id	sid	tid	token	lemma	pos
ejpam-2650	1	1	european	european	PROPN
ejpam-2650	1	2	journal	journal	PROPN
ejpam-2650	1	3	of	of	ADP
ejpam-2650	1	4	pure	pure	ADJ
ejpam-2650	1	5	and	and	CCONJ
ejpam-2650	1	6	applied	apply	VERB
ejpam-2650	1	7	mathematics	mathematic	NOUN
ejpam-2650	1	8	vol	vol	NOUN
ejpam-2650	1	9	.	.	PROPN
ejpam-2650	2	1	10	10	NUM
ejpam-2650	2	2	,	,	PUNCT
ejpam-2650	2	3	no	no	INTJ
ejpam-2650	2	4	.	.	NOUN
ejpam-2650	2	5	5	5	NUM
ejpam-2650	2	6	,	,	PUNCT
ejpam-2650	2	7	2017	2017	NUM
ejpam-2650	2	8	,	,	PUNCT
ejpam-2650	2	9	1112	1112	NUM
ejpam-2650	2	10	-	-	SYM
ejpam-2650	2	11	1123	1123	NUM
ejpam-2650	2	12	issn	issn	PROPN
ejpam-2650	2	13	1307	1307	NUM
ejpam-2650	2	14	-	-	SYM
ejpam-2650	2	15	5543	5543	NUM
ejpam-2650	2	16	–	–	PUNCT
ejpam-2650	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2650	2	18	published	publish	VERB
ejpam-2650	2	19	by	by	ADP
ejpam-2650	2	20	new	new	PROPN
ejpam-2650	2	21	york	york	PROPN
ejpam-2650	2	22	business	business	PROPN
ejpam-2650	2	23	global	global	ADJ
ejpam-2650	2	24	optimal	optimal	ADJ
ejpam-2650	2	25	divisible	divisible	ADJ
ejpam-2650	2	26	binary	binary	NOUN
ejpam-2650	2	27	codes	code	NOUN
ejpam-2650	2	28	from	from	ADP
ejpam-2650	2	29	gray	gray	ADJ
ejpam-2650	2	30	-	-	PUNCT
ejpam-2650	2	31	homogeneous	homogeneous	ADJ
ejpam-2650	2	32	images	image	NOUN
ejpam-2650	2	33	of	of	ADP
ejpam-2650	2	34	codes	code	NOUN
ejpam-2650	2	35	over	over	ADP
ejpam-2650	2	36	rk	rk	NOUN
ejpam-2650	2	37	,	,	PUNCT
ejpam-2650	2	38	m	m	VERB
ejpam-2650	2	39	bahattin	bahattin	PROPN
ejpam-2650	2	40	yildiz1,∗	yildiz1,∗	PROPN
ejpam-2650	2	41	,	,	PUNCT
ejpam-2650	2	42	nesibe	nesibe	VERB
ejpam-2650	2	43	tufekci	tufekci	PROPN
ejpam-2650	2	44	1	1	NUM
ejpam-2650	2	45	department	department	NOUN
ejpam-2650	2	46	of	of	ADP
ejpam-2650	2	47	mathematics	mathematics	PROPN
ejpam-2650	2	48	&	&	CCONJ
ejpam-2650	2	49	statistics	statistics	PROPN
ejpam-2650	2	50	,	,	PUNCT
ejpam-2650	2	51	northern	northern	PROPN
ejpam-2650	2	52	arizona	arizona	PROPN
ejpam-2650	2	53	university	university	PROPN
ejpam-2650	2	54	,	,	PUNCT
ejpam-2650	2	55	flagstaff	flagstaff	PROPN
ejpam-2650	2	56	,	,	PUNCT
ejpam-2650	2	57	az	az	PROPN
ejpam-2650	2	58	86001	86001	NUM
ejpam-2650	2	59	,	,	PUNCT
ejpam-2650	2	60	usa	usa	PROPN
ejpam-2650	2	61	abstract	abstract	NOUN
ejpam-2650	2	62	.	.	PUNCT
ejpam-2650	3	1	in	in	ADP
ejpam-2650	3	2	this	this	DET
ejpam-2650	3	3	work	work	NOUN
ejpam-2650	3	4	,	,	PUNCT
ejpam-2650	3	5	we	we	PRON
ejpam-2650	3	6	find	find	VERB
ejpam-2650	3	7	a	a	DET
ejpam-2650	3	8	form	form	NOUN
ejpam-2650	3	9	for	for	ADP
ejpam-2650	3	10	the	the	DET
ejpam-2650	3	11	homogeneous	homogeneous	ADJ
ejpam-2650	3	12	weight	weight	NOUN
ejpam-2650	3	13	over	over	ADP
ejpam-2650	3	14	the	the	DET
ejpam-2650	3	15	ring	ring	NOUN
ejpam-2650	3	16	rk	rk	NOUN
ejpam-2650	3	17	,	,	PUNCT
ejpam-2650	3	18	m	m	PRON
ejpam-2650	3	19	,	,	PUNCT
ejpam-2650	3	20	using	use	VERB
ejpam-2650	3	21	the	the	DET
ejpam-2650	3	22	related	related	ADJ
ejpam-2650	3	23	theoretical	theoretical	ADJ
ejpam-2650	3	24	results	result	NOUN
ejpam-2650	3	25	from	from	ADP
ejpam-2650	3	26	the	the	DET
ejpam-2650	3	27	literature	literature	NOUN
ejpam-2650	3	28	.	.	PUNCT
ejpam-2650	4	1	we	we	PRON
ejpam-2650	4	2	then	then	ADV
ejpam-2650	4	3	use	use	VERB
ejpam-2650	4	4	the	the	DET
ejpam-2650	4	5	first	first	ADJ
ejpam-2650	4	6	order	order	NOUN
ejpam-2650	4	7	reed	reed	NOUN
ejpam-2650	4	8	-	-	PUNCT
ejpam-2650	4	9	muller	muller	PROPN
ejpam-2650	4	10	codes	code	NOUN
ejpam-2650	4	11	to	to	PART
ejpam-2650	4	12	find	find	VERB
ejpam-2650	4	13	a	a	DET
ejpam-2650	4	14	distance	distance	NOUN
ejpam-2650	4	15	-	-	PUNCT
ejpam-2650	4	16	preserving	preserve	VERB
ejpam-2650	4	17	map	map	NOUN
ejpam-2650	4	18	that	that	PRON
ejpam-2650	4	19	takes	take	VERB
ejpam-2650	4	20	codes	code	NOUN
ejpam-2650	4	21	over	over	ADP
ejpam-2650	4	22	rk	rk	NOUN
ejpam-2650	4	23	,	,	PUNCT
ejpam-2650	4	24	m	m	VERB
ejpam-2650	4	25	to	to	ADP
ejpam-2650	4	26	binary	binary	ADJ
ejpam-2650	4	27	codes	code	NOUN
ejpam-2650	4	28	.	.	PUNCT
ejpam-2650	5	1	by	by	ADP
ejpam-2650	5	2	considering	consider	VERB
ejpam-2650	5	3	cyclic	cyclic	ADJ
ejpam-2650	5	4	,	,	PUNCT
ejpam-2650	5	5	constacyclic	constacyclic	ADJ
ejpam-2650	5	6	and	and	CCONJ
ejpam-2650	5	7	quasicyclic	quasicyclic	ADJ
ejpam-2650	5	8	codes	code	NOUN
ejpam-2650	5	9	over	over	ADP
ejpam-2650	5	10	rk	rk	NOUN
ejpam-2650	5	11	,	,	PUNCT
ejpam-2650	5	12	m	m	NOUN
ejpam-2650	5	13	of	of	ADP
ejpam-2650	5	14	different	different	ADJ
ejpam-2650	5	15	lengths	length	NOUN
ejpam-2650	5	16	for	for	ADP
ejpam-2650	5	17	different	different	ADJ
ejpam-2650	5	18	values	value	NOUN
ejpam-2650	5	19	of	of	ADP
ejpam-2650	5	20	k	k	PROPN
ejpam-2650	5	21	and	and	CCONJ
ejpam-2650	5	22	m	m	PROPN
ejpam-2650	5	23	,	,	PUNCT
ejpam-2650	5	24	we	we	PRON
ejpam-2650	5	25	construct	construct	VERB
ejpam-2650	5	26	a	a	DET
ejpam-2650	5	27	considerable	considerable	ADJ
ejpam-2650	5	28	number	number	NOUN
ejpam-2650	5	29	of	of	ADP
ejpam-2650	5	30	optimal	optimal	ADJ
ejpam-2650	5	31	binary	binary	ADJ
ejpam-2650	5	32	codes	code	NOUN
ejpam-2650	5	33	that	that	PRON
ejpam-2650	5	34	are	be	AUX
ejpam-2650	5	35	divisible	divisible	ADJ
ejpam-2650	5	36	with	with	ADP
ejpam-2650	5	37	high	high	ADJ
ejpam-2650	5	38	levels	level	NOUN
ejpam-2650	5	39	of	of	ADP
ejpam-2650	5	40	divisibility	divisibility	NOUN
ejpam-2650	5	41	.	.	PUNCT
ejpam-2650	6	1	the	the	DET
ejpam-2650	6	2	codes	code	NOUN
ejpam-2650	6	3	we	we	PRON
ejpam-2650	6	4	have	have	AUX
ejpam-2650	6	5	obtained	obtain	VERB
ejpam-2650	6	6	are	be	AUX
ejpam-2650	6	7	also	also	ADV
ejpam-2650	6	8	quasicyclic	quasicyclic	ADJ
ejpam-2650	6	9	with	with	ADP
ejpam-2650	6	10	high	high	ADJ
ejpam-2650	6	11	indices	index	NOUN
ejpam-2650	6	12	and	and	CCONJ
ejpam-2650	6	13	they	they	PRON
ejpam-2650	6	14	are	be	AUX
ejpam-2650	6	15	all	all	PRON
ejpam-2650	6	16	self	self	NOUN
ejpam-2650	6	17	-	-	PUNCT
ejpam-2650	6	18	orthogonal	orthogonal	ADJ
ejpam-2650	6	19	when	when	SCONJ
ejpam-2650	6	20	km	km	PROPN
ejpam-2650	6	21	≥	≥	NUM
ejpam-2650	6	22	4	4	NUM
ejpam-2650	6	23	.	.	PUNCT
ejpam-2650	7	1	the	the	DET
ejpam-2650	7	2	results	result	NOUN
ejpam-2650	7	3	,	,	PUNCT
ejpam-2650	7	4	which	which	PRON
ejpam-2650	7	5	have	have	AUX
ejpam-2650	7	6	been	be	AUX
ejpam-2650	7	7	obtained	obtain	VERB
ejpam-2650	7	8	by	by	ADP
ejpam-2650	7	9	computer	computer	NOUN
ejpam-2650	7	10	search	search	NOUN
ejpam-2650	7	11	are	be	AUX
ejpam-2650	7	12	tabulated	tabulate	VERB
ejpam-2650	7	13	.	.	PUNCT
ejpam-2650	8	1	2010	2010	NUM
ejpam-2650	8	2	mathematics	mathematic	NOUN
ejpam-2650	8	3	subject	subject	NOUN
ejpam-2650	8	4	classifications	classification	NOUN
ejpam-2650	8	5	:	:	PUNCT
ejpam-2650	8	6	94b05	94b05	NUM
ejpam-2650	8	7	,	,	PUNCT
ejpam-2650	8	8	94b99	94b99	NUM
ejpam-2650	8	9	key	key	ADJ
ejpam-2650	8	10	words	word	NOUN
ejpam-2650	8	11	and	and	CCONJ
ejpam-2650	8	12	phrases	phrase	NOUN
ejpam-2650	8	13	:	:	PUNCT
ejpam-2650	8	14	homogeneous	homogeneous	ADJ
ejpam-2650	8	15	weight	weight	NOUN
ejpam-2650	8	16	,	,	PUNCT
ejpam-2650	8	17	frobenius	frobenius	NOUN
ejpam-2650	8	18	rings	ring	NOUN
ejpam-2650	8	19	,	,	PUNCT
ejpam-2650	8	20	divisible	divisible	ADJ
ejpam-2650	8	21	codes	code	NOUN
ejpam-2650	8	22	,	,	PUNCT
ejpam-2650	8	23	self	self	NOUN
ejpam-2650	8	24	-	-	PUNCT
ejpam-2650	8	25	orthogonal	orthogonal	ADJ
ejpam-2650	8	26	quasicyclic	quasicyclic	NOUN
ejpam-2650	8	27	codes	code	NOUN
ejpam-2650	8	28	,	,	PUNCT
ejpam-2650	8	29	optimal	optimal	ADJ
ejpam-2650	8	30	codes	code	NOUN
ejpam-2650	8	31	1	1	NUM
ejpam-2650	8	32	.	.	PUNCT
ejpam-2650	9	1	introduction	introduction	NOUN
ejpam-2650	9	2	the	the	DET
ejpam-2650	9	3	homogeneous	homogeneous	ADJ
ejpam-2650	9	4	weight	weight	NOUN
ejpam-2650	9	5	was	be	AUX
ejpam-2650	9	6	introduced	introduce	VERB
ejpam-2650	9	7	for	for	ADP
ejpam-2650	9	8	codes	code	NOUN
ejpam-2650	9	9	over	over	ADP
ejpam-2650	9	10	rings	ring	NOUN
ejpam-2650	9	11	as	as	ADP
ejpam-2650	9	12	an	an	DET
ejpam-2650	9	13	alternative	alternative	NOUN
ejpam-2650	9	14	to	to	ADP
ejpam-2650	9	15	the	the	DET
ejpam-2650	9	16	hamming	hamming	NOUN
ejpam-2650	9	17	weight	weight	NOUN
ejpam-2650	9	18	.	.	PUNCT
ejpam-2650	10	1	the	the	DET
ejpam-2650	10	2	theoretical	theoretical	ADJ
ejpam-2650	10	3	work	work	NOUN
ejpam-2650	10	4	on	on	ADP
ejpam-2650	10	5	the	the	DET
ejpam-2650	10	6	homogeneous	homogeneous	ADJ
ejpam-2650	10	7	weight	weight	NOUN
ejpam-2650	10	8	and	and	CCONJ
ejpam-2650	10	9	its	its	PRON
ejpam-2650	10	10	form	form	NOUN
ejpam-2650	10	11	for	for	ADP
ejpam-2650	10	12	frobenius	frobenius	ADJ
ejpam-2650	10	13	rings	ring	NOUN
ejpam-2650	10	14	can	can	AUX
ejpam-2650	10	15	be	be	AUX
ejpam-2650	10	16	found	find	VERB
ejpam-2650	10	17	in	in	ADP
ejpam-2650	10	18	such	such	ADJ
ejpam-2650	10	19	works	work	NOUN
ejpam-2650	10	20	as	as	ADP
ejpam-2650	10	21	[	[	X
ejpam-2650	10	22	4	4	NUM
ejpam-2650	10	23	]	]	PUNCT
ejpam-2650	10	24	,	,	PUNCT
ejpam-2650	10	25	[	[	X
ejpam-2650	10	26	6	6	NUM
ejpam-2650	10	27	]	]	PUNCT
ejpam-2650	10	28	and	and	CCONJ
ejpam-2650	10	29	[	[	X
ejpam-2650	10	30	8	8	NUM
ejpam-2650	10	31	]	]	PUNCT
ejpam-2650	10	32	.	.	PUNCT
ejpam-2650	11	1	different	different	ADJ
ejpam-2650	11	2	characterizations	characterization	NOUN
ejpam-2650	11	3	for	for	ADP
ejpam-2650	11	4	the	the	DET
ejpam-2650	11	5	homogeneous	homogeneous	ADJ
ejpam-2650	11	6	weight	weight	NOUN
ejpam-2650	11	7	on	on	ADP
ejpam-2650	11	8	frobenius	frobenius	ADJ
ejpam-2650	11	9	rings	ring	NOUN
ejpam-2650	11	10	were	be	AUX
ejpam-2650	11	11	given	give	VERB
ejpam-2650	11	12	in	in	ADP
ejpam-2650	11	13	these	these	DET
ejpam-2650	11	14	works	work	NOUN
ejpam-2650	11	15	.	.	PUNCT
ejpam-2650	12	1	the	the	DET
ejpam-2650	12	2	mobius	mobius	PROPN
ejpam-2650	12	3	function	function	NOUN
ejpam-2650	12	4	or	or	CCONJ
ejpam-2650	12	5	the	the	DET
ejpam-2650	12	6	generating	generate	VERB
ejpam-2650	12	7	character	character	NOUN
ejpam-2650	12	8	of	of	ADP
ejpam-2650	12	9	the	the	DET
ejpam-2650	12	10	ring	ring	NOUN
ejpam-2650	12	11	seem	seem	VERB
ejpam-2650	12	12	to	to	PART
ejpam-2650	12	13	be	be	AUX
ejpam-2650	12	14	the	the	DET
ejpam-2650	12	15	prevalent	prevalent	ADJ
ejpam-2650	12	16	tools	tool	NOUN
ejpam-2650	12	17	used	use	VERB
ejpam-2650	12	18	in	in	ADP
ejpam-2650	12	19	these	these	DET
ejpam-2650	12	20	constructions	construction	NOUN
ejpam-2650	12	21	.	.	PUNCT
ejpam-2650	13	1	in	in	ADP
ejpam-2650	13	2	most	most	ADJ
ejpam-2650	13	3	works	work	NOUN
ejpam-2650	13	4	related	relate	VERB
ejpam-2650	13	5	to	to	ADP
ejpam-2650	13	6	the	the	DET
ejpam-2650	13	7	homogeneous	homogeneous	ADJ
ejpam-2650	13	8	weight	weight	NOUN
ejpam-2650	13	9	,	,	PUNCT
ejpam-2650	13	10	the	the	DET
ejpam-2650	13	11	average	average	ADJ
ejpam-2650	13	12	weight	weight	NOUN
ejpam-2650	13	13	γ	γ	NOUN
ejpam-2650	13	14	is	be	AUX
ejpam-2650	13	15	unassigned	unassigned	ADJ
ejpam-2650	13	16	.	.	PUNCT
ejpam-2650	14	1	in	in	ADP
ejpam-2650	14	2	a	a	DET
ejpam-2650	14	3	number	number	NOUN
ejpam-2650	14	4	of	of	ADP
ejpam-2650	14	5	recent	recent	ADJ
ejpam-2650	14	6	works	work	NOUN
ejpam-2650	14	7	involving	involve	VERB
ejpam-2650	14	8	different	different	ADJ
ejpam-2650	14	9	alphabets	alphabet	NOUN
ejpam-2650	14	10	,	,	PUNCT
ejpam-2650	14	11	γ	γ	NOUN
ejpam-2650	14	12	was	be	AUX
ejpam-2650	14	13	given	give	VERB
ejpam-2650	14	14	a	a	DET
ejpam-2650	14	15	fixed	fix	VERB
ejpam-2650	14	16	value	value	NOUN
ejpam-2650	14	17	and	and	CCONJ
ejpam-2650	14	18	then	then	ADV
ejpam-2650	14	19	a	a	DET
ejpam-2650	14	20	distance	distance	NOUN
ejpam-2650	14	21	-	-	PUNCT
ejpam-2650	14	22	preserving	preserve	VERB
ejpam-2650	14	23	isometry	isometry	NOUN
ejpam-2650	14	24	was	be	AUX
ejpam-2650	14	25	defined	define	VERB
ejpam-2650	14	26	using	use	VERB
ejpam-2650	14	27	different	different	ADJ
ejpam-2650	14	28	methods	method	NOUN
ejpam-2650	14	29	and	and	CCONJ
ejpam-2650	14	30	tools	tool	NOUN
ejpam-2650	14	31	.	.	PUNCT
ejpam-2650	15	1	we	we	PRON
ejpam-2650	15	2	will	will	AUX
ejpam-2650	15	3	call	call	VERB
ejpam-2650	15	4	such	such	DET
ejpam-2650	15	5	an	an	DET
ejpam-2650	15	6	isometry	isometry	NOUN
ejpam-2650	15	7	a	a	DET
ejpam-2650	15	8	gray	gray	ADJ
ejpam-2650	15	9	-	-	PUNCT
ejpam-2650	15	10	homogeneous	homogeneous	ADJ
ejpam-2650	15	11	map	map	NOUN
ejpam-2650	15	12	here	here	ADV
ejpam-2650	15	13	.	.	PUNCT
ejpam-2650	16	1	in	in	ADP
ejpam-2650	16	2	[	[	X
ejpam-2650	16	3	17	17	NUM
ejpam-2650	16	4	]	]	PUNCT
ejpam-2650	16	5	and	and	CCONJ
ejpam-2650	16	6	[	[	X
ejpam-2650	16	7	16	16	NUM
ejpam-2650	16	8	]	]	X
ejpam-2650	16	9	an	an	DET
ejpam-2650	16	10	algebraic	algebraic	ADJ
ejpam-2650	16	11	and	and	CCONJ
ejpam-2650	16	12	a	a	DET
ejpam-2650	16	13	combinatorial	combinatorial	ADJ
ejpam-2650	16	14	construction	construction	NOUN
ejpam-2650	16	15	was	be	AUX
ejpam-2650	16	16	given	give	VERB
ejpam-2650	16	17	respectively	respectively	ADV
ejpam-2650	16	18	,	,	PUNCT
ejpam-2650	16	19	for	for	ADP
ejpam-2650	16	20	the	the	DET
ejpam-2650	16	21	gray	gray	ADJ
ejpam-2650	16	22	-	-	PUNCT
ejpam-2650	16	23	homogeneous	homogeneous	ADJ
ejpam-2650	16	24	map	map	NOUN
ejpam-2650	16	25	on	on	ADP
ejpam-2650	16	26	galois	galois	PROPN
ejpam-2650	16	27	rings	ring	NOUN
ejpam-2650	16	28	.	.	PUNCT
ejpam-2650	17	1	in	in	ADP
ejpam-2650	17	2	[	[	X
ejpam-2650	17	3	11	11	NUM
ejpam-2650	17	4	]	]	PUNCT
ejpam-2650	17	5	,	,	PUNCT
ejpam-2650	17	6	combinatorial	combinatorial	ADJ
ejpam-2650	17	7	constructions	construction	NOUN
ejpam-2650	17	8	using	use	VERB
ejpam-2650	17	9	projective	projective	ADJ
ejpam-2650	17	10	geometries	geometry	NOUN
ejpam-2650	17	11	were	be	AUX
ejpam-2650	17	12	given	give	VERB
ejpam-2650	17	13	for	for	ADP
ejpam-2650	17	14	the	the	DET
ejpam-2650	17	15	gray	gray	ADJ
ejpam-2650	17	16	-	-	PUNCT
ejpam-2650	17	17	homogeneous	homogeneous	ADJ
ejpam-2650	17	18	maps	map	NOUN
ejpam-2650	17	19	on	on	ADP
ejpam-2650	17	20	finite	finite	ADJ
ejpam-2650	17	21	chain	chain	NOUN
ejpam-2650	17	22	rings	ring	NOUN
ejpam-2650	17	23	and	and	CCONJ
ejpam-2650	17	24	some	some	DET
ejpam-2650	17	25	other	other	ADJ
ejpam-2650	17	26	families	family	NOUN
ejpam-2650	17	27	of	of	ADP
ejpam-2650	17	28	rings	ring	NOUN
ejpam-2650	17	29	.	.	PUNCT
ejpam-2650	18	1	in	in	ADP
ejpam-2650	18	2	∗corresponding	∗corresponde	VERB
ejpam-2650	18	3	author	author	NOUN
ejpam-2650	18	4	.	.	PUNCT
ejpam-2650	19	1	email	email	NOUN
ejpam-2650	19	2	addresses	address	NOUN
ejpam-2650	19	3	:	:	PUNCT
ejpam-2650	19	4	bahattin.yildiz@nau.edu	bahattin.yildiz@nau.edu	PROPN
ejpam-2650	19	5	(	(	PUNCT
ejpam-2650	19	6	b.	b.	PROPN
ejpam-2650	19	7	yildiz	yildiz	PROPN
ejpam-2650	19	8	)	)	PUNCT
ejpam-2650	19	9	,	,	PUNCT
ejpam-2650	19	10	nesibe	nesibe	NOUN
ejpam-2650	19	11	tufekci@hotmail.com	tufekci@hotmail.com	PROPN
ejpam-2650	20	1	(	(	PUNCT
ejpam-2650	20	2	n.	n.	PROPN
ejpam-2650	20	3	tufekci	tufekci	PROPN
ejpam-2650	20	4	)	)	PUNCT
ejpam-2650	20	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2650	21	1	1112	1112	NUM
ejpam-2650	21	2	c	c	X
ejpam-2650	21	3	©	©	PROPN
ejpam-2650	21	4	2017	2017	NUM
ejpam-2650	21	5	ejpam	ejpam	VERB
ejpam-2650	21	6	all	all	DET
ejpam-2650	21	7	rights	right	NOUN
ejpam-2650	21	8	reserved	reserve	VERB
ejpam-2650	21	9	.	.	PUNCT
ejpam-2650	22	1	b.	b.	PROPN
ejpam-2650	22	2	yildiz	yildiz	PROPN
ejpam-2650	22	3	,	,	PUNCT
ejpam-2650	22	4	n.	n.	PROPN
ejpam-2650	22	5	tufekci	tufekci	PROPN
ejpam-2650	22	6	/	/	SYM
ejpam-2650	22	7	eur	eur	PROPN
ejpam-2650	22	8	.	.	PUNCT
ejpam-2650	23	1	j.	j.	PROPN
ejpam-2650	23	2	pure	pure	PROPN
ejpam-2650	23	3	appl	appl	PROPN
ejpam-2650	23	4	.	.	PROPN
ejpam-2650	23	5	math	math	PROPN
ejpam-2650	23	6	,	,	PUNCT
ejpam-2650	23	7	10	10	NUM
ejpam-2650	23	8	(	(	PUNCT
ejpam-2650	23	9	5	5	NUM
ejpam-2650	23	10	)	)	PUNCT
ejpam-2650	23	11	(	(	PUNCT
ejpam-2650	23	12	2017	2017	NUM
ejpam-2650	23	13	)	)	PUNCT
ejpam-2650	23	14	,	,	PUNCT
ejpam-2650	23	15	1112	1112	NUM
ejpam-2650	23	16	-	-	SYM
ejpam-2650	23	17	1123	1123	NUM
ejpam-2650	23	18	1113	1113	NUM
ejpam-2650	23	19	[	[	X
ejpam-2650	23	20	15	15	NUM
ejpam-2650	23	21	]	]	X
ejpam-2650	23	22	,	,	PUNCT
ejpam-2650	23	23	a	a	DET
ejpam-2650	23	24	construction	construction	NOUN
ejpam-2650	23	25	for	for	ADP
ejpam-2650	23	26	the	the	DET
ejpam-2650	23	27	gray	gray	ADJ
ejpam-2650	23	28	-	-	PUNCT
ejpam-2650	23	29	homogeneous	homogeneous	ADJ
ejpam-2650	23	30	map	map	NOUN
ejpam-2650	23	31	using	use	VERB
ejpam-2650	23	32	reed	reed	NOUN
ejpam-2650	23	33	-	-	PUNCT
ejpam-2650	23	34	muller	muller	NOUN
ejpam-2650	23	35	codes	code	NOUN
ejpam-2650	23	36	was	be	AUX
ejpam-2650	23	37	given	give	VERB
ejpam-2650	23	38	for	for	ADP
ejpam-2650	23	39	codes	code	NOUN
ejpam-2650	23	40	over	over	ADP
ejpam-2650	23	41	the	the	DET
ejpam-2650	23	42	ring	ring	NOUN
ejpam-2650	23	43	family	family	NOUN
ejpam-2650	23	44	of	of	ADP
ejpam-2650	23	45	rk	rk	NOUN
ejpam-2650	23	46	,	,	PUNCT
ejpam-2650	23	47	and	and	CCONJ
ejpam-2650	23	48	many	many	ADJ
ejpam-2650	23	49	new	new	ADJ
ejpam-2650	23	50	quasicyclic	quasicyclic	NOUN
ejpam-2650	23	51	codes	code	NOUN
ejpam-2650	23	52	were	be	AUX
ejpam-2650	23	53	obtained	obtain	VERB
ejpam-2650	23	54	as	as	ADP
ejpam-2650	23	55	images	image	NOUN
ejpam-2650	23	56	.	.	PUNCT
ejpam-2650	24	1	in	in	ADP
ejpam-2650	24	2	this	this	DET
ejpam-2650	24	3	work	work	NOUN
ejpam-2650	24	4	,	,	PUNCT
ejpam-2650	24	5	we	we	PRON
ejpam-2650	24	6	consider	consider	VERB
ejpam-2650	24	7	the	the	DET
ejpam-2650	24	8	homogeneous	homogeneous	ADJ
ejpam-2650	24	9	weight	weight	NOUN
ejpam-2650	24	10	on	on	ADP
ejpam-2650	24	11	the	the	DET
ejpam-2650	24	12	ring	ring	NOUN
ejpam-2650	24	13	family	family	PROPN
ejpam-2650	24	14	rk	rk	PROPN
ejpam-2650	24	15	,	,	PUNCT
ejpam-2650	24	16	m	m	PRON
ejpam-2650	24	17	,	,	PUNCT
ejpam-2650	24	18	a	a	DET
ejpam-2650	24	19	characteristic	characteristic	ADJ
ejpam-2650	24	20	2	2	NUM
ejpam-2650	24	21	family	family	NOUN
ejpam-2650	24	22	of	of	ADP
ejpam-2650	24	23	frobenius	frobenius	ADJ
ejpam-2650	24	24	rings	ring	NOUN
ejpam-2650	24	25	,	,	PUNCT
ejpam-2650	24	26	intrduced	intrduce	VERB
ejpam-2650	24	27	in	in	ADP
ejpam-2650	24	28	[	[	X
ejpam-2650	24	29	13	13	NUM
ejpam-2650	24	30	]	]	PUNCT
ejpam-2650	24	31	.	.	PUNCT
ejpam-2650	25	1	using	use	VERB
ejpam-2650	25	2	the	the	DET
ejpam-2650	25	3	generating	generate	VERB
ejpam-2650	25	4	character	character	NOUN
ejpam-2650	25	5	characterization	characterization	NOUN
ejpam-2650	25	6	of	of	ADP
ejpam-2650	25	7	the	the	DET
ejpam-2650	25	8	homogeneous	homogeneous	ADJ
ejpam-2650	25	9	weight	weight	NOUN
ejpam-2650	25	10	we	we	PRON
ejpam-2650	25	11	find	find	VERB
ejpam-2650	25	12	a	a	DET
ejpam-2650	25	13	form	form	NOUN
ejpam-2650	25	14	for	for	ADP
ejpam-2650	25	15	the	the	DET
ejpam-2650	25	16	homogeneous	homogeneous	ADJ
ejpam-2650	25	17	weight	weight	NOUN
ejpam-2650	25	18	on	on	ADP
ejpam-2650	25	19	rk	rk	NOUN
ejpam-2650	25	20	,	,	PUNCT
ejpam-2650	25	21	m.	m.	NOUN
ejpam-2650	25	22	we	we	PRON
ejpam-2650	25	23	assign	assign	VERB
ejpam-2650	25	24	a	a	DET
ejpam-2650	25	25	value	value	NOUN
ejpam-2650	25	26	to	to	ADP
ejpam-2650	25	27	the	the	DET
ejpam-2650	25	28	average	average	ADJ
ejpam-2650	25	29	weight	weight	NOUN
ejpam-2650	25	30	γ	γ	NOUN
ejpam-2650	25	31	,	,	PUNCT
ejpam-2650	25	32	giving	give	VERB
ejpam-2650	25	33	algebraic	algebraic	ADJ
ejpam-2650	25	34	and	and	CCONJ
ejpam-2650	25	35	combinatorial	combinatorial	ADJ
ejpam-2650	25	36	justifications	justification	NOUN
ejpam-2650	25	37	.	.	PUNCT
ejpam-2650	26	1	we	we	PRON
ejpam-2650	26	2	then	then	ADV
ejpam-2650	26	3	construct	construct	VERB
ejpam-2650	26	4	the	the	DET
ejpam-2650	26	5	gray	gray	ADJ
ejpam-2650	26	6	-	-	PUNCT
ejpam-2650	26	7	homogeneous	homogeneous	ADJ
ejpam-2650	26	8	map	map	NOUN
ejpam-2650	26	9	using	use	VERB
ejpam-2650	26	10	reed	reed	NOUN
ejpam-2650	26	11	-	-	PUNCT
ejpam-2650	26	12	muller	muller	NOUN
ejpam-2650	26	13	codes	code	NOUN
ejpam-2650	26	14	.	.	PUNCT
ejpam-2650	27	1	using	use	VERB
ejpam-2650	27	2	the	the	DET
ejpam-2650	27	3	images	image	NOUN
ejpam-2650	27	4	of	of	ADP
ejpam-2650	27	5	cyclic	cyclic	ADJ
ejpam-2650	27	6	,	,	PUNCT
ejpam-2650	27	7	constacyclic	constacyclic	ADJ
ejpam-2650	27	8	and	and	CCONJ
ejpam-2650	27	9	quasicyclic	quasicyclic	ADJ
ejpam-2650	27	10	codes	code	NOUN
ejpam-2650	27	11	overrk	overrk	NOUN
ejpam-2650	27	12	,	,	PUNCT
ejpam-2650	27	13	m	m	NOUN
ejpam-2650	27	14	of	of	ADP
ejpam-2650	27	15	different	different	ADJ
ejpam-2650	27	16	lengths	length	NOUN
ejpam-2650	27	17	with	with	ADP
ejpam-2650	27	18	suitable	suitable	ADJ
ejpam-2650	27	19	k	k	NOUN
ejpam-2650	27	20	,	,	PUNCT
ejpam-2650	27	21	m	m	AUX
ejpam-2650	27	22	we	we	PRON
ejpam-2650	27	23	are	be	AUX
ejpam-2650	27	24	able	able	ADJ
ejpam-2650	27	25	to	to	PART
ejpam-2650	27	26	construct	construct	VERB
ejpam-2650	27	27	many	many	ADJ
ejpam-2650	27	28	optimal	optimal	ADJ
ejpam-2650	27	29	binary	binary	ADJ
ejpam-2650	27	30	codes	code	NOUN
ejpam-2650	27	31	that	that	PRON
ejpam-2650	27	32	are	be	AUX
ejpam-2650	27	33	divisible	divisible	ADJ
ejpam-2650	27	34	with	with	ADP
ejpam-2650	27	35	high	high	ADJ
ejpam-2650	27	36	levels	level	NOUN
ejpam-2650	27	37	of	of	ADP
ejpam-2650	27	38	divisibility	divisibility	NOUN
ejpam-2650	27	39	.	.	PUNCT
ejpam-2650	28	1	the	the	DET
ejpam-2650	28	2	codes	code	NOUN
ejpam-2650	28	3	we	we	PRON
ejpam-2650	28	4	have	have	AUX
ejpam-2650	28	5	obtained	obtain	VERB
ejpam-2650	28	6	are	be	AUX
ejpam-2650	28	7	also	also	ADV
ejpam-2650	28	8	quasicyclic	quasicyclic	ADJ
ejpam-2650	28	9	with	with	ADP
ejpam-2650	28	10	high	high	ADJ
ejpam-2650	28	11	indices	index	NOUN
ejpam-2650	28	12	and	and	CCONJ
ejpam-2650	28	13	they	they	PRON
ejpam-2650	28	14	are	be	AUX
ejpam-2650	28	15	all	all	PRON
ejpam-2650	28	16	self	self	NOUN
ejpam-2650	28	17	-	-	PUNCT
ejpam-2650	28	18	orthogonal	orthogonal	ADJ
ejpam-2650	28	19	when	when	SCONJ
ejpam-2650	28	20	km	km	PROPN
ejpam-2650	28	21	≥	≥	NUM
ejpam-2650	28	22	4	4	NUM
ejpam-2650	28	23	.	.	PUNCT
ejpam-2650	29	1	thus	thus	ADV
ejpam-2650	29	2	we	we	PRON
ejpam-2650	29	3	obtain	obtain	VERB
ejpam-2650	29	4	many	many	ADJ
ejpam-2650	29	5	optimal	optimal	ADJ
ejpam-2650	29	6	,	,	PUNCT
ejpam-2650	29	7	self	self	NOUN
ejpam-2650	29	8	-	-	PUNCT
ejpam-2650	29	9	orthogonal	orthogonal	ADJ
ejpam-2650	29	10	quasicyclic	quasicyclic	ADJ
ejpam-2650	29	11	binary	binary	NOUN
ejpam-2650	29	12	codes	code	NOUN
ejpam-2650	29	13	,	,	PUNCT
ejpam-2650	29	14	which	which	PRON
ejpam-2650	29	15	have	have	AUX
ejpam-2650	29	16	been	be	AUX
ejpam-2650	29	17	shown	show	VERB
ejpam-2650	29	18	to	to	PART
ejpam-2650	29	19	be	be	AUX
ejpam-2650	29	20	of	of	ADP
ejpam-2650	29	21	importance	importance	NOUN
ejpam-2650	29	22	in	in	ADP
ejpam-2650	29	23	[	[	X
ejpam-2650	29	24	12	12	NUM
ejpam-2650	29	25	]	]	PUNCT
ejpam-2650	29	26	,	,	PUNCT
ejpam-2650	29	27	for	for	ADP
ejpam-2650	29	28	their	their	PRON
ejpam-2650	29	29	connection	connection	NOUN
ejpam-2650	29	30	to	to	ADP
ejpam-2650	29	31	difference	difference	NOUN
ejpam-2650	29	32	sets	set	NOUN
ejpam-2650	29	33	and	and	CCONJ
ejpam-2650	29	34	their	their	PRON
ejpam-2650	29	35	near	near	ADJ
ejpam-2650	29	36	-	-	PUNCT
ejpam-2650	29	37	bch	bch	NOUN
ejpam-2650	29	38	performance	performance	NOUN
ejpam-2650	29	39	.	.	PUNCT
ejpam-2650	30	1	the	the	DET
ejpam-2650	30	2	rest	rest	NOUN
ejpam-2650	30	3	of	of	ADP
ejpam-2650	30	4	the	the	DET
ejpam-2650	30	5	work	work	NOUN
ejpam-2650	30	6	is	be	AUX
ejpam-2650	30	7	organized	organize	VERB
ejpam-2650	30	8	as	as	SCONJ
ejpam-2650	30	9	follows	follow	VERB
ejpam-2650	30	10	.	.	PUNCT
ejpam-2650	31	1	in	in	ADP
ejpam-2650	31	2	section	section	NOUN
ejpam-2650	31	3	2	2	NUM
ejpam-2650	31	4	,	,	PUNCT
ejpam-2650	31	5	we	we	PRON
ejpam-2650	31	6	give	give	VERB
ejpam-2650	31	7	some	some	DET
ejpam-2650	31	8	preliminaries	preliminary	NOUN
ejpam-2650	31	9	on	on	ADP
ejpam-2650	31	10	the	the	DET
ejpam-2650	31	11	ring	ring	NOUN
ejpam-2650	31	12	family	family	PROPN
ejpam-2650	31	13	rk	rk	PROPN
ejpam-2650	31	14	,	,	PUNCT
ejpam-2650	31	15	m	m	PRON
ejpam-2650	31	16	,	,	PUNCT
ejpam-2650	31	17	mainly	mainly	ADV
ejpam-2650	31	18	citing	cite	VERB
ejpam-2650	31	19	from	from	ADP
ejpam-2650	31	20	[	[	X
ejpam-2650	31	21	13	13	NUM
ejpam-2650	31	22	]	]	PUNCT
ejpam-2650	31	23	.	.	PUNCT
ejpam-2650	32	1	in	in	ADP
ejpam-2650	32	2	section	section	NOUN
ejpam-2650	32	3	3	3	NUM
ejpam-2650	32	4	,	,	PUNCT
ejpam-2650	32	5	we	we	PRON
ejpam-2650	32	6	recall	recall	VERB
ejpam-2650	32	7	the	the	DET
ejpam-2650	32	8	definitions	definition	NOUN
ejpam-2650	32	9	of	of	ADP
ejpam-2650	32	10	the	the	DET
ejpam-2650	32	11	homogeneous	homogeneous	ADJ
ejpam-2650	32	12	weight	weight	NOUN
ejpam-2650	32	13	from	from	ADP
ejpam-2650	32	14	the	the	DET
ejpam-2650	32	15	relevant	relevant	ADJ
ejpam-2650	32	16	literature	literature	NOUN
ejpam-2650	32	17	and	and	CCONJ
ejpam-2650	32	18	applying	apply	VERB
ejpam-2650	32	19	the	the	DET
ejpam-2650	32	20	definitions	definition	NOUN
ejpam-2650	32	21	to	to	PART
ejpam-2650	32	22	rk	rk	VERB
ejpam-2650	32	23	,	,	PUNCT
ejpam-2650	32	24	m	m	PRON
ejpam-2650	32	25	,	,	PUNCT
ejpam-2650	32	26	we	we	PRON
ejpam-2650	32	27	find	find	VERB
ejpam-2650	32	28	the	the	DET
ejpam-2650	32	29	homogeneous	homogeneous	ADJ
ejpam-2650	32	30	weight	weight	NOUN
ejpam-2650	32	31	for	for	ADP
ejpam-2650	32	32	codes	code	NOUN
ejpam-2650	32	33	over	over	ADP
ejpam-2650	32	34	rk	rk	NOUN
ejpam-2650	32	35	,	,	PUNCT
ejpam-2650	32	36	m.	m.	NOUN
ejpam-2650	32	37	we	we	PRON
ejpam-2650	32	38	also	also	ADV
ejpam-2650	32	39	construct	construct	VERB
ejpam-2650	32	40	the	the	DET
ejpam-2650	32	41	gray	gray	ADJ
ejpam-2650	32	42	-	-	PUNCT
ejpam-2650	32	43	homogeneous	homogeneous	ADJ
ejpam-2650	32	44	map	map	NOUN
ejpam-2650	32	45	.	.	PUNCT
ejpam-2650	33	1	section	section	NOUN
ejpam-2650	33	2	4	4	NUM
ejpam-2650	33	3	contains	contain	VERB
ejpam-2650	33	4	the	the	DET
ejpam-2650	33	5	computational	computational	ADJ
ejpam-2650	33	6	results	result	NOUN
ejpam-2650	33	7	obtained	obtain	VERB
ejpam-2650	33	8	using	use	VERB
ejpam-2650	33	9	a	a	DET
ejpam-2650	33	10	computer	computer	NOUN
ejpam-2650	33	11	search	search	NOUN
ejpam-2650	33	12	,	,	PUNCT
ejpam-2650	33	13	with	with	ADP
ejpam-2650	33	14	the	the	DET
ejpam-2650	33	15	help	help	NOUN
ejpam-2650	33	16	of	of	ADP
ejpam-2650	33	17	magma	magma	NOUN
ejpam-2650	33	18	,	,	PUNCT
ejpam-2650	33	19	[	[	X
ejpam-2650	33	20	2	2	NUM
ejpam-2650	33	21	]	]	PUNCT
ejpam-2650	33	22	.	.	PUNCT
ejpam-2650	34	1	we	we	PRON
ejpam-2650	34	2	then	then	ADV
ejpam-2650	34	3	finish	finish	VERB
ejpam-2650	34	4	with	with	ADP
ejpam-2650	34	5	concluding	conclude	VERB
ejpam-2650	34	6	remarks	remark	NOUN
ejpam-2650	34	7	in	in	ADP
ejpam-2650	34	8	section	section	NOUN
ejpam-2650	34	9	5	5	NUM
ejpam-2650	34	10	.	.	NOUN
ejpam-2650	34	11	2	2	NUM
ejpam-2650	34	12	.	.	NOUN
ejpam-2650	34	13	preliminaries	preliminary	NOUN
ejpam-2650	34	14	the	the	DET
ejpam-2650	34	15	ring	ring	NOUN
ejpam-2650	34	16	denoted	denote	VERB
ejpam-2650	34	17	by	by	ADP
ejpam-2650	34	18	rk	rk	PRON
ejpam-2650	34	19	,	,	PUNCT
ejpam-2650	34	20	m	m	VERB
ejpam-2650	34	21	is	be	AUX
ejpam-2650	34	22	a	a	DET
ejpam-2650	34	23	characteristic	characteristic	ADJ
ejpam-2650	34	24	2	2	NUM
ejpam-2650	34	25	ring	ring	NOUN
ejpam-2650	34	26	of	of	ADP
ejpam-2650	34	27	size	size	NOUN
ejpam-2650	34	28	2	2	NUM
ejpam-2650	34	29	km	km	NOUN
ejpam-2650	34	30	,	,	PUNCT
ejpam-2650	34	31	that	that	PRON
ejpam-2650	34	32	was	be	AUX
ejpam-2650	34	33	introduced	introduce	VERB
ejpam-2650	34	34	in	in	ADP
ejpam-2650	34	35	[	[	X
ejpam-2650	34	36	13	13	NUM
ejpam-2650	34	37	]	]	PUNCT
ejpam-2650	34	38	,	,	PUNCT
ejpam-2650	34	39	and	and	CCONJ
ejpam-2650	34	40	is	be	AUX
ejpam-2650	34	41	defined	define	VERB
ejpam-2650	34	42	as	as	SCONJ
ejpam-2650	34	43	follows	follow	VERB
ejpam-2650	34	44	for	for	ADP
ejpam-2650	34	45	k	k	PROPN
ejpam-2650	34	46	≥	≥	PROPN
ejpam-2650	34	47	m	m	PROPN
ejpam-2650	34	48	≥	≥	NOUN
ejpam-2650	34	49	1	1	NUM
ejpam-2650	34	50	:	:	PUNCT
ejpam-2650	34	51	rk	rk	VERB
ejpam-2650	34	52	,	,	PUNCT
ejpam-2650	34	53	m	m	VERB
ejpam-2650	34	54	=	=	ADJ
ejpam-2650	34	55	f2[u	f2[u	PROPN
ejpam-2650	34	56	,	,	PUNCT
ejpam-2650	34	57	v]/	v]/	X
ejpam-2650	34	58	〈	〈	PROPN
ejpam-2650	34	59	uk	uk	PROPN
ejpam-2650	34	60	,	,	PUNCT
ejpam-2650	34	61	vm	vm	PROPN
ejpam-2650	34	62	,	,	PUNCT
ejpam-2650	34	63	uv	uv	NOUN
ejpam-2650	34	64	−	−	PROPN
ejpam-2650	34	65	vu	vu	X
ejpam-2650	34	66	〉	〉	NOUN
ejpam-2650	34	67	.	.	PUNCT
ejpam-2650	35	1	note	note	VERB
ejpam-2650	35	2	that	that	SCONJ
ejpam-2650	35	3	when	when	SCONJ
ejpam-2650	35	4	k	k	PROPN
ejpam-2650	35	5	=	=	SYM
ejpam-2650	35	6	2,m	2,m	NOUN
ejpam-2650	35	7	=	=	SYM
ejpam-2650	35	8	1	1	NUM
ejpam-2650	35	9	the	the	DET
ejpam-2650	35	10	ring	ring	NOUN
ejpam-2650	35	11	is	be	AUX
ejpam-2650	35	12	f2	f2	ADJ
ejpam-2650	35	13	+	+	CCONJ
ejpam-2650	35	14	uf2	uf2	NOUN
ejpam-2650	35	15	,	,	PUNCT
ejpam-2650	35	16	when	when	SCONJ
ejpam-2650	35	17	k	k	PROPN
ejpam-2650	35	18	=	=	PUNCT
ejpam-2650	35	19	m	m	VERB
ejpam-2650	35	20	=	=	SYM
ejpam-2650	35	21	2	2	NUM
ejpam-2650	35	22	the	the	DET
ejpam-2650	35	23	ring	ring	NOUN
ejpam-2650	35	24	is	be	AUX
ejpam-2650	35	25	f2	f2	ADJ
ejpam-2650	35	26	+	+	CCONJ
ejpam-2650	35	27	uf2	uf2	NOUN
ejpam-2650	35	28	+	+	CCONJ
ejpam-2650	35	29	vf2	vf2	NOUN
ejpam-2650	35	30	+	+	CCONJ
ejpam-2650	35	31	uvf2	uvf2	PROPN
ejpam-2650	35	32	,	,	PUNCT
ejpam-2650	35	33	both	both	CCONJ
ejpam-2650	35	34	quite	quite	ADV
ejpam-2650	35	35	commonly	commonly	ADV
ejpam-2650	35	36	-	-	PUNCT
ejpam-2650	35	37	used	use	VERB
ejpam-2650	35	38	in	in	ADP
ejpam-2650	35	39	the	the	DET
ejpam-2650	35	40	recent	recent	ADJ
ejpam-2650	35	41	literature	literature	NOUN
ejpam-2650	35	42	of	of	ADP
ejpam-2650	35	43	coding	code	VERB
ejpam-2650	35	44	theory	theory	NOUN
ejpam-2650	35	45	.	.	PUNCT
ejpam-2650	36	1	any	any	DET
ejpam-2650	36	2	element	element	NOUN
ejpam-2650	36	3	of	of	ADP
ejpam-2650	36	4	rk	rk	NOUN
ejpam-2650	36	5	,	,	PUNCT
ejpam-2650	36	6	m	m	VERB
ejpam-2650	36	7	can	can	AUX
ejpam-2650	36	8	be	be	AUX
ejpam-2650	36	9	represented	represent	VERB
ejpam-2650	36	10	as∑	as∑	ADJ
ejpam-2650	36	11	0≤i≤k−1	0≤i≤k−1	NUM
ejpam-2650	36	12	0≤j≤m−1	0≤j≤m−1	NUM
ejpam-2650	36	13	ciju	ciju	NOUN
ejpam-2650	36	14	ivj	ivj	NOUN
ejpam-2650	36	15	,	,	PUNCT
ejpam-2650	36	16	cij	cij	PROPN
ejpam-2650	36	17	∈	∈	PROPN
ejpam-2650	36	18	f2	f2	PROPN
ejpam-2650	36	19	.	.	PUNCT
ejpam-2650	37	1	(	(	PUNCT
ejpam-2650	37	2	1	1	X
ejpam-2650	37	3	)	)	PUNCT
ejpam-2650	37	4	the	the	DET
ejpam-2650	37	5	following	follow	VERB
ejpam-2650	37	6	lemmas	lemma	VERB
ejpam-2650	37	7	from	from	ADP
ejpam-2650	37	8	[	[	NOUN
ejpam-2650	37	9	13	13	NUM
ejpam-2650	37	10	]	]	PUNCT
ejpam-2650	37	11	describes	describe	VERB
ejpam-2650	37	12	the	the	DET
ejpam-2650	37	13	algebraic	algebraic	ADJ
ejpam-2650	37	14	structure	structure	NOUN
ejpam-2650	37	15	of	of	ADP
ejpam-2650	37	16	these	these	DET
ejpam-2650	37	17	rings	ring	NOUN
ejpam-2650	37	18	.	.	PUNCT
ejpam-2650	38	1	lemma	lemma	PROPN
ejpam-2650	38	2	1	1	NUM
ejpam-2650	38	3	.	.	PUNCT
ejpam-2650	39	1	an	an	DET
ejpam-2650	39	2	element	element	NOUN
ejpam-2650	39	3	in	in	ADP
ejpam-2650	39	4	rk	rk	NOUN
ejpam-2650	39	5	,	,	PUNCT
ejpam-2650	39	6	m	m	NOUN
ejpam-2650	39	7	of	of	ADP
ejpam-2650	39	8	the	the	DET
ejpam-2650	39	9	form	form	NOUN
ejpam-2650	39	10	given	give	VERB
ejpam-2650	39	11	in	in	ADP
ejpam-2650	39	12	(	(	PUNCT
ejpam-2650	39	13	1	1	NUM
ejpam-2650	39	14	)	)	PUNCT
ejpam-2650	39	15	is	be	AUX
ejpam-2650	39	16	a	a	DET
ejpam-2650	39	17	unit	unit	NOUN
ejpam-2650	39	18	if	if	SCONJ
ejpam-2650	39	19	and	and	CCONJ
ejpam-2650	39	20	only	only	ADV
ejpam-2650	39	21	if	if	SCONJ
ejpam-2650	39	22	c00	c00	NOUN
ejpam-2650	39	23	is	be	AUX
ejpam-2650	39	24	1	1	NUM
ejpam-2650	39	25	.	.	PUNCT
ejpam-2650	40	1	lemma	lemma	PROPN
ejpam-2650	40	2	2	2	NUM
ejpam-2650	40	3	.	.	PUNCT
ejpam-2650	41	1	the	the	DET
ejpam-2650	41	2	ring	ring	NOUN
ejpam-2650	41	3	rk	rk	NOUN
ejpam-2650	41	4	,	,	PUNCT
ejpam-2650	41	5	m	m	VERB
ejpam-2650	41	6	is	be	AUX
ejpam-2650	41	7	a	a	DET
ejpam-2650	41	8	local	local	ADJ
ejpam-2650	41	9	ring	ring	NOUN
ejpam-2650	41	10	with	with	ADP
ejpam-2650	41	11	a	a	DET
ejpam-2650	41	12	unique	unique	ADJ
ejpam-2650	41	13	maximal	maximal	ADJ
ejpam-2650	41	14	ideal	ideal	NOUN
ejpam-2650	41	15	iu	iu	ADP
ejpam-2650	41	16	,	,	PUNCT
ejpam-2650	41	17	v	v	NOUN
ejpam-2650	41	18	=	=	SYM
ejpam-2650	41	19	〈	〈	PROPN
ejpam-2650	41	20	u	u	NOUN
ejpam-2650	41	21	,	,	PUNCT
ejpam-2650	41	22	v	v	PROPN
ejpam-2650	41	23	〉	〉	NOUN
ejpam-2650	41	24	.	.	PUNCT
ejpam-2650	42	1	this	this	DET
ejpam-2650	42	2	ideal	ideal	NOUN
ejpam-2650	42	3	consists	consist	VERB
ejpam-2650	42	4	of	of	ADP
ejpam-2650	42	5	all	all	DET
ejpam-2650	42	6	non	non	NOUN
ejpam-2650	42	7	-	-	NOUN
ejpam-2650	42	8	units	unit	NOUN
ejpam-2650	42	9	and	and	CCONJ
ejpam-2650	42	10	satisfies	satisfie	NOUN
ejpam-2650	42	11	|iu	|iu	NOUN
ejpam-2650	42	12	,	,	PUNCT
ejpam-2650	42	13	v|	v|	NOUN
ejpam-2650	42	14	=	=	SYM
ejpam-2650	42	15	|rk	|rk	NOUN
ejpam-2650	42	16	,	,	PUNCT
ejpam-2650	42	17	m|	m|	NOUN
ejpam-2650	42	18	2	2	NUM
ejpam-2650	42	19	.	.	PUNCT
ejpam-2650	43	1	b.	b.	PROPN
ejpam-2650	43	2	yildiz	yildiz	PROPN
ejpam-2650	43	3	,	,	PUNCT
ejpam-2650	43	4	n.	n.	PROPN
ejpam-2650	43	5	tufekci	tufekci	PROPN
ejpam-2650	43	6	/	/	SYM
ejpam-2650	43	7	eur	eur	PROPN
ejpam-2650	43	8	.	.	PUNCT
ejpam-2650	44	1	j.	j.	PROPN
ejpam-2650	44	2	pure	pure	PROPN
ejpam-2650	44	3	appl	appl	PROPN
ejpam-2650	44	4	.	.	PROPN
ejpam-2650	44	5	math	math	PROPN
ejpam-2650	44	6	,	,	PUNCT
ejpam-2650	44	7	10	10	NUM
ejpam-2650	44	8	(	(	PUNCT
ejpam-2650	44	9	5	5	NUM
ejpam-2650	44	10	)	)	PUNCT
ejpam-2650	44	11	(	(	PUNCT
ejpam-2650	44	12	2017	2017	NUM
ejpam-2650	44	13	)	)	PUNCT
ejpam-2650	44	14	,	,	PUNCT
ejpam-2650	44	15	1112	1112	NUM
ejpam-2650	44	16	-	-	SYM
ejpam-2650	44	17	1123	1123	NUM
ejpam-2650	44	18	1114	1114	NUM
ejpam-2650	44	19	by	by	ADP
ejpam-2650	44	20	u(rk	u(rk	NOUN
ejpam-2650	44	21	,	,	PUNCT
ejpam-2650	44	22	m	m	NOUN
ejpam-2650	44	23	)	)	PUNCT
ejpam-2650	44	24	,	,	PUNCT
ejpam-2650	44	25	denote	denote	VERB
ejpam-2650	44	26	the	the	DET
ejpam-2650	44	27	units	unit	NOUN
ejpam-2650	44	28	of	of	ADP
ejpam-2650	44	29	rk	rk	NOUN
ejpam-2650	44	30	,	,	PUNCT
ejpam-2650	44	31	m	m	PRON
ejpam-2650	44	32	and	and	CCONJ
ejpam-2650	44	33	by	by	ADP
ejpam-2650	44	34	d(rk	d(rk	PROPN
ejpam-2650	44	35	,	,	PUNCT
ejpam-2650	44	36	m	m	PROPN
ejpam-2650	44	37	)	)	PUNCT
ejpam-2650	44	38	,	,	PUNCT
ejpam-2650	44	39	the	the	DET
ejpam-2650	44	40	set	set	NOUN
ejpam-2650	44	41	of	of	ADP
ejpam-2650	44	42	non	non	NOUN
ejpam-2650	44	43	-	-	NOUN
ejpam-2650	44	44	units	unit	NOUN
ejpam-2650	44	45	in	in	ADP
ejpam-2650	44	46	rk	rk	NOUN
ejpam-2650	44	47	,	,	PUNCT
ejpam-2650	44	48	m.	m.	NOUN
ejpam-2650	44	49	it	it	PRON
ejpam-2650	44	50	is	be	AUX
ejpam-2650	44	51	easy	easy	ADJ
ejpam-2650	44	52	to	to	PART
ejpam-2650	44	53	see	see	VERB
ejpam-2650	44	54	that	that	PRON
ejpam-2650	44	55	|u(rk	|u(rk	ADJ
ejpam-2650	44	56	,	,	PUNCT
ejpam-2650	44	57	m)|	m)|	ADJ
ejpam-2650	44	58	=	=	SYM
ejpam-2650	44	59	|d(rk	|d(rk	PROPN
ejpam-2650	44	60	,	,	PUNCT
ejpam-2650	44	61	m)|	m)|	NOUN
ejpam-2650	44	62	=	=	SYM
ejpam-2650	44	63	|rk	|rk	NOUN
ejpam-2650	44	64	,	,	PUNCT
ejpam-2650	44	65	m|	m|	NOUN
ejpam-2650	44	66	2	2	NUM
ejpam-2650	44	67	and	and	CCONJ
ejpam-2650	44	68	that	that	SCONJ
ejpam-2650	44	69	u(rk	u(rk	ADV
ejpam-2650	44	70	,	,	PUNCT
ejpam-2650	44	71	m	m	NOUN
ejpam-2650	44	72	)	)	PUNCT
ejpam-2650	44	73	=	=	SYM
ejpam-2650	45	1	1	1	NUM
ejpam-2650	45	2	+	+	NOUN
ejpam-2650	45	3	d(rk	d(rk	PROPN
ejpam-2650	45	4	,	,	PUNCT
ejpam-2650	45	5	m	m	PROPN
ejpam-2650	45	6	)	)	PUNCT
ejpam-2650	45	7	.	.	PUNCT
ejpam-2650	46	1	we	we	PRON
ejpam-2650	46	2	easily	easily	ADV
ejpam-2650	46	3	observe	observe	VERB
ejpam-2650	46	4	that	that	SCONJ
ejpam-2650	46	5	when	when	SCONJ
ejpam-2650	46	6	m	m	VERB
ejpam-2650	46	7	>	>	X
ejpam-2650	46	8	1	1	NUM
ejpam-2650	46	9	,	,	PUNCT
ejpam-2650	46	10	rk	rk	NOUN
ejpam-2650	46	11	,	,	PUNCT
ejpam-2650	46	12	m	m	VERB
ejpam-2650	46	13	is	be	AUX
ejpam-2650	46	14	not	not	PART
ejpam-2650	46	15	a	a	DET
ejpam-2650	46	16	chain	chain	NOUN
ejpam-2650	46	17	ring	ring	NOUN
ejpam-2650	46	18	.	.	PUNCT
ejpam-2650	47	1	however	however	ADV
ejpam-2650	47	2	,	,	PUNCT
ejpam-2650	47	3	as	as	SCONJ
ejpam-2650	47	4	was	be	AUX
ejpam-2650	47	5	also	also	ADV
ejpam-2650	47	6	pointed	point	VERB
ejpam-2650	47	7	out	out	ADP
ejpam-2650	47	8	in	in	ADP
ejpam-2650	47	9	[	[	X
ejpam-2650	47	10	13	13	NUM
ejpam-2650	47	11	]	]	PUNCT
ejpam-2650	47	12	,	,	PUNCT
ejpam-2650	47	13	since	since	SCONJ
ejpam-2650	47	14	rk	rk	PRON
ejpam-2650	47	15	,	,	PUNCT
ejpam-2650	47	16	m	m	NOUN
ejpam-2650	47	17	/	/	SYM
ejpam-2650	47	18	rad(rk	rad(rk	NOUN
ejpam-2650	47	19	,	,	PUNCT
ejpam-2650	47	20	m	m	NOUN
ejpam-2650	47	21	)	)	PUNCT
ejpam-2650	47	22	'	'	PUNCT
ejpam-2650	47	23	soc(rk	soc(rk	PROPN
ejpam-2650	47	24	,	,	PUNCT
ejpam-2650	47	25	m	m	NOUN
ejpam-2650	47	26	)	)	PUNCT
ejpam-2650	47	27	the	the	DET
ejpam-2650	47	28	ring	ring	NOUN
ejpam-2650	47	29	rk	rk	NOUN
ejpam-2650	47	30	,	,	PUNCT
ejpam-2650	47	31	m	m	VERB
ejpam-2650	47	32	is	be	AUX
ejpam-2650	47	33	a	a	DET
ejpam-2650	47	34	frobenius	frobenius	ADJ
ejpam-2650	47	35	ring	ring	NOUN
ejpam-2650	47	36	.	.	PUNCT
ejpam-2650	48	1	as	as	ADP
ejpam-2650	48	2	a	a	DET
ejpam-2650	48	3	frobenius	frobenius	NOUN
ejpam-2650	48	4	ring	ring	NOUN
ejpam-2650	48	5	,	,	PUNCT
ejpam-2650	48	6	rk	rk	NOUN
ejpam-2650	48	7	,	,	PUNCT
ejpam-2650	48	8	m	m	VERB
ejpam-2650	48	9	has	have	VERB
ejpam-2650	48	10	a	a	DET
ejpam-2650	48	11	generating	generate	VERB
ejpam-2650	48	12	character	character	NOUN
ejpam-2650	48	13	.	.	PUNCT
ejpam-2650	49	1	it	it	PRON
ejpam-2650	49	2	was	be	AUX
ejpam-2650	49	3	shown	show	VERB
ejpam-2650	49	4	in	in	ADP
ejpam-2650	49	5	[	[	X
ejpam-2650	49	6	13	13	NUM
ejpam-2650	49	7	]	]	PUNCT
ejpam-2650	49	8	that	that	SCONJ
ejpam-2650	49	9	the	the	DET
ejpam-2650	49	10	generating	generate	VERB
ejpam-2650	49	11	character	character	NOUN
ejpam-2650	49	12	of	of	ADP
ejpam-2650	49	13	rk	rk	PROPN
ejpam-2650	49	14	,	,	PUNCT
ejpam-2650	49	15	m	m	AUX
ejpam-2650	49	16	is	be	AUX
ejpam-2650	49	17	given	give	VERB
ejpam-2650	49	18	by	by	ADP
ejpam-2650	49	19	χ	χ	X
ejpam-2650	49	20	:	:	PUNCT
ejpam-2650	49	21	(	(	PUNCT
ejpam-2650	49	22	rk	rk	NOUN
ejpam-2650	49	23	,	,	PUNCT
ejpam-2650	49	24	m,+	m,+	PROPN
ejpam-2650	49	25	)	)	PUNCT
ejpam-2650	49	26	→	→	X
ejpam-2650	49	27	(	(	PUNCT
ejpam-2650	49	28	{	{	PUNCT
ejpam-2650	49	29	−1	−1	NOUN
ejpam-2650	49	30	,	,	PUNCT
ejpam-2650	49	31	1	1	NUM
ejpam-2650	49	32	}	}	PUNCT
ejpam-2650	49	33	,	,	PUNCT
ejpam-2650	49	34	.)∑	.)∑	PUNCT
ejpam-2650	50	1	0≤i≤k−1	0≤i≤k−1	NUM
ejpam-2650	50	2	0≤j≤m−1	0≤j≤m−1	NUM
ejpam-2650	50	3	ciju	ciju	NOUN
ejpam-2650	50	4	ivj	ivj	NOUN
ejpam-2650	50	5	7→	7→	NUM
ejpam-2650	50	6	(	(	PUNCT
ejpam-2650	50	7	−1)wh(c	−1)wh(c	NOUN
ejpam-2650	50	8	)	)	PUNCT
ejpam-2650	50	9	,	,	PUNCT
ejpam-2650	50	10	(	(	PUNCT
ejpam-2650	50	11	2	2	X
ejpam-2650	50	12	)	)	PUNCT
ejpam-2650	50	13	where	where	SCONJ
ejpam-2650	50	14	c	c	NOUN
ejpam-2650	50	15	=	=	SYM
ejpam-2650	50	16	(	(	PUNCT
ejpam-2650	50	17	cij	cij	PROPN
ejpam-2650	50	18	)	)	PUNCT
ejpam-2650	50	19	is	be	AUX
ejpam-2650	50	20	the	the	DET
ejpam-2650	50	21	binary	binary	ADJ
ejpam-2650	50	22	vector	vector	NOUN
ejpam-2650	50	23	consisting	consist	VERB
ejpam-2650	50	24	of	of	ADP
ejpam-2650	50	25	all	all	DET
ejpam-2650	50	26	the	the	DET
ejpam-2650	50	27	coefficients	coefficient	NOUN
ejpam-2650	50	28	cij	cij	PROPN
ejpam-2650	50	29	’s	’s	NOUN
ejpam-2650	50	30	of	of	ADP
ejpam-2650	50	31	a	a	DET
ejpam-2650	50	32	typical	typical	ADJ
ejpam-2650	50	33	element	element	NOUN
ejpam-2650	50	34	in	in	ADP
ejpam-2650	50	35	rk	rk	PROPN
ejpam-2650	50	36	,	,	PUNCT
ejpam-2650	50	37	m	m	PRON
ejpam-2650	50	38	,	,	PUNCT
ejpam-2650	50	39	and	and	CCONJ
ejpam-2650	50	40	wh(c	wh(c	NOUN
ejpam-2650	50	41	)	)	PUNCT
ejpam-2650	50	42	denotes	denote	VERB
ejpam-2650	50	43	the	the	DET
ejpam-2650	50	44	hamming	hamming	NOUN
ejpam-2650	50	45	weight	weight	NOUN
ejpam-2650	50	46	of	of	ADP
ejpam-2650	50	47	c.	c.	NOUN
ejpam-2650	50	48	for	for	ADP
ejpam-2650	50	49	example	example	NOUN
ejpam-2650	50	50	,	,	PUNCT
ejpam-2650	50	51	in	in	ADP
ejpam-2650	50	52	the	the	DET
ejpam-2650	50	53	case	case	NOUN
ejpam-2650	50	54	when	when	SCONJ
ejpam-2650	50	55	k	k	PROPN
ejpam-2650	50	56	=	=	SYM
ejpam-2650	50	57	2,m	2,m	NOUN
ejpam-2650	50	58	=	=	SYM
ejpam-2650	50	59	1	1	NUM
ejpam-2650	50	60	,	,	PUNCT
ejpam-2650	50	61	i.e.	i.e.	X
ejpam-2650	50	62	,	,	PUNCT
ejpam-2650	50	63	when	when	SCONJ
ejpam-2650	50	64	the	the	DET
ejpam-2650	50	65	ring	ring	NOUN
ejpam-2650	50	66	is	be	AUX
ejpam-2650	50	67	f2	f2	ADJ
ejpam-2650	50	68	+	+	CCONJ
ejpam-2650	50	69	uf2	uf2	NOUN
ejpam-2650	50	70	,	,	PUNCT
ejpam-2650	50	71	the	the	DET
ejpam-2650	50	72	generating	generate	VERB
ejpam-2650	50	73	character	character	NOUN
ejpam-2650	50	74	takes	take	VERB
ejpam-2650	50	75	on	on	ADP
ejpam-2650	50	76	the	the	DET
ejpam-2650	50	77	values	value	NOUN
ejpam-2650	50	78	:	:	PUNCT
ejpam-2650	50	79	χ(0	χ(0	NOUN
ejpam-2650	50	80	)	)	PUNCT
ejpam-2650	50	81	=	=	SYM
ejpam-2650	50	82	1	1	NUM
ejpam-2650	50	83	,	,	PUNCT
ejpam-2650	50	84	χ(1	χ(1	PROPN
ejpam-2650	50	85	)	)	PUNCT
ejpam-2650	50	86	=	=	SYM
ejpam-2650	50	87	χ(u	χ(u	NOUN
ejpam-2650	50	88	)	)	PUNCT
ejpam-2650	50	89	=	=	SYM
ejpam-2650	50	90	−1	−1	NOUN
ejpam-2650	50	91	and	and	CCONJ
ejpam-2650	50	92	χ(1	χ(1	PROPN
ejpam-2650	50	93	+	+	CCONJ
ejpam-2650	50	94	u	u	NOUN
ejpam-2650	50	95	)	)	PUNCT
ejpam-2650	50	96	=	=	SYM
ejpam-2650	51	1	1	1	X
ejpam-2650	51	2	.	.	X
ejpam-2650	51	3	a	a	DET
ejpam-2650	51	4	linear	linear	ADJ
ejpam-2650	51	5	code	code	NOUN
ejpam-2650	51	6	c	c	NOUN
ejpam-2650	51	7	of	of	ADP
ejpam-2650	51	8	length	length	NOUN
ejpam-2650	51	9	n	n	CCONJ
ejpam-2650	51	10	over	over	ADP
ejpam-2650	51	11	rk	rk	NOUN
ejpam-2650	51	12	,	,	PUNCT
ejpam-2650	51	13	m	m	VERB
ejpam-2650	51	14	is	be	AUX
ejpam-2650	51	15	an	an	DET
ejpam-2650	51	16	rk	rk	NOUN
ejpam-2650	51	17	,	,	PUNCT
ejpam-2650	51	18	m	m	NOUN
ejpam-2650	51	19	-	-	NOUN
ejpam-2650	51	20	submodule	submodule	NOUN
ejpam-2650	51	21	of	of	ADP
ejpam-2650	51	22	rnk	rnk	PROPN
ejpam-2650	51	23	,	,	PUNCT
ejpam-2650	51	24	m.	m.	NOUN
ejpam-2650	51	25	special	special	ADJ
ejpam-2650	51	26	types	type	NOUN
ejpam-2650	51	27	of	of	ADP
ejpam-2650	51	28	codes	code	NOUN
ejpam-2650	51	29	such	such	ADJ
ejpam-2650	51	30	as	as	ADP
ejpam-2650	51	31	cyclic	cyclic	ADJ
ejpam-2650	51	32	and	and	CCONJ
ejpam-2650	51	33	quasicyclic	quasicyclic	NOUN
ejpam-2650	51	34	codes	code	NOUN
ejpam-2650	51	35	are	be	AUX
ejpam-2650	51	36	also	also	ADV
ejpam-2650	51	37	defined	define	VERB
ejpam-2650	51	38	over	over	ADP
ejpam-2650	51	39	rk	rk	NOUN
ejpam-2650	51	40	,	,	PUNCT
ejpam-2650	51	41	m	m	VERB
ejpam-2650	51	42	in	in	ADP
ejpam-2650	51	43	the	the	DET
ejpam-2650	51	44	natural	natural	ADJ
ejpam-2650	51	45	way	way	NOUN
ejpam-2650	51	46	they	they	PRON
ejpam-2650	51	47	are	be	AUX
ejpam-2650	51	48	defined	define	VERB
ejpam-2650	51	49	over	over	ADP
ejpam-2650	51	50	rings	ring	NOUN
ejpam-2650	51	51	.	.	PUNCT
ejpam-2650	52	1	for	for	ADP
ejpam-2650	52	2	more	more	ADJ
ejpam-2650	52	3	details	detail	NOUN
ejpam-2650	52	4	on	on	ADP
ejpam-2650	52	5	the	the	DET
ejpam-2650	52	6	structural	structural	ADJ
ejpam-2650	52	7	properties	property	NOUN
ejpam-2650	52	8	of	of	ADP
ejpam-2650	52	9	the	the	DET
ejpam-2650	52	10	rings	ring	NOUN
ejpam-2650	52	11	as	as	ADV
ejpam-2650	52	12	well	well	ADV
ejpam-2650	52	13	as	as	ADP
ejpam-2650	52	14	a	a	DET
ejpam-2650	52	15	lee	lee	PROPN
ejpam-2650	52	16	weight	weight	NOUN
ejpam-2650	52	17	and	and	CCONJ
ejpam-2650	52	18	related	relate	VERB
ejpam-2650	52	19	gray	gray	ADJ
ejpam-2650	52	20	maps	map	NOUN
ejpam-2650	52	21	we	we	PRON
ejpam-2650	52	22	refer	refer	VERB
ejpam-2650	52	23	to	to	ADP
ejpam-2650	52	24	[	[	X
ejpam-2650	52	25	13	13	NUM
ejpam-2650	52	26	]	]	PUNCT
ejpam-2650	52	27	.	.	PUNCT
ejpam-2650	53	1	3	3	X
ejpam-2650	53	2	.	.	X
ejpam-2650	53	3	the	the	DET
ejpam-2650	53	4	homogeneous	homogeneous	ADJ
ejpam-2650	53	5	weight	weight	NOUN
ejpam-2650	53	6	and	and	CCONJ
ejpam-2650	53	7	the	the	DET
ejpam-2650	53	8	corresponding	corresponding	ADJ
ejpam-2650	53	9	gray	gray	ADJ
ejpam-2650	53	10	map	map	NOUN
ejpam-2650	53	11	on	on	ADP
ejpam-2650	53	12	rk	rk	NOUN
ejpam-2650	53	13	,	,	PUNCT
ejpam-2650	53	14	m	m	VERB
ejpam-2650	53	15	homogeneous	homogeneous	ADJ
ejpam-2650	53	16	weights	weight	NOUN
ejpam-2650	53	17	were	be	AUX
ejpam-2650	53	18	first	first	ADV
ejpam-2650	53	19	introduced	introduce	VERB
ejpam-2650	53	20	in	in	ADP
ejpam-2650	53	21	1997	1997	NUM
ejpam-2650	53	22	by	by	ADP
ejpam-2650	53	23	heise	heise	PROPN
ejpam-2650	53	24	and	and	CCONJ
ejpam-2650	53	25	constantinescu	constantinescu	NOUN
ejpam-2650	53	26	in	in	ADP
ejpam-2650	53	27	[	[	X
ejpam-2650	53	28	4	4	NUM
ejpam-2650	53	29	]	]	PUNCT
ejpam-2650	53	30	.	.	PUNCT
ejpam-2650	54	1	they	they	PRON
ejpam-2650	54	2	have	have	AUX
ejpam-2650	54	3	been	be	AUX
ejpam-2650	54	4	studied	study	VERB
ejpam-2650	54	5	especially	especially	ADV
ejpam-2650	54	6	within	within	ADP
ejpam-2650	54	7	the	the	DET
ejpam-2650	54	8	context	context	NOUN
ejpam-2650	54	9	of	of	ADP
ejpam-2650	54	10	frobenius	frobenius	ADJ
ejpam-2650	54	11	rings	ring	NOUN
ejpam-2650	54	12	.	.	PUNCT
ejpam-2650	55	1	[	[	X
ejpam-2650	55	2	8	8	NUM
ejpam-2650	55	3	]	]	PUNCT
ejpam-2650	55	4	and	and	CCONJ
ejpam-2650	55	5	[	[	X
ejpam-2650	55	6	6	6	NUM
ejpam-2650	55	7	]	]	PUNCT
ejpam-2650	55	8	can	can	AUX
ejpam-2650	55	9	be	be	AUX
ejpam-2650	55	10	cited	cite	VERB
ejpam-2650	55	11	for	for	ADP
ejpam-2650	55	12	this	this	DET
ejpam-2650	55	13	purpose	purpose	NOUN
ejpam-2650	55	14	.	.	PUNCT
ejpam-2650	56	1	the	the	DET
ejpam-2650	56	2	homogeneous	homogeneous	ADJ
ejpam-2650	56	3	weight	weight	NOUN
ejpam-2650	56	4	is	be	AUX
ejpam-2650	56	5	defined	define	VERB
ejpam-2650	56	6	with	with	ADP
ejpam-2650	56	7	two	two	NUM
ejpam-2650	56	8	conditions	condition	NOUN
ejpam-2650	56	9	for	for	ADP
ejpam-2650	56	10	arbitrary	arbitrary	ADJ
ejpam-2650	56	11	finite	finite	NOUN
ejpam-2650	56	12	rings	ring	NOUN
ejpam-2650	56	13	as	as	SCONJ
ejpam-2650	56	14	follows	follow	VERB
ejpam-2650	56	15	in	in	ADP
ejpam-2650	56	16	[	[	X
ejpam-2650	56	17	6	6	NUM
ejpam-2650	56	18	]	]	PUNCT
ejpam-2650	56	19	:	:	PUNCT
ejpam-2650	56	20	definition	definition	NOUN
ejpam-2650	56	21	1	1	NUM
ejpam-2650	56	22	.	.	PUNCT
ejpam-2650	57	1	a	a	DET
ejpam-2650	57	2	real	real	ADV
ejpam-2650	57	3	valued	value	VERB
ejpam-2650	57	4	function	function	NOUN
ejpam-2650	57	5	ω	ω	PROPN
ejpam-2650	57	6	on	on	ADP
ejpam-2650	57	7	the	the	DET
ejpam-2650	57	8	finite	finite	NOUN
ejpam-2650	57	9	ring	ring	NOUN
ejpam-2650	57	10	r	r	NOUN
ejpam-2650	57	11	is	be	AUX
ejpam-2650	57	12	called	call	VERB
ejpam-2650	57	13	a	a	DET
ejpam-2650	57	14	(	(	PUNCT
ejpam-2650	57	15	left	left	ADJ
ejpam-2650	57	16	)	)	PUNCT
ejpam-2650	57	17	homogeneous	homogeneous	ADJ
ejpam-2650	57	18	weight	weight	NOUN
ejpam-2650	57	19	if	if	SCONJ
ejpam-2650	57	20	ω(0	ω(0	NUM
ejpam-2650	57	21	)	)	PUNCT
ejpam-2650	57	22	=	=	SYM
ejpam-2650	57	23	0	0	NUM
ejpam-2650	57	24	and	and	CCONJ
ejpam-2650	57	25	the	the	DET
ejpam-2650	57	26	following	follow	VERB
ejpam-2650	57	27	is	be	AUX
ejpam-2650	57	28	true	true	ADJ
ejpam-2650	57	29	:	:	PUNCT
ejpam-2650	57	30	(	(	PUNCT
ejpam-2650	57	31	h1	h1	PROPN
ejpam-2650	57	32	)	)	PUNCT
ejpam-2650	57	33	for	for	ADP
ejpam-2650	57	34	all	all	DET
ejpam-2650	57	35	x	x	NOUN
ejpam-2650	57	36	,	,	PUNCT
ejpam-2650	57	37	y	y	PROPN
ejpam-2650	57	38	∈	∈	PROPN
ejpam-2650	57	39	r	r	NOUN
ejpam-2650	57	40	,	,	PUNCT
ejpam-2650	57	41	rx	rx	X
ejpam-2650	57	42	=	=	VERB
ejpam-2650	57	43	ry	ry	NOUN
ejpam-2650	57	44	implies	imply	VERB
ejpam-2650	57	45	ω(x	ω(x	NOUN
ejpam-2650	57	46	)	)	PUNCT
ejpam-2650	57	47	=	=	SYM
ejpam-2650	57	48	ω(y	ω(y	PROPN
ejpam-2650	57	49	)	)	PUNCT
ejpam-2650	57	50	holds	hold	VERB
ejpam-2650	57	51	.	.	PUNCT
ejpam-2650	58	1	(	(	PUNCT
ejpam-2650	58	2	h2	h2	NOUN
ejpam-2650	58	3	)	)	PUNCT
ejpam-2650	58	4	there	there	PRON
ejpam-2650	58	5	exists	exist	VERB
ejpam-2650	58	6	a	a	DET
ejpam-2650	58	7	real	real	ADJ
ejpam-2650	58	8	number	number	NOUN
ejpam-2650	58	9	γ	γ	ADP
ejpam-2650	58	10	such	such	ADJ
ejpam-2650	58	11	that∑	that∑	NOUN
ejpam-2650	58	12	y∈rx	y∈rx	NOUN
ejpam-2650	58	13	ω(y	ω(y	PROPN
ejpam-2650	58	14	)	)	PUNCT
ejpam-2650	58	15	=	=	SYM
ejpam-2650	58	16	γ	γ	X
ejpam-2650	58	17	|rx|	|rx|	NOUN
ejpam-2650	58	18	for	for	ADP
ejpam-2650	58	19	all	all	DET
ejpam-2650	58	20	x	x	SYM
ejpam-2650	58	21	∈	∈	PROPN
ejpam-2650	58	22	r\{0	r\{0	PROPN
ejpam-2650	58	23	}	}	PUNCT
ejpam-2650	58	24	it	it	PRON
ejpam-2650	58	25	has	have	AUX
ejpam-2650	58	26	been	be	AUX
ejpam-2650	58	27	shown	show	VERB
ejpam-2650	58	28	that	that	SCONJ
ejpam-2650	58	29	all	all	DET
ejpam-2650	58	30	frobenius	frobenius	NOUN
ejpam-2650	58	31	rings	ring	NOUN
ejpam-2650	58	32	are	be	AUX
ejpam-2650	58	33	equipped	equip	VERB
ejpam-2650	58	34	with	with	ADP
ejpam-2650	58	35	a	a	DET
ejpam-2650	58	36	homogeneous	homogeneous	ADJ
ejpam-2650	58	37	weight	weight	NOUN
ejpam-2650	58	38	.	.	PUNCT
ejpam-2650	59	1	different	different	ADJ
ejpam-2650	59	2	characterizations	characterization	NOUN
ejpam-2650	59	3	of	of	ADP
ejpam-2650	59	4	the	the	DET
ejpam-2650	59	5	homogeneous	homogeneous	ADJ
ejpam-2650	59	6	weight	weight	NOUN
ejpam-2650	59	7	for	for	ADP
ejpam-2650	59	8	frobenus	frobenus	NOUN
ejpam-2650	59	9	rings	ring	NOUN
ejpam-2650	59	10	have	have	AUX
ejpam-2650	59	11	been	be	AUX
ejpam-2650	59	12	given	give	VERB
ejpam-2650	59	13	.	.	PUNCT
ejpam-2650	60	1	some	some	PRON
ejpam-2650	60	2	of	of	ADP
ejpam-2650	60	3	these	these	PRON
ejpam-2650	60	4	use	use	VERB
ejpam-2650	60	5	the	the	DET
ejpam-2650	60	6	mobius	mobius	NOUN
ejpam-2650	60	7	function	function	NOUN
ejpam-2650	60	8	,	,	PUNCT
ejpam-2650	60	9	and	and	CCONJ
ejpam-2650	60	10	some	some	PRON
ejpam-2650	60	11	use	use	VERB
ejpam-2650	60	12	the	the	DET
ejpam-2650	60	13	generating	generate	VERB
ejpam-2650	60	14	character	character	NOUN
ejpam-2650	60	15	of	of	ADP
ejpam-2650	60	16	frobenius	frobenius	ADJ
ejpam-2650	60	17	rings	ring	NOUN
ejpam-2650	60	18	.	.	PUNCT
ejpam-2650	61	1	in	in	ADP
ejpam-2650	61	2	our	our	PRON
ejpam-2650	61	3	work	work	NOUN
ejpam-2650	61	4	we	we	PRON
ejpam-2650	61	5	will	will	AUX
ejpam-2650	61	6	use	use	VERB
ejpam-2650	61	7	the	the	DET
ejpam-2650	61	8	following	follow	VERB
ejpam-2650	61	9	proposition	proposition	NOUN
ejpam-2650	61	10	from	from	ADP
ejpam-2650	61	11	[	[	X
ejpam-2650	61	12	8	8	NUM
ejpam-2650	61	13	]	]	PUNCT
ejpam-2650	61	14	,	,	PUNCT
ejpam-2650	61	15	which	which	PRON
ejpam-2650	61	16	describes	describe	VERB
ejpam-2650	61	17	the	the	DET
ejpam-2650	61	18	homogeneous	homogeneous	ADJ
ejpam-2650	61	19	weight	weight	NOUN
ejpam-2650	61	20	in	in	ADP
ejpam-2650	61	21	terms	term	NOUN
ejpam-2650	61	22	of	of	ADP
ejpam-2650	61	23	the	the	DET
ejpam-2650	61	24	generating	generate	VERB
ejpam-2650	61	25	character	character	NOUN
ejpam-2650	61	26	of	of	ADP
ejpam-2650	61	27	the	the	DET
ejpam-2650	61	28	ring	ring	NOUN
ejpam-2650	61	29	:	:	PUNCT
ejpam-2650	61	30	b.	b.	PROPN
ejpam-2650	61	31	yildiz	yildiz	PROPN
ejpam-2650	61	32	,	,	PUNCT
ejpam-2650	61	33	n.	n.	PROPN
ejpam-2650	61	34	tufekci	tufekci	PROPN
ejpam-2650	61	35	/	/	SYM
ejpam-2650	61	36	eur	eur	PROPN
ejpam-2650	61	37	.	.	PUNCT
ejpam-2650	62	1	j.	j.	PROPN
ejpam-2650	62	2	pure	pure	PROPN
ejpam-2650	62	3	appl	appl	PROPN
ejpam-2650	62	4	.	.	PROPN
ejpam-2650	62	5	math	math	PROPN
ejpam-2650	62	6	,	,	PUNCT
ejpam-2650	62	7	10	10	NUM
ejpam-2650	62	8	(	(	PUNCT
ejpam-2650	62	9	5	5	NUM
ejpam-2650	62	10	)	)	PUNCT
ejpam-2650	62	11	(	(	PUNCT
ejpam-2650	62	12	2017	2017	NUM
ejpam-2650	62	13	)	)	PUNCT
ejpam-2650	62	14	,	,	PUNCT
ejpam-2650	62	15	1112	1112	NUM
ejpam-2650	62	16	-	-	SYM
ejpam-2650	62	17	1123	1123	NUM
ejpam-2650	62	18	1115	1115	NUM
ejpam-2650	62	19	proposition	proposition	NOUN
ejpam-2650	62	20	1	1	NUM
ejpam-2650	62	21	.	.	PUNCT
ejpam-2650	63	1	(	(	PUNCT
ejpam-2650	63	2	[	[	X
ejpam-2650	63	3	8	8	NUM
ejpam-2650	63	4	]	]	PUNCT
ejpam-2650	63	5	)	)	PUNCT
ejpam-2650	63	6	the	the	DET
ejpam-2650	63	7	homogeneous	homogeneous	ADJ
ejpam-2650	63	8	weight	weight	NOUN
ejpam-2650	63	9	function	function	NOUN
ejpam-2650	63	10	for	for	ADP
ejpam-2650	63	11	a	a	DET
ejpam-2650	63	12	finite	finite	ADJ
ejpam-2650	63	13	ring	ring	NOUN
ejpam-2650	63	14	r	r	NOUN
ejpam-2650	63	15	with	with	ADP
ejpam-2650	63	16	generating	generate	VERB
ejpam-2650	63	17	character	character	NOUN
ejpam-2650	63	18	χ	χ	NOUN
ejpam-2650	63	19	is	be	AUX
ejpam-2650	63	20	of	of	ADP
ejpam-2650	63	21	the	the	DET
ejpam-2650	63	22	form	form	NOUN
ejpam-2650	63	23	ω	ω	NOUN
ejpam-2650	63	24	:	:	PUNCT
ejpam-2650	63	25	r	r	NOUN
ejpam-2650	63	26	→	→	SYM
ejpam-2650	63	27	r	r	NOUN
ejpam-2650	63	28	x	x	SYM
ejpam-2650	63	29	7→	7→	NUM
ejpam-2650	63	30	γ	γ	NOUN
ejpam-2650	63	31	[	[	PUNCT
ejpam-2650	63	32	1−	1−	NUM
ejpam-2650	63	33	1	1	NUM
ejpam-2650	63	34	|r×|	|r×|	X
ejpam-2650	63	35	∑	∑	ADP
ejpam-2650	63	36	ρ∈r×	ρ∈r×	PROPN
ejpam-2650	63	37	χ(xρ	χ(xρ	NOUN
ejpam-2650	63	38	)	)	PUNCT
ejpam-2650	63	39	]	]	PUNCT
ejpam-2650	63	40	,	,	PUNCT
ejpam-2650	63	41	(	(	PUNCT
ejpam-2650	63	42	3	3	X
ejpam-2650	63	43	)	)	PUNCT
ejpam-2650	63	44	where	where	SCONJ
ejpam-2650	63	45	r×	r×	NOUN
ejpam-2650	63	46	,	,	PUNCT
ejpam-2650	63	47	represents	represent	VERB
ejpam-2650	63	48	the	the	DET
ejpam-2650	63	49	group	group	NOUN
ejpam-2650	63	50	of	of	ADP
ejpam-2650	63	51	units	unit	NOUN
ejpam-2650	63	52	of	of	ADP
ejpam-2650	63	53	r.	r.	PROPN
ejpam-2650	63	54	the	the	DET
ejpam-2650	63	55	γ	γ	NOUN
ejpam-2650	63	56	that	that	PRON
ejpam-2650	63	57	appears	appear	VERB
ejpam-2650	63	58	in	in	ADP
ejpam-2650	63	59	the	the	DET
ejpam-2650	63	60	weight	weight	NOUN
ejpam-2650	63	61	function	function	NOUN
ejpam-2650	63	62	is	be	AUX
ejpam-2650	63	63	also	also	ADV
ejpam-2650	63	64	called	call	VERB
ejpam-2650	63	65	the	the	DET
ejpam-2650	63	66	average	average	ADJ
ejpam-2650	63	67	weight	weight	NOUN
ejpam-2650	63	68	and	and	CCONJ
ejpam-2650	63	69	further	further	ADJ
ejpam-2650	63	70	satisfies	satisfie	NOUN
ejpam-2650	63	71	the	the	DET
ejpam-2650	63	72	following	follow	VERB
ejpam-2650	63	73	property	property	NOUN
ejpam-2650	63	74	:	:	PUNCT
ejpam-2650	63	75	proposition	proposition	NOUN
ejpam-2650	63	76	2	2	NUM
ejpam-2650	63	77	.	.	PUNCT
ejpam-2650	64	1	(	(	PUNCT
ejpam-2650	64	2	[	[	X
ejpam-2650	64	3	8	8	NUM
ejpam-2650	64	4	]	]	PUNCT
ejpam-2650	64	5	)	)	PUNCT
ejpam-2650	64	6	let	let	VERB
ejpam-2650	64	7	i	i	PRON
ejpam-2650	64	8	be	be	AUX
ejpam-2650	64	9	either	either	CCONJ
ejpam-2650	64	10	a	a	DET
ejpam-2650	64	11	left	left	NOUN
ejpam-2650	64	12	or	or	CCONJ
ejpam-2650	64	13	a	a	DET
ejpam-2650	64	14	right	right	ADJ
ejpam-2650	64	15	ideal	ideal	NOUN
ejpam-2650	64	16	of	of	ADP
ejpam-2650	64	17	a	a	DET
ejpam-2650	64	18	finite	finite	ADJ
ejpam-2650	64	19	frobenius	frobenius	NOUN
ejpam-2650	64	20	ring	ring	NOUN
ejpam-2650	64	21	r	r	NOUN
ejpam-2650	64	22	,	,	PUNCT
ejpam-2650	64	23	and	and	CCONJ
ejpam-2650	64	24	let	let	VERB
ejpam-2650	64	25	y	y	PROPN
ejpam-2650	64	26	∈	∈	PROPN
ejpam-2650	64	27	r.	r.	PROPN
ejpam-2650	64	28	then	then	ADV
ejpam-2650	64	29	∑	∑	PROPN
ejpam-2650	64	30	r∈i+y	r∈i+y	PROPN
ejpam-2650	64	31	ω(r	ω(r	NUM
ejpam-2650	64	32	)	)	PUNCT
ejpam-2650	65	1	=	=	PUNCT
ejpam-2650	65	2	γ	γ	NOUN
ejpam-2650	65	3	|i|	|i|	PROPN
ejpam-2650	65	4	.	.	PUNCT
ejpam-2650	65	5	applying	apply	VERB
ejpam-2650	65	6	proposition	proposition	NOUN
ejpam-2650	65	7	1	1	NUM
ejpam-2650	65	8	to	to	ADP
ejpam-2650	65	9	the	the	DET
ejpam-2650	65	10	ring	ring	NOUN
ejpam-2650	65	11	rk	rk	PROPN
ejpam-2650	65	12	,	,	PUNCT
ejpam-2650	65	13	m	m	PRON
ejpam-2650	65	14	,	,	PUNCT
ejpam-2650	65	15	we	we	PRON
ejpam-2650	65	16	can	can	AUX
ejpam-2650	65	17	obtain	obtain	VERB
ejpam-2650	65	18	a	a	DET
ejpam-2650	65	19	form	form	NOUN
ejpam-2650	65	20	for	for	ADP
ejpam-2650	65	21	the	the	DET
ejpam-2650	65	22	homogeneous	homogeneous	ADJ
ejpam-2650	65	23	weight	weight	NOUN
ejpam-2650	65	24	for	for	ADP
ejpam-2650	65	25	codes	code	NOUN
ejpam-2650	65	26	over	over	ADP
ejpam-2650	65	27	the	the	DET
ejpam-2650	65	28	ring	ring	NOUN
ejpam-2650	65	29	rk	rk	NOUN
ejpam-2650	65	30	,	,	PUNCT
ejpam-2650	65	31	m	m	PRON
ejpam-2650	65	32	:	:	PUNCT
ejpam-2650	65	33	theorem	theorem	NOUN
ejpam-2650	65	34	1	1	NUM
ejpam-2650	65	35	.	.	PUNCT
ejpam-2650	66	1	the	the	DET
ejpam-2650	66	2	homogeneous	homogeneous	ADJ
ejpam-2650	66	3	weight	weight	NOUN
ejpam-2650	66	4	for	for	ADP
ejpam-2650	66	5	the	the	DET
ejpam-2650	66	6	ring	ring	NOUN
ejpam-2650	66	7	rk	rk	NOUN
ejpam-2650	66	8	,	,	PUNCT
ejpam-2650	66	9	m	m	VERB
ejpam-2650	66	10	is	be	AUX
ejpam-2650	66	11	of	of	ADP
ejpam-2650	66	12	the	the	DET
ejpam-2650	66	13	form	form	NOUN
ejpam-2650	66	14	ωhom(x	ωhom(x	NOUN
ejpam-2650	66	15	)	)	PUNCT
ejpam-2650	66	16			PUNCT
ejpam-2650	66	17	0	0	NUM
ejpam-2650	66	18	x	x	SYM
ejpam-2650	66	19	=	=	SYM
ejpam-2650	66	20	0	0	NUM
ejpam-2650	66	21	,	,	PUNCT
ejpam-2650	66	22	2γ	2γ	NOUN
ejpam-2650	66	23	,	,	PUNCT
ejpam-2650	66	24	x	x	SYM
ejpam-2650	66	25	=	=	SYM
ejpam-2650	66	26	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	66	27	,	,	PUNCT
ejpam-2650	66	28	γ	γ	X
ejpam-2650	66	29	,	,	PUNCT
ejpam-2650	66	30	otherwise	otherwise	ADV
ejpam-2650	66	31	.	.	PUNCT
ejpam-2650	67	1	proof	proof	NOUN
ejpam-2650	67	2	.	.	PUNCT
ejpam-2650	68	1	we	we	PRON
ejpam-2650	68	2	first	first	ADV
ejpam-2650	68	3	note	note	VERB
ejpam-2650	68	4	that	that	SCONJ
ejpam-2650	68	5	uk−1vm−1ρ	uk−1vm−1ρ	ADV
ejpam-2650	68	6	=	=	SYM
ejpam-2650	68	7	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	68	8	for	for	ADP
ejpam-2650	68	9	all	all	DET
ejpam-2650	68	10	ρ	ρ	NOUN
ejpam-2650	68	11	∈	∈	PROPN
ejpam-2650	68	12	u(rk	u(rk	NOUN
ejpam-2650	68	13	,	,	PUNCT
ejpam-2650	68	14	m	m	NOUN
ejpam-2650	68	15	)	)	PUNCT
ejpam-2650	68	16	and	and	CCONJ
ejpam-2650	68	17	so	so	ADV
ejpam-2650	68	18	we	we	PRON
ejpam-2650	68	19	have	have	VERB
ejpam-2650	68	20	χ(uk−1vm−1ρ	χ(uk−1vm−1ρ	NOUN
ejpam-2650	68	21	)	)	PUNCT
ejpam-2650	68	22	=	=	SYM
ejpam-2650	68	23	(	(	PUNCT
ejpam-2650	68	24	−1	−1	NOUN
ejpam-2650	68	25	)	)	PUNCT
ejpam-2650	68	26	for	for	ADP
ejpam-2650	68	27	all	all	DET
ejpam-2650	68	28	ρ	ρ	NOUN
ejpam-2650	68	29	∈	∈	PROPN
ejpam-2650	68	30	u(rk	u(rk	NOUN
ejpam-2650	68	31	,	,	PUNCT
ejpam-2650	68	32	m	m	NOUN
ejpam-2650	68	33	)	)	PUNCT
ejpam-2650	68	34	.	.	PUNCT
ejpam-2650	69	1	putting	put	VERB
ejpam-2650	69	2	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	69	3	into	into	ADP
ejpam-2650	69	4	equation	equation	NOUN
ejpam-2650	69	5	3	3	NUM
ejpam-2650	69	6	we	we	PRON
ejpam-2650	69	7	see	see	VERB
ejpam-2650	69	8	that	that	SCONJ
ejpam-2650	69	9	we	we	PRON
ejpam-2650	69	10	have	have	VERB
ejpam-2650	69	11	ωhom(uk−1vm−1	ωhom(uk−1vm−1	NUM
ejpam-2650	69	12	)	)	PUNCT
ejpam-2650	70	1	=	=	SYM
ejpam-2650	70	2	γ	γ	X
ejpam-2650	70	3	[	[	PUNCT
ejpam-2650	70	4	1−	1−	NUM
ejpam-2650	70	5	1	1	NUM
ejpam-2650	70	6	2km−1	2km−1	PROPN
ejpam-2650	70	7	∑	∑	NOUN
ejpam-2650	70	8	ρ∈u(rk	ρ∈u(rk	PROPN
ejpam-2650	70	9	,	,	PUNCT
ejpam-2650	70	10	m	m	PROPN
ejpam-2650	70	11	)	)	PUNCT
ejpam-2650	70	12	(	(	PUNCT
ejpam-2650	70	13	−1	−1	NOUN
ejpam-2650	70	14	)	)	PUNCT
ejpam-2650	70	15	]	]	PUNCT
ejpam-2650	71	1	=	=	SYM
ejpam-2650	71	2	2γ	2γ	NOUN
ejpam-2650	71	3	.	.	PUNCT
ejpam-2650	72	1	on	on	ADP
ejpam-2650	72	2	the	the	DET
ejpam-2650	72	3	other	other	ADJ
ejpam-2650	72	4	hand	hand	NOUN
ejpam-2650	72	5	,	,	PUNCT
ejpam-2650	72	6	following	follow	VERB
ejpam-2650	72	7	the	the	DET
ejpam-2650	72	8	same	same	ADJ
ejpam-2650	72	9	arguments	argument	NOUN
ejpam-2650	72	10	as	as	SCONJ
ejpam-2650	72	11	were	be	AUX
ejpam-2650	72	12	used	use	VERB
ejpam-2650	72	13	in	in	ADP
ejpam-2650	72	14	[	[	X
ejpam-2650	72	15	15	15	NUM
ejpam-2650	72	16	]	]	X
ejpam-2650	72	17	we	we	PRON
ejpam-2650	72	18	can	can	AUX
ejpam-2650	72	19	prove	prove	VERB
ejpam-2650	72	20	that	that	SCONJ
ejpam-2650	72	21	,	,	PUNCT
ejpam-2650	72	22	for	for	ADP
ejpam-2650	72	23	any	any	DET
ejpam-2650	72	24	element	element	NOUN
ejpam-2650	72	25	x	x	PUNCT
ejpam-2650	72	26	in	in	ADP
ejpam-2650	72	27	rk	rk	NOUN
ejpam-2650	72	28	,	,	PUNCT
ejpam-2650	72	29	m	m	VERB
ejpam-2650	72	30	such	such	ADJ
ejpam-2650	72	31	that	that	SCONJ
ejpam-2650	72	32	x	x	PROPN
ejpam-2650	72	33	6=	6=	ADP
ejpam-2650	72	34	0	0	NUM
ejpam-2650	72	35	,	,	PUNCT
ejpam-2650	72	36	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	72	37	,	,	PUNCT
ejpam-2650	72	38	we	we	PRON
ejpam-2650	72	39	have∑	have∑	VERB
ejpam-2650	72	40	α∈u(rk	α∈u(rk	PROPN
ejpam-2650	72	41	,	,	PUNCT
ejpam-2650	72	42	m	m	NOUN
ejpam-2650	72	43	)	)	PUNCT
ejpam-2650	72	44	χ(αx	χ(αx	PROPN
ejpam-2650	72	45	)	)	PUNCT
ejpam-2650	72	46	=	=	SYM
ejpam-2650	73	1	0	0	X
ejpam-2650	73	2	.	.	PUNCT
ejpam-2650	74	1	thus	thus	ADV
ejpam-2650	74	2	we	we	PRON
ejpam-2650	74	3	obtain	obtain	VERB
ejpam-2650	74	4	ωhom(x	ωhom(x	NOUN
ejpam-2650	74	5	)	)	PUNCT
ejpam-2650	74	6	=	=	SYM
ejpam-2650	74	7	γ	γ	X
ejpam-2650	74	8	[	[	PUNCT
ejpam-2650	74	9	1−	1−	NUM
ejpam-2650	74	10	1	1	NUM
ejpam-2650	74	11	2km−1	2km−1	NOUN
ejpam-2650	74	12	0	0	NUM
ejpam-2650	74	13	]	]	PUNCT
ejpam-2650	74	14	=	=	PUNCT
ejpam-2650	74	15	γ	γ	NOUN
ejpam-2650	74	16	for	for	ADP
ejpam-2650	74	17	all	all	DET
ejpam-2650	74	18	x	x	SYM
ejpam-2650	74	19	6=	6=	ADP
ejpam-2650	74	20	0	0	NUM
ejpam-2650	74	21	,	,	PUNCT
ejpam-2650	74	22	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	74	23	.	.	PUNCT
ejpam-2650	75	1	having	having	AUX
ejpam-2650	75	2	settled	settle	VERB
ejpam-2650	75	3	the	the	DET
ejpam-2650	75	4	form	form	NOUN
ejpam-2650	75	5	of	of	ADP
ejpam-2650	75	6	the	the	DET
ejpam-2650	75	7	homogeneous	homogeneous	ADJ
ejpam-2650	75	8	weight	weight	NOUN
ejpam-2650	75	9	,	,	PUNCT
ejpam-2650	75	10	we	we	PRON
ejpam-2650	75	11	now	now	ADV
ejpam-2650	75	12	want	want	VERB
ejpam-2650	75	13	to	to	PART
ejpam-2650	75	14	choose	choose	VERB
ejpam-2650	75	15	a	a	DET
ejpam-2650	75	16	specific	specific	ADJ
ejpam-2650	75	17	value	value	NOUN
ejpam-2650	75	18	for	for	ADP
ejpam-2650	75	19	γ	γ	NOUN
ejpam-2650	75	20	so	so	SCONJ
ejpam-2650	75	21	that	that	SCONJ
ejpam-2650	75	22	we	we	PRON
ejpam-2650	75	23	can	can	AUX
ejpam-2650	75	24	find	find	VERB
ejpam-2650	75	25	a	a	DET
ejpam-2650	75	26	distance	distance	NOUN
ejpam-2650	75	27	preserving	preserve	VERB
ejpam-2650	75	28	isometry	isometry	NOUN
ejpam-2650	75	29	from	from	ADP
ejpam-2650	75	30	rk	rk	PRON
ejpam-2650	75	31	,	,	PUNCT
ejpam-2650	75	32	m	m	VERB
ejpam-2650	75	33	to	to	ADP
ejpam-2650	75	34	fs2	fs2	PROPN
ejpam-2650	75	35	for	for	ADP
ejpam-2650	75	36	a	a	DET
ejpam-2650	75	37	suitable	suitable	ADJ
ejpam-2650	75	38	s.	s.	PROPN
ejpam-2650	75	39	we	we	PRON
ejpam-2650	75	40	will	will	AUX
ejpam-2650	75	41	call	call	VERB
ejpam-2650	75	42	this	this	DET
ejpam-2650	75	43	map	map	NOUN
ejpam-2650	75	44	the	the	DET
ejpam-2650	75	45	gray	gray	ADJ
ejpam-2650	75	46	-	-	PUNCT
ejpam-2650	75	47	homogeneous	homogeneous	ADJ
ejpam-2650	75	48	map	map	NOUN
ejpam-2650	75	49	.	.	PUNCT
ejpam-2650	76	1	we	we	PRON
ejpam-2650	76	2	recall	recall	VERB
ejpam-2650	76	3	some	some	PRON
ejpam-2650	76	4	of	of	ADP
ejpam-2650	76	5	the	the	DET
ejpam-2650	76	6	work	work	NOUN
ejpam-2650	76	7	done	do	VERB
ejpam-2650	76	8	in	in	ADP
ejpam-2650	76	9	this	this	DET
ejpam-2650	76	10	direction	direction	NOUN
ejpam-2650	76	11	.	.	PUNCT
ejpam-2650	77	1	an	an	DET
ejpam-2650	77	2	inductive	inductive	ADJ
ejpam-2650	77	3	algebraic	algebraic	ADJ
ejpam-2650	77	4	construction	construction	NOUN
ejpam-2650	77	5	of	of	ADP
ejpam-2650	77	6	a	a	DET
ejpam-2650	77	7	distance	distance	NOUN
ejpam-2650	77	8	preserving	preserve	VERB
ejpam-2650	77	9	gray	gray	ADJ
ejpam-2650	77	10	map	map	NOUN
ejpam-2650	77	11	was	be	AUX
ejpam-2650	77	12	given	give	VERB
ejpam-2650	77	13	by	by	ADP
ejpam-2650	77	14	yildiz	yildiz	NOUN
ejpam-2650	77	15	from	from	ADP
ejpam-2650	77	16	galois	galois	PROPN
ejpam-2650	77	17	rings	ring	NOUN
ejpam-2650	77	18	with	with	ADP
ejpam-2650	77	19	the	the	DET
ejpam-2650	77	20	homogeneous	homogeneous	ADJ
ejpam-2650	77	21	distance	distance	NOUN
ejpam-2650	77	22	to	to	ADP
ejpam-2650	77	23	the	the	DET
ejpam-2650	77	24	field	field	NOUN
ejpam-2650	77	25	of	of	ADP
ejpam-2650	77	26	prime	prime	ADJ
ejpam-2650	77	27	size	size	NOUN
ejpam-2650	77	28	with	with	ADP
ejpam-2650	77	29	the	the	DET
ejpam-2650	77	30	hamming	hamming	NOUN
ejpam-2650	77	31	distance	distance	NOUN
ejpam-2650	77	32	in	in	ADP
ejpam-2650	77	33	[	[	X
ejpam-2650	77	34	17	17	NUM
ejpam-2650	77	35	]	]	PUNCT
ejpam-2650	77	36	as	as	ADV
ejpam-2650	77	37	well	well	ADV
ejpam-2650	77	38	as	as	ADP
ejpam-2650	77	39	a	a	DET
ejpam-2650	77	40	combinatorial	combinatorial	ADJ
ejpam-2650	77	41	construction	construction	NOUN
ejpam-2650	77	42	b.	b.	PROPN
ejpam-2650	77	43	yildiz	yildiz	PROPN
ejpam-2650	77	44	,	,	PUNCT
ejpam-2650	77	45	n.	n.	PROPN
ejpam-2650	77	46	tufekci	tufekci	PROPN
ejpam-2650	77	47	/	/	SYM
ejpam-2650	77	48	eur	eur	PROPN
ejpam-2650	77	49	.	.	PUNCT
ejpam-2650	78	1	j.	j.	PROPN
ejpam-2650	78	2	pure	pure	PROPN
ejpam-2650	78	3	appl	appl	PROPN
ejpam-2650	78	4	.	.	PROPN
ejpam-2650	78	5	math	math	PROPN
ejpam-2650	78	6	,	,	PUNCT
ejpam-2650	78	7	10	10	NUM
ejpam-2650	78	8	(	(	PUNCT
ejpam-2650	78	9	5	5	NUM
ejpam-2650	78	10	)	)	PUNCT
ejpam-2650	78	11	(	(	PUNCT
ejpam-2650	78	12	2017	2017	NUM
ejpam-2650	78	13	)	)	PUNCT
ejpam-2650	78	14	,	,	PUNCT
ejpam-2650	78	15	1112	1112	NUM
ejpam-2650	78	16	-	-	SYM
ejpam-2650	78	17	1123	1123	NUM
ejpam-2650	78	18	1116	1116	NUM
ejpam-2650	78	19	of	of	ADP
ejpam-2650	78	20	the	the	DET
ejpam-2650	78	21	gray	gray	ADJ
ejpam-2650	78	22	map	map	NOUN
ejpam-2650	78	23	for	for	ADP
ejpam-2650	78	24	galois	galois	PROPN
ejpam-2650	78	25	rings	ring	NOUN
ejpam-2650	78	26	by	by	ADP
ejpam-2650	78	27	using	use	VERB
ejpam-2650	78	28	affine	affine	NOUN
ejpam-2650	78	29	geometries	geometry	NOUN
ejpam-2650	78	30	in	in	ADP
ejpam-2650	78	31	[	[	X
ejpam-2650	78	32	16	16	NUM
ejpam-2650	78	33	]	]	PUNCT
ejpam-2650	78	34	.	.	PUNCT
ejpam-2650	79	1	later	later	ADV
ejpam-2650	79	2	,	,	PUNCT
ejpam-2650	79	3	projective	projective	PROPN
ejpam-2650	79	4	geometries	geometry	NOUN
ejpam-2650	79	5	pgn(q	pgn(q	NOUN
ejpam-2650	79	6	)	)	PUNCT
ejpam-2650	79	7	were	be	AUX
ejpam-2650	79	8	used	use	VERB
ejpam-2650	79	9	to	to	PART
ejpam-2650	79	10	construct	construct	VERB
ejpam-2650	79	11	the	the	DET
ejpam-2650	79	12	gray	gray	ADJ
ejpam-2650	79	13	map	map	NOUN
ejpam-2650	79	14	for	for	ADP
ejpam-2650	79	15	linear	linear	PROPN
ejpam-2650	79	16	codes	code	NOUN
ejpam-2650	79	17	over	over	ADP
ejpam-2650	79	18	a	a	DET
ejpam-2650	79	19	family	family	NOUN
ejpam-2650	79	20	of	of	ADP
ejpam-2650	79	21	frobenius	frobenius	ADJ
ejpam-2650	79	22	rings	ring	NOUN
ejpam-2650	79	23	in	in	ADP
ejpam-2650	79	24	[	[	X
ejpam-2650	79	25	11	11	NUM
ejpam-2650	79	26	]	]	PUNCT
ejpam-2650	79	27	.	.	PUNCT
ejpam-2650	80	1	considering	consider	VERB
ejpam-2650	80	2	the	the	DET
ejpam-2650	80	3	hyperplanes	hyperplane	NOUN
ejpam-2650	80	4	and	and	CCONJ
ejpam-2650	80	5	projective	projective	ADJ
ejpam-2650	80	6	spaces	space	NOUN
ejpam-2650	80	7	,	,	PUNCT
ejpam-2650	80	8	the	the	DET
ejpam-2650	80	9	work	work	NOUN
ejpam-2650	80	10	in	in	ADP
ejpam-2650	80	11	[	[	X
ejpam-2650	80	12	11	11	NUM
ejpam-2650	80	13	]	]	PUNCT
ejpam-2650	80	14	suggests	suggest	VERB
ejpam-2650	80	15	the	the	DET
ejpam-2650	80	16	use	use	NOUN
ejpam-2650	80	17	of	of	ADP
ejpam-2650	80	18	the	the	DET
ejpam-2650	80	19	projective	projective	ADJ
ejpam-2650	80	20	geometry	geometry	NOUN
ejpam-2650	80	21	pgkm−1(f2	pgkm−1(f2	NOUN
ejpam-2650	80	22	)	)	PUNCT
ejpam-2650	80	23	.	.	PUNCT
ejpam-2650	81	1	this	this	PRON
ejpam-2650	81	2	requires	require	VERB
ejpam-2650	81	3	the	the	DET
ejpam-2650	81	4	s	s	NOUN
ejpam-2650	81	5	to	to	PART
ejpam-2650	81	6	be	be	AUX
ejpam-2650	81	7	2km−1	2km−1	PROPN
ejpam-2650	81	8	.	.	PUNCT
ejpam-2650	82	1	however	however	ADV
ejpam-2650	82	2	,	,	PUNCT
ejpam-2650	82	3	as	as	SCONJ
ejpam-2650	82	4	was	be	AUX
ejpam-2650	82	5	later	later	ADV
ejpam-2650	82	6	done	do	VERB
ejpam-2650	82	7	in	in	ADP
ejpam-2650	82	8	[	[	X
ejpam-2650	82	9	15	15	NUM
ejpam-2650	82	10	]	]	PUNCT
ejpam-2650	82	11	,	,	PUNCT
ejpam-2650	82	12	the	the	DET
ejpam-2650	82	13	first	first	ADJ
ejpam-2650	82	14	order	order	NOUN
ejpam-2650	82	15	reed	reed	NOUN
ejpam-2650	82	16	-	-	PUNCT
ejpam-2650	82	17	muller	muller	NOUN
ejpam-2650	82	18	codes	code	NOUN
ejpam-2650	82	19	seem	seem	VERB
ejpam-2650	82	20	to	to	PART
ejpam-2650	82	21	give	give	VERB
ejpam-2650	82	22	us	we	PRON
ejpam-2650	82	23	a	a	DET
ejpam-2650	82	24	more	more	ADV
ejpam-2650	82	25	constructive	constructive	ADJ
ejpam-2650	82	26	method	method	NOUN
ejpam-2650	82	27	of	of	ADP
ejpam-2650	82	28	finding	find	VERB
ejpam-2650	82	29	this	this	DET
ejpam-2650	82	30	map	map	NOUN
ejpam-2650	82	31	.	.	PUNCT
ejpam-2650	83	1	we	we	PRON
ejpam-2650	83	2	recall	recall	VERB
ejpam-2650	83	3	that	that	SCONJ
ejpam-2650	83	4	the	the	DET
ejpam-2650	83	5	first	first	ADJ
ejpam-2650	83	6	order	order	NOUN
ejpam-2650	83	7	reed	reed	NOUN
ejpam-2650	83	8	-	-	PUNCT
ejpam-2650	83	9	muller	muller	NOUN
ejpam-2650	83	10	codes	code	NOUN
ejpam-2650	83	11	rm(1,m	rm(1,m	ADJ
ejpam-2650	83	12	)	)	PUNCT
ejpam-2650	83	13	are	be	AUX
ejpam-2650	83	14	a	a	DET
ejpam-2650	83	15	family	family	NOUN
ejpam-2650	83	16	of	of	ADP
ejpam-2650	83	17	binary	binary	PROPN
ejpam-2650	83	18	linear	linear	PROPN
ejpam-2650	83	19	codes	code	NOUN
ejpam-2650	83	20	of	of	ADP
ejpam-2650	83	21	parameters	parameter	NOUN
ejpam-2650	83	22	[	[	X
ejpam-2650	83	23	2m	2m	NUM
ejpam-2650	83	24	,	,	PUNCT
ejpam-2650	83	25	m	m	VERB
ejpam-2650	83	26	+	+	NOUN
ejpam-2650	83	27	1	1	NUM
ejpam-2650	83	28	,	,	PUNCT
ejpam-2650	83	29	2m−1	2m−1	NUM
ejpam-2650	83	30	]	]	PUNCT
ejpam-2650	83	31	,	,	PUNCT
ejpam-2650	83	32	for	for	ADP
ejpam-2650	83	33	each	each	DET
ejpam-2650	83	34	positive	positive	ADJ
ejpam-2650	83	35	integer	integer	NOUN
ejpam-2650	83	36	m.	m.	NOUN
ejpam-2650	83	37	the	the	DET
ejpam-2650	83	38	important	important	ADJ
ejpam-2650	83	39	property	property	NOUN
ejpam-2650	83	40	of	of	ADP
ejpam-2650	83	41	the	the	DET
ejpam-2650	83	42	first	first	ADJ
ejpam-2650	83	43	order	order	NOUN
ejpam-2650	83	44	reed	reed	NOUN
ejpam-2650	83	45	-	-	PUNCT
ejpam-2650	83	46	muller	muller	NOUN
ejpam-2650	83	47	codes	code	NOUN
ejpam-2650	83	48	is	be	AUX
ejpam-2650	83	49	that	that	SCONJ
ejpam-2650	83	50	there	there	PRON
ejpam-2650	83	51	is	be	VERB
ejpam-2650	83	52	one	one	NUM
ejpam-2650	83	53	codeword	codeword	NOUN
ejpam-2650	83	54	with	with	ADP
ejpam-2650	83	55	weight	weight	NOUN
ejpam-2650	83	56	2	2	NUM
ejpam-2650	83	57	m	m	NOUN
ejpam-2650	83	58	and	and	CCONJ
ejpam-2650	83	59	all	all	DET
ejpam-2650	83	60	the	the	DET
ejpam-2650	83	61	other	other	ADJ
ejpam-2650	83	62	non	non	ADJ
ejpam-2650	83	63	-	-	ADJ
ejpam-2650	83	64	zero	zero	ADJ
ejpam-2650	83	65	codewords	codeword	NOUN
ejpam-2650	83	66	have	have	VERB
ejpam-2650	83	67	weight	weight	NOUN
ejpam-2650	83	68	2m−1	2m−1	NUM
ejpam-2650	83	69	.	.	PUNCT
ejpam-2650	84	1	because	because	SCONJ
ejpam-2650	84	2	of	of	ADP
ejpam-2650	84	3	the	the	DET
ejpam-2650	84	4	structure	structure	NOUN
ejpam-2650	84	5	of	of	ADP
ejpam-2650	84	6	the	the	DET
ejpam-2650	84	7	homogeneous	homogeneous	ADJ
ejpam-2650	84	8	weight	weight	NOUN
ejpam-2650	84	9	,	,	PUNCT
ejpam-2650	84	10	it	it	PRON
ejpam-2650	84	11	is	be	AUX
ejpam-2650	84	12	clear	clear	ADJ
ejpam-2650	84	13	that	that	SCONJ
ejpam-2650	84	14	first	first	ADJ
ejpam-2650	84	15	order	order	NOUN
ejpam-2650	84	16	reed	reed	NOUN
ejpam-2650	84	17	-	-	PUNCT
ejpam-2650	84	18	muller	muller	NOUN
ejpam-2650	84	19	codes	code	NOUN
ejpam-2650	84	20	can	can	AUX
ejpam-2650	84	21	be	be	AUX
ejpam-2650	84	22	used	use	VERB
ejpam-2650	84	23	to	to	PART
ejpam-2650	84	24	construct	construct	VERB
ejpam-2650	84	25	the	the	DET
ejpam-2650	84	26	gray	gray	ADJ
ejpam-2650	84	27	map	map	NOUN
ejpam-2650	84	28	.	.	PUNCT
ejpam-2650	85	1	since	since	SCONJ
ejpam-2650	85	2	|rk	|rk	NUM
ejpam-2650	85	3	,	,	PUNCT
ejpam-2650	85	4	m|	m|	NOUN
ejpam-2650	85	5	=	=	SYM
ejpam-2650	85	6	2	2	NUM
ejpam-2650	85	7	km	km	NOUN
ejpam-2650	85	8	,	,	PUNCT
ejpam-2650	85	9	we	we	PRON
ejpam-2650	85	10	clearly	clearly	ADV
ejpam-2650	85	11	need	need	VERB
ejpam-2650	85	12	rm(1	rm(1	NOUN
ejpam-2650	85	13	,	,	PUNCT
ejpam-2650	85	14	s	s	NOUN
ejpam-2650	85	15	)	)	PUNCT
ejpam-2650	85	16	where	where	SCONJ
ejpam-2650	85	17	s	s	VERB
ejpam-2650	85	18	+	+	CCONJ
ejpam-2650	85	19	1	1	NUM
ejpam-2650	85	20	=	=	SYM
ejpam-2650	85	21	km	km	NOUN
ejpam-2650	85	22	.	.	PUNCT
ejpam-2650	86	1	thus	thus	ADV
ejpam-2650	86	2	,	,	PUNCT
ejpam-2650	86	3	to	to	PART
ejpam-2650	86	4	define	define	VERB
ejpam-2650	86	5	a	a	DET
ejpam-2650	86	6	distance	distance	NOUN
ejpam-2650	86	7	preserving	preserve	VERB
ejpam-2650	86	8	gray	gray	ADJ
ejpam-2650	86	9	map	map	NOUN
ejpam-2650	86	10	for	for	ADP
ejpam-2650	86	11	the	the	DET
ejpam-2650	86	12	homogeneous	homogeneous	ADJ
ejpam-2650	86	13	weight	weight	NOUN
ejpam-2650	86	14	on	on	ADP
ejpam-2650	86	15	rk	rk	NOUN
ejpam-2650	86	16	,	,	PUNCT
ejpam-2650	86	17	m	m	AUX
ejpam-2650	86	18	we	we	PRON
ejpam-2650	86	19	use	use	VERB
ejpam-2650	86	20	the	the	DET
ejpam-2650	86	21	first	first	ADJ
ejpam-2650	86	22	order	order	NOUN
ejpam-2650	86	23	reed	reed	NOUN
ejpam-2650	86	24	-	-	PUNCT
ejpam-2650	86	25	muller	muller	NOUN
ejpam-2650	86	26	codes	code	NOUN
ejpam-2650	86	27	rm(1	rm(1	NOUN
ejpam-2650	86	28	,	,	PUNCT
ejpam-2650	86	29	km−1	km−1	PROPN
ejpam-2650	86	30	)	)	PUNCT
ejpam-2650	86	31	,	,	PUNCT
ejpam-2650	86	32	of	of	ADP
ejpam-2650	86	33	length	length	NOUN
ejpam-2650	86	34	2km−1	2km−1	PROPN
ejpam-2650	86	35	.	.	PUNCT
ejpam-2650	87	1	this	this	PRON
ejpam-2650	87	2	coincides	coincide	VERB
ejpam-2650	87	3	with	with	ADP
ejpam-2650	87	4	length	length	NOUN
ejpam-2650	87	5	of	of	ADP
ejpam-2650	87	6	the	the	DET
ejpam-2650	87	7	image	image	NOUN
ejpam-2650	87	8	suggested	suggest	VERB
ejpam-2650	87	9	in	in	ADP
ejpam-2650	87	10	[	[	X
ejpam-2650	87	11	11	11	NUM
ejpam-2650	87	12	]	]	PUNCT
ejpam-2650	87	13	,	,	PUNCT
ejpam-2650	87	14	which	which	PRON
ejpam-2650	87	15	adds	add	VERB
ejpam-2650	87	16	an	an	DET
ejpam-2650	87	17	added	add	VERB
ejpam-2650	87	18	motivation	motivation	NOUN
ejpam-2650	87	19	for	for	ADP
ejpam-2650	87	20	the	the	DET
ejpam-2650	87	21	choice	choice	NOUN
ejpam-2650	87	22	of	of	ADP
ejpam-2650	87	23	γ	γ	NOUN
ejpam-2650	87	24	for	for	ADP
ejpam-2650	87	25	us	we	PRON
ejpam-2650	87	26	.	.	PUNCT
ejpam-2650	88	1	thus	thus	ADV
ejpam-2650	88	2	we	we	PRON
ejpam-2650	88	3	choose	choose	VERB
ejpam-2650	88	4	γ	γ	X
ejpam-2650	88	5	=	=	SYM
ejpam-2650	88	6	2km−2	2km−2	PROPN
ejpam-2650	88	7	.	.	PUNCT
ejpam-2650	89	1	this	this	PRON
ejpam-2650	89	2	means	mean	VERB
ejpam-2650	89	3	that	that	SCONJ
ejpam-2650	89	4	for	for	ADP
ejpam-2650	89	5	us	we	PRON
ejpam-2650	89	6	,	,	PUNCT
ejpam-2650	89	7	the	the	DET
ejpam-2650	89	8	homogeneous	homogeneous	ADJ
ejpam-2650	89	9	weight	weight	NOUN
ejpam-2650	89	10	will	will	AUX
ejpam-2650	89	11	have	have	VERB
ejpam-2650	89	12	the	the	DET
ejpam-2650	89	13	following	follow	VERB
ejpam-2650	89	14	form	form	NOUN
ejpam-2650	89	15	:	:	PUNCT
ejpam-2650	89	16	ωhom(x	ωhom(x	VERB
ejpam-2650	89	17	)	)	PUNCT
ejpam-2650	89	18			PUNCT
ejpam-2650	89	19	0	0	PUNCT
ejpam-2650	90	1	if	if	SCONJ
ejpam-2650	90	2	x	x	X
ejpam-2650	90	3	=	=	SYM
ejpam-2650	90	4	0	0	NUM
ejpam-2650	90	5	,	,	PUNCT
ejpam-2650	90	6	2km−1	2km−1	NOUN
ejpam-2650	90	7	if	if	SCONJ
ejpam-2650	90	8	x	x	PROPN
ejpam-2650	90	9	=	=	SYM
ejpam-2650	90	10	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	90	11	,	,	PUNCT
ejpam-2650	90	12	2km−2	2km−2	PROPN
ejpam-2650	90	13	otherwise	otherwise	ADV
ejpam-2650	90	14	.	.	PUNCT
ejpam-2650	91	1	now	now	ADV
ejpam-2650	91	2	,	,	PUNCT
ejpam-2650	91	3	in	in	ADP
ejpam-2650	91	4	order	order	NOUN
ejpam-2650	91	5	to	to	PART
ejpam-2650	91	6	define	define	VERB
ejpam-2650	91	7	the	the	DET
ejpam-2650	91	8	gray	gray	ADJ
ejpam-2650	91	9	-	-	PUNCT
ejpam-2650	91	10	homogeneous	homogeneous	ADJ
ejpam-2650	91	11	map	map	NOUN
ejpam-2650	91	12	on	on	ADP
ejpam-2650	91	13	rk	rk	NOUN
ejpam-2650	91	14	,	,	PUNCT
ejpam-2650	91	15	m	m	PRON
ejpam-2650	91	16	,	,	PUNCT
ejpam-2650	91	17	we	we	PRON
ejpam-2650	91	18	first	first	ADV
ejpam-2650	91	19	note	note	VERB
ejpam-2650	91	20	that	that	SCONJ
ejpam-2650	91	21	rk	rk	NOUN
ejpam-2650	91	22	,	,	PUNCT
ejpam-2650	91	23	m	m	VERB
ejpam-2650	91	24	can	can	AUX
ejpam-2650	91	25	be	be	AUX
ejpam-2650	91	26	viewed	view	VERB
ejpam-2650	91	27	as	as	ADP
ejpam-2650	91	28	an	an	DET
ejpam-2650	91	29	f2	f2	ADJ
ejpam-2650	91	30	-	-	PUNCT
ejpam-2650	91	31	vector	vector	NOUN
ejpam-2650	91	32	space	space	NOUN
ejpam-2650	91	33	with	with	ADP
ejpam-2650	91	34	a	a	DET
ejpam-2650	91	35	basis	basis	NOUN
ejpam-2650	91	36	β	β	X
ejpam-2650	91	37	=	=	PUNCT
ejpam-2650	91	38	{	{	PUNCT
ejpam-2650	91	39	1	1	NUM
ejpam-2650	91	40	,	,	PUNCT
ejpam-2650	91	41	u	u	NOUN
ejpam-2650	91	42	,	,	PUNCT
ejpam-2650	91	43	.	.	PUNCT
ejpam-2650	91	44	.	.	PUNCT
ejpam-2650	92	1	.	.	PUNCT
ejpam-2650	93	1	,	,	PUNCT
ejpam-2650	93	2	uk−1	uk−1	PROPN
ejpam-2650	93	3	,	,	PUNCT
ejpam-2650	93	4	v	v	NOUN
ejpam-2650	93	5	,	,	PUNCT
ejpam-2650	93	6	.	.	PUNCT
ejpam-2650	93	7	.	.	PUNCT
ejpam-2650	94	1	.	.	PUNCT
ejpam-2650	95	1	,	,	PUNCT
ejpam-2650	95	2	vm−1	vm−1	NOUN
ejpam-2650	95	3	,	,	PUNCT
ejpam-2650	95	4	uv	uv	NOUN
ejpam-2650	95	5	,	,	PUNCT
ejpam-2650	95	6	.	.	PUNCT
ejpam-2650	95	7	.	.	PUNCT
ejpam-2650	96	1	.	.	PUNCT
ejpam-2650	97	1	,	,	PUNCT
ejpam-2650	97	2	uk−1vm−1	uk−1vm−1	PROPN
ejpam-2650	97	3	}	}	PUNCT
ejpam-2650	97	4	.	.	PUNCT
ejpam-2650	98	1	rm(1	rm(1	NOUN
ejpam-2650	98	2	,	,	PUNCT
ejpam-2650	98	3	2km−	2km−	NUM
ejpam-2650	98	4	1	1	NUM
ejpam-2650	98	5	)	)	PUNCT
ejpam-2650	98	6	has	have	VERB
ejpam-2650	98	7	exactly	exactly	ADV
ejpam-2650	98	8	km	km	NOUN
ejpam-2650	98	9	basis	basis	NOUN
ejpam-2650	98	10	elements	element	NOUN
ejpam-2650	98	11	,	,	PUNCT
ejpam-2650	98	12	which	which	PRON
ejpam-2650	98	13	are	be	AUX
ejpam-2650	98	14	binary	binary	ADJ
ejpam-2650	98	15	vectors	vector	NOUN
ejpam-2650	98	16	of	of	ADP
ejpam-2650	98	17	length	length	NOUN
ejpam-2650	98	18	2km−1	2km−1	PROPN
ejpam-2650	98	19	,	,	PUNCT
ejpam-2650	98	20	including	include	VERB
ejpam-2650	98	21	(	(	PUNCT
ejpam-2650	98	22	1	1	NUM
ejpam-2650	98	23	,	,	PUNCT
ejpam-2650	98	24	1	1	NUM
ejpam-2650	98	25	,	,	PUNCT
ejpam-2650	98	26	.	.	PUNCT
ejpam-2650	98	27	.	.	PUNCT
ejpam-2650	99	1	.	.	PUNCT
ejpam-2650	100	1	,	,	PUNCT
ejpam-2650	100	2	1	1	NUM
ejpam-2650	100	3	)	)	PUNCT
ejpam-2650	100	4	.	.	PUNCT
ejpam-2650	101	1	so	so	ADV
ejpam-2650	101	2	,	,	PUNCT
ejpam-2650	101	3	we	we	PRON
ejpam-2650	101	4	first	first	ADV
ejpam-2650	101	5	let	let	VERB
ejpam-2650	101	6	φhom	φhom	ADP
ejpam-2650	101	7	map	map	VERB
ejpam-2650	101	8	elements	element	NOUN
ejpam-2650	101	9	of	of	ADP
ejpam-2650	101	10	the	the	DET
ejpam-2650	101	11	minimal	minimal	ADJ
ejpam-2650	101	12	ideal	ideal	NOUN
ejpam-2650	101	13	iuk−1vm−1	iuk−1vm−1	PROPN
ejpam-2650	101	14	to	to	ADP
ejpam-2650	101	15	the	the	DET
ejpam-2650	101	16	two	two	NUM
ejpam-2650	101	17	elements	element	NOUN
ejpam-2650	101	18	of	of	ADP
ejpam-2650	101	19	rm(1	rm(1	NOUN
ejpam-2650	101	20	,	,	PUNCT
ejpam-2650	101	21	km	km	NOUN
ejpam-2650	101	22	−	−	NOUN
ejpam-2650	101	23	1	1	NUM
ejpam-2650	101	24	)	)	PUNCT
ejpam-2650	101	25	,	,	PUNCT
ejpam-2650	101	26	given	give	VERB
ejpam-2650	101	27	by	by	ADP
ejpam-2650	101	28	(	(	PUNCT
ejpam-2650	101	29	0	0	NUM
ejpam-2650	101	30	.	.	PUNCT
ejpam-2650	101	31	.	.	PUNCT
ejpam-2650	102	1	.	.	PUNCT
ejpam-2650	103	1	0	0	X
ejpam-2650	103	2	)	)	PUNCT
ejpam-2650	103	3	and	and	CCONJ
ejpam-2650	103	4	(	(	PUNCT
ejpam-2650	103	5	1	1	NUM
ejpam-2650	103	6	.	.	PUNCT
ejpam-2650	103	7	.	.	PUNCT
ejpam-2650	103	8	.	.	PUNCT
ejpam-2650	104	1	1	1	NUM
ejpam-2650	104	2	)	)	PUNCT
ejpam-2650	104	3	,	,	PUNCT
ejpam-2650	104	4	respectively	respectively	ADV
ejpam-2650	104	5	.	.	PUNCT
ejpam-2650	105	1	the	the	DET
ejpam-2650	105	2	remaining	remain	VERB
ejpam-2650	105	3	elements	element	NOUN
ejpam-2650	105	4	of	of	ADP
ejpam-2650	105	5	the	the	DET
ejpam-2650	105	6	basis	basis	NOUN
ejpam-2650	105	7	are	be	AUX
ejpam-2650	105	8	mapped	map	VERB
ejpam-2650	105	9	to	to	ADP
ejpam-2650	105	10	basic	basic	ADJ
ejpam-2650	105	11	generators	generator	NOUN
ejpam-2650	105	12	of	of	ADP
ejpam-2650	105	13	rm(1	rm(1	NOUN
ejpam-2650	105	14	,	,	PUNCT
ejpam-2650	105	15	km−	km−	PROPN
ejpam-2650	105	16	1	1	NUM
ejpam-2650	105	17	)	)	PUNCT
ejpam-2650	105	18	except	except	SCONJ
ejpam-2650	105	19	(	(	PUNCT
ejpam-2650	105	20	1	1	NUM
ejpam-2650	105	21	.	.	PUNCT
ejpam-2650	105	22	.	.	PUNCT
ejpam-2650	106	1	.	.	PUNCT
ejpam-2650	107	1	1	1	NUM
ejpam-2650	107	2	)	)	PUNCT
ejpam-2650	107	3	.	.	PUNCT
ejpam-2650	108	1	taking	take	VERB
ejpam-2650	108	2	all	all	DET
ejpam-2650	108	3	the	the	DET
ejpam-2650	108	4	possible	possible	ADJ
ejpam-2650	108	5	linear	linear	ADJ
ejpam-2650	108	6	combinations	combination	NOUN
ejpam-2650	108	7	,	,	PUNCT
ejpam-2650	108	8	we	we	PRON
ejpam-2650	108	9	extend	extend	VERB
ejpam-2650	108	10	the	the	DET
ejpam-2650	108	11	map	map	NOUN
ejpam-2650	108	12	φhom	φhom	ADV
ejpam-2650	108	13	to	to	ADP
ejpam-2650	108	14	rk	rk	PRON
ejpam-2650	108	15	,	,	PUNCT
ejpam-2650	108	16	m.	m.	NOUN
ejpam-2650	108	17	the	the	DET
ejpam-2650	108	18	map	map	NOUN
ejpam-2650	108	19	is	be	AUX
ejpam-2650	108	20	then	then	ADV
ejpam-2650	108	21	extended	extend	VERB
ejpam-2650	108	22	in	in	ADP
ejpam-2650	108	23	the	the	DET
ejpam-2650	108	24	natural	natural	ADJ
ejpam-2650	108	25	way	way	NOUN
ejpam-2650	108	26	rnk	rnk	X
ejpam-2650	108	27	,	,	PUNCT
ejpam-2650	108	28	m	m	VERB
ejpam-2650	108	29	:	:	PUNCT
ejpam-2650	108	30	φhom	φhom	ADV
ejpam-2650	108	31	:	:	PUNCT
ejpam-2650	108	32	(	(	PUNCT
ejpam-2650	108	33	rk	rk	NOUN
ejpam-2650	108	34	,	,	PUNCT
ejpam-2650	108	35	m)n	m)n	X
ejpam-2650	108	36	→	→	SYM
ejpam-2650	108	37	f(2km−1)n	f(2km−1)n	PROPN
ejpam-2650	108	38	2	2	NUM
ejpam-2650	108	39	(	(	PUNCT
ejpam-2650	108	40	c1	c1	PROPN
ejpam-2650	108	41	,	,	PUNCT
ejpam-2650	108	42	c2	c2	PROPN
ejpam-2650	108	43	,	,	PUNCT
ejpam-2650	108	44	.	.	PUNCT
ejpam-2650	108	45	.	.	PUNCT
ejpam-2650	109	1	.	.	PUNCT
ejpam-2650	110	1	,	,	PUNCT
ejpam-2650	110	2	cn	cn	PROPN
ejpam-2650	110	3	)	)	PUNCT
ejpam-2650	110	4	7→	7→	PROPN
ejpam-2650	110	5	(	(	PUNCT
ejpam-2650	110	6	φhom(c1	φhom(c1	NOUN
ejpam-2650	110	7	)	)	PUNCT
ejpam-2650	110	8	,	,	PUNCT
ejpam-2650	110	9	φhom(c2	φhom(c2	NOUN
ejpam-2650	110	10	)	)	PUNCT
ejpam-2650	110	11	,	,	PUNCT
ejpam-2650	110	12	.	.	PUNCT
ejpam-2650	110	13	.	.	PUNCT
ejpam-2650	111	1	.	.	PUNCT
ejpam-2650	112	1	,	,	PUNCT
ejpam-2650	112	2	φhom(cn	φhom(cn	PROPN
ejpam-2650	112	3	)	)	PUNCT
ejpam-2650	112	4	)	)	PUNCT
ejpam-2650	112	5	.	.	PUNCT
ejpam-2650	113	1	(	(	PUNCT
ejpam-2650	113	2	4	4	X
ejpam-2650	113	3	)	)	PUNCT
ejpam-2650	113	4	the	the	DET
ejpam-2650	113	5	properties	property	NOUN
ejpam-2650	113	6	of	of	ADP
ejpam-2650	113	7	the	the	DET
ejpam-2650	113	8	reed	reed	NOUN
ejpam-2650	113	9	-	-	PUNCT
ejpam-2650	113	10	muller	muller	PROPN
ejpam-2650	113	11	codes	code	NOUN
ejpam-2650	113	12	then	then	ADV
ejpam-2650	113	13	result	result	VERB
ejpam-2650	113	14	in	in	ADP
ejpam-2650	113	15	the	the	DET
ejpam-2650	113	16	following	following	NOUN
ejpam-2650	113	17	:	:	PUNCT
ejpam-2650	113	18	theorem	theorem	NOUN
ejpam-2650	113	19	2	2	NUM
ejpam-2650	113	20	.	.	NUM
ejpam-2650	113	21	φhom	φhom	PROPN
ejpam-2650	113	22	is	be	AUX
ejpam-2650	113	23	a	a	DET
ejpam-2650	113	24	distance	distance	NOUN
ejpam-2650	113	25	preserving	preserve	VERB
ejpam-2650	113	26	isometry	isometry	NOUN
ejpam-2650	113	27	from	from	ADP
ejpam-2650	113	28	(	(	PUNCT
ejpam-2650	113	29	rnk	rnk	X
ejpam-2650	113	30	,	,	PUNCT
ejpam-2650	113	31	m	m	PROPN
ejpam-2650	113	32	,	,	PUNCT
ejpam-2650	113	33	homogeneous	homogeneous	ADJ
ejpam-2650	113	34	distance	distance	NOUN
ejpam-2650	113	35	)	)	PUNCT
ejpam-2650	113	36	to	to	ADP
ejpam-2650	113	37	(	(	PUNCT
ejpam-2650	113	38	f2km−1n	f2km−1n	NOUN
ejpam-2650	113	39	2	2	NUM
ejpam-2650	113	40	,	,	PUNCT
ejpam-2650	113	41	hamming	hamming	NOUN
ejpam-2650	113	42	distance	distance	NOUN
ejpam-2650	113	43	)	)	PUNCT
ejpam-2650	113	44	.	.	PUNCT
ejpam-2650	114	1	thus	thus	ADV
ejpam-2650	114	2	if	if	SCONJ
ejpam-2650	114	3	c	c	PROPN
ejpam-2650	114	4	is	be	AUX
ejpam-2650	114	5	a	a	DET
ejpam-2650	114	6	linear	linear	ADJ
ejpam-2650	114	7	code	code	NOUN
ejpam-2650	114	8	over	over	ADP
ejpam-2650	114	9	rk	rk	PROPN
ejpam-2650	114	10	,	,	PUNCT
ejpam-2650	114	11	m	m	NOUN
ejpam-2650	114	12	of	of	ADP
ejpam-2650	114	13	length	length	NOUN
ejpam-2650	114	14	n	n	NOUN
ejpam-2650	114	15	and	and	CCONJ
ejpam-2650	114	16	minimum	minimum	ADJ
ejpam-2650	114	17	homogeneous	homogeneous	ADJ
ejpam-2650	114	18	weight	weight	NOUN
ejpam-2650	114	19	d	d	NOUN
ejpam-2650	114	20	,	,	PUNCT
ejpam-2650	114	21	then	then	ADV
ejpam-2650	114	22	φhom(c	φhom(c	NUM
ejpam-2650	114	23	)	)	PUNCT
ejpam-2650	114	24	is	be	AUX
ejpam-2650	114	25	a	a	DET
ejpam-2650	114	26	binary	binary	ADJ
ejpam-2650	114	27	linear	linear	PROPN
ejpam-2650	114	28	code	code	NOUN
ejpam-2650	114	29	of	of	ADP
ejpam-2650	114	30	length	length	NOUN
ejpam-2650	114	31	2km−1n	2km−1n	ADV
ejpam-2650	114	32	,	,	PUNCT
ejpam-2650	114	33	and	and	CCONJ
ejpam-2650	114	34	minimum	minimum	ADJ
ejpam-2650	114	35	hamming	hamming	NOUN
ejpam-2650	114	36	weight	weight	NOUN
ejpam-2650	114	37	d.	d.	NOUN
ejpam-2650	114	38	moreover	moreover	ADV
ejpam-2650	114	39	,	,	PUNCT
ejpam-2650	114	40	the	the	DET
ejpam-2650	114	41	homogeneous	homogeneous	ADJ
ejpam-2650	114	42	weight	weight	NOUN
ejpam-2650	114	43	distribution	distribution	NOUN
ejpam-2650	114	44	of	of	ADP
ejpam-2650	114	45	c	c	PROPN
ejpam-2650	114	46	is	be	AUX
ejpam-2650	114	47	the	the	DET
ejpam-2650	114	48	same	same	ADJ
ejpam-2650	114	49	as	as	ADP
ejpam-2650	114	50	the	the	DET
ejpam-2650	114	51	hamming	hamming	NOUN
ejpam-2650	114	52	weight	weight	NOUN
ejpam-2650	114	53	distribution	distribution	NOUN
ejpam-2650	114	54	of	of	ADP
ejpam-2650	114	55	φhom(c	φhom(c	PROPN
ejpam-2650	114	56	)	)	PUNCT
ejpam-2650	114	57	.	.	PUNCT
ejpam-2650	115	1	b.	b.	PROPN
ejpam-2650	115	2	yildiz	yildiz	PROPN
ejpam-2650	115	3	,	,	PUNCT
ejpam-2650	115	4	n.	n.	PROPN
ejpam-2650	115	5	tufekci	tufekci	PROPN
ejpam-2650	115	6	/	/	SYM
ejpam-2650	115	7	eur	eur	PROPN
ejpam-2650	115	8	.	.	PUNCT
ejpam-2650	116	1	j.	j.	PROPN
ejpam-2650	116	2	pure	pure	PROPN
ejpam-2650	116	3	appl	appl	PROPN
ejpam-2650	116	4	.	.	PROPN
ejpam-2650	116	5	math	math	PROPN
ejpam-2650	116	6	,	,	PUNCT
ejpam-2650	116	7	10	10	NUM
ejpam-2650	116	8	(	(	PUNCT
ejpam-2650	116	9	5	5	NUM
ejpam-2650	116	10	)	)	PUNCT
ejpam-2650	116	11	(	(	PUNCT
ejpam-2650	116	12	2017	2017	NUM
ejpam-2650	116	13	)	)	PUNCT
ejpam-2650	116	14	,	,	PUNCT
ejpam-2650	116	15	1112	1112	NUM
ejpam-2650	116	16	-	-	SYM
ejpam-2650	116	17	1123	1123	NUM
ejpam-2650	116	18	1117	1117	NUM
ejpam-2650	116	19	we	we	PRON
ejpam-2650	116	20	finish	finish	VERB
ejpam-2650	116	21	this	this	DET
ejpam-2650	116	22	section	section	NOUN
ejpam-2650	116	23	with	with	ADP
ejpam-2650	116	24	a	a	DET
ejpam-2650	116	25	few	few	ADJ
ejpam-2650	116	26	examples	example	NOUN
ejpam-2650	116	27	:	:	PUNCT
ejpam-2650	116	28	the	the	DET
ejpam-2650	116	29	homogeneous	homogeneous	ADJ
ejpam-2650	116	30	weight	weight	NOUN
ejpam-2650	116	31	forr2,1	forr2,1	PROPN
ejpam-2650	116	32	=	=	PUNCT
ejpam-2650	117	1	f+uf2	f+uf2	PROPN
ejpam-2650	117	2	coincides	coincide	VERB
ejpam-2650	117	3	with	with	ADP
ejpam-2650	117	4	the	the	DET
ejpam-2650	117	5	lee	lee	PROPN
ejpam-2650	117	6	weight	weight	NOUN
ejpam-2650	117	7	defined	define	VERB
ejpam-2650	117	8	on	on	ADP
ejpam-2650	117	9	f2	f2	PROPN
ejpam-2650	117	10	+	+	CCONJ
ejpam-2650	117	11	uf2	uf2	NOUN
ejpam-2650	117	12	and	and	CCONJ
ejpam-2650	117	13	the	the	DET
ejpam-2650	117	14	gray	gray	ADJ
ejpam-2650	117	15	-	-	PUNCT
ejpam-2650	117	16	homogeneous	homogeneous	ADJ
ejpam-2650	117	17	map	map	NOUN
ejpam-2650	117	18	also	also	ADV
ejpam-2650	117	19	coincides	coincide	VERB
ejpam-2650	117	20	with	with	ADP
ejpam-2650	117	21	the	the	DET
ejpam-2650	117	22	usual	usual	ADJ
ejpam-2650	117	23	gray	gray	ADJ
ejpam-2650	117	24	map	map	NOUN
ejpam-2650	117	25	for	for	ADP
ejpam-2650	117	26	f2	f2	PROPN
ejpam-2650	117	27	+	+	CCONJ
ejpam-2650	117	28	uf2	uf2	NOUN
ejpam-2650	117	29	,	,	PUNCT
ejpam-2650	117	30	that	that	PRON
ejpam-2650	117	31	is	be	AUX
ejpam-2650	117	32	well	well	ADV
ejpam-2650	117	33	-	-	PUNCT
ejpam-2650	117	34	known	know	VERB
ejpam-2650	117	35	in	in	ADP
ejpam-2650	117	36	the	the	DET
ejpam-2650	117	37	literature	literature	NOUN
ejpam-2650	117	38	.	.	PUNCT
ejpam-2650	118	1	let	let	VERB
ejpam-2650	118	2	us	we	PRON
ejpam-2650	118	3	consider	consider	VERB
ejpam-2650	118	4	r3,1	r3,1	PROPN
ejpam-2650	118	5	=	=	SYM
ejpam-2650	118	6	f2	f2	PROPN
ejpam-2650	118	7	+	+	CCONJ
ejpam-2650	118	8	uf2	uf2	NOUN
ejpam-2650	118	9	+	+	CCONJ
ejpam-2650	118	10	u2f2	u2f2	PROPN
ejpam-2650	118	11	.	.	PUNCT
ejpam-2650	119	1	the	the	DET
ejpam-2650	119	2	homogeneous	homogeneous	ADJ
ejpam-2650	119	3	weight	weight	NOUN
ejpam-2650	119	4	then	then	ADV
ejpam-2650	119	5	is	be	AUX
ejpam-2650	119	6	found	find	VERB
ejpam-2650	119	7	to	to	PART
ejpam-2650	119	8	be	be	AUX
ejpam-2650	119	9	ωhom(x	ωhom(x	VERB
ejpam-2650	119	10	)	)	PUNCT
ejpam-2650	119	11			PUNCT
ejpam-2650	119	12	0	0	PUNCT
ejpam-2650	120	1	if	if	SCONJ
ejpam-2650	120	2	x	x	X
ejpam-2650	120	3	=	=	SYM
ejpam-2650	120	4	0	0	NUM
ejpam-2650	120	5	,	,	PUNCT
ejpam-2650	120	6	4	4	NUM
ejpam-2650	120	7	if	if	SCONJ
ejpam-2650	120	8	x	x	X
ejpam-2650	120	9	=	=	SYM
ejpam-2650	120	10	u2	u2	PROPN
ejpam-2650	120	11	,	,	PUNCT
ejpam-2650	120	12	2	2	NUM
ejpam-2650	120	13	otherwise	otherwise	ADV
ejpam-2650	120	14	.	.	PUNCT
ejpam-2650	121	1	the	the	DET
ejpam-2650	121	2	gray	gray	ADJ
ejpam-2650	121	3	-	-	PUNCT
ejpam-2650	121	4	homogeneous	homogeneous	ADJ
ejpam-2650	121	5	map	map	NOUN
ejpam-2650	121	6	will	will	AUX
ejpam-2650	121	7	then	then	ADV
ejpam-2650	121	8	be	be	AUX
ejpam-2650	121	9	given	give	VERB
ejpam-2650	121	10	by	by	ADP
ejpam-2650	121	11	φhom(u2	φhom(u2	NOUN
ejpam-2650	121	12	)	)	PUNCT
ejpam-2650	121	13	=	=	PUNCT
ejpam-2650	121	14	(	(	PUNCT
ejpam-2650	121	15	1	1	NUM
ejpam-2650	121	16	,	,	PUNCT
ejpam-2650	121	17	1	1	NUM
ejpam-2650	121	18	,	,	PUNCT
ejpam-2650	121	19	1	1	NUM
ejpam-2650	121	20	,	,	PUNCT
ejpam-2650	121	21	1	1	NUM
ejpam-2650	121	22	)	)	PUNCT
ejpam-2650	121	23	,	,	PUNCT
ejpam-2650	121	24	φhom(u	φhom(u	VERB
ejpam-2650	121	25	)	)	PUNCT
ejpam-2650	121	26	=	=	SYM
ejpam-2650	121	27	(	(	PUNCT
ejpam-2650	121	28	1	1	NUM
ejpam-2650	121	29	,	,	PUNCT
ejpam-2650	121	30	1	1	NUM
ejpam-2650	121	31	,	,	PUNCT
ejpam-2650	121	32	0	0	NUM
ejpam-2650	121	33	,	,	PUNCT
ejpam-2650	121	34	0	0	NUM
ejpam-2650	121	35	)	)	PUNCT
ejpam-2650	121	36	,	,	PUNCT
ejpam-2650	121	37	φhom(1	φhom(1	NOUN
ejpam-2650	121	38	)	)	PUNCT
ejpam-2650	121	39	=	=	PUNCT
ejpam-2650	121	40	(	(	PUNCT
ejpam-2650	121	41	1	1	NUM
ejpam-2650	121	42	,	,	PUNCT
ejpam-2650	121	43	0	0	NUM
ejpam-2650	121	44	,	,	PUNCT
ejpam-2650	121	45	1	1	NUM
ejpam-2650	121	46	,	,	PUNCT
ejpam-2650	121	47	0	0	NUM
ejpam-2650	121	48	)	)	PUNCT
ejpam-2650	121	49	.	.	PUNCT
ejpam-2650	122	1	the	the	DET
ejpam-2650	122	2	map	map	NOUN
ejpam-2650	122	3	is	be	AUX
ejpam-2650	122	4	then	then	ADV
ejpam-2650	122	5	extended	extend	VERB
ejpam-2650	122	6	to	to	ADP
ejpam-2650	122	7	r3,1	r3,1	PROPN
ejpam-2650	122	8	by	by	ADP
ejpam-2650	122	9	taking	take	VERB
ejpam-2650	122	10	the	the	DET
ejpam-2650	122	11	f2	f2	ADJ
ejpam-2650	122	12	-	-	PUNCT
ejpam-2650	122	13	linear	linear	NOUN
ejpam-2650	122	14	combinations	combination	NOUN
ejpam-2650	122	15	.	.	PUNCT
ejpam-2650	123	1	consequently	consequently	ADV
ejpam-2650	123	2	we	we	PRON
ejpam-2650	123	3	have	have	VERB
ejpam-2650	123	4	φhom(a+	φhom(a+	ADJ
ejpam-2650	123	5	bu+	bu+	NOUN
ejpam-2650	123	6	cu2	cu2	NOUN
ejpam-2650	123	7	)	)	PUNCT
ejpam-2650	124	1	=	=	SYM
ejpam-2650	124	2	(	(	PUNCT
ejpam-2650	124	3	a+	a+	X
ejpam-2650	124	4	b+	b+	X
ejpam-2650	124	5	c	c	X
ejpam-2650	124	6	,	,	PUNCT
ejpam-2650	124	7	b+	b+	VERB
ejpam-2650	124	8	c	c	X
ejpam-2650	124	9	,	,	PUNCT
ejpam-2650	124	10	a+	a+	PUNCT
ejpam-2650	124	11	c	c	X
ejpam-2650	124	12	,	,	PUNCT
ejpam-2650	124	13	c	c	NOUN
ejpam-2650	124	14	)	)	PUNCT
ejpam-2650	124	15	,	,	PUNCT
ejpam-2650	124	16	a	a	DET
ejpam-2650	124	17	,	,	PUNCT
ejpam-2650	124	18	b	b	NOUN
ejpam-2650	124	19	,	,	PUNCT
ejpam-2650	124	20	c	c	PROPN
ejpam-2650	124	21	∈	∈	PROPN
ejpam-2650	124	22	f2	f2	PROPN
ejpam-2650	124	23	.	.	PUNCT
ejpam-2650	125	1	4	4	X
ejpam-2650	125	2	.	.	X
ejpam-2650	125	3	divisible	divisible	ADJ
ejpam-2650	125	4	codes	code	NOUN
ejpam-2650	125	5	over	over	ADP
ejpam-2650	125	6	rk	rk	NOUN
ejpam-2650	125	7	,	,	PUNCT
ejpam-2650	125	8	m	m	VERB
ejpam-2650	125	9	divisible	divisible	ADJ
ejpam-2650	125	10	codes	code	NOUN
ejpam-2650	125	11	were	be	AUX
ejpam-2650	125	12	first	first	ADV
ejpam-2650	125	13	introduced	introduce	VERB
ejpam-2650	125	14	by	by	ADP
ejpam-2650	125	15	ward	ward	NOUN
ejpam-2650	125	16	in	in	ADP
ejpam-2650	125	17	1981	1981	NUM
ejpam-2650	125	18	in	in	ADP
ejpam-2650	125	19	[	[	X
ejpam-2650	125	20	14	14	NUM
ejpam-2650	125	21	]	]	PUNCT
ejpam-2650	125	22	.	.	PUNCT
ejpam-2650	126	1	a	a	DET
ejpam-2650	126	2	code	code	NOUN
ejpam-2650	126	3	is	be	AUX
ejpam-2650	126	4	divisible	divisible	ADJ
ejpam-2650	126	5	if	if	SCONJ
ejpam-2650	126	6	the	the	DET
ejpam-2650	126	7	weights	weight	NOUN
ejpam-2650	126	8	of	of	ADP
ejpam-2650	126	9	all	all	DET
ejpam-2650	126	10	the	the	DET
ejpam-2650	126	11	codewords	codeword	NOUN
ejpam-2650	126	12	have	have	VERB
ejpam-2650	126	13	a	a	DET
ejpam-2650	126	14	common	common	ADJ
ejpam-2650	126	15	divisor	divisor	NOUN
ejpam-2650	126	16	∆	∆	PROPN
ejpam-2650	126	17	>	>	X
ejpam-2650	127	1	1	1	X
ejpam-2650	127	2	.	.	PUNCT
ejpam-2650	128	1	the	the	DET
ejpam-2650	128	2	replicated	replicate	VERB
ejpam-2650	128	3	code	code	NOUN
ejpam-2650	128	4	,	,	PUNCT
ejpam-2650	128	5	constructed	construct	VERB
ejpam-2650	128	6	by	by	ADP
ejpam-2650	128	7	repeating	repeat	VERB
ejpam-2650	128	8	each	each	DET
ejpam-2650	128	9	coordinate	coordinate	NOUN
ejpam-2650	128	10	of	of	ADP
ejpam-2650	128	11	a	a	DET
ejpam-2650	128	12	selected	select	VERB
ejpam-2650	128	13	code	code	NOUN
ejpam-2650	128	14	a	a	DET
ejpam-2650	128	15	certain	certain	ADJ
ejpam-2650	128	16	number	number	NOUN
ejpam-2650	128	17	of	of	ADP
ejpam-2650	128	18	times	time	NOUN
ejpam-2650	128	19	is	be	AUX
ejpam-2650	128	20	the	the	DET
ejpam-2650	128	21	simplest	simple	ADJ
ejpam-2650	128	22	divisible	divisible	ADJ
ejpam-2650	128	23	code	code	NOUN
ejpam-2650	128	24	.	.	PUNCT
ejpam-2650	129	1	moreover	moreover	ADV
ejpam-2650	129	2	,	,	PUNCT
ejpam-2650	129	3	ward	ward	PROPN
ejpam-2650	129	4	proved	prove	VERB
ejpam-2650	129	5	that	that	SCONJ
ejpam-2650	129	6	a	a	DET
ejpam-2650	129	7	divisible	divisible	ADJ
ejpam-2650	129	8	code	code	NOUN
ejpam-2650	129	9	is	be	AUX
ejpam-2650	129	10	equivalent	equivalent	ADJ
ejpam-2650	129	11	to	to	ADP
ejpam-2650	129	12	a	a	DET
ejpam-2650	129	13	∆-fold	∆-fold	NOUN
ejpam-2650	129	14	replicated	replicate	VERB
ejpam-2650	129	15	code	code	NOUN
ejpam-2650	129	16	if	if	SCONJ
ejpam-2650	129	17	the	the	DET
ejpam-2650	129	18	divisor	divisor	NOUN
ejpam-2650	129	19	∆	∆	PROPN
ejpam-2650	129	20	of	of	ADP
ejpam-2650	129	21	the	the	DET
ejpam-2650	129	22	code	code	NOUN
ejpam-2650	129	23	is	be	AUX
ejpam-2650	129	24	relatively	relatively	ADV
ejpam-2650	129	25	prime	prime	ADJ
ejpam-2650	129	26	to	to	ADP
ejpam-2650	129	27	the	the	DET
ejpam-2650	129	28	field	field	NOUN
ejpam-2650	129	29	characteristic	characteristic	ADJ
ejpam-2650	129	30	in	in	ADP
ejpam-2650	129	31	[	[	X
ejpam-2650	129	32	14	14	NUM
ejpam-2650	129	33	]	]	PUNCT
ejpam-2650	129	34	.	.	PUNCT
ejpam-2650	130	1	a	a	DET
ejpam-2650	130	2	divisible	divisible	ADJ
ejpam-2650	130	3	code	code	NOUN
ejpam-2650	130	4	is	be	AUX
ejpam-2650	130	5	said	say	VERB
ejpam-2650	130	6	to	to	PART
ejpam-2650	130	7	be	be	AUX
ejpam-2650	130	8	of	of	ADP
ejpam-2650	130	9	“	"	PUNCT
ejpam-2650	130	10	level	level	NOUN
ejpam-2650	130	11	e	e	NOUN
ejpam-2650	130	12	”	"	PUNCT
ejpam-2650	130	13	,	,	PUNCT
ejpam-2650	130	14	if	if	SCONJ
ejpam-2650	130	15	the	the	DET
ejpam-2650	130	16	greatest	great	ADJ
ejpam-2650	130	17	common	common	ADJ
ejpam-2650	130	18	divisor	divisor	NOUN
ejpam-2650	130	19	of	of	ADP
ejpam-2650	130	20	weights	weight	NOUN
ejpam-2650	130	21	of	of	ADP
ejpam-2650	130	22	codewords	codeword	NOUN
ejpam-2650	130	23	in	in	ADP
ejpam-2650	130	24	c	c	PROPN
ejpam-2650	130	25	equals	equal	VERB
ejpam-2650	130	26	pe	pe	PRON
ejpam-2650	130	27	for	for	ADP
ejpam-2650	130	28	some	some	DET
ejpam-2650	130	29	integer	integer	NOUN
ejpam-2650	130	30	e	e	X
ejpam-2650	130	31	≥	≥	NUM
ejpam-2650	130	32	1	1	NUM
ejpam-2650	130	33	.	.	PUNCT
ejpam-2650	130	34	reed	reed	NOUN
ejpam-2650	130	35	-	-	PUNCT
ejpam-2650	130	36	muller	muller	PROPN
ejpam-2650	130	37	codes	code	NOUN
ejpam-2650	130	38	are	be	AUX
ejpam-2650	130	39	an	an	DET
ejpam-2650	130	40	example	example	NOUN
ejpam-2650	130	41	of	of	ADP
ejpam-2650	130	42	divisible	divisible	ADJ
ejpam-2650	130	43	codes	code	NOUN
ejpam-2650	130	44	,	,	PUNCT
ejpam-2650	130	45	by	by	ADP
ejpam-2650	130	46	the	the	DET
ejpam-2650	130	47	following	following	NOUN
ejpam-2650	130	48	theorem	theorem	NOUN
ejpam-2650	130	49	in	in	ADP
ejpam-2650	130	50	[	[	X
ejpam-2650	130	51	10	10	NUM
ejpam-2650	130	52	]	]	NUM
ejpam-2650	130	53	:	:	PUNCT
ejpam-2650	130	54	theorem	theorem	NOUN
ejpam-2650	130	55	3	3	NUM
ejpam-2650	130	56	.	.	PUNCT
ejpam-2650	131	1	the	the	DET
ejpam-2650	131	2	weight	weight	NOUN
ejpam-2650	131	3	of	of	ADP
ejpam-2650	131	4	every	every	DET
ejpam-2650	131	5	codeword	codeword	NOUN
ejpam-2650	131	6	in	in	ADP
ejpam-2650	131	7	rm(r	rm(r	PROPN
ejpam-2650	131	8	,	,	PUNCT
ejpam-2650	131	9	m	m	PRON
ejpam-2650	131	10	)	)	PUNCT
ejpam-2650	131	11	is	be	AUX
ejpam-2650	131	12	divisible	divisible	ADJ
ejpam-2650	131	13	by	by	ADP
ejpam-2650	131	14	2[(m−1)/r	2[(m−1)/r	NUM
ejpam-2650	131	15	]	]	X
ejpam-2650	131	16	.	.	PUNCT
ejpam-2650	132	1	because	because	SCONJ
ejpam-2650	132	2	of	of	ADP
ejpam-2650	132	3	the	the	DET
ejpam-2650	132	4	homogeneous	homogeneous	ADJ
ejpam-2650	132	5	weight	weight	NOUN
ejpam-2650	132	6	on	on	ADP
ejpam-2650	132	7	rk	rk	NOUN
ejpam-2650	132	8	,	,	PUNCT
ejpam-2650	132	9	m	m	AUX
ejpam-2650	132	10	we	we	PRON
ejpam-2650	132	11	can	can	AUX
ejpam-2650	132	12	easily	easily	ADV
ejpam-2650	132	13	observe	observe	VERB
ejpam-2650	132	14	the	the	DET
ejpam-2650	132	15	following	following	NOUN
ejpam-2650	132	16	:	:	PUNCT
ejpam-2650	132	17	theorem	theorem	NOUN
ejpam-2650	132	18	4	4	NUM
ejpam-2650	132	19	.	.	PUNCT
ejpam-2650	133	1	any	any	DET
ejpam-2650	133	2	linear	linear	PROPN
ejpam-2650	133	3	code	code	NOUN
ejpam-2650	133	4	c	c	NOUN
ejpam-2650	133	5	over	over	ADP
ejpam-2650	133	6	rk	rk	PROPN
ejpam-2650	133	7	,	,	PUNCT
ejpam-2650	133	8	m	m	VERB
ejpam-2650	133	9	is	be	AUX
ejpam-2650	133	10	divisible	divisible	ADJ
ejpam-2650	133	11	with	with	ADP
ejpam-2650	133	12	∆	∆	PROPN
ejpam-2650	133	13	≥	≥	NUM
ejpam-2650	133	14	γ	γ	X
ejpam-2650	133	15	.	.	PROPN
ejpam-2650	134	1	in	in	ADP
ejpam-2650	134	2	particular	particular	ADJ
ejpam-2650	134	3	with	with	ADP
ejpam-2650	134	4	our	our	PRON
ejpam-2650	134	5	choice	choice	NOUN
ejpam-2650	134	6	of	of	ADP
ejpam-2650	134	7	γ	γ	X
ejpam-2650	134	8	,	,	PUNCT
ejpam-2650	134	9	we	we	PRON
ejpam-2650	134	10	see	see	VERB
ejpam-2650	134	11	that	that	SCONJ
ejpam-2650	134	12	if	if	SCONJ
ejpam-2650	134	13	c	c	PROPN
ejpam-2650	134	14	is	be	AUX
ejpam-2650	134	15	a	a	DET
ejpam-2650	134	16	linear	linear	ADJ
ejpam-2650	134	17	code	code	NOUN
ejpam-2650	134	18	over	over	ADP
ejpam-2650	134	19	rk	rk	PROPN
ejpam-2650	134	20	,	,	PUNCT
ejpam-2650	134	21	m	m	NOUN
ejpam-2650	134	22	of	of	ADP
ejpam-2650	134	23	length	length	NOUN
ejpam-2650	134	24	n	n	CCONJ
ejpam-2650	134	25	,	,	PUNCT
ejpam-2650	134	26	then	then	ADV
ejpam-2650	134	27	φhom(c	φhom(c	NUM
ejpam-2650	134	28	)	)	PUNCT
ejpam-2650	134	29	is	be	AUX
ejpam-2650	134	30	a	a	DET
ejpam-2650	134	31	divisible	divisible	ADJ
ejpam-2650	134	32	binary	binary	NOUN
ejpam-2650	134	33	code	code	NOUN
ejpam-2650	134	34	of	of	ADP
ejpam-2650	134	35	length	length	NOUN
ejpam-2650	134	36	2km−1n	2km−1n	ADV
ejpam-2650	134	37	with	with	ADP
ejpam-2650	134	38	∆	∆	PROPN
ejpam-2650	134	39	≥	≥	NUM
ejpam-2650	134	40	2km−2	2km−2	NUM
ejpam-2650	134	41	.	.	PUNCT
ejpam-2650	135	1	thus	thus	ADV
ejpam-2650	135	2	any	any	DET
ejpam-2650	135	3	such	such	ADJ
ejpam-2650	135	4	code	code	NOUN
ejpam-2650	135	5	is	be	AUX
ejpam-2650	135	6	of	of	ADP
ejpam-2650	135	7	level	level	NOUN
ejpam-2650	135	8	e	e	NOUN
ejpam-2650	135	9	≥	≥	NOUN
ejpam-2650	135	10	km−	km−	X
ejpam-2650	135	11	2	2	X
ejpam-2650	135	12	.	.	PUNCT
ejpam-2650	136	1	it	it	PRON
ejpam-2650	136	2	is	be	AUX
ejpam-2650	136	3	well	well	ADV
ejpam-2650	136	4	known	know	VERB
ejpam-2650	136	5	that	that	SCONJ
ejpam-2650	136	6	binary	binary	ADJ
ejpam-2650	136	7	linear	linear	ADJ
ejpam-2650	136	8	divisible	divisible	ADJ
ejpam-2650	136	9	codes	code	NOUN
ejpam-2650	136	10	with	with	ADP
ejpam-2650	136	11	∆	∆	PROPN
ejpam-2650	136	12	=	=	SYM
ejpam-2650	136	13	2k	2k	NUM
ejpam-2650	136	14	,	,	PUNCT
ejpam-2650	136	15	k	k	PROPN
ejpam-2650	136	16	≥	≥	NUM
ejpam-2650	136	17	2	2	NUM
ejpam-2650	136	18	are	be	AUX
ejpam-2650	136	19	also	also	ADV
ejpam-2650	136	20	selforthogonal	selforthogonal	ADJ
ejpam-2650	136	21	.	.	PUNCT
ejpam-2650	137	1	thus	thus	ADV
ejpam-2650	137	2	we	we	PRON
ejpam-2650	137	3	have	have	VERB
ejpam-2650	137	4	the	the	DET
ejpam-2650	137	5	following	follow	VERB
ejpam-2650	137	6	corollary	corollary	ADJ
ejpam-2650	137	7	:	:	PUNCT
ejpam-2650	137	8	corollary	corollary	ADJ
ejpam-2650	137	9	1	1	NUM
ejpam-2650	137	10	.	.	PUNCT
ejpam-2650	138	1	let	let	VERB
ejpam-2650	138	2	c	c	PRON
ejpam-2650	138	3	be	be	AUX
ejpam-2650	138	4	any	any	DET
ejpam-2650	138	5	linear	linear	ADJ
ejpam-2650	138	6	code	code	NOUN
ejpam-2650	138	7	over	over	ADP
ejpam-2650	138	8	rk	rk	PROPN
ejpam-2650	138	9	,	,	PUNCT
ejpam-2650	138	10	m.	m.	NOUN
ejpam-2650	138	11	then	then	ADV
ejpam-2650	138	12	φhom(c	φhom(c	NUM
ejpam-2650	138	13	)	)	PUNCT
ejpam-2650	138	14	is	be	AUX
ejpam-2650	138	15	a	a	DET
ejpam-2650	138	16	binary	binary	ADJ
ejpam-2650	138	17	selforthogonal	selforthogonal	PROPN
ejpam-2650	138	18	linear	linear	PROPN
ejpam-2650	138	19	code	code	PROPN
ejpam-2650	138	20	if	if	SCONJ
ejpam-2650	138	21	km	km	PROPN
ejpam-2650	138	22	≥	≥	NOUN
ejpam-2650	138	23	4	4	NUM
ejpam-2650	138	24	.	.	PUNCT
ejpam-2650	139	1	in	in	ADP
ejpam-2650	139	2	what	what	PRON
ejpam-2650	139	3	follows	follow	VERB
ejpam-2650	139	4	,	,	PUNCT
ejpam-2650	139	5	we	we	PRON
ejpam-2650	139	6	will	will	AUX
ejpam-2650	139	7	search	search	VERB
ejpam-2650	139	8	for	for	ADP
ejpam-2650	139	9	binary	binary	ADJ
ejpam-2650	139	10	divisible	divisible	ADJ
ejpam-2650	139	11	codes	code	NOUN
ejpam-2650	139	12	with	with	ADP
ejpam-2650	139	13	various	various	ADJ
ejpam-2650	139	14	divisors	divisor	NOUN
ejpam-2650	139	15	from	from	ADP
ejpam-2650	139	16	the	the	DET
ejpam-2650	139	17	gray	gray	ADJ
ejpam-2650	139	18	-	-	PUNCT
ejpam-2650	139	19	homogeneous	homogeneous	ADJ
ejpam-2650	139	20	images	image	NOUN
ejpam-2650	139	21	of	of	ADP
ejpam-2650	139	22	cyclic	cyclic	ADJ
ejpam-2650	139	23	,	,	PUNCT
ejpam-2650	139	24	constacyclic	constacyclic	ADJ
ejpam-2650	139	25	and	and	CCONJ
ejpam-2650	139	26	quasicyclic	quasicyclic	ADJ
ejpam-2650	139	27	codes	code	NOUN
ejpam-2650	139	28	over	over	ADP
ejpam-2650	139	29	rk	rk	NOUN
ejpam-2650	139	30	,	,	PUNCT
ejpam-2650	139	31	m	m	NOUN
ejpam-2650	139	32	of	of	ADP
ejpam-2650	139	33	some	some	DET
ejpam-2650	139	34	lengths	length	NOUN
ejpam-2650	139	35	.	.	PUNCT
ejpam-2650	140	1	because	because	SCONJ
ejpam-2650	140	2	of	of	ADP
ejpam-2650	140	3	the	the	DET
ejpam-2650	140	4	increased	increase	VERB
ejpam-2650	140	5	size	size	NOUN
ejpam-2650	140	6	of	of	ADP
ejpam-2650	140	7	the	the	DET
ejpam-2650	140	8	rings	ring	NOUN
ejpam-2650	140	9	,	,	PUNCT
ejpam-2650	140	10	we	we	PRON
ejpam-2650	140	11	will	will	AUX
ejpam-2650	140	12	mostly	mostly	ADV
ejpam-2650	140	13	consider	consider	VERB
ejpam-2650	140	14	the	the	DET
ejpam-2650	140	15	rings	ring	NOUN
ejpam-2650	140	16	r3,1	r3,1	PROPN
ejpam-2650	140	17	,	,	PUNCT
ejpam-2650	140	18	r4,1	r4,1	PROPN
ejpam-2650	140	19	and	and	CCONJ
ejpam-2650	140	20	r5,1	r5,1	PROPN
ejpam-2650	140	21	.	.	PUNCT
ejpam-2650	141	1	the	the	DET
ejpam-2650	141	2	examples	example	NOUN
ejpam-2650	141	3	that	that	PRON
ejpam-2650	141	4	we	we	PRON
ejpam-2650	141	5	give	give	VERB
ejpam-2650	141	6	are	be	AUX
ejpam-2650	141	7	mainly	mainly	ADV
ejpam-2650	141	8	optimal	optimal	ADJ
ejpam-2650	141	9	.	.	PUNCT
ejpam-2650	142	1	b.	b.	PROPN
ejpam-2650	142	2	yildiz	yildiz	PROPN
ejpam-2650	142	3	,	,	PUNCT
ejpam-2650	142	4	n.	n.	PROPN
ejpam-2650	142	5	tufekci	tufekci	PROPN
ejpam-2650	142	6	/	/	SYM
ejpam-2650	142	7	eur	eur	PROPN
ejpam-2650	142	8	.	.	PUNCT
ejpam-2650	143	1	j.	j.	PROPN
ejpam-2650	143	2	pure	pure	PROPN
ejpam-2650	143	3	appl	appl	PROPN
ejpam-2650	143	4	.	.	PROPN
ejpam-2650	143	5	math	math	PROPN
ejpam-2650	143	6	,	,	PUNCT
ejpam-2650	143	7	10	10	NUM
ejpam-2650	143	8	(	(	PUNCT
ejpam-2650	143	9	5	5	NUM
ejpam-2650	143	10	)	)	PUNCT
ejpam-2650	143	11	(	(	PUNCT
ejpam-2650	143	12	2017	2017	NUM
ejpam-2650	143	13	)	)	PUNCT
ejpam-2650	143	14	,	,	PUNCT
ejpam-2650	143	15	1112	1112	NUM
ejpam-2650	143	16	-	-	SYM
ejpam-2650	143	17	1123	1123	NUM
ejpam-2650	143	18	1118	1118	NUM
ejpam-2650	143	19	4.1	4.1	NUM
ejpam-2650	143	20	.	.	PUNCT
ejpam-2650	144	1	divisible	divisible	ADJ
ejpam-2650	144	2	cyclic	cyclic	NOUN
ejpam-2650	144	3	codes	code	NOUN
ejpam-2650	144	4	over	over	ADP
ejpam-2650	144	5	rk	rk	NOUN
ejpam-2650	144	6	,	,	PUNCT
ejpam-2650	144	7	m	m	VERB
ejpam-2650	144	8	recall	recall	VERB
ejpam-2650	144	9	that	that	SCONJ
ejpam-2650	144	10	a	a	DET
ejpam-2650	144	11	linear	linear	ADJ
ejpam-2650	144	12	code	code	NOUN
ejpam-2650	144	13	c	c	PROPN
ejpam-2650	144	14	of	of	ADP
ejpam-2650	144	15	length	length	NOUN
ejpam-2650	144	16	n	n	PRON
ejpam-2650	144	17	overrk	overrk	NOUN
ejpam-2650	144	18	,	,	PUNCT
ejpam-2650	144	19	m	m	VERB
ejpam-2650	144	20	is	be	AUX
ejpam-2650	144	21	a	a	DET
ejpam-2650	144	22	cyclic	cyclic	ADJ
ejpam-2650	144	23	code	code	NOUN
ejpam-2650	144	24	if	if	SCONJ
ejpam-2650	144	25	τ(c̄	τ(c̄	NOUN
ejpam-2650	144	26	)	)	PUNCT
ejpam-2650	144	27	=	=	SYM
ejpam-2650	145	1	(	(	PUNCT
ejpam-2650	145	2	cn−1	cn−1	PROPN
ejpam-2650	145	3	,	,	PUNCT
ejpam-2650	145	4	c0	c0	NOUN
ejpam-2650	145	5	,	,	PUNCT
ejpam-2650	145	6	.	.	PUNCT
ejpam-2650	145	7	.	.	PUNCT
ejpam-2650	146	1	.	.	PUNCT
ejpam-2650	147	1	,	,	PUNCT
ejpam-2650	147	2	cn−2	cn−2	PROPN
ejpam-2650	147	3	)	)	PUNCT
ejpam-2650	147	4	∈	∈	PROPN
ejpam-2650	147	5	c	c	NOUN
ejpam-2650	147	6	for	for	ADP
ejpam-2650	147	7	all	all	PRON
ejpam-2650	147	8	c̄	c̄	PROPN
ejpam-2650	147	9	=	=	SYM
ejpam-2650	147	10	(	(	PUNCT
ejpam-2650	147	11	c0	c0	NOUN
ejpam-2650	147	12	,	,	PUNCT
ejpam-2650	147	13	c1	c1	PROPN
ejpam-2650	147	14	.	.	PUNCT
ejpam-2650	147	15	.	.	PUNCT
ejpam-2650	148	1	.	.	PUNCT
ejpam-2650	149	1	,	,	PUNCT
ejpam-2650	149	2	cn−1	cn−1	X
ejpam-2650	149	3	)	)	PUNCT
ejpam-2650	149	4	∈	∈	PROPN
ejpam-2650	149	5	c	c	NOUN
ejpam-2650	149	6	,	,	PUNCT
ejpam-2650	149	7	where	where	SCONJ
ejpam-2650	149	8	τ	τ	PROPN
ejpam-2650	149	9	is	be	AUX
ejpam-2650	149	10	the	the	DET
ejpam-2650	149	11	cyclic	cyclic	ADJ
ejpam-2650	149	12	shift	shift	NOUN
ejpam-2650	149	13	.	.	PUNCT
ejpam-2650	150	1	considering	consider	VERB
ejpam-2650	150	2	the	the	DET
ejpam-2650	150	3	polynomial	polynomial	ADJ
ejpam-2650	150	4	correspondence	correspondence	NOUN
ejpam-2650	150	5	π	π	NOUN
ejpam-2650	150	6	:	:	PUNCT
ejpam-2650	150	7	(	(	PUNCT
ejpam-2650	150	8	rk	rk	NOUN
ejpam-2650	150	9	,	,	PUNCT
ejpam-2650	150	10	m)n	m)n	X
ejpam-2650	150	11	→	→	SYM
ejpam-2650	150	12	rk	rk	NOUN
ejpam-2650	150	13	,	,	PUNCT
ejpam-2650	150	14	m[x	m[x	NOUN
ejpam-2650	150	15	]	]	X
ejpam-2650	150	16	c̄	c̄	PROPN
ejpam-2650	150	17	=	=	SYM
ejpam-2650	150	18	(	(	PUNCT
ejpam-2650	150	19	c0	c0	PROPN
ejpam-2650	150	20	,	,	PUNCT
ejpam-2650	150	21	c1	c1	PROPN
ejpam-2650	150	22	.	.	PUNCT
ejpam-2650	150	23	.	.	PUNCT
ejpam-2650	151	1	.	.	PUNCT
ejpam-2650	152	1	,	,	PUNCT
ejpam-2650	152	2	cn−1	cn−1	NOUN
ejpam-2650	152	3	)	)	PUNCT
ejpam-2650	153	1	7→	7→	NUM
ejpam-2650	153	2	c0	c0	NOUN
ejpam-2650	153	3	+	+	CCONJ
ejpam-2650	153	4	c1x+	c1x+	NOUN
ejpam-2650	153	5	.	.	PUNCT
ejpam-2650	153	6	.	.	PUNCT
ejpam-2650	154	1	.+	.+	NOUN
ejpam-2650	154	2	cn−1x	cn−1x	VERB
ejpam-2650	154	3	n−1	n−1	PROPN
ejpam-2650	154	4	we	we	PRON
ejpam-2650	154	5	know	know	VERB
ejpam-2650	154	6	that	that	SCONJ
ejpam-2650	154	7	a	a	DET
ejpam-2650	154	8	code	code	NOUN
ejpam-2650	154	9	c	c	NOUN
ejpam-2650	154	10	of	of	ADP
ejpam-2650	154	11	length	length	NOUN
ejpam-2650	154	12	n	n	CCONJ
ejpam-2650	154	13	over	over	ADP
ejpam-2650	154	14	rk	rk	NOUN
ejpam-2650	154	15	,	,	PUNCT
ejpam-2650	154	16	m	m	VERB
ejpam-2650	154	17	is	be	AUX
ejpam-2650	154	18	cyclic	cyclic	ADJ
ejpam-2650	154	19	if	if	SCONJ
ejpam-2650	154	20	and	and	CCONJ
ejpam-2650	154	21	only	only	ADV
ejpam-2650	154	22	if	if	SCONJ
ejpam-2650	154	23	π(c	π(c	PROPN
ejpam-2650	154	24	)	)	PUNCT
ejpam-2650	154	25	is	be	AUX
ejpam-2650	154	26	an	an	DET
ejpam-2650	154	27	ideal	ideal	NOUN
ejpam-2650	154	28	in	in	ADP
ejpam-2650	154	29	the	the	DET
ejpam-2650	154	30	ring	ring	NOUN
ejpam-2650	154	31	rk	rk	NOUN
ejpam-2650	154	32	,	,	PUNCT
ejpam-2650	154	33	m[x]/(xn−1	m[x]/(xn−1	PROPN
ejpam-2650	154	34	)	)	PUNCT
ejpam-2650	154	35	.	.	PUNCT
ejpam-2650	155	1	there	there	PRON
ejpam-2650	155	2	are	be	VERB
ejpam-2650	155	3	a	a	DET
ejpam-2650	155	4	lot	lot	NOUN
ejpam-2650	155	5	of	of	ADP
ejpam-2650	155	6	results	result	NOUN
ejpam-2650	155	7	concerning	concern	VERB
ejpam-2650	155	8	the	the	DET
ejpam-2650	155	9	structural	structural	ADJ
ejpam-2650	155	10	properties	property	NOUN
ejpam-2650	155	11	of	of	ADP
ejpam-2650	155	12	cyclic	cyclic	ADJ
ejpam-2650	155	13	codes	code	NOUN
ejpam-2650	155	14	over	over	ADP
ejpam-2650	155	15	rings	ring	NOUN
ejpam-2650	155	16	,	,	PUNCT
ejpam-2650	155	17	in	in	ADP
ejpam-2650	155	18	particular	particular	ADJ
ejpam-2650	155	19	over	over	ADP
ejpam-2650	155	20	finite	finite	ADJ
ejpam-2650	155	21	chain	chain	NOUN
ejpam-2650	155	22	rings	ring	NOUN
ejpam-2650	155	23	.	.	PUNCT
ejpam-2650	156	1	the	the	DET
ejpam-2650	156	2	rings	ring	NOUN
ejpam-2650	156	3	that	that	PRON
ejpam-2650	156	4	we	we	PRON
ejpam-2650	156	5	consider	consider	VERB
ejpam-2650	156	6	for	for	ADP
ejpam-2650	156	7	the	the	DET
ejpam-2650	156	8	purposes	purpose	NOUN
ejpam-2650	156	9	in	in	ADP
ejpam-2650	156	10	this	this	DET
ejpam-2650	156	11	section	section	NOUN
ejpam-2650	156	12	,	,	PUNCT
ejpam-2650	156	13	r3,1	r3,1	PROPN
ejpam-2650	156	14	,	,	PUNCT
ejpam-2650	156	15	r4,1	r4,1	NOUN
ejpam-2650	156	16	being	be	AUX
ejpam-2650	156	17	finite	finite	ADJ
ejpam-2650	156	18	chain	chain	NOUN
ejpam-2650	156	19	,	,	PUNCT
ejpam-2650	156	20	we	we	PRON
ejpam-2650	156	21	are	be	AUX
ejpam-2650	156	22	not	not	PART
ejpam-2650	156	23	going	go	VERB
ejpam-2650	156	24	to	to	PART
ejpam-2650	156	25	go	go	VERB
ejpam-2650	156	26	into	into	ADP
ejpam-2650	156	27	the	the	DET
ejpam-2650	156	28	theoretical	theoretical	ADJ
ejpam-2650	156	29	aspects	aspect	NOUN
ejpam-2650	156	30	of	of	ADP
ejpam-2650	156	31	cyclic	cyclic	ADJ
ejpam-2650	156	32	codes	code	NOUN
ejpam-2650	156	33	.	.	PUNCT
ejpam-2650	157	1	instead	instead	ADV
ejpam-2650	157	2	we	we	PRON
ejpam-2650	157	3	will	will	AUX
ejpam-2650	157	4	demonstrate	demonstrate	VERB
ejpam-2650	157	5	how	how	SCONJ
ejpam-2650	157	6	some	some	DET
ejpam-2650	157	7	onegenerator	onegenerator	NOUN
ejpam-2650	157	8	cyclic	cyclic	NOUN
ejpam-2650	157	9	codes	code	NOUN
ejpam-2650	157	10	over	over	ADP
ejpam-2650	157	11	these	these	DET
ejpam-2650	157	12	rings	ring	NOUN
ejpam-2650	157	13	lead	lead	VERB
ejpam-2650	157	14	to	to	ADP
ejpam-2650	157	15	optimal	optimal	ADJ
ejpam-2650	157	16	divisible	divisible	ADJ
ejpam-2650	157	17	binary	binary	ADJ
ejpam-2650	157	18	linear	linear	PROPN
ejpam-2650	157	19	codes	code	NOUN
ejpam-2650	157	20	under	under	ADP
ejpam-2650	157	21	the	the	DET
ejpam-2650	157	22	gray	gray	ADJ
ejpam-2650	157	23	-	-	PUNCT
ejpam-2650	157	24	homogeneous	homogeneous	ADJ
ejpam-2650	157	25	map	map	NOUN
ejpam-2650	157	26	.	.	PUNCT
ejpam-2650	158	1	since	since	SCONJ
ejpam-2650	158	2	the	the	DET
ejpam-2650	158	3	gray	gray	ADJ
ejpam-2650	158	4	-	-	PUNCT
ejpam-2650	158	5	homogeneous	homogeneous	ADJ
ejpam-2650	158	6	image	image	NOUN
ejpam-2650	158	7	of	of	ADP
ejpam-2650	158	8	a	a	DET
ejpam-2650	158	9	cyclic	cyclic	ADJ
ejpam-2650	158	10	code	code	NOUN
ejpam-2650	158	11	over	over	ADP
ejpam-2650	158	12	rk	rk	PROPN
ejpam-2650	158	13	,	,	PUNCT
ejpam-2650	158	14	m	m	VERB
ejpam-2650	158	15	is	be	AUX
ejpam-2650	158	16	a	a	DET
ejpam-2650	158	17	2km−1	2km−1	PROPN
ejpam-2650	158	18	-	-	PUNCT
ejpam-2650	158	19	quasicyclic	quasicyclic	ADJ
ejpam-2650	158	20	binary	binary	PROPN
ejpam-2650	158	21	code	code	PROPN
ejpam-2650	158	22	,	,	PUNCT
ejpam-2650	158	23	the	the	DET
ejpam-2650	158	24	binary	binary	NOUN
ejpam-2650	158	25	codes	code	NOUN
ejpam-2650	158	26	that	that	PRON
ejpam-2650	158	27	we	we	PRON
ejpam-2650	158	28	have	have	AUX
ejpam-2650	158	29	constructed	construct	VERB
ejpam-2650	158	30	have	have	VERB
ejpam-2650	158	31	the	the	DET
ejpam-2650	158	32	additional	additional	ADJ
ejpam-2650	158	33	property	property	NOUN
ejpam-2650	158	34	that	that	PRON
ejpam-2650	158	35	they	they	PRON
ejpam-2650	158	36	are	be	AUX
ejpam-2650	158	37	4	4	NUM
ejpam-2650	158	38	-	-	NUM
ejpam-2650	158	39	quasicyclic	quasicyclic	NOUN
ejpam-2650	158	40	or	or	CCONJ
ejpam-2650	158	41	8	8	NUM
ejpam-2650	158	42	-	-	NUM
ejpam-2650	158	43	quasicyclic	quasicyclic	NOUN
ejpam-2650	158	44	according	accord	VERB
ejpam-2650	158	45	as	as	SCONJ
ejpam-2650	158	46	we	we	PRON
ejpam-2650	158	47	are	be	AUX
ejpam-2650	158	48	on	on	ADP
ejpam-2650	158	49	the	the	DET
ejpam-2650	158	50	ring	ring	NOUN
ejpam-2650	158	51	r3,1	r3,1	PROPN
ejpam-2650	158	52	or	or	CCONJ
ejpam-2650	158	53	r4,1	r4,1	NOUN
ejpam-2650	158	54	.	.	PUNCT
ejpam-2650	158	55	table	table	NOUN
ejpam-2650	158	56	1	1	NUM
ejpam-2650	158	57	:	:	PUNCT
ejpam-2650	158	58	divisible	divisible	ADJ
ejpam-2650	158	59	cyclic	cyclic	NOUN
ejpam-2650	158	60	codes	code	NOUN
ejpam-2650	158	61	over	over	ADP
ejpam-2650	158	62	r3,1	r3,1	PROPN
ejpam-2650	158	63	of	of	ADP
ejpam-2650	158	64	length	length	NOUN
ejpam-2650	158	65	n	n	PROPN
ejpam-2650	158	66	and	and	CCONJ
ejpam-2650	158	67	the	the	DET
ejpam-2650	158	68	binary	binary	ADJ
ejpam-2650	158	69	images	image	NOUN
ejpam-2650	158	70	n	n	PRON
ejpam-2650	158	71	g(x	g(x	NOUN
ejpam-2650	158	72	)	)	PUNCT
ejpam-2650	158	73	φhom(〈g(x	φhom(〈g(x	ADJ
ejpam-2650	158	74	)	)	PUNCT
ejpam-2650	158	75	〉	〉	PROPN
ejpam-2650	158	76	)	)	PUNCT
ejpam-2650	158	77	∆	∆	PROPN
ejpam-2650	158	78	level	level	NOUN
ejpam-2650	158	79	3	3	NUM
ejpam-2650	159	1	u2x+	u2x+	ADV
ejpam-2650	160	1	u2x2	u2x2	ADP
ejpam-2650	161	1	[	[	X
ejpam-2650	161	2	12	12	NUM
ejpam-2650	161	3	,	,	PUNCT
ejpam-2650	161	4	2	2	NUM
ejpam-2650	161	5	,	,	PUNCT
ejpam-2650	161	6	8	8	NUM
ejpam-2650	161	7	]	]	SYM
ejpam-2650	161	8	8	8	NUM
ejpam-2650	161	9	3	3	NUM
ejpam-2650	161	10	3	3	NUM
ejpam-2650	161	11	1	1	NUM
ejpam-2650	161	12	+	+	NUM
ejpam-2650	161	13	x2	x2	NOUN
ejpam-2650	162	1	[	[	X
ejpam-2650	162	2	12	12	NUM
ejpam-2650	162	3	,	,	PUNCT
ejpam-2650	162	4	3	3	NUM
ejpam-2650	162	5	,	,	PUNCT
ejpam-2650	162	6	6	6	NUM
ejpam-2650	162	7	]	]	SYM
ejpam-2650	162	8	6	6	NUM
ejpam-2650	162	9	1	1	NUM
ejpam-2650	162	10	4	4	NUM
ejpam-2650	162	11	ux+	ux+	ADJ
ejpam-2650	162	12	u2x2	u2x2	ADP
ejpam-2650	162	13	+	+	NUM
ejpam-2650	162	14	ux3	ux3	NOUN
ejpam-2650	163	1	[	[	X
ejpam-2650	163	2	16	16	NUM
ejpam-2650	163	3	,	,	PUNCT
ejpam-2650	163	4	4	4	NUM
ejpam-2650	163	5	,	,	PUNCT
ejpam-2650	163	6	8	8	NUM
ejpam-2650	163	7	]	]	SYM
ejpam-2650	163	8	8	8	NUM
ejpam-2650	163	9	3	3	NUM
ejpam-2650	163	10	4	4	NUM
ejpam-2650	163	11	1	1	NUM
ejpam-2650	163	12	+	+	CCONJ
ejpam-2650	163	13	x+	x+	ADJ
ejpam-2650	163	14	x2	x2	NOUN
ejpam-2650	164	1	+	+	CCONJ
ejpam-2650	164	2	(	(	PUNCT
ejpam-2650	164	3	1	1	NUM
ejpam-2650	164	4	+	+	NUM
ejpam-2650	164	5	u2)x3	u2)x3	NOUN
ejpam-2650	164	6	[	[	X
ejpam-2650	164	7	16	16	NUM
ejpam-2650	164	8	,	,	PUNCT
ejpam-2650	164	9	5	5	NUM
ejpam-2650	164	10	,	,	PUNCT
ejpam-2650	164	11	8	8	NUM
ejpam-2650	164	12	]	]	SYM
ejpam-2650	164	13	8	8	NUM
ejpam-2650	164	14	3	3	NUM
ejpam-2650	164	15	4	4	NUM
ejpam-2650	164	16	x+	x+	VERB
ejpam-2650	164	17	ux2	ux2	NOUN
ejpam-2650	164	18	+	+	CCONJ
ejpam-2650	164	19	(	(	PUNCT
ejpam-2650	164	20	u+	u+	NUM
ejpam-2650	164	21	1)x3	1)x3	NUM
ejpam-2650	164	22	[	[	SYM
ejpam-2650	164	23	16	16	NUM
ejpam-2650	164	24	,	,	PUNCT
ejpam-2650	164	25	6	6	NUM
ejpam-2650	164	26	,	,	PUNCT
ejpam-2650	164	27	6	6	NUM
ejpam-2650	164	28	]	]	SYM
ejpam-2650	164	29	2	2	NUM
ejpam-2650	164	30	1	1	NUM
ejpam-2650	164	31	4	4	NUM
ejpam-2650	164	32	x2	x2	NOUN
ejpam-2650	165	1	+	+	CCONJ
ejpam-2650	165	2	x3	x3	ADJ
ejpam-2650	166	1	[	[	X
ejpam-2650	166	2	16	16	NUM
ejpam-2650	166	3	,	,	PUNCT
ejpam-2650	166	4	9	9	NUM
ejpam-2650	166	5	,	,	PUNCT
ejpam-2650	166	6	4	4	NUM
ejpam-2650	166	7	]	]	SYM
ejpam-2650	166	8	2	2	NUM
ejpam-2650	166	9	1	1	NUM
ejpam-2650	166	10	4	4	NUM
ejpam-2650	166	11	x3	x3	NOUN
ejpam-2650	167	1	[	[	X
ejpam-2650	167	2	16	16	NUM
ejpam-2650	167	3	,	,	PUNCT
ejpam-2650	167	4	12	12	NUM
ejpam-2650	167	5	,	,	PUNCT
ejpam-2650	167	6	2	2	NUM
ejpam-2650	167	7	]	]	SYM
ejpam-2650	167	8	2	2	NUM
ejpam-2650	167	9	1	1	NUM
ejpam-2650	167	10	5	5	NUM
ejpam-2650	167	11	x3	x3	ADJ
ejpam-2650	167	12	+	+	CCONJ
ejpam-2650	168	1	x4	x4	PROPN
ejpam-2650	169	1	[	[	X
ejpam-2650	169	2	20	20	NUM
ejpam-2650	169	3	,	,	PUNCT
ejpam-2650	169	4	12	12	NUM
ejpam-2650	169	5	,	,	PUNCT
ejpam-2650	169	6	4	4	NUM
ejpam-2650	169	7	]	]	SYM
ejpam-2650	169	8	2	2	NUM
ejpam-2650	169	9	1	1	NUM
ejpam-2650	169	10	5	5	NUM
ejpam-2650	169	11	x3	x3	ADJ
ejpam-2650	169	12	+	+	CCONJ
ejpam-2650	169	13	(	(	PUNCT
ejpam-2650	169	14	1	1	NUM
ejpam-2650	170	1	+	+	NUM
ejpam-2650	170	2	u2)x4	u2)x4	NOUN
ejpam-2650	170	3	[	[	X
ejpam-2650	170	4	20	20	NUM
ejpam-2650	170	5	,	,	PUNCT
ejpam-2650	170	6	13	13	NUM
ejpam-2650	170	7	,	,	PUNCT
ejpam-2650	170	8	4	4	NUM
ejpam-2650	170	9	]	]	SYM
ejpam-2650	170	10	2	2	NUM
ejpam-2650	170	11	1	1	NUM
ejpam-2650	170	12	6	6	NUM
ejpam-2650	170	13	ux+	ux+	ADJ
ejpam-2650	170	14	ux2	ux2	NOUN
ejpam-2650	170	15	+	+	CCONJ
ejpam-2650	170	16	u2x3	u2x3	PROPN
ejpam-2650	170	17	+	+	NUM
ejpam-2650	170	18	ux4	ux4	NOUN
ejpam-2650	170	19	+	+	CCONJ
ejpam-2650	170	20	(	(	PUNCT
ejpam-2650	170	21	u+	u+	NUM
ejpam-2650	170	22	u2)x5	u2)x5	PROPN
ejpam-2650	170	23	[	[	X
ejpam-2650	170	24	24	24	NUM
ejpam-2650	170	25	,	,	PUNCT
ejpam-2650	170	26	4	4	NUM
ejpam-2650	170	27	,	,	PUNCT
ejpam-2650	170	28	12	12	NUM
ejpam-2650	170	29	]	]	SYM
ejpam-2650	170	30	4	4	NUM
ejpam-2650	170	31	2	2	NUM
ejpam-2650	170	32	6	6	NUM
ejpam-2650	170	33	x4	x4	ADV
ejpam-2650	170	34	+	+	NUM
ejpam-2650	170	35	x5	x5	NOUN
ejpam-2650	171	1	[	[	X
ejpam-2650	171	2	24	24	NUM
ejpam-2650	171	3	,	,	PUNCT
ejpam-2650	171	4	15	15	NUM
ejpam-2650	171	5	,	,	PUNCT
ejpam-2650	171	6	4	4	NUM
ejpam-2650	171	7	]	]	SYM
ejpam-2650	171	8	2	2	NUM
ejpam-2650	171	9	1	1	NUM
ejpam-2650	171	10	6	6	NUM
ejpam-2650	171	11	x4	x4	NOUN
ejpam-2650	171	12	+	+	X
ejpam-2650	171	13	(	(	PUNCT
ejpam-2650	171	14	1	1	NUM
ejpam-2650	171	15	+	+	X
ejpam-2650	171	16	u)x5	u)x5	PROPN
ejpam-2650	171	17	[	[	X
ejpam-2650	171	18	24	24	NUM
ejpam-2650	171	19	,	,	PUNCT
ejpam-2650	171	20	16	16	NUM
ejpam-2650	171	21	,	,	PUNCT
ejpam-2650	171	22	4	4	NUM
ejpam-2650	171	23	]	]	SYM
ejpam-2650	171	24	2	2	NUM
ejpam-2650	171	25	1	1	NUM
ejpam-2650	171	26	7	7	NUM
ejpam-2650	171	27	u2x2	u2x2	ADP
ejpam-2650	171	28	+	+	CCONJ
ejpam-2650	171	29	u2x4	u2x4	X
ejpam-2650	171	30	+	+	ADJ
ejpam-2650	171	31	u2x5	u2x5	NOUN
ejpam-2650	172	1	+	+	CCONJ
ejpam-2650	172	2	u2x6	u2x6	ADJ
ejpam-2650	172	3	[	[	X
ejpam-2650	172	4	28	28	NUM
ejpam-2650	172	5	,	,	PUNCT
ejpam-2650	172	6	3	3	NUM
ejpam-2650	172	7	,	,	PUNCT
ejpam-2650	172	8	16	16	NUM
ejpam-2650	172	9	]	]	SYM
ejpam-2650	172	10	16	16	NUM
ejpam-2650	172	11	4	4	NUM
ejpam-2650	172	12	7	7	NUM
ejpam-2650	172	13	1	1	NUM
ejpam-2650	172	14	+	+	CCONJ
ejpam-2650	172	15	x+	x+	ADJ
ejpam-2650	172	16	x2	x2	NOUN
ejpam-2650	173	1	+	+	CCONJ
ejpam-2650	173	2	(	(	PUNCT
ejpam-2650	173	3	1	1	NUM
ejpam-2650	173	4	+	+	NUM
ejpam-2650	173	5	u2)x3	u2)x3	NOUN
ejpam-2650	173	6	+	+	CCONJ
ejpam-2650	173	7	x4	x4	PROPN
ejpam-2650	174	1	+	+	CCONJ
ejpam-2650	175	1	(	(	PUNCT
ejpam-2650	175	2	1	1	NUM
ejpam-2650	175	3	+	+	NUM
ejpam-2650	175	4	u2)x5	u2)x5	PROPN
ejpam-2650	175	5	+	+	CCONJ
ejpam-2650	175	6	(	(	PUNCT
ejpam-2650	175	7	1	1	NUM
ejpam-2650	175	8	+	+	CCONJ
ejpam-2650	175	9	u2)x6	u2)x6	ADJ
ejpam-2650	175	10	[	[	X
ejpam-2650	175	11	28	28	NUM
ejpam-2650	175	12	,	,	PUNCT
ejpam-2650	175	13	6	6	NUM
ejpam-2650	175	14	,	,	PUNCT
ejpam-2650	175	15	12	12	NUM
ejpam-2650	175	16	]	]	SYM
ejpam-2650	175	17	2	2	NUM
ejpam-2650	175	18	1	1	NUM
ejpam-2650	175	19	7	7	NUM
ejpam-2650	175	20	x2	x2	NOUN
ejpam-2650	175	21	+	+	CCONJ
ejpam-2650	175	22	x4	x4	PROPN
ejpam-2650	175	23	+	+	CCONJ
ejpam-2650	175	24	(	(	PUNCT
ejpam-2650	175	25	1	1	NUM
ejpam-2650	175	26	+	+	NUM
ejpam-2650	175	27	u2)x5	u2)x5	PROPN
ejpam-2650	175	28	+	+	CCONJ
ejpam-2650	175	29	(	(	PUNCT
ejpam-2650	175	30	1	1	NUM
ejpam-2650	175	31	+	+	CCONJ
ejpam-2650	175	32	u2)x6	u2)x6	ADJ
ejpam-2650	175	33	[	[	X
ejpam-2650	175	34	28	28	NUM
ejpam-2650	175	35	,	,	PUNCT
ejpam-2650	175	36	12	12	NUM
ejpam-2650	175	37	,	,	PUNCT
ejpam-2650	175	38	8	8	NUM
ejpam-2650	175	39	]	]	SYM
ejpam-2650	175	40	4	4	NUM
ejpam-2650	175	41	2	2	NUM
ejpam-2650	175	42	7	7	NUM
ejpam-2650	175	43	x5	x5	NOUN
ejpam-2650	175	44	+	+	CCONJ
ejpam-2650	175	45	(	(	PUNCT
ejpam-2650	175	46	1	1	NUM
ejpam-2650	175	47	+	+	CCONJ
ejpam-2650	175	48	u2)x6	u2)x6	ADJ
ejpam-2650	175	49	[	[	X
ejpam-2650	175	50	28	28	NUM
ejpam-2650	175	51	,	,	PUNCT
ejpam-2650	175	52	19	19	NUM
ejpam-2650	175	53	,	,	PUNCT
ejpam-2650	175	54	4	4	NUM
ejpam-2650	175	55	]	]	SYM
ejpam-2650	175	56	2	2	NUM
ejpam-2650	175	57	1	1	NUM
ejpam-2650	175	58	8	8	NUM
ejpam-2650	175	59	x3	x3	ADJ
ejpam-2650	175	60	+	+	CCONJ
ejpam-2650	175	61	ux5	ux5	PROPN
ejpam-2650	176	1	+	+	CCONJ
ejpam-2650	176	2	ux6	ux6	NOUN
ejpam-2650	176	3	+	+	CCONJ
ejpam-2650	176	4	x7	x7	NOUN
ejpam-2650	177	1	[	[	X
ejpam-2650	177	2	32	32	NUM
ejpam-2650	177	3	,	,	PUNCT
ejpam-2650	177	4	14	14	NUM
ejpam-2650	177	5	,	,	PUNCT
ejpam-2650	177	6	8	8	NUM
ejpam-2650	177	7	]	]	SYM
ejpam-2650	177	8	2	2	NUM
ejpam-2650	177	9	1	1	NUM
ejpam-2650	177	10	8	8	NUM
ejpam-2650	177	11	x4	x4	PROPN
ejpam-2650	177	12	+	+	NUM
ejpam-2650	177	13	x5	x5	NOUN
ejpam-2650	177	14	+	+	CCONJ
ejpam-2650	177	15	(	(	PUNCT
ejpam-2650	177	16	1	1	NUM
ejpam-2650	177	17	+	+	X
ejpam-2650	177	18	u)x6	u)x6	ADJ
ejpam-2650	177	19	+	+	CCONJ
ejpam-2650	177	20	(	(	PUNCT
ejpam-2650	177	21	1	1	NUM
ejpam-2650	177	22	+	+	NUM
ejpam-2650	177	23	u+	u+	NOUN
ejpam-2650	177	24	u2)x7	u2)x7	NOUN
ejpam-2650	177	25	[	[	X
ejpam-2650	177	26	32	32	NUM
ejpam-2650	177	27	,	,	PUNCT
ejpam-2650	177	28	15	15	NUM
ejpam-2650	177	29	,	,	PUNCT
ejpam-2650	177	30	8	8	NUM
ejpam-2650	177	31	]	]	SYM
ejpam-2650	177	32	2	2	NUM
ejpam-2650	177	33	1	1	NUM
ejpam-2650	177	34	b.	b.	PROPN
ejpam-2650	177	35	yildiz	yildiz	PROPN
ejpam-2650	177	36	,	,	PUNCT
ejpam-2650	177	37	n.	n.	PROPN
ejpam-2650	177	38	tufekci	tufekci	PROPN
ejpam-2650	177	39	/	/	SYM
ejpam-2650	177	40	eur	eur	PROPN
ejpam-2650	177	41	.	.	PUNCT
ejpam-2650	178	1	j.	j.	PROPN
ejpam-2650	178	2	pure	pure	PROPN
ejpam-2650	178	3	appl	appl	PROPN
ejpam-2650	178	4	.	.	PROPN
ejpam-2650	178	5	math	math	PROPN
ejpam-2650	178	6	,	,	PUNCT
ejpam-2650	178	7	10	10	NUM
ejpam-2650	178	8	(	(	PUNCT
ejpam-2650	178	9	5	5	NUM
ejpam-2650	178	10	)	)	PUNCT
ejpam-2650	178	11	(	(	PUNCT
ejpam-2650	178	12	2017	2017	NUM
ejpam-2650	178	13	)	)	PUNCT
ejpam-2650	178	14	,	,	PUNCT
ejpam-2650	178	15	1112	1112	NUM
ejpam-2650	178	16	-	-	SYM
ejpam-2650	178	17	1123	1123	NUM
ejpam-2650	178	18	1119	1119	NUM
ejpam-2650	178	19	table	table	NOUN
ejpam-2650	178	20	2	2	NUM
ejpam-2650	178	21	:	:	PUNCT
ejpam-2650	178	22	divisible	divisible	ADJ
ejpam-2650	178	23	cyclic	cyclic	NOUN
ejpam-2650	178	24	codes	code	NOUN
ejpam-2650	178	25	over	over	ADP
ejpam-2650	178	26	r4,1	r4,1	NOUN
ejpam-2650	178	27	of	of	ADP
ejpam-2650	178	28	length	length	NOUN
ejpam-2650	178	29	n	n	PROPN
ejpam-2650	178	30	and	and	CCONJ
ejpam-2650	178	31	the	the	DET
ejpam-2650	178	32	binary	binary	ADJ
ejpam-2650	178	33	images	image	NOUN
ejpam-2650	178	34	n	n	PRON
ejpam-2650	178	35	g(x	g(x	NOUN
ejpam-2650	178	36	)	)	PUNCT
ejpam-2650	178	37	φhom(〈g(x	φhom(〈g(x	ADJ
ejpam-2650	178	38	)	)	PUNCT
ejpam-2650	178	39	〉	〉	PROPN
ejpam-2650	178	40	)	)	PUNCT
ejpam-2650	178	41	∆	∆	PROPN
ejpam-2650	178	42	level	level	NOUN
ejpam-2650	178	43	2	2	NUM
ejpam-2650	178	44	u+	u+	NOUN
ejpam-2650	178	45	ux	ux	NOUN
ejpam-2650	178	46	[	[	X
ejpam-2650	178	47	16	16	NUM
ejpam-2650	178	48	,	,	PUNCT
ejpam-2650	178	49	3	3	NUM
ejpam-2650	178	50	,	,	PUNCT
ejpam-2650	178	51	8	8	NUM
ejpam-2650	178	52	]	]	SYM
ejpam-2650	178	53	8	8	NUM
ejpam-2650	178	54	3	3	NUM
ejpam-2650	178	55	3	3	NUM
ejpam-2650	178	56	u3x+	u3x+	NOUN
ejpam-2650	178	57	u3x2	u3x2	PROPN
ejpam-2650	179	1	[	[	X
ejpam-2650	179	2	24	24	NUM
ejpam-2650	179	3	,	,	PUNCT
ejpam-2650	179	4	2	2	NUM
ejpam-2650	179	5	,	,	PUNCT
ejpam-2650	179	6	16	16	NUM
ejpam-2650	179	7	]	]	SYM
ejpam-2650	179	8	16	16	NUM
ejpam-2650	179	9	4	4	NUM
ejpam-2650	179	10	3	3	NUM
ejpam-2650	179	11	x+	x+	VERB
ejpam-2650	179	12	x2	x2	PROPN
ejpam-2650	180	1	[	[	X
ejpam-2650	180	2	24	24	NUM
ejpam-2650	180	3	,	,	PUNCT
ejpam-2650	180	4	8	8	NUM
ejpam-2650	180	5	,	,	PUNCT
ejpam-2650	180	6	8	8	NUM
ejpam-2650	180	7	]	]	SYM
ejpam-2650	180	8	4	4	NUM
ejpam-2650	180	9	2	2	NUM
ejpam-2650	180	10	3	3	NUM
ejpam-2650	180	11	x+	x+	X
ejpam-2650	180	12	(	(	PUNCT
ejpam-2650	180	13	1	1	NUM
ejpam-2650	180	14	+	+	NUM
ejpam-2650	180	15	u3)x2	u3)x2	NOUN
ejpam-2650	181	1	[	[	X
ejpam-2650	181	2	24	24	NUM
ejpam-2650	181	3	,	,	PUNCT
ejpam-2650	181	4	9	9	NUM
ejpam-2650	181	5	,	,	PUNCT
ejpam-2650	181	6	8	8	NUM
ejpam-2650	181	7	]	]	SYM
ejpam-2650	181	8	4	4	NUM
ejpam-2650	181	9	2	2	NUM
ejpam-2650	181	10	4	4	NUM
ejpam-2650	181	11	u2x+	u2x+	ADV
ejpam-2650	181	12	u3x2	u3x2	INTJ
ejpam-2650	182	1	+	+	CCONJ
ejpam-2650	182	2	u2x3	u2x3	X
ejpam-2650	182	3	[	[	X
ejpam-2650	182	4	32	32	NUM
ejpam-2650	182	5	,	,	PUNCT
ejpam-2650	182	6	4	4	NUM
ejpam-2650	182	7	,	,	PUNCT
ejpam-2650	182	8	16	16	NUM
ejpam-2650	182	9	]	]	SYM
ejpam-2650	182	10	16	16	NUM
ejpam-2650	182	11	4	4	NUM
ejpam-2650	182	12	4	4	NUM
ejpam-2650	182	13	1	1	NUM
ejpam-2650	182	14	+	+	CCONJ
ejpam-2650	182	15	x+	x+	NUM
ejpam-2650	182	16	(	(	PUNCT
ejpam-2650	182	17	1	1	NUM
ejpam-2650	182	18	+	+	NUM
ejpam-2650	182	19	u3)x2	u3)x2	NOUN
ejpam-2650	183	1	+	+	CCONJ
ejpam-2650	183	2	(	(	PUNCT
ejpam-2650	183	3	1	1	NUM
ejpam-2650	183	4	+	+	NUM
ejpam-2650	183	5	u3)x3	u3)x3	NOUN
ejpam-2650	183	6	[	[	X
ejpam-2650	183	7	32	32	NUM
ejpam-2650	183	8	,	,	PUNCT
ejpam-2650	183	9	5	5	NUM
ejpam-2650	183	10	,	,	PUNCT
ejpam-2650	183	11	16	16	NUM
ejpam-2650	183	12	]	]	SYM
ejpam-2650	183	13	16	16	NUM
ejpam-2650	183	14	4	4	NUM
ejpam-2650	183	15	4	4	NUM
ejpam-2650	183	16	1	1	NUM
ejpam-2650	183	17	+	+	CCONJ
ejpam-2650	183	18	x+	x+	ADJ
ejpam-2650	183	19	x2	x2	NOUN
ejpam-2650	184	1	+	+	CCONJ
ejpam-2650	184	2	(	(	PUNCT
ejpam-2650	184	3	1	1	NUM
ejpam-2650	184	4	+	+	NUM
ejpam-2650	184	5	u3)x3	u3)x3	NOUN
ejpam-2650	184	6	[	[	X
ejpam-2650	184	7	32	32	NUM
ejpam-2650	184	8	,	,	PUNCT
ejpam-2650	184	9	6	6	NUM
ejpam-2650	184	10	,	,	PUNCT
ejpam-2650	184	11	16	16	NUM
ejpam-2650	184	12	]	]	SYM
ejpam-2650	184	13	16	16	NUM
ejpam-2650	184	14	4	4	NUM
ejpam-2650	184	15	6	6	NUM
ejpam-2650	184	16	u3x+	u3x+	ADJ
ejpam-2650	184	17	u3x2	u3x2	PROPN
ejpam-2650	185	1	+	+	NUM
ejpam-2650	185	2	u3x4	u3x4	PROPN
ejpam-2650	185	3	+	+	NUM
ejpam-2650	185	4	u3x5	u3x5	X
ejpam-2650	186	1	[	[	X
ejpam-2650	186	2	48	48	NUM
ejpam-2650	186	3	,	,	PUNCT
ejpam-2650	186	4	2	2	NUM
ejpam-2650	186	5	,	,	PUNCT
ejpam-2650	186	6	32	32	NUM
ejpam-2650	186	7	]	]	SYM
ejpam-2650	186	8	32	32	NUM
ejpam-2650	186	9	5	5	NUM
ejpam-2650	186	10	6	6	NUM
ejpam-2650	186	11	u2x+	u2x+	ADV
ejpam-2650	187	1	u2x2	u2x2	ADP
ejpam-2650	187	2	+	+	X
ejpam-2650	187	3	u3x3	u3x3	X
ejpam-2650	187	4	+	+	CCONJ
ejpam-2650	187	5	u2x4	u2x4	X
ejpam-2650	187	6	+	+	X
ejpam-2650	187	7	(	(	PUNCT
ejpam-2650	187	8	u2	u2	PROPN
ejpam-2650	187	9	+	+	CCONJ
ejpam-2650	187	10	u3)x5	u3)x5	PROPN
ejpam-2650	188	1	[	[	X
ejpam-2650	188	2	48	48	NUM
ejpam-2650	188	3	,	,	PUNCT
ejpam-2650	188	4	4	4	NUM
ejpam-2650	188	5	,	,	PUNCT
ejpam-2650	188	6	24	24	NUM
ejpam-2650	188	7	]	]	SYM
ejpam-2650	188	8	8	8	NUM
ejpam-2650	188	9	3	3	NUM
ejpam-2650	188	10	remark	remark	NOUN
ejpam-2650	188	11	1	1	NUM
ejpam-2650	188	12	.	.	PUNCT
ejpam-2650	189	1	all	all	DET
ejpam-2650	189	2	the	the	DET
ejpam-2650	189	3	binary	binary	ADJ
ejpam-2650	189	4	codes	code	NOUN
ejpam-2650	189	5	given	give	VERB
ejpam-2650	189	6	in	in	ADP
ejpam-2650	189	7	the	the	DET
ejpam-2650	189	8	above	above	ADJ
ejpam-2650	189	9	tables	table	NOUN
ejpam-2650	189	10	are	be	AUX
ejpam-2650	189	11	optimal	optimal	ADJ
ejpam-2650	189	12	or	or	CCONJ
ejpam-2650	189	13	best	well	ADV
ejpam-2650	189	14	known	know	VERB
ejpam-2650	189	15	codes	code	NOUN
ejpam-2650	189	16	,	,	PUNCT
ejpam-2650	189	17	meaning	mean	VERB
ejpam-2650	189	18	that	that	SCONJ
ejpam-2650	189	19	they	they	PRON
ejpam-2650	189	20	either	either	CCONJ
ejpam-2650	189	21	attain	attain	VERB
ejpam-2650	189	22	upper	upper	ADJ
ejpam-2650	189	23	bounds	bound	NOUN
ejpam-2650	189	24	or	or	CCONJ
ejpam-2650	189	25	have	have	VERB
ejpam-2650	189	26	the	the	DET
ejpam-2650	189	27	best	well	ADV
ejpam-2650	189	28	known	know	VERB
ejpam-2650	189	29	minimum	minimum	NOUN
ejpam-2650	189	30	distance	distance	NOUN
ejpam-2650	189	31	according	accord	VERB
ejpam-2650	189	32	to	to	ADP
ejpam-2650	189	33	[	[	X
ejpam-2650	189	34	5	5	NUM
ejpam-2650	189	35	]	]	PUNCT
ejpam-2650	189	36	.	.	PUNCT
ejpam-2650	190	1	the	the	DET
ejpam-2650	190	2	codes	code	NOUN
ejpam-2650	190	3	given	give	VERB
ejpam-2650	190	4	in	in	ADP
ejpam-2650	190	5	table	table	NOUN
ejpam-2650	190	6	2	2	NUM
ejpam-2650	190	7	have	have	VERB
ejpam-2650	190	8	the	the	DET
ejpam-2650	190	9	additional	additional	ADJ
ejpam-2650	190	10	property	property	NOUN
ejpam-2650	190	11	that	that	PRON
ejpam-2650	190	12	they	they	PRON
ejpam-2650	190	13	are	be	AUX
ejpam-2650	190	14	all	all	PRON
ejpam-2650	190	15	self	self	NOUN
ejpam-2650	190	16	-	-	PUNCT
ejpam-2650	190	17	orthogonal	orthogonal	ADJ
ejpam-2650	190	18	quasicyclic	quasicyclic	NOUN
ejpam-2650	190	19	codes	code	NOUN
ejpam-2650	190	20	of	of	ADP
ejpam-2650	190	21	the	the	DET
ejpam-2650	190	22	best	good	ADJ
ejpam-2650	190	23	possible	possible	ADJ
ejpam-2650	190	24	parameters	parameter	NOUN
ejpam-2650	190	25	.	.	PUNCT
ejpam-2650	191	1	4.2	4.2	NUM
ejpam-2650	191	2	.	.	PUNCT
ejpam-2650	191	3	divisible	divisible	ADJ
ejpam-2650	191	4	constacyclic	constacyclic	ADJ
ejpam-2650	191	5	codes	code	NOUN
ejpam-2650	191	6	over	over	ADP
ejpam-2650	191	7	rk	rk	PROPN
ejpam-2650	191	8	,	,	PUNCT
ejpam-2650	191	9	m	m	PROPN
ejpam-2650	191	10	constacyclic	constacyclic	ADJ
ejpam-2650	191	11	codes	code	NOUN
ejpam-2650	191	12	are	be	AUX
ejpam-2650	191	13	a	a	DET
ejpam-2650	191	14	natural	natural	ADJ
ejpam-2650	191	15	generalization	generalization	NOUN
ejpam-2650	191	16	of	of	ADP
ejpam-2650	191	17	cyclic	cyclic	ADJ
ejpam-2650	191	18	codes	code	NOUN
ejpam-2650	191	19	.	.	PUNCT
ejpam-2650	192	1	for	for	ADP
ejpam-2650	192	2	a	a	DET
ejpam-2650	192	3	unit	unit	NOUN
ejpam-2650	192	4	α	α	NOUN
ejpam-2650	192	5	∈	∈	PROPN
ejpam-2650	192	6	r	r	NOUN
ejpam-2650	192	7	,	,	PUNCT
ejpam-2650	192	8	a	a	DET
ejpam-2650	192	9	constacyclic	constacyclic	ADJ
ejpam-2650	192	10	shift	shift	NOUN
ejpam-2650	192	11	on	on	ADP
ejpam-2650	192	12	rn	rn	PROPN
ejpam-2650	192	13	is	be	AUX
ejpam-2650	192	14	given	give	VERB
ejpam-2650	192	15	by	by	ADP
ejpam-2650	192	16	τα(c0	τα(c0	PROPN
ejpam-2650	192	17	,	,	PUNCT
ejpam-2650	192	18	c1	c1	PROPN
ejpam-2650	192	19	,	,	PUNCT
ejpam-2650	192	20	.	.	PUNCT
ejpam-2650	192	21	.	.	PUNCT
ejpam-2650	193	1	.	.	PUNCT
ejpam-2650	194	1	,	,	PUNCT
ejpam-2650	194	2	cn−1	cn−1	X
ejpam-2650	194	3	)	)	PUNCT
ejpam-2650	194	4	=	=	SYM
ejpam-2650	194	5	(	(	PUNCT
ejpam-2650	195	1	αcn−1	αcn−1	PROPN
ejpam-2650	195	2	,	,	PUNCT
ejpam-2650	195	3	c0	c0	NOUN
ejpam-2650	195	4	,	,	PUNCT
ejpam-2650	195	5	c1	c1	PROPN
ejpam-2650	195	6	,	,	PUNCT
ejpam-2650	195	7	.	.	PUNCT
ejpam-2650	195	8	.	.	PUNCT
ejpam-2650	196	1	.	.	PUNCT
ejpam-2650	197	1	,	,	PUNCT
ejpam-2650	197	2	cn−2	cn−2	PROPN
ejpam-2650	197	3	)	)	PUNCT
ejpam-2650	197	4	.	.	PUNCT
ejpam-2650	198	1	a	a	DET
ejpam-2650	198	2	code	code	NOUN
ejpam-2650	198	3	c	c	NOUN
ejpam-2650	198	4	over	over	ADP
ejpam-2650	198	5	r	r	NOUN
ejpam-2650	198	6	is	be	AUX
ejpam-2650	198	7	said	say	VERB
ejpam-2650	198	8	to	to	PART
ejpam-2650	198	9	be	be	AUX
ejpam-2650	198	10	α	α	NOUN
ejpam-2650	198	11	-	-	NOUN
ejpam-2650	198	12	constacyclic	constacyclic	ADJ
ejpam-2650	198	13	if	if	SCONJ
ejpam-2650	198	14	it	it	PRON
ejpam-2650	198	15	is	be	AUX
ejpam-2650	198	16	invariant	invariant	ADJ
ejpam-2650	198	17	under	under	ADP
ejpam-2650	198	18	the	the	DET
ejpam-2650	198	19	α	α	ADJ
ejpam-2650	198	20	-	-	ADJ
ejpam-2650	198	21	constacyclic	constacyclic	ADJ
ejpam-2650	198	22	shift	shift	NOUN
ejpam-2650	198	23	,	,	PUNCT
ejpam-2650	198	24	i.e.	i.e.	X
ejpam-2650	198	25	,	,	PUNCT
ejpam-2650	198	26	τα(c	τα(c	NUM
ejpam-2650	198	27	)	)	PUNCT
ejpam-2650	198	28	=	=	SYM
ejpam-2650	198	29	c.	c.	NOUN
ejpam-2650	198	30	in	in	ADP
ejpam-2650	198	31	exactly	exactly	ADV
ejpam-2650	198	32	the	the	DET
ejpam-2650	198	33	same	same	ADJ
ejpam-2650	198	34	way	way	NOUN
ejpam-2650	198	35	as	as	ADP
ejpam-2650	198	36	the	the	DET
ejpam-2650	198	37	cyclic	cyclic	ADJ
ejpam-2650	198	38	codes	code	NOUN
ejpam-2650	198	39	,	,	PUNCT
ejpam-2650	198	40	constacylic	constacylic	ADJ
ejpam-2650	198	41	codes	code	NOUN
ejpam-2650	198	42	are	be	AUX
ejpam-2650	198	43	also	also	ADV
ejpam-2650	198	44	endowed	endow	VERB
ejpam-2650	198	45	with	with	ADP
ejpam-2650	198	46	an	an	DET
ejpam-2650	198	47	algebraic	algebraic	ADJ
ejpam-2650	198	48	structure	structure	NOUN
ejpam-2650	198	49	.	.	PUNCT
ejpam-2650	199	1	more	more	ADV
ejpam-2650	199	2	precisely	precisely	ADV
ejpam-2650	199	3	,	,	PUNCT
ejpam-2650	199	4	constacyclic	constacyclic	ADJ
ejpam-2650	199	5	codes	code	NOUN
ejpam-2650	199	6	over	over	ADP
ejpam-2650	199	7	r	r	NOUN
ejpam-2650	199	8	are	be	AUX
ejpam-2650	199	9	in	in	ADP
ejpam-2650	199	10	one	one	NUM
ejpam-2650	199	11	-	-	PUNCT
ejpam-2650	199	12	to	to	ADP
ejpam-2650	199	13	-	-	PUNCT
ejpam-2650	199	14	one	one	NUM
ejpam-2650	199	15	correspondence	correspondence	NOUN
ejpam-2650	199	16	with	with	ADP
ejpam-2650	199	17	ideals	ideal	NOUN
ejpam-2650	199	18	in	in	ADP
ejpam-2650	199	19	the	the	DET
ejpam-2650	199	20	quoient	quoient	NOUN
ejpam-2650	199	21	ring	ring	NOUN
ejpam-2650	199	22	r[x]/(xn	r[x]/(xn	PUNCT
ejpam-2650	200	1	−	−	NOUN
ejpam-2650	200	2	α	α	NOUN
ejpam-2650	200	3	)	)	PUNCT
ejpam-2650	200	4	.	.	PUNCT
ejpam-2650	201	1	structural	structural	ADJ
ejpam-2650	201	2	properties	property	NOUN
ejpam-2650	201	3	of	of	ADP
ejpam-2650	201	4	constacyclic	constacyclic	ADJ
ejpam-2650	201	5	codes	code	NOUN
ejpam-2650	201	6	over	over	ADP
ejpam-2650	201	7	different	different	ADJ
ejpam-2650	201	8	alphabets	alphabet	NOUN
ejpam-2650	201	9	have	have	AUX
ejpam-2650	201	10	been	be	AUX
ejpam-2650	201	11	studied	study	VERB
ejpam-2650	201	12	quite	quite	ADV
ejpam-2650	201	13	extensively	extensively	ADV
ejpam-2650	201	14	in	in	ADP
ejpam-2650	201	15	the	the	DET
ejpam-2650	201	16	literature	literature	NOUN
ejpam-2650	201	17	.	.	PUNCT
ejpam-2650	202	1	in	in	ADP
ejpam-2650	202	2	[	[	X
ejpam-2650	202	3	9	9	NUM
ejpam-2650	202	4	]	]	PUNCT
ejpam-2650	202	5	,	,	PUNCT
ejpam-2650	202	6	karadeniz	karadeniz	PROPN
ejpam-2650	202	7	and	and	CCONJ
ejpam-2650	202	8	yildiz	yildiz	PROPN
ejpam-2650	202	9	studied	study	VERB
ejpam-2650	202	10	(	(	PUNCT
ejpam-2650	202	11	1	1	NUM
ejpam-2650	202	12	+	+	NOUN
ejpam-2650	202	13	v)-constacyclic	v)-constacyclic	ADJ
ejpam-2650	202	14	codes	code	NOUN
ejpam-2650	202	15	over	over	ADP
ejpam-2650	202	16	r2,2	r2,2	PROPN
ejpam-2650	202	17	=	=	SYM
ejpam-2650	202	18	f2	f2	PROPN
ejpam-2650	202	19	+	+	CCONJ
ejpam-2650	202	20	uf2	uf2	NOUN
ejpam-2650	202	21	+	+	CCONJ
ejpam-2650	202	22	vf2	vf2	NOUN
ejpam-2650	202	23	+	+	CCONJ
ejpam-2650	202	24	uvf2	uvf2	PROPN
ejpam-2650	202	25	.	.	PUNCT
ejpam-2650	203	1	it	it	PRON
ejpam-2650	203	2	is	be	AUX
ejpam-2650	203	3	well	well	ADV
ejpam-2650	203	4	known	know	VERB
ejpam-2650	203	5	that	that	SCONJ
ejpam-2650	203	6	if	if	SCONJ
ejpam-2650	203	7	r	r	NOUN
ejpam-2650	203	8	is	be	AUX
ejpam-2650	203	9	a	a	DET
ejpam-2650	203	10	ring	ring	NOUN
ejpam-2650	203	11	of	of	ADP
ejpam-2650	203	12	characteristic	characteristic	ADJ
ejpam-2650	203	13	2	2	NUM
ejpam-2650	203	14	,	,	PUNCT
ejpam-2650	203	15	and	and	CCONJ
ejpam-2650	203	16	α	α	PRON
ejpam-2650	203	17	∈	∈	NOUN
ejpam-2650	203	18	r	r	NOUN
ejpam-2650	203	19	satisfies	satisfie	NOUN
ejpam-2650	203	20	α2	α2	PROPN
ejpam-2650	203	21	=	=	SYM
ejpam-2650	204	1	1	1	NUM
ejpam-2650	204	2	,	,	PUNCT
ejpam-2650	204	3	then	then	ADV
ejpam-2650	204	4	α	α	X
ejpam-2650	204	5	-	-	ADJ
ejpam-2650	204	6	constacyclic	constacyclic	ADJ
ejpam-2650	204	7	codes	code	NOUN
ejpam-2650	204	8	over	over	ADP
ejpam-2650	204	9	r	r	NOUN
ejpam-2650	204	10	are	be	AUX
ejpam-2650	204	11	also	also	ADV
ejpam-2650	204	12	cyclic	cyclic	ADJ
ejpam-2650	204	13	.	.	PUNCT
ejpam-2650	205	1	in	in	ADP
ejpam-2650	205	2	r2,2	r2,2	PROPN
ejpam-2650	205	3	as	as	ADV
ejpam-2650	205	4	well	well	ADV
ejpam-2650	205	5	as	as	ADP
ejpam-2650	205	6	in	in	ADP
ejpam-2650	205	7	the	the	DET
ejpam-2650	205	8	latter	latter	ADJ
ejpam-2650	205	9	generalizations	generalization	NOUN
ejpam-2650	205	10	rk	rk	VERB
ejpam-2650	205	11	,	,	PUNCT
ejpam-2650	205	12	[	[	X
ejpam-2650	205	13	15	15	NUM
ejpam-2650	205	14	]	]	X
ejpam-2650	205	15	,	,	PUNCT
ejpam-2650	205	16	every	every	DET
ejpam-2650	205	17	unit	unit	NOUN
ejpam-2650	205	18	satisfies	satisfy	VERB
ejpam-2650	205	19	this	this	DET
ejpam-2650	205	20	property	property	NOUN
ejpam-2650	205	21	.	.	PUNCT
ejpam-2650	206	1	so	so	ADV
ejpam-2650	206	2	,	,	PUNCT
ejpam-2650	206	3	constacyclic	constacyclic	ADJ
ejpam-2650	206	4	codes	code	NOUN
ejpam-2650	206	5	over	over	ADP
ejpam-2650	206	6	these	these	DET
ejpam-2650	206	7	rings	ring	NOUN
ejpam-2650	206	8	of	of	ADP
ejpam-2650	206	9	odd	odd	ADJ
ejpam-2650	206	10	lengths	length	NOUN
ejpam-2650	206	11	are	be	AUX
ejpam-2650	206	12	just	just	ADV
ejpam-2650	206	13	cyclic	cyclic	ADJ
ejpam-2650	206	14	.	.	PUNCT
ejpam-2650	207	1	however	however	ADV
ejpam-2650	207	2	,	,	PUNCT
ejpam-2650	207	3	the	the	DET
ejpam-2650	207	4	cases	case	NOUN
ejpam-2650	207	5	that	that	PRON
ejpam-2650	207	6	we	we	PRON
ejpam-2650	207	7	look	look	VERB
ejpam-2650	207	8	at	at	ADP
ejpam-2650	207	9	,	,	PUNCT
ejpam-2650	207	10	namely	namely	ADV
ejpam-2650	207	11	in	in	ADP
ejpam-2650	207	12	r3,1	r3,1	PROPN
ejpam-2650	207	13	,	,	PUNCT
ejpam-2650	207	14	r4,1	r4,1	PROPN
ejpam-2650	207	15	and	and	CCONJ
ejpam-2650	207	16	r5,1	r5,1	PROPN
ejpam-2650	207	17	this	this	PRON
ejpam-2650	207	18	is	be	AUX
ejpam-2650	207	19	not	not	PART
ejpam-2650	207	20	true	true	ADJ
ejpam-2650	207	21	.	.	PUNCT
ejpam-2650	208	1	if	if	SCONJ
ejpam-2650	208	2	we	we	PRON
ejpam-2650	208	3	take	take	VERB
ejpam-2650	208	4	α	α	NOUN
ejpam-2650	208	5	=	=	SYM
ejpam-2650	208	6	1	1	NUM
ejpam-2650	208	7	+	+	NUM
ejpam-2650	208	8	u	u	NOUN
ejpam-2650	208	9	,	,	PUNCT
ejpam-2650	208	10	then	then	ADV
ejpam-2650	208	11	(	(	PUNCT
ejpam-2650	208	12	1	1	NUM
ejpam-2650	208	13	+	+	CCONJ
ejpam-2650	208	14	u)2	u)2	NOUN
ejpam-2650	208	15	6=	6=	NUM
ejpam-2650	208	16	1	1	NUM
ejpam-2650	208	17	in	in	ADP
ejpam-2650	208	18	the	the	DET
ejpam-2650	208	19	rings	ring	NOUN
ejpam-2650	208	20	mentioned	mention	VERB
ejpam-2650	208	21	above	above	ADV
ejpam-2650	208	22	.	.	PUNCT
ejpam-2650	209	1	in	in	ADP
ejpam-2650	209	2	what	what	PRON
ejpam-2650	209	3	follows	follow	VERB
ejpam-2650	209	4	,	,	PUNCT
ejpam-2650	209	5	we	we	PRON
ejpam-2650	209	6	have	have	AUX
ejpam-2650	209	7	listed	list	VERB
ejpam-2650	209	8	some	some	DET
ejpam-2650	209	9	examples	example	NOUN
ejpam-2650	209	10	of	of	ADP
ejpam-2650	209	11	one	one	NUM
ejpam-2650	209	12	-	-	PUNCT
ejpam-2650	209	13	generator	generator	NOUN
ejpam-2650	209	14	(	(	PUNCT
ejpam-2650	209	15	1	1	NUM
ejpam-2650	209	16	+	+	CCONJ
ejpam-2650	209	17	u)-constacyclic	u)-constacyclic	ADJ
ejpam-2650	209	18	codes	code	NOUN
ejpam-2650	209	19	over	over	ADP
ejpam-2650	209	20	rk	rk	NOUN
ejpam-2650	209	21	,	,	PUNCT
ejpam-2650	209	22	m	m	PRON
ejpam-2650	209	23	and	and	CCONJ
ejpam-2650	209	24	their	their	PRON
ejpam-2650	209	25	homogeneous	homogeneous	ADJ
ejpam-2650	209	26	gray	gray	ADJ
ejpam-2650	209	27	images	image	NOUN
ejpam-2650	209	28	,	,	PUNCT
ejpam-2650	209	29	which	which	PRON
ejpam-2650	209	30	turn	turn	VERB
ejpam-2650	209	31	out	out	ADP
ejpam-2650	209	32	to	to	PART
ejpam-2650	209	33	be	be	AUX
ejpam-2650	209	34	divisible	divisible	ADJ
ejpam-2650	209	35	,	,	PUNCT
ejpam-2650	209	36	optimal	optimal	ADJ
ejpam-2650	209	37	and	and	CCONJ
ejpam-2650	209	38	in	in	ADP
ejpam-2650	209	39	some	some	DET
ejpam-2650	209	40	cases	case	NOUN
ejpam-2650	209	41	self	self	NOUN
ejpam-2650	209	42	-	-	PUNCT
ejpam-2650	209	43	orthogonal	orthogonal	NOUN
ejpam-2650	209	44	:	:	PUNCT
ejpam-2650	209	45	b.	b.	PROPN
ejpam-2650	209	46	yildiz	yildiz	PROPN
ejpam-2650	209	47	,	,	PUNCT
ejpam-2650	209	48	n.	n.	PROPN
ejpam-2650	209	49	tufekci	tufekci	PROPN
ejpam-2650	209	50	/	/	SYM
ejpam-2650	209	51	eur	eur	PROPN
ejpam-2650	209	52	.	.	PUNCT
ejpam-2650	210	1	j.	j.	PROPN
ejpam-2650	210	2	pure	pure	PROPN
ejpam-2650	210	3	appl	appl	PROPN
ejpam-2650	210	4	.	.	PROPN
ejpam-2650	210	5	math	math	PROPN
ejpam-2650	210	6	,	,	PUNCT
ejpam-2650	210	7	10	10	NUM
ejpam-2650	210	8	(	(	PUNCT
ejpam-2650	210	9	5	5	NUM
ejpam-2650	210	10	)	)	PUNCT
ejpam-2650	210	11	(	(	PUNCT
ejpam-2650	210	12	2017	2017	NUM
ejpam-2650	210	13	)	)	PUNCT
ejpam-2650	210	14	,	,	PUNCT
ejpam-2650	210	15	1112	1112	NUM
ejpam-2650	210	16	-	-	SYM
ejpam-2650	210	17	1123	1123	NUM
ejpam-2650	210	18	1120	1120	NUM
ejpam-2650	210	19	table	table	NOUN
ejpam-2650	210	20	3	3	NUM
ejpam-2650	210	21	:	:	PUNCT
ejpam-2650	210	22	divisible	divisible	ADJ
ejpam-2650	210	23	(	(	PUNCT
ejpam-2650	210	24	1	1	NUM
ejpam-2650	210	25	+	+	CCONJ
ejpam-2650	210	26	u)-constacyclic	u)-constacyclic	ADJ
ejpam-2650	210	27	codes	code	NOUN
ejpam-2650	210	28	over	over	ADP
ejpam-2650	210	29	rk,1	rk,1	NOUN
ejpam-2650	210	30	of	of	ADP
ejpam-2650	210	31	length	length	NOUN
ejpam-2650	210	32	n	n	PROPN
ejpam-2650	210	33	and	and	CCONJ
ejpam-2650	210	34	the	the	DET
ejpam-2650	210	35	binary	binary	ADJ
ejpam-2650	210	36	images	image	NOUN
ejpam-2650	210	37	rk,1	rk,1	PROPN
ejpam-2650	210	38	n	n	PRON
ejpam-2650	210	39	generator	generator	NOUN
ejpam-2650	210	40	of	of	ADP
ejpam-2650	210	41	the	the	DET
ejpam-2650	210	42	code	code	NOUN
ejpam-2650	210	43	φhom(〈g(x	φhom(〈g(x	NOUN
ejpam-2650	210	44	)	)	PUNCT
ejpam-2650	210	45	〉	〉	PROPN
ejpam-2650	210	46	)	)	PUNCT
ejpam-2650	210	47	∆	∆	PROPN
ejpam-2650	210	48	level	level	NOUN
ejpam-2650	210	49	r3,1	r3,1	PROPN
ejpam-2650	210	50	6	6	NUM
ejpam-2650	210	51	(	(	PUNCT
ejpam-2650	210	52	0	0	NUM
ejpam-2650	210	53	,	,	PUNCT
ejpam-2650	210	54	u2	u2	NOUN
ejpam-2650	210	55	,	,	PUNCT
ejpam-2650	210	56	u2	u2	NOUN
ejpam-2650	210	57	,	,	PUNCT
ejpam-2650	210	58	0	0	NUM
ejpam-2650	210	59	,	,	PUNCT
ejpam-2650	210	60	u2	u2	NOUN
ejpam-2650	210	61	,	,	PUNCT
ejpam-2650	210	62	u2	u2	PROPN
ejpam-2650	210	63	)	)	PUNCT
ejpam-2650	211	1	[	[	X
ejpam-2650	211	2	24	24	NUM
ejpam-2650	211	3	,	,	PUNCT
ejpam-2650	211	4	2	2	NUM
ejpam-2650	211	5	,	,	PUNCT
ejpam-2650	211	6	16	16	NUM
ejpam-2650	211	7	]	]	SYM
ejpam-2650	211	8	16	16	NUM
ejpam-2650	211	9	4	4	NUM
ejpam-2650	211	10	r3,1	r3,1	PROPN
ejpam-2650	211	11	6	6	NUM
ejpam-2650	211	12	(	(	PUNCT
ejpam-2650	211	13	0	0	NUM
ejpam-2650	211	14	,	,	PUNCT
ejpam-2650	211	15	0	0	NUM
ejpam-2650	211	16	,	,	PUNCT
ejpam-2650	211	17	0	0	NUM
ejpam-2650	211	18	,	,	PUNCT
ejpam-2650	211	19	1	1	NUM
ejpam-2650	211	20	,	,	PUNCT
ejpam-2650	211	21	u	u	NOUN
ejpam-2650	211	22	,	,	PUNCT
ejpam-2650	211	23	1	1	NUM
ejpam-2650	211	24	)	)	PUNCT
ejpam-2650	212	1	[	[	X
ejpam-2650	212	2	24	24	NUM
ejpam-2650	212	3	,	,	PUNCT
ejpam-2650	212	4	15	15	NUM
ejpam-2650	212	5	,	,	PUNCT
ejpam-2650	212	6	4	4	NUM
ejpam-2650	212	7	]	]	SYM
ejpam-2650	212	8	2	2	NUM
ejpam-2650	212	9	1	1	NUM
ejpam-2650	212	10	r3,1	r3,1	PROPN
ejpam-2650	212	11	7	7	NUM
ejpam-2650	212	12	(	(	PUNCT
ejpam-2650	212	13	0	0	NUM
ejpam-2650	212	14	,	,	PUNCT
ejpam-2650	212	15	0	0	NUM
ejpam-2650	212	16	,	,	PUNCT
ejpam-2650	212	17	u2	u2	NOUN
ejpam-2650	212	18	,	,	PUNCT
ejpam-2650	212	19	0	0	NUM
ejpam-2650	212	20	,	,	PUNCT
ejpam-2650	212	21	u2	u2	NOUN
ejpam-2650	212	22	,	,	PUNCT
ejpam-2650	212	23	u2	u2	NOUN
ejpam-2650	212	24	,	,	PUNCT
ejpam-2650	212	25	u2	u2	PROPN
ejpam-2650	212	26	)	)	PUNCT
ejpam-2650	213	1	[	[	X
ejpam-2650	213	2	28	28	NUM
ejpam-2650	213	3	,	,	PUNCT
ejpam-2650	213	4	3	3	NUM
ejpam-2650	213	5	,	,	PUNCT
ejpam-2650	213	6	16	16	NUM
ejpam-2650	213	7	]	]	SYM
ejpam-2650	213	8	16	16	NUM
ejpam-2650	213	9	4	4	NUM
ejpam-2650	213	10	r3,1	r3,1	PROPN
ejpam-2650	213	11	7	7	NUM
ejpam-2650	213	12	(	(	PUNCT
ejpam-2650	213	13	1	1	NUM
ejpam-2650	213	14	,	,	PUNCT
ejpam-2650	213	15	u+	u+	NUM
ejpam-2650	213	16	1	1	NUM
ejpam-2650	213	17	,	,	PUNCT
ejpam-2650	213	18	1	1	NUM
ejpam-2650	213	19	,	,	PUNCT
ejpam-2650	213	20	u+	u+	NUM
ejpam-2650	213	21	1	1	NUM
ejpam-2650	213	22	,	,	PUNCT
ejpam-2650	213	23	1	1	NUM
ejpam-2650	213	24	,	,	PUNCT
ejpam-2650	213	25	u2	u2	PROPN
ejpam-2650	213	26	+	+	CCONJ
ejpam-2650	213	27	u+	u+	NUM
ejpam-2650	213	28	1	1	NUM
ejpam-2650	213	29	,	,	PUNCT
ejpam-2650	213	30	u2	u2	NOUN
ejpam-2650	213	31	+	+	CCONJ
ejpam-2650	213	32	1	1	NUM
ejpam-2650	213	33	)	)	PUNCT
ejpam-2650	214	1	[	[	X
ejpam-2650	214	2	28	28	NUM
ejpam-2650	214	3	,	,	PUNCT
ejpam-2650	214	4	6	6	NUM
ejpam-2650	214	5	,	,	PUNCT
ejpam-2650	214	6	12	12	NUM
ejpam-2650	214	7	]	]	SYM
ejpam-2650	214	8	2	2	NUM
ejpam-2650	214	9	1	1	NUM
ejpam-2650	214	10	r3,1	r3,1	PROPN
ejpam-2650	214	11	7	7	NUM
ejpam-2650	214	12	(	(	PUNCT
ejpam-2650	214	13	0	0	NUM
ejpam-2650	214	14	,	,	PUNCT
ejpam-2650	214	15	0	0	NUM
ejpam-2650	214	16	,	,	PUNCT
ejpam-2650	214	17	1	1	NUM
ejpam-2650	214	18	,	,	PUNCT
ejpam-2650	214	19	0	0	NUM
ejpam-2650	214	20	,	,	PUNCT
ejpam-2650	214	21	1	1	NUM
ejpam-2650	214	22	,	,	PUNCT
ejpam-2650	214	23	u+	u+	NUM
ejpam-2650	214	24	1	1	NUM
ejpam-2650	214	25	,	,	PUNCT
ejpam-2650	214	26	1	1	NUM
ejpam-2650	214	27	)	)	PUNCT
ejpam-2650	215	1	[	[	X
ejpam-2650	215	2	28	28	NUM
ejpam-2650	215	3	,	,	PUNCT
ejpam-2650	215	4	12	12	NUM
ejpam-2650	215	5	,	,	PUNCT
ejpam-2650	215	6	8	8	NUM
ejpam-2650	215	7	]	]	SYM
ejpam-2650	215	8	4	4	NUM
ejpam-2650	215	9	2	2	NUM
ejpam-2650	215	10	r3,1	r3,1	PROPN
ejpam-2650	215	11	7	7	NUM
ejpam-2650	215	12	(	(	PUNCT
ejpam-2650	215	13	0	0	NUM
ejpam-2650	215	14	,	,	PUNCT
ejpam-2650	215	15	0	0	NUM
ejpam-2650	215	16	,	,	PUNCT
ejpam-2650	215	17	0	0	NUM
ejpam-2650	215	18	,	,	PUNCT
ejpam-2650	215	19	0	0	NUM
ejpam-2650	215	20	,	,	PUNCT
ejpam-2650	215	21	0	0	NUM
ejpam-2650	215	22	,	,	PUNCT
ejpam-2650	215	23	1	1	NUM
ejpam-2650	215	24	,	,	PUNCT
ejpam-2650	215	25	u2	u2	PROPN
ejpam-2650	215	26	+	+	CCONJ
ejpam-2650	215	27	u+	u+	NUM
ejpam-2650	215	28	1	1	NUM
ejpam-2650	215	29	)	)	PUNCT
ejpam-2650	216	1	[	[	X
ejpam-2650	216	2	28	28	NUM
ejpam-2650	216	3	,	,	PUNCT
ejpam-2650	216	4	19	19	NUM
ejpam-2650	216	5	,	,	PUNCT
ejpam-2650	216	6	4	4	NUM
ejpam-2650	216	7	]	]	SYM
ejpam-2650	216	8	2	2	NUM
ejpam-2650	216	9	1	1	NUM
ejpam-2650	216	10	r3,1	r3,1	PROPN
ejpam-2650	216	11	9	9	NUM
ejpam-2650	216	12	(	(	PUNCT
ejpam-2650	216	13	0	0	NUM
ejpam-2650	216	14	,	,	PUNCT
ejpam-2650	216	15	u2	u2	NOUN
ejpam-2650	216	16	,	,	PUNCT
ejpam-2650	216	17	u2	u2	NOUN
ejpam-2650	216	18	,	,	PUNCT
ejpam-2650	216	19	0	0	NUM
ejpam-2650	216	20	,	,	PUNCT
ejpam-2650	216	21	u2	u2	NOUN
ejpam-2650	216	22	,	,	PUNCT
ejpam-2650	216	23	u2	u2	NOUN
ejpam-2650	216	24	,	,	PUNCT
ejpam-2650	216	25	0	0	NUM
ejpam-2650	216	26	,	,	PUNCT
ejpam-2650	216	27	u2	u2	NOUN
ejpam-2650	216	28	,	,	PUNCT
ejpam-2650	216	29	u2	u2	PROPN
ejpam-2650	216	30	)	)	PUNCT
ejpam-2650	217	1	[	[	X
ejpam-2650	217	2	36	36	NUM
ejpam-2650	217	3	,	,	PUNCT
ejpam-2650	217	4	2	2	NUM
ejpam-2650	217	5	,	,	PUNCT
ejpam-2650	217	6	24	24	NUM
ejpam-2650	217	7	]	]	SYM
ejpam-2650	217	8	24	24	NUM
ejpam-2650	217	9	r4,1	r4,1	NOUN
ejpam-2650	217	10	2	2	NUM
ejpam-2650	217	11	(	(	PUNCT
ejpam-2650	217	12	u2	u2	NOUN
ejpam-2650	217	13	,	,	PUNCT
ejpam-2650	217	14	u2	u2	PROPN
ejpam-2650	217	15	)	)	PUNCT
ejpam-2650	218	1	[	[	X
ejpam-2650	218	2	16	16	NUM
ejpam-2650	218	3	,	,	PUNCT
ejpam-2650	218	4	3	3	NUM
ejpam-2650	218	5	,	,	PUNCT
ejpam-2650	218	6	8	8	NUM
ejpam-2650	218	7	]	]	SYM
ejpam-2650	218	8	8	8	NUM
ejpam-2650	218	9	3	3	NUM
ejpam-2650	218	10	r4,1	r4,1	NOUN
ejpam-2650	218	11	3	3	NUM
ejpam-2650	218	12	(	(	PUNCT
ejpam-2650	218	13	0	0	NUM
ejpam-2650	218	14	,	,	PUNCT
ejpam-2650	218	15	1	1	NUM
ejpam-2650	218	16	,	,	PUNCT
ejpam-2650	218	17	u+	u+	NUM
ejpam-2650	218	18	1	1	NUM
ejpam-2650	218	19	)	)	PUNCT
ejpam-2650	219	1	[	[	X
ejpam-2650	219	2	24	24	NUM
ejpam-2650	219	3	,	,	PUNCT
ejpam-2650	219	4	8	8	NUM
ejpam-2650	219	5	,	,	PUNCT
ejpam-2650	219	6	8	8	NUM
ejpam-2650	219	7	]	]	SYM
ejpam-2650	219	8	4	4	NUM
ejpam-2650	219	9	2	2	NUM
ejpam-2650	219	10	r4,1	r4,1	NOUN
ejpam-2650	219	11	3	3	NUM
ejpam-2650	219	12	(	(	PUNCT
ejpam-2650	219	13	0	0	NUM
ejpam-2650	219	14	,	,	PUNCT
ejpam-2650	219	15	1	1	NUM
ejpam-2650	219	16	,	,	PUNCT
ejpam-2650	219	17	u3	u3	NOUN
ejpam-2650	219	18	+	+	CCONJ
ejpam-2650	219	19	u+	u+	NUM
ejpam-2650	219	20	1	1	NUM
ejpam-2650	219	21	)	)	PUNCT
ejpam-2650	220	1	[	[	X
ejpam-2650	220	2	24	24	NUM
ejpam-2650	220	3	,	,	PUNCT
ejpam-2650	220	4	9	9	NUM
ejpam-2650	220	5	,	,	PUNCT
ejpam-2650	220	6	8	8	NUM
ejpam-2650	220	7	]	]	SYM
ejpam-2650	220	8	4	4	NUM
ejpam-2650	220	9	2	2	NUM
ejpam-2650	220	10	r4,1	r4,1	NOUN
ejpam-2650	220	11	5	5	NUM
ejpam-2650	220	12	(	(	PUNCT
ejpam-2650	220	13	1	1	NUM
ejpam-2650	220	14	,	,	PUNCT
ejpam-2650	220	15	u3	u3	NOUN
ejpam-2650	220	16	+	+	CCONJ
ejpam-2650	220	17	u2	u2	PROPN
ejpam-2650	220	18	+	+	CCONJ
ejpam-2650	220	19	u+	u+	NUM
ejpam-2650	220	20	1	1	NUM
ejpam-2650	220	21	,	,	PUNCT
ejpam-2650	220	22	u2	u2	NOUN
ejpam-2650	220	23	+	+	CCONJ
ejpam-2650	220	24	1	1	NUM
ejpam-2650	220	25	,	,	PUNCT
ejpam-2650	220	26	u+	u+	NUM
ejpam-2650	220	27	1	1	NUM
ejpam-2650	220	28	,	,	PUNCT
ejpam-2650	220	29	1	1	NUM
ejpam-2650	220	30	)	)	PUNCT
ejpam-2650	221	1	[	[	X
ejpam-2650	221	2	40	40	NUM
ejpam-2650	221	3	,	,	PUNCT
ejpam-2650	221	4	4	4	NUM
ejpam-2650	221	5	,	,	PUNCT
ejpam-2650	221	6	20	20	NUM
ejpam-2650	221	7	]	]	SYM
ejpam-2650	221	8	20	20	NUM
ejpam-2650	221	9	r4,1	r4,1	NOUN
ejpam-2650	221	10	7	7	NUM
ejpam-2650	221	11	(	(	PUNCT
ejpam-2650	221	12	0	0	NUM
ejpam-2650	221	13	,	,	PUNCT
ejpam-2650	221	14	0	0	NUM
ejpam-2650	221	15	,	,	PUNCT
ejpam-2650	221	16	u3	u3	NOUN
ejpam-2650	221	17	,	,	PUNCT
ejpam-2650	221	18	0	0	NUM
ejpam-2650	221	19	,	,	PUNCT
ejpam-2650	221	20	u3	u3	NOUN
ejpam-2650	221	21	,	,	PUNCT
ejpam-2650	221	22	u3	u3	NOUN
ejpam-2650	221	23	,	,	PUNCT
ejpam-2650	221	24	u3	u3	NOUN
ejpam-2650	221	25	)	)	PUNCT
ejpam-2650	221	26	[	[	X
ejpam-2650	221	27	56	56	NUM
ejpam-2650	221	28	,	,	PUNCT
ejpam-2650	221	29	3	3	NUM
ejpam-2650	221	30	,	,	PUNCT
ejpam-2650	221	31	32	32	NUM
ejpam-2650	221	32	]	]	SYM
ejpam-2650	221	33	32	32	NUM
ejpam-2650	221	34	5	5	NUM
ejpam-2650	221	35	r5,1	r5,1	NOUN
ejpam-2650	221	36	3	3	NUM
ejpam-2650	221	37	(	(	PUNCT
ejpam-2650	221	38	0	0	NUM
ejpam-2650	221	39	,	,	PUNCT
ejpam-2650	221	40	u4	u4	PROPN
ejpam-2650	221	41	,	,	PUNCT
ejpam-2650	221	42	u4	u4	PROPN
ejpam-2650	221	43	)	)	PUNCT
ejpam-2650	221	44	[	[	X
ejpam-2650	221	45	48	48	NUM
ejpam-2650	221	46	,	,	PUNCT
ejpam-2650	221	47	2	2	NUM
ejpam-2650	221	48	,	,	PUNCT
ejpam-2650	221	49	32	32	NUM
ejpam-2650	221	50	]	]	SYM
ejpam-2650	221	51	32	32	NUM
ejpam-2650	221	52	5	5	NUM
ejpam-2650	221	53	r5,1	r5,1	NOUN
ejpam-2650	221	54	3	3	NUM
ejpam-2650	221	55	(	(	PUNCT
ejpam-2650	221	56	u	u	NOUN
ejpam-2650	221	57	,	,	PUNCT
ejpam-2650	221	58	u2	u2	PROPN
ejpam-2650	221	59	+	+	CCONJ
ejpam-2650	221	60	u	u	PROPN
ejpam-2650	221	61	,	,	PUNCT
ejpam-2650	221	62	u3	u3	NOUN
ejpam-2650	221	63	+	+	CCONJ
ejpam-2650	221	64	u	u	NOUN
ejpam-2650	221	65	)	)	PUNCT
ejpam-2650	222	1	[	[	X
ejpam-2650	222	2	48	48	NUM
ejpam-2650	222	3	,	,	PUNCT
ejpam-2650	222	4	4	4	NUM
ejpam-2650	222	5	,	,	PUNCT
ejpam-2650	222	6	24	24	NUM
ejpam-2650	222	7	]	]	SYM
ejpam-2650	222	8	24	24	NUM
ejpam-2650	222	9	r5,1	r5,1	NOUN
ejpam-2650	222	10	3	3	NUM
ejpam-2650	222	11	(	(	PUNCT
ejpam-2650	222	12	1	1	NUM
ejpam-2650	222	13	,	,	PUNCT
ejpam-2650	222	14	1	1	NUM
ejpam-2650	222	15	+	+	NUM
ejpam-2650	222	16	u+	u+	X
ejpam-2650	222	17	u4	u4	NOUN
ejpam-2650	222	18	,	,	PUNCT
ejpam-2650	222	19	1	1	NUM
ejpam-2650	222	20	+	+	NUM
ejpam-2650	222	21	u2	u2	NOUN
ejpam-2650	222	22	)	)	PUNCT
ejpam-2650	223	1	[	[	X
ejpam-2650	223	2	48	48	NUM
ejpam-2650	223	3	,	,	PUNCT
ejpam-2650	223	4	5	5	NUM
ejpam-2650	223	5	,	,	PUNCT
ejpam-2650	223	6	24	24	NUM
ejpam-2650	223	7	]	]	SYM
ejpam-2650	223	8	24	24	NUM
ejpam-2650	223	9	r5,1	r5,1	NOUN
ejpam-2650	223	10	5	5	NUM
ejpam-2650	223	11	(	(	PUNCT
ejpam-2650	223	12	1	1	NUM
ejpam-2650	223	13	,	,	PUNCT
ejpam-2650	223	14	u3	u3	NOUN
ejpam-2650	223	15	+	+	CCONJ
ejpam-2650	223	16	u2	u2	PROPN
ejpam-2650	223	17	+	+	CCONJ
ejpam-2650	223	18	u+	u+	NUM
ejpam-2650	223	19	1	1	NUM
ejpam-2650	223	20	,	,	PUNCT
ejpam-2650	223	21	u4	u4	PROPN
ejpam-2650	223	22	+	+	CCONJ
ejpam-2650	223	23	u2	u2	PROPN
ejpam-2650	223	24	+	+	CCONJ
ejpam-2650	223	25	1	1	NUM
ejpam-2650	223	26	,	,	PUNCT
ejpam-2650	223	27	u+	u+	NUM
ejpam-2650	223	28	1	1	NUM
ejpam-2650	223	29	,	,	PUNCT
ejpam-2650	223	30	u4	u4	PROPN
ejpam-2650	223	31	+	+	PROPN
ejpam-2650	223	32	1	1	NUM
ejpam-2650	223	33	)	)	PUNCT
ejpam-2650	224	1	[	[	X
ejpam-2650	224	2	80	80	NUM
ejpam-2650	224	3	,	,	PUNCT
ejpam-2650	224	4	5	5	NUM
ejpam-2650	224	5	,	,	PUNCT
ejpam-2650	224	6	40	40	NUM
ejpam-2650	224	7	]	]	SYM
ejpam-2650	224	8	40	40	NUM
ejpam-2650	224	9	remark	remark	NOUN
ejpam-2650	224	10	2	2	NUM
ejpam-2650	224	11	.	.	PUNCT
ejpam-2650	225	1	if	if	SCONJ
ejpam-2650	225	2	c	c	PROPN
ejpam-2650	225	3	is	be	AUX
ejpam-2650	225	4	an	an	DET
ejpam-2650	225	5	α	α	NOUN
ejpam-2650	225	6	-	-	ADJ
ejpam-2650	225	7	constacyclic	constacyclic	ADJ
ejpam-2650	225	8	code	code	NOUN
ejpam-2650	225	9	over	over	ADP
ejpam-2650	225	10	rk	rk	PROPN
ejpam-2650	225	11	,	,	PUNCT
ejpam-2650	225	12	m	m	PRON
ejpam-2650	225	13	,	,	PUNCT
ejpam-2650	225	14	then	then	ADV
ejpam-2650	225	15	φhom(c	φhom(c	NUM
ejpam-2650	225	16	)	)	PUNCT
ejpam-2650	225	17	might	might	AUX
ejpam-2650	225	18	not	not	PART
ejpam-2650	225	19	be	be	AUX
ejpam-2650	225	20	a	a	DET
ejpam-2650	225	21	2km−1quasicyclic	2km−1quasicyclic	NUM
ejpam-2650	225	22	binary	binary	ADJ
ejpam-2650	225	23	code	code	NOUN
ejpam-2650	225	24	,	,	PUNCT
ejpam-2650	225	25	however	however	ADV
ejpam-2650	225	26	it	it	PRON
ejpam-2650	225	27	can	can	AUX
ejpam-2650	225	28	easily	easily	ADV
ejpam-2650	225	29	be	be	AUX
ejpam-2650	225	30	shown	show	VERB
ejpam-2650	225	31	that	that	SCONJ
ejpam-2650	225	32	φhom(c	φhom(c	NOUN
ejpam-2650	225	33	)	)	PUNCT
ejpam-2650	225	34	is	be	AUX
ejpam-2650	225	35	equivalent	equivalent	ADJ
ejpam-2650	225	36	to	to	ADP
ejpam-2650	225	37	a	a	DET
ejpam-2650	225	38	2km−1	2km−1	PROPN
ejpam-2650	225	39	-	-	PUNCT
ejpam-2650	225	40	quasicyclic	quasicyclic	ADJ
ejpam-2650	225	41	binary	binary	PROPN
ejpam-2650	225	42	code	code	NOUN
ejpam-2650	225	43	.	.	PUNCT
ejpam-2650	226	1	thus	thus	ADV
ejpam-2650	226	2	all	all	DET
ejpam-2650	226	3	the	the	DET
ejpam-2650	226	4	codes	code	NOUN
ejpam-2650	226	5	given	give	VERB
ejpam-2650	226	6	in	in	ADP
ejpam-2650	226	7	the	the	DET
ejpam-2650	226	8	above	above	ADJ
ejpam-2650	226	9	table	table	NOUN
ejpam-2650	226	10	are	be	AUX
ejpam-2650	226	11	equivalent	equivalent	ADJ
ejpam-2650	226	12	to	to	ADP
ejpam-2650	226	13	binary	binary	ADJ
ejpam-2650	226	14	quasicyclic	quasicyclic	PROPN
ejpam-2650	226	15	codes	code	NOUN
ejpam-2650	226	16	and	and	CCONJ
ejpam-2650	226	17	they	they	PRON
ejpam-2650	226	18	are	be	AUX
ejpam-2650	226	19	also	also	ADV
ejpam-2650	226	20	self	self	NOUN
ejpam-2650	226	21	-	-	PUNCT
ejpam-2650	226	22	orthogonal	orthogonal	ADJ
ejpam-2650	227	1	when	when	SCONJ
ejpam-2650	227	2	∆	∆	PROPN
ejpam-2650	227	3	≥	≥	NOUN
ejpam-2650	227	4	4	4	NUM
ejpam-2650	227	5	.	.	NUM
ejpam-2650	227	6	4.3	4.3	NUM
ejpam-2650	227	7	.	.	PUNCT
ejpam-2650	228	1	some	some	DET
ejpam-2650	228	2	results	result	NOUN
ejpam-2650	228	3	on	on	ADP
ejpam-2650	228	4	divisible	divisible	ADJ
ejpam-2650	228	5	quasicyclic	quasicyclic	NOUN
ejpam-2650	228	6	codes	code	NOUN
ejpam-2650	228	7	over	over	ADP
ejpam-2650	228	8	rk	rk	NOUN
ejpam-2650	228	9	,	,	PUNCT
ejpam-2650	228	10	m	m	VERB
ejpam-2650	228	11	quasicyclic	quasicyclic	ADJ
ejpam-2650	228	12	codes	code	NOUN
ejpam-2650	228	13	are	be	AUX
ejpam-2650	228	14	another	another	DET
ejpam-2650	228	15	generalization	generalization	NOUN
ejpam-2650	228	16	of	of	ADP
ejpam-2650	228	17	cyclic	cyclic	ADJ
ejpam-2650	228	18	codes	code	NOUN
ejpam-2650	228	19	and	and	CCONJ
ejpam-2650	228	20	have	have	AUX
ejpam-2650	228	21	generated	generate	VERB
ejpam-2650	228	22	a	a	DET
ejpam-2650	228	23	lot	lot	NOUN
ejpam-2650	228	24	of	of	ADP
ejpam-2650	228	25	interest	interest	NOUN
ejpam-2650	228	26	.	.	PUNCT
ejpam-2650	229	1	they	they	PRON
ejpam-2650	229	2	have	have	VERB
ejpam-2650	229	3	algebraic	algebraic	ADJ
ejpam-2650	229	4	structure	structure	NOUN
ejpam-2650	229	5	and	and	CCONJ
ejpam-2650	229	6	they	they	PRON
ejpam-2650	229	7	also	also	ADV
ejpam-2650	229	8	satisfy	satisfy	VERB
ejpam-2650	229	9	a	a	DET
ejpam-2650	229	10	modified	modify	VERB
ejpam-2650	229	11	version	version	NOUN
ejpam-2650	229	12	of	of	ADP
ejpam-2650	229	13	the	the	DET
ejpam-2650	229	14	gilbert	gilbert	PROPN
ejpam-2650	229	15	-	-	PUNCT
ejpam-2650	229	16	varshamov	varshamov	PROPN
ejpam-2650	229	17	bound	bind	VERB
ejpam-2650	229	18	.	.	PUNCT
ejpam-2650	230	1	many	many	ADJ
ejpam-2650	230	2	optimal	optimal	ADJ
ejpam-2650	230	3	good	good	ADJ
ejpam-2650	230	4	binary	binary	ADJ
ejpam-2650	230	5	codes	code	NOUN
ejpam-2650	230	6	are	be	AUX
ejpam-2650	230	7	quasicyclic	quasicyclic	ADJ
ejpam-2650	230	8	.	.	PUNCT
ejpam-2650	231	1	a	a	DET
ejpam-2650	231	2	lot	lot	NOUN
ejpam-2650	231	3	of	of	ADP
ejpam-2650	231	4	good	good	ADJ
ejpam-2650	231	5	codes	code	NOUN
ejpam-2650	231	6	have	have	AUX
ejpam-2650	231	7	been	be	AUX
ejpam-2650	231	8	constructed	construct	VERB
ejpam-2650	231	9	using	use	VERB
ejpam-2650	231	10	quasicyclic	quasicyclic	ADJ
ejpam-2650	231	11	codes	code	NOUN
ejpam-2650	231	12	over	over	ADP
ejpam-2650	231	13	different	different	ADJ
ejpam-2650	231	14	alphabets	alphabet	NOUN
ejpam-2650	231	15	,	,	PUNCT
ejpam-2650	231	16	such	such	ADJ
ejpam-2650	231	17	as	as	ADP
ejpam-2650	231	18	[	[	X
ejpam-2650	231	19	1	1	NUM
ejpam-2650	231	20	]	]	PUNCT
ejpam-2650	231	21	and	and	CCONJ
ejpam-2650	231	22	[	[	X
ejpam-2650	231	23	3	3	NUM
ejpam-2650	231	24	]	]	PUNCT
ejpam-2650	231	25	.	.	PUNCT
ejpam-2650	232	1	a	a	DET
ejpam-2650	232	2	definition	definition	NOUN
ejpam-2650	232	3	can	can	AUX
ejpam-2650	232	4	be	be	AUX
ejpam-2650	232	5	given	give	VERB
ejpam-2650	232	6	from	from	ADP
ejpam-2650	232	7	[	[	X
ejpam-2650	232	8	10	10	NUM
ejpam-2650	232	9	]	]	PUNCT
ejpam-2650	232	10	:	:	PUNCT
ejpam-2650	232	11	definition	definition	NOUN
ejpam-2650	232	12	2	2	NUM
ejpam-2650	232	13	.	.	PUNCT
ejpam-2650	232	14	a	a	DET
ejpam-2650	232	15	code	code	NOUN
ejpam-2650	232	16	c	c	NOUN
ejpam-2650	232	17	of	of	ADP
ejpam-2650	232	18	length	length	NOUN
ejpam-2650	232	19	n	n	NUM
ejpam-2650	232	20	is	be	AUX
ejpam-2650	232	21	called	call	VERB
ejpam-2650	232	22	`	`	PUNCT
ejpam-2650	232	23	−quasicyclic	−quasicyclic	ADJ
ejpam-2650	232	24	if	if	SCONJ
ejpam-2650	232	25	`	`	PUNCT
ejpam-2650	232	26	|n	|n	ADJ
ejpam-2650	232	27	and	and	CCONJ
ejpam-2650	232	28	τ	τ	NUM
ejpam-2650	232	29	`	`	PUNCT
ejpam-2650	232	30	(	(	PUNCT
ejpam-2650	232	31	c	c	NOUN
ejpam-2650	232	32	)	)	PUNCT
ejpam-2650	233	1	=	=	SYM
ejpam-2650	233	2	c.	c.	NOUN
ejpam-2650	233	3	note	note	VERB
ejpam-2650	233	4	that	that	SCONJ
ejpam-2650	233	5	when	when	SCONJ
ejpam-2650	233	6	`	`	PUNCT
ejpam-2650	233	7	=	=	SYM
ejpam-2650	233	8	1	1	NUM
ejpam-2650	233	9	,	,	PUNCT
ejpam-2650	233	10	1	1	NUM
ejpam-2650	233	11	-	-	PUNCT
ejpam-2650	233	12	quasicyclic	quasicyclic	NOUN
ejpam-2650	233	13	codes	code	NOUN
ejpam-2650	233	14	are	be	AUX
ejpam-2650	233	15	just	just	ADV
ejpam-2650	233	16	cyclic	cyclic	ADJ
ejpam-2650	233	17	codes	code	NOUN
ejpam-2650	233	18	.	.	PUNCT
ejpam-2650	234	1	structurally	structurally	ADV
ejpam-2650	234	2	,	,	PUNCT
ejpam-2650	234	3	the	the	DET
ejpam-2650	234	4	generator	generator	NOUN
ejpam-2650	234	5	matrix	matrix	NOUN
ejpam-2650	234	6	of	of	ADP
ejpam-2650	234	7	a	a	DET
ejpam-2650	234	8	t	t	NOUN
ejpam-2650	234	9	generator	generator	NOUN
ejpam-2650	234	10	`	`	PUNCT
ejpam-2650	234	11	−quasicyclic	−quasicyclic	PROPN
ejpam-2650	234	12	code	code	NOUN
ejpam-2650	234	13	can	can	AUX
ejpam-2650	234	14	be	be	AUX
ejpam-2650	234	15	shown	show	VERB
ejpam-2650	234	16	to	to	PART
ejpam-2650	234	17	be	be	AUX
ejpam-2650	234	18	of	of	ADP
ejpam-2650	234	19	the	the	DET
ejpam-2650	234	20	following	follow	VERB
ejpam-2650	234	21	form	form	NOUN
ejpam-2650	234	22	:	:	PUNCT
ejpam-2650	234	23			PROPN
ejpam-2650	234	24	c00	c00	PROPN
ejpam-2650	234	25	c01	c01	PROPN
ejpam-2650	234	26	.	.	PUNCT
ejpam-2650	234	27	.	.	PUNCT
ejpam-2650	234	28	.	.	PUNCT
ejpam-2650	235	1	c0,`−1	c0,`−1	ADV
ejpam-2650	235	2	c10	c10	VERB
ejpam-2650	235	3	c11	c11	NOUN
ejpam-2650	235	4	.	.	PUNCT
ejpam-2650	235	5	.	.	PUNCT
ejpam-2650	235	6	.	.	PUNCT
ejpam-2650	236	1	c1,`−1	c1,`−1	ADJ
ejpam-2650	236	2	...	...	PUNCT
ejpam-2650	236	3	...	...	PUNCT
ejpam-2650	236	4	...	...	PUNCT
ejpam-2650	236	5	...	...	PUNCT
ejpam-2650	237	1	ct,0	ct,0	VERB
ejpam-2650	237	2	ct,1	ct,1	PROPN
ejpam-2650	237	3	.	.	PUNCT
ejpam-2650	237	4	.	.	PUNCT
ejpam-2650	237	5	.	.	PUNCT
ejpam-2650	238	1	ct,`−1	ct,`−1	PROPN
ejpam-2650	238	2			VERB
ejpam-2650	238	3	where	where	SCONJ
ejpam-2650	238	4	cij	cij	PROPN
ejpam-2650	238	5	are	be	AUX
ejpam-2650	238	6	m×m	m×m	ADJ
ejpam-2650	238	7	circulant	circulant	ADJ
ejpam-2650	238	8	matrices	matrix	NOUN
ejpam-2650	238	9	.	.	PUNCT
ejpam-2650	239	1	in	in	ADP
ejpam-2650	239	2	such	such	DET
ejpam-2650	239	3	a	a	DET
ejpam-2650	239	4	case	case	NOUN
ejpam-2650	239	5	,	,	PUNCT
ejpam-2650	239	6	the	the	DET
ejpam-2650	239	7	length	length	NOUN
ejpam-2650	239	8	n	n	PROPN
ejpam-2650	239	9	of	of	ADP
ejpam-2650	239	10	the	the	DET
ejpam-2650	239	11	`	`	PUNCT
ejpam-2650	239	12	−quasicyclic	−quasicyclic	PROPN
ejpam-2650	239	13	code	code	PROPN
ejpam-2650	239	14	c	c	PROPN
ejpam-2650	239	15	is	be	AUX
ejpam-2650	239	16	m×	m×	PROPN
ejpam-2650	239	17	`	`	PUNCT
ejpam-2650	239	18	.	.	PUNCT
ejpam-2650	240	1	we	we	PRON
ejpam-2650	240	2	refer	refer	VERB
ejpam-2650	240	3	to	to	ADP
ejpam-2650	240	4	[	[	X
ejpam-2650	240	5	12	12	NUM
ejpam-2650	240	6	,	,	PUNCT
ejpam-2650	240	7	3	3	NUM
ejpam-2650	240	8	]	]	PUNCT
ejpam-2650	240	9	for	for	ADP
ejpam-2650	240	10	more	more	ADJ
ejpam-2650	240	11	information	information	NOUN
ejpam-2650	240	12	on	on	ADP
ejpam-2650	240	13	quasicyclic	quasicyclic	ADJ
ejpam-2650	240	14	codes	code	NOUN
ejpam-2650	240	15	.	.	PUNCT
ejpam-2650	241	1	b.	b.	PROPN
ejpam-2650	241	2	yildiz	yildiz	PROPN
ejpam-2650	241	3	,	,	PUNCT
ejpam-2650	241	4	n.	n.	PROPN
ejpam-2650	241	5	tufekci	tufekci	PROPN
ejpam-2650	241	6	/	/	SYM
ejpam-2650	241	7	eur	eur	PROPN
ejpam-2650	241	8	.	.	PUNCT
ejpam-2650	242	1	j.	j.	PROPN
ejpam-2650	242	2	pure	pure	PROPN
ejpam-2650	242	3	appl	appl	PROPN
ejpam-2650	242	4	.	.	PROPN
ejpam-2650	242	5	math	math	PROPN
ejpam-2650	242	6	,	,	PUNCT
ejpam-2650	242	7	10	10	NUM
ejpam-2650	242	8	(	(	PUNCT
ejpam-2650	242	9	5	5	NUM
ejpam-2650	242	10	)	)	PUNCT
ejpam-2650	242	11	(	(	PUNCT
ejpam-2650	242	12	2017	2017	NUM
ejpam-2650	242	13	)	)	PUNCT
ejpam-2650	242	14	,	,	PUNCT
ejpam-2650	242	15	1112	1112	NUM
ejpam-2650	242	16	-	-	SYM
ejpam-2650	242	17	1123	1123	NUM
ejpam-2650	242	18	1121	1121	NUM
ejpam-2650	242	19	we	we	PRON
ejpam-2650	242	20	have	have	AUX
ejpam-2650	242	21	searched	search	VERB
ejpam-2650	242	22	through	through	ADP
ejpam-2650	242	23	one	one	NUM
ejpam-2650	242	24	generator	generator	NOUN
ejpam-2650	242	25	`	`	PUNCT
ejpam-2650	242	26	-quasicyclic	-quasicyclic	ADJ
ejpam-2650	242	27	codes	code	NOUN
ejpam-2650	242	28	over	over	ADP
ejpam-2650	242	29	rk	rk	NOUN
ejpam-2650	242	30	,	,	PUNCT
ejpam-2650	242	31	m	m	VERB
ejpam-2650	242	32	to	to	PART
ejpam-2650	242	33	get	get	VERB
ejpam-2650	242	34	divisible	divisible	ADJ
ejpam-2650	242	35	codes	code	NOUN
ejpam-2650	242	36	of	of	ADP
ejpam-2650	242	37	various	various	ADJ
ejpam-2650	242	38	lengths	length	NOUN
ejpam-2650	242	39	.	.	PUNCT
ejpam-2650	243	1	we	we	PRON
ejpam-2650	243	2	have	have	AUX
ejpam-2650	243	3	listed	list	VERB
ejpam-2650	243	4	in	in	ADP
ejpam-2650	243	5	the	the	DET
ejpam-2650	243	6	following	follow	VERB
ejpam-2650	243	7	table	table	NOUN
ejpam-2650	243	8	,	,	PUNCT
ejpam-2650	243	9	divisible	divisible	ADJ
ejpam-2650	243	10	,	,	PUNCT
ejpam-2650	243	11	optimal	optimal	ADJ
ejpam-2650	243	12	binary	binary	ADJ
ejpam-2650	243	13	codes	code	NOUN
ejpam-2650	243	14	obtained	obtain	VERB
ejpam-2650	243	15	as	as	ADP
ejpam-2650	243	16	the	the	DET
ejpam-2650	243	17	φhom	φhom	NOUN
ejpam-2650	243	18	-	-	PUNCT
ejpam-2650	243	19	images	image	NOUN
ejpam-2650	243	20	of	of	ADP
ejpam-2650	243	21	quasi	quasi	ADJ
ejpam-2650	243	22	cyclic	cyclic	NOUN
ejpam-2650	243	23	codes	code	NOUN
ejpam-2650	243	24	over	over	ADP
ejpam-2650	243	25	rk	rk	PROPN
ejpam-2650	243	26	,	,	PUNCT
ejpam-2650	243	27	m	m	PRON
ejpam-2650	243	28	:	:	PUNCT
ejpam-2650	243	29	table	table	NOUN
ejpam-2650	243	30	4	4	NUM
ejpam-2650	243	31	:	:	PUNCT
ejpam-2650	243	32	divisible	divisible	ADJ
ejpam-2650	243	33	`	`	PUNCT
ejpam-2650	243	34	-quasicyclic	-quasicyclic	ADJ
ejpam-2650	243	35	codes	code	NOUN
ejpam-2650	243	36	over	over	ADP
ejpam-2650	243	37	rk,1	rk,1	NOUN
ejpam-2650	243	38	and	and	CCONJ
ejpam-2650	243	39	the	the	DET
ejpam-2650	243	40	binary	binary	ADJ
ejpam-2650	243	41	images	image	NOUN
ejpam-2650	243	42	rk,1	rk,1	NOUN
ejpam-2650	243	43	`	`	PUNCT
ejpam-2650	243	44	generator	generator	NOUN
ejpam-2650	243	45	of	of	ADP
ejpam-2650	243	46	the	the	DET
ejpam-2650	243	47	code	code	NOUN
ejpam-2650	243	48	φhom(〈g(x	φhom(〈g(x	NOUN
ejpam-2650	243	49	)	)	PUNCT
ejpam-2650	243	50	〉	〉	PROPN
ejpam-2650	243	51	)	)	PUNCT
ejpam-2650	243	52	∆	∆	PROPN
ejpam-2650	243	53	level	level	NOUN
ejpam-2650	243	54	r3,1	r3,1	PROPN
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ejpam-2650	243	56	(	(	PUNCT
ejpam-2650	243	57	0	0	NUM
ejpam-2650	243	58	,	,	PUNCT
ejpam-2650	243	59	1	1	NUM
ejpam-2650	243	60	,	,	PUNCT
ejpam-2650	243	61	1	1	NUM
ejpam-2650	243	62	,	,	PUNCT
ejpam-2650	243	63	0	0	NUM
ejpam-2650	243	64	,	,	PUNCT
ejpam-2650	243	65	1	1	NUM
ejpam-2650	243	66	,	,	PUNCT
ejpam-2650	243	67	1	1	NUM
ejpam-2650	243	68	+	+	CCONJ
ejpam-2650	243	69	u2	u2	PROPN
ejpam-2650	243	70	,	,	PUNCT
ejpam-2650	243	71	u	u	NOUN
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ejpam-2650	243	73	u	u	NOUN
ejpam-2650	243	74	,	,	PUNCT
ejpam-2650	243	75	u2	u2	PROPN
ejpam-2650	243	76	)	)	PUNCT
ejpam-2650	244	1	[	[	X
ejpam-2650	244	2	36	36	NUM
ejpam-2650	244	3	,	,	PUNCT
ejpam-2650	244	4	2	2	NUM
ejpam-2650	244	5	,	,	PUNCT
ejpam-2650	244	6	24	24	NUM
ejpam-2650	244	7	]	]	SYM
ejpam-2650	244	8	24	24	NUM
ejpam-2650	244	9	3	3	NUM
ejpam-2650	244	10	(	(	PUNCT
ejpam-2650	244	11	0	0	NUM
ejpam-2650	244	12	,	,	PUNCT
ejpam-2650	244	13	u	u	NOUN
ejpam-2650	244	14	,	,	PUNCT
ejpam-2650	244	15	u	u	NOUN
ejpam-2650	244	16	,	,	PUNCT
ejpam-2650	244	17	0	0	NUM
ejpam-2650	244	18	,	,	PUNCT
ejpam-2650	244	19	u	u	NOUN
ejpam-2650	244	20	,	,	PUNCT
ejpam-2650	244	21	u2	u2	PROPN
ejpam-2650	244	22	+	+	CCONJ
ejpam-2650	244	23	u	u	PROPN
ejpam-2650	244	24	,	,	PUNCT
ejpam-2650	244	25	u	u	NOUN
ejpam-2650	244	26	,	,	PUNCT
ejpam-2650	244	27	u	u	NOUN
ejpam-2650	244	28	,	,	PUNCT
ejpam-2650	244	29	u2	u2	PROPN
ejpam-2650	244	30	)	)	PUNCT
ejpam-2650	245	1	[	[	X
ejpam-2650	245	2	36	36	NUM
ejpam-2650	245	3	,	,	PUNCT
ejpam-2650	245	4	5	5	NUM
ejpam-2650	245	5	,	,	PUNCT
ejpam-2650	245	6	16	16	NUM
ejpam-2650	245	7	]	]	SYM
ejpam-2650	246	1	4	4	NUM
ejpam-2650	246	2	2	2	NUM
ejpam-2650	246	3	3	3	NUM
ejpam-2650	246	4	(	(	PUNCT
ejpam-2650	246	5	0	0	NUM
ejpam-2650	246	6	,	,	PUNCT
ejpam-2650	246	7	1	1	NUM
ejpam-2650	246	8	,	,	PUNCT
ejpam-2650	246	9	1	1	NUM
ejpam-2650	246	10	,	,	PUNCT
ejpam-2650	246	11	0	0	NUM
ejpam-2650	246	12	,	,	PUNCT
ejpam-2650	246	13	u	u	NOUN
ejpam-2650	246	14	,	,	PUNCT
ejpam-2650	246	15	u	u	NOUN
ejpam-2650	246	16	,	,	PUNCT
ejpam-2650	246	17	1	1	NUM
ejpam-2650	246	18	,	,	PUNCT
ejpam-2650	246	19	u2	u2	NOUN
ejpam-2650	246	20	,	,	PUNCT
ejpam-2650	246	21	u2	u2	PROPN
ejpam-2650	246	22	+	+	CCONJ
ejpam-2650	246	23	1	1	NUM
ejpam-2650	246	24	)	)	PUNCT
ejpam-2650	247	1	[	[	X
ejpam-2650	247	2	36	36	NUM
ejpam-2650	247	3	,	,	PUNCT
ejpam-2650	247	4	6	6	NUM
ejpam-2650	247	5	,	,	PUNCT
ejpam-2650	247	6	16	16	NUM
ejpam-2650	247	7	]	]	SYM
ejpam-2650	247	8	4	4	NUM
ejpam-2650	247	9	2	2	NUM
ejpam-2650	247	10	3	3	NUM
ejpam-2650	247	11	(	(	PUNCT
ejpam-2650	247	12	0	0	NUM
ejpam-2650	247	13	,	,	PUNCT
ejpam-2650	247	14	1	1	NUM
ejpam-2650	247	15	,	,	PUNCT
ejpam-2650	247	16	1	1	NUM
ejpam-2650	247	17	,	,	PUNCT
ejpam-2650	247	18	0	0	NUM
ejpam-2650	247	19	,	,	PUNCT
ejpam-2650	247	20	1	1	NUM
ejpam-2650	247	21	,	,	PUNCT
ejpam-2650	247	22	u2	u2	PROPN
ejpam-2650	247	23	+	+	CCONJ
ejpam-2650	247	24	1	1	NUM
ejpam-2650	247	25	,	,	PUNCT
ejpam-2650	247	26	u	u	NOUN
ejpam-2650	247	27	,	,	PUNCT
ejpam-2650	247	28	u	u	NOUN
ejpam-2650	247	29	,	,	PUNCT
ejpam-2650	247	30	u2	u2	PROPN
ejpam-2650	247	31	)	)	PUNCT
ejpam-2650	248	1	[	[	X
ejpam-2650	248	2	36	36	NUM
ejpam-2650	248	3	,	,	PUNCT
ejpam-2650	248	4	7	7	NUM
ejpam-2650	248	5	,	,	PUNCT
ejpam-2650	248	6	16	16	NUM
ejpam-2650	248	7	]	]	SYM
ejpam-2650	248	8	4	4	NUM
ejpam-2650	248	9	2	2	NUM
ejpam-2650	248	10	3	3	NUM
ejpam-2650	248	11	(	(	PUNCT
ejpam-2650	248	12	1	1	NUM
ejpam-2650	248	13	,	,	PUNCT
ejpam-2650	248	14	1	1	NUM
ejpam-2650	248	15	,	,	PUNCT
ejpam-2650	248	16	u2	u2	PROPN
ejpam-2650	248	17	+	+	CCONJ
ejpam-2650	248	18	1	1	NUM
ejpam-2650	248	19	,	,	PUNCT
ejpam-2650	248	20	u2	u2	NOUN
ejpam-2650	248	21	+	+	CCONJ
ejpam-2650	248	22	1	1	NUM
ejpam-2650	248	23	,	,	PUNCT
ejpam-2650	248	24	1	1	NUM
ejpam-2650	248	25	,	,	PUNCT
ejpam-2650	248	26	1	1	NUM
ejpam-2650	248	27	,	,	PUNCT
ejpam-2650	248	28	u2	u2	PROPN
ejpam-2650	248	29	+	+	CCONJ
ejpam-2650	248	30	1	1	NUM
ejpam-2650	248	31	,	,	PUNCT
ejpam-2650	248	32	u2	u2	NOUN
ejpam-2650	248	33	+	+	CCONJ
ejpam-2650	248	34	1	1	NUM
ejpam-2650	248	35	,	,	PUNCT
ejpam-2650	248	36	1	1	NUM
ejpam-2650	248	37	,	,	PUNCT
ejpam-2650	248	38	1	1	NUM
ejpam-2650	248	39	,	,	PUNCT
ejpam-2650	248	40	u2	u2	PROPN
ejpam-2650	248	41	+	+	CCONJ
ejpam-2650	248	42	1	1	NUM
ejpam-2650	248	43	,	,	PUNCT
ejpam-2650	248	44	u2	u2	NOUN
ejpam-2650	248	45	+	+	CCONJ
ejpam-2650	248	46	1	1	NUM
ejpam-2650	248	47	)	)	PUNCT
ejpam-2650	249	1	[	[	X
ejpam-2650	249	2	48	48	NUM
ejpam-2650	249	3	,	,	PUNCT
ejpam-2650	249	4	4	4	NUM
ejpam-2650	249	5	,	,	PUNCT
ejpam-2650	249	6	24	24	NUM
ejpam-2650	249	7	]	]	SYM
ejpam-2650	249	8	24	24	NUM
ejpam-2650	249	9	3	3	NUM
ejpam-2650	249	10	(	(	PUNCT
ejpam-2650	249	11	0	0	NUM
ejpam-2650	249	12	,	,	PUNCT
ejpam-2650	249	13	u	u	NOUN
ejpam-2650	249	14	,	,	PUNCT
ejpam-2650	249	15	u2	u2	NOUN
ejpam-2650	249	16	,	,	PUNCT
ejpam-2650	249	17	u2	u2	PROPN
ejpam-2650	249	18	+	+	CCONJ
ejpam-2650	249	19	u	u	PROPN
ejpam-2650	249	20	,	,	PUNCT
ejpam-2650	249	21	1	1	NUM
ejpam-2650	249	22	,	,	PUNCT
ejpam-2650	249	23	1	1	NUM
ejpam-2650	249	24	,	,	PUNCT
ejpam-2650	249	25	u2	u2	PROPN
ejpam-2650	249	26	+	+	CCONJ
ejpam-2650	249	27	1	1	NUM
ejpam-2650	249	28	,	,	PUNCT
ejpam-2650	249	29	u2	u2	NOUN
ejpam-2650	249	30	+	+	CCONJ
ejpam-2650	249	31	1	1	NUM
ejpam-2650	249	32	,	,	PUNCT
ejpam-2650	249	33	1	1	NUM
ejpam-2650	249	34	,	,	PUNCT
ejpam-2650	249	35	u+	u+	NUM
ejpam-2650	249	36	1	1	NUM
ejpam-2650	249	37	,	,	PUNCT
ejpam-2650	249	38	1	1	NUM
ejpam-2650	249	39	,	,	PUNCT
ejpam-2650	249	40	u+	u+	NUM
ejpam-2650	249	41	1	1	NUM
ejpam-2650	249	42	)	)	PUNCT
ejpam-2650	250	1	[	[	X
ejpam-2650	250	2	48	48	NUM
ejpam-2650	250	3	,	,	PUNCT
ejpam-2650	250	4	5	5	NUM
ejpam-2650	250	5	,	,	PUNCT
ejpam-2650	250	6	24	24	NUM
ejpam-2650	250	7	]	]	SYM
ejpam-2650	250	8	8	8	NUM
ejpam-2650	250	9	3	3	NUM
ejpam-2650	250	10	2	2	NUM
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ejpam-2650	250	12	0	0	NUM
ejpam-2650	250	13	,	,	PUNCT
ejpam-2650	250	14	1	1	NUM
ejpam-2650	250	15	,	,	PUNCT
ejpam-2650	250	16	1	1	NUM
ejpam-2650	250	17	,	,	PUNCT
ejpam-2650	250	18	u2	u2	NOUN
ejpam-2650	250	19	,	,	PUNCT
ejpam-2650	250	20	1	1	NUM
ejpam-2650	250	21	,	,	PUNCT
ejpam-2650	250	22	u2	u2	PROPN
ejpam-2650	250	23	+	+	CCONJ
ejpam-2650	250	24	1	1	NUM
ejpam-2650	250	25	,	,	PUNCT
ejpam-2650	250	26	u2	u2	PROPN
ejpam-2650	250	27	+	+	CCONJ
ejpam-2650	250	28	u	u	PROPN
ejpam-2650	250	29	,	,	PUNCT
ejpam-2650	250	30	1	1	NUM
ejpam-2650	250	31	,	,	PUNCT
ejpam-2650	250	32	u2	u2	PROPN
ejpam-2650	250	33	+	+	CCONJ
ejpam-2650	250	34	u+	u+	NUM
ejpam-2650	250	35	1	1	NUM
ejpam-2650	250	36	,	,	PUNCT
ejpam-2650	250	37	u	u	NOUN
ejpam-2650	250	38	,	,	PUNCT
ejpam-2650	250	39	1	1	NUM
ejpam-2650	250	40	,	,	PUNCT
ejpam-2650	250	41	u+	u+	NUM
ejpam-2650	250	42	1	1	NUM
ejpam-2650	250	43	)	)	PUNCT
ejpam-2650	251	1	[	[	X
ejpam-2650	251	2	48	48	NUM
ejpam-2650	251	3	,	,	PUNCT
ejpam-2650	251	4	6	6	NUM
ejpam-2650	251	5	,	,	PUNCT
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ejpam-2650	251	7	]	]	SYM
ejpam-2650	251	8	8	8	NUM
ejpam-2650	251	9	3	3	NUM
ejpam-2650	251	10	2	2	NUM
ejpam-2650	251	11	(	(	PUNCT
ejpam-2650	251	12	0	0	NUM
ejpam-2650	251	13	,	,	PUNCT
ejpam-2650	251	14	0	0	NUM
ejpam-2650	251	15	,	,	PUNCT
ejpam-2650	251	16	0	0	NUM
ejpam-2650	251	17	,	,	PUNCT
ejpam-2650	251	18	u	u	NOUN
ejpam-2650	251	19	,	,	PUNCT
ejpam-2650	251	20	u	u	NOUN
ejpam-2650	251	21	,	,	PUNCT
ejpam-2650	251	22	0	0	NUM
ejpam-2650	251	23	,	,	PUNCT
ejpam-2650	251	24	u2	u2	NOUN
ejpam-2650	251	25	,	,	PUNCT
ejpam-2650	251	26	u	u	NOUN
ejpam-2650	251	27	,	,	PUNCT
ejpam-2650	251	28	u	u	NOUN
ejpam-2650	251	29	,	,	PUNCT
ejpam-2650	251	30	u2	u2	PROPN
ejpam-2650	251	31	)	)	PUNCT
ejpam-2650	252	1	[	[	X
ejpam-2650	252	2	40	40	NUM
ejpam-2650	252	3	,	,	PUNCT
ejpam-2650	252	4	8	8	NUM
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ejpam-2650	252	8	8	8	NUM
ejpam-2650	252	9	3	3	NUM
ejpam-2650	252	10	3	3	NUM
ejpam-2650	252	11	(	(	PUNCT
ejpam-2650	252	12	1	1	NUM
ejpam-2650	252	13	,	,	PUNCT
ejpam-2650	252	14	1	1	NUM
ejpam-2650	252	15	,	,	PUNCT
ejpam-2650	252	16	1	1	NUM
ejpam-2650	252	17	,	,	PUNCT
ejpam-2650	252	18	1	1	NUM
ejpam-2650	252	19	,	,	PUNCT
ejpam-2650	252	20	u2	u2	PROPN
ejpam-2650	252	21	+	+	CCONJ
ejpam-2650	252	22	1	1	NUM
ejpam-2650	252	23	,	,	PUNCT
ejpam-2650	252	24	1	1	NUM
ejpam-2650	252	25	,	,	PUNCT
ejpam-2650	252	26	1	1	NUM
ejpam-2650	252	27	,	,	PUNCT
ejpam-2650	252	28	1	1	NUM
ejpam-2650	252	29	,	,	PUNCT
ejpam-2650	252	30	u2	u2	PROPN
ejpam-2650	252	31	+	+	CCONJ
ejpam-2650	252	32	1	1	NUM
ejpam-2650	252	33	,	,	PUNCT
ejpam-2650	252	34	u2	u2	NOUN
ejpam-2650	252	35	+	+	CCONJ
ejpam-2650	252	36	1	1	NUM
ejpam-2650	252	37	,	,	PUNCT
ejpam-2650	252	38	1	1	NUM
ejpam-2650	252	39	,	,	PUNCT
ejpam-2650	252	40	1	1	NUM
ejpam-2650	252	41	,	,	PUNCT
ejpam-2650	252	42	u2	u2	PROPN
ejpam-2650	252	43	+	+	CCONJ
ejpam-2650	252	44	1	1	NUM
ejpam-2650	252	45	,	,	PUNCT
ejpam-2650	252	46	1	1	NUM
ejpam-2650	252	47	,	,	PUNCT
ejpam-2650	252	48	u2	u2	NOUN
ejpam-2650	252	49	+	+	CCONJ
ejpam-2650	252	50	1	1	NUM
ejpam-2650	252	51	)	)	PUNCT
ejpam-2650	253	1	[	[	X
ejpam-2650	253	2	60	60	NUM
ejpam-2650	253	3	,	,	PUNCT
ejpam-2650	253	4	7	7	NUM
ejpam-2650	253	5	,	,	PUNCT
ejpam-2650	253	6	28	28	NUM
ejpam-2650	253	7	]	]	SYM
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ejpam-2650	253	9	1	1	NUM
ejpam-2650	253	10	3	3	NUM
ejpam-2650	253	11	(	(	PUNCT
ejpam-2650	253	12	0	0	NUM
ejpam-2650	253	13	,	,	PUNCT
ejpam-2650	253	14	0	0	NUM
ejpam-2650	253	15	,	,	PUNCT
ejpam-2650	253	16	0	0	NUM
ejpam-2650	253	17	,	,	PUNCT
ejpam-2650	253	18	1	1	NUM
ejpam-2650	253	19	,	,	PUNCT
ejpam-2650	253	20	1	1	NUM
ejpam-2650	253	21	,	,	PUNCT
ejpam-2650	253	22	0	0	NUM
ejpam-2650	253	23	,	,	PUNCT
ejpam-2650	253	24	u	u	NOUN
ejpam-2650	253	25	,	,	PUNCT
ejpam-2650	253	26	1	1	NUM
ejpam-2650	253	27	,	,	PUNCT
ejpam-2650	253	28	u	u	NOUN
ejpam-2650	253	29	,	,	PUNCT
ejpam-2650	253	30	1	1	NUM
ejpam-2650	253	31	,	,	PUNCT
ejpam-2650	253	32	1	1	NUM
ejpam-2650	253	33	,	,	PUNCT
ejpam-2650	253	34	u+	u+	NUM
ejpam-2650	253	35	1	1	NUM
ejpam-2650	253	36	,	,	PUNCT
ejpam-2650	253	37	u2	u2	NOUN
ejpam-2650	253	38	,	,	PUNCT
ejpam-2650	253	39	1	1	NUM
ejpam-2650	253	40	,	,	PUNCT
ejpam-2650	253	41	u2	u2	PROPN
ejpam-2650	253	42	+	+	CCONJ
ejpam-2650	253	43	u+	u+	NUM
ejpam-2650	253	44	1	1	NUM
ejpam-2650	253	45	)	)	PUNCT
ejpam-2650	254	1	[	[	X
ejpam-2650	254	2	60	60	NUM
ejpam-2650	254	3	,	,	PUNCT
ejpam-2650	254	4	12	12	NUM
ejpam-2650	254	5	,	,	PUNCT
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ejpam-2650	254	7	]	]	SYM
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ejpam-2650	254	9	2	2	NUM
ejpam-2650	254	10	r4,1	r4,1	NOUN
ejpam-2650	254	11	2	2	NUM
ejpam-2650	254	12	(	(	PUNCT
ejpam-2650	254	13	1	1	NUM
ejpam-2650	254	14	,	,	PUNCT
ejpam-2650	254	15	1	1	NUM
ejpam-2650	254	16	,	,	PUNCT
ejpam-2650	254	17	u3	u3	NOUN
ejpam-2650	254	18	+	+	CCONJ
ejpam-2650	254	19	1	1	NUM
ejpam-2650	254	20	,	,	PUNCT
ejpam-2650	254	21	u3	u3	NOUN
ejpam-2650	254	22	+	+	CCONJ
ejpam-2650	254	23	1	1	NUM
ejpam-2650	254	24	,	,	PUNCT
ejpam-2650	254	25	1	1	NUM
ejpam-2650	254	26	,	,	PUNCT
ejpam-2650	254	27	1	1	NUM
ejpam-2650	254	28	,	,	PUNCT
ejpam-2650	254	29	u3	u3	NOUN
ejpam-2650	254	30	+	+	CCONJ
ejpam-2650	254	31	1	1	NUM
ejpam-2650	254	32	,	,	PUNCT
ejpam-2650	254	33	u3	u3	NOUN
ejpam-2650	254	34	+	+	CCONJ
ejpam-2650	254	35	1	1	NUM
ejpam-2650	254	36	)	)	PUNCT
ejpam-2650	255	1	[	[	X
ejpam-2650	255	2	64	64	NUM
ejpam-2650	255	3	,	,	PUNCT
ejpam-2650	255	4	5	5	NUM
ejpam-2650	255	5	,	,	PUNCT
ejpam-2650	255	6	32	32	NUM
ejpam-2650	255	7	]	]	SYM
ejpam-2650	255	8	32	32	NUM
ejpam-2650	255	9	5	5	NUM
ejpam-2650	255	10	2	2	NUM
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ejpam-2650	255	12	1	1	NUM
ejpam-2650	255	13	,	,	PUNCT
ejpam-2650	255	14	1	1	NUM
ejpam-2650	255	15	,	,	PUNCT
ejpam-2650	255	16	1	1	NUM
ejpam-2650	255	17	,	,	PUNCT
ejpam-2650	255	18	u3	u3	NOUN
ejpam-2650	255	19	+	+	CCONJ
ejpam-2650	255	20	1	1	NUM
ejpam-2650	255	21	,	,	PUNCT
ejpam-2650	255	22	1	1	NUM
ejpam-2650	255	23	,	,	PUNCT
ejpam-2650	255	24	1	1	NUM
ejpam-2650	255	25	,	,	PUNCT
ejpam-2650	255	26	1	1	NUM
ejpam-2650	255	27	,	,	PUNCT
ejpam-2650	255	28	u3	u3	NOUN
ejpam-2650	255	29	+	+	CCONJ
ejpam-2650	255	30	1	1	NUM
ejpam-2650	255	31	)	)	PUNCT
ejpam-2650	256	1	[	[	X
ejpam-2650	256	2	64	64	NUM
ejpam-2650	256	3	,	,	PUNCT
ejpam-2650	256	4	6	6	NUM
ejpam-2650	256	5	,	,	PUNCT
ejpam-2650	256	6	32	32	NUM
ejpam-2650	256	7	]	]	SYM
ejpam-2650	256	8	32	32	NUM
ejpam-2650	256	9	5	5	NUM
ejpam-2650	256	10	2	2	NUM
ejpam-2650	256	11	(	(	PUNCT
ejpam-2650	256	12	1	1	NUM
ejpam-2650	256	13	,	,	PUNCT
ejpam-2650	256	14	1	1	NUM
ejpam-2650	256	15	,	,	PUNCT
ejpam-2650	256	16	u2	u2	PROPN
ejpam-2650	256	17	+	+	CCONJ
ejpam-2650	256	18	1	1	NUM
ejpam-2650	256	19	,	,	PUNCT
ejpam-2650	256	20	u3	u3	NOUN
ejpam-2650	256	21	+	+	CCONJ
ejpam-2650	256	22	u2	u2	PROPN
ejpam-2650	256	23	+	+	CCONJ
ejpam-2650	256	24	1	1	NUM
ejpam-2650	256	25	,	,	PUNCT
ejpam-2650	256	26	1	1	NUM
ejpam-2650	256	27	,	,	PUNCT
ejpam-2650	256	28	1	1	NUM
ejpam-2650	256	29	,	,	PUNCT
ejpam-2650	256	30	u3	u3	NOUN
ejpam-2650	256	31	+	+	CCONJ
ejpam-2650	256	32	u2	u2	PROPN
ejpam-2650	256	33	+	+	CCONJ
ejpam-2650	256	34	1	1	NUM
ejpam-2650	256	35	,	,	PUNCT
ejpam-2650	256	36	u2	u2	NOUN
ejpam-2650	256	37	+	+	CCONJ
ejpam-2650	256	38	1	1	NUM
ejpam-2650	256	39	)	)	PUNCT
ejpam-2650	257	1	[	[	X
ejpam-2650	257	2	64	64	NUM
ejpam-2650	257	3	,	,	PUNCT
ejpam-2650	257	4	7	7	NUM
ejpam-2650	257	5	,	,	PUNCT
ejpam-2650	257	6	32	32	NUM
ejpam-2650	257	7	]	]	SYM
ejpam-2650	257	8	32	32	NUM
ejpam-2650	257	9	5	5	NUM
ejpam-2650	257	10	3	3	NUM
ejpam-2650	257	11	(	(	PUNCT
ejpam-2650	257	12	1	1	NUM
ejpam-2650	257	13	,	,	PUNCT
ejpam-2650	257	14	1	1	NUM
ejpam-2650	257	15	,	,	PUNCT
ejpam-2650	257	16	u3	u3	NOUN
ejpam-2650	257	17	+	+	CCONJ
ejpam-2650	257	18	1	1	NUM
ejpam-2650	257	19	,	,	PUNCT
ejpam-2650	257	20	1	1	NUM
ejpam-2650	257	21	,	,	PUNCT
ejpam-2650	257	22	1	1	NUM
ejpam-2650	257	23	,	,	PUNCT
ejpam-2650	257	24	u3	u3	NOUN
ejpam-2650	257	25	+	+	CCONJ
ejpam-2650	257	26	1	1	NUM
ejpam-2650	257	27	,	,	PUNCT
ejpam-2650	257	28	1	1	NUM
ejpam-2650	257	29	,	,	PUNCT
ejpam-2650	257	30	1	1	NUM
ejpam-2650	257	31	,	,	PUNCT
ejpam-2650	257	32	u3	u3	NOUN
ejpam-2650	257	33	+	+	CCONJ
ejpam-2650	257	34	1	1	NUM
ejpam-2650	257	35	)	)	PUNCT
ejpam-2650	258	1	[	[	X
ejpam-2650	258	2	72	72	NUM
ejpam-2650	258	3	,	,	PUNCT
ejpam-2650	258	4	5	5	NUM
ejpam-2650	258	5	,	,	PUNCT
ejpam-2650	258	6	36	36	NUM
ejpam-2650	258	7	]	]	SYM
ejpam-2650	258	8	12	12	NUM
ejpam-2650	258	9	3	3	NUM
ejpam-2650	258	10	(	(	PUNCT
ejpam-2650	258	11	1	1	NUM
ejpam-2650	258	12	,	,	PUNCT
ejpam-2650	258	13	1	1	NUM
ejpam-2650	258	14	,	,	PUNCT
ejpam-2650	258	15	1	1	NUM
ejpam-2650	258	16	,	,	PUNCT
ejpam-2650	258	17	u3	u3	NOUN
ejpam-2650	258	18	+	+	CCONJ
ejpam-2650	258	19	1	1	NUM
ejpam-2650	258	20	,	,	PUNCT
ejpam-2650	258	21	1	1	NUM
ejpam-2650	258	22	,	,	PUNCT
ejpam-2650	258	23	1	1	NUM
ejpam-2650	258	24	,	,	PUNCT
ejpam-2650	258	25	1	1	NUM
ejpam-2650	258	26	,	,	PUNCT
ejpam-2650	258	27	u3	u3	NOUN
ejpam-2650	258	28	+	+	CCONJ
ejpam-2650	258	29	1	1	NUM
ejpam-2650	258	30	,	,	PUNCT
ejpam-2650	258	31	1	1	NUM
ejpam-2650	258	32	,	,	PUNCT
ejpam-2650	258	33	1	1	NUM
ejpam-2650	258	34	,	,	PUNCT
ejpam-2650	258	35	1	1	NUM
ejpam-2650	258	36	,	,	PUNCT
ejpam-2650	258	37	u3	u3	NOUN
ejpam-2650	258	38	+	+	CCONJ
ejpam-2650	258	39	1	1	NUM
ejpam-2650	258	40	)	)	PUNCT
ejpam-2650	259	1	[	[	X
ejpam-2650	259	2	96	96	NUM
ejpam-2650	259	3	,	,	PUNCT
ejpam-2650	259	4	6	6	NUM
ejpam-2650	259	5	,	,	PUNCT
ejpam-2650	259	6	48	48	NUM
ejpam-2650	259	7	]	]	SYM
ejpam-2650	259	8	48	48	NUM
ejpam-2650	259	9	remark	remark	NOUN
ejpam-2650	259	10	3	3	NUM
ejpam-2650	259	11	.	.	PUNCT
ejpam-2650	260	1	it	it	PRON
ejpam-2650	260	2	can	can	AUX
ejpam-2650	260	3	easily	easily	ADV
ejpam-2650	260	4	be	be	AUX
ejpam-2650	260	5	shown	show	VERB
ejpam-2650	260	6	that	that	SCONJ
ejpam-2650	260	7	the	the	DET
ejpam-2650	260	8	gray	gray	ADJ
ejpam-2650	260	9	-	-	PUNCT
ejpam-2650	260	10	homogeneous	homogeneous	ADJ
ejpam-2650	260	11	image	image	NOUN
ejpam-2650	260	12	of	of	ADP
ejpam-2650	260	13	an	an	DET
ejpam-2650	260	14	`	`	PUNCT
ejpam-2650	260	15	-quasicyclic	-quasicyclic	ADJ
ejpam-2650	260	16	code	code	NOUN
ejpam-2650	260	17	is	be	AUX
ejpam-2650	260	18	a	a	DET
ejpam-2650	260	19	(	(	PUNCT
ejpam-2650	260	20	2km−1`)-quasicyclic	2km−1`)-quasicyclic	NUM
ejpam-2650	260	21	binary	binary	PROPN
ejpam-2650	260	22	code	code	NOUN
ejpam-2650	260	23	.	.	PUNCT
ejpam-2650	261	1	so	so	ADV
ejpam-2650	261	2	,	,	PUNCT
ejpam-2650	261	3	the	the	DET
ejpam-2650	261	4	binary	binary	NOUN
ejpam-2650	261	5	codes	code	NOUN
ejpam-2650	261	6	constructed	construct	VERB
ejpam-2650	261	7	above	above	ADV
ejpam-2650	261	8	are	be	AUX
ejpam-2650	261	9	all	all	PRON
ejpam-2650	261	10	(	(	PUNCT
ejpam-2650	261	11	2km−1`)-quasicyclic	2km−1`)-quasicyclic	NUM
ejpam-2650	261	12	for	for	ADP
ejpam-2650	261	13	the	the	DET
ejpam-2650	261	14	appropriate	appropriate	ADJ
ejpam-2650	261	15	values	value	NOUN
ejpam-2650	261	16	of	of	ADP
ejpam-2650	261	17	`	`	PUNCT
ejpam-2650	261	18	,	,	PUNCT
ejpam-2650	261	19	k	k	NOUN
ejpam-2650	261	20	,	,	PUNCT
ejpam-2650	261	21	m.	m.	NOUN
ejpam-2650	261	22	in	in	ADP
ejpam-2650	261	23	all	all	PRON
ejpam-2650	261	24	but	but	SCONJ
ejpam-2650	261	25	one	one	NUM
ejpam-2650	261	26	of	of	ADP
ejpam-2650	261	27	the	the	DET
ejpam-2650	261	28	cases	case	NOUN
ejpam-2650	261	29	they	they	PRON
ejpam-2650	261	30	are	be	AUX
ejpam-2650	261	31	self	self	NOUN
ejpam-2650	261	32	-	-	PUNCT
ejpam-2650	261	33	orthogonal	orthogonal	ADJ
ejpam-2650	261	34	as	as	ADV
ejpam-2650	261	35	well	well	ADV
ejpam-2650	261	36	.	.	PUNCT
ejpam-2650	262	1	thus	thus	ADV
ejpam-2650	262	2	almost	almost	ADV
ejpam-2650	262	3	all	all	DET
ejpam-2650	262	4	the	the	DET
ejpam-2650	262	5	codes	code	NOUN
ejpam-2650	262	6	given	give	VERB
ejpam-2650	262	7	in	in	ADP
ejpam-2650	262	8	the	the	DET
ejpam-2650	262	9	above	above	ADJ
ejpam-2650	262	10	table	table	NOUN
ejpam-2650	262	11	are	be	AUX
ejpam-2650	262	12	optimal	optimal	ADJ
ejpam-2650	262	13	self	self	NOUN
ejpam-2650	262	14	-	-	PUNCT
ejpam-2650	262	15	orthogonal	orthogonal	ADJ
ejpam-2650	262	16	quasicyclic	quasicyclic	NOUN
ejpam-2650	262	17	codes	code	NOUN
ejpam-2650	262	18	.	.	PUNCT
ejpam-2650	263	1	4.4	4.4	NUM
ejpam-2650	263	2	.	.	PUNCT
ejpam-2650	264	1	griesmer	griesmer	PROPN
ejpam-2650	264	2	code	code	NOUN
ejpam-2650	264	3	the	the	DET
ejpam-2650	264	4	griesmer	griesmer	NOUN
ejpam-2650	264	5	bound	bind	VERB
ejpam-2650	264	6	,	,	PUNCT
ejpam-2650	264	7	introduced	introduce	VERB
ejpam-2650	264	8	in	in	ADP
ejpam-2650	264	9	[	[	X
ejpam-2650	264	10	7	7	NUM
ejpam-2650	264	11	]	]	PUNCT
ejpam-2650	264	12	is	be	AUX
ejpam-2650	264	13	one	one	NUM
ejpam-2650	264	14	of	of	ADP
ejpam-2650	264	15	the	the	DET
ejpam-2650	264	16	many	many	ADJ
ejpam-2650	264	17	bounds	bound	NOUN
ejpam-2650	264	18	that	that	PRON
ejpam-2650	264	19	exist	exist	VERB
ejpam-2650	264	20	for	for	ADP
ejpam-2650	264	21	codes	code	NOUN
ejpam-2650	264	22	,	,	PUNCT
ejpam-2650	264	23	and	and	CCONJ
ejpam-2650	264	24	can	can	AUX
ejpam-2650	264	25	be	be	AUX
ejpam-2650	264	26	stated	state	VERB
ejpam-2650	264	27	as	as	SCONJ
ejpam-2650	264	28	follows	follow	VERB
ejpam-2650	264	29	:	:	PUNCT
ejpam-2650	264	30	for	for	ADP
ejpam-2650	264	31	a	a	DET
ejpam-2650	264	32	linear	linear	ADJ
ejpam-2650	264	33	[	[	X
ejpam-2650	264	34	n	n	CCONJ
ejpam-2650	264	35	,	,	PUNCT
ejpam-2650	264	36	k	k	NOUN
ejpam-2650	264	37	,	,	PUNCT
ejpam-2650	264	38	d]-code	d]-code	NOUN
ejpam-2650	264	39	over	over	ADP
ejpam-2650	264	40	fq	fq	PROPN
ejpam-2650	264	41	,	,	PUNCT
ejpam-2650	264	42	we	we	PRON
ejpam-2650	264	43	have	have	VERB
ejpam-2650	264	44	n	n	NUM
ejpam-2650	264	45	≥	≥	NOUN
ejpam-2650	264	46	k−1∑	k−1∑	PROPN
ejpam-2650	264	47	i=0	i=0	PROPN
ejpam-2650	264	48	d	d	PROPN
ejpam-2650	264	49	d	d	X
ejpam-2650	264	50	qi	qi	PROPN
ejpam-2650	264	51	e	e	PROPN
ejpam-2650	264	52	,	,	PUNCT
ejpam-2650	264	53	(	(	PUNCT
ejpam-2650	264	54	5	5	NUM
ejpam-2650	264	55	)	)	PUNCT
ejpam-2650	264	56	where	where	SCONJ
ejpam-2650	264	57	dxe	dxe	PROPN
ejpam-2650	264	58	denotes	denote	VERB
ejpam-2650	264	59	the	the	DET
ejpam-2650	264	60	smallest	small	ADJ
ejpam-2650	264	61	integer	integer	NOUN
ejpam-2650	264	62	greater	great	ADJ
ejpam-2650	264	63	than	than	ADP
ejpam-2650	264	64	or	or	CCONJ
ejpam-2650	264	65	equal	equal	ADJ
ejpam-2650	264	66	to	to	ADP
ejpam-2650	264	67	x.	x.	NOUN
ejpam-2650	264	68	linear	linear	PROPN
ejpam-2650	264	69	codes	code	NOUN
ejpam-2650	264	70	meeting	meet	VERB
ejpam-2650	264	71	this	this	DET
ejpam-2650	264	72	bound	bind	VERB
ejpam-2650	264	73	are	be	AUX
ejpam-2650	264	74	called	call	VERB
ejpam-2650	264	75	griesmer	griesmer	ADJ
ejpam-2650	264	76	codes	code	NOUN
ejpam-2650	264	77	.	.	PUNCT
ejpam-2650	265	1	let	let	VERB
ejpam-2650	265	2	us	we	PRON
ejpam-2650	265	3	consider	consider	VERB
ejpam-2650	265	4	a	a	DET
ejpam-2650	265	5	one	one	NUM
ejpam-2650	265	6	generator	generator	NOUN
ejpam-2650	265	7	cyclic	cyclic	PROPN
ejpam-2650	265	8	code	code	NOUN
ejpam-2650	265	9	ckm	ckm	NOUN
ejpam-2650	265	10	of	of	ADP
ejpam-2650	265	11	length	length	NOUN
ejpam-2650	265	12	n	n	CCONJ
ejpam-2650	265	13	over	over	ADP
ejpam-2650	265	14	rk	rk	NOUN
ejpam-2650	265	15	,	,	PUNCT
ejpam-2650	265	16	m	m	VERB
ejpam-2650	265	17	with	with	ADP
ejpam-2650	265	18	the	the	DET
ejpam-2650	265	19	generator	generator	NOUN
ejpam-2650	265	20	vector	vector	NOUN
ejpam-2650	265	21	(	(	PUNCT
ejpam-2650	265	22	11	11	NUM
ejpam-2650	265	23	.	.	PUNCT
ejpam-2650	265	24	.	.	PUNCT
ejpam-2650	266	1	.	.	PUNCT
ejpam-2650	267	1	1	1	NUM
ejpam-2650	267	2	)	)	PUNCT
ejpam-2650	267	3	.	.	PUNCT
ejpam-2650	268	1	this	this	PRON
ejpam-2650	268	2	is	be	AUX
ejpam-2650	268	3	actually	actually	ADV
ejpam-2650	268	4	the	the	DET
ejpam-2650	268	5	repetition	repetition	NOUN
ejpam-2650	268	6	code	code	PROPN
ejpam-2650	268	7	.	.	PUNCT
ejpam-2650	269	1	it	it	PRON
ejpam-2650	269	2	is	be	AUX
ejpam-2650	269	3	clear	clear	ADJ
ejpam-2650	269	4	to	to	PART
ejpam-2650	269	5	see	see	VERB
ejpam-2650	269	6	that	that	SCONJ
ejpam-2650	269	7	the	the	DET
ejpam-2650	269	8	gray	gray	ADJ
ejpam-2650	269	9	-	-	PUNCT
ejpam-2650	269	10	homogeneous	homogeneous	ADJ
ejpam-2650	269	11	image	image	NOUN
ejpam-2650	269	12	of	of	ADP
ejpam-2650	269	13	this	this	DET
ejpam-2650	269	14	code	code	NOUN
ejpam-2650	269	15	is	be	AUX
ejpam-2650	269	16	a	a	DET
ejpam-2650	269	17	binary	binary	ADJ
ejpam-2650	269	18	linear	linear	PROPN
ejpam-2650	269	19	code	code	NOUN
ejpam-2650	269	20	of	of	ADP
ejpam-2650	269	21	the	the	DET
ejpam-2650	269	22	parameters	parameter	NOUN
ejpam-2650	270	1	[	[	X
ejpam-2650	270	2	2km−1n	2km−1n	ADJ
ejpam-2650	270	3	,	,	PUNCT
ejpam-2650	270	4	km	km	PROPN
ejpam-2650	270	5	,	,	PUNCT
ejpam-2650	270	6	2km−2n	2km−2n	PROPN
ejpam-2650	270	7	]	]	PUNCT
ejpam-2650	270	8	.	.	PUNCT
ejpam-2650	271	1	thus	thus	ADV
ejpam-2650	271	2	,	,	PUNCT
ejpam-2650	271	3	the	the	DET
ejpam-2650	271	4	images	image	NOUN
ejpam-2650	271	5	of	of	ADP
ejpam-2650	271	6	this	this	DET
ejpam-2650	271	7	code	code	NOUN
ejpam-2650	271	8	are	be	AUX
ejpam-2650	271	9	binary	binary	ADJ
ejpam-2650	271	10	divisible	divisible	ADJ
ejpam-2650	271	11	codes	code	NOUN
ejpam-2650	271	12	with	with	ADP
ejpam-2650	271	13	divisor	divisor	NOUN
ejpam-2650	271	14	at	at	ADV
ejpam-2650	271	15	least	least	ADJ
ejpam-2650	271	16	2km−2	2km−2	NUM
ejpam-2650	271	17	.	.	PUNCT
ejpam-2650	272	1	we	we	PRON
ejpam-2650	272	2	may	may	AUX
ejpam-2650	272	3	construct	construct	VERB
ejpam-2650	272	4	many	many	ADJ
ejpam-2650	272	5	optimal	optimal	ADJ
ejpam-2650	272	6	linear	linear	ADJ
ejpam-2650	272	7	codes	code	NOUN
ejpam-2650	272	8	,	,	PUNCT
ejpam-2650	272	9	which	which	PRON
ejpam-2650	272	10	otherwise	otherwise	ADV
ejpam-2650	272	11	may	may	AUX
ejpam-2650	272	12	references	reference	VERB
ejpam-2650	272	13	1122	1122	NUM
ejpam-2650	272	14	have	have	VERB
ejpam-2650	272	15	complicated	complicated	ADJ
ejpam-2650	272	16	constructions	construction	NOUN
ejpam-2650	272	17	,	,	PUNCT
ejpam-2650	272	18	in	in	ADP
ejpam-2650	272	19	a	a	DET
ejpam-2650	272	20	relatively	relatively	ADV
ejpam-2650	272	21	easier	easy	ADJ
ejpam-2650	272	22	way	way	NOUN
ejpam-2650	272	23	from	from	ADP
ejpam-2650	272	24	ckm	ckm	PROPN
ejpam-2650	272	25	.	.	PROPN
ejpam-2650	273	1	as	as	ADP
ejpam-2650	273	2	an	an	DET
ejpam-2650	273	3	illustration	illustration	NOUN
ejpam-2650	273	4	of	of	ADP
ejpam-2650	273	5	this	this	DET
ejpam-2650	273	6	idea	idea	NOUN
ejpam-2650	273	7	,	,	PUNCT
ejpam-2650	273	8	consider	consider	VERB
ejpam-2650	273	9	,	,	PUNCT
ejpam-2650	273	10	the	the	DET
ejpam-2650	273	11	gray	gray	ADJ
ejpam-2650	273	12	-	-	PUNCT
ejpam-2650	273	13	homogeneous	homogeneous	ADJ
ejpam-2650	273	14	images	image	NOUN
ejpam-2650	273	15	of	of	ADP
ejpam-2650	273	16	c51	c51	NOUN
ejpam-2650	273	17	and	and	CCONJ
ejpam-2650	273	18	c32	c32	NOUN
ejpam-2650	273	19	of	of	ADP
ejpam-2650	273	20	length	length	NOUN
ejpam-2650	273	21	n.	n.	PROPN
ejpam-2650	273	22	these	these	PRON
ejpam-2650	273	23	will	will	AUX
ejpam-2650	273	24	be	be	AUX
ejpam-2650	273	25	binary	binary	ADJ
ejpam-2650	273	26	codes	code	NOUN
ejpam-2650	273	27	of	of	ADP
ejpam-2650	273	28	parameters	parameter	NOUN
ejpam-2650	273	29	[	[	X
ejpam-2650	273	30	16n	16n	NUM
ejpam-2650	273	31	,	,	PUNCT
ejpam-2650	273	32	5	5	NUM
ejpam-2650	273	33	,	,	PUNCT
ejpam-2650	273	34	8n	8n	NOUN
ejpam-2650	273	35	]	]	PUNCT
ejpam-2650	273	36	and	and	CCONJ
ejpam-2650	273	37	[	[	X
ejpam-2650	273	38	32n	32n	NOUN
ejpam-2650	273	39	,	,	PUNCT
ejpam-2650	273	40	6	6	NUM
ejpam-2650	273	41	,	,	PUNCT
ejpam-2650	273	42	16n	16n	NUM
ejpam-2650	273	43	]	]	PUNCT
ejpam-2650	273	44	,	,	PUNCT
ejpam-2650	273	45	respectively	respectively	ADV
ejpam-2650	273	46	.	.	PUNCT
ejpam-2650	274	1	according	accord	VERB
ejpam-2650	274	2	to	to	ADP
ejpam-2650	274	3	[	[	X
ejpam-2650	274	4	5	5	NUM
ejpam-2650	274	5	]	]	PUNCT
ejpam-2650	274	6	,	,	PUNCT
ejpam-2650	274	7	these	these	DET
ejpam-2650	274	8	codes	code	NOUN
ejpam-2650	274	9	are	be	AUX
ejpam-2650	274	10	all	all	ADV
ejpam-2650	274	11	optimal	optimal	ADJ
ejpam-2650	274	12	when	when	SCONJ
ejpam-2650	274	13	1	1	NUM
ejpam-2650	274	14	≤	≤	NUM
ejpam-2650	274	15	n	n	PRON
ejpam-2650	274	16	≤	≤	NUM
ejpam-2650	274	17	8	8	NUM
ejpam-2650	274	18	.	.	PUNCT
ejpam-2650	275	1	we	we	PRON
ejpam-2650	275	2	finish	finish	VERB
ejpam-2650	275	3	this	this	DET
ejpam-2650	275	4	section	section	NOUN
ejpam-2650	275	5	by	by	ADP
ejpam-2650	275	6	noticing	notice	VERB
ejpam-2650	275	7	that	that	SCONJ
ejpam-2650	275	8	φhom(ckm)s	φhom(ckm)s	PROPN
ejpam-2650	275	9	are	be	AUX
ejpam-2650	275	10	griesmer	griesmer	ADJ
ejpam-2650	275	11	codes	code	NOUN
ejpam-2650	275	12	,	,	PUNCT
ejpam-2650	275	13	when	when	SCONJ
ejpam-2650	275	14	n	n	X
ejpam-2650	275	15	=	=	SYM
ejpam-2650	275	16	1	1	NUM
ejpam-2650	275	17	,	,	PUNCT
ejpam-2650	275	18	for	for	SCONJ
ejpam-2650	275	19	all	all	DET
ejpam-2650	275	20	k	k	PROPN
ejpam-2650	275	21	and	and	CCONJ
ejpam-2650	275	22	m.	m.	NOUN
ejpam-2650	275	23	theorem	theorem	VERB
ejpam-2650	275	24	5	5	NUM
ejpam-2650	275	25	.	.	PUNCT
ejpam-2650	276	1	the	the	DET
ejpam-2650	276	2	binary	binary	PROPN
ejpam-2650	276	3	linear	linear	PROPN
ejpam-2650	276	4	code	code	PROPN
ejpam-2650	276	5	φhom(ckm	φhom(ckm	PROPN
ejpam-2650	276	6	)	)	PUNCT
ejpam-2650	276	7	is	be	AUX
ejpam-2650	276	8	a	a	DET
ejpam-2650	276	9	griesmer	griesmer	ADJ
ejpam-2650	276	10	code	code	NOUN
ejpam-2650	276	11	for	for	ADP
ejpam-2650	276	12	n	n	NOUN
ejpam-2650	276	13	=	=	SYM
ejpam-2650	276	14	1	1	NUM
ejpam-2650	276	15	,	,	PUNCT
ejpam-2650	276	16	and	and	CCONJ
ejpam-2650	276	17	for	for	ADP
ejpam-2650	276	18	all	all	DET
ejpam-2650	276	19	k	k	PROPN
ejpam-2650	276	20	,	,	PUNCT
ejpam-2650	276	21	m.	m.	NOUN
ejpam-2650	276	22	proof	proof	NOUN
ejpam-2650	276	23	.	.	PUNCT
ejpam-2650	277	1	when	when	SCONJ
ejpam-2650	277	2	n	n	X
ejpam-2650	277	3	=	=	SYM
ejpam-2650	277	4	1	1	NUM
ejpam-2650	277	5	,	,	PUNCT
ejpam-2650	277	6	φhom(ckm	φhom(ckm	NOUN
ejpam-2650	277	7	)	)	PUNCT
ejpam-2650	277	8	is	be	AUX
ejpam-2650	277	9	a	a	DET
ejpam-2650	277	10	km	km	NOUN
ejpam-2650	277	11	-	-	PUNCT
ejpam-2650	277	12	dimensional	dimensional	ADJ
ejpam-2650	277	13	linear	linear	ADJ
ejpam-2650	277	14	code	code	NOUN
ejpam-2650	277	15	with	with	ADP
ejpam-2650	277	16	minimum	minimum	NOUN
ejpam-2650	277	17	distance	distance	NOUN
ejpam-2650	277	18	2km−2	2km−2	NUM
ejpam-2650	277	19	.	.	PUNCT
ejpam-2650	278	1	calculating	calculate	VERB
ejpam-2650	278	2	the	the	DET
ejpam-2650	278	3	griesmer	griesmer	NOUN
ejpam-2650	278	4	lower	lower	ADV
ejpam-2650	278	5	bound	bind	VERB
ejpam-2650	278	6	according	accord	VERB
ejpam-2650	278	7	to	to	ADP
ejpam-2650	278	8	5	5	NUM
ejpam-2650	278	9	,	,	PUNCT
ejpam-2650	278	10	we	we	PRON
ejpam-2650	278	11	see	see	VERB
ejpam-2650	278	12	that	that	SCONJ
ejpam-2650	278	13	the	the	DET
ejpam-2650	278	14	lower	low	ADJ
ejpam-2650	278	15	bound	bind	VERB
ejpam-2650	278	16	must	must	AUX
ejpam-2650	278	17	be	be	AUX
ejpam-2650	278	18	km−1∑	km−1∑	VERB
ejpam-2650	278	19	i=0	i=0	PROPN
ejpam-2650	278	20	d	d	PROPN
ejpam-2650	279	1	d	d	X
ejpam-2650	279	2	2i	2i	NUM
ejpam-2650	279	3	e	e	X
ejpam-2650	279	4	=	=	SYM
ejpam-2650	279	5	d2	d2	PROPN
ejpam-2650	279	6	km−2	km−2	PROPN
ejpam-2650	279	7	20	20	NUM
ejpam-2650	279	8	e+	e+	NUM
ejpam-2650	279	9	d2	d2	PROPN
ejpam-2650	279	10	km−2	km−2	PROPN
ejpam-2650	279	11	21	21	NUM
ejpam-2650	279	12	e+	e+	X
ejpam-2650	279	13	·	·	PUNCT
ejpam-2650	279	14	·	·	PUNCT
ejpam-2650	279	15	·	·	PUNCT
ejpam-2650	279	16	+	+	NUM
ejpam-2650	279	17	d2	d2	PROPN
ejpam-2650	279	18	km−2	km−2	PROPN
ejpam-2650	279	19	2km−2	2km−2	NUM
ejpam-2650	279	20	e+	e+	PUNCT
ejpam-2650	279	21	d2	d2	PROPN
ejpam-2650	279	22	km−2	km−2	PROPN
ejpam-2650	279	23	2km−1	2km−1	PROPN
ejpam-2650	279	24	e	e	NOUN
ejpam-2650	279	25	=	=	SYM
ejpam-2650	279	26	2km−2	2km−2	NUM
ejpam-2650	280	1	+	+	NUM
ejpam-2650	280	2	2km−3	2km−3	NUM
ejpam-2650	280	3	+	+	X
ejpam-2650	280	4	·	·	PUNCT
ejpam-2650	281	1	·	·	PUNCT
ejpam-2650	281	2	·	·	PUNCT
ejpam-2650	281	3	+	+	SYM
ejpam-2650	281	4	1	1	NUM
ejpam-2650	281	5	+	+	SYM
ejpam-2650	281	6	1	1	NUM
ejpam-2650	281	7	=	=	SYM
ejpam-2650	281	8	(	(	PUNCT
ejpam-2650	281	9	2km−1	2km−1	NOUN
ejpam-2650	281	10	−	−	NOUN
ejpam-2650	281	11	1	1	NUM
ejpam-2650	281	12	)	)	PUNCT
ejpam-2650	281	13	+	+	CCONJ
ejpam-2650	281	14	1	1	NUM
ejpam-2650	281	15	=	=	SYM
ejpam-2650	281	16	2km−1	2km−1	PROPN
ejpam-2650	281	17	,	,	PUNCT
ejpam-2650	281	18	which	which	PRON
ejpam-2650	281	19	is	be	AUX
ejpam-2650	281	20	precisely	precisely	ADV
ejpam-2650	281	21	the	the	DET
ejpam-2650	281	22	length	length	NOUN
ejpam-2650	281	23	of	of	ADP
ejpam-2650	281	24	φhom(ckm	φhom(ckm	NOUN
ejpam-2650	281	25	)	)	PUNCT
ejpam-2650	281	26	,	,	PUNCT
ejpam-2650	281	27	when	when	SCONJ
ejpam-2650	281	28	n	n	X
ejpam-2650	281	29	=	=	SYM
ejpam-2650	281	30	1	1	NUM
ejpam-2650	281	31	.	.	NOUN
ejpam-2650	281	32	5	5	NUM
ejpam-2650	281	33	.	.	X
ejpam-2650	281	34	conclusion	conclusion	NOUN
ejpam-2650	281	35	finding	find	VERB
ejpam-2650	281	36	optimal	optimal	ADJ
ejpam-2650	281	37	binary	binary	ADJ
ejpam-2650	281	38	codes	code	NOUN
ejpam-2650	281	39	is	be	AUX
ejpam-2650	281	40	a	a	DET
ejpam-2650	281	41	relevant	relevant	ADJ
ejpam-2650	281	42	question	question	NOUN
ejpam-2650	281	43	in	in	ADP
ejpam-2650	281	44	coding	code	VERB
ejpam-2650	281	45	theory	theory	NOUN
ejpam-2650	281	46	.	.	PUNCT
ejpam-2650	282	1	the	the	DET
ejpam-2650	282	2	database	database	NOUN
ejpam-2650	282	3	given	give	VERB
ejpam-2650	282	4	in	in	ADP
ejpam-2650	282	5	[	[	NOUN
ejpam-2650	282	6	5	5	NUM
ejpam-2650	282	7	]	]	PUNCT
ejpam-2650	282	8	is	be	AUX
ejpam-2650	282	9	a	a	DET
ejpam-2650	282	10	dynamic	dynamic	ADJ
ejpam-2650	282	11	source	source	NOUN
ejpam-2650	282	12	of	of	ADP
ejpam-2650	282	13	such	such	ADJ
ejpam-2650	282	14	codes	code	NOUN
ejpam-2650	282	15	together	together	ADV
ejpam-2650	282	16	with	with	ADP
ejpam-2650	282	17	different	different	ADJ
ejpam-2650	282	18	suggested	suggest	VERB
ejpam-2650	282	19	constructions	construction	NOUN
ejpam-2650	282	20	.	.	PUNCT
ejpam-2650	283	1	in	in	ADP
ejpam-2650	283	2	our	our	PRON
ejpam-2650	283	3	work	work	NOUN
ejpam-2650	283	4	,	,	PUNCT
ejpam-2650	283	5	we	we	PRON
ejpam-2650	283	6	were	be	AUX
ejpam-2650	283	7	able	able	ADJ
ejpam-2650	283	8	to	to	PART
ejpam-2650	283	9	reconstruct	reconstruct	VERB
ejpam-2650	283	10	many	many	ADJ
ejpam-2650	283	11	of	of	ADP
ejpam-2650	283	12	the	the	DET
ejpam-2650	283	13	optimal	optimal	ADJ
ejpam-2650	283	14	codes	code	NOUN
ejpam-2650	283	15	by	by	ADP
ejpam-2650	283	16	using	use	VERB
ejpam-2650	283	17	different	different	ADJ
ejpam-2650	283	18	constructions	construction	NOUN
ejpam-2650	283	19	over	over	ADP
ejpam-2650	283	20	the	the	DET
ejpam-2650	283	21	rings	ring	NOUN
ejpam-2650	283	22	rk	rk	PROPN
ejpam-2650	283	23	,	,	PUNCT
ejpam-2650	283	24	m.	m.	VERB
ejpam-2650	283	25	the	the	DET
ejpam-2650	283	26	codes	code	NOUN
ejpam-2650	283	27	that	that	PRON
ejpam-2650	283	28	are	be	AUX
ejpam-2650	283	29	obtained	obtain	VERB
ejpam-2650	283	30	,	,	PUNCT
ejpam-2650	283	31	are	be	AUX
ejpam-2650	283	32	not	not	PART
ejpam-2650	283	33	only	only	ADV
ejpam-2650	283	34	all	all	PRON
ejpam-2650	283	35	optimal	optimal	ADJ
ejpam-2650	283	36	,	,	PUNCT
ejpam-2650	283	37	but	but	CCONJ
ejpam-2650	283	38	they	they	PRON
ejpam-2650	283	39	possess	possess	VERB
ejpam-2650	283	40	some	some	DET
ejpam-2650	283	41	further	further	ADJ
ejpam-2650	283	42	properties	property	NOUN
ejpam-2650	283	43	such	such	ADJ
ejpam-2650	283	44	as	as	ADP
ejpam-2650	283	45	being	be	AUX
ejpam-2650	283	46	divisible	divisible	ADJ
ejpam-2650	283	47	with	with	ADP
ejpam-2650	283	48	high	high	ADJ
ejpam-2650	283	49	levels	level	NOUN
ejpam-2650	283	50	of	of	ADP
ejpam-2650	283	51	divisibility	divisibility	NOUN
ejpam-2650	283	52	,	,	PUNCT
ejpam-2650	283	53	and	and	CCONJ
ejpam-2650	283	54	in	in	ADP
ejpam-2650	283	55	many	many	ADJ
ejpam-2650	283	56	cases	case	NOUN
ejpam-2650	283	57	self	self	NOUN
ejpam-2650	283	58	-	-	PUNCT
ejpam-2650	283	59	orthogonal	orthogonal	NOUN
ejpam-2650	283	60	.	.	PUNCT
ejpam-2650	284	1	they	they	PRON
ejpam-2650	284	2	are	be	AUX
ejpam-2650	284	3	also	also	ADV
ejpam-2650	284	4	quasicyclic	quasicyclic	ADJ
ejpam-2650	284	5	with	with	ADP
ejpam-2650	284	6	high	high	ADJ
ejpam-2650	284	7	indices	index	NOUN
ejpam-2650	284	8	.	.	PUNCT
ejpam-2650	285	1	this	this	PRON
ejpam-2650	285	2	means	mean	VERB
ejpam-2650	285	3	that	that	SCONJ
ejpam-2650	285	4	the	the	DET
ejpam-2650	285	5	binary	binary	PROPN
ejpam-2650	285	6	codes	code	NOUN
ejpam-2650	285	7	that	that	PRON
ejpam-2650	285	8	we	we	PRON
ejpam-2650	285	9	have	have	AUX
ejpam-2650	285	10	obtained	obtain	VERB
ejpam-2650	285	11	from	from	ADP
ejpam-2650	285	12	the	the	DET
ejpam-2650	285	13	gray	gray	ADJ
ejpam-2650	285	14	-	-	PUNCT
ejpam-2650	285	15	homogeneous	homogeneous	ADJ
ejpam-2650	285	16	images	image	NOUN
ejpam-2650	285	17	of	of	ADP
ejpam-2650	285	18	codes	code	NOUN
ejpam-2650	285	19	over	over	ADP
ejpam-2650	285	20	rk	rk	NOUN
ejpam-2650	285	21	,	,	PUNCT
ejpam-2650	285	22	m	m	VERB
ejpam-2650	285	23	are	be	AUX
ejpam-2650	285	24	rather	rather	ADV
ejpam-2650	285	25	special	special	ADJ
ejpam-2650	285	26	examples	example	NOUN
ejpam-2650	285	27	of	of	ADP
ejpam-2650	285	28	codes	code	NOUN
ejpam-2650	285	29	that	that	PRON
ejpam-2650	285	30	appear	appear	VERB
ejpam-2650	285	31	in	in	ADP
ejpam-2650	285	32	[	[	X
ejpam-2650	285	33	5	5	NUM
ejpam-2650	285	34	]	]	PUNCT
ejpam-2650	285	35	.	.	PUNCT
ejpam-2650	286	1	considering	consider	VERB
ejpam-2650	286	2	that	that	SCONJ
ejpam-2650	286	3	many	many	ADJ
ejpam-2650	286	4	of	of	ADP
ejpam-2650	286	5	the	the	DET
ejpam-2650	286	6	codes	code	NOUN
ejpam-2650	286	7	we	we	PRON
ejpam-2650	286	8	have	have	AUX
ejpam-2650	286	9	obtained	obtain	VERB
ejpam-2650	286	10	fall	fall	NOUN
ejpam-2650	286	11	into	into	ADP
ejpam-2650	286	12	the	the	DET
ejpam-2650	286	13	class	class	NOUN
ejpam-2650	286	14	of	of	ADP
ejpam-2650	286	15	self	self	NOUN
ejpam-2650	286	16	-	-	PUNCT
ejpam-2650	286	17	orthogonal	orthogonal	ADJ
ejpam-2650	286	18	quasicyclic	quasicyclic	NOUN
ejpam-2650	286	19	codes	code	NOUN
ejpam-2650	286	20	,	,	PUNCT
ejpam-2650	286	21	they	they	PRON
ejpam-2650	286	22	are	be	AUX
ejpam-2650	286	23	of	of	ADP
ejpam-2650	286	24	interest	interest	NOUN
ejpam-2650	286	25	within	within	ADP
ejpam-2650	286	26	the	the	DET
ejpam-2650	286	27	context	context	NOUN
ejpam-2650	286	28	of	of	ADP
ejpam-2650	286	29	[	[	X
ejpam-2650	286	30	12	12	NUM
ejpam-2650	286	31	]	]	PUNCT
ejpam-2650	286	32	as	as	ADV
ejpam-2650	286	33	well	well	ADV
ejpam-2650	286	34	.	.	PUNCT
ejpam-2650	287	1	the	the	DET
ejpam-2650	287	2	relative	relative	ADJ
ejpam-2650	287	3	ease	ease	NOUN
ejpam-2650	287	4	with	with	ADP
ejpam-2650	287	5	which	which	PRON
ejpam-2650	287	6	we	we	PRON
ejpam-2650	287	7	obtained	obtain	VERB
ejpam-2650	287	8	the	the	DET
ejpam-2650	287	9	codes	code	NOUN
ejpam-2650	287	10	and	and	CCONJ
ejpam-2650	287	11	usually	usually	ADV
ejpam-2650	287	12	simple	simple	ADJ
ejpam-2650	287	13	constructions	construction	NOUN
ejpam-2650	287	14	suggest	suggest	VERB
ejpam-2650	287	15	that	that	SCONJ
ejpam-2650	287	16	,	,	PUNCT
ejpam-2650	287	17	the	the	DET
ejpam-2650	287	18	idea	idea	NOUN
ejpam-2650	287	19	of	of	ADP
ejpam-2650	287	20	using	use	VERB
ejpam-2650	287	21	rk	rk	PRON
ejpam-2650	287	22	,	,	PUNCT
ejpam-2650	287	23	m	m	PRON
ejpam-2650	287	24	and	and	CCONJ
ejpam-2650	287	25	the	the	DET
ejpam-2650	287	26	gray	gray	ADJ
ejpam-2650	287	27	-	-	PUNCT
ejpam-2650	287	28	homogeneous	homogeneous	ADJ
ejpam-2650	287	29	map	map	NOUN
ejpam-2650	287	30	is	be	AUX
ejpam-2650	287	31	worth	worth	ADJ
ejpam-2650	287	32	pursuing	pursue	VERB
ejpam-2650	287	33	in	in	ADP
ejpam-2650	287	34	many	many	ADJ
ejpam-2650	287	35	other	other	ADJ
ejpam-2650	287	36	contexts	context	NOUN
ejpam-2650	287	37	as	as	ADV
ejpam-2650	287	38	well	well	ADV
ejpam-2650	287	39	.	.	PUNCT
ejpam-2650	288	1	references	reference	NOUN
ejpam-2650	288	2	[	[	X
ejpam-2650	288	3	1	1	NUM
ejpam-2650	288	4	]	]	PUNCT
ejpam-2650	288	5	n	n	CCONJ
ejpam-2650	288	6	aydin	aydin	NOUN
ejpam-2650	288	7	,	,	PUNCT
ejpam-2650	288	8	s	s	PROPN
ejpam-2650	288	9	karadeniz	karadeniz	NOUN
ejpam-2650	288	10	and	and	CCONJ
ejpam-2650	288	11	b	b	PROPN
ejpam-2650	288	12	yildiz	yildiz	NOUN
ejpam-2650	288	13	.	.	PUNCT
ejpam-2650	289	1	some	some	DET
ejpam-2650	289	2	new	new	ADJ
ejpam-2650	289	3	binary	binary	ADJ
ejpam-2650	289	4	quasi	quasi	ADJ
ejpam-2650	289	5	-	-	ADJ
ejpam-2650	289	6	cyclic	cyclic	ADJ
ejpam-2650	289	7	codes	code	NOUN
ejpam-2650	289	8	from	from	ADP
ejpam-2650	289	9	codes	code	NOUN
ejpam-2650	289	10	over	over	ADP
ejpam-2650	289	11	the	the	DET
ejpam-2650	289	12	ring	ring	NOUN
ejpam-2650	289	13	f2+uf2+vf2+uvf2	f2+uf2+vf2+uvf2	PROPN
ejpam-2650	289	14	,	,	PUNCT
ejpam-2650	289	15	applicable	applicable	ADJ
ejpam-2650	289	16	algebra	algebra	NOUN
ejpam-2650	289	17	in	in	ADP
ejpam-2650	289	18	engineering	engineering	NOUN
ejpam-2650	289	19	,	,	PUNCT
ejpam-2650	289	20	communication	communication	NOUN
ejpam-2650	289	21	and	and	CCONJ
ejpam-2650	289	22	computing	computing	NOUN
ejpam-2650	289	23	,	,	PUNCT
ejpam-2650	289	24	24:355	24:355	NUM
ejpam-2650	289	25	-	-	SYM
ejpam-2650	289	26	367	367	NUM
ejpam-2650	289	27	,	,	PUNCT
ejpam-2650	289	28	2013	2013	NUM
ejpam-2650	289	29	.	.	PUNCT
ejpam-2650	290	1	references	reference	NOUN
ejpam-2650	290	2	1123	1123	NUM
ejpam-2650	290	3	[	[	X
ejpam-2650	290	4	2	2	NUM
ejpam-2650	290	5	]	]	PUNCT
ejpam-2650	290	6	w	w	PROPN
ejpam-2650	290	7	bosma	bosma	PROPN
ejpam-2650	290	8	,	,	PUNCT
ejpam-2650	290	9	j	j	PROPN
ejpam-2650	290	10	cannon	cannon	NOUN
ejpam-2650	290	11	and	and	CCONJ
ejpam-2650	290	12	c	c	PROPN
ejpam-2650	290	13	playoust	playoust	NOUN
ejpam-2650	290	14	.	.	PUNCT
ejpam-2650	291	1	the	the	DET
ejpam-2650	291	2	magma	magma	NOUN
ejpam-2650	291	3	algebra	algebra	NOUN
ejpam-2650	291	4	system	system	NOUN
ejpam-2650	291	5	i.	i.	PROPN
ejpam-2650	291	6	the	the	DET
ejpam-2650	291	7	user	user	NOUN
ejpam-2650	291	8	language	language	PROPN
ejpam-2650	291	9	,	,	PUNCT
ejpam-2650	291	10	journal	journal	NOUN
ejpam-2650	291	11	of	of	ADP
ejpam-2650	291	12	symbolic	symbolic	ADJ
ejpam-2650	291	13	computation	computation	NOUN
ejpam-2650	291	14	,	,	PUNCT
ejpam-2650	291	15	24:235–265	24:235–265	NUM
ejpam-2650	291	16	,	,	PUNCT
ejpam-2650	291	17	1997	1997	NUM
ejpam-2650	291	18	.	.	PUNCT
ejpam-2650	292	1	[	[	X
ejpam-2650	292	2	3	3	X
ejpam-2650	292	3	]	]	X
ejpam-2650	292	4	z	z	PROPN
ejpam-2650	292	5	chen	chen	PROPN
ejpam-2650	292	6	.	.	PUNCT
ejpam-2650	293	1	six	six	NUM
ejpam-2650	293	2	new	new	ADJ
ejpam-2650	293	3	binary	binary	ADJ
ejpam-2650	293	4	quasi	quasi	ADJ
ejpam-2650	293	5	-	-	ADJ
ejpam-2650	293	6	cyclic	cyclic	ADJ
ejpam-2650	293	7	codes	code	NOUN
ejpam-2650	293	8	,	,	PUNCT
ejpam-2650	293	9	ieee	ieee	NOUN
ejpam-2650	293	10	transactions	transaction	NOUN
ejpam-2650	293	11	on	on	ADP
ejpam-2650	293	12	information	information	NOUN
ejpam-2650	293	13	theory	theory	NOUN
ejpam-2650	293	14	,	,	PUNCT
ejpam-2650	293	15	40(5):1666–1667	40(5):1666–1667	PROPN
ejpam-2650	293	16	,	,	PUNCT
ejpam-2650	293	17	1994	1994	NUM
ejpam-2650	293	18	.	.	PUNCT
ejpam-2650	294	1	[	[	X
ejpam-2650	294	2	4	4	X
ejpam-2650	294	3	]	]	X
ejpam-2650	294	4	i	i	PRON
ejpam-2650	294	5	constantinescu	constantinescu	PROPN
ejpam-2650	294	6	and	and	CCONJ
ejpam-2650	294	7	w	w	PROPN
ejpam-2650	294	8	heise	heise	PROPN
ejpam-2650	294	9	.	.	PUNCT
ejpam-2650	295	1	a	a	DET
ejpam-2650	295	2	metric	metric	NOUN
ejpam-2650	295	3	for	for	ADP
ejpam-2650	295	4	codes	code	NOUN
ejpam-2650	295	5	over	over	ADP
ejpam-2650	295	6	residue	residue	NOUN
ejpam-2650	295	7	class	class	NOUN
ejpam-2650	295	8	rings	ring	NOUN
ejpam-2650	295	9	of	of	ADP
ejpam-2650	295	10	integers	integer	NOUN
ejpam-2650	295	11	,	,	PUNCT
ejpam-2650	295	12	problemy	problemy	PROPN
ejpam-2650	295	13	peredachi	peredachi	PROPN
ejpam-2650	295	14	informatsii	informatsii	VERB
ejpam-2650	295	15	,	,	PUNCT
ejpam-2650	295	16	33(3):22–28	33(3):22–28	NUM
ejpam-2650	295	17	,	,	PUNCT
ejpam-2650	295	18	1997	1997	NUM
ejpam-2650	295	19	.	.	PUNCT
ejpam-2650	296	1	[	[	X
ejpam-2650	296	2	5	5	NUM
ejpam-2650	296	3	]	]	PUNCT
ejpam-2650	296	4	m	m	AUX
ejpam-2650	296	5	grassl	grassl	VERB
ejpam-2650	296	6	.	.	PUNCT
ejpam-2650	297	1	bound	bind	VERB
ejpam-2650	297	2	on	on	ADP
ejpam-2650	297	3	the	the	DET
ejpam-2650	297	4	minimum	minimum	ADJ
ejpam-2650	297	5	distance	distance	NOUN
ejpam-2650	297	6	of	of	ADP
ejpam-2650	297	7	linear	linear	PROPN
ejpam-2650	297	8	codes	code	NOUN
ejpam-2650	297	9	and	and	CCONJ
ejpam-2650	297	10	quantum	quantum	NOUN
ejpam-2650	297	11	codes	code	NOUN
ejpam-2650	297	12	,	,	PUNCT
ejpam-2650	297	13	online	online	ADV
ejpam-2650	297	14	available	available	ADJ
ejpam-2650	297	15	at	at	ADP
ejpam-2650	297	16	:	:	PUNCT
ejpam-2650	297	17	www.codetables.de(accessed	www.codetables.de(accesse	VERB
ejpam-2650	297	18	on	on	ADP
ejpam-2650	297	19	2015/12/01	2015/12/01	NUM
ejpam-2650	297	20	)	)	PUNCT
ejpam-2650	297	21	.	.	PUNCT
ejpam-2650	298	1	[	[	X
ejpam-2650	298	2	6	6	NUM
ejpam-2650	298	3	]	]	PUNCT
ejpam-2650	298	4	m	m	VERB
ejpam-2650	298	5	greferath	greferath	NOUN
ejpam-2650	298	6	and	and	CCONJ
ejpam-2650	298	7	m	m	PROPN
ejpam-2650	298	8	e	e	NOUN
ejpam-2650	298	9	osullivan	osullivan	NOUN
ejpam-2650	298	10	.	.	PUNCT
ejpam-2650	299	1	on	on	ADP
ejpam-2650	299	2	bounds	bound	NOUN
ejpam-2650	299	3	for	for	ADP
ejpam-2650	299	4	codes	code	NOUN
ejpam-2650	299	5	over	over	ADP
ejpam-2650	299	6	frobenius	frobenius	ADJ
ejpam-2650	299	7	rings	ring	NOUN
ejpam-2650	299	8	under	under	ADP
ejpam-2650	299	9	homogeneous	homogeneous	ADJ
ejpam-2650	299	10	weights	weight	NOUN
ejpam-2650	299	11	,	,	PUNCT
ejpam-2650	299	12	discrete	discrete	ADJ
ejpam-2650	299	13	mathematics	mathematic	NOUN
ejpam-2650	299	14	,	,	PUNCT
ejpam-2650	299	15	289:11	289:11	PROPN
ejpam-2650	299	16	-	-	SYM
ejpam-2650	299	17	24	24	NUM
ejpam-2650	299	18	,	,	PUNCT
ejpam-2650	299	19	2004	2004	NUM
ejpam-2650	299	20	.	.	PUNCT
ejpam-2650	300	1	[	[	X
ejpam-2650	300	2	7	7	X
ejpam-2650	300	3	]	]	X
ejpam-2650	300	4	j	j	PROPN
ejpam-2650	300	5	h	h	PROPN
ejpam-2650	300	6	griesmer	griesmer	NOUN
ejpam-2650	300	7	.	.	PUNCT
ejpam-2650	301	1	a	a	DET
ejpam-2650	301	2	bound	bind	VERB
ejpam-2650	301	3	for	for	ADP
ejpam-2650	301	4	error	error	NOUN
ejpam-2650	301	5	correcting	correct	VERB
ejpam-2650	301	6	codes	code	NOUN
ejpam-2650	301	7	,	,	PUNCT
ejpam-2650	301	8	ibm	ibm	PROPN
ejpam-2650	301	9	journal	journal	NOUN
ejpam-2650	301	10	of	of	ADP
ejpam-2650	301	11	research	research	NOUN
ejpam-2650	301	12	and	and	CCONJ
ejpam-2650	301	13	development	development	NOUN
ejpam-2650	301	14	,	,	PUNCT
ejpam-2650	301	15	4:532–542	4:532–542	NOUN
ejpam-2650	301	16	,	,	PUNCT
ejpam-2650	301	17	1960	1960	NUM
ejpam-2650	301	18	.	.	PUNCT
ejpam-2650	302	1	[	[	X
ejpam-2650	302	2	8	8	NUM
ejpam-2650	302	3	]	]	PUNCT
ejpam-2650	302	4	t	t	PROPN
ejpam-2650	302	5	honold	honold	PROPN
ejpam-2650	302	6	.	.	PUNCT
ejpam-2650	303	1	a	a	DET
ejpam-2650	303	2	characterization	characterization	NOUN
ejpam-2650	303	3	of	of	ADP
ejpam-2650	303	4	finite	finite	ADJ
ejpam-2650	303	5	frobenius	frobenius	PROPN
ejpam-2650	303	6	rings	ring	NOUN
ejpam-2650	303	7	,	,	PUNCT
ejpam-2650	303	8	archiv	archiv	PROPN
ejpam-2650	303	9	der	der	PROPN
ejpam-2650	303	10	mathematik	mathematik	PROPN
ejpam-2650	303	11	,	,	PUNCT
ejpam-2650	303	12	76:406	76:406	PROPN
ejpam-2650	303	13	-	-	NUM
ejpam-2650	303	14	415	415	NUM
ejpam-2650	303	15	,	,	PUNCT
ejpam-2650	303	16	2001	2001	NUM
ejpam-2650	303	17	.	.	PUNCT
ejpam-2650	304	1	[	[	X
ejpam-2650	304	2	9	9	NUM
ejpam-2650	304	3	]	]	SYM
ejpam-2650	304	4	s	s	PART
ejpam-2650	304	5	karadeniz	karadeniz	NOUN
ejpam-2650	304	6	and	and	CCONJ
ejpam-2650	304	7	b	b	PROPN
ejpam-2650	304	8	yildiz	yildiz	NOUN
ejpam-2650	304	9	.	.	PUNCT
ejpam-2650	305	1	(	(	PUNCT
ejpam-2650	305	2	1	1	NUM
ejpam-2650	305	3	+	+	CCONJ
ejpam-2650	305	4	v)-constacylic	v)-constacylic	NOUN
ejpam-2650	305	5	codes	code	NOUN
ejpam-2650	305	6	over	over	ADP
ejpam-2650	305	7	f2	f2	PROPN
ejpam-2650	305	8	+	+	CCONJ
ejpam-2650	305	9	uf2	uf2	NOUN
ejpam-2650	305	10	+	+	CCONJ
ejpam-2650	305	11	vf2	vf2	NOUN
ejpam-2650	305	12	+	+	CCONJ
ejpam-2650	305	13	uvf2	uvf2	PROPN
ejpam-2650	305	14	,	,	PUNCT
ejpam-2650	305	15	journal	journal	NOUN
ejpam-2650	305	16	of	of	ADP
ejpam-2650	305	17	the	the	DET
ejpam-2650	305	18	franklin	franklin	PROPN
ejpam-2650	305	19	institute	institute	PROPN
ejpam-2650	305	20	,	,	PUNCT
ejpam-2650	305	21	348:2625–2632	348:2625–2632	PROPN
ejpam-2650	305	22	,	,	PUNCT
ejpam-2650	305	23	2011	2011	NUM
ejpam-2650	305	24	.	.	PUNCT
ejpam-2650	306	1	[	[	X
ejpam-2650	306	2	10	10	NUM
ejpam-2650	306	3	]	]	X
ejpam-2650	306	4	f	f	PROPN
ejpam-2650	306	5	j	j	PROPN
ejpam-2650	306	6	macwilliams	macwilliams	PROPN
ejpam-2650	306	7	and	and	CCONJ
ejpam-2650	306	8	n	n	PRON
ejpam-2650	306	9	j	j	PROPN
ejpam-2650	306	10	a	a	DET
ejpam-2650	306	11	sloane	sloane	NOUN
ejpam-2650	306	12	.	.	PUNCT
ejpam-2650	307	1	the	the	DET
ejpam-2650	307	2	theory	theory	NOUN
ejpam-2650	307	3	of	of	ADP
ejpam-2650	307	4	error	error	NOUN
ejpam-2650	307	5	-	-	PUNCT
ejpam-2650	307	6	correcting	correct	VERB
ejpam-2650	307	7	codes	code	NOUN
ejpam-2650	307	8	,	,	PUNCT
ejpam-2650	307	9	northholland	northholland	NOUN
ejpam-2650	307	10	publishing	publish	VERB
ejpam-2650	307	11	company	company	NOUN
ejpam-2650	307	12	,	,	PUNCT
ejpam-2650	307	13	1977	1977	NUM
ejpam-2650	307	14	.	.	PUNCT
ejpam-2650	308	1	[	[	X
ejpam-2650	308	2	11	11	NUM
ejpam-2650	308	3	]	]	PUNCT
ejpam-2650	308	4	a	a	DET
ejpam-2650	308	5	pasa	pasa	NOUN
ejpam-2650	308	6	and	and	CCONJ
ejpam-2650	308	7	b	b	PROPN
ejpam-2650	308	8	yildiz	yildiz	NOUN
ejpam-2650	308	9	.	.	PUNCT
ejpam-2650	309	1	constructing	construct	VERB
ejpam-2650	309	2	gray	gray	ADJ
ejpam-2650	309	3	maps	map	NOUN
ejpam-2650	309	4	from	from	ADP
ejpam-2650	309	5	combinatorial	combinatorial	ADJ
ejpam-2650	309	6	geometries	geometry	NOUN
ejpam-2650	309	7	,	,	PUNCT
ejpam-2650	309	8	communications	communication	NOUN
ejpam-2650	309	9	de	de	X
ejpam-2650	309	10	la	la	X
ejpam-2650	309	11	facult	facult	PROPN
ejpam-2650	309	12	des	des	PROPN
ejpam-2650	309	13	sciences	sciences	PROPN
ejpam-2650	309	14	de	de	ADP
ejpam-2650	309	15	l’universit	l’universit	PROPN
ejpam-2650	309	16	d’ankara	d’ankara	PROPN
ejpam-2650	309	17	serie	serie	PROPN
ejpam-2650	309	18	a1	a1	PROPN
ejpam-2650	309	19	,	,	PUNCT
ejpam-2650	309	20	63:147–161	63:147–161	NOUN
ejpam-2650	309	21	,	,	PUNCT
ejpam-2650	309	22	2014	2014	NUM
ejpam-2650	309	23	.	.	PUNCT
ejpam-2650	310	1	[	[	X
ejpam-2650	310	2	12	12	NUM
ejpam-2650	310	3	]	]	X
ejpam-2650	310	4	r	r	NOUN
ejpam-2650	310	5	l	l	NOUN
ejpam-2650	310	6	townsend	townsend	PROPN
ejpam-2650	310	7	and	and	CCONJ
ejpam-2650	310	8	e	e	NOUN
ejpam-2650	310	9	weldon	weldon	PROPN
ejpam-2650	310	10	.	.	PUNCT
ejpam-2650	311	1	self	self	NOUN
ejpam-2650	311	2	-	-	PUNCT
ejpam-2650	311	3	orthogonal	orthogonal	ADJ
ejpam-2650	311	4	quasi	quasi	ADJ
ejpam-2650	311	5	-	-	ADJ
ejpam-2650	311	6	cyclic	cyclic	ADJ
ejpam-2650	311	7	codes	code	NOUN
ejpam-2650	311	8	,	,	PUNCT
ejpam-2650	311	9	ieee	ieee	NOUN
ejpam-2650	311	10	transactions	transaction	NOUN
ejpam-2650	311	11	on	on	ADP
ejpam-2650	311	12	information	information	NOUN
ejpam-2650	311	13	theory	theory	NOUN
ejpam-2650	311	14	,	,	PUNCT
ejpam-2650	311	15	13(2):183–195	13(2):183–195	PROPN
ejpam-2650	311	16	,	,	PUNCT
ejpam-2650	311	17	1967	1967	NUM
ejpam-2650	311	18	.	.	PUNCT
ejpam-2650	312	1	[	[	X
ejpam-2650	312	2	13	13	NUM
ejpam-2650	312	3	]	]	PUNCT
ejpam-2650	312	4	n	n	CCONJ
ejpam-2650	312	5	tufekci	tufekci	NOUN
ejpam-2650	312	6	and	and	CCONJ
ejpam-2650	312	7	b	b	NOUN
ejpam-2650	312	8	yildiz	yildiz	NOUN
ejpam-2650	312	9	.	.	PUNCT
ejpam-2650	313	1	on	on	ADP
ejpam-2650	313	2	codes	code	NOUN
ejpam-2650	313	3	overrk	overrk	NOUN
ejpam-2650	313	4	,	,	PUNCT
ejpam-2650	313	5	m	m	PRON
ejpam-2650	313	6	and	and	CCONJ
ejpam-2650	313	7	constructions	construction	NOUN
ejpam-2650	313	8	for	for	ADP
ejpam-2650	313	9	new	new	ADJ
ejpam-2650	313	10	binary	binary	ADJ
ejpam-2650	313	11	self	self	NOUN
ejpam-2650	313	12	-	-	PUNCT
ejpam-2650	313	13	dual	dual	ADJ
ejpam-2650	313	14	codes	code	NOUN
ejpam-2650	313	15	,	,	PUNCT
ejpam-2650	313	16	mathematica	mathematica	PROPN
ejpam-2650	313	17	slovaca	slovaca	PROPN
ejpam-2650	313	18	,	,	PUNCT
ejpam-2650	313	19	66(6):1511–1526	66(6):1511–1526	NUM
ejpam-2650	313	20	,	,	PUNCT
ejpam-2650	313	21	2016	2016	NUM
ejpam-2650	313	22	.	.	PUNCT
ejpam-2650	314	1	[	[	X
ejpam-2650	314	2	14	14	NUM
ejpam-2650	314	3	]	]	X
ejpam-2650	314	4	h	h	NOUN
ejpam-2650	314	5	n	n	NOUN
ejpam-2650	314	6	ward	ward	NOUN
ejpam-2650	314	7	.	.	PUNCT
ejpam-2650	315	1	divisible	divisible	ADJ
ejpam-2650	315	2	codes	code	NOUN
ejpam-2650	315	3	,	,	PUNCT
ejpam-2650	315	4	archive	archive	ADJ
ejpam-2650	315	5	der	der	NOUN
ejpam-2650	315	6	mathematik	mathematik	PROPN
ejpam-2650	315	7	,	,	PUNCT
ejpam-2650	315	8	36:485	36:485	NUM
ejpam-2650	315	9	-	-	SYM
ejpam-2650	315	10	499	499	NUM
ejpam-2650	315	11	,	,	PUNCT
ejpam-2650	315	12	1981	1981	NUM
ejpam-2650	315	13	.	.	PUNCT
ejpam-2650	316	1	[	[	X
ejpam-2650	316	2	15	15	NUM
ejpam-2650	316	3	]	]	X
ejpam-2650	316	4	b	b	X
ejpam-2650	316	5	yildiz	yildiz	NOUN
ejpam-2650	316	6	and	and	CCONJ
ejpam-2650	316	7	i	i	PRON
ejpam-2650	316	8	g	g	PROPN
ejpam-2650	316	9	kelebek	kelebek	PROPN
ejpam-2650	316	10	.	.	PUNCT
ejpam-2650	317	1	the	the	DET
ejpam-2650	317	2	homogeneous	homogeneous	ADJ
ejpam-2650	317	3	weight	weight	NOUN
ejpam-2650	317	4	for	for	ADP
ejpam-2650	317	5	rk	rk	NOUN
ejpam-2650	317	6	,	,	PUNCT
ejpam-2650	317	7	related	relate	VERB
ejpam-2650	317	8	gray	gray	ADJ
ejpam-2650	317	9	map	map	NOUN
ejpam-2650	317	10	and	and	CCONJ
ejpam-2650	317	11	new	new	ADJ
ejpam-2650	317	12	binary	binary	ADJ
ejpam-2650	317	13	quasicyclic	quasicyclic	PROPN
ejpam-2650	317	14	codes	code	NOUN
ejpam-2650	317	15	,	,	PUNCT
ejpam-2650	317	16	arxiv	arxiv	NOUN
ejpam-2650	317	17	:	:	PUNCT
ejpam-2650	317	18	1504.04111	1504.04111	NUM
ejpam-2650	317	19	,	,	PUNCT
ejpam-2650	317	20	2014	2014	NUM
ejpam-2650	317	21	.	.	PUNCT
ejpam-2650	318	1	[	[	X
ejpam-2650	318	2	16	16	NUM
ejpam-2650	318	3	]	]	SYM
ejpam-2650	318	4	b	b	PROPN
ejpam-2650	318	5	yildiz	yildiz	NOUN
ejpam-2650	318	6	.	.	PUNCT
ejpam-2650	319	1	a	a	DET
ejpam-2650	319	2	combinatorial	combinatorial	ADJ
ejpam-2650	319	3	construction	construction	NOUN
ejpam-2650	319	4	of	of	ADP
ejpam-2650	319	5	the	the	DET
ejpam-2650	319	6	gray	gray	ADJ
ejpam-2650	319	7	map	map	NOUN
ejpam-2650	319	8	over	over	ADP
ejpam-2650	319	9	galois	galois	PROPN
ejpam-2650	319	10	rings	ring	NOUN
ejpam-2650	319	11	,	,	PUNCT
ejpam-2650	319	12	discrete	discrete	ADJ
ejpam-2650	319	13	mathematics	mathematic	NOUN
ejpam-2650	319	14	,	,	PUNCT
ejpam-2650	319	15	309:3408–3412	309:3408–3412	NUM
ejpam-2650	319	16	,	,	PUNCT
ejpam-2650	319	17	2009	2009	NUM
ejpam-2650	319	18	.	.	PUNCT
ejpam-2650	320	1	[	[	X
ejpam-2650	320	2	17	17	NUM
ejpam-2650	320	3	]	]	SYM
ejpam-2650	320	4	b	b	PROPN
ejpam-2650	320	5	yildiz	yildiz	NOUN
ejpam-2650	320	6	.	.	PUNCT
ejpam-2650	321	1	weight	weight	NOUN
ejpam-2650	321	2	enumerators	enumerator	NOUN
ejpam-2650	321	3	and	and	CCONJ
ejpam-2650	321	4	gray	gray	ADJ
ejpam-2650	321	5	maps	map	NOUN
ejpam-2650	321	6	of	of	ADP
ejpam-2650	321	7	linear	linear	PROPN
ejpam-2650	321	8	codes	code	NOUN
ejpam-2650	321	9	over	over	ADP
ejpam-2650	321	10	rings	ring	NOUN
ejpam-2650	321	11	,	,	PUNCT
ejpam-2650	321	12	ph.d	ph.d	PROPN
ejpam-2650	321	13	.	.	PUNCT
ejpam-2650	322	1	thesis	thesis	NOUN
ejpam-2650	322	2	:	:	PUNCT
ejpam-2650	322	3	california	california	PROPN
ejpam-2650	322	4	institute	institute	PROPN
ejpam-2650	322	5	of	of	ADP
ejpam-2650	322	6	technology	technology	PROPN
ejpam-2650	322	7	,	,	PUNCT
ejpam-2650	322	8	2006	2006	NUM
ejpam-2650	322	9	.	.	PUNCT