72	14	y.	y.	PROPN
ejpam-2537	72	15	cengellenmis	cengellenmis	PROPN
ejpam-2537	72	16	/	/	SYM
ejpam-2537	72	17	eur	eur	PROPN
ejpam-2537	72	18	.	.	PUNCT
ejpam-2537	73	1	j.	j.	PROPN
ejpam-2537	73	2	pure	pure	PROPN
ejpam-2537	73	3	appl	appl	PROPN
ejpam-2537	73	4	.	.	PROPN
ejpam-2537	73	5	math	math	PROPN
ejpam-2537	73	6	,	,	PUNCT
ejpam-2537	73	7	9	9	NUM
ejpam-2537	73	8	(	(	PUNCT
ejpam-2537	73	9	2016	2016	NUM
ejpam-2537	73	10	)	)	PUNCT
ejpam-2537	73	11	,	,	PUNCT
ejpam-2537	73	12	305	305	NUM
ejpam-2537	73	13	-	-	SYM
ejpam-2537	73	14	313	313	NUM
ejpam-2537	73	15	307	307	NUM
ejpam-2537	73	16	usual	usual	ADJ
ejpam-2537	73	17	cyclic	cyclic	ADJ
ejpam-2537	73	18	shift	shift	NOUN
ejpam-2537	73	19	(	(	PUNCT
ejpam-2537	73	20	c0	c0	NOUN
ejpam-2537	73	21	,	,	PUNCT
ejpam-2537	73	22	.	.	PUNCT
ejpam-2537	73	23	.	.	PUNCT
ejpam-2537	74	1	.	.	PUNCT
ejpam-2537	75	1	,	,	PUNCT
ejpam-2537	75	2	cn−1	cn−1	NOUN
ejpam-2537	75	3	)	)	PUNCT
ejpam-2537	75	4	7−→	7−→	NOUN
ejpam-2537	75	5	(	(	PUNCT
ejpam-2537	75	6	cn−1	cn−1	PROPN
ejpam-2537	75	7	,	,	PUNCT
ejpam-2537	75	8	c0	c0	NOUN
ejpam-2537	75	9	,	,	PUNCT
ejpam-2537	75	10	.	.	PUNCT
ejpam-2537	75	11	.	.	PUNCT
ejpam-2537	75	12	.	.	PUNCT
ejpam-2537	76	1	,	,	PUNCT
ejpam-2537	76	2	cn−2	cn−2	PROPN
ejpam-2537	76	3	)	)	PUNCT
ejpam-2537	76	4	on	on	ADP
ejpam-2537	76	5	f	f	PROPN
ejpam-2537	76	6	n	n	PRON
ejpam-2537	76	7	2	2	NUM
ejpam-2537	76	8	.	.	PUNCT
ejpam-2537	77	1	a	a	DET
ejpam-2537	77	2	code	code	NOUN
ejpam-2537	77	3	c̃	c̃	PROPN
ejpam-2537	77	4	of	of	ADP
ejpam-2537	77	5	length	length	NOUN
ejpam-2537	77	6	3n	3n	NUM
ejpam-2537	77	7	over	over	ADP
ejpam-2537	77	8	f2	f2	PROPN
ejpam-2537	77	9	is	be	AUX
ejpam-2537	77	10	said	say	VERB
ejpam-2537	77	11	to	to	PART
ejpam-2537	77	12	be	be	AUX
ejpam-2537	77	13	quasi	quasi	ADJ
ejpam-2537	77	14	-	-	ADJ
ejpam-2537	77	15	cyclic	cyclic	ADJ
ejpam-2537	77	16	of	of	ADP
ejpam-2537	77	17	index	index	NOUN
ejpam-2537	77	18	3	3	NUM
ejpam-2537	77	19	if	if	SCONJ
ejpam-2537	77	20	σ⊗3(c̃	σ⊗3(c̃	NUM
ejpam-2537	77	21	)	)	PUNCT
ejpam-2537	77	22	=	=	SYM
ejpam-2537	77	23	c̃	c̃	PROPN
ejpam-2537	77	24	.	.	PUNCT
ejpam-2537	78	1	the	the	DET
ejpam-2537	78	2	hamming	hamming	NOUN
ejpam-2537	78	3	weight	weight	NOUN
ejpam-2537	78	4	wh(x	wh(x	PUNCT
ejpam-2537	78	5	)	)	PUNCT
ejpam-2537	78	6	of	of	ADP
ejpam-2537	78	7	a	a	DET
ejpam-2537	78	8	codeword	codeword	NOUN
ejpam-2537	78	9	x	x	PUNCT
ejpam-2537	78	10	is	be	AUX
ejpam-2537	78	11	the	the	DET
ejpam-2537	78	12	number	number	NOUN
ejpam-2537	78	13	of	of	ADP
ejpam-2537	78	14	nonzero	nonzero	PROPN
ejpam-2537	78	15	components	component	NOUN
ejpam-2537	78	16	in	in	ADP
ejpam-2537	78	17	x	x	X
ejpam-2537	78	18	.	.	PUNCT
ejpam-2537	79	1	the	the	DET
ejpam-2537	79	2	hamming	hamming	NOUN
ejpam-2537	79	3	distance	distance	NOUN
ejpam-2537	79	4	d(x	d(x	PROPN
ejpam-2537	79	5	,	,	PUNCT
ejpam-2537	79	6	y	y	PROPN
ejpam-2537	79	7	)	)	PUNCT
ejpam-2537	79	8	between	between	ADP
ejpam-2537	79	9	two	two	NUM
ejpam-2537	79	10	codewords	codeword	NOUN
ejpam-2537	79	11	x	x	PUNCT
ejpam-2537	79	12	and	and	CCONJ
ejpam-2537	79	13	y	y	PROPN
ejpam-2537	79	14	is	be	AUX
ejpam-2537	79	15	the	the	DET
ejpam-2537	79	16	hamming	hamming	ADJ
ejpam-2537	79	17	weight	weight	NOUN
ejpam-2537	79	18	of	of	ADP
ejpam-2537	79	19	the	the	DET
ejpam-2537	79	20	codewords	codeword	NOUN
ejpam-2537	79	21	x	x	PUNCT
ejpam-2537	79	22	−	−	PROPN
ejpam-2537	79	23	y	y	NOUN
ejpam-2537	79	24	.	.	PUNCT
ejpam-2537	80	1	the	the	DET
ejpam-2537	80	2	minimum	minimum	ADJ
ejpam-2537	80	3	hamming	hamming	NOUN
ejpam-2537	80	4	distance	distance	NOUN
ejpam-2537	80	5	dh	dh	NOUN
ejpam-2537	80	6	of	of	ADP
ejpam-2537	80	7	c	c	PROPN
ejpam-2537	80	8	is	be	AUX
ejpam-2537	80	9	defined	define	VERB
ejpam-2537	80	10	as	as	ADP
ejpam-2537	80	11	min{dh(x	min{dh(x	PROPN
ejpam-2537	80	12	,	,	PUNCT
ejpam-2537	80	13	y)|x	y)|x	NOUN
ejpam-2537	80	14	,	,	PUNCT
ejpam-2537	80	15	y	y	PROPN
ejpam-2537	80	16	∈	∈	PROPN
ejpam-2537	80	17	c	c	NOUN
ejpam-2537	80	18	,	,	PUNCT
ejpam-2537	80	19	x	x	PROPN
ejpam-2537	80	20	6=	6=	ADP
ejpam-2537	80	21	y	y	NOUN
ejpam-2537	80	22	}	}	PUNCT
ejpam-2537	80	23	.	.	PUNCT
ejpam-2537	81	1	let	let	VERB
ejpam-2537	81	2	x	x	PUNCT
ejpam-2537	81	3	=	=	SYM
ejpam-2537	81	4	(	(	PUNCT
ejpam-2537	81	5	x1	x1	PROPN
ejpam-2537	81	6	,	,	PUNCT
ejpam-2537	81	7	.	.	PUNCT
ejpam-2537	81	8	.	.	PUNCT
ejpam-2537	81	9	.	.	PUNCT
ejpam-2537	82	1	,	,	PUNCT
ejpam-2537	82	2	xn	xn	X
ejpam-2537	82	3	)	)	PUNCT
ejpam-2537	82	4	and	and	CCONJ
ejpam-2537	82	5	y	y	PROPN
ejpam-2537	82	6	=	=	SYM
ejpam-2537	82	7	(	(	PUNCT
ejpam-2537	82	8	y1	y1	INTJ
ejpam-2537	82	9	,	,	PUNCT
ejpam-2537	82	10	.	.	PUNCT
ejpam-2537	82	11	.	.	PUNCT
ejpam-2537	82	12	.	.	PUNCT
ejpam-2537	83	1	,	,	PUNCT
ejpam-2537	83	2	yn	yn	PROPN
ejpam-2537	83	3	)	)	PUNCT
ejpam-2537	83	4	be	be	VERB
ejpam-2537	83	5	two	two	NUM
ejpam-2537	83	6	vectors	vector	NOUN
ejpam-2537	83	7	of	of	ADP
ejpam-2537	83	8	rn	rn	PROPN
ejpam-2537	83	9	.	.	PUNCT
ejpam-2537	84	1	the	the	DET
ejpam-2537	84	2	euclidean	euclidean	ADJ
ejpam-2537	84	3	inner	inner	ADJ
ejpam-2537	84	4	product	product	NOUN
ejpam-2537	84	5	of	of	ADP
ejpam-2537	84	6	x	x	PUNCT
ejpam-2537	84	7	and	and	CCONJ
ejpam-2537	84	8	y	y	PROPN
ejpam-2537	84	9	is	be	AUX
ejpam-2537	84	10	defined	define	VERB
ejpam-2537	84	11	x	x	PUNCT
ejpam-2537	84	12	y	y	PROPN
ejpam-2537	84	13	=	=	SYM
ejpam-2537	84	14	n	n	PROPN
ejpam-2537	84	15	∑	∑	ADV
ejpam-2537	84	16	i=1	i=1	PROPN
ejpam-2537	84	17	x	x	PUNCT
ejpam-2537	85	1	i	i	PRON
ejpam-2537	85	2	yi	yi	PROPN
ejpam-2537	85	3	.	.	PUNCT
ejpam-2537	86	1	the	the	DET
ejpam-2537	86	2	dual	dual	PROPN
ejpam-2537	86	3	code	code	NOUN
ejpam-2537	86	4	c⊥	c⊥	NOUN
ejpam-2537	86	5	of	of	ADP
ejpam-2537	86	6	c	c	PROPN
ejpam-2537	86	7	is	be	AUX
ejpam-2537	86	8	defined	define	VERB
ejpam-2537	86	9	as	as	ADP
ejpam-2537	86	10	c⊥	c⊥	X
ejpam-2537	86	11	=	=	PUNCT
ejpam-2537	86	12	{	{	PUNCT
ejpam-2537	86	13	x	x	PUNCT
ejpam-2537	86	14	∈	∈	NOUN
ejpam-2537	86	15	rn|xc	rn|xc	NOUN
ejpam-2537	86	16	=	=	NOUN
ejpam-2537	86	17	0	0	NUM
ejpam-2537	86	18	for	for	ADP
ejpam-2537	86	19	all	all	DET
ejpam-2537	86	20	c	c	NOUN
ejpam-2537	86	21	∈	∈	PROPN
ejpam-2537	86	22	c	c	NOUN
ejpam-2537	86	23	}	}	PUNCT
ejpam-2537	86	24	.	.	PUNCT
ejpam-2537	87	1	c	c	PROPN
ejpam-2537	87	2	is	be	AUX
ejpam-2537	87	3	said	say	VERB
ejpam-2537	87	4	to	to	PART
ejpam-2537	87	5	be	be	AUX
ejpam-2537	87	6	self	self	NOUN
ejpam-2537	87	7	orthogonal	orthogonal	ADJ
ejpam-2537	87	8	if	if	SCONJ
ejpam-2537	87	9	c	c	PROPN
ejpam-2537	87	10	⊆	⊆	NUM
ejpam-2537	87	11	c⊥	c⊥	NOUN
ejpam-2537	87	12	and	and	CCONJ
ejpam-2537	87	13	c	c	PROPN
ejpam-2537	87	14	is	be	AUX
ejpam-2537	87	15	said	say	VERB
ejpam-2537	87	16	to	to	PART
ejpam-2537	87	17	be	be	AUX
ejpam-2537	87	18	self	self	NOUN
ejpam-2537	87	19	dual	dual	ADJ
ejpam-2537	87	20	if	if	SCONJ
ejpam-2537	87	21	c	c	NOUN
ejpam-2537	87	22	=	=	SYM
ejpam-2537	87	23	c⊥.	c⊥.	NOUN
ejpam-2537	87	24	recall	recall	NOUN
ejpam-2537	87	25	that	that	SCONJ
ejpam-2537	87	26	the	the	DET
ejpam-2537	87	27	gray	gray	ADJ
ejpam-2537	87	28	map	map	NOUN
ejpam-2537	87	29	φ1	φ1	PROPN
ejpam-2537	87	30	on	on	ADP
ejpam-2537	87	31	f2	f2	PROPN
ejpam-2537	87	32	+	+	CCONJ
ejpam-2537	87	33	uf2,u2	uf2,u2	NOUN
ejpam-2537	87	34	=	=	SYM
ejpam-2537	87	35	0	0	NUM
ejpam-2537	87	36	is	be	AUX
ejpam-2537	87	37	defined	define	VERB
ejpam-2537	87	38	as	as	ADP
ejpam-2537	87	39	φ1(z	φ1(z	NOUN
ejpam-2537	87	40	)	)	PUNCT
ejpam-2537	87	41	=	=	SYM
ejpam-2537	87	42	(	(	PUNCT
ejpam-2537	87	43	r	r	NOUN
ejpam-2537	87	44	,	,	PUNCT
ejpam-2537	87	45	r	r	NOUN
ejpam-2537	87	46	+	+	NOUN
ejpam-2537	87	47	q	q	X
ejpam-2537	87	48	)	)	PUNCT
ejpam-2537	87	49	where	where	SCONJ
ejpam-2537	87	50	z	z	NOUN
ejpam-2537	87	51	=	=	SYM
ejpam-2537	87	52	q+ur	q+ur	NOUN
ejpam-2537	87	53	with	with	ADP
ejpam-2537	87	54	r	r	NOUN
ejpam-2537	87	55	,	,	PUNCT
ejpam-2537	87	56	q	q	NOUN
ejpam-2537	87	57	∈	∈	PROPN
ejpam-2537	87	58	f2	f2	PROPN
ejpam-2537	87	59	and	and	CCONJ
ejpam-2537	87	60	the	the	DET
ejpam-2537	87	61	gray	gray	ADJ
ejpam-2537	87	62	mapφ2	mapφ2	NOUN
ejpam-2537	87	63	on	on	ADP
ejpam-2537	87	64	f2+vf2	f2+vf2	NUM
ejpam-2537	87	65	,	,	PUNCT
ejpam-2537	87	66	v2	v2	PROPN
ejpam-2537	87	67	=	=	SYM
ejpam-2537	87	68	v	v	NOUN
ejpam-2537	87	69	is	be	AUX
ejpam-2537	87	70	defined	define	VERB
ejpam-2537	87	71	asφ2(s	asφ2(s	NUM
ejpam-2537	87	72	)	)	PUNCT
ejpam-2537	87	73	=	=	PUNCT
ejpam-2537	87	74	(	(	PUNCT
ejpam-2537	87	75	m	m	PROPN
ejpam-2537	87	76	,	,	PUNCT
ejpam-2537	87	77	m+t	m+t	NUM
ejpam-2537	87	78	)	)	PUNCT
ejpam-2537	87	79	where	where	SCONJ
ejpam-2537	87	80	s	s	AUX
ejpam-2537	87	81	=	=	X
ejpam-2537	87	82	m+	m+	PROPN
ejpam-2537	87	83	vt	vt	PROPN
ejpam-2537	87	84	with	with	ADP
ejpam-2537	87	85	m	m	PROPN
ejpam-2537	87	86	,	,	PUNCT
ejpam-2537	87	87	t	t	PROPN
ejpam-2537	87	88	∈	∈	PROPN
ejpam-2537	87	89	f2	f2	PROPN
ejpam-2537	87	90	.	.	PUNCT
ejpam-2537	88	1	the	the	DET
ejpam-2537	88	2	maps	map	NOUN
ejpam-2537	88	3	φ1	φ1	PROPN
ejpam-2537	88	4	and	and	CCONJ
ejpam-2537	88	5	φ2	φ2	PROPN
ejpam-2537	88	6	can	can	AUX
ejpam-2537	88	7	be	be	AUX
ejpam-2537	88	8	extended	extend	VERB
ejpam-2537	88	9	to	to	ADP
ejpam-2537	88	10	(	(	PUNCT
ejpam-2537	88	11	f2	f2	PROPN
ejpam-2537	88	12	+	+	NUM
ejpam-2537	88	13	uf2	uf2	NOUN
ejpam-2537	88	14	)	)	PUNCT
ejpam-2537	88	15	n	n	NOUN
ejpam-2537	88	16	and	and	CCONJ
ejpam-2537	88	17	(	(	PUNCT
ejpam-2537	88	18	f2	f2	PROPN
ejpam-2537	88	19	+	+	CCONJ
ejpam-2537	88	20	vf2	vf2	ADJ
ejpam-2537	88	21	)	)	PUNCT
ejpam-2537	88	22	n	n	CCONJ
ejpam-2537	88	23	,	,	PUNCT
ejpam-2537	88	24	respectively	respectively	ADV
ejpam-2537	88	25	as	as	SCONJ
ejpam-2537	88	26	follows	follow	VERB
ejpam-2537	88	27	,	,	PUNCT
ejpam-2537	88	28	φ1	φ1	PROPN
ejpam-2537	88	29	:(	:(	PROPN
ejpam-2537	89	1	f2	f2	PROPN
ejpam-2537	89	2	+	+	X
ejpam-2537	89	3	uf2	uf2	NOUN
ejpam-2537	89	4	)	)	PUNCT
ejpam-2537	89	5	n→	n→	ADV
ejpam-2537	89	6	f2n	f2n	PROPN
ejpam-2537	89	7	2	2	NUM
ejpam-2537	89	8	(	(	PUNCT
ejpam-2537	89	9	z0	z0	PROPN
ejpam-2537	89	10	,	,	PUNCT
ejpam-2537	89	11	.	.	PUNCT
ejpam-2537	89	12	.	.	PUNCT
ejpam-2537	90	1	.	.	PUNCT
ejpam-2537	91	1	,	,	PUNCT
ejpam-2537	91	2	zn−1	zn−1	PROPN
ejpam-2537	91	3	)	)	PUNCT
ejpam-2537	91	4	7→	7→	PROPN
ejpam-2537	91	5	(	(	PUNCT
ejpam-2537	91	6	r0	r0	NOUN
ejpam-2537	91	7	,	,	PUNCT
ejpam-2537	91	8	.	.	PUNCT
ejpam-2537	91	9	.	.	PUNCT
ejpam-2537	92	1	.	.	PUNCT
ejpam-2537	93	1	,	,	PUNCT
ejpam-2537	93	2	rn−1	rn−1	PROPN
ejpam-2537	93	3	,	,	PUNCT
ejpam-2537	93	4	r0	r0	NOUN
ejpam-2537	93	5	⊕	⊕	PROPN
ejpam-2537	93	6	q0	q0	PROPN
ejpam-2537	93	7	,	,	PUNCT
ejpam-2537	93	8	.	.	PUNCT
ejpam-2537	93	9	.	.	PUNCT
ejpam-2537	94	1	.	.	PUNCT
ejpam-2537	95	1	,	,	PUNCT
ejpam-2537	95	2	rn−1	rn−1	PROPN
ejpam-2537	95	3	⊕	⊕	PROPN
ejpam-2537	95	4	qn−1	qn−1	PROPN
ejpam-2537	95	5	)	)	PUNCT
ejpam-2537	95	6	φ2	φ2	NOUN
ejpam-2537	95	7	:(	:(	PROPN
ejpam-2537	96	1	f2	f2	PROPN
ejpam-2537	96	2	+	+	CCONJ
ejpam-2537	96	3	vf2	vf2	NUM
ejpam-2537	96	4	)	)	PUNCT
ejpam-2537	96	5	n→	n→	ADV
ejpam-2537	96	6	f2n	f2n	ADJ
ejpam-2537	96	7	2	2	NUM
ejpam-2537	96	8	(	(	PUNCT
ejpam-2537	96	9	s0	s0	PROPN
ejpam-2537	96	10	,	,	PUNCT
ejpam-2537	96	11	.	.	PUNCT
ejpam-2537	96	12	.	.	PUNCT
ejpam-2537	97	1	.	.	PUNCT
ejpam-2537	98	1	,	,	PUNCT
ejpam-2537	98	2	sn−1	sn−1	PROPN
ejpam-2537	98	3	)	)	PUNCT
ejpam-2537	98	4	7→	7→	PROPN
ejpam-2537	98	5	(	(	PUNCT
ejpam-2537	98	6	m0	m0	NOUN
ejpam-2537	98	7	,	,	PUNCT
ejpam-2537	98	8	.	.	PUNCT
ejpam-2537	98	9	.	.	PUNCT
ejpam-2537	98	10	.	.	PUNCT
ejpam-2537	99	1	,	,	PUNCT
ejpam-2537	99	2	mn−1	mn−1	PROPN
ejpam-2537	99	3	,	,	PUNCT
ejpam-2537	99	4	m0	m0	PROPN
ejpam-2537	99	5	⊕	⊕	PROPN
ejpam-2537	99	6	t0	t0	PROPN
ejpam-2537	99	7	,	,	PUNCT
ejpam-2537	99	8	.	.	PUNCT
ejpam-2537	99	9	.	.	PUNCT
ejpam-2537	99	10	.	.	PUNCT
ejpam-2537	100	1	,	,	PUNCT
ejpam-2537	100	2	mn−1	mn−1	PROPN
ejpam-2537	100	3	⊕	⊕	PROPN
ejpam-2537	100	4	tn−1	tn−1	PROPN
ejpam-2537	100	5	)	)	PUNCT
ejpam-2537	101	1	where	where	SCONJ
ejpam-2537	101	2	zi	zi	NOUN
ejpam-2537	101	3	=	=	PUNCT
ejpam-2537	101	4	ri+uqi	ri+uqi	PROPN
ejpam-2537	101	5	,	,	PUNCT
ejpam-2537	101	6	si	si	X
ejpam-2537	101	7	=	=	PUNCT
ejpam-2537	101	8	mi+vt	mi+vt	NOUN
ejpam-2537	101	9	i	i	PRON
ejpam-2537	101	10	and	and	CCONJ
ejpam-2537	101	11	qi	qi	PROPN
ejpam-2537	101	12	,	,	PUNCT
ejpam-2537	101	13	ri	ri	PROPN
ejpam-2537	101	14	,	,	PUNCT
ejpam-2537	101	15	mi	mi	PROPN
ejpam-2537	101	16	,	,	PUNCT
ejpam-2537	101	17	t	t	PROPN
ejpam-2537	101	18	i	i	PRON
ejpam-2537	101	19	∈	∈	PROPN
ejpam-2537	101	20	f2	f2	PROPN
ejpam-2537	101	21	for	for	ADP
ejpam-2537	101	22	0≤	0≤	NUM
ejpam-2537	102	1	i	i	PRON
ejpam-2537	102	2	≤	≤	ADV
ejpam-2537	102	3	n−1	n−1	PROPN
ejpam-2537	102	4	and	and	CCONJ
ejpam-2537	102	5	⊕	⊕	PROPN
ejpam-2537	102	6	is	be	AUX
ejpam-2537	102	7	componentwise	componentwise	NOUN
ejpam-2537	102	8	addition	addition	NOUN
ejpam-2537	102	9	in	in	ADP
ejpam-2537	102	10	f2	f2	PROPN
ejpam-2537	102	11	.	.	PUNCT
ejpam-2537	103	1	each	each	DET
ejpam-2537	103	2	element	element	NOUN
ejpam-2537	103	3	c	c	PROPN
ejpam-2537	103	4	∈	∈	NOUN
ejpam-2537	103	5	r	r	NOUN
ejpam-2537	103	6	=	=	SYM
ejpam-2537	103	7	f2	f2	PROPN
ejpam-2537	103	8	+	+	NUM
ejpam-2537	103	9	uf2	uf2	NOUN
ejpam-2537	103	10	+	+	CCONJ
ejpam-2537	103	11	vf2	vf2	NOUN
ejpam-2537	103	12	can	can	AUX
ejpam-2537	103	13	be	be	AUX
ejpam-2537	103	14	expressed	express	VERB
ejpam-2537	103	15	c	c	NOUN
ejpam-2537	103	16	=	=	PUNCT
ejpam-2537	103	17	a	a	PROPN
ejpam-2537	104	1	+	+	X
ejpam-2537	104	2	ub	ub	INTJ
ejpam-2537	104	3	where	where	SCONJ
ejpam-2537	104	4	a	a	PRON
ejpam-2537	104	5	,	,	PUNCT
ejpam-2537	104	6	b	b	PROPN
ejpam-2537	104	7	∈	∈	PROPN
ejpam-2537	104	8	f2	f2	PROPN
ejpam-2537	104	9	+	+	CCONJ
ejpam-2537	104	10	vf2	vf2	ADJ
ejpam-2537	104	11	.	.	PUNCT
ejpam-2537	105	1	the	the	DET
ejpam-2537	105	2	map	map	NOUN
ejpam-2537	105	3	φ1,1	φ1,1	NOUN
ejpam-2537	105	4	is	be	AUX
ejpam-2537	105	5	defined	define	VERB
ejpam-2537	105	6	as	as	ADP
ejpam-2537	105	7	φ1,1	φ1,1	NOUN
ejpam-2537	105	8	:	:	PUNCT
ejpam-2537	105	9	rn→	rn→	X
ejpam-2537	105	10	(	(	PUNCT
ejpam-2537	105	11	f2	f2	PROPN
ejpam-2537	105	12	+	+	CCONJ
ejpam-2537	105	13	vf2	vf2	ADJ
ejpam-2537	105	14	)	)	PUNCT
ejpam-2537	105	15	2n	2n	NUM
ejpam-2537	105	16	(	(	PUNCT
ejpam-2537	105	17	c0	c0	NOUN
ejpam-2537	105	18	,	,	PUNCT
ejpam-2537	105	19	.	.	PUNCT
ejpam-2537	105	20	.	.	PUNCT
ejpam-2537	106	1	.	.	PUNCT
ejpam-2537	107	1	,	,	PUNCT
ejpam-2537	107	2	cn−1	cn−1	NOUN
ejpam-2537	107	3	)	)	PUNCT
ejpam-2537	107	4	7→	7→	PROPN
ejpam-2537	107	5	(	(	PUNCT
ejpam-2537	107	6	b0	b0	NOUN
ejpam-2537	107	7	,	,	PUNCT
ejpam-2537	107	8	.	.	PUNCT
ejpam-2537	107	9	.	.	PUNCT
ejpam-2537	108	1	.	.	PUNCT
ejpam-2537	109	1	,	,	PUNCT
ejpam-2537	109	2	bn−1	bn−1	NOUN
ejpam-2537	109	3	,	,	PUNCT
ejpam-2537	109	4	b0	b0	NOUN
ejpam-2537	109	5	+	+	CCONJ
ejpam-2537	109	6	a0	a0	NOUN
ejpam-2537	109	7	,	,	PUNCT
ejpam-2537	109	8	.	.	PUNCT
ejpam-2537	109	9	.	.	PUNCT
ejpam-2537	110	1	.	.	PUNCT
ejpam-2537	111	1	,	,	PUNCT
ejpam-2537	111	2	bn−1	bn−1	PRON
ejpam-2537	111	3	+	+	CCONJ
ejpam-2537	111	4	an−1	an−1	ADJ
ejpam-2537	111	5	)	)	PUNCT
ejpam-2537	111	6	where	where	SCONJ
ejpam-2537	111	7	ci	ci	NOUN
ejpam-2537	111	8	=	=	VERB
ejpam-2537	111	9	ai	ai	VERB
ejpam-2537	111	10	+	+	X
ejpam-2537	111	11	ubi	ubi	ADJ
ejpam-2537	111	12	with	with	ADP
ejpam-2537	111	13	ai	ai	PROPN
ejpam-2537	111	14	,	,	PUNCT
ejpam-2537	111	15	bi	bi	NOUN
ejpam-2537	111	16	∈	∈	PROPN
ejpam-2537	111	17	f2	f2	PROPN
ejpam-2537	111	18	+	+	CCONJ
ejpam-2537	111	19	vf2	vf2	NOUN
ejpam-2537	111	20	for	for	ADP
ejpam-2537	111	21	0≤	0≤	ADJ
ejpam-2537	112	1	i	i	PRON
ejpam-2537	112	2	≤	≤	ADJ
ejpam-2537	112	3	n−	n−	NOUN
ejpam-2537	112	4	1	1	NUM
ejpam-2537	112	5	.	.	PUNCT
ejpam-2537	113	1	each	each	DET
ejpam-2537	113	2	element	element	NOUN
ejpam-2537	113	3	c	c	PROPN
ejpam-2537	113	4	∈	∈	PROPN
ejpam-2537	113	5	r=	r=	PROPN
ejpam-2537	113	6	f2	f2	PROPN
ejpam-2537	113	7	+	+	CCONJ
ejpam-2537	113	8	uf2	uf2	NOUN
ejpam-2537	113	9	+	+	CCONJ
ejpam-2537	113	10	vf2	vf2	NOUN
ejpam-2537	113	11	can	can	AUX
ejpam-2537	113	12	be	be	AUX
ejpam-2537	113	13	also	also	ADV
ejpam-2537	113	14	expressed	express	VERB
ejpam-2537	113	15	c	c	NOUN
ejpam-2537	113	16	=	=	PUNCT
ejpam-2537	113	17	a′	a′	PROPN
ejpam-2537	113	18	+	+	NUM
ejpam-2537	113	19	vb′	vb′	NOUN
ejpam-2537	113	20	where	where	SCONJ
ejpam-2537	113	21	a′	a′	PROPN
ejpam-2537	113	22	,	,	PUNCT
ejpam-2537	113	23	b′	b′	NUM
ejpam-2537	113	24	∈	∈	NOUN
ejpam-2537	113	25	f2	f2	PROPN
ejpam-2537	113	26	+	+	X
ejpam-2537	113	27	uf2	uf2	NOUN
ejpam-2537	113	28	.	.	PUNCT
ejpam-2537	114	1	the	the	DET
ejpam-2537	114	2	map	map	NOUN
ejpam-2537	114	3	φ2,1	φ2,1	NOUN
ejpam-2537	114	4	is	be	AUX
ejpam-2537	114	5	defined	define	VERB
ejpam-2537	114	6	as	as	ADP
ejpam-2537	114	7	φ2,1	φ2,1	PROPN
ejpam-2537	114	8	:	:	PUNCT
ejpam-2537	114	9	rn→	rn→	X
ejpam-2537	114	10	(	(	PUNCT
ejpam-2537	114	11	f2	f2	PROPN
ejpam-2537	114	12	+	+	NUM
ejpam-2537	114	13	uf2	uf2	NOUN
ejpam-2537	114	14	)	)	PUNCT
ejpam-2537	114	15	2n	2n	NUM
ejpam-2537	114	16	(	(	PUNCT
ejpam-2537	114	17	c0	c0	NOUN
ejpam-2537	114	18	,	,	PUNCT
ejpam-2537	114	19	.	.	PUNCT
ejpam-2537	114	20	.	.	PUNCT
ejpam-2537	115	1	.	.	PUNCT
ejpam-2537	116	1	,	,	PUNCT
ejpam-2537	116	2	cn−1	cn−1	NOUN
ejpam-2537	116	3	)	)	PUNCT
ejpam-2537	116	4	7→	7→	NUM
ejpam-2537	116	5	(	(	PUNCT
ejpam-2537	116	6	a	a	DET
ejpam-2537	116	7	′	′	NOUN
ejpam-2537	116	8	0	0	NUM
ejpam-2537	116	9	,	,	PUNCT
ejpam-2537	116	10	.	.	PUNCT
ejpam-2537	116	11	.	.	PUNCT
ejpam-2537	117	1	.	.	PUNCT
ejpam-2537	118	1	,	,	PUNCT
ejpam-2537	118	2	a′n−1	a′n−1	PROPN
ejpam-2537	118	3	,	,	PUNCT
ejpam-2537	118	4	b′0	b′0	X
ejpam-2537	118	5	+	+	CCONJ
ejpam-2537	118	6	a′0	a′0	ADJ
ejpam-2537	118	7	,	,	PUNCT
ejpam-2537	118	8	.	.	PUNCT
ejpam-2537	118	9	.	.	PUNCT
ejpam-2537	119	1	.	.	PUNCT
ejpam-2537	120	1	,	,	PUNCT
ejpam-2537	120	2	b′n−1	b′n−1	PROPN
ejpam-2537	120	3	+	+	CCONJ
ejpam-2537	120	4	a′n−1	a′n−1	PROPN
ejpam-2537	120	5	)	)	PUNCT
ejpam-2537	121	1	where	where	SCONJ
ejpam-2537	121	2	ci	ci	NOUN
ejpam-2537	121	3	=	=	PUNCT
ejpam-2537	121	4	a′	a′	PROPN
ejpam-2537	122	1	i	i	PRON
ejpam-2537	122	2	+	+	CCONJ
ejpam-2537	122	3	vb′	vb′	VERB
ejpam-2537	122	4	i	i	PRON
ejpam-2537	122	5	with	with	ADP
ejpam-2537	122	6	a′	a′	PROPN
ejpam-2537	122	7	i	i	PRON
ejpam-2537	122	8	,	,	PUNCT
ejpam-2537	122	9	b′	b′	NOUN
ejpam-2537	122	10	i	i	PRON
ejpam-2537	122	11	∈	∈	VERB
ejpam-2537	122	12	f2	f2	PROPN
ejpam-2537	122	13	+	+	CCONJ
ejpam-2537	122	14	uf2	uf2	NOUN
ejpam-2537	122	15	for	for	ADP
ejpam-2537	122	16	0≤	0≤	NUM
ejpam-2537	123	1	i	i	PRON
ejpam-2537	123	2	≤	≤	ADJ
ejpam-2537	123	3	n−	n−	NOUN
ejpam-2537	123	4	1	1	NUM
ejpam-2537	123	5	.	.	PUNCT
ejpam-2537	124	1	a	a	DET
ejpam-2537	124	2	gray	gray	ADJ
ejpam-2537	124	3	map	map	NOUN
ejpam-2537	124	4	φ	φ	NOUN
ejpam-2537	124	5	from	from	ADP
ejpam-2537	124	6	r	r	NOUN
ejpam-2537	124	7	to	to	ADP
ejpam-2537	124	8	f	f	PROPN
ejpam-2537	124	9	m	m	VERB
ejpam-2537	124	10	2	2	NUM
ejpam-2537	124	11	which	which	PRON
ejpam-2537	124	12	is	be	AUX
ejpam-2537	124	13	the	the	DET
ejpam-2537	124	14	composition	composition	NOUN
ejpam-2537	124	15	of	of	ADP
ejpam-2537	124	16	φ1,1	φ1,1	PROPN
ejpam-2537	124	17	and	and	CCONJ
ejpam-2537	124	18	φ2	φ2	PROPN
ejpam-2537	124	19	or	or	CCONJ
ejpam-2537	124	20	φ2,1	φ2,1	PROPN
ejpam-2537	124	21	and	and	CCONJ
ejpam-2537	124	22	φ1	φ1	PROPN
ejpam-2537	124	23	can	can	AUX
ejpam-2537	124	24	be	be	AUX
ejpam-2537	124	25	obtained	obtain	VERB
ejpam-2537	124	26	.	.	PUNCT
ejpam-2537	125	1	a.	a.	NOUN
ejpam-2537	125	2	dertli	dertli	PROPN
ejpam-2537	125	3	,	,	PUNCT
ejpam-2537	125	4	y.	y.	PROPN
ejpam-2537	125	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	125	6	/	/	SYM
ejpam-2537	125	7	eur	eur	PROPN
ejpam-2537	125	8	.	.	PUNCT
ejpam-2537	126	1	j.	j.	PROPN
ejpam-2537	126	2	pure	pure	PROPN
ejpam-2537	126	3	appl	appl	PROPN
ejpam-2537	126	4	.	.	PROPN
ejpam-2537	126	5	math	math	PROPN
ejpam-2537	126	6	,	,	PUNCT
ejpam-2537	126	7	9	9	NUM
ejpam-2537	126	8	(	(	PUNCT
ejpam-2537	126	9	2016	2016	NUM
ejpam-2537	126	10	)	)	PUNCT
ejpam-2537	126	11	,	,	PUNCT
ejpam-2537	126	12	305	305	NUM
ejpam-2537	126	13	-	-	SYM
ejpam-2537	126	14	313	313	NUM
ejpam-2537	126	15	308	308	NUM
ejpam-2537	126	16	the	the	DET
ejpam-2537	126	17	lee	lee	PROPN
ejpam-2537	126	18	weights	weight	NOUN
ejpam-2537	126	19	of	of	ADP
ejpam-2537	126	20	0,1,u	0,1,u	NOUN
ejpam-2537	126	21	,	,	PUNCT
ejpam-2537	126	22	1	1	NUM
ejpam-2537	126	23	+	+	NUM
ejpam-2537	126	24	u	u	NOUN
ejpam-2537	126	25	∈	∈	NOUN
ejpam-2537	126	26	f2	f2	PROPN
ejpam-2537	126	27	+	+	CCONJ
ejpam-2537	126	28	uf2	uf2	NOUN
ejpam-2537	126	29	are	be	AUX
ejpam-2537	126	30	0,1,2,1	0,1,2,1	NUM
ejpam-2537	126	31	respectively	respectively	ADV
ejpam-2537	126	32	.	.	PUNCT
ejpam-2537	127	1	the	the	DET
ejpam-2537	127	2	lee	lee	PROPN
ejpam-2537	127	3	weights	weight	NOUN
ejpam-2537	127	4	of	of	ADP
ejpam-2537	127	5	0,1	0,1	NUM
ejpam-2537	127	6	,	,	PUNCT
ejpam-2537	127	7	v	v	NOUN
ejpam-2537	127	8	,	,	PUNCT
ejpam-2537	127	9	1	1	NUM
ejpam-2537	127	10	+	+	SYM
ejpam-2537	127	11	v	v	NUM
ejpam-2537	127	12	∈	∈	NOUN
ejpam-2537	127	13	f2	f2	PROPN
ejpam-2537	127	14	+	+	CCONJ
ejpam-2537	127	15	vf2	vf2	NOUN
ejpam-2537	127	16	are	be	AUX
ejpam-2537	127	17	0,2,1,1	0,2,1,1	NUM
ejpam-2537	127	18	respectively	respectively	ADV
ejpam-2537	127	19	.	.	PUNCT
ejpam-2537	128	1	these	these	DET
ejpam-2537	128	2	lee	lee	PROPN
ejpam-2537	128	3	weights	weight	NOUN
ejpam-2537	128	4	can	can	AUX
ejpam-2537	128	5	be	be	AUX
ejpam-2537	128	6	extended	extend	VERB
ejpam-2537	128	7	to	to	ADP
ejpam-2537	128	8	(	(	PUNCT
ejpam-2537	128	9	f2	f2	PROPN
ejpam-2537	128	10	+	+	NUM
ejpam-2537	128	11	uf2	uf2	NOUN
ejpam-2537	128	12	)	)	PUNCT
ejpam-2537	128	13	n	n	NOUN
ejpam-2537	128	14	and	and	CCONJ
ejpam-2537	128	15	(	(	PUNCT
ejpam-2537	128	16	f2	f2	PROPN
ejpam-2537	128	17	+	+	CCONJ
ejpam-2537	128	18	vf2	vf2	ADJ
ejpam-2537	128	19	)	)	PUNCT
ejpam-2537	128	20	n.	n.	NOUN
ejpam-2537	128	21	it	it	PRON
ejpam-2537	128	22	is	be	AUX
ejpam-2537	128	23	known	know	VERB
ejpam-2537	128	24	that	that	SCONJ
ejpam-2537	128	25	φ1	φ1	PROPN
ejpam-2537	128	26	and	and	CCONJ
ejpam-2537	128	27	φ2	φ2	PROPN
ejpam-2537	128	28	are	be	AUX
ejpam-2537	128	29	distance	distance	NOUN
ejpam-2537	128	30	-	-	PUNCT
ejpam-2537	128	31	preserving	preserve	VERB
ejpam-2537	128	32	map	map	NOUN
ejpam-2537	128	33	from	from	ADP
ejpam-2537	128	34	(	(	PUNCT
ejpam-2537	128	35	f2	f2	PROPN
ejpam-2537	128	36	+	+	NUM
ejpam-2537	128	37	uf2	uf2	NOUN
ejpam-2537	128	38	)	)	PUNCT
ejpam-2537	128	39	n	n	PROPN
ejpam-2537	128	40	(	(	PUNCT
ejpam-2537	128	41	lee	lee	PROPN
ejpam-2537	128	42	distance	distance	PROPN
ejpam-2537	128	43	)	)	PUNCT
ejpam-2537	128	44	to	to	ADP
ejpam-2537	128	45	f2n	f2n	PROPN
ejpam-2537	128	46	2	2	NUM
ejpam-2537	128	47	(	(	PUNCT
ejpam-2537	128	48	hamming	hamming	NOUN
ejpam-2537	128	49	distance	distance	NOUN
ejpam-2537	128	50	)	)	PUNCT
ejpam-2537	128	51	and	and	CCONJ
ejpam-2537	128	52	(	(	PUNCT
ejpam-2537	128	53	f2	f2	PROPN
ejpam-2537	128	54	+	+	CCONJ
ejpam-2537	128	55	vf2	vf2	NOUN
ejpam-2537	128	56	)	)	PUNCT
ejpam-2537	128	57	n	n	PROPN
ejpam-2537	128	58	(	(	PUNCT
ejpam-2537	128	59	lee	lee	PROPN
ejpam-2537	128	60	distance	distance	PROPN
ejpam-2537	128	61	)	)	PUNCT
ejpam-2537	128	62	to	to	ADP
ejpam-2537	128	63	f2n	f2n	PROPN
ejpam-2537	128	64	2	2	NUM
ejpam-2537	128	65	(	(	PUNCT
ejpam-2537	128	66	hamming	hamming	NOUN
ejpam-2537	128	67	distance	distance	NOUN
ejpam-2537	128	68	)	)	PUNCT
ejpam-2537	128	69	,	,	PUNCT
ejpam-2537	128	70	respectively	respectively	ADV
ejpam-2537	128	71	.	.	PUNCT
ejpam-2537	129	1	for	for	ADP
ejpam-2537	129	2	any	any	DET
ejpam-2537	129	3	element	element	NOUN
ejpam-2537	129	4	a+vb	a+vb	NOUN
ejpam-2537	129	5	∈	∈	PROPN
ejpam-2537	129	6	r	r	NOUN
ejpam-2537	129	7	with	with	ADP
ejpam-2537	129	8	a	a	DET
ejpam-2537	129	9	,	,	PUNCT
ejpam-2537	129	10	b	b	PROPN
ejpam-2537	129	11	∈	∈	PROPN
ejpam-2537	129	12	f2+uf2	f2+uf2	NOUN
ejpam-2537	129	13	,	,	PUNCT
ejpam-2537	129	14	it	it	PRON
ejpam-2537	129	15	is	be	AUX
ejpam-2537	129	16	defined	define	VERB
ejpam-2537	129	17	lee	lee	PROPN
ejpam-2537	129	18	weight	weight	PROPN
ejpam-2537	129	19	,	,	PUNCT
ejpam-2537	129	20	denoted	denote	VERB
ejpam-2537	129	21	by	by	ADP
ejpam-2537	129	22	wl	wl	NOUN
ejpam-2537	129	23	as	as	ADP
ejpam-2537	129	24	wl(a	wl(a	NUM
ejpam-2537	129	25	+	+	CCONJ
ejpam-2537	129	26	vb	vb	NOUN
ejpam-2537	129	27	)	)	PUNCT
ejpam-2537	129	28	=	=	SYM
ejpam-2537	129	29	wl(b	wl(b	X
ejpam-2537	129	30	,	,	PUNCT
ejpam-2537	129	31	b	b	NOUN
ejpam-2537	129	32	+	+	CCONJ
ejpam-2537	129	33	a	a	X
ejpam-2537	129	34	)	)	PUNCT
ejpam-2537	129	35	.	.	PUNCT
ejpam-2537	130	1	the	the	DET
ejpam-2537	130	2	lee	lee	PROPN
ejpam-2537	130	3	distance	distance	NOUN
ejpam-2537	130	4	of	of	ADP
ejpam-2537	130	5	a	a	DET
ejpam-2537	130	6	linear	linear	ADJ
ejpam-2537	130	7	code	code	NOUN
ejpam-2537	130	8	over	over	ADP
ejpam-2537	130	9	r	r	NOUN
ejpam-2537	130	10	,	,	PUNCT
ejpam-2537	130	11	denoted	denote	VERB
ejpam-2537	130	12	by	by	ADP
ejpam-2537	130	13	dl(c	dl(c	PROPN
ejpam-2537	130	14	)	)	PUNCT
ejpam-2537	130	15	is	be	AUX
ejpam-2537	130	16	defined	define	VERB
ejpam-2537	130	17	as	as	ADP
ejpam-2537	130	18	minimum	minimum	ADJ
ejpam-2537	130	19	lee	lee	PROPN
ejpam-2537	130	20	weight	weight	NOUN
ejpam-2537	130	21	of	of	ADP
ejpam-2537	130	22	nonzero	nonzero	PROPN
ejpam-2537	130	23	codewords	codeword	NOUN
ejpam-2537	130	24	of	of	ADP
ejpam-2537	130	25	c	c	PROPN
ejpam-2537	130	26	.	.	PUNCT
ejpam-2537	131	1	φ1	φ1	PROPN
ejpam-2537	131	2	:(	:(	PROPN
ejpam-2537	132	1	f2	f2	PROPN
ejpam-2537	132	2	+	+	X
ejpam-2537	132	3	uf2	uf2	NOUN
ejpam-2537	132	4	)	)	PUNCT
ejpam-2537	132	5	n	n	PROPN
ejpam-2537	132	6	(	(	PUNCT
ejpam-2537	132	7	lee	lee	PROPN
ejpam-2537	132	8	distance	distance	PROPN
ejpam-2537	132	9	)	)	PUNCT
ejpam-2537	132	10	→	→	SYM
ejpam-2537	132	11	f2n	f2n	ADJ
ejpam-2537	132	12	2	2	NUM
ejpam-2537	132	13	(	(	PUNCT
ejpam-2537	132	14	hamming	hamming	NOUN
ejpam-2537	132	15	distance	distance	NOUN
ejpam-2537	132	16	)	)	PUNCT
ejpam-2537	132	17	φ2	φ2	NOUN
ejpam-2537	132	18	:(	:(	PROPN
ejpam-2537	133	1	f2	f2	PROPN
ejpam-2537	133	2	+	+	CCONJ
ejpam-2537	133	3	vf2	vf2	ADJ
ejpam-2537	133	4	)	)	PUNCT
ejpam-2537	133	5	n	n	PROPN
ejpam-2537	133	6	(	(	PUNCT
ejpam-2537	133	7	lee	lee	PROPN
ejpam-2537	133	8	distance	distance	PROPN
ejpam-2537	133	9	)	)	PUNCT
ejpam-2537	133	10	→	→	SYM
ejpam-2537	133	11	f2n	f2n	ADJ
ejpam-2537	133	12	2	2	NUM
ejpam-2537	133	13	(	(	PUNCT
ejpam-2537	133	14	hamming	hamming	NOUN
ejpam-2537	133	15	distance	distance	NOUN
ejpam-2537	133	16	)	)	PUNCT
ejpam-2537	134	1	φ1,1	φ1,1	NOUN
ejpam-2537	134	2	:	:	PUNCT
ejpam-2537	134	3	rn	rn	PROPN
ejpam-2537	134	4	(	(	PUNCT
ejpam-2537	134	5	lee	lee	PROPN
ejpam-2537	134	6	distance	distance	PROPN
ejpam-2537	134	7	)	)	PUNCT
ejpam-2537	134	8	→	→	PUNCT
ejpam-2537	134	9	(	(	PUNCT
ejpam-2537	134	10	f2	f2	PROPN
ejpam-2537	134	11	+	+	CCONJ
ejpam-2537	134	12	vf2	vf2	ADJ
ejpam-2537	134	13	)	)	PUNCT
ejpam-2537	134	14	2n	2n	NUM
ejpam-2537	134	15	(	(	PUNCT
ejpam-2537	134	16	lee	lee	PROPN
ejpam-2537	134	17	distance	distance	PROPN
ejpam-2537	134	18	)	)	PUNCT
ejpam-2537	134	19	φ2,1	φ2,1	PROPN
ejpam-2537	134	20	:	:	PUNCT
ejpam-2537	135	1	rn	rn	PROPN
ejpam-2537	135	2	(	(	PUNCT
ejpam-2537	135	3	lee	lee	PROPN
ejpam-2537	135	4	distance	distance	PROPN
ejpam-2537	135	5	)	)	PUNCT
ejpam-2537	135	6	→	→	PUNCT
ejpam-2537	135	7	(	(	PUNCT
ejpam-2537	135	8	f2	f2	PROPN
ejpam-2537	135	9	+	+	NUM
ejpam-2537	135	10	uf2	uf2	NOUN
ejpam-2537	135	11	)	)	PUNCT
ejpam-2537	135	12	2n	2n	NUM
ejpam-2537	135	13	(	(	PUNCT
ejpam-2537	135	14	lee	lee	PROPN
ejpam-2537	135	15	distance	distance	PROPN
ejpam-2537	135	16	)	)	PUNCT
ejpam-2537	135	17	now	now	ADV
ejpam-2537	135	18	,	,	PUNCT
ejpam-2537	135	19	it	it	PRON
ejpam-2537	135	20	will	will	AUX
ejpam-2537	135	21	be	be	AUX
ejpam-2537	135	22	characterized	characterize	VERB
ejpam-2537	135	23	codes	code	NOUN
ejpam-2537	135	24	over	over	ADP
ejpam-2537	135	25	f2	f2	PROPN
ejpam-2537	135	26	+	+	CCONJ
ejpam-2537	135	27	vf2	vf2	NOUN
ejpam-2537	135	28	which	which	PRON
ejpam-2537	135	29	are	be	AUX
ejpam-2537	135	30	the	the	DET
ejpam-2537	135	31	images	image	NOUN
ejpam-2537	135	32	of	of	ADP
ejpam-2537	135	33	(	(	PUNCT
ejpam-2537	135	34	1	1	NUM
ejpam-2537	135	35	+	+	CCONJ
ejpam-2537	135	36	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	135	37	and	and	CCONJ
ejpam-2537	135	38	cyclic	cyclic	ADJ
ejpam-2537	135	39	codes	code	NOUN
ejpam-2537	135	40	over	over	ADP
ejpam-2537	135	41	r.	r.	PROPN
ejpam-2537	135	42	proposition	proposition	NOUN
ejpam-2537	136	1	1	1	NUM
ejpam-2537	136	2	.	.	PUNCT
ejpam-2537	137	1	let	let	VERB
ejpam-2537	137	2	φ1,1	φ1,1	INTJ
ejpam-2537	137	3	be	be	AUX
ejpam-2537	137	4	defined	define	VERB
ejpam-2537	137	5	as	as	ADP
ejpam-2537	137	6	above	above	ADV
ejpam-2537	137	7	.	.	PUNCT
ejpam-2537	138	1	let	let	VERB
ejpam-2537	138	2	ν	ν	NOUN
ejpam-2537	138	3	be	be	AUX
ejpam-2537	138	4	(	(	PUNCT
ejpam-2537	138	5	1	1	NUM
ejpam-2537	138	6	+	+	CCONJ
ejpam-2537	138	7	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	138	8	shift	shift	NOUN
ejpam-2537	138	9	on	on	ADP
ejpam-2537	138	10	rn	rn	PROPN
ejpam-2537	138	11	and	and	CCONJ
ejpam-2537	138	12	σ	σ	NUM
ejpam-2537	138	13	the	the	DET
ejpam-2537	138	14	cyclic	cyclic	ADJ
ejpam-2537	138	15	shift	shift	NOUN
ejpam-2537	138	16	on	on	ADP
ejpam-2537	138	17	(	(	PUNCT
ejpam-2537	138	18	f2	f2	PROPN
ejpam-2537	138	19	+	+	CCONJ
ejpam-2537	138	20	vf2	vf2	ADJ
ejpam-2537	138	21	)	)	PUNCT
ejpam-2537	138	22	2n	2n	NUM
ejpam-2537	138	23	.	.	PUNCT
ejpam-2537	139	1	then	then	ADV
ejpam-2537	139	2	φ1,1ν=	φ1,1ν=	NUM
ejpam-2537	139	3	σφ1,1	σφ1,1	NOUN
ejpam-2537	139	4	.	.	PUNCT
ejpam-2537	140	1	proof	proof	NOUN
ejpam-2537	140	2	.	.	PUNCT
ejpam-2537	141	1	let	let	VERB
ejpam-2537	141	2	z	z	NOUN
ejpam-2537	141	3	=	=	SYM
ejpam-2537	141	4	(	(	PUNCT
ejpam-2537	141	5	z0	z0	PROPN
ejpam-2537	141	6	,	,	PUNCT
ejpam-2537	141	7	.	.	PUNCT
ejpam-2537	141	8	.	.	PUNCT
ejpam-2537	142	1	.	.	PUNCT
ejpam-2537	143	1	,	,	PUNCT
ejpam-2537	143	2	zn−1	zn−1	PROPN
ejpam-2537	143	3	)	)	PUNCT
ejpam-2537	143	4	∈	∈	PROPN
ejpam-2537	143	5	rn	rn	PROPN
ejpam-2537	143	6	where	where	SCONJ
ejpam-2537	143	7	ci	ci	PROPN
ejpam-2537	143	8	=	=	PROPN
ejpam-2537	143	9	qi	qi	PROPN
ejpam-2537	143	10	+	+	PROPN
ejpam-2537	143	11	uri	uri	PROPN
ejpam-2537	143	12	and	and	CCONJ
ejpam-2537	143	13	qi	qi	PROPN
ejpam-2537	143	14	,	,	PUNCT
ejpam-2537	143	15	ri	ri	PROPN
ejpam-2537	143	16	∈	∈	PROPN
ejpam-2537	143	17	f2	f2	PROPN
ejpam-2537	143	18	+	+	CCONJ
ejpam-2537	143	19	vf2	vf2	NOUN
ejpam-2537	143	20	for	for	ADP
ejpam-2537	143	21	0≤	0≤	NUM
ejpam-2537	144	1	i	i	NOUN
ejpam-2537	144	2	≤	≤	PUNCT
ejpam-2537	144	3	n−1	n−1	PROPN
ejpam-2537	144	4	.	.	PROPN
ejpam-2537	145	1	from	from	ADP
ejpam-2537	145	2	definition	definition	NOUN
ejpam-2537	145	3	,	,	PUNCT
ejpam-2537	145	4	we	we	PRON
ejpam-2537	145	5	get	get	VERB
ejpam-2537	145	6	,	,	PUNCT
ejpam-2537	145	7	φ1,1(z	φ1,1(z	PROPN
ejpam-2537	145	8	)	)	PUNCT
ejpam-2537	145	9	=	=	PUNCT
ejpam-2537	145	10	(	(	PUNCT
ejpam-2537	145	11	r0	r0	NOUN
ejpam-2537	145	12	,	,	PUNCT
ejpam-2537	145	13	.	.	PUNCT
ejpam-2537	145	14	.	.	PUNCT
ejpam-2537	146	1	.	.	PUNCT
ejpam-2537	147	1	,	,	PUNCT
ejpam-2537	147	2	rn−1	rn−1	NOUN
ejpam-2537	147	3	,	,	PUNCT
ejpam-2537	147	4	r0	r0	NOUN
ejpam-2537	147	5	+	+	CCONJ
ejpam-2537	147	6	q0	q0	ADJ
ejpam-2537	147	7	,	,	PUNCT
ejpam-2537	147	8	.	.	PUNCT
ejpam-2537	147	9	.	.	PUNCT
ejpam-2537	148	1	.	.	PUNCT
ejpam-2537	149	1	,	,	PUNCT
ejpam-2537	149	2	rn−1	rn−1	PROPN
ejpam-2537	149	3	+	+	CCONJ
ejpam-2537	149	4	qn−1	qn−1	ADJ
ejpam-2537	149	5	)	)	PUNCT
ejpam-2537	149	6	and	and	CCONJ
ejpam-2537	149	7	σ(φ1,1(z	σ(φ1,1(z	VERB
ejpam-2537	149	8	)	)	PUNCT
ejpam-2537	149	9	)	)	PUNCT
ejpam-2537	150	1	=	=	SYM
ejpam-2537	150	2	(	(	PUNCT
ejpam-2537	150	3	rn−1	rn−1	PROPN
ejpam-2537	150	4	+	+	CCONJ
ejpam-2537	150	5	qn−1	qn−1	ADJ
ejpam-2537	150	6	,	,	PUNCT
ejpam-2537	150	7	r0	r0	NOUN
ejpam-2537	150	8	,	,	PUNCT
ejpam-2537	150	9	.	.	PUNCT
ejpam-2537	150	10	.	.	PUNCT
ejpam-2537	151	1	.	.	PUNCT
ejpam-2537	152	1	,	,	PUNCT
ejpam-2537	152	2	rn−1	rn−1	NOUN
ejpam-2537	152	3	,	,	PUNCT
ejpam-2537	152	4	r0	r0	NOUN
ejpam-2537	152	5	+	+	CCONJ
ejpam-2537	152	6	q0	q0	ADJ
ejpam-2537	152	7	,	,	PUNCT
ejpam-2537	152	8	.	.	PUNCT
ejpam-2537	152	9	.	.	PUNCT
ejpam-2537	153	1	.	.	PUNCT
ejpam-2537	154	1	,	,	PUNCT
ejpam-2537	154	2	rn−2	rn−2	PROPN
ejpam-2537	154	3	+	+	CCONJ
ejpam-2537	154	4	qn−2	qn−2	PROPN
ejpam-2537	154	5	)	)	PUNCT
ejpam-2537	154	6	on	on	ADP
ejpam-2537	154	7	the	the	DET
ejpam-2537	154	8	other	other	ADJ
ejpam-2537	154	9	hand	hand	NOUN
ejpam-2537	154	10	,	,	PUNCT
ejpam-2537	154	11	ν(z	ν(z	NOUN
ejpam-2537	154	12	)	)	PUNCT
ejpam-2537	154	13	=	=	PRON
ejpam-2537	155	1	(	(	PUNCT
ejpam-2537	155	2	(	(	PUNCT
ejpam-2537	155	3	1	1	NUM
ejpam-2537	155	4	+	+	NUM
ejpam-2537	155	5	u)zn−1	u)zn−1	ADJ
ejpam-2537	155	6	,	,	PUNCT
ejpam-2537	155	7	z0	z0	PROPN
ejpam-2537	155	8	,	,	PUNCT
ejpam-2537	155	9	.	.	PUNCT
ejpam-2537	155	10	.	.	PUNCT
ejpam-2537	156	1	.	.	PUNCT
ejpam-2537	157	1	,	,	PUNCT
ejpam-2537	157	2	zn−2	zn−2	PROPN
ejpam-2537	157	3	)	)	PUNCT
ejpam-2537	157	4	=	=	PUNCT
ejpam-2537	157	5	(	(	PUNCT
ejpam-2537	157	6	qn−1	qn−1	PROPN
ejpam-2537	157	7	+	+	NUM
ejpam-2537	157	8	u(qn−1	u(qn−1	X
ejpam-2537	158	1	+	+	CCONJ
ejpam-2537	158	2	rn−1),q0	rn−1),q0	ADJ
ejpam-2537	158	3	+	+	CCONJ
ejpam-2537	158	4	ur0	ur0	NOUN
ejpam-2537	158	5	,	,	PUNCT
ejpam-2537	158	6	.	.	PUNCT
ejpam-2537	158	7	.	.	PUNCT
ejpam-2537	158	8	.	.	PUNCT
ejpam-2537	159	1	,	,	PUNCT
ejpam-2537	159	2	qn−2	qn−2	NOUN
ejpam-2537	159	3	+	+	CCONJ
ejpam-2537	159	4	urn−2	urn−2	PROPN
ejpam-2537	159	5	)	)	PUNCT
ejpam-2537	159	6	and	and	CCONJ
ejpam-2537	159	7	φ1,1(ν(z	φ1,1(ν(z	PROPN
ejpam-2537	159	8	)	)	PUNCT
ejpam-2537	159	9	)	)	PUNCT
ejpam-2537	160	1	=	=	SYM
ejpam-2537	160	2	(	(	PUNCT
ejpam-2537	160	3	qn−1	qn−1	PROPN
ejpam-2537	160	4	+	+	CCONJ
ejpam-2537	160	5	rn−1	rn−1	PROPN
ejpam-2537	160	6	,	,	PUNCT
ejpam-2537	160	7	r0	r0	NOUN
ejpam-2537	160	8	,	,	PUNCT
ejpam-2537	160	9	.	.	PUNCT
ejpam-2537	160	10	.	.	PUNCT
ejpam-2537	161	1	.	.	PUNCT
ejpam-2537	162	1	,	,	PUNCT
ejpam-2537	162	2	qn−2	qn−2	PROPN
ejpam-2537	162	3	+	+	X
ejpam-2537	162	4	rn−2	rn−2	PROPN
ejpam-2537	162	5	)	)	PUNCT
ejpam-2537	162	6	.	.	PUNCT
ejpam-2537	163	1	theorem	theorem	NOUN
ejpam-2537	163	2	1	1	NUM
ejpam-2537	163	3	.	.	PUNCT
ejpam-2537	164	1	a	a	DET
ejpam-2537	164	2	linear	linear	ADJ
ejpam-2537	164	3	code	code	NOUN
ejpam-2537	164	4	c	c	NOUN
ejpam-2537	164	5	of	of	ADP
ejpam-2537	164	6	length	length	NOUN
ejpam-2537	164	7	n	n	CCONJ
ejpam-2537	164	8	over	over	ADP
ejpam-2537	164	9	r	r	NOUN
ejpam-2537	164	10	is	be	AUX
ejpam-2537	164	11	a	a	DET
ejpam-2537	164	12	(	(	PUNCT
ejpam-2537	164	13	1	1	NUM
ejpam-2537	164	14	+	+	NUM
ejpam-2537	164	15	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	164	16	code	code	NOUN
ejpam-2537	164	17	iff	iff	PROPN
ejpam-2537	164	18	φ1,1(c	φ1,1(c	PROPN
ejpam-2537	164	19	)	)	PUNCT
ejpam-2537	165	1	is	be	AUX
ejpam-2537	165	2	a	a	DET
ejpam-2537	165	3	cyclic	cyclic	ADJ
ejpam-2537	165	4	code	code	NOUN
ejpam-2537	165	5	of	of	ADP
ejpam-2537	165	6	length	length	NOUN
ejpam-2537	165	7	2n	2n	NUM
ejpam-2537	165	8	over	over	ADP
ejpam-2537	165	9	f2	f2	PROPN
ejpam-2537	165	10	+	+	CCONJ
ejpam-2537	165	11	vf2	vf2	ADJ
ejpam-2537	165	12	.	.	PUNCT
ejpam-2537	166	1	proof	proof	NOUN
ejpam-2537	166	2	.	.	PUNCT
ejpam-2537	167	1	if	if	SCONJ
ejpam-2537	167	2	c	c	PROPN
ejpam-2537	167	3	is	be	AUX
ejpam-2537	167	4	(	(	PUNCT
ejpam-2537	167	5	1	1	NUM
ejpam-2537	167	6	+	+	NUM
ejpam-2537	167	7	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	167	8	code	code	NOUN
ejpam-2537	167	9	,	,	PUNCT
ejpam-2537	167	10	from	from	ADP
ejpam-2537	167	11	proposition	proposition	NOUN
ejpam-2537	167	12	1	1	NUM
ejpam-2537	167	13	we	we	PRON
ejpam-2537	167	14	get	get	VERB
ejpam-2537	167	15	φ1,1(ν(c	φ1,1(ν(c	X
ejpam-2537	167	16	)	)	PUNCT
ejpam-2537	167	17	)	)	PUNCT
ejpam-2537	168	1	=	=	SYM
ejpam-2537	168	2	σ(φ1,1(c	σ(φ1,1(c	NOUN
ejpam-2537	168	3	)	)	PUNCT
ejpam-2537	168	4	)	)	PUNCT
ejpam-2537	168	5	.	.	PUNCT
ejpam-2537	169	1	so	so	ADV
ejpam-2537	169	2	φ1,1(c	φ1,1(c	NOUN
ejpam-2537	169	3	)	)	PUNCT
ejpam-2537	169	4	is	be	AUX
ejpam-2537	169	5	a	a	DET
ejpam-2537	169	6	cyclic	cyclic	ADJ
ejpam-2537	169	7	code	code	NOUN
ejpam-2537	169	8	of	of	ADP
ejpam-2537	169	9	length	length	NOUN
ejpam-2537	169	10	2n	2n	NUM
ejpam-2537	169	11	over	over	ADP
ejpam-2537	169	12	f2	f2	PROPN
ejpam-2537	169	13	+	+	CCONJ
ejpam-2537	169	14	vf2	vf2	ADJ
ejpam-2537	169	15	.	.	PUNCT
ejpam-2537	170	1	conversely	conversely	ADV
ejpam-2537	170	2	,	,	PUNCT
ejpam-2537	170	3	if	if	SCONJ
ejpam-2537	170	4	φ1,1(c	φ1,1(c	NOUN
ejpam-2537	170	5	)	)	PUNCT
ejpam-2537	170	6	is	be	AUX
ejpam-2537	170	7	a	a	DET
ejpam-2537	170	8	cyclic	cyclic	ADJ
ejpam-2537	170	9	code	code	NOUN
ejpam-2537	170	10	of	of	ADP
ejpam-2537	170	11	length	length	NOUN
ejpam-2537	170	12	2n	2n	NUM
ejpam-2537	170	13	over	over	ADP
ejpam-2537	170	14	f2	f2	PROPN
ejpam-2537	170	15	+	+	CCONJ
ejpam-2537	170	16	vf2	vf2	ADJ
ejpam-2537	170	17	,	,	PUNCT
ejpam-2537	170	18	from	from	ADP
ejpam-2537	170	19	proposition	proposition	NOUN
ejpam-2537	170	20	1	1	NUM
ejpam-2537	170	21	,	,	PUNCT
ejpam-2537	170	22	we	we	PRON
ejpam-2537	170	23	get	get	VERB
ejpam-2537	170	24	φ1,1(ν(c	φ1,1(ν(c	X
ejpam-2537	170	25	)	)	PUNCT
ejpam-2537	170	26	)	)	PUNCT
ejpam-2537	171	1	=	=	SYM
ejpam-2537	171	2	σ(φ1,1(c	σ(φ1,1(c	NOUN
ejpam-2537	171	3	)	)	PUNCT
ejpam-2537	171	4	)	)	PUNCT
ejpam-2537	172	1	=	=	SYM
ejpam-2537	172	2	φ1,1(c	φ1,1(c	NOUN
ejpam-2537	172	3	)	)	PUNCT
ejpam-2537	172	4	.	.	PUNCT
ejpam-2537	173	1	by	by	ADP
ejpam-2537	173	2	using	use	VERB
ejpam-2537	173	3	φ1,1	φ1,1	PROPN
ejpam-2537	173	4	is	be	AUX
ejpam-2537	173	5	injection	injection	NOUN
ejpam-2537	173	6	,	,	PUNCT
ejpam-2537	173	7	hence	hence	ADV
ejpam-2537	173	8	ν(c	ν(c	NOUN
ejpam-2537	173	9	)	)	PUNCT
ejpam-2537	174	1	=	=	SYM
ejpam-2537	174	2	c	c	X
ejpam-2537	174	3	.	.	PUNCT
ejpam-2537	175	1	corollary	corollary	ADJ
ejpam-2537	175	2	1	1	NUM
ejpam-2537	175	3	.	.	PUNCT
ejpam-2537	176	1	the	the	DET
ejpam-2537	176	2	image	image	NOUN
ejpam-2537	176	3	of	of	ADP
ejpam-2537	176	4	a	a	DET
ejpam-2537	176	5	(	(	PUNCT
ejpam-2537	176	6	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	176	7	code	code	NOUN
ejpam-2537	176	8	of	of	ADP
ejpam-2537	176	9	length	length	NOUN
ejpam-2537	176	10	n	n	CCONJ
ejpam-2537	176	11	over	over	ADP
ejpam-2537	176	12	r	r	NOUN
ejpam-2537	176	13	under	under	ADP
ejpam-2537	176	14	the	the	DET
ejpam-2537	176	15	map	map	NOUN
ejpam-2537	176	16	φ1,1	φ1,1	NOUN
ejpam-2537	176	17	is	be	AUX
ejpam-2537	176	18	a	a	DET
ejpam-2537	176	19	distance	distance	NOUN
ejpam-2537	176	20	invariant	invariant	ADJ
ejpam-2537	176	21	cyclic	cyclic	ADJ
ejpam-2537	176	22	code	code	NOUN
ejpam-2537	176	23	of	of	ADP
ejpam-2537	176	24	length	length	NOUN
ejpam-2537	176	25	2n	2n	NUM
ejpam-2537	176	26	over	over	ADP
ejpam-2537	176	27	f2	f2	PROPN
ejpam-2537	176	28	+	+	CCONJ
ejpam-2537	176	29	vf2	vf2	ADJ
ejpam-2537	176	30	.	.	PUNCT
ejpam-2537	177	1	a.	a.	NOUN
ejpam-2537	177	2	dertli	dertli	PROPN
ejpam-2537	177	3	,	,	PUNCT
ejpam-2537	177	4	y.	y.	PROPN
ejpam-2537	177	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	177	6	/	/	SYM
ejpam-2537	177	7	eur	eur	PROPN
ejpam-2537	177	8	.	.	PUNCT
ejpam-2537	178	1	j.	j.	PROPN
ejpam-2537	178	2	pure	pure	PROPN
ejpam-2537	178	3	appl	appl	PROPN
ejpam-2537	178	4	.	.	PROPN
ejpam-2537	178	5	math	math	PROPN
ejpam-2537	178	6	,	,	PUNCT
ejpam-2537	178	7	9	9	NUM
ejpam-2537	178	8	(	(	PUNCT
ejpam-2537	178	9	2016	2016	NUM
ejpam-2537	178	10	)	)	PUNCT
ejpam-2537	178	11	,	,	PUNCT
ejpam-2537	178	12	305	305	NUM
ejpam-2537	178	13	-	-	SYM
ejpam-2537	178	14	313	313	NUM
ejpam-2537	178	15	309	309	NUM
ejpam-2537	178	16	note	note	NOUN
ejpam-2537	179	1	that	that	SCONJ
ejpam-2537	179	2	(	(	PUNCT
ejpam-2537	179	3	1	1	NUM
ejpam-2537	179	4	+	+	NUM
ejpam-2537	179	5	u)n	u)n	NOUN
ejpam-2537	179	6	=	=	SYM
ejpam-2537	179	7	1	1	NUM
ejpam-2537	179	8	+	+	NUM
ejpam-2537	179	9	u	u	NOUN
ejpam-2537	179	10	if	if	SCONJ
ejpam-2537	179	11	n	n	NOUN
ejpam-2537	179	12	is	be	AUX
ejpam-2537	179	13	odd	odd	ADJ
ejpam-2537	179	14	,	,	PUNCT
ejpam-2537	179	15	(	(	PUNCT
ejpam-2537	179	16	1	1	NUM
ejpam-2537	179	17	+	+	NUM
ejpam-2537	179	18	u)n	u)n	NOUN
ejpam-2537	179	19	=	=	SYM
ejpam-2537	179	20	1	1	NUM
ejpam-2537	179	21	if	if	SCONJ
ejpam-2537	179	22	n	n	PRON
ejpam-2537	179	23	is	be	AUX
ejpam-2537	179	24	even	even	ADV
ejpam-2537	179	25	.	.	PUNCT
ejpam-2537	180	1	in	in	ADP
ejpam-2537	180	2	here	here	ADV
ejpam-2537	180	3	,	,	PUNCT
ejpam-2537	180	4	it	it	PRON
ejpam-2537	180	5	is	be	AUX
ejpam-2537	180	6	studied	study	VERB
ejpam-2537	180	7	the	the	DET
ejpam-2537	180	8	properties	property	NOUN
ejpam-2537	180	9	of	of	ADP
ejpam-2537	180	10	(	(	PUNCT
ejpam-2537	180	11	1	1	NUM
ejpam-2537	180	12	+	+	NUM
ejpam-2537	180	13	u	u	NOUN
ejpam-2537	180	14	)	)	PUNCT
ejpam-2537	180	15	cyclic	cyclic	ADJ
ejpam-2537	180	16	codes	code	NOUN
ejpam-2537	180	17	of	of	ADP
ejpam-2537	180	18	odd	odd	ADJ
ejpam-2537	180	19	length	length	NOUN
ejpam-2537	180	20	in	in	ADP
ejpam-2537	180	21	this	this	DET
ejpam-2537	180	22	section	section	NOUN
ejpam-2537	180	23	.	.	PUNCT
ejpam-2537	181	1	let	let	VERB
ejpam-2537	181	2	µ	µ	X
ejpam-2537	181	3	be	be	AUX
ejpam-2537	181	4	the	the	DET
ejpam-2537	181	5	map	map	NOUN
ejpam-2537	181	6	of	of	ADP
ejpam-2537	181	7	r[x]/〈xn−1	r[x]/〈xn−1	PROPN
ejpam-2537	181	8	〉	〉	NOUN
ejpam-2537	181	9	into	into	ADP
ejpam-2537	181	10	r[x]/〈xn−(1+u	r[x]/〈xn−(1+u	NOUN
ejpam-2537	181	11	)	)	PUNCT
ejpam-2537	181	12	〉	〉	NOUN
ejpam-2537	181	13	defined	define	VERB
ejpam-2537	181	14	by	by	ADP
ejpam-2537	181	15	µ(c(x	µ(c(x	PROPN
ejpam-2537	181	16	)	)	PUNCT
ejpam-2537	181	17	)	)	PUNCT
ejpam-2537	182	1	=	=	PUNCT
ejpam-2537	182	2	c((1+u)x	c((1+u)x	PROPN
ejpam-2537	182	3	)	)	PUNCT
ejpam-2537	182	4	.	.	PUNCT
ejpam-2537	183	1	if	if	SCONJ
ejpam-2537	183	2	n	n	NOUN
ejpam-2537	183	3	is	be	AUX
ejpam-2537	183	4	odd	odd	ADJ
ejpam-2537	183	5	,	,	PUNCT
ejpam-2537	183	6	then	then	ADV
ejpam-2537	183	7	µ	µ	NOUN
ejpam-2537	183	8	is	be	AUX
ejpam-2537	183	9	a	a	DET
ejpam-2537	183	10	ring	ring	NOUN
ejpam-2537	183	11	isomorphism	isomorphism	NOUN
ejpam-2537	183	12	.	.	PUNCT
ejpam-2537	184	1	hence	hence	ADV
ejpam-2537	184	2	i	i	PRON
ejpam-2537	184	3	is	be	AUX
ejpam-2537	184	4	an	an	DET
ejpam-2537	184	5	ideal	ideal	NOUN
ejpam-2537	184	6	of	of	ADP
ejpam-2537	184	7	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2537	184	8	−	−	NOUN
ejpam-2537	184	9	1	1	NUM
ejpam-2537	184	10	〉	〉	NOUN
ejpam-2537	184	11	if	if	SCONJ
ejpam-2537	184	12	and	and	CCONJ
ejpam-2537	184	13	only	only	ADV
ejpam-2537	184	14	if	if	SCONJ
ejpam-2537	184	15	µ(i	µ(i	PROPN
ejpam-2537	184	16	)	)	PUNCT
ejpam-2537	184	17	is	be	AUX
ejpam-2537	184	18	an	an	DET
ejpam-2537	184	19	ideal	ideal	NOUN
ejpam-2537	184	20	of	of	ADP
ejpam-2537	184	21	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2537	184	22	−	−	PROPN
ejpam-2537	184	23	(	(	PUNCT
ejpam-2537	184	24	1	1	NUM
ejpam-2537	184	25	+	+	NUM
ejpam-2537	184	26	u	u	NOUN
ejpam-2537	184	27	)	)	PUNCT
ejpam-2537	184	28	〉	〉	NOUN
ejpam-2537	184	29	.	.	PUNCT
ejpam-2537	185	1	if	if	SCONJ
ejpam-2537	185	2	µ̄′	µ̄′	PROPN
ejpam-2537	185	3	is	be	AUX
ejpam-2537	185	4	the	the	DET
ejpam-2537	185	5	map	map	NOUN
ejpam-2537	185	6	µ̄′	µ̄′	NOUN
ejpam-2537	185	7	:	:	PUNCT
ejpam-2537	185	8	rn→	rn→	PROPN
ejpam-2537	185	9	rn	rn	PROPN
ejpam-2537	185	10	z	z	PROPN
ejpam-2537	185	11	7→	7→	PROPN
ejpam-2537	185	12	(	(	PUNCT
ejpam-2537	185	13	z0	z0	PROPN
ejpam-2537	185	14	,	,	PUNCT
ejpam-2537	185	15	(	(	PUNCT
ejpam-2537	185	16	1	1	NUM
ejpam-2537	185	17	+	+	NUM
ejpam-2537	185	18	u)z1	u)z1	NOUN
ejpam-2537	185	19	,	,	PUNCT
ejpam-2537	185	20	(	(	PUNCT
ejpam-2537	185	21	1	1	NUM
ejpam-2537	185	22	+	+	CCONJ
ejpam-2537	185	23	u)2z2	u)2z2	NOUN
ejpam-2537	185	24	,	,	PUNCT
ejpam-2537	185	25	.	.	PUNCT
ejpam-2537	185	26	.	.	PUNCT
ejpam-2537	186	1	.	.	PUNCT
ejpam-2537	187	1	,	,	PUNCT
ejpam-2537	187	2	(	(	PUNCT
ejpam-2537	187	3	1	1	NUM
ejpam-2537	187	4	+	+	NUM
ejpam-2537	187	5	u)n−1zn−1	u)n−1zn−1	ADJ
ejpam-2537	187	6	)	)	PUNCT
ejpam-2537	187	7	where	where	SCONJ
ejpam-2537	187	8	zi	zi	NOUN
ejpam-2537	187	9	=	=	SYM
ejpam-2537	187	10	qi	qi	PROPN
ejpam-2537	187	11	+	+	CCONJ
ejpam-2537	187	12	uri	uri	PROPN
ejpam-2537	187	13	and	and	CCONJ
ejpam-2537	187	14	ri	ri	PROPN
ejpam-2537	187	15	,	,	PUNCT
ejpam-2537	187	16	qi	qi	PROPN
ejpam-2537	187	17	∈	∈	PROPN
ejpam-2537	187	18	f2	f2	PROPN
ejpam-2537	187	19	+	+	CCONJ
ejpam-2537	187	20	vf2	vf2	NOUN
ejpam-2537	187	21	for	for	ADP
ejpam-2537	187	22	0≤	0≤	ADJ
ejpam-2537	187	23	i	i	PRON
ejpam-2537	187	24	≤	≤	ADJ
ejpam-2537	187	25	n−	n−	NOUN
ejpam-2537	187	26	1	1	NUM
ejpam-2537	187	27	,	,	PUNCT
ejpam-2537	187	28	then	then	ADV
ejpam-2537	187	29	it	it	PRON
ejpam-2537	187	30	also	also	ADV
ejpam-2537	187	31	follows	follow	VERB
ejpam-2537	187	32	that	that	SCONJ
ejpam-2537	187	33	:	:	PUNCT
ejpam-2537	187	34	proposition	proposition	NOUN
ejpam-2537	187	35	2	2	NUM
ejpam-2537	187	36	.	.	PUNCT
ejpam-2537	188	1	the	the	DET
ejpam-2537	188	2	set	set	NOUN
ejpam-2537	188	3	c	c	PROPN
ejpam-2537	188	4	⊆	⊆	NUM
ejpam-2537	188	5	rn	rn	PROPN
ejpam-2537	188	6	is	be	AUX
ejpam-2537	188	7	a	a	DET
ejpam-2537	188	8	linear	linear	ADJ
ejpam-2537	188	9	cyclic	cyclic	ADJ
ejpam-2537	188	10	code	code	NOUN
ejpam-2537	189	1	if	if	SCONJ
ejpam-2537	189	2	and	and	CCONJ
ejpam-2537	189	3	only	only	ADV
ejpam-2537	189	4	if	if	SCONJ
ejpam-2537	189	5	µ̄′(c	µ̄′(c	NOUN
ejpam-2537	189	6	)	)	PUNCT
ejpam-2537	189	7	is	be	AUX
ejpam-2537	189	8	a	a	DET
ejpam-2537	189	9	linear	linear	ADJ
ejpam-2537	189	10	(	(	PUNCT
ejpam-2537	189	11	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	189	12	code	code	NOUN
ejpam-2537	189	13	.	.	PUNCT
ejpam-2537	190	1	let	let	VERB
ejpam-2537	190	2	τ′	τ′	NOUN
ejpam-2537	190	3	be	be	AUX
ejpam-2537	190	4	the	the	DET
ejpam-2537	190	5	following	follow	VERB
ejpam-2537	190	6	permutation	permutation	NOUN
ejpam-2537	190	7	of	of	ADP
ejpam-2537	190	8	{	{	PUNCT
ejpam-2537	190	9	0,1,2	0,1,2	NOUN
ejpam-2537	190	10	,	,	PUNCT
ejpam-2537	190	11	.	.	PUNCT
ejpam-2537	190	12	.	.	PUNCT
ejpam-2537	191	1	.	.	PUNCT
ejpam-2537	192	1	,	,	PUNCT
ejpam-2537	193	1	2n−1}with	2n−1}with	NUM
ejpam-2537	193	2	n	n	CCONJ
ejpam-2537	193	3	odd	odd	ADJ
ejpam-2537	193	4	:	:	PUNCT
ejpam-2537	193	5	τ′	τ′	X
ejpam-2537	193	6	=	=	SYM
ejpam-2537	193	7	(	(	PUNCT
ejpam-2537	193	8	1	1	NUM
ejpam-2537	193	9	,	,	PUNCT
ejpam-2537	193	10	n+1)(3	n+1)(3	NOUN
ejpam-2537	193	11	,	,	PUNCT
ejpam-2537	193	12	n+	n+	PRON
ejpam-2537	193	13	3	3	NUM
ejpam-2537	193	14	)	)	PUNCT
ejpam-2537	193	15	.	.	PUNCT
ejpam-2537	193	16	.	.	PUNCT
ejpam-2537	193	17	.	.	PUNCT
ejpam-2537	194	1	(	(	PUNCT
ejpam-2537	194	2	n−	n−	NOUN
ejpam-2537	194	3	2,2n−	2,2n−	NOUN
ejpam-2537	194	4	2	2	NUM
ejpam-2537	194	5	)	)	PUNCT
ejpam-2537	194	6	.	.	PUNCT
ejpam-2537	195	1	the	the	DET
ejpam-2537	195	2	nechaev	nechaev	NOUN
ejpam-2537	195	3	permutation	permutation	NOUN
ejpam-2537	195	4	π′	π′	NUM
ejpam-2537	195	5	of	of	ADP
ejpam-2537	195	6	(	(	PUNCT
ejpam-2537	195	7	f2	f2	PROPN
ejpam-2537	195	8	+	+	CCONJ
ejpam-2537	195	9	vf2	vf2	ADJ
ejpam-2537	195	10	)	)	PUNCT
ejpam-2537	195	11	2n	2n	NUM
ejpam-2537	195	12	is	be	AUX
ejpam-2537	195	13	defined	define	VERB
ejpam-2537	195	14	by	by	ADP
ejpam-2537	195	15	π′(r0	π′(r0	NOUN
ejpam-2537	195	16	,	,	PUNCT
ejpam-2537	195	17	r1	r1	PROPN
ejpam-2537	195	18	,	,	PUNCT
ejpam-2537	195	19	.	.	PUNCT
ejpam-2537	195	20	.	.	PUNCT
ejpam-2537	196	1	.	.	PUNCT
ejpam-2537	197	1	,	,	PUNCT
ejpam-2537	197	2	r2n−1	r2n−1	PROPN
ejpam-2537	197	3	)	)	PUNCT
ejpam-2537	197	4	=	=	PUNCT
ejpam-2537	197	5	(	(	PUNCT
ejpam-2537	198	1	rτ′(0	rτ′(0	NOUN
ejpam-2537	198	2	)	)	PUNCT
ejpam-2537	198	3	,	,	PUNCT
ejpam-2537	198	4	rτ′(1	rτ′(1	PROPN
ejpam-2537	198	5	)	)	PUNCT
ejpam-2537	198	6	,	,	PUNCT
ejpam-2537	198	7	.	.	PUNCT
ejpam-2537	198	8	.	.	PUNCT
ejpam-2537	199	1	.	.	PUNCT
ejpam-2537	200	1	,	,	PUNCT
ejpam-2537	200	2	rτ′(2n−1	rτ′(2n−1	PROPN
ejpam-2537	200	3	)	)	PUNCT
ejpam-2537	200	4	)	)	PUNCT
ejpam-2537	200	5	.	.	PUNCT
ejpam-2537	201	1	proposition	proposition	NOUN
ejpam-2537	201	2	3	3	NUM
ejpam-2537	201	3	.	.	PUNCT
ejpam-2537	201	4	assume	assume	VERB
ejpam-2537	201	5	n	n	PRON
ejpam-2537	201	6	odd	odd	ADJ
ejpam-2537	201	7	,	,	PUNCT
ejpam-2537	201	8	let	let	VERB
ejpam-2537	201	9	µ̄′	µ̄′	PROPN
ejpam-2537	201	10	be	be	AUX
ejpam-2537	201	11	the	the	DET
ejpam-2537	201	12	permutation	permutation	NOUN
ejpam-2537	201	13	of	of	ADP
ejpam-2537	201	14	rn	rn	PROPN
ejpam-2537	201	15	such	such	ADJ
ejpam-2537	201	16	that	that	SCONJ
ejpam-2537	201	17	µ̄′(z0	µ̄′(z0	PROPN
ejpam-2537	201	18	,	,	PUNCT
ejpam-2537	201	19	.	.	PUNCT
ejpam-2537	201	20	.	.	PUNCT
ejpam-2537	202	1	.	.	PUNCT
ejpam-2537	203	1	,	,	PUNCT
ejpam-2537	203	2	zn−1	zn−1	PROPN
ejpam-2537	203	3	)	)	PUNCT
ejpam-2537	203	4	=	=	PUNCT
ejpam-2537	203	5	(	(	PUNCT
ejpam-2537	203	6	z0	z0	PROPN
ejpam-2537	203	7	,	,	PUNCT
ejpam-2537	203	8	(	(	PUNCT
ejpam-2537	204	1	1	1	NUM
ejpam-2537	204	2	+	+	NUM
ejpam-2537	204	3	u)z1	u)z1	NOUN
ejpam-2537	204	4	,	,	PUNCT
ejpam-2537	204	5	.	.	PUNCT
ejpam-2537	204	6	.	.	PUNCT
ejpam-2537	205	1	.	.	PUNCT
ejpam-2537	206	1	,	,	PUNCT
ejpam-2537	206	2	(	(	PUNCT
ejpam-2537	206	3	1	1	NUM
ejpam-2537	206	4	+	+	NUM
ejpam-2537	206	5	u)n−1zn−1	u)n−1zn−1	ADJ
ejpam-2537	206	6	)	)	PUNCT
ejpam-2537	206	7	.	.	PUNCT
ejpam-2537	207	1	then	then	ADV
ejpam-2537	207	2	φ1,1µ̄	φ1,1µ̄	ADP
ejpam-2537	207	3	′	′	NUM
ejpam-2537	207	4	=	=	PUNCT
ejpam-2537	207	5	π′φ1,1	π′φ1,1	ADJ
ejpam-2537	207	6	.	.	PUNCT
ejpam-2537	208	1	corollary	corollary	ADJ
ejpam-2537	208	2	2	2	NUM
ejpam-2537	208	3	.	.	PUNCT
ejpam-2537	209	1	if	if	SCONJ
ejpam-2537	209	2	c̃	c̃	PROPN
ejpam-2537	209	3	is	be	AUX
ejpam-2537	209	4	the	the	DET
ejpam-2537	209	5	gray	gray	ADJ
ejpam-2537	209	6	image	image	NOUN
ejpam-2537	209	7	of	of	ADP
ejpam-2537	209	8	a	a	DET
ejpam-2537	209	9	linear	linear	ADJ
ejpam-2537	209	10	cyclic	cyclic	ADJ
ejpam-2537	209	11	code	code	NOUN
ejpam-2537	209	12	of	of	ADP
ejpam-2537	209	13	length	length	NOUN
ejpam-2537	209	14	n	n	CCONJ
ejpam-2537	209	15	over	over	ADP
ejpam-2537	209	16	r	r	NOUN
ejpam-2537	209	17	,	,	PUNCT
ejpam-2537	209	18	then	then	ADV
ejpam-2537	209	19	c̃	c̃	PROPN
ejpam-2537	209	20	is	be	AUX
ejpam-2537	209	21	permutation	permutation	NOUN
ejpam-2537	209	22	equivalent	equivalent	ADJ
ejpam-2537	209	23	to	to	ADP
ejpam-2537	209	24	a	a	DET
ejpam-2537	209	25	cyclic	cyclic	ADJ
ejpam-2537	209	26	code	code	NOUN
ejpam-2537	209	27	and	and	CCONJ
ejpam-2537	209	28	length	length	NOUN
ejpam-2537	209	29	2n	2n	NUM
ejpam-2537	209	30	over	over	ADP
ejpam-2537	209	31	f2	f2	PROPN
ejpam-2537	209	32	+	+	CCONJ
ejpam-2537	209	33	vf2	vf2	ADJ
ejpam-2537	209	34	.	.	PUNCT
ejpam-2537	210	1	proof	proof	NOUN
ejpam-2537	210	2	.	.	PUNCT
ejpam-2537	211	1	from	from	ADP
ejpam-2537	211	2	proposition	proposition	NOUN
ejpam-2537	211	3	2	2	NUM
ejpam-2537	211	4	,	,	PUNCT
ejpam-2537	211	5	a	a	DET
ejpam-2537	211	6	code	code	NOUN
ejpam-2537	211	7	c	c	NOUN
ejpam-2537	211	8	of	of	ADP
ejpam-2537	211	9	length	length	NOUN
ejpam-2537	211	10	n	n	CCONJ
ejpam-2537	211	11	over	over	ADP
ejpam-2537	211	12	r	r	NOUN
ejpam-2537	211	13	is	be	AUX
ejpam-2537	211	14	linear	linear	ADJ
ejpam-2537	211	15	cyclic	cyclic	PROPN
ejpam-2537	211	16	code	code	NOUN
ejpam-2537	211	17	if	if	SCONJ
ejpam-2537	211	18	and	and	CCONJ
ejpam-2537	211	19	only	only	ADV
ejpam-2537	211	20	if	if	SCONJ
ejpam-2537	211	21	µ̄′(c	µ̄′(c	NOUN
ejpam-2537	211	22	)	)	PUNCT
ejpam-2537	211	23	is	be	AUX
ejpam-2537	211	24	linear	linear	ADJ
ejpam-2537	211	25	(	(	PUNCT
ejpam-2537	211	26	1	1	NUM
ejpam-2537	211	27	+	+	CCONJ
ejpam-2537	211	28	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	211	29	.	.	PUNCT
ejpam-2537	212	1	from	from	ADP
ejpam-2537	212	2	theorem	theorem	NOUN
ejpam-2537	212	3	1	1	NUM
ejpam-2537	212	4	,	,	PUNCT
ejpam-2537	212	5	this	this	PRON
ejpam-2537	212	6	is	be	AUX
ejpam-2537	212	7	also	also	ADV
ejpam-2537	212	8	so	so	ADV
ejpam-2537	212	9	if	if	SCONJ
ejpam-2537	213	1	and	and	CCONJ
ejpam-2537	213	2	only	only	ADV
ejpam-2537	213	3	if	if	SCONJ
ejpam-2537	213	4	φ1,1(µ̄	φ1,1(µ̄	NOUN
ejpam-2537	213	5	′(c	′(c	ADP
ejpam-2537	213	6	)	)	PUNCT
ejpam-2537	213	7	)	)	PUNCT
ejpam-2537	213	8	is	be	AUX
ejpam-2537	213	9	permutation	permutation	NOUN
ejpam-2537	213	10	equivalent	equivalent	ADJ
ejpam-2537	213	11	to	to	ADP
ejpam-2537	213	12	a	a	DET
ejpam-2537	213	13	linear	linear	ADJ
ejpam-2537	213	14	cyclic	cyclic	ADJ
ejpam-2537	213	15	code	code	NOUN
ejpam-2537	213	16	over	over	ADP
ejpam-2537	213	17	f2	f2	PROPN
ejpam-2537	213	18	+	+	CCONJ
ejpam-2537	213	19	vf2	vf2	ADJ
ejpam-2537	213	20	.	.	PUNCT
ejpam-2537	214	1	from	from	ADP
ejpam-2537	214	2	proposition	proposition	NOUN
ejpam-2537	214	3	3	3	NUM
ejpam-2537	214	4	,	,	PUNCT
ejpam-2537	214	5	φ1,1(c	φ1,1(c	PROPN
ejpam-2537	214	6	)	)	PUNCT
ejpam-2537	214	7	is	be	AUX
ejpam-2537	214	8	permutation	permutation	NOUN
ejpam-2537	214	9	equivalent	equivalent	ADJ
ejpam-2537	214	10	to	to	PART
ejpam-2537	214	11	linear	linear	VERB
ejpam-2537	214	12	cyclic	cyclic	NOUN
ejpam-2537	214	13	over	over	ADP
ejpam-2537	214	14	f2	f2	PROPN
ejpam-2537	214	15	+	+	CCONJ
ejpam-2537	214	16	vf2	vf2	ADJ
ejpam-2537	214	17	.	.	PUNCT
ejpam-2537	215	1	3	3	X
ejpam-2537	215	2	.	.	X
ejpam-2537	215	3	a	a	DET
ejpam-2537	215	4	representation	representation	NOUN
ejpam-2537	215	5	of	of	ADP
ejpam-2537	215	6	a	a	DET
ejpam-2537	215	7	code	code	NOUN
ejpam-2537	215	8	over	over	ADP
ejpam-2537	215	9	r	r	NOUN
ejpam-2537	215	10	in	in	ADP
ejpam-2537	215	11	this	this	DET
ejpam-2537	215	12	section	section	NOUN
ejpam-2537	215	13	,	,	PUNCT
ejpam-2537	215	14	it	it	PRON
ejpam-2537	215	15	will	will	AUX
ejpam-2537	215	16	be	be	AUX
ejpam-2537	215	17	obtained	obtain	VERB
ejpam-2537	215	18	a	a	DET
ejpam-2537	215	19	representation	representation	NOUN
ejpam-2537	215	20	of	of	ADP
ejpam-2537	215	21	a	a	DET
ejpam-2537	215	22	linear	linear	ADJ
ejpam-2537	215	23	code	code	NOUN
ejpam-2537	215	24	of	of	ADP
ejpam-2537	215	25	length	length	NOUN
ejpam-2537	215	26	n	n	CCONJ
ejpam-2537	215	27	over	over	ADP
ejpam-2537	215	28	r	r	NOUN
ejpam-2537	215	29	by	by	ADP
ejpam-2537	215	30	means	mean	NOUN
ejpam-2537	215	31	of	of	ADP
ejpam-2537	215	32	c1	c1	PROPN
ejpam-2537	215	33	and	and	CCONJ
ejpam-2537	215	34	c2	c2	PROPN
ejpam-2537	215	35	which	which	PRON
ejpam-2537	215	36	are	be	AUX
ejpam-2537	215	37	linear	linear	NOUN
ejpam-2537	215	38	codes	code	NOUN
ejpam-2537	215	39	of	of	ADP
ejpam-2537	215	40	length	length	NOUN
ejpam-2537	215	41	n	n	NOUN
ejpam-2537	215	42	over	over	ADP
ejpam-2537	215	43	f2	f2	PROPN
ejpam-2537	215	44	+	+	CCONJ
ejpam-2537	215	45	uf2	uf2	NOUN
ejpam-2537	215	46	.	.	PUNCT
ejpam-2537	216	1	theorem	theorem	VERB
ejpam-2537	216	2	2	2	NUM
ejpam-2537	216	3	.	.	PUNCT
ejpam-2537	217	1	the	the	DET
ejpam-2537	217	2	map	map	NOUN
ejpam-2537	217	3	φ2,1	φ2,1	PROPN
ejpam-2537	217	4	:	:	PUNCT
ejpam-2537	217	5	rn→	rn→	X
ejpam-2537	217	6	(	(	PUNCT
ejpam-2537	217	7	f2	f2	PROPN
ejpam-2537	217	8	+	+	NUM
ejpam-2537	217	9	uf2	uf2	NOUN
ejpam-2537	217	10	)	)	PUNCT
ejpam-2537	217	11	2n	2n	NUM
ejpam-2537	217	12	is	be	AUX
ejpam-2537	217	13	a	a	DET
ejpam-2537	217	14	linear	linear	ADJ
ejpam-2537	217	15	isometry	isometry	NOUN
ejpam-2537	217	16	.	.	PUNCT
ejpam-2537	218	1	proof	proof	NOUN
ejpam-2537	218	2	.	.	PUNCT
ejpam-2537	219	1	for	for	ADP
ejpam-2537	219	2	any	any	DET
ejpam-2537	219	3	m	m	NOUN
ejpam-2537	219	4	,	,	PUNCT
ejpam-2537	219	5	k	k	PROPN
ejpam-2537	219	6	∈	∈	PROPN
ejpam-2537	219	7	rn	rn	PROPN
ejpam-2537	219	8	and	and	CCONJ
ejpam-2537	219	9	s	s	PROPN
ejpam-2537	219	10	,	,	PUNCT
ejpam-2537	219	11	t	t	PROPN
ejpam-2537	219	12	∈	∈	PROPN
ejpam-2537	219	13	f2	f2	PROPN
ejpam-2537	219	14	+	+	CCONJ
ejpam-2537	219	15	uf2	uf2	NOUN
ejpam-2537	219	16	,	,	PUNCT
ejpam-2537	219	17	it	it	PRON
ejpam-2537	219	18	is	be	AUX
ejpam-2537	219	19	verified	verify	VERB
ejpam-2537	219	20	that	that	SCONJ
ejpam-2537	219	21	φ2,1(sm+	φ2,1(sm+	PROPN
ejpam-2537	219	22	tk	tk	PROPN
ejpam-2537	219	23	)	)	PUNCT
ejpam-2537	219	24	=	=	SYM
ejpam-2537	219	25	sφ2,1(m	sφ2,1(m	PROPN
ejpam-2537	219	26	)	)	PUNCT
ejpam-2537	219	27	+	+	NUM
ejpam-2537	220	1	tφ2,1(k	tφ2,1(k	NOUN
ejpam-2537	220	2	)	)	PUNCT
ejpam-2537	220	3	,	,	PUNCT
ejpam-2537	220	4	so	so	ADV
ejpam-2537	220	5	φ2,1	φ2,1	PROPN
ejpam-2537	220	6	is	be	AUX
ejpam-2537	220	7	linear	linear	ADJ
ejpam-2537	220	8	.	.	PUNCT
ejpam-2537	221	1	for	for	ADP
ejpam-2537	221	2	isometry	isometry	NOUN
ejpam-2537	221	3	,	,	PUNCT
ejpam-2537	221	4	we	we	PRON
ejpam-2537	221	5	get	get	VERB
ejpam-2537	221	6	dl(φ2,1(m),φ2,1(k	dl(φ2,1(m),φ2,1(k	NOUN
ejpam-2537	221	7	)	)	PUNCT
ejpam-2537	221	8	)	)	PUNCT
ejpam-2537	222	1	=	=	PRON
ejpam-2537	222	2	wl(φ2,1(m−	wl(φ2,1(m−	X
ejpam-2537	222	3	k	k	NOUN
ejpam-2537	222	4	)	)	PUNCT
ejpam-2537	222	5	)	)	PUNCT
ejpam-2537	223	1	=	=	SYM
ejpam-2537	224	1	wl(m−	wl(m−	X
ejpam-2537	224	2	k	k	X
ejpam-2537	224	3	)	)	PUNCT
ejpam-2537	224	4	=	=	SYM
ejpam-2537	224	5	dl(m	dl(m	PROPN
ejpam-2537	224	6	,	,	PUNCT
ejpam-2537	224	7	k	k	NOUN
ejpam-2537	224	8	)	)	PUNCT
ejpam-2537	224	9	.	.	PUNCT
ejpam-2537	225	1	a.	a.	PROPN
ejpam-2537	225	2	dertli	dertli	PROPN
ejpam-2537	225	3	,	,	PUNCT
ejpam-2537	225	4	y.	y.	PROPN
ejpam-2537	225	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	225	6	/	/	SYM
ejpam-2537	225	7	eur	eur	PROPN
ejpam-2537	225	8	.	.	PUNCT
ejpam-2537	226	1	j.	j.	PROPN
ejpam-2537	226	2	pure	pure	PROPN
ejpam-2537	226	3	appl	appl	PROPN
ejpam-2537	226	4	.	.	PROPN
ejpam-2537	226	5	math	math	PROPN
ejpam-2537	226	6	,	,	PUNCT
ejpam-2537	226	7	9	9	NUM
ejpam-2537	226	8	(	(	PUNCT
ejpam-2537	226	9	2016	2016	NUM
ejpam-2537	226	10	)	)	PUNCT
ejpam-2537	226	11	,	,	PUNCT
ejpam-2537	226	12	305	305	NUM
ejpam-2537	226	13	-	-	SYM
ejpam-2537	226	14	313	313	NUM
ejpam-2537	226	15	310	310	NUM
ejpam-2537	226	16	theorem	theorem	NOUN
ejpam-2537	226	17	3	3	NUM
ejpam-2537	226	18	.	.	PUNCT
ejpam-2537	227	1	if	if	SCONJ
ejpam-2537	227	2	c	c	PROPN
ejpam-2537	227	3	is	be	AUX
ejpam-2537	227	4	a	a	DET
ejpam-2537	227	5	linear	linear	ADJ
ejpam-2537	227	6	code	code	NOUN
ejpam-2537	227	7	of	of	ADP
ejpam-2537	227	8	length	length	NOUN
ejpam-2537	227	9	n	n	CCONJ
ejpam-2537	227	10	over	over	ADP
ejpam-2537	227	11	r	r	NOUN
ejpam-2537	227	12	,	,	PUNCT
ejpam-2537	227	13	then	then	ADV
ejpam-2537	227	14	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	227	15	)	)	PUNCT
ejpam-2537	227	16	is	be	AUX
ejpam-2537	227	17	a	a	DET
ejpam-2537	227	18	linear	linear	ADJ
ejpam-2537	227	19	code	code	NOUN
ejpam-2537	227	20	of	of	ADP
ejpam-2537	227	21	length	length	NOUN
ejpam-2537	227	22	2n	2n	NUM
ejpam-2537	227	23	over	over	ADP
ejpam-2537	227	24	f2	f2	PROPN
ejpam-2537	227	25	+	+	X
ejpam-2537	227	26	uf2	uf2	NOUN
ejpam-2537	227	27	.	.	PUNCT
ejpam-2537	228	1	proof	proof	NOUN
ejpam-2537	228	2	.	.	PUNCT
ejpam-2537	229	1	it	it	PRON
ejpam-2537	229	2	is	be	AUX
ejpam-2537	229	3	seen	see	VERB
ejpam-2537	229	4	from	from	ADP
ejpam-2537	229	5	linearity	linearity	NOUN
ejpam-2537	229	6	of	of	ADP
ejpam-2537	229	7	φ2,1	φ2,1	PROPN
ejpam-2537	229	8	.	.	PUNCT
ejpam-2537	230	1	let	let	VERB
ejpam-2537	230	2	a	a	PRON
ejpam-2537	230	3	and	and	CCONJ
ejpam-2537	230	4	b	b	NOUN
ejpam-2537	230	5	be	be	AUX
ejpam-2537	230	6	two	two	NUM
ejpam-2537	230	7	codes	code	NOUN
ejpam-2537	230	8	.	.	PUNCT
ejpam-2537	231	1	the	the	DET
ejpam-2537	231	2	direct	direct	ADJ
ejpam-2537	231	3	product	product	NOUN
ejpam-2537	231	4	and	and	CCONJ
ejpam-2537	231	5	sum	sum	NOUN
ejpam-2537	231	6	of	of	ADP
ejpam-2537	231	7	a	a	PRON
ejpam-2537	231	8	and	and	CCONJ
ejpam-2537	231	9	b	b	NOUN
ejpam-2537	231	10	are	be	AUX
ejpam-2537	231	11	defined	define	VERB
ejpam-2537	231	12	by	by	ADP
ejpam-2537	231	13	,	,	PUNCT
ejpam-2537	231	14	respectively	respectively	ADV
ejpam-2537	231	15	a⊗	a⊗	PROPN
ejpam-2537	231	16	b	b	PROPN
ejpam-2537	231	17	=	=	NOUN
ejpam-2537	231	18	{	{	PUNCT
ejpam-2537	231	19	(	(	PUNCT
ejpam-2537	231	20	a	a	PRON
ejpam-2537	231	21	,	,	PUNCT
ejpam-2537	231	22	b)|a	b)|a	NOUN
ejpam-2537	231	23	∈	∈	PROPN
ejpam-2537	231	24	a	a	PRON
ejpam-2537	231	25	,	,	PUNCT
ejpam-2537	231	26	b	b	PROPN
ejpam-2537	231	27	∈	∈	PROPN
ejpam-2537	231	28	b	b	PROPN
ejpam-2537	231	29	}	}	PUNCT
ejpam-2537	232	1	a⊕	a⊕	NOUN
ejpam-2537	232	2	b	b	NOUN
ejpam-2537	232	3	=	=	NOUN
ejpam-2537	232	4	{	{	PUNCT
ejpam-2537	232	5	a+	a+	PRON
ejpam-2537	232	6	b|a	b|a	PROPN
ejpam-2537	232	7	∈	∈	PROPN
ejpam-2537	232	8	a	a	PRON
ejpam-2537	232	9	,	,	PUNCT
ejpam-2537	232	10	b	b	PROPN
ejpam-2537	232	11	∈	∈	PROPN
ejpam-2537	232	12	b	b	NOUN
ejpam-2537	232	13	}	}	PUNCT
ejpam-2537	232	14	.	.	PUNCT
ejpam-2537	233	1	theorem	theorem	NOUN
ejpam-2537	233	2	4	4	NUM
ejpam-2537	233	3	.	.	PUNCT
ejpam-2537	234	1	if	if	SCONJ
ejpam-2537	234	2	c	c	PRON
ejpam-2537	234	3	be	be	AUX
ejpam-2537	234	4	a	a	DET
ejpam-2537	234	5	linear	linear	ADJ
ejpam-2537	234	6	code	code	NOUN
ejpam-2537	234	7	of	of	ADP
ejpam-2537	234	8	length	length	NOUN
ejpam-2537	234	9	n	n	CCONJ
ejpam-2537	234	10	over	over	ADP
ejpam-2537	234	11	r	r	NOUN
ejpam-2537	234	12	,	,	PUNCT
ejpam-2537	234	13	then	then	ADV
ejpam-2537	234	14	c	c	X
ejpam-2537	234	15	=	=	SYM
ejpam-2537	234	16	(	(	PUNCT
ejpam-2537	234	17	1	1	NUM
ejpam-2537	234	18	+	+	NUM
ejpam-2537	234	19	v)c1⊕	v)c1⊕	PROPN
ejpam-2537	234	20	vc2	vc2	PROPN
ejpam-2537	234	21	,	,	PUNCT
ejpam-2537	234	22	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	234	23	)	)	PUNCT
ejpam-2537	234	24	=	=	SYM
ejpam-2537	234	25	c1⊗c2	c1⊗c2	PROPN
ejpam-2537	234	26	and	and	CCONJ
ejpam-2537	234	27	|c	|c	PROPN
ejpam-2537	234	28	|	|	NOUN
ejpam-2537	234	29	=	=	SYM
ejpam-2537	234	30	|c1||c2|	|c1||c2|	PROPN
ejpam-2537	234	31	where	where	SCONJ
ejpam-2537	234	32	c1	c1	PROPN
ejpam-2537	234	33	=	=	PUNCT
ejpam-2537	234	34	{	{	PUNCT
ejpam-2537	234	35	m	m	VERB
ejpam-2537	234	36	∈	∈	PROPN
ejpam-2537	234	37	(	(	PUNCT
ejpam-2537	234	38	f2	f2	PROPN
ejpam-2537	234	39	+	+	NUM
ejpam-2537	234	40	uf2	uf2	NOUN
ejpam-2537	234	41	)	)	PUNCT
ejpam-2537	234	42	n|m	n|m	PUNCT
ejpam-2537	235	1	+	+	CCONJ
ejpam-2537	235	2	vt	vt	PROPN
ejpam-2537	235	3	∈	∈	PROPN
ejpam-2537	235	4	c	c	PROPN
ejpam-2537	235	5	for	for	ADP
ejpam-2537	235	6	some	some	DET
ejpam-2537	235	7	t	t	NOUN
ejpam-2537	235	8	∈	∈	PROPN
ejpam-2537	235	9	(	(	PUNCT
ejpam-2537	235	10	f2	f2	PROPN
ejpam-2537	235	11	+	+	NUM
ejpam-2537	235	12	uf2	uf2	NOUN
ejpam-2537	235	13	)	)	PUNCT
ejpam-2537	235	14	n	n	CCONJ
ejpam-2537	235	15	}	}	PUNCT
ejpam-2537	235	16	and	and	CCONJ
ejpam-2537	235	17	c2	c2	PROPN
ejpam-2537	235	18	=	=	SYM
ejpam-2537	235	19	{	{	PUNCT
ejpam-2537	235	20	m+	m+	NOUN
ejpam-2537	235	21	t	t	PROPN
ejpam-2537	235	22	∈	∈	PROPN
ejpam-2537	235	23	(	(	PUNCT
ejpam-2537	235	24	f2	f2	PROPN
ejpam-2537	235	25	+	+	NUM
ejpam-2537	235	26	uf2	uf2	NOUN
ejpam-2537	235	27	)	)	PUNCT
ejpam-2537	235	28	n|m+	n|m+	ADP
ejpam-2537	235	29	vt	vt	PROPN
ejpam-2537	235	30	∈	∈	PROPN
ejpam-2537	235	31	c	c	PROPN
ejpam-2537	235	32	for	for	ADP
ejpam-2537	235	33	some	some	DET
ejpam-2537	235	34	m	m	NOUN
ejpam-2537	235	35	∈	∈	NOUN
ejpam-2537	235	36	(	(	PUNCT
ejpam-2537	235	37	f2	f2	PROPN
ejpam-2537	235	38	+	+	NUM
ejpam-2537	235	39	uf2	uf2	NOUN
ejpam-2537	235	40	)	)	PUNCT
ejpam-2537	235	41	n	n	CCONJ
ejpam-2537	235	42	}	}	PUNCT
ejpam-2537	235	43	.	.	PUNCT
ejpam-2537	236	1	proof	proof	NOUN
ejpam-2537	236	2	.	.	PUNCT
ejpam-2537	237	1	let	let	VERB
ejpam-2537	237	2	c	c	NOUN
ejpam-2537	237	3	=	=	VERB
ejpam-2537	237	4	m	m	PROPN
ejpam-2537	237	5	+	+	NUM
ejpam-2537	237	6	vt	vt	PROPN
ejpam-2537	237	7	∈	∈	PROPN
ejpam-2537	237	8	c	c	PROPN
ejpam-2537	237	9	for	for	ADP
ejpam-2537	237	10	some	some	DET
ejpam-2537	237	11	m	m	NOUN
ejpam-2537	237	12	,	,	PUNCT
ejpam-2537	237	13	t	t	PROPN
ejpam-2537	237	14	∈	∈	PROPN
ejpam-2537	237	15	(	(	PUNCT
ejpam-2537	237	16	f2	f2	PROPN
ejpam-2537	237	17	+	+	NUM
ejpam-2537	237	18	uf2	uf2	NOUN
ejpam-2537	237	19	)	)	PUNCT
ejpam-2537	237	20	n.	n.	NOUN
ejpam-2537	238	1	so	so	ADV
ejpam-2537	238	2	m	m	PROPN
ejpam-2537	238	3	∈	∈	PROPN
ejpam-2537	238	4	c1	c1	NOUN
ejpam-2537	238	5	,	,	PUNCT
ejpam-2537	238	6	m	m	PROPN
ejpam-2537	238	7	+	+	NUM
ejpam-2537	238	8	t	t	PROPN
ejpam-2537	238	9	∈	∈	PROPN
ejpam-2537	238	10	c2	c2	PROPN
ejpam-2537	238	11	.	.	PUNCT
ejpam-2537	239	1	hence	hence	ADV
ejpam-2537	239	2	c	c	NOUN
ejpam-2537	240	1	=	=	PUNCT
ejpam-2537	240	2	(	(	PUNCT
ejpam-2537	240	3	1	1	NUM
ejpam-2537	240	4	+	+	NUM
ejpam-2537	240	5	v)m+	v)m+	NUM
ejpam-2537	240	6	v(m+	v(m+	X
ejpam-2537	240	7	t	t	X
ejpam-2537	240	8	)	)	PUNCT
ejpam-2537	240	9	∈	∈	PROPN
ejpam-2537	240	10	(	(	PUNCT
ejpam-2537	240	11	1	1	NUM
ejpam-2537	240	12	+	+	NUM
ejpam-2537	240	13	v)c1	v)c1	PROPN
ejpam-2537	240	14	⊕	⊕	PROPN
ejpam-2537	240	15	vc2	vc2	PROPN
ejpam-2537	240	16	.	.	PUNCT
ejpam-2537	241	1	we	we	PRON
ejpam-2537	241	2	have	have	VERB
ejpam-2537	241	3	c	c	NOUN
ejpam-2537	241	4	⊆	⊆	NUM
ejpam-2537	241	5	(	(	PUNCT
ejpam-2537	241	6	1	1	NUM
ejpam-2537	241	7	+	+	NUM
ejpam-2537	241	8	v)c1	v)c1	PROPN
ejpam-2537	241	9	⊕	⊕	PROPN
ejpam-2537	241	10	vc2	vc2	PROPN
ejpam-2537	241	11	.	.	PUNCT
ejpam-2537	242	1	on	on	ADP
ejpam-2537	242	2	the	the	DET
ejpam-2537	242	3	other	other	ADJ
ejpam-2537	242	4	hand	hand	NOUN
ejpam-2537	242	5	,	,	PUNCT
ejpam-2537	242	6	(	(	PUNCT
ejpam-2537	242	7	1	1	NUM
ejpam-2537	242	8	+	+	NUM
ejpam-2537	242	9	v)m	v)m	X
ejpam-2537	243	1	+	+	CCONJ
ejpam-2537	243	2	v(m	v(m	PROPN
ejpam-2537	243	3	+	+	NUM
ejpam-2537	243	4	t	t	NOUN
ejpam-2537	243	5	)	)	PUNCT
ejpam-2537	243	6	∈	∈	PROPN
ejpam-2537	243	7	(	(	PUNCT
ejpam-2537	243	8	1	1	NUM
ejpam-2537	243	9	+	+	NUM
ejpam-2537	243	10	v)c1	v)c1	PROPN
ejpam-2537	243	11	⊕	⊕	PROPN
ejpam-2537	243	12	vc2	vc2	PROPN
ejpam-2537	243	13	where	where	SCONJ
ejpam-2537	243	14	m	m	PROPN
ejpam-2537	243	15	∈	∈	PROPN
ejpam-2537	243	16	c1	c1	PROPN
ejpam-2537	243	17	and	and	CCONJ
ejpam-2537	243	18	t	t	PROPN
ejpam-2537	243	19	∈	∈	PROPN
ejpam-2537	243	20	c2	c2	PROPN
ejpam-2537	243	21	,	,	PUNCT
ejpam-2537	243	22	there	there	PRON
ejpam-2537	243	23	exist	exist	VERB
ejpam-2537	243	24	a	a	DET
ejpam-2537	243	25	,	,	PUNCT
ejpam-2537	243	26	b	b	PROPN
ejpam-2537	243	27	∈	∈	PROPN
ejpam-2537	243	28	c	c	NOUN
ejpam-2537	243	29	and	and	CCONJ
ejpam-2537	243	30	r	r	NOUN
ejpam-2537	243	31	,	,	PUNCT
ejpam-2537	243	32	q	q	NOUN
ejpam-2537	243	33	∈	∈	PROPN
ejpam-2537	243	34	(	(	PUNCT
ejpam-2537	243	35	f2	f2	PROPN
ejpam-2537	243	36	+	+	NUM
ejpam-2537	243	37	uf2	uf2	NOUN
ejpam-2537	243	38	)	)	PUNCT
ejpam-2537	243	39	n	n	PRON
ejpam-2537	243	40	such	such	ADJ
ejpam-2537	243	41	that	that	SCONJ
ejpam-2537	243	42	a	a	DET
ejpam-2537	243	43	=	=	SYM
ejpam-2537	243	44	m+	m+	NUM
ejpam-2537	243	45	vr	vr	PROPN
ejpam-2537	243	46	and	and	CCONJ
ejpam-2537	243	47	b	b	X
ejpam-2537	243	48	=	=	SYM
ejpam-2537	243	49	m+	m+	NUM
ejpam-2537	243	50	t	t	NOUN
ejpam-2537	243	51	+	+	CCONJ
ejpam-2537	243	52	(	(	PUNCT
ejpam-2537	243	53	1	1	NUM
ejpam-2537	243	54	+	+	NUM
ejpam-2537	243	55	v)q	v)q	NOUN
ejpam-2537	243	56	.	.	PUNCT
ejpam-2537	244	1	as	as	SCONJ
ejpam-2537	244	2	c	c	PROPN
ejpam-2537	244	3	is	be	AUX
ejpam-2537	244	4	linear	linear	ADJ
ejpam-2537	244	5	over	over	ADP
ejpam-2537	244	6	r	r	NOUN
ejpam-2537	244	7	,	,	PUNCT
ejpam-2537	244	8	from	from	ADP
ejpam-2537	244	9	c	c	NOUN
ejpam-2537	244	10	=	=	SYM
ejpam-2537	244	11	(	(	PUNCT
ejpam-2537	244	12	1	1	NUM
ejpam-2537	244	13	+	+	SYM
ejpam-2537	244	14	v)a+	v)a+	NUM
ejpam-2537	244	15	vb	vb	X
ejpam-2537	244	16	∈	∈	NOUN
ejpam-2537	244	17	c	c	NOUN
ejpam-2537	244	18	we	we	PRON
ejpam-2537	244	19	have	have	VERB
ejpam-2537	244	20	(	(	PUNCT
ejpam-2537	244	21	1	1	NUM
ejpam-2537	244	22	+	+	NUM
ejpam-2537	244	23	v)c1	v)c1	PROPN
ejpam-2537	244	24	⊕	⊕	PROPN
ejpam-2537	244	25	vc2	vc2	PROPN
ejpam-2537	245	1	⊆	⊆	NUM
ejpam-2537	245	2	c	c	NOUN
ejpam-2537	245	3	.	.	PUNCT
ejpam-2537	246	1	theorem	theorem	ADJ
ejpam-2537	246	2	5	5	NUM
ejpam-2537	246	3	.	.	PUNCT
ejpam-2537	247	1	a	a	DET
ejpam-2537	247	2	linear	linear	ADJ
ejpam-2537	247	3	code	code	NOUN
ejpam-2537	247	4	c	c	NOUN
ejpam-2537	247	5	=	=	PUNCT
ejpam-2537	247	6	(	(	PUNCT
ejpam-2537	247	7	1	1	NUM
ejpam-2537	247	8	+	+	NUM
ejpam-2537	247	9	v)c1⊕	v)c1⊕	PRON
ejpam-2537	247	10	vc2	vc2	PROPN
ejpam-2537	247	11	cyclic	cyclic	NOUN
ejpam-2537	247	12	over	over	ADP
ejpam-2537	247	13	r	r	NOUN
ejpam-2537	247	14	if	if	SCONJ
ejpam-2537	248	1	and	and	CCONJ
ejpam-2537	248	2	only	only	ADV
ejpam-2537	248	3	if	if	SCONJ
ejpam-2537	248	4	c1	c1	PROPN
ejpam-2537	248	5	and	and	CCONJ
ejpam-2537	248	6	c2	c2	PROPN
ejpam-2537	248	7	are	be	AUX
ejpam-2537	248	8	all	all	PRON
ejpam-2537	248	9	cyclic	cyclic	ADJ
ejpam-2537	248	10	codes	code	NOUN
ejpam-2537	248	11	over	over	ADP
ejpam-2537	248	12	f2	f2	PROPN
ejpam-2537	248	13	+	+	X
ejpam-2537	248	14	uf2	uf2	NOUN
ejpam-2537	248	15	.	.	PUNCT
ejpam-2537	249	1	proof	proof	NOUN
ejpam-2537	249	2	.	.	PUNCT
ejpam-2537	250	1	let	let	VERB
ejpam-2537	250	2	(	(	PUNCT
ejpam-2537	250	3	r0	r0	VERB
ejpam-2537	250	4	,	,	PUNCT
ejpam-2537	250	5	.	.	PUNCT
ejpam-2537	250	6	.	.	PUNCT
ejpam-2537	251	1	.	.	PUNCT
ejpam-2537	252	1	,	,	PUNCT
ejpam-2537	252	2	rn−1	rn−1	NOUN
ejpam-2537	252	3	)	)	PUNCT
ejpam-2537	252	4	∈	∈	PROPN
ejpam-2537	252	5	c1	c1	PROPN
ejpam-2537	252	6	and	and	CCONJ
ejpam-2537	252	7	(	(	PUNCT
ejpam-2537	252	8	s0	s0	PROPN
ejpam-2537	252	9	,	,	PUNCT
ejpam-2537	252	10	.	.	PUNCT
ejpam-2537	252	11	.	.	PUNCT
ejpam-2537	253	1	.	.	PUNCT
ejpam-2537	254	1	,	,	PUNCT
ejpam-2537	254	2	sn−1	sn−1	PROPN
ejpam-2537	254	3	)	)	PUNCT
ejpam-2537	254	4	∈	∈	PROPN
ejpam-2537	254	5	c2	c2	PROPN
ejpam-2537	254	6	.	.	PUNCT
ejpam-2537	254	7	suppose	suppose	VERB
ejpam-2537	254	8	that	that	SCONJ
ejpam-2537	254	9	ci	ci	PROPN
ejpam-2537	254	10	=	=	PUNCT
ejpam-2537	254	11	(	(	PUNCT
ejpam-2537	254	12	1	1	NUM
ejpam-2537	254	13	+	+	NUM
ejpam-2537	254	14	v)ri	v)ri	PROPN
ejpam-2537	254	15	+	+	CCONJ
ejpam-2537	254	16	vsi	vsi	PROPN
ejpam-2537	254	17	for	for	ADP
ejpam-2537	254	18	i	i	PROPN
ejpam-2537	254	19	=	=	NOUN
ejpam-2537	254	20	0	0	NUM
ejpam-2537	254	21	,	,	PUNCT
ejpam-2537	254	22	.	.	PUNCT
ejpam-2537	254	23	.	.	PUNCT
ejpam-2537	255	1	.	.	PUNCT
ejpam-2537	256	1	,	,	PUNCT
ejpam-2537	256	2	n−1	n−1	PROPN
ejpam-2537	256	3	.	.	PUNCT
ejpam-2537	256	4	let	let	VERB
ejpam-2537	256	5	c	c	NOUN
ejpam-2537	256	6	=	=	SYM
ejpam-2537	256	7	(	(	PUNCT
ejpam-2537	256	8	c0	c0	NOUN
ejpam-2537	256	9	,	,	PUNCT
ejpam-2537	256	10	.	.	PUNCT
ejpam-2537	256	11	.	.	PUNCT
ejpam-2537	257	1	.	.	PUNCT
ejpam-2537	258	1	,	,	PUNCT
ejpam-2537	258	2	cn−1	cn−1	X
ejpam-2537	258	3	)	)	PUNCT
ejpam-2537	258	4	∈	∈	PROPN
ejpam-2537	258	5	c	c	NOUN
ejpam-2537	258	6	.	.	PUNCT
ejpam-2537	259	1	as	as	SCONJ
ejpam-2537	259	2	c	c	PROPN
ejpam-2537	259	3	is	be	AUX
ejpam-2537	259	4	cyclic	cyclic	ADJ
ejpam-2537	259	5	,	,	PUNCT
ejpam-2537	259	6	it	it	PRON
ejpam-2537	259	7	follows	follow	VERB
ejpam-2537	259	8	that	that	SCONJ
ejpam-2537	259	9	(	(	PUNCT
ejpam-2537	259	10	cn−1	cn−1	PROPN
ejpam-2537	259	11	,	,	PUNCT
ejpam-2537	259	12	c0	c0	NOUN
ejpam-2537	259	13	,	,	PUNCT
ejpam-2537	259	14	.	.	PUNCT
ejpam-2537	259	15	.	.	PUNCT
ejpam-2537	260	1	.	.	PUNCT
ejpam-2537	261	1	,	,	PUNCT
ejpam-2537	261	2	cn−2	cn−2	PROPN
ejpam-2537	261	3	)	)	PUNCT
ejpam-2537	261	4	∈	∈	PROPN
ejpam-2537	261	5	c	c	PROPN
ejpam-2537	261	6	.	.	PUNCT
ejpam-2537	262	1	note	note	VERB
ejpam-2537	262	2	that	that	SCONJ
ejpam-2537	262	3	(	(	PUNCT
ejpam-2537	262	4	cn−1	cn−1	PROPN
ejpam-2537	262	5	,	,	PUNCT
ejpam-2537	262	6	c0	c0	NOUN
ejpam-2537	262	7	,	,	PUNCT
ejpam-2537	262	8	.	.	PUNCT
ejpam-2537	262	9	.	.	PUNCT
ejpam-2537	263	1	.	.	PUNCT
ejpam-2537	264	1	,	,	PUNCT
ejpam-2537	264	2	cn−2	cn−2	PROPN
ejpam-2537	264	3	)	)	PUNCT
ejpam-2537	264	4	=	=	PUNCT
ejpam-2537	265	1	(	(	PUNCT
ejpam-2537	265	2	1	1	NUM
ejpam-2537	265	3	+	+	CCONJ
ejpam-2537	265	4	v)(rn−1	v)(rn−1	PROPN
ejpam-2537	265	5	,	,	PUNCT
ejpam-2537	265	6	r0	r0	NOUN
ejpam-2537	265	7	,	,	PUNCT
ejpam-2537	265	8	.	.	PUNCT
ejpam-2537	265	9	.	.	PUNCT
ejpam-2537	266	1	.	.	PUNCT
ejpam-2537	267	1	,	,	PUNCT
ejpam-2537	267	2	rn−2	rn−2	PROPN
ejpam-2537	267	3	)	)	PUNCT
ejpam-2537	267	4	+	+	NUM
ejpam-2537	267	5	v(sn−1	v(sn−1	PROPN
ejpam-2537	267	6	,	,	PUNCT
ejpam-2537	267	7	s0	s0	PROPN
ejpam-2537	267	8	,	,	PUNCT
ejpam-2537	267	9	.	.	PUNCT
ejpam-2537	267	10	.	.	PUNCT
ejpam-2537	268	1	.	.	PUNCT
ejpam-2537	269	1	,	,	PUNCT
ejpam-2537	269	2	sn−2	sn−2	PROPN
ejpam-2537	269	3	)	)	PUNCT
ejpam-2537	269	4	.	.	PUNCT
ejpam-2537	270	1	so	so	ADV
ejpam-2537	270	2	(	(	PUNCT
ejpam-2537	270	3	rn−1	rn−1	PROPN
ejpam-2537	270	4	,	,	PUNCT
ejpam-2537	270	5	r0	r0	NOUN
ejpam-2537	270	6	,	,	PUNCT
ejpam-2537	270	7	.	.	PUNCT
ejpam-2537	270	8	.	.	PUNCT
ejpam-2537	271	1	.	.	PUNCT
ejpam-2537	272	1	,	,	PUNCT
ejpam-2537	272	2	rn−2	rn−2	PROPN
ejpam-2537	272	3	)	)	PUNCT
ejpam-2537	272	4	∈	∈	PROPN
ejpam-2537	272	5	c1	c1	NOUN
ejpam-2537	272	6	,	,	PUNCT
ejpam-2537	272	7	(	(	PUNCT
ejpam-2537	272	8	sn−1	sn−1	PROPN
ejpam-2537	272	9	,	,	PUNCT
ejpam-2537	272	10	s0	s0	PROPN
ejpam-2537	272	11	,	,	PUNCT
ejpam-2537	272	12	.	.	PUNCT
ejpam-2537	272	13	.	.	PUNCT
ejpam-2537	272	14	.	.	PUNCT
ejpam-2537	273	1	,	,	PUNCT
ejpam-2537	273	2	sn−2	sn−2	PROPN
ejpam-2537	273	3	)	)	PUNCT
ejpam-2537	273	4	∈	∈	PROPN
ejpam-2537	273	5	c2	c2	PROPN
ejpam-2537	273	6	,	,	PUNCT
ejpam-2537	273	7	that	that	PRON
ejpam-2537	273	8	is	be	AUX
ejpam-2537	273	9	c1	c1	PROPN
ejpam-2537	273	10	,	,	PUNCT
ejpam-2537	273	11	c2	c2	PROPN
ejpam-2537	273	12	are	be	AUX
ejpam-2537	273	13	cyclic	cyclic	ADJ
ejpam-2537	273	14	codes	code	NOUN
ejpam-2537	273	15	over	over	ADP
ejpam-2537	273	16	f2	f2	PROPN
ejpam-2537	273	17	+	+	X
ejpam-2537	273	18	uf2	uf2	NOUN
ejpam-2537	273	19	.	.	PUNCT
ejpam-2537	274	1	conversely	conversely	ADV
ejpam-2537	274	2	,	,	PUNCT
ejpam-2537	274	3	let	let	VERB
ejpam-2537	274	4	c1	c1	PROPN
ejpam-2537	274	5	,	,	PUNCT
ejpam-2537	274	6	c2	c2	PROPN
ejpam-2537	274	7	be	be	VERB
ejpam-2537	274	8	cyclic	cyclic	ADJ
ejpam-2537	274	9	codes	code	NOUN
ejpam-2537	274	10	over	over	ADP
ejpam-2537	274	11	f2	f2	PROPN
ejpam-2537	274	12	+	+	X
ejpam-2537	274	13	uf2	uf2	NOUN
ejpam-2537	274	14	.	.	PUNCT
ejpam-2537	275	1	let	let	VERB
ejpam-2537	275	2	(	(	PUNCT
ejpam-2537	275	3	cn−1	cn−1	PROPN
ejpam-2537	275	4	,	,	PUNCT
ejpam-2537	275	5	c0	c0	NOUN
ejpam-2537	275	6	,	,	PUNCT
ejpam-2537	275	7	.	.	PUNCT
ejpam-2537	275	8	.	.	PUNCT
ejpam-2537	276	1	.	.	PUNCT
ejpam-2537	277	1	,	,	PUNCT
ejpam-2537	277	2	cn−2	cn−2	PROPN
ejpam-2537	277	3	)	)	PUNCT
ejpam-2537	277	4	∈	∈	PROPN
ejpam-2537	278	1	c	c	PROPN
ejpam-2537	278	2	where	where	SCONJ
ejpam-2537	278	3	ci	ci	NOUN
ejpam-2537	278	4	=	=	PUNCT
ejpam-2537	278	5	(	(	PUNCT
ejpam-2537	278	6	1	1	NUM
ejpam-2537	278	7	+	+	NUM
ejpam-2537	278	8	v)ri	v)ri	PROPN
ejpam-2537	278	9	+	+	CCONJ
ejpam-2537	278	10	vsi	vsi	PROPN
ejpam-2537	278	11	for	for	ADP
ejpam-2537	278	12	i	i	PROPN
ejpam-2537	278	13	=	=	NOUN
ejpam-2537	278	14	0	0	NUM
ejpam-2537	278	15	,	,	PUNCT
ejpam-2537	278	16	.	.	PUNCT
ejpam-2537	278	17	.	.	PUNCT
ejpam-2537	278	18	.	.	PUNCT
ejpam-2537	279	1	,	,	PUNCT
ejpam-2537	279	2	n−	n−	NOUN
ejpam-2537	279	3	1	1	NUM
ejpam-2537	279	4	.	.	PUNCT
ejpam-2537	280	1	then	then	ADV
ejpam-2537	280	2	(	(	PUNCT
ejpam-2537	280	3	r0	r0	NOUN
ejpam-2537	280	4	,	,	PUNCT
ejpam-2537	280	5	.	.	PUNCT
ejpam-2537	280	6	.	.	PUNCT
ejpam-2537	281	1	.	.	PUNCT
ejpam-2537	282	1	,	,	PUNCT
ejpam-2537	282	2	rn−1	rn−1	NOUN
ejpam-2537	282	3	)	)	PUNCT
ejpam-2537	282	4	∈	∈	PROPN
ejpam-2537	282	5	c1	c1	PROPN
ejpam-2537	282	6	and	and	CCONJ
ejpam-2537	282	7	(	(	PUNCT
ejpam-2537	282	8	s0	s0	PROPN
ejpam-2537	282	9	,	,	PUNCT
ejpam-2537	282	10	.	.	PUNCT
ejpam-2537	282	11	.	.	PUNCT
ejpam-2537	283	1	.	.	PUNCT
ejpam-2537	284	1	,	,	PUNCT
ejpam-2537	284	2	sn−1	sn−1	PROPN
ejpam-2537	284	3	)	)	PUNCT
ejpam-2537	284	4	∈	∈	PROPN
ejpam-2537	284	5	c2	c2	PROPN
ejpam-2537	284	6	.	.	PUNCT
ejpam-2537	285	1	note	note	VERB
ejpam-2537	285	2	that	that	SCONJ
ejpam-2537	285	3	(	(	PUNCT
ejpam-2537	285	4	cn−1	cn−1	PROPN
ejpam-2537	285	5	,	,	PUNCT
ejpam-2537	285	6	c0	c0	NOUN
ejpam-2537	285	7	,	,	PUNCT
ejpam-2537	285	8	.	.	PUNCT
ejpam-2537	285	9	.	.	PUNCT
ejpam-2537	286	1	.	.	PUNCT
ejpam-2537	287	1	,	,	PUNCT
ejpam-2537	287	2	cn−2	cn−2	PROPN
ejpam-2537	287	3	)	)	PUNCT
ejpam-2537	288	1	=	=	PUNCT
ejpam-2537	288	2	(	(	PUNCT
ejpam-2537	288	3	1+v)(rn−1	1+v)(rn−1	PROPN
ejpam-2537	288	4	,	,	PUNCT
ejpam-2537	288	5	r0	r0	NOUN
ejpam-2537	288	6	,	,	PUNCT
ejpam-2537	288	7	.	.	PUNCT
ejpam-2537	288	8	.	.	PUNCT
ejpam-2537	289	1	.	.	PUNCT
ejpam-2537	290	1	,	,	PUNCT
ejpam-2537	290	2	rn−2)+v(sn−1	rn−2)+v(sn−1	NUM
ejpam-2537	290	3	,	,	PUNCT
ejpam-2537	290	4	s0	s0	NOUN
ejpam-2537	290	5	,	,	PUNCT
ejpam-2537	290	6	.	.	PUNCT
ejpam-2537	290	7	.	.	PUNCT
ejpam-2537	291	1	.	.	PUNCT
ejpam-2537	292	1	,	,	PUNCT
ejpam-2537	292	2	sn−2	sn−2	PROPN
ejpam-2537	292	3	)	)	PUNCT
ejpam-2537	292	4	∈	∈	PROPN
ejpam-2537	292	5	(	(	PUNCT
ejpam-2537	292	6	1+v)c1⊕vc2	1+v)c1⊕vc2	NUM
ejpam-2537	292	7	=	=	SYM
ejpam-2537	292	8	c	c	X
ejpam-2537	292	9	.	.	PUNCT
ejpam-2537	293	1	so	so	ADV
ejpam-2537	293	2	c	c	PROPN
ejpam-2537	293	3	is	be	AUX
ejpam-2537	293	4	a	a	DET
ejpam-2537	293	5	cyclic	cyclic	ADJ
ejpam-2537	293	6	code	code	NOUN
ejpam-2537	293	7	.	.	PUNCT
ejpam-2537	294	1	theorem	theorem	VERB
ejpam-2537	294	2	6	6	NUM
ejpam-2537	294	3	.	.	PUNCT
ejpam-2537	295	1	let	let	VERB
ejpam-2537	295	2	c	c	PRON
ejpam-2537	295	3	be	be	AUX
ejpam-2537	295	4	a	a	DET
ejpam-2537	295	5	linear	linear	ADJ
ejpam-2537	295	6	code	code	NOUN
ejpam-2537	295	7	of	of	ADP
ejpam-2537	295	8	length	length	NOUN
ejpam-2537	295	9	n	n	PROPN
ejpam-2537	295	10	over	over	ADP
ejpam-2537	295	11	r.	r.	PROPN
ejpam-2537	295	12	then	then	ADV
ejpam-2537	295	13	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	295	14	⊥	⊥	NUM
ejpam-2537	295	15	)	)	PUNCT
ejpam-2537	296	1	=	=	SYM
ejpam-2537	296	2	(	(	PUNCT
ejpam-2537	296	3	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	296	4	)	)	PUNCT
ejpam-2537	296	5	)	)	PUNCT
ejpam-2537	297	1	⊥.	⊥.	NUM
ejpam-2537	297	2	proof	proof	NOUN
ejpam-2537	297	3	.	.	PUNCT
ejpam-2537	298	1	by	by	ADP
ejpam-2537	298	2	using	use	VERB
ejpam-2537	298	3	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	298	4	⊥	⊥	NUM
ejpam-2537	298	5	)	)	PUNCT
ejpam-2537	298	6	⊆	⊆	NUM
ejpam-2537	298	7	(	(	PUNCT
ejpam-2537	298	8	φ2,1(c	φ2,1(c	PROPN
ejpam-2537	298	9	)	)	PUNCT
ejpam-2537	298	10	)	)	PUNCT
ejpam-2537	299	1	⊥	⊥	NOUN
ejpam-2537	299	2	and	and	CCONJ
ejpam-2537	299	3	|φ2,1(c	|φ2,1(c	NOUN
ejpam-2537	299	4	⊥)|	⊥)|	NOUN
ejpam-2537	299	5	=	=	SYM
ejpam-2537	299	6	|(φ2,1(c	|(φ2,1(c	NOUN
ejpam-2537	299	7	)	)	PUNCT
ejpam-2537	299	8	)	)	PUNCT
ejpam-2537	299	9	⊥|	⊥|	PROPN
ejpam-2537	299	10	,	,	PUNCT
ejpam-2537	299	11	we	we	PRON
ejpam-2537	299	12	have	have	AUX
ejpam-2537	299	13	expected	expect	VERB
ejpam-2537	299	14	result	result	NOUN
ejpam-2537	299	15	.	.	PUNCT
ejpam-2537	300	1	theorem	theorem	ADJ
ejpam-2537	300	2	7	7	NUM
ejpam-2537	300	3	.	.	PUNCT
ejpam-2537	301	1	if	if	SCONJ
ejpam-2537	301	2	c	c	PROPN
ejpam-2537	301	3	is	be	AUX
ejpam-2537	301	4	a	a	DET
ejpam-2537	301	5	linear	linear	ADJ
ejpam-2537	301	6	code	code	NOUN
ejpam-2537	301	7	of	of	ADP
ejpam-2537	301	8	length	length	NOUN
ejpam-2537	301	9	n	n	CCONJ
ejpam-2537	301	10	over	over	ADP
ejpam-2537	301	11	r	r	NOUN
ejpam-2537	301	12	such	such	ADJ
ejpam-2537	301	13	that	that	DET
ejpam-2537	301	14	c	c	NOUN
ejpam-2537	301	15	=	=	SYM
ejpam-2537	301	16	(	(	PUNCT
ejpam-2537	301	17	1	1	NUM
ejpam-2537	301	18	+	+	NUM
ejpam-2537	301	19	v)c1	v)c1	PROPN
ejpam-2537	301	20	⊕	⊕	PROPN
ejpam-2537	301	21	vc2	vc2	PROPN
ejpam-2537	301	22	,	,	PUNCT
ejpam-2537	301	23	then	then	ADV
ejpam-2537	301	24	c⊥	c⊥	VERB
ejpam-2537	301	25	=	=	PUNCT
ejpam-2537	301	26	(	(	PUNCT
ejpam-2537	301	27	1	1	NUM
ejpam-2537	301	28	+	+	NUM
ejpam-2537	301	29	v)c⊥1	v)c⊥1	PROPN
ejpam-2537	301	30	⊕	⊕	PROPN
ejpam-2537	301	31	vc⊥2	vc⊥2	NOUN
ejpam-2537	301	32	.	.	PUNCT
ejpam-2537	302	1	moreover	moreover	ADV
ejpam-2537	302	2	c	c	PROPN
ejpam-2537	302	3	is	be	AUX
ejpam-2537	302	4	self	self	NOUN
ejpam-2537	302	5	dual	dual	ADJ
ejpam-2537	302	6	if	if	SCONJ
ejpam-2537	303	1	and	and	CCONJ
ejpam-2537	303	2	only	only	ADV
ejpam-2537	303	3	if	if	SCONJ
ejpam-2537	303	4	c1	c1	PROPN
ejpam-2537	303	5	,	,	PUNCT
ejpam-2537	303	6	c2	c2	PROPN
ejpam-2537	303	7	are	be	AUX
ejpam-2537	303	8	self	self	NOUN
ejpam-2537	303	9	dual	dual	ADJ
ejpam-2537	303	10	over	over	ADP
ejpam-2537	303	11	f2	f2	PROPN
ejpam-2537	303	12	+	+	CCONJ
ejpam-2537	303	13	uf2	uf2	NOUN
ejpam-2537	303	14	.	.	PUNCT
ejpam-2537	304	1	theorem	theorem	VERB
ejpam-2537	304	2	8	8	NUM
ejpam-2537	304	3	.	.	PUNCT
ejpam-2537	305	1	let	let	VERB
ejpam-2537	305	2	c	c	NOUN
ejpam-2537	305	3	=	=	SYM
ejpam-2537	305	4	(	(	PUNCT
ejpam-2537	305	5	1	1	NUM
ejpam-2537	305	6	+	+	NUM
ejpam-2537	305	7	v)c1	v)c1	PROPN
ejpam-2537	305	8	⊕	⊕	PROPN
ejpam-2537	305	9	vc2	vc2	PROPN
ejpam-2537	305	10	be	be	AUX
ejpam-2537	305	11	a	a	DET
ejpam-2537	305	12	linear	linear	ADJ
ejpam-2537	305	13	code	code	NOUN
ejpam-2537	305	14	of	of	ADP
ejpam-2537	305	15	length	length	NOUN
ejpam-2537	305	16	n	n	PROPN
ejpam-2537	305	17	over	over	ADP
ejpam-2537	305	18	r.	r.	PROPN
ejpam-2537	305	19	then	then	ADV
ejpam-2537	305	20	dmin(c	dmin(c	PROPN
ejpam-2537	305	21	)	)	PUNCT
ejpam-2537	305	22	=	=	SYM
ejpam-2537	305	23	min{d1	min{d1	VERB
ejpam-2537	305	24	,	,	PUNCT
ejpam-2537	305	25	d2	d2	PROPN
ejpam-2537	305	26	}	}	PUNCT
ejpam-2537	305	27	where	where	SCONJ
ejpam-2537	305	28	dmin	dmin	PROPN
ejpam-2537	305	29	,	,	PUNCT
ejpam-2537	305	30	d1	d1	PROPN
ejpam-2537	305	31	and	and	CCONJ
ejpam-2537	305	32	d2	d2	PROPN
ejpam-2537	305	33	are	be	AUX
ejpam-2537	305	34	minimum	minimum	ADJ
ejpam-2537	305	35	lee	lee	PROPN
ejpam-2537	305	36	distance	distance	NOUN
ejpam-2537	305	37	of	of	ADP
ejpam-2537	305	38	c	c	PROPN
ejpam-2537	305	39	,	,	PUNCT
ejpam-2537	305	40	c1	c1	PROPN
ejpam-2537	305	41	and	and	CCONJ
ejpam-2537	305	42	c2	c2	PROPN
ejpam-2537	305	43	,	,	PUNCT
ejpam-2537	305	44	respectively	respectively	ADV
ejpam-2537	305	45	.	.	PUNCT
ejpam-2537	306	1	a.	a.	NOUN
ejpam-2537	306	2	dertli	dertli	PROPN
ejpam-2537	306	3	,	,	PUNCT
ejpam-2537	306	4	y.	y.	PROPN
ejpam-2537	306	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	306	6	/	/	SYM
ejpam-2537	306	7	eur	eur	PROPN
ejpam-2537	306	8	.	.	PUNCT
ejpam-2537	307	1	j.	j.	PROPN
ejpam-2537	307	2	pure	pure	PROPN
ejpam-2537	307	3	appl	appl	PROPN
ejpam-2537	307	4	.	.	PROPN
ejpam-2537	307	5	math	math	PROPN
ejpam-2537	307	6	,	,	PUNCT
ejpam-2537	307	7	9	9	NUM
ejpam-2537	307	8	(	(	PUNCT
ejpam-2537	307	9	2016	2016	NUM
ejpam-2537	307	10	)	)	PUNCT
ejpam-2537	307	11	,	,	PUNCT
ejpam-2537	307	12	305	305	NUM
ejpam-2537	307	13	-	-	SYM
ejpam-2537	307	14	313	313	NUM
ejpam-2537	307	15	311	311	NUM
ejpam-2537	307	16	4	4	NUM
ejpam-2537	307	17	.	.	PUNCT
ejpam-2537	308	1	the	the	DET
ejpam-2537	308	2	gray	gray	ADJ
ejpam-2537	308	3	images	image	NOUN
ejpam-2537	308	4	of	of	ADP
ejpam-2537	308	5	(	(	PUNCT
ejpam-2537	308	6	1	1	NUM
ejpam-2537	308	7	+	+	CCONJ
ejpam-2537	308	8	u)−	u)−	PROPN
ejpam-2537	308	9	cyclic	cyclic	ADJ
ejpam-2537	308	10	codes	code	NOUN
ejpam-2537	308	11	and	and	CCONJ
ejpam-2537	308	12	cyclic	cyclic	NOUN
ejpam-2537	308	13	over	over	ADP
ejpam-2537	308	14	f2	f2	PROPN
ejpam-2537	308	15	+	+	CCONJ
ejpam-2537	308	16	uf2	uf2	NOUN
ejpam-2537	308	17	+	+	CCONJ
ejpam-2537	308	18	vf2	vf2	NOUN
ejpam-2537	308	19	in	in	ADP
ejpam-2537	308	20	this	this	DET
ejpam-2537	308	21	section	section	NOUN
ejpam-2537	308	22	,	,	PUNCT
ejpam-2537	308	23	by	by	ADP
ejpam-2537	308	24	using	use	VERB
ejpam-2537	308	25	the	the	DET
ejpam-2537	308	26	gray	gray	ADJ
ejpam-2537	308	27	map	map	NOUN
ejpam-2537	308	28	which	which	PRON
ejpam-2537	308	29	is	be	AUX
ejpam-2537	308	30	defined	define	VERB
ejpam-2537	308	31	by	by	ADP
ejpam-2537	308	32	liu	liu	PROPN
ejpam-2537	308	33	xiusheng	xiusheng	PROPN
ejpam-2537	308	34	,	,	PUNCT
ejpam-2537	308	35	liu	liu	PROPN
ejpam-2537	308	36	hualu	hualu	PROPN
ejpam-2537	308	37	,	,	PUNCT
ejpam-2537	308	38	we	we	PRON
ejpam-2537	308	39	will	will	AUX
ejpam-2537	308	40	characterize	characterize	VERB
ejpam-2537	308	41	codes	code	NOUN
ejpam-2537	308	42	over	over	ADP
ejpam-2537	308	43	f2	f2	PROPN
ejpam-2537	308	44	which	which	PRON
ejpam-2537	308	45	are	be	AUX
ejpam-2537	308	46	the	the	DET
ejpam-2537	308	47	gray	gray	ADJ
ejpam-2537	308	48	images	image	NOUN
ejpam-2537	308	49	of	of	ADP
ejpam-2537	308	50	(	(	PUNCT
ejpam-2537	308	51	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	308	52	and	and	CCONJ
ejpam-2537	308	53	cyclic	cyclic	ADJ
ejpam-2537	308	54	codes	code	NOUN
ejpam-2537	308	55	over	over	ADP
ejpam-2537	308	56	r.	r.	PROPN
ejpam-2537	308	57	in	in	ADP
ejpam-2537	308	58	[	[	X
ejpam-2537	308	59	9	9	NUM
ejpam-2537	308	60	]	]	PUNCT
ejpam-2537	308	61	,	,	PUNCT
ejpam-2537	308	62	it	it	PRON
ejpam-2537	308	63	was	be	AUX
ejpam-2537	308	64	defined	define	VERB
ejpam-2537	308	65	the	the	DET
ejpam-2537	308	66	gray	gray	ADJ
ejpam-2537	308	67	map	map	NOUN
ejpam-2537	308	68	φ	φ	PROPN
ejpam-2537	308	69	on	on	ADP
ejpam-2537	308	70	rn	rn	PROPN
ejpam-2537	308	71	as	as	SCONJ
ejpam-2537	308	72	follows	follow	VERB
ejpam-2537	308	73	φ	φ	PROPN
ejpam-2537	308	74	:	:	PUNCT
ejpam-2537	308	75	r→	r→	PROPN
ejpam-2537	308	76	f3	f3	PROPN
ejpam-2537	308	77	2	2	NUM
ejpam-2537	308	78	a+	a+	PUNCT
ejpam-2537	308	79	ub+	ub+	NOUN
ejpam-2537	308	80	vc	vc	PROPN
ejpam-2537	308	81	7→	7→	PROPN
ejpam-2537	308	82	(	(	PUNCT
ejpam-2537	308	83	c	c	NOUN
ejpam-2537	308	84	,	,	PUNCT
ejpam-2537	308	85	b+	b+	X
ejpam-2537	308	86	c	c	X
ejpam-2537	308	87	,	,	PUNCT
ejpam-2537	308	88	a+	a+	X
ejpam-2537	308	89	b+	b+	X
ejpam-2537	308	90	c	c	NOUN
ejpam-2537	308	91	)	)	PUNCT
ejpam-2537	308	92	.	.	PUNCT
ejpam-2537	309	1	this	this	DET
ejpam-2537	309	2	map	map	NOUN
ejpam-2537	309	3	can	can	AUX
ejpam-2537	309	4	be	be	AUX
ejpam-2537	309	5	extended	extend	VERB
ejpam-2537	309	6	to	to	ADP
ejpam-2537	309	7	rn	rn	PROPN
ejpam-2537	309	8	in	in	ADP
ejpam-2537	309	9	a	a	DET
ejpam-2537	309	10	natural	natural	ADJ
ejpam-2537	309	11	way	way	NOUN
ejpam-2537	309	12	.	.	PUNCT
ejpam-2537	310	1	for	for	ADP
ejpam-2537	310	2	z	z	NOUN
ejpam-2537	310	3	=	=	SYM
ejpam-2537	310	4	(	(	PUNCT
ejpam-2537	310	5	z0	z0	PROPN
ejpam-2537	310	6	,	,	PUNCT
ejpam-2537	310	7	.	.	PUNCT
ejpam-2537	310	8	.	.	PUNCT
ejpam-2537	310	9	.	.	PUNCT
ejpam-2537	311	1	,	,	PUNCT
ejpam-2537	311	2	zn−1	zn−1	PROPN
ejpam-2537	311	3	)	)	PUNCT
ejpam-2537	311	4	∈	∈	PROPN
ejpam-2537	311	5	rn	rn	PROPN
ejpam-2537	311	6	,	,	PUNCT
ejpam-2537	311	7	φ	φ	PROPN
ejpam-2537	311	8	:	:	PUNCT
ejpam-2537	311	9	rn→	rn→	PROPN
ejpam-2537	311	10	f3n	f3n	NUM
ejpam-2537	311	11	2	2	NUM
ejpam-2537	311	12	z	z	NOUN
ejpam-2537	311	13	=	=	PUNCT
ejpam-2537	311	14	(	(	PUNCT
ejpam-2537	311	15	z0	z0	PROPN
ejpam-2537	311	16	,	,	PUNCT
ejpam-2537	311	17	.	.	PUNCT
ejpam-2537	311	18	.	.	PUNCT
ejpam-2537	312	1	.	.	PUNCT
ejpam-2537	313	1	,	,	PUNCT
ejpam-2537	313	2	zn−1	zn−1	PROPN
ejpam-2537	313	3	)	)	PUNCT
ejpam-2537	313	4	7→	7→	PROPN
ejpam-2537	313	5	(	(	PUNCT
ejpam-2537	313	6	s0	s0	PROPN
ejpam-2537	313	7	,	,	PUNCT
ejpam-2537	313	8	.	.	PUNCT
ejpam-2537	313	9	.	.	PUNCT
ejpam-2537	314	1	.	.	PUNCT
ejpam-2537	315	1	,	,	PUNCT
ejpam-2537	315	2	sn−1	sn−1	PROPN
ejpam-2537	315	3	,	,	PUNCT
ejpam-2537	315	4	s0	s0	PROPN
ejpam-2537	315	5	⊕	⊕	PROPN
ejpam-2537	315	6	q0	q0	PROPN
ejpam-2537	315	7	,	,	PUNCT
ejpam-2537	315	8	.	.	PUNCT
ejpam-2537	315	9	.	.	PUNCT
ejpam-2537	315	10	.	.	PUNCT
ejpam-2537	316	1	,	,	PUNCT
ejpam-2537	316	2	sn−1	sn−1	PROPN
ejpam-2537	316	3	⊕	⊕	PROPN
ejpam-2537	316	4	qn−1	qn−1	PROPN
ejpam-2537	316	5	,	,	PUNCT
ejpam-2537	316	6	r0	r0	PROPN
ejpam-2537	316	7	⊕	⊕	PROPN
ejpam-2537	316	8	q0	q0	PROPN
ejpam-2537	316	9	⊕	⊕	PROPN
ejpam-2537	316	10	s0	s0	PROPN
ejpam-2537	316	11	,	,	PUNCT
ejpam-2537	316	12	.	.	PUNCT
ejpam-2537	316	13	.	.	PUNCT
ejpam-2537	317	1	.	.	PUNCT
ejpam-2537	318	1	,	,	PUNCT
ejpam-2537	318	2	rn−1	rn−1	PROPN
ejpam-2537	318	3	⊕	⊕	PROPN
ejpam-2537	318	4	qn−1	qn−1	PROPN
ejpam-2537	318	5	⊕	⊕	PROPN
ejpam-2537	318	6	sn−1	sn−1	PROPN
ejpam-2537	318	7	)	)	PUNCT
ejpam-2537	319	1	where	where	SCONJ
ejpam-2537	319	2	zi	zi	NOUN
ejpam-2537	319	3	=	=	SYM
ejpam-2537	319	4	ri	ri	PROPN
ejpam-2537	320	1	+	+	NUM
ejpam-2537	320	2	uqi	uqi	PROPN
ejpam-2537	320	3	+	+	CCONJ
ejpam-2537	320	4	vsi	vsi	PROPN
ejpam-2537	320	5	,	,	PUNCT
ejpam-2537	320	6	for	for	ADP
ejpam-2537	320	7	0≤	0≤	NUM
ejpam-2537	321	1	i	i	PRON
ejpam-2537	321	2	≤	≤	ADJ
ejpam-2537	321	3	n−	n−	NOUN
ejpam-2537	321	4	1	1	NUM
ejpam-2537	321	5	and	and	CCONJ
ejpam-2537	321	6	⊕	⊕	PROPN
ejpam-2537	321	7	is	be	AUX
ejpam-2537	321	8	componentwise	componentwise	NOUN
ejpam-2537	321	9	addition	addition	NOUN
ejpam-2537	321	10	in	in	ADP
ejpam-2537	321	11	f2	f2	PROPN
ejpam-2537	321	12	.	.	PUNCT
ejpam-2537	322	1	in	in	ADP
ejpam-2537	322	2	[	[	X
ejpam-2537	322	3	9	9	NUM
ejpam-2537	322	4	]	]	PUNCT
ejpam-2537	322	5	,	,	PUNCT
ejpam-2537	322	6	they	they	PRON
ejpam-2537	322	7	extended	extend	VERB
ejpam-2537	322	8	the	the	DET
ejpam-2537	322	9	definition	definition	NOUN
ejpam-2537	322	10	of	of	ADP
ejpam-2537	322	11	the	the	DET
ejpam-2537	322	12	lee	lee	PROPN
ejpam-2537	322	13	weight	weight	NOUN
ejpam-2537	322	14	from	from	ADP
ejpam-2537	322	15	f2+vf2	f2+vf2	NUM
ejpam-2537	322	16	to	to	ADP
ejpam-2537	322	17	the	the	DET
ejpam-2537	322	18	ring	ring	NOUN
ejpam-2537	322	19	f2+uf2+vf2	f2+uf2+vf2	PROPN
ejpam-2537	322	20	.	.	PUNCT
ejpam-2537	323	1	the	the	DET
ejpam-2537	323	2	lee	lee	PROPN
ejpam-2537	323	3	weight	weight	PROPN
ejpam-2537	323	4	wl(x	wl(x	PROPN
ejpam-2537	323	5	)	)	PUNCT
ejpam-2537	323	6	of	of	ADP
ejpam-2537	323	7	a	a	DET
ejpam-2537	323	8	codeword	codeword	NOUN
ejpam-2537	323	9	x	x	X
ejpam-2537	323	10	=	=	SYM
ejpam-2537	323	11	(	(	PUNCT
ejpam-2537	323	12	x1	x1	PROPN
ejpam-2537	323	13	,	,	PUNCT
ejpam-2537	323	14	.	.	PUNCT
ejpam-2537	323	15	.	.	PUNCT
ejpam-2537	323	16	.	.	PUNCT
ejpam-2537	324	1	,	,	PUNCT
ejpam-2537	324	2	xn	xn	X
ejpam-2537	324	3	)	)	PUNCT
ejpam-2537	324	4	was	be	AUX
ejpam-2537	324	5	defined	define	VERB
ejpam-2537	324	6	as	as	ADP
ejpam-2537	324	7	∑n	∑n	PROPN
ejpam-2537	324	8	i=1	i=1	PROPN
ejpam-2537	324	9	wl(x	wl(x	PROPN
ejpam-2537	324	10	i	i	PROPN
ejpam-2537	324	11	)	)	PUNCT
ejpam-2537	324	12	where	where	SCONJ
ejpam-2537	324	13	wl(x	wl(x	X
ejpam-2537	324	14	)	)	PUNCT
ejpam-2537	325	1	=	=	PUNCT
ejpam-2537	325	2			PROPN
ejpam-2537	325	3			X
ejpam-2537	325	4			PROPN
ejpam-2537	325	5			PROPN
ejpam-2537	325	6			NOUN
ejpam-2537	325	7			PROPN
ejpam-2537	325	8			PROPN
ejpam-2537	325	9			PROPN
ejpam-2537	325	10			NOUN
ejpam-2537	325	11	0	0	PUNCT
ejpam-2537	326	1	if	if	SCONJ
ejpam-2537	326	2	x	x	X
ejpam-2537	326	3	i	i	NOUN
ejpam-2537	326	4	=	=	NOUN
ejpam-2537	326	5	0	0	NUM
ejpam-2537	326	6	1	1	NUM
ejpam-2537	326	7	if	if	SCONJ
ejpam-2537	326	8	x	x	PROPN
ejpam-2537	326	9	i	i	NOUN
ejpam-2537	326	10	=	=	PUNCT
ejpam-2537	326	11	1,1	1,1	NUM
ejpam-2537	326	12	+	+	SYM
ejpam-2537	326	13	u	u	NOUN
ejpam-2537	326	14	,	,	PUNCT
ejpam-2537	326	15	u+	u+	NOUN
ejpam-2537	326	16	v	v	ADP
ejpam-2537	326	17	2	2	NUM
ejpam-2537	326	18	if	if	SCONJ
ejpam-2537	326	19	x	x	PROPN
ejpam-2537	326	20	i	i	NOUN
ejpam-2537	326	21	=	=	SYM
ejpam-2537	326	22	u	u	PROPN
ejpam-2537	326	23	,	,	PUNCT
ejpam-2537	326	24	1	1	NUM
ejpam-2537	326	25	+	+	NUM
ejpam-2537	326	26	v	v	NOUN
ejpam-2537	326	27	,	,	PUNCT
ejpam-2537	326	28	1	1	NUM
ejpam-2537	326	29	+	+	NUM
ejpam-2537	326	30	u+	u+	NOUN
ejpam-2537	326	31	v	v	ADP
ejpam-2537	326	32	3	3	NUM
ejpam-2537	326	33	if	if	SCONJ
ejpam-2537	326	34	x	x	PROPN
ejpam-2537	327	1	i	i	NOUN
ejpam-2537	327	2	=	=	PUNCT
ejpam-2537	327	3	v	v	ADP
ejpam-2537	327	4	the	the	DET
ejpam-2537	327	5	lee	lee	PROPN
ejpam-2537	327	6	distance	distance	PROPN
ejpam-2537	327	7	dl(x	dl(x	X
ejpam-2537	327	8	,	,	PUNCT
ejpam-2537	327	9	y	y	PROPN
ejpam-2537	327	10	)	)	PUNCT
ejpam-2537	327	11	between	between	ADP
ejpam-2537	327	12	two	two	NUM
ejpam-2537	327	13	codewords	codeword	NOUN
ejpam-2537	327	14	x	x	PUNCT
ejpam-2537	327	15	and	and	CCONJ
ejpam-2537	327	16	y	y	PROPN
ejpam-2537	327	17	is	be	AUX
ejpam-2537	327	18	the	the	DET
ejpam-2537	327	19	lee	lee	PROPN
ejpam-2537	327	20	weight	weight	NOUN
ejpam-2537	327	21	of	of	ADP
ejpam-2537	327	22	x−	x−	PROPN
ejpam-2537	327	23	y	y	PROPN
ejpam-2537	327	24	.	.	PUNCT
ejpam-2537	328	1	the	the	DET
ejpam-2537	328	2	gray	gray	ADJ
ejpam-2537	328	3	map	map	NOUN
ejpam-2537	328	4	φ	φ	PROPN
ejpam-2537	328	5	is	be	AUX
ejpam-2537	328	6	an	an	DET
ejpam-2537	328	7	isometry	isometry	NOUN
ejpam-2537	328	8	from	from	ADP
ejpam-2537	328	9	(	(	PUNCT
ejpam-2537	328	10	rn	rn	PROPN
ejpam-2537	328	11	,	,	PUNCT
ejpam-2537	328	12	dlee	dlee	PROPN
ejpam-2537	328	13	)	)	PUNCT
ejpam-2537	328	14	to	to	ADP
ejpam-2537	328	15	f3n	f3n	PROPN
ejpam-2537	328	16	2	2	NUM
ejpam-2537	328	17	under	under	ADP
ejpam-2537	328	18	the	the	DET
ejpam-2537	328	19	hamming	hamming	NOUN
ejpam-2537	328	20	distance	distance	NOUN
ejpam-2537	328	21	.	.	PUNCT
ejpam-2537	329	1	proposition	proposition	NOUN
ejpam-2537	329	2	4	4	NUM
ejpam-2537	329	3	.	.	PUNCT
ejpam-2537	330	1	φν	φν	X
ejpam-2537	330	2	=	=	PUNCT
ejpam-2537	331	1	ρσ⊗3φ	ρσ⊗3φ	NUM
ejpam-2537	331	2	where	where	SCONJ
ejpam-2537	331	3	ρ	ρ	PROPN
ejpam-2537	331	4	is	be	AUX
ejpam-2537	331	5	a	a	DET
ejpam-2537	331	6	permutation	permutation	NOUN
ejpam-2537	331	7	of	of	ADP
ejpam-2537	331	8	{	{	PUNCT
ejpam-2537	331	9	0	0	NUM
ejpam-2537	331	10	,	,	PUNCT
ejpam-2537	331	11	.	.	PUNCT
ejpam-2537	331	12	.	.	PUNCT
ejpam-2537	332	1	.	.	PUNCT
ejpam-2537	333	1	,	,	PUNCT
ejpam-2537	333	2	3n	3n	NUM
ejpam-2537	333	3	−	−	NOUN
ejpam-2537	333	4	1	1	NUM
ejpam-2537	333	5	}	}	PUNCT
ejpam-2537	333	6	which	which	PRON
ejpam-2537	333	7	is	be	AUX
ejpam-2537	333	8	defined	define	VERB
ejpam-2537	333	9	ρ	ρ	NOUN
ejpam-2537	333	10	=	=	SYM
ejpam-2537	333	11	(	(	PUNCT
ejpam-2537	333	12	n+	n+	NUM
ejpam-2537	333	13	1,2n+	1,2n+	NUM
ejpam-2537	333	14	1	1	NUM
ejpam-2537	333	15	)	)	PUNCT
ejpam-2537	333	16	.	.	PUNCT
ejpam-2537	334	1	proof	proof	NOUN
ejpam-2537	334	2	.	.	PUNCT
ejpam-2537	335	1	let	let	VERB
ejpam-2537	335	2	z	z	NOUN
ejpam-2537	335	3	=	=	SYM
ejpam-2537	335	4	(	(	PUNCT
ejpam-2537	335	5	z0	z0	PROPN
ejpam-2537	335	6	,	,	PUNCT
ejpam-2537	335	7	z1	z1	NOUN
ejpam-2537	335	8	,	,	PUNCT
ejpam-2537	335	9	.	.	PUNCT
ejpam-2537	335	10	.	.	PUNCT
ejpam-2537	336	1	.	.	PUNCT
ejpam-2537	337	1	,	,	PUNCT
ejpam-2537	337	2	zn−1	zn−1	PROPN
ejpam-2537	337	3	)	)	PUNCT
ejpam-2537	337	4	∈	∈	PROPN
ejpam-2537	337	5	rn	rn	PROPN
ejpam-2537	337	6	.	.	PROPN
ejpam-2537	338	1	let	let	VERB
ejpam-2537	338	2	ri	ri	PROPN
ejpam-2537	338	3	,	,	PUNCT
ejpam-2537	338	4	qi	qi	PROPN
ejpam-2537	339	1	,	,	PUNCT
ejpam-2537	339	2	si	si	PROPN
ejpam-2537	339	3	∈	∈	PROPN
ejpam-2537	339	4	f2	f2	PRON
ejpam-2537	339	5	such	such	ADJ
ejpam-2537	339	6	that	that	DET
ejpam-2537	339	7	zi	zi	NOUN
ejpam-2537	339	8	=	=	SYM
ejpam-2537	339	9	ri	ri	PROPN
ejpam-2537	340	1	+	+	NUM
ejpam-2537	340	2	uqi	uqi	PROPN
ejpam-2537	340	3	+	+	CCONJ
ejpam-2537	340	4	vsi	vsi	PROPN
ejpam-2537	340	5	,	,	PUNCT
ejpam-2537	340	6	for	for	ADP
ejpam-2537	340	7	0≤	0≤	NUM
ejpam-2537	340	8	i	i	PRON
ejpam-2537	340	9	≤	≤	ADJ
ejpam-2537	340	10	n−	n−	NOUN
ejpam-2537	340	11	1	1	NUM
ejpam-2537	340	12	.	.	PUNCT
ejpam-2537	341	1	we	we	PRON
ejpam-2537	341	2	have	have	VERB
ejpam-2537	341	3	φ(z	φ(z	PROPN
ejpam-2537	341	4	)	)	PUNCT
ejpam-2537	342	1	=	=	PUNCT
ejpam-2537	342	2	(	(	PUNCT
ejpam-2537	342	3	s0	s0	PROPN
ejpam-2537	342	4	,	,	PUNCT
ejpam-2537	342	5	.	.	PUNCT
ejpam-2537	342	6	.	.	PUNCT
ejpam-2537	343	1	.	.	PUNCT
ejpam-2537	344	1	,	,	PUNCT
ejpam-2537	344	2	sn−1	sn−1	PROPN
ejpam-2537	344	3	,	,	PUNCT
ejpam-2537	344	4	s0	s0	PROPN
ejpam-2537	344	5	⊕	⊕	PROPN
ejpam-2537	344	6	q0	q0	PROPN
ejpam-2537	344	7	,	,	PUNCT
ejpam-2537	344	8	.	.	PUNCT
ejpam-2537	344	9	.	.	PUNCT
ejpam-2537	344	10	.	.	PUNCT
ejpam-2537	345	1	,	,	PUNCT
ejpam-2537	345	2	sn−1	sn−1	PROPN
ejpam-2537	345	3	⊕	⊕	PROPN
ejpam-2537	345	4	qn−1	qn−1	PROPN
ejpam-2537	345	5	,	,	PUNCT
ejpam-2537	345	6	r0	r0	PROPN
ejpam-2537	345	7	⊕	⊕	PROPN
ejpam-2537	345	8	q0	q0	PROPN
ejpam-2537	345	9	⊕	⊕	PROPN
ejpam-2537	345	10	s0	s0	PROPN
ejpam-2537	345	11	,	,	PUNCT
ejpam-2537	345	12	.	.	PUNCT
ejpam-2537	345	13	.	.	PUNCT
ejpam-2537	346	1	.	.	PUNCT
ejpam-2537	347	1	,	,	PUNCT
ejpam-2537	347	2	rn−1	rn−1	PROPN
ejpam-2537	347	3	⊕	⊕	PROPN
ejpam-2537	347	4	qn−1	qn−1	PROPN
ejpam-2537	347	5	⊕	⊕	PROPN
ejpam-2537	347	6	sn−1	sn−1	PROPN
ejpam-2537	347	7	)	)	PUNCT
ejpam-2537	347	8	.	.	PUNCT
ejpam-2537	348	1	then	then	ADV
ejpam-2537	348	2	σ⊗3(φ(z	σ⊗3(φ(z	NOUN
ejpam-2537	348	3	)	)	PUNCT
ejpam-2537	348	4	)	)	PUNCT
ejpam-2537	349	1	=(	=(	PROPN
ejpam-2537	349	2	sn−1	sn−1	PROPN
ejpam-2537	349	3	,	,	PUNCT
ejpam-2537	349	4	s0	s0	PROPN
ejpam-2537	349	5	,	,	PUNCT
ejpam-2537	349	6	.	.	PUNCT
ejpam-2537	349	7	.	.	PUNCT
ejpam-2537	350	1	.	.	PUNCT
ejpam-2537	351	1	,	,	PUNCT
ejpam-2537	351	2	sn−2	sn−2	ADV
ejpam-2537	351	3	,	,	PUNCT
ejpam-2537	351	4	sn−1	sn−1	PROPN
ejpam-2537	351	5	⊕	⊕	PROPN
ejpam-2537	351	6	qn−1	qn−1	PROPN
ejpam-2537	351	7	,	,	PUNCT
ejpam-2537	351	8	s0	s0	PROPN
ejpam-2537	351	9	⊕	⊕	PROPN
ejpam-2537	351	10	q0	q0	PROPN
ejpam-2537	351	11	,	,	PUNCT
ejpam-2537	351	12	.	.	PUNCT
ejpam-2537	351	13	.	.	PUNCT
ejpam-2537	352	1	.	.	PUNCT
ejpam-2537	353	1	,	,	PUNCT
ejpam-2537	353	2	sn−2	sn−2	PROPN
ejpam-2537	353	3	⊕	⊕	PROPN
ejpam-2537	353	4	qn−2	qn−2	PROPN
ejpam-2537	353	5	,	,	PUNCT
ejpam-2537	353	6	rn−1	rn−1	PROPN
ejpam-2537	353	7	⊕	⊕	PROPN
ejpam-2537	353	8	qn−1	qn−1	PROPN
ejpam-2537	353	9	⊕	⊕	PROPN
ejpam-2537	353	10	sn−1	sn−1	PROPN
ejpam-2537	353	11	,	,	PUNCT
ejpam-2537	353	12	r0	r0	PROPN
ejpam-2537	353	13	⊕	⊕	PROPN
ejpam-2537	353	14	q0	q0	PROPN
ejpam-2537	353	15	⊕	⊕	PROPN
ejpam-2537	353	16	s0	s0	PROPN
ejpam-2537	353	17	,	,	PUNCT
ejpam-2537	353	18	.	.	PUNCT
ejpam-2537	353	19	.	.	PUNCT
ejpam-2537	354	1	.	.	PUNCT
ejpam-2537	355	1	,	,	PUNCT
ejpam-2537	355	2	rn−2	rn−2	PROPN
ejpam-2537	355	3	⊕	⊕	PROPN
ejpam-2537	355	4	qn−2	qn−2	PROPN
ejpam-2537	355	5	⊕	⊕	PROPN
ejpam-2537	355	6	sn−2	sn−2	PROPN
ejpam-2537	355	7	)	)	PUNCT
ejpam-2537	355	8	.	.	PUNCT
ejpam-2537	356	1	on	on	ADP
ejpam-2537	356	2	the	the	DET
ejpam-2537	356	3	other	other	ADJ
ejpam-2537	356	4	hand	hand	NOUN
ejpam-2537	356	5	,	,	PUNCT
ejpam-2537	356	6	ν(z	ν(z	NOUN
ejpam-2537	356	7	)	)	PUNCT
ejpam-2537	356	8	=	=	PRON
ejpam-2537	357	1	(	(	PUNCT
ejpam-2537	357	2	(	(	PUNCT
ejpam-2537	357	3	1	1	NUM
ejpam-2537	357	4	+	+	NUM
ejpam-2537	357	5	u)zn−1	u)zn−1	ADJ
ejpam-2537	357	6	,	,	PUNCT
ejpam-2537	357	7	z0	z0	PROPN
ejpam-2537	357	8	,	,	PUNCT
ejpam-2537	357	9	.	.	PUNCT
ejpam-2537	357	10	.	.	PUNCT
ejpam-2537	358	1	.	.	PUNCT
ejpam-2537	359	1	,	,	PUNCT
ejpam-2537	359	2	zn−2	zn−2	PROPN
ejpam-2537	359	3	)	)	PUNCT
ejpam-2537	359	4	where	where	SCONJ
ejpam-2537	359	5	(	(	PUNCT
ejpam-2537	359	6	1	1	NUM
ejpam-2537	359	7	+	+	NUM
ejpam-2537	359	8	u)zn−1	u)zn−1	ADJ
ejpam-2537	359	9	=	=	NOUN
ejpam-2537	359	10	rn−1	rn−1	PROPN
ejpam-2537	359	11	+	+	CCONJ
ejpam-2537	359	12	u(rn−1	u(rn−1	PROPN
ejpam-2537	359	13	+	+	CCONJ
ejpam-2537	359	14	qn−1	qn−1	ADJ
ejpam-2537	359	15	)	)	PUNCT
ejpam-2537	360	1	+	+	X
ejpam-2537	361	1	vsn−1	vsn−1	ADJ
ejpam-2537	361	2	.	.	PUNCT
ejpam-2537	362	1	we	we	PRON
ejpam-2537	362	2	have	have	VERB
ejpam-2537	362	3	φ(ν(z	φ(ν(z	NOUN
ejpam-2537	362	4	)	)	PUNCT
ejpam-2537	362	5	)	)	PUNCT
ejpam-2537	363	1	=(	=(	NOUN
ejpam-2537	363	2	sn−1	sn−1	PROPN
ejpam-2537	363	3	,	,	PUNCT
ejpam-2537	363	4	s0	s0	PROPN
ejpam-2537	363	5	,	,	PUNCT
ejpam-2537	363	6	.	.	PUNCT
ejpam-2537	363	7	.	.	PUNCT
ejpam-2537	364	1	.	.	PUNCT
ejpam-2537	365	1	,	,	PUNCT
ejpam-2537	365	2	sn−2	sn−2	ADV
ejpam-2537	365	3	,	,	PUNCT
ejpam-2537	365	4	rn−1	rn−1	PROPN
ejpam-2537	365	5	⊕	⊕	PROPN
ejpam-2537	365	6	qn−1	qn−1	PROPN
ejpam-2537	365	7	⊕	⊕	PROPN
ejpam-2537	365	8	sn−1,q0	sn−1,q0	PROPN
ejpam-2537	365	9	⊕	⊕	PROPN
ejpam-2537	365	10	s0	s0	PROPN
ejpam-2537	365	11	,	,	PUNCT
ejpam-2537	365	12	.	.	PUNCT
ejpam-2537	365	13	.	.	PUNCT
ejpam-2537	366	1	.	.	PUNCT
ejpam-2537	367	1	,	,	PUNCT
ejpam-2537	367	2	qn−2	qn−2	PROPN
ejpam-2537	367	3	⊕	⊕	PROPN
ejpam-2537	367	4	sn−2	sn−2	PROPN
ejpam-2537	367	5	,	,	PUNCT
ejpam-2537	367	6	rn−1	rn−1	PROPN
ejpam-2537	367	7	⊕	⊕	PROPN
ejpam-2537	367	8	qn−1	qn−1	PROPN
ejpam-2537	367	9	,	,	PUNCT
ejpam-2537	367	10	r0	r0	PROPN
ejpam-2537	367	11	⊕	⊕	PROPN
ejpam-2537	367	12	q0	q0	PROPN
ejpam-2537	367	13	⊕	⊕	PROPN
ejpam-2537	367	14	s0	s0	PROPN
ejpam-2537	367	15	,	,	PUNCT
ejpam-2537	367	16	.	.	PUNCT
ejpam-2537	367	17	.	.	PUNCT
ejpam-2537	368	1	.	.	PUNCT
ejpam-2537	369	1	,	,	PUNCT
ejpam-2537	369	2	rn−2	rn−2	PROPN
ejpam-2537	369	3	⊕	⊕	PROPN
ejpam-2537	369	4	qn−2	qn−2	PROPN
ejpam-2537	369	5	⊕	⊕	PROPN
ejpam-2537	369	6	sn−2	sn−2	PROPN
ejpam-2537	369	7	)	)	PUNCT
ejpam-2537	369	8	.	.	PUNCT
ejpam-2537	370	1	hence	hence	ADV
ejpam-2537	370	2	φν=	φν=	PROPN
ejpam-2537	370	3	ρσ⊗3φ	ρσ⊗3φ	PROPN
ejpam-2537	370	4	.	.	PUNCT
ejpam-2537	371	1	so	so	ADV
ejpam-2537	371	2	we	we	PRON
ejpam-2537	371	3	have	have	VERB
ejpam-2537	371	4	the	the	DET
ejpam-2537	371	5	following	follow	VERB
ejpam-2537	371	6	theorem	theorem	PROPN
ejpam-2537	371	7	.	.	PUNCT
ejpam-2537	371	8	a.	a.	PROPN
ejpam-2537	371	9	dertli	dertli	PROPN
ejpam-2537	371	10	,	,	PUNCT
ejpam-2537	371	11	y.	y.	PROPN
ejpam-2537	371	12	cengellenmis	cengellenmis	PROPN
ejpam-2537	371	13	/	/	SYM
ejpam-2537	371	14	eur	eur	PROPN
ejpam-2537	371	15	.	.	PUNCT
ejpam-2537	372	1	j.	j.	PROPN
ejpam-2537	372	2	pure	pure	PROPN
ejpam-2537	372	3	appl	appl	PROPN
ejpam-2537	372	4	.	.	PROPN
ejpam-2537	372	5	math	math	PROPN
ejpam-2537	372	6	,	,	PUNCT
ejpam-2537	372	7	9	9	NUM
ejpam-2537	372	8	(	(	PUNCT
ejpam-2537	372	9	2016	2016	NUM
ejpam-2537	372	10	)	)	PUNCT
ejpam-2537	372	11	,	,	PUNCT
ejpam-2537	372	12	305	305	NUM
ejpam-2537	372	13	-	-	SYM
ejpam-2537	372	14	313	313	NUM
ejpam-2537	372	15	312	312	NUM
ejpam-2537	372	16	theorem	theorem	NOUN
ejpam-2537	372	17	9	9	NUM
ejpam-2537	372	18	.	.	PUNCT
ejpam-2537	373	1	a	a	DET
ejpam-2537	373	2	code	code	NOUN
ejpam-2537	373	3	c	c	NOUN
ejpam-2537	373	4	of	of	ADP
ejpam-2537	373	5	length	length	NOUN
ejpam-2537	373	6	n	n	CCONJ
ejpam-2537	373	7	over	over	ADP
ejpam-2537	373	8	r	r	NOUN
ejpam-2537	373	9	is	be	AUX
ejpam-2537	373	10	(	(	PUNCT
ejpam-2537	373	11	1	1	NUM
ejpam-2537	373	12	+	+	CCONJ
ejpam-2537	373	13	u)−cyclic	u)−cyclic	ADJ
ejpam-2537	373	14	if	if	SCONJ
ejpam-2537	373	15	and	and	CCONJ
ejpam-2537	373	16	only	only	ADV
ejpam-2537	373	17	if	if	SCONJ
ejpam-2537	373	18	φ(c	φ(c	NOUN
ejpam-2537	373	19	)	)	PUNCT
ejpam-2537	373	20	is	be	AUX
ejpam-2537	373	21	permutation	permutation	NOUN
ejpam-2537	373	22	equivalent	equivalent	ADJ
ejpam-2537	373	23	to	to	ADP
ejpam-2537	373	24	quasi	quasi	NOUN
ejpam-2537	373	25	-	-	ADJ
ejpam-2537	373	26	cyclic	cyclic	ADJ
ejpam-2537	373	27	of	of	ADP
ejpam-2537	373	28	index	index	NOUN
ejpam-2537	373	29	3	3	NUM
ejpam-2537	373	30	and	and	CCONJ
ejpam-2537	373	31	length	length	NOUN
ejpam-2537	373	32	3n	3n	NUM
ejpam-2537	373	33	over	over	ADP
ejpam-2537	373	34	f2	f2	PROPN
ejpam-2537	373	35	.	.	PUNCT
ejpam-2537	374	1	proof	proof	NOUN
ejpam-2537	374	2	.	.	PUNCT
ejpam-2537	375	1	suppose	suppose	VERB
ejpam-2537	375	2	c	c	NOUN
ejpam-2537	375	3	is	be	AUX
ejpam-2537	375	4	(	(	PUNCT
ejpam-2537	375	5	1	1	NUM
ejpam-2537	375	6	+	+	CCONJ
ejpam-2537	375	7	u)−cyclic	u)−cyclic	ADJ
ejpam-2537	375	8	.	.	PUNCT
ejpam-2537	376	1	as	as	ADP
ejpam-2537	376	2	ρ(σ⊗3(φ(c	ρ(σ⊗3(φ(c	NUM
ejpam-2537	376	3	)	)	PUNCT
ejpam-2537	376	4	)	)	PUNCT
ejpam-2537	376	5	)	)	PUNCT
ejpam-2537	377	1	=	=	PUNCT
ejpam-2537	377	2	φ(ν(c	φ(ν(c	NOUN
ejpam-2537	377	3	)	)	PUNCT
ejpam-2537	377	4	)	)	PUNCT
ejpam-2537	377	5	,	,	PUNCT
ejpam-2537	377	6	φ(c	φ(c	NOUN
ejpam-2537	377	7	)	)	PUNCT
ejpam-2537	377	8	is	be	AUX
ejpam-2537	377	9	permutation	permutation	NOUN
ejpam-2537	377	10	equivalent	equivalent	ADJ
ejpam-2537	377	11	to	to	ADP
ejpam-2537	377	12	a	a	DET
ejpam-2537	377	13	quasi	quasi	NOUN
ejpam-2537	377	14	-	-	NOUN
ejpam-2537	377	15	cyclic	cyclic	ADJ
ejpam-2537	377	16	of	of	ADP
ejpam-2537	377	17	index	index	NOUN
ejpam-2537	377	18	3	3	NUM
ejpam-2537	377	19	.	.	PUNCT
ejpam-2537	378	1	conversely	conversely	ADV
ejpam-2537	378	2	,	,	PUNCT
ejpam-2537	378	3	if	if	SCONJ
ejpam-2537	378	4	φ(c	φ(c	NOUN
ejpam-2537	378	5	)	)	PUNCT
ejpam-2537	378	6	is	be	AUX
ejpam-2537	378	7	permutation	permutation	NOUN
ejpam-2537	378	8	equivalent	equivalent	ADJ
ejpam-2537	378	9	to	to	ADP
ejpam-2537	378	10	quasicyclic	quasicyclic	NOUN
ejpam-2537	378	11	of	of	ADP
ejpam-2537	378	12	index	index	NOUN
ejpam-2537	378	13	3	3	NUM
ejpam-2537	378	14	,	,	PUNCT
ejpam-2537	378	15	then	then	ADV
ejpam-2537	378	16	φ(ν(c	φ(ν(c	NOUN
ejpam-2537	378	17	)	)	PUNCT
ejpam-2537	378	18	)	)	PUNCT
ejpam-2537	379	1	=	=	SYM
ejpam-2537	379	2	ρ(σ⊗3(φ(c	ρ(σ⊗3(φ(c	NUM
ejpam-2537	379	3	)	)	PUNCT
ejpam-2537	379	4	)	)	PUNCT
ejpam-2537	379	5	)	)	PUNCT
ejpam-2537	380	1	=	=	SYM
ejpam-2537	380	2	φ(c	φ(c	NOUN
ejpam-2537	380	3	)	)	PUNCT
ejpam-2537	380	4	.	.	PUNCT
ejpam-2537	381	1	since	since	SCONJ
ejpam-2537	381	2	φ	φ	PROPN
ejpam-2537	381	3	is	be	AUX
ejpam-2537	381	4	isometry	isometry	ADJ
ejpam-2537	381	5	,	,	PUNCT
ejpam-2537	381	6	so	so	SCONJ
ejpam-2537	381	7	ν(c	ν(c	PROPN
ejpam-2537	381	8	)	)	PUNCT
ejpam-2537	382	1	=	=	PUNCT
ejpam-2537	382	2	c	c	NOUN
ejpam-2537	382	3	,	,	PUNCT
ejpam-2537	382	4	that	that	PRON
ejpam-2537	382	5	is	is	ADV
ejpam-2537	382	6	c	c	NOUN
ejpam-2537	382	7	is	be	AUX
ejpam-2537	382	8	(	(	PUNCT
ejpam-2537	382	9	1	1	NUM
ejpam-2537	382	10	+	+	CCONJ
ejpam-2537	382	11	u)−	u)−	PROPN
ejpam-2537	382	12	cyclic	cyclic	ADJ
ejpam-2537	382	13	code	code	NOUN
ejpam-2537	382	14	.	.	PUNCT
ejpam-2537	383	1	note	note	VERB
ejpam-2537	383	2	that	that	SCONJ
ejpam-2537	383	3	(	(	PUNCT
ejpam-2537	383	4	1	1	NUM
ejpam-2537	383	5	+	+	NUM
ejpam-2537	383	6	u)n	u)n	NOUN
ejpam-2537	383	7	=	=	SYM
ejpam-2537	383	8	1	1	NUM
ejpam-2537	383	9	+	+	NUM
ejpam-2537	383	10	u	u	NOUN
ejpam-2537	383	11	if	if	SCONJ
ejpam-2537	383	12	n	n	NOUN
ejpam-2537	383	13	is	be	AUX
ejpam-2537	383	14	odd	odd	ADJ
ejpam-2537	383	15	,	,	PUNCT
ejpam-2537	383	16	(	(	PUNCT
ejpam-2537	383	17	1	1	NUM
ejpam-2537	383	18	+	+	NUM
ejpam-2537	383	19	u)n	u)n	NOUN
ejpam-2537	383	20	=	=	SYM
ejpam-2537	383	21	1	1	NUM
ejpam-2537	383	22	if	if	SCONJ
ejpam-2537	383	23	n	n	PRON
ejpam-2537	383	24	is	be	AUX
ejpam-2537	383	25	even	even	ADV
ejpam-2537	383	26	.	.	PUNCT
ejpam-2537	384	1	in	in	ADP
ejpam-2537	384	2	here	here	ADV
ejpam-2537	384	3	,	,	PUNCT
ejpam-2537	384	4	it	it	PRON
ejpam-2537	384	5	is	be	AUX
ejpam-2537	384	6	studied	study	VERB
ejpam-2537	384	7	the	the	DET
ejpam-2537	384	8	properties	property	NOUN
ejpam-2537	384	9	of	of	ADP
ejpam-2537	384	10	(	(	PUNCT
ejpam-2537	384	11	1	1	NUM
ejpam-2537	384	12	+	+	NUM
ejpam-2537	384	13	u	u	NOUN
ejpam-2537	384	14	)	)	PUNCT
ejpam-2537	384	15	cyclic	cyclic	ADJ
ejpam-2537	384	16	codes	code	NOUN
ejpam-2537	384	17	of	of	ADP
ejpam-2537	384	18	odd	odd	ADJ
ejpam-2537	384	19	length	length	NOUN
ejpam-2537	384	20	in	in	ADP
ejpam-2537	384	21	this	this	DET
ejpam-2537	384	22	section	section	NOUN
ejpam-2537	384	23	.	.	PUNCT
ejpam-2537	385	1	let	let	VERB
ejpam-2537	385	2	µ	µ	X
ejpam-2537	385	3	be	be	AUX
ejpam-2537	385	4	the	the	DET
ejpam-2537	385	5	map	map	NOUN
ejpam-2537	385	6	of	of	ADP
ejpam-2537	385	7	r[x]/〈xn−1	r[x]/〈xn−1	PROPN
ejpam-2537	385	8	〉	〉	NOUN
ejpam-2537	385	9	into	into	ADP
ejpam-2537	385	10	r[x]/〈xn−(1+u	r[x]/〈xn−(1+u	NOUN
ejpam-2537	385	11	)	)	PUNCT
ejpam-2537	385	12	〉	〉	NOUN
ejpam-2537	385	13	defined	define	VERB
ejpam-2537	385	14	by	by	ADP
ejpam-2537	385	15	µ(c(x	µ(c(x	PROPN
ejpam-2537	385	16	)	)	PUNCT
ejpam-2537	385	17	)	)	PUNCT
ejpam-2537	386	1	=	=	PUNCT
ejpam-2537	386	2	c((1+u)x	c((1+u)x	PROPN
ejpam-2537	386	3	)	)	PUNCT
ejpam-2537	386	4	.	.	PUNCT
ejpam-2537	387	1	if	if	SCONJ
ejpam-2537	387	2	n	n	NOUN
ejpam-2537	387	3	is	be	AUX
ejpam-2537	387	4	odd	odd	ADJ
ejpam-2537	387	5	,	,	PUNCT
ejpam-2537	387	6	then	then	ADV
ejpam-2537	387	7	µ	µ	NOUN
ejpam-2537	387	8	is	be	AUX
ejpam-2537	387	9	a	a	DET
ejpam-2537	387	10	ring	ring	NOUN
ejpam-2537	387	11	isomorphism	isomorphism	NOUN
ejpam-2537	387	12	.	.	PUNCT
ejpam-2537	388	1	hence	hence	ADV
ejpam-2537	388	2	i	i	PRON
ejpam-2537	388	3	is	be	AUX
ejpam-2537	388	4	an	an	DET
ejpam-2537	388	5	ideal	ideal	NOUN
ejpam-2537	388	6	of	of	ADP
ejpam-2537	388	7	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2537	388	8	−	−	NOUN
ejpam-2537	388	9	1	1	NUM
ejpam-2537	388	10	〉	〉	NOUN
ejpam-2537	388	11	if	if	SCONJ
ejpam-2537	388	12	and	and	CCONJ
ejpam-2537	388	13	only	only	ADV
ejpam-2537	388	14	if	if	SCONJ
ejpam-2537	388	15	µ(i	µ(i	PROPN
ejpam-2537	388	16	)	)	PUNCT
ejpam-2537	388	17	is	be	AUX
ejpam-2537	388	18	an	an	DET
ejpam-2537	388	19	ideal	ideal	NOUN
ejpam-2537	388	20	of	of	ADP
ejpam-2537	388	21	r[x]/〈xn	r[x]/〈xn	NOUN
ejpam-2537	388	22	−	−	PROPN
ejpam-2537	388	23	(	(	PUNCT
ejpam-2537	388	24	1	1	NUM
ejpam-2537	388	25	+	+	NUM
ejpam-2537	388	26	u	u	NOUN
ejpam-2537	388	27	)	)	PUNCT
ejpam-2537	388	28	〉	〉	NOUN
ejpam-2537	388	29	.	.	PUNCT
ejpam-2537	389	1	if	if	SCONJ
ejpam-2537	389	2	µ̄	µ̄	PROPN
ejpam-2537	389	3	is	be	AUX
ejpam-2537	389	4	the	the	DET
ejpam-2537	389	5	map	map	NOUN
ejpam-2537	389	6	µ̄	µ̄	PROPN
ejpam-2537	389	7	:	:	PUNCT
ejpam-2537	389	8	rn→	rn→	PROPN
ejpam-2537	389	9	rn	rn	PROPN
ejpam-2537	389	10	z	z	PROPN
ejpam-2537	389	11	7→	7→	PROPN
ejpam-2537	389	12	(	(	PUNCT
ejpam-2537	389	13	z0	z0	PROPN
ejpam-2537	389	14	,	,	PUNCT
ejpam-2537	389	15	(	(	PUNCT
ejpam-2537	389	16	1	1	NUM
ejpam-2537	389	17	+	+	NUM
ejpam-2537	389	18	u)z1	u)z1	NOUN
ejpam-2537	389	19	,	,	PUNCT
ejpam-2537	389	20	(	(	PUNCT
ejpam-2537	389	21	1	1	NUM
ejpam-2537	389	22	+	+	CCONJ
ejpam-2537	389	23	u)2z2	u)2z2	NOUN
ejpam-2537	389	24	,	,	PUNCT
ejpam-2537	389	25	.	.	PUNCT
ejpam-2537	389	26	.	.	PUNCT
ejpam-2537	390	1	.	.	PUNCT
ejpam-2537	391	1	,	,	PUNCT
ejpam-2537	391	2	(	(	PUNCT
ejpam-2537	391	3	1	1	NUM
ejpam-2537	391	4	+	+	NUM
ejpam-2537	391	5	u)n−1zn−1	u)n−1zn−1	ADJ
ejpam-2537	391	6	)	)	PUNCT
ejpam-2537	391	7	where	where	SCONJ
ejpam-2537	391	8	zi	zi	NOUN
ejpam-2537	391	9	=	=	PUNCT
ejpam-2537	391	10	si	si	PROPN
ejpam-2537	391	11	+	+	CCONJ
ejpam-2537	391	12	ut	ut	PROPN
ejpam-2537	391	13	i	i	PROPN
ejpam-2537	391	14	+	+	CCONJ
ejpam-2537	391	15	v	v	VERB
ejpam-2537	391	16	yi	yi	NOUN
ejpam-2537	391	17	and	and	CCONJ
ejpam-2537	391	18	si	si	PROPN
ejpam-2537	391	19	,	,	PUNCT
ejpam-2537	391	20	t	t	PROPN
ejpam-2537	391	21	i	i	PRON
ejpam-2537	391	22	,	,	PUNCT
ejpam-2537	391	23	yi	yi	PROPN
ejpam-2537	391	24	∈	∈	PROPN
ejpam-2537	391	25	f2	f2	PROPN
ejpam-2537	391	26	for	for	ADP
ejpam-2537	391	27	0≤	0≤	NUM
ejpam-2537	392	1	i	i	PRON
ejpam-2537	392	2	≤	≤	ADJ
ejpam-2537	392	3	n−	n−	NOUN
ejpam-2537	392	4	1	1	NUM
ejpam-2537	392	5	,	,	PUNCT
ejpam-2537	392	6	then	then	ADV
ejpam-2537	392	7	it	it	PRON
ejpam-2537	392	8	also	also	ADV
ejpam-2537	392	9	follows	follow	VERB
ejpam-2537	392	10	that	that	SCONJ
ejpam-2537	392	11	:	:	PUNCT
ejpam-2537	392	12	proposition	proposition	NOUN
ejpam-2537	392	13	5	5	NUM
ejpam-2537	392	14	.	.	PUNCT
ejpam-2537	393	1	the	the	DET
ejpam-2537	393	2	set	set	NOUN
ejpam-2537	393	3	c	c	PROPN
ejpam-2537	393	4	⊆	⊆	NUM
ejpam-2537	393	5	rn	rn	PROPN
ejpam-2537	393	6	is	be	AUX
ejpam-2537	393	7	a	a	DET
ejpam-2537	393	8	linear	linear	ADJ
ejpam-2537	393	9	cyclic	cyclic	ADJ
ejpam-2537	393	10	code	code	NOUN
ejpam-2537	394	1	if	if	SCONJ
ejpam-2537	394	2	and	and	CCONJ
ejpam-2537	394	3	only	only	ADV
ejpam-2537	394	4	if	if	SCONJ
ejpam-2537	394	5	µ̄(c	µ̄(c	NOUN
ejpam-2537	394	6	)	)	PUNCT
ejpam-2537	394	7	is	be	AUX
ejpam-2537	394	8	a	a	DET
ejpam-2537	394	9	linear	linear	ADJ
ejpam-2537	394	10	(	(	PUNCT
ejpam-2537	394	11	1	1	NUM
ejpam-2537	394	12	+	+	NUM
ejpam-2537	394	13	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	394	14	code	code	NOUN
ejpam-2537	394	15	.	.	PUNCT
ejpam-2537	395	1	let	let	VERB
ejpam-2537	395	2	τ	τ	PROPN
ejpam-2537	395	3	be	be	AUX
ejpam-2537	395	4	the	the	DET
ejpam-2537	395	5	following	follow	VERB
ejpam-2537	395	6	permutation	permutation	NOUN
ejpam-2537	395	7	of	of	ADP
ejpam-2537	395	8	{	{	PUNCT
ejpam-2537	395	9	0,1,2	0,1,2	NOUN
ejpam-2537	395	10	,	,	PUNCT
ejpam-2537	395	11	.	.	PUNCT
ejpam-2537	395	12	.	.	PUNCT
ejpam-2537	396	1	.	.	PUNCT
ejpam-2537	397	1	,	,	PUNCT
ejpam-2537	398	1	3n−	3n−	PROPN
ejpam-2537	398	2	1	1	NUM
ejpam-2537	398	3	}	}	PUNCT
ejpam-2537	398	4	with	with	ADP
ejpam-2537	398	5	n	n	PRON
ejpam-2537	398	6	odd	odd	ADJ
ejpam-2537	398	7	:	:	PUNCT
ejpam-2537	398	8	τ=	τ=	PRON
ejpam-2537	398	9	(	(	PUNCT
ejpam-2537	398	10	n+	n+	NUM
ejpam-2537	398	11	1,2n+	1,2n+	NUM
ejpam-2537	398	12	1)(n+	1)(n+	NUM
ejpam-2537	398	13	3,2n+	3,2n+	NUM
ejpam-2537	398	14	3)(n+	3)(n+	NUM
ejpam-2537	398	15	5,2n+	5,2n+	NUM
ejpam-2537	398	16	5	5	NUM
ejpam-2537	398	17	)	)	PUNCT
ejpam-2537	398	18	.	.	PUNCT
ejpam-2537	398	19	.	.	PUNCT
ejpam-2537	398	20	.	.	PUNCT
ejpam-2537	399	1	(	(	PUNCT
ejpam-2537	399	2	2n−	2n−	NUM
ejpam-2537	399	3	2,3n−	2,3n−	NUM
ejpam-2537	399	4	2	2	NUM
ejpam-2537	399	5	)	)	PUNCT
ejpam-2537	399	6	the	the	DET
ejpam-2537	399	7	permutation	permutation	NOUN
ejpam-2537	399	8	π	π	PROPN
ejpam-2537	399	9	of	of	ADP
ejpam-2537	399	10	f3n	f3n	PROPN
ejpam-2537	399	11	2	2	NUM
ejpam-2537	399	12	is	be	AUX
ejpam-2537	399	13	defined	define	VERB
ejpam-2537	399	14	by	by	ADP
ejpam-2537	399	15	π(r0	π(r0	ADJ
ejpam-2537	399	16	,	,	PUNCT
ejpam-2537	399	17	r1	r1	PROPN
ejpam-2537	399	18	,	,	PUNCT
ejpam-2537	399	19	.	.	PUNCT
ejpam-2537	399	20	.	.	PUNCT
ejpam-2537	400	1	.	.	PUNCT
ejpam-2537	401	1	,	,	PUNCT
ejpam-2537	401	2	r3n−1	r3n−1	PROPN
ejpam-2537	401	3	)	)	PUNCT
ejpam-2537	401	4	=	=	PRON
ejpam-2537	401	5	(	(	PUNCT
ejpam-2537	401	6	rτ(0	rτ(0	NOUN
ejpam-2537	401	7	)	)	PUNCT
ejpam-2537	401	8	,	,	PUNCT
ejpam-2537	401	9	rτ(1	rτ(1	NOUN
ejpam-2537	401	10	)	)	PUNCT
ejpam-2537	401	11	,	,	PUNCT
ejpam-2537	401	12	.	.	PUNCT
ejpam-2537	401	13	.	.	PUNCT
ejpam-2537	402	1	.	.	PUNCT
ejpam-2537	403	1	,	,	PUNCT
ejpam-2537	403	2	rτ(3n−1	rτ(3n−1	NOUN
ejpam-2537	403	3	)	)	PUNCT
ejpam-2537	403	4	)	)	PUNCT
ejpam-2537	403	5	proposition	proposition	NOUN
ejpam-2537	403	6	6	6	NUM
ejpam-2537	403	7	.	.	PUNCT
ejpam-2537	404	1	assume	assume	VERB
ejpam-2537	404	2	n	n	PRON
ejpam-2537	404	3	odd	odd	ADJ
ejpam-2537	404	4	,	,	PUNCT
ejpam-2537	404	5	let	let	VERB
ejpam-2537	404	6	µ̄	µ̄	NOUN
ejpam-2537	404	7	be	be	AUX
ejpam-2537	404	8	the	the	DET
ejpam-2537	404	9	permutation	permutation	NOUN
ejpam-2537	404	10	of	of	ADP
ejpam-2537	404	11	rn	rn	PROPN
ejpam-2537	404	12	such	such	ADJ
ejpam-2537	404	13	that	that	SCONJ
ejpam-2537	404	14	µ̄(z0	µ̄(z0	ADV
ejpam-2537	404	15	,	,	PUNCT
ejpam-2537	404	16	.	.	PUNCT
ejpam-2537	404	17	.	.	PUNCT
ejpam-2537	405	1	.	.	PUNCT
ejpam-2537	406	1	,	,	PUNCT
ejpam-2537	406	2	zn−1	zn−1	PROPN
ejpam-2537	406	3	)	)	PUNCT
ejpam-2537	406	4	=	=	PUNCT
ejpam-2537	406	5	(	(	PUNCT
ejpam-2537	406	6	z0	z0	PROPN
ejpam-2537	406	7	,	,	PUNCT
ejpam-2537	406	8	(	(	PUNCT
ejpam-2537	407	1	1	1	NUM
ejpam-2537	407	2	+	+	NUM
ejpam-2537	407	3	u)z1	u)z1	NOUN
ejpam-2537	407	4	,	,	PUNCT
ejpam-2537	407	5	.	.	PUNCT
ejpam-2537	407	6	.	.	PUNCT
ejpam-2537	408	1	.	.	PUNCT
ejpam-2537	409	1	,	,	PUNCT
ejpam-2537	409	2	(	(	PUNCT
ejpam-2537	409	3	1	1	NUM
ejpam-2537	409	4	+	+	NUM
ejpam-2537	409	5	u)n−1zn−1	u)n−1zn−1	ADJ
ejpam-2537	409	6	)	)	PUNCT
ejpam-2537	409	7	.	.	PUNCT
ejpam-2537	410	1	then	then	ADV
ejpam-2537	410	2	φµ̄=	φµ̄=	NUM
ejpam-2537	410	3	πφ	πφ	PROPN
ejpam-2537	410	4	.	.	PROPN
ejpam-2537	410	5	corollary	corollary	ADJ
ejpam-2537	410	6	3	3	NUM
ejpam-2537	410	7	.	.	PUNCT
ejpam-2537	411	1	if	if	SCONJ
ejpam-2537	411	2	c̃	c̃	PROPN
ejpam-2537	411	3	is	be	AUX
ejpam-2537	411	4	the	the	DET
ejpam-2537	411	5	gray	gray	ADJ
ejpam-2537	411	6	image	image	NOUN
ejpam-2537	411	7	of	of	ADP
ejpam-2537	411	8	a	a	DET
ejpam-2537	411	9	linear	linear	ADJ
ejpam-2537	411	10	cyclic	cyclic	ADJ
ejpam-2537	411	11	code	code	NOUN
ejpam-2537	411	12	of	of	ADP
ejpam-2537	411	13	length	length	NOUN
ejpam-2537	411	14	n	n	CCONJ
ejpam-2537	411	15	over	over	ADP
ejpam-2537	411	16	r	r	NOUN
ejpam-2537	411	17	,	,	PUNCT
ejpam-2537	411	18	then	then	ADV
ejpam-2537	411	19	c̃	c̃	PROPN
ejpam-2537	411	20	is	be	AUX
ejpam-2537	411	21	permutation	permutation	NOUN
ejpam-2537	411	22	equivalent	equivalent	ADJ
ejpam-2537	411	23	to	to	ADP
ejpam-2537	411	24	a	a	DET
ejpam-2537	411	25	quasi	quasi	ADJ
ejpam-2537	411	26	-	-	ADJ
ejpam-2537	411	27	cyclic	cyclic	ADJ
ejpam-2537	411	28	code	code	NOUN
ejpam-2537	411	29	of	of	ADP
ejpam-2537	411	30	index	index	NOUN
ejpam-2537	411	31	3	3	NUM
ejpam-2537	411	32	and	and	CCONJ
ejpam-2537	411	33	length	length	NOUN
ejpam-2537	411	34	3n	3n	NUM
ejpam-2537	411	35	over	over	ADP
ejpam-2537	411	36	f2	f2	PROPN
ejpam-2537	411	37	.	.	PUNCT
ejpam-2537	412	1	proof	proof	NOUN
ejpam-2537	412	2	.	.	PUNCT
ejpam-2537	413	1	from	from	ADP
ejpam-2537	413	2	proposition	proposition	NOUN
ejpam-2537	413	3	5	5	NUM
ejpam-2537	413	4	,	,	PUNCT
ejpam-2537	413	5	a	a	DET
ejpam-2537	413	6	code	code	NOUN
ejpam-2537	413	7	c	c	NOUN
ejpam-2537	413	8	of	of	ADP
ejpam-2537	413	9	length	length	NOUN
ejpam-2537	413	10	n	n	CCONJ
ejpam-2537	413	11	over	over	ADP
ejpam-2537	413	12	r	r	NOUN
ejpam-2537	413	13	is	be	AUX
ejpam-2537	413	14	linear	linear	ADJ
ejpam-2537	413	15	cyclic	cyclic	PROPN
ejpam-2537	413	16	code	code	NOUN
ejpam-2537	413	17	if	if	SCONJ
ejpam-2537	413	18	and	and	CCONJ
ejpam-2537	413	19	only	only	ADV
ejpam-2537	413	20	if	if	SCONJ
ejpam-2537	413	21	µ̄(c	µ̄(c	NOUN
ejpam-2537	413	22	)	)	PUNCT
ejpam-2537	413	23	is	be	AUX
ejpam-2537	413	24	linear	linear	ADJ
ejpam-2537	413	25	(	(	PUNCT
ejpam-2537	413	26	1	1	NUM
ejpam-2537	413	27	+	+	CCONJ
ejpam-2537	413	28	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	413	29	.	.	PUNCT
ejpam-2537	414	1	from	from	ADP
ejpam-2537	414	2	theorem	theorem	NOUN
ejpam-2537	414	3	9	9	NUM
ejpam-2537	414	4	,	,	PUNCT
ejpam-2537	414	5	this	this	PRON
ejpam-2537	414	6	is	be	AUX
ejpam-2537	414	7	also	also	ADV
ejpam-2537	414	8	so	so	ADV
ejpam-2537	414	9	if	if	SCONJ
ejpam-2537	414	10	and	and	CCONJ
ejpam-2537	414	11	only	only	ADV
ejpam-2537	414	12	if	if	SCONJ
ejpam-2537	414	13	φ(µ̄(c	φ(µ̄(c	NOUN
ejpam-2537	414	14	)	)	PUNCT
ejpam-2537	414	15	)	)	PUNCT
ejpam-2537	415	1	is	be	AUX
ejpam-2537	415	2	permutation	permutation	NOUN
ejpam-2537	415	3	equivalent	equivalent	ADJ
ejpam-2537	415	4	to	to	ADP
ejpam-2537	415	5	a	a	DET
ejpam-2537	415	6	linear	linear	ADJ
ejpam-2537	415	7	quasi	quasi	ADJ
ejpam-2537	415	8	-	-	ADJ
ejpam-2537	415	9	cyclic	cyclic	ADJ
ejpam-2537	415	10	code	code	NOUN
ejpam-2537	415	11	of	of	ADP
ejpam-2537	415	12	index	index	NOUN
ejpam-2537	415	13	3	3	NUM
ejpam-2537	415	14	over	over	ADP
ejpam-2537	415	15	f2	f2	PROPN
ejpam-2537	415	16	.	.	PUNCT
ejpam-2537	416	1	from	from	ADP
ejpam-2537	416	2	proposition	proposition	NOUN
ejpam-2537	416	3	6	6	NUM
ejpam-2537	416	4	,	,	PUNCT
ejpam-2537	416	5	φ(c	φ(c	NOUN
ejpam-2537	416	6	)	)	PUNCT
ejpam-2537	416	7	is	be	AUX
ejpam-2537	416	8	permutation	permutation	NOUN
ejpam-2537	416	9	equivalent	equivalent	ADJ
ejpam-2537	416	10	to	to	PART
ejpam-2537	416	11	linear	linear	VERB
ejpam-2537	416	12	quasi	quasi	X
ejpam-2537	416	13	cyclic	cyclic	NOUN
ejpam-2537	416	14	of	of	ADP
ejpam-2537	416	15	index	index	NOUN
ejpam-2537	416	16	3	3	NUM
ejpam-2537	416	17	over	over	ADP
ejpam-2537	416	18	f2	f2	PROPN
ejpam-2537	416	19	.	.	PUNCT
ejpam-2537	417	1	references	reference	NOUN
ejpam-2537	417	2	313	313	NUM
ejpam-2537	417	3	5	5	NUM
ejpam-2537	417	4	.	.	PUNCT
ejpam-2537	418	1	conclusion	conclusion	NOUN
ejpam-2537	418	2	it	it	PRON
ejpam-2537	418	3	is	be	AUX
ejpam-2537	418	4	introduced	introduce	VERB
ejpam-2537	419	1	(	(	PUNCT
ejpam-2537	419	2	1+u)-cyclic	1+u)-cyclic	NUM
ejpam-2537	419	3	codes	code	NOUN
ejpam-2537	419	4	and	and	CCONJ
ejpam-2537	419	5	cyclic	cyclic	ADJ
ejpam-2537	419	6	codes	code	NOUN
ejpam-2537	419	7	over	over	ADP
ejpam-2537	419	8	r.	r.	PROPN
ejpam-2537	419	9	firstly	firstly	ADV
ejpam-2537	419	10	,	,	PUNCT
ejpam-2537	419	11	it	it	PRON
ejpam-2537	419	12	is	be	AUX
ejpam-2537	419	13	characterized	characterize	VERB
ejpam-2537	419	14	codes	code	NOUN
ejpam-2537	419	15	over	over	ADP
ejpam-2537	419	16	f2	f2	PROPN
ejpam-2537	419	17	+	+	CCONJ
ejpam-2537	419	18	vf2	vf2	NOUN
ejpam-2537	419	19	which	which	PRON
ejpam-2537	419	20	are	be	AUX
ejpam-2537	419	21	the	the	DET
ejpam-2537	419	22	gray	gray	ADJ
ejpam-2537	419	23	images	image	NOUN
ejpam-2537	419	24	of	of	ADP
ejpam-2537	419	25	(	(	PUNCT
ejpam-2537	419	26	1	1	NUM
ejpam-2537	419	27	+	+	NUM
ejpam-2537	419	28	u)-cyclic	u)-cyclic	ADJ
ejpam-2537	419	29	codes	code	NOUN
ejpam-2537	419	30	and	and	CCONJ
ejpam-2537	419	31	cyclic	cyclic	ADJ
ejpam-2537	419	32	codes	code	NOUN
ejpam-2537	419	33	over	over	ADP
ejpam-2537	419	34	r.	r.	PROPN
ejpam-2537	419	35	it	it	PRON
ejpam-2537	419	36	is	be	AUX
ejpam-2537	419	37	obtained	obtain	VERB
ejpam-2537	419	38	a	a	DET
ejpam-2537	419	39	representation	representation	NOUN
ejpam-2537	419	40	of	of	ADP
ejpam-2537	419	41	a	a	DET
ejpam-2537	419	42	linear	linear	ADJ
ejpam-2537	419	43	code	code	NOUN
ejpam-2537	419	44	of	of	ADP
ejpam-2537	419	45	length	length	NOUN
ejpam-2537	419	46	n	n	CCONJ
ejpam-2537	419	47	over	over	ADP
ejpam-2537	419	48	r	r	NOUN
ejpam-2537	419	49	by	by	ADP
ejpam-2537	419	50	means	mean	NOUN
ejpam-2537	419	51	of	of	ADP
ejpam-2537	419	52	c1	c1	PROPN
ejpam-2537	419	53	and	and	CCONJ
ejpam-2537	419	54	c2	c2	PROPN
ejpam-2537	419	55	which	which	PRON
ejpam-2537	419	56	are	be	AUX
ejpam-2537	419	57	linear	linear	NOUN
ejpam-2537	419	58	codes	code	NOUN
ejpam-2537	419	59	of	of	ADP
ejpam-2537	419	60	length	length	NOUN
ejpam-2537	419	61	n	n	NOUN
ejpam-2537	419	62	over	over	ADP
ejpam-2537	419	63	f2	f2	PROPN
ejpam-2537	419	64	+	+	CCONJ
ejpam-2537	419	65	uf2	uf2	NOUN
ejpam-2537	419	66	.	.	PUNCT
ejpam-2537	420	1	it	it	PRON
ejpam-2537	420	2	is	be	AUX
ejpam-2537	420	3	characterized	characterize	VERB
ejpam-2537	420	4	codes	code	NOUN
ejpam-2537	420	5	over	over	ADP
ejpam-2537	420	6	f2	f2	PROPN
ejpam-2537	420	7	which	which	PRON
ejpam-2537	420	8	are	be	AUX
ejpam-2537	420	9	the	the	DET
ejpam-2537	420	10	gray	gray	ADJ
ejpam-2537	420	11	images	image	NOUN
ejpam-2537	420	12	of	of	ADP
ejpam-2537	420	13	(	(	PUNCT
ejpam-2537	420	14	1	1	NUM
ejpam-2537	420	15	+	+	CCONJ
ejpam-2537	420	16	u)cyclic	u)cyclic	ADJ
ejpam-2537	420	17	codes	code	NOUN
ejpam-2537	420	18	or	or	CCONJ
ejpam-2537	420	19	cyclic	cyclic	ADJ
ejpam-2537	420	20	codes	code	NOUN
ejpam-2537	420	21	over	over	ADP
ejpam-2537	420	22	r.	r.	PROPN
ejpam-2537	420	23	references	reference	NOUN
ejpam-2537	420	24	[	[	X
ejpam-2537	420	25	1	1	NUM
ejpam-2537	420	26	]	]	PUNCT
ejpam-2537	420	27	m.	m.	NOUN
ejpam-2537	420	28	c.	c.	PROPN
ejpam-2537	420	29	v.	v.	PROPN
ejpam-2537	420	30	amarra	amarra	PROPN
ejpam-2537	420	31	and	and	CCONJ
ejpam-2537	420	32	f.	f.	PROPN
ejpam-2537	420	33	r.	r.	PROPN
ejpam-2537	420	34	nemenzo	nemenzo	PROPN
ejpam-2537	420	35	.	.	PUNCT
ejpam-2537	421	1	on	on	ADP
ejpam-2537	421	2	(	(	PUNCT
ejpam-2537	421	3	1	1	NUM
ejpam-2537	421	4	−	−	PROPN
ejpam-2537	421	5	u)−	u)−	PROPN
ejpam-2537	421	6	cyclic	cyclic	NOUN
ejpam-2537	421	7	codes	code	NOUN
ejpam-2537	421	8	over	over	ADP
ejpam-2537	421	9	fpk	fpk	NOUN
ejpam-2537	421	10	+	+	CCONJ
ejpam-2537	421	11	ufpk	ufpk	NOUN
ejpam-2537	421	12	,	,	PUNCT
ejpam-2537	421	13	applied	apply	VERB
ejpam-2537	421	14	mathematics	mathematics	NOUN
ejpam-2537	421	15	letters	letter	NOUN
ejpam-2537	421	16	,	,	PUNCT
ejpam-2537	421	17	21	21	NUM
ejpam-2537	421	18	,	,	PUNCT
ejpam-2537	421	19	1129–1133	1129–1133	NUM
ejpam-2537	421	20	.	.	PUNCT
ejpam-2537	421	21	2008	2008	NUM
ejpam-2537	421	22	.	.	PUNCT
ejpam-2537	422	1	[	[	X
ejpam-2537	422	2	2	2	X
ejpam-2537	422	3	]	]	X
ejpam-2537	422	4	y.	y.	PROPN
ejpam-2537	422	5	cengellenmis	cengellenmis	PROPN
ejpam-2537	422	6	,	,	PUNCT
ejpam-2537	422	7	on	on	ADP
ejpam-2537	422	8	(	(	PUNCT
ejpam-2537	422	9	1−	1−	NUM
ejpam-2537	422	10	um)-cyclic	um)-cyclic	ADJ
ejpam-2537	422	11	codes	code	NOUN
ejpam-2537	422	12	over	over	ADP
ejpam-2537	422	13	f2	f2	PROPN
ejpam-2537	422	14	+	+	CCONJ
ejpam-2537	422	15	uf2	uf2	NOUN
ejpam-2537	422	16	+	+	NUM
ejpam-2537	422	17	u2f2	u2f2	ADJ
ejpam-2537	422	18	+	+	CCONJ
ejpam-2537	422	19	u3f2	u3f2	NOUN
ejpam-2537	422	20	+	+	NUM
ejpam-2537	422	21	.	.	PUNCT
ejpam-2537	422	22	.	.	PUNCT
ejpam-2537	423	1	.+	.+	NOUN
ejpam-2537	423	2	umf2	umf2	PROPN
ejpam-2537	423	3	,	,	PUNCT
ejpam-2537	423	4	international	international	ADJ
ejpam-2537	423	5	journal	journal	NOUN
ejpam-2537	423	6	of	of	ADP
ejpam-2537	423	7	contemporary	contemporary	PROPN
ejpam-2537	423	8	mathematical	mathematical	PROPN
ejpam-2537	423	9	sciences	sciences	PROPN
ejpam-2537	423	10	4	4	NUM
ejpam-2537	423	11	,	,	PUNCT
ejpam-2537	423	12	987	987	NUM
ejpam-2537	423	13	-	-	SYM
ejpam-2537	423	14	992	992	NUM
ejpam-2537	423	15	.	.	PUNCT
ejpam-2537	423	16	2009	2009	NUM
ejpam-2537	423	17	.	.	PUNCT
ejpam-2537	424	1	[	[	X
ejpam-2537	424	2	3	3	X
ejpam-2537	424	3	]	]	PUNCT
ejpam-2537	424	4	x.	x.	NOUN
ejpam-2537	424	5	kai	kai	PROPN
ejpam-2537	424	6	,	,	PUNCT
ejpam-2537	424	7	s.	s.	PROPN
ejpam-2537	424	8	zhu	zhu	PROPN
ejpam-2537	424	9	,	,	PUNCT
ejpam-2537	424	10	and	and	CCONJ
ejpam-2537	424	11	l.	l.	PROPN
ejpam-2537	424	12	wang	wang	PROPN
ejpam-2537	424	13	.	.	PUNCT
ejpam-2537	425	1	a	a	DET
ejpam-2537	425	2	family	family	NOUN
ejpam-2537	425	3	of	of	ADP
ejpam-2537	425	4	constacyclic	constacyclic	ADJ
ejpam-2537	425	5	codes	code	NOUN
ejpam-2537	425	6	over	over	ADP
ejpam-2537	425	7	f2	f2	PROPN
ejpam-2537	425	8	+	+	CCONJ
ejpam-2537	425	9	uf2	uf2	NOUN
ejpam-2537	425	10	+	+	CCONJ
ejpam-2537	425	11	vf2	vf2	NOUN
ejpam-2537	425	12	+	+	CCONJ
ejpam-2537	425	13	uvf2	uvf2	PROPN
ejpam-2537	425	14	,	,	PUNCT
ejpam-2537	425	15	journal	journal	NOUN
ejpam-2537	425	16	of	of	ADP
ejpam-2537	425	17	systems	system	NOUN
ejpam-2537	425	18	science	science	NOUN
ejpam-2537	425	19	and	and	CCONJ
ejpam-2537	425	20	complexity	complexity	NOUN
ejpam-2537	425	21	,	,	PUNCT
ejpam-2537	425	22	25	25	NUM
ejpam-2537	425	23	,	,	PUNCT
ejpam-2537	425	24	1023	1023	NUM
ejpam-2537	425	25	-	-	SYM
ejpam-2537	425	26	1040	1040	NUM
ejpam-2537	425	27	.	.	PUNCT
ejpam-2537	425	28	2012	2012	NUM
ejpam-2537	425	29	.	.	PUNCT
ejpam-2537	426	1	[	[	X
ejpam-2537	426	2	4	4	X
ejpam-2537	426	3	]	]	PUNCT
ejpam-2537	426	4	s.	s.	PROPN
ejpam-2537	426	5	karadeniz	karadeniz	PROPN
ejpam-2537	426	6	and	and	CCONJ
ejpam-2537	426	7	b.	b.	PROPN
ejpam-2537	426	8	yildiz	yildiz	PROPN
ejpam-2537	426	9	.	.	PUNCT
ejpam-2537	427	1	(	(	PUNCT
ejpam-2537	427	2	1	1	NUM
ejpam-2537	427	3	+	+	NOUN
ejpam-2537	427	4	v)-constacyclic	v)-constacyclic	ADJ
ejpam-2537	427	5	codes	code	NOUN
ejpam-2537	427	6	over	over	ADP
ejpam-2537	427	7	f2	f2	PROPN
ejpam-2537	427	8	+	+	CCONJ
ejpam-2537	427	9	uf2	uf2	NOUN
ejpam-2537	427	10	+	+	CCONJ
ejpam-2537	427	11	vf2	vf2	NOUN
ejpam-2537	427	12	+	+	CCONJ
ejpam-2537	427	13	uvf2	uvf2	PROPN
ejpam-2537	427	14	,	,	PUNCT
ejpam-2537	427	15	journal	journal	NOUN
ejpam-2537	427	16	of	of	ADP
ejpam-2537	427	17	the	the	DET
ejpam-2537	427	18	franklin	franklin	PROPN
ejpam-2537	427	19	institute	institute	PROPN
ejpam-2537	427	20	,	,	PUNCT
ejpam-2537	427	21	doi:10.1016	doi:10.1016	PROPN
ejpam-2537	427	22	/	/	SYM
ejpam-2537	427	23	j.jfranklin.2011.08.005	j.jfranklin.2011.08.005	PROPN
ejpam-2537	427	24	,	,	PUNCT
ejpam-2537	427	25	2011	2011	NUM
ejpam-2537	427	26	.	.	PUNCT
ejpam-2537	428	1	[	[	X
ejpam-2537	428	2	5	5	X
ejpam-2537	428	3	]	]	PUNCT
ejpam-2537	428	4	j.	j.	PROPN
ejpam-2537	428	5	f.	f.	PROPN
ejpam-2537	428	6	qian	qian	PROPN
ejpam-2537	428	7	,	,	PUNCT
ejpam-2537	428	8	l.	l.	PROPN
ejpam-2537	428	9	n.	n.	PROPN
ejpam-2537	428	10	zhang	zhang	PROPN
ejpam-2537	428	11	,	,	PUNCT
ejpam-2537	428	12	and	and	CCONJ
ejpam-2537	428	13	s.	s.	PROPN
ejpam-2537	428	14	x.	x.	PROPN
ejpam-2537	428	15	zhu	zhu	PROPN
ejpam-2537	428	16	.	.	PUNCT
ejpam-2537	429	1	constacyclic	constacyclic	ADJ
ejpam-2537	429	2	and	and	CCONJ
ejpam-2537	429	3	cyclic	cyclic	ADJ
ejpam-2537	429	4	codes	code	NOUN
ejpam-2537	429	5	over	over	ADP
ejpam-2537	429	6	f2	f2	PROPN
ejpam-2537	429	7	+	+	CCONJ
ejpam-2537	429	8	uf2	uf2	NOUN
ejpam-2537	429	9	+	+	SYM
ejpam-2537	429	10	u2f2	u2f2	PROPN
ejpam-2537	429	11	,	,	PUNCT
ejpam-2537	429	12	ieice	ieice	NOUN
ejpam-2537	429	13	transactions	transaction	NOUN
ejpam-2537	429	14	on	on	ADP
ejpam-2537	429	15	fundamentals	fundamental	NOUN
ejpam-2537	429	16	of	of	ADP
ejpam-2537	429	17	electronics	electronics	NOUN
ejpam-2537	429	18	communications	communication	NOUN
ejpam-2537	429	19	and	and	CCONJ
ejpam-2537	429	20	computer	computer	NOUN
ejpam-2537	429	21	sciences	science	NOUN
ejpam-2537	429	22	,	,	PUNCT
ejpam-2537	429	23	e89	e89	PROPN
ejpam-2537	429	24	-	-	PUNCT
ejpam-2537	429	25	a(6	a(6	PROPN
ejpam-2537	429	26	)	)	PUNCT
ejpam-2537	429	27	,	,	PUNCT
ejpam-2537	429	28	1863–1865	1863–1865	NUM
ejpam-2537	429	29	.	.	NOUN
ejpam-2537	429	30	2006	2006	NUM
ejpam-2537	429	31	.	.	PUNCT
ejpam-2537	430	1	[	[	X
ejpam-2537	430	2	6	6	NUM
ejpam-2537	430	3	]	]	PUNCT
ejpam-2537	430	4	j.	j.	PROPN
ejpam-2537	430	5	f.	f.	PROPN
ejpam-2537	430	6	qian	qian	PROPN
ejpam-2537	430	7	,	,	PUNCT
ejpam-2537	430	8	l.	l.	PROPN
ejpam-2537	430	9	n.	n.	PROPN
ejpam-2537	430	10	zhang	zhang	PROPN
ejpam-2537	430	11	,	,	PUNCT
ejpam-2537	430	12	and	and	CCONJ
ejpam-2537	430	13	s.	s.	PROPN
ejpam-2537	430	14	x.	x.	PROPN
ejpam-2537	430	15	zhu	zhu	PROPN
ejpam-2537	430	16	.	.	PUNCT
ejpam-2537	431	1	(	(	PUNCT
ejpam-2537	431	2	1	1	NUM
ejpam-2537	431	3	+	+	NUM
ejpam-2537	431	4	u	u	NOUN
ejpam-2537	431	5	)	)	PUNCT
ejpam-2537	431	6	constacyclic	constacyclic	ADJ
ejpam-2537	431	7	and	and	CCONJ
ejpam-2537	431	8	cyclic	cyclic	ADJ
ejpam-2537	431	9	codes	code	NOUN
ejpam-2537	431	10	over	over	ADP
ejpam-2537	431	11	f2	f2	PROPN
ejpam-2537	431	12	+	+	CCONJ
ejpam-2537	431	13	uf2	uf2	NOUN
ejpam-2537	431	14	,	,	PUNCT
ejpam-2537	431	15	applied	apply	VERB
ejpam-2537	431	16	mathematics	mathematic	NOUN
ejpam-2537	431	17	letters	letter	NOUN
ejpam-2537	431	18	,	,	PUNCT
ejpam-2537	431	19	19	19	NUM
ejpam-2537	431	20	,	,	PUNCT
ejpam-2537	431	21	820–823	820–823	NUM
ejpam-2537	431	22	.	.	NOUN
ejpam-2537	431	23	2006	2006	NUM
ejpam-2537	431	24	.	.	PUNCT
ejpam-2537	432	1	[	[	X
ejpam-2537	432	2	7	7	X
ejpam-2537	432	3	]	]	X
ejpam-2537	432	4	b.	b.	NOUN
ejpam-2537	432	5	srinivasulu	srinivasulu	PROPN
ejpam-2537	432	6	and	and	CCONJ
ejpam-2537	432	7	m.	m.	NOUN
ejpam-2537	432	8	bhaintwal	bhaintwal	NOUN
ejpam-2537	432	9	.	.	PUNCT
ejpam-2537	433	1	on	on	ADP
ejpam-2537	433	2	linear	linear	PROPN
ejpam-2537	433	3	codes	code	NOUN
ejpam-2537	433	4	over	over	ADP
ejpam-2537	433	5	a	a	DET
ejpam-2537	433	6	non	non	ADJ
ejpam-2537	433	7	chain	chain	NOUN
ejpam-2537	433	8	extension	extension	NOUN
ejpam-2537	433	9	of	of	ADP
ejpam-2537	433	10	f2	f2	PROPN
ejpam-2537	433	11	+	+	CCONJ
ejpam-2537	433	12	uf2	uf2	NOUN
ejpam-2537	433	13	,	,	PUNCT
ejpam-2537	433	14	computer	computer	NOUN
ejpam-2537	433	15	,	,	PUNCT
ejpam-2537	433	16	communication	communication	NOUN
ejpam-2537	433	17	,	,	PUNCT
ejpam-2537	433	18	control	control	NOUN
ejpam-2537	433	19	and	and	CCONJ
ejpam-2537	433	20	information	information	NOUN
ejpam-2537	433	21	technology	technology	NOUN
ejpam-2537	433	22	(	(	PUNCT
ejpam-2537	433	23	c3it	c3it	NUM
ejpam-2537	433	24	)	)	PUNCT
ejpam-2537	433	25	,	,	PUNCT
ejpam-2537	433	26	2015	2015	NUM
ejpam-2537	433	27	third	third	ADJ
ejpam-2537	433	28	international	international	ADJ
ejpam-2537	433	29	conference	conference	NOUN
ejpam-2537	433	30	on	on	ADP
ejpam-2537	433	31	ieee	ieee	NOUN
ejpam-2537	433	32	,	,	PUNCT
ejpam-2537	433	33	2015	2015	NUM
ejpam-2537	433	34	.	.	PUNCT
ejpam-2537	434	1	doi:10.1109	doi:10.1109	VERB
ejpam-2537	434	2	/	/	SYM
ejpam-2537	434	3	c3it.2015.7060155	c3it.2015.7060155	NOUN
ejpam-2537	434	4	[	[	X
ejpam-2537	434	5	8	8	NUM
ejpam-2537	434	6	]	]	PUNCT
ejpam-2537	434	7	p.	p.	NOUN
ejpam-2537	434	8	udomkavanich	udomkavanich	PROPN
ejpam-2537	434	9	and	and	CCONJ
ejpam-2537	434	10	s.	s.	PROPN
ejpam-2537	434	11	jitman	jitman	PROPN
ejpam-2537	434	12	.	.	PUNCT
ejpam-2537	435	1	on	on	ADP
ejpam-2537	435	2	the	the	DET
ejpam-2537	435	3	gray	gray	ADJ
ejpam-2537	435	4	image	image	NOUN
ejpam-2537	435	5	of	of	ADP
ejpam-2537	435	6	(	(	PUNCT
ejpam-2537	435	7	1−um)-cyclic	1−um)-cyclic	NUM
ejpam-2537	435	8	codes	code	NOUN
ejpam-2537	435	9	over	over	ADP
ejpam-2537	435	10	fpk+ufpk+	fpk+ufpk+	NOUN
ejpam-2537	435	11	.	.	PUNCT
ejpam-2537	435	12	.	.	PUNCT
ejpam-2537	436	1	.+umfpk	.+umfpk	PUNCT
ejpam-2537	436	2	,	,	PUNCT
ejpam-2537	436	3	international	international	ADJ
ejpam-2537	436	4	journal	journal	NOUN
ejpam-2537	436	5	of	of	ADP
ejpam-2537	436	6	contemporary	contemporary	PROPN
ejpam-2537	436	7	mathematical	mathematical	PROPN
ejpam-2537	436	8	sciences	sciences	PROPN
ejpam-2537	436	9	4	4	NUM
ejpam-2537	436	10	,	,	PUNCT
ejpam-2537	436	11	1265	1265	NUM
ejpam-2537	436	12	-	-	SYM
ejpam-2537	436	13	1272	1272	NUM
ejpam-2537	436	14	.	.	PUNCT
ejpam-2537	436	15	2009	2009	NUM
ejpam-2537	436	16	.	.	PUNCT
ejpam-2537	437	1	[	[	X
ejpam-2537	437	2	9	9	NUM
ejpam-2537	437	3	]	]	PUNCT
ejpam-2537	437	4	l.	l.	PROPN
ejpam-2537	437	5	xiusheng	xiusheng	PROPN
ejpam-2537	437	6	and	and	CCONJ
ejpam-2537	437	7	l.	l.	PROPN
ejpam-2537	437	8	hualu	hualu	PROPN
ejpam-2537	437	9	.	.	PUNCT
ejpam-2537	438	1	macwilliams	macwilliam	NOUN
ejpam-2537	438	2	identities	identity	NOUN
ejpam-2537	438	3	of	of	ADP
ejpam-2537	438	4	linear	linear	PROPN
ejpam-2537	438	5	codes	code	NOUN
ejpam-2537	438	6	over	over	ADP
ejpam-2537	438	7	the	the	DET
ejpam-2537	438	8	ring	ring	NOUN
ejpam-2537	438	9	f2+uf2+vf2	f2+uf2+vf2	PROPN
ejpam-2537	438	10	,	,	PUNCT
ejpam-2537	438	11	doi:10.1007	doi:10.1007	X
ejpam-2537	438	12	s11424	s11424	VERB
ejpam-2537	438	13	-	-	PUNCT
ejpam-2537	438	14	015	015	NUM
ejpam-2537	438	15	-	-	PUNCT
ejpam-2537	438	16	2246	2246	NUM
ejpam-2537	438	17	-	-	PUNCT
ejpam-2537	438	18	x	x	NOUN
ejpam-2537	438	19	,	,	PUNCT
ejpam-2537	438	20	journal	journal	NOUN
ejpam-2537	438	21	of	of	ADP
ejpam-2537	438	22	systems	system	NOUN
ejpam-2537	438	23	science	science	NOUN
ejpam-2537	438	24	and	and	CCONJ
ejpam-2537	438	25	complexity	complexity	NOUN
ejpam-2537	438	26	,	,	PUNCT
ejpam-2537	438	27	28	28	NUM
ejpam-2537	438	28	,	,	PUNCT
ejpam-2537	438	29	691701	691701	NUM
ejpam-2537	439	1	.	.	PUNCT
ejpam-2537	440	1	2015	2015	NUM
ejpam-2537	440	2	.	.	PUNCT