id	sid	tid	token	lemma	pos
ejpam-4867	1	1	european	european	PROPN
ejpam-4867	1	2	journal	journal	PROPN
ejpam-4867	1	3	of	of	ADP
ejpam-4867	1	4	pure	pure	ADJ
ejpam-4867	1	5	and	and	CCONJ
ejpam-4867	1	6	applied	apply	VERB
ejpam-4867	1	7	mathematics	mathematic	NOUN
ejpam-4867	1	8	vol	vol	NOUN
ejpam-4867	1	9	.	.	PROPN
ejpam-4867	2	1	17	17	NUM
ejpam-4867	2	2	,	,	PUNCT
ejpam-4867	2	3	no	no	INTJ
ejpam-4867	2	4	.	.	NOUN
ejpam-4867	2	5	2	2	NUM
ejpam-4867	2	6	,	,	PUNCT
ejpam-4867	2	7	2024	2024	NUM
ejpam-4867	2	8	,	,	PUNCT
ejpam-4867	2	9	1369	1369	NUM
ejpam-4867	2	10	-	-	SYM
ejpam-4867	2	11	1384	1384	NUM
ejpam-4867	2	12	issn	issn	PROPN
ejpam-4867	2	13	1307	1307	NUM
ejpam-4867	2	14	-	-	SYM
ejpam-4867	2	15	5543	5543	NUM
ejpam-4867	2	16	–	–	PUNCT
ejpam-4867	2	17	ejpam.com	ejpam.com	X
ejpam-4867	2	18	published	publish	VERB
ejpam-4867	2	19	by	by	ADP
ejpam-4867	2	20	new	new	PROPN
ejpam-4867	2	21	york	york	PROPN
ejpam-4867	2	22	business	business	PROPN
ejpam-4867	2	23	global	global	ADJ
ejpam-4867	2	24	vertex	vertex	NOUN
ejpam-4867	2	25	-	-	PUNCT
ejpam-4867	2	26	weighted	weight	VERB
ejpam-4867	2	27	(	(	PUNCT
ejpam-4867	2	28	k1	k1	NOUN
ejpam-4867	2	29	,	,	PUNCT
ejpam-4867	2	30	k2	k2	ADJ
ejpam-4867	2	31	)	)	PUNCT
ejpam-4867	3	1	e	e	NOUN
ejpam-4867	3	2	-	-	NOUN
ejpam-4867	3	3	torsion	torsion	NOUN
ejpam-4867	3	4	graph	graph	NOUN
ejpam-4867	3	5	of	of	ADP
ejpam-4867	3	6	quasi	quasi	NOUN
ejpam-4867	3	7	self	self	NOUN
ejpam-4867	3	8	-	-	PUNCT
ejpam-4867	3	9	dual	dual	ADJ
ejpam-4867	3	10	codes	code	NOUN
ejpam-4867	3	11	jupiter	jupiter	PROPN
ejpam-4867	3	12	g.	g.	PROPN
ejpam-4867	3	13	pilongo1	pilongo1	PROPN
ejpam-4867	3	14	,	,	PUNCT
ejpam-4867	3	15	leonard	leonard	PROPN
ejpam-4867	3	16	m.	m.	PROPN
ejpam-4867	3	17	paleta1,∗	paleta1,∗	PROPN
ejpam-4867	3	18	,	,	PUNCT
ejpam-4867	4	1	philip	philip	PROPN
ejpam-4867	4	2	lester	lester	PROPN
ejpam-4867	4	3	p.	p.	PROPN
ejpam-4867	4	4	benjamin1	benjamin1	NOUN
ejpam-4867	4	5	1	1	NUM
ejpam-4867	4	6	department	department	NOUN
ejpam-4867	4	7	of	of	ADP
ejpam-4867	4	8	mathematics	mathematic	NOUN
ejpam-4867	4	9	and	and	CCONJ
ejpam-4867	4	10	statistics	statistic	NOUN
ejpam-4867	4	11	,	,	PUNCT
ejpam-4867	4	12	college	college	NOUN
ejpam-4867	4	13	of	of	ADP
ejpam-4867	4	14	science	science	NOUN
ejpam-4867	4	15	and	and	CCONJ
ejpam-4867	4	16	mathematics	mathematic	NOUN
ejpam-4867	4	17	,	,	PUNCT
ejpam-4867	4	18	university	university	NOUN
ejpam-4867	4	19	of	of	ADP
ejpam-4867	4	20	southern	southern	ADJ
ejpam-4867	4	21	mindanao	mindanao	PROPN
ejpam-4867	4	22	,	,	PUNCT
ejpam-4867	4	23	9407	9407	NUM
ejpam-4867	4	24	kabacan	kabacan	NOUN
ejpam-4867	4	25	,	,	PUNCT
ejpam-4867	4	26	north	north	NOUN
ejpam-4867	4	27	cotabato	cotabato	PROPN
ejpam-4867	4	28	,	,	PUNCT
ejpam-4867	4	29	philippines	philippine	NOUN
ejpam-4867	4	30	abstract	abstract	ADJ
ejpam-4867	4	31	.	.	PUNCT
ejpam-4867	5	1	in	in	ADP
ejpam-4867	5	2	this	this	DET
ejpam-4867	5	3	paper	paper	NOUN
ejpam-4867	5	4	,	,	PUNCT
ejpam-4867	5	5	we	we	PRON
ejpam-4867	5	6	have	have	AUX
ejpam-4867	5	7	introduced	introduce	VERB
ejpam-4867	5	8	a	a	DET
ejpam-4867	5	9	graph	graph	NOUN
ejpam-4867	5	10	gec	gec	NOUN
ejpam-4867	5	11	generated	generate	VERB
ejpam-4867	5	12	by	by	ADP
ejpam-4867	5	13	type-(k1	type-(k1	ADJ
ejpam-4867	5	14	,	,	PUNCT
ejpam-4867	5	15	k2	k2	ADJ
ejpam-4867	5	16	)	)	PUNCT
ejpam-4867	5	17	e	e	X
ejpam-4867	5	18	-	-	NOUN
ejpam-4867	5	19	codes	code	NOUN
ejpam-4867	5	20	which	which	PRON
ejpam-4867	5	21	is	be	AUX
ejpam-4867	5	22	(	(	PUNCT
ejpam-4867	5	23	k1	k1	X
ejpam-4867	5	24	,	,	PUNCT
ejpam-4867	5	25	k2	k2	ADJ
ejpam-4867	5	26	)	)	PUNCT
ejpam-4867	5	27	e	e	NOUN
ejpam-4867	5	28	-	-	NOUN
ejpam-4867	5	29	torsion	torsion	NOUN
ejpam-4867	5	30	graph	graph	NOUN
ejpam-4867	5	31	.	.	PUNCT
ejpam-4867	6	1	the	the	DET
ejpam-4867	6	2	binary	binary	PROPN
ejpam-4867	6	3	codewords	codeword	NOUN
ejpam-4867	6	4	of	of	ADP
ejpam-4867	6	5	the	the	DET
ejpam-4867	6	6	torsion	torsion	NOUN
ejpam-4867	6	7	code	code	NOUN
ejpam-4867	6	8	of	of	ADP
ejpam-4867	6	9	c	c	PROPN
ejpam-4867	6	10	are	be	AUX
ejpam-4867	6	11	the	the	DET
ejpam-4867	6	12	set	set	NOUN
ejpam-4867	6	13	of	of	ADP
ejpam-4867	6	14	vertices	vertex	NOUN
ejpam-4867	6	15	,	,	PUNCT
ejpam-4867	6	16	and	and	CCONJ
ejpam-4867	6	17	the	the	DET
ejpam-4867	6	18	edges	edge	NOUN
ejpam-4867	6	19	are	be	AUX
ejpam-4867	6	20	defined	define	VERB
ejpam-4867	6	21	using	use	VERB
ejpam-4867	6	22	the	the	DET
ejpam-4867	6	23	construction	construction	NOUN
ejpam-4867	6	24	of	of	ADP
ejpam-4867	6	25	e	e	NOUN
ejpam-4867	6	26	-	-	NOUN
ejpam-4867	6	27	codes	code	NOUN
ejpam-4867	6	28	.	.	PUNCT
ejpam-4867	7	1	moreover	moreover	ADV
ejpam-4867	7	2	,	,	PUNCT
ejpam-4867	7	3	we	we	PRON
ejpam-4867	7	4	characterized	characterize	VERB
ejpam-4867	7	5	the	the	DET
ejpam-4867	7	6	graph	graph	NOUN
ejpam-4867	7	7	obtained	obtain	VERB
ejpam-4867	7	8	when	when	SCONJ
ejpam-4867	7	9	k1	k1	PROPN
ejpam-4867	7	10	=	=	SYM
ejpam-4867	7	11	0	0	NUM
ejpam-4867	7	12	and	and	CCONJ
ejpam-4867	7	13	k2	k2	PROPN
ejpam-4867	7	14	=	=	SYM
ejpam-4867	7	15	0	0	PUNCT
ejpam-4867	7	16	and	and	CCONJ
ejpam-4867	7	17	calculated	calculate	VERB
ejpam-4867	7	18	the	the	DET
ejpam-4867	7	19	degrees	degree	NOUN
ejpam-4867	7	20	of	of	ADP
ejpam-4867	7	21	every	every	DET
ejpam-4867	7	22	vertex	vertex	NOUN
ejpam-4867	7	23	and	and	CCONJ
ejpam-4867	7	24	the	the	DET
ejpam-4867	7	25	number	number	NOUN
ejpam-4867	7	26	of	of	ADP
ejpam-4867	7	27	edges	edge	NOUN
ejpam-4867	7	28	of	of	ADP
ejpam-4867	7	29	gec	gec	NOUN
ejpam-4867	7	30	.	.	PUNCT
ejpam-4867	8	1	moreover	moreover	ADV
ejpam-4867	8	2	,	,	PUNCT
ejpam-4867	8	3	we	we	PRON
ejpam-4867	8	4	presented	present	VERB
ejpam-4867	8	5	necessary	necessary	ADJ
ejpam-4867	8	6	and	and	CCONJ
ejpam-4867	8	7	sufficient	sufficient	ADJ
ejpam-4867	8	8	conditions	condition	NOUN
ejpam-4867	8	9	for	for	ADP
ejpam-4867	8	10	a	a	DET
ejpam-4867	8	11	vertex	vertex	NOUN
ejpam-4867	8	12	to	to	PART
ejpam-4867	8	13	be	be	AUX
ejpam-4867	8	14	in	in	ADP
ejpam-4867	8	15	the	the	DET
ejpam-4867	8	16	center	center	NOUN
ejpam-4867	8	17	of	of	ADP
ejpam-4867	8	18	a	a	DET
ejpam-4867	8	19	graph	graph	NOUN
ejpam-4867	8	20	given	give	VERB
ejpam-4867	8	21	the	the	DET
ejpam-4867	8	22	property	property	NOUN
ejpam-4867	8	23	of	of	ADP
ejpam-4867	8	24	the	the	DET
ejpam-4867	8	25	codeword	codeword	NOUN
ejpam-4867	8	26	corresponding	correspond	VERB
ejpam-4867	8	27	to	to	ADP
ejpam-4867	8	28	the	the	DET
ejpam-4867	8	29	vertex	vertex	NOUN
ejpam-4867	8	30	.	.	PUNCT
ejpam-4867	9	1	finally	finally	ADV
ejpam-4867	9	2	,	,	PUNCT
ejpam-4867	9	3	we	we	PRON
ejpam-4867	9	4	represent	represent	VERB
ejpam-4867	9	5	every	every	DET
ejpam-4867	9	6	quasi	quasi	NOUN
ejpam-4867	9	7	self	self	NOUN
ejpam-4867	9	8	-	-	PUNCT
ejpam-4867	9	9	dual	dual	ADJ
ejpam-4867	9	10	codes	code	NOUN
ejpam-4867	9	11	of	of	ADP
ejpam-4867	9	12	short	short	ADJ
ejpam-4867	9	13	length	length	NOUN
ejpam-4867	9	14	by	by	ADP
ejpam-4867	9	15	defining	define	VERB
ejpam-4867	9	16	the	the	DET
ejpam-4867	9	17	vertex	vertex	NOUN
ejpam-4867	9	18	-	-	PUNCT
ejpam-4867	9	19	weighted	weight	VERB
ejpam-4867	9	20	(	(	PUNCT
ejpam-4867	9	21	k1	k1	NOUN
ejpam-4867	9	22	,	,	PUNCT
ejpam-4867	9	23	k2	k2	ADJ
ejpam-4867	9	24	)	)	PUNCT
ejpam-4867	9	25	e	e	NOUN
ejpam-4867	9	26	-	-	NOUN
ejpam-4867	9	27	torsion	torsion	NOUN
ejpam-4867	9	28	graph	graph	NOUN
ejpam-4867	9	29	,	,	PUNCT
ejpam-4867	9	30	where	where	SCONJ
ejpam-4867	9	31	the	the	DET
ejpam-4867	9	32	weight	weight	NOUN
ejpam-4867	9	33	of	of	ADP
ejpam-4867	9	34	every	every	DET
ejpam-4867	9	35	vertex	vertex	NOUN
ejpam-4867	9	36	is	be	AUX
ejpam-4867	9	37	the	the	DET
ejpam-4867	9	38	weight	weight	NOUN
ejpam-4867	9	39	of	of	ADP
ejpam-4867	9	40	the	the	DET
ejpam-4867	9	41	codeword	codeword	NOUN
ejpam-4867	9	42	corresponding	correspond	VERB
ejpam-4867	9	43	to	to	ADP
ejpam-4867	9	44	the	the	DET
ejpam-4867	9	45	vertex	vertex	NOUN
ejpam-4867	9	46	.	.	PUNCT
ejpam-4867	10	1	2020	2020	NUM
ejpam-4867	10	2	mathematics	mathematic	NOUN
ejpam-4867	10	3	subject	subject	NOUN
ejpam-4867	10	4	classifications	classification	NOUN
ejpam-4867	10	5	:	:	PUNCT
ejpam-4867	10	6	05c25	05c25	NUM
ejpam-4867	10	7	,	,	PUNCT
ejpam-4867	10	8	05c60	05c60	NOUN
ejpam-4867	10	9	,	,	PUNCT
ejpam-4867	10	10	05c62	05c62	NUM
ejpam-4867	10	11	,	,	PUNCT
ejpam-4867	10	12	05c90	05c90	NUM
ejpam-4867	10	13	,	,	PUNCT
ejpam-4867	10	14	11h71	11h71	NUM
ejpam-4867	10	15	,	,	PUNCT
ejpam-4867	10	16	14g50	14g50	NUM
ejpam-4867	10	17	key	key	ADJ
ejpam-4867	10	18	words	word	NOUN
ejpam-4867	10	19	and	and	CCONJ
ejpam-4867	10	20	phrases	phrase	NOUN
ejpam-4867	10	21	:	:	PUNCT
ejpam-4867	10	22	quasi	quasi	ADJ
ejpam-4867	10	23	-	-	ADJ
ejpam-4867	10	24	self	self	ADJ
ejpam-4867	10	25	dual	dual	ADJ
ejpam-4867	10	26	codes	code	NOUN
ejpam-4867	10	27	,	,	PUNCT
ejpam-4867	10	28	rings	ring	NOUN
ejpam-4867	10	29	,	,	PUNCT
ejpam-4867	10	30	torsion	torsion	NOUN
ejpam-4867	10	31	codes	code	NOUN
ejpam-4867	10	32	,	,	PUNCT
ejpam-4867	10	33	e	e	NOUN
ejpam-4867	10	34	-	-	NOUN
ejpam-4867	10	35	codes	code	NOUN
ejpam-4867	10	36	,	,	PUNCT
ejpam-4867	10	37	e	e	NOUN
ejpam-4867	10	38	-	-	NOUN
ejpam-4867	10	39	torsion	torsion	NOUN
ejpam-4867	10	40	graphs	graph	NOUN
ejpam-4867	10	41	,	,	PUNCT
ejpam-4867	10	42	graph	graph	NOUN
ejpam-4867	10	43	representation	representation	NOUN
ejpam-4867	10	44	,	,	PUNCT
ejpam-4867	10	45	quasi	quasi	ADJ
ejpam-4867	10	46	-	-	ADJ
ejpam-4867	10	47	self	self	ADJ
ejpam-4867	10	48	dual	dual	ADJ
ejpam-4867	10	49	codes	code	NOUN
ejpam-4867	10	50	1	1	NUM
ejpam-4867	10	51	.	.	PUNCT
ejpam-4867	11	1	introduction	introduction	NOUN
ejpam-4867	11	2	linear	linear	PROPN
ejpam-4867	11	3	codes	code	NOUN
ejpam-4867	11	4	,	,	PUNCT
ejpam-4867	11	5	well	well	ADV
ejpam-4867	11	6	-	-	PUNCT
ejpam-4867	11	7	studied	study	VERB
ejpam-4867	11	8	objects	object	NOUN
ejpam-4867	11	9	in	in	ADP
ejpam-4867	11	10	coding	code	VERB
ejpam-4867	11	11	theory	theory	NOUN
ejpam-4867	11	12	,	,	PUNCT
ejpam-4867	11	13	have	have	AUX
ejpam-4867	11	14	traditionally	traditionally	ADV
ejpam-4867	11	15	been	be	AUX
ejpam-4867	11	16	explored	explore	VERB
ejpam-4867	11	17	over	over	ADP
ejpam-4867	11	18	fields	field	NOUN
ejpam-4867	11	19	or	or	CCONJ
ejpam-4867	11	20	rings	ring	NOUN
ejpam-4867	11	21	with	with	ADP
ejpam-4867	11	22	unity	unity	NOUN
ejpam-4867	11	23	.	.	PUNCT
ejpam-4867	12	1	however	however	ADV
ejpam-4867	12	2	,	,	PUNCT
ejpam-4867	12	3	recent	recent	ADJ
ejpam-4867	12	4	researches	research	NOUN
ejpam-4867	13	1	[	[	X
ejpam-4867	13	2	2–4	2–4	NUM
ejpam-4867	13	3	,	,	PUNCT
ejpam-4867	13	4	14	14	NUM
ejpam-4867	13	5	]	]	PUNCT
ejpam-4867	13	6	have	have	AUX
ejpam-4867	13	7	unveiled	unveil	VERB
ejpam-4867	13	8	a	a	DET
ejpam-4867	13	9	fascinating	fascinating	ADJ
ejpam-4867	13	10	avenue	avenue	NOUN
ejpam-4867	13	11	of	of	ADP
ejpam-4867	13	12	investigation	investigation	NOUN
ejpam-4867	13	13	by	by	ADP
ejpam-4867	13	14	extending	extend	VERB
ejpam-4867	13	15	the	the	DET
ejpam-4867	13	16	study	study	NOUN
ejpam-4867	13	17	of	of	ADP
ejpam-4867	13	18	linear	linear	PROPN
ejpam-4867	13	19	codes	code	NOUN
ejpam-4867	13	20	to	to	ADP
ejpam-4867	13	21	non	non	ADJ
ejpam-4867	13	22	-	-	ADJ
ejpam-4867	13	23	unital	unital	ADJ
ejpam-4867	13	24	rings	ring	NOUN
ejpam-4867	13	25	.	.	PUNCT
ejpam-4867	14	1	for	for	ADP
ejpam-4867	14	2	instance	instance	NOUN
ejpam-4867	14	3	,	,	PUNCT
ejpam-4867	14	4	alahmadi	alahmadi	PROPN
ejpam-4867	14	5	,	,	PUNCT
ejpam-4867	14	6	et	et	NOUN
ejpam-4867	14	7	al	al	PROPN
ejpam-4867	15	1	[	[	X
ejpam-4867	15	2	1	1	NUM
ejpam-4867	15	3	]	]	PUNCT
ejpam-4867	15	4	,	,	PUNCT
ejpam-4867	15	5	introduced	introduce	VERB
ejpam-4867	15	6	the	the	DET
ejpam-4867	15	7	notion	notion	NOUN
ejpam-4867	15	8	of	of	ADP
ejpam-4867	15	9	quasi	quasi	ADJ
ejpam-4867	15	10	self	self	NOUN
ejpam-4867	15	11	-	-	PUNCT
ejpam-4867	15	12	dual	dual	ADJ
ejpam-4867	15	13	codes	code	NOUN
ejpam-4867	15	14	(	(	PUNCT
ejpam-4867	15	15	qsd	qsd	NOUN
ejpam-4867	15	16	codes	code	NOUN
ejpam-4867	15	17	)	)	PUNCT
ejpam-4867	15	18	,	,	PUNCT
ejpam-4867	15	19	self	self	NOUN
ejpam-4867	15	20	-	-	PUNCT
ejpam-4867	15	21	orthogonal	orthogonal	ADJ
ejpam-4867	15	22	linear	linear	NOUN
ejpam-4867	15	23	codes	code	NOUN
ejpam-4867	15	24	of	of	ADP
ejpam-4867	15	25	length	length	NOUN
ejpam-4867	15	26	n	n	NOUN
ejpam-4867	15	27	over	over	ADP
ejpam-4867	15	28	a	a	DET
ejpam-4867	15	29	non	non	ADJ
ejpam-4867	15	30	-	-	ADJ
ejpam-4867	15	31	unital	unital	ADJ
ejpam-4867	15	32	ring	ring	NOUN
ejpam-4867	15	33	e	e	NOUN
ejpam-4867	15	34	such	such	ADJ
ejpam-4867	15	35	that	that	SCONJ
ejpam-4867	15	36	the	the	DET
ejpam-4867	15	37	size	size	NOUN
ejpam-4867	15	38	of	of	ADP
ejpam-4867	15	39	the	the	DET
ejpam-4867	15	40	code	code	NOUN
ejpam-4867	15	41	is	be	AUX
ejpam-4867	15	42	2n	2n	NUM
ejpam-4867	15	43	.	.	PUNCT
ejpam-4867	16	1	moreover	moreover	ADV
ejpam-4867	16	2	,	,	PUNCT
ejpam-4867	16	3	there	there	PRON
ejpam-4867	16	4	are	be	VERB
ejpam-4867	16	5	some	some	DET
ejpam-4867	16	6	interesting	interesting	ADJ
ejpam-4867	16	7	researches	research	NOUN
ejpam-4867	16	8	in	in	ADP
ejpam-4867	16	9	binary	binary	ADJ
ejpam-4867	16	10	codes	code	NOUN
ejpam-4867	16	11	in	in	ADP
ejpam-4867	16	12	the	the	DET
ejpam-4867	16	13	literature	literature	NOUN
ejpam-4867	16	14	,	,	PUNCT
ejpam-4867	16	15	for	for	ADP
ejpam-4867	16	16	instance	instance	NOUN
ejpam-4867	16	17	,	,	PUNCT
ejpam-4867	16	18	[	[	X
ejpam-4867	16	19	15	15	NUM
ejpam-4867	16	20	]	]	PUNCT
ejpam-4867	16	21	explored	explore	VERB
ejpam-4867	16	22	the	the	DET
ejpam-4867	16	23	z2	z2	NUM
ejpam-4867	16	24	-	-	PUNCT
ejpam-4867	16	25	triple	triple	ADJ
ejpam-4867	16	26	cycle	cycle	NOUN
ejpam-4867	16	27	codes	code	NOUN
ejpam-4867	16	28	and	and	CCONJ
ejpam-4867	16	29	their	their	PRON
ejpam-4867	16	30	duals	dual	NOUN
ejpam-4867	16	31	,	,	PUNCT
ejpam-4867	16	32	[	[	X
ejpam-4867	16	33	11	11	NUM
ejpam-4867	16	34	]	]	X
ejpam-4867	16	35	cyclic	cyclic	ADJ
ejpam-4867	16	36	codes	code	NOUN
ejpam-4867	16	37	from	from	ADP
ejpam-4867	16	38	a	a	DET
ejpam-4867	16	39	sequence	sequence	NOUN
ejpam-4867	16	40	over	over	ADP
ejpam-4867	16	41	finite	finite	ADJ
ejpam-4867	16	42	fields	field	NOUN
ejpam-4867	16	43	,	,	PUNCT
ejpam-4867	16	44	and	and	CCONJ
ejpam-4867	16	45	[	[	X
ejpam-4867	16	46	6	6	NUM
ejpam-4867	16	47	]	]	PUNCT
ejpam-4867	16	48	studied	study	VERB
ejpam-4867	16	49	self	self	NOUN
ejpam-4867	16	50	-	-	PUNCT
ejpam-4867	16	51	dual	dual	ADJ
ejpam-4867	16	52	codes	code	NOUN
ejpam-4867	16	53	over	over	ADP
ejpam-4867	16	54	rk	rk	NOUN
ejpam-4867	16	55	and	and	CCONJ
ejpam-4867	16	56	binary	binary	NOUN
ejpam-4867	16	57	self	self	NOUN
ejpam-4867	16	58	-	-	PUNCT
ejpam-4867	16	59	dual	dual	ADJ
ejpam-4867	16	60	codes	code	NOUN
ejpam-4867	16	61	.	.	PUNCT
ejpam-4867	17	1	in	in	ADP
ejpam-4867	17	2	continuation	continuation	NOUN
ejpam-4867	17	3	to	to	ADP
ejpam-4867	17	4	the	the	DET
ejpam-4867	17	5	codes	code	NOUN
ejpam-4867	17	6	over	over	ADP
ejpam-4867	17	7	e	e	PROPN
ejpam-4867	17	8	,	,	PUNCT
ejpam-4867	17	9	shi	shi	PROPN
ejpam-4867	17	10	,	,	PUNCT
ejpam-4867	17	11	minjia	minjia	PROPN
ejpam-4867	17	12	,	,	PUNCT
ejpam-4867	17	13	et	et	PROPN
ejpam-4867	17	14	al	al	PROPN
ejpam-4867	17	15	.	.	PUNCT
ejpam-4867	18	1	[	[	X
ejpam-4867	18	2	14	14	NUM
ejpam-4867	18	3	]	]	PUNCT
ejpam-4867	18	4	presented	present	VERB
ejpam-4867	18	5	a	a	DET
ejpam-4867	18	6	special	special	ADJ
ejpam-4867	18	7	construction	construction	NOUN
ejpam-4867	18	8	of	of	ADP
ejpam-4867	18	9	qsd	qsd	NOUN
ejpam-4867	18	10	codes	code	NOUN
ejpam-4867	18	11	over	over	ADP
ejpam-4867	18	12	e	e	NOUN
ejpam-4867	18	13	,	,	PUNCT
ejpam-4867	18	14	based	base	VERB
ejpam-4867	18	15	on	on	ADP
ejpam-4867	18	16	combinatorial	combinatorial	ADJ
ejpam-4867	18	17	matrices	matrix	NOUN
ejpam-4867	18	18	∗corresponding	∗corresponde	VERB
ejpam-4867	18	19	author	author	NOUN
ejpam-4867	18	20	.	.	PUNCT
ejpam-4867	19	1	doi	doi	NOUN
ejpam-4867	19	2	:	:	PUNCT
ejpam-4867	19	3	https://doi.org/10.29020/nybg.ejpam.v17i2.4867	https://doi.org/10.29020/nybg.ejpam.v17i2.4867	PROPN
ejpam-4867	19	4	email	email	NOUN
ejpam-4867	19	5	addresses	address	NOUN
ejpam-4867	19	6	:	:	PUNCT
ejpam-4867	19	7	jgpilongo@usm.edu.ph	jgpilongo@usm.edu.ph	PROPN
ejpam-4867	19	8	(	(	PUNCT
ejpam-4867	19	9	j.	j.	PROPN
ejpam-4867	19	10	pilongo	pilongo	PROPN
ejpam-4867	19	11	)	)	PUNCT
ejpam-4867	19	12	,	,	PUNCT
ejpam-4867	19	13	lmpaleta@usm.edu.ph	lmpaleta@usm.edu.ph	PROPN
ejpam-4867	19	14	(	(	PUNCT
ejpam-4867	19	15	l.	l.	PROPN
ejpam-4867	19	16	paleta	paleta	PROPN
ejpam-4867	19	17	)	)	PUNCT
ejpam-4867	19	18	,	,	PUNCT
ejpam-4867	19	19	plbenj@usm.edu.ph	plbenj@usm.edu.ph	PROPN
ejpam-4867	19	20	(	(	PUNCT
ejpam-4867	19	21	p.	p.	NOUN
ejpam-4867	19	22	benjamin	benjamin	PROPN
ejpam-4867	19	23	)	)	PUNCT
ejpam-4867	19	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4867	19	25	1369	1369	NUM
ejpam-4867	19	26	©	©	ADP
ejpam-4867	19	27	2024	2024	NUM
ejpam-4867	19	28	ejpam	ejpam	NOUN
ejpam-4867	19	29	all	all	DET
ejpam-4867	19	30	rights	right	NOUN
ejpam-4867	19	31	reserved	reserve	VERB
ejpam-4867	19	32	.	.	PUNCT
ejpam-4867	20	1	j.	j.	PROPN
ejpam-4867	20	2	pilongo	pilongo	PROPN
ejpam-4867	20	3	,	,	PUNCT
ejpam-4867	20	4	l.	l.	PROPN
ejpam-4867	20	5	paleta	paleta	PROPN
ejpam-4867	20	6	,	,	PUNCT
ejpam-4867	20	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	20	8	/	/	SYM
ejpam-4867	20	9	eur	eur	PROPN
ejpam-4867	20	10	.	.	PUNCT
ejpam-4867	21	1	j.	j.	PROPN
ejpam-4867	21	2	pure	pure	PROPN
ejpam-4867	21	3	appl	appl	PROPN
ejpam-4867	21	4	.	.	PROPN
ejpam-4867	21	5	math	math	PROPN
ejpam-4867	21	6	,	,	PUNCT
ejpam-4867	21	7	17	17	NUM
ejpam-4867	21	8	(	(	PUNCT
ejpam-4867	21	9	2	2	NUM
ejpam-4867	21	10	)	)	PUNCT
ejpam-4867	21	11	(	(	PUNCT
ejpam-4867	21	12	2024	2024	NUM
ejpam-4867	21	13	)	)	PUNCT
ejpam-4867	21	14	,	,	PUNCT
ejpam-4867	21	15	1369	1369	NUM
ejpam-4867	21	16	-	-	SYM
ejpam-4867	21	17	1384	1384	NUM
ejpam-4867	21	18	1370	1370	NUM
ejpam-4867	21	19	related	relate	VERB
ejpam-4867	21	20	to	to	ADP
ejpam-4867	21	21	two	two	NUM
ejpam-4867	21	22	-	-	PUNCT
ejpam-4867	21	23	class	class	NOUN
ejpam-4867	21	24	association	association	NOUN
ejpam-4867	21	25	schemes	scheme	NOUN
ejpam-4867	21	26	,	,	PUNCT
ejpam-4867	21	27	strongly	strongly	ADV
ejpam-4867	21	28	regular	regular	ADJ
ejpam-4867	21	29	graphs	graph	NOUN
ejpam-4867	21	30	(	(	PUNCT
ejpam-4867	21	31	srg	srg	NOUN
ejpam-4867	21	32	)	)	PUNCT
ejpam-4867	21	33	,	,	PUNCT
ejpam-4867	21	34	and	and	CCONJ
ejpam-4867	21	35	doubly	doubly	ADV
ejpam-4867	21	36	regular	regular	ADJ
ejpam-4867	21	37	tournaments	tournament	NOUN
ejpam-4867	21	38	(	(	PUNCT
ejpam-4867	21	39	drt	drt	NOUN
ejpam-4867	21	40	)	)	PUNCT
ejpam-4867	21	41	.	.	PUNCT
ejpam-4867	22	1	in	in	ADP
ejpam-4867	22	2	this	this	DET
ejpam-4867	22	3	article	article	NOUN
ejpam-4867	22	4	,	,	PUNCT
ejpam-4867	22	5	we	we	PRON
ejpam-4867	22	6	delved	delve	VERB
ejpam-4867	22	7	into	into	ADP
ejpam-4867	22	8	the	the	DET
ejpam-4867	22	9	analysis	analysis	NOUN
ejpam-4867	22	10	of	of	ADP
ejpam-4867	22	11	graphs	graph	NOUN
ejpam-4867	22	12	generated	generate	VERB
ejpam-4867	22	13	from	from	ADP
ejpam-4867	22	14	linear	linear	PROPN
ejpam-4867	22	15	codes	code	NOUN
ejpam-4867	22	16	over	over	ADP
ejpam-4867	22	17	e	e	NOUN
ejpam-4867	22	18	,	,	PUNCT
ejpam-4867	22	19	called	call	VERB
ejpam-4867	22	20	linear	linear	PROPN
ejpam-4867	22	21	e	e	NOUN
ejpam-4867	22	22	-	-	NOUN
ejpam-4867	22	23	codes	code	NOUN
ejpam-4867	22	24	and	and	CCONJ
ejpam-4867	22	25	examine	examine	VERB
ejpam-4867	22	26	their	their	PRON
ejpam-4867	22	27	properties	property	NOUN
ejpam-4867	22	28	and	and	CCONJ
ejpam-4867	22	29	use	use	VERB
ejpam-4867	22	30	these	these	DET
ejpam-4867	22	31	concepts	concept	NOUN
ejpam-4867	22	32	to	to	PART
ejpam-4867	22	33	formulate	formulate	VERB
ejpam-4867	22	34	a	a	DET
ejpam-4867	22	35	definition	definition	NOUN
ejpam-4867	22	36	of	of	ADP
ejpam-4867	22	37	graph	graph	NOUN
ejpam-4867	22	38	.	.	PUNCT
ejpam-4867	23	1	graph	graph	NOUN
ejpam-4867	23	2	theory	theory	NOUN
ejpam-4867	23	3	provides	provide	VERB
ejpam-4867	23	4	a	a	DET
ejpam-4867	23	5	powerful	powerful	ADJ
ejpam-4867	23	6	framework	framework	NOUN
ejpam-4867	23	7	for	for	ADP
ejpam-4867	23	8	visualizing	visualize	VERB
ejpam-4867	23	9	and	and	CCONJ
ejpam-4867	23	10	understanding	understand	VERB
ejpam-4867	23	11	complex	complex	ADJ
ejpam-4867	23	12	systems	system	NOUN
ejpam-4867	23	13	,	,	PUNCT
ejpam-4867	23	14	making	make	VERB
ejpam-4867	23	15	it	it	PRON
ejpam-4867	23	16	an	an	DET
ejpam-4867	23	17	ideal	ideal	ADJ
ejpam-4867	23	18	tool	tool	NOUN
ejpam-4867	23	19	for	for	ADP
ejpam-4867	23	20	investigating	investigate	VERB
ejpam-4867	23	21	linear	linear	ADJ
ejpam-4867	23	22	codes	code	NOUN
ejpam-4867	23	23	over	over	ADP
ejpam-4867	23	24	non	non	ADJ
ejpam-4867	23	25	-	-	ADJ
ejpam-4867	23	26	unital	unital	ADJ
ejpam-4867	23	27	rings	ring	NOUN
ejpam-4867	23	28	.	.	PUNCT
ejpam-4867	24	1	by	by	ADP
ejpam-4867	24	2	associating	associate	VERB
ejpam-4867	24	3	codes	code	NOUN
ejpam-4867	24	4	with	with	ADP
ejpam-4867	24	5	corresponding	correspond	VERB
ejpam-4867	24	6	graphs	graph	NOUN
ejpam-4867	24	7	,	,	PUNCT
ejpam-4867	24	8	we	we	PRON
ejpam-4867	24	9	can	can	AUX
ejpam-4867	24	10	gain	gain	VERB
ejpam-4867	24	11	insights	insight	NOUN
ejpam-4867	24	12	into	into	ADP
ejpam-4867	24	13	the	the	DET
ejpam-4867	24	14	structure	structure	NOUN
ejpam-4867	24	15	and	and	CCONJ
ejpam-4867	24	16	behavior	behavior	NOUN
ejpam-4867	24	17	of	of	ADP
ejpam-4867	24	18	these	these	DET
ejpam-4867	24	19	codes	code	NOUN
ejpam-4867	24	20	,	,	PUNCT
ejpam-4867	24	21	enabling	enable	VERB
ejpam-4867	24	22	us	we	PRON
ejpam-4867	24	23	to	to	PART
ejpam-4867	24	24	extract	extract	VERB
ejpam-4867	24	25	valuable	valuable	ADJ
ejpam-4867	24	26	information	information	NOUN
ejpam-4867	24	27	related	relate	VERB
ejpam-4867	24	28	to	to	ADP
ejpam-4867	24	29	error	error	NOUN
ejpam-4867	24	30	correction	correction	NOUN
ejpam-4867	24	31	,	,	PUNCT
ejpam-4867	24	32	network	network	NOUN
ejpam-4867	24	33	coding	coding	NOUN
ejpam-4867	24	34	,	,	PUNCT
ejpam-4867	24	35	and	and	CCONJ
ejpam-4867	24	36	other	other	ADJ
ejpam-4867	24	37	areas	area	NOUN
ejpam-4867	24	38	of	of	ADP
ejpam-4867	24	39	interest	interest	NOUN
ejpam-4867	24	40	.	.	PUNCT
ejpam-4867	25	1	for	for	ADP
ejpam-4867	25	2	standard	standard	ADJ
ejpam-4867	25	3	notations	notation	NOUN
ejpam-4867	25	4	and	and	CCONJ
ejpam-4867	25	5	concepts	concept	NOUN
ejpam-4867	25	6	in	in	ADP
ejpam-4867	25	7	graph	graph	NOUN
ejpam-4867	25	8	theory	theory	NOUN
ejpam-4867	25	9	,	,	PUNCT
ejpam-4867	25	10	the	the	DET
ejpam-4867	25	11	readers	reader	NOUN
ejpam-4867	25	12	are	be	AUX
ejpam-4867	25	13	advised	advise	VERB
ejpam-4867	25	14	to	to	PART
ejpam-4867	25	15	refer	refer	VERB
ejpam-4867	25	16	to	to	ADP
ejpam-4867	25	17	[	[	X
ejpam-4867	25	18	9	9	NUM
ejpam-4867	25	19	]	]	PUNCT
ejpam-4867	25	20	.	.	PUNCT
ejpam-4867	26	1	in	in	ADP
ejpam-4867	26	2	this	this	DET
ejpam-4867	26	3	study	study	NOUN
ejpam-4867	26	4	,	,	PUNCT
ejpam-4867	26	5	we	we	PRON
ejpam-4867	26	6	will	will	AUX
ejpam-4867	26	7	first	first	ADV
ejpam-4867	26	8	establish	establish	VERB
ejpam-4867	26	9	the	the	DET
ejpam-4867	26	10	foundations	foundation	NOUN
ejpam-4867	26	11	of	of	ADP
ejpam-4867	26	12	linear	linear	PROPN
ejpam-4867	26	13	codes	code	NOUN
ejpam-4867	26	14	over	over	ADP
ejpam-4867	26	15	e	e	NOUN
ejpam-4867	26	16	,	,	PUNCT
ejpam-4867	26	17	elucidating	elucidate	VERB
ejpam-4867	26	18	the	the	DET
ejpam-4867	26	19	necessary	necessary	ADJ
ejpam-4867	26	20	definitions	definition	NOUN
ejpam-4867	26	21	,	,	PUNCT
ejpam-4867	26	22	properties	property	NOUN
ejpam-4867	26	23	,	,	PUNCT
ejpam-4867	26	24	and	and	CCONJ
ejpam-4867	26	25	construction	construction	NOUN
ejpam-4867	26	26	methods	method	NOUN
ejpam-4867	26	27	.	.	PUNCT
ejpam-4867	27	1	next	next	ADV
ejpam-4867	27	2	,	,	PUNCT
ejpam-4867	27	3	we	we	PRON
ejpam-4867	27	4	will	will	AUX
ejpam-4867	27	5	introduce	introduce	VERB
ejpam-4867	27	6	the	the	DET
ejpam-4867	27	7	graph	graph	NOUN
ejpam-4867	27	8	representation	representation	NOUN
ejpam-4867	27	9	of	of	ADP
ejpam-4867	27	10	such	such	ADJ
ejpam-4867	27	11	linear	linear	ADJ
ejpam-4867	27	12	codes	code	NOUN
ejpam-4867	27	13	,	,	PUNCT
ejpam-4867	27	14	by	by	ADP
ejpam-4867	27	15	defining	define	VERB
ejpam-4867	27	16	(	(	PUNCT
ejpam-4867	27	17	k1	k1	NOUN
ejpam-4867	27	18	,	,	PUNCT
ejpam-4867	27	19	k2	k2	ADJ
ejpam-4867	27	20	)	)	PUNCT
ejpam-4867	27	21	e	e	NOUN
ejpam-4867	27	22	-	-	NOUN
ejpam-4867	27	23	torsion	torsion	NOUN
ejpam-4867	27	24	graph	graph	NOUN
ejpam-4867	27	25	of	of	ADP
ejpam-4867	27	26	an	an	DET
ejpam-4867	27	27	e	e	NOUN
ejpam-4867	27	28	-	-	NOUN
ejpam-4867	27	29	code	code	NOUN
ejpam-4867	27	30	,	,	PUNCT
ejpam-4867	27	31	and	and	CCONJ
ejpam-4867	27	32	will	will	AUX
ejpam-4867	27	33	discuss	discuss	VERB
ejpam-4867	27	34	the	the	DET
ejpam-4867	27	35	construction	construction	NOUN
ejpam-4867	27	36	of	of	ADP
ejpam-4867	27	37	such	such	ADJ
ejpam-4867	27	38	graphs	graph	NOUN
ejpam-4867	27	39	and	and	CCONJ
ejpam-4867	27	40	explore	explore	VERB
ejpam-4867	27	41	the	the	DET
ejpam-4867	27	42	relationship	relationship	NOUN
ejpam-4867	27	43	between	between	ADP
ejpam-4867	27	44	the	the	DET
ejpam-4867	27	45	code	code	NOUN
ejpam-4867	27	46	’s	’s	PART
ejpam-4867	27	47	properties	property	NOUN
ejpam-4867	27	48	and	and	CCONJ
ejpam-4867	27	49	the	the	DET
ejpam-4867	27	50	resulting	result	VERB
ejpam-4867	27	51	graph	graph	NOUN
ejpam-4867	27	52	structure	structure	NOUN
ejpam-4867	27	53	.	.	PUNCT
ejpam-4867	28	1	moreover	moreover	ADV
ejpam-4867	28	2	,	,	PUNCT
ejpam-4867	28	3	we	we	PRON
ejpam-4867	28	4	will	will	AUX
ejpam-4867	28	5	study	study	VERB
ejpam-4867	28	6	vertex	vertex	NOUN
ejpam-4867	28	7	-	-	PUNCT
ejpam-4867	28	8	weighted	weight	VERB
ejpam-4867	28	9	graph	graph	NOUN
ejpam-4867	28	10	to	to	PART
ejpam-4867	28	11	separate	separate	VERB
ejpam-4867	28	12	the	the	DET
ejpam-4867	28	13	isomorphic	isomorphic	ADJ
ejpam-4867	28	14	graph	graph	NOUN
ejpam-4867	28	15	generated	generate	VERB
ejpam-4867	28	16	by	by	ADP
ejpam-4867	28	17	two	two	NUM
ejpam-4867	28	18	inequivalent	inequivalent	ADJ
ejpam-4867	28	19	e	e	NOUN
ejpam-4867	28	20	-	-	NOUN
ejpam-4867	28	21	codes	code	NOUN
ejpam-4867	28	22	.	.	PUNCT
ejpam-4867	29	1	the	the	DET
ejpam-4867	29	2	study	study	NOUN
ejpam-4867	29	3	of	of	ADP
ejpam-4867	29	4	coding	code	VERB
ejpam-4867	29	5	theory	theory	NOUN
ejpam-4867	29	6	in	in	ADP
ejpam-4867	29	7	relation	relation	NOUN
ejpam-4867	29	8	to	to	PART
ejpam-4867	29	9	graph	graph	NOUN
ejpam-4867	29	10	theory	theory	NOUN
ejpam-4867	29	11	is	be	AUX
ejpam-4867	29	12	not	not	PART
ejpam-4867	29	13	well	well	ADV
ejpam-4867	29	14	-	-	PUNCT
ejpam-4867	29	15	established	establish	VERB
ejpam-4867	29	16	topic	topic	NOUN
ejpam-4867	29	17	.	.	PUNCT
ejpam-4867	30	1	however	however	ADV
ejpam-4867	30	2	,	,	PUNCT
ejpam-4867	30	3	few	few	ADJ
ejpam-4867	30	4	researchers	researcher	NOUN
ejpam-4867	30	5	tried	try	VERB
ejpam-4867	30	6	to	to	PART
ejpam-4867	30	7	focus	focus	VERB
ejpam-4867	30	8	on	on	ADP
ejpam-4867	30	9	the	the	DET
ejpam-4867	30	10	subject	subject	NOUN
ejpam-4867	30	11	such	such	ADJ
ejpam-4867	30	12	as	as	ADP
ejpam-4867	30	13	graph	graph	NOUN
ejpam-4867	30	14	theoretic	theoretic	ADJ
ejpam-4867	30	15	methods	method	NOUN
ejpam-4867	30	16	in	in	ADP
ejpam-4867	30	17	coding	code	VERB
ejpam-4867	30	18	theory	theory	NOUN
ejpam-4867	30	19	[	[	X
ejpam-4867	30	20	13	13	NUM
ejpam-4867	30	21	]	]	PUNCT
ejpam-4867	30	22	,	,	PUNCT
ejpam-4867	30	23	where	where	SCONJ
ejpam-4867	30	24	it	it	PRON
ejpam-4867	30	25	discusses	discuss	VERB
ejpam-4867	30	26	the	the	DET
ejpam-4867	30	27	application	application	NOUN
ejpam-4867	30	28	of	of	ADP
ejpam-4867	30	29	graph	graph	NOUN
ejpam-4867	30	30	theory	theory	NOUN
ejpam-4867	30	31	in	in	ADP
ejpam-4867	30	32	coding	code	VERB
ejpam-4867	30	33	theory	theory	NOUN
ejpam-4867	30	34	,	,	PUNCT
ejpam-4867	30	35	and	and	CCONJ
ejpam-4867	30	36	codes	code	NOUN
ejpam-4867	30	37	on	on	ADP
ejpam-4867	30	38	graphs	graph	NOUN
ejpam-4867	30	39	[	[	X
ejpam-4867	30	40	8	8	NUM
ejpam-4867	30	41	]	]	PUNCT
ejpam-4867	30	42	,	,	PUNCT
ejpam-4867	30	43	where	where	SCONJ
ejpam-4867	30	44	it	it	PRON
ejpam-4867	30	45	developed	develop	VERB
ejpam-4867	30	46	a	a	DET
ejpam-4867	30	47	fundamental	fundamental	ADJ
ejpam-4867	30	48	theory	theory	NOUN
ejpam-4867	30	49	of	of	ADP
ejpam-4867	30	50	realizations	realization	NOUN
ejpam-4867	30	51	of	of	ADP
ejpam-4867	30	52	linear	linear	PROPN
ejpam-4867	30	53	and	and	CCONJ
ejpam-4867	30	54	group	group	NOUN
ejpam-4867	30	55	codes	code	NOUN
ejpam-4867	30	56	on	on	ADP
ejpam-4867	30	57	general	general	ADJ
ejpam-4867	30	58	graphs	graph	NOUN
ejpam-4867	30	59	using	use	VERB
ejpam-4867	30	60	elementary	elementary	ADJ
ejpam-4867	30	61	group	group	NOUN
ejpam-4867	30	62	theory	theory	NOUN
ejpam-4867	30	63	,	,	PUNCT
ejpam-4867	30	64	including	include	VERB
ejpam-4867	30	65	basic	basic	ADJ
ejpam-4867	30	66	group	group	NOUN
ejpam-4867	30	67	duality	duality	NOUN
ejpam-4867	30	68	theory	theory	NOUN
ejpam-4867	30	69	.	.	PUNCT
ejpam-4867	31	1	through	through	ADP
ejpam-4867	31	2	our	our	PRON
ejpam-4867	31	3	comprehensive	comprehensive	ADJ
ejpam-4867	31	4	analysis	analysis	NOUN
ejpam-4867	31	5	of	of	ADP
ejpam-4867	31	6	graphs	graph	NOUN
ejpam-4867	31	7	produced	produce	VERB
ejpam-4867	31	8	from	from	ADP
ejpam-4867	31	9	linear	linear	PROPN
ejpam-4867	31	10	codes	code	NOUN
ejpam-4867	31	11	over	over	ADP
ejpam-4867	31	12	the	the	DET
ejpam-4867	31	13	non	non	ADJ
ejpam-4867	31	14	-	-	ADJ
ejpam-4867	31	15	unital	unital	ADJ
ejpam-4867	31	16	ring	ring	NOUN
ejpam-4867	31	17	e	e	NOUN
ejpam-4867	31	18	,	,	PUNCT
ejpam-4867	31	19	this	this	DET
ejpam-4867	31	20	article	article	NOUN
ejpam-4867	31	21	seeks	seek	VERB
ejpam-4867	31	22	to	to	PART
ejpam-4867	31	23	contribute	contribute	VERB
ejpam-4867	31	24	to	to	ADP
ejpam-4867	31	25	the	the	DET
ejpam-4867	31	26	expanding	expand	VERB
ejpam-4867	31	27	field	field	NOUN
ejpam-4867	31	28	of	of	ADP
ejpam-4867	31	29	coding	code	VERB
ejpam-4867	31	30	theory	theory	NOUN
ejpam-4867	31	31	and	and	CCONJ
ejpam-4867	31	32	its	its	PRON
ejpam-4867	31	33	applications	application	NOUN
ejpam-4867	31	34	in	in	ADP
ejpam-4867	31	35	diverse	diverse	ADJ
ejpam-4867	31	36	domains	domain	NOUN
ejpam-4867	31	37	.	.	PUNCT
ejpam-4867	32	1	by	by	ADP
ejpam-4867	32	2	exploring	explore	VERB
ejpam-4867	32	3	the	the	DET
ejpam-4867	32	4	interplay	interplay	NOUN
ejpam-4867	32	5	between	between	ADP
ejpam-4867	32	6	graph	graph	NOUN
ejpam-4867	32	7	theory	theory	NOUN
ejpam-4867	32	8	and	and	CCONJ
ejpam-4867	32	9	linear	linear	ADJ
ejpam-4867	32	10	codes	code	NOUN
ejpam-4867	32	11	over	over	ADP
ejpam-4867	32	12	non	non	ADJ
ejpam-4867	32	13	-	-	ADJ
ejpam-4867	32	14	unital	unital	ADJ
ejpam-4867	32	15	rings	ring	NOUN
ejpam-4867	32	16	,	,	PUNCT
ejpam-4867	32	17	we	we	PRON
ejpam-4867	32	18	strive	strive	VERB
ejpam-4867	32	19	to	to	PART
ejpam-4867	32	20	unlock	unlock	VERB
ejpam-4867	32	21	new	new	ADJ
ejpam-4867	32	22	perspectives	perspective	NOUN
ejpam-4867	32	23	,	,	PUNCT
ejpam-4867	32	24	insights	insight	NOUN
ejpam-4867	32	25	,	,	PUNCT
ejpam-4867	32	26	and	and	CCONJ
ejpam-4867	32	27	practical	practical	ADJ
ejpam-4867	32	28	solutions	solution	NOUN
ejpam-4867	32	29	that	that	PRON
ejpam-4867	32	30	can	can	AUX
ejpam-4867	32	31	address	address	VERB
ejpam-4867	32	32	challenges	challenge	NOUN
ejpam-4867	32	33	in	in	ADP
ejpam-4867	32	34	error	error	NOUN
ejpam-4867	32	35	correction	correction	NOUN
ejpam-4867	32	36	,	,	PUNCT
ejpam-4867	32	37	information	information	NOUN
ejpam-4867	32	38	transmission	transmission	NOUN
ejpam-4867	32	39	,	,	PUNCT
ejpam-4867	32	40	and	and	CCONJ
ejpam-4867	32	41	beyond	beyond	ADP
ejpam-4867	32	42	.	.	NOUN
ejpam-4867	33	1	2	2	X
ejpam-4867	33	2	.	.	X
ejpam-4867	33	3	background	background	NOUN
ejpam-4867	33	4	2.1	2.1	NUM
ejpam-4867	33	5	.	.	PUNCT
ejpam-4867	34	1	binary	binary	ADJ
ejpam-4867	34	2	codes	code	NOUN
ejpam-4867	34	3	as	as	SCONJ
ejpam-4867	34	4	defined	define	VERB
ejpam-4867	34	5	in	in	ADP
ejpam-4867	34	6	[	[	X
ejpam-4867	34	7	14	14	NUM
ejpam-4867	34	8	]	]	PUNCT
ejpam-4867	34	9	,	,	PUNCT
ejpam-4867	34	10	denoted	denote	VERB
ejpam-4867	34	11	by	by	ADP
ejpam-4867	34	12	wt(x	wt(x	NOUN
ejpam-4867	34	13	)	)	PUNCT
ejpam-4867	34	14	the	the	DET
ejpam-4867	34	15	hamming	hamming	NOUN
ejpam-4867	34	16	weight	weight	NOUN
ejpam-4867	34	17	of	of	ADP
ejpam-4867	34	18	x	x	PUNCT
ejpam-4867	34	19	∈	∈	PROPN
ejpam-4867	34	20	fn	fn	NOUN
ejpam-4867	34	21	2	2	NUM
ejpam-4867	34	22	.	.	PUNCT
ejpam-4867	35	1	the	the	DET
ejpam-4867	35	2	dual	dual	ADJ
ejpam-4867	35	3	of	of	ADP
ejpam-4867	35	4	a	a	DET
ejpam-4867	35	5	binary	binary	PROPN
ejpam-4867	35	6	code	code	NOUN
ejpam-4867	35	7	c	c	PROPN
ejpam-4867	35	8	is	be	AUX
ejpam-4867	35	9	denoted	denote	VERB
ejpam-4867	35	10	by	by	ADP
ejpam-4867	35	11	c⊥	c⊥	PROPN
ejpam-4867	35	12	and	and	CCONJ
ejpam-4867	35	13	defined	define	VERB
ejpam-4867	35	14	as	as	ADP
ejpam-4867	35	15	c⊥	c⊥	X
ejpam-4867	35	16	=	=	X
ejpam-4867	35	17	{	{	PUNCT
ejpam-4867	35	18	y	y	PROPN
ejpam-4867	35	19	∈	∈	PROPN
ejpam-4867	35	20	fn	fn	NOUN
ejpam-4867	35	21	2	2	NUM
ejpam-4867	35	22	|∀x	|∀x	NOUN
ejpam-4867	35	23	∈	∈	PROPN
ejpam-4867	35	24	c	c	NOUN
ejpam-4867	35	25	,	,	PUNCT
ejpam-4867	35	26	(	(	PUNCT
ejpam-4867	35	27	x	x	NOUN
ejpam-4867	35	28	,	,	PUNCT
ejpam-4867	35	29	y	y	NOUN
ejpam-4867	35	30	)	)	PUNCT
ejpam-4867	35	31	=	=	SYM
ejpam-4867	35	32	0	0	NUM
ejpam-4867	35	33	,	,	PUNCT
ejpam-4867	35	34	}	}	PUNCT
ejpam-4867	35	35	where	where	SCONJ
ejpam-4867	35	36	(	(	PUNCT
ejpam-4867	35	37	x	x	NOUN
ejpam-4867	35	38	,	,	PUNCT
ejpam-4867	35	39	y	y	NOUN
ejpam-4867	35	40	)	)	PUNCT
ejpam-4867	35	41	=	=	PUNCT
ejpam-4867	36	1	n∑	n∑	PROPN
ejpam-4867	36	2	i=1	i=1	PROPN
ejpam-4867	37	1	xiyi	xiyi	PROPN
ejpam-4867	37	2	,	,	PUNCT
ejpam-4867	37	3	j.	j.	PROPN
ejpam-4867	37	4	pilongo	pilongo	PROPN
ejpam-4867	37	5	,	,	PUNCT
ejpam-4867	37	6	l.	l.	PROPN
ejpam-4867	37	7	paleta	paleta	PROPN
ejpam-4867	37	8	,	,	PUNCT
ejpam-4867	37	9	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	37	10	/	/	SYM
ejpam-4867	37	11	eur	eur	PROPN
ejpam-4867	37	12	.	.	PUNCT
ejpam-4867	38	1	j.	j.	PROPN
ejpam-4867	38	2	pure	pure	PROPN
ejpam-4867	38	3	appl	appl	PROPN
ejpam-4867	38	4	.	.	PROPN
ejpam-4867	38	5	math	math	PROPN
ejpam-4867	38	6	,	,	PUNCT
ejpam-4867	38	7	17	17	NUM
ejpam-4867	38	8	(	(	PUNCT
ejpam-4867	38	9	2	2	NUM
ejpam-4867	38	10	)	)	PUNCT
ejpam-4867	38	11	(	(	PUNCT
ejpam-4867	38	12	2024	2024	NUM
ejpam-4867	38	13	)	)	PUNCT
ejpam-4867	38	14	,	,	PUNCT
ejpam-4867	38	15	1369	1369	NUM
ejpam-4867	38	16	-	-	SYM
ejpam-4867	38	17	1384	1384	NUM
ejpam-4867	38	18	1371	1371	NUM
ejpam-4867	38	19	denotes	denote	VERB
ejpam-4867	38	20	the	the	DET
ejpam-4867	38	21	standard	standard	ADJ
ejpam-4867	38	22	inner	inner	ADJ
ejpam-4867	38	23	product	product	NOUN
ejpam-4867	38	24	.	.	PUNCT
ejpam-4867	39	1	a	a	DET
ejpam-4867	39	2	code	code	NOUN
ejpam-4867	39	3	c	c	NOUN
ejpam-4867	39	4	is	be	AUX
ejpam-4867	39	5	self	self	NOUN
ejpam-4867	39	6	-	-	PUNCT
ejpam-4867	39	7	orthogonal	orthogonal	ADJ
ejpam-4867	39	8	if	if	SCONJ
ejpam-4867	39	9	it	it	PRON
ejpam-4867	39	10	is	be	AUX
ejpam-4867	39	11	included	include	VERB
ejpam-4867	39	12	in	in	ADP
ejpam-4867	39	13	its	its	PRON
ejpam-4867	39	14	dual	dual	NOUN
ejpam-4867	39	15	:	:	PUNCT
ejpam-4867	39	16	c	c	PROPN
ejpam-4867	39	17	⊆	⊆	NUM
ejpam-4867	39	18	c⊥.	c⊥.	NOUN
ejpam-4867	39	19	two	two	NUM
ejpam-4867	39	20	binary	binary	ADJ
ejpam-4867	39	21	codes	code	NOUN
ejpam-4867	39	22	are	be	AUX
ejpam-4867	39	23	equivalent	equivalent	ADJ
ejpam-4867	39	24	if	if	SCONJ
ejpam-4867	39	25	there	there	PRON
ejpam-4867	39	26	is	be	VERB
ejpam-4867	39	27	a	a	DET
ejpam-4867	39	28	permutation	permutation	NOUN
ejpam-4867	39	29	of	of	ADP
ejpam-4867	39	30	coordinates	coordinate	NOUN
ejpam-4867	39	31	that	that	PRON
ejpam-4867	39	32	maps	map	VERB
ejpam-4867	39	33	one	one	NUM
ejpam-4867	39	34	to	to	ADP
ejpam-4867	39	35	the	the	DET
ejpam-4867	39	36	other	other	ADJ
ejpam-4867	39	37	.	.	PUNCT
ejpam-4867	40	1	2.2	2.2	NUM
ejpam-4867	40	2	.	.	PUNCT
ejpam-4867	40	3	ring	ring	NOUN
ejpam-4867	40	4	theory	theory	NOUN
ejpam-4867	40	5	we	we	PRON
ejpam-4867	40	6	describe	describe	VERB
ejpam-4867	40	7	the	the	DET
ejpam-4867	40	8	main	main	ADJ
ejpam-4867	40	9	properties	property	NOUN
ejpam-4867	40	10	of	of	ADP
ejpam-4867	40	11	the	the	DET
ejpam-4867	40	12	ring	ring	NOUN
ejpam-4867	40	13	e	e	NOUN
ejpam-4867	40	14	of	of	ADP
ejpam-4867	40	15	order	order	NOUN
ejpam-4867	40	16	four	four	NUM
ejpam-4867	40	17	.	.	PUNCT
ejpam-4867	41	1	the	the	DET
ejpam-4867	41	2	ring	ring	NOUN
ejpam-4867	41	3	e	e	NOUN
ejpam-4867	41	4	is	be	AUX
ejpam-4867	41	5	defined	define	VERB
ejpam-4867	41	6	by	by	ADP
ejpam-4867	41	7	the	the	DET
ejpam-4867	41	8	relations	relation	NOUN
ejpam-4867	41	9	on	on	ADP
ejpam-4867	41	10	two	two	NUM
ejpam-4867	41	11	generators	generator	NOUN
ejpam-4867	41	12	a	a	DET
ejpam-4867	41	13	,	,	PUNCT
ejpam-4867	41	14	b	b	NOUN
ejpam-4867	42	1	and	and	CCONJ
ejpam-4867	42	2	we	we	PRON
ejpam-4867	42	3	shall	shall	AUX
ejpam-4867	42	4	write	write	VERB
ejpam-4867	42	5	c	c	NOUN
ejpam-4867	42	6	=	=	SYM
ejpam-4867	42	7	a+	a+	PUNCT
ejpam-4867	42	8	b	b	NOUN
ejpam-4867	42	9	for	for	ADP
ejpam-4867	42	10	the	the	DET
ejpam-4867	42	11	given	give	VERB
ejpam-4867	42	12	ring	ring	NOUN
ejpam-4867	42	13	.	.	PUNCT
ejpam-4867	43	1	the	the	DET
ejpam-4867	43	2	ring	ring	NOUN
ejpam-4867	43	3	e	e	NOUN
ejpam-4867	43	4	is	be	AUX
ejpam-4867	43	5	defined	define	VERB
ejpam-4867	43	6	by	by	ADP
ejpam-4867	43	7	e	e	PROPN
ejpam-4867	43	8	=	=	SYM
ejpam-4867	43	9	⟨a	⟨a	PROPN
ejpam-4867	43	10	,	,	PUNCT
ejpam-4867	43	11	b|2a	b|2a	NOUN
ejpam-4867	43	12	=	=	SYM
ejpam-4867	43	13	2b	2b	NUM
ejpam-4867	43	14	=	=	SYM
ejpam-4867	43	15	0	0	NUM
ejpam-4867	43	16	,	,	PUNCT
ejpam-4867	43	17	a2	a2	PROPN
ejpam-4867	43	18	=	=	SYM
ejpam-4867	43	19	a	a	PRON
ejpam-4867	43	20	,	,	PUNCT
ejpam-4867	43	21	b2	b2	NOUN
ejpam-4867	43	22	=	=	SYM
ejpam-4867	43	23	b	b	PROPN
ejpam-4867	43	24	,	,	PUNCT
ejpam-4867	43	25	ab	ab	PROPN
ejpam-4867	43	26	=	=	PUNCT
ejpam-4867	43	27	a	a	PROPN
ejpam-4867	43	28	,	,	PUNCT
ejpam-4867	43	29	ba	ba	PROPN
ejpam-4867	43	30	=	=	NOUN
ejpam-4867	43	31	b⟩.	b⟩.	NOUN
ejpam-4867	43	32	it	it	PRON
ejpam-4867	43	33	is	be	AUX
ejpam-4867	43	34	a	a	DET
ejpam-4867	43	35	non	non	ADJ
ejpam-4867	43	36	-	-	ADJ
ejpam-4867	43	37	unital	unital	ADJ
ejpam-4867	43	38	ring	ring	NOUN
ejpam-4867	43	39	and	and	CCONJ
ejpam-4867	43	40	non	non	ADJ
ejpam-4867	43	41	-	-	ADJ
ejpam-4867	43	42	commutative	commutative	ADJ
ejpam-4867	43	43	ring	ring	NOUN
ejpam-4867	43	44	with	with	ADP
ejpam-4867	43	45	characteristic	characteristic	ADJ
ejpam-4867	43	46	two	two	NUM
ejpam-4867	43	47	.	.	PUNCT
ejpam-4867	44	1	for	for	SCONJ
ejpam-4867	44	2	more	more	ADJ
ejpam-4867	44	3	details	detail	NOUN
ejpam-4867	44	4	refer	refer	VERB
ejpam-4867	44	5	to	to	ADP
ejpam-4867	44	6	[	[	X
ejpam-4867	44	7	3	3	NUM
ejpam-4867	44	8	,	,	PUNCT
ejpam-4867	44	9	7	7	NUM
ejpam-4867	44	10	,	,	PUNCT
ejpam-4867	44	11	12	12	NUM
ejpam-4867	44	12	]	]	PUNCT
ejpam-4867	44	13	.	.	PUNCT
ejpam-4867	45	1	the	the	DET
ejpam-4867	45	2	ring	ring	NOUN
ejpam-4867	45	3	is	be	AUX
ejpam-4867	45	4	local	local	ADJ
ejpam-4867	45	5	with	with	ADP
ejpam-4867	45	6	maximal	maximal	ADJ
ejpam-4867	45	7	ideal	ideal	NOUN
ejpam-4867	45	8	{	{	PUNCT
ejpam-4867	45	9	0	0	NUM
ejpam-4867	45	10	,	,	PUNCT
ejpam-4867	45	11	c	c	NOUN
ejpam-4867	45	12	}	}	PUNCT
ejpam-4867	45	13	.	.	PUNCT
ejpam-4867	46	1	its	its	PRON
ejpam-4867	46	2	multiplication	multiplication	NOUN
ejpam-4867	46	3	table	table	NOUN
ejpam-4867	46	4	is	be	AUX
ejpam-4867	46	5	given	give	VERB
ejpam-4867	46	6	in	in	ADP
ejpam-4867	46	7	table	table	NOUN
ejpam-4867	46	8	1	1	NUM
ejpam-4867	46	9	.	.	PUNCT
ejpam-4867	47	1	×	×	NOUN
ejpam-4867	47	2	0	0	NUM
ejpam-4867	47	3	a	a	DET
ejpam-4867	47	4	b	b	NOUN
ejpam-4867	47	5	c	c	NOUN
ejpam-4867	47	6	0	0	NUM
ejpam-4867	47	7	0	0	NUM
ejpam-4867	47	8	0	0	NUM
ejpam-4867	47	9	0	0	NUM
ejpam-4867	47	10	0	0	NUM
ejpam-4867	48	1	a	a	DET
ejpam-4867	48	2	0	0	NUM
ejpam-4867	48	3	a	a	DET
ejpam-4867	48	4	0	0	NUM
ejpam-4867	48	5	0	0	NUM
ejpam-4867	48	6	b	b	NOUN
ejpam-4867	48	7	0	0	NUM
ejpam-4867	48	8	b	b	PROPN
ejpam-4867	48	9	b	b	PROPN
ejpam-4867	48	10	0	0	NUM
ejpam-4867	48	11	c	c	NOUN
ejpam-4867	48	12	0	0	PUNCT
ejpam-4867	48	13	c	c	NOUN
ejpam-4867	48	14	c	c	NOUN
ejpam-4867	48	15	0	0	NUM
ejpam-4867	48	16	table	table	NOUN
ejpam-4867	48	17	1	1	NUM
ejpam-4867	48	18	:	:	PUNCT
ejpam-4867	48	19	multiplication	multiplication	NOUN
ejpam-4867	48	20	table	table	NOUN
ejpam-4867	48	21	for	for	ADP
ejpam-4867	48	22	the	the	DET
ejpam-4867	48	23	ring	ring	NOUN
ejpam-4867	48	24	e	e	NOUN
ejpam-4867	48	25	from	from	ADP
ejpam-4867	48	26	table	table	NOUN
ejpam-4867	48	27	1	1	NUM
ejpam-4867	49	1	,	,	PUNCT
ejpam-4867	49	2	it	it	PRON
ejpam-4867	49	3	is	be	AUX
ejpam-4867	49	4	clear	clear	ADJ
ejpam-4867	49	5	e	e	NOUN
ejpam-4867	49	6	is	be	AUX
ejpam-4867	49	7	not	not	PART
ejpam-4867	49	8	commutative	commutative	ADJ
ejpam-4867	49	9	,	,	PUNCT
ejpam-4867	49	10	and	and	CCONJ
ejpam-4867	49	11	non	non	ADJ
ejpam-4867	49	12	-	-	ADJ
ejpam-4867	49	13	unital	unital	ADJ
ejpam-4867	49	14	.	.	PUNCT
ejpam-4867	50	1	it	it	PRON
ejpam-4867	50	2	is	be	AUX
ejpam-4867	50	3	local	local	ADJ
ejpam-4867	50	4	with	with	ADP
ejpam-4867	50	5	the	the	DET
ejpam-4867	50	6	maximal	maximal	ADJ
ejpam-4867	50	7	ideal	ideal	NOUN
ejpam-4867	50	8	j	j	PROPN
ejpam-4867	51	1	=	=	PUNCT
ejpam-4867	51	2	{	{	PUNCT
ejpam-4867	51	3	0	0	NUM
ejpam-4867	51	4	,	,	PUNCT
ejpam-4867	51	5	c	c	NOUN
ejpam-4867	51	6	}	}	PUNCT
ejpam-4867	51	7	,	,	PUNCT
ejpam-4867	51	8	and	and	CCONJ
ejpam-4867	51	9	residue	residue	NOUN
ejpam-4867	51	10	field	field	NOUN
ejpam-4867	51	11	e	e	NOUN
ejpam-4867	51	12	/	/	SYM
ejpam-4867	51	13	j	j	PROPN
ejpam-4867	51	14	=	=	SYM
ejpam-4867	51	15	f	f	PROPN
ejpam-4867	51	16	=	=	PUNCT
ejpam-4867	51	17	{	{	PUNCT
ejpam-4867	51	18	0	0	NUM
ejpam-4867	51	19	,	,	PUNCT
ejpam-4867	51	20	1	1	NUM
ejpam-4867	51	21	}	}	PUNCT
ejpam-4867	51	22	,	,	PUNCT
ejpam-4867	51	23	the	the	DET
ejpam-4867	51	24	finite	finite	NOUN
ejpam-4867	51	25	filed	file	VERB
ejpam-4867	51	26	of	of	ADP
ejpam-4867	51	27	order	order	NOUN
ejpam-4867	51	28	2	2	X
ejpam-4867	51	29	.	.	PUNCT
ejpam-4867	52	1	if	if	SCONJ
ejpam-4867	52	2	we	we	PRON
ejpam-4867	52	3	denote	denote	VERB
ejpam-4867	52	4	α	α	X
ejpam-4867	52	5	:	:	PUNCT
ejpam-4867	52	6	e	e	X
ejpam-4867	52	7	→	→	SYM
ejpam-4867	52	8	e	e	PROPN
ejpam-4867	52	9	/	/	SYM
ejpam-4867	52	10	j	j	PROPN
ejpam-4867	52	11	=	=	SYM
ejpam-4867	52	12	f2	f2	PROPN
ejpam-4867	52	13	,	,	PUNCT
ejpam-4867	52	14	the	the	DET
ejpam-4867	52	15	map	map	NOUN
ejpam-4867	52	16	of	of	ADP
ejpam-4867	52	17	reduction	reduction	NOUN
ejpam-4867	52	18	modulo	modulo	VERB
ejpam-4867	52	19	j	j	PROPN
ejpam-4867	52	20	.	.	PUNCT
ejpam-4867	53	1	it	it	PRON
ejpam-4867	53	2	follows	follow	VERB
ejpam-4867	53	3	that	that	SCONJ
ejpam-4867	53	4	α(0	α(0	NOUN
ejpam-4867	53	5	)	)	PUNCT
ejpam-4867	53	6	=	=	SYM
ejpam-4867	53	7	α(c	α(c	NOUN
ejpam-4867	53	8	)	)	PUNCT
ejpam-4867	53	9	=	=	SYM
ejpam-4867	53	10	0	0	NUM
ejpam-4867	53	11	,	,	PUNCT
ejpam-4867	53	12	and	and	CCONJ
ejpam-4867	53	13	α(a	α(a	NOUN
ejpam-4867	53	14	)	)	PUNCT
ejpam-4867	53	15	=	=	PUNCT
ejpam-4867	53	16	α(b	α(b	NOUN
ejpam-4867	53	17	)	)	PUNCT
ejpam-4867	53	18	=	=	SYM
ejpam-4867	54	1	1	1	X
ejpam-4867	54	2	.	.	PUNCT
ejpam-4867	55	1	this	this	DET
ejpam-4867	55	2	function	function	NOUN
ejpam-4867	55	3	α	α	PROPN
ejpam-4867	55	4	is	be	AUX
ejpam-4867	55	5	extended	extend	VERB
ejpam-4867	55	6	in	in	ADP
ejpam-4867	55	7	the	the	DET
ejpam-4867	55	8	natural	natural	ADJ
ejpam-4867	55	9	way	way	NOUN
ejpam-4867	55	10	in	in	ADP
ejpam-4867	55	11	a	a	DET
ejpam-4867	55	12	map	map	NOUN
ejpam-4867	55	13	from	from	ADP
ejpam-4867	55	14	en	en	ADP
ejpam-4867	55	15	to	to	ADP
ejpam-4867	55	16	fn	fn	PROPN
ejpam-4867	55	17	2	2	NUM
ejpam-4867	55	18	.	.	PUNCT
ejpam-4867	56	1	readers	reader	NOUN
ejpam-4867	56	2	who	who	PRON
ejpam-4867	56	3	wanted	want	VERB
ejpam-4867	56	4	further	further	ADJ
ejpam-4867	56	5	details	detail	NOUN
ejpam-4867	56	6	on	on	ADP
ejpam-4867	56	7	the	the	DET
ejpam-4867	56	8	properties	property	NOUN
ejpam-4867	56	9	of	of	ADP
ejpam-4867	56	10	ring	ring	NOUN
ejpam-4867	56	11	r	r	NOUN
ejpam-4867	56	12	,	,	PUNCT
ejpam-4867	56	13	we	we	PRON
ejpam-4867	56	14	refer	refer	VERB
ejpam-4867	56	15	the	the	DET
ejpam-4867	56	16	readers	reader	NOUN
ejpam-4867	56	17	to	to	ADP
ejpam-4867	56	18	[	[	X
ejpam-4867	56	19	1–3	1–3	NOUN
ejpam-4867	56	20	,	,	PUNCT
ejpam-4867	56	21	10	10	NUM
ejpam-4867	56	22	]	]	PUNCT
ejpam-4867	56	23	.	.	PUNCT
ejpam-4867	57	1	j.	j.	PROPN
ejpam-4867	57	2	pilongo	pilongo	PROPN
ejpam-4867	57	3	,	,	PUNCT
ejpam-4867	57	4	l.	l.	PROPN
ejpam-4867	57	5	paleta	paleta	PROPN
ejpam-4867	57	6	,	,	PUNCT
ejpam-4867	57	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	57	8	/	/	SYM
ejpam-4867	57	9	eur	eur	PROPN
ejpam-4867	57	10	.	.	PUNCT
ejpam-4867	58	1	j.	j.	PROPN
ejpam-4867	58	2	pure	pure	PROPN
ejpam-4867	58	3	appl	appl	PROPN
ejpam-4867	58	4	.	.	PROPN
ejpam-4867	58	5	math	math	PROPN
ejpam-4867	58	6	,	,	PUNCT
ejpam-4867	58	7	17	17	NUM
ejpam-4867	58	8	(	(	PUNCT
ejpam-4867	58	9	2	2	NUM
ejpam-4867	58	10	)	)	PUNCT
ejpam-4867	58	11	(	(	PUNCT
ejpam-4867	58	12	2024	2024	NUM
ejpam-4867	58	13	)	)	PUNCT
ejpam-4867	58	14	,	,	PUNCT
ejpam-4867	58	15	1369	1369	NUM
ejpam-4867	58	16	-	-	SYM
ejpam-4867	58	17	1384	1384	NUM
ejpam-4867	58	18	1372	1372	NUM
ejpam-4867	58	19	2.3	2.3	NUM
ejpam-4867	58	20	.	.	PUNCT
ejpam-4867	59	1	codes	code	NOUN
ejpam-4867	59	2	over	over	ADP
ejpam-4867	59	3	e	e	PROPN
ejpam-4867	59	4	a	a	DET
ejpam-4867	59	5	linear	linear	ADJ
ejpam-4867	59	6	e	e	NOUN
ejpam-4867	59	7	-	-	NOUN
ejpam-4867	59	8	code	code	NOUN
ejpam-4867	59	9	of	of	ADP
ejpam-4867	59	10	length	length	NOUN
ejpam-4867	59	11	n	n	PROPN
ejpam-4867	59	12	is	be	AUX
ejpam-4867	59	13	a	a	DET
ejpam-4867	59	14	one	one	NUM
ejpam-4867	59	15	-	-	PUNCT
ejpam-4867	59	16	sided	sided	ADJ
ejpam-4867	59	17	e	e	NOUN
ejpam-4867	59	18	-	-	NOUN
ejpam-4867	59	19	submodule	submodule	NOUN
ejpam-4867	59	20	of	of	ADP
ejpam-4867	59	21	en	en	X
ejpam-4867	59	22	.	.	PUNCT
ejpam-4867	60	1	let	let	VERB
ejpam-4867	60	2	c	c	PRON
ejpam-4867	60	3	be	be	AUX
ejpam-4867	60	4	a	a	DET
ejpam-4867	60	5	code	code	NOUN
ejpam-4867	60	6	of	of	ADP
ejpam-4867	60	7	length	length	NOUN
ejpam-4867	60	8	n	n	PROPN
ejpam-4867	60	9	over	over	ADP
ejpam-4867	60	10	e.	e.	PROPN
ejpam-4867	60	11	with	with	ADP
ejpam-4867	60	12	the	the	DET
ejpam-4867	60	13	code	code	NOUN
ejpam-4867	60	14	,	,	PUNCT
ejpam-4867	60	15	there	there	PRON
ejpam-4867	60	16	are	be	VERB
ejpam-4867	60	17	two	two	NUM
ejpam-4867	60	18	binary	binary	ADJ
ejpam-4867	60	19	codes	code	NOUN
ejpam-4867	60	20	of	of	ADP
ejpam-4867	60	21	length	length	NOUN
ejpam-4867	60	22	n	n	CCONJ
ejpam-4867	60	23	:	:	PUNCT
ejpam-4867	60	24	(	(	PUNCT
ejpam-4867	60	25	i	i	NOUN
ejpam-4867	60	26	)	)	PUNCT
ejpam-4867	60	27	the	the	DET
ejpam-4867	60	28	residue	residue	NOUN
ejpam-4867	60	29	code	code	NOUN
ejpam-4867	60	30	defined	define	VERB
ejpam-4867	60	31	by	by	ADP
ejpam-4867	60	32	res(c	res(c	PROPN
ejpam-4867	60	33	)	)	PUNCT
ejpam-4867	60	34	=	=	PRON
ejpam-4867	60	35	{	{	PUNCT
ejpam-4867	60	36	α(y)|y	α(y)|y	PROPN
ejpam-4867	60	37	∈	∈	PROPN
ejpam-4867	60	38	c	c	NOUN
ejpam-4867	60	39	}	}	PUNCT
ejpam-4867	60	40	,	,	PUNCT
ejpam-4867	60	41	(	(	PUNCT
ejpam-4867	60	42	ii	ii	NOUN
ejpam-4867	60	43	)	)	PUNCT
ejpam-4867	60	44	the	the	DET
ejpam-4867	60	45	torsion	torsion	NOUN
ejpam-4867	60	46	code	code	NOUN
ejpam-4867	60	47	defined	define	VERB
ejpam-4867	60	48	by	by	ADP
ejpam-4867	60	49	tor(c	tor(c	PROPN
ejpam-4867	60	50	)	)	PUNCT
ejpam-4867	60	51	=	=	PRON
ejpam-4867	61	1	{	{	PUNCT
ejpam-4867	61	2	x	x	SYM
ejpam-4867	61	3	∈	∈	NOUN
ejpam-4867	61	4	fn	fn	NOUN
ejpam-4867	61	5	2	2	NUM
ejpam-4867	61	6	|cx	|cx	NUM
ejpam-4867	61	7	∈	∈	PROPN
ejpam-4867	61	8	c	c	NOUN
ejpam-4867	61	9	}	}	PUNCT
ejpam-4867	61	10	.	.	PUNCT
ejpam-4867	62	1	the	the	DET
ejpam-4867	62	2	right	right	ADJ
ejpam-4867	62	3	dual	dual	ADJ
ejpam-4867	62	4	c⊥r	c⊥r	PROPN
ejpam-4867	62	5	of	of	ADP
ejpam-4867	62	6	c	c	PROPN
ejpam-4867	62	7	is	be	AUX
ejpam-4867	62	8	the	the	DET
ejpam-4867	62	9	right	right	ADJ
ejpam-4867	62	10	module	module	NOUN
ejpam-4867	62	11	defined	define	VERB
ejpam-4867	62	12	by	by	ADP
ejpam-4867	62	13	c⊥r	c⊥r	PROPN
ejpam-4867	62	14	=	=	PUNCT
ejpam-4867	62	15	{	{	PUNCT
ejpam-4867	62	16	y	y	PROPN
ejpam-4867	62	17	∈	∈	PROPN
ejpam-4867	62	18	en|∀x	en|∀x	PROPN
ejpam-4867	62	19	∈	∈	PROPN
ejpam-4867	62	20	c	c	NOUN
ejpam-4867	62	21	,	,	PUNCT
ejpam-4867	62	22	(	(	PUNCT
ejpam-4867	62	23	x	x	NOUN
ejpam-4867	62	24	,	,	PUNCT
ejpam-4867	62	25	y	y	NOUN
ejpam-4867	62	26	)	)	PUNCT
ejpam-4867	62	27	=	=	PUNCT
ejpam-4867	62	28	0	0	NUM
ejpam-4867	62	29	}	}	PUNCT
ejpam-4867	62	30	.	.	PUNCT
ejpam-4867	63	1	the	the	DET
ejpam-4867	63	2	left	left	ADJ
ejpam-4867	63	3	dual	dual	ADJ
ejpam-4867	63	4	c⊥r	c⊥r	PROPN
ejpam-4867	63	5	of	of	ADP
ejpam-4867	63	6	c	c	PROPN
ejpam-4867	63	7	is	be	AUX
ejpam-4867	63	8	the	the	DET
ejpam-4867	63	9	left	left	ADJ
ejpam-4867	63	10	module	module	NOUN
ejpam-4867	63	11	defined	define	VERB
ejpam-4867	63	12	by	by	ADP
ejpam-4867	63	13	c⊥l	c⊥l	PROPN
ejpam-4867	63	14	=	=	PUNCT
ejpam-4867	63	15	{	{	PUNCT
ejpam-4867	63	16	y	y	PROPN
ejpam-4867	63	17	∈	∈	PROPN
ejpam-4867	63	18	en|∀x	en|∀x	PROPN
ejpam-4867	63	19	∈	∈	PROPN
ejpam-4867	63	20	c	c	PROPN
ejpam-4867	63	21	,	,	PUNCT
ejpam-4867	63	22	(	(	PUNCT
ejpam-4867	63	23	y	y	NOUN
ejpam-4867	63	24	,	,	PUNCT
ejpam-4867	63	25	x	x	NOUN
ejpam-4867	63	26	)	)	PUNCT
ejpam-4867	63	27	=	=	SYM
ejpam-4867	63	28	0	0	NUM
ejpam-4867	63	29	}	}	PUNCT
ejpam-4867	63	30	.	.	PUNCT
ejpam-4867	64	1	an	an	DET
ejpam-4867	64	2	e	e	NOUN
ejpam-4867	64	3	-	-	NOUN
ejpam-4867	64	4	code	code	ADJ
ejpam-4867	64	5	c	c	NOUN
ejpam-4867	64	6	is	be	AUX
ejpam-4867	64	7	self	self	NOUN
ejpam-4867	64	8	-	-	PUNCT
ejpam-4867	64	9	orthogonal	orthogonal	ADJ
ejpam-4867	64	10	if	if	SCONJ
ejpam-4867	64	11	∀x	∀x	NUM
ejpam-4867	64	12	,	,	PUNCT
ejpam-4867	65	1	y	y	PROPN
ejpam-4867	65	2	∈	∈	PROPN
ejpam-4867	65	3	c	c	PROPN
ejpam-4867	65	4	,	,	PUNCT
ejpam-4867	65	5	(	(	PUNCT
ejpam-4867	65	6	x	x	NOUN
ejpam-4867	65	7	,	,	PUNCT
ejpam-4867	65	8	y	y	NOUN
ejpam-4867	65	9	)	)	PUNCT
ejpam-4867	65	10	=	=	SYM
ejpam-4867	66	1	0	0	X
ejpam-4867	66	2	.	.	PUNCT
ejpam-4867	67	1	it	it	PRON
ejpam-4867	67	2	follows	follow	VERB
ejpam-4867	67	3	that	that	SCONJ
ejpam-4867	67	4	c	c	PROPN
ejpam-4867	67	5	is	be	AUX
ejpam-4867	67	6	self	self	NOUN
ejpam-4867	67	7	-	-	PUNCT
ejpam-4867	67	8	orthogonal	orthogonal	ADJ
ejpam-4867	67	9	if	if	SCONJ
ejpam-4867	68	1	and	and	CCONJ
ejpam-4867	68	2	only	only	ADV
ejpam-4867	68	3	if	if	SCONJ
ejpam-4867	68	4	c	c	PROPN
ejpam-4867	68	5	⊆	⊆	NUM
ejpam-4867	68	6	c⊥l	c⊥l	PROPN
ejpam-4867	68	7	.	.	PUNCT
ejpam-4867	69	1	similarly	similarly	ADV
ejpam-4867	69	2	,	,	PUNCT
ejpam-4867	69	3	c	c	PROPN
ejpam-4867	69	4	is	be	AUX
ejpam-4867	69	5	self	self	NOUN
ejpam-4867	69	6	-	-	PUNCT
ejpam-4867	69	7	orthogonal	orthogonal	ADJ
ejpam-4867	69	8	if	if	SCONJ
ejpam-4867	69	9	and	and	CCONJ
ejpam-4867	69	10	only	only	ADV
ejpam-4867	69	11	if	if	SCONJ
ejpam-4867	69	12	c	c	PROPN
ejpam-4867	69	13	⊆	⊆	NUM
ejpam-4867	69	14	c⊥r	c⊥r	NOUN
ejpam-4867	69	15	.	.	PUNCT
ejpam-4867	70	1	hence	hence	ADV
ejpam-4867	70	2	,	,	PUNCT
ejpam-4867	70	3	for	for	ADP
ejpam-4867	70	4	a	a	DET
ejpam-4867	70	5	self	self	NOUN
ejpam-4867	70	6	-	-	PUNCT
ejpam-4867	70	7	orthogonal	orthogonal	ADJ
ejpam-4867	70	8	code	code	NOUN
ejpam-4867	70	9	c	c	NOUN
ejpam-4867	70	10	,	,	PUNCT
ejpam-4867	70	11	it	it	PRON
ejpam-4867	70	12	satisfies	satisfy	VERB
ejpam-4867	70	13	that	that	SCONJ
ejpam-4867	70	14	c	c	PROPN
ejpam-4867	70	15	⊆	⊆	NUM
ejpam-4867	70	16	c⊥l	c⊥l	PROPN
ejpam-4867	70	17	∩	∩	NOUN
ejpam-4867	70	18	c⊥r	c⊥r	PROPN
ejpam-4867	70	19	.	.	PUNCT
ejpam-4867	71	1	an	an	DET
ejpam-4867	71	2	e−code	e−code	NOUN
ejpam-4867	71	3	of	of	ADP
ejpam-4867	71	4	length	length	NOUN
ejpam-4867	71	5	n	n	PROPN
ejpam-4867	71	6	is	be	AUX
ejpam-4867	71	7	quasi	quasi	ADJ
ejpam-4867	71	8	self	self	NOUN
ejpam-4867	71	9	-	-	PUNCT
ejpam-4867	71	10	dual	dual	ADJ
ejpam-4867	71	11	(	(	PUNCT
ejpam-4867	71	12	qsd	qsd	NOUN
ejpam-4867	71	13	for	for	ADP
ejpam-4867	71	14	short	short	ADJ
ejpam-4867	71	15	)	)	PUNCT
ejpam-4867	72	1	[	[	X
ejpam-4867	72	2	14	14	NUM
ejpam-4867	72	3	]	]	X
ejpam-4867	72	4	if	if	SCONJ
ejpam-4867	72	5	it	it	PRON
ejpam-4867	72	6	is	be	AUX
ejpam-4867	72	7	self	self	NOUN
ejpam-4867	72	8	-	-	PUNCT
ejpam-4867	72	9	orthogonal	orthogonal	ADJ
ejpam-4867	72	10	and	and	CCONJ
ejpam-4867	72	11	of	of	ADP
ejpam-4867	72	12	size	size	NOUN
ejpam-4867	72	13	2n	2n	NUM
ejpam-4867	72	14	.	.	PUNCT
ejpam-4867	73	1	a	a	DET
ejpam-4867	73	2	quasi	quasi	ADJ
ejpam-4867	73	3	-	-	ADJ
ejpam-4867	73	4	self	self	ADJ
ejpam-4867	73	5	dual	dual	ADJ
ejpam-4867	73	6	code	code	NOUN
ejpam-4867	73	7	is	be	AUX
ejpam-4867	73	8	type	type	NOUN
ejpam-4867	73	9	iv	iv	NUM
ejpam-4867	73	10	if	if	SCONJ
ejpam-4867	73	11	all	all	DET
ejpam-4867	73	12	its	its	PRON
ejpam-4867	73	13	codewords	codeword	NOUN
ejpam-4867	73	14	have	have	AUX
ejpam-4867	73	15	even	even	ADV
ejpam-4867	73	16	weight	weight	NOUN
ejpam-4867	73	17	[	[	X
ejpam-4867	73	18	5	5	NUM
ejpam-4867	73	19	]	]	PUNCT
ejpam-4867	73	20	.	.	PUNCT
ejpam-4867	74	1	3	3	X
ejpam-4867	74	2	.	.	X
ejpam-4867	75	1	some	some	DET
ejpam-4867	75	2	results	result	NOUN
ejpam-4867	75	3	in	in	ADP
ejpam-4867	75	4	linear	linear	ADJ
ejpam-4867	75	5	e	e	NOUN
ejpam-4867	75	6	-	-	NOUN
ejpam-4867	75	7	codes	code	NOUN
ejpam-4867	75	8	3.1	3.1	NUM
ejpam-4867	75	9	.	.	PUNCT
ejpam-4867	76	1	linear	linear	PROPN
ejpam-4867	76	2	e	e	NOUN
ejpam-4867	76	3	-	-	NOUN
ejpam-4867	76	4	codes	code	NOUN
ejpam-4867	76	5	definition	definition	NOUN
ejpam-4867	76	6	1	1	NUM
ejpam-4867	76	7	.	.	PUNCT
ejpam-4867	77	1	[	[	X
ejpam-4867	77	2	3	3	X
ejpam-4867	77	3	]	]	PUNCT
ejpam-4867	77	4	let	let	VERB
ejpam-4867	77	5	c	c	PRON
ejpam-4867	77	6	be	be	AUX
ejpam-4867	77	7	a	a	DET
ejpam-4867	77	8	linear	linear	ADJ
ejpam-4867	77	9	e	e	NOUN
ejpam-4867	77	10	-	-	NOUN
ejpam-4867	77	11	code	code	NOUN
ejpam-4867	77	12	.	.	PUNCT
ejpam-4867	78	1	then	then	ADV
ejpam-4867	78	2	c	c	PROPN
ejpam-4867	78	3	is	be	AUX
ejpam-4867	78	4	a	a	DET
ejpam-4867	78	5	type-(k1	type-(k1	ADJ
ejpam-4867	78	6	,	,	PUNCT
ejpam-4867	78	7	k2	k2	ADJ
ejpam-4867	78	8	)	)	PUNCT
ejpam-4867	78	9	code	code	NOUN
ejpam-4867	78	10	if	if	SCONJ
ejpam-4867	78	11	dim(res(c	dim(res(c	NOUN
ejpam-4867	78	12	)	)	PUNCT
ejpam-4867	78	13	)	)	PUNCT
ejpam-4867	79	1	=	=	SYM
ejpam-4867	79	2	k1	k1	NOUN
ejpam-4867	79	3	and	and	CCONJ
ejpam-4867	79	4	dim(tor(c	dim(tor(c	NOUN
ejpam-4867	79	5	)	)	PUNCT
ejpam-4867	79	6	)	)	PUNCT
ejpam-4867	80	1	=	=	SYM
ejpam-4867	80	2	k1	k1	PROPN
ejpam-4867	80	3	+	+	X
ejpam-4867	80	4	k2	k2	PROPN
ejpam-4867	80	5	.	.	PUNCT
ejpam-4867	81	1	j.	j.	PROPN
ejpam-4867	81	2	pilongo	pilongo	PROPN
ejpam-4867	81	3	,	,	PUNCT
ejpam-4867	81	4	l.	l.	PROPN
ejpam-4867	81	5	paleta	paleta	PROPN
ejpam-4867	81	6	,	,	PUNCT
ejpam-4867	81	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	81	8	/	/	SYM
ejpam-4867	81	9	eur	eur	PROPN
ejpam-4867	81	10	.	.	PUNCT
ejpam-4867	82	1	j.	j.	PROPN
ejpam-4867	82	2	pure	pure	PROPN
ejpam-4867	82	3	appl	appl	PROPN
ejpam-4867	82	4	.	.	PROPN
ejpam-4867	82	5	math	math	PROPN
ejpam-4867	82	6	,	,	PUNCT
ejpam-4867	82	7	17	17	NUM
ejpam-4867	82	8	(	(	PUNCT
ejpam-4867	82	9	2	2	NUM
ejpam-4867	82	10	)	)	PUNCT
ejpam-4867	82	11	(	(	PUNCT
ejpam-4867	82	12	2024	2024	NUM
ejpam-4867	82	13	)	)	PUNCT
ejpam-4867	82	14	,	,	PUNCT
ejpam-4867	82	15	1369	1369	NUM
ejpam-4867	82	16	-	-	SYM
ejpam-4867	82	17	1384	1384	NUM
ejpam-4867	82	18	1373	1373	NUM
ejpam-4867	82	19	theorem	theorem	NOUN
ejpam-4867	82	20	1	1	NUM
ejpam-4867	82	21	.	.	PUNCT
ejpam-4867	83	1	[	[	X
ejpam-4867	83	2	3	3	X
ejpam-4867	83	3	]	]	X
ejpam-4867	83	4	let	let	VERB
ejpam-4867	83	5	b	b	PRON
ejpam-4867	83	6	be	be	AUX
ejpam-4867	83	7	a	a	DET
ejpam-4867	83	8	self	self	NOUN
ejpam-4867	83	9	-	-	PUNCT
ejpam-4867	83	10	orthogonal	orthogonal	ADJ
ejpam-4867	83	11	binary	binary	NOUN
ejpam-4867	83	12	code	code	NOUN
ejpam-4867	83	13	of	of	ADP
ejpam-4867	83	14	length	length	NOUN
ejpam-4867	83	15	n.	n.	PROPN
ejpam-4867	83	16	the	the	DET
ejpam-4867	83	17	code	code	NOUN
ejpam-4867	83	18	c	c	NOUN
ejpam-4867	83	19	defined	define	VERB
ejpam-4867	83	20	by	by	ADP
ejpam-4867	83	21	the	the	DET
ejpam-4867	83	22	relation	relation	NOUN
ejpam-4867	83	23	c	c	NOUN
ejpam-4867	83	24	=	=	SYM
ejpam-4867	83	25	ab	ab	PROPN
ejpam-4867	83	26	+	+	NUM
ejpam-4867	83	27	cb⊥	cb⊥	PROPN
ejpam-4867	83	28	,	,	PUNCT
ejpam-4867	83	29	is	be	AUX
ejpam-4867	83	30	a	a	DET
ejpam-4867	83	31	quasi	quasi	NOUN
ejpam-4867	83	32	self	self	NOUN
ejpam-4867	83	33	-	-	PUNCT
ejpam-4867	83	34	dual	dual	ADJ
ejpam-4867	83	35	code	code	NOUN
ejpam-4867	83	36	.	.	PUNCT
ejpam-4867	84	1	its	its	PRON
ejpam-4867	84	2	residue	residue	NOUN
ejpam-4867	84	3	code	code	NOUN
ejpam-4867	84	4	is	be	AUX
ejpam-4867	84	5	b	b	NOUN
ejpam-4867	84	6	and	and	CCONJ
ejpam-4867	84	7	its	its	PRON
ejpam-4867	84	8	torsion	torsion	NOUN
ejpam-4867	84	9	code	code	NOUN
ejpam-4867	84	10	is	be	AUX
ejpam-4867	84	11	b⊥.	b⊥.	NOUN
ejpam-4867	84	12	corollary	corollary	ADJ
ejpam-4867	84	13	1	1	NUM
ejpam-4867	84	14	.	.	PUNCT
ejpam-4867	85	1	[	[	X
ejpam-4867	85	2	3	3	X
ejpam-4867	85	3	]	]	X
ejpam-4867	85	4	let	let	AUX
ejpam-4867	85	5	b	b	NOUN
ejpam-4867	85	6	and	and	CCONJ
ejpam-4867	85	7	b′	b′	NUM
ejpam-4867	85	8	be	be	VERB
ejpam-4867	85	9	a	a	DET
ejpam-4867	85	10	binary	binary	ADJ
ejpam-4867	85	11	code	code	NOUN
ejpam-4867	85	12	of	of	ADP
ejpam-4867	85	13	length	length	NOUN
ejpam-4867	85	14	n	n	PRON
ejpam-4867	85	15	such	such	ADJ
ejpam-4867	85	16	that	that	DET
ejpam-4867	85	17	b	b	PROPN
ejpam-4867	85	18	is	be	AUX
ejpam-4867	85	19	self	self	NOUN
ejpam-4867	85	20	-	-	PUNCT
ejpam-4867	85	21	orthogonal	orthogonal	ADJ
ejpam-4867	85	22	and	and	CCONJ
ejpam-4867	85	23	b	b	NOUN
ejpam-4867	85	24	⊆	⊆	NUM
ejpam-4867	85	25	b′.	b′.	NOUN
ejpam-4867	85	26	then	then	ADV
ejpam-4867	85	27	c	c	PROPN
ejpam-4867	85	28	is	be	AUX
ejpam-4867	85	29	a	a	DET
ejpam-4867	85	30	linear	linear	ADJ
ejpam-4867	85	31	e	e	NOUN
ejpam-4867	85	32	-	-	NOUN
ejpam-4867	85	33	code	code	NOUN
ejpam-4867	85	34	defined	define	VERB
ejpam-4867	85	35	by	by	ADP
ejpam-4867	85	36	the	the	DET
ejpam-4867	85	37	relation	relation	NOUN
ejpam-4867	85	38	c	c	NOUN
ejpam-4867	85	39	=	=	SYM
ejpam-4867	85	40	ab	ab	PROPN
ejpam-4867	85	41	+	+	CCONJ
ejpam-4867	85	42	cb′.	cb′.	PROPN
ejpam-4867	85	43	4	4	X
ejpam-4867	86	1	.	.	X
ejpam-4867	86	2	results	result	NOUN
ejpam-4867	86	3	in	in	ADP
ejpam-4867	86	4	(	(	PUNCT
ejpam-4867	86	5	k1	k1	NOUN
ejpam-4867	86	6	,	,	PUNCT
ejpam-4867	86	7	k2	k2	ADJ
ejpam-4867	86	8	)	)	PUNCT
ejpam-4867	86	9	e	e	NOUN
ejpam-4867	86	10	-	-	NOUN
ejpam-4867	86	11	torsion	torsion	NOUN
ejpam-4867	86	12	graph	graph	NOUN
ejpam-4867	86	13	of	of	ADP
ejpam-4867	86	14	an	an	DET
ejpam-4867	86	15	e	e	NOUN
ejpam-4867	86	16	-	-	NOUN
ejpam-4867	86	17	code	code	ADJ
ejpam-4867	86	18	definition	definition	NOUN
ejpam-4867	86	19	2	2	NUM
ejpam-4867	86	20	.	.	PUNCT
ejpam-4867	87	1	let	let	VERB
ejpam-4867	87	2	c	c	PRON
ejpam-4867	87	3	be	be	AUX
ejpam-4867	87	4	a	a	DET
ejpam-4867	87	5	linear	linear	ADJ
ejpam-4867	87	6	e	e	NOUN
ejpam-4867	87	7	-	-	NOUN
ejpam-4867	87	8	code	code	NOUN
ejpam-4867	87	9	and	and	CCONJ
ejpam-4867	87	10	b′	b′	NUM
ejpam-4867	87	11	be	be	AUX
ejpam-4867	87	12	the	the	DET
ejpam-4867	87	13	torsion	torsion	NOUN
ejpam-4867	87	14	code	code	NOUN
ejpam-4867	87	15	of	of	ADP
ejpam-4867	87	16	c.	c.	PROPN
ejpam-4867	87	17	then	then	ADV
ejpam-4867	87	18	the	the	DET
ejpam-4867	87	19	simple	simple	ADJ
ejpam-4867	87	20	graph	graph	NOUN
ejpam-4867	87	21	gec	gec	NOUN
ejpam-4867	87	22	such	such	ADJ
ejpam-4867	87	23	that	that	SCONJ
ejpam-4867	87	24	the	the	DET
ejpam-4867	87	25	vertex	vertex	NOUN
ejpam-4867	87	26	set	set	VERB
ejpam-4867	87	27	v	v	NOUN
ejpam-4867	87	28	(	(	PUNCT
ejpam-4867	87	29	gec	gec	NOUN
ejpam-4867	87	30	)	)	PUNCT
ejpam-4867	87	31	=	=	PUNCT
ejpam-4867	88	1	b′	b′	NUM
ejpam-4867	88	2	and	and	CCONJ
ejpam-4867	88	3	xy	xy	PROPN
ejpam-4867	88	4	∈	∈	PROPN
ejpam-4867	88	5	e(gec	e(gec	PROPN
ejpam-4867	88	6	)	)	PUNCT
ejpam-4867	88	7	,	,	PUNCT
ejpam-4867	88	8	the	the	DET
ejpam-4867	88	9	edge	edge	NOUN
ejpam-4867	88	10	set	set	VERB
ejpam-4867	88	11	and	and	CCONJ
ejpam-4867	88	12	x	x	SYM
ejpam-4867	88	13	̸=	̸=	PROPN
ejpam-4867	88	14	y	y	NUM
ejpam-4867	88	15	,	,	PUNCT
ejpam-4867	88	16	if	if	SCONJ
ejpam-4867	88	17	ax+	ax+	ADJ
ejpam-4867	88	18	cy	cy	PROPN
ejpam-4867	88	19	∈	∈	PROPN
ejpam-4867	88	20	c	c	PROPN
ejpam-4867	88	21	or	or	CCONJ
ejpam-4867	88	22	ay	ay	NOUN
ejpam-4867	88	23	+	+	CCONJ
ejpam-4867	88	24	cx	cx	PROPN
ejpam-4867	88	25	∈	∈	PROPN
ejpam-4867	88	26	c	c	NOUN
ejpam-4867	88	27	,	,	PUNCT
ejpam-4867	88	28	is	be	AUX
ejpam-4867	88	29	called	call	VERB
ejpam-4867	88	30	the	the	DET
ejpam-4867	88	31	(	(	PUNCT
ejpam-4867	88	32	k1	k1	NOUN
ejpam-4867	88	33	,	,	PUNCT
ejpam-4867	88	34	k2	k2	ADJ
ejpam-4867	88	35	)	)	PUNCT
ejpam-4867	88	36	e	e	NOUN
ejpam-4867	88	37	-	-	NOUN
ejpam-4867	88	38	torsion	torsion	NOUN
ejpam-4867	88	39	graph	graph	NOUN
ejpam-4867	88	40	of	of	ADP
ejpam-4867	88	41	c.	c.	NOUN
ejpam-4867	88	42	to	to	PART
ejpam-4867	88	43	avoid	avoid	VERB
ejpam-4867	88	44	the	the	DET
ejpam-4867	88	45	confusion	confusion	NOUN
ejpam-4867	88	46	to	to	ADP
ejpam-4867	88	47	whether	whether	SCONJ
ejpam-4867	88	48	the	the	DET
ejpam-4867	88	49	binary	binary	PROPN
ejpam-4867	88	50	code	code	PROPN
ejpam-4867	88	51	is	be	AUX
ejpam-4867	88	52	viewed	view	VERB
ejpam-4867	88	53	as	as	ADP
ejpam-4867	88	54	a	a	DET
ejpam-4867	88	55	codeword	codeword	NOUN
ejpam-4867	88	56	in	in	ADP
ejpam-4867	88	57	tor(c	tor(c	PROPN
ejpam-4867	88	58	)	)	PUNCT
ejpam-4867	88	59	or	or	CCONJ
ejpam-4867	88	60	vertex	vertex	NOUN
ejpam-4867	88	61	in	in	ADP
ejpam-4867	88	62	gec	gec	NOUN
ejpam-4867	88	63	,	,	PUNCT
ejpam-4867	88	64	we	we	PRON
ejpam-4867	88	65	denote	denote	VERB
ejpam-4867	88	66	the	the	DET
ejpam-4867	88	67	vertex	vertex	NOUN
ejpam-4867	88	68	x̂	x̂	NOUN
ejpam-4867	89	1	which	which	PRON
ejpam-4867	89	2	corresponds	correspond	VERB
ejpam-4867	89	3	to	to	ADP
ejpam-4867	89	4	the	the	DET
ejpam-4867	89	5	codeword	codeword	NOUN
ejpam-4867	89	6	x.	x.	NOUN
ejpam-4867	89	7	this	this	PRON
ejpam-4867	89	8	means	mean	VERB
ejpam-4867	89	9	that	that	SCONJ
ejpam-4867	89	10	if	if	SCONJ
ejpam-4867	89	11	x	x	PROPN
ejpam-4867	89	12	∈	∈	PROPN
ejpam-4867	89	13	tor(c	tor(c	PROPN
ejpam-4867	89	14	)	)	PUNCT
ejpam-4867	89	15	,	,	PUNCT
ejpam-4867	89	16	then	then	ADV
ejpam-4867	89	17	x̂	x̂	PUNCT
ejpam-4867	89	18	∈	∈	PROPN
ejpam-4867	89	19	v	v	PROPN
ejpam-4867	89	20	(	(	PUNCT
ejpam-4867	89	21	gec	gec	NOUN
ejpam-4867	89	22	)	)	PUNCT
ejpam-4867	89	23	.	.	PUNCT
ejpam-4867	90	1	example	example	NOUN
ejpam-4867	91	1	1	1	X
ejpam-4867	91	2	.	.	PUNCT
ejpam-4867	91	3	let	let	VERB
ejpam-4867	91	4	c	c	NOUN
ejpam-4867	91	5	=	=	SYM
ejpam-4867	91	6	ab	ab	PROPN
ejpam-4867	92	1	+	+	CCONJ
ejpam-4867	92	2	cb′	cb′	PROPN
ejpam-4867	92	3	where	where	SCONJ
ejpam-4867	92	4	b	b	NOUN
ejpam-4867	92	5	=	=	SYM
ejpam-4867	92	6	⟨1100⟩	⟨1100⟩	PROPN
ejpam-4867	92	7	and	and	CCONJ
ejpam-4867	92	8	b′	b′	NUM
ejpam-4867	92	9	=	=	NOUN
ejpam-4867	92	10	⟨1100	⟨1100	PROPN
ejpam-4867	92	11	,	,	PUNCT
ejpam-4867	92	12	0011⟩	0011⟩	PROPN
ejpam-4867	92	13	.	.	PUNCT
ejpam-4867	93	1	this	this	PRON
ejpam-4867	93	2	means	mean	VERB
ejpam-4867	93	3	that	that	SCONJ
ejpam-4867	93	4	v	v	X
ejpam-4867	93	5	(	(	PUNCT
ejpam-4867	93	6	gec	gec	NOUN
ejpam-4867	93	7	)	)	PUNCT
ejpam-4867	93	8	=	=	PRON
ejpam-4867	93	9	{	{	PUNCT
ejpam-4867	93	10	0̂000	0̂000	NUM
ejpam-4867	93	11	,	,	PUNCT
ejpam-4867	93	12	1̂100	1̂100	NUM
ejpam-4867	93	13	,	,	PUNCT
ejpam-4867	93	14	0̂011	0̂011	NUM
ejpam-4867	93	15	,	,	PUNCT
ejpam-4867	93	16	1̂111	1̂111	NUM
ejpam-4867	93	17	}	}	PUNCT
ejpam-4867	93	18	.	.	PUNCT
ejpam-4867	94	1	by	by	ADP
ejpam-4867	94	2	computation	computation	NOUN
ejpam-4867	94	3	,	,	PUNCT
ejpam-4867	94	4	we	we	PRON
ejpam-4867	94	5	get	get	VERB
ejpam-4867	94	6	e(gec	e(gec	NOUN
ejpam-4867	94	7	)	)	PUNCT
ejpam-4867	94	8	=	=	PRON
ejpam-4867	94	9	{	{	PUNCT
ejpam-4867	94	10	(	(	PUNCT
ejpam-4867	94	11	0̂000	0̂000	NUM
ejpam-4867	94	12	,	,	PUNCT
ejpam-4867	94	13	1̂100	1̂100	NUM
ejpam-4867	94	14	)	)	PUNCT
ejpam-4867	94	15	,	,	PUNCT
ejpam-4867	94	16	(	(	PUNCT
ejpam-4867	94	17	0̂000	0̂000	NUM
ejpam-4867	94	18	,	,	PUNCT
ejpam-4867	94	19	0̂011	0̂011	NUM
ejpam-4867	94	20	)	)	PUNCT
ejpam-4867	94	21	,	,	PUNCT
ejpam-4867	94	22	(	(	PUNCT
ejpam-4867	94	23	0̂000	0̂000	NUM
ejpam-4867	94	24	,	,	PUNCT
ejpam-4867	94	25	1̂111	1̂111	NUM
ejpam-4867	94	26	)	)	PUNCT
ejpam-4867	94	27	,	,	PUNCT
ejpam-4867	94	28	(	(	PUNCT
ejpam-4867	94	29	1̂100	1̂100	NUM
ejpam-4867	94	30	,	,	PUNCT
ejpam-4867	94	31	0̂011	0̂011	NUM
ejpam-4867	94	32	)	)	PUNCT
ejpam-4867	94	33	,	,	PUNCT
ejpam-4867	94	34	(	(	PUNCT
ejpam-4867	94	35	1̂100	1̂100	NUM
ejpam-4867	94	36	,	,	PUNCT
ejpam-4867	94	37	1̂111	1̂111	NUM
ejpam-4867	94	38	)	)	PUNCT
ejpam-4867	94	39	}	}	PUNCT
ejpam-4867	94	40	.	.	PUNCT
ejpam-4867	95	1	thus	thus	ADV
ejpam-4867	95	2	,	,	PUNCT
ejpam-4867	95	3	the	the	DET
ejpam-4867	95	4	(	(	PUNCT
ejpam-4867	95	5	k1	k1	NOUN
ejpam-4867	95	6	,	,	PUNCT
ejpam-4867	95	7	k2)-torsion	k2)-torsion	NOUN
ejpam-4867	95	8	graph	graph	NOUN
ejpam-4867	95	9	of	of	ADP
ejpam-4867	95	10	c	c	PROPN
ejpam-4867	95	11	,	,	PUNCT
ejpam-4867	95	12	gec	gec	PROPN
ejpam-4867	95	13	,	,	PUNCT
ejpam-4867	95	14	is	be	AUX
ejpam-4867	95	15	illustrated	illustrate	VERB
ejpam-4867	95	16	in	in	ADP
ejpam-4867	95	17	figure	figure	NOUN
ejpam-4867	95	18	1	1	NUM
ejpam-4867	95	19	.	.	PUNCT
ejpam-4867	96	1	j.	j.	PROPN
ejpam-4867	96	2	pilongo	pilongo	PROPN
ejpam-4867	96	3	,	,	PUNCT
ejpam-4867	96	4	l.	l.	PROPN
ejpam-4867	96	5	paleta	paleta	PROPN
ejpam-4867	96	6	,	,	PUNCT
ejpam-4867	96	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	96	8	/	/	SYM
ejpam-4867	96	9	eur	eur	PROPN
ejpam-4867	96	10	.	.	PUNCT
ejpam-4867	97	1	j.	j.	PROPN
ejpam-4867	97	2	pure	pure	PROPN
ejpam-4867	97	3	appl	appl	PROPN
ejpam-4867	97	4	.	.	PROPN
ejpam-4867	97	5	math	math	PROPN
ejpam-4867	97	6	,	,	PUNCT
ejpam-4867	97	7	17	17	NUM
ejpam-4867	97	8	(	(	PUNCT
ejpam-4867	97	9	2	2	NUM
ejpam-4867	97	10	)	)	PUNCT
ejpam-4867	97	11	(	(	PUNCT
ejpam-4867	97	12	2024	2024	NUM
ejpam-4867	97	13	)	)	PUNCT
ejpam-4867	97	14	,	,	PUNCT
ejpam-4867	97	15	1369	1369	NUM
ejpam-4867	97	16	-	-	SYM
ejpam-4867	97	17	1384	1384	NUM
ejpam-4867	97	18	1374	1374	NUM
ejpam-4867	97	19	figure	figure	NOUN
ejpam-4867	97	20	1	1	NUM
ejpam-4867	97	21	:	:	PUNCT
ejpam-4867	97	22	(	(	PUNCT
ejpam-4867	97	23	k1	k1	X
ejpam-4867	97	24	,	,	PUNCT
ejpam-4867	97	25	k2	k2	ADJ
ejpam-4867	97	26	)	)	PUNCT
ejpam-4867	98	1	e	e	NOUN
ejpam-4867	98	2	-	-	NOUN
ejpam-4867	98	3	torsion	torsion	NOUN
ejpam-4867	98	4	graph	graph	NOUN
ejpam-4867	98	5	of	of	ADP
ejpam-4867	98	6	c	c	NOUN
ejpam-4867	98	7	theorem	theorem	NOUN
ejpam-4867	98	8	2	2	NUM
ejpam-4867	98	9	.	.	PUNCT
ejpam-4867	99	1	if	if	SCONJ
ejpam-4867	99	2	c	c	PROPN
ejpam-4867	99	3	is	be	AUX
ejpam-4867	99	4	a	a	DET
ejpam-4867	99	5	type-(k1	type-(k1	ADJ
ejpam-4867	99	6	,	,	PUNCT
ejpam-4867	99	7	k2	k2	NOUN
ejpam-4867	99	8	)	)	PUNCT
ejpam-4867	99	9	of	of	ADP
ejpam-4867	99	10	an	an	DET
ejpam-4867	99	11	e	e	NOUN
ejpam-4867	99	12	-	-	NOUN
ejpam-4867	99	13	code	code	NOUN
ejpam-4867	99	14	,	,	PUNCT
ejpam-4867	99	15	then	then	ADV
ejpam-4867	99	16	|v	|v	PROPN
ejpam-4867	99	17	(	(	PUNCT
ejpam-4867	99	18	gec)|	gec)|	NOUN
ejpam-4867	99	19	=	=	SYM
ejpam-4867	99	20	2k1+k2	2k1+k2	NUM
ejpam-4867	99	21	and	and	CCONJ
ejpam-4867	99	22	|e(gec)|	|e(gec)|	PROPN
ejpam-4867	100	1	=	=	SYM
ejpam-4867	100	2	2k1∑	2k1∑	NUM
ejpam-4867	100	3	i=1	i=1	PRON
ejpam-4867	100	4	2k1+k2	2k1+k2	NUM
ejpam-4867	101	1	−	−	NOUN
ejpam-4867	102	1	i.	i.	NOUN
ejpam-4867	102	2	proof	proof	NOUN
ejpam-4867	102	3	.	.	PUNCT
ejpam-4867	103	1	the	the	DET
ejpam-4867	103	2	equation	equation	NOUN
ejpam-4867	103	3	|v	|v	NOUN
ejpam-4867	103	4	(	(	PUNCT
ejpam-4867	103	5	gec)|	gec)|	NOUN
ejpam-4867	103	6	=	=	SYM
ejpam-4867	103	7	2k1+k2	2k1+k2	NUM
ejpam-4867	103	8	follows	follow	VERB
ejpam-4867	103	9	from	from	ADP
ejpam-4867	103	10	the	the	DET
ejpam-4867	103	11	fact	fact	NOUN
ejpam-4867	103	12	that	that	SCONJ
ejpam-4867	103	13	the	the	DET
ejpam-4867	103	14	torsion	torsion	NOUN
ejpam-4867	103	15	of	of	ADP
ejpam-4867	103	16	a	a	PRON
ejpam-4867	103	17	type-(k1	type-(k1	ADJ
ejpam-4867	103	18	,	,	PUNCT
ejpam-4867	103	19	k2	k2	ADJ
ejpam-4867	103	20	)	)	PUNCT
ejpam-4867	103	21	e	e	NOUN
ejpam-4867	103	22	-	-	NOUN
ejpam-4867	103	23	code	code	NOUN
ejpam-4867	103	24	has	have	AUX
ejpam-4867	103	25	dimension	dimension	NOUN
ejpam-4867	103	26	k1	k1	NOUN
ejpam-4867	103	27	+	+	X
ejpam-4867	103	28	k2	k2	ADJ
ejpam-4867	103	29	.	.	PUNCT
ejpam-4867	104	1	on	on	ADP
ejpam-4867	104	2	the	the	DET
ejpam-4867	104	3	other	other	ADJ
ejpam-4867	104	4	hand	hand	NOUN
ejpam-4867	104	5	,	,	PUNCT
ejpam-4867	104	6	from	from	ADP
ejpam-4867	104	7	the	the	DET
ejpam-4867	104	8	definition	definition	NOUN
ejpam-4867	104	9	of	of	ADP
ejpam-4867	104	10	e(gec	e(gec	PROPN
ejpam-4867	104	11	)	)	PUNCT
ejpam-4867	104	12	,	,	PUNCT
ejpam-4867	104	13	e(gec	e(gec	PROPN
ejpam-4867	104	14	)	)	PUNCT
ejpam-4867	104	15	=	=	PRON
ejpam-4867	104	16	{	{	PUNCT
ejpam-4867	104	17	(	(	PUNCT
ejpam-4867	104	18	x̂	x̂	NOUN
ejpam-4867	104	19	,	,	PUNCT
ejpam-4867	104	20	ŷ	ŷ	NUM
ejpam-4867	104	21	)	)	PUNCT
ejpam-4867	104	22	:	:	PUNCT
ejpam-4867	105	1	x	x	X
ejpam-4867	105	2	∈	∈	PROPN
ejpam-4867	105	3	res(c	res(c	PROPN
ejpam-4867	105	4	)	)	PUNCT
ejpam-4867	105	5	,	,	PUNCT
ejpam-4867	105	6	y	y	PROPN
ejpam-4867	105	7	∈	∈	PROPN
ejpam-4867	105	8	tor(c	tor(c	PROPN
ejpam-4867	105	9	)	)	PUNCT
ejpam-4867	105	10	}	}	PUNCT
ejpam-4867	105	11	,	,	PUNCT
ejpam-4867	105	12	that	that	ADV
ejpam-4867	105	13	is	is	ADV
ejpam-4867	105	14	,	,	PUNCT
ejpam-4867	105	15	each	each	PRON
ejpam-4867	105	16	of	of	ADP
ejpam-4867	105	17	the	the	DET
ejpam-4867	105	18	2k1	2k1	NUM
ejpam-4867	105	19	elements	element	NOUN
ejpam-4867	105	20	of	of	ADP
ejpam-4867	105	21	the	the	DET
ejpam-4867	105	22	residue	residue	NOUN
ejpam-4867	105	23	will	will	AUX
ejpam-4867	105	24	be	be	AUX
ejpam-4867	105	25	connected	connect	VERB
ejpam-4867	105	26	by	by	ADP
ejpam-4867	105	27	an	an	DET
ejpam-4867	105	28	edge	edge	NOUN
ejpam-4867	105	29	to	to	ADP
ejpam-4867	105	30	the	the	DET
ejpam-4867	105	31	2k1+k2	2k1+k2	NUM
ejpam-4867	105	32	−	−	NOUN
ejpam-4867	105	33	1	1	NUM
ejpam-4867	105	34	elements	element	NOUN
ejpam-4867	105	35	of	of	ADP
ejpam-4867	105	36	the	the	DET
ejpam-4867	105	37	torsion	torsion	NOUN
ejpam-4867	105	38	.	.	PUNCT
ejpam-4867	106	1	we	we	PRON
ejpam-4867	106	2	can	can	AUX
ejpam-4867	106	3	enumerate	enumerate	VERB
ejpam-4867	106	4	the	the	DET
ejpam-4867	106	5	edges	edge	NOUN
ejpam-4867	106	6	by	by	ADP
ejpam-4867	106	7	starting	start	VERB
ejpam-4867	106	8	at	at	ADP
ejpam-4867	106	9	an	an	DET
ejpam-4867	106	10	element	element	NOUN
ejpam-4867	106	11	in	in	ADP
ejpam-4867	106	12	the	the	DET
ejpam-4867	106	13	residue	residue	NOUN
ejpam-4867	106	14	with	with	ADP
ejpam-4867	106	15	2k1+k2	2k1+k2	NUM
ejpam-4867	106	16	−	−	NUM
ejpam-4867	106	17	1	1	NUM
ejpam-4867	106	18	edges	edge	NOUN
ejpam-4867	106	19	containing	contain	VERB
ejpam-4867	106	20	that	that	DET
ejpam-4867	106	21	element	element	NOUN
ejpam-4867	106	22	,	,	PUNCT
ejpam-4867	106	23	then	then	ADV
ejpam-4867	106	24	if	if	SCONJ
ejpam-4867	106	25	there	there	PRON
ejpam-4867	106	26	is	be	VERB
ejpam-4867	106	27	another	another	DET
ejpam-4867	106	28	element	element	NOUN
ejpam-4867	106	29	of	of	ADP
ejpam-4867	106	30	the	the	DET
ejpam-4867	106	31	residue	residue	NOUN
ejpam-4867	106	32	,	,	PUNCT
ejpam-4867	106	33	we	we	PRON
ejpam-4867	106	34	will	will	AUX
ejpam-4867	106	35	enumerate	enumerate	VERB
ejpam-4867	106	36	the	the	DET
ejpam-4867	106	37	2k1+k2	2k1+k2	NUM
ejpam-4867	106	38	−	−	NOUN
ejpam-4867	106	39	2	2	NUM
ejpam-4867	106	40	edges	edge	NOUN
ejpam-4867	106	41	containing	contain	VERB
ejpam-4867	106	42	the	the	DET
ejpam-4867	106	43	second	second	ADJ
ejpam-4867	106	44	element	element	NOUN
ejpam-4867	106	45	,	,	PUNCT
ejpam-4867	106	46	since	since	SCONJ
ejpam-4867	106	47	there	there	PRON
ejpam-4867	106	48	is	be	VERB
ejpam-4867	106	49	one	one	NUM
ejpam-4867	106	50	edge	edge	NOUN
ejpam-4867	106	51	common	common	ADJ
ejpam-4867	106	52	to	to	ADP
ejpam-4867	106	53	the	the	DET
ejpam-4867	106	54	set	set	NOUN
ejpam-4867	106	55	of	of	ADP
ejpam-4867	106	56	edges	edge	NOUN
ejpam-4867	106	57	containing	contain	VERB
ejpam-4867	106	58	the	the	DET
ejpam-4867	106	59	first	first	ADJ
ejpam-4867	106	60	element	element	NOUN
ejpam-4867	106	61	and	and	CCONJ
ejpam-4867	106	62	set	set	NOUN
ejpam-4867	106	63	of	of	ADP
ejpam-4867	106	64	edges	edge	NOUN
ejpam-4867	106	65	containing	contain	VERB
ejpam-4867	106	66	the	the	DET
ejpam-4867	106	67	second	second	ADJ
ejpam-4867	106	68	element	element	NOUN
ejpam-4867	106	69	,	,	PUNCT
ejpam-4867	106	70	hence	hence	ADV
ejpam-4867	106	71	the	the	DET
ejpam-4867	106	72	second	second	ADJ
ejpam-4867	106	73	set	set	NOUN
ejpam-4867	106	74	of	of	ADP
ejpam-4867	106	75	edges	edge	NOUN
ejpam-4867	106	76	is	be	AUX
ejpam-4867	106	77	1	1	NUM
ejpam-4867	106	78	less	less	ADJ
ejpam-4867	106	79	than	than	ADP
ejpam-4867	106	80	the	the	DET
ejpam-4867	106	81	previous	previous	ADJ
ejpam-4867	106	82	set	set	NOUN
ejpam-4867	106	83	of	of	ADP
ejpam-4867	106	84	edges	edge	NOUN
ejpam-4867	106	85	.	.	PUNCT
ejpam-4867	107	1	we	we	PRON
ejpam-4867	107	2	continue	continue	VERB
ejpam-4867	107	3	the	the	DET
ejpam-4867	107	4	process	process	NOUN
ejpam-4867	107	5	by	by	ADP
ejpam-4867	107	6	subtracting	subtract	VERB
ejpam-4867	107	7	1	1	NUM
ejpam-4867	107	8	from	from	ADP
ejpam-4867	107	9	the	the	DET
ejpam-4867	107	10	number	number	NOUN
ejpam-4867	107	11	of	of	ADP
ejpam-4867	107	12	the	the	DET
ejpam-4867	107	13	previous	previous	ADJ
ejpam-4867	107	14	set	set	NOUN
ejpam-4867	107	15	of	of	ADP
ejpam-4867	107	16	edges	edge	NOUN
ejpam-4867	107	17	.	.	PUNCT
ejpam-4867	108	1	using	use	VERB
ejpam-4867	108	2	this	this	DET
ejpam-4867	108	3	algorithm	algorithm	NOUN
ejpam-4867	108	4	,	,	PUNCT
ejpam-4867	108	5	the	the	DET
ejpam-4867	108	6	number	number	NOUN
ejpam-4867	108	7	of	of	ADP
ejpam-4867	108	8	distinct	distinct	ADJ
ejpam-4867	108	9	pairs	pair	NOUN
ejpam-4867	108	10	would	would	AUX
ejpam-4867	108	11	be	be	AUX
ejpam-4867	108	12	2k1∑	2k1∑	NUM
ejpam-4867	108	13	i=1	i=1	PROPN
ejpam-4867	108	14	2k1+k2	2k1+k2	NUM
ejpam-4867	109	1	−	−	PROPN
ejpam-4867	109	2	i.	i.	PROPN
ejpam-4867	109	3	■	■	PUNCT
ejpam-4867	109	4	j.	j.	PROPN
ejpam-4867	109	5	pilongo	pilongo	PROPN
ejpam-4867	109	6	,	,	PUNCT
ejpam-4867	109	7	l.	l.	PROPN
ejpam-4867	109	8	paleta	paleta	PROPN
ejpam-4867	109	9	,	,	PUNCT
ejpam-4867	109	10	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	109	11	/	/	SYM
ejpam-4867	109	12	eur	eur	PROPN
ejpam-4867	109	13	.	.	PUNCT
ejpam-4867	110	1	j.	j.	PROPN
ejpam-4867	110	2	pure	pure	PROPN
ejpam-4867	110	3	appl	appl	PROPN
ejpam-4867	110	4	.	.	PROPN
ejpam-4867	110	5	math	math	PROPN
ejpam-4867	110	6	,	,	PUNCT
ejpam-4867	110	7	17	17	NUM
ejpam-4867	110	8	(	(	PUNCT
ejpam-4867	110	9	2	2	NUM
ejpam-4867	110	10	)	)	PUNCT
ejpam-4867	110	11	(	(	PUNCT
ejpam-4867	110	12	2024	2024	NUM
ejpam-4867	110	13	)	)	PUNCT
ejpam-4867	110	14	,	,	PUNCT
ejpam-4867	110	15	1369	1369	NUM
ejpam-4867	110	16	-	-	SYM
ejpam-4867	110	17	1384	1384	NUM
ejpam-4867	110	18	1375	1375	NUM
ejpam-4867	110	19	corollary	corollary	NOUN
ejpam-4867	110	20	2	2	NUM
ejpam-4867	110	21	.	.	PUNCT
ejpam-4867	111	1	let	let	VERB
ejpam-4867	111	2	x̂	x̂	PUNCT
ejpam-4867	111	3	∈	∈	PROPN
ejpam-4867	111	4	v	v	PROPN
ejpam-4867	111	5	(	(	PUNCT
ejpam-4867	111	6	gec	gec	NOUN
ejpam-4867	111	7	)	)	PUNCT
ejpam-4867	111	8	.	.	PUNCT
ejpam-4867	112	1	if	if	SCONJ
ejpam-4867	112	2	x	x	SYM
ejpam-4867	112	3	∈	∈	PROPN
ejpam-4867	112	4	res(c	res(c	PROPN
ejpam-4867	112	5	)	)	PUNCT
ejpam-4867	112	6	,	,	PUNCT
ejpam-4867	112	7	then	then	ADV
ejpam-4867	112	8	deg(x̂	deg(x̂	PROPN
ejpam-4867	112	9	)	)	PUNCT
ejpam-4867	112	10	=	=	PUNCT
ejpam-4867	113	1	2k1+k2	2k1+k2	NUM
ejpam-4867	113	2	−	−	NOUN
ejpam-4867	113	3	1	1	X
ejpam-4867	113	4	.	.	PUNCT
ejpam-4867	114	1	if	if	SCONJ
ejpam-4867	114	2	x	x	PRON
ejpam-4867	114	3	/∈	/∈	PUNCT
ejpam-4867	114	4	res(c	res(c	ADJ
ejpam-4867	114	5	)	)	PUNCT
ejpam-4867	114	6	,	,	PUNCT
ejpam-4867	114	7	then	then	ADV
ejpam-4867	114	8	deg(x̂	deg(x̂	PROPN
ejpam-4867	114	9	)	)	PUNCT
ejpam-4867	114	10	=	=	SYM
ejpam-4867	114	11	2k1	2k1	NUM
ejpam-4867	114	12	.	.	PUNCT
ejpam-4867	115	1	proof	proof	NOUN
ejpam-4867	115	2	.	.	PUNCT
ejpam-4867	116	1	the	the	DET
ejpam-4867	116	2	proof	proof	NOUN
ejpam-4867	116	3	follows	follow	VERB
ejpam-4867	116	4	from	from	ADP
ejpam-4867	116	5	theorem	theorem	ADJ
ejpam-4867	116	6	2	2	NUM
ejpam-4867	116	7	.	.	PUNCT
ejpam-4867	117	1	■	■	PUNCT
ejpam-4867	117	2	corollary	corollary	ADJ
ejpam-4867	117	3	3	3	X
ejpam-4867	117	4	.	.	PUNCT
ejpam-4867	118	1	if	if	SCONJ
ejpam-4867	118	2	c	c	PROPN
ejpam-4867	118	3	is	be	AUX
ejpam-4867	118	4	a	a	DET
ejpam-4867	118	5	type-(k1	type-(k1	ADJ
ejpam-4867	118	6	,	,	PUNCT
ejpam-4867	118	7	k2	k2	ADJ
ejpam-4867	118	8	)	)	PUNCT
ejpam-4867	118	9	e	e	NOUN
ejpam-4867	118	10	-	-	NOUN
ejpam-4867	118	11	code	code	NOUN
ejpam-4867	118	12	,	,	PUNCT
ejpam-4867	118	13	then	then	ADV
ejpam-4867	118	14	|e(gec)|	|e(gec)|	PROPN
ejpam-4867	119	1	=	=	SYM
ejpam-4867	119	2	22k1+k2	22k1+k2	NUM
ejpam-4867	119	3	−	−	NOUN
ejpam-4867	119	4	22k1−1	22k1−1	NUM
ejpam-4867	119	5	−	−	PROPN
ejpam-4867	119	6	2k1−1	2k1−1	NUM
ejpam-4867	119	7	.	.	PUNCT
ejpam-4867	120	1	proof	proof	NOUN
ejpam-4867	120	2	.	.	PUNCT
ejpam-4867	121	1	the	the	DET
ejpam-4867	121	2	proof	proof	NOUN
ejpam-4867	121	3	follows	follow	VERB
ejpam-4867	121	4	directly	directly	ADV
ejpam-4867	121	5	from	from	ADP
ejpam-4867	121	6	corollary	corollary	ADJ
ejpam-4867	121	7	2	2	NUM
ejpam-4867	121	8	.	.	PUNCT
ejpam-4867	122	1	■	■	PUNCT
ejpam-4867	122	2	lemma	lemma	PROPN
ejpam-4867	122	3	1	1	NUM
ejpam-4867	122	4	.	.	PUNCT
ejpam-4867	122	5	r(gec	r(gec	NOUN
ejpam-4867	122	6	)	)	PUNCT
ejpam-4867	122	7	=	=	SYM
ejpam-4867	122	8	1	1	X
ejpam-4867	122	9	.	.	PUNCT
ejpam-4867	123	1	proof	proof	NOUN
ejpam-4867	123	2	.	.	PUNCT
ejpam-4867	124	1	if	if	SCONJ
ejpam-4867	124	2	x	x	SYM
ejpam-4867	124	3	∈	∈	PROPN
ejpam-4867	124	4	res(c	res(c	PROPN
ejpam-4867	124	5	)	)	PUNCT
ejpam-4867	124	6	,	,	PUNCT
ejpam-4867	124	7	then	then	ADV
ejpam-4867	124	8	the	the	DET
ejpam-4867	124	9	eccentricity	eccentricity	NOUN
ejpam-4867	124	10	of	of	ADP
ejpam-4867	124	11	x̂	x̂	PROPN
ejpam-4867	124	12	is	be	AUX
ejpam-4867	124	13	1	1	NUM
ejpam-4867	124	14	since	since	SCONJ
ejpam-4867	124	15	x̂	x̂	NUM
ejpam-4867	124	16	is	be	AUX
ejpam-4867	124	17	connected	connect	VERB
ejpam-4867	124	18	by	by	ADP
ejpam-4867	124	19	an	an	DET
ejpam-4867	124	20	edge	edge	NOUN
ejpam-4867	124	21	to	to	ADP
ejpam-4867	124	22	every	every	DET
ejpam-4867	124	23	vertex	vertex	NOUN
ejpam-4867	124	24	in	in	ADP
ejpam-4867	124	25	gec	gec	NOUN
ejpam-4867	124	26	.	.	PUNCT
ejpam-4867	125	1	if	if	SCONJ
ejpam-4867	125	2	x	x	PRON
ejpam-4867	125	3	/∈	/∈	PUNCT
ejpam-4867	125	4	res(c	res(c	ADJ
ejpam-4867	125	5	)	)	PUNCT
ejpam-4867	125	6	,	,	PUNCT
ejpam-4867	125	7	then	then	ADV
ejpam-4867	125	8	the	the	DET
ejpam-4867	125	9	eccentricity	eccentricity	NOUN
ejpam-4867	125	10	of	of	ADP
ejpam-4867	125	11	x̂	x̂	PROPN
ejpam-4867	125	12	is	be	AUX
ejpam-4867	125	13	2	2	NUM
ejpam-4867	125	14	since	since	SCONJ
ejpam-4867	125	15	every	every	DET
ejpam-4867	125	16	vertex	vertex	NOUN
ejpam-4867	125	17	in	in	ADP
ejpam-4867	125	18	gec	gec	NOUN
ejpam-4867	125	19	is	be	AUX
ejpam-4867	125	20	connected	connect	VERB
ejpam-4867	125	21	through	through	ADP
ejpam-4867	125	22	a	a	DET
ejpam-4867	125	23	vertex	vertex	NOUN
ejpam-4867	125	24	in	in	ADP
ejpam-4867	125	25	res(c	res(c	ADJ
ejpam-4867	125	26	)	)	PUNCT
ejpam-4867	125	27	to	to	ADP
ejpam-4867	125	28	all	all	DET
ejpam-4867	125	29	other	other	ADJ
ejpam-4867	125	30	vertex	vertex	NOUN
ejpam-4867	125	31	not	not	PART
ejpam-4867	125	32	in	in	ADP
ejpam-4867	125	33	res(c	res(c	ADJ
ejpam-4867	125	34	)	)	PUNCT
ejpam-4867	125	35	.	.	PUNCT
ejpam-4867	126	1	therefore	therefore	ADV
ejpam-4867	126	2	,	,	PUNCT
ejpam-4867	126	3	r(gec	r(gec	NOUN
ejpam-4867	126	4	)	)	PUNCT
ejpam-4867	126	5	=	=	SYM
ejpam-4867	126	6	1	1	X
ejpam-4867	126	7	.	.	X
ejpam-4867	127	1	■	■	PUNCT
ejpam-4867	127	2	lemma	lemma	PROPN
ejpam-4867	127	3	2	2	X
ejpam-4867	127	4	.	.	PUNCT
ejpam-4867	127	5	let	let	VERB
ejpam-4867	127	6	gec	gec	NOUN
ejpam-4867	127	7	̸=	̸=	PROPN
ejpam-4867	127	8	p2	p2	NOUN
ejpam-4867	127	9	,	,	PUNCT
ejpam-4867	127	10	path	path	NOUN
ejpam-4867	127	11	of	of	ADP
ejpam-4867	127	12	order	order	NOUN
ejpam-4867	127	13	2	2	X
ejpam-4867	127	14	.	.	PUNCT
ejpam-4867	128	1	if	if	SCONJ
ejpam-4867	128	2	there	there	PRON
ejpam-4867	128	3	exists	exist	VERB
ejpam-4867	128	4	x	x	X
ejpam-4867	128	5	/∈	/∈	PUNCT
ejpam-4867	128	6	res(c	res(c	ADJ
ejpam-4867	128	7	)	)	PUNCT
ejpam-4867	128	8	,	,	PUNCT
ejpam-4867	128	9	then	then	ADV
ejpam-4867	128	10	there	there	PRON
ejpam-4867	128	11	exists	exist	VERB
ejpam-4867	128	12	y	y	PROPN
ejpam-4867	128	13	̸=	̸=	PROPN
ejpam-4867	128	14	x	x	PUNCT
ejpam-4867	128	15	such	such	ADJ
ejpam-4867	128	16	that	that	SCONJ
ejpam-4867	128	17	y	y	PROPN
ejpam-4867	128	18	/∈	/∈	PUNCT
ejpam-4867	129	1	res(c	res(c	ADJ
ejpam-4867	129	2	)	)	PUNCT
ejpam-4867	129	3	.	.	PUNCT
ejpam-4867	130	1	proof	proof	NOUN
ejpam-4867	130	2	.	.	PUNCT
ejpam-4867	131	1	let	let	VERB
ejpam-4867	131	2	x	x	PRON
ejpam-4867	131	3	/∈	/∈	PUNCT
ejpam-4867	132	1	res(c	res(c	ADJ
ejpam-4867	132	2	)	)	PUNCT
ejpam-4867	132	3	.	.	PUNCT
ejpam-4867	133	1	then	then	ADV
ejpam-4867	133	2	|res(c)|	|res(c)|	PROPN
ejpam-4867	133	3	<	<	X
ejpam-4867	133	4	|tor(c)|	|tor(c)|	PROPN
ejpam-4867	133	5	.	.	PUNCT
ejpam-4867	134	1	this	this	PRON
ejpam-4867	134	2	means	mean	VERB
ejpam-4867	134	3	k1	k1	PROPN
ejpam-4867	134	4	<	<	X
ejpam-4867	134	5	k1	k1	PROPN
ejpam-4867	134	6	+	+	X
ejpam-4867	134	7	k2	k2	NOUN
ejpam-4867	134	8	,	,	PUNCT
ejpam-4867	134	9	that	that	ADV
ejpam-4867	134	10	is	be	AUX
ejpam-4867	134	11	,	,	PUNCT
ejpam-4867	134	12	k2	k2	X
ejpam-4867	134	13	>	>	X
ejpam-4867	134	14	0	0	X
ejpam-4867	134	15	.	.	PUNCT
ejpam-4867	135	1	now	now	ADV
ejpam-4867	135	2	,	,	PUNCT
ejpam-4867	135	3	|tor(c)|	|tor(c)|	PROPN
ejpam-4867	135	4	−	−	PROPN
ejpam-4867	135	5	|res(c)|	|res(c)|	PROPN
ejpam-4867	135	6	=	=	SYM
ejpam-4867	136	1	2k1+k2	2k1+k2	NUM
ejpam-4867	136	2	−	−	NUM
ejpam-4867	136	3	2k1	2k1	NUM
ejpam-4867	136	4	=	=	SYM
ejpam-4867	136	5	2k1	2k1	NUM
ejpam-4867	136	6	(	(	PUNCT
ejpam-4867	136	7	2k2	2k2	NUM
ejpam-4867	136	8	−	−	NOUN
ejpam-4867	136	9	1	1	NUM
ejpam-4867	136	10	)	)	PUNCT
ejpam-4867	136	11	.	.	PUNCT
ejpam-4867	137	1	note	note	VERB
ejpam-4867	137	2	that	that	SCONJ
ejpam-4867	137	3	if	if	SCONJ
ejpam-4867	137	4	k1	k1	PROPN
ejpam-4867	137	5	=	=	SYM
ejpam-4867	137	6	0	0	NUM
ejpam-4867	137	7	and	and	CCONJ
ejpam-4867	137	8	k2	k2	PROPN
ejpam-4867	137	9	=	=	SYM
ejpam-4867	137	10	1	1	NUM
ejpam-4867	137	11	,	,	PUNCT
ejpam-4867	137	12	gec	gec	NOUN
ejpam-4867	137	13	̸=	̸=	PROPN
ejpam-4867	137	14	p2	p2	NOUN
ejpam-4867	137	15	,	,	PUNCT
ejpam-4867	137	16	which	which	PRON
ejpam-4867	137	17	is	be	AUX
ejpam-4867	137	18	a	a	DET
ejpam-4867	137	19	contradiction	contradiction	NOUN
ejpam-4867	137	20	.	.	PUNCT
ejpam-4867	138	1	thus	thus	ADV
ejpam-4867	138	2	,	,	PUNCT
ejpam-4867	138	3	2k1	2k1	NUM
ejpam-4867	138	4	(	(	PUNCT
ejpam-4867	138	5	2k2	2k2	NUM
ejpam-4867	138	6	−	−	NUM
ejpam-4867	138	7	1	1	NUM
ejpam-4867	138	8	)	)	PUNCT
ejpam-4867	138	9	≥	≥	NOUN
ejpam-4867	138	10	2	2	NUM
ejpam-4867	138	11	.	.	PUNCT
ejpam-4867	138	12	■	■	PUNCT
ejpam-4867	138	13	theorem	theorem	ADJ
ejpam-4867	138	14	3	3	X
ejpam-4867	138	15	.	.	PUNCT
ejpam-4867	139	1	let	let	VERB
ejpam-4867	139	2	c	c	PRON
ejpam-4867	139	3	be	be	AUX
ejpam-4867	139	4	an	an	DET
ejpam-4867	139	5	e	e	NOUN
ejpam-4867	139	6	-	-	NOUN
ejpam-4867	139	7	code	code	NOUN
ejpam-4867	139	8	and	and	CCONJ
ejpam-4867	139	9	gec	gec	NOUN
ejpam-4867	139	10	be	be	AUX
ejpam-4867	139	11	the	the	DET
ejpam-4867	139	12	(	(	PUNCT
ejpam-4867	139	13	k1	k1	NOUN
ejpam-4867	139	14	,	,	PUNCT
ejpam-4867	139	15	k2	k2	ADJ
ejpam-4867	139	16	)	)	PUNCT
ejpam-4867	140	1	e	e	NOUN
ejpam-4867	140	2	-	-	NOUN
ejpam-4867	140	3	torsion	torsion	NOUN
ejpam-4867	140	4	graph	graph	NOUN
ejpam-4867	140	5	of	of	ADP
ejpam-4867	140	6	c	c	NOUN
ejpam-4867	140	7	which	which	PRON
ejpam-4867	140	8	is	be	AUX
ejpam-4867	140	9	not	not	PART
ejpam-4867	140	10	p2	p2	NOUN
ejpam-4867	140	11	.	.	PUNCT
ejpam-4867	141	1	then	then	ADV
ejpam-4867	141	2	vertex	vertex	NOUN
ejpam-4867	141	3	x̂	x̂	PUNCT
ejpam-4867	141	4	∈	∈	PROPN
ejpam-4867	141	5	c(gec	c(gec	PROPN
ejpam-4867	141	6	)	)	PUNCT
ejpam-4867	142	1	if	if	SCONJ
ejpam-4867	142	2	and	and	CCONJ
ejpam-4867	142	3	only	only	ADV
ejpam-4867	142	4	if	if	SCONJ
ejpam-4867	142	5	x	x	PROPN
ejpam-4867	142	6	∈	∈	PROPN
ejpam-4867	142	7	res(c	res(c	PROPN
ejpam-4867	142	8	)	)	PUNCT
ejpam-4867	142	9	.	.	PUNCT
ejpam-4867	143	1	j.	j.	PROPN
ejpam-4867	143	2	pilongo	pilongo	PROPN
ejpam-4867	143	3	,	,	PUNCT
ejpam-4867	143	4	l.	l.	PROPN
ejpam-4867	143	5	paleta	paleta	PROPN
ejpam-4867	143	6	,	,	PUNCT
ejpam-4867	143	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	143	8	/	/	SYM
ejpam-4867	143	9	eur	eur	PROPN
ejpam-4867	143	10	.	.	PUNCT
ejpam-4867	144	1	j.	j.	PROPN
ejpam-4867	144	2	pure	pure	PROPN
ejpam-4867	144	3	appl	appl	PROPN
ejpam-4867	144	4	.	.	PROPN
ejpam-4867	144	5	math	math	PROPN
ejpam-4867	144	6	,	,	PUNCT
ejpam-4867	144	7	17	17	NUM
ejpam-4867	144	8	(	(	PUNCT
ejpam-4867	144	9	2	2	NUM
ejpam-4867	144	10	)	)	PUNCT
ejpam-4867	144	11	(	(	PUNCT
ejpam-4867	144	12	2024	2024	NUM
ejpam-4867	144	13	)	)	PUNCT
ejpam-4867	144	14	,	,	PUNCT
ejpam-4867	144	15	1369	1369	NUM
ejpam-4867	144	16	-	-	SYM
ejpam-4867	144	17	1384	1384	NUM
ejpam-4867	144	18	1376	1376	NUM
ejpam-4867	144	19	proof	proof	NOUN
ejpam-4867	144	20	.	.	PUNCT
ejpam-4867	145	1	let	let	VERB
ejpam-4867	145	2	x̂	x̂	PROPN
ejpam-4867	145	3	∈	∈	PROPN
ejpam-4867	145	4	c(gec	c(gec	PROPN
ejpam-4867	145	5	)	)	PUNCT
ejpam-4867	145	6	.	.	PUNCT
ejpam-4867	146	1	suppose	suppose	VERB
ejpam-4867	146	2	x	x	X
ejpam-4867	146	3	/∈	/∈	PUNCT
ejpam-4867	147	1	res(c	res(c	ADJ
ejpam-4867	147	2	)	)	PUNCT
ejpam-4867	147	3	.	.	PUNCT
ejpam-4867	148	1	then	then	ADV
ejpam-4867	148	2	,	,	PUNCT
ejpam-4867	148	3	by	by	ADP
ejpam-4867	148	4	lemma	lemma	PROPN
ejpam-4867	148	5	2	2	NUM
ejpam-4867	148	6	there	there	ADV
ejpam-4867	148	7	exists	exist	VERB
ejpam-4867	148	8	y	y	PROPN
ejpam-4867	148	9	∈	∈	PROPN
ejpam-4867	148	10	tor(c	tor(c	PROPN
ejpam-4867	148	11	)	)	PUNCT
ejpam-4867	148	12	such	such	ADJ
ejpam-4867	148	13	that	that	SCONJ
ejpam-4867	148	14	both	both	DET
ejpam-4867	148	15	ax+	ax+	VERB
ejpam-4867	148	16	cy	cy	NOUN
ejpam-4867	148	17	and	and	CCONJ
ejpam-4867	148	18	ay	ay	PROPN
ejpam-4867	148	19	+	+	CCONJ
ejpam-4867	148	20	cx	cx	NOUN
ejpam-4867	148	21	not	not	PART
ejpam-4867	148	22	in	in	ADP
ejpam-4867	148	23	c.	c.	PROPN
ejpam-4867	148	24	it	it	PRON
ejpam-4867	148	25	follows	follow	VERB
ejpam-4867	148	26	that	that	SCONJ
ejpam-4867	148	27	eccentricity	eccentricity	NOUN
ejpam-4867	148	28	of	of	ADP
ejpam-4867	148	29	x̂	x̂	NOUN
ejpam-4867	148	30	is	be	AUX
ejpam-4867	148	31	greater	great	ADJ
ejpam-4867	148	32	than	than	ADP
ejpam-4867	148	33	1	1	NUM
ejpam-4867	148	34	,	,	PUNCT
ejpam-4867	148	35	a	a	DET
ejpam-4867	148	36	contradiction	contradiction	NOUN
ejpam-4867	148	37	that	that	PRON
ejpam-4867	148	38	x̂	x̂	PUNCT
ejpam-4867	148	39	∈	∈	PROPN
ejpam-4867	148	40	c(gec	c(gec	PROPN
ejpam-4867	148	41	)	)	PUNCT
ejpam-4867	148	42	by	by	ADP
ejpam-4867	148	43	lemma	lemma	PROPN
ejpam-4867	148	44	1	1	NUM
ejpam-4867	148	45	.	.	PUNCT
ejpam-4867	148	46	conversely	conversely	ADV
ejpam-4867	148	47	,	,	PUNCT
ejpam-4867	148	48	suppose	suppose	VERB
ejpam-4867	148	49	x	x	X
ejpam-4867	148	50	∈	∈	PROPN
ejpam-4867	148	51	res(c	res(c	PROPN
ejpam-4867	148	52	)	)	PUNCT
ejpam-4867	148	53	.	.	PUNCT
ejpam-4867	149	1	then	then	ADV
ejpam-4867	149	2	x̂	x̂	NUM
ejpam-4867	149	3	is	be	AUX
ejpam-4867	149	4	connected	connect	VERB
ejpam-4867	149	5	by	by	ADP
ejpam-4867	149	6	an	an	DET
ejpam-4867	149	7	edge	edge	NOUN
ejpam-4867	149	8	to	to	ADP
ejpam-4867	149	9	every	every	DET
ejpam-4867	149	10	vertex	vertex	NOUN
ejpam-4867	149	11	in	in	ADP
ejpam-4867	149	12	gec	gec	NOUN
ejpam-4867	149	13	.	.	PUNCT
ejpam-4867	150	1	thus	thus	ADV
ejpam-4867	150	2	,	,	PUNCT
ejpam-4867	150	3	the	the	DET
ejpam-4867	150	4	eccentricity	eccentricity	NOUN
ejpam-4867	150	5	of	of	ADP
ejpam-4867	150	6	vertex	vertex	NOUN
ejpam-4867	150	7	x̂	x̂	NUM
ejpam-4867	150	8	is	be	AUX
ejpam-4867	150	9	1	1	NUM
ejpam-4867	150	10	,	,	PUNCT
ejpam-4867	150	11	that	that	ADV
ejpam-4867	150	12	is	is	ADV
ejpam-4867	150	13	,	,	PUNCT
ejpam-4867	150	14	x̂	x̂	PROPN
ejpam-4867	150	15	∈	∈	PROPN
ejpam-4867	150	16	c(gec	c(gec	PROPN
ejpam-4867	150	17	)	)	PUNCT
ejpam-4867	150	18	.	.	PUNCT
ejpam-4867	151	1	■	■	PUNCT
ejpam-4867	151	2	4.1	4.1	NUM
ejpam-4867	151	3	.	.	PUNCT
ejpam-4867	151	4	(	(	PUNCT
ejpam-4867	151	5	k1	k1	NOUN
ejpam-4867	151	6	,	,	PUNCT
ejpam-4867	151	7	k2	k2	ADJ
ejpam-4867	151	8	)	)	PUNCT
ejpam-4867	151	9	e	e	NOUN
ejpam-4867	151	10	-	-	NOUN
ejpam-4867	151	11	torsion	torsion	NOUN
ejpam-4867	151	12	graph	graph	NOUN
ejpam-4867	151	13	of	of	ADP
ejpam-4867	151	14	qsd	qsd	NOUN
ejpam-4867	151	15	codes	code	NOUN
ejpam-4867	151	16	quasi	quasi	VERB
ejpam-4867	151	17	self	self	NOUN
ejpam-4867	151	18	-	-	PUNCT
ejpam-4867	151	19	dual	dual	ADJ
ejpam-4867	151	20	codes	code	NOUN
ejpam-4867	151	21	are	be	AUX
ejpam-4867	151	22	classified	classify	VERB
ejpam-4867	151	23	in	in	ADP
ejpam-4867	151	24	[	[	X
ejpam-4867	151	25	3	3	NUM
ejpam-4867	151	26	]	]	PUNCT
ejpam-4867	151	27	using	use	VERB
ejpam-4867	151	28	their	their	PRON
ejpam-4867	151	29	residue	residue	NOUN
ejpam-4867	151	30	codes	code	NOUN
ejpam-4867	151	31	.	.	PUNCT
ejpam-4867	152	1	but	but	CCONJ
ejpam-4867	152	2	since	since	SCONJ
ejpam-4867	152	3	every	every	DET
ejpam-4867	152	4	residue	residue	NOUN
ejpam-4867	152	5	code	code	NOUN
ejpam-4867	152	6	corresponds	correspond	VERB
ejpam-4867	152	7	to	to	ADP
ejpam-4867	152	8	a	a	DET
ejpam-4867	152	9	unique	unique	ADJ
ejpam-4867	152	10	torsion	torsion	NOUN
ejpam-4867	152	11	code	code	NOUN
ejpam-4867	152	12	,	,	PUNCT
ejpam-4867	152	13	the	the	DET
ejpam-4867	152	14	study	study	NOUN
ejpam-4867	152	15	of	of	ADP
ejpam-4867	152	16	the	the	DET
ejpam-4867	152	17	structure	structure	NOUN
ejpam-4867	152	18	of	of	ADP
ejpam-4867	152	19	gec	gec	NOUN
ejpam-4867	152	20	of	of	ADP
ejpam-4867	152	21	a	a	DET
ejpam-4867	152	22	qsd	qsd	NOUN
ejpam-4867	152	23	code	code	NOUN
ejpam-4867	152	24	will	will	AUX
ejpam-4867	152	25	be	be	AUX
ejpam-4867	152	26	concentrated	concentrate	VERB
ejpam-4867	152	27	in	in	ADP
ejpam-4867	152	28	this	this	DET
ejpam-4867	152	29	section	section	NOUN
ejpam-4867	152	30	.	.	PUNCT
ejpam-4867	153	1	example	example	NOUN
ejpam-4867	154	1	2	2	NUM
ejpam-4867	154	2	.	.	PUNCT
ejpam-4867	154	3	let	let	VERB
ejpam-4867	154	4	c	c	NOUN
ejpam-4867	154	5	=	=	SYM
ejpam-4867	154	6	ab	ab	PROPN
ejpam-4867	154	7	+	+	NUM
ejpam-4867	154	8	cb⊥	cb⊥	PROPN
ejpam-4867	154	9	,	,	PUNCT
ejpam-4867	154	10	where	where	SCONJ
ejpam-4867	154	11	b	b	X
ejpam-4867	154	12	=	=	SYM
ejpam-4867	154	13	⟨1100	⟨1100	PROPN
ejpam-4867	154	14	,	,	PUNCT
ejpam-4867	154	15	0011⟩	0011⟩	PROPN
ejpam-4867	154	16	.	.	PUNCT
ejpam-4867	155	1	then	then	ADV
ejpam-4867	155	2	b⊥	b⊥	VERB
ejpam-4867	155	3	=	=	SYM
ejpam-4867	155	4	⟨1100	⟨1100	PROPN
ejpam-4867	155	5	,	,	PUNCT
ejpam-4867	155	6	0011⟩	0011⟩	NUM
ejpam-4867	155	7	by	by	ADP
ejpam-4867	155	8	theorem	theorem	NOUN
ejpam-4867	155	9	1	1	NUM
ejpam-4867	155	10	,	,	PUNCT
ejpam-4867	155	11	c	c	PROPN
ejpam-4867	155	12	is	be	AUX
ejpam-4867	155	13	a	a	DET
ejpam-4867	155	14	qsd	qsd	NOUN
ejpam-4867	155	15	code	code	NOUN
ejpam-4867	155	16	.	.	PUNCT
ejpam-4867	156	1	v	v	X
ejpam-4867	156	2	(	(	PUNCT
ejpam-4867	156	3	gec	gec	NOUN
ejpam-4867	156	4	)	)	PUNCT
ejpam-4867	156	5	=	=	PRON
ejpam-4867	156	6	{	{	PUNCT
ejpam-4867	156	7	0̂000	0̂000	NUM
ejpam-4867	156	8	,	,	PUNCT
ejpam-4867	156	9	1̂100	1̂100	NUM
ejpam-4867	156	10	,	,	PUNCT
ejpam-4867	156	11	0̂011	0̂011	NUM
ejpam-4867	156	12	,	,	PUNCT
ejpam-4867	156	13	1̂111	1̂111	NUM
ejpam-4867	156	14	}	}	PUNCT
ejpam-4867	156	15	.	.	PUNCT
ejpam-4867	157	1	by	by	ADP
ejpam-4867	157	2	corollary	corollary	ADJ
ejpam-4867	157	3	3	3	NUM
ejpam-4867	157	4	,	,	PUNCT
ejpam-4867	157	5	|e(gec)|	|e(gec)|	NOUN
ejpam-4867	157	6	=	=	SYM
ejpam-4867	157	7	16−	16−	VERB
ejpam-4867	157	8	8−	8−	NUM
ejpam-4867	157	9	2	2	NUM
ejpam-4867	157	10	=	=	SYM
ejpam-4867	157	11	6	6	NUM
ejpam-4867	157	12	,	,	PUNCT
ejpam-4867	157	13	that	that	ADV
ejpam-4867	157	14	is	is	ADV
ejpam-4867	157	15	,	,	PUNCT
ejpam-4867	157	16	gec	gec	PROPN
ejpam-4867	157	17	is	be	AUX
ejpam-4867	157	18	a	a	DET
ejpam-4867	157	19	complete	complete	ADJ
ejpam-4867	157	20	graph	graph	NOUN
ejpam-4867	157	21	.	.	PUNCT
ejpam-4867	158	1	theorem	theorem	NOUN
ejpam-4867	158	2	4	4	NUM
ejpam-4867	158	3	.	.	PUNCT
ejpam-4867	159	1	let	let	VERB
ejpam-4867	159	2	gec	gec	PROPN
ejpam-4867	159	3	be	be	AUX
ejpam-4867	159	4	the	the	DET
ejpam-4867	159	5	(	(	PUNCT
ejpam-4867	159	6	k1	k1	NOUN
ejpam-4867	159	7	,	,	PUNCT
ejpam-4867	159	8	k2	k2	ADJ
ejpam-4867	159	9	)	)	PUNCT
ejpam-4867	159	10	e	e	NOUN
ejpam-4867	159	11	-	-	NOUN
ejpam-4867	159	12	torsion	torsion	NOUN
ejpam-4867	159	13	graph	graph	NOUN
ejpam-4867	159	14	of	of	ADP
ejpam-4867	159	15	a	a	DET
ejpam-4867	159	16	qsd	qsd	NOUN
ejpam-4867	159	17	code	code	NOUN
ejpam-4867	159	18	c	c	NOUN
ejpam-4867	160	1	=	=	SYM
ejpam-4867	160	2	ab	ab	PROPN
ejpam-4867	161	1	+	+	CCONJ
ejpam-4867	161	2	cb⊥	cb⊥	PROPN
ejpam-4867	161	3	where	where	SCONJ
ejpam-4867	161	4	b	b	NOUN
ejpam-4867	161	5	is	be	AUX
ejpam-4867	161	6	a	a	DET
ejpam-4867	161	7	binary	binary	PROPN
ejpam-4867	161	8	code	code	NOUN
ejpam-4867	161	9	.	.	PUNCT
ejpam-4867	162	1	then	then	ADV
ejpam-4867	162	2	b	b	PROPN
ejpam-4867	162	3	is	be	AUX
ejpam-4867	162	4	self	self	NOUN
ejpam-4867	162	5	-	-	PUNCT
ejpam-4867	162	6	dual	dual	ADJ
ejpam-4867	162	7	if	if	SCONJ
ejpam-4867	163	1	and	and	CCONJ
ejpam-4867	163	2	only	only	ADV
ejpam-4867	163	3	if	if	SCONJ
ejpam-4867	163	4	gec	gec	NOUN
ejpam-4867	163	5	is	be	AUX
ejpam-4867	163	6	a	a	DET
ejpam-4867	163	7	complete	complete	ADJ
ejpam-4867	163	8	graph	graph	NOUN
ejpam-4867	163	9	.	.	PUNCT
ejpam-4867	164	1	proof	proof	NOUN
ejpam-4867	164	2	.	.	PUNCT
ejpam-4867	165	1	let	let	VERB
ejpam-4867	165	2	b	b	NOUN
ejpam-4867	165	3	be	be	AUX
ejpam-4867	165	4	self	self	NOUN
ejpam-4867	165	5	-	-	PUNCT
ejpam-4867	165	6	dual	dual	ADJ
ejpam-4867	165	7	.	.	PUNCT
ejpam-4867	166	1	then	then	ADV
ejpam-4867	166	2	res(c	res(c	PROPN
ejpam-4867	166	3	)	)	PUNCT
ejpam-4867	166	4	=	=	SYM
ejpam-4867	166	5	tor(c	tor(c	PROPN
ejpam-4867	166	6	)	)	PUNCT
ejpam-4867	166	7	.	.	PUNCT
ejpam-4867	167	1	by	by	ADP
ejpam-4867	167	2	corollary	corollary	ADJ
ejpam-4867	167	3	2	2	NUM
ejpam-4867	167	4	,	,	PUNCT
ejpam-4867	167	5	the	the	DET
ejpam-4867	167	6	degree	degree	NOUN
ejpam-4867	167	7	of	of	ADP
ejpam-4867	167	8	every	every	DET
ejpam-4867	167	9	vertex	vertex	NOUN
ejpam-4867	167	10	of	of	ADP
ejpam-4867	167	11	gec	gec	NOUN
ejpam-4867	167	12	is	be	AUX
ejpam-4867	167	13	2k1+k2	2k1+k2	NUM
ejpam-4867	167	14	−	−	NOUN
ejpam-4867	167	15	1	1	NUM
ejpam-4867	167	16	,	,	PUNCT
ejpam-4867	167	17	j.	j.	PROPN
ejpam-4867	167	18	pilongo	pilongo	PROPN
ejpam-4867	167	19	,	,	PUNCT
ejpam-4867	167	20	l.	l.	PROPN
ejpam-4867	167	21	paleta	paleta	PROPN
ejpam-4867	167	22	,	,	PUNCT
ejpam-4867	167	23	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	167	24	/	/	SYM
ejpam-4867	167	25	eur	eur	PROPN
ejpam-4867	167	26	.	.	PUNCT
ejpam-4867	168	1	j.	j.	PROPN
ejpam-4867	168	2	pure	pure	PROPN
ejpam-4867	168	3	appl	appl	PROPN
ejpam-4867	168	4	.	.	PROPN
ejpam-4867	168	5	math	math	PROPN
ejpam-4867	168	6	,	,	PUNCT
ejpam-4867	168	7	17	17	NUM
ejpam-4867	168	8	(	(	PUNCT
ejpam-4867	168	9	2	2	NUM
ejpam-4867	168	10	)	)	PUNCT
ejpam-4867	168	11	(	(	PUNCT
ejpam-4867	168	12	2024	2024	NUM
ejpam-4867	168	13	)	)	PUNCT
ejpam-4867	168	14	,	,	PUNCT
ejpam-4867	168	15	1369	1369	NUM
ejpam-4867	168	16	-	-	SYM
ejpam-4867	168	17	1384	1384	NUM
ejpam-4867	168	18	1377	1377	NUM
ejpam-4867	168	19	that	that	PRON
ejpam-4867	168	20	is	be	AUX
ejpam-4867	168	21	,	,	PUNCT
ejpam-4867	168	22	gec	gec	PROPN
ejpam-4867	168	23	is	be	AUX
ejpam-4867	168	24	a	a	DET
ejpam-4867	168	25	complete	complete	ADJ
ejpam-4867	168	26	graph	graph	NOUN
ejpam-4867	168	27	.	.	PUNCT
ejpam-4867	169	1	conversely	conversely	ADV
ejpam-4867	169	2	,	,	PUNCT
ejpam-4867	169	3	suppose	suppose	VERB
ejpam-4867	169	4	that	that	SCONJ
ejpam-4867	169	5	gec	gec	PROPN
ejpam-4867	169	6	is	be	AUX
ejpam-4867	169	7	a	a	DET
ejpam-4867	169	8	complete	complete	ADJ
ejpam-4867	169	9	graph	graph	NOUN
ejpam-4867	169	10	.	.	PUNCT
ejpam-4867	170	1	let	let	VERB
ejpam-4867	170	2	x	x	SYM
ejpam-4867	170	3	∈	∈	PROPN
ejpam-4867	170	4	tor(c	tor(c	PROPN
ejpam-4867	170	5	)	)	PUNCT
ejpam-4867	170	6	.	.	PUNCT
ejpam-4867	171	1	then	then	ADV
ejpam-4867	171	2	(	(	PUNCT
ejpam-4867	171	3	x̂	x̂	NUM
ejpam-4867	171	4	,	,	PUNCT
ejpam-4867	171	5	ŷ	ŷ	NUM
ejpam-4867	171	6	)	)	PUNCT
ejpam-4867	171	7	∈	∈	PROPN
ejpam-4867	171	8	e(gec	e(gec	PROPN
ejpam-4867	171	9	)	)	PUNCT
ejpam-4867	171	10	since	since	SCONJ
ejpam-4867	171	11	gec	gec	NOUN
ejpam-4867	171	12	is	be	AUX
ejpam-4867	171	13	complete	complete	ADJ
ejpam-4867	171	14	.	.	PUNCT
ejpam-4867	172	1	it	it	PRON
ejpam-4867	172	2	follows	follow	VERB
ejpam-4867	172	3	that	that	DET
ejpam-4867	172	4	ax+	ax+	NOUN
ejpam-4867	172	5	cy	cy	PROPN
ejpam-4867	172	6	∈	∈	PROPN
ejpam-4867	172	7	c	c	PROPN
ejpam-4867	172	8	for	for	ADP
ejpam-4867	172	9	all	all	DET
ejpam-4867	172	10	y	y	PROPN
ejpam-4867	172	11	∈	∈	PROPN
ejpam-4867	172	12	tor(c	tor(c	PROPN
ejpam-4867	172	13	)	)	PUNCT
ejpam-4867	172	14	.	.	PUNCT
ejpam-4867	173	1	applying	apply	VERB
ejpam-4867	173	2	α	α	NUM
ejpam-4867	173	3	,	,	PUNCT
ejpam-4867	173	4	we	we	PRON
ejpam-4867	173	5	have	have	VERB
ejpam-4867	173	6	x	x	X
ejpam-4867	173	7	∈	∈	PROPN
ejpam-4867	173	8	res(c	res(c	PROPN
ejpam-4867	173	9	)	)	PUNCT
ejpam-4867	173	10	,	,	PUNCT
ejpam-4867	173	11	that	that	ADV
ejpam-4867	173	12	is	is	ADV
ejpam-4867	173	13	,	,	PUNCT
ejpam-4867	173	14	tor(c	tor(c	PROPN
ejpam-4867	173	15	)	)	PUNCT
ejpam-4867	173	16	⊆	⊆	NUM
ejpam-4867	173	17	res(c	res(c	NUM
ejpam-4867	173	18	)	)	PUNCT
ejpam-4867	173	19	.	.	PUNCT
ejpam-4867	174	1	■	■	PUNCT
ejpam-4867	174	2	corollary	corollary	ADJ
ejpam-4867	174	3	4	4	NUM
ejpam-4867	174	4	.	.	PUNCT
ejpam-4867	175	1	if	if	SCONJ
ejpam-4867	175	2	c	c	PROPN
ejpam-4867	175	3	is	be	AUX
ejpam-4867	175	4	a	a	DET
ejpam-4867	175	5	qsd	qsd	NOUN
ejpam-4867	175	6	code	code	NOUN
ejpam-4867	175	7	of	of	ADP
ejpam-4867	175	8	type-(k1	type-(k1	PROPN
ejpam-4867	175	9	,	,	PUNCT
ejpam-4867	175	10	0	0	NUM
ejpam-4867	175	11	)	)	PUNCT
ejpam-4867	175	12	,	,	PUNCT
ejpam-4867	175	13	then	then	ADV
ejpam-4867	175	14	gec	gec	PROPN
ejpam-4867	175	15	is	be	AUX
ejpam-4867	175	16	a	a	DET
ejpam-4867	175	17	complete	complete	ADJ
ejpam-4867	175	18	graph	graph	NOUN
ejpam-4867	175	19	.	.	PUNCT
ejpam-4867	176	1	theorem	theorem	NOUN
ejpam-4867	176	2	5	5	NUM
ejpam-4867	176	3	.	.	PUNCT
ejpam-4867	177	1	if	if	SCONJ
ejpam-4867	177	2	c	c	PROPN
ejpam-4867	177	3	is	be	AUX
ejpam-4867	177	4	a	a	DET
ejpam-4867	177	5	qsd	qsd	NOUN
ejpam-4867	177	6	code	code	NOUN
ejpam-4867	177	7	of	of	ADP
ejpam-4867	177	8	type-(0	type-(0	PROPN
ejpam-4867	177	9	,	,	PUNCT
ejpam-4867	177	10	k2	k2	NOUN
ejpam-4867	177	11	)	)	PUNCT
ejpam-4867	177	12	,	,	PUNCT
ejpam-4867	177	13	then	then	ADV
ejpam-4867	177	14	gec	gec	PROPN
ejpam-4867	177	15	is	be	AUX
ejpam-4867	177	16	a	a	DET
ejpam-4867	177	17	star	star	NOUN
ejpam-4867	177	18	graph	graph	NOUN
ejpam-4867	177	19	.	.	PUNCT
ejpam-4867	178	1	proof	proof	NOUN
ejpam-4867	178	2	.	.	PUNCT
ejpam-4867	179	1	if	if	SCONJ
ejpam-4867	179	2	k1	k1	NOUN
ejpam-4867	179	3	=	=	SYM
ejpam-4867	179	4	0	0	NUM
ejpam-4867	179	5	,	,	PUNCT
ejpam-4867	179	6	then	then	ADV
ejpam-4867	179	7	res(c	res(c	PROPN
ejpam-4867	179	8	)	)	PUNCT
ejpam-4867	179	9	is	be	AUX
ejpam-4867	179	10	the	the	DET
ejpam-4867	179	11	trivial	trivial	ADJ
ejpam-4867	179	12	code	code	NOUN
ejpam-4867	179	13	which	which	PRON
ejpam-4867	179	14	contains	contain	VERB
ejpam-4867	179	15	only	only	ADV
ejpam-4867	179	16	the	the	DET
ejpam-4867	179	17	zero	zero	NUM
ejpam-4867	179	18	vector	vector	NOUN
ejpam-4867	179	19	.	.	PUNCT
ejpam-4867	180	1	it	it	PRON
ejpam-4867	180	2	follows	follow	VERB
ejpam-4867	180	3	that	that	SCONJ
ejpam-4867	180	4	tor(c	tor(c	PROPN
ejpam-4867	180	5	)	)	PUNCT
ejpam-4867	180	6	=	=	SYM
ejpam-4867	180	7	fn	fn	NOUN
ejpam-4867	180	8	2	2	NUM
ejpam-4867	180	9	.	.	PUNCT
ejpam-4867	181	1	hence	hence	ADV
ejpam-4867	181	2	,	,	PUNCT
ejpam-4867	181	3	e(gec	e(gec	PROPN
ejpam-4867	181	4	)	)	PUNCT
ejpam-4867	181	5	=	=	PRON
ejpam-4867	181	6	{	{	PUNCT
ejpam-4867	181	7	(	(	PUNCT
ejpam-4867	181	8	0̂v	0̂v	NUM
ejpam-4867	181	9	,	,	PUNCT
ejpam-4867	181	10	x̂	x̂	NUM
ejpam-4867	181	11	)	)	PUNCT
ejpam-4867	181	12	:	:	PUNCT
ejpam-4867	182	1	x	x	PUNCT
ejpam-4867	182	2	∈	∈	NOUN
ejpam-4867	182	3	fn	fn	NOUN
ejpam-4867	182	4	2	2	NUM
ejpam-4867	182	5	}	}	PUNCT
ejpam-4867	182	6	.	.	PUNCT
ejpam-4867	183	1	■	■	PUNCT
ejpam-4867	183	2	remark	remark	NOUN
ejpam-4867	183	3	1	1	NUM
ejpam-4867	183	4	.	.	PUNCT
ejpam-4867	184	1	let	let	VERB
ejpam-4867	184	2	k1	k1	PROPN
ejpam-4867	184	3	,	,	PUNCT
ejpam-4867	184	4	k2	k2	PROPN
ejpam-4867	184	5	∈	∈	PROPN
ejpam-4867	184	6	z+	z+	NUM
ejpam-4867	184	7	and	and	CCONJ
ejpam-4867	184	8	c1	c1	PROPN
ejpam-4867	184	9	,	,	PUNCT
ejpam-4867	184	10	c2	c2	PROPN
ejpam-4867	184	11	be	be	VERB
ejpam-4867	184	12	type-(k1	type-(k1	ADJ
ejpam-4867	184	13	,	,	PUNCT
ejpam-4867	184	14	k2	k2	ADJ
ejpam-4867	184	15	)	)	PUNCT
ejpam-4867	184	16	linear	linear	NOUN
ejpam-4867	184	17	e	e	NOUN
ejpam-4867	184	18	-	-	NOUN
ejpam-4867	184	19	codes	code	NOUN
ejpam-4867	184	20	.	.	PUNCT
ejpam-4867	185	1	then	then	ADV
ejpam-4867	185	2	gec1	gec1	PROPN
ejpam-4867	185	3	∼=	∼=	PROPN
ejpam-4867	185	4	gec2	gec2	NOUN
ejpam-4867	185	5	.	.	PUNCT
ejpam-4867	186	1	looking	look	VERB
ejpam-4867	186	2	at	at	ADP
ejpam-4867	186	3	remark	remark	NOUN
ejpam-4867	186	4	1	1	NUM
ejpam-4867	186	5	,	,	PUNCT
ejpam-4867	186	6	(	(	PUNCT
ejpam-4867	186	7	k1	k1	X
ejpam-4867	186	8	,	,	PUNCT
ejpam-4867	186	9	k2	k2	ADJ
ejpam-4867	186	10	)	)	PUNCT
ejpam-4867	186	11	e	e	NOUN
ejpam-4867	186	12	-	-	NOUN
ejpam-4867	186	13	torsion	torsion	NOUN
ejpam-4867	186	14	graph	graph	NOUN
ejpam-4867	186	15	alone	alone	ADV
ejpam-4867	186	16	can	can	AUX
ejpam-4867	186	17	not	not	PART
ejpam-4867	186	18	be	be	AUX
ejpam-4867	186	19	used	use	VERB
ejpam-4867	186	20	to	to	PART
ejpam-4867	186	21	classify	classify	VERB
ejpam-4867	186	22	qsd	qsd	NOUN
ejpam-4867	186	23	codes	code	NOUN
ejpam-4867	186	24	since	since	SCONJ
ejpam-4867	186	25	two	two	NUM
ejpam-4867	186	26	inequivalent	inequivalent	NOUN
ejpam-4867	186	27	codes	code	NOUN
ejpam-4867	186	28	under	under	ADP
ejpam-4867	186	29	the	the	DET
ejpam-4867	186	30	same	same	ADJ
ejpam-4867	186	31	type-(k1	type-(k1	NOUN
ejpam-4867	186	32	,	,	PUNCT
ejpam-4867	186	33	k2	k2	ADJ
ejpam-4867	186	34	)	)	PUNCT
ejpam-4867	186	35	code	code	NOUN
ejpam-4867	186	36	have	have	VERB
ejpam-4867	186	37	the	the	DET
ejpam-4867	186	38	same	same	ADJ
ejpam-4867	186	39	(	(	PUNCT
ejpam-4867	186	40	k1	k1	NOUN
ejpam-4867	186	41	,	,	PUNCT
ejpam-4867	186	42	k2	k2	ADJ
ejpam-4867	186	43	)	)	PUNCT
ejpam-4867	186	44	e	e	NOUN
ejpam-4867	186	45	-	-	NOUN
ejpam-4867	186	46	torsion	torsion	NOUN
ejpam-4867	186	47	graph	graph	NOUN
ejpam-4867	186	48	.	.	PUNCT
ejpam-4867	187	1	so	so	ADV
ejpam-4867	187	2	to	to	PART
ejpam-4867	187	3	separate	separate	VERB
ejpam-4867	187	4	these	these	DET
ejpam-4867	187	5	two	two	NUM
ejpam-4867	187	6	inequivalent	inequivalent	ADJ
ejpam-4867	187	7	qsd	qsd	NOUN
ejpam-4867	187	8	codes	code	NOUN
ejpam-4867	187	9	,	,	PUNCT
ejpam-4867	187	10	we	we	PRON
ejpam-4867	187	11	use	use	VERB
ejpam-4867	187	12	the	the	DET
ejpam-4867	187	13	concept	concept	NOUN
ejpam-4867	187	14	of	of	ADP
ejpam-4867	187	15	vertex	vertex	NOUN
ejpam-4867	187	16	-	-	PUNCT
ejpam-4867	187	17	weighted	weight	VERB
ejpam-4867	187	18	graph	graph	NOUN
ejpam-4867	187	19	which	which	PRON
ejpam-4867	187	20	is	be	AUX
ejpam-4867	187	21	defined	define	VERB
ejpam-4867	187	22	in	in	ADP
ejpam-4867	187	23	the	the	DET
ejpam-4867	187	24	following	following	NOUN
ejpam-4867	187	25	.	.	PUNCT
ejpam-4867	188	1	definition	definition	NOUN
ejpam-4867	188	2	3	3	NUM
ejpam-4867	188	3	.	.	PUNCT
ejpam-4867	189	1	the	the	DET
ejpam-4867	189	2	vertex	vertex	NOUN
ejpam-4867	189	3	-	-	PUNCT
ejpam-4867	189	4	weighted	weight	VERB
ejpam-4867	189	5	(	(	PUNCT
ejpam-4867	189	6	k1	k1	NOUN
ejpam-4867	189	7	,	,	PUNCT
ejpam-4867	189	8	k2	k2	ADJ
ejpam-4867	189	9	)	)	PUNCT
ejpam-4867	189	10	e	e	NOUN
ejpam-4867	189	11	-	-	NOUN
ejpam-4867	189	12	torsion	torsion	NOUN
ejpam-4867	189	13	graph	graph	NOUN
ejpam-4867	189	14	of	of	ADP
ejpam-4867	189	15	a	a	DET
ejpam-4867	189	16	qsd	qsd	NOUN
ejpam-4867	189	17	code	code	NOUN
ejpam-4867	189	18	is	be	AUX
ejpam-4867	189	19	the	the	DET
ejpam-4867	189	20	vertex	vertex	NOUN
ejpam-4867	189	21	-	-	PUNCT
ejpam-4867	189	22	weighted	weight	VERB
ejpam-4867	189	23	graph	graph	NOUN
ejpam-4867	189	24	where	where	SCONJ
ejpam-4867	189	25	the	the	DET
ejpam-4867	189	26	weight	weight	NOUN
ejpam-4867	189	27	of	of	ADP
ejpam-4867	189	28	a	a	DET
ejpam-4867	189	29	vertex	vertex	NOUN
ejpam-4867	189	30	x	x	SYM
ejpam-4867	189	31	∈	∈	PROPN
ejpam-4867	189	32	gec	gec	NOUN
ejpam-4867	189	33	is	be	AUX
ejpam-4867	189	34	the	the	DET
ejpam-4867	189	35	weight	weight	NOUN
ejpam-4867	189	36	of	of	ADP
ejpam-4867	189	37	the	the	DET
ejpam-4867	189	38	codeword	codeword	NOUN
ejpam-4867	189	39	wt(x	wt(x	PUNCT
ejpam-4867	189	40	)	)	PUNCT
ejpam-4867	189	41	of	of	ADP
ejpam-4867	189	42	x	x	PROPN
ejpam-4867	189	43	∈	∈	PROPN
ejpam-4867	189	44	tor(c	tor(c	PROPN
ejpam-4867	189	45	)	)	PUNCT
ejpam-4867	189	46	.	.	PUNCT
ejpam-4867	189	47	example	example	NOUN
ejpam-4867	190	1	3	3	X
ejpam-4867	190	2	.	.	PUNCT
ejpam-4867	190	3	let	let	VERB
ejpam-4867	190	4	c1	c1	PROPN
ejpam-4867	190	5	=	=	PUNCT
ejpam-4867	191	1	ab1	ab1	PROPN
ejpam-4867	192	1	+	+	CCONJ
ejpam-4867	192	2	cb⊥	cb⊥	PROPN
ejpam-4867	192	3	1	1	NUM
ejpam-4867	192	4	and	and	CCONJ
ejpam-4867	192	5	c2	c2	PROPN
ejpam-4867	192	6	=	=	PUNCT
ejpam-4867	192	7	ab2	ab2	PROPN
ejpam-4867	192	8	+	+	CCONJ
ejpam-4867	192	9	cb⊥	cb⊥	PROPN
ejpam-4867	192	10	2	2	NUM
ejpam-4867	192	11	j.	j.	PROPN
ejpam-4867	192	12	pilongo	pilongo	PROPN
ejpam-4867	192	13	,	,	PUNCT
ejpam-4867	192	14	l.	l.	PROPN
ejpam-4867	192	15	paleta	paleta	PROPN
ejpam-4867	192	16	,	,	PUNCT
ejpam-4867	192	17	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	192	18	/	/	SYM
ejpam-4867	192	19	eur	eur	PROPN
ejpam-4867	192	20	.	.	PUNCT
ejpam-4867	193	1	j.	j.	PROPN
ejpam-4867	193	2	pure	pure	PROPN
ejpam-4867	193	3	appl	appl	PROPN
ejpam-4867	193	4	.	.	PROPN
ejpam-4867	193	5	math	math	PROPN
ejpam-4867	193	6	,	,	PUNCT
ejpam-4867	193	7	17	17	NUM
ejpam-4867	193	8	(	(	PUNCT
ejpam-4867	193	9	2	2	NUM
ejpam-4867	193	10	)	)	PUNCT
ejpam-4867	193	11	(	(	PUNCT
ejpam-4867	193	12	2024	2024	NUM
ejpam-4867	193	13	)	)	PUNCT
ejpam-4867	193	14	,	,	PUNCT
ejpam-4867	193	15	1369	1369	NUM
ejpam-4867	193	16	-	-	SYM
ejpam-4867	193	17	1384	1384	NUM
ejpam-4867	193	18	1378	1378	NUM
ejpam-4867	193	19	where	where	SCONJ
ejpam-4867	193	20	b1	b1	NOUN
ejpam-4867	193	21	=	=	SYM
ejpam-4867	193	22	⟨1100⟩	⟨1100⟩	X
ejpam-4867	193	23	and	and	CCONJ
ejpam-4867	193	24	b2	b2	NOUN
ejpam-4867	193	25	=	=	SYM
ejpam-4867	193	26	⟨1111⟩	⟨1111⟩	PROPN
ejpam-4867	193	27	.	.	PUNCT
ejpam-4867	193	28	note	note	VERB
ejpam-4867	193	29	that	that	SCONJ
ejpam-4867	193	30	c1	c1	PROPN
ejpam-4867	193	31	and	and	CCONJ
ejpam-4867	193	32	c2	c2	PROPN
ejpam-4867	193	33	are	be	AUX
ejpam-4867	193	34	two	two	NUM
ejpam-4867	193	35	nonequivalents	nonequivalent	NOUN
ejpam-4867	193	36	e	e	NOUN
ejpam-4867	193	37	-	-	NOUN
ejpam-4867	193	38	codes	code	NOUN
ejpam-4867	193	39	.	.	PUNCT
ejpam-4867	194	1	now	now	ADV
ejpam-4867	194	2	,	,	PUNCT
ejpam-4867	194	3	v	v	INTJ
ejpam-4867	194	4	(	(	PUNCT
ejpam-4867	194	5	gec1	gec1	PROPN
ejpam-4867	194	6	)	)	PUNCT
ejpam-4867	194	7	=	=	PUNCT
ejpam-4867	194	8	{	{	PUNCT
ejpam-4867	194	9	0̂000	0̂000	NUM
ejpam-4867	194	10	,	,	PUNCT
ejpam-4867	194	11	1̂100	1̂100	NUM
ejpam-4867	194	12	,	,	PUNCT
ejpam-4867	194	13	0̂010	0̂010	NUM
ejpam-4867	194	14	,	,	PUNCT
ejpam-4867	194	15	1̂110	1̂110	NUM
ejpam-4867	194	16	,	,	PUNCT
ejpam-4867	194	17	0̂001	0̂001	NUM
ejpam-4867	194	18	,	,	PUNCT
ejpam-4867	194	19	1̂101	1̂101	NUM
ejpam-4867	194	20	,	,	PUNCT
ejpam-4867	194	21	0̂011	0̂011	NUM
ejpam-4867	194	22	,	,	PUNCT
ejpam-4867	194	23	1̂111	1̂111	NUM
ejpam-4867	194	24	}	}	PUNCT
ejpam-4867	194	25	and	and	CCONJ
ejpam-4867	194	26	v	v	X
ejpam-4867	194	27	(	(	PUNCT
ejpam-4867	194	28	gec2	gec2	PROPN
ejpam-4867	194	29	)	)	PUNCT
ejpam-4867	194	30	=	=	PRON
ejpam-4867	194	31	{	{	PUNCT
ejpam-4867	194	32	0̂000	0̂000	NUM
ejpam-4867	194	33	,	,	PUNCT
ejpam-4867	194	34	1̂111	1̂111	NUM
ejpam-4867	194	35	,	,	PUNCT
ejpam-4867	194	36	1̂100	1̂100	NUM
ejpam-4867	194	37	,	,	PUNCT
ejpam-4867	194	38	0̂011	0̂011	NUM
ejpam-4867	194	39	,	,	PUNCT
ejpam-4867	194	40	0̂110	0̂110	NUM
ejpam-4867	194	41	,	,	PUNCT
ejpam-4867	194	42	1̂001	1̂001	NUM
ejpam-4867	194	43	,	,	PUNCT
ejpam-4867	194	44	1̂010	1̂010	NUM
ejpam-4867	194	45	,	,	PUNCT
ejpam-4867	194	46	0̂101	0̂101	NUM
ejpam-4867	194	47	}	}	PUNCT
ejpam-4867	194	48	.	.	PUNCT
ejpam-4867	195	1	figure	figure	NOUN
ejpam-4867	195	2	2	2	NUM
ejpam-4867	195	3	shows	show	VERB
ejpam-4867	195	4	the	the	DET
ejpam-4867	195	5	graph	graph	NOUN
ejpam-4867	195	6	representation	representation	NOUN
ejpam-4867	195	7	of	of	ADP
ejpam-4867	195	8	gec1	gec1	PROPN
ejpam-4867	195	9	:	:	PUNCT
ejpam-4867	195	10	figure	figure	NOUN
ejpam-4867	195	11	2	2	NUM
ejpam-4867	195	12	:	:	PUNCT
ejpam-4867	195	13	(	(	PUNCT
ejpam-4867	195	14	k1	k1	X
ejpam-4867	195	15	,	,	PUNCT
ejpam-4867	195	16	k2	k2	ADJ
ejpam-4867	195	17	)	)	PUNCT
ejpam-4867	195	18	e	e	NOUN
ejpam-4867	195	19	-	-	NOUN
ejpam-4867	195	20	torsion	torsion	NOUN
ejpam-4867	195	21	graph	graph	NOUN
ejpam-4867	195	22	of	of	ADP
ejpam-4867	195	23	gec1	gec1	PROPN
ejpam-4867	195	24	furthermore	furthermore	ADV
ejpam-4867	195	25	,	,	PUNCT
ejpam-4867	195	26	figure	figure	NOUN
ejpam-4867	195	27	3	3	NUM
ejpam-4867	195	28	is	be	AUX
ejpam-4867	195	29	the	the	DET
ejpam-4867	195	30	graph	graph	NOUN
ejpam-4867	195	31	representation	representation	NOUN
ejpam-4867	195	32	of	of	ADP
ejpam-4867	195	33	graph	graph	NOUN
ejpam-4867	195	34	gec2	gec2	PROPN
ejpam-4867	195	35	.	.	PUNCT
ejpam-4867	196	1	figure	figure	VERB
ejpam-4867	196	2	3	3	NUM
ejpam-4867	196	3	:	:	PUNCT
ejpam-4867	196	4	(	(	PUNCT
ejpam-4867	196	5	k1	k1	X
ejpam-4867	196	6	,	,	PUNCT
ejpam-4867	196	7	k2	k2	ADJ
ejpam-4867	196	8	)	)	PUNCT
ejpam-4867	197	1	e	e	NOUN
ejpam-4867	197	2	-	-	NOUN
ejpam-4867	197	3	torsion	torsion	NOUN
ejpam-4867	197	4	graph	graph	NOUN
ejpam-4867	197	5	of	of	ADP
ejpam-4867	197	6	gec2	gec2	PROPN
ejpam-4867	197	7	note	note	NOUN
ejpam-4867	197	8	that	that	SCONJ
ejpam-4867	197	9	the	the	DET
ejpam-4867	197	10	two	two	NUM
ejpam-4867	197	11	graphs	graph	NOUN
ejpam-4867	197	12	are	be	AUX
ejpam-4867	197	13	isomorphic	isomorphic	ADJ
ejpam-4867	197	14	.	.	PUNCT
ejpam-4867	198	1	however	however	ADV
ejpam-4867	198	2	,	,	PUNCT
ejpam-4867	198	3	if	if	SCONJ
ejpam-4867	198	4	we	we	PRON
ejpam-4867	198	5	look	look	VERB
ejpam-4867	198	6	at	at	ADP
ejpam-4867	198	7	the	the	DET
ejpam-4867	198	8	vertex	vertex	NOUN
ejpam-4867	198	9	-	-	PUNCT
ejpam-4867	198	10	weighted	weight	VERB
ejpam-4867	198	11	graph	graph	NOUN
ejpam-4867	198	12	of	of	ADP
ejpam-4867	198	13	gec1	gec1	PROPN
ejpam-4867	198	14	and	and	CCONJ
ejpam-4867	198	15	gec2	gec2	PROPN
ejpam-4867	198	16	,	,	PUNCT
ejpam-4867	198	17	respectively	respectively	ADV
ejpam-4867	198	18	,	,	PUNCT
ejpam-4867	198	19	(	(	PUNCT
ejpam-4867	198	20	see	see	VERB
ejpam-4867	198	21	figure	figure	NOUN
ejpam-4867	198	22	4	4	NUM
ejpam-4867	198	23	and	and	CCONJ
ejpam-4867	198	24	5	5	NUM
ejpam-4867	198	25	)	)	PUNCT
ejpam-4867	198	26	using	use	VERB
ejpam-4867	198	27	the	the	DET
ejpam-4867	198	28	weights	weight	NOUN
ejpam-4867	198	29	of	of	ADP
ejpam-4867	198	30	every	every	DET
ejpam-4867	198	31	codeword	codeword	NOUN
ejpam-4867	198	32	,	,	PUNCT
ejpam-4867	198	33	we	we	PRON
ejpam-4867	198	34	see	see	VERB
ejpam-4867	198	35	the	the	DET
ejpam-4867	198	36	difference	difference	NOUN
ejpam-4867	198	37	between	between	ADP
ejpam-4867	198	38	these	these	DET
ejpam-4867	198	39	two	two	NUM
ejpam-4867	198	40	vertex	vertex	NOUN
ejpam-4867	198	41	-	-	PUNCT
ejpam-4867	198	42	weighted	weight	VERB
ejpam-4867	198	43	(	(	PUNCT
ejpam-4867	198	44	1	1	NUM
ejpam-4867	198	45	,	,	PUNCT
ejpam-4867	198	46	2	2	NUM
ejpam-4867	198	47	)	)	PUNCT
ejpam-4867	198	48	e	e	NOUN
ejpam-4867	198	49	-	-	NOUN
ejpam-4867	198	50	torsion	torsion	NOUN
ejpam-4867	198	51	graphs	graph	NOUN
ejpam-4867	198	52	.	.	PUNCT
ejpam-4867	199	1	hence	hence	ADV
ejpam-4867	199	2	,	,	PUNCT
ejpam-4867	199	3	two	two	NUM
ejpam-4867	199	4	codes	code	NOUN
ejpam-4867	199	5	can	can	AUX
ejpam-4867	199	6	have	have	VERB
ejpam-4867	199	7	isomorphic	isomorphic	ADJ
ejpam-4867	199	8	graphs	graph	NOUN
ejpam-4867	199	9	but	but	CCONJ
ejpam-4867	199	10	different	different	ADJ
ejpam-4867	199	11	vertex	vertex	NOUN
ejpam-4867	199	12	-	-	PUNCT
ejpam-4867	199	13	weighted	weight	VERB
ejpam-4867	199	14	(	(	PUNCT
ejpam-4867	199	15	k1	k1	NOUN
ejpam-4867	199	16	,	,	PUNCT
ejpam-4867	199	17	k2	k2	ADJ
ejpam-4867	199	18	)	)	PUNCT
ejpam-4867	199	19	etorsion	etorsion	NOUN
ejpam-4867	199	20	graphs	graph	NOUN
ejpam-4867	199	21	.	.	PUNCT
ejpam-4867	200	1	j.	j.	PROPN
ejpam-4867	200	2	pilongo	pilongo	PROPN
ejpam-4867	200	3	,	,	PUNCT
ejpam-4867	200	4	l.	l.	PROPN
ejpam-4867	200	5	paleta	paleta	PROPN
ejpam-4867	200	6	,	,	PUNCT
ejpam-4867	200	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	200	8	/	/	SYM
ejpam-4867	200	9	eur	eur	PROPN
ejpam-4867	200	10	.	.	PUNCT
ejpam-4867	201	1	j.	j.	PROPN
ejpam-4867	201	2	pure	pure	PROPN
ejpam-4867	201	3	appl	appl	PROPN
ejpam-4867	201	4	.	.	PROPN
ejpam-4867	201	5	math	math	PROPN
ejpam-4867	201	6	,	,	PUNCT
ejpam-4867	201	7	17	17	NUM
ejpam-4867	201	8	(	(	PUNCT
ejpam-4867	201	9	2	2	NUM
ejpam-4867	201	10	)	)	PUNCT
ejpam-4867	201	11	(	(	PUNCT
ejpam-4867	201	12	2024	2024	NUM
ejpam-4867	201	13	)	)	PUNCT
ejpam-4867	201	14	,	,	PUNCT
ejpam-4867	201	15	1369	1369	NUM
ejpam-4867	201	16	-	-	SYM
ejpam-4867	201	17	1384	1384	NUM
ejpam-4867	201	18	1379	1379	NUM
ejpam-4867	201	19	figure	figure	NOUN
ejpam-4867	201	20	4	4	NUM
ejpam-4867	201	21	:	:	PUNCT
ejpam-4867	201	22	(	(	PUNCT
ejpam-4867	201	23	k1	k1	X
ejpam-4867	201	24	,	,	PUNCT
ejpam-4867	201	25	k2	k2	ADJ
ejpam-4867	201	26	)	)	PUNCT
ejpam-4867	201	27	e	e	NOUN
ejpam-4867	201	28	-	-	NOUN
ejpam-4867	201	29	torsion	torsion	NOUN
ejpam-4867	201	30	graph	graph	NOUN
ejpam-4867	201	31	of	of	ADP
ejpam-4867	201	32	gec1	gec1	PROPN
ejpam-4867	201	33	figure	figure	NOUN
ejpam-4867	201	34	5	5	NUM
ejpam-4867	201	35	:	:	PUNCT
ejpam-4867	201	36	(	(	PUNCT
ejpam-4867	201	37	k1	k1	X
ejpam-4867	201	38	,	,	PUNCT
ejpam-4867	201	39	k2	k2	ADJ
ejpam-4867	201	40	)	)	PUNCT
ejpam-4867	201	41	e	e	NOUN
ejpam-4867	201	42	-	-	NOUN
ejpam-4867	201	43	torsion	torsion	NOUN
ejpam-4867	201	44	graph	graph	NOUN
ejpam-4867	201	45	of	of	ADP
ejpam-4867	201	46	gec2	gec2	PROPN
ejpam-4867	201	47	5	5	NUM
ejpam-4867	201	48	.	.	PUNCT
ejpam-4867	201	49	vertex	vertex	NOUN
ejpam-4867	201	50	-	-	PUNCT
ejpam-4867	201	51	weighted	weight	VERB
ejpam-4867	201	52	(	(	PUNCT
ejpam-4867	201	53	k1	k1	NOUN
ejpam-4867	201	54	,	,	PUNCT
ejpam-4867	201	55	k2	k2	ADJ
ejpam-4867	201	56	)	)	PUNCT
ejpam-4867	201	57	e	e	NOUN
ejpam-4867	201	58	-	-	NOUN
ejpam-4867	201	59	torsion	torsion	NOUN
ejpam-4867	201	60	graph	graph	NOUN
ejpam-4867	201	61	of	of	ADP
ejpam-4867	201	62	qsd	qsd	NOUN
ejpam-4867	201	63	codes	code	NOUN
ejpam-4867	201	64	with	with	ADP
ejpam-4867	201	65	n	n	DET
ejpam-4867	201	66	≤	≤	NUM
ejpam-4867	201	67	4	4	NUM
ejpam-4867	201	68	quasi	quasi	NOUN
ejpam-4867	201	69	self	self	NOUN
ejpam-4867	201	70	-	-	PUNCT
ejpam-4867	201	71	dual	dual	ADJ
ejpam-4867	201	72	e	e	NOUN
ejpam-4867	201	73	-	-	NOUN
ejpam-4867	201	74	codes	code	NOUN
ejpam-4867	201	75	of	of	ADP
ejpam-4867	201	76	short	short	ADJ
ejpam-4867	201	77	length	length	NOUN
ejpam-4867	201	78	were	be	AUX
ejpam-4867	201	79	classified	classify	VERB
ejpam-4867	201	80	in	in	ADP
ejpam-4867	201	81	[	[	X
ejpam-4867	201	82	3	3	NUM
ejpam-4867	201	83	]	]	PUNCT
ejpam-4867	201	84	.	.	PUNCT
ejpam-4867	202	1	in	in	ADP
ejpam-4867	202	2	this	this	DET
ejpam-4867	202	3	section	section	NOUN
ejpam-4867	202	4	,	,	PUNCT
ejpam-4867	202	5	we	we	PRON
ejpam-4867	202	6	will	will	AUX
ejpam-4867	202	7	illustrate	illustrate	VERB
ejpam-4867	202	8	those	those	DET
ejpam-4867	202	9	qsd	qsd	NOUN
ejpam-4867	202	10	codes	code	NOUN
ejpam-4867	202	11	using	use	VERB
ejpam-4867	202	12	their	their	PRON
ejpam-4867	202	13	vertex	vertex	NOUN
ejpam-4867	202	14	-	-	PUNCT
ejpam-4867	202	15	weighted	weight	VERB
ejpam-4867	202	16	(	(	PUNCT
ejpam-4867	202	17	k1	k1	NOUN
ejpam-4867	202	18	,	,	PUNCT
ejpam-4867	202	19	k2	k2	ADJ
ejpam-4867	202	20	)	)	PUNCT
ejpam-4867	202	21	e	e	NOUN
ejpam-4867	202	22	-	-	NOUN
ejpam-4867	202	23	torsion	torsion	NOUN
ejpam-4867	202	24	graphs	graph	NOUN
ejpam-4867	202	25	up	up	ADP
ejpam-4867	202	26	to	to	ADP
ejpam-4867	202	27	n	n	NOUN
ejpam-4867	202	28	=	=	SYM
ejpam-4867	202	29	4	4	NUM
ejpam-4867	202	30	.	.	NOUN
ejpam-4867	202	31	5.1	5.1	NUM
ejpam-4867	202	32	.	.	PUNCT
ejpam-4867	203	1	(	(	PUNCT
ejpam-4867	203	2	k1	k1	NOUN
ejpam-4867	203	3	,	,	PUNCT
ejpam-4867	203	4	k2	k2	ADJ
ejpam-4867	203	5	)	)	PUNCT
ejpam-4867	203	6	e	e	NOUN
ejpam-4867	203	7	-	-	NOUN
ejpam-4867	203	8	torsion	torsion	NOUN
ejpam-4867	203	9	graph	graph	NOUN
ejpam-4867	203	10	of	of	ADP
ejpam-4867	203	11	qsd	qsd	NOUN
ejpam-4867	203	12	codes	code	NOUN
ejpam-4867	203	13	for	for	ADP
ejpam-4867	203	14	n=2	n=2	X
ejpam-4867	203	15	.	.	PUNCT
ejpam-4867	204	1	for	for	ADP
ejpam-4867	204	2	c1	c1	PROPN
ejpam-4867	204	3	=	=	PROPN
ejpam-4867	204	4	a	a	DET
ejpam-4867	204	5	⟨00⟩+	⟨00⟩+	PROPN
ejpam-4867	204	6	c	c	PROPN
ejpam-4867	204	7	⟨10	⟨10	PROPN
ejpam-4867	204	8	,	,	PUNCT
ejpam-4867	204	9	01⟩	01⟩	NUM
ejpam-4867	204	10	,	,	PUNCT
ejpam-4867	204	11	we	we	PRON
ejpam-4867	204	12	have	have	VERB
ejpam-4867	204	13	a	a	DET
ejpam-4867	204	14	(	(	PUNCT
ejpam-4867	204	15	0	0	NUM
ejpam-4867	204	16	,	,	PUNCT
ejpam-4867	204	17	2	2	NUM
ejpam-4867	204	18	)	)	PUNCT
ejpam-4867	204	19	e	e	NOUN
ejpam-4867	204	20	-	-	NOUN
ejpam-4867	204	21	torsion	torsion	NOUN
ejpam-4867	204	22	graph	graph	NOUN
ejpam-4867	204	23	which	which	PRON
ejpam-4867	204	24	is	be	AUX
ejpam-4867	204	25	illustrated	illustrate	VERB
ejpam-4867	204	26	in	in	ADP
ejpam-4867	204	27	figure	figure	NOUN
ejpam-4867	204	28	6	6	NUM
ejpam-4867	204	29	.	.	PUNCT
ejpam-4867	205	1	figure	figure	VERB
ejpam-4867	205	2	6	6	NUM
ejpam-4867	205	3	:	:	PUNCT
ejpam-4867	205	4	vertex	vertex	NOUN
ejpam-4867	205	5	-	-	PUNCT
ejpam-4867	205	6	weighted	weight	VERB
ejpam-4867	205	7	(	(	PUNCT
ejpam-4867	205	8	k1	k1	NOUN
ejpam-4867	205	9	,	,	PUNCT
ejpam-4867	205	10	k2	k2	ADJ
ejpam-4867	205	11	)	)	PUNCT
ejpam-4867	205	12	e	e	NOUN
ejpam-4867	205	13	-	-	NOUN
ejpam-4867	205	14	torsion	torsion	NOUN
ejpam-4867	205	15	graph	graph	NOUN
ejpam-4867	205	16	of	of	ADP
ejpam-4867	205	17	c1	c1	PROPN
ejpam-4867	205	18	j.	j.	PROPN
ejpam-4867	205	19	pilongo	pilongo	PROPN
ejpam-4867	205	20	,	,	PUNCT
ejpam-4867	205	21	l.	l.	PROPN
ejpam-4867	205	22	paleta	paleta	PROPN
ejpam-4867	205	23	,	,	PUNCT
ejpam-4867	205	24	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	205	25	/	/	SYM
ejpam-4867	205	26	eur	eur	PROPN
ejpam-4867	205	27	.	.	PUNCT
ejpam-4867	206	1	j.	j.	PROPN
ejpam-4867	206	2	pure	pure	PROPN
ejpam-4867	206	3	appl	appl	PROPN
ejpam-4867	206	4	.	.	PROPN
ejpam-4867	206	5	math	math	PROPN
ejpam-4867	206	6	,	,	PUNCT
ejpam-4867	206	7	17	17	NUM
ejpam-4867	206	8	(	(	PUNCT
ejpam-4867	206	9	2	2	NUM
ejpam-4867	206	10	)	)	PUNCT
ejpam-4867	206	11	(	(	PUNCT
ejpam-4867	206	12	2024	2024	NUM
ejpam-4867	206	13	)	)	PUNCT
ejpam-4867	206	14	,	,	PUNCT
ejpam-4867	206	15	1369	1369	NUM
ejpam-4867	206	16	-	-	SYM
ejpam-4867	206	17	1384	1384	NUM
ejpam-4867	206	18	1380	1380	NUM
ejpam-4867	206	19	for	for	ADP
ejpam-4867	206	20	c2	c2	PROPN
ejpam-4867	206	21	=	=	PUNCT
ejpam-4867	207	1	a	a	DET
ejpam-4867	207	2	⟨11⟩+	⟨11⟩+	PROPN
ejpam-4867	207	3	c	c	PROPN
ejpam-4867	207	4	⟨11⟩	⟨11⟩	NOUN
ejpam-4867	207	5	,	,	PUNCT
ejpam-4867	207	6	we	we	PRON
ejpam-4867	207	7	have	have	VERB
ejpam-4867	207	8	a	a	DET
ejpam-4867	207	9	(	(	PUNCT
ejpam-4867	207	10	1	1	NUM
ejpam-4867	207	11	,	,	PUNCT
ejpam-4867	207	12	0	0	NUM
ejpam-4867	207	13	)	)	PUNCT
ejpam-4867	207	14	e	e	NOUN
ejpam-4867	207	15	-	-	NOUN
ejpam-4867	207	16	torsion	torsion	NOUN
ejpam-4867	207	17	graph	graph	NOUN
ejpam-4867	207	18	which	which	PRON
ejpam-4867	207	19	is	be	AUX
ejpam-4867	207	20	illustrated	illustrate	VERB
ejpam-4867	207	21	in	in	ADP
ejpam-4867	207	22	figure	figure	NOUN
ejpam-4867	207	23	7	7	NUM
ejpam-4867	207	24	.	.	PUNCT
ejpam-4867	207	25	figure	figure	VERB
ejpam-4867	207	26	7	7	NUM
ejpam-4867	207	27	:	:	PUNCT
ejpam-4867	207	28	vertex	vertex	NOUN
ejpam-4867	207	29	-	-	PUNCT
ejpam-4867	207	30	weighted	weight	VERB
ejpam-4867	207	31	(	(	PUNCT
ejpam-4867	207	32	k1	k1	NOUN
ejpam-4867	207	33	,	,	PUNCT
ejpam-4867	207	34	k2	k2	ADJ
ejpam-4867	207	35	)	)	PUNCT
ejpam-4867	208	1	e	e	NOUN
ejpam-4867	208	2	-	-	NOUN
ejpam-4867	208	3	torsion	torsion	NOUN
ejpam-4867	208	4	graph	graph	NOUN
ejpam-4867	208	5	of	of	ADP
ejpam-4867	208	6	c2	c2	PROPN
ejpam-4867	208	7	5.2	5.2	NUM
ejpam-4867	208	8	.	.	PUNCT
ejpam-4867	209	1	(	(	PUNCT
ejpam-4867	209	2	k1	k1	NOUN
ejpam-4867	209	3	,	,	PUNCT
ejpam-4867	209	4	k2	k2	ADJ
ejpam-4867	209	5	)	)	PUNCT
ejpam-4867	209	6	e	e	NOUN
ejpam-4867	209	7	-	-	NOUN
ejpam-4867	209	8	torsion	torsion	NOUN
ejpam-4867	209	9	graph	graph	NOUN
ejpam-4867	209	10	of	of	ADP
ejpam-4867	209	11	qsd	qsd	NOUN
ejpam-4867	209	12	codes	code	NOUN
ejpam-4867	209	13	for	for	ADP
ejpam-4867	209	14	n=3	n=3	NOUN
ejpam-4867	209	15	.	.	NOUN
ejpam-4867	209	16	for	for	ADP
ejpam-4867	209	17	c3	c3	PROPN
ejpam-4867	209	18	=	=	PUNCT
ejpam-4867	209	19	a	a	DET
ejpam-4867	209	20	⟨000⟩+	⟨000⟩+	PROPN
ejpam-4867	209	21	c	c	NOUN
ejpam-4867	209	22	⟨100	⟨100	NOUN
ejpam-4867	209	23	,	,	PUNCT
ejpam-4867	209	24	010	010	NUM
ejpam-4867	209	25	,	,	PUNCT
ejpam-4867	209	26	001⟩	001⟩	NOUN
ejpam-4867	209	27	,	,	PUNCT
ejpam-4867	209	28	we	we	PRON
ejpam-4867	209	29	have	have	VERB
ejpam-4867	209	30	a	a	DET
ejpam-4867	209	31	(	(	PUNCT
ejpam-4867	209	32	0	0	NUM
ejpam-4867	209	33	,	,	PUNCT
ejpam-4867	209	34	3	3	X
ejpam-4867	209	35	)	)	PUNCT
ejpam-4867	209	36	e	e	NOUN
ejpam-4867	209	37	-	-	NOUN
ejpam-4867	209	38	torsion	torsion	NOUN
ejpam-4867	209	39	graph	graph	NOUN
ejpam-4867	209	40	which	which	PRON
ejpam-4867	209	41	is	be	AUX
ejpam-4867	209	42	illustrated	illustrate	VERB
ejpam-4867	209	43	in	in	ADP
ejpam-4867	209	44	figure	figure	NOUN
ejpam-4867	209	45	8	8	NUM
ejpam-4867	209	46	.	.	PUNCT
ejpam-4867	210	1	figure	figure	VERB
ejpam-4867	210	2	8	8	NUM
ejpam-4867	210	3	:	:	PUNCT
ejpam-4867	210	4	vertex	vertex	NOUN
ejpam-4867	210	5	-	-	PUNCT
ejpam-4867	210	6	weighted	weight	VERB
ejpam-4867	210	7	(	(	PUNCT
ejpam-4867	210	8	k1	k1	NOUN
ejpam-4867	210	9	,	,	PUNCT
ejpam-4867	210	10	k2	k2	ADJ
ejpam-4867	210	11	)	)	PUNCT
ejpam-4867	210	12	e	e	NOUN
ejpam-4867	210	13	-	-	NOUN
ejpam-4867	210	14	torsion	torsion	NOUN
ejpam-4867	210	15	graph	graph	NOUN
ejpam-4867	210	16	of	of	ADP
ejpam-4867	210	17	c3	c3	PROPN
ejpam-4867	210	18	5.3	5.3	NUM
ejpam-4867	210	19	.	.	PUNCT
ejpam-4867	211	1	(	(	PUNCT
ejpam-4867	211	2	k1	k1	NOUN
ejpam-4867	211	3	,	,	PUNCT
ejpam-4867	211	4	k2	k2	ADJ
ejpam-4867	211	5	)	)	PUNCT
ejpam-4867	211	6	e	e	NOUN
ejpam-4867	211	7	-	-	NOUN
ejpam-4867	211	8	torsion	torsion	NOUN
ejpam-4867	211	9	graph	graph	NOUN
ejpam-4867	211	10	of	of	ADP
ejpam-4867	211	11	qsd	qsd	NOUN
ejpam-4867	211	12	codes	code	NOUN
ejpam-4867	211	13	for	for	ADP
ejpam-4867	211	14	n=4	n=4	PROPN
ejpam-4867	211	15	.	.	PROPN
ejpam-4867	211	16	for	for	ADP
ejpam-4867	211	17	c5	c5	PROPN
ejpam-4867	211	18	=	=	PUNCT
ejpam-4867	212	1	a	a	DET
ejpam-4867	212	2	⟨0000⟩+	⟨0000⟩+	PROPN
ejpam-4867	212	3	c	c	NOUN
ejpam-4867	212	4	⟨1000	⟨1000	PROPN
ejpam-4867	212	5	,	,	PUNCT
ejpam-4867	212	6	0100	0100	NUM
ejpam-4867	212	7	,	,	PUNCT
ejpam-4867	212	8	0010	0010	NUM
ejpam-4867	212	9	,	,	PUNCT
ejpam-4867	212	10	0001⟩	0001⟩	PROPN
ejpam-4867	212	11	,	,	PUNCT
ejpam-4867	212	12	we	we	PRON
ejpam-4867	212	13	have	have	VERB
ejpam-4867	212	14	a	a	DET
ejpam-4867	212	15	(	(	PUNCT
ejpam-4867	212	16	0	0	NUM
ejpam-4867	212	17	,	,	PUNCT
ejpam-4867	212	18	4	4	NUM
ejpam-4867	212	19	)	)	PUNCT
ejpam-4867	212	20	e	e	NOUN
ejpam-4867	212	21	-	-	NOUN
ejpam-4867	212	22	torsion	torsion	NOUN
ejpam-4867	212	23	graph	graph	NOUN
ejpam-4867	212	24	which	which	PRON
ejpam-4867	212	25	is	be	AUX
ejpam-4867	212	26	illustrated	illustrate	VERB
ejpam-4867	212	27	in	in	ADP
ejpam-4867	212	28	figure	figure	NOUN
ejpam-4867	212	29	10	10	NUM
ejpam-4867	212	30	.	.	PUNCT
ejpam-4867	213	1	j.	j.	PROPN
ejpam-4867	213	2	pilongo	pilongo	PROPN
ejpam-4867	213	3	,	,	PUNCT
ejpam-4867	213	4	l.	l.	PROPN
ejpam-4867	213	5	paleta	paleta	PROPN
ejpam-4867	213	6	,	,	PUNCT
ejpam-4867	213	7	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	213	8	/	/	SYM
ejpam-4867	213	9	eur	eur	PROPN
ejpam-4867	213	10	.	.	PUNCT
ejpam-4867	214	1	j.	j.	PROPN
ejpam-4867	214	2	pure	pure	PROPN
ejpam-4867	214	3	appl	appl	PROPN
ejpam-4867	214	4	.	.	PROPN
ejpam-4867	214	5	math	math	PROPN
ejpam-4867	214	6	,	,	PUNCT
ejpam-4867	214	7	17	17	NUM
ejpam-4867	214	8	(	(	PUNCT
ejpam-4867	214	9	2	2	NUM
ejpam-4867	214	10	)	)	PUNCT
ejpam-4867	214	11	(	(	PUNCT
ejpam-4867	214	12	2024	2024	NUM
ejpam-4867	214	13	)	)	PUNCT
ejpam-4867	214	14	,	,	PUNCT
ejpam-4867	214	15	1369	1369	NUM
ejpam-4867	214	16	-	-	SYM
ejpam-4867	214	17	1384	1384	NUM
ejpam-4867	214	18	1381	1381	NUM
ejpam-4867	214	19	for	for	ADP
ejpam-4867	214	20	c4	c4	NOUN
ejpam-4867	214	21	=	=	PUNCT
ejpam-4867	214	22	a	a	DET
ejpam-4867	214	23	⟨101⟩+	⟨101⟩+	NOUN
ejpam-4867	214	24	c	c	X
ejpam-4867	214	25	⟨101	⟨101	NOUN
ejpam-4867	214	26	,	,	PUNCT
ejpam-4867	214	27	010⟩	010⟩	NOUN
ejpam-4867	214	28	,	,	PUNCT
ejpam-4867	214	29	we	we	PRON
ejpam-4867	214	30	have	have	VERB
ejpam-4867	214	31	a	a	DET
ejpam-4867	214	32	(	(	PUNCT
ejpam-4867	214	33	1	1	NUM
ejpam-4867	214	34	,	,	PUNCT
ejpam-4867	214	35	1	1	NUM
ejpam-4867	214	36	)	)	PUNCT
ejpam-4867	214	37	e	e	NOUN
ejpam-4867	214	38	-	-	NOUN
ejpam-4867	214	39	torsion	torsion	NOUN
ejpam-4867	214	40	graph	graph	NOUN
ejpam-4867	214	41	which	which	PRON
ejpam-4867	214	42	is	be	AUX
ejpam-4867	214	43	illustrated	illustrate	VERB
ejpam-4867	214	44	in	in	ADP
ejpam-4867	214	45	figure	figure	NOUN
ejpam-4867	214	46	9	9	NUM
ejpam-4867	214	47	.	.	PUNCT
ejpam-4867	214	48	figure	figure	VERB
ejpam-4867	214	49	9	9	NUM
ejpam-4867	214	50	:	:	PUNCT
ejpam-4867	214	51	vertex	vertex	NOUN
ejpam-4867	214	52	-	-	PUNCT
ejpam-4867	214	53	weighted	weight	VERB
ejpam-4867	214	54	(	(	PUNCT
ejpam-4867	214	55	k1	k1	NOUN
ejpam-4867	214	56	,	,	PUNCT
ejpam-4867	214	57	k2	k2	ADJ
ejpam-4867	214	58	)	)	PUNCT
ejpam-4867	214	59	e	e	NOUN
ejpam-4867	214	60	-	-	NOUN
ejpam-4867	214	61	torsion	torsion	NOUN
ejpam-4867	214	62	graph	graph	NOUN
ejpam-4867	214	63	of	of	ADP
ejpam-4867	214	64	c4	c4	NOUN
ejpam-4867	214	65	figure	figure	NOUN
ejpam-4867	214	66	10	10	NUM
ejpam-4867	214	67	:	:	PUNCT
ejpam-4867	214	68	vertex	vertex	NOUN
ejpam-4867	214	69	-	-	PUNCT
ejpam-4867	214	70	weighted	weight	VERB
ejpam-4867	214	71	(	(	PUNCT
ejpam-4867	214	72	k1	k1	NOUN
ejpam-4867	214	73	,	,	PUNCT
ejpam-4867	214	74	k2	k2	ADJ
ejpam-4867	214	75	)	)	PUNCT
ejpam-4867	214	76	e	e	NOUN
ejpam-4867	214	77	-	-	NOUN
ejpam-4867	214	78	torsion	torsion	NOUN
ejpam-4867	214	79	graph	graph	NOUN
ejpam-4867	214	80	of	of	ADP
ejpam-4867	214	81	c5	c5	PROPN
ejpam-4867	214	82	for	for	ADP
ejpam-4867	214	83	c6	c6	PROPN
ejpam-4867	214	84	=	=	PUNCT
ejpam-4867	215	1	a	a	DET
ejpam-4867	215	2	⟨1100⟩+	⟨1100⟩+	PROPN
ejpam-4867	215	3	c	c	PROPN
ejpam-4867	215	4	⟨1100	⟨1100	PROPN
ejpam-4867	215	5	,	,	PUNCT
ejpam-4867	215	6	0010	0010	NUM
ejpam-4867	215	7	,	,	PUNCT
ejpam-4867	215	8	0001⟩	0001⟩	PROPN
ejpam-4867	215	9	,	,	PUNCT
ejpam-4867	215	10	we	we	PRON
ejpam-4867	215	11	have	have	VERB
ejpam-4867	215	12	a	a	DET
ejpam-4867	215	13	(	(	PUNCT
ejpam-4867	215	14	1	1	NUM
ejpam-4867	215	15	,	,	PUNCT
ejpam-4867	215	16	2	2	NUM
ejpam-4867	215	17	)	)	PUNCT
ejpam-4867	215	18	e	e	NOUN
ejpam-4867	215	19	-	-	NOUN
ejpam-4867	215	20	torsion	torsion	NOUN
ejpam-4867	215	21	graph	graph	NOUN
ejpam-4867	215	22	which	which	PRON
ejpam-4867	215	23	is	be	AUX
ejpam-4867	215	24	illustrated	illustrate	VERB
ejpam-4867	215	25	in	in	ADP
ejpam-4867	215	26	figure	figure	NOUN
ejpam-4867	215	27	11	11	NUM
ejpam-4867	215	28	.	.	PUNCT
ejpam-4867	216	1	figure	figure	VERB
ejpam-4867	216	2	11	11	NUM
ejpam-4867	216	3	:	:	PUNCT
ejpam-4867	216	4	vertex	vertex	NOUN
ejpam-4867	216	5	-	-	PUNCT
ejpam-4867	216	6	weighted	weight	VERB
ejpam-4867	216	7	(	(	PUNCT
ejpam-4867	216	8	k1	k1	NOUN
ejpam-4867	216	9	,	,	PUNCT
ejpam-4867	216	10	k2	k2	ADJ
ejpam-4867	216	11	)	)	PUNCT
ejpam-4867	216	12	e	e	NOUN
ejpam-4867	216	13	-	-	NOUN
ejpam-4867	216	14	torsion	torsion	NOUN
ejpam-4867	216	15	graph	graph	NOUN
ejpam-4867	216	16	of	of	ADP
ejpam-4867	216	17	c6	c6	PROPN
ejpam-4867	216	18	j.	j.	PROPN
ejpam-4867	216	19	pilongo	pilongo	PROPN
ejpam-4867	216	20	,	,	PUNCT
ejpam-4867	216	21	l.	l.	PROPN
ejpam-4867	216	22	paleta	paleta	PROPN
ejpam-4867	216	23	,	,	PUNCT
ejpam-4867	216	24	p.l.benjamin	p.l.benjamin	NOUN
ejpam-4867	216	25	/	/	SYM
ejpam-4867	216	26	eur	eur	PROPN
ejpam-4867	216	27	.	.	PUNCT
ejpam-4867	217	1	j.	j.	PROPN
ejpam-4867	217	2	pure	pure	PROPN
ejpam-4867	217	3	appl	appl	PROPN
ejpam-4867	217	4	.	.	PROPN
ejpam-4867	217	5	math	math	PROPN
ejpam-4867	217	6	,	,	PUNCT
ejpam-4867	217	7	17	17	NUM
ejpam-4867	217	8	(	(	PUNCT
ejpam-4867	217	9	2	2	NUM
ejpam-4867	217	10	)	)	PUNCT
ejpam-4867	217	11	(	(	PUNCT
ejpam-4867	217	12	2024	2024	NUM
ejpam-4867	217	13	)	)	PUNCT
ejpam-4867	217	14	,	,	PUNCT
ejpam-4867	217	15	1369	1369	NUM
ejpam-4867	217	16	-	-	SYM
ejpam-4867	217	17	1384	1384	NUM
ejpam-4867	217	18	1382	1382	NUM
ejpam-4867	217	19	for	for	ADP
ejpam-4867	217	20	c7	c7	PROPN
ejpam-4867	217	21	=	=	PUNCT
ejpam-4867	217	22	a	a	DET
ejpam-4867	217	23	⟨1111⟩+	⟨1111⟩+	NUM
ejpam-4867	217	24	c	c	NOUN
ejpam-4867	217	25	⟨1111	⟨1111	NOUN
ejpam-4867	217	26	,	,	PUNCT
ejpam-4867	217	27	1100	1100	NUM
ejpam-4867	217	28	,	,	PUNCT
ejpam-4867	217	29	0110⟩	0110⟩	PROPN
ejpam-4867	217	30	,	,	PUNCT
ejpam-4867	217	31	we	we	PRON
ejpam-4867	217	32	have	have	VERB
ejpam-4867	217	33	a	a	DET
ejpam-4867	217	34	(	(	PUNCT
ejpam-4867	217	35	1	1	NUM
ejpam-4867	217	36	,	,	PUNCT
ejpam-4867	217	37	2	2	NUM
ejpam-4867	217	38	)	)	PUNCT
ejpam-4867	217	39	e	e	NOUN
ejpam-4867	217	40	-	-	NOUN
ejpam-4867	217	41	torsion	torsion	NOUN
ejpam-4867	217	42	graph	graph	NOUN
ejpam-4867	217	43	which	which	PRON
ejpam-4867	217	44	is	be	AUX
ejpam-4867	217	45	illustrated	illustrate	VERB
ejpam-4867	217	46	in	in	ADP
ejpam-4867	217	47	figure	figure	NOUN
ejpam-4867	217	48	12	12	NUM
ejpam-4867	217	49	.	.	PUNCT
ejpam-4867	218	1	figure	figure	NOUN
ejpam-4867	218	2	12	12	NUM
ejpam-4867	218	3	:	:	PUNCT
ejpam-4867	218	4	vertex	vertex	NOUN
ejpam-4867	218	5	-	-	PUNCT
ejpam-4867	218	6	weighted	weight	VERB
ejpam-4867	218	7	(	(	PUNCT
ejpam-4867	218	8	k1	k1	NOUN
ejpam-4867	218	9	,	,	PUNCT
ejpam-4867	218	10	k2	k2	ADJ
ejpam-4867	218	11	)	)	PUNCT
ejpam-4867	218	12	e	e	NOUN
ejpam-4867	218	13	-	-	NOUN
ejpam-4867	218	14	torsion	torsion	NOUN
ejpam-4867	218	15	graph	graph	NOUN
ejpam-4867	218	16	of	of	ADP
ejpam-4867	218	17	c7	c7	PROPN
ejpam-4867	218	18	for	for	ADP
ejpam-4867	218	19	c8	c8	PROPN
ejpam-4867	218	20	=	=	PROPN
ejpam-4867	218	21	a	a	DET
ejpam-4867	218	22	⟨1100	⟨1100	NOUN
ejpam-4867	218	23	,	,	PUNCT
ejpam-4867	218	24	0011⟩+	0011⟩+	PROPN
ejpam-4867	218	25	c	c	NOUN
ejpam-4867	218	26	⟨1100	⟨1100	PROPN
ejpam-4867	218	27	,	,	PUNCT
ejpam-4867	218	28	0011⟩	0011⟩	NUM
ejpam-4867	218	29	,	,	PUNCT
ejpam-4867	218	30	we	we	PRON
ejpam-4867	218	31	have	have	VERB
ejpam-4867	218	32	a	a	DET
ejpam-4867	218	33	(	(	PUNCT
ejpam-4867	218	34	2	2	NUM
ejpam-4867	218	35	,	,	PUNCT
ejpam-4867	218	36	0	0	NUM
ejpam-4867	218	37	)	)	PUNCT
ejpam-4867	218	38	e	e	NOUN
ejpam-4867	218	39	-	-	NOUN
ejpam-4867	218	40	torsion	torsion	NOUN
ejpam-4867	218	41	graph	graph	NOUN
ejpam-4867	218	42	which	which	PRON
ejpam-4867	218	43	is	be	AUX
ejpam-4867	218	44	illustrated	illustrate	VERB
ejpam-4867	218	45	in	in	ADP
ejpam-4867	218	46	figure	figure	NOUN
ejpam-4867	218	47	13	13	NUM
ejpam-4867	218	48	.	.	PUNCT
ejpam-4867	219	1	figure	figure	VERB
ejpam-4867	219	2	13	13	NUM
ejpam-4867	219	3	:	:	PUNCT
ejpam-4867	219	4	vertex	vertex	NOUN
ejpam-4867	219	5	-	-	PUNCT
ejpam-4867	219	6	weighted	weight	VERB
ejpam-4867	219	7	(	(	PUNCT
ejpam-4867	219	8	k1	k1	NOUN
ejpam-4867	219	9	,	,	PUNCT
ejpam-4867	219	10	k2	k2	ADJ
ejpam-4867	219	11	)	)	PUNCT
ejpam-4867	219	12	e	e	NOUN
ejpam-4867	219	13	-	-	NOUN
ejpam-4867	219	14	torsion	torsion	NOUN
ejpam-4867	219	15	graph	graph	NOUN
ejpam-4867	219	16	of	of	ADP
ejpam-4867	219	17	c8	c8	PROPN
ejpam-4867	219	18	references	reference	NOUN
ejpam-4867	219	19	1383	1383	NUM
ejpam-4867	219	20	6	6	NUM
ejpam-4867	219	21	.	.	PUNCT
ejpam-4867	220	1	conclusion	conclusion	NOUN
ejpam-4867	220	2	in	in	ADP
ejpam-4867	220	3	this	this	DET
ejpam-4867	220	4	paper	paper	NOUN
ejpam-4867	220	5	,	,	PUNCT
ejpam-4867	220	6	we	we	PRON
ejpam-4867	220	7	studied	study	VERB
ejpam-4867	220	8	the	the	DET
ejpam-4867	220	9	(	(	PUNCT
ejpam-4867	220	10	k1	k1	NOUN
ejpam-4867	220	11	,	,	PUNCT
ejpam-4867	220	12	k2	k2	ADJ
ejpam-4867	220	13	)	)	PUNCT
ejpam-4867	220	14	e	e	NOUN
ejpam-4867	220	15	-	-	NOUN
ejpam-4867	220	16	torsion	torsion	NOUN
ejpam-4867	220	17	graph	graph	NOUN
ejpam-4867	220	18	of	of	ADP
ejpam-4867	220	19	a	a	DET
ejpam-4867	220	20	type-(k1	type-(k1	ADJ
ejpam-4867	220	21	,	,	PUNCT
ejpam-4867	220	22	k2	k2	ADJ
ejpam-4867	220	23	)	)	PUNCT
ejpam-4867	220	24	e	e	NOUN
ejpam-4867	220	25	-	-	NOUN
ejpam-4867	220	26	codes	code	NOUN
ejpam-4867	220	27	.	.	PUNCT
ejpam-4867	221	1	in	in	ADP
ejpam-4867	221	2	particular	particular	ADJ
ejpam-4867	221	3	,	,	PUNCT
ejpam-4867	221	4	the	the	DET
ejpam-4867	221	5	size	size	NOUN
ejpam-4867	221	6	of	of	ADP
ejpam-4867	221	7	the	the	DET
ejpam-4867	221	8	set	set	NOUN
ejpam-4867	221	9	of	of	ADP
ejpam-4867	221	10	vertices	vertex	NOUN
ejpam-4867	221	11	and	and	CCONJ
ejpam-4867	221	12	set	set	NOUN
ejpam-4867	221	13	of	of	ADP
ejpam-4867	221	14	edges	edge	NOUN
ejpam-4867	221	15	.	.	PUNCT
ejpam-4867	222	1	we	we	PRON
ejpam-4867	222	2	also	also	ADV
ejpam-4867	222	3	characterized	characterize	VERB
ejpam-4867	222	4	(	(	PUNCT
ejpam-4867	222	5	k1	k1	NOUN
ejpam-4867	222	6	,	,	PUNCT
ejpam-4867	222	7	k2	k2	ADJ
ejpam-4867	222	8	)	)	PUNCT
ejpam-4867	222	9	e	e	NOUN
ejpam-4867	222	10	-	-	NOUN
ejpam-4867	222	11	torsion	torsion	NOUN
ejpam-4867	222	12	graph	graph	NOUN
ejpam-4867	222	13	when	when	SCONJ
ejpam-4867	222	14	k1	k1	PROPN
ejpam-4867	222	15	=	=	SYM
ejpam-4867	222	16	0	0	NUM
ejpam-4867	222	17	and	and	CCONJ
ejpam-4867	222	18	k2	k2	PROPN
ejpam-4867	222	19	=	=	SYM
ejpam-4867	222	20	0	0	PUNCT
ejpam-4867	222	21	and	and	CCONJ
ejpam-4867	222	22	introduced	introduce	VERB
ejpam-4867	222	23	the	the	DET
ejpam-4867	222	24	notion	notion	NOUN
ejpam-4867	222	25	of	of	ADP
ejpam-4867	222	26	vertex	vertex	NOUN
ejpam-4867	222	27	-	-	PUNCT
ejpam-4867	222	28	weighted	weight	VERB
ejpam-4867	222	29	(	(	PUNCT
ejpam-4867	222	30	k1	k1	NOUN
ejpam-4867	222	31	,	,	PUNCT
ejpam-4867	222	32	k2	k2	ADJ
ejpam-4867	222	33	)	)	PUNCT
ejpam-4867	222	34	e	e	NOUN
ejpam-4867	222	35	-	-	NOUN
ejpam-4867	222	36	torsion	torsion	NOUN
ejpam-4867	222	37	graph	graph	NOUN
ejpam-4867	222	38	to	to	PART
ejpam-4867	222	39	differentiate	differentiate	VERB
ejpam-4867	222	40	inequivalent	inequivalent	NOUN
ejpam-4867	222	41	qsd	qsd	NOUN
ejpam-4867	222	42	codes	code	NOUN
ejpam-4867	222	43	of	of	ADP
ejpam-4867	222	44	the	the	DET
ejpam-4867	222	45	same	same	ADJ
ejpam-4867	222	46	type	type	NOUN
ejpam-4867	222	47	.	.	PUNCT
ejpam-4867	223	1	finally	finally	ADV
ejpam-4867	223	2	,	,	PUNCT
ejpam-4867	223	3	we	we	PRON
ejpam-4867	223	4	were	be	AUX
ejpam-4867	223	5	able	able	ADJ
ejpam-4867	223	6	to	to	PART
ejpam-4867	223	7	represent	represent	VERB
ejpam-4867	223	8	qsd	qsd	NOUN
ejpam-4867	223	9	codes	code	NOUN
ejpam-4867	223	10	which	which	PRON
ejpam-4867	223	11	were	be	AUX
ejpam-4867	223	12	classified	classify	VERB
ejpam-4867	223	13	in	in	ADP
ejpam-4867	223	14	[	[	X
ejpam-4867	223	15	3	3	X
ejpam-4867	223	16	]	]	PUNCT
ejpam-4867	223	17	up	up	ADP
ejpam-4867	223	18	to	to	ADP
ejpam-4867	223	19	n	n	NOUN
ejpam-4867	223	20	=	=	NOUN
ejpam-4867	223	21	4	4	NUM
ejpam-4867	223	22	using	use	VERB
ejpam-4867	223	23	the	the	DET
ejpam-4867	223	24	vertex	vertex	NOUN
ejpam-4867	223	25	-	-	PUNCT
ejpam-4867	223	26	weighted	weight	VERB
ejpam-4867	223	27	(	(	PUNCT
ejpam-4867	223	28	k1	k1	NOUN
ejpam-4867	223	29	,	,	PUNCT
ejpam-4867	223	30	k2	k2	ADJ
ejpam-4867	223	31	)	)	PUNCT
ejpam-4867	223	32	e	e	NOUN
ejpam-4867	223	33	-	-	NOUN
ejpam-4867	223	34	torsion	torsion	NOUN
ejpam-4867	223	35	graph	graph	NOUN
ejpam-4867	223	36	.	.	PUNCT
ejpam-4867	224	1	by	by	ADP
ejpam-4867	224	2	defining	define	VERB
ejpam-4867	224	3	a	a	DET
ejpam-4867	224	4	(	(	PUNCT
ejpam-4867	224	5	k1	k1	NOUN
ejpam-4867	224	6	,	,	PUNCT
ejpam-4867	224	7	k2	k2	ADJ
ejpam-4867	224	8	)	)	PUNCT
ejpam-4867	224	9	e	e	NOUN
ejpam-4867	224	10	-	-	NOUN
ejpam-4867	224	11	torsion	torsion	NOUN
ejpam-4867	224	12	graph	graph	NOUN
ejpam-4867	224	13	g	g	ADP
ejpam-4867	224	14	such	such	ADJ
ejpam-4867	224	15	that	that	SCONJ
ejpam-4867	224	16	the	the	DET
ejpam-4867	224	17	v	v	NOUN
ejpam-4867	224	18	(	(	PUNCT
ejpam-4867	224	19	g	g	NOUN
ejpam-4867	224	20	)	)	PUNCT
ejpam-4867	224	21	=	=	SYM
ejpam-4867	225	1	2k1+k2	2k1+k2	NUM
ejpam-4867	225	2	,	,	PUNCT
ejpam-4867	225	3	there	there	PRON
ejpam-4867	225	4	are	be	VERB
ejpam-4867	225	5	2k1	2k1	NUM
ejpam-4867	225	6	vertices	vertex	NOUN
ejpam-4867	225	7	that	that	PRON
ejpam-4867	225	8	have	have	VERB
ejpam-4867	225	9	degree	degree	NOUN
ejpam-4867	225	10	2k1+k2	2k1+k2	NUM
ejpam-4867	225	11	−	−	NOUN
ejpam-4867	225	12	1	1	NUM
ejpam-4867	225	13	with	with	ADP
ejpam-4867	225	14	the	the	DET
ejpam-4867	225	15	rest	rest	NOUN
ejpam-4867	225	16	vertices	vertex	NOUN
ejpam-4867	225	17	,	,	PUNCT
ejpam-4867	225	18	if	if	SCONJ
ejpam-4867	225	19	there	there	PRON
ejpam-4867	225	20	exist	exist	VERB
ejpam-4867	225	21	,	,	PUNCT
ejpam-4867	225	22	have	have	VERB
ejpam-4867	225	23	degree	degree	NOUN
ejpam-4867	225	24	2k1	2k1	NUM
ejpam-4867	225	25	.	.	PUNCT
ejpam-4867	226	1	for	for	ADP
ejpam-4867	226	2	future	future	ADJ
ejpam-4867	226	3	study	study	NOUN
ejpam-4867	226	4	,	,	PUNCT
ejpam-4867	226	5	after	after	ADP
ejpam-4867	226	6	graph	graph	NOUN
ejpam-4867	226	7	operations	operation	NOUN
ejpam-4867	226	8	of	of	ADP
ejpam-4867	226	9	two	two	NUM
ejpam-4867	226	10	(	(	PUNCT
ejpam-4867	226	11	k1	k1	NOUN
ejpam-4867	226	12	,	,	PUNCT
ejpam-4867	226	13	k2	k2	ADJ
ejpam-4867	226	14	)	)	PUNCT
ejpam-4867	226	15	e	e	NOUN
ejpam-4867	226	16	-	-	NOUN
ejpam-4867	226	17	torsion	torsion	NOUN
ejpam-4867	226	18	graphs	graph	NOUN
ejpam-4867	226	19	is	be	AUX
ejpam-4867	226	20	a	a	DET
ejpam-4867	226	21	(	(	PUNCT
ejpam-4867	226	22	k1	k1	NOUN
ejpam-4867	226	23	,	,	PUNCT
ejpam-4867	226	24	k2	k2	ADJ
ejpam-4867	226	25	)	)	PUNCT
ejpam-4867	226	26	e	e	NOUN
ejpam-4867	226	27	-	-	NOUN
ejpam-4867	226	28	torsion	torsion	NOUN
ejpam-4867	226	29	graph	graph	NOUN
ejpam-4867	226	30	?	?	PUNCT
ejpam-4867	227	1	also	also	ADV
ejpam-4867	227	2	,	,	PUNCT
ejpam-4867	227	3	one	one	PRON
ejpam-4867	227	4	can	can	AUX
ejpam-4867	227	5	explore	explore	VERB
ejpam-4867	227	6	center	center	NOUN
ejpam-4867	227	7	of	of	ADP
ejpam-4867	227	8	(	(	PUNCT
ejpam-4867	227	9	k1	k1	PROPN
ejpam-4867	227	10	,	,	PUNCT
ejpam-4867	227	11	k2	k2	ADJ
ejpam-4867	227	12	)	)	PUNCT
ejpam-4867	227	13	e	e	NOUN
ejpam-4867	227	14	-	-	NOUN
ejpam-4867	227	15	torsion	torsion	NOUN
ejpam-4867	227	16	graphs	graph	NOUN
ejpam-4867	227	17	and	and	CCONJ
ejpam-4867	227	18	the	the	DET
ejpam-4867	227	19	dominating	dominating	NOUN
ejpam-4867	227	20	sets	set	NOUN
ejpam-4867	227	21	of	of	ADP
ejpam-4867	227	22	(	(	PUNCT
ejpam-4867	227	23	k1	k1	NOUN
ejpam-4867	227	24	,	,	PUNCT
ejpam-4867	227	25	k2	k2	ADJ
ejpam-4867	227	26	)	)	PUNCT
ejpam-4867	227	27	e	e	NOUN
ejpam-4867	227	28	-	-	NOUN
ejpam-4867	227	29	torsion	torsion	NOUN
ejpam-4867	227	30	graphs	graph	NOUN
ejpam-4867	227	31	.	.	PUNCT
ejpam-4867	228	1	references	reference	NOUN
ejpam-4867	228	2	[	[	X
ejpam-4867	228	3	1	1	NUM
ejpam-4867	228	4	]	]	PUNCT
ejpam-4867	228	5	a.	a.	NOUN
ejpam-4867	228	6	alahmadi	alahmadi	PROPN
ejpam-4867	228	7	,	,	PUNCT
ejpam-4867	228	8	a.	a.	NOUN
ejpam-4867	228	9	alkathiry	alkathiry	NOUN
ejpam-4867	228	10	,	,	PUNCT
ejpam-4867	228	11	a.	a.	NOUN
ejpam-4867	228	12	altassan	altassan	PROPN
ejpam-4867	228	13	,	,	PUNCT
ejpam-4867	228	14	w.	w.	PROPN
ejpam-4867	228	15	basaffar	basaffar	PROPN
ejpam-4867	228	16	,	,	PUNCT
ejpam-4867	228	17	a.	a.	NOUN
ejpam-4867	228	18	bonnecaze	bonnecaze	NOUN
ejpam-4867	228	19	,	,	PUNCT
ejpam-4867	228	20	h.	h.	PROPN
ejpam-4867	228	21	shoaib	shoaib	PROPN
ejpam-4867	228	22	,	,	PUNCT
ejpam-4867	228	23	and	and	CCONJ
ejpam-4867	228	24	p.	p.	PROPN
ejpam-4867	228	25	sole	sole	NOUN
ejpam-4867	228	26	’	'	PUNCT
ejpam-4867	228	27	.	.	PUNCT
ejpam-4867	229	1	quasi	quasi	NOUN
ejpam-4867	229	2	self	self	NOUN
ejpam-4867	229	3	-	-	PUNCT
ejpam-4867	229	4	dual	dual	ADJ
ejpam-4867	229	5	codes	code	NOUN
ejpam-4867	229	6	over	over	ADP
ejpam-4867	229	7	non	non	ADJ
ejpam-4867	229	8	-	-	ADJ
ejpam-4867	229	9	unital	unital	ADJ
ejpam-4867	229	10	rings	ring	NOUN
ejpam-4867	229	11	of	of	ADP
ejpam-4867	229	12	order	order	NOUN
ejpam-4867	229	13	six	six	NUM
ejpam-4867	229	14	.	.	PUNCT
ejpam-4867	230	1	proyecciones	proyeccione	NOUN
ejpam-4867	230	2	(	(	PUNCT
ejpam-4867	230	3	antofagasta	antofagasta	PROPN
ejpam-4867	230	4	)	)	PUNCT
ejpam-4867	230	5	,	,	PUNCT
ejpam-4867	230	6	39(4):1083–1095	39(4):1083–1095	NUM
ejpam-4867	230	7	,	,	PUNCT
ejpam-4867	230	8	2020	2020	NUM
ejpam-4867	230	9	.	.	PUNCT
ejpam-4867	231	1	[	[	X
ejpam-4867	231	2	2	2	NUM
ejpam-4867	231	3	]	]	PUNCT
ejpam-4867	231	4	a.	a.	NOUN
ejpam-4867	231	5	alahmadi	alahmadi	PROPN
ejpam-4867	231	6	,	,	PUNCT
ejpam-4867	231	7	a.	a.	NOUN
ejpam-4867	231	8	alkathiry	alkathiry	NOUN
ejpam-4867	231	9	,	,	PUNCT
ejpam-4867	231	10	a.	a.	NOUN
ejpam-4867	231	11	altassan	altassan	PROPN
ejpam-4867	231	12	,	,	PUNCT
ejpam-4867	231	13	w.	w.	PROPN
ejpam-4867	231	14	basaffar	basaffar	PROPN
ejpam-4867	231	15	,	,	PUNCT
ejpam-4867	231	16	a.	a.	NOUN
ejpam-4867	231	17	bonnecaze	bonnecaze	NOUN
ejpam-4867	231	18	,	,	PUNCT
ejpam-4867	231	19	h.	h.	PROPN
ejpam-4867	231	20	shoaib	shoaib	PROPN
ejpam-4867	231	21	,	,	PUNCT
ejpam-4867	231	22	and	and	CCONJ
ejpam-4867	231	23	p.	p.	PROPN
ejpam-4867	231	24	sole	sole	NOUN
ejpam-4867	231	25	’	'	PUNCT
ejpam-4867	231	26	.	.	PUNCT
ejpam-4867	232	1	type	type	NOUN
ejpam-4867	232	2	iv	iv	NUM
ejpam-4867	232	3	codes	code	NOUN
ejpam-4867	232	4	over	over	ADP
ejpam-4867	232	5	a	a	DET
ejpam-4867	232	6	non	non	ADJ
ejpam-4867	232	7	-	-	ADJ
ejpam-4867	232	8	local	local	ADJ
ejpam-4867	232	9	non	non	ADJ
ejpam-4867	232	10	-	-	ADJ
ejpam-4867	232	11	unital	unital	ADJ
ejpam-4867	232	12	ring	ring	NOUN
ejpam-4867	232	13	.	.	PUNCT
ejpam-4867	233	1	proyecciones	proyecciones	PROPN
ejpam-4867	233	2	(	(	PUNCT
ejpam-4867	233	3	antofagasta	antofagasta	PROPN
ejpam-4867	233	4	,	,	PUNCT
ejpam-4867	233	5	online	online	ADJ
ejpam-4867	233	6	)	)	PUNCT
ejpam-4867	233	7	,	,	PUNCT
ejpam-4867	233	8	39(4):963–978	39(4):963–978	PROPN
ejpam-4867	233	9	,	,	PUNCT
ejpam-4867	233	10	2022	2022	NUM
ejpam-4867	233	11	.	.	PUNCT
ejpam-4867	234	1	[	[	X
ejpam-4867	234	2	3	3	NUM
ejpam-4867	234	3	]	]	PUNCT
ejpam-4867	234	4	a.	a.	NOUN
ejpam-4867	234	5	alahmadi	alahmadi	PROPN
ejpam-4867	234	6	,	,	PUNCT
ejpam-4867	234	7	a.	a.	NOUN
ejpam-4867	234	8	altassan	altassan	PROPN
ejpam-4867	234	9	,	,	PUNCT
ejpam-4867	234	10	w.	w.	PROPN
ejpam-4867	234	11	basaffar	basaffar	PROPN
ejpam-4867	234	12	,	,	PUNCT
ejpam-4867	234	13	a.	a.	NOUN
ejpam-4867	234	14	bonnecaze	bonnecaze	NOUN
ejpam-4867	234	15	,	,	PUNCT
ejpam-4867	234	16	and	and	CCONJ
ejpam-4867	234	17	p.	p.	PROPN
ejpam-4867	234	18	sole	sole	NOUN
ejpam-4867	234	19	’	'	PUNCT
ejpam-4867	234	20	.	.	PUNCT
ejpam-4867	235	1	type	type	NOUN
ejpam-4867	235	2	iv	iv	NUM
ejpam-4867	235	3	codes	code	NOUN
ejpam-4867	235	4	over	over	ADP
ejpam-4867	235	5	a	a	DET
ejpam-4867	235	6	non	non	ADJ
ejpam-4867	235	7	-	-	ADJ
ejpam-4867	235	8	unital	unital	ADJ
ejpam-4867	235	9	ring	ring	NOUN
ejpam-4867	235	10	.	.	PUNCT
ejpam-4867	236	1	journal	journal	PROPN
ejpam-4867	236	2	of	of	ADP
ejpam-4867	236	3	algebra	algebra	PROPN
ejpam-4867	236	4	and	and	CCONJ
ejpam-4867	236	5	its	its	PRON
ejpam-4867	236	6	applications	application	NOUN
ejpam-4867	236	7	,	,	PUNCT
ejpam-4867	236	8	2(7	2(7	NUM
ejpam-4867	236	9	)	)	PUNCT
ejpam-4867	236	10	,	,	PUNCT
ejpam-4867	236	11	2021	2021	NUM
ejpam-4867	236	12	.	.	PUNCT
ejpam-4867	237	1	[	[	X
ejpam-4867	237	2	4	4	NUM
ejpam-4867	237	3	]	]	PUNCT
ejpam-4867	237	4	a.	a.	NOUN
ejpam-4867	237	5	alahmadi	alahmadi	PROPN
ejpam-4867	237	6	,	,	PUNCT
ejpam-4867	237	7	a.	a.	NOUN
ejpam-4867	237	8	melaibari	melaibari	PROPN
ejpam-4867	237	9	,	,	PUNCT
ejpam-4867	237	10	and	and	CCONJ
ejpam-4867	237	11	p.	p.	PROPN
ejpam-4867	237	12	sole	sole	NOUN
ejpam-4867	237	13	’	'	PUNCT
ejpam-4867	237	14	.	.	PUNCT
ejpam-4867	238	1	duality	duality	NOUN
ejpam-4867	238	2	of	of	ADP
ejpam-4867	238	3	codes	code	NOUN
ejpam-4867	238	4	over	over	ADP
ejpam-4867	238	5	non	non	ADJ
ejpam-4867	238	6	-	-	ADJ
ejpam-4867	238	7	unital	unital	ADJ
ejpam-4867	238	8	rings	ring	NOUN
ejpam-4867	238	9	of	of	ADP
ejpam-4867	238	10	order	order	NOUN
ejpam-4867	238	11	four	four	NUM
ejpam-4867	238	12	.	.	PUNCT
ejpam-4867	239	1	ieee	ieee	NOUN
ejpam-4867	239	2	access	access	NOUN
ejpam-4867	239	3	,	,	PUNCT
ejpam-4867	239	4	2023	2023	NUM
ejpam-4867	239	5	.	.	PUNCT
ejpam-4867	240	1	[	[	X
ejpam-4867	240	2	5	5	X
ejpam-4867	240	3	]	]	PUNCT
ejpam-4867	240	4	s.	s.	PROPN
ejpam-4867	240	5	t.	t.	PROPN
ejpam-4867	240	6	dougherty	dougherty	PROPN
ejpam-4867	240	7	,	,	PUNCT
ejpam-4867	240	8	p.	p.	NOUN
ejpam-4867	240	9	gaborit	gaborit	PROPN
ejpam-4867	240	10	,	,	PUNCT
ejpam-4867	240	11	m.	m.	PROPN
ejpam-4867	240	12	harada	harada	PROPN
ejpam-4867	240	13	,	,	PUNCT
ejpam-4867	240	14	a.	a.	NOUN
ejpam-4867	240	15	munemasa	munemasa	PROPN
ejpam-4867	240	16	,	,	PUNCT
ejpam-4867	240	17	and	and	CCONJ
ejpam-4867	240	18	p.	p.	PROPN
ejpam-4867	240	19	sole	sole	NOUN
ejpam-4867	240	20	’	'	PUNCT
ejpam-4867	240	21	.	.	PUNCT
ejpam-4867	241	1	type	type	NOUN
ejpam-4867	241	2	iv	iv	NUM
ejpam-4867	241	3	self	self	NOUN
ejpam-4867	241	4	-	-	PUNCT
ejpam-4867	241	5	dual	dual	ADJ
ejpam-4867	241	6	codes	code	NOUN
ejpam-4867	241	7	over	over	ADP
ejpam-4867	241	8	rings	ring	NOUN
ejpam-4867	241	9	.	.	PUNCT
ejpam-4867	242	1	ieee	ieee	PROPN
ejpam-4867	242	2	trans	trans	PROPN
ejpam-4867	242	3	.	.	PUNCT
ejpam-4867	243	1	information	information	NOUN
ejpam-4867	243	2	theory	theory	NOUN
ejpam-4867	243	3	,	,	PUNCT
ejpam-4867	243	4	45:2345–2360	45:2345–2360	NUM
ejpam-4867	243	5	,	,	PUNCT
ejpam-4867	243	6	1999	1999	NUM
ejpam-4867	243	7	.	.	PUNCT
ejpam-4867	244	1	[	[	X
ejpam-4867	244	2	6	6	NUM
ejpam-4867	244	3	]	]	PUNCT
ejpam-4867	244	4	s.	s.	PROPN
ejpam-4867	244	5	t.	t.	PROPN
ejpam-4867	244	6	dougherty	dougherty	PROPN
ejpam-4867	244	7	,	,	PUNCT
ejpam-4867	244	8	b.	b.	PROPN
ejpam-4867	244	9	yildiz	yildiz	PROPN
ejpam-4867	244	10	,	,	PUNCT
ejpam-4867	244	11	and	and	CCONJ
ejpam-4867	244	12	s.	s.	PROPN
ejpam-4867	244	13	karadeniz	karadeniz	PROPN
ejpam-4867	244	14	.	.	PUNCT
ejpam-4867	244	15	self	self	NOUN
ejpam-4867	244	16	-	-	PUNCT
ejpam-4867	244	17	dual	dual	ADJ
ejpam-4867	244	18	codes	code	NOUN
ejpam-4867	244	19	over	over	ADP
ejpam-4867	244	20	rk	rk	NOUN
ejpam-4867	244	21	and	and	CCONJ
ejpam-4867	244	22	binary	binary	NOUN
ejpam-4867	244	23	self	self	NOUN
ejpam-4867	244	24	-	-	PUNCT
ejpam-4867	244	25	dual	dual	ADJ
ejpam-4867	244	26	codes	code	NOUN
ejpam-4867	244	27	.	.	PUNCT
ejpam-4867	245	1	european	european	ADJ
ejpam-4867	245	2	journal	journal	PROPN
ejpam-4867	245	3	of	of	ADP
ejpam-4867	245	4	pure	pure	ADJ
ejpam-4867	245	5	and	and	CCONJ
ejpam-4867	245	6	applied	applied	ADJ
ejpam-4867	245	7	mathematics	mathematic	NOUN
ejpam-4867	245	8	,	,	PUNCT
ejpam-4867	245	9	6(1):89–106	6(1):89–106	NUM
ejpam-4867	245	10	,	,	PUNCT
ejpam-4867	245	11	2013	2013	NUM
ejpam-4867	245	12	.	.	PUNCT
ejpam-4867	246	1	[	[	X
ejpam-4867	246	2	7	7	X
ejpam-4867	246	3	]	]	X
ejpam-4867	246	4	b.	b.	NOUN
ejpam-4867	246	5	fine	fine	PROPN
ejpam-4867	246	6	.	.	PUNCT
ejpam-4867	247	1	classification	classification	NOUN
ejpam-4867	247	2	of	of	ADP
ejpam-4867	247	3	finite	finite	ADJ
ejpam-4867	247	4	rings	ring	NOUN
ejpam-4867	247	5	of	of	ADP
ejpam-4867	247	6	order	order	NOUN
ejpam-4867	247	7	p2	p2	NOUN
ejpam-4867	247	8	.	.	PUNCT
ejpam-4867	248	1	mathematics	mathematic	NOUN
ejpam-4867	248	2	magazine	magazine	NOUN
ejpam-4867	248	3	,	,	PUNCT
ejpam-4867	248	4	66(4):248	66(4):248	NUM
ejpam-4867	248	5	–	–	PUNCT
ejpam-4867	248	6	252	252	NUM
ejpam-4867	248	7	,	,	PUNCT
ejpam-4867	248	8	1993	1993	NUM
ejpam-4867	248	9	.	.	PUNCT
ejpam-4867	249	1	[	[	X
ejpam-4867	249	2	8	8	NUM
ejpam-4867	249	3	]	]	X
ejpam-4867	249	4	g.	g.	PROPN
ejpam-4867	249	5	d.	d.	PROPN
ejpam-4867	249	6	forney	forney	PROPN
ejpam-4867	249	7	.	.	PUNCT
ejpam-4867	250	1	codes	code	NOUN
ejpam-4867	250	2	on	on	ADP
ejpam-4867	250	3	graphs	graph	NOUN
ejpam-4867	250	4	:	:	PUNCT
ejpam-4867	250	5	fundamentals	fundamental	NOUN
ejpam-4867	250	6	.	.	PUNCT
ejpam-4867	251	1	ieee	ieee	NOUN
ejpam-4867	251	2	transactions	transaction	NOUN
ejpam-4867	251	3	on	on	ADP
ejpam-4867	251	4	information	information	NOUN
ejpam-4867	251	5	theory	theory	NOUN
ejpam-4867	251	6	,	,	PUNCT
ejpam-4867	251	7	60(10):5809–5826	60(10):5809–5826	NOUN
ejpam-4867	251	8	,	,	PUNCT
ejpam-4867	251	9	2014	2014	NUM
ejpam-4867	251	10	.	.	PUNCT
ejpam-4867	252	1	[	[	X
ejpam-4867	252	2	9	9	NUM
ejpam-4867	252	3	]	]	PUNCT
ejpam-4867	252	4	f.	f.	PROPN
ejpam-4867	252	5	harrary	harrary	PROPN
ejpam-4867	252	6	.	.	PUNCT
ejpam-4867	253	1	graph	graph	NOUN
ejpam-4867	253	2	theory	theory	NOUN
ejpam-4867	253	3	.	.	PUNCT
ejpam-4867	254	1	addison	addison	PROPN
ejpam-4867	254	2	-	-	PUNCT
ejpam-4867	254	3	wesley	wesley	PROPN
ejpam-4867	254	4	,	,	PUNCT
ejpam-4867	254	5	1994	1994	NUM
ejpam-4867	254	6	.	.	PUNCT
ejpam-4867	255	1	[	[	X
ejpam-4867	255	2	10	10	NUM
ejpam-4867	255	3	]	]	PUNCT
ejpam-4867	255	4	t.	t.	PROPN
ejpam-4867	255	5	w.	w.	PROPN
ejpam-4867	255	6	hungerford	hungerford	PROPN
ejpam-4867	255	7	.	.	PUNCT
ejpam-4867	256	1	algebra	algebra	PROPN
ejpam-4867	256	2	.	.	PUNCT
ejpam-4867	257	1	springer	springer	NOUN
ejpam-4867	257	2	,	,	PUNCT
ejpam-4867	257	3	1974	1974	NUM
ejpam-4867	257	4	.	.	PUNCT
ejpam-4867	258	1	references	reference	NOUN
ejpam-4867	258	2	1384	1384	NUM
ejpam-4867	258	3	[	[	X
ejpam-4867	258	4	11	11	NUM
ejpam-4867	258	5	]	]	X
ejpam-4867	258	6	n.	n.	PROPN
ejpam-4867	258	7	nopendri	nopendri	PROPN
ejpam-4867	258	8	,	,	PUNCT
ejpam-4867	258	9	i.	i.	PROPN
ejpam-4867	258	10	muchtadi	muchtadi	PROPN
ejpam-4867	258	11	-	-	PUNCT
ejpam-4867	258	12	alamsyah	alamsyah	PROPN
ejpam-4867	258	13	,	,	PUNCT
ejpam-4867	258	14	d.	d.	PROPN
ejpam-4867	258	15	suprijanto	suprijanto	PROPN
ejpam-4867	258	16	,	,	PUNCT
ejpam-4867	258	17	and	and	CCONJ
ejpam-4867	258	18	a.	a.	NOUN
ejpam-4867	258	19	barra	barra	PROPN
ejpam-4867	258	20	.	.	PUNCT
ejpam-4867	259	1	cyclic	cyclic	ADJ
ejpam-4867	259	2	codes	code	NOUN
ejpam-4867	259	3	from	from	ADP
ejpam-4867	259	4	a	a	DET
ejpam-4867	259	5	sequence	sequence	NOUN
ejpam-4867	259	6	over	over	ADP
ejpam-4867	259	7	finite	finite	ADJ
ejpam-4867	259	8	fields	field	NOUN
ejpam-4867	259	9	.	.	PUNCT
ejpam-4867	260	1	european	european	ADJ
ejpam-4867	260	2	journal	journal	PROPN
ejpam-4867	260	3	of	of	ADP
ejpam-4867	260	4	pure	pure	ADJ
ejpam-4867	260	5	and	and	CCONJ
ejpam-4867	260	6	applied	applied	ADJ
ejpam-4867	260	7	mathematics	mathematic	NOUN
ejpam-4867	260	8	,	,	PUNCT
ejpam-4867	260	9	14(3):685–694	14(3):685–694	NUM
ejpam-4867	260	10	,	,	PUNCT
ejpam-4867	260	11	2021	2021	NUM
ejpam-4867	260	12	.	.	PUNCT
ejpam-4867	261	1	[	[	X
ejpam-4867	261	2	12	12	NUM
ejpam-4867	261	3	]	]	X
ejpam-4867	261	4	r.	r.	PROPN
ejpam-4867	261	5	raghavendran	raghavendran	PROPN
ejpam-4867	261	6	.	.	PUNCT
ejpam-4867	262	1	finite	finite	PROPN
ejpam-4867	262	2	associative	associative	PROPN
ejpam-4867	262	3	rings	ring	NOUN
ejpam-4867	262	4	.	.	PUNCT
ejpam-4867	263	1	compositio	compositio	PROPN
ejpam-4867	263	2	mathematica	mathematica	PROPN
ejpam-4867	263	3	,	,	PUNCT
ejpam-4867	263	4	21(2):195–229	21(2):195–229	PROPN
ejpam-4867	263	5	,	,	PUNCT
ejpam-4867	263	6	1969	1969	NUM
ejpam-4867	263	7	.	.	PUNCT
ejpam-4867	264	1	[	[	X
ejpam-4867	264	2	13	13	NUM
ejpam-4867	264	3	]	]	PUNCT
ejpam-4867	264	4	s.	s.	PROPN
ejpam-4867	264	5	e.	e.	PROPN
ejpam-4867	264	6	rouayheb	rouayheb	PROPN
ejpam-4867	264	7	and	and	CCONJ
ejpam-4867	264	8	c.	c.	PROPN
ejpam-4867	264	9	georghiades	georghiade	NOUN
ejpam-4867	264	10	.	.	PUNCT
ejpam-4867	265	1	graph	graph	NOUN
ejpam-4867	265	2	theoretic	theoretic	ADJ
ejpam-4867	265	3	methods	method	NOUN
ejpam-4867	265	4	in	in	ADP
ejpam-4867	265	5	coding	code	VERB
ejpam-4867	265	6	theory	theory	NOUN
ejpam-4867	265	7	.	.	PUNCT
ejpam-4867	266	1	in	in	ADP
ejpam-4867	266	2	springer	springer	NOUN
ejpam-4867	266	3	ebooks	ebook	NOUN
ejpam-4867	266	4	,	,	PUNCT
ejpam-4867	266	5	pages	page	NOUN
ejpam-4867	266	6	53–62	53–62	NUM
ejpam-4867	266	7	.	.	NOUN
ejpam-4867	266	8	2011	2011	NUM
ejpam-4867	266	9	.	.	PUNCT
ejpam-4867	267	1	[	[	X
ejpam-4867	267	2	14	14	NUM
ejpam-4867	267	3	]	]	PUNCT
ejpam-4867	267	4	m.	m.	PROPN
ejpam-4867	267	5	shi	shi	PROPN
ejpam-4867	267	6	,	,	PUNCT
ejpam-4867	267	7	s.	s.	PROPN
ejpam-4867	267	8	wang	wang	PROPN
ejpam-4867	267	9	,	,	PUNCT
ejpam-4867	267	10	j.	j.	PROPN
ejpam-4867	267	11	l.	l.	PROPN
ejpam-4867	267	12	kim	kim	PROPN
ejpam-4867	267	13	,	,	PUNCT
ejpam-4867	267	14	and	and	CCONJ
ejpam-4867	267	15	p.	p.	NOUN
ejpam-4867	267	16	solé.	solé.	PROPN
ejpam-4867	267	17	self	self	NOUN
ejpam-4867	267	18	-	-	PUNCT
ejpam-4867	267	19	orthogonal	orthogonal	ADJ
ejpam-4867	267	20	codes	code	NOUN
ejpam-4867	267	21	over	over	ADP
ejpam-4867	267	22	a	a	DET
ejpam-4867	267	23	non	non	ADJ
ejpam-4867	267	24	-	-	ADJ
ejpam-4867	267	25	unital	unital	ADJ
ejpam-4867	267	26	ring	ring	NOUN
ejpam-4867	267	27	and	and	CCONJ
ejpam-4867	267	28	combinatorial	combinatorial	ADJ
ejpam-4867	267	29	matrices	matrix	NOUN
ejpam-4867	267	30	.	.	PUNCT
ejpam-4867	268	1	designs	design	NOUN
ejpam-4867	268	2	,	,	PUNCT
ejpam-4867	268	3	codes	code	NOUN
ejpam-4867	268	4	and	and	CCONJ
ejpam-4867	268	5	cryptography	cryptography	NOUN
ejpam-4867	268	6	,	,	PUNCT
ejpam-4867	268	7	pages	page	NOUN
ejpam-4867	268	8	1–13	1–13	NOUN
ejpam-4867	268	9	,	,	PUNCT
ejpam-4867	268	10	2021	2021	NUM
ejpam-4867	268	11	.	.	PUNCT
ejpam-4867	269	1	[	[	X
ejpam-4867	269	2	15	15	NUM
ejpam-4867	269	3	]	]	X
ejpam-4867	269	4	b.	b.	PROPN
ejpam-4867	269	5	shinivasulu	shinivasulu	PROPN
ejpam-4867	269	6	and	and	CCONJ
ejpam-4867	269	7	m.	m.	NOUN
ejpam-4867	269	8	bhaintwal	bhaintwal	NOUN
ejpam-4867	269	9	.	.	PUNCT
ejpam-4867	270	1	z2	z2	ADJ
ejpam-4867	270	2	-	-	PUNCT
ejpam-4867	270	3	triple	triple	ADJ
ejpam-4867	270	4	cyclic	cyclic	ADJ
ejpam-4867	270	5	codes	code	NOUN
ejpam-4867	270	6	and	and	CCONJ
ejpam-4867	270	7	their	their	PRON
ejpam-4867	270	8	duals	dual	NOUN
ejpam-4867	270	9	.	.	PUNCT
ejpam-4867	271	1	european	european	ADJ
ejpam-4867	271	2	journal	journal	PROPN
ejpam-4867	271	3	of	of	ADP
ejpam-4867	271	4	pure	pure	ADJ
ejpam-4867	271	5	and	and	CCONJ
ejpam-4867	271	6	applied	applied	ADJ
ejpam-4867	271	7	mathematics	mathematic	NOUN
ejpam-4867	271	8	,	,	PUNCT
ejpam-4867	271	9	10(2):392–409	10(2):392–409	PROPN
ejpam-4867	271	10	,	,	PUNCT
ejpam-4867	271	11	2016	2016	NUM
ejpam-4867	271	12	.	.	PUNCT