id	sid	tid	token	lemma	pos
ejpam-3565	1	1	european	european	PROPN
ejpam-3565	1	2	journal	journal	PROPN
ejpam-3565	1	3	of	of	ADP
ejpam-3565	1	4	pure	pure	ADJ
ejpam-3565	1	5	and	and	CCONJ
ejpam-3565	1	6	applied	apply	VERB
ejpam-3565	1	7	mathematics	mathematic	NOUN
ejpam-3565	1	8	vol	vol	NOUN
ejpam-3565	1	9	.	.	PROPN
ejpam-3565	2	1	12	12	NUM
ejpam-3565	2	2	,	,	PUNCT
ejpam-3565	2	3	no	no	INTJ
ejpam-3565	2	4	.	.	NOUN
ejpam-3565	2	5	4	4	NUM
ejpam-3565	2	6	,	,	PUNCT
ejpam-3565	2	7	2019	2019	NUM
ejpam-3565	2	8	,	,	PUNCT
ejpam-3565	2	9	1701	1701	NUM
ejpam-3565	2	10	-	-	SYM
ejpam-3565	2	11	1716	1716	NUM
ejpam-3565	2	12	issn	issn	VERB
ejpam-3565	2	13	1307	1307	NUM
ejpam-3565	2	14	-	-	SYM
ejpam-3565	2	15	5543	5543	NUM
ejpam-3565	2	16	–	–	PUNCT
ejpam-3565	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3565	2	18	published	publish	VERB
ejpam-3565	2	19	by	by	ADP
ejpam-3565	2	20	new	new	PROPN
ejpam-3565	2	21	york	york	PROPN
ejpam-3565	2	22	business	business	PROPN
ejpam-3565	2	23	global	global	ADJ
ejpam-3565	2	24	mass	mass	NOUN
ejpam-3565	2	25	formula	formula	NOUN
ejpam-3565	2	26	for	for	ADP
ejpam-3565	2	27	self	self	NOUN
ejpam-3565	2	28	-	-	PUNCT
ejpam-3565	2	29	dual	dual	ADJ
ejpam-3565	2	30	codes	code	NOUN
ejpam-3565	2	31	over	over	ADP
ejpam-3565	2	32	galois	galois	PROPN
ejpam-3565	2	33	rings	ring	NOUN
ejpam-3565	2	34	gr(p3	gr(p3	PROPN
ejpam-3565	2	35	,	,	PUNCT
ejpam-3565	2	36	r	r	NOUN
ejpam-3565	2	37	)	)	PUNCT
ejpam-3565	2	38	trilbe	trilbe	NOUN
ejpam-3565	2	39	lizann	lizann	PROPN
ejpam-3565	2	40	e.	e.	PROPN
ejpam-3565	2	41	vasquez1,∗	vasquez1,∗	PROPN
ejpam-3565	2	42	,	,	PUNCT
ejpam-3565	2	43	gaudencio	gaudencio	PROPN
ejpam-3565	2	44	c.	c.	PROPN
ejpam-3565	2	45	petalcorin	petalcorin	PROPN
ejpam-3565	2	46	,	,	PUNCT
ejpam-3565	2	47	jr.1	jr.1	PROPN
ejpam-3565	2	48	1	1	NUM
ejpam-3565	2	49	department	department	NOUN
ejpam-3565	2	50	of	of	ADP
ejpam-3565	2	51	mathematics	mathematic	NOUN
ejpam-3565	2	52	and	and	CCONJ
ejpam-3565	2	53	statistics	statistic	NOUN
ejpam-3565	2	54	,	,	PUNCT
ejpam-3565	2	55	college	college	NOUN
ejpam-3565	2	56	of	of	ADP
ejpam-3565	2	57	science	science	NOUN
ejpam-3565	2	58	and	and	CCONJ
ejpam-3565	2	59	mathematics	mathematic	NOUN
ejpam-3565	2	60	,	,	PUNCT
ejpam-3565	2	61	mindanao	mindanao	PROPN
ejpam-3565	2	62	state	state	PROPN
ejpam-3565	2	63	university	university	PROPN
ejpam-3565	2	64	iligan	iligan	PROPN
ejpam-3565	2	65	institute	institute	PROPN
ejpam-3565	2	66	of	of	ADP
ejpam-3565	2	67	technology	technology	PROPN
ejpam-3565	2	68	,	,	PUNCT
ejpam-3565	2	69	9200	9200	NUM
ejpam-3565	2	70	iligan	iligan	ADJ
ejpam-3565	2	71	city	city	NOUN
ejpam-3565	2	72	,	,	PUNCT
ejpam-3565	3	1	philippines	philippine	NOUN
ejpam-3565	3	2	abstract	abstract	ADJ
ejpam-3565	3	3	.	.	PUNCT
ejpam-3565	4	1	let	let	VERB
ejpam-3565	4	2	p	p	PRON
ejpam-3565	4	3	be	be	AUX
ejpam-3565	4	4	an	an	DET
ejpam-3565	4	5	odd	odd	ADJ
ejpam-3565	4	6	prime	prime	NOUN
ejpam-3565	4	7	and	and	CCONJ
ejpam-3565	4	8	r	r	NOUN
ejpam-3565	4	9	a	a	DET
ejpam-3565	4	10	positive	positive	ADJ
ejpam-3565	4	11	integer	integer	NOUN
ejpam-3565	4	12	.	.	PUNCT
ejpam-3565	5	1	let	let	VERB
ejpam-3565	5	2	gr(p3	gr(p3	NOUN
ejpam-3565	5	3	,	,	PUNCT
ejpam-3565	5	4	r	r	NOUN
ejpam-3565	5	5	)	)	PUNCT
ejpam-3565	5	6	be	be	VERB
ejpam-3565	5	7	the	the	DET
ejpam-3565	5	8	galois	galois	PROPN
ejpam-3565	5	9	ring	ring	NOUN
ejpam-3565	5	10	of	of	ADP
ejpam-3565	5	11	characteristic	characteristic	ADJ
ejpam-3565	5	12	p3	p3	PROPN
ejpam-3565	5	13	and	and	CCONJ
ejpam-3565	5	14	cardinality	cardinality	PROPN
ejpam-3565	5	15	p3r	p3r	PROPN
ejpam-3565	5	16	.	.	PROPN
ejpam-3565	6	1	in	in	ADP
ejpam-3565	6	2	this	this	DET
ejpam-3565	6	3	paper	paper	NOUN
ejpam-3565	6	4	,	,	PUNCT
ejpam-3565	6	5	we	we	PRON
ejpam-3565	6	6	investigate	investigate	VERB
ejpam-3565	6	7	the	the	DET
ejpam-3565	6	8	self	self	NOUN
ejpam-3565	6	9	-	-	PUNCT
ejpam-3565	6	10	dual	dual	ADJ
ejpam-3565	6	11	codes	code	NOUN
ejpam-3565	6	12	over	over	ADP
ejpam-3565	6	13	gr(p3	gr(p3	PROPN
ejpam-3565	6	14	,	,	PUNCT
ejpam-3565	6	15	r	r	NOUN
ejpam-3565	6	16	)	)	PUNCT
ejpam-3565	6	17	and	and	CCONJ
ejpam-3565	6	18	give	give	VERB
ejpam-3565	6	19	a	a	DET
ejpam-3565	6	20	method	method	NOUN
ejpam-3565	6	21	to	to	PART
ejpam-3565	6	22	construct	construct	VERB
ejpam-3565	6	23	self	self	NOUN
ejpam-3565	6	24	-	-	PUNCT
ejpam-3565	6	25	dual	dual	ADJ
ejpam-3565	6	26	codes	code	NOUN
ejpam-3565	6	27	over	over	ADP
ejpam-3565	6	28	this	this	DET
ejpam-3565	6	29	ring	ring	NOUN
ejpam-3565	6	30	.	.	PUNCT
ejpam-3565	7	1	we	we	PRON
ejpam-3565	7	2	establish	establish	VERB
ejpam-3565	7	3	a	a	DET
ejpam-3565	7	4	mass	mass	ADJ
ejpam-3565	7	5	formula	formula	NOUN
ejpam-3565	7	6	for	for	ADP
ejpam-3565	7	7	self	self	NOUN
ejpam-3565	7	8	-	-	PUNCT
ejpam-3565	7	9	dual	dual	ADJ
ejpam-3565	7	10	codes	code	NOUN
ejpam-3565	7	11	over	over	ADP
ejpam-3565	7	12	gr(p3	gr(p3	PROPN
ejpam-3565	7	13	,	,	PUNCT
ejpam-3565	7	14	r	r	NOUN
ejpam-3565	7	15	)	)	PUNCT
ejpam-3565	7	16	and	and	CCONJ
ejpam-3565	7	17	classify	classify	VERB
ejpam-3565	7	18	self	self	NOUN
ejpam-3565	7	19	-	-	PUNCT
ejpam-3565	7	20	dual	dual	ADJ
ejpam-3565	7	21	codes	code	NOUN
ejpam-3565	7	22	over	over	ADP
ejpam-3565	7	23	gr(p3	gr(p3	PROPN
ejpam-3565	7	24	,	,	PUNCT
ejpam-3565	7	25	2	2	NUM
ejpam-3565	7	26	)	)	PUNCT
ejpam-3565	7	27	of	of	ADP
ejpam-3565	7	28	length	length	NOUN
ejpam-3565	7	29	4	4	NUM
ejpam-3565	7	30	for	for	ADP
ejpam-3565	7	31	p	p	NOUN
ejpam-3565	7	32	=	=	SYM
ejpam-3565	7	33	3	3	NUM
ejpam-3565	7	34	,	,	PUNCT
ejpam-3565	7	35	5	5	NUM
ejpam-3565	7	36	.	.	SYM
ejpam-3565	7	37	2010	2010	NUM
ejpam-3565	7	38	mathematics	mathematic	NOUN
ejpam-3565	7	39	subject	subject	NOUN
ejpam-3565	7	40	classifications	classification	NOUN
ejpam-3565	7	41	:	:	PUNCT
ejpam-3565	7	42	94b05	94b05	NUM
ejpam-3565	7	43	key	key	ADJ
ejpam-3565	7	44	words	word	NOUN
ejpam-3565	7	45	and	and	CCONJ
ejpam-3565	7	46	phrases	phrase	NOUN
ejpam-3565	7	47	:	:	PUNCT
ejpam-3565	7	48	mass	mass	ADJ
ejpam-3565	7	49	formula	formula	NOUN
ejpam-3565	7	50	,	,	PUNCT
ejpam-3565	7	51	self	self	NOUN
ejpam-3565	7	52	-	-	PUNCT
ejpam-3565	7	53	dual	dual	ADJ
ejpam-3565	7	54	codes	code	NOUN
ejpam-3565	7	55	,	,	PUNCT
ejpam-3565	7	56	finite	finite	PROPN
ejpam-3565	7	57	ring	ring	NOUN
ejpam-3565	7	58	,	,	PUNCT
ejpam-3565	7	59	galois	galois	PROPN
ejpam-3565	7	60	ring	ring	NOUN
ejpam-3565	7	61	,	,	PUNCT
ejpam-3565	7	62	classification	classification	NOUN
ejpam-3565	7	63	1	1	NUM
ejpam-3565	7	64	.	.	PUNCT
ejpam-3565	8	1	introduction	introduction	NOUN
ejpam-3565	8	2	it	it	PRON
ejpam-3565	8	3	was	be	AUX
ejpam-3565	8	4	shown	show	VERB
ejpam-3565	8	5	in	in	ADP
ejpam-3565	8	6	[	[	X
ejpam-3565	8	7	6	6	NUM
ejpam-3565	8	8	]	]	PUNCT
ejpam-3565	8	9	that	that	SCONJ
ejpam-3565	8	10	several	several	ADJ
ejpam-3565	8	11	well	well	ADV
ejpam-3565	8	12	-	-	PUNCT
ejpam-3565	8	13	known	know	VERB
ejpam-3565	8	14	families	family	NOUN
ejpam-3565	8	15	of	of	ADP
ejpam-3565	8	16	non	non	ADJ
ejpam-3565	8	17	-	-	ADJ
ejpam-3565	8	18	linear	linear	ADJ
ejpam-3565	8	19	binary	binary	ADJ
ejpam-3565	8	20	codes	code	NOUN
ejpam-3565	8	21	can	can	AUX
ejpam-3565	8	22	be	be	AUX
ejpam-3565	8	23	viewed	view	VERB
ejpam-3565	8	24	as	as	ADP
ejpam-3565	8	25	linear	linear	ADJ
ejpam-3565	8	26	codes	code	NOUN
ejpam-3565	8	27	over	over	ADP
ejpam-3565	8	28	the	the	DET
ejpam-3565	8	29	ring	ring	NOUN
ejpam-3565	8	30	z4	z4	PROPN
ejpam-3565	8	31	of	of	ADP
ejpam-3565	8	32	integers	integer	NOUN
ejpam-3565	8	33	modulo	modulo	VERB
ejpam-3565	8	34	4	4	NUM
ejpam-3565	8	35	.	.	PUNCT
ejpam-3565	9	1	this	this	DET
ejpam-3565	9	2	discovery	discovery	NOUN
ejpam-3565	9	3	led	lead	VERB
ejpam-3565	9	4	to	to	ADP
ejpam-3565	9	5	much	much	ADJ
ejpam-3565	9	6	interest	interest	NOUN
ejpam-3565	9	7	and	and	CCONJ
ejpam-3565	9	8	attention	attention	NOUN
ejpam-3565	9	9	given	give	VERB
ejpam-3565	9	10	to	to	ADP
ejpam-3565	9	11	codes	code	NOUN
ejpam-3565	9	12	over	over	ADP
ejpam-3565	9	13	the	the	DET
ejpam-3565	9	14	ring	ring	NOUN
ejpam-3565	9	15	zm	zm	PROPN
ejpam-3565	9	16	of	of	ADP
ejpam-3565	9	17	integers	integer	NOUN
ejpam-3565	9	18	modulo	modulo	VERB
ejpam-3565	9	19	m	m	VERB
ejpam-3565	9	20	and	and	CCONJ
ejpam-3565	9	21	finite	finite	ADJ
ejpam-3565	9	22	rings	ring	NOUN
ejpam-3565	9	23	in	in	ADP
ejpam-3565	9	24	general	general	ADJ
ejpam-3565	9	25	.	.	PUNCT
ejpam-3565	10	1	self	self	NOUN
ejpam-3565	10	2	-	-	PUNCT
ejpam-3565	10	3	dual	dual	ADJ
ejpam-3565	10	4	codes	code	NOUN
ejpam-3565	10	5	are	be	AUX
ejpam-3565	10	6	an	an	DET
ejpam-3565	10	7	important	important	ADJ
ejpam-3565	10	8	class	class	NOUN
ejpam-3565	10	9	of	of	ADP
ejpam-3565	10	10	linear	linear	PROPN
ejpam-3565	10	11	codes	code	NOUN
ejpam-3565	10	12	for	for	ADP
ejpam-3565	10	13	both	both	CCONJ
ejpam-3565	10	14	theoretical	theoretical	ADJ
ejpam-3565	10	15	and	and	CCONJ
ejpam-3565	10	16	practical	practical	ADJ
ejpam-3565	10	17	reasons	reason	NOUN
ejpam-3565	10	18	.	.	PUNCT
ejpam-3565	11	1	it	it	PRON
ejpam-3565	11	2	is	be	AUX
ejpam-3565	11	3	a	a	DET
ejpam-3565	11	4	fundamental	fundamental	ADJ
ejpam-3565	11	5	problem	problem	NOUN
ejpam-3565	11	6	to	to	PART
ejpam-3565	11	7	classify	classify	VERB
ejpam-3565	11	8	self	self	NOUN
ejpam-3565	11	9	-	-	PUNCT
ejpam-3565	11	10	dual	dual	ADJ
ejpam-3565	11	11	codes	code	NOUN
ejpam-3565	11	12	,	,	PUNCT
ejpam-3565	11	13	that	that	ADV
ejpam-3565	11	14	is	is	ADV
ejpam-3565	11	15	,	,	PUNCT
ejpam-3565	11	16	to	to	PART
ejpam-3565	11	17	find	find	VERB
ejpam-3565	11	18	a	a	DET
ejpam-3565	11	19	representative	representative	NOUN
ejpam-3565	11	20	for	for	ADP
ejpam-3565	11	21	each	each	DET
ejpam-3565	11	22	equivalence	equivalence	NOUN
ejpam-3565	11	23	class	class	NOUN
ejpam-3565	11	24	of	of	ADP
ejpam-3565	11	25	self	self	NOUN
ejpam-3565	11	26	-	-	PUNCT
ejpam-3565	11	27	dual	dual	ADJ
ejpam-3565	11	28	codes	code	NOUN
ejpam-3565	11	29	.	.	PUNCT
ejpam-3565	12	1	however	however	ADV
ejpam-3565	12	2	,	,	PUNCT
ejpam-3565	12	3	determining	determine	VERB
ejpam-3565	12	4	the	the	DET
ejpam-3565	12	5	number	number	NOUN
ejpam-3565	12	6	of	of	ADP
ejpam-3565	12	7	equivalence	equivalence	NOUN
ejpam-3565	12	8	classes	class	NOUN
ejpam-3565	12	9	is	be	AUX
ejpam-3565	12	10	difficult	difficult	ADJ
ejpam-3565	12	11	.	.	PUNCT
ejpam-3565	13	1	this	this	DET
ejpam-3565	13	2	task	task	NOUN
ejpam-3565	13	3	will	will	AUX
ejpam-3565	13	4	be	be	AUX
ejpam-3565	13	5	made	make	VERB
ejpam-3565	13	6	easier	easy	ADJ
ejpam-3565	13	7	by	by	ADP
ejpam-3565	13	8	a	a	DET
ejpam-3565	13	9	mass	mass	ADJ
ejpam-3565	13	10	formula	formula	NOUN
ejpam-3565	13	11	,	,	PUNCT
ejpam-3565	13	12	which	which	PRON
ejpam-3565	13	13	will	will	AUX
ejpam-3565	13	14	tell	tell	VERB
ejpam-3565	13	15	us	we	PRON
ejpam-3565	13	16	when	when	SCONJ
ejpam-3565	13	17	we	we	PRON
ejpam-3565	13	18	have	have	VERB
ejpam-3565	13	19	a	a	DET
ejpam-3565	13	20	complete	complete	ADJ
ejpam-3565	13	21	set	set	NOUN
ejpam-3565	13	22	of	of	ADP
ejpam-3565	13	23	representatives	representative	NOUN
ejpam-3565	13	24	from	from	ADP
ejpam-3565	13	25	each	each	DET
ejpam-3565	13	26	equivalence	equivalence	NOUN
ejpam-3565	13	27	class	class	NOUN
ejpam-3565	13	28	.	.	PUNCT
ejpam-3565	14	1	mass	mass	ADJ
ejpam-3565	14	2	formula	formula	NOUN
ejpam-3565	14	3	for	for	ADP
ejpam-3565	14	4	self	self	NOUN
ejpam-3565	14	5	-	-	PUNCT
ejpam-3565	14	6	dual	dual	ADJ
ejpam-3565	14	7	codes	code	NOUN
ejpam-3565	14	8	over	over	ADP
ejpam-3565	14	9	the	the	DET
ejpam-3565	14	10	ring	ring	NOUN
ejpam-3565	14	11	zpe	zpe	NOUN
ejpam-3565	14	12	for	for	ADP
ejpam-3565	14	13	any	any	DET
ejpam-3565	14	14	prime	prime	NOUN
ejpam-3565	14	15	p	p	NOUN
ejpam-3565	14	16	and	and	CCONJ
ejpam-3565	14	17	for	for	ADP
ejpam-3565	14	18	any	any	DET
ejpam-3565	14	19	positive	positive	ADJ
ejpam-3565	14	20	integer	integer	NOUN
ejpam-3565	14	21	e	e	NOUN
ejpam-3565	14	22	are	be	AUX
ejpam-3565	14	23	established	establish	VERB
ejpam-3565	14	24	by	by	ADP
ejpam-3565	14	25	the	the	DET
ejpam-3565	14	26	effort	effort	NOUN
ejpam-3565	14	27	of	of	ADP
ejpam-3565	14	28	many	many	ADJ
ejpam-3565	14	29	authors	author	NOUN
ejpam-3565	14	30	[	[	X
ejpam-3565	14	31	1	1	NUM
ejpam-3565	14	32	,	,	PUNCT
ejpam-3565	14	33	5	5	NUM
ejpam-3565	14	34	,	,	PUNCT
ejpam-3565	14	35	9–11	9–11	NOUN
ejpam-3565	14	36	]	]	PUNCT
ejpam-3565	14	37	.	.	PUNCT
ejpam-3565	15	1	a	a	DET
ejpam-3565	15	2	classification	classification	NOUN
ejpam-3565	15	3	method	method	NOUN
ejpam-3565	15	4	of	of	ADP
ejpam-3565	15	5	self	self	NOUN
ejpam-3565	15	6	-	-	PUNCT
ejpam-3565	15	7	dual	dual	ADJ
ejpam-3565	15	8	codes	code	NOUN
ejpam-3565	15	9	over	over	ADP
ejpam-3565	15	10	zm	zm	PROPN
ejpam-3565	15	11	for	for	ADP
ejpam-3565	15	12	arbitrary	arbitrary	ADJ
ejpam-3565	15	13	integer	integer	NOUN
ejpam-3565	15	14	m	m	AUX
ejpam-3565	15	15	is	be	AUX
ejpam-3565	15	16	given	give	VERB
ejpam-3565	15	17	in	in	ADP
ejpam-3565	15	18	[	[	PUNCT
ejpam-3565	15	19	13	13	NUM
ejpam-3565	15	20	]	]	PUNCT
ejpam-3565	15	21	.	.	PUNCT
ejpam-3565	16	1	in	in	ADP
ejpam-3565	16	2	particular	particular	ADJ
ejpam-3565	16	3	,	,	PUNCT
ejpam-3565	16	4	selfdual	selfdual	ADJ
ejpam-3565	16	5	codes	code	NOUN
ejpam-3565	16	6	of	of	ADP
ejpam-3565	16	7	length	length	NOUN
ejpam-3565	16	8	4	4	NUM
ejpam-3565	16	9	over	over	ADP
ejpam-3565	16	10	zp	zp	PROPN
ejpam-3565	16	11	were	be	AUX
ejpam-3565	16	12	classified	classify	VERB
ejpam-3565	16	13	in	in	ADP
ejpam-3565	16	14	[	[	X
ejpam-3565	16	15	13	13	NUM
ejpam-3565	16	16	]	]	PUNCT
ejpam-3565	16	17	for	for	ADP
ejpam-3565	16	18	all	all	DET
ejpam-3565	16	19	primes	prime	NOUN
ejpam-3565	16	20	p	p	NOUN
ejpam-3565	16	21	in	in	ADP
ejpam-3565	16	22	terms	term	NOUN
ejpam-3565	16	23	of	of	ADP
ejpam-3565	16	24	their	their	PRON
ejpam-3565	16	25	automorphism	automorphism	NOUN
ejpam-3565	16	26	groups	group	NOUN
ejpam-3565	16	27	.	.	PUNCT
ejpam-3565	17	1	the	the	DET
ejpam-3565	17	2	galois	galois	PROPN
ejpam-3565	17	3	ring	ring	NOUN
ejpam-3565	17	4	gr(pe	gr(pe	NOUN
ejpam-3565	17	5	,	,	PUNCT
ejpam-3565	17	6	r	r	NOUN
ejpam-3565	17	7	)	)	PUNCT
ejpam-3565	17	8	,	,	PUNCT
ejpam-3565	17	9	where	where	SCONJ
ejpam-3565	17	10	p	p	NOUN
ejpam-3565	17	11	is	be	AUX
ejpam-3565	17	12	prime	prime	ADJ
ejpam-3565	17	13	,	,	PUNCT
ejpam-3565	17	14	e	e	NOUN
ejpam-3565	17	15	and	and	CCONJ
ejpam-3565	17	16	r	r	NOUN
ejpam-3565	17	17	are	be	AUX
ejpam-3565	17	18	positive	positive	ADJ
ejpam-3565	17	19	integers	integer	NOUN
ejpam-3565	17	20	,	,	PUNCT
ejpam-3565	17	21	is	be	AUX
ejpam-3565	17	22	the	the	DET
ejpam-3565	17	23	unique	unique	ADJ
ejpam-3565	17	24	galois	galois	NOUN
ejpam-3565	17	25	extension	extension	NOUN
ejpam-3565	17	26	of	of	ADP
ejpam-3565	17	27	zpe	zpe	NOUN
ejpam-3565	17	28	of	of	ADP
ejpam-3565	17	29	degree	degree	NOUN
ejpam-3565	17	30	r.	r.	NOUN
ejpam-3565	17	31	using	use	VERB
ejpam-3565	17	32	a	a	DET
ejpam-3565	17	33	similar	similar	ADJ
ejpam-3565	17	34	argument	argument	NOUN
ejpam-3565	17	35	in	in	ADP
ejpam-3565	17	36	[	[	X
ejpam-3565	17	37	1	1	NUM
ejpam-3565	17	38	]	]	PUNCT
ejpam-3565	17	39	,	,	PUNCT
ejpam-3565	17	40	the	the	DET
ejpam-3565	17	41	mass	mass	ADJ
ejpam-3565	17	42	formula	formula	NOUN
ejpam-3565	17	43	∗corresponding	∗corresponde	VERB
ejpam-3565	17	44	author	author	NOUN
ejpam-3565	17	45	.	.	PUNCT
ejpam-3565	18	1	doi	doi	NOUN
ejpam-3565	18	2	:	:	PUNCT
ejpam-3565	18	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3565	https://doi.org/10.29020/nybg.ejpam.v12i4.3565	ADJ
ejpam-3565	18	4	email	email	NOUN
ejpam-3565	18	5	addresses	address	NOUN
ejpam-3565	18	6	:	:	PUNCT
ejpam-3565	18	7	trilbelizann.vasquez@g.msuiit.edu.ph	trilbelizann.vasquez@g.msuiit.edu.ph	PROPN
ejpam-3565	18	8	(	(	PUNCT
ejpam-3565	18	9	t.l	t.l	PROPN
ejpam-3565	18	10	.	.	PUNCT
ejpam-3565	18	11	vasquez	vasquez	PROPN
ejpam-3565	18	12	)	)	PUNCT
ejpam-3565	18	13	,	,	PUNCT
ejpam-3565	18	14	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-3565	18	15	(	(	PUNCT
ejpam-3565	18	16	g.	g.	PROPN
ejpam-3565	18	17	petalcorin	petalcorin	PROPN
ejpam-3565	18	18	)	)	PUNCT
ejpam-3565	18	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3565	18	20	1701	1701	NUM
ejpam-3565	18	21	c	c	X
ejpam-3565	18	22	©	©	PROPN
ejpam-3565	18	23	2019	2019	NUM
ejpam-3565	18	24	ejpam	ejpam	NOUN
ejpam-3565	18	25	all	all	DET
ejpam-3565	18	26	rights	right	NOUN
ejpam-3565	18	27	reserved	reserve	VERB
ejpam-3565	18	28	.	.	PUNCT
ejpam-3565	19	1	t.	t.	PROPN
ejpam-3565	19	2	l.	l.	PROPN
ejpam-3565	19	3	vasquez	vasquez	PROPN
ejpam-3565	19	4	,	,	PUNCT
ejpam-3565	19	5	g.	g.	PROPN
ejpam-3565	19	6	petalcorin	petalcorin	PROPN
ejpam-3565	19	7	/	/	SYM
ejpam-3565	19	8	eur	eur	PROPN
ejpam-3565	19	9	.	.	PUNCT
ejpam-3565	20	1	j.	j.	PROPN
ejpam-3565	20	2	pure	pure	PROPN
ejpam-3565	20	3	appl	appl	PROPN
ejpam-3565	20	4	.	.	PROPN
ejpam-3565	20	5	math	math	PROPN
ejpam-3565	20	6	,	,	PUNCT
ejpam-3565	20	7	12	12	NUM
ejpam-3565	20	8	(	(	PUNCT
ejpam-3565	20	9	4	4	NUM
ejpam-3565	20	10	)	)	PUNCT
ejpam-3565	20	11	(	(	PUNCT
ejpam-3565	20	12	2019	2019	NUM
ejpam-3565	20	13	)	)	PUNCT
ejpam-3565	20	14	,	,	PUNCT
ejpam-3565	20	15	1701	1701	NUM
ejpam-3565	20	16	-	-	SYM
ejpam-3565	20	17	1716	1716	NUM
ejpam-3565	20	18	1702	1702	NUM
ejpam-3565	20	19	for	for	ADP
ejpam-3565	20	20	self	self	NOUN
ejpam-3565	20	21	-	-	PUNCT
ejpam-3565	20	22	dual	dual	ADJ
ejpam-3565	20	23	codes	code	NOUN
ejpam-3565	20	24	over	over	ADP
ejpam-3565	20	25	gr(p2	gr(p2	VERB
ejpam-3565	20	26	,	,	PUNCT
ejpam-3565	20	27	2	2	NUM
ejpam-3565	20	28	)	)	PUNCT
ejpam-3565	20	29	for	for	ADP
ejpam-3565	20	30	odd	odd	ADJ
ejpam-3565	20	31	primes	prime	NOUN
ejpam-3565	20	32	p	p	NOUN
ejpam-3565	20	33	is	be	AUX
ejpam-3565	20	34	obtained	obtain	VERB
ejpam-3565	20	35	in	in	ADP
ejpam-3565	20	36	[	[	X
ejpam-3565	20	37	3	3	NUM
ejpam-3565	20	38	]	]	PUNCT
ejpam-3565	20	39	.	.	PUNCT
ejpam-3565	21	1	moreover	moreover	ADV
ejpam-3565	21	2	,	,	PUNCT
ejpam-3565	21	3	self	self	NOUN
ejpam-3565	21	4	-	-	PUNCT
ejpam-3565	21	5	dual	dual	ADJ
ejpam-3565	21	6	codes	code	NOUN
ejpam-3565	21	7	of	of	ADP
ejpam-3565	21	8	length	length	NOUN
ejpam-3565	21	9	4	4	NUM
ejpam-3565	21	10	over	over	ADP
ejpam-3565	21	11	gr(p	gr(p	NOUN
ejpam-3565	21	12	,	,	PUNCT
ejpam-3565	21	13	2	2	NUM
ejpam-3565	21	14	)	)	PUNCT
ejpam-3565	21	15	and	and	CCONJ
ejpam-3565	21	16	gr(p2	gr(p2	NOUN
ejpam-3565	21	17	,	,	PUNCT
ejpam-3565	21	18	2	2	NUM
ejpam-3565	21	19	)	)	PUNCT
ejpam-3565	21	20	are	be	AUX
ejpam-3565	21	21	classified	classify	VERB
ejpam-3565	21	22	in	in	ADP
ejpam-3565	21	23	[	[	X
ejpam-3565	21	24	4	4	X
ejpam-3565	21	25	]	]	PUNCT
ejpam-3565	21	26	for	for	ADP
ejpam-3565	21	27	all	all	DET
ejpam-3565	21	28	primes	prime	NOUN
ejpam-3565	21	29	p	p	NOUN
ejpam-3565	21	30	up	up	ADP
ejpam-3565	21	31	to	to	ADP
ejpam-3565	21	32	equivalence	equivalence	NOUN
ejpam-3565	21	33	in	in	ADP
ejpam-3565	21	34	terms	term	NOUN
ejpam-3565	21	35	of	of	ADP
ejpam-3565	21	36	automorphism	automorphism	NOUN
ejpam-3565	21	37	group	group	NOUN
ejpam-3565	21	38	.	.	PUNCT
ejpam-3565	22	1	in	in	ADP
ejpam-3565	22	2	this	this	DET
ejpam-3565	22	3	paper	paper	NOUN
ejpam-3565	22	4	,	,	PUNCT
ejpam-3565	22	5	we	we	PRON
ejpam-3565	22	6	build	build	VERB
ejpam-3565	22	7	on	on	ADP
ejpam-3565	22	8	the	the	DET
ejpam-3565	22	9	method	method	NOUN
ejpam-3565	22	10	in	in	ADP
ejpam-3565	22	11	[	[	X
ejpam-3565	22	12	10	10	NUM
ejpam-3565	22	13	]	]	PUNCT
ejpam-3565	22	14	to	to	PART
ejpam-3565	22	15	establish	establish	VERB
ejpam-3565	22	16	a	a	DET
ejpam-3565	22	17	mass	mass	ADJ
ejpam-3565	22	18	formula	formula	NOUN
ejpam-3565	22	19	for	for	ADP
ejpam-3565	22	20	self	self	NOUN
ejpam-3565	22	21	-	-	PUNCT
ejpam-3565	22	22	dual	dual	ADJ
ejpam-3565	22	23	codes	code	NOUN
ejpam-3565	22	24	over	over	ADP
ejpam-3565	22	25	gr(p3	gr(p3	PROPN
ejpam-3565	22	26	,	,	PUNCT
ejpam-3565	22	27	r	r	NOUN
ejpam-3565	22	28	)	)	PUNCT
ejpam-3565	22	29	,	,	PUNCT
ejpam-3565	22	30	where	where	SCONJ
ejpam-3565	22	31	p	p	NOUN
ejpam-3565	22	32	is	be	AUX
ejpam-3565	22	33	an	an	DET
ejpam-3565	22	34	odd	odd	ADJ
ejpam-3565	22	35	prime	prime	NOUN
ejpam-3565	22	36	and	and	CCONJ
ejpam-3565	22	37	r	r	NOUN
ejpam-3565	22	38	is	be	AUX
ejpam-3565	22	39	a	a	DET
ejpam-3565	22	40	positive	positive	ADJ
ejpam-3565	22	41	integer	integer	NOUN
ejpam-3565	22	42	.	.	PUNCT
ejpam-3565	23	1	using	use	VERB
ejpam-3565	23	2	the	the	DET
ejpam-3565	23	3	mass	mass	ADJ
ejpam-3565	23	4	formula	formula	NOUN
ejpam-3565	23	5	,	,	PUNCT
ejpam-3565	23	6	we	we	PRON
ejpam-3565	23	7	classify	classify	VERB
ejpam-3565	23	8	self	self	NOUN
ejpam-3565	23	9	-	-	PUNCT
ejpam-3565	23	10	dual	dual	ADJ
ejpam-3565	23	11	codes	code	NOUN
ejpam-3565	23	12	of	of	ADP
ejpam-3565	23	13	length	length	NOUN
ejpam-3565	23	14	4	4	NUM
ejpam-3565	23	15	over	over	ADP
ejpam-3565	23	16	gr(p3	gr(p3	PROPN
ejpam-3565	23	17	,	,	PUNCT
ejpam-3565	23	18	2	2	NUM
ejpam-3565	23	19	)	)	PUNCT
ejpam-3565	23	20	for	for	ADP
ejpam-3565	23	21	p	p	NOUN
ejpam-3565	23	22	=	=	SYM
ejpam-3565	23	23	3	3	NUM
ejpam-3565	23	24	,	,	PUNCT
ejpam-3565	23	25	5	5	NUM
ejpam-3565	23	26	.	.	SYM
ejpam-3565	23	27	2	2	NUM
ejpam-3565	23	28	.	.	X
ejpam-3565	23	29	preliminaries	preliminary	NOUN
ejpam-3565	23	30	let	let	VERB
ejpam-3565	23	31	p	p	PRON
ejpam-3565	23	32	be	be	AUX
ejpam-3565	23	33	prime	prime	ADJ
ejpam-3565	23	34	and	and	CCONJ
ejpam-3565	23	35	e	e	X
ejpam-3565	23	36	a	a	DET
ejpam-3565	23	37	positive	positive	ADJ
ejpam-3565	23	38	integer	integer	NOUN
ejpam-3565	23	39	.	.	PUNCT
ejpam-3565	24	1	the	the	DET
ejpam-3565	24	2	modulo	modulo	NOUN
ejpam-3565	24	3	p	p	NOUN
ejpam-3565	24	4	reduction	reduction	NOUN
ejpam-3565	24	5	mapping	mapping	NOUN
ejpam-3565	24	6	µ	µ	X
ejpam-3565	24	7	:	:	PUNCT
ejpam-3565	24	8	zpe	zpe	PROPN
ejpam-3565	24	9	→	→	SYM
ejpam-3565	24	10	zp	zp	PROPN
ejpam-3565	24	11	,	,	PUNCT
ejpam-3565	24	12	a	a	DET
ejpam-3565	24	13	7→	7→	NUM
ejpam-3565	24	14	ā	ā	NOUN
ejpam-3565	24	15	=	=	PUNCT
ejpam-3565	24	16	a	a	DET
ejpam-3565	24	17	(	(	PUNCT
ejpam-3565	24	18	mod	mod	NOUN
ejpam-3565	24	19	p	p	NOUN
ejpam-3565	24	20	)	)	PUNCT
ejpam-3565	24	21	induces	induce	VERB
ejpam-3565	24	22	the	the	DET
ejpam-3565	24	23	following	follow	VERB
ejpam-3565	24	24	modulo	modulo	NOUN
ejpam-3565	24	25	p	p	NOUN
ejpam-3565	24	26	reduction	reduction	NOUN
ejpam-3565	24	27	mapping	mapping	NOUN
ejpam-3565	24	28	between	between	ADP
ejpam-3565	24	29	polynomial	polynomial	ADJ
ejpam-3565	24	30	rings	ring	NOUN
ejpam-3565	24	31	µ	µ	X
ejpam-3565	24	32	:	:	PUNCT
ejpam-3565	24	33	zpe	zpe	NOUN
ejpam-3565	25	1	[	[	X
ejpam-3565	25	2	x]→	x]→	X
ejpam-3565	25	3	zp[x	zp[x	VERB
ejpam-3565	25	4	]	]	X
ejpam-3565	25	5	,	,	PUNCT
ejpam-3565	25	6	f(x	f(x	PROPN
ejpam-3565	25	7	)	)	PUNCT
ejpam-3565	25	8	=	=	PUNCT
ejpam-3565	25	9	∑	∑	PUNCT
ejpam-3565	25	10	aix	aix	PROPN
ejpam-3565	25	11	i	i	PROPN
ejpam-3565	25	12	7→	7→	NUM
ejpam-3565	25	13	f̄(x	f̄(x	NUM
ejpam-3565	25	14	)	)	PUNCT
ejpam-3565	25	15	=	=	SYM
ejpam-3565	25	16	∑	∑	PUNCT
ejpam-3565	25	17	āix	āix	PROPN
ejpam-3565	25	18	i.	i.	PROPN
ejpam-3565	25	19	an	an	DET
ejpam-3565	25	20	irreducible	irreducible	ADJ
ejpam-3565	25	21	polynomial	polynomial	ADJ
ejpam-3565	25	22	f(x	f(x	PROPN
ejpam-3565	25	23	)	)	PUNCT
ejpam-3565	25	24	in	in	ADP
ejpam-3565	25	25	zpe	zpe	PROPN
ejpam-3565	25	26	[	[	X
ejpam-3565	25	27	x	x	X
ejpam-3565	25	28	]	]	X
ejpam-3565	25	29	is	be	AUX
ejpam-3565	25	30	said	say	VERB
ejpam-3565	25	31	to	to	PART
ejpam-3565	25	32	be	be	AUX
ejpam-3565	25	33	basic	basic	ADJ
ejpam-3565	25	34	if	if	SCONJ
ejpam-3565	25	35	f̄(x	f̄(x	NOUN
ejpam-3565	25	36	)	)	PUNCT
ejpam-3565	25	37	is	be	AUX
ejpam-3565	25	38	irreducible	irreducible	ADJ
ejpam-3565	25	39	.	.	PUNCT
ejpam-3565	26	1	let	let	VERB
ejpam-3565	26	2	f(x	f(x	PROPN
ejpam-3565	26	3	)	)	PUNCT
ejpam-3565	26	4	be	be	AUX
ejpam-3565	26	5	a	a	DET
ejpam-3565	26	6	monic	monic	ADJ
ejpam-3565	26	7	basic	basic	ADJ
ejpam-3565	26	8	irreducible	irreducible	ADJ
ejpam-3565	26	9	polynomial	polynomial	NOUN
ejpam-3565	26	10	over	over	ADP
ejpam-3565	26	11	zpe	zpe	PROPN
ejpam-3565	27	1	[	[	X
ejpam-3565	27	2	x	x	X
ejpam-3565	27	3	]	]	X
ejpam-3565	27	4	of	of	ADP
ejpam-3565	27	5	degree	degree	NOUN
ejpam-3565	27	6	r.	r.	NOUN
ejpam-3565	27	7	we	we	PRON
ejpam-3565	27	8	can	can	AUX
ejpam-3565	27	9	choose	choose	VERB
ejpam-3565	27	10	f(x	f(x	PROPN
ejpam-3565	27	11	)	)	PUNCT
ejpam-3565	27	12	so	so	SCONJ
ejpam-3565	27	13	that	that	SCONJ
ejpam-3565	27	14	ω	ω	X
ejpam-3565	27	15	=	=	SYM
ejpam-3565	27	16	x+	x+	PROPN
ejpam-3565	27	17	〈	〈	PROPN
ejpam-3565	27	18	f(x	f(x	PROPN
ejpam-3565	27	19	)	)	PUNCT
ejpam-3565	27	20	〉	〉	PROPN
ejpam-3565	27	21	is	be	AUX
ejpam-3565	27	22	a	a	DET
ejpam-3565	27	23	primitive	primitive	ADJ
ejpam-3565	27	24	(	(	PUNCT
ejpam-3565	27	25	pr	pr	NOUN
ejpam-3565	27	26	−	−	PROPN
ejpam-3565	27	27	1)st	1)st	NUM
ejpam-3565	27	28	root	root	NOUN
ejpam-3565	27	29	of	of	ADP
ejpam-3565	27	30	unity	unity	NOUN
ejpam-3565	27	31	.	.	PUNCT
ejpam-3565	28	1	the	the	DET
ejpam-3565	28	2	galois	galois	PROPN
ejpam-3565	28	3	ring	ring	NOUN
ejpam-3565	28	4	gr(pe	gr(pe	NOUN
ejpam-3565	28	5	,	,	PUNCT
ejpam-3565	28	6	r	r	NOUN
ejpam-3565	28	7	)	)	PUNCT
ejpam-3565	28	8	of	of	ADP
ejpam-3565	28	9	characteristic	characteristic	ADJ
ejpam-3565	28	10	pe	pe	INTJ
ejpam-3565	28	11	and	and	CCONJ
ejpam-3565	28	12	cardinality	cardinality	NOUN
ejpam-3565	28	13	per	per	ADP
ejpam-3565	28	14	is	be	AUX
ejpam-3565	28	15	defined	define	VERB
ejpam-3565	28	16	as	as	ADP
ejpam-3565	28	17	gr(pe	gr(pe	NOUN
ejpam-3565	28	18	,	,	PUNCT
ejpam-3565	28	19	r	r	NOUN
ejpam-3565	28	20	)	)	PUNCT
ejpam-3565	29	1	=	=	SYM
ejpam-3565	29	2	zpe	zpe	NOUN
ejpam-3565	30	1	[	[	X
ejpam-3565	30	2	x]/〈f(x	x]/〈f(x	PROPN
ejpam-3565	30	3	)	)	PUNCT
ejpam-3565	30	4	〉	〉	PROPN
ejpam-3565	30	5	=	=	SYM
ejpam-3565	30	6	zpe	zpe	PROPN
ejpam-3565	31	1	[	[	X
ejpam-3565	31	2	ω	ω	X
ejpam-3565	31	3	]	]	X
ejpam-3565	31	4	.	.	PUNCT
ejpam-3565	32	1	every	every	DET
ejpam-3565	32	2	element	element	NOUN
ejpam-3565	32	3	of	of	ADP
ejpam-3565	32	4	gr(pe	gr(pe	NOUN
ejpam-3565	32	5	,	,	PUNCT
ejpam-3565	32	6	r	r	NOUN
ejpam-3565	32	7	)	)	PUNCT
ejpam-3565	32	8	can	can	AUX
ejpam-3565	32	9	be	be	AUX
ejpam-3565	32	10	expressed	express	VERB
ejpam-3565	32	11	uniquely	uniquely	ADV
ejpam-3565	32	12	in	in	ADP
ejpam-3565	32	13	the	the	DET
ejpam-3565	32	14	ω	ω	ADJ
ejpam-3565	32	15	-	-	ADJ
ejpam-3565	32	16	adic	adic	ADJ
ejpam-3565	32	17	representation	representation	NOUN
ejpam-3565	32	18	a0	a0	NOUN
ejpam-3565	32	19	+	+	CCONJ
ejpam-3565	32	20	a1ω	a1ω	PROPN
ejpam-3565	32	21	+	+	CCONJ
ejpam-3565	32	22	a2ω	a2ω	PROPN
ejpam-3565	32	23	2	2	NUM
ejpam-3565	32	24	+	+	CCONJ
ejpam-3565	32	25	·	·	PUNCT
ejpam-3565	32	26	·	·	PUNCT
ejpam-3565	32	27	·	·	PUNCT
ejpam-3565	33	1	+	+	NUM
ejpam-3565	33	2	ar−1ω	ar−1ω	NUM
ejpam-3565	33	3	r−1	r−1	PROPN
ejpam-3565	33	4	,	,	PUNCT
ejpam-3565	33	5	where	where	SCONJ
ejpam-3565	33	6	ai	ai	VERB
ejpam-3565	33	7	∈	∈	PROPN
ejpam-3565	33	8	zpe	zpe	PROPN
ejpam-3565	33	9	.	.	PUNCT
ejpam-3565	33	10	note	note	VERB
ejpam-3565	33	11	that	that	SCONJ
ejpam-3565	33	12	gr(pe	gr(pe	NOUN
ejpam-3565	33	13	,	,	PUNCT
ejpam-3565	33	14	1	1	X
ejpam-3565	33	15	)	)	PUNCT
ejpam-3565	33	16	=	=	SYM
ejpam-3565	33	17	zpe	zpe	PROPN
ejpam-3565	33	18	and	and	CCONJ
ejpam-3565	33	19	gr(p	gr(p	PROPN
ejpam-3565	33	20	,	,	PUNCT
ejpam-3565	33	21	r	r	NOUN
ejpam-3565	33	22	)	)	PUNCT
ejpam-3565	33	23	=	=	NOUN
ejpam-3565	33	24	fpr	fpr	NOUN
ejpam-3565	33	25	,	,	PUNCT
ejpam-3565	33	26	the	the	DET
ejpam-3565	33	27	galois	galois	PROPN
ejpam-3565	33	28	field	field	NOUN
ejpam-3565	33	29	of	of	ADP
ejpam-3565	33	30	pr	pr	NOUN
ejpam-3565	33	31	elements	element	NOUN
ejpam-3565	33	32	.	.	PUNCT
ejpam-3565	34	1	the	the	DET
ejpam-3565	34	2	modulo	modulo	ADJ
ejpam-3565	34	3	p	p	NOUN
ejpam-3565	34	4	reduction	reduction	NOUN
ejpam-3565	34	5	can	can	AUX
ejpam-3565	34	6	be	be	AUX
ejpam-3565	34	7	naturally	naturally	ADV
ejpam-3565	34	8	extended	extend	VERB
ejpam-3565	34	9	to	to	ADP
ejpam-3565	34	10	µ	µ	NOUN
ejpam-3565	34	11	:	:	PUNCT
ejpam-3565	34	12	gr(pe	gr(pe	NOUN
ejpam-3565	34	13	,	,	PUNCT
ejpam-3565	34	14	r	r	NOUN
ejpam-3565	34	15	)	)	PUNCT
ejpam-3565	35	1	=	=	SYM
ejpam-3565	35	2	zpe	zpe	NOUN
ejpam-3565	36	1	[	[	X
ejpam-3565	36	2	x]/〈f(x	x]/〈f(x	PROPN
ejpam-3565	36	3	)	)	PUNCT
ejpam-3565	36	4	〉	〉	PROPN
ejpam-3565	36	5	→	→	SYM
ejpam-3565	36	6	zp[x]/〈f̄(x	zp[x]/〈f̄(x	PROPN
ejpam-3565	36	7	)	)	PUNCT
ejpam-3565	36	8	〉	〉	NOUN
ejpam-3565	36	9	=	=	NOUN
ejpam-3565	36	10	fpr	fpr	NOUN
ejpam-3565	36	11	,	,	PUNCT
ejpam-3565	36	12	a	a	DET
ejpam-3565	36	13	7→	7→	NUM
ejpam-3565	36	14	ā	ā	NOUN
ejpam-3565	36	15	=	=	PUNCT
ejpam-3565	36	16	a	a	PRON
ejpam-3565	36	17	(	(	PUNCT
ejpam-3565	36	18	mod	mod	NOUN
ejpam-3565	36	19	p	p	NOUN
ejpam-3565	36	20	)	)	PUNCT
ejpam-3565	36	21	.	.	PUNCT
ejpam-3565	37	1	let	let	VERB
ejpam-3565	37	2	tpr	tpr	PROPN
ejpam-3565	37	3	=	=	X
ejpam-3565	37	4	{	{	PUNCT
ejpam-3565	37	5	0	0	NUM
ejpam-3565	37	6	,	,	PUNCT
ejpam-3565	37	7	1	1	NUM
ejpam-3565	37	8	,	,	PUNCT
ejpam-3565	37	9	ω	ω	NOUN
ejpam-3565	37	10	,	,	PUNCT
ejpam-3565	37	11	.	.	PUNCT
ejpam-3565	37	12	.	.	PUNCT
ejpam-3565	38	1	.	.	PUNCT
ejpam-3565	39	1	,	,	PUNCT
ejpam-3565	39	2	ωpr−2	ωpr−2	ADP
ejpam-3565	39	3	}	}	PUNCT
ejpam-3565	39	4	.	.	PUNCT
ejpam-3565	40	1	observe	observe	VERB
ejpam-3565	40	2	that	that	SCONJ
ejpam-3565	40	3	the	the	DET
ejpam-3565	40	4	function	function	NOUN
ejpam-3565	40	5	µ|tpr	µ|tpr	NOUN
ejpam-3565	40	6	:	:	PUNCT
ejpam-3565	40	7	tpr	tpr	NOUN
ejpam-3565	40	8	→	→	X
ejpam-3565	40	9	fpr	fpr	X
ejpam-3565	40	10	is	be	AUX
ejpam-3565	40	11	one	one	NUM
ejpam-3565	40	12	-	-	PUNCT
ejpam-3565	40	13	to	to	ADP
ejpam-3565	40	14	-	-	PUNCT
ejpam-3565	40	15	one	one	NUM
ejpam-3565	40	16	and	and	CCONJ
ejpam-3565	40	17	onto	onto	ADP
ejpam-3565	40	18	.	.	PUNCT
ejpam-3565	41	1	any	any	DET
ejpam-3565	41	2	element	element	NOUN
ejpam-3565	41	3	of	of	ADP
ejpam-3565	41	4	gr(pe	gr(pe	NOUN
ejpam-3565	41	5	,	,	PUNCT
ejpam-3565	41	6	r	r	NOUN
ejpam-3565	41	7	)	)	PUNCT
ejpam-3565	41	8	can	can	AUX
ejpam-3565	41	9	be	be	AUX
ejpam-3565	41	10	written	write	VERB
ejpam-3565	41	11	uniquely	uniquely	ADV
ejpam-3565	41	12	in	in	ADP
ejpam-3565	41	13	the	the	DET
ejpam-3565	41	14	p	p	NOUN
ejpam-3565	41	15	-	-	PUNCT
ejpam-3565	41	16	adic	adic	NOUN
ejpam-3565	41	17	representation	representation	NOUN
ejpam-3565	41	18	b0	b0	NOUN
ejpam-3565	41	19	+	+	CCONJ
ejpam-3565	41	20	pb1	pb1	NOUN
ejpam-3565	41	21	+	+	CCONJ
ejpam-3565	41	22	p2b2	p2b2	X
ejpam-3565	42	1	+	+	X
ejpam-3565	42	2	·	·	PUNCT
ejpam-3565	42	3	·	·	PUNCT
ejpam-3565	42	4	·	·	PUNCT
ejpam-3565	42	5	+	+	NUM
ejpam-3565	42	6	pe−1be−1	pe−1be−1	PROPN
ejpam-3565	42	7	,	,	PUNCT
ejpam-3565	42	8	where	where	SCONJ
ejpam-3565	42	9	bi	bi	PROPN
ejpam-3565	42	10	∈	∈	PROPN
ejpam-3565	42	11	tpr	tpr	PROPN
ejpam-3565	42	12	.	.	PUNCT
ejpam-3565	43	1	an	an	DET
ejpam-3565	43	2	element	element	NOUN
ejpam-3565	43	3	a	a	DET
ejpam-3565	43	4	∈	∈	PROPN
ejpam-3565	43	5	gr(pe	gr(pe	NOUN
ejpam-3565	43	6	,	,	PUNCT
ejpam-3565	43	7	r	r	NOUN
ejpam-3565	43	8	)	)	PUNCT
ejpam-3565	43	9	is	be	AUX
ejpam-3565	43	10	a	a	DET
ejpam-3565	43	11	unit	unit	NOUN
ejpam-3565	43	12	if	if	SCONJ
ejpam-3565	43	13	and	and	CCONJ
ejpam-3565	43	14	only	only	ADV
ejpam-3565	43	15	if	if	SCONJ
ejpam-3565	43	16	ā	ā	PROPN
ejpam-3565	43	17	6=	6=	PROPN
ejpam-3565	43	18	0	0	NUM
ejpam-3565	43	19	.	.	PUNCT
ejpam-3565	44	1	for	for	ADP
ejpam-3565	44	2	the	the	DET
ejpam-3565	44	3	further	further	ADJ
ejpam-3565	44	4	study	study	NOUN
ejpam-3565	44	5	of	of	ADP
ejpam-3565	44	6	galois	galois	PROPN
ejpam-3565	44	7	rings	ring	NOUN
ejpam-3565	44	8	,	,	PUNCT
ejpam-3565	44	9	see	see	VERB
ejpam-3565	44	10	[	[	X
ejpam-3565	44	11	8	8	NUM
ejpam-3565	44	12	,	,	PUNCT
ejpam-3565	44	13	16	16	NUM
ejpam-3565	44	14	]	]	PUNCT
ejpam-3565	44	15	.	.	PUNCT
ejpam-3565	45	1	let	let	VERB
ejpam-3565	45	2	n	n	PRON
ejpam-3565	45	3	be	be	AUX
ejpam-3565	45	4	a	a	DET
ejpam-3565	45	5	positive	positive	ADJ
ejpam-3565	45	6	integer	integer	NOUN
ejpam-3565	45	7	and	and	CCONJ
ejpam-3565	45	8	let	let	VERB
ejpam-3565	45	9	sn	sn	PROPN
ejpam-3565	45	10	denote	denote	VERB
ejpam-3565	45	11	the	the	DET
ejpam-3565	45	12	collection	collection	NOUN
ejpam-3565	45	13	of	of	ADP
ejpam-3565	45	14	n	n	CCONJ
ejpam-3565	45	15	-	-	PUNCT
ejpam-3565	45	16	tuples	tuple	NOUN
ejpam-3565	45	17	over	over	ADP
ejpam-3565	45	18	a	a	DET
ejpam-3565	45	19	finite	finite	NOUN
ejpam-3565	45	20	set	set	VERB
ejpam-3565	45	21	s.	s.	PROPN
ejpam-3565	45	22	a	a	DET
ejpam-3565	45	23	code	code	NOUN
ejpam-3565	45	24	of	of	ADP
ejpam-3565	45	25	length	length	NOUN
ejpam-3565	45	26	n	n	CCONJ
ejpam-3565	45	27	over	over	ADP
ejpam-3565	45	28	a	a	DET
ejpam-3565	45	29	finite	finite	ADJ
ejpam-3565	45	30	field	field	NOUN
ejpam-3565	45	31	f	f	PROPN
ejpam-3565	45	32	or	or	CCONJ
ejpam-3565	45	33	a	a	DET
ejpam-3565	45	34	finite	finite	NOUN
ejpam-3565	45	35	ring	ring	NOUN
ejpam-3565	45	36	r	r	NOUN
ejpam-3565	45	37	is	be	AUX
ejpam-3565	45	38	a	a	DET
ejpam-3565	45	39	subspace	subspace	NOUN
ejpam-3565	45	40	of	of	ADP
ejpam-3565	45	41	fn	fn	NOUN
ejpam-3565	45	42	or	or	CCONJ
ejpam-3565	45	43	an	an	DET
ejpam-3565	45	44	r	r	NOUN
ejpam-3565	45	45	-	-	PUNCT
ejpam-3565	45	46	submodule	submodule	NOUN
ejpam-3565	45	47	of	of	ADP
ejpam-3565	45	48	rn	rn	PROPN
ejpam-3565	45	49	,	,	PUNCT
ejpam-3565	45	50	respectively	respectively	ADV
ejpam-3565	45	51	.	.	PUNCT
ejpam-3565	46	1	every	every	DET
ejpam-3565	46	2	element	element	NOUN
ejpam-3565	46	3	of	of	ADP
ejpam-3565	46	4	the	the	DET
ejpam-3565	46	5	code	code	NOUN
ejpam-3565	46	6	is	be	AUX
ejpam-3565	46	7	called	call	VERB
ejpam-3565	46	8	a	a	DET
ejpam-3565	46	9	codeword	codeword	NOUN
ejpam-3565	46	10	.	.	PUNCT
ejpam-3565	47	1	a	a	DET
ejpam-3565	47	2	matrix	matrix	NOUN
ejpam-3565	47	3	g	g	NOUN
ejpam-3565	47	4	is	be	AUX
ejpam-3565	47	5	called	call	VERB
ejpam-3565	47	6	a	a	DET
ejpam-3565	47	7	generator	generator	NOUN
ejpam-3565	47	8	matrix	matrix	NOUN
ejpam-3565	47	9	for	for	ADP
ejpam-3565	47	10	a	a	DET
ejpam-3565	47	11	code	code	NOUN
ejpam-3565	47	12	c	c	NOUN
ejpam-3565	47	13	if	if	SCONJ
ejpam-3565	47	14	the	the	DET
ejpam-3565	47	15	rows	row	NOUN
ejpam-3565	47	16	of	of	ADP
ejpam-3565	47	17	g	g	PROPN
ejpam-3565	47	18	generate	generate	VERB
ejpam-3565	47	19	all	all	DET
ejpam-3565	47	20	the	the	DET
ejpam-3565	47	21	elements	element	NOUN
ejpam-3565	47	22	of	of	ADP
ejpam-3565	47	23	c	c	NOUN
ejpam-3565	47	24	and	and	CCONJ
ejpam-3565	47	25	none	none	NOUN
ejpam-3565	47	26	of	of	ADP
ejpam-3565	47	27	the	the	DET
ejpam-3565	47	28	rows	row	NOUN
ejpam-3565	47	29	can	can	AUX
ejpam-3565	47	30	be	be	AUX
ejpam-3565	47	31	written	write	VERB
ejpam-3565	47	32	as	as	ADP
ejpam-3565	47	33	a	a	DET
ejpam-3565	47	34	linear	linear	ADJ
ejpam-3565	47	35	combination	combination	NOUN
ejpam-3565	47	36	of	of	ADP
ejpam-3565	47	37	the	the	DET
ejpam-3565	47	38	other	other	ADJ
ejpam-3565	47	39	rows	row	NOUN
ejpam-3565	47	40	.	.	PUNCT
ejpam-3565	48	1	two	two	NUM
ejpam-3565	48	2	codewords	codeword	NOUN
ejpam-3565	48	3	x	x	PUNCT
ejpam-3565	48	4	=	=	PUNCT
ejpam-3565	48	5	(	(	PUNCT
ejpam-3565	48	6	x1	x1	PROPN
ejpam-3565	48	7	,	,	PUNCT
ejpam-3565	48	8	.	.	PUNCT
ejpam-3565	48	9	.	.	PUNCT
ejpam-3565	48	10	.	.	PUNCT
ejpam-3565	48	11	,	,	PUNCT
ejpam-3565	48	12	xn	xn	X
ejpam-3565	48	13	)	)	PUNCT
ejpam-3565	48	14	and	and	CCONJ
ejpam-3565	48	15	y	y	PROPN
ejpam-3565	48	16	=	=	SYM
ejpam-3565	48	17	(	(	PUNCT
ejpam-3565	48	18	y1	y1	INTJ
ejpam-3565	48	19	,	,	PUNCT
ejpam-3565	48	20	.	.	PUNCT
ejpam-3565	48	21	.	.	PUNCT
ejpam-3565	48	22	.	.	PUNCT
ejpam-3565	49	1	,	,	PUNCT
ejpam-3565	49	2	yn	yn	X
ejpam-3565	49	3	)	)	PUNCT
ejpam-3565	49	4	are	be	AUX
ejpam-3565	49	5	orthogonal	orthogonal	ADJ
ejpam-3565	49	6	if	if	SCONJ
ejpam-3565	49	7	their	their	PRON
ejpam-3565	49	8	euclidean	euclidean	ADJ
ejpam-3565	49	9	inner	inner	ADJ
ejpam-3565	49	10	product	product	NOUN
ejpam-3565	49	11	∑n	∑n	PROPN
ejpam-3565	49	12	i=1	i=1	PROPN
ejpam-3565	49	13	xiyi	xiyi	PROPN
ejpam-3565	49	14	is	be	AUX
ejpam-3565	49	15	zero	zero	NUM
ejpam-3565	49	16	.	.	PUNCT
ejpam-3565	50	1	the	the	DET
ejpam-3565	50	2	dual	dual	ADJ
ejpam-3565	50	3	c⊥	c⊥	NOUN
ejpam-3565	50	4	of	of	ADP
ejpam-3565	50	5	a	a	DET
ejpam-3565	50	6	code	code	NOUN
ejpam-3565	50	7	c	c	NOUN
ejpam-3565	50	8	of	of	ADP
ejpam-3565	50	9	length	length	NOUN
ejpam-3565	50	10	n	n	CCONJ
ejpam-3565	50	11	over	over	ADP
ejpam-3565	50	12	s	s	VERB
ejpam-3565	50	13	consists	consist	NOUN
ejpam-3565	50	14	of	of	ADP
ejpam-3565	50	15	t.	t.	PROPN
ejpam-3565	50	16	l.	l.	PROPN
ejpam-3565	50	17	vasquez	vasquez	PROPN
ejpam-3565	50	18	,	,	PUNCT
ejpam-3565	50	19	g.	g.	PROPN
ejpam-3565	50	20	petalcorin	petalcorin	PROPN
ejpam-3565	50	21	/	/	SYM
ejpam-3565	50	22	eur	eur	PROPN
ejpam-3565	50	23	.	.	PUNCT
ejpam-3565	51	1	j.	j.	PROPN
ejpam-3565	51	2	pure	pure	PROPN
ejpam-3565	51	3	appl	appl	PROPN
ejpam-3565	51	4	.	.	PROPN
ejpam-3565	51	5	math	math	PROPN
ejpam-3565	51	6	,	,	PUNCT
ejpam-3565	51	7	12	12	NUM
ejpam-3565	51	8	(	(	PUNCT
ejpam-3565	51	9	4	4	NUM
ejpam-3565	51	10	)	)	PUNCT
ejpam-3565	51	11	(	(	PUNCT
ejpam-3565	51	12	2019	2019	NUM
ejpam-3565	51	13	)	)	PUNCT
ejpam-3565	51	14	,	,	PUNCT
ejpam-3565	51	15	1701	1701	NUM
ejpam-3565	51	16	-	-	SYM
ejpam-3565	51	17	1716	1716	NUM
ejpam-3565	51	18	1703	1703	NUM
ejpam-3565	51	19	all	all	PRON
ejpam-3565	51	20	x	x	SYM
ejpam-3565	51	21	∈	∈	PROPN
ejpam-3565	51	22	sn	sn	PROPN
ejpam-3565	51	23	which	which	PRON
ejpam-3565	51	24	are	be	AUX
ejpam-3565	51	25	orthogonal	orthogonal	ADJ
ejpam-3565	51	26	to	to	ADP
ejpam-3565	51	27	every	every	DET
ejpam-3565	51	28	codeword	codeword	NOUN
ejpam-3565	51	29	in	in	ADP
ejpam-3565	51	30	c.	c.	PROPN
ejpam-3565	51	31	if	if	SCONJ
ejpam-3565	51	32	c	c	PROPN
ejpam-3565	51	33	⊆	⊆	NUM
ejpam-3565	51	34	c⊥	c⊥	PROPN
ejpam-3565	51	35	,	,	PUNCT
ejpam-3565	51	36	then	then	ADV
ejpam-3565	51	37	c	c	PROPN
ejpam-3565	51	38	is	be	AUX
ejpam-3565	51	39	said	say	VERB
ejpam-3565	51	40	to	to	PART
ejpam-3565	51	41	be	be	AUX
ejpam-3565	51	42	self	self	NOUN
ejpam-3565	51	43	-	-	PUNCT
ejpam-3565	51	44	orthogonal	orthogonal	ADJ
ejpam-3565	51	45	.	.	PUNCT
ejpam-3565	52	1	if	if	SCONJ
ejpam-3565	52	2	c	c	NOUN
ejpam-3565	52	3	=	=	SYM
ejpam-3565	52	4	c⊥	c⊥	PROPN
ejpam-3565	52	5	,	,	PUNCT
ejpam-3565	52	6	then	then	ADV
ejpam-3565	52	7	c	c	PROPN
ejpam-3565	52	8	is	be	AUX
ejpam-3565	52	9	said	say	VERB
ejpam-3565	52	10	to	to	PART
ejpam-3565	52	11	be	be	AUX
ejpam-3565	52	12	self	self	NOUN
ejpam-3565	52	13	-	-	PUNCT
ejpam-3565	52	14	dual	dual	ADJ
ejpam-3565	52	15	.	.	PUNCT
ejpam-3565	53	1	a	a	DET
ejpam-3565	53	2	code	code	NOUN
ejpam-3565	53	3	of	of	ADP
ejpam-3565	53	4	length	length	NOUN
ejpam-3565	53	5	n	n	PROPN
ejpam-3565	53	6	and	and	CCONJ
ejpam-3565	53	7	dimension	dimension	NOUN
ejpam-3565	53	8	k	k	PROPN
ejpam-3565	53	9	over	over	ADP
ejpam-3565	53	10	a	a	DET
ejpam-3565	53	11	finite	finite	ADJ
ejpam-3565	53	12	field	field	NOUN
ejpam-3565	53	13	f	f	PROPN
ejpam-3565	53	14	is	be	AUX
ejpam-3565	53	15	called	call	VERB
ejpam-3565	53	16	an	an	DET
ejpam-3565	53	17	[	[	NOUN
ejpam-3565	53	18	n	n	CCONJ
ejpam-3565	53	19	,	,	PUNCT
ejpam-3565	53	20	k	k	X
ejpam-3565	53	21	]	]	X
ejpam-3565	53	22	code	code	NOUN
ejpam-3565	53	23	and	and	CCONJ
ejpam-3565	53	24	contains	contain	VERB
ejpam-3565	53	25	|f|k	|f|k	NUM
ejpam-3565	53	26	codewords	codeword	NOUN
ejpam-3565	53	27	.	.	PUNCT
ejpam-3565	54	1	an	an	DET
ejpam-3565	54	2	[	[	NOUN
ejpam-3565	54	3	n	n	CCONJ
ejpam-3565	54	4	,	,	PUNCT
ejpam-3565	54	5	k	k	X
ejpam-3565	54	6	]	]	X
ejpam-3565	54	7	code	code	NOUN
ejpam-3565	54	8	is	be	AUX
ejpam-3565	54	9	self	self	NOUN
ejpam-3565	54	10	-	-	PUNCT
ejpam-3565	54	11	dual	dual	ADJ
ejpam-3565	54	12	if	if	SCONJ
ejpam-3565	55	1	and	and	CCONJ
ejpam-3565	55	2	only	only	ADV
ejpam-3565	55	3	if	if	SCONJ
ejpam-3565	55	4	it	it	PRON
ejpam-3565	55	5	is	be	AUX
ejpam-3565	55	6	self	self	NOUN
ejpam-3565	55	7	-	-	PUNCT
ejpam-3565	55	8	orthogonal	orthogonal	ADJ
ejpam-3565	55	9	and	and	CCONJ
ejpam-3565	55	10	k	k	NOUN
ejpam-3565	55	11	=	=	PROPN
ejpam-3565	55	12	n	n	PRON
ejpam-3565	55	13	2	2	NUM
ejpam-3565	55	14	.	.	PUNCT
ejpam-3565	56	1	we	we	PRON
ejpam-3565	56	2	say	say	VERB
ejpam-3565	56	3	that	that	SCONJ
ejpam-3565	56	4	a	a	DET
ejpam-3565	56	5	generator	generator	NOUN
ejpam-3565	56	6	matrix	matrix	NOUN
ejpam-3565	56	7	g	g	NOUN
ejpam-3565	56	8	for	for	ADP
ejpam-3565	56	9	an	an	DET
ejpam-3565	56	10	[	[	NOUN
ejpam-3565	56	11	n	n	CCONJ
ejpam-3565	56	12	,	,	PUNCT
ejpam-3565	56	13	k	k	X
ejpam-3565	56	14	]	]	X
ejpam-3565	56	15	code	code	NOUN
ejpam-3565	56	16	is	be	AUX
ejpam-3565	56	17	in	in	ADP
ejpam-3565	56	18	standard	standard	ADJ
ejpam-3565	56	19	form	form	NOUN
ejpam-3565	56	20	if	if	SCONJ
ejpam-3565	56	21	g	g	NOUN
ejpam-3565	56	22	=	=	SYM
ejpam-3565	57	1	[	[	X
ejpam-3565	57	2	ik	ik	PROPN
ejpam-3565	57	3	a	a	X
ejpam-3565	57	4	]	]	X
ejpam-3565	57	5	,	,	PUNCT
ejpam-3565	57	6	where	where	SCONJ
ejpam-3565	57	7	ik	ik	PROPN
ejpam-3565	57	8	denotes	denote	VERB
ejpam-3565	57	9	the	the	DET
ejpam-3565	57	10	k×	k×	PROPN
ejpam-3565	57	11	k	k	PROPN
ejpam-3565	57	12	identity	identity	NOUN
ejpam-3565	57	13	matrix	matrix	NOUN
ejpam-3565	57	14	and	and	CCONJ
ejpam-3565	57	15	a	a	PRON
ejpam-3565	57	16	is	be	AUX
ejpam-3565	57	17	some	some	DET
ejpam-3565	57	18	k×	k×	PROPN
ejpam-3565	57	19	(	(	PUNCT
ejpam-3565	57	20	n−	n−	NOUN
ejpam-3565	57	21	k	k	NOUN
ejpam-3565	57	22	)	)	PUNCT
ejpam-3565	57	23	matrix	matrix	NOUN
ejpam-3565	57	24	.	.	PUNCT
ejpam-3565	58	1	let	let	VERB
ejpam-3565	58	2	c	c	PRON
ejpam-3565	58	3	be	be	AUX
ejpam-3565	58	4	a	a	DET
ejpam-3565	58	5	code	code	NOUN
ejpam-3565	58	6	of	of	ADP
ejpam-3565	58	7	length	length	NOUN
ejpam-3565	58	8	n	n	CCONJ
ejpam-3565	58	9	over	over	ADP
ejpam-3565	58	10	the	the	DET
ejpam-3565	58	11	galois	galois	PROPN
ejpam-3565	58	12	ring	ring	NOUN
ejpam-3565	58	13	gr(pe	gr(pe	NOUN
ejpam-3565	58	14	,	,	PUNCT
ejpam-3565	58	15	r	r	NOUN
ejpam-3565	58	16	)	)	PUNCT
ejpam-3565	58	17	.	.	PUNCT
ejpam-3565	59	1	c	c	PROPN
ejpam-3565	59	2	has	have	VERB
ejpam-3565	59	3	a	a	DET
ejpam-3565	59	4	generator	generator	NOUN
ejpam-3565	59	5	matrix	matrix	NOUN
ejpam-3565	59	6	which	which	PRON
ejpam-3565	59	7	,	,	PUNCT
ejpam-3565	59	8	after	after	ADP
ejpam-3565	59	9	a	a	DET
ejpam-3565	59	10	suitable	suitable	ADJ
ejpam-3565	59	11	permutation	permutation	NOUN
ejpam-3565	59	12	of	of	ADP
ejpam-3565	59	13	coordinates	coordinate	NOUN
ejpam-3565	59	14	,	,	PUNCT
ejpam-3565	59	15	can	can	AUX
ejpam-3565	59	16	be	be	AUX
ejpam-3565	59	17	written	write	VERB
ejpam-3565	59	18	as	as	ADP
ejpam-3565	59	19	g	g	NOUN
ejpam-3565	59	20	=	=	NOUN
ejpam-3565	59	21			NOUN
ejpam-3565	59	22	ik0	ik0	VERB
ejpam-3565	59	23	a0,1	a0,1	PROPN
ejpam-3565	59	24	a0,2	a0,2	PROPN
ejpam-3565	59	25	·	·	PUNCT
ejpam-3565	59	26	·	·	PUNCT
ejpam-3565	59	27	·	·	PUNCT
ejpam-3565	60	1	a0,e−1	a0,e−1	PROPN
ejpam-3565	60	2	a0,e	a0,e	PROPN
ejpam-3565	60	3	0	0	NUM
ejpam-3565	60	4	pik1	pik1	ADJ
ejpam-3565	60	5	pa1,2	pa1,2	NOUN
ejpam-3565	60	6	·	·	PUNCT
ejpam-3565	60	7	·	·	PUNCT
ejpam-3565	60	8	·	·	PUNCT
ejpam-3565	60	9	pa1,e−1	pa1,e−1	NOUN
ejpam-3565	60	10	pa1,e	pa1,e	NOUN
ejpam-3565	60	11	0	0	NUM
ejpam-3565	60	12	0	0	NUM
ejpam-3565	60	13	p2ik2	p2ik2	NOUN
ejpam-3565	60	14	·	·	PUNCT
ejpam-3565	60	15	·	·	PUNCT
ejpam-3565	60	16	·	·	PUNCT
ejpam-3565	60	17	p2a2,e−1	p2a2,e−1	PROPN
ejpam-3565	60	18	p2a2,e	p2a2,e	NOUN
ejpam-3565	60	19	...	...	PUNCT
ejpam-3565	60	20	...	...	PUNCT
ejpam-3565	60	21	...	...	PUNCT
ejpam-3565	60	22	.	.	PUNCT
ejpam-3565	60	23	.	.	PUNCT
ejpam-3565	60	24	.	.	PUNCT
ejpam-3565	61	1	...	...	PUNCT
ejpam-3565	62	1	...	...	PUNCT
ejpam-3565	63	1	0	0	NUM
ejpam-3565	63	2	0	0	NUM
ejpam-3565	63	3	0	0	NUM
ejpam-3565	63	4	·	·	PUNCT
ejpam-3565	63	5	·	·	PUNCT
ejpam-3565	63	6	·	·	PUNCT
ejpam-3565	64	1	pe−1ike−1	pe−1ike−1	NOUN
ejpam-3565	64	2	pe−1ae−1,e	pe−1ae−1,e	NOUN
ejpam-3565	64	3			PUNCT
ejpam-3565	64	4	(	(	PUNCT
ejpam-3565	64	5	1	1	NUM
ejpam-3565	64	6	)	)	PUNCT
ejpam-3565	64	7	where	where	SCONJ
ejpam-3565	64	8	iki	iki	PROPN
ejpam-3565	64	9	is	be	AUX
ejpam-3565	64	10	the	the	DET
ejpam-3565	64	11	ki×	ki×	PROPN
ejpam-3565	64	12	ki	ki	PROPN
ejpam-3565	64	13	identity	identity	NOUN
ejpam-3565	64	14	matrix	matrix	NOUN
ejpam-3565	64	15	and	and	CCONJ
ejpam-3565	64	16	the	the	DET
ejpam-3565	64	17	aijs	aijs	PROPN
ejpam-3565	64	18	are	be	AUX
ejpam-3565	64	19	matrices	matrix	NOUN
ejpam-3565	64	20	of	of	ADP
ejpam-3565	64	21	appropriate	appropriate	ADJ
ejpam-3565	64	22	sizes	size	NOUN
ejpam-3565	64	23	over	over	ADP
ejpam-3565	64	24	gr(pe	gr(pe	NOUN
ejpam-3565	64	25	,	,	PUNCT
ejpam-3565	64	26	r	r	NOUN
ejpam-3565	64	27	)	)	PUNCT
ejpam-3565	64	28	.	.	PUNCT
ejpam-3565	65	1	the	the	DET
ejpam-3565	65	2	columns	column	NOUN
ejpam-3565	65	3	are	be	AUX
ejpam-3565	65	4	grouped	group	VERB
ejpam-3565	65	5	into	into	ADP
ejpam-3565	65	6	blocks	block	NOUN
ejpam-3565	65	7	of	of	ADP
ejpam-3565	65	8	sizes	size	NOUN
ejpam-3565	65	9	k0	k0	PROPN
ejpam-3565	65	10	,	,	PUNCT
ejpam-3565	65	11	k1	k1	NOUN
ejpam-3565	65	12	,	,	PUNCT
ejpam-3565	65	13	.	.	PUNCT
ejpam-3565	65	14	.	.	PUNCT
ejpam-3565	66	1	.	.	PUNCT
ejpam-3565	67	1	,	,	PUNCT
ejpam-3565	67	2	ke−1	ke−1	PROPN
ejpam-3565	67	3	,	,	PUNCT
ejpam-3565	67	4	ke	ke	NOUN
ejpam-3565	67	5	=	=	PUNCT
ejpam-3565	68	1	n−	n−	PROPN
ejpam-3565	68	2	∑e−1	∑e−1	NOUN
ejpam-3565	69	1	i=0	i=0	PROPN
ejpam-3565	69	2	ki	ki	PROPN
ejpam-3565	69	3	.	.	PUNCT
ejpam-3565	70	1	a	a	DET
ejpam-3565	70	2	code	code	NOUN
ejpam-3565	70	3	c	c	NOUN
ejpam-3565	70	4	with	with	ADP
ejpam-3565	70	5	generator	generator	NOUN
ejpam-3565	70	6	matrix	matrix	NOUN
ejpam-3565	70	7	g	g	NOUN
ejpam-3565	70	8	as	as	ADP
ejpam-3565	70	9	in	in	ADP
ejpam-3565	70	10	(	(	PUNCT
ejpam-3565	70	11	1	1	NUM
ejpam-3565	70	12	)	)	PUNCT
ejpam-3565	70	13	is	be	AUX
ejpam-3565	70	14	said	say	VERB
ejpam-3565	70	15	to	to	PART
ejpam-3565	70	16	be	be	AUX
ejpam-3565	70	17	of	of	ADP
ejpam-3565	70	18	type	type	NOUN
ejpam-3565	70	19	{	{	PUNCT
ejpam-3565	70	20	k0	k0	PROPN
ejpam-3565	70	21	,	,	PUNCT
ejpam-3565	70	22	k1	k1	NOUN
ejpam-3565	70	23	,	,	PUNCT
ejpam-3565	70	24	.	.	PUNCT
ejpam-3565	70	25	.	.	PUNCT
ejpam-3565	71	1	.	.	PUNCT
ejpam-3565	72	1	,	,	PUNCT
ejpam-3565	72	2	ke−1	ke−1	PROPN
ejpam-3565	72	3	}	}	PUNCT
ejpam-3565	72	4	and	and	CCONJ
ejpam-3565	72	5	has	have	VERB
ejpam-3565	72	6	(	(	PUNCT
ejpam-3565	72	7	pr	pr	NOUN
ejpam-3565	72	8	)	)	PUNCT
ejpam-3565	72	9	∑e−1	∑e−1	NOUN
ejpam-3565	73	1	i=0	i=0	PROPN
ejpam-3565	73	2	(	(	PUNCT
ejpam-3565	73	3	e−i)ki	e−i)ki	PROPN
ejpam-3565	73	4	codewords	codeword	NOUN
ejpam-3565	73	5	.	.	PUNCT
ejpam-3565	74	1	the	the	DET
ejpam-3565	74	2	dual	dual	ADJ
ejpam-3565	74	3	c⊥	c⊥	NOUN
ejpam-3565	74	4	of	of	ADP
ejpam-3565	74	5	c	c	PROPN
ejpam-3565	74	6	is	be	AUX
ejpam-3565	74	7	of	of	ADP
ejpam-3565	74	8	type	type	NOUN
ejpam-3565	74	9	{	{	PUNCT
ejpam-3565	74	10	ke	ke	PROPN
ejpam-3565	74	11	,	,	PUNCT
ejpam-3565	74	12	ke−1	ke−1	PROPN
ejpam-3565	74	13	,	,	PUNCT
ejpam-3565	74	14	.	.	PUNCT
ejpam-3565	74	15	.	.	PUNCT
ejpam-3565	75	1	.	.	PUNCT
ejpam-3565	76	1	,	,	PUNCT
ejpam-3565	76	2	k1	k1	NOUN
ejpam-3565	76	3	}	}	PUNCT
ejpam-3565	76	4	.	.	PUNCT
ejpam-3565	77	1	it	it	PRON
ejpam-3565	77	2	is	be	AUX
ejpam-3565	77	3	known	know	VERB
ejpam-3565	77	4	that	that	SCONJ
ejpam-3565	77	5	|c||c⊥|	|c||c⊥|	ADV
ejpam-3565	77	6	=	=	SYM
ejpam-3565	77	7	pern	pern	NOUN
ejpam-3565	77	8	.	.	PUNCT
ejpam-3565	78	1	if	if	SCONJ
ejpam-3565	78	2	c	c	PROPN
ejpam-3565	78	3	is	be	AUX
ejpam-3565	78	4	a	a	DET
ejpam-3565	78	5	self	self	NOUN
ejpam-3565	78	6	-	-	PUNCT
ejpam-3565	78	7	dual	dual	ADJ
ejpam-3565	78	8	code	code	NOUN
ejpam-3565	78	9	of	of	ADP
ejpam-3565	78	10	type	type	NOUN
ejpam-3565	78	11	{	{	PUNCT
ejpam-3565	78	12	k0	k0	PROPN
ejpam-3565	78	13	,	,	PUNCT
ejpam-3565	78	14	k1	k1	NOUN
ejpam-3565	78	15	,	,	PUNCT
ejpam-3565	78	16	.	.	PUNCT
ejpam-3565	78	17	.	.	PUNCT
ejpam-3565	79	1	.	.	PUNCT
ejpam-3565	80	1	,	,	PUNCT
ejpam-3565	80	2	ke−1	ke−1	PROPN
ejpam-3565	80	3	}	}	PUNCT
ejpam-3565	80	4	,	,	PUNCT
ejpam-3565	80	5	then	then	ADV
ejpam-3565	80	6	we	we	PRON
ejpam-3565	80	7	must	must	AUX
ejpam-3565	80	8	have	have	VERB
ejpam-3565	80	9	ki	ki	PROPN
ejpam-3565	80	10	=	=	PUNCT
ejpam-3565	80	11	ke−i	ke−i	PROPN
ejpam-3565	80	12	for	for	ADP
ejpam-3565	80	13	all	all	DET
ejpam-3565	80	14	i.	i.	NOUN
ejpam-3565	80	15	for	for	ADP
ejpam-3565	80	16	0	0	NUM
ejpam-3565	80	17	≤	≤	NUM
ejpam-3565	81	1	i	i	PRON
ejpam-3565	81	2	≤	≤	NOUN
ejpam-3565	81	3	e−	e−	PROPN
ejpam-3565	81	4	1	1	NUM
ejpam-3565	81	5	,	,	PUNCT
ejpam-3565	81	6	define	define	VERB
ejpam-3565	81	7	tori(c	tori(c	NOUN
ejpam-3565	81	8	)	)	PUNCT
ejpam-3565	81	9	=	=	PRON
ejpam-3565	82	1	{	{	PUNCT
ejpam-3565	82	2	v̄	v̄	NOUN
ejpam-3565	82	3	:	:	PUNCT
ejpam-3565	82	4	piv̄	piv̄	NOUN
ejpam-3565	82	5	∈	∈	PROPN
ejpam-3565	82	6	c	c	X
ejpam-3565	82	7	}	}	PUNCT
ejpam-3565	82	8	,	,	PUNCT
ejpam-3565	82	9	where	where	SCONJ
ejpam-3565	82	10	v̄	v̄	NOUN
ejpam-3565	82	11	is	be	AUX
ejpam-3565	82	12	the	the	DET
ejpam-3565	82	13	image	image	NOUN
ejpam-3565	82	14	of	of	ADP
ejpam-3565	82	15	v	v	NOUN
ejpam-3565	82	16	under	under	ADP
ejpam-3565	82	17	the	the	DET
ejpam-3565	82	18	projection	projection	NOUN
ejpam-3565	82	19	µ	µ	NOUN
ejpam-3565	82	20	:	:	PUNCT
ejpam-3565	82	21	gr(pe	gr(pe	NOUN
ejpam-3565	82	22	,	,	PUNCT
ejpam-3565	82	23	r)n	r)n	PUNCT
ejpam-3565	82	24	→	→	PUNCT
ejpam-3565	82	25	fn	fn	NOUN
ejpam-3565	82	26	pr	pr	NOUN
ejpam-3565	82	27	.	.	PUNCT
ejpam-3565	83	1	tori(c	tori(c	NOUN
ejpam-3565	83	2	)	)	PUNCT
ejpam-3565	83	3	is	be	AUX
ejpam-3565	83	4	an	an	DET
ejpam-3565	83	5	[	[	NOUN
ejpam-3565	83	6	n	n	CCONJ
ejpam-3565	83	7	,	,	PUNCT
ejpam-3565	83	8	k0	k0	PROPN
ejpam-3565	83	9	+	+	X
ejpam-3565	83	10	.	.	PUNCT
ejpam-3565	83	11	.	.	PUNCT
ejpam-3565	83	12	.	.	PUNCT
ejpam-3565	84	1	+	+	CCONJ
ejpam-3565	84	2	ki	ki	PROPN
ejpam-3565	84	3	]	]	X
ejpam-3565	84	4	code	code	NOUN
ejpam-3565	84	5	over	over	ADP
ejpam-3565	84	6	fpr	fpr	NOUN
ejpam-3565	84	7	and	and	CCONJ
ejpam-3565	84	8	is	be	AUX
ejpam-3565	84	9	called	call	VERB
ejpam-3565	84	10	the	the	DET
ejpam-3565	84	11	ith	ith	PROPN
ejpam-3565	84	12	torsion	torsion	NOUN
ejpam-3565	84	13	code	code	NOUN
ejpam-3565	84	14	of	of	ADP
ejpam-3565	84	15	c.	c.	PROPN
ejpam-3565	84	16	in	in	ADP
ejpam-3565	84	17	particular	particular	ADJ
ejpam-3565	84	18	,	,	PUNCT
ejpam-3565	84	19	tor0(c	tor0(c	NUM
ejpam-3565	84	20	)	)	PUNCT
ejpam-3565	84	21	is	be	AUX
ejpam-3565	84	22	called	call	VERB
ejpam-3565	84	23	the	the	DET
ejpam-3565	84	24	residue	residue	NOUN
ejpam-3565	84	25	code	code	NOUN
ejpam-3565	84	26	and	and	CCONJ
ejpam-3565	84	27	is	be	AUX
ejpam-3565	84	28	denoted	denote	VERB
ejpam-3565	84	29	by	by	ADP
ejpam-3565	84	30	res(c	res(c	PROPN
ejpam-3565	84	31	)	)	PUNCT
ejpam-3565	84	32	.	.	PUNCT
ejpam-3565	85	1	if	if	SCONJ
ejpam-3565	85	2	c	c	PROPN
ejpam-3565	85	3	has	have	VERB
ejpam-3565	85	4	generator	generator	NOUN
ejpam-3565	85	5	matrix	matrix	NOUN
ejpam-3565	85	6	g	g	NOUN
ejpam-3565	85	7	in	in	ADP
ejpam-3565	85	8	(	(	PUNCT
ejpam-3565	85	9	1	1	NUM
ejpam-3565	85	10	)	)	PUNCT
ejpam-3565	85	11	,	,	PUNCT
ejpam-3565	85	12	then	then	ADV
ejpam-3565	85	13	tori(c	tori(c	PROPN
ejpam-3565	85	14	)	)	PUNCT
ejpam-3565	85	15	has	have	VERB
ejpam-3565	85	16	a	a	DET
ejpam-3565	85	17	generator	generator	NOUN
ejpam-3565	85	18	matrix	matrix	NOUN
ejpam-3565	85	19	of	of	ADP
ejpam-3565	85	20	the	the	DET
ejpam-3565	85	21	form	form	NOUN
ejpam-3565	85	22	gi	gi	NOUN
ejpam-3565	85	23	=	=	PUNCT
ejpam-3565	85	24			PROPN
ejpam-3565	85	25	ik0	ik0	VERB
ejpam-3565	85	26	a0,1	a0,1	PROPN
ejpam-3565	85	27	a0,2	a0,2	PROPN
ejpam-3565	85	28	·	·	PUNCT
ejpam-3565	85	29	·	·	PUNCT
ejpam-3565	85	30	·	·	PUNCT
ejpam-3565	86	1	a0,i−1	a0,i−1	PROPN
ejpam-3565	86	2	·	·	PUNCT
ejpam-3565	86	3	·	·	PUNCT
ejpam-3565	86	4	·	·	PUNCT
ejpam-3565	87	1	a0,e	a0,e	PROPN
ejpam-3565	87	2	0	0	NUM
ejpam-3565	87	3	ik1	ik1	PROPN
ejpam-3565	87	4	a1,2	a1,2	PROPN
ejpam-3565	87	5	·	·	PUNCT
ejpam-3565	87	6	·	·	PUNCT
ejpam-3565	87	7	·	·	PUNCT
ejpam-3565	87	8	a1,i−1	a1,i−1	PUNCT
ejpam-3565	87	9	·	·	PUNCT
ejpam-3565	87	10	·	·	PUNCT
ejpam-3565	87	11	·	·	PUNCT
ejpam-3565	87	12	a1,e	a1,e	PROPN
ejpam-3565	87	13	...	...	PUNCT
ejpam-3565	87	14	...	...	PUNCT
ejpam-3565	87	15	...	...	PUNCT
ejpam-3565	87	16	.	.	PUNCT
ejpam-3565	87	17	.	.	PUNCT
ejpam-3565	87	18	.	.	PUNCT
ejpam-3565	87	19	...	...	PUNCT
ejpam-3565	87	20	.	.	PUNCT
ejpam-3565	87	21	.	.	PUNCT
ejpam-3565	87	22	.	.	PUNCT
ejpam-3565	88	1	...	...	PUNCT
ejpam-3565	89	1	0	0	NUM
ejpam-3565	89	2	0	0	NUM
ejpam-3565	89	3	0	0	NUM
ejpam-3565	89	4	·	·	PUNCT
ejpam-3565	89	5	·	·	PUNCT
ejpam-3565	89	6	·	·	PUNCT
ejpam-3565	89	7	iki	iki	X
ejpam-3565	89	8	·	·	PUNCT
ejpam-3565	89	9	·	·	PUNCT
ejpam-3565	89	10	·	·	PUNCT
ejpam-3565	89	11	ai	ai	VERB
ejpam-3565	89	12	,	,	PUNCT
ejpam-3565	89	13	e	e	X
ejpam-3565	89	14			VERB
ejpam-3565	89	15	,	,	PUNCT
ejpam-3565	89	16	where	where	SCONJ
ejpam-3565	89	17	a	a	DET
ejpam-3565	89	18	=	=	X
ejpam-3565	89	19	(	(	PUNCT
ejpam-3565	89	20	āij	āij	PROPN
ejpam-3565	89	21	)	)	PUNCT
ejpam-3565	89	22	whenever	whenever	SCONJ
ejpam-3565	89	23	a	a	DET
ejpam-3565	89	24	=	=	X
ejpam-3565	89	25	(	(	PUNCT
ejpam-3565	89	26	aij	aij	PROPN
ejpam-3565	89	27	)	)	PUNCT
ejpam-3565	89	28	.	.	PUNCT
ejpam-3565	90	1	two	two	NUM
ejpam-3565	90	2	codes	code	NOUN
ejpam-3565	90	3	over	over	ADP
ejpam-3565	90	4	gr(pe	gr(pe	NOUN
ejpam-3565	90	5	,	,	PUNCT
ejpam-3565	90	6	r	r	NOUN
ejpam-3565	90	7	)	)	PUNCT
ejpam-3565	90	8	are	be	AUX
ejpam-3565	90	9	said	say	VERB
ejpam-3565	90	10	to	to	PART
ejpam-3565	90	11	be	be	AUX
ejpam-3565	90	12	equivalent	equivalent	ADJ
ejpam-3565	90	13	if	if	SCONJ
ejpam-3565	90	14	one	one	PRON
ejpam-3565	90	15	can	can	AUX
ejpam-3565	90	16	be	be	AUX
ejpam-3565	90	17	obtained	obtain	VERB
ejpam-3565	90	18	from	from	ADP
ejpam-3565	90	19	the	the	DET
ejpam-3565	90	20	other	other	ADJ
ejpam-3565	90	21	by	by	ADP
ejpam-3565	90	22	permuting	permute	VERB
ejpam-3565	90	23	the	the	DET
ejpam-3565	90	24	coordinates	coordinate	NOUN
ejpam-3565	90	25	and	and	CCONJ
ejpam-3565	90	26	(	(	PUNCT
ejpam-3565	90	27	if	if	SCONJ
ejpam-3565	90	28	necessary	necessary	ADJ
ejpam-3565	90	29	)	)	PUNCT
ejpam-3565	90	30	changing	change	VERB
ejpam-3565	90	31	the	the	DET
ejpam-3565	90	32	signs	sign	NOUN
ejpam-3565	90	33	of	of	ADP
ejpam-3565	90	34	certain	certain	ADJ
ejpam-3565	90	35	coordinates	coordinate	NOUN
ejpam-3565	90	36	.	.	PUNCT
ejpam-3565	91	1	thus	thus	ADV
ejpam-3565	91	2	two	two	NUM
ejpam-3565	91	3	codes	code	NOUN
ejpam-3565	91	4	c1	c1	PROPN
ejpam-3565	91	5	and	and	CCONJ
ejpam-3565	91	6	c2	c2	PROPN
ejpam-3565	91	7	of	of	ADP
ejpam-3565	91	8	length	length	NOUN
ejpam-3565	91	9	n	n	CCONJ
ejpam-3565	91	10	over	over	ADP
ejpam-3565	91	11	gr(pe	gr(pe	NOUN
ejpam-3565	91	12	,	,	PUNCT
ejpam-3565	91	13	r	r	NOUN
ejpam-3565	91	14	)	)	PUNCT
ejpam-3565	91	15	are	be	AUX
ejpam-3565	91	16	equivalent	equivalent	ADJ
ejpam-3565	91	17	if	if	SCONJ
ejpam-3565	91	18	there	there	PRON
ejpam-3565	91	19	exists	exist	VERB
ejpam-3565	91	20	a	a	DET
ejpam-3565	91	21	monomial	monomial	ADJ
ejpam-3565	91	22	matrix	matrix	NOUN
ejpam-3565	91	23	p	p	NOUN
ejpam-3565	91	24	such	such	ADJ
ejpam-3565	91	25	that	that	DET
ejpam-3565	91	26	c2	c2	PROPN
ejpam-3565	91	27	=	=	PUNCT
ejpam-3565	91	28	c1p	c1p	NOUN
ejpam-3565	91	29	=	=	SYM
ejpam-3565	91	30	{	{	PUNCT
ejpam-3565	91	31	cp	cp	INTJ
ejpam-3565	91	32	:	:	PUNCT
ejpam-3565	91	33	c	c	PROPN
ejpam-3565	91	34	∈	∈	PROPN
ejpam-3565	91	35	c1	c1	PROPN
ejpam-3565	91	36	}	}	PUNCT
ejpam-3565	91	37	,	,	PUNCT
ejpam-3565	91	38	where	where	SCONJ
ejpam-3565	91	39	p	p	NOUN
ejpam-3565	91	40	has	have	VERB
ejpam-3565	91	41	exactly	exactly	ADV
ejpam-3565	91	42	one	one	NUM
ejpam-3565	91	43	entry	entry	NOUN
ejpam-3565	91	44	±1	±1	VERB
ejpam-3565	91	45	in	in	ADP
ejpam-3565	91	46	every	every	DET
ejpam-3565	91	47	row	row	NOUN
ejpam-3565	91	48	and	and	CCONJ
ejpam-3565	91	49	every	every	DET
ejpam-3565	91	50	column	column	NOUN
ejpam-3565	91	51	and	and	CCONJ
ejpam-3565	91	52	all	all	DET
ejpam-3565	91	53	the	the	DET
ejpam-3565	91	54	other	other	ADJ
ejpam-3565	91	55	entries	entry	NOUN
ejpam-3565	91	56	are	be	AUX
ejpam-3565	91	57	zero	zero	NUM
ejpam-3565	91	58	.	.	PUNCT
ejpam-3565	92	1	the	the	DET
ejpam-3565	92	2	automorphism	automorphism	NOUN
ejpam-3565	92	3	group	group	NOUN
ejpam-3565	92	4	aut(c	aut(c	PROPN
ejpam-3565	92	5	)	)	PUNCT
ejpam-3565	92	6	of	of	ADP
ejpam-3565	92	7	a	a	DET
ejpam-3565	92	8	code	code	NOUN
ejpam-3565	92	9	c	c	NOUN
ejpam-3565	92	10	of	of	ADP
ejpam-3565	92	11	length	length	NOUN
ejpam-3565	92	12	n	n	CCONJ
ejpam-3565	92	13	over	over	ADP
ejpam-3565	92	14	gr(pe	gr(pe	NOUN
ejpam-3565	92	15	,	,	PUNCT
ejpam-3565	92	16	r	r	NOUN
ejpam-3565	92	17	)	)	PUNCT
ejpam-3565	92	18	is	be	AUX
ejpam-3565	92	19	the	the	DET
ejpam-3565	92	20	group	group	NOUN
ejpam-3565	92	21	of	of	ADP
ejpam-3565	92	22	all	all	DET
ejpam-3565	92	23	such	such	ADJ
ejpam-3565	92	24	matrices	matrix	NOUN
ejpam-3565	92	25	p	p	VERB
ejpam-3565	92	26	such	such	ADJ
ejpam-3565	92	27	that	that	DET
ejpam-3565	92	28	c	c	NOUN
ejpam-3565	92	29	=	=	SYM
ejpam-3565	92	30	cp	cp	INTJ
ejpam-3565	92	31	.	.	PUNCT
ejpam-3565	93	1	t.	t.	PROPN
ejpam-3565	93	2	l.	l.	PROPN
ejpam-3565	93	3	vasquez	vasquez	PROPN
ejpam-3565	93	4	,	,	PUNCT
ejpam-3565	93	5	g.	g.	PROPN
ejpam-3565	93	6	petalcorin	petalcorin	PROPN
ejpam-3565	93	7	/	/	SYM
ejpam-3565	93	8	eur	eur	PROPN
ejpam-3565	93	9	.	.	PUNCT
ejpam-3565	94	1	j.	j.	PROPN
ejpam-3565	94	2	pure	pure	PROPN
ejpam-3565	94	3	appl	appl	PROPN
ejpam-3565	94	4	.	.	PROPN
ejpam-3565	94	5	math	math	PROPN
ejpam-3565	94	6	,	,	PUNCT
ejpam-3565	94	7	12	12	NUM
ejpam-3565	94	8	(	(	PUNCT
ejpam-3565	94	9	4	4	NUM
ejpam-3565	94	10	)	)	PUNCT
ejpam-3565	94	11	(	(	PUNCT
ejpam-3565	94	12	2019	2019	NUM
ejpam-3565	94	13	)	)	PUNCT
ejpam-3565	94	14	,	,	PUNCT
ejpam-3565	94	15	1701	1701	NUM
ejpam-3565	94	16	-	-	SYM
ejpam-3565	94	17	1716	1716	NUM
ejpam-3565	94	18	1704	1704	NUM
ejpam-3565	94	19	let	let	VERB
ejpam-3565	94	20	en	en	X
ejpam-3565	94	21	be	be	AUX
ejpam-3565	94	22	the	the	DET
ejpam-3565	94	23	signed	sign	VERB
ejpam-3565	94	24	symmetric	symmetric	ADJ
ejpam-3565	94	25	group	group	NOUN
ejpam-3565	94	26	of	of	ADP
ejpam-3565	94	27	order	order	NOUN
ejpam-3565	94	28	|en|	|en|	NUM
ejpam-3565	94	29	=	=	SYM
ejpam-3565	94	30	2nn	2nn	ADJ
ejpam-3565	94	31	!	!	PUNCT
ejpam-3565	94	32	.	.	PUNCT
ejpam-3565	95	1	the	the	DET
ejpam-3565	95	2	number	number	NOUN
ejpam-3565	95	3	of	of	ADP
ejpam-3565	95	4	codes	code	NOUN
ejpam-3565	95	5	equivalent	equivalent	ADJ
ejpam-3565	95	6	to	to	ADP
ejpam-3565	95	7	a	a	DET
ejpam-3565	95	8	code	code	NOUN
ejpam-3565	95	9	c	c	NOUN
ejpam-3565	95	10	over	over	ADP
ejpam-3565	95	11	gr(p3	gr(p3	PROPN
ejpam-3565	95	12	,	,	PUNCT
ejpam-3565	95	13	r	r	NOUN
ejpam-3565	95	14	)	)	PUNCT
ejpam-3565	95	15	of	of	ADP
ejpam-3565	95	16	length	length	NOUN
ejpam-3565	95	17	n	n	NUM
ejpam-3565	95	18	is	be	AUX
ejpam-3565	95	19	|en|	|en|	NUM
ejpam-3565	95	20	|aut(c)|	|aut(c)|	NOUN
ejpam-3565	95	21	and	and	CCONJ
ejpam-3565	95	22	hence	hence	ADV
ejpam-3565	95	23	the	the	DET
ejpam-3565	95	24	number	number	NOUN
ejpam-3565	95	25	np3,r(n	np3,r(n	NOUN
ejpam-3565	95	26	)	)	PUNCT
ejpam-3565	95	27	of	of	ADP
ejpam-3565	95	28	distinct	distinct	ADJ
ejpam-3565	95	29	self	self	NOUN
ejpam-3565	95	30	-	-	PUNCT
ejpam-3565	95	31	dual	dual	ADJ
ejpam-3565	95	32	codes	code	NOUN
ejpam-3565	95	33	over	over	ADP
ejpam-3565	95	34	gr(p3	gr(p3	PROPN
ejpam-3565	95	35	,	,	PUNCT
ejpam-3565	95	36	r	r	NOUN
ejpam-3565	95	37	)	)	PUNCT
ejpam-3565	95	38	of	of	ADP
ejpam-3565	95	39	length	length	NOUN
ejpam-3565	95	40	n	n	NUM
ejpam-3565	95	41	is	be	AUX
ejpam-3565	95	42	np3,r(n	np3,r(n	NOUN
ejpam-3565	95	43	)	)	PUNCT
ejpam-3565	95	44	=	=	PUNCT
ejpam-3565	96	1	∑	∑	PUNCT
ejpam-3565	96	2	c	c	NOUN
ejpam-3565	96	3	|en|	|en|	NUM
ejpam-3565	96	4	|aut(c)|	|aut(c)|	NUM
ejpam-3565	96	5	where	where	SCONJ
ejpam-3565	96	6	the	the	DET
ejpam-3565	96	7	sum	sum	NOUN
ejpam-3565	96	8	runs	run	VERB
ejpam-3565	96	9	through	through	ADP
ejpam-3565	96	10	all	all	DET
ejpam-3565	96	11	inequivalent	inequivalent	NOUN
ejpam-3565	96	12	self	self	NOUN
ejpam-3565	96	13	-	-	PUNCT
ejpam-3565	96	14	dual	dual	ADJ
ejpam-3565	96	15	codes	code	NOUN
ejpam-3565	96	16	c	c	PROPN
ejpam-3565	96	17	over	over	ADP
ejpam-3565	96	18	gr(p3	gr(p3	PROPN
ejpam-3565	96	19	,	,	PUNCT
ejpam-3565	96	20	r	r	NOUN
ejpam-3565	96	21	)	)	PUNCT
ejpam-3565	96	22	of	of	ADP
ejpam-3565	96	23	length	length	NOUN
ejpam-3565	96	24	n.	n.	PROPN
ejpam-3565	96	25	an	an	DET
ejpam-3565	96	26	explicit	explicit	ADJ
ejpam-3565	96	27	formula	formula	NOUN
ejpam-3565	96	28	for	for	ADP
ejpam-3565	96	29	np3,r(n	np3,r(n	NOUN
ejpam-3565	96	30	)	)	PUNCT
ejpam-3565	96	31	,	,	PUNCT
ejpam-3565	96	32	called	call	VERB
ejpam-3565	96	33	the	the	DET
ejpam-3565	96	34	mass	mass	ADJ
ejpam-3565	96	35	formula	formula	NOUN
ejpam-3565	96	36	,	,	PUNCT
ejpam-3565	96	37	would	would	AUX
ejpam-3565	96	38	thus	thus	ADV
ejpam-3565	96	39	be	be	AUX
ejpam-3565	96	40	useful	useful	ADJ
ejpam-3565	96	41	for	for	ADP
ejpam-3565	96	42	finding	find	VERB
ejpam-3565	96	43	all	all	DET
ejpam-3565	96	44	inequivalent	inequivalent	NOUN
ejpam-3565	96	45	self	self	NOUN
ejpam-3565	96	46	-	-	PUNCT
ejpam-3565	96	47	dual	dual	ADJ
ejpam-3565	96	48	codes	code	NOUN
ejpam-3565	96	49	over	over	ADP
ejpam-3565	96	50	gr(p3	gr(p3	PROPN
ejpam-3565	96	51	,	,	PUNCT
ejpam-3565	96	52	r	r	NOUN
ejpam-3565	96	53	)	)	PUNCT
ejpam-3565	96	54	of	of	ADP
ejpam-3565	96	55	given	give	VERB
ejpam-3565	96	56	length	length	NOUN
ejpam-3565	96	57	.	.	PUNCT
ejpam-3565	97	1	for	for	ADP
ejpam-3565	97	2	the	the	DET
ejpam-3565	97	3	further	further	ADJ
ejpam-3565	97	4	study	study	NOUN
ejpam-3565	97	5	of	of	ADP
ejpam-3565	97	6	codes	code	NOUN
ejpam-3565	97	7	over	over	ADP
ejpam-3565	97	8	finite	finite	ADJ
ejpam-3565	97	9	fields	field	NOUN
ejpam-3565	97	10	and	and	CCONJ
ejpam-3565	97	11	finite	finite	ADJ
ejpam-3565	97	12	rings	ring	NOUN
ejpam-3565	97	13	,	,	PUNCT
ejpam-3565	97	14	see	see	VERB
ejpam-3565	97	15	[	[	X
ejpam-3565	97	16	7	7	NUM
ejpam-3565	97	17	,	,	PUNCT
ejpam-3565	97	18	12	12	NUM
ejpam-3565	97	19	]	]	PUNCT
ejpam-3565	97	20	.	.	PUNCT
ejpam-3565	98	1	we	we	PRON
ejpam-3565	98	2	will	will	AUX
ejpam-3565	98	3	need	need	VERB
ejpam-3565	98	4	the	the	DET
ejpam-3565	98	5	following	follow	VERB
ejpam-3565	98	6	lemmas	lemmas	PROPN
ejpam-3565	98	7	,	,	PUNCT
ejpam-3565	98	8	the	the	DET
ejpam-3565	98	9	proofs	proof	NOUN
ejpam-3565	98	10	of	of	ADP
ejpam-3565	98	11	which	which	PRON
ejpam-3565	98	12	are	be	AUX
ejpam-3565	98	13	known	know	VERB
ejpam-3565	98	14	.	.	PUNCT
ejpam-3565	99	1	lemma	lemma	PROPN
ejpam-3565	99	2	1	1	NUM
ejpam-3565	99	3	.	.	PUNCT
ejpam-3565	100	1	[	[	X
ejpam-3565	100	2	14	14	NUM
ejpam-3565	100	3	]	]	PUNCT
ejpam-3565	100	4	let	let	VERB
ejpam-3565	100	5	σq(n	σq(n	NOUN
ejpam-3565	100	6	,	,	PUNCT
ejpam-3565	100	7	k	k	X
ejpam-3565	100	8	)	)	PUNCT
ejpam-3565	100	9	be	be	VERB
ejpam-3565	100	10	the	the	DET
ejpam-3565	100	11	number	number	NOUN
ejpam-3565	100	12	of	of	ADP
ejpam-3565	100	13	self	self	NOUN
ejpam-3565	100	14	-	-	PUNCT
ejpam-3565	100	15	orthogonal	orthogonal	ADJ
ejpam-3565	100	16	codes	code	NOUN
ejpam-3565	100	17	of	of	ADP
ejpam-3565	100	18	even	even	ADV
ejpam-3565	100	19	length	length	NOUN
ejpam-3565	100	20	n	n	PROPN
ejpam-3565	100	21	and	and	CCONJ
ejpam-3565	100	22	dimension	dimension	NOUN
ejpam-3565	101	1	k	k	PROPN
ejpam-3565	101	2	over	over	ADP
ejpam-3565	101	3	fq	fq	PROPN
ejpam-3565	101	4	.	.	PROPN
ejpam-3565	102	1	if	if	SCONJ
ejpam-3565	102	2	char	char	PROPN
ejpam-3565	102	3	fq	fq	PROPN
ejpam-3565	102	4	6=	6=	PROPN
ejpam-3565	102	5	2	2	NUM
ejpam-3565	102	6	,	,	PUNCT
ejpam-3565	102	7	then	then	ADV
ejpam-3565	102	8	σq(n	σq(n	NOUN
ejpam-3565	102	9	,	,	PUNCT
ejpam-3565	102	10	k	k	NOUN
ejpam-3565	102	11	)	)	PUNCT
ejpam-3565	102	12	=	=	SYM
ejpam-3565	102	13	(	(	PUNCT
ejpam-3565	102	14	qn−k	qn−k	NOUN
ejpam-3565	102	15	−	−	PROPN
ejpam-3565	102	16	εqn/2−k	εqn/2−k	NOUN
ejpam-3565	102	17	+	+	CCONJ
ejpam-3565	102	18	εqn/2	εqn/2	PROPN
ejpam-3565	102	19	−	−	ADP
ejpam-3565	102	20	1	1	X
ejpam-3565	102	21	)	)	PUNCT
ejpam-3565	103	1	k−1∏	k−1∏	PROPN
ejpam-3565	103	2	i=1	i=1	PROPN
ejpam-3565	103	3	(	(	PUNCT
ejpam-3565	103	4	qn−2i	qn−2i	NUM
ejpam-3565	103	5	−	−	NOUN
ejpam-3565	103	6	1	1	X
ejpam-3565	103	7	)	)	PUNCT
ejpam-3565	103	8	k∏	k∏	PROPN
ejpam-3565	103	9	i=1	i=1	PROPN
ejpam-3565	103	10	(	(	PUNCT
ejpam-3565	103	11	qi	qi	NOUN
ejpam-3565	103	12	−	−	PROPN
ejpam-3565	103	13	1	1	NUM
ejpam-3565	103	14	)	)	PUNCT
ejpam-3565	103	15	,	,	PUNCT
ejpam-3565	103	16	k	k	PROPN
ejpam-3565	103	17	≥	≥	PROPN
ejpam-3565	103	18	2	2	NUM
ejpam-3565	103	19	where	where	SCONJ
ejpam-3565	103	20	ε	ε	PROPN
ejpam-3565	103	21	=	=	SYM
ejpam-3565	103	22	1	1	NUM
ejpam-3565	103	23	if	if	SCONJ
ejpam-3565	103	24	(	(	PUNCT
ejpam-3565	103	25	−1)n/2	−1)n/2	NOUN
ejpam-3565	103	26	is	be	AUX
ejpam-3565	103	27	a	a	DET
ejpam-3565	103	28	square	square	NOUN
ejpam-3565	103	29	and	and	CCONJ
ejpam-3565	103	30	ε	ε	PROPN
ejpam-3565	103	31	=	=	SYM
ejpam-3565	103	32	−1	−1	NOUN
ejpam-3565	103	33	if	if	SCONJ
ejpam-3565	103	34	(	(	PUNCT
ejpam-3565	103	35	−1)n/2	−1)n/2	NOUN
ejpam-3565	103	36	is	be	AUX
ejpam-3565	103	37	not	not	PART
ejpam-3565	103	38	a	a	DET
ejpam-3565	103	39	square	square	NOUN
ejpam-3565	103	40	.	.	PUNCT
ejpam-3565	104	1	lemma	lemma	PROPN
ejpam-3565	104	2	2	2	NUM
ejpam-3565	104	3	.	.	PUNCT
ejpam-3565	105	1	[	[	X
ejpam-3565	105	2	15	15	NUM
ejpam-3565	105	3	]	]	PUNCT
ejpam-3565	105	4	let	let	VERB
ejpam-3565	105	5	v	v	PART
ejpam-3565	105	6	be	be	AUX
ejpam-3565	105	7	an	an	DET
ejpam-3565	105	8	n	n	ADV
ejpam-3565	105	9	-	-	PUNCT
ejpam-3565	105	10	dimensional	dimensional	ADJ
ejpam-3565	105	11	vector	vector	NOUN
ejpam-3565	105	12	space	space	NOUN
ejpam-3565	105	13	over	over	ADP
ejpam-3565	105	14	fq	fq	PROPN
ejpam-3565	105	15	.	.	PUNCT
ejpam-3565	106	1	the	the	DET
ejpam-3565	106	2	number	number	NOUN
ejpam-3565	106	3	(	(	PUNCT
ejpam-3565	106	4	n	n	NOUN
ejpam-3565	106	5	k	k	NOUN
ejpam-3565	106	6	)	)	PUNCT
ejpam-3565	106	7	q	q	NOUN
ejpam-3565	106	8	of	of	ADP
ejpam-3565	106	9	subspaces	subspace	NOUN
ejpam-3565	106	10	u	u	PROPN
ejpam-3565	106	11	⊂	⊂	X
ejpam-3565	106	12	v	v	NOUN
ejpam-3565	106	13	of	of	ADP
ejpam-3565	106	14	dimension	dimension	NOUN
ejpam-3565	106	15	k	k	PROPN
ejpam-3565	106	16	≤	≤	PROPN
ejpam-3565	106	17	n	n	VERB
ejpam-3565	106	18	is	be	AUX
ejpam-3565	106	19	given	give	VERB
ejpam-3565	106	20	by	by	ADP
ejpam-3565	106	21	(	(	PUNCT
ejpam-3565	106	22	n	n	PROPN
ejpam-3565	106	23	k	k	NOUN
ejpam-3565	106	24	)	)	PUNCT
ejpam-3565	106	25	q	q	PROPN
ejpam-3565	107	1	=	=	PUNCT
ejpam-3565	107	2	(	(	PUNCT
ejpam-3565	107	3	qn	qn	NOUN
ejpam-3565	107	4	−	−	PROPN
ejpam-3565	107	5	1)(qn	1)(qn	NUM
ejpam-3565	107	6	−	−	PROPN
ejpam-3565	107	7	q	q	NOUN
ejpam-3565	107	8	)	)	PUNCT
ejpam-3565	107	9	·	·	PUNCT
ejpam-3565	107	10	·	·	PUNCT
ejpam-3565	107	11	·	·	PUNCT
ejpam-3565	107	12	(	(	PUNCT
ejpam-3565	107	13	qn	qn	INTJ
ejpam-3565	107	14	−	−	PROPN
ejpam-3565	107	15	qk−1	qk−1	PROPN
ejpam-3565	107	16	)	)	PUNCT
ejpam-3565	107	17	(	(	PUNCT
ejpam-3565	107	18	qk	qk	ADP
ejpam-3565	107	19	−	−	PROPN
ejpam-3565	107	20	1)(qk	1)(qk	NUM
ejpam-3565	107	21	−	−	NOUN
ejpam-3565	107	22	q	q	NOUN
ejpam-3565	107	23	)	)	PUNCT
ejpam-3565	107	24	·	·	PUNCT
ejpam-3565	107	25	·	·	PUNCT
ejpam-3565	107	26	·	·	PUNCT
ejpam-3565	107	27	(	(	PUNCT
ejpam-3565	107	28	qk	qk	ADP
ejpam-3565	107	29	−	−	PROPN
ejpam-3565	107	30	qk−1	qk−1	PROPN
ejpam-3565	107	31	)	)	PUNCT
ejpam-3565	107	32	.	.	PUNCT
ejpam-3565	108	1	3	3	X
ejpam-3565	108	2	.	.	X
ejpam-3565	108	3	codes	code	NOUN
ejpam-3565	108	4	over	over	ADP
ejpam-3565	108	5	gr(p3	gr(p3	PROPN
ejpam-3565	108	6	,	,	PUNCT
ejpam-3565	108	7	r	r	NOUN
ejpam-3565	108	8	)	)	PUNCT
ejpam-3565	108	9	let	let	VERB
ejpam-3565	108	10	c	c	NOUN
ejpam-3565	108	11	be	be	AUX
ejpam-3565	108	12	a	a	DET
ejpam-3565	108	13	code	code	NOUN
ejpam-3565	108	14	of	of	ADP
ejpam-3565	108	15	length	length	NOUN
ejpam-3565	108	16	n	n	PROPN
ejpam-3565	108	17	over	over	ADP
ejpam-3565	108	18	gr(p3	gr(p3	PROPN
ejpam-3565	108	19	,	,	PUNCT
ejpam-3565	108	20	r	r	NOUN
ejpam-3565	108	21	)	)	PUNCT
ejpam-3565	108	22	and	and	CCONJ
ejpam-3565	108	23	let	let	VERB
ejpam-3565	108	24	g	g	PRON
ejpam-3565	108	25	be	be	AUX
ejpam-3565	108	26	a	a	DET
ejpam-3565	108	27	generator	generator	NOUN
ejpam-3565	108	28	matrix	matrix	NOUN
ejpam-3565	108	29	for	for	ADP
ejpam-3565	108	30	c.	c.	NOUN
ejpam-3565	108	31	we	we	PRON
ejpam-3565	108	32	can	can	AUX
ejpam-3565	108	33	write	write	VERB
ejpam-3565	108	34	g	g	NOUN
ejpam-3565	108	35	in	in	ADP
ejpam-3565	108	36	the	the	DET
ejpam-3565	108	37	following	follow	VERB
ejpam-3565	108	38	form	form	NOUN
ejpam-3565	108	39	:	:	PUNCT
ejpam-3565	108	40	g	g	PROPN
ejpam-3565	108	41	=	=	SYM
ejpam-3565	108	42			PROPN
ejpam-3565	108	43	a	a	PRON
ejpam-3565	108	44	pb	pb	ADP
ejpam-3565	108	45	p2c	p2c	ADV
ejpam-3565	108	46			NOUN
ejpam-3565	108	47	=	=	SYM
ejpam-3565	108	48	ik	ik	PROPN
ejpam-3565	108	49	a2	a2	PROPN
ejpam-3565	108	50	a3	a3	PROPN
ejpam-3565	108	51	a4	a4	PROPN
ejpam-3565	108	52	0	0	NUM
ejpam-3565	108	53	pil	pil	NOUN
ejpam-3565	108	54	pb3	pb3	NOUN
ejpam-3565	108	55	pb4	pb4	NOUN
ejpam-3565	108	56	0	0	NUM
ejpam-3565	108	57	0	0	NUM
ejpam-3565	108	58	p2im	p2im	NOUN
ejpam-3565	108	59	p2c4	p2c4	NOUN
ejpam-3565	108	60			NOUN
ejpam-3565	108	61	,	,	PUNCT
ejpam-3565	108	62	(	(	PUNCT
ejpam-3565	108	63	2	2	X
ejpam-3565	108	64	)	)	PUNCT
ejpam-3565	108	65	where	where	SCONJ
ejpam-3565	108	66	ir	ir	PROPN
ejpam-3565	108	67	is	be	AUX
ejpam-3565	108	68	the	the	DET
ejpam-3565	108	69	identity	identity	NOUN
ejpam-3565	108	70	matrix	matrix	NOUN
ejpam-3565	108	71	of	of	ADP
ejpam-3565	108	72	order	order	NOUN
ejpam-3565	108	73	r	r	NOUN
ejpam-3565	108	74	,	,	PUNCT
ejpam-3565	108	75	and	and	CCONJ
ejpam-3565	108	76	the	the	DET
ejpam-3565	108	77	other	other	ADJ
ejpam-3565	108	78	matrices	matrix	NOUN
ejpam-3565	108	79	have	have	VERB
ejpam-3565	108	80	entries	entry	NOUN
ejpam-3565	108	81	from	from	ADP
ejpam-3565	108	82	gr(p3	gr(p3	PROPN
ejpam-3565	108	83	,	,	PUNCT
ejpam-3565	108	84	r	r	NOUN
ejpam-3565	108	85	)	)	PUNCT
ejpam-3565	108	86	and	and	CCONJ
ejpam-3565	108	87	are	be	AUX
ejpam-3565	108	88	described	describe	VERB
ejpam-3565	108	89	as	as	SCONJ
ejpam-3565	108	90	follows	follow	VERB
ejpam-3565	108	91	.	.	PUNCT
ejpam-3565	109	1	we	we	PRON
ejpam-3565	109	2	write	write	VERB
ejpam-3565	109	3	a3	a3	NOUN
ejpam-3565	109	4	,	,	PUNCT
ejpam-3565	109	5	b4	b4	NOUN
ejpam-3565	109	6	and	and	CCONJ
ejpam-3565	109	7	a4	a4	NOUN
ejpam-3565	109	8	in	in	ADP
ejpam-3565	109	9	their	their	PRON
ejpam-3565	109	10	p	p	ADJ
ejpam-3565	109	11	-	-	PUNCT
ejpam-3565	109	12	adic	adic	ADJ
ejpam-3565	109	13	expansions	expansion	NOUN
ejpam-3565	109	14	t.	t.	PROPN
ejpam-3565	109	15	l.	l.	PROPN
ejpam-3565	109	16	vasquez	vasquez	PROPN
ejpam-3565	109	17	,	,	PUNCT
ejpam-3565	109	18	g.	g.	PROPN
ejpam-3565	109	19	petalcorin	petalcorin	PROPN
ejpam-3565	109	20	/	/	SYM
ejpam-3565	109	21	eur	eur	PROPN
ejpam-3565	109	22	.	.	PUNCT
ejpam-3565	110	1	j.	j.	PROPN
ejpam-3565	110	2	pure	pure	PROPN
ejpam-3565	110	3	appl	appl	PROPN
ejpam-3565	110	4	.	.	PROPN
ejpam-3565	110	5	math	math	PROPN
ejpam-3565	110	6	,	,	PUNCT
ejpam-3565	110	7	12	12	NUM
ejpam-3565	110	8	(	(	PUNCT
ejpam-3565	110	9	4	4	NUM
ejpam-3565	110	10	)	)	PUNCT
ejpam-3565	110	11	(	(	PUNCT
ejpam-3565	110	12	2019	2019	NUM
ejpam-3565	110	13	)	)	PUNCT
ejpam-3565	110	14	,	,	PUNCT
ejpam-3565	110	15	1701	1701	NUM
ejpam-3565	110	16	-	-	SYM
ejpam-3565	110	17	1716	1716	NUM
ejpam-3565	110	18	1705	1705	NUM
ejpam-3565	110	19	a3	a3	NOUN
ejpam-3565	110	20	=	=	PRON
ejpam-3565	110	21	a30	a30	NOUN
ejpam-3565	110	22	+	+	CCONJ
ejpam-3565	111	1	pa31	pa31	PROPN
ejpam-3565	111	2	,	,	PUNCT
ejpam-3565	111	3	b4	b4	NOUN
ejpam-3565	111	4	=	=	SYM
ejpam-3565	111	5	b40	b40	NOUN
ejpam-3565	111	6	+	+	CCONJ
ejpam-3565	111	7	pb41	pb41	PROPN
ejpam-3565	111	8	,	,	PUNCT
ejpam-3565	111	9	a4	a4	NOUN
ejpam-3565	111	10	=	=	SYM
ejpam-3565	111	11	a40	a40	NOUN
ejpam-3565	111	12	+	+	CCONJ
ejpam-3565	112	1	pa41	pa41	ADJ
ejpam-3565	112	2	+	+	NUM
ejpam-3565	112	3	p2a42	p2a42	NOUN
ejpam-3565	112	4	,	,	PUNCT
ejpam-3565	112	5	and	and	CCONJ
ejpam-3565	112	6	the	the	DET
ejpam-3565	112	7	matrices	matrix	NOUN
ejpam-3565	112	8	a2	a2	PROPN
ejpam-3565	112	9	,	,	PUNCT
ejpam-3565	112	10	b3	b3	PROPN
ejpam-3565	112	11	,	,	PUNCT
ejpam-3565	112	12	c4	c4	NOUN
ejpam-3565	112	13	,	,	PUNCT
ejpam-3565	112	14	aij	aij	PROPN
ejpam-3565	112	15	and	and	CCONJ
ejpam-3565	112	16	bij	bij	PROPN
ejpam-3565	112	17	have	have	VERB
ejpam-3565	112	18	entries	entry	NOUN
ejpam-3565	112	19	from	from	ADP
ejpam-3565	112	20	tpr	tpr	PROPN
ejpam-3565	112	21	.	.	PUNCT
ejpam-3565	113	1	the	the	DET
ejpam-3565	113	2	columns	column	NOUN
ejpam-3565	113	3	are	be	AUX
ejpam-3565	113	4	grouped	group	VERB
ejpam-3565	113	5	in	in	ADP
ejpam-3565	113	6	blocks	block	NOUN
ejpam-3565	113	7	of	of	ADP
ejpam-3565	113	8	sizes	size	NOUN
ejpam-3565	113	9	k	k	PROPN
ejpam-3565	113	10	,	,	PUNCT
ejpam-3565	113	11	l	l	NOUN
ejpam-3565	113	12	,	,	PUNCT
ejpam-3565	113	13	m	m	NOUN
ejpam-3565	113	14	and	and	CCONJ
ejpam-3565	113	15	h	h	NOUN
ejpam-3565	113	16	=	=	SYM
ejpam-3565	113	17	n	n	PROPN
ejpam-3565	113	18	−	−	PROPN
ejpam-3565	113	19	(	(	PUNCT
ejpam-3565	113	20	k	k	PROPN
ejpam-3565	114	1	+	+	PROPN
ejpam-3565	114	2	l	l	NOUN
ejpam-3565	114	3	+	+	X
ejpam-3565	114	4	m	m	NOUN
ejpam-3565	114	5	)	)	PUNCT
ejpam-3565	114	6	.	.	PUNCT
ejpam-3565	115	1	the	the	DET
ejpam-3565	115	2	code	code	NOUN
ejpam-3565	115	3	c	c	PROPN
ejpam-3565	115	4	is	be	AUX
ejpam-3565	115	5	said	say	VERB
ejpam-3565	115	6	to	to	PART
ejpam-3565	115	7	be	be	AUX
ejpam-3565	115	8	of	of	ADP
ejpam-3565	115	9	type	type	NOUN
ejpam-3565	115	10	{	{	PUNCT
ejpam-3565	115	11	k	k	NOUN
ejpam-3565	115	12	,	,	PUNCT
ejpam-3565	115	13	l	l	NOUN
ejpam-3565	115	14	,	,	PUNCT
ejpam-3565	115	15	m	m	VERB
ejpam-3565	115	16	}	}	PUNCT
ejpam-3565	115	17	and	and	CCONJ
ejpam-3565	115	18	has	have	VERB
ejpam-3565	115	19	pr(3k+2l+m	pr(3k+2l+m	NOUN
ejpam-3565	115	20	)	)	PUNCT
ejpam-3565	115	21	codewords	codeword	NOUN
ejpam-3565	115	22	.	.	PUNCT
ejpam-3565	116	1	the	the	DET
ejpam-3565	116	2	dual	dual	PROPN
ejpam-3565	116	3	code	code	NOUN
ejpam-3565	116	4	c⊥	c⊥	NOUN
ejpam-3565	116	5	is	be	AUX
ejpam-3565	116	6	of	of	ADP
ejpam-3565	116	7	type	type	NOUN
ejpam-3565	116	8	{	{	PUNCT
ejpam-3565	116	9	h	h	NOUN
ejpam-3565	116	10	,	,	PUNCT
ejpam-3565	116	11	m	m	PROPN
ejpam-3565	116	12	,	,	PUNCT
ejpam-3565	116	13	l	l	NOUN
ejpam-3565	116	14	}	}	PUNCT
ejpam-3565	116	15	and	and	CCONJ
ejpam-3565	116	16	has	have	VERB
ejpam-3565	116	17	pr(3h+2m+l	pr(3h+2m+l	ADJ
ejpam-3565	116	18	)	)	PUNCT
ejpam-3565	116	19	codewords	codeword	NOUN
ejpam-3565	116	20	.	.	PUNCT
ejpam-3565	117	1	if	if	SCONJ
ejpam-3565	117	2	the	the	DET
ejpam-3565	117	3	code	code	NOUN
ejpam-3565	117	4	c	c	PROPN
ejpam-3565	117	5	has	have	VERB
ejpam-3565	117	6	generator	generator	NOUN
ejpam-3565	117	7	matrix	matrix	NOUN
ejpam-3565	117	8	g	g	NOUN
ejpam-3565	117	9	in	in	ADP
ejpam-3565	117	10	(	(	PUNCT
ejpam-3565	117	11	2	2	NUM
ejpam-3565	117	12	)	)	PUNCT
ejpam-3565	117	13	,	,	PUNCT
ejpam-3565	117	14	then	then	ADV
ejpam-3565	117	15	the	the	DET
ejpam-3565	117	16	residue	residue	NOUN
ejpam-3565	117	17	code	code	NOUN
ejpam-3565	117	18	res(c	res(c	PROPN
ejpam-3565	117	19	)	)	PUNCT
ejpam-3565	117	20	has	have	VERB
ejpam-3565	117	21	dimension	dimension	NOUN
ejpam-3565	117	22	k	k	PROPN
ejpam-3565	117	23	and	and	CCONJ
ejpam-3565	117	24	generator	generator	PROPN
ejpam-3565	117	25	matrix	matrix	NOUN
ejpam-3565	117	26	t0	t0	NOUN
ejpam-3565	117	27	=	=	PUNCT
ejpam-3565	117	28	a	a	DET
ejpam-3565	117	29	(	(	PUNCT
ejpam-3565	117	30	mod	mod	NOUN
ejpam-3565	117	31	p	p	NOUN
ejpam-3565	117	32	)	)	PUNCT
ejpam-3565	117	33	=	=	PUNCT
ejpam-3565	117	34	[	[	PUNCT
ejpam-3565	117	35	ik	ik	PROPN
ejpam-3565	117	36	a2	a2	PROPN
ejpam-3565	117	37	a30	a30	PROPN
ejpam-3565	117	38	a40	a40	PROPN
ejpam-3565	117	39	]	]	PUNCT
ejpam-3565	117	40	,	,	PUNCT
ejpam-3565	117	41	(	(	PUNCT
ejpam-3565	117	42	3	3	X
ejpam-3565	117	43	)	)	PUNCT
ejpam-3565	117	44	the	the	DET
ejpam-3565	117	45	first	first	ADJ
ejpam-3565	117	46	torsion	torsion	NOUN
ejpam-3565	117	47	code	code	NOUN
ejpam-3565	117	48	tor1(c	tor1(c	NOUN
ejpam-3565	117	49	)	)	PUNCT
ejpam-3565	117	50	has	have	AUX
ejpam-3565	117	51	dimension	dimension	NOUN
ejpam-3565	117	52	k	k	PROPN
ejpam-3565	118	1	+	+	CCONJ
ejpam-3565	118	2	l	l	NOUN
ejpam-3565	118	3	and	and	CCONJ
ejpam-3565	118	4	generator	generator	NOUN
ejpam-3565	118	5	matrix	matrix	NOUN
ejpam-3565	118	6	t1	t1	NOUN
ejpam-3565	118	7	=	=	PUNCT
ejpam-3565	119	1	[	[	PUNCT
ejpam-3565	119	2	a	a	DET
ejpam-3565	119	3	b	b	NOUN
ejpam-3565	119	4	]	]	X
ejpam-3565	119	5	(	(	PUNCT
ejpam-3565	119	6	mod	mod	PROPN
ejpam-3565	119	7	p	p	X
ejpam-3565	119	8	)	)	PUNCT
ejpam-3565	119	9	=	=	PUNCT
ejpam-3565	119	10	[	[	PUNCT
ejpam-3565	119	11	ik	ik	PROPN
ejpam-3565	119	12	a2	a2	PROPN
ejpam-3565	119	13	a30	a30	VERB
ejpam-3565	119	14	a40	a40	PROPN
ejpam-3565	119	15	0	0	NUM
ejpam-3565	119	16	il	il	PROPN
ejpam-3565	119	17	b3	b3	PROPN
ejpam-3565	119	18	b40	b40	PROPN
ejpam-3565	119	19	]	]	PUNCT
ejpam-3565	119	20	,	,	PUNCT
ejpam-3565	119	21	(	(	PUNCT
ejpam-3565	119	22	4	4	NUM
ejpam-3565	119	23	)	)	PUNCT
ejpam-3565	119	24	and	and	CCONJ
ejpam-3565	119	25	the	the	DET
ejpam-3565	119	26	second	second	ADJ
ejpam-3565	119	27	torsion	torsion	NOUN
ejpam-3565	119	28	code	code	NOUN
ejpam-3565	119	29	tor2(c	tor2(c	NOUN
ejpam-3565	119	30	)	)	PUNCT
ejpam-3565	119	31	has	have	AUX
ejpam-3565	119	32	dimension	dimension	NOUN
ejpam-3565	119	33	k	k	PROPN
ejpam-3565	120	1	+	+	PUNCT
ejpam-3565	120	2	l	l	PUNCT
ejpam-3565	120	3	+	+	NOUN
ejpam-3565	120	4	m	m	PRON
ejpam-3565	120	5	and	and	CCONJ
ejpam-3565	120	6	generator	generator	NOUN
ejpam-3565	120	7	matrix	matrix	NOUN
ejpam-3565	120	8	t2	t2	NOUN
ejpam-3565	120	9	=	=	SYM
ejpam-3565	120	10	ab	ab	PROPN
ejpam-3565	120	11	c	c	NOUN
ejpam-3565	120	12			NOUN
ejpam-3565	120	13	(	(	PUNCT
ejpam-3565	120	14	mod	mod	PROPN
ejpam-3565	120	15	p	p	X
ejpam-3565	120	16	)	)	PUNCT
ejpam-3565	120	17	=	=	SYM
ejpam-3565	120	18	ik	ik	PROPN
ejpam-3565	120	19	a2	a2	PROPN
ejpam-3565	120	20	a30	a30	VERB
ejpam-3565	120	21	a40	a40	PROPN
ejpam-3565	120	22	0	0	NUM
ejpam-3565	120	23	il	il	PROPN
ejpam-3565	120	24	b3	b3	PROPN
ejpam-3565	120	25	b40	b40	NOUN
ejpam-3565	120	26	0	0	NUM
ejpam-3565	120	27	0	0	PUNCT
ejpam-3565	121	1	i	i	PRON
ejpam-3565	121	2	m	m	VERB
ejpam-3565	121	3	c4	c4	NOUN
ejpam-3565	121	4			NOUN
ejpam-3565	121	5	.	.	PUNCT
ejpam-3565	122	1	(	(	PUNCT
ejpam-3565	122	2	5	5	X
ejpam-3565	122	3	)	)	PUNCT
ejpam-3565	122	4	the	the	DET
ejpam-3565	122	5	following	follow	VERB
ejpam-3565	122	6	proposition	proposition	NOUN
ejpam-3565	122	7	gives	give	VERB
ejpam-3565	122	8	a	a	DET
ejpam-3565	122	9	characterization	characterization	NOUN
ejpam-3565	122	10	of	of	ADP
ejpam-3565	122	11	self	self	NOUN
ejpam-3565	122	12	-	-	PUNCT
ejpam-3565	122	13	duality	duality	NOUN
ejpam-3565	122	14	in	in	ADP
ejpam-3565	122	15	gr(p3	gr(p3	PROPN
ejpam-3565	122	16	,	,	PUNCT
ejpam-3565	122	17	r	r	NOUN
ejpam-3565	122	18	)	)	PUNCT
ejpam-3565	122	19	.	.	PUNCT
ejpam-3565	123	1	proposition	proposition	NOUN
ejpam-3565	123	2	1	1	NUM
ejpam-3565	123	3	.	.	PUNCT
ejpam-3565	124	1	let	let	VERB
ejpam-3565	124	2	c	c	PRON
ejpam-3565	124	3	be	be	AUX
ejpam-3565	124	4	a	a	DET
ejpam-3565	124	5	code	code	NOUN
ejpam-3565	124	6	over	over	ADP
ejpam-3565	124	7	gr(p3	gr(p3	PROPN
ejpam-3565	124	8	,	,	PUNCT
ejpam-3565	124	9	r	r	NOUN
ejpam-3565	124	10	)	)	PUNCT
ejpam-3565	124	11	with	with	ADP
ejpam-3565	124	12	generator	generator	NOUN
ejpam-3565	124	13	matrix	matrix	NOUN
ejpam-3565	124	14	g	g	NOUN
ejpam-3565	124	15	as	as	ADP
ejpam-3565	124	16	in	in	ADP
ejpam-3565	124	17	(	(	PUNCT
ejpam-3565	124	18	2	2	NUM
ejpam-3565	124	19	)	)	PUNCT
ejpam-3565	124	20	.	.	PUNCT
ejpam-3565	125	1	then	then	ADV
ejpam-3565	125	2	c	c	PROPN
ejpam-3565	125	3	is	be	AUX
ejpam-3565	125	4	self	self	NOUN
ejpam-3565	125	5	-	-	PUNCT
ejpam-3565	125	6	dual	dual	ADJ
ejpam-3565	125	7	if	if	SCONJ
ejpam-3565	126	1	and	and	CCONJ
ejpam-3565	126	2	only	only	ADV
ejpam-3565	126	3	if	if	SCONJ
ejpam-3565	126	4	k	k	PROPN
ejpam-3565	126	5	=	=	SYM
ejpam-3565	126	6	h	h	NOUN
ejpam-3565	126	7	,	,	PUNCT
ejpam-3565	126	8	l	l	NOUN
ejpam-3565	126	9	=	=	PUNCT
ejpam-3565	126	10	m	m	NOUN
ejpam-3565	126	11	and	and	CCONJ
ejpam-3565	126	12	the	the	DET
ejpam-3565	126	13	following	follow	VERB
ejpam-3565	126	14	hold	hold	NOUN
ejpam-3565	126	15	:	:	PUNCT
ejpam-3565	126	16	aat	aat	PROPN
ejpam-3565	126	17	≡	≡	PROPN
ejpam-3565	126	18	0	0	NUM
ejpam-3565	127	1	(	(	PUNCT
ejpam-3565	127	2	mod	mod	PROPN
ejpam-3565	127	3	p3	p3	PROPN
ejpam-3565	127	4	)	)	PUNCT
ejpam-3565	127	5	(	(	PUNCT
ejpam-3565	127	6	6	6	X
ejpam-3565	127	7	)	)	PUNCT
ejpam-3565	127	8	abt	abt	INTJ
ejpam-3565	127	9	≡	≡	PROPN
ejpam-3565	127	10	0	0	PUNCT
ejpam-3565	128	1	(	(	PUNCT
ejpam-3565	128	2	mod	mod	ADJ
ejpam-3565	128	3	p2	p2	PROPN
ejpam-3565	128	4	)	)	PUNCT
ejpam-3565	128	5	(	(	PUNCT
ejpam-3565	128	6	7	7	X
ejpam-3565	128	7	)	)	PUNCT
ejpam-3565	128	8	bbt	bbt	PROPN
ejpam-3565	128	9	≡	≡	PROPN
ejpam-3565	128	10	0	0	PUNCT
ejpam-3565	129	1	(	(	PUNCT
ejpam-3565	129	2	mod	mod	PROPN
ejpam-3565	129	3	p	p	X
ejpam-3565	129	4	)	)	PUNCT
ejpam-3565	129	5	(	(	PUNCT
ejpam-3565	129	6	8)	8)	NUM
ejpam-3565	129	7	act	act	NOUN
ejpam-3565	129	8	≡	≡	PROPN
ejpam-3565	129	9	0	0	PUNCT
ejpam-3565	130	1	(	(	PUNCT
ejpam-3565	130	2	mod	mod	PROPN
ejpam-3565	130	3	p	p	NOUN
ejpam-3565	130	4	)	)	PUNCT
ejpam-3565	130	5	.	.	PUNCT
ejpam-3565	131	1	(	(	PUNCT
ejpam-3565	131	2	9	9	X
ejpam-3565	131	3	)	)	PUNCT
ejpam-3565	131	4	proof	proof	NOUN
ejpam-3565	131	5	.	.	PUNCT
ejpam-3565	132	1	suppose	suppose	VERB
ejpam-3565	132	2	c	c	NOUN
ejpam-3565	132	3	is	be	AUX
ejpam-3565	132	4	a	a	DET
ejpam-3565	132	5	self	self	NOUN
ejpam-3565	132	6	-	-	PUNCT
ejpam-3565	132	7	dual	dual	ADJ
ejpam-3565	132	8	code	code	NOUN
ejpam-3565	132	9	over	over	ADP
ejpam-3565	132	10	gr(p3	gr(p3	PROPN
ejpam-3565	132	11	,	,	PUNCT
ejpam-3565	132	12	r	r	NOUN
ejpam-3565	132	13	)	)	PUNCT
ejpam-3565	132	14	.	.	PUNCT
ejpam-3565	133	1	we	we	PRON
ejpam-3565	133	2	then	then	ADV
ejpam-3565	133	3	have	have	VERB
ejpam-3565	133	4	ggt	ggt	PROPN
ejpam-3565	133	5	≡	≡	PROPN
ejpam-3565	133	6	0	0	PROPN
ejpam-3565	134	1	(	(	PUNCT
ejpam-3565	134	2	mod	mod	PROPN
ejpam-3565	134	3	p3	p3	PROPN
ejpam-3565	134	4	)	)	PUNCT
ejpam-3565	134	5	,	,	PUNCT
ejpam-3565	134	6	that	that	ADV
ejpam-3565	134	7	is	is	ADV
ejpam-3565	134	8	,	,	PUNCT
ejpam-3565	134	9	aat	aat	X
ejpam-3565	134	10	≡	≡	PROPN
ejpam-3565	134	11	0	0	NUM
ejpam-3565	134	12	(	(	PUNCT
ejpam-3565	134	13	mod	mod	PROPN
ejpam-3565	134	14	p3	p3	PROPN
ejpam-3565	134	15	)	)	PUNCT
ejpam-3565	134	16	pabt	pabt	NOUN
ejpam-3565	134	17	≡	≡	PROPN
ejpam-3565	134	18	0	0	PUNCT
ejpam-3565	135	1	(	(	PUNCT
ejpam-3565	135	2	mod	mod	PROPN
ejpam-3565	135	3	p3	p3	PROPN
ejpam-3565	135	4	)	)	PUNCT
ejpam-3565	135	5	p2bbt	p2bbt	PROPN
ejpam-3565	135	6	≡	≡	PROPN
ejpam-3565	135	7	0	0	PUNCT
ejpam-3565	136	1	(	(	PUNCT
ejpam-3565	136	2	mod	mod	PROPN
ejpam-3565	136	3	p3	p3	PROPN
ejpam-3565	136	4	)	)	PUNCT
ejpam-3565	136	5	p2act	p2act	PROPN
ejpam-3565	136	6	≡	≡	PROPN
ejpam-3565	136	7	0	0	PUNCT
ejpam-3565	136	8	(	(	PUNCT
ejpam-3565	136	9	mod	mod	PROPN
ejpam-3565	136	10	p3	p3	PROPN
ejpam-3565	136	11	)	)	PUNCT
ejpam-3565	136	12	,	,	PUNCT
ejpam-3565	136	13	which	which	PRON
ejpam-3565	136	14	is	be	AUX
ejpam-3565	136	15	equivalent	equivalent	ADJ
ejpam-3565	136	16	to	to	ADP
ejpam-3565	136	17	the	the	DET
ejpam-3565	136	18	set	set	NOUN
ejpam-3565	136	19	of	of	ADP
ejpam-3565	136	20	conditions	condition	NOUN
ejpam-3565	136	21	(	(	PUNCT
ejpam-3565	136	22	6)-(9	6)-(9	NOUN
ejpam-3565	136	23	)	)	PUNCT
ejpam-3565	136	24	.	.	PUNCT
ejpam-3565	137	1	now	now	ADV
ejpam-3565	137	2	,	,	PUNCT
ejpam-3565	137	3	c	c	PROPN
ejpam-3565	137	4	is	be	AUX
ejpam-3565	137	5	of	of	ADP
ejpam-3565	137	6	type	type	NOUN
ejpam-3565	137	7	{	{	PUNCT
ejpam-3565	137	8	k	k	NOUN
ejpam-3565	137	9	,	,	PUNCT
ejpam-3565	137	10	l	l	NOUN
ejpam-3565	137	11	,	,	PUNCT
ejpam-3565	137	12	m	m	NOUN
ejpam-3565	137	13	}	}	PUNCT
ejpam-3565	137	14	and	and	CCONJ
ejpam-3565	137	15	its	its	PRON
ejpam-3565	137	16	dual	dual	ADJ
ejpam-3565	137	17	code	code	NOUN
ejpam-3565	137	18	c⊥	c⊥	NOUN
ejpam-3565	137	19	is	be	AUX
ejpam-3565	137	20	of	of	ADP
ejpam-3565	137	21	type	type	NOUN
ejpam-3565	137	22	{	{	PUNCT
ejpam-3565	137	23	h	h	NOUN
ejpam-3565	137	24	,	,	PUNCT
ejpam-3565	137	25	m	m	PROPN
ejpam-3565	137	26	,	,	PUNCT
ejpam-3565	137	27	l	l	NOUN
ejpam-3565	137	28	}	}	PUNCT
ejpam-3565	137	29	.	.	PUNCT
ejpam-3565	138	1	since	since	SCONJ
ejpam-3565	138	2	c	c	PROPN
ejpam-3565	138	3	is	be	AUX
ejpam-3565	138	4	self	self	NOUN
ejpam-3565	138	5	-	-	PUNCT
ejpam-3565	138	6	dual	dual	ADJ
ejpam-3565	138	7	,	,	PUNCT
ejpam-3565	138	8	we	we	PRON
ejpam-3565	138	9	then	then	ADV
ejpam-3565	138	10	have	have	VERB
ejpam-3565	138	11	k	k	NOUN
ejpam-3565	138	12	=	=	PUNCT
ejpam-3565	138	13	h	h	NOUN
ejpam-3565	138	14	and	and	CCONJ
ejpam-3565	138	15	l	l	NOUN
ejpam-3565	138	16	=	=	SYM
ejpam-3565	138	17	m.	m.	NOUN
ejpam-3565	138	18	conversely	conversely	ADV
ejpam-3565	138	19	,	,	PUNCT
ejpam-3565	138	20	let	let	VERB
ejpam-3565	138	21	c	c	PRON
ejpam-3565	138	22	be	be	AUX
ejpam-3565	138	23	a	a	DET
ejpam-3565	138	24	code	code	NOUN
ejpam-3565	138	25	such	such	ADJ
ejpam-3565	138	26	that	that	SCONJ
ejpam-3565	138	27	k	k	PROPN
ejpam-3565	138	28	=	=	SYM
ejpam-3565	138	29	h	h	NOUN
ejpam-3565	138	30	,	,	PUNCT
ejpam-3565	138	31	l	l	NOUN
ejpam-3565	138	32	=	=	PUNCT
ejpam-3565	138	33	m	m	NOUN
ejpam-3565	138	34	and	and	CCONJ
ejpam-3565	138	35	conditions	condition	NOUN
ejpam-3565	138	36	(	(	PUNCT
ejpam-3565	138	37	6)-(9	6)-(9	NOUN
ejpam-3565	138	38	)	)	PUNCT
ejpam-3565	138	39	hold	hold	NOUN
ejpam-3565	138	40	.	.	PUNCT
ejpam-3565	139	1	now	now	ADV
ejpam-3565	139	2	,	,	PUNCT
ejpam-3565	139	3	conditions	condition	NOUN
ejpam-3565	139	4	(	(	PUNCT
ejpam-3565	139	5	6)-(9	6)-(9	NOUN
ejpam-3565	139	6	)	)	PUNCT
ejpam-3565	139	7	imply	imply	VERB
ejpam-3565	139	8	that	that	SCONJ
ejpam-3565	139	9	ggt	ggt	PROPN
ejpam-3565	139	10	≡	≡	PROPN
ejpam-3565	139	11	0	0	PUNCT
ejpam-3565	140	1	(	(	PUNCT
ejpam-3565	140	2	mod	mod	PROPN
ejpam-3565	140	3	p3	p3	PROPN
ejpam-3565	140	4	)	)	PUNCT
ejpam-3565	140	5	.	.	PUNCT
ejpam-3565	141	1	so	so	ADV
ejpam-3565	141	2	c	c	PROPN
ejpam-3565	141	3	is	be	AUX
ejpam-3565	141	4	a	a	DET
ejpam-3565	141	5	self	self	NOUN
ejpam-3565	141	6	-	-	PUNCT
ejpam-3565	141	7	orthogonal	orthogonal	ADJ
ejpam-3565	141	8	code	code	NOUN
ejpam-3565	141	9	,	,	PUNCT
ejpam-3565	141	10	i.e.	i.e.	X
ejpam-3565	141	11	c	c	PROPN
ejpam-3565	141	12	⊆	⊆	NUM
ejpam-3565	141	13	c⊥.	c⊥.	NOUN
ejpam-3565	141	14	moreover	moreover	ADV
ejpam-3565	141	15	,	,	PUNCT
ejpam-3565	141	16	since	since	SCONJ
ejpam-3565	141	17	k	k	PROPN
ejpam-3565	141	18	=	=	PUNCT
ejpam-3565	141	19	h	h	PROPN
ejpam-3565	141	20	and	and	CCONJ
ejpam-3565	141	21	l	l	NOUN
ejpam-3565	141	22	=	=	SYM
ejpam-3565	141	23	m	m	PROPN
ejpam-3565	141	24	,	,	PUNCT
ejpam-3565	141	25	we	we	PRON
ejpam-3565	141	26	then	then	ADV
ejpam-3565	141	27	have	have	VERB
ejpam-3565	141	28	|c|	|c|	PROPN
ejpam-3565	141	29	=	=	SYM
ejpam-3565	141	30	|c⊥|	|c⊥|	PROPN
ejpam-3565	141	31	.	.	PUNCT
ejpam-3565	142	1	therefore	therefore	ADV
ejpam-3565	142	2	c	c	X
ejpam-3565	142	3	=	=	SYM
ejpam-3565	142	4	c⊥.	c⊥.	NOUN
ejpam-3565	142	5	t.	t.	PROPN
ejpam-3565	142	6	l.	l.	PROPN
ejpam-3565	142	7	vasquez	vasquez	PROPN
ejpam-3565	142	8	,	,	PUNCT
ejpam-3565	142	9	g.	g.	PROPN
ejpam-3565	142	10	petalcorin	petalcorin	PROPN
ejpam-3565	142	11	/	/	SYM
ejpam-3565	142	12	eur	eur	PROPN
ejpam-3565	142	13	.	.	PUNCT
ejpam-3565	143	1	j.	j.	PROPN
ejpam-3565	143	2	pure	pure	PROPN
ejpam-3565	143	3	appl	appl	PROPN
ejpam-3565	143	4	.	.	PROPN
ejpam-3565	143	5	math	math	PROPN
ejpam-3565	143	6	,	,	PUNCT
ejpam-3565	143	7	12	12	NUM
ejpam-3565	143	8	(	(	PUNCT
ejpam-3565	143	9	4	4	NUM
ejpam-3565	143	10	)	)	PUNCT
ejpam-3565	143	11	(	(	PUNCT
ejpam-3565	143	12	2019	2019	NUM
ejpam-3565	143	13	)	)	PUNCT
ejpam-3565	143	14	,	,	PUNCT
ejpam-3565	143	15	1701	1701	NUM
ejpam-3565	143	16	-	-	SYM
ejpam-3565	143	17	1716	1716	NUM
ejpam-3565	143	18	1706	1706	NUM
ejpam-3565	143	19	corollary	corollary	ADJ
ejpam-3565	143	20	1	1	NUM
ejpam-3565	143	21	.	.	PUNCT
ejpam-3565	144	1	a	a	DET
ejpam-3565	144	2	self	self	NOUN
ejpam-3565	144	3	-	-	PUNCT
ejpam-3565	144	4	dual	dual	ADJ
ejpam-3565	144	5	code	code	NOUN
ejpam-3565	144	6	c	c	PROPN
ejpam-3565	144	7	over	over	ADP
ejpam-3565	144	8	gr(p3	gr(p3	PROPN
ejpam-3565	144	9	,	,	PUNCT
ejpam-3565	144	10	r	r	NOUN
ejpam-3565	144	11	)	)	PUNCT
ejpam-3565	144	12	of	of	ADP
ejpam-3565	144	13	type	type	NOUN
ejpam-3565	144	14	{	{	PUNCT
ejpam-3565	144	15	k	k	NOUN
ejpam-3565	144	16	,	,	PUNCT
ejpam-3565	144	17	l	l	NOUN
ejpam-3565	144	18	,	,	PUNCT
ejpam-3565	144	19	l	l	NOUN
ejpam-3565	144	20	}	}	PUNCT
ejpam-3565	144	21	is	be	AUX
ejpam-3565	144	22	of	of	ADP
ejpam-3565	144	23	even	even	ADV
ejpam-3565	144	24	length	length	NOUN
ejpam-3565	144	25	n	n	NOUN
ejpam-3565	144	26	=	=	SYM
ejpam-3565	144	27	2(k	2(k	NUM
ejpam-3565	144	28	+	+	CCONJ
ejpam-3565	144	29	l	l	NOUN
ejpam-3565	144	30	)	)	PUNCT
ejpam-3565	144	31	.	.	PUNCT
ejpam-3565	145	1	corollary	corollary	ADJ
ejpam-3565	145	2	2	2	NUM
ejpam-3565	145	3	.	.	PUNCT
ejpam-3565	146	1	let	let	VERB
ejpam-3565	146	2	c	c	PRON
ejpam-3565	146	3	be	be	AUX
ejpam-3565	146	4	a	a	DET
ejpam-3565	146	5	self	self	NOUN
ejpam-3565	146	6	-	-	PUNCT
ejpam-3565	146	7	dual	dual	ADJ
ejpam-3565	146	8	code	code	NOUN
ejpam-3565	146	9	over	over	ADP
ejpam-3565	146	10	gr(p3	gr(p3	PROPN
ejpam-3565	146	11	,	,	PUNCT
ejpam-3565	146	12	r	r	NOUN
ejpam-3565	146	13	)	)	PUNCT
ejpam-3565	146	14	of	of	ADP
ejpam-3565	146	15	length	length	NOUN
ejpam-3565	146	16	n	n	PROPN
ejpam-3565	146	17	and	and	CCONJ
ejpam-3565	146	18	of	of	ADP
ejpam-3565	146	19	type	type	NOUN
ejpam-3565	146	20	{	{	PUNCT
ejpam-3565	146	21	k	k	NOUN
ejpam-3565	146	22	,	,	PUNCT
ejpam-3565	146	23	l	l	NOUN
ejpam-3565	146	24	,	,	PUNCT
ejpam-3565	146	25	l	l	NOUN
ejpam-3565	146	26	}	}	PUNCT
ejpam-3565	146	27	.	.	PUNCT
ejpam-3565	147	1	then	then	ADV
ejpam-3565	147	2	res(c	res(c	PROPN
ejpam-3565	147	3	)	)	PUNCT
ejpam-3565	147	4	is	be	AUX
ejpam-3565	147	5	self	self	NOUN
ejpam-3565	147	6	-	-	PUNCT
ejpam-3565	147	7	orthogonal	orthogonal	ADJ
ejpam-3565	147	8	,	,	PUNCT
ejpam-3565	147	9	tor1(c	tor1(c	NUM
ejpam-3565	147	10	)	)	PUNCT
ejpam-3565	147	11	is	be	AUX
ejpam-3565	147	12	self	self	NOUN
ejpam-3565	147	13	-	-	PUNCT
ejpam-3565	147	14	dual	dual	ADJ
ejpam-3565	147	15	,	,	PUNCT
ejpam-3565	147	16	and	and	CCONJ
ejpam-3565	147	17	tor2(c	tor2(c	NOUN
ejpam-3565	148	1	)	)	PUNCT
ejpam-3565	148	2	=	=	SYM
ejpam-3565	148	3	res(c)⊥.	res(c)⊥.	NOUN
ejpam-3565	148	4	proof	proof	NOUN
ejpam-3565	148	5	.	.	PUNCT
ejpam-3565	149	1	suppose	suppose	VERB
ejpam-3565	149	2	c	c	NOUN
ejpam-3565	149	3	has	have	VERB
ejpam-3565	149	4	generator	generator	NOUN
ejpam-3565	149	5	matrix	matrix	NOUN
ejpam-3565	149	6	g	g	NOUN
ejpam-3565	149	7	as	as	ADP
ejpam-3565	149	8	in	in	ADP
ejpam-3565	149	9	(	(	PUNCT
ejpam-3565	149	10	2	2	NUM
ejpam-3565	149	11	)	)	PUNCT
ejpam-3565	149	12	.	.	PUNCT
ejpam-3565	150	1	then	then	ADV
ejpam-3565	150	2	the	the	DET
ejpam-3565	150	3	torsion	torsion	NOUN
ejpam-3565	150	4	codes	code	NOUN
ejpam-3565	150	5	res(c	res(c	ADV
ejpam-3565	150	6	)	)	PUNCT
ejpam-3565	150	7	,	,	PUNCT
ejpam-3565	150	8	tor1(c	tor1(c	NOUN
ejpam-3565	150	9	)	)	PUNCT
ejpam-3565	150	10	and	and	CCONJ
ejpam-3565	150	11	tor2(c	tor2(c	NUM
ejpam-3565	150	12	)	)	PUNCT
ejpam-3565	150	13	have	have	VERB
ejpam-3565	150	14	generator	generator	NOUN
ejpam-3565	150	15	matrices	matrix	NOUN
ejpam-3565	150	16	t0	t0	PROPN
ejpam-3565	150	17	,	,	PUNCT
ejpam-3565	150	18	t1	t1	NOUN
ejpam-3565	150	19	and	and	CCONJ
ejpam-3565	150	20	t2	t2	NOUN
ejpam-3565	150	21	as	as	ADP
ejpam-3565	150	22	in	in	ADP
ejpam-3565	150	23	(	(	PUNCT
ejpam-3565	150	24	3	3	NUM
ejpam-3565	150	25	)	)	PUNCT
ejpam-3565	150	26	,	,	PUNCT
ejpam-3565	150	27	(	(	PUNCT
ejpam-3565	150	28	4	4	NUM
ejpam-3565	150	29	)	)	PUNCT
ejpam-3565	150	30	and	and	CCONJ
ejpam-3565	150	31	(	(	PUNCT
ejpam-3565	150	32	5	5	NUM
ejpam-3565	150	33	)	)	PUNCT
ejpam-3565	150	34	respectively	respectively	ADV
ejpam-3565	150	35	.	.	PUNCT
ejpam-3565	151	1	from	from	ADP
ejpam-3565	151	2	conditions	condition	NOUN
ejpam-3565	151	3	(	(	PUNCT
ejpam-3565	151	4	6	6	NUM
ejpam-3565	151	5	)	)	PUNCT
ejpam-3565	151	6	and	and	CCONJ
ejpam-3565	151	7	(	(	PUNCT
ejpam-3565	151	8	7	7	NUM
ejpam-3565	151	9	)	)	PUNCT
ejpam-3565	151	10	,	,	PUNCT
ejpam-3565	151	11	we	we	PRON
ejpam-3565	151	12	obtain	obtain	VERB
ejpam-3565	151	13	aat	aat	ADJ
ejpam-3565	151	14	≡	≡	PROPN
ejpam-3565	151	15	0	0	PUNCT
ejpam-3565	152	1	(	(	PUNCT
ejpam-3565	152	2	mod	mod	PROPN
ejpam-3565	152	3	p	p	X
ejpam-3565	152	4	)	)	PUNCT
ejpam-3565	152	5	(	(	PUNCT
ejpam-3565	152	6	10	10	NUM
ejpam-3565	152	7	)	)	PUNCT
ejpam-3565	152	8	abt	abt	VERB
ejpam-3565	152	9	≡	≡	PROPN
ejpam-3565	152	10	0	0	PUNCT
ejpam-3565	153	1	(	(	PUNCT
ejpam-3565	153	2	mod	mod	PROPN
ejpam-3565	153	3	p	p	NOUN
ejpam-3565	153	4	)	)	PUNCT
ejpam-3565	153	5	.	.	PUNCT
ejpam-3565	154	1	(	(	PUNCT
ejpam-3565	154	2	11	11	X
ejpam-3565	154	3	)	)	PUNCT
ejpam-3565	154	4	it	it	PRON
ejpam-3565	154	5	immediately	immediately	ADV
ejpam-3565	154	6	follows	follow	VERB
ejpam-3565	154	7	from	from	ADP
ejpam-3565	154	8	(	(	PUNCT
ejpam-3565	154	9	10	10	NUM
ejpam-3565	154	10	)	)	PUNCT
ejpam-3565	154	11	that	that	PRON
ejpam-3565	155	1	t0	t0	VERB
ejpam-3565	155	2	t	t	PROPN
ejpam-3565	155	3	t	t	PROPN
ejpam-3565	155	4	0	0	NUM
ejpam-3565	156	1	≡	≡	PROPN
ejpam-3565	156	2	0	0	PUNCT
ejpam-3565	156	3	(	(	PUNCT
ejpam-3565	156	4	mod	mod	PROPN
ejpam-3565	156	5	p	p	X
ejpam-3565	156	6	)	)	PUNCT
ejpam-3565	156	7	,	,	PUNCT
ejpam-3565	156	8	and	and	CCONJ
ejpam-3565	156	9	so	so	ADV
ejpam-3565	156	10	res(c	res(c	ADJ
ejpam-3565	156	11	)	)	PUNCT
ejpam-3565	156	12	is	be	AUX
ejpam-3565	156	13	self	self	NOUN
ejpam-3565	156	14	-	-	PUNCT
ejpam-3565	156	15	orthogonal	orthogonal	ADJ
ejpam-3565	156	16	.	.	PUNCT
ejpam-3565	157	1	conditions	condition	NOUN
ejpam-3565	157	2	(	(	PUNCT
ejpam-3565	157	3	8)	8)	NUM
ejpam-3565	157	4	,	,	PUNCT
ejpam-3565	157	5	(	(	PUNCT
ejpam-3565	157	6	10	10	NUM
ejpam-3565	157	7	)	)	PUNCT
ejpam-3565	157	8	and	and	CCONJ
ejpam-3565	157	9	(	(	PUNCT
ejpam-3565	157	10	11	11	NUM
ejpam-3565	157	11	)	)	PUNCT
ejpam-3565	157	12	imply	imply	VERB
ejpam-3565	157	13	that	that	SCONJ
ejpam-3565	157	14	t1	t1	PROPN
ejpam-3565	157	15	t	t	PROPN
ejpam-3565	157	16	t	t	PROPN
ejpam-3565	157	17	1	1	NUM
ejpam-3565	157	18	≡	≡	PROPN
ejpam-3565	157	19	0	0	NUM
ejpam-3565	158	1	(	(	PUNCT
ejpam-3565	158	2	mod	mod	PROPN
ejpam-3565	158	3	p	p	X
ejpam-3565	158	4	)	)	PUNCT
ejpam-3565	158	5	,	,	PUNCT
ejpam-3565	159	1	so	so	SCONJ
ejpam-3565	159	2	that	that	PRON
ejpam-3565	159	3	tor1(c	tor1(c	NOUN
ejpam-3565	159	4	)	)	PUNCT
ejpam-3565	159	5	is	be	AUX
ejpam-3565	159	6	selforthogonal	selforthogonal	ADJ
ejpam-3565	159	7	.	.	PUNCT
ejpam-3565	160	1	since	since	SCONJ
ejpam-3565	160	2	c	c	PROPN
ejpam-3565	160	3	is	be	AUX
ejpam-3565	160	4	self	self	NOUN
ejpam-3565	160	5	-	-	PUNCT
ejpam-3565	160	6	dual	dual	ADJ
ejpam-3565	160	7	,	,	PUNCT
ejpam-3565	160	8	then	then	ADV
ejpam-3565	160	9	dim	dim	VERB
ejpam-3565	160	10	tor1(c	tor1(c	NOUN
ejpam-3565	160	11	)	)	PUNCT
ejpam-3565	161	1	=	=	SYM
ejpam-3565	161	2	k	k	X
ejpam-3565	162	1	+	+	PUNCT
ejpam-3565	162	2	l	l	NOUN
ejpam-3565	162	3	=	=	SYM
ejpam-3565	162	4	n	n	PRON
ejpam-3565	162	5	2	2	NUM
ejpam-3565	162	6	.	.	PUNCT
ejpam-3565	162	7	thus	thus	ADV
ejpam-3565	162	8	tor1(c	tor1(c	NUM
ejpam-3565	162	9	)	)	PUNCT
ejpam-3565	162	10	is	be	AUX
ejpam-3565	162	11	self	self	NOUN
ejpam-3565	162	12	-	-	PUNCT
ejpam-3565	162	13	dual	dual	ADJ
ejpam-3565	162	14	.	.	PUNCT
ejpam-3565	163	1	from	from	ADP
ejpam-3565	163	2	conditions	condition	NOUN
ejpam-3565	163	3	(	(	PUNCT
ejpam-3565	163	4	9)-(11	9)-(11	NUM
ejpam-3565	163	5	)	)	PUNCT
ejpam-3565	163	6	,	,	PUNCT
ejpam-3565	163	7	it	it	PRON
ejpam-3565	163	8	follows	follow	VERB
ejpam-3565	163	9	that	that	SCONJ
ejpam-3565	163	10	t2	t2	PROPN
ejpam-3565	163	11	t	t	PROPN
ejpam-3565	163	12	t	t	PROPN
ejpam-3565	163	13	0	0	NUM
ejpam-3565	164	1	≡	≡	PROPN
ejpam-3565	164	2	0	0	PUNCT
ejpam-3565	164	3	(	(	PUNCT
ejpam-3565	164	4	mod	mod	PROPN
ejpam-3565	164	5	p	p	X
ejpam-3565	164	6	)	)	PUNCT
ejpam-3565	164	7	,	,	PUNCT
ejpam-3565	164	8	so	so	ADV
ejpam-3565	164	9	tor2(c	tor2(c	NOUN
ejpam-3565	164	10	)	)	PUNCT
ejpam-3565	164	11	⊆	⊆	NUM
ejpam-3565	164	12	res(c)⊥.	res(c)⊥.	NOUN
ejpam-3565	164	13	from	from	ADP
ejpam-3565	164	14	corollary	corollary	ADJ
ejpam-3565	164	15	1	1	NUM
ejpam-3565	164	16	,	,	PUNCT
ejpam-3565	164	17	dim	dim	ADJ
ejpam-3565	164	18	tor2(c	tor2(c	NOUN
ejpam-3565	164	19	)	)	PUNCT
ejpam-3565	164	20	=	=	SYM
ejpam-3565	164	21	k+2l	k+2l	PROPN
ejpam-3565	164	22	=	=	PUNCT
ejpam-3565	164	23	n−k	n−k	NOUN
ejpam-3565	164	24	=	=	SYM
ejpam-3565	164	25	dim	dim	ADJ
ejpam-3565	164	26	res(c)⊥.	res(c)⊥.	NOUN
ejpam-3565	164	27	consequently	consequently	ADV
ejpam-3565	164	28	,	,	PUNCT
ejpam-3565	164	29	|tor2(c)|	|tor2(c)|	NOUN
ejpam-3565	164	30	=	=	X
ejpam-3565	164	31	|res(c)⊥|	|res(c)⊥|	NOUN
ejpam-3565	164	32	and	and	CCONJ
ejpam-3565	164	33	so	so	ADV
ejpam-3565	164	34	tor2(c	tor2(c	NUM
ejpam-3565	164	35	)	)	PUNCT
ejpam-3565	164	36	=	=	PRON
ejpam-3565	164	37	res(c)⊥.	res(c)⊥.	NOUN
ejpam-3565	164	38	4	4	NUM
ejpam-3565	164	39	.	.	PUNCT
ejpam-3565	164	40	codes	code	NOUN
ejpam-3565	164	41	over	over	ADP
ejpam-3565	164	42	gr(p3	gr(p3	PROPN
ejpam-3565	164	43	,	,	PUNCT
ejpam-3565	164	44	r	r	NOUN
ejpam-3565	164	45	)	)	PUNCT
ejpam-3565	164	46	from	from	ADP
ejpam-3565	164	47	a	a	DET
ejpam-3565	164	48	code	code	NOUN
ejpam-3565	164	49	over	over	ADP
ejpam-3565	164	50	fr	fr	PROPN
ejpam-3565	164	51	p	p	NOUN
ejpam-3565	164	52	we	we	PRON
ejpam-3565	164	53	now	now	ADV
ejpam-3565	164	54	use	use	VERB
ejpam-3565	164	55	proposition	proposition	NOUN
ejpam-3565	164	56	1	1	NUM
ejpam-3565	164	57	to	to	PART
ejpam-3565	164	58	construct	construct	VERB
ejpam-3565	164	59	self	self	NOUN
ejpam-3565	164	60	-	-	PUNCT
ejpam-3565	164	61	dual	dual	ADJ
ejpam-3565	164	62	codes	code	NOUN
ejpam-3565	164	63	over	over	ADP
ejpam-3565	164	64	gr(p3	gr(p3	PROPN
ejpam-3565	164	65	,	,	PUNCT
ejpam-3565	164	66	r	r	NOUN
ejpam-3565	164	67	)	)	PUNCT
ejpam-3565	164	68	with	with	ADP
ejpam-3565	164	69	prescribed	prescribe	VERB
ejpam-3565	164	70	first	first	ADJ
ejpam-3565	164	71	torsion	torsion	NOUN
ejpam-3565	164	72	code	code	NOUN
ejpam-3565	164	73	.	.	PUNCT
ejpam-3565	165	1	we	we	PRON
ejpam-3565	165	2	start	start	VERB
ejpam-3565	165	3	with	with	ADP
ejpam-3565	165	4	a	a	DET
ejpam-3565	165	5	self	self	NOUN
ejpam-3565	165	6	-	-	PUNCT
ejpam-3565	165	7	dual	dual	ADJ
ejpam-3565	165	8	[	[	X
ejpam-3565	165	9	n	n	CCONJ
ejpam-3565	165	10	,	,	PUNCT
ejpam-3565	165	11	k	k	PROPN
ejpam-3565	165	12	+	+	NUM
ejpam-3565	165	13	l	l	NOUN
ejpam-3565	165	14	]	]	X
ejpam-3565	165	15	code	code	NOUN
ejpam-3565	165	16	c1	c1	NOUN
ejpam-3565	165	17	over	over	ADP
ejpam-3565	165	18	fpr	fpr	NOUN
ejpam-3565	165	19	with	with	ADP
ejpam-3565	165	20	generator	generator	NOUN
ejpam-3565	165	21	matrix	matrix	NOUN
ejpam-3565	165	22	g′	g′	NOUN
ejpam-3565	166	1	=	=	PUNCT
ejpam-3565	167	1	[	[	PUNCT
ejpam-3565	167	2	a′	a′	PROPN
ejpam-3565	167	3	b′	b′	NOUN
ejpam-3565	167	4	]	]	PUNCT
ejpam-3565	168	1	=	=	PUNCT
ejpam-3565	168	2	[	[	PUNCT
ejpam-3565	168	3	ik	ik	X
ejpam-3565	168	4	a′2	a′2	PROPN
ejpam-3565	168	5	a′30	a′30	PROPN
ejpam-3565	168	6	a′40	a′40	PROPN
ejpam-3565	168	7	0	0	NUM
ejpam-3565	168	8	il	il	PROPN
ejpam-3565	168	9	b′3	b′3	NOUN
ejpam-3565	168	10	b′40	b′40	VERB
ejpam-3565	168	11	]	]	PUNCT
ejpam-3565	168	12	,	,	PUNCT
ejpam-3565	168	13	where	where	SCONJ
ejpam-3565	168	14	the	the	DET
ejpam-3565	168	15	columns	column	NOUN
ejpam-3565	168	16	are	be	AUX
ejpam-3565	168	17	grouped	group	VERB
ejpam-3565	168	18	into	into	ADP
ejpam-3565	168	19	blocks	block	NOUN
ejpam-3565	168	20	of	of	ADP
ejpam-3565	168	21	sizes	size	NOUN
ejpam-3565	168	22	k	k	PROPN
ejpam-3565	168	23	,	,	PUNCT
ejpam-3565	168	24	l	l	NOUN
ejpam-3565	168	25	,	,	PUNCT
ejpam-3565	168	26	l	l	PROPN
ejpam-3565	168	27	and	and	CCONJ
ejpam-3565	168	28	k.	k.	PROPN
ejpam-3565	168	29	note	note	VERB
ejpam-3565	169	1	that	that	SCONJ
ejpam-3565	169	2	2(k	2(k	NUM
ejpam-3565	169	3	+	+	NUM
ejpam-3565	169	4	l	l	NOUN
ejpam-3565	169	5	)	)	PUNCT
ejpam-3565	170	1	=	=	VERB
ejpam-3565	170	2	n.	n.	NOUN
ejpam-3565	170	3	we	we	PRON
ejpam-3565	170	4	want	want	VERB
ejpam-3565	170	5	to	to	PART
ejpam-3565	170	6	obtain	obtain	VERB
ejpam-3565	170	7	the	the	DET
ejpam-3565	170	8	number	number	NOUN
ejpam-3565	170	9	of	of	ADP
ejpam-3565	170	10	self	self	NOUN
ejpam-3565	170	11	-	-	PUNCT
ejpam-3565	170	12	dual	dual	ADJ
ejpam-3565	170	13	codes	code	NOUN
ejpam-3565	170	14	c	c	PROPN
ejpam-3565	170	15	over	over	ADP
ejpam-3565	170	16	gr(p3	gr(p3	PROPN
ejpam-3565	170	17	,	,	PUNCT
ejpam-3565	170	18	r	r	NOUN
ejpam-3565	170	19	)	)	PUNCT
ejpam-3565	170	20	such	such	ADJ
ejpam-3565	170	21	that	that	DET
ejpam-3565	170	22	tor1(c	tor1(c	NOUN
ejpam-3565	170	23	)	)	PUNCT
ejpam-3565	170	24	=	=	SYM
ejpam-3565	170	25	c1	c1	PROPN
ejpam-3565	170	26	.	.	PUNCT
ejpam-3565	171	1	since	since	SCONJ
ejpam-3565	171	2	c1	c1	PROPN
ejpam-3565	171	3	is	be	AUX
ejpam-3565	171	4	self	self	NOUN
ejpam-3565	171	5	-	-	PUNCT
ejpam-3565	171	6	dual	dual	ADJ
ejpam-3565	171	7	,	,	PUNCT
ejpam-3565	171	8	then	then	ADV
ejpam-3565	171	9	g′g′t	g′g′t	PROPN
ejpam-3565	171	10	≡	≡	PROPN
ejpam-3565	171	11	0	0	PUNCT
ejpam-3565	172	1	(	(	PUNCT
ejpam-3565	172	2	mod	mod	PROPN
ejpam-3565	172	3	p	p	X
ejpam-3565	172	4	)	)	PUNCT
ejpam-3565	172	5	and	and	CCONJ
ejpam-3565	172	6	we	we	PRON
ejpam-3565	172	7	obtain	obtain	VERB
ejpam-3565	172	8	ik	ik	PROPN
ejpam-3565	172	9	+	+	NOUN
ejpam-3565	172	10	a′2a	a′2a	NOUN
ejpam-3565	172	11	′	′	NUM
ejpam-3565	172	12	2	2	NUM
ejpam-3565	172	13	t	t	NOUN
ejpam-3565	173	1	+	+	ADP
ejpam-3565	173	2	a′30a	a′30a	PROPN
ejpam-3565	173	3	′	′	NUM
ejpam-3565	173	4	30	30	NUM
ejpam-3565	173	5	t	t	NOUN
ejpam-3565	173	6	+	+	NOUN
ejpam-3565	173	7	a′40a	a′40a	ADJ
ejpam-3565	173	8	′	′	NUM
ejpam-3565	173	9	40	40	NUM
ejpam-3565	173	10	t	t	NOUN
ejpam-3565	173	11	≡	≡	PROPN
ejpam-3565	173	12	0	0	PUNCT
ejpam-3565	174	1	(	(	PUNCT
ejpam-3565	174	2	mod	mod	PROPN
ejpam-3565	174	3	p	p	X
ejpam-3565	174	4	)	)	PUNCT
ejpam-3565	174	5	(	(	PUNCT
ejpam-3565	174	6	12	12	NUM
ejpam-3565	174	7	)	)	PUNCT
ejpam-3565	174	8	a′2	a′2	NOUN
ejpam-3565	175	1	+	+	ADJ
ejpam-3565	175	2	a′30b	a′30b	NOUN
ejpam-3565	175	3	′	′	ADJ
ejpam-3565	175	4	3	3	NUM
ejpam-3565	175	5	t	t	NOUN
ejpam-3565	175	6	+	+	NOUN
ejpam-3565	175	7	a′40b	a′40b	PROPN
ejpam-3565	175	8	′	′	NUM
ejpam-3565	175	9	40	40	NUM
ejpam-3565	175	10	t	t	NOUN
ejpam-3565	175	11	≡	≡	PROPN
ejpam-3565	175	12	0	0	PUNCT
ejpam-3565	176	1	(	(	PUNCT
ejpam-3565	176	2	mod	mod	PROPN
ejpam-3565	176	3	p	p	X
ejpam-3565	176	4	)	)	PUNCT
ejpam-3565	176	5	(	(	PUNCT
ejpam-3565	176	6	13	13	NUM
ejpam-3565	176	7	)	)	PUNCT
ejpam-3565	176	8	il	il	NOUN
ejpam-3565	177	1	+	+	PUNCT
ejpam-3565	177	2	b′3b	b′3b	NOUN
ejpam-3565	177	3	′	′	NUM
ejpam-3565	177	4	3	3	NUM
ejpam-3565	177	5	t	t	NOUN
ejpam-3565	177	6	+	+	NOUN
ejpam-3565	177	7	b′40b	b′40b	PROPN
ejpam-3565	177	8	′	′	NUM
ejpam-3565	177	9	40	40	NUM
ejpam-3565	177	10	t	t	NOUN
ejpam-3565	177	11	≡	≡	PROPN
ejpam-3565	177	12	0	0	PUNCT
ejpam-3565	178	1	(	(	PUNCT
ejpam-3565	178	2	mod	mod	PROPN
ejpam-3565	178	3	p	p	NOUN
ejpam-3565	178	4	)	)	PUNCT
ejpam-3565	178	5	.	.	PUNCT
ejpam-3565	179	1	(	(	PUNCT
ejpam-3565	179	2	14	14	NUM
ejpam-3565	179	3	)	)	PUNCT
ejpam-3565	179	4	let	let	VERB
ejpam-3565	179	5	h	h	NOUN
ejpam-3565	179	6	=	=	PRON
ejpam-3565	180	1	[	[	PUNCT
ejpam-3565	180	2	a′30	a′30	NOUN
ejpam-3565	180	3	a′40	a′40	NOUN
ejpam-3565	180	4	b′3	b′3	NOUN
ejpam-3565	180	5	b′40	b′40	NOUN
ejpam-3565	180	6	]	]	PUNCT
ejpam-3565	180	7	and	and	CCONJ
ejpam-3565	180	8	j	j	PROPN
ejpam-3565	181	1	=	=	PRON
ejpam-3565	181	2	[	[	PUNCT
ejpam-3565	181	3	ik	ik	X
ejpam-3565	181	4	−a′2	−a′2	PROPN
ejpam-3565	181	5	−a′2	−a′2	NUM
ejpam-3565	181	6	t	t	PROPN
ejpam-3565	181	7	il	il	PROPN
ejpam-3565	182	1	+	+	PROPN
ejpam-3565	182	2	a′2	a′2	ADJ
ejpam-3565	182	3	ta′2	ta′2	VERB
ejpam-3565	182	4	]	]	PUNCT
ejpam-3565	182	5	.	.	PUNCT
ejpam-3565	183	1	note	note	VERB
ejpam-3565	183	2	that	that	SCONJ
ejpam-3565	183	3	h	h	PROPN
ejpam-3565	183	4	and	and	CCONJ
ejpam-3565	183	5	j	j	PROPN
ejpam-3565	183	6	are	be	AUX
ejpam-3565	183	7	both	both	PRON
ejpam-3565	183	8	square	square	ADJ
ejpam-3565	183	9	matrices	matrix	NOUN
ejpam-3565	183	10	of	of	ADP
ejpam-3565	183	11	order	order	NOUN
ejpam-3565	184	1	k	k	PROPN
ejpam-3565	184	2	+	+	PUNCT
ejpam-3565	184	3	l.	l.	PROPN
ejpam-3565	184	4	from	from	ADP
ejpam-3565	184	5	(	(	PUNCT
ejpam-3565	184	6	12)-(14	12)-(14	NUM
ejpam-3565	184	7	)	)	PUNCT
ejpam-3565	184	8	,	,	PUNCT
ejpam-3565	184	9	we	we	PRON
ejpam-3565	184	10	have	have	VERB
ejpam-3565	184	11	h(−htj	h(−htj	PROPN
ejpam-3565	184	12	)	)	PUNCT
ejpam-3565	184	13	≡	≡	PROPN
ejpam-3565	184	14	ik+l	ik+l	PROPN
ejpam-3565	185	1	(	(	PUNCT
ejpam-3565	185	2	mod	mod	PROPN
ejpam-3565	185	3	p	p	X
ejpam-3565	185	4	)	)	PUNCT
ejpam-3565	185	5	.	.	PUNCT
ejpam-3565	186	1	hence	hence	ADV
ejpam-3565	186	2	,	,	PUNCT
ejpam-3565	186	3	h	h	PROPN
ejpam-3565	186	4	is	be	AUX
ejpam-3565	186	5	invertible	invertible	ADJ
ejpam-3565	186	6	modulo	modulo	NOUN
ejpam-3565	186	7	p.	p.	NOUN
ejpam-3565	186	8	by	by	ADP
ejpam-3565	186	9	a	a	DET
ejpam-3565	186	10	permutation	permutation	NOUN
ejpam-3565	186	11	of	of	ADP
ejpam-3565	186	12	columns	column	NOUN
ejpam-3565	186	13	of	of	ADP
ejpam-3565	186	14	h	h	NOUN
ejpam-3565	186	15	,	,	PUNCT
ejpam-3565	186	16	we	we	PRON
ejpam-3565	186	17	can	can	AUX
ejpam-3565	186	18	assume	assume	VERB
ejpam-3565	186	19	that	that	SCONJ
ejpam-3565	186	20	the	the	DET
ejpam-3565	186	21	k	k	PROPN
ejpam-3565	186	22	×	×	PROPN
ejpam-3565	186	23	k	k	PROPN
ejpam-3565	186	24	matrix	matrix	NOUN
ejpam-3565	186	25	a′40	a′40	NOUN
ejpam-3565	186	26	is	be	AUX
ejpam-3565	186	27	invertible	invertible	ADJ
ejpam-3565	186	28	modulo	modulo	NOUN
ejpam-3565	186	29	p.	p.	NOUN
ejpam-3565	186	30	t.	t.	PROPN
ejpam-3565	186	31	l.	l.	PROPN
ejpam-3565	186	32	vasquez	vasquez	PROPN
ejpam-3565	186	33	,	,	PUNCT
ejpam-3565	186	34	g.	g.	PROPN
ejpam-3565	186	35	petalcorin	petalcorin	PROPN
ejpam-3565	186	36	/	/	SYM
ejpam-3565	186	37	eur	eur	PROPN
ejpam-3565	186	38	.	.	PUNCT
ejpam-3565	187	1	j.	j.	PROPN
ejpam-3565	187	2	pure	pure	PROPN
ejpam-3565	187	3	appl	appl	PROPN
ejpam-3565	187	4	.	.	PROPN
ejpam-3565	187	5	math	math	PROPN
ejpam-3565	187	6	,	,	PUNCT
ejpam-3565	187	7	12	12	NUM
ejpam-3565	187	8	(	(	PUNCT
ejpam-3565	187	9	4	4	NUM
ejpam-3565	187	10	)	)	PUNCT
ejpam-3565	187	11	(	(	PUNCT
ejpam-3565	187	12	2019	2019	NUM
ejpam-3565	187	13	)	)	PUNCT
ejpam-3565	187	14	,	,	PUNCT
ejpam-3565	187	15	1701	1701	NUM
ejpam-3565	187	16	-	-	SYM
ejpam-3565	187	17	1716	1716	NUM
ejpam-3565	187	18	1707	1707	NUM
ejpam-3565	187	19	let	let	VERB
ejpam-3565	187	20	c0	c0	PROPN
ejpam-3565	187	21	be	be	AUX
ejpam-3565	187	22	the	the	DET
ejpam-3565	187	23	k	k	ADJ
ejpam-3565	187	24	-	-	ADJ
ejpam-3565	187	25	dimensional	dimensional	ADJ
ejpam-3565	187	26	subspace	subspace	NOUN
ejpam-3565	187	27	of	of	ADP
ejpam-3565	187	28	c1	c1	PROPN
ejpam-3565	187	29	with	with	ADP
ejpam-3565	187	30	generator	generator	NOUN
ejpam-3565	187	31	matrix	matrix	NOUN
ejpam-3565	187	32	a′	a′	NOUN
ejpam-3565	188	1	=	=	PUNCT
ejpam-3565	188	2	[	[	PUNCT
ejpam-3565	188	3	ik	ik	X
ejpam-3565	188	4	a′2	a′2	PROPN
ejpam-3565	188	5	a′30	a′30	PROPN
ejpam-3565	188	6	a′40	a′40	PROPN
ejpam-3565	188	7	]	]	PUNCT
ejpam-3565	188	8	.	.	PUNCT
ejpam-3565	189	1	from	from	ADP
ejpam-3565	189	2	(	(	PUNCT
ejpam-3565	189	3	12	12	NUM
ejpam-3565	189	4	)	)	PUNCT
ejpam-3565	189	5	and	and	CCONJ
ejpam-3565	189	6	(	(	PUNCT
ejpam-3565	189	7	13	13	NUM
ejpam-3565	189	8	)	)	PUNCT
ejpam-3565	189	9	,	,	PUNCT
ejpam-3565	189	10	c0	c0	PROPN
ejpam-3565	189	11	is	be	AUX
ejpam-3565	189	12	a	a	DET
ejpam-3565	189	13	self	self	NOUN
ejpam-3565	189	14	-	-	PUNCT
ejpam-3565	189	15	orthogonal	orthogonal	ADJ
ejpam-3565	189	16	code	code	NOUN
ejpam-3565	189	17	and	and	CCONJ
ejpam-3565	189	18	c0	c0	PROPN
ejpam-3565	189	19	⊆	⊆	NUM
ejpam-3565	189	20	c1	c1	PROPN
ejpam-3565	189	21	⊆	⊆	NUM
ejpam-3565	189	22	c⊥0	c⊥0	PROPN
ejpam-3565	189	23	.	.	PUNCT
ejpam-3565	190	1	now	now	ADV
ejpam-3565	190	2	,	,	PUNCT
ejpam-3565	190	3	the	the	DET
ejpam-3565	190	4	dual	dual	ADJ
ejpam-3565	190	5	of	of	ADP
ejpam-3565	190	6	c⊥0	c⊥0	VERB
ejpam-3565	190	7	has	have	AUX
ejpam-3565	190	8	dimension	dimension	VERB
ejpam-3565	190	9	n−	n−	PROPN
ejpam-3565	190	10	k	k	NOUN
ejpam-3565	190	11	=	=	PUNCT
ejpam-3565	190	12	k	k	PROPN
ejpam-3565	191	1	+	+	CCONJ
ejpam-3565	191	2	2l	2l	NUM
ejpam-3565	191	3	.	.	PUNCT
ejpam-3565	192	1	hence	hence	ADV
ejpam-3565	192	2	we	we	PRON
ejpam-3565	192	3	can	can	AUX
ejpam-3565	192	4	write	write	VERB
ejpam-3565	192	5	the	the	DET
ejpam-3565	192	6	generator	generator	NOUN
ejpam-3565	192	7	matrix	matrix	NOUN
ejpam-3565	192	8	of	of	ADP
ejpam-3565	192	9	c⊥0	c⊥0	PUNCT
ejpam-3565	192	10	asa′b′	asa′b′	VERB
ejpam-3565	192	11	c	c	NOUN
ejpam-3565	192	12	′	′	NOUN
ejpam-3565	192	13			NOUN
ejpam-3565	192	14	=	=	SYM
ejpam-3565	192	15	ik	ik	PROPN
ejpam-3565	192	16	a′2	a′2	NUM
ejpam-3565	192	17	a′30	a′30	PROPN
ejpam-3565	192	18	a′40	a′40	PROPN
ejpam-3565	192	19	0	0	NUM
ejpam-3565	192	20	il	il	PROPN
ejpam-3565	192	21	b′3	b′3	NOUN
ejpam-3565	192	22	b′40	b′40	VERB
ejpam-3565	192	23	0	0	NUM
ejpam-3565	192	24	0	0	NUM
ejpam-3565	192	25	il	il	PROPN
ejpam-3565	192	26	c	c	NOUN
ejpam-3565	192	27	′4	′4	ADJ
ejpam-3565	192	28			NOUN
ejpam-3565	192	29	,	,	PUNCT
ejpam-3565	192	30	where	where	SCONJ
ejpam-3565	192	31	c	c	PROPN
ejpam-3565	192	32	′4	′4	PROPN
ejpam-3565	192	33	is	be	AUX
ejpam-3565	192	34	an	an	DET
ejpam-3565	192	35	l	l	NOUN
ejpam-3565	192	36	×	×	NOUN
ejpam-3565	192	37	k	k	PROPN
ejpam-3565	192	38	matrix	matrix	NOUN
ejpam-3565	192	39	over	over	ADP
ejpam-3565	192	40	fpr	fpr	PRON
ejpam-3565	192	41	.	.	PUNCT
ejpam-3565	193	1	we	we	PRON
ejpam-3565	193	2	wish	wish	VERB
ejpam-3565	193	3	to	to	PART
ejpam-3565	193	4	find	find	VERB
ejpam-3565	193	5	matrices	matrix	NOUN
ejpam-3565	193	6	a2	a2	NOUN
ejpam-3565	193	7	,	,	PUNCT
ejpam-3565	193	8	a3	a3	NOUN
ejpam-3565	193	9	,	,	PUNCT
ejpam-3565	193	10	a4	a4	PROPN
ejpam-3565	193	11	,	,	PUNCT
ejpam-3565	193	12	b3	b3	NOUN
ejpam-3565	193	13	,	,	PUNCT
ejpam-3565	193	14	b4	b4	NOUN
ejpam-3565	193	15	and	and	CCONJ
ejpam-3565	193	16	c4	c4	NOUN
ejpam-3565	193	17	with	with	ADP
ejpam-3565	193	18	entries	entry	NOUN
ejpam-3565	193	19	from	from	ADP
ejpam-3565	193	20	gr(pe	gr(pe	NOUN
ejpam-3565	193	21	,	,	PUNCT
ejpam-3565	193	22	r	r	NOUN
ejpam-3565	193	23	)	)	PUNCT
ejpam-3565	193	24	satisfying	satisfy	VERB
ejpam-3565	193	25	conditions	condition	NOUN
ejpam-3565	193	26	(	(	PUNCT
ejpam-3565	193	27	6)-(9	6)-(9	NOUN
ejpam-3565	193	28	)	)	PUNCT
ejpam-3565	193	29	,	,	PUNCT
ejpam-3565	193	30	which	which	PRON
ejpam-3565	193	31	are	be	AUX
ejpam-3565	193	32	equivalent	equivalent	ADJ
ejpam-3565	193	33	to	to	ADP
ejpam-3565	193	34	ik	ik	PROPN
ejpam-3565	194	1	+	+	PROPN
ejpam-3565	194	2	a2a	a2a	PROPN
ejpam-3565	194	3	t	t	PROPN
ejpam-3565	194	4	2	2	NUM
ejpam-3565	195	1	+	+	NOUN
ejpam-3565	195	2	a3a	a3a	PROPN
ejpam-3565	195	3	t	t	NOUN
ejpam-3565	195	4	3	3	NUM
ejpam-3565	195	5	+	+	NOUN
ejpam-3565	195	6	a4a	a4a	ADJ
ejpam-3565	195	7	t	t	PROPN
ejpam-3565	195	8	4	4	NUM
ejpam-3565	195	9	≡	≡	PROPN
ejpam-3565	195	10	0	0	PUNCT
ejpam-3565	196	1	(	(	PUNCT
ejpam-3565	196	2	mod	mod	PROPN
ejpam-3565	196	3	p3	p3	PROPN
ejpam-3565	196	4	)	)	PUNCT
ejpam-3565	196	5	(	(	PUNCT
ejpam-3565	196	6	15	15	X
ejpam-3565	196	7	)	)	PUNCT
ejpam-3565	196	8	a2	a2	PROPN
ejpam-3565	196	9	+	+	PROPN
ejpam-3565	196	10	a3b	a3b	NOUN
ejpam-3565	196	11	t	t	NOUN
ejpam-3565	196	12	3	3	NUM
ejpam-3565	196	13	+	+	NOUN
ejpam-3565	196	14	a4b	a4b	PROPN
ejpam-3565	196	15	t	t	PROPN
ejpam-3565	196	16	4	4	NUM
ejpam-3565	196	17	≡	≡	PROPN
ejpam-3565	196	18	0	0	PUNCT
ejpam-3565	197	1	(	(	PUNCT
ejpam-3565	197	2	mod	mod	ADJ
ejpam-3565	197	3	p2	p2	PROPN
ejpam-3565	197	4	)	)	PUNCT
ejpam-3565	197	5	(	(	PUNCT
ejpam-3565	197	6	16	16	NUM
ejpam-3565	197	7	)	)	PUNCT
ejpam-3565	197	8	il	il	PROPN
ejpam-3565	198	1	+	+	PROPN
ejpam-3565	198	2	b3b	b3b	PROPN
ejpam-3565	198	3	t	t	NOUN
ejpam-3565	198	4	3	3	NUM
ejpam-3565	199	1	+	+	NOUN
ejpam-3565	199	2	b4b	b4b	NOUN
ejpam-3565	199	3	t	t	NOUN
ejpam-3565	199	4	4	4	NUM
ejpam-3565	199	5	≡	≡	PROPN
ejpam-3565	199	6	0	0	PUNCT
ejpam-3565	200	1	(	(	PUNCT
ejpam-3565	200	2	mod	mod	PROPN
ejpam-3565	200	3	p	p	X
ejpam-3565	200	4	)	)	PUNCT
ejpam-3565	200	5	(	(	PUNCT
ejpam-3565	200	6	17	17	NUM
ejpam-3565	200	7	)	)	PUNCT
ejpam-3565	200	8	a3	a3	NOUN
ejpam-3565	201	1	+	+	PROPN
ejpam-3565	201	2	a4c	a4c	PROPN
ejpam-3565	201	3	t	t	PROPN
ejpam-3565	201	4	4	4	NUM
ejpam-3565	201	5	≡	≡	PROPN
ejpam-3565	201	6	0	0	PUNCT
ejpam-3565	202	1	(	(	PUNCT
ejpam-3565	202	2	mod	mod	PROPN
ejpam-3565	202	3	p	p	NOUN
ejpam-3565	202	4	)	)	PUNCT
ejpam-3565	202	5	.	.	PUNCT
ejpam-3565	203	1	(	(	PUNCT
ejpam-3565	203	2	18	18	NUM
ejpam-3565	203	3	)	)	PUNCT
ejpam-3565	203	4	the	the	DET
ejpam-3565	203	5	matrices	matrix	NOUN
ejpam-3565	203	6	a2	a2	PROPN
ejpam-3565	203	7	,	,	PUNCT
ejpam-3565	203	8	b3	b3	PROPN
ejpam-3565	203	9	and	and	CCONJ
ejpam-3565	203	10	c4	c4	NOUN
ejpam-3565	203	11	are	be	AUX
ejpam-3565	203	12	considered	consider	VERB
ejpam-3565	203	13	modulo	modulo	ADJ
ejpam-3565	203	14	p	p	NOUN
ejpam-3565	203	15	,	,	PUNCT
ejpam-3565	203	16	a3	a3	NOUN
ejpam-3565	203	17	and	and	CCONJ
ejpam-3565	203	18	b4	b4	NOUN
ejpam-3565	203	19	are	be	AUX
ejpam-3565	203	20	considered	consider	VERB
ejpam-3565	203	21	modulo	modulo	ADJ
ejpam-3565	203	22	p2	p2	NOUN
ejpam-3565	203	23	,	,	PUNCT
ejpam-3565	203	24	and	and	CCONJ
ejpam-3565	203	25	a4	a4	NOUN
ejpam-3565	203	26	modulo	modulo	PROPN
ejpam-3565	203	27	p3	p3	PROPN
ejpam-3565	203	28	.	.	PUNCT
ejpam-3565	204	1	as	as	SCONJ
ejpam-3565	204	2	previously	previously	ADV
ejpam-3565	204	3	done	do	VERB
ejpam-3565	204	4	,	,	PUNCT
ejpam-3565	204	5	we	we	PRON
ejpam-3565	204	6	write	write	VERB
ejpam-3565	204	7	the	the	DET
ejpam-3565	204	8	matrices	matrix	NOUN
ejpam-3565	204	9	in	in	ADP
ejpam-3565	204	10	p	p	ADJ
ejpam-3565	204	11	-	-	PUNCT
ejpam-3565	204	12	adic	adic	ADJ
ejpam-3565	204	13	expansion	expansion	NOUN
ejpam-3565	204	14	:	:	PUNCT
ejpam-3565	204	15	a3	a3	NOUN
ejpam-3565	204	16	=	=	SYM
ejpam-3565	204	17	a30	a30	NOUN
ejpam-3565	204	18	+	+	CCONJ
ejpam-3565	205	1	pa31	pa31	PROPN
ejpam-3565	205	2	,	,	PUNCT
ejpam-3565	205	3	b4	b4	NOUN
ejpam-3565	205	4	=	=	SYM
ejpam-3565	205	5	b40	b40	NOUN
ejpam-3565	205	6	+	+	CCONJ
ejpam-3565	205	7	pb41	pb41	PROPN
ejpam-3565	205	8	and	and	CCONJ
ejpam-3565	205	9	a4	a4	NOUN
ejpam-3565	205	10	=	=	SYM
ejpam-3565	205	11	a40	a40	NOUN
ejpam-3565	205	12	+	+	CCONJ
ejpam-3565	206	1	pa41	pa41	PROPN
ejpam-3565	206	2	+	+	NUM
ejpam-3565	206	3	p2a42	p2a42	NOUN
ejpam-3565	206	4	,	,	PUNCT
ejpam-3565	206	5	where	where	SCONJ
ejpam-3565	206	6	a31	a31	NOUN
ejpam-3565	206	7	,	,	PUNCT
ejpam-3565	206	8	b41	b41	NOUN
ejpam-3565	206	9	,	,	PUNCT
ejpam-3565	206	10	a41	a41	NOUN
ejpam-3565	206	11	and	and	CCONJ
ejpam-3565	206	12	a42	a42	NOUN
ejpam-3565	206	13	have	have	VERB
ejpam-3565	206	14	entries	entry	NOUN
ejpam-3565	206	15	from	from	ADP
ejpam-3565	206	16	tpr	tpr	PROPN
ejpam-3565	206	17	.	.	PUNCT
ejpam-3565	207	1	let	let	VERB
ejpam-3565	207	2	a2	a2	PROPN
ejpam-3565	207	3	,	,	PUNCT
ejpam-3565	207	4	a30	a30	NOUN
ejpam-3565	207	5	,	,	PUNCT
ejpam-3565	207	6	a40	a40	NOUN
ejpam-3565	207	7	,	,	PUNCT
ejpam-3565	207	8	b3	b3	PROPN
ejpam-3565	207	9	and	and	CCONJ
ejpam-3565	207	10	b40	b40	NOUN
ejpam-3565	207	11	be	be	AUX
ejpam-3565	207	12	the	the	DET
ejpam-3565	207	13	matrices	matrix	NOUN
ejpam-3565	207	14	over	over	ADP
ejpam-3565	207	15	tpr	tpr	NOUN
ejpam-3565	207	16	such	such	ADJ
ejpam-3565	207	17	that	that	DET
ejpam-3565	207	18	a2	a2	PROPN
ejpam-3565	207	19	=	=	SYM
ejpam-3565	207	20	a′2	a′2	ADJ
ejpam-3565	207	21	,	,	PUNCT
ejpam-3565	207	22	a30	a30	NOUN
ejpam-3565	207	23	=	=	SYM
ejpam-3565	207	24	a′30	a′30	NOUN
ejpam-3565	207	25	,	,	PUNCT
ejpam-3565	207	26	a40	a40	PROPN
ejpam-3565	207	27	=	=	PUNCT
ejpam-3565	207	28	a′40	a′40	PROPN
ejpam-3565	207	29	,	,	PUNCT
ejpam-3565	207	30	b3	b3	NOUN
ejpam-3565	207	31	=	=	PUNCT
ejpam-3565	207	32	b′3	b′3	NOUN
ejpam-3565	207	33	and	and	CCONJ
ejpam-3565	207	34	b40	b40	NOUN
ejpam-3565	207	35	=	=	SYM
ejpam-3565	207	36	b′40	b′40	NOUN
ejpam-3565	207	37	.	.	PUNCT
ejpam-3565	208	1	from	from	ADP
ejpam-3565	208	2	(	(	PUNCT
ejpam-3565	208	3	12	12	NUM
ejpam-3565	208	4	)	)	PUNCT
ejpam-3565	208	5	and	and	CCONJ
ejpam-3565	208	6	(	(	PUNCT
ejpam-3565	208	7	13	13	NUM
ejpam-3565	208	8	)	)	PUNCT
ejpam-3565	208	9	,	,	PUNCT
ejpam-3565	208	10	there	there	PRON
ejpam-3565	208	11	exist	exist	VERB
ejpam-3565	208	12	matrices	matrix	NOUN
ejpam-3565	208	13	(	(	PUNCT
ejpam-3565	208	14	fij	fij	PROPN
ejpam-3565	208	15	)	)	PUNCT
ejpam-3565	208	16	and	and	CCONJ
ejpam-3565	208	17	d	d	X
ejpam-3565	208	18	with	with	ADP
ejpam-3565	208	19	entries	entry	NOUN
ejpam-3565	208	20	from	from	ADP
ejpam-3565	208	21	gr(p3	gr(p3	PROPN
ejpam-3565	208	22	,	,	PUNCT
ejpam-3565	208	23	r	r	NOUN
ejpam-3565	208	24	)	)	PUNCT
ejpam-3565	208	25	such	such	ADJ
ejpam-3565	208	26	that	that	DET
ejpam-3565	208	27	a2	a2	PROPN
ejpam-3565	209	1	+	+	PROPN
ejpam-3565	209	2	a30b	a30b	PROPN
ejpam-3565	209	3	t	t	PROPN
ejpam-3565	209	4	3	3	NUM
ejpam-3565	210	1	+	+	NOUN
ejpam-3565	210	2	a40b	a40b	ADJ
ejpam-3565	210	3	t	t	NOUN
ejpam-3565	210	4	40	40	NUM
ejpam-3565	210	5	=	=	SYM
ejpam-3565	210	6	pd	pd	X
ejpam-3565	210	7	(	(	PUNCT
ejpam-3565	210	8	19	19	NUM
ejpam-3565	210	9	)	)	PUNCT
ejpam-3565	210	10	and	and	CCONJ
ejpam-3565	210	11	ik	ik	PROPN
ejpam-3565	210	12	+	+	PROPN
ejpam-3565	210	13	a2a	a2a	PROPN
ejpam-3565	210	14	t	t	PROPN
ejpam-3565	210	15	2	2	NUM
ejpam-3565	210	16	+	+	NOUN
ejpam-3565	210	17	a30a	a30a	ADJ
ejpam-3565	210	18	t	t	NOUN
ejpam-3565	210	19	30	30	NUM
ejpam-3565	210	20	+	+	NUM
ejpam-3565	210	21	a40a	a40a	X
ejpam-3565	210	22	t	t	PROPN
ejpam-3565	210	23	40	40	NUM
ejpam-3565	210	24	=	=	SYM
ejpam-3565	210	25	p(fij	p(fij	PROPN
ejpam-3565	210	26	)	)	PUNCT
ejpam-3565	210	27	.	.	PUNCT
ejpam-3565	211	1	(	(	PUNCT
ejpam-3565	211	2	20	20	NUM
ejpam-3565	211	3	)	)	PUNCT
ejpam-3565	211	4	as	as	ADP
ejpam-3565	211	5	in	in	ADP
ejpam-3565	211	6	[	[	X
ejpam-3565	211	7	10	10	NUM
ejpam-3565	211	8	]	]	PUNCT
ejpam-3565	211	9	,	,	PUNCT
ejpam-3565	211	10	b41	b41	NOUN
ejpam-3565	211	11	and	and	CCONJ
ejpam-3565	211	12	c4	c4	NOUN
ejpam-3565	211	13	are	be	AUX
ejpam-3565	211	14	uniquely	uniquely	ADV
ejpam-3565	211	15	determined	determine	VERB
ejpam-3565	211	16	by	by	ADP
ejpam-3565	211	17	bt	bt	PROPN
ejpam-3565	211	18	41	41	NUM
ejpam-3565	211	19	≡	≡	PROPN
ejpam-3565	211	20	−a−1	−a−1	NUM
ejpam-3565	211	21	40	40	NUM
ejpam-3565	211	22	(	(	PUNCT
ejpam-3565	212	1	d	d	X
ejpam-3565	212	2	+	+	PROPN
ejpam-3565	212	3	a31b	a31b	ADJ
ejpam-3565	212	4	t	t	NOUN
ejpam-3565	212	5	3	3	NUM
ejpam-3565	213	1	+	+	NOUN
ejpam-3565	213	2	a41b	a41b	NOUN
ejpam-3565	213	3	t	t	NOUN
ejpam-3565	213	4	40	40	NUM
ejpam-3565	213	5	)	)	PUNCT
ejpam-3565	213	6	(	(	PUNCT
ejpam-3565	213	7	mod	mod	PROPN
ejpam-3565	213	8	p	p	X
ejpam-3565	213	9	)	)	PUNCT
ejpam-3565	213	10	(	(	PUNCT
ejpam-3565	213	11	21	21	NUM
ejpam-3565	213	12	)	)	PUNCT
ejpam-3565	213	13	and	and	CCONJ
ejpam-3565	213	14	ct	ct	NUM
ejpam-3565	213	15	4	4	NUM
ejpam-3565	213	16	≡	≡	NOUN
ejpam-3565	213	17	−a−1	−a−1	NUM
ejpam-3565	213	18	40	40	NUM
ejpam-3565	213	19	a30	a30	NOUN
ejpam-3565	213	20	(	(	PUNCT
ejpam-3565	213	21	mod	mod	NOUN
ejpam-3565	213	22	p	p	PROPN
ejpam-3565	213	23	)	)	PUNCT
ejpam-3565	213	24	,	,	PUNCT
ejpam-3565	213	25	(	(	PUNCT
ejpam-3565	213	26	22	22	NUM
ejpam-3565	213	27	)	)	PUNCT
ejpam-3565	213	28	which	which	PRON
ejpam-3565	213	29	are	be	AUX
ejpam-3565	213	30	sufficient	sufficient	ADJ
ejpam-3565	213	31	conditions	condition	NOUN
ejpam-3565	213	32	for	for	ADP
ejpam-3565	213	33	(	(	PUNCT
ejpam-3565	213	34	16	16	NUM
ejpam-3565	213	35	)	)	PUNCT
ejpam-3565	213	36	and	and	CCONJ
ejpam-3565	213	37	(	(	PUNCT
ejpam-3565	213	38	18	18	NUM
ejpam-3565	213	39	)	)	PUNCT
ejpam-3565	213	40	.	.	PUNCT
ejpam-3565	214	1	since	since	SCONJ
ejpam-3565	214	2	(	(	PUNCT
ejpam-3565	214	3	14	14	NUM
ejpam-3565	214	4	)	)	PUNCT
ejpam-3565	214	5	is	be	AUX
ejpam-3565	214	6	the	the	DET
ejpam-3565	214	7	same	same	ADJ
ejpam-3565	214	8	as	as	ADP
ejpam-3565	214	9	(	(	PUNCT
ejpam-3565	214	10	17	17	NUM
ejpam-3565	214	11	)	)	PUNCT
ejpam-3565	214	12	,	,	PUNCT
ejpam-3565	214	13	we	we	PRON
ejpam-3565	214	14	only	only	ADV
ejpam-3565	214	15	have	have	VERB
ejpam-3565	214	16	to	to	PART
ejpam-3565	214	17	look	look	VERB
ejpam-3565	214	18	at	at	ADP
ejpam-3565	214	19	(	(	PUNCT
ejpam-3565	214	20	15	15	NUM
ejpam-3565	214	21	)	)	PUNCT
ejpam-3565	214	22	.	.	PUNCT
ejpam-3565	215	1	it	it	PRON
ejpam-3565	215	2	then	then	ADV
ejpam-3565	215	3	follows	follow	VERB
ejpam-3565	215	4	that	that	SCONJ
ejpam-3565	215	5	the	the	DET
ejpam-3565	215	6	code	code	NOUN
ejpam-3565	215	7	c	c	PROPN
ejpam-3565	215	8	is	be	AUX
ejpam-3565	215	9	self	self	NOUN
ejpam-3565	215	10	-	-	PUNCT
ejpam-3565	215	11	dual	dual	ADJ
ejpam-3565	215	12	if	if	SCONJ
ejpam-3565	215	13	and	and	CCONJ
ejpam-3565	215	14	only	only	ADV
ejpam-3565	215	15	if	if	SCONJ
ejpam-3565	215	16	fij	fij	PROPN
ejpam-3565	215	17	+	+	CCONJ
ejpam-3565	215	18	ã30at	ã30at	NOUN
ejpam-3565	215	19	31	31	NUM
ejpam-3565	215	20	+	+	NUM
ejpam-3565	215	21	ã40at	ã40at	NUM
ejpam-3565	215	22	41	41	NUM
ejpam-3565	215	23	+	+	SYM
ejpam-3565	215	24	p(a31a	p(a31a	NOUN
ejpam-3565	215	25	t	t	NOUN
ejpam-3565	215	26	31	31	NUM
ejpam-3565	216	1	+	+	NOUN
ejpam-3565	216	2	a41a	a41a	NOUN
ejpam-3565	216	3	t	t	NOUN
ejpam-3565	216	4	41	41	NUM
ejpam-3565	216	5	+	+	CCONJ
ejpam-3565	216	6	ã40at	ã40at	NUM
ejpam-3565	216	7	42	42	NUM
ejpam-3565	216	8	)	)	PUNCT
ejpam-3565	216	9	≡	≡	PROPN
ejpam-3565	216	10	0	0	PUNCT
ejpam-3565	217	1	(	(	PUNCT
ejpam-3565	217	2	mod	mod	ADJ
ejpam-3565	217	3	p2	p2	PROPN
ejpam-3565	217	4	)	)	PUNCT
ejpam-3565	217	5	(	(	PUNCT
ejpam-3565	217	6	23	23	NUM
ejpam-3565	217	7	)	)	PUNCT
ejpam-3565	217	8	our	our	PRON
ejpam-3565	217	9	goal	goal	NOUN
ejpam-3565	217	10	is	be	AUX
ejpam-3565	217	11	to	to	PART
ejpam-3565	217	12	count	count	VERB
ejpam-3565	217	13	the	the	DET
ejpam-3565	217	14	number	number	NOUN
ejpam-3565	217	15	of	of	ADP
ejpam-3565	217	16	matrices	matrix	NOUN
ejpam-3565	217	17	a31	a31	NOUN
ejpam-3565	217	18	,	,	PUNCT
ejpam-3565	217	19	a41	a41	NOUN
ejpam-3565	217	20	and	and	CCONJ
ejpam-3565	217	21	a42	a42	NOUN
ejpam-3565	217	22	satisfying	satisfying	ADJ
ejpam-3565	217	23	(	(	PUNCT
ejpam-3565	217	24	23	23	NUM
ejpam-3565	217	25	)	)	PUNCT
ejpam-3565	217	26	.	.	PUNCT
ejpam-3565	218	1	t.	t.	PROPN
ejpam-3565	218	2	l.	l.	PROPN
ejpam-3565	218	3	vasquez	vasquez	PROPN
ejpam-3565	218	4	,	,	PUNCT
ejpam-3565	218	5	g.	g.	PROPN
ejpam-3565	218	6	petalcorin	petalcorin	PROPN
ejpam-3565	218	7	/	/	SYM
ejpam-3565	218	8	eur	eur	PROPN
ejpam-3565	218	9	.	.	PUNCT
ejpam-3565	219	1	j.	j.	PROPN
ejpam-3565	219	2	pure	pure	PROPN
ejpam-3565	219	3	appl	appl	PROPN
ejpam-3565	219	4	.	.	PROPN
ejpam-3565	219	5	math	math	PROPN
ejpam-3565	219	6	,	,	PUNCT
ejpam-3565	219	7	12	12	NUM
ejpam-3565	219	8	(	(	PUNCT
ejpam-3565	219	9	4	4	NUM
ejpam-3565	219	10	)	)	PUNCT
ejpam-3565	219	11	(	(	PUNCT
ejpam-3565	219	12	2019	2019	NUM
ejpam-3565	219	13	)	)	PUNCT
ejpam-3565	219	14	,	,	PUNCT
ejpam-3565	219	15	1701	1701	NUM
ejpam-3565	219	16	-	-	SYM
ejpam-3565	219	17	1716	1716	NUM
ejpam-3565	219	18	1708	1708	NUM
ejpam-3565	219	19	for	for	ADP
ejpam-3565	219	20	the	the	DET
ejpam-3565	219	21	remainder	remainder	NOUN
ejpam-3565	219	22	of	of	ADP
ejpam-3565	219	23	this	this	DET
ejpam-3565	219	24	paper	paper	NOUN
ejpam-3565	220	1	,	,	PUNCT
ejpam-3565	220	2	we	we	PRON
ejpam-3565	220	3	assume	assume	VERB
ejpam-3565	220	4	that	that	SCONJ
ejpam-3565	220	5	p	p	NOUN
ejpam-3565	220	6	is	be	AUX
ejpam-3565	220	7	an	an	DET
ejpam-3565	220	8	odd	odd	ADJ
ejpam-3565	220	9	prime	prime	NOUN
ejpam-3565	220	10	.	.	PUNCT
ejpam-3565	221	1	following	follow	VERB
ejpam-3565	221	2	the	the	DET
ejpam-3565	221	3	argument	argument	NOUN
ejpam-3565	221	4	in	in	ADP
ejpam-3565	221	5	section	section	NOUN
ejpam-3565	221	6	2.1	2.1	NUM
ejpam-3565	221	7	of	of	ADP
ejpam-3565	221	8	[	[	X
ejpam-3565	221	9	10	10	NUM
ejpam-3565	221	10	]	]	PUNCT
ejpam-3565	221	11	,	,	PUNCT
ejpam-3565	221	12	there	there	PRON
ejpam-3565	221	13	are	be	VERB
ejpam-3565	221	14	prkl	prkl	NOUN
ejpam-3565	221	15	possible	possible	ADJ
ejpam-3565	221	16	choices	choice	NOUN
ejpam-3565	221	17	for	for	ADP
ejpam-3565	221	18	a31	a31	NOUN
ejpam-3565	221	19	,	,	PUNCT
ejpam-3565	221	20	p	p	NOUN
ejpam-3565	221	21	rk(k−1	rk(k−1	NOUN
ejpam-3565	221	22	)	)	PUNCT
ejpam-3565	221	23	2	2	NUM
ejpam-3565	221	24	for	for	ADP
ejpam-3565	221	25	a41	a41	NOUN
ejpam-3565	221	26	and	and	CCONJ
ejpam-3565	221	27	p	p	NOUN
ejpam-3565	221	28	rk(k−1	rk(k−1	PROPN
ejpam-3565	221	29	)	)	PUNCT
ejpam-3565	221	30	2	2	NUM
ejpam-3565	221	31	for	for	ADP
ejpam-3565	221	32	a42	a42	NOUN
ejpam-3565	221	33	.	.	PUNCT
ejpam-3565	222	1	therefore	therefore	ADV
ejpam-3565	222	2	,	,	PUNCT
ejpam-3565	222	3	we	we	PRON
ejpam-3565	222	4	have	have	VERB
ejpam-3565	222	5	prk(n	prk(n	PROPN
ejpam-3565	222	6	2	2	NUM
ejpam-3565	222	7	−1	−1	NOUN
ejpam-3565	222	8	)	)	PUNCT
ejpam-3565	222	9	possible	possible	ADJ
ejpam-3565	222	10	choices	choice	NOUN
ejpam-3565	222	11	for	for	ADP
ejpam-3565	222	12	the	the	DET
ejpam-3565	222	13	matrices	matrix	NOUN
ejpam-3565	222	14	a31	a31	NOUN
ejpam-3565	222	15	,	,	PUNCT
ejpam-3565	222	16	a41	a41	NOUN
ejpam-3565	222	17	and	and	CCONJ
ejpam-3565	222	18	a42	a42	NOUN
ejpam-3565	222	19	.	.	PUNCT
ejpam-3565	223	1	we	we	PRON
ejpam-3565	223	2	have	have	AUX
ejpam-3565	223	3	proved	prove	VERB
ejpam-3565	223	4	the	the	DET
ejpam-3565	223	5	following	follow	VERB
ejpam-3565	223	6	result	result	NOUN
ejpam-3565	223	7	,	,	PUNCT
ejpam-3565	223	8	which	which	PRON
ejpam-3565	223	9	is	be	AUX
ejpam-3565	223	10	analogous	analogous	ADJ
ejpam-3565	223	11	to	to	PART
ejpam-3565	223	12	proposition	proposition	VERB
ejpam-3565	223	13	2.2	2.2	NUM
ejpam-3565	223	14	of	of	ADP
ejpam-3565	223	15	[	[	X
ejpam-3565	223	16	10	10	NUM
ejpam-3565	223	17	]	]	PUNCT
ejpam-3565	223	18	.	.	PUNCT
ejpam-3565	224	1	proposition	proposition	NOUN
ejpam-3565	224	2	2	2	NUM
ejpam-3565	224	3	.	.	PUNCT
ejpam-3565	224	4	let	let	VERB
ejpam-3565	224	5	p	p	PRON
ejpam-3565	224	6	be	be	AUX
ejpam-3565	224	7	an	an	DET
ejpam-3565	224	8	odd	odd	ADJ
ejpam-3565	224	9	prime	prime	NOUN
ejpam-3565	224	10	.	.	PUNCT
ejpam-3565	225	1	a	a	DET
ejpam-3565	225	2	self	self	NOUN
ejpam-3565	225	3	-	-	PUNCT
ejpam-3565	225	4	dual	dual	ADJ
ejpam-3565	225	5	code	code	NOUN
ejpam-3565	225	6	over	over	ADP
ejpam-3565	225	7	gr(p3	gr(p3	PROPN
ejpam-3565	225	8	,	,	PUNCT
ejpam-3565	225	9	r	r	NOUN
ejpam-3565	225	10	)	)	PUNCT
ejpam-3565	225	11	can	can	AUX
ejpam-3565	225	12	be	be	AUX
ejpam-3565	225	13	induced	induce	VERB
ejpam-3565	225	14	from	from	ADP
ejpam-3565	225	15	a	a	DET
ejpam-3565	225	16	self	self	NOUN
ejpam-3565	225	17	-	-	PUNCT
ejpam-3565	225	18	dual	dual	ADJ
ejpam-3565	225	19	code	code	NOUN
ejpam-3565	225	20	c1	c1	PROPN
ejpam-3565	225	21	over	over	ADP
ejpam-3565	225	22	fpr	fpr	PRON
ejpam-3565	225	23	.	.	PUNCT
ejpam-3565	226	1	there	there	PRON
ejpam-3565	226	2	are	be	VERB
ejpam-3565	226	3	prk(n	prk(n	PROPN
ejpam-3565	226	4	2	2	NUM
ejpam-3565	226	5	−1	−1	NOUN
ejpam-3565	226	6	)	)	PUNCT
ejpam-3565	226	7	self	self	NOUN
ejpam-3565	226	8	-	-	PUNCT
ejpam-3565	226	9	dual	dual	ADJ
ejpam-3565	226	10	codes	code	NOUN
ejpam-3565	226	11	over	over	ADP
ejpam-3565	226	12	gr(p3	gr(p3	PROPN
ejpam-3565	226	13	,	,	PUNCT
ejpam-3565	226	14	r	r	NOUN
ejpam-3565	226	15	)	)	PUNCT
ejpam-3565	226	16	of	of	ADP
ejpam-3565	226	17	length	length	NOUN
ejpam-3565	226	18	n	n	ADP
ejpam-3565	226	19	corresponding	correspond	VERB
ejpam-3565	226	20	to	to	ADP
ejpam-3565	226	21	each	each	DET
ejpam-3565	226	22	subspace	subspace	NOUN
ejpam-3565	226	23	of	of	ADP
ejpam-3565	226	24	c1	c1	PROPN
ejpam-3565	226	25	of	of	ADP
ejpam-3565	226	26	dimension	dimension	PROPN
ejpam-3565	226	27	k	k	PROPN
ejpam-3565	226	28	,	,	PUNCT
ejpam-3565	226	29	where	where	SCONJ
ejpam-3565	226	30	0	0	NUM
ejpam-3565	226	31	≤	≤	NUM
ejpam-3565	226	32	k	k	NOUN
ejpam-3565	226	33	≤	≤	NUM
ejpam-3565	226	34	n	n	DET
ejpam-3565	226	35	2	2	NUM
ejpam-3565	226	36	.	.	PUNCT
ejpam-3565	227	1	for	for	ADP
ejpam-3565	227	2	the	the	DET
ejpam-3565	227	3	sake	sake	NOUN
ejpam-3565	227	4	of	of	ADP
ejpam-3565	227	5	completeness	completeness	NOUN
ejpam-3565	227	6	,	,	PUNCT
ejpam-3565	227	7	we	we	PRON
ejpam-3565	227	8	describe	describe	VERB
ejpam-3565	227	9	the	the	DET
ejpam-3565	227	10	matrices	matrix	NOUN
ejpam-3565	227	11	a31	a31	NOUN
ejpam-3565	227	12	,	,	PUNCT
ejpam-3565	227	13	a41	a41	NOUN
ejpam-3565	227	14	and	and	CCONJ
ejpam-3565	227	15	a42	a42	PROPN
ejpam-3565	227	16	.	.	PUNCT
ejpam-3565	228	1	a31	a31	PROPN
ejpam-3565	228	2	is	be	AUX
ejpam-3565	228	3	an	an	DET
ejpam-3565	228	4	arbitrary	arbitrary	ADJ
ejpam-3565	228	5	k	k	NOUN
ejpam-3565	228	6	×	×	PROPN
ejpam-3565	228	7	l	l	NOUN
ejpam-3565	228	8	matrix	matrix	NOUN
ejpam-3565	228	9	with	with	ADP
ejpam-3565	228	10	entries	entry	NOUN
ejpam-3565	228	11	from	from	ADP
ejpam-3565	228	12	tpr	tpr	PROPN
ejpam-3565	228	13	,	,	PUNCT
ejpam-3565	228	14	a41	a41	PROPN
ejpam-3565	228	15	is	be	AUX
ejpam-3565	228	16	determined	determine	VERB
ejpam-3565	228	17	by	by	ADP
ejpam-3565	228	18	fij	fij	PROPN
ejpam-3565	229	1	+	+	CCONJ
ejpam-3565	229	2	ã30at	ã30at	NOUN
ejpam-3565	229	3	31	31	NUM
ejpam-3565	229	4	+	+	ADP
ejpam-3565	229	5	ã40at	ã40at	NUM
ejpam-3565	229	6	41	41	NUM
ejpam-3565	229	7	≡	≡	PROPN
ejpam-3565	229	8	0	0	PUNCT
ejpam-3565	230	1	(	(	PUNCT
ejpam-3565	230	2	mod	mod	PROPN
ejpam-3565	230	3	p	p	X
ejpam-3565	230	4	)	)	PUNCT
ejpam-3565	230	5	,	,	PUNCT
ejpam-3565	230	6	(	(	PUNCT
ejpam-3565	230	7	24	24	NUM
ejpam-3565	230	8	)	)	PUNCT
ejpam-3565	230	9	while	while	SCONJ
ejpam-3565	230	10	a42	a42	NOUN
ejpam-3565	230	11	is	be	AUX
ejpam-3565	230	12	determined	determine	VERB
ejpam-3565	230	13	by	by	ADP
ejpam-3565	230	14	(	(	PUNCT
ejpam-3565	230	15	hij	hij	NOUN
ejpam-3565	230	16	)	)	PUNCT
ejpam-3565	230	17	+	+	CCONJ
ejpam-3565	230	18	ã40at	ã40at	NUM
ejpam-3565	230	19	42	42	NUM
ejpam-3565	230	20	≡	≡	PROPN
ejpam-3565	230	21	0	0	NUM
ejpam-3565	231	1	(	(	PUNCT
ejpam-3565	231	2	mod	mod	PROPN
ejpam-3565	231	3	p	p	X
ejpam-3565	231	4	)	)	PUNCT
ejpam-3565	232	1	,	,	PUNCT
ejpam-3565	232	2	(	(	PUNCT
ejpam-3565	232	3	25	25	NUM
ejpam-3565	232	4	)	)	PUNCT
ejpam-3565	232	5	where	where	SCONJ
ejpam-3565	232	6	(	(	PUNCT
ejpam-3565	232	7	fij	fij	PROPN
ejpam-3565	232	8	)	)	PUNCT
ejpam-3565	233	1	+	+	CCONJ
ejpam-3565	233	2	ã30at	ã30at	NOUN
ejpam-3565	233	3	31	31	NUM
ejpam-3565	233	4	+	+	NUM
ejpam-3565	233	5	ã40at	ã40at	NUM
ejpam-3565	233	6	41	41	NUM
ejpam-3565	233	7	+	+	SYM
ejpam-3565	233	8	p(a31a	p(a31a	NOUN
ejpam-3565	233	9	t	t	NOUN
ejpam-3565	233	10	31	31	NUM
ejpam-3565	234	1	+	+	NOUN
ejpam-3565	234	2	a41a	a41a	NOUN
ejpam-3565	234	3	t	t	NOUN
ejpam-3565	234	4	41	41	NUM
ejpam-3565	234	5	)	)	PUNCT
ejpam-3565	234	6	=	=	SYM
ejpam-3565	234	7	p(hij	p(hij	NOUN
ejpam-3565	234	8	)	)	PUNCT
ejpam-3565	234	9	.	.	PUNCT
ejpam-3565	235	1	(	(	PUNCT
ejpam-3565	235	2	26	26	NUM
ejpam-3565	235	3	)	)	PUNCT
ejpam-3565	235	4	5	5	NUM
ejpam-3565	235	5	.	.	PUNCT
ejpam-3565	235	6	mass	mass	ADJ
ejpam-3565	235	7	formula	formula	NOUN
ejpam-3565	235	8	and	and	CCONJ
ejpam-3565	235	9	classification	classification	NOUN
ejpam-3565	235	10	recall	recall	NOUN
ejpam-3565	235	11	from	from	ADP
ejpam-3565	235	12	lemma	lemma	PROPN
ejpam-3565	235	13	1	1	NUM
ejpam-3565	235	14	that	that	SCONJ
ejpam-3565	235	15	σpr(n	σpr(n	PROPN
ejpam-3565	235	16	,	,	PUNCT
ejpam-3565	235	17	k	k	NOUN
ejpam-3565	235	18	)	)	PUNCT
ejpam-3565	235	19	is	be	AUX
ejpam-3565	235	20	the	the	DET
ejpam-3565	235	21	number	number	NOUN
ejpam-3565	235	22	of	of	ADP
ejpam-3565	235	23	self	self	NOUN
ejpam-3565	235	24	-	-	PUNCT
ejpam-3565	235	25	orthogonal	orthogonal	ADJ
ejpam-3565	235	26	codes	code	NOUN
ejpam-3565	235	27	of	of	ADP
ejpam-3565	235	28	even	even	ADV
ejpam-3565	235	29	length	length	NOUN
ejpam-3565	235	30	n	n	PROPN
ejpam-3565	235	31	and	and	CCONJ
ejpam-3565	235	32	dimension	dimension	NOUN
ejpam-3565	235	33	k	k	PROPN
ejpam-3565	235	34	over	over	ADP
ejpam-3565	235	35	fpr	fpr	PRON
ejpam-3565	235	36	.	.	PUNCT
ejpam-3565	236	1	also	also	ADV
ejpam-3565	236	2	,	,	PUNCT
ejpam-3565	236	3	from	from	ADP
ejpam-3565	236	4	lemma	lemma	PROPN
ejpam-3565	236	5	2	2	NUM
ejpam-3565	236	6	,	,	PUNCT
ejpam-3565	236	7	(	(	PUNCT
ejpam-3565	236	8	n	n	X
ejpam-3565	236	9	k	k	NOUN
ejpam-3565	236	10	)	)	PUNCT
ejpam-3565	236	11	pr	pr	NOUN
ejpam-3565	236	12	is	be	AUX
ejpam-3565	236	13	the	the	DET
ejpam-3565	236	14	number	number	NOUN
ejpam-3565	236	15	of	of	ADP
ejpam-3565	236	16	kdimensional	kdimensional	ADJ
ejpam-3565	236	17	subspaces	subspace	NOUN
ejpam-3565	236	18	of	of	ADP
ejpam-3565	236	19	an	an	DET
ejpam-3565	236	20	n	n	ADV
ejpam-3565	236	21	-	-	PUNCT
ejpam-3565	236	22	dimensional	dimensional	ADJ
ejpam-3565	236	23	vector	vector	NOUN
ejpam-3565	236	24	space	space	NOUN
ejpam-3565	236	25	over	over	ADP
ejpam-3565	236	26	fpr	fpr	NOUN
ejpam-3565	236	27	,	,	PUNCT
ejpam-3565	236	28	where	where	SCONJ
ejpam-3565	236	29	0	0	NUM
ejpam-3565	236	30	≤	≤	NUM
ejpam-3565	236	31	k	k	X
ejpam-3565	236	32	≤	≤	PROPN
ejpam-3565	236	33	n.	n.	NOUN
ejpam-3565	236	34	the	the	DET
ejpam-3565	236	35	following	follow	VERB
ejpam-3565	236	36	theorem	theorem	NOUN
ejpam-3565	236	37	gives	give	VERB
ejpam-3565	236	38	the	the	DET
ejpam-3565	236	39	mass	mass	ADJ
ejpam-3565	236	40	formula	formula	NOUN
ejpam-3565	236	41	for	for	ADP
ejpam-3565	236	42	self	self	NOUN
ejpam-3565	236	43	-	-	PUNCT
ejpam-3565	236	44	dual	dual	ADJ
ejpam-3565	236	45	codes	code	NOUN
ejpam-3565	236	46	over	over	ADP
ejpam-3565	236	47	gr(p3	gr(p3	PROPN
ejpam-3565	236	48	,	,	PUNCT
ejpam-3565	236	49	r	r	NOUN
ejpam-3565	236	50	)	)	PUNCT
ejpam-3565	236	51	.	.	PUNCT
ejpam-3565	237	1	theorem	theorem	NOUN
ejpam-3565	237	2	1	1	NUM
ejpam-3565	237	3	.	.	PUNCT
ejpam-3565	238	1	let	let	VERB
ejpam-3565	238	2	p	p	PRON
ejpam-3565	238	3	be	be	AUX
ejpam-3565	238	4	an	an	DET
ejpam-3565	238	5	odd	odd	ADJ
ejpam-3565	238	6	prime	prime	NOUN
ejpam-3565	238	7	and	and	CCONJ
ejpam-3565	238	8	let	let	VERB
ejpam-3565	238	9	np3,r(n	np3,r(n	NOUN
ejpam-3565	238	10	)	)	PUNCT
ejpam-3565	238	11	denote	denote	VERB
ejpam-3565	238	12	the	the	DET
ejpam-3565	238	13	number	number	NOUN
ejpam-3565	238	14	of	of	ADP
ejpam-3565	238	15	distinct	distinct	ADJ
ejpam-3565	238	16	self	self	NOUN
ejpam-3565	238	17	-	-	PUNCT
ejpam-3565	238	18	dual	dual	ADJ
ejpam-3565	238	19	codes	code	NOUN
ejpam-3565	238	20	of	of	ADP
ejpam-3565	238	21	even	even	ADV
ejpam-3565	238	22	length	length	NOUN
ejpam-3565	238	23	n	n	NOUN
ejpam-3565	238	24	=	=	SYM
ejpam-3565	238	25	2	2	NUM
ejpam-3565	238	26	m	m	NOUN
ejpam-3565	238	27	over	over	ADP
ejpam-3565	238	28	gr(p3	gr(p3	PROPN
ejpam-3565	238	29	,	,	PUNCT
ejpam-3565	238	30	r	r	NOUN
ejpam-3565	238	31	)	)	PUNCT
ejpam-3565	238	32	.	.	PUNCT
ejpam-3565	239	1	then	then	ADV
ejpam-3565	239	2	np3,r(n	np3,r(n	X
ejpam-3565	239	3	)	)	PUNCT
ejpam-3565	239	4	=	=	SYM
ejpam-3565	239	5	σpr	σpr	X
ejpam-3565	239	6	(	(	PUNCT
ejpam-3565	239	7	n	n	CCONJ
ejpam-3565	239	8	,	,	PUNCT
ejpam-3565	239	9	m	m	NOUN
ejpam-3565	239	10	)	)	PUNCT
ejpam-3565	239	11	m∑	m∑	CCONJ
ejpam-3565	239	12	k=0	k=0	PROPN
ejpam-3565	239	13	(	(	PUNCT
ejpam-3565	239	14	m	m	VERB
ejpam-3565	239	15	k	k	NOUN
ejpam-3565	239	16	)	)	PUNCT
ejpam-3565	239	17	pr	pr	VERB
ejpam-3565	239	18	prk(n/2−1	prk(n/2−1	NOUN
ejpam-3565	239	19	)	)	PUNCT
ejpam-3565	239	20	.	.	PUNCT
ejpam-3565	240	1	proof	proof	NOUN
ejpam-3565	240	2	.	.	PUNCT
ejpam-3565	241	1	from	from	ADP
ejpam-3565	241	2	lemma	lemma	PROPN
ejpam-3565	241	3	1	1	NUM
ejpam-3565	241	4	,	,	PUNCT
ejpam-3565	241	5	there	there	PRON
ejpam-3565	241	6	are	be	VERB
ejpam-3565	241	7	σpr(n	σpr(n	PROPN
ejpam-3565	241	8	,	,	PUNCT
ejpam-3565	241	9	m	m	NOUN
ejpam-3565	241	10	)	)	PUNCT
ejpam-3565	241	11	self	self	NOUN
ejpam-3565	241	12	-	-	PUNCT
ejpam-3565	241	13	dual	dual	ADJ
ejpam-3565	241	14	codes	code	NOUN
ejpam-3565	241	15	of	of	ADP
ejpam-3565	241	16	length	length	NOUN
ejpam-3565	241	17	n	n	NOUN
ejpam-3565	241	18	over	over	ADP
ejpam-3565	241	19	fpr	fpr	NOUN
ejpam-3565	241	20	.	.	PUNCT
ejpam-3565	242	1	let	let	VERB
ejpam-3565	242	2	c1	c1	PROPN
ejpam-3565	242	3	be	be	AUX
ejpam-3565	242	4	one	one	NUM
ejpam-3565	242	5	such	such	ADJ
ejpam-3565	242	6	self	self	NOUN
ejpam-3565	242	7	-	-	PUNCT
ejpam-3565	242	8	dual	dual	ADJ
ejpam-3565	242	9	code	code	NOUN
ejpam-3565	242	10	.	.	PUNCT
ejpam-3565	243	1	lemma	lemma	PROPN
ejpam-3565	243	2	2	2	PROPN
ejpam-3565	243	3	tells	tell	VERB
ejpam-3565	243	4	us	we	PRON
ejpam-3565	243	5	that	that	SCONJ
ejpam-3565	243	6	there	there	PRON
ejpam-3565	243	7	are	be	VERB
ejpam-3565	243	8	(	(	PUNCT
ejpam-3565	243	9	m	m	PROPN
ejpam-3565	243	10	k	k	NOUN
ejpam-3565	243	11	)	)	PUNCT
ejpam-3565	243	12	pr	pr	NOUN
ejpam-3565	243	13	subspaces	subspace	NOUN
ejpam-3565	243	14	c0	c0	PROPN
ejpam-3565	243	15	⊆	⊆	NUM
ejpam-3565	243	16	c1	c1	NOUN
ejpam-3565	243	17	of	of	ADP
ejpam-3565	243	18	dimension	dimension	PROPN
ejpam-3565	243	19	k	k	PROPN
ejpam-3565	243	20	,	,	PUNCT
ejpam-3565	243	21	where	where	SCONJ
ejpam-3565	243	22	0	0	NUM
ejpam-3565	243	23	≤	≤	NUM
ejpam-3565	243	24	k	k	X
ejpam-3565	243	25	≤	≤	PROPN
ejpam-3565	243	26	m.	m.	NOUN
ejpam-3565	243	27	finally	finally	ADV
ejpam-3565	243	28	,	,	PUNCT
ejpam-3565	243	29	from	from	ADP
ejpam-3565	243	30	proposition	proposition	NOUN
ejpam-3565	243	31	2	2	NUM
ejpam-3565	243	32	,	,	PUNCT
ejpam-3565	243	33	there	there	PRON
ejpam-3565	243	34	are	be	VERB
ejpam-3565	243	35	prk(m−1	prk(m−1	NOUN
ejpam-3565	243	36	)	)	PUNCT
ejpam-3565	243	37	self	self	NOUN
ejpam-3565	243	38	-	-	PUNCT
ejpam-3565	243	39	dual	dual	ADJ
ejpam-3565	243	40	codes	code	NOUN
ejpam-3565	243	41	over	over	ADP
ejpam-3565	243	42	gr(p3	gr(p3	PROPN
ejpam-3565	243	43	,	,	PUNCT
ejpam-3565	243	44	r	r	NOUN
ejpam-3565	243	45	)	)	PUNCT
ejpam-3565	243	46	corresponding	correspond	VERB
ejpam-3565	243	47	to	to	ADP
ejpam-3565	243	48	c0	c0	PROPN
ejpam-3565	243	49	.	.	PUNCT
ejpam-3565	244	1	the	the	DET
ejpam-3565	244	2	result	result	NOUN
ejpam-3565	244	3	immediately	immediately	ADV
ejpam-3565	244	4	follows	follow	VERB
ejpam-3565	244	5	.	.	PUNCT
ejpam-3565	245	1	when	when	SCONJ
ejpam-3565	245	2	r	r	NOUN
ejpam-3565	245	3	=	=	SYM
ejpam-3565	245	4	1	1	NUM
ejpam-3565	245	5	,	,	PUNCT
ejpam-3565	245	6	theorem	theorem	VERB
ejpam-3565	245	7	1	1	NUM
ejpam-3565	245	8	coincides	coincide	VERB
ejpam-3565	245	9	with	with	ADP
ejpam-3565	245	10	the	the	DET
ejpam-3565	245	11	result	result	NOUN
ejpam-3565	245	12	in	in	ADP
ejpam-3565	245	13	[	[	X
ejpam-3565	245	14	10	10	NUM
ejpam-3565	245	15	]	]	PUNCT
ejpam-3565	245	16	for	for	ADP
ejpam-3565	245	17	zp3	zp3	X
ejpam-3565	245	18	.	.	PUNCT
ejpam-3565	246	1	we	we	PRON
ejpam-3565	246	2	now	now	ADV
ejpam-3565	246	3	give	give	VERB
ejpam-3565	246	4	a	a	DET
ejpam-3565	246	5	classification	classification	NOUN
ejpam-3565	246	6	of	of	ADP
ejpam-3565	246	7	self	self	NOUN
ejpam-3565	246	8	-	-	PUNCT
ejpam-3565	246	9	dual	dual	ADJ
ejpam-3565	246	10	codes	code	NOUN
ejpam-3565	246	11	over	over	ADP
ejpam-3565	246	12	gr(p3	gr(p3	PROPN
ejpam-3565	246	13	,	,	PUNCT
ejpam-3565	246	14	2	2	NUM
ejpam-3565	246	15	)	)	PUNCT
ejpam-3565	246	16	of	of	ADP
ejpam-3565	246	17	length	length	NOUN
ejpam-3565	246	18	4	4	NUM
ejpam-3565	246	19	for	for	ADP
ejpam-3565	246	20	p	p	NOUN
ejpam-3565	246	21	=	=	SYM
ejpam-3565	246	22	3	3	NUM
ejpam-3565	246	23	,	,	PUNCT
ejpam-3565	246	24	5	5	NUM
ejpam-3565	246	25	.	.	PUNCT
ejpam-3565	247	1	our	our	PRON
ejpam-3565	247	2	goal	goal	NOUN
ejpam-3565	247	3	is	be	AUX
ejpam-3565	247	4	to	to	PART
ejpam-3565	247	5	find	find	VERB
ejpam-3565	247	6	a	a	DET
ejpam-3565	247	7	representative	representative	NOUN
ejpam-3565	247	8	for	for	ADP
ejpam-3565	247	9	each	each	DET
ejpam-3565	247	10	equivalence	equivalence	NOUN
ejpam-3565	247	11	classes	class	NOUN
ejpam-3565	247	12	of	of	ADP
ejpam-3565	247	13	codes	code	NOUN
ejpam-3565	247	14	.	.	PUNCT
ejpam-3565	248	1	in	in	ADP
ejpam-3565	248	2	defining	define	VERB
ejpam-3565	248	3	the	the	DET
ejpam-3565	248	4	equivalence	equivalence	NOUN
ejpam-3565	248	5	of	of	ADP
ejpam-3565	248	6	codes	code	NOUN
ejpam-3565	248	7	over	over	ADP
ejpam-3565	248	8	gr(p3	gr(p3	PROPN
ejpam-3565	248	9	,	,	PUNCT
ejpam-3565	248	10	2	2	NUM
ejpam-3565	248	11	)	)	PUNCT
ejpam-3565	248	12	,	,	PUNCT
ejpam-3565	248	13	we	we	PRON
ejpam-3565	248	14	allow	allow	VERB
ejpam-3565	248	15	permutation	permutation	NOUN
ejpam-3565	248	16	of	of	ADP
ejpam-3565	248	17	coordinates	coordinate	NOUN
ejpam-3565	248	18	and	and	CCONJ
ejpam-3565	248	19	(	(	PUNCT
ejpam-3565	248	20	if	if	SCONJ
ejpam-3565	248	21	necessary	necessary	ADJ
ejpam-3565	248	22	)	)	PUNCT
ejpam-3565	248	23	multiplying	multiply	VERB
ejpam-3565	248	24	certain	certain	ADJ
ejpam-3565	248	25	coordinates	coordinate	NOUN
ejpam-3565	248	26	by	by	ADP
ejpam-3565	248	27	−1	−1	NOUN
ejpam-3565	248	28	.	.	PUNCT
ejpam-3565	249	1	all	all	DET
ejpam-3565	249	2	computations	computation	NOUN
ejpam-3565	249	3	for	for	ADP
ejpam-3565	249	4	this	this	DET
ejpam-3565	249	5	paper	paper	NOUN
ejpam-3565	249	6	were	be	AUX
ejpam-3565	249	7	done	do	VERB
ejpam-3565	249	8	with	with	ADP
ejpam-3565	249	9	the	the	DET
ejpam-3565	249	10	computer	computer	NOUN
ejpam-3565	249	11	algebra	algebra	NOUN
ejpam-3565	249	12	package	package	NOUN
ejpam-3565	249	13	magma	magma	NOUN
ejpam-3565	249	14	[	[	X
ejpam-3565	249	15	2	2	NUM
ejpam-3565	249	16	]	]	PUNCT
ejpam-3565	249	17	.	.	PUNCT
ejpam-3565	250	1	t.	t.	PROPN
ejpam-3565	250	2	l.	l.	PROPN
ejpam-3565	250	3	vasquez	vasquez	PROPN
ejpam-3565	250	4	,	,	PUNCT
ejpam-3565	250	5	g.	g.	PROPN
ejpam-3565	250	6	petalcorin	petalcorin	PROPN
ejpam-3565	250	7	/	/	SYM
ejpam-3565	250	8	eur	eur	PROPN
ejpam-3565	250	9	.	.	PUNCT
ejpam-3565	251	1	j.	j.	PROPN
ejpam-3565	251	2	pure	pure	PROPN
ejpam-3565	251	3	appl	appl	PROPN
ejpam-3565	251	4	.	.	PROPN
ejpam-3565	251	5	math	math	PROPN
ejpam-3565	251	6	,	,	PUNCT
ejpam-3565	251	7	12	12	NUM
ejpam-3565	251	8	(	(	PUNCT
ejpam-3565	251	9	4	4	NUM
ejpam-3565	251	10	)	)	PUNCT
ejpam-3565	251	11	(	(	PUNCT
ejpam-3565	251	12	2019	2019	NUM
ejpam-3565	251	13	)	)	PUNCT
ejpam-3565	251	14	,	,	PUNCT
ejpam-3565	251	15	1701	1701	NUM
ejpam-3565	251	16	-	-	SYM
ejpam-3565	251	17	1716	1716	NUM
ejpam-3565	251	18	1709	1709	NUM
ejpam-3565	251	19	5.1	5.1	NUM
ejpam-3565	251	20	.	.	PUNCT
ejpam-3565	252	1	building	build	VERB
ejpam-3565	252	2	-	-	PUNCT
ejpam-3565	252	3	up	up	ADP
ejpam-3565	252	4	using	use	VERB
ejpam-3565	252	5	the	the	DET
ejpam-3565	252	6	construction	construction	NOUN
ejpam-3565	252	7	method	method	NOUN
ejpam-3565	252	8	discussed	discuss	VERB
ejpam-3565	252	9	in	in	ADP
ejpam-3565	252	10	section	section	NOUN
ejpam-3565	252	11	4	4	NUM
ejpam-3565	252	12	,	,	PUNCT
ejpam-3565	252	13	a	a	DET
ejpam-3565	252	14	general	general	ADJ
ejpam-3565	252	15	way	way	NOUN
ejpam-3565	252	16	to	to	PART
ejpam-3565	252	17	construct	construct	VERB
ejpam-3565	252	18	selfdual	selfdual	ADJ
ejpam-3565	252	19	codes	code	NOUN
ejpam-3565	252	20	over	over	ADP
ejpam-3565	252	21	gr(p3	gr(p3	PROPN
ejpam-3565	252	22	,	,	PUNCT
ejpam-3565	252	23	2	2	NUM
ejpam-3565	252	24	)	)	PUNCT
ejpam-3565	252	25	of	of	ADP
ejpam-3565	252	26	length	length	NOUN
ejpam-3565	252	27	4	4	NUM
ejpam-3565	252	28	can	can	AUX
ejpam-3565	252	29	be	be	AUX
ejpam-3565	252	30	described	describe	VERB
ejpam-3565	252	31	.	.	PUNCT
ejpam-3565	253	1	note	note	VERB
ejpam-3565	253	2	that	that	SCONJ
ejpam-3565	253	3	a	a	DET
ejpam-3565	253	4	self	self	NOUN
ejpam-3565	253	5	-	-	PUNCT
ejpam-3565	253	6	dual	dual	ADJ
ejpam-3565	253	7	code	code	NOUN
ejpam-3565	253	8	of	of	ADP
ejpam-3565	253	9	length	length	NOUN
ejpam-3565	253	10	4	4	NUM
ejpam-3565	253	11	over	over	ADP
ejpam-3565	253	12	gr(p3	gr(p3	PROPN
ejpam-3565	253	13	,	,	PUNCT
ejpam-3565	253	14	2	2	NUM
ejpam-3565	253	15	)	)	PUNCT
ejpam-3565	253	16	has	have	VERB
ejpam-3565	253	17	one	one	NUM
ejpam-3565	253	18	of	of	ADP
ejpam-3565	253	19	the	the	DET
ejpam-3565	253	20	following	following	ADJ
ejpam-3565	253	21	three	three	NUM
ejpam-3565	253	22	types	type	NOUN
ejpam-3565	253	23	:	:	PUNCT
ejpam-3565	253	24	{	{	PUNCT
ejpam-3565	253	25	0	0	NUM
ejpam-3565	253	26	,	,	PUNCT
ejpam-3565	253	27	2	2	NUM
ejpam-3565	253	28	,	,	PUNCT
ejpam-3565	253	29	2	2	NUM
ejpam-3565	253	30	}	}	PUNCT
ejpam-3565	253	31	,	,	PUNCT
ejpam-3565	253	32	{	{	PUNCT
ejpam-3565	253	33	1	1	NUM
ejpam-3565	253	34	,	,	PUNCT
ejpam-3565	253	35	1	1	NUM
ejpam-3565	253	36	,	,	PUNCT
ejpam-3565	253	37	1	1	NUM
ejpam-3565	253	38	}	}	PUNCT
ejpam-3565	253	39	or	or	CCONJ
ejpam-3565	253	40	{	{	PUNCT
ejpam-3565	253	41	2	2	NUM
ejpam-3565	253	42	,	,	PUNCT
ejpam-3565	253	43	0	0	NUM
ejpam-3565	253	44	,	,	PUNCT
ejpam-3565	253	45	0	0	NUM
ejpam-3565	253	46	}	}	PUNCT
ejpam-3565	253	47	.	.	PUNCT
ejpam-3565	254	1	we	we	PRON
ejpam-3565	254	2	start	start	VERB
ejpam-3565	254	3	with	with	ADP
ejpam-3565	254	4	a	a	DET
ejpam-3565	254	5	self	self	NOUN
ejpam-3565	254	6	-	-	PUNCT
ejpam-3565	254	7	dual	dual	ADJ
ejpam-3565	254	8	code	code	NOUN
ejpam-3565	254	9	c[4]p	c[4]p	NOUN
ejpam-3565	254	10	over	over	ADP
ejpam-3565	254	11	fp2	fp2	PROPN
ejpam-3565	254	12	of	of	ADP
ejpam-3565	254	13	length	length	NOUN
ejpam-3565	254	14	4	4	NUM
ejpam-3565	254	15	with	with	ADP
ejpam-3565	254	16	generator	generator	NOUN
ejpam-3565	254	17	matrix	matrix	NOUN
ejpam-3565	254	18	[	[	X
ejpam-3565	254	19	i2	i2	PROPN
ejpam-3565	254	20	a	a	X
ejpam-3565	254	21	]	]	X
ejpam-3565	254	22	,	,	PUNCT
ejpam-3565	254	23	where	where	SCONJ
ejpam-3565	254	24	a	a	PRON
ejpam-3565	254	25	is	be	AUX
ejpam-3565	254	26	a	a	DET
ejpam-3565	254	27	2	2	NUM
ejpam-3565	254	28	×	×	NOUN
ejpam-3565	254	29	2	2	NUM
ejpam-3565	254	30	matrix	matrix	NOUN
ejpam-3565	254	31	over	over	ADP
ejpam-3565	254	32	fp2	fp2	PROPN
ejpam-3565	254	33	and	and	CCONJ
ejpam-3565	254	34	aat	aat	PROPN
ejpam-3565	254	35	≡	≡	PROPN
ejpam-3565	254	36	−i2	−i2	PROPN
ejpam-3565	254	37	(	(	PUNCT
ejpam-3565	254	38	mod	mod	PROPN
ejpam-3565	254	39	p	p	X
ejpam-3565	254	40	)	)	PUNCT
ejpam-3565	254	41	.	.	PUNCT
ejpam-3565	255	1	let	let	VERB
ejpam-3565	255	2	c[4,k]p	c[4,k]p	PRON
ejpam-3565	255	3	be	be	AUX
ejpam-3565	255	4	a	a	DET
ejpam-3565	255	5	self	self	NOUN
ejpam-3565	255	6	-	-	PUNCT
ejpam-3565	255	7	dual	dual	ADJ
ejpam-3565	255	8	code	code	NOUN
ejpam-3565	255	9	over	over	ADP
ejpam-3565	255	10	gr(p3	gr(p3	PROPN
ejpam-3565	255	11	,	,	PUNCT
ejpam-3565	255	12	2	2	NUM
ejpam-3565	255	13	)	)	PUNCT
ejpam-3565	255	14	of	of	ADP
ejpam-3565	255	15	length	length	NOUN
ejpam-3565	255	16	4	4	NUM
ejpam-3565	255	17	and	and	CCONJ
ejpam-3565	255	18	type	type	NOUN
ejpam-3565	255	19	{	{	PUNCT
ejpam-3565	255	20	k	k	NOUN
ejpam-3565	255	21	,	,	PUNCT
ejpam-3565	255	22	l	l	NOUN
ejpam-3565	255	23	,	,	PUNCT
ejpam-3565	255	24	l	l	NOUN
ejpam-3565	255	25	}	}	PUNCT
ejpam-3565	255	26	induced	induce	VERB
ejpam-3565	255	27	from	from	ADP
ejpam-3565	255	28	c[4]p	c[4]p	NOUN
ejpam-3565	255	29	,	,	PUNCT
ejpam-3565	255	30	where	where	SCONJ
ejpam-3565	255	31	k	k	PROPN
ejpam-3565	255	32	=	=	SYM
ejpam-3565	255	33	0	0	NUM
ejpam-3565	255	34	,	,	PUNCT
ejpam-3565	255	35	1	1	NUM
ejpam-3565	255	36	,	,	PUNCT
ejpam-3565	255	37	2	2	NUM
ejpam-3565	255	38	and	and	CCONJ
ejpam-3565	255	39	l	l	NOUN
ejpam-3565	255	40	=	=	SYM
ejpam-3565	255	41	2−	2−	NUM
ejpam-3565	255	42	k.	k.	NOUN
ejpam-3565	255	43	for	for	ADP
ejpam-3565	255	44	α	α	PROPN
ejpam-3565	255	45	∈	∈	PROPN
ejpam-3565	255	46	fpr	fpr	NOUN
ejpam-3565	255	47	,	,	PUNCT
ejpam-3565	255	48	we	we	PRON
ejpam-3565	255	49	denote	denote	VERB
ejpam-3565	255	50	by	by	ADP
ejpam-3565	255	51	α̂	α̂	NOUN
ejpam-3565	255	52	the	the	DET
ejpam-3565	255	53	element	element	NOUN
ejpam-3565	255	54	in	in	ADP
ejpam-3565	255	55	tpr	tpr	NOUN
ejpam-3565	255	56	such	such	ADJ
ejpam-3565	255	57	that	that	PRON
ejpam-3565	255	58	α̂	α̂	NUM
ejpam-3565	256	1	=	=	SYM
ejpam-3565	256	2	α	α	X
ejpam-3565	256	3	.	.	PUNCT
ejpam-3565	256	4	given	give	VERB
ejpam-3565	256	5	a	a	DET
ejpam-3565	256	6	matrix	matrix	NOUN
ejpam-3565	256	7	m	m	NOUN
ejpam-3565	256	8	=	=	PUNCT
ejpam-3565	256	9	(	(	PUNCT
ejpam-3565	256	10	αij	αij	NOUN
ejpam-3565	256	11	)	)	PUNCT
ejpam-3565	256	12	over	over	ADP
ejpam-3565	256	13	fpr	fpr	NOUN
ejpam-3565	256	14	,	,	PUNCT
ejpam-3565	256	15	we	we	PRON
ejpam-3565	256	16	denote	denote	VERB
ejpam-3565	256	17	by	by	ADP
ejpam-3565	256	18	m̂	m̂	PROPN
ejpam-3565	256	19	the	the	DET
ejpam-3565	256	20	matrix	matrix	NOUN
ejpam-3565	256	21	(	(	PUNCT
ejpam-3565	256	22	α̂ij	α̂ij	NOUN
ejpam-3565	256	23	)	)	PUNCT
ejpam-3565	256	24	over	over	ADP
ejpam-3565	256	25	tpr	tpr	PROPN
ejpam-3565	256	26	.	.	PUNCT
ejpam-3565	257	1	proposition	proposition	NOUN
ejpam-3565	257	2	3	3	NUM
ejpam-3565	257	3	.	.	PUNCT
ejpam-3565	258	1	c[4,0]p	c[4,0]p	NOUN
ejpam-3565	258	2	has	have	VERB
ejpam-3565	258	3	generator	generator	NOUN
ejpam-3565	258	4	matrix	matrix	NOUN
ejpam-3565	258	5	mp(â	mp(â	NOUN
ejpam-3565	258	6	)	)	PUNCT
ejpam-3565	258	7	=	=	PUNCT
ejpam-3565	259	1	[	[	PUNCT
ejpam-3565	259	2	pi2	pi2	NUM
ejpam-3565	259	3	pâ	pâ	PROPN
ejpam-3565	259	4	0	0	PUNCT
ejpam-3565	260	1	p2i2	p2i2	X
ejpam-3565	260	2	]	]	PUNCT
ejpam-3565	260	3	.	.	PUNCT
ejpam-3565	261	1	proof	proof	NOUN
ejpam-3565	261	2	.	.	PUNCT
ejpam-3565	262	1	this	this	PRON
ejpam-3565	262	2	immediately	immediately	ADV
ejpam-3565	262	3	follows	follow	VERB
ejpam-3565	262	4	from	from	ADP
ejpam-3565	262	5	the	the	DET
ejpam-3565	262	6	construction	construction	NOUN
ejpam-3565	262	7	method	method	NOUN
ejpam-3565	262	8	discussed	discuss	VERB
ejpam-3565	262	9	in	in	ADP
ejpam-3565	262	10	section	section	NOUN
ejpam-3565	262	11	4	4	NUM
ejpam-3565	262	12	,	,	PUNCT
ejpam-3565	262	13	where	where	SCONJ
ejpam-3565	262	14	we	we	PRON
ejpam-3565	262	15	take	take	VERB
ejpam-3565	262	16	k	k	NOUN
ejpam-3565	262	17	=	=	PUNCT
ejpam-3565	262	18	0	0	NUM
ejpam-3565	262	19	and	and	CCONJ
ejpam-3565	262	20	l	l	NOUN
ejpam-3565	262	21	=	=	NOUN
ejpam-3565	263	1	2	2	X
ejpam-3565	263	2	.	.	X
ejpam-3565	263	3	we	we	PRON
ejpam-3565	263	4	now	now	ADV
ejpam-3565	263	5	describe	describe	VERB
ejpam-3565	263	6	the	the	DET
ejpam-3565	263	7	generator	generator	NOUN
ejpam-3565	263	8	matrix	matrix	NOUN
ejpam-3565	263	9	of	of	ADP
ejpam-3565	263	10	c[4,1]p	c[4,1]p	PROPN
ejpam-3565	263	11	.	.	PUNCT
ejpam-3565	264	1	let	let	VERB
ejpam-3565	264	2	a1	a1	PROPN
ejpam-3565	264	3	∈	∈	PROPN
ejpam-3565	264	4	fp2	fp2	X
ejpam-3565	264	5	.	.	PUNCT
ejpam-3565	265	1	by	by	ADP
ejpam-3565	265	2	adding	add	VERB
ejpam-3565	265	3	a1	a1	NOUN
ejpam-3565	265	4	times	time	NOUN
ejpam-3565	265	5	the	the	DET
ejpam-3565	265	6	second	second	ADJ
ejpam-3565	265	7	row	row	NOUN
ejpam-3565	265	8	of	of	ADP
ejpam-3565	265	9	the	the	DET
ejpam-3565	265	10	matrix	matrix	NOUN
ejpam-3565	265	11	[	[	X
ejpam-3565	265	12	i2	i2	PROPN
ejpam-3565	265	13	a	a	X
ejpam-3565	265	14	]	]	X
ejpam-3565	265	15	to	to	ADP
ejpam-3565	265	16	its	its	PRON
ejpam-3565	265	17	first	first	ADJ
ejpam-3565	265	18	row	row	NOUN
ejpam-3565	265	19	,	,	PUNCT
ejpam-3565	265	20	and	and	CCONJ
ejpam-3565	265	21	permuting	permute	VERB
ejpam-3565	265	22	the	the	DET
ejpam-3565	265	23	last	last	ADJ
ejpam-3565	265	24	two	two	NUM
ejpam-3565	265	25	columns	column	NOUN
ejpam-3565	265	26	whenever	whenever	SCONJ
ejpam-3565	265	27	necessary	necessary	ADJ
ejpam-3565	265	28	so	so	SCONJ
ejpam-3565	265	29	that	that	SCONJ
ejpam-3565	265	30	the	the	DET
ejpam-3565	265	31	(	(	PUNCT
ejpam-3565	265	32	1,4	1,4	NUM
ejpam-3565	265	33	)	)	PUNCT
ejpam-3565	265	34	entry	entry	NOUN
ejpam-3565	265	35	is	be	AUX
ejpam-3565	265	36	nonzero	nonzero	ADJ
ejpam-3565	265	37	,	,	PUNCT
ejpam-3565	265	38	we	we	PRON
ejpam-3565	265	39	obtain	obtain	VERB
ejpam-3565	265	40	a	a	DET
ejpam-3565	265	41	matrix	matrix	NOUN
ejpam-3565	265	42	over	over	ADP
ejpam-3565	265	43	fp2	fp2	PROPN
ejpam-3565	265	44	of	of	ADP
ejpam-3565	265	45	the	the	DET
ejpam-3565	265	46	form	form	NOUN
ejpam-3565	265	47	g	g	NOUN
ejpam-3565	265	48	=	=	PUNCT
ejpam-3565	265	49	[	[	PUNCT
ejpam-3565	265	50	1	1	NUM
ejpam-3565	265	51	a1	a1	NOUN
ejpam-3565	265	52	b1	b1	NOUN
ejpam-3565	265	53	c1	c1	PROPN
ejpam-3565	265	54	0	0	NUM
ejpam-3565	265	55	1	1	NUM
ejpam-3565	265	56	d1	d1	NOUN
ejpam-3565	265	57	e1	e1	PROPN
ejpam-3565	265	58	]	]	PUNCT
ejpam-3565	265	59	,	,	PUNCT
ejpam-3565	265	60	where	where	SCONJ
ejpam-3565	265	61	a1	a1	NOUN
ejpam-3565	265	62	,	,	PUNCT
ejpam-3565	265	63	b1	b1	NOUN
ejpam-3565	265	64	,	,	PUNCT
ejpam-3565	265	65	c1	c1	NOUN
ejpam-3565	265	66	,	,	PUNCT
ejpam-3565	265	67	d1	d1	PROPN
ejpam-3565	265	68	,	,	PUNCT
ejpam-3565	265	69	e1	e1	NOUN
ejpam-3565	265	70	∈	∈	PROPN
ejpam-3565	265	71	fpr	fpr	NOUN
ejpam-3565	265	72	and	and	CCONJ
ejpam-3565	265	73	c1	c1	PROPN
ejpam-3565	265	74	6=	6=	ADP
ejpam-3565	265	75	0	0	PROPN
ejpam-3565	265	76	.	.	PUNCT
ejpam-3565	266	1	the	the	DET
ejpam-3565	266	2	code	code	NOUN
ejpam-3565	266	3	c[4]p	c[4]p	NOUN
ejpam-3565	266	4	is	be	AUX
ejpam-3565	266	5	equivalent	equivalent	ADJ
ejpam-3565	266	6	to	to	ADP
ejpam-3565	266	7	the	the	DET
ejpam-3565	266	8	code	code	NOUN
ejpam-3565	266	9	with	with	ADP
ejpam-3565	266	10	generator	generator	NOUN
ejpam-3565	266	11	matrix	matrix	NOUN
ejpam-3565	266	12	g.	g.	NOUN
ejpam-3565	266	13	let	let	VERB
ejpam-3565	266	14	ĝ	ĝ	X
ejpam-3565	266	15	=	=	PUNCT
ejpam-3565	267	1	[	[	PUNCT
ejpam-3565	267	2	1	1	NUM
ejpam-3565	267	3	a	a	DET
ejpam-3565	267	4	b	b	NOUN
ejpam-3565	267	5	c	c	NOUN
ejpam-3565	267	6	0	0	NUM
ejpam-3565	267	7	1	1	NUM
ejpam-3565	267	8	d	d	NOUN
ejpam-3565	267	9	e	e	X
ejpam-3565	267	10	]	]	PUNCT
ejpam-3565	267	11	.	.	PUNCT
ejpam-3565	268	1	since	since	SCONJ
ejpam-3565	268	2	c1	c1	PROPN
ejpam-3565	268	3	is	be	AUX
ejpam-3565	268	4	nonzero	nonzero	ADJ
ejpam-3565	268	5	,	,	PUNCT
ejpam-3565	268	6	then	then	ADV
ejpam-3565	268	7	c	c	PROPN
ejpam-3565	268	8	is	be	AUX
ejpam-3565	268	9	a	a	DET
ejpam-3565	268	10	nonzero	nonzero	ADJ
ejpam-3565	268	11	element	element	NOUN
ejpam-3565	268	12	of	of	ADP
ejpam-3565	268	13	tpr	tpr	PROPN
ejpam-3565	268	14	.	.	PUNCT
ejpam-3565	269	1	thus	thus	ADV
ejpam-3565	269	2	,	,	PUNCT
ejpam-3565	269	3	c	c	PROPN
ejpam-3565	269	4	is	be	AUX
ejpam-3565	269	5	a	a	DET
ejpam-3565	269	6	unit	unit	NOUN
ejpam-3565	269	7	of	of	ADP
ejpam-3565	269	8	gr(p3	gr(p3	PROPN
ejpam-3565	269	9	,	,	PUNCT
ejpam-3565	269	10	2	2	NUM
ejpam-3565	269	11	)	)	PUNCT
ejpam-3565	269	12	.	.	PUNCT
ejpam-3565	270	1	proposition	proposition	NOUN
ejpam-3565	270	2	4	4	NUM
ejpam-3565	270	3	.	.	PUNCT
ejpam-3565	271	1	c[4,1]p	c[4,1]p	PROPN
ejpam-3565	271	2	has	have	VERB
ejpam-3565	271	3	generator	generator	NOUN
ejpam-3565	271	4	matrix	matrix	NOUN
ejpam-3565	271	5	mp(ĝ	mp(ĝ	NOUN
ejpam-3565	271	6	,	,	PUNCT
ejpam-3565	271	7	x	x	NOUN
ejpam-3565	271	8	)	)	PUNCT
ejpam-3565	271	9	=	=	SYM
ejpam-3565	271	10	1	1	NOUN
ejpam-3565	271	11	a	a	DET
ejpam-3565	271	12	b+	b+	X
ejpam-3565	271	13	px	px	X
ejpam-3565	271	14	c+	c+	VERB
ejpam-3565	271	15	py	py	PROPN
ejpam-3565	271	16	+	+	CCONJ
ejpam-3565	271	17	p2z	p2z	PROPN
ejpam-3565	271	18	0	0	NUM
ejpam-3565	272	1	p	p	X
ejpam-3565	272	2	pd	pd	PROPN
ejpam-3565	272	3	pe+	pe+	NOUN
ejpam-3565	272	4	p2q	p2q	NOUN
ejpam-3565	272	5	0	0	NUM
ejpam-3565	272	6	0	0	NUM
ejpam-3565	272	7	p2	p2	PROPN
ejpam-3565	272	8	p2r	p2r	NOUN
ejpam-3565	272	9			NOUN
ejpam-3565	272	10	,	,	PUNCT
ejpam-3565	272	11	where	where	SCONJ
ejpam-3565	272	12	x	x	PRON
ejpam-3565	272	13	is	be	AUX
ejpam-3565	272	14	an	an	DET
ejpam-3565	272	15	arbitrary	arbitrary	ADJ
ejpam-3565	272	16	element	element	NOUN
ejpam-3565	272	17	of	of	ADP
ejpam-3565	272	18	tpr	tpr	PROPN
ejpam-3565	272	19	and	and	CCONJ
ejpam-3565	272	20	y	y	PROPN
ejpam-3565	272	21	,	,	PUNCT
ejpam-3565	272	22	z	z	PROPN
ejpam-3565	272	23	,	,	PUNCT
ejpam-3565	272	24	q	q	INTJ
ejpam-3565	272	25	,	,	PUNCT
ejpam-3565	272	26	r	r	NOUN
ejpam-3565	272	27	∈	∈	PROPN
ejpam-3565	272	28	tpr	tpr	NOUN
ejpam-3565	272	29	such	such	ADJ
ejpam-3565	272	30	that	that	SCONJ
ejpam-3565	272	31	y	y	PROPN
ejpam-3565	272	32	≡	≡	PROPN
ejpam-3565	273	1	−(2c)−1(f	−(2c)−1(f	PROPN
ejpam-3565	273	2	+	+	CCONJ
ejpam-3565	273	3	2bx	2bx	ADJ
ejpam-3565	273	4	)	)	PUNCT
ejpam-3565	273	5	(	(	PUNCT
ejpam-3565	273	6	mod	mod	PROPN
ejpam-3565	273	7	p	p	X
ejpam-3565	273	8	)	)	PUNCT
ejpam-3565	273	9	z	z	PROPN
ejpam-3565	273	10	≡	≡	PROPN
ejpam-3565	273	11	−(2c)−1h	−(2c)−1h	NOUN
ejpam-3565	273	12	(	(	PUNCT
ejpam-3565	273	13	mod	mod	PROPN
ejpam-3565	273	14	p	p	NOUN
ejpam-3565	273	15	)	)	PUNCT
ejpam-3565	273	16	q	q	PROPN
ejpam-3565	273	17	≡	≡	PROPN
ejpam-3565	273	18	−c−1(d	−c−1(d	NOUN
ejpam-3565	273	19	+	+	CCONJ
ejpam-3565	273	20	dx+	dx+	ADJ
ejpam-3565	273	21	ey	ey	NOUN
ejpam-3565	273	22	)	)	PUNCT
ejpam-3565	273	23	(	(	PUNCT
ejpam-3565	273	24	mod	mod	PROPN
ejpam-3565	273	25	p	p	X
ejpam-3565	273	26	)	)	PUNCT
ejpam-3565	273	27	r	r	NOUN
ejpam-3565	273	28	≡	≡	PROPN
ejpam-3565	273	29	−c−1b	−c−1b	X
ejpam-3565	274	1	(	(	PUNCT
ejpam-3565	274	2	mod	mod	PROPN
ejpam-3565	274	3	p	p	X
ejpam-3565	274	4	)	)	PUNCT
ejpam-3565	274	5	,	,	PUNCT
ejpam-3565	274	6	with	with	ADP
ejpam-3565	274	7	f	f	PROPN
ejpam-3565	274	8	=	=	SYM
ejpam-3565	274	9	1	1	NUM
ejpam-3565	274	10	p(1	p(1	PROPN
ejpam-3565	274	11	+	+	NUM
ejpam-3565	274	12	a2	a2	PROPN
ejpam-3565	274	13	+	+	CCONJ
ejpam-3565	274	14	b2	b2	NOUN
ejpam-3565	274	15	+	+	CCONJ
ejpam-3565	274	16	c2	c2	PROPN
ejpam-3565	274	17	)	)	PUNCT
ejpam-3565	274	18	t.	t.	PROPN
ejpam-3565	274	19	l.	l.	PROPN
ejpam-3565	274	20	vasquez	vasquez	PROPN
ejpam-3565	274	21	,	,	PUNCT
ejpam-3565	274	22	g.	g.	PROPN
ejpam-3565	274	23	petalcorin	petalcorin	PROPN
ejpam-3565	274	24	/	/	SYM
ejpam-3565	274	25	eur	eur	PROPN
ejpam-3565	274	26	.	.	PUNCT
ejpam-3565	275	1	j.	j.	PROPN
ejpam-3565	275	2	pure	pure	PROPN
ejpam-3565	275	3	appl	appl	PROPN
ejpam-3565	275	4	.	.	PROPN
ejpam-3565	275	5	math	math	PROPN
ejpam-3565	275	6	,	,	PUNCT
ejpam-3565	275	7	12	12	NUM
ejpam-3565	275	8	(	(	PUNCT
ejpam-3565	275	9	4	4	NUM
ejpam-3565	275	10	)	)	PUNCT
ejpam-3565	275	11	(	(	PUNCT
ejpam-3565	275	12	2019	2019	NUM
ejpam-3565	275	13	)	)	PUNCT
ejpam-3565	275	14	,	,	PUNCT
ejpam-3565	275	15	1701	1701	NUM
ejpam-3565	275	16	-	-	SYM
ejpam-3565	275	17	1716	1716	NUM
ejpam-3565	275	18	1710	1710	NUM
ejpam-3565	275	19	h	h	NOUN
ejpam-3565	275	20	=	=	SYM
ejpam-3565	275	21	1	1	NUM
ejpam-3565	275	22	p(f	p(f	PROPN
ejpam-3565	275	23	+	+	CCONJ
ejpam-3565	275	24	2bx+	2bx+	NUM
ejpam-3565	275	25	2cy	2cy	NOUN
ejpam-3565	275	26	+	+	CCONJ
ejpam-3565	275	27	px2	px2	NOUN
ejpam-3565	275	28	+	+	CCONJ
ejpam-3565	275	29	py2	py2	NOUN
ejpam-3565	275	30	)	)	PUNCT
ejpam-3565	276	1	d	d	NOUN
ejpam-3565	276	2	=	=	SYM
ejpam-3565	276	3	1	1	NUM
ejpam-3565	276	4	p(a+	p(a+	PROPN
ejpam-3565	276	5	bd+	bd+	PROPN
ejpam-3565	276	6	ce	ce	PROPN
ejpam-3565	276	7	)	)	PUNCT
ejpam-3565	276	8	proof	proof	NOUN
ejpam-3565	276	9	.	.	PUNCT
ejpam-3565	277	1	let	let	VERB
ejpam-3565	277	2	a2	a2	PROPN
ejpam-3565	277	3	=	=	PRON
ejpam-3565	277	4	(	(	PUNCT
ejpam-3565	277	5	a	a	NOUN
ejpam-3565	277	6	)	)	PUNCT
ejpam-3565	277	7	,	,	PUNCT
ejpam-3565	277	8	a30	a30	NOUN
ejpam-3565	277	9	=	=	SYM
ejpam-3565	277	10	(	(	PUNCT
ejpam-3565	277	11	b	b	NOUN
ejpam-3565	277	12	)	)	PUNCT
ejpam-3565	277	13	,	,	PUNCT
ejpam-3565	277	14	a40	a40	PROPN
ejpam-3565	277	15	=	=	SYM
ejpam-3565	277	16	(	(	PUNCT
ejpam-3565	277	17	c	c	NOUN
ejpam-3565	277	18	)	)	PUNCT
ejpam-3565	277	19	.	.	PUNCT
ejpam-3565	278	1	from	from	ADP
ejpam-3565	278	2	(	(	PUNCT
ejpam-3565	278	3	20	20	NUM
ejpam-3565	278	4	)	)	PUNCT
ejpam-3565	278	5	,	,	PUNCT
ejpam-3565	278	6	we	we	PRON
ejpam-3565	278	7	obtain	obtain	VERB
ejpam-3565	278	8	pf	pf	NOUN
ejpam-3565	278	9	=	=	PUNCT
ejpam-3565	278	10	(	(	PUNCT
ejpam-3565	278	11	1	1	NUM
ejpam-3565	278	12	+	+	NUM
ejpam-3565	278	13	a2	a2	PROPN
ejpam-3565	278	14	+	+	CCONJ
ejpam-3565	278	15	b2	b2	NOUN
ejpam-3565	278	16	+	+	CCONJ
ejpam-3565	278	17	c2	c2	PROPN
ejpam-3565	278	18	)	)	PUNCT
ejpam-3565	278	19	,	,	PUNCT
ejpam-3565	278	20	where	where	SCONJ
ejpam-3565	278	21	f	f	PROPN
ejpam-3565	278	22	=	=	SYM
ejpam-3565	278	23	(	(	PUNCT
ejpam-3565	278	24	fij	fij	PROPN
ejpam-3565	278	25	)	)	PUNCT
ejpam-3565	278	26	.	.	PUNCT
ejpam-3565	279	1	the	the	DET
ejpam-3565	279	2	matrices	matrix	NOUN
ejpam-3565	279	3	a31	a31	NOUN
ejpam-3565	279	4	=	=	SYM
ejpam-3565	279	5	(	(	PUNCT
ejpam-3565	279	6	x	x	NOUN
ejpam-3565	279	7	)	)	PUNCT
ejpam-3565	279	8	and	and	CCONJ
ejpam-3565	279	9	a41	a41	NOUN
ejpam-3565	279	10	=	=	SYM
ejpam-3565	279	11	(	(	PUNCT
ejpam-3565	279	12	y	y	NOUN
ejpam-3565	279	13	)	)	PUNCT
ejpam-3565	279	14	satisfy	satisfy	NOUN
ejpam-3565	279	15	(	(	PUNCT
ejpam-3565	279	16	24	24	NUM
ejpam-3565	279	17	)	)	PUNCT
ejpam-3565	279	18	.	.	PUNCT
ejpam-3565	280	1	hence	hence	ADV
ejpam-3565	280	2	,	,	PUNCT
ejpam-3565	280	3	we	we	PRON
ejpam-3565	280	4	have	have	VERB
ejpam-3565	280	5	f	f	NOUN
ejpam-3565	280	6	+	+	CCONJ
ejpam-3565	280	7	2bx+	2bx+	NUM
ejpam-3565	280	8	2cy	2cy	ADJ
ejpam-3565	280	9	≡	≡	PROPN
ejpam-3565	280	10	0	0	PUNCT
ejpam-3565	281	1	(	(	PUNCT
ejpam-3565	281	2	mod	mod	PROPN
ejpam-3565	281	3	p	p	X
ejpam-3565	281	4	)	)	PUNCT
ejpam-3565	281	5	y	y	PROPN
ejpam-3565	281	6	≡	≡	PROPN
ejpam-3565	281	7	−(2c)−1(f	−(2c)−1(f	PROPN
ejpam-3565	281	8	+	+	CCONJ
ejpam-3565	281	9	2bx	2bx	ADJ
ejpam-3565	281	10	)	)	PUNCT
ejpam-3565	281	11	(	(	PUNCT
ejpam-3565	281	12	mod	mod	PROPN
ejpam-3565	281	13	p	p	X
ejpam-3565	281	14	)	)	PUNCT
ejpam-3565	281	15	.	.	PUNCT
ejpam-3565	282	1	next	next	ADV
ejpam-3565	282	2	,	,	PUNCT
ejpam-3565	282	3	we	we	PRON
ejpam-3565	282	4	obtain	obtain	VERB
ejpam-3565	282	5	ph	ph	NOUN
ejpam-3565	282	6	=	=	PUNCT
ejpam-3565	282	7	(	(	PUNCT
ejpam-3565	282	8	f	f	PROPN
ejpam-3565	282	9	+	+	CCONJ
ejpam-3565	282	10	2bx+	2bx+	NUM
ejpam-3565	282	11	2cy	2cy	NOUN
ejpam-3565	282	12	+	+	CCONJ
ejpam-3565	282	13	px2	px2	NOUN
ejpam-3565	282	14	+	+	CCONJ
ejpam-3565	282	15	py2	py2	NOUN
ejpam-3565	282	16	)	)	PUNCT
ejpam-3565	282	17	from	from	ADP
ejpam-3565	282	18	(	(	PUNCT
ejpam-3565	282	19	26	26	NUM
ejpam-3565	282	20	)	)	PUNCT
ejpam-3565	282	21	,	,	PUNCT
ejpam-3565	282	22	where	where	SCONJ
ejpam-3565	282	23	h	h	NOUN
ejpam-3565	282	24	=	=	SYM
ejpam-3565	282	25	(	(	PUNCT
ejpam-3565	282	26	hij	hij	NOUN
ejpam-3565	282	27	)	)	PUNCT
ejpam-3565	282	28	.	.	PUNCT
ejpam-3565	283	1	the	the	DET
ejpam-3565	283	2	matrix	matrix	NOUN
ejpam-3565	283	3	a42	a42	NOUN
ejpam-3565	283	4	=	=	SYM
ejpam-3565	283	5	(	(	PUNCT
ejpam-3565	283	6	z	z	NOUN
ejpam-3565	283	7	)	)	PUNCT
ejpam-3565	283	8	satisfies	satisfie	NOUN
ejpam-3565	283	9	(	(	PUNCT
ejpam-3565	283	10	25	25	NUM
ejpam-3565	283	11	)	)	PUNCT
ejpam-3565	283	12	,	,	PUNCT
ejpam-3565	283	13	which	which	PRON
ejpam-3565	283	14	gives	give	VERB
ejpam-3565	283	15	us	we	PRON
ejpam-3565	283	16	h	h	NOUN
ejpam-3565	283	17	+	+	CCONJ
ejpam-3565	283	18	2cz	2cz	ADJ
ejpam-3565	283	19	≡	≡	PROPN
ejpam-3565	283	20	0	0	PUNCT
ejpam-3565	284	1	(	(	PUNCT
ejpam-3565	284	2	mod	mod	PROPN
ejpam-3565	284	3	p	p	NOUN
ejpam-3565	284	4	)	)	PUNCT
ejpam-3565	284	5	z	z	PROPN
ejpam-3565	284	6	≡	≡	PROPN
ejpam-3565	284	7	−(2c)−1h	−(2c)−1h	NOUN
ejpam-3565	284	8	(	(	PUNCT
ejpam-3565	284	9	mod	mod	PROPN
ejpam-3565	284	10	p	p	NOUN
ejpam-3565	284	11	)	)	PUNCT
ejpam-3565	284	12	.	.	PUNCT
ejpam-3565	285	1	now	now	ADV
ejpam-3565	285	2	,	,	PUNCT
ejpam-3565	285	3	let	let	VERB
ejpam-3565	285	4	c4	c4	NOUN
ejpam-3565	285	5	=	=	SYM
ejpam-3565	285	6	(	(	PUNCT
ejpam-3565	285	7	r	r	NOUN
ejpam-3565	285	8	)	)	PUNCT
ejpam-3565	285	9	.	.	PUNCT
ejpam-3565	286	1	from	from	ADP
ejpam-3565	286	2	(	(	PUNCT
ejpam-3565	286	3	22	22	NUM
ejpam-3565	286	4	)	)	PUNCT
ejpam-3565	286	5	,	,	PUNCT
ejpam-3565	286	6	we	we	PRON
ejpam-3565	286	7	have	have	VERB
ejpam-3565	286	8	r	r	NOUN
ejpam-3565	286	9	≡	≡	PROPN
ejpam-3565	286	10	c−1b	c−1b	X
ejpam-3565	287	1	(	(	PUNCT
ejpam-3565	287	2	mod	mod	PROPN
ejpam-3565	287	3	p	p	X
ejpam-3565	287	4	)	)	PUNCT
ejpam-3565	287	5	.	.	PUNCT
ejpam-3565	288	1	finally	finally	ADV
ejpam-3565	288	2	,	,	PUNCT
ejpam-3565	288	3	let	let	VERB
ejpam-3565	288	4	b3	b3	PROPN
ejpam-3565	288	5	=	=	SYM
ejpam-3565	288	6	(	(	PUNCT
ejpam-3565	288	7	d	d	NOUN
ejpam-3565	288	8	)	)	PUNCT
ejpam-3565	288	9	,	,	PUNCT
ejpam-3565	288	10	b40	b40	NOUN
ejpam-3565	288	11	=	=	SYM
ejpam-3565	288	12	(	(	PUNCT
ejpam-3565	288	13	e	e	NOUN
ejpam-3565	288	14	)	)	PUNCT
ejpam-3565	288	15	and	and	CCONJ
ejpam-3565	288	16	b41	b41	NOUN
ejpam-3565	288	17	=	=	SYM
ejpam-3565	288	18	(	(	PUNCT
ejpam-3565	288	19	q	q	NOUN
ejpam-3565	288	20	)	)	PUNCT
ejpam-3565	288	21	.	.	PUNCT
ejpam-3565	289	1	we	we	PRON
ejpam-3565	289	2	compute	compute	VERB
ejpam-3565	289	3	pd	pd	PROPN
ejpam-3565	290	1	=	=	PRON
ejpam-3565	290	2	(	(	PUNCT
ejpam-3565	290	3	a+	a+	X
ejpam-3565	290	4	bd+	bd+	PROPN
ejpam-3565	290	5	ce	ce	PROPN
ejpam-3565	290	6	)	)	PUNCT
ejpam-3565	290	7	from	from	ADP
ejpam-3565	290	8	(	(	PUNCT
ejpam-3565	290	9	19	19	NUM
ejpam-3565	290	10	)	)	PUNCT
ejpam-3565	290	11	.	.	PUNCT
ejpam-3565	291	1	then	then	ADV
ejpam-3565	291	2	from	from	ADP
ejpam-3565	291	3	(	(	PUNCT
ejpam-3565	291	4	21	21	NUM
ejpam-3565	291	5	)	)	PUNCT
ejpam-3565	291	6	,	,	PUNCT
ejpam-3565	291	7	it	it	PRON
ejpam-3565	291	8	follows	follow	VERB
ejpam-3565	291	9	that	that	SCONJ
ejpam-3565	291	10	q	q	PROPN
ejpam-3565	291	11	≡	≡	PROPN
ejpam-3565	291	12	−c−1(d	−c−1(d	NOUN
ejpam-3565	291	13	+	+	CCONJ
ejpam-3565	291	14	dx+	dx+	ADJ
ejpam-3565	291	15	ey	ey	NOUN
ejpam-3565	291	16	)	)	PUNCT
ejpam-3565	291	17	(	(	PUNCT
ejpam-3565	291	18	mod	mod	PROPN
ejpam-3565	291	19	p	p	X
ejpam-3565	291	20	)	)	PUNCT
ejpam-3565	291	21	.	.	PUNCT
ejpam-3565	292	1	we	we	PRON
ejpam-3565	292	2	now	now	ADV
ejpam-3565	292	3	describe	describe	VERB
ejpam-3565	292	4	the	the	DET
ejpam-3565	292	5	generator	generator	NOUN
ejpam-3565	292	6	matrix	matrix	NOUN
ejpam-3565	292	7	of	of	ADP
ejpam-3565	292	8	c[4,2]p	c[4,2]p	PROPN
ejpam-3565	292	9	.	.	PUNCT
ejpam-3565	293	1	we	we	PRON
ejpam-3565	293	2	permute	permute	VERB
ejpam-3565	293	3	the	the	DET
ejpam-3565	293	4	columns	column	NOUN
ejpam-3565	293	5	of	of	ADP
ejpam-3565	293	6	the	the	DET
ejpam-3565	293	7	matrix	matrix	NOUN
ejpam-3565	294	1	[	[	X
ejpam-3565	294	2	i2	i2	PROPN
ejpam-3565	294	3	a	a	X
ejpam-3565	294	4	]	]	X
ejpam-3565	294	5	whenever	whenever	SCONJ
ejpam-3565	294	6	necessary	necessary	ADJ
ejpam-3565	294	7	,	,	PUNCT
ejpam-3565	294	8	so	so	SCONJ
ejpam-3565	294	9	that	that	SCONJ
ejpam-3565	294	10	the	the	DET
ejpam-3565	294	11	(	(	PUNCT
ejpam-3565	294	12	1,1	1,1	NUM
ejpam-3565	294	13	)	)	PUNCT
ejpam-3565	294	14	entry	entry	NOUN
ejpam-3565	294	15	of	of	ADP
ejpam-3565	294	16	a	a	PRON
ejpam-3565	294	17	is	be	AUX
ejpam-3565	294	18	nonzero	nonzero	NOUN
ejpam-3565	294	19	.	.	PUNCT
ejpam-3565	295	1	we	we	PRON
ejpam-3565	295	2	write	write	VERB
ejpam-3565	295	3	[	[	X
ejpam-3565	295	4	i2	i2	PROPN
ejpam-3565	295	5	a	a	X
ejpam-3565	295	6	]	]	X
ejpam-3565	296	1	=	=	PUNCT
ejpam-3565	297	1	[	[	PUNCT
ejpam-3565	297	2	1	1	NUM
ejpam-3565	297	3	0	0	NUM
ejpam-3565	297	4	s1	s1	NOUN
ejpam-3565	297	5	t1	t1	NOUN
ejpam-3565	297	6	0	0	NUM
ejpam-3565	297	7	1	1	NUM
ejpam-3565	297	8	u1	u1	NOUN
ejpam-3565	297	9	v1	v1	NOUN
ejpam-3565	297	10	]	]	PUNCT
ejpam-3565	297	11	,	,	PUNCT
ejpam-3565	298	1	where	where	SCONJ
ejpam-3565	298	2	s1	s1	NOUN
ejpam-3565	298	3	,	,	PUNCT
ejpam-3565	298	4	t1	t1	NOUN
ejpam-3565	298	5	,	,	PUNCT
ejpam-3565	298	6	u1	u1	NOUN
ejpam-3565	298	7	,	,	PUNCT
ejpam-3565	298	8	v1	v1	NOUN
ejpam-3565	298	9	∈	∈	NOUN
ejpam-3565	298	10	fpr	fpr	NOUN
ejpam-3565	298	11	and	and	CCONJ
ejpam-3565	298	12	s1	s1	PROPN
ejpam-3565	298	13	6=	6=	ADP
ejpam-3565	298	14	0	0	X
ejpam-3565	298	15	.	.	PUNCT
ejpam-3565	298	16	let	let	VERB
ejpam-3565	298	17	â	â	PUNCT
ejpam-3565	298	18	=	=	PUNCT
ejpam-3565	299	1	[	[	PUNCT
ejpam-3565	299	2	s	s	X
ejpam-3565	299	3	t	t	X
ejpam-3565	299	4	u	u	NOUN
ejpam-3565	299	5	v	v	ADP
ejpam-3565	299	6	]	]	PUNCT
ejpam-3565	299	7	.	.	PUNCT
ejpam-3565	300	1	since	since	SCONJ
ejpam-3565	300	2	s1	s1	PROPN
ejpam-3565	300	3	is	be	AUX
ejpam-3565	300	4	nonzero	nonzero	ADJ
ejpam-3565	300	5	,	,	PUNCT
ejpam-3565	300	6	then	then	ADV
ejpam-3565	300	7	s	s	VERB
ejpam-3565	300	8	is	be	AUX
ejpam-3565	300	9	a	a	DET
ejpam-3565	300	10	nonzero	nonzero	ADJ
ejpam-3565	300	11	element	element	NOUN
ejpam-3565	300	12	of	of	ADP
ejpam-3565	300	13	tp2	tp2	PROPN
ejpam-3565	300	14	,	,	PUNCT
ejpam-3565	300	15	and	and	CCONJ
ejpam-3565	300	16	thus	thus	ADV
ejpam-3565	300	17	,	,	PUNCT
ejpam-3565	300	18	is	be	AUX
ejpam-3565	300	19	a	a	DET
ejpam-3565	300	20	unit	unit	NOUN
ejpam-3565	300	21	of	of	ADP
ejpam-3565	300	22	gr(p3	gr(p3	PROPN
ejpam-3565	300	23	,	,	PUNCT
ejpam-3565	300	24	2	2	NUM
ejpam-3565	300	25	)	)	PUNCT
ejpam-3565	300	26	.	.	PUNCT
ejpam-3565	301	1	also	also	ADV
ejpam-3565	301	2	,	,	PUNCT
ejpam-3565	301	3	since	since	SCONJ
ejpam-3565	301	4	a	a	PRON
ejpam-3565	301	5	has	have	VERB
ejpam-3565	301	6	an	an	DET
ejpam-3565	301	7	inverse	inverse	NOUN
ejpam-3565	301	8	modulo	modulo	NOUN
ejpam-3565	302	1	p	p	X
ejpam-3565	302	2	,	,	PUNCT
ejpam-3565	302	3	then	then	ADV
ejpam-3565	302	4	deta	deta	NOUN
ejpam-3565	302	5	=	=	SYM
ejpam-3565	302	6	s1v1	s1v1	AUX
ejpam-3565	302	7	−	−	ADP
ejpam-3565	302	8	t1u1	t1u1	SYM
ejpam-3565	302	9	6=	6=	ADP
ejpam-3565	302	10	0	0	NUM
ejpam-3565	302	11	,	,	PUNCT
ejpam-3565	302	12	which	which	PRON
ejpam-3565	302	13	implies	imply	VERB
ejpam-3565	302	14	that	that	SCONJ
ejpam-3565	303	1	sv	sv	INTJ
ejpam-3565	303	2	−	−	PROPN
ejpam-3565	303	3	tu	tu	PROPN
ejpam-3565	303	4	6=	6=	ADP
ejpam-3565	303	5	0	0	NUM
ejpam-3565	304	1	and	and	CCONJ
ejpam-3565	304	2	(	(	PUNCT
ejpam-3565	304	3	sv	sv	INTJ
ejpam-3565	304	4	−	−	PROPN
ejpam-3565	304	5	tu)/s	tu)/s	PROPN
ejpam-3565	304	6	=	=	SYM
ejpam-3565	304	7	v	v	ADP
ejpam-3565	304	8	−	−	PROPN
ejpam-3565	304	9	tus−1	tus−1	NOUN
ejpam-3565	304	10	has	have	VERB
ejpam-3565	304	11	an	an	DET
ejpam-3565	304	12	inverse	inverse	NOUN
ejpam-3565	304	13	modulo	modulo	NOUN
ejpam-3565	304	14	p.	p.	NOUN
ejpam-3565	304	15	proposition	proposition	NOUN
ejpam-3565	304	16	5	5	NUM
ejpam-3565	304	17	.	.	PUNCT
ejpam-3565	305	1	c[4,2]p	c[4,2]p	PROPN
ejpam-3565	305	2	has	have	VERB
ejpam-3565	305	3	generator	generator	NOUN
ejpam-3565	305	4	matrix	matrix	NOUN
ejpam-3565	305	5	mp(â	mp(â	NOUN
ejpam-3565	305	6	,	,	PUNCT
ejpam-3565	305	7	y12	y12	PROPN
ejpam-3565	305	8	,	,	PUNCT
ejpam-3565	305	9	z12	z12	NUM
ejpam-3565	305	10	)	)	PUNCT
ejpam-3565	305	11	=	=	PUNCT
ejpam-3565	306	1	[	[	X
ejpam-3565	306	2	i2	i2	PROPN
ejpam-3565	306	3	â+	â+	PROPN
ejpam-3565	306	4	py	py	PROPN
ejpam-3565	306	5	+	+	CCONJ
ejpam-3565	306	6	p2z	p2z	PROPN
ejpam-3565	306	7	]	]	X
ejpam-3565	306	8	,	,	PUNCT
ejpam-3565	306	9	t.	t.	PROPN
ejpam-3565	306	10	l.	l.	PROPN
ejpam-3565	306	11	vasquez	vasquez	PROPN
ejpam-3565	306	12	,	,	PUNCT
ejpam-3565	306	13	g.	g.	PROPN
ejpam-3565	306	14	petalcorin	petalcorin	PROPN
ejpam-3565	306	15	/	/	SYM
ejpam-3565	306	16	eur	eur	PROPN
ejpam-3565	306	17	.	.	PUNCT
ejpam-3565	307	1	j.	j.	PROPN
ejpam-3565	307	2	pure	pure	PROPN
ejpam-3565	307	3	appl	appl	PROPN
ejpam-3565	307	4	.	.	PROPN
ejpam-3565	307	5	math	math	PROPN
ejpam-3565	307	6	,	,	PUNCT
ejpam-3565	307	7	12	12	NUM
ejpam-3565	307	8	(	(	PUNCT
ejpam-3565	307	9	4	4	NUM
ejpam-3565	307	10	)	)	PUNCT
ejpam-3565	307	11	(	(	PUNCT
ejpam-3565	307	12	2019	2019	NUM
ejpam-3565	307	13	)	)	PUNCT
ejpam-3565	307	14	,	,	PUNCT
ejpam-3565	307	15	1701	1701	NUM
ejpam-3565	307	16	-	-	SYM
ejpam-3565	307	17	1716	1716	NUM
ejpam-3565	307	18	1711	1711	NUM
ejpam-3565	307	19	where	where	SCONJ
ejpam-3565	307	20	y12	y12	PROPN
ejpam-3565	307	21	and	and	CCONJ
ejpam-3565	307	22	z12	z12	PROPN
ejpam-3565	307	23	are	be	AUX
ejpam-3565	307	24	arbitrary	arbitrary	ADJ
ejpam-3565	307	25	elements	element	NOUN
ejpam-3565	307	26	of	of	ADP
ejpam-3565	307	27	tp2	tp2	PROPN
ejpam-3565	307	28	and	and	CCONJ
ejpam-3565	307	29	y	y	PROPN
ejpam-3565	307	30	=	=	SYM
ejpam-3565	307	31	(	(	PUNCT
ejpam-3565	307	32	yij	yij	NOUN
ejpam-3565	307	33	)	)	PUNCT
ejpam-3565	307	34	and	and	CCONJ
ejpam-3565	307	35	z	z	NOUN
ejpam-3565	307	36	=	=	SYM
ejpam-3565	307	37	(	(	PUNCT
ejpam-3565	307	38	zij	zij	PROPN
ejpam-3565	307	39	)	)	PUNCT
ejpam-3565	307	40	are	be	AUX
ejpam-3565	307	41	matrices	matrix	NOUN
ejpam-3565	307	42	over	over	ADP
ejpam-3565	307	43	tp2	tp2	PROPN
ejpam-3565	307	44	satisfying	satisfy	VERB
ejpam-3565	307	45	f	f	PROPN
ejpam-3565	307	46	+	+	CCONJ
ejpam-3565	307	47	˜̂	˜̂	NOUN
ejpam-3565	307	48	ay	ay	PROPN
ejpam-3565	307	49	t	t	PROPN
ejpam-3565	307	50	≡	≡	PROPN
ejpam-3565	307	51	0	0	PUNCT
ejpam-3565	308	1	(	(	PUNCT
ejpam-3565	308	2	mod	mod	PROPN
ejpam-3565	308	3	p	p	NOUN
ejpam-3565	308	4	)	)	PUNCT
ejpam-3565	308	5	h	h	NOUN
ejpam-3565	308	6	+	+	CCONJ
ejpam-3565	308	7	˜̂	˜̂	NOUN
ejpam-3565	308	8	azt	azt	PROPN
ejpam-3565	308	9	≡	≡	PROPN
ejpam-3565	308	10	0	0	PUNCT
ejpam-3565	309	1	(	(	PUNCT
ejpam-3565	309	2	mod	mod	PROPN
ejpam-3565	309	3	p	p	X
ejpam-3565	309	4	)	)	PUNCT
ejpam-3565	309	5	,	,	PUNCT
ejpam-3565	309	6	with	with	ADP
ejpam-3565	309	7	f	f	PROPN
ejpam-3565	309	8	=	=	SYM
ejpam-3565	309	9	1	1	NUM
ejpam-3565	309	10	p(i2	p(i2	NOUN
ejpam-3565	309	11	+	+	SYM
ejpam-3565	309	12	âât	âât	NOUN
ejpam-3565	309	13	)	)	PUNCT
ejpam-3565	310	1	and	and	CCONJ
ejpam-3565	310	2	h	h	NOUN
ejpam-3565	310	3	=	=	NOUN
ejpam-3565	310	4	1	1	NUM
ejpam-3565	310	5	p	p	NOUN
ejpam-3565	310	6	(	(	PUNCT
ejpam-3565	310	7	f	f	PROPN
ejpam-3565	310	8	+	+	CCONJ
ejpam-3565	310	9	˜̂	˜̂	NOUN
ejpam-3565	310	10	ay	ay	PROPN
ejpam-3565	310	11	t	t	PROPN
ejpam-3565	311	1	+	+	CCONJ
ejpam-3565	311	2	py	py	PROPN
ejpam-3565	311	3	y	y	PROPN
ejpam-3565	311	4	t	t	PROPN
ejpam-3565	311	5	)	)	PUNCT
ejpam-3565	311	6	.	.	PUNCT
ejpam-3565	312	1	proof	proof	NOUN
ejpam-3565	312	2	.	.	PUNCT
ejpam-3565	313	1	let	let	VERB
ejpam-3565	313	2	a40	a40	PROPN
ejpam-3565	313	3	=	=	PUNCT
ejpam-3565	313	4	â.	â.	ADV
ejpam-3565	313	5	from	from	ADP
ejpam-3565	313	6	(	(	PUNCT
ejpam-3565	313	7	20	20	NUM
ejpam-3565	313	8	)	)	PUNCT
ejpam-3565	313	9	,	,	PUNCT
ejpam-3565	313	10	we	we	PRON
ejpam-3565	313	11	compute	compute	VERB
ejpam-3565	313	12	pf	pf	PROPN
ejpam-3565	313	13	=	=	PROPN
ejpam-3565	313	14	i2	i2	PROPN
ejpam-3565	313	15	+	+	CCONJ
ejpam-3565	313	16	âât	âât	PROPN
ejpam-3565	313	17	,	,	PUNCT
ejpam-3565	313	18	where	where	SCONJ
ejpam-3565	313	19	f	f	PROPN
ejpam-3565	313	20	=	=	SYM
ejpam-3565	313	21	(	(	PUNCT
ejpam-3565	313	22	fij	fij	PROPN
ejpam-3565	313	23	)	)	PUNCT
ejpam-3565	313	24	.	.	PUNCT
ejpam-3565	314	1	note	note	VERB
ejpam-3565	314	2	that	that	SCONJ
ejpam-3565	314	3	f	f	PROPN
ejpam-3565	314	4	is	be	AUX
ejpam-3565	314	5	a	a	DET
ejpam-3565	314	6	symmetric	symmetric	ADJ
ejpam-3565	314	7	matrix	matrix	NOUN
ejpam-3565	314	8	.	.	PUNCT
ejpam-3565	315	1	the	the	DET
ejpam-3565	315	2	matrix	matrix	NOUN
ejpam-3565	315	3	a41	a41	NOUN
ejpam-3565	315	4	=	=	SYM
ejpam-3565	315	5	y	y	PROPN
ejpam-3565	315	6	=	=	SYM
ejpam-3565	315	7	(	(	PUNCT
ejpam-3565	315	8	yij	yij	NOUN
ejpam-3565	315	9	)	)	PUNCT
ejpam-3565	315	10	,	,	PUNCT
ejpam-3565	315	11	with	with	ADP
ejpam-3565	315	12	entries	entry	NOUN
ejpam-3565	315	13	from	from	ADP
ejpam-3565	315	14	tp2	tp2	PROPN
ejpam-3565	315	15	,	,	PUNCT
ejpam-3565	315	16	satisfies	satisfie	NOUN
ejpam-3565	315	17	(	(	PUNCT
ejpam-3565	315	18	24	24	NUM
ejpam-3565	315	19	)	)	PUNCT
ejpam-3565	315	20	.	.	PUNCT
ejpam-3565	316	1	we	we	PRON
ejpam-3565	316	2	then	then	ADV
ejpam-3565	316	3	have	have	VERB
ejpam-3565	316	4	f	f	PROPN
ejpam-3565	316	5	+	+	NUM
ejpam-3565	316	6	˜̂	˜̂	NOUN
ejpam-3565	316	7	ay	ay	PROPN
ejpam-3565	316	8	t	t	PROPN
ejpam-3565	316	9	≡	≡	PROPN
ejpam-3565	316	10	0	0	PUNCT
ejpam-3565	317	1	(	(	PUNCT
ejpam-3565	317	2	mod	mod	PROPN
ejpam-3565	317	3	p	p	X
ejpam-3565	317	4	)	)	PUNCT
ejpam-3565	317	5	,	,	PUNCT
ejpam-3565	317	6	that	that	ADV
ejpam-3565	317	7	is	be	AUX
ejpam-3565	317	8	,	,	PUNCT
ejpam-3565	317	9	[	[	PUNCT
ejpam-3565	317	10	f11	f11	PROPN
ejpam-3565	317	11	f12	f12	NOUN
ejpam-3565	317	12	f12	f12	NOUN
ejpam-3565	317	13	f22	f22	NOUN
ejpam-3565	317	14	]	]	PUNCT
ejpam-3565	318	1	+	+	CCONJ
ejpam-3565	318	2	[	[	PUNCT
ejpam-3565	318	3	s	s	X
ejpam-3565	318	4	t	t	X
ejpam-3565	318	5	u	u	NOUN
ejpam-3565	318	6	v	v	X
ejpam-3565	318	7	]	]	X
ejpam-3565	318	8	[	[	PUNCT
ejpam-3565	318	9	y11	y11	NOUN
ejpam-3565	318	10	y21	y21	PROPN
ejpam-3565	318	11	y12	y12	PROPN
ejpam-3565	318	12	y22	y22	PROPN
ejpam-3565	318	13	]	]	PUNCT
ejpam-3565	319	1	+	+	CCONJ
ejpam-3565	319	2	[	[	PUNCT
ejpam-3565	319	3	y11	y11	NUM
ejpam-3565	319	4	y12	y12	PROPN
ejpam-3565	319	5	y21	y21	PROPN
ejpam-3565	319	6	y22	y22	PROPN
ejpam-3565	319	7	]	]	PUNCT
ejpam-3565	319	8	[	[	PUNCT
ejpam-3565	319	9	s	s	X
ejpam-3565	319	10	u	u	NOUN
ejpam-3565	319	11	t	t	X
ejpam-3565	319	12	v	v	X
ejpam-3565	319	13	]	]	PUNCT
ejpam-3565	319	14	≡	≡	PROPN
ejpam-3565	319	15	0	0	PUNCT
ejpam-3565	320	1	(	(	PUNCT
ejpam-3565	320	2	mod	mod	PROPN
ejpam-3565	320	3	p	p	X
ejpam-3565	320	4	)	)	PUNCT
ejpam-3565	320	5	.	.	PUNCT
ejpam-3565	321	1	hence	hence	ADV
ejpam-3565	321	2	y	y	PROPN
ejpam-3565	321	3	satisfies	satisfy	VERB
ejpam-3565	321	4	f11	f11	VERB
ejpam-3565	321	5	+	+	CCONJ
ejpam-3565	321	6	2sy11	2sy11	NUM
ejpam-3565	321	7	+	+	CCONJ
ejpam-3565	321	8	2ty12	2ty12	NUM
ejpam-3565	321	9	≡	≡	PROPN
ejpam-3565	321	10	0	0	PUNCT
ejpam-3565	322	1	(	(	PUNCT
ejpam-3565	322	2	mod	mod	PROPN
ejpam-3565	322	3	p	p	NOUN
ejpam-3565	322	4	)	)	PUNCT
ejpam-3565	322	5	f22	f22	NOUN
ejpam-3565	323	1	+	+	CCONJ
ejpam-3565	323	2	2uy21	2uy21	NUM
ejpam-3565	324	1	+	+	CCONJ
ejpam-3565	324	2	2vy22	2vy22	NUM
ejpam-3565	324	3	≡	≡	PROPN
ejpam-3565	324	4	0	0	PUNCT
ejpam-3565	324	5	(	(	PUNCT
ejpam-3565	324	6	mod	mod	PROPN
ejpam-3565	324	7	p	p	NOUN
ejpam-3565	324	8	)	)	PUNCT
ejpam-3565	324	9	f12	f12	NOUN
ejpam-3565	324	10	+	+	X
ejpam-3565	324	11	sy21	sy21	PROPN
ejpam-3565	324	12	+	+	PROPN
ejpam-3565	324	13	ty22	ty22	PROPN
ejpam-3565	324	14	+	+	CCONJ
ejpam-3565	324	15	uy11	uy11	PROPN
ejpam-3565	324	16	+	+	CCONJ
ejpam-3565	324	17	vy12	vy12	PROPN
ejpam-3565	324	18	≡	≡	PROPN
ejpam-3565	324	19	0	0	PUNCT
ejpam-3565	325	1	(	(	PUNCT
ejpam-3565	325	2	mod	mod	PROPN
ejpam-3565	325	3	p	p	X
ejpam-3565	325	4	)	)	PUNCT
ejpam-3565	325	5	observe	observe	VERB
ejpam-3565	325	6	that	that	DET
ejpam-3565	325	7	y11	y11	NOUN
ejpam-3565	325	8	,	,	PUNCT
ejpam-3565	325	9	y21	y21	PROPN
ejpam-3565	325	10	and	and	CCONJ
ejpam-3565	325	11	y22	y22	PROPN
ejpam-3565	325	12	can	can	AUX
ejpam-3565	325	13	each	each	PRON
ejpam-3565	325	14	be	be	AUX
ejpam-3565	325	15	expressed	express	VERB
ejpam-3565	325	16	in	in	ADP
ejpam-3565	325	17	terms	term	NOUN
ejpam-3565	325	18	of	of	ADP
ejpam-3565	325	19	y12	y12	PROPN
ejpam-3565	325	20	.	.	PUNCT
ejpam-3565	326	1	thus	thus	ADV
ejpam-3565	326	2	y11	y11	NOUN
ejpam-3565	326	3	,	,	PUNCT
ejpam-3565	326	4	y21	y21	PROPN
ejpam-3565	326	5	and	and	CCONJ
ejpam-3565	326	6	y22	y22	PROPN
ejpam-3565	326	7	are	be	AUX
ejpam-3565	326	8	determined	determine	VERB
ejpam-3565	326	9	by	by	ADP
ejpam-3565	326	10	â	â	PROPN
ejpam-3565	326	11	and	and	CCONJ
ejpam-3565	326	12	y12	y12	PROPN
ejpam-3565	326	13	.	.	PUNCT
ejpam-3565	327	1	next	next	ADV
ejpam-3565	327	2	we	we	PRON
ejpam-3565	327	3	compute	compute	VERB
ejpam-3565	327	4	ph	ph	NOUN
ejpam-3565	327	5	=	=	SYM
ejpam-3565	327	6	f	f	PROPN
ejpam-3565	327	7	+	+	NUM
ejpam-3565	327	8	˜̂	˜̂	NOUN
ejpam-3565	327	9	ay	ay	PROPN
ejpam-3565	327	10	t	t	PROPN
ejpam-3565	328	1	+	+	CCONJ
ejpam-3565	328	2	py	py	PROPN
ejpam-3565	328	3	y	y	PROPN
ejpam-3565	328	4	t	t	PROPN
ejpam-3565	328	5	from	from	ADP
ejpam-3565	328	6	(	(	PUNCT
ejpam-3565	328	7	26	26	NUM
ejpam-3565	328	8	)	)	PUNCT
ejpam-3565	328	9	,	,	PUNCT
ejpam-3565	328	10	where	where	SCONJ
ejpam-3565	328	11	h	h	NOUN
ejpam-3565	328	12	=	=	SYM
ejpam-3565	328	13	(	(	PUNCT
ejpam-3565	328	14	hij	hij	NOUN
ejpam-3565	328	15	)	)	PUNCT
ejpam-3565	328	16	.	.	PUNCT
ejpam-3565	329	1	the	the	DET
ejpam-3565	329	2	matrix	matrix	NOUN
ejpam-3565	329	3	a42	a42	NOUN
ejpam-3565	329	4	=	=	PUNCT
ejpam-3565	329	5	z	z	NOUN
ejpam-3565	329	6	=	=	SYM
ejpam-3565	329	7	(	(	PUNCT
ejpam-3565	329	8	zij	zij	PROPN
ejpam-3565	329	9	)	)	PUNCT
ejpam-3565	329	10	,	,	PUNCT
ejpam-3565	329	11	with	with	ADP
ejpam-3565	329	12	entries	entry	NOUN
ejpam-3565	329	13	from	from	ADP
ejpam-3565	329	14	tp2	tp2	PROPN
ejpam-3565	329	15	,	,	PUNCT
ejpam-3565	329	16	satisfies	satisfie	NOUN
ejpam-3565	329	17	(	(	PUNCT
ejpam-3565	329	18	25	25	NUM
ejpam-3565	329	19	)	)	PUNCT
ejpam-3565	329	20	.	.	PUNCT
ejpam-3565	330	1	hence	hence	ADV
ejpam-3565	330	2	z	z	NOUN
ejpam-3565	330	3	satisfies	satisfy	VERB
ejpam-3565	330	4	h	h	NOUN
ejpam-3565	330	5	+	+	CCONJ
ejpam-3565	330	6	˜̂	˜̂	NOUN
ejpam-3565	330	7	azt	azt	PROPN
ejpam-3565	330	8	≡	≡	PROPN
ejpam-3565	330	9	0	0	PUNCT
ejpam-3565	331	1	(	(	PUNCT
ejpam-3565	331	2	mod	mod	PROPN
ejpam-3565	331	3	p	p	X
ejpam-3565	331	4	)	)	PUNCT
ejpam-3565	331	5	,	,	PUNCT
ejpam-3565	331	6	that	that	ADV
ejpam-3565	331	7	is	be	AUX
ejpam-3565	331	8	,	,	PUNCT
ejpam-3565	331	9	[	[	PUNCT
ejpam-3565	331	10	h11	h11	PROPN
ejpam-3565	331	11	h12	h12	PROPN
ejpam-3565	331	12	h12	h12	PROPN
ejpam-3565	331	13	h22	h22	PROPN
ejpam-3565	331	14	]	]	X
ejpam-3565	332	1	+	+	CCONJ
ejpam-3565	332	2	[	[	PUNCT
ejpam-3565	332	3	s	s	X
ejpam-3565	332	4	t	t	X
ejpam-3565	332	5	u	u	NOUN
ejpam-3565	332	6	v	v	X
ejpam-3565	332	7	]	]	PUNCT
ejpam-3565	332	8	[	[	PUNCT
ejpam-3565	332	9	z11	z11	PROPN
ejpam-3565	332	10	z21	z21	PROPN
ejpam-3565	332	11	z12	z12	PROPN
ejpam-3565	332	12	z22	z22	PROPN
ejpam-3565	332	13	]	]	X
ejpam-3565	333	1	+	+	CCONJ
ejpam-3565	333	2	[	[	PUNCT
ejpam-3565	333	3	z11	z11	PROPN
ejpam-3565	333	4	z12	z12	PROPN
ejpam-3565	333	5	z21	z21	PROPN
ejpam-3565	333	6	z22	z22	NOUN
ejpam-3565	333	7	]	]	X
ejpam-3565	333	8	[	[	PUNCT
ejpam-3565	333	9	s	s	X
ejpam-3565	333	10	u	u	NOUN
ejpam-3565	333	11	t	t	X
ejpam-3565	333	12	v	v	X
ejpam-3565	333	13	]	]	PUNCT
ejpam-3565	333	14	≡	≡	PROPN
ejpam-3565	333	15	0	0	PUNCT
ejpam-3565	334	1	(	(	PUNCT
ejpam-3565	334	2	mod	mod	PROPN
ejpam-3565	334	3	p	p	X
ejpam-3565	334	4	)	)	PUNCT
ejpam-3565	334	5	.	.	PUNCT
ejpam-3565	335	1	using	use	VERB
ejpam-3565	335	2	a	a	DET
ejpam-3565	335	3	similar	similar	ADJ
ejpam-3565	335	4	argument	argument	NOUN
ejpam-3565	335	5	as	as	ADP
ejpam-3565	335	6	earlier	early	ADV
ejpam-3565	335	7	,	,	PUNCT
ejpam-3565	335	8	we	we	PRON
ejpam-3565	335	9	see	see	VERB
ejpam-3565	335	10	that	that	SCONJ
ejpam-3565	335	11	z11	z11	NOUN
ejpam-3565	335	12	,	,	PUNCT
ejpam-3565	335	13	z21	z21	NOUN
ejpam-3565	335	14	and	and	CCONJ
ejpam-3565	335	15	z22	z22	NOUN
ejpam-3565	335	16	are	be	AUX
ejpam-3565	335	17	determined	determine	VERB
ejpam-3565	335	18	by	by	ADP
ejpam-3565	335	19	â	â	PROPN
ejpam-3565	335	20	and	and	CCONJ
ejpam-3565	335	21	z12	z12	NUM
ejpam-3565	335	22	.	.	PROPN
ejpam-3565	336	1	5.2	5.2	NUM
ejpam-3565	336	2	.	.	PUNCT
ejpam-3565	337	1	self	self	NOUN
ejpam-3565	337	2	-	-	PUNCT
ejpam-3565	337	3	dual	dual	ADJ
ejpam-3565	337	4	codes	code	NOUN
ejpam-3565	337	5	over	over	ADP
ejpam-3565	337	6	gr(27	gr(27	PROPN
ejpam-3565	337	7	,	,	PUNCT
ejpam-3565	337	8	2	2	NUM
ejpam-3565	337	9	)	)	PUNCT
ejpam-3565	337	10	we	we	PRON
ejpam-3565	337	11	consider	consider	VERB
ejpam-3565	337	12	gr(27	gr(27	PROPN
ejpam-3565	337	13	,	,	PUNCT
ejpam-3565	337	14	2	2	NUM
ejpam-3565	337	15	)	)	PUNCT
ejpam-3565	337	16	=	=	SYM
ejpam-3565	337	17	z27[ω	z27[ω	NOUN
ejpam-3565	337	18	]	]	X
ejpam-3565	337	19	,	,	PUNCT
ejpam-3565	337	20	where	where	SCONJ
ejpam-3565	337	21	ω2	ω2	ADJ
ejpam-3565	337	22	+	+	CCONJ
ejpam-3565	337	23	5ω+	5ω+	NUM
ejpam-3565	337	24	26	26	NUM
ejpam-3565	337	25	=	=	SYM
ejpam-3565	337	26	0	0	NUM
ejpam-3565	337	27	and	and	CCONJ
ejpam-3565	337	28	ω8	ω8	NOUN
ejpam-3565	337	29	=	=	SYM
ejpam-3565	337	30	1	1	NUM
ejpam-3565	337	31	,	,	PUNCT
ejpam-3565	337	32	and	and	CCONJ
ejpam-3565	337	33	f9	f9	PROPN
ejpam-3565	337	34	=	=	PUNCT
ejpam-3565	337	35	z3[ω̄	z3[ω̄	PROPN
ejpam-3565	337	36	]	]	PUNCT
ejpam-3565	337	37	,	,	PUNCT
ejpam-3565	337	38	where	where	SCONJ
ejpam-3565	337	39	ω̄2	ω̄2	NUM
ejpam-3565	337	40	+	+	NUM
ejpam-3565	337	41	2ω	2ω	NUM
ejpam-3565	337	42	+	+	CCONJ
ejpam-3565	337	43	2	2	NUM
ejpam-3565	337	44	=	=	SYM
ejpam-3565	337	45	0	0	NUM
ejpam-3565	337	46	and	and	CCONJ
ejpam-3565	337	47	ω̄8	ω̄8	NUM
ejpam-3565	337	48	=	=	SYM
ejpam-3565	337	49	1	1	X
ejpam-3565	337	50	.	.	PUNCT
ejpam-3565	337	51	t.	t.	PROPN
ejpam-3565	337	52	l.	l.	PROPN
ejpam-3565	337	53	vasquez	vasquez	PROPN
ejpam-3565	337	54	,	,	PUNCT
ejpam-3565	337	55	g.	g.	PROPN
ejpam-3565	337	56	petalcorin	petalcorin	PROPN
ejpam-3565	337	57	/	/	SYM
ejpam-3565	337	58	eur	eur	PROPN
ejpam-3565	337	59	.	.	PUNCT
ejpam-3565	338	1	j.	j.	PROPN
ejpam-3565	338	2	pure	pure	PROPN
ejpam-3565	338	3	appl	appl	PROPN
ejpam-3565	338	4	.	.	PROPN
ejpam-3565	338	5	math	math	PROPN
ejpam-3565	338	6	,	,	PUNCT
ejpam-3565	338	7	12	12	NUM
ejpam-3565	338	8	(	(	PUNCT
ejpam-3565	338	9	4	4	NUM
ejpam-3565	338	10	)	)	PUNCT
ejpam-3565	338	11	(	(	PUNCT
ejpam-3565	338	12	2019	2019	NUM
ejpam-3565	338	13	)	)	PUNCT
ejpam-3565	338	14	,	,	PUNCT
ejpam-3565	338	15	1701	1701	NUM
ejpam-3565	338	16	-	-	SYM
ejpam-3565	338	17	1716	1716	NUM
ejpam-3565	338	18	1712	1712	NUM
ejpam-3565	338	19	from	from	ADP
ejpam-3565	338	20	[	[	X
ejpam-3565	338	21	4	4	NUM
ejpam-3565	338	22	]	]	PUNCT
ejpam-3565	338	23	,	,	PUNCT
ejpam-3565	338	24	there	there	PRON
ejpam-3565	338	25	exist	exist	VERB
ejpam-3565	338	26	two	two	NUM
ejpam-3565	338	27	inequivalent	inequivalent	NOUN
ejpam-3565	338	28	self	self	NOUN
ejpam-3565	338	29	-	-	PUNCT
ejpam-3565	338	30	dual	dual	ADJ
ejpam-3565	338	31	codes	code	NOUN
ejpam-3565	338	32	of	of	ADP
ejpam-3565	338	33	length	length	NOUN
ejpam-3565	338	34	4	4	NUM
ejpam-3565	338	35	over	over	ADP
ejpam-3565	338	36	f9	f9	PROPN
ejpam-3565	338	37	:	:	PUNCT
ejpam-3565	338	38	c[4]3	c[4]3	NOUN
ejpam-3565	338	39	1	1	NUM
ejpam-3565	338	40	and	and	CCONJ
ejpam-3565	338	41	c[4]3	c[4]3	NOUN
ejpam-3565	338	42	2	2	NUM
ejpam-3565	338	43	with	with	ADP
ejpam-3565	338	44	generator	generator	NOUN
ejpam-3565	338	45	matrices	matrix	NOUN
ejpam-3565	338	46	[	[	X
ejpam-3565	338	47	i2	i2	NOUN
ejpam-3565	338	48	a3,1	a3,1	PROPN
ejpam-3565	338	49	]	]	PUNCT
ejpam-3565	339	1	=	=	PUNCT
ejpam-3565	339	2	[	[	PUNCT
ejpam-3565	339	3	1	1	NUM
ejpam-3565	339	4	0	0	NUM
ejpam-3565	339	5	ω̄2	ω̄2	NUM
ejpam-3565	339	6	0	0	NUM
ejpam-3565	339	7	0	0	NUM
ejpam-3565	339	8	1	1	NUM
ejpam-3565	339	9	0	0	NUM
ejpam-3565	339	10	ω̄2	ω̄2	NUM
ejpam-3565	339	11	]	]	PUNCT
ejpam-3565	339	12	and	and	CCONJ
ejpam-3565	339	13	[	[	X
ejpam-3565	339	14	i2	i2	PROPN
ejpam-3565	339	15	a3,2	a3,2	PROPN
ejpam-3565	339	16	]	]	X
ejpam-3565	339	17	=	=	PUNCT
ejpam-3565	339	18	[	[	PUNCT
ejpam-3565	339	19	1	1	NUM
ejpam-3565	339	20	0	0	NUM
ejpam-3565	339	21	1	1	NUM
ejpam-3565	339	22	1	1	NUM
ejpam-3565	339	23	0	0	NUM
ejpam-3565	339	24	1	1	NUM
ejpam-3565	339	25	ω̄4	ω̄4	NOUN
ejpam-3565	339	26	1	1	NUM
ejpam-3565	339	27	]	]	PUNCT
ejpam-3565	339	28	,	,	PUNCT
ejpam-3565	339	29	respectively	respectively	ADV
ejpam-3565	339	30	.	.	PUNCT
ejpam-3565	340	1	the	the	DET
ejpam-3565	340	2	matrices	matrix	NOUN
ejpam-3565	340	3	g3,1,0	g3,1,0	NOUN
ejpam-3565	340	4	=	=	PUNCT
ejpam-3565	340	5	[	[	PUNCT
ejpam-3565	340	6	1	1	NUM
ejpam-3565	340	7	0	0	NUM
ejpam-3565	340	8	0	0	NUM
ejpam-3565	340	9	ω̄2	ω̄2	NUM
ejpam-3565	340	10	0	0	NUM
ejpam-3565	340	11	1	1	NUM
ejpam-3565	340	12	ω̄2	ω̄2	NUM
ejpam-3565	340	13	0	0	NUM
ejpam-3565	340	14	]	]	PUNCT
ejpam-3565	340	15	,	,	PUNCT
ejpam-3565	340	16	g3,1,1	g3,1,1	PROPN
ejpam-3565	340	17	=	=	PUNCT
ejpam-3565	341	1	[	[	PUNCT
ejpam-3565	341	2	1	1	NUM
ejpam-3565	341	3	1	1	NUM
ejpam-3565	341	4	ω̄2	ω̄2	NUM
ejpam-3565	341	5	ω̄2	ω̄2	NUM
ejpam-3565	341	6	0	0	NUM
ejpam-3565	341	7	1	1	NUM
ejpam-3565	341	8	0	0	NUM
ejpam-3565	341	9	ω̄2	ω̄2	NUM
ejpam-3565	341	10	]	]	PUNCT
ejpam-3565	341	11	and	and	CCONJ
ejpam-3565	341	12	g3,1,ω̄	g3,1,ω̄	NOUN
ejpam-3565	342	1	=	=	PUNCT
ejpam-3565	342	2	[	[	PUNCT
ejpam-3565	342	3	1	1	NUM
ejpam-3565	342	4	ω̄	ω̄	NUM
ejpam-3565	342	5	ω̄2	ω̄2	NUM
ejpam-3565	342	6	ω̄3	ω̄3	NUM
ejpam-3565	342	7	0	0	NUM
ejpam-3565	342	8	1	1	NUM
ejpam-3565	342	9	0	0	NUM
ejpam-3565	342	10	ω̄2	ω̄2	NUM
ejpam-3565	342	11	]	]	PUNCT
ejpam-3565	342	12	generate	generate	VERB
ejpam-3565	342	13	codes	code	NOUN
ejpam-3565	342	14	which	which	PRON
ejpam-3565	342	15	are	be	AUX
ejpam-3565	342	16	equivalent	equivalent	ADJ
ejpam-3565	342	17	to	to	ADP
ejpam-3565	342	18	c[4]3	c[4]3	NOUN
ejpam-3565	342	19	1	1	NUM
ejpam-3565	342	20	,	,	PUNCT
ejpam-3565	342	21	while	while	SCONJ
ejpam-3565	342	22	the	the	DET
ejpam-3565	342	23	matrices	matrix	NOUN
ejpam-3565	342	24	g3,2,0	g3,2,0	X
ejpam-3565	342	25	=	=	PUNCT
ejpam-3565	343	1	[	[	X
ejpam-3565	343	2	i2	i2	PROPN
ejpam-3565	343	3	a3,2	a3,2	PROPN
ejpam-3565	343	4	]	]	PUNCT
ejpam-3565	343	5	and	and	CCONJ
ejpam-3565	343	6	g3,2,ω̄	g3,2,ω̄	NOUN
ejpam-3565	343	7	=	=	PUNCT
ejpam-3565	343	8	[	[	PUNCT
ejpam-3565	343	9	1	1	NUM
ejpam-3565	343	10	ω̄	ω̄	NUM
ejpam-3565	343	11	ω̄3	ω̄3	NUM
ejpam-3565	343	12	ω̄2	ω̄2	NUM
ejpam-3565	343	13	0	0	NUM
ejpam-3565	343	14	1	1	NUM
ejpam-3565	343	15	ω̄4	ω̄4	NUM
ejpam-3565	343	16	1	1	NUM
ejpam-3565	343	17	]	]	PUNCT
ejpam-3565	343	18	generate	generate	VERB
ejpam-3565	343	19	codes	code	NOUN
ejpam-3565	343	20	which	which	PRON
ejpam-3565	343	21	are	be	AUX
ejpam-3565	343	22	equivalent	equivalent	ADJ
ejpam-3565	343	23	to	to	ADP
ejpam-3565	343	24	c[4]3	c[4]3	NOUN
ejpam-3565	343	25	2	2	NUM
ejpam-3565	343	26	.	.	PUNCT
ejpam-3565	343	27	table	table	NOUN
ejpam-3565	343	28	1	1	NUM
ejpam-3565	343	29	:	:	PUNCT
ejpam-3565	343	30	self	self	NOUN
ejpam-3565	343	31	-	-	PUNCT
ejpam-3565	343	32	dual	dual	ADJ
ejpam-3565	343	33	codes	code	NOUN
ejpam-3565	343	34	of	of	ADP
ejpam-3565	343	35	length	length	NOUN
ejpam-3565	343	36	4	4	NUM
ejpam-3565	343	37	over	over	ADP
ejpam-3565	343	38	gr(27	gr(27	PROPN
ejpam-3565	343	39	,	,	PUNCT
ejpam-3565	343	40	2	2	NUM
ejpam-3565	343	41	)	)	PUNCT
ejpam-3565	343	42	.	.	PUNCT
ejpam-3565	344	1	type	type	NOUN
ejpam-3565	344	2	generator	generator	PROPN
ejpam-3565	344	3	matrix	matrix	NOUN
ejpam-3565	344	4	no	no	INTJ
ejpam-3565	344	5	.	.	PUNCT
ejpam-3565	345	1	of	of	ADP
ejpam-3565	345	2	codes	code	NOUN
ejpam-3565	345	3	|aut(c)|	|aut(c)|	ADJ
ejpam-3565	345	4	{	{	PUNCT
ejpam-3565	345	5	0	0	NUM
ejpam-3565	345	6	,	,	PUNCT
ejpam-3565	345	7	2	2	NUM
ejpam-3565	345	8	,	,	PUNCT
ejpam-3565	345	9	2	2	NUM
ejpam-3565	345	10	}	}	PUNCT
ejpam-3565	345	11	m3(â3,1	m3(â3,1	NOUN
ejpam-3565	345	12	)	)	PUNCT
ejpam-3565	345	13	1	1	NUM
ejpam-3565	345	14	32	32	NUM
ejpam-3565	345	15	m3(â3,2	m3(â3,2	NOUN
ejpam-3565	345	16	)	)	PUNCT
ejpam-3565	345	17	1	1	NUM
ejpam-3565	345	18	48	48	NUM
ejpam-3565	345	19	{	{	PUNCT
ejpam-3565	345	20	1	1	NUM
ejpam-3565	345	21	,	,	PUNCT
ejpam-3565	345	22	1	1	NUM
ejpam-3565	345	23	,	,	PUNCT
ejpam-3565	345	24	1	1	NUM
ejpam-3565	345	25	}	}	PUNCT
ejpam-3565	345	26	m3(ĝ3,1,0	m3(ĝ3,1,0	PROPN
ejpam-3565	345	27	,	,	PUNCT
ejpam-3565	345	28	0	0	NUM
ejpam-3565	345	29	)	)	PUNCT
ejpam-3565	345	30	1	1	NUM
ejpam-3565	345	31	16	16	NUM
ejpam-3565	345	32	m3(ĝ3,1,1	m3(ĝ3,1,1	NOUN
ejpam-3565	345	33	,	,	PUNCT
ejpam-3565	345	34	0	0	NUM
ejpam-3565	345	35	)	)	PUNCT
ejpam-3565	345	36	,	,	PUNCT
ejpam-3565	345	37	m3(ĝ3,1,ω̄	m3(ĝ3,1,ω̄	NOUN
ejpam-3565	345	38	,	,	PUNCT
ejpam-3565	345	39	0	0	NUM
ejpam-3565	345	40	)	)	PUNCT
ejpam-3565	345	41	,	,	PUNCT
ejpam-3565	345	42	m3(ĝ3,2,ω̄	m3(ĝ3,2,ω̄	NOUN
ejpam-3565	345	43	,	,	PUNCT
ejpam-3565	345	44	0	0	NUM
ejpam-3565	345	45	)	)	PUNCT
ejpam-3565	345	46	3	3	NUM
ejpam-3565	345	47	8	8	NUM
ejpam-3565	345	48	m3(ĝ3,1,0	m3(ĝ3,1,0	NOUN
ejpam-3565	345	49	,	,	PUNCT
ejpam-3565	345	50	x	x	NOUN
ejpam-3565	345	51	)	)	PUNCT
ejpam-3565	345	52	,	,	PUNCT
ejpam-3565	345	53	where	where	SCONJ
ejpam-3565	345	54	x	x	X
ejpam-3565	345	55	∈	∈	PROPN
ejpam-3565	345	56	{	{	PUNCT
ejpam-3565	345	57	1	1	NUM
ejpam-3565	345	58	,	,	PUNCT
ejpam-3565	345	59	ω	ω	NOUN
ejpam-3565	345	60	}	}	PUNCT
ejpam-3565	345	61	11	11	NUM
ejpam-3565	345	62	4	4	NUM
ejpam-3565	345	63	m3(ĝ3,1,1	m3(ĝ3,1,1	ADJ
ejpam-3565	345	64	,	,	PUNCT
ejpam-3565	345	65	x	x	NOUN
ejpam-3565	345	66	)	)	PUNCT
ejpam-3565	345	67	,	,	PUNCT
ejpam-3565	345	68	where	where	SCONJ
ejpam-3565	345	69	x	x	X
ejpam-3565	345	70	∈	∈	PROPN
ejpam-3565	345	71	{	{	PUNCT
ejpam-3565	345	72	1	1	NUM
ejpam-3565	345	73	,	,	PUNCT
ejpam-3565	345	74	ω	ω	PROPN
ejpam-3565	345	75	,	,	PUNCT
ejpam-3565	345	76	ω2	ω2	ADJ
ejpam-3565	345	77	,	,	PUNCT
ejpam-3565	345	78	ω3	ω3	ADJ
ejpam-3565	345	79	}	}	PUNCT
ejpam-3565	345	80	m3(ĝ3,2,0	m3(ĝ3,2,0	PROPN
ejpam-3565	345	81	,	,	PUNCT
ejpam-3565	345	82	0	0	NUM
ejpam-3565	345	83	)	)	PUNCT
ejpam-3565	345	84	,	,	PUNCT
ejpam-3565	345	85	m3(ĝ3,2,ω̄	m3(ĝ3,2,ω̄	NOUN
ejpam-3565	345	86	,	,	PUNCT
ejpam-3565	345	87	x	x	NOUN
ejpam-3565	345	88	)	)	PUNCT
ejpam-3565	345	89	,	,	PUNCT
ejpam-3565	346	1	where	where	SCONJ
ejpam-3565	346	2	x	x	X
ejpam-3565	346	3	∈	∈	NOUN
ejpam-3565	346	4	{	{	PUNCT
ejpam-3565	346	5	1	1	NUM
ejpam-3565	346	6	,	,	PUNCT
ejpam-3565	346	7	ω2	ω2	ADJ
ejpam-3565	346	8	,	,	PUNCT
ejpam-3565	346	9	ω3	ω3	PROPN
ejpam-3565	346	10	,	,	PUNCT
ejpam-3565	346	11	ω5	ω5	NOUN
ejpam-3565	346	12	}	}	PUNCT
ejpam-3565	346	13	m3(ĝ3,1,ω̄	m3(ĝ3,1,ω̄	NOUN
ejpam-3565	346	14	,	,	PUNCT
ejpam-3565	346	15	x	x	NOUN
ejpam-3565	346	16	)	)	PUNCT
ejpam-3565	346	17	,	,	PUNCT
ejpam-3565	346	18	where	where	SCONJ
ejpam-3565	346	19	x	x	X
ejpam-3565	346	20	∈	∈	PROPN
ejpam-3565	346	21	{	{	PUNCT
ejpam-3565	346	22	1	1	NUM
ejpam-3565	346	23	,	,	PUNCT
ejpam-3565	346	24	ω	ω	NOUN
ejpam-3565	346	25	}	}	PUNCT
ejpam-3565	346	26	,	,	PUNCT
ejpam-3565	346	27	3	3	NUM
ejpam-3565	346	28	2	2	NUM
ejpam-3565	346	29	m3(ĝ3,2,0	m3(ĝ3,2,0	NOUN
ejpam-3565	346	30	,	,	PUNCT
ejpam-3565	346	31	ω	ω	NOUN
ejpam-3565	346	32	)	)	PUNCT
ejpam-3565	346	33	{	{	PUNCT
ejpam-3565	346	34	2	2	NUM
ejpam-3565	346	35	,	,	PUNCT
ejpam-3565	346	36	0	0	NUM
ejpam-3565	346	37	,	,	PUNCT
ejpam-3565	346	38	0	0	NUM
ejpam-3565	346	39	}	}	PUNCT
ejpam-3565	346	40	m3(â3,1	m3(â3,1	NOUN
ejpam-3565	346	41	,	,	PUNCT
ejpam-3565	346	42	0	0	NUM
ejpam-3565	346	43	,	,	PUNCT
ejpam-3565	346	44	0	0	NUM
ejpam-3565	346	45	)	)	PUNCT
ejpam-3565	346	46	1	1	NUM
ejpam-3565	346	47	32	32	NUM
ejpam-3565	346	48	m3(â3,2	m3(â3,2	NOUN
ejpam-3565	346	49	,	,	PUNCT
ejpam-3565	346	50	0	0	NUM
ejpam-3565	346	51	,	,	PUNCT
ejpam-3565	346	52	0	0	NUM
ejpam-3565	346	53	)	)	PUNCT
ejpam-3565	346	54	1	1	NUM
ejpam-3565	346	55	16	16	NUM
ejpam-3565	346	56	m3(â3,1	m3(â3,1	NOUN
ejpam-3565	346	57	,	,	PUNCT
ejpam-3565	346	58	0	0	NUM
ejpam-3565	346	59	,	,	PUNCT
ejpam-3565	346	60	z	z	NOUN
ejpam-3565	346	61	)	)	PUNCT
ejpam-3565	346	62	,	,	PUNCT
ejpam-3565	346	63	where	where	SCONJ
ejpam-3565	346	64	z	z	PROPN
ejpam-3565	346	65	∈	∈	PROPN
ejpam-3565	346	66	{	{	PUNCT
ejpam-3565	346	67	1	1	NUM
ejpam-3565	346	68	,	,	PUNCT
ejpam-3565	346	69	ω	ω	NOUN
ejpam-3565	346	70	}	}	PUNCT
ejpam-3565	346	71	33	33	NUM
ejpam-3565	346	72	8	8	NUM
ejpam-3565	346	73	m3(â3,1	m3(â3,1	NOUN
ejpam-3565	346	74	,	,	PUNCT
ejpam-3565	346	75	1	1	NUM
ejpam-3565	346	76	,	,	PUNCT
ejpam-3565	346	77	z	z	NOUN
ejpam-3565	346	78	)	)	PUNCT
ejpam-3565	346	79	,	,	PUNCT
ejpam-3565	346	80	where	where	SCONJ
ejpam-3565	346	81	z	z	PROPN
ejpam-3565	346	82	∈	∈	PROPN
ejpam-3565	346	83	{	{	PUNCT
ejpam-3565	346	84	0	0	NUM
ejpam-3565	346	85	,	,	PUNCT
ejpam-3565	346	86	1	1	NUM
ejpam-3565	346	87	,	,	PUNCT
ejpam-3565	346	88	ω	ω	NOUN
ejpam-3565	346	89	,	,	PUNCT
ejpam-3565	346	90	.	.	PUNCT
ejpam-3565	346	91	.	.	PUNCT
ejpam-3565	346	92	.	.	PUNCT
ejpam-3565	346	93	,	,	PUNCT
ejpam-3565	346	94	ω7	ω7	NOUN
ejpam-3565	346	95	}	}	PUNCT
ejpam-3565	346	96	m3(â3,1	m3(â3,1	NOUN
ejpam-3565	346	97	,	,	PUNCT
ejpam-3565	346	98	ω	ω	NOUN
ejpam-3565	346	99	,	,	PUNCT
ejpam-3565	346	100	z	z	NOUN
ejpam-3565	346	101	)	)	PUNCT
ejpam-3565	346	102	,	,	PUNCT
ejpam-3565	346	103	where	where	SCONJ
ejpam-3565	346	104	z	z	PROPN
ejpam-3565	346	105	∈	∈	PROPN
ejpam-3565	346	106	{	{	PUNCT
ejpam-3565	346	107	0	0	NUM
ejpam-3565	346	108	,	,	PUNCT
ejpam-3565	346	109	1	1	NUM
ejpam-3565	346	110	,	,	PUNCT
ejpam-3565	346	111	ω	ω	NOUN
ejpam-3565	346	112	,	,	PUNCT
ejpam-3565	346	113	.	.	PUNCT
ejpam-3565	346	114	.	.	PUNCT
ejpam-3565	346	115	.	.	PUNCT
ejpam-3565	347	1	,	,	PUNCT
ejpam-3565	347	2	ω7	ω7	NOUN
ejpam-3565	347	3	}	}	PUNCT
ejpam-3565	347	4	m3(â3,2	m3(â3,2	PROPN
ejpam-3565	347	5	,	,	PUNCT
ejpam-3565	347	6	0	0	NUM
ejpam-3565	347	7	,	,	PUNCT
ejpam-3565	347	8	z	z	NOUN
ejpam-3565	347	9	)	)	PUNCT
ejpam-3565	347	10	,	,	PUNCT
ejpam-3565	348	1	where	where	SCONJ
ejpam-3565	348	2	z	z	PROPN
ejpam-3565	348	3	∈	∈	PROPN
ejpam-3565	348	4	{	{	PUNCT
ejpam-3565	348	5	1	1	NUM
ejpam-3565	348	6	,	,	PUNCT
ejpam-3565	348	7	ω	ω	PROPN
ejpam-3565	348	8	,	,	PUNCT
ejpam-3565	348	9	ω2	ω2	ADJ
ejpam-3565	348	10	,	,	PUNCT
ejpam-3565	348	11	ω3	ω3	ADJ
ejpam-3565	348	12	}	}	PUNCT
ejpam-3565	348	13	m3(â3,2	m3(â3,2	PROPN
ejpam-3565	348	14	,	,	PUNCT
ejpam-3565	348	15	ω	ω	PROPN
ejpam-3565	348	16	,	,	PUNCT
ejpam-3565	348	17	z	z	NOUN
ejpam-3565	348	18	)	)	PUNCT
ejpam-3565	348	19	,	,	PUNCT
ejpam-3565	348	20	where	where	SCONJ
ejpam-3565	348	21	z	z	PROPN
ejpam-3565	348	22	∈	∈	PROPN
ejpam-3565	348	23	{	{	PUNCT
ejpam-3565	348	24	0	0	NUM
ejpam-3565	348	25	,	,	PUNCT
ejpam-3565	348	26	1	1	NUM
ejpam-3565	348	27	,	,	PUNCT
ejpam-3565	348	28	ω	ω	NOUN
ejpam-3565	348	29	,	,	PUNCT
ejpam-3565	348	30	.	.	PUNCT
ejpam-3565	348	31	.	.	PUNCT
ejpam-3565	348	32	.	.	PUNCT
ejpam-3565	348	33	,	,	PUNCT
ejpam-3565	348	34	ω7	ω7	NOUN
ejpam-3565	348	35	}	}	PUNCT
ejpam-3565	348	36	in	in	ADP
ejpam-3565	348	37	table	table	NOUN
ejpam-3565	348	38	1	1	NUM
ejpam-3565	348	39	,	,	PUNCT
ejpam-3565	348	40	we	we	PRON
ejpam-3565	348	41	give	give	VERB
ejpam-3565	348	42	the	the	DET
ejpam-3565	348	43	list	list	NOUN
ejpam-3565	348	44	of	of	ADP
ejpam-3565	348	45	inequivalent	inequivalent	NOUN
ejpam-3565	348	46	self	self	NOUN
ejpam-3565	348	47	-	-	PUNCT
ejpam-3565	348	48	dual	dual	ADJ
ejpam-3565	348	49	codes	code	NOUN
ejpam-3565	348	50	over	over	ADP
ejpam-3565	348	51	gr(27	gr(27	PROPN
ejpam-3565	348	52	,	,	PUNCT
ejpam-3565	348	53	2	2	NUM
ejpam-3565	348	54	)	)	PUNCT
ejpam-3565	348	55	of	of	ADP
ejpam-3565	348	56	length	length	NOUN
ejpam-3565	348	57	4	4	NUM
ejpam-3565	348	58	.	.	PUNCT
ejpam-3565	348	59	using	use	VERB
ejpam-3565	348	60	the	the	DET
ejpam-3565	348	61	mass	mass	ADJ
ejpam-3565	348	62	formula	formula	NOUN
ejpam-3565	348	63	in	in	ADP
ejpam-3565	348	64	theorem	theorem	NOUN
ejpam-3565	348	65	1	1	NUM
ejpam-3565	348	66	,	,	PUNCT
ejpam-3565	348	67	we	we	PRON
ejpam-3565	348	68	make	make	VERB
ejpam-3565	348	69	the	the	DET
ejpam-3565	348	70	following	follow	VERB
ejpam-3565	348	71	computations	computation	NOUN
ejpam-3565	348	72	,	,	PUNCT
ejpam-3565	348	73	confirming	confirm	VERB
ejpam-3565	348	74	that	that	SCONJ
ejpam-3565	348	75	table	table	NOUN
ejpam-3565	348	76	1	1	NUM
ejpam-3565	348	77	gives	give	VERB
ejpam-3565	348	78	a	a	DET
ejpam-3565	348	79	complete	complete	ADJ
ejpam-3565	348	80	classification	classification	NOUN
ejpam-3565	348	81	.	.	PUNCT
ejpam-3565	349	1	n27,2(4	n27,2(4	NOUN
ejpam-3565	349	2	)	)	PUNCT
ejpam-3565	350	1	=	=	SYM
ejpam-3565	350	2	σ9(4	σ9(4	NOUN
ejpam-3565	350	3	,	,	PUNCT
ejpam-3565	350	4	2	2	NUM
ejpam-3565	350	5	)	)	PUNCT
ejpam-3565	350	6	2∑	2∑	NOUN
ejpam-3565	350	7	k=0	k=0	X
ejpam-3565	350	8	(	(	PUNCT
ejpam-3565	350	9	2	2	NUM
ejpam-3565	350	10	k	k	NOUN
ejpam-3565	350	11	)	)	PUNCT
ejpam-3565	350	12	9	9	NUM
ejpam-3565	350	13	32k	32k	NOUN
ejpam-3565	350	14	=	=	SYM
ejpam-3565	350	15	20	20	NUM
ejpam-3565	350	16	+	+	NUM
ejpam-3565	350	17	1800	1800	NUM
ejpam-3565	350	18	+	+	SYM
ejpam-3565	350	19	1620	1620	NUM
ejpam-3565	350	20	=	=	SYM
ejpam-3565	350	21	∑	∑	PUNCT
ejpam-3565	350	22	c	c	PROPN
ejpam-3565	350	23	24	24	NUM
ejpam-3565	350	24	·	·	SYM
ejpam-3565	350	25	4	4	X
ejpam-3565	350	26	!	!	PUNCT
ejpam-3565	350	27	|aut(c)|	|aut(c)|	NOUN
ejpam-3565	350	28	.	.	PUNCT
ejpam-3565	351	1	t.	t.	PROPN
ejpam-3565	351	2	l.	l.	PROPN
ejpam-3565	351	3	vasquez	vasquez	PROPN
ejpam-3565	351	4	,	,	PUNCT
ejpam-3565	351	5	g.	g.	PROPN
ejpam-3565	351	6	petalcorin	petalcorin	PROPN
ejpam-3565	351	7	/	/	SYM
ejpam-3565	351	8	eur	eur	PROPN
ejpam-3565	351	9	.	.	PUNCT
ejpam-3565	352	1	j.	j.	PROPN
ejpam-3565	352	2	pure	pure	PROPN
ejpam-3565	352	3	appl	appl	PROPN
ejpam-3565	352	4	.	.	PROPN
ejpam-3565	352	5	math	math	PROPN
ejpam-3565	352	6	,	,	PUNCT
ejpam-3565	352	7	12	12	NUM
ejpam-3565	352	8	(	(	PUNCT
ejpam-3565	352	9	4	4	NUM
ejpam-3565	352	10	)	)	PUNCT
ejpam-3565	352	11	(	(	PUNCT
ejpam-3565	352	12	2019	2019	NUM
ejpam-3565	352	13	)	)	PUNCT
ejpam-3565	352	14	,	,	PUNCT
ejpam-3565	352	15	1701	1701	NUM
ejpam-3565	352	16	-	-	SYM
ejpam-3565	352	17	1716	1716	NUM
ejpam-3565	352	18	1713	1713	NUM
ejpam-3565	352	19	hence	hence	ADV
ejpam-3565	352	20	there	there	PRON
ejpam-3565	352	21	are	be	VERB
ejpam-3565	352	22	55	55	NUM
ejpam-3565	352	23	self	self	NOUN
ejpam-3565	352	24	-	-	PUNCT
ejpam-3565	352	25	dual	dual	ADJ
ejpam-3565	352	26	codes	code	NOUN
ejpam-3565	352	27	of	of	ADP
ejpam-3565	352	28	length	length	NOUN
ejpam-3565	352	29	4	4	NUM
ejpam-3565	352	30	over	over	ADP
ejpam-3565	352	31	gr(27	gr(27	PROPN
ejpam-3565	352	32	,	,	PUNCT
ejpam-3565	352	33	2	2	NUM
ejpam-3565	352	34	)	)	PUNCT
ejpam-3565	352	35	.	.	PUNCT
ejpam-3565	353	1	5.3	5.3	NUM
ejpam-3565	353	2	.	.	PUNCT
ejpam-3565	353	3	self	self	NOUN
ejpam-3565	353	4	-	-	PUNCT
ejpam-3565	353	5	dual	dual	ADJ
ejpam-3565	353	6	codes	code	NOUN
ejpam-3565	353	7	over	over	ADP
ejpam-3565	353	8	gr(125	gr(125	PROPN
ejpam-3565	353	9	,	,	PUNCT
ejpam-3565	353	10	2	2	X
ejpam-3565	353	11	)	)	PUNCT
ejpam-3565	353	12	we	we	PRON
ejpam-3565	353	13	consider	consider	VERB
ejpam-3565	353	14	gr(125	gr(125	NOUN
ejpam-3565	353	15	,	,	PUNCT
ejpam-3565	353	16	2	2	X
ejpam-3565	353	17	)	)	PUNCT
ejpam-3565	353	18	=	=	NOUN
ejpam-3565	354	1	z125[ω	z125[ω	PROPN
ejpam-3565	354	2	]	]	PUNCT
ejpam-3565	354	3	,	,	PUNCT
ejpam-3565	354	4	where	where	SCONJ
ejpam-3565	354	5	ω2	ω2	ADJ
ejpam-3565	354	6	+	+	NOUN
ejpam-3565	354	7	89ω	89ω	NOUN
ejpam-3565	354	8	+	+	CCONJ
ejpam-3565	354	9	57	57	NUM
ejpam-3565	354	10	=	=	SYM
ejpam-3565	354	11	0	0	NUM
ejpam-3565	354	12	and	and	CCONJ
ejpam-3565	354	13	ω24	ω24	NOUN
ejpam-3565	354	14	=	=	SYM
ejpam-3565	354	15	1	1	NUM
ejpam-3565	354	16	,	,	PUNCT
ejpam-3565	354	17	and	and	CCONJ
ejpam-3565	354	18	f25	f25	NOUN
ejpam-3565	354	19	=	=	SYM
ejpam-3565	354	20	z5[ω̄	z5[ω̄	PROPN
ejpam-3565	354	21	]	]	PUNCT
ejpam-3565	354	22	,	,	PUNCT
ejpam-3565	354	23	where	where	SCONJ
ejpam-3565	354	24	ω̄2	ω̄2	NUM
ejpam-3565	354	25	+	+	NUM
ejpam-3565	354	26	4ω	4ω	NOUN
ejpam-3565	354	27	+	+	CCONJ
ejpam-3565	354	28	2	2	NUM
ejpam-3565	354	29	=	=	SYM
ejpam-3565	354	30	0	0	NUM
ejpam-3565	354	31	and	and	CCONJ
ejpam-3565	354	32	ω̄24	ω̄24	NUM
ejpam-3565	354	33	=	=	SYM
ejpam-3565	354	34	1	1	X
ejpam-3565	354	35	.	.	PUNCT
ejpam-3565	354	36	from	from	ADP
ejpam-3565	354	37	[	[	X
ejpam-3565	354	38	4	4	NUM
ejpam-3565	354	39	]	]	PUNCT
ejpam-3565	354	40	,	,	PUNCT
ejpam-3565	354	41	there	there	PRON
ejpam-3565	354	42	exist	exist	VERB
ejpam-3565	354	43	three	three	NUM
ejpam-3565	354	44	inequivalent	inequivalent	NOUN
ejpam-3565	354	45	self	self	NOUN
ejpam-3565	354	46	-	-	PUNCT
ejpam-3565	354	47	dual	dual	ADJ
ejpam-3565	354	48	codes	code	NOUN
ejpam-3565	354	49	of	of	ADP
ejpam-3565	354	50	length	length	NOUN
ejpam-3565	354	51	4	4	NUM
ejpam-3565	354	52	over	over	ADP
ejpam-3565	354	53	f25	f25	PROPN
ejpam-3565	354	54	:	:	PUNCT
ejpam-3565	354	55	c[4]5	c[4]5	VERB
ejpam-3565	354	56	1	1	NUM
ejpam-3565	354	57	,	,	PUNCT
ejpam-3565	354	58	c[4]5	c[4]5	VERB
ejpam-3565	354	59	2	2	NUM
ejpam-3565	354	60	and	and	CCONJ
ejpam-3565	354	61	c[4]5	c[4]5	VERB
ejpam-3565	354	62	3	3	NUM
ejpam-3565	354	63	with	with	ADP
ejpam-3565	354	64	generator	generator	NOUN
ejpam-3565	354	65	matrices	matrix	NOUN
ejpam-3565	354	66	[	[	X
ejpam-3565	354	67	i2	i2	NOUN
ejpam-3565	354	68	a5,1	a5,1	PROPN
ejpam-3565	354	69	]	]	PUNCT
ejpam-3565	354	70	,	,	PUNCT
ejpam-3565	354	71	[	[	X
ejpam-3565	354	72	i2	i2	PROPN
ejpam-3565	354	73	a5,2	a5,2	NOUN
ejpam-3565	354	74	]	]	PUNCT
ejpam-3565	354	75	and	and	CCONJ
ejpam-3565	354	76	[	[	X
ejpam-3565	354	77	i2	i2	PROPN
ejpam-3565	354	78	a5,3	a5,3	PROPN
ejpam-3565	354	79	]	]	PUNCT
ejpam-3565	354	80	respectively	respectively	ADV
ejpam-3565	354	81	,	,	PUNCT
ejpam-3565	354	82	where	where	SCONJ
ejpam-3565	354	83	a5,1	a5,1	ADV
ejpam-3565	354	84	=	=	PUNCT
ejpam-3565	354	85	[	[	PUNCT
ejpam-3565	354	86	ω̄6	ω̄6	NUM
ejpam-3565	354	87	0	0	NUM
ejpam-3565	354	88	0	0	NUM
ejpam-3565	354	89	ω̄6	ω̄6	NOUN
ejpam-3565	354	90	]	]	PUNCT
ejpam-3565	354	91	,	,	PUNCT
ejpam-3565	354	92	a5,2	a5,2	NOUN
ejpam-3565	354	93	=	=	SYM
ejpam-3565	354	94	[	[	PUNCT
ejpam-3565	354	95	ω̄8	ω̄8	X
ejpam-3565	354	96	ω̄4	ω̄4	NUM
ejpam-3565	354	97	ω̄16	ω̄16	NUM
ejpam-3565	354	98	ω̄8	ω̄8	X
ejpam-3565	354	99	]	]	PUNCT
ejpam-3565	354	100	and	and	CCONJ
ejpam-3565	354	101	a5,3	a5,3	PROPN
ejpam-3565	354	102	=	=	PUNCT
ejpam-3565	355	1	[	[	PUNCT
ejpam-3565	355	2	1	1	NUM
ejpam-3565	355	3	ω̄21	ω̄21	NUM
ejpam-3565	355	4	ω̄9	ω̄9	NUM
ejpam-3565	355	5	1	1	NUM
ejpam-3565	355	6	]	]	PUNCT
ejpam-3565	355	7	,	,	PUNCT
ejpam-3565	355	8	respectively	respectively	ADV
ejpam-3565	355	9	.	.	PUNCT
ejpam-3565	356	1	c[4]5	c[4]5	VERB
ejpam-3565	356	2	1	1	NUM
ejpam-3565	356	3	is	be	AUX
ejpam-3565	356	4	equivalent	equivalent	ADJ
ejpam-3565	356	5	to	to	ADP
ejpam-3565	356	6	codes	code	NOUN
ejpam-3565	356	7	with	with	ADP
ejpam-3565	356	8	generator	generator	NOUN
ejpam-3565	356	9	matrices	matrix	NOUN
ejpam-3565	356	10	g5,1,0	g5,1,0	X
ejpam-3565	356	11	=	=	PUNCT
ejpam-3565	357	1	[	[	PUNCT
ejpam-3565	357	2	1	1	NUM
ejpam-3565	357	3	0	0	NUM
ejpam-3565	357	4	0	0	NUM
ejpam-3565	357	5	ω̄6	ω̄6	NOUN
ejpam-3565	357	6	0	0	NUM
ejpam-3565	357	7	1	1	NUM
ejpam-3565	357	8	ω̄6	ω̄6	NOUN
ejpam-3565	357	9	1	1	NUM
ejpam-3565	357	10	]	]	PUNCT
ejpam-3565	357	11	,	,	PUNCT
ejpam-3565	357	12	g5,1,1	g5,1,1	PROPN
ejpam-3565	357	13	=	=	PUNCT
ejpam-3565	358	1	[	[	PUNCT
ejpam-3565	358	2	1	1	NUM
ejpam-3565	358	3	1	1	NUM
ejpam-3565	358	4	ω̄6	ω̄6	NOUN
ejpam-3565	358	5	ω̄6	ω̄6	NOUN
ejpam-3565	358	6	0	0	NUM
ejpam-3565	358	7	1	1	NUM
ejpam-3565	358	8	0	0	NUM
ejpam-3565	358	9	ω̄6	ω̄6	NOUN
ejpam-3565	358	10	]	]	PUNCT
ejpam-3565	358	11	,	,	PUNCT
ejpam-3565	358	12	g5,1,ω̄	g5,1,ω̄	NOUN
ejpam-3565	359	1	=	=	PUNCT
ejpam-3565	359	2	[	[	PUNCT
ejpam-3565	359	3	1	1	NUM
ejpam-3565	359	4	ω̄	ω̄	NUM
ejpam-3565	359	5	ω̄6	ω̄6	NUM
ejpam-3565	359	6	ω̄7	ω̄7	NOUN
ejpam-3565	359	7	0	0	NUM
ejpam-3565	359	8	1	1	NUM
ejpam-3565	359	9	0	0	NUM
ejpam-3565	359	10	ω̄6	ω̄6	NOUN
ejpam-3565	359	11	]	]	PUNCT
ejpam-3565	359	12	,	,	PUNCT
ejpam-3565	359	13	g5,1,ω̄2	g5,1,ω̄2	PROPN
ejpam-3565	359	14	=	=	PUNCT
ejpam-3565	359	15	[	[	PUNCT
ejpam-3565	359	16	1	1	NUM
ejpam-3565	359	17	ω̄2	ω̄2	NUM
ejpam-3565	359	18	ω̄6	ω̄6	X
ejpam-3565	359	19	ω̄8	ω̄8	X
ejpam-3565	359	20	0	0	NUM
ejpam-3565	359	21	1	1	NUM
ejpam-3565	359	22	0	0	NUM
ejpam-3565	359	23	ω̄6	ω̄6	NOUN
ejpam-3565	359	24	]	]	PUNCT
ejpam-3565	359	25	and	and	CCONJ
ejpam-3565	359	26	g5,1,ω̄3	g5,1,ω̄3	PROPN
ejpam-3565	359	27	=	=	PUNCT
ejpam-3565	359	28	[	[	PUNCT
ejpam-3565	359	29	1	1	NUM
ejpam-3565	359	30	ω̄3	ω̄3	NUM
ejpam-3565	359	31	ω̄6	ω̄6	VERB
ejpam-3565	359	32	ω̄9	ω̄9	NUM
ejpam-3565	359	33	0	0	NUM
ejpam-3565	359	34	1	1	NUM
ejpam-3565	359	35	0	0	NUM
ejpam-3565	359	36	ω̄6	ω̄6	NOUN
ejpam-3565	359	37	]	]	PUNCT
ejpam-3565	359	38	,	,	PUNCT
ejpam-3565	359	39	c[4]5	c[4]5	VERB
ejpam-3565	359	40	2	2	NUM
ejpam-3565	359	41	is	be	AUX
ejpam-3565	359	42	equivalent	equivalent	ADJ
ejpam-3565	359	43	to	to	ADP
ejpam-3565	359	44	codes	code	NOUN
ejpam-3565	359	45	with	with	ADP
ejpam-3565	359	46	generator	generator	NOUN
ejpam-3565	359	47	matrices	matrix	NOUN
ejpam-3565	359	48	g5,2,0	g5,2,0	NOUN
ejpam-3565	359	49	=	=	PUNCT
ejpam-3565	360	1	[	[	X
ejpam-3565	360	2	i2	i2	PROPN
ejpam-3565	360	3	a5,2	a5,2	PROPN
ejpam-3565	360	4	]	]	PUNCT
ejpam-3565	360	5	,	,	PUNCT
ejpam-3565	360	6	g5,2,1	g5,2,1	PROPN
ejpam-3565	360	7	=	=	PUNCT
ejpam-3565	361	1	[	[	PUNCT
ejpam-3565	361	2	1	1	NUM
ejpam-3565	361	3	1	1	NUM
ejpam-3565	361	4	ω̄12	ω̄12	NUM
ejpam-3565	361	5	ω̄3	ω̄3	NUM
ejpam-3565	361	6	0	0	NUM
ejpam-3565	361	7	1	1	NUM
ejpam-3565	361	8	ω̄16	ω̄16	NUM
ejpam-3565	361	9	ω̄8	ω̄8	X
ejpam-3565	361	10	]	]	PUNCT
ejpam-3565	361	11	,	,	PUNCT
ejpam-3565	361	12	g5,2,ω̄	g5,2,ω̄	NOUN
ejpam-3565	362	1	=	=	PUNCT
ejpam-3565	362	2	[	[	PUNCT
ejpam-3565	362	3	1	1	NUM
ejpam-3565	362	4	ω̄	ω̄	ADP
ejpam-3565	362	5	ω̄19	ω̄19	NUM
ejpam-3565	362	6	ω̄18	ω̄18	NUM
ejpam-3565	362	7	0	0	NUM
ejpam-3565	362	8	1	1	NUM
ejpam-3565	362	9	ω̄16	ω̄16	NUM
ejpam-3565	362	10	ω̄8	ω̄8	NOUN
ejpam-3565	362	11	]	]	PUNCT
ejpam-3565	362	12	and	and	CCONJ
ejpam-3565	362	13	g5,2,ω̄2	g5,2,ω̄2	VERB
ejpam-3565	362	14	=	=	PUNCT
ejpam-3565	362	15	[	[	PUNCT
ejpam-3565	362	16	1	1	NUM
ejpam-3565	362	17	ω̄2	ω̄2	NUM
ejpam-3565	362	18	ω̄21	ω̄21	NUM
ejpam-3565	362	19	ω̄22	ω̄22	NUM
ejpam-3565	362	20	0	0	NUM
ejpam-3565	362	21	1	1	NUM
ejpam-3565	362	22	ω̄16	ω̄16	NUM
ejpam-3565	362	23	ω̄8	ω̄8	NOUN
ejpam-3565	362	24	]	]	PUNCT
ejpam-3565	362	25	,	,	PUNCT
ejpam-3565	362	26	while	while	SCONJ
ejpam-3565	362	27	c[4]5	c[4]5	ADJ
ejpam-3565	362	28	3	3	NUM
ejpam-3565	362	29	is	be	AUX
ejpam-3565	362	30	equivalent	equivalent	ADJ
ejpam-3565	362	31	to	to	ADP
ejpam-3565	362	32	codes	code	NOUN
ejpam-3565	362	33	with	with	ADP
ejpam-3565	362	34	generator	generator	NOUN
ejpam-3565	362	35	matrices	matrix	NOUN
ejpam-3565	362	36	g5,3,0	g5,3,0	PROPN
ejpam-3565	362	37	=	=	PUNCT
ejpam-3565	363	1	[	[	X
ejpam-3565	363	2	i2	i2	PROPN
ejpam-3565	363	3	a5,3	a5,3	PROPN
ejpam-3565	363	4	]	]	X
ejpam-3565	363	5	,	,	PUNCT
ejpam-3565	363	6	g5,3,1	g5,3,1	PROPN
ejpam-3565	363	7	=	=	PUNCT
ejpam-3565	363	8	[	[	PUNCT
ejpam-3565	363	9	1	1	NUM
ejpam-3565	363	10	1	1	NUM
ejpam-3565	363	11	ω̄11	ω̄11	NUM
ejpam-3565	363	12	ω̄7	ω̄7	NUM
ejpam-3565	363	13	0	0	NUM
ejpam-3565	363	14	1	1	NUM
ejpam-3565	363	15	ω̄9	ω̄9	NUM
ejpam-3565	363	16	1	1	NUM
ejpam-3565	363	17	]	]	PUNCT
ejpam-3565	363	18	,	,	PUNCT
ejpam-3565	363	19	g5,3,ω̄2	g5,3,ω̄2	NOUN
ejpam-3565	363	20	=	=	PUNCT
ejpam-3565	363	21	[	[	PUNCT
ejpam-3565	363	22	1	1	NUM
ejpam-3565	363	23	ω̄2	ω̄2	NUM
ejpam-3565	363	24	ω̄16	ω̄16	NUM
ejpam-3565	363	25	ω̄11	ω̄11	NUM
ejpam-3565	363	26	0	0	NUM
ejpam-3565	363	27	1	1	NUM
ejpam-3565	363	28	ω̄9	ω̄9	NUM
ejpam-3565	363	29	1	1	NUM
ejpam-3565	363	30	]	]	PUNCT
ejpam-3565	363	31	,	,	PUNCT
ejpam-3565	363	32	g5,3,ω̄6	g5,3,ω̄6	NOUN
ejpam-3565	363	33	=	=	SYM
ejpam-3565	363	34	[	[	PUNCT
ejpam-3565	363	35	1	1	NUM
ejpam-3565	363	36	ω̄6	ω̄6	NOUN
ejpam-3565	363	37	ω̄2	ω̄2	NUM
ejpam-3565	363	38	ω̄8	ω̄8	X
ejpam-3565	363	39	0	0	NUM
ejpam-3565	363	40	1	1	NUM
ejpam-3565	363	41	ω̄9	ω̄9	NUM
ejpam-3565	363	42	1	1	NUM
ejpam-3565	363	43	]	]	PUNCT
ejpam-3565	363	44	and	and	CCONJ
ejpam-3565	363	45	g5,3,ω̄15	g5,3,ω̄15	PROPN
ejpam-3565	363	46	=	=	SYM
ejpam-3565	363	47	[	[	PUNCT
ejpam-3565	363	48	1	1	NUM
ejpam-3565	363	49	ω̄15	ω̄15	NUM
ejpam-3565	363	50	ω̄6	ω̄6	NOUN
ejpam-3565	363	51	ω̄9	ω̄9	NUM
ejpam-3565	363	52	0	0	NUM
ejpam-3565	363	53	1	1	NUM
ejpam-3565	363	54	ω̄9	ω̄9	NUM
ejpam-3565	363	55	1	1	NUM
ejpam-3565	363	56	]	]	PUNCT
ejpam-3565	363	57	.	.	PUNCT
ejpam-3565	364	1	let	let	VERB
ejpam-3565	364	2	j1	j1	PROPN
ejpam-3565	364	3	and	and	CCONJ
ejpam-3565	364	4	j2	j2	PROPN
ejpam-3565	364	5	be	be	VERB
ejpam-3565	364	6	subsets	subset	NOUN
ejpam-3565	364	7	of	of	ADP
ejpam-3565	364	8	t25	t25	NOUN
ejpam-3565	364	9	,	,	PUNCT
ejpam-3565	364	10	with	with	ADP
ejpam-3565	364	11	j1	j1	PROPN
ejpam-3565	364	12	=	=	SYM
ejpam-3565	364	13	{	{	PUNCT
ejpam-3565	364	14	0	0	NUM
ejpam-3565	364	15	,	,	PUNCT
ejpam-3565	364	16	1	1	NUM
ejpam-3565	364	17	,	,	PUNCT
ejpam-3565	364	18	ω	ω	PROPN
ejpam-3565	364	19	,	,	PUNCT
ejpam-3565	364	20	ω2	ω2	ADJ
ejpam-3565	364	21	,	,	PUNCT
ejpam-3565	364	22	ω4	ω4	NUM
ejpam-3565	364	23	,	,	PUNCT
ejpam-3565	364	24	ω5	ω5	NOUN
ejpam-3565	364	25	,	,	PUNCT
ejpam-3565	364	26	ω7	ω7	NOUN
ejpam-3565	364	27	,	,	PUNCT
ejpam-3565	364	28	ω9	ω9	PROPN
ejpam-3565	364	29	,	,	PUNCT
ejpam-3565	364	30	ω10	ω10	NUM
ejpam-3565	364	31	,	,	PUNCT
ejpam-3565	364	32	ω11	ω11	ADV
ejpam-3565	364	33	,	,	PUNCT
ejpam-3565	364	34	ω13	ω13	PROPN
ejpam-3565	364	35	,	,	PUNCT
ejpam-3565	364	36	ω17	ω17	ADJ
ejpam-3565	364	37	}	}	PUNCT
ejpam-3565	364	38	j2	j2	NOUN
ejpam-3565	364	39	=	=	SYM
ejpam-3565	364	40	{	{	PUNCT
ejpam-3565	364	41	0	0	NUM
ejpam-3565	364	42	,	,	PUNCT
ejpam-3565	364	43	1	1	NUM
ejpam-3565	364	44	,	,	PUNCT
ejpam-3565	364	45	ω	ω	PROPN
ejpam-3565	364	46	,	,	PUNCT
ejpam-3565	364	47	ω2	ω2	ADJ
ejpam-3565	364	48	,	,	PUNCT
ejpam-3565	364	49	ω4	ω4	NUM
ejpam-3565	364	50	,	,	PUNCT
ejpam-3565	364	51	ω5	ω5	PROPN
ejpam-3565	364	52	,	,	PUNCT
ejpam-3565	364	53	ω6	ω6	PROPN
ejpam-3565	364	54	,	,	PUNCT
ejpam-3565	364	55	ω7	ω7	NOUN
ejpam-3565	364	56	,	,	PUNCT
ejpam-3565	364	57	ω10	ω10	NUM
ejpam-3565	364	58	,	,	PUNCT
ejpam-3565	364	59	ω11	ω11	NUM
ejpam-3565	364	60	,	,	PUNCT
ejpam-3565	364	61	ω15	ω15	PROPN
ejpam-3565	364	62	,	,	PUNCT
ejpam-3565	364	63	ω16	ω16	VERB
ejpam-3565	364	64	}	}	PUNCT
ejpam-3565	364	65	.	.	PUNCT
ejpam-3565	365	1	table	table	NOUN
ejpam-3565	365	2	2	2	NUM
ejpam-3565	365	3	gives	give	VERB
ejpam-3565	365	4	the	the	DET
ejpam-3565	365	5	list	list	NOUN
ejpam-3565	365	6	of	of	ADP
ejpam-3565	365	7	inequivalent	inequivalent	NOUN
ejpam-3565	365	8	self	self	NOUN
ejpam-3565	365	9	-	-	PUNCT
ejpam-3565	365	10	dual	dual	ADJ
ejpam-3565	365	11	codes	code	NOUN
ejpam-3565	365	12	over	over	ADP
ejpam-3565	365	13	gr(125	gr(125	PROPN
ejpam-3565	365	14	,	,	PUNCT
ejpam-3565	365	15	2	2	NUM
ejpam-3565	365	16	)	)	PUNCT
ejpam-3565	365	17	of	of	ADP
ejpam-3565	365	18	length	length	NOUN
ejpam-3565	365	19	4	4	NUM
ejpam-3565	365	20	.	.	PUNCT
ejpam-3565	365	21	using	use	VERB
ejpam-3565	365	22	the	the	DET
ejpam-3565	365	23	mass	mass	ADJ
ejpam-3565	365	24	formula	formula	NOUN
ejpam-3565	365	25	in	in	ADP
ejpam-3565	365	26	theorem	theorem	NOUN
ejpam-3565	365	27	1	1	NUM
ejpam-3565	365	28	,	,	PUNCT
ejpam-3565	365	29	we	we	PRON
ejpam-3565	365	30	make	make	VERB
ejpam-3565	365	31	the	the	DET
ejpam-3565	365	32	following	follow	VERB
ejpam-3565	365	33	computations	computation	NOUN
ejpam-3565	365	34	,	,	PUNCT
ejpam-3565	365	35	confirming	confirm	VERB
ejpam-3565	365	36	that	that	SCONJ
ejpam-3565	365	37	table	table	NOUN
ejpam-3565	365	38	2	2	NUM
ejpam-3565	365	39	gives	give	VERB
ejpam-3565	365	40	a	a	DET
ejpam-3565	365	41	complete	complete	ADJ
ejpam-3565	365	42	classification	classification	NOUN
ejpam-3565	365	43	.	.	PUNCT
ejpam-3565	366	1	n125,2(4	n125,2(4	ADJ
ejpam-3565	366	2	)	)	PUNCT
ejpam-3565	366	3	=	=	SYM
ejpam-3565	366	4	σ25(4	σ25(4	PROPN
ejpam-3565	366	5	,	,	PUNCT
ejpam-3565	366	6	2	2	NUM
ejpam-3565	366	7	)	)	PUNCT
ejpam-3565	366	8	2∑	2∑	NOUN
ejpam-3565	367	1	k=0	k=0	X
ejpam-3565	367	2	(	(	PUNCT
ejpam-3565	367	3	2	2	NUM
ejpam-3565	367	4	k	k	NOUN
ejpam-3565	367	5	)	)	PUNCT
ejpam-3565	367	6	25	25	NUM
ejpam-3565	367	7	52k	52k	NOUN
ejpam-3565	367	8	=	=	SYM
ejpam-3565	367	9	52	52	NUM
ejpam-3565	367	10	+	+	SYM
ejpam-3565	367	11	33800	33800	NUM
ejpam-3565	367	12	+	+	CCONJ
ejpam-3565	367	13	32500	32500	NUM
ejpam-3565	367	14	=	=	SYM
ejpam-3565	367	15	∑	∑	PUNCT
ejpam-3565	367	16	c	c	PROPN
ejpam-3565	367	17	24	24	NUM
ejpam-3565	367	18	·	·	SYM
ejpam-3565	367	19	4	4	X
ejpam-3565	367	20	!	!	NUM
ejpam-3565	367	21	|aut(c)|	|aut(c)|	NOUN
ejpam-3565	367	22	.	.	PUNCT
ejpam-3565	368	1	hence	hence	ADV
ejpam-3565	368	2	there	there	PRON
ejpam-3565	368	3	are	be	VERB
ejpam-3565	368	4	904	904	NUM
ejpam-3565	368	5	self	self	NOUN
ejpam-3565	368	6	-	-	PUNCT
ejpam-3565	368	7	dual	dual	ADJ
ejpam-3565	368	8	codes	code	NOUN
ejpam-3565	368	9	of	of	ADP
ejpam-3565	368	10	length	length	NOUN
ejpam-3565	368	11	4	4	NUM
ejpam-3565	368	12	over	over	ADP
ejpam-3565	368	13	gr(125	gr(125	ADJ
ejpam-3565	368	14	,	,	PUNCT
ejpam-3565	368	15	2	2	NUM
ejpam-3565	368	16	)	)	PUNCT
ejpam-3565	368	17	.	.	PUNCT
ejpam-3565	369	1	t.	t.	PROPN
ejpam-3565	369	2	l.	l.	PROPN
ejpam-3565	369	3	vasquez	vasquez	PROPN
ejpam-3565	369	4	,	,	PUNCT
ejpam-3565	369	5	g.	g.	PROPN
ejpam-3565	369	6	petalcorin	petalcorin	PROPN
ejpam-3565	369	7	/	/	SYM
ejpam-3565	369	8	eur	eur	PROPN
ejpam-3565	369	9	.	.	PUNCT
ejpam-3565	370	1	j.	j.	PROPN
ejpam-3565	370	2	pure	pure	PROPN
ejpam-3565	370	3	appl	appl	PROPN
ejpam-3565	370	4	.	.	PROPN
ejpam-3565	370	5	math	math	PROPN
ejpam-3565	370	6	,	,	PUNCT
ejpam-3565	370	7	12	12	NUM
ejpam-3565	370	8	(	(	PUNCT
ejpam-3565	370	9	4	4	NUM
ejpam-3565	370	10	)	)	PUNCT
ejpam-3565	370	11	(	(	PUNCT
ejpam-3565	370	12	2019	2019	NUM
ejpam-3565	370	13	)	)	PUNCT
ejpam-3565	370	14	,	,	PUNCT
ejpam-3565	370	15	1701	1701	NUM
ejpam-3565	370	16	-	-	SYM
ejpam-3565	370	17	1716	1716	NUM
ejpam-3565	370	18	1714	1714	NUM
ejpam-3565	370	19	table	table	NOUN
ejpam-3565	370	20	2	2	NUM
ejpam-3565	370	21	:	:	PUNCT
ejpam-3565	370	22	self	self	NOUN
ejpam-3565	370	23	-	-	PUNCT
ejpam-3565	370	24	dual	dual	ADJ
ejpam-3565	370	25	codes	code	NOUN
ejpam-3565	370	26	of	of	ADP
ejpam-3565	370	27	length	length	NOUN
ejpam-3565	370	28	4	4	NUM
ejpam-3565	370	29	over	over	ADP
ejpam-3565	370	30	gr(125	gr(125	ADJ
ejpam-3565	370	31	,	,	PUNCT
ejpam-3565	370	32	2	2	NUM
ejpam-3565	370	33	)	)	PUNCT
ejpam-3565	370	34	.	.	PUNCT
ejpam-3565	371	1	type	type	NOUN
ejpam-3565	371	2	generator	generator	PROPN
ejpam-3565	371	3	matrix	matrix	NOUN
ejpam-3565	371	4	no	no	INTJ
ejpam-3565	371	5	.	.	PUNCT
ejpam-3565	372	1	of	of	ADP
ejpam-3565	372	2	codes	code	NOUN
ejpam-3565	372	3	|aut(c)|	|aut(c)|	PUNCT
ejpam-3565	372	4	{	{	PUNCT
ejpam-3565	372	5	0,2,2	0,2,2	NUM
ejpam-3565	372	6	}	}	SYM
ejpam-3565	372	7	m5(â5,1	m5(â5,1	PROPN
ejpam-3565	372	8	)	)	PUNCT
ejpam-3565	372	9	1	1	NUM
ejpam-3565	372	10	32	32	NUM
ejpam-3565	372	11	m5(â5,2	m5(â5,2	NOUN
ejpam-3565	372	12	)	)	PUNCT
ejpam-3565	372	13	1	1	NUM
ejpam-3565	372	14	24	24	NUM
ejpam-3565	372	15	m5(â5,3	m5(â5,3	PROPN
ejpam-3565	372	16	)	)	PUNCT
ejpam-3565	372	17	1	1	NUM
ejpam-3565	372	18	16	16	NUM
ejpam-3565	372	19	{	{	PUNCT
ejpam-3565	372	20	1,1,1	1,1,1	NUM
ejpam-3565	372	21	}	}	PUNCT
ejpam-3565	372	22	m5(ĝ5,1,0	m5(ĝ5,1,0	ADJ
ejpam-3565	372	23	,	,	PUNCT
ejpam-3565	372	24	0	0	NUM
ejpam-3565	372	25	)	)	PUNCT
ejpam-3565	372	26	1	1	NUM
ejpam-3565	372	27	16	16	NUM
ejpam-3565	372	28	m5(ĝ5,1,1	m5(ĝ5,1,1	NOUN
ejpam-3565	372	29	,	,	PUNCT
ejpam-3565	372	30	0	0	NUM
ejpam-3565	372	31	)	)	PUNCT
ejpam-3565	372	32	,	,	PUNCT
ejpam-3565	372	33	m5(ĝ5,1,ω̄3	m5(ĝ5,1,ω̄3	PROPN
ejpam-3565	372	34	,	,	PUNCT
ejpam-3565	372	35	0	0	NUM
ejpam-3565	372	36	)	)	PUNCT
ejpam-3565	372	37	,	,	PUNCT
ejpam-3565	372	38	m5(ĝ5,3,ω̄15	m5(ĝ5,3,ω̄15	X
ejpam-3565	372	39	,	,	PUNCT
ejpam-3565	372	40	0	0	NUM
ejpam-3565	372	41	)	)	PUNCT
ejpam-3565	372	42	3	3	NUM
ejpam-3565	372	43	8	8	NUM
ejpam-3565	372	44	m5(ĝ5,2,0	m5(ĝ5,2,0	NOUN
ejpam-3565	372	45	,	,	PUNCT
ejpam-3565	372	46	0	0	NUM
ejpam-3565	372	47	)	)	PUNCT
ejpam-3565	372	48	,	,	PUNCT
ejpam-3565	372	49	m5(ĝ5,2,1	m5(ĝ5,2,1	PROPN
ejpam-3565	372	50	,	,	PUNCT
ejpam-3565	372	51	0	0	NUM
ejpam-3565	372	52	)	)	PUNCT
ejpam-3565	372	53	2	2	NUM
ejpam-3565	372	54	6	6	NUM
ejpam-3565	372	55	m5(ĝ5,1,ω̄	m5(ĝ5,1,ω̄	NOUN
ejpam-3565	372	56	,	,	PUNCT
ejpam-3565	372	57	0	0	NUM
ejpam-3565	372	58	)	)	PUNCT
ejpam-3565	372	59	,	,	PUNCT
ejpam-3565	372	60	m5(ĝ5,1,ω̄2	m5(ĝ5,1,ω̄2	PROPN
ejpam-3565	372	61	,	,	PUNCT
ejpam-3565	372	62	0),m5(ĝ5,3,0	0),m5(ĝ5,3,0	NUM
ejpam-3565	372	63	,	,	PUNCT
ejpam-3565	372	64	0	0	NUM
ejpam-3565	372	65	)	)	PUNCT
ejpam-3565	372	66	,	,	PUNCT
ejpam-3565	372	67	83	83	NUM
ejpam-3565	372	68	4	4	NUM
ejpam-3565	372	69	m5(ĝ5,1,0	m5(ĝ5,1,0	ADJ
ejpam-3565	372	70	,	,	PUNCT
ejpam-3565	372	71	x	x	NOUN
ejpam-3565	372	72	)	)	PUNCT
ejpam-3565	372	73	,	,	PUNCT
ejpam-3565	372	74	where	where	SCONJ
ejpam-3565	372	75	x	x	X
ejpam-3565	372	76	∈	∈	PROPN
ejpam-3565	372	77	{	{	PUNCT
ejpam-3565	372	78	1	1	NUM
ejpam-3565	372	79	,	,	PUNCT
ejpam-3565	372	80	ω	ω	PROPN
ejpam-3565	372	81	,	,	PUNCT
ejpam-3565	372	82	.	.	PUNCT
ejpam-3565	372	83	.	.	PUNCT
ejpam-3565	372	84	.	.	PUNCT
ejpam-3565	373	1	,	,	PUNCT
ejpam-3565	373	2	ω5	ω5	PROPN
ejpam-3565	373	3	}	}	PUNCT
ejpam-3565	373	4	,	,	PUNCT
ejpam-3565	373	5	m5(ĝ5,1,1	m5(ĝ5,1,1	NOUN
ejpam-3565	373	6	,	,	PUNCT
ejpam-3565	373	7	x	x	NOUN
ejpam-3565	373	8	)	)	PUNCT
ejpam-3565	373	9	,	,	PUNCT
ejpam-3565	373	10	where	where	SCONJ
ejpam-3565	373	11	x	x	X
ejpam-3565	373	12	∈	∈	PROPN
ejpam-3565	373	13	{	{	PUNCT
ejpam-3565	373	14	1	1	NUM
ejpam-3565	373	15	,	,	PUNCT
ejpam-3565	373	16	ω	ω	PROPN
ejpam-3565	373	17	,	,	PUNCT
ejpam-3565	373	18	.	.	PUNCT
ejpam-3565	373	19	.	.	PUNCT
ejpam-3565	374	1	.	.	PUNCT
ejpam-3565	375	1	,	,	PUNCT
ejpam-3565	375	2	ω11	ω11	ADV
ejpam-3565	375	3	}	}	PUNCT
ejpam-3565	375	4	,	,	PUNCT
ejpam-3565	375	5	m5(ĝ5,2,ω̄	m5(ĝ5,2,ω̄	NOUN
ejpam-3565	375	6	,	,	PUNCT
ejpam-3565	375	7	x	x	NOUN
ejpam-3565	375	8	)	)	PUNCT
ejpam-3565	375	9	,	,	PUNCT
ejpam-3565	375	10	where	where	SCONJ
ejpam-3565	375	11	x	x	X
ejpam-3565	375	12	∈	∈	PROPN
ejpam-3565	375	13	{	{	PUNCT
ejpam-3565	375	14	0	0	NUM
ejpam-3565	375	15	,	,	PUNCT
ejpam-3565	375	16	1	1	NUM
ejpam-3565	375	17	,	,	PUNCT
ejpam-3565	375	18	ω	ω	NOUN
ejpam-3565	375	19	,	,	PUNCT
ejpam-3565	375	20	.	.	PUNCT
ejpam-3565	375	21	.	.	PUNCT
ejpam-3565	375	22	.	.	PUNCT
ejpam-3565	376	1	,	,	PUNCT
ejpam-3565	376	2	ω23	ω23	NUM
ejpam-3565	376	3	}	}	PUNCT
ejpam-3565	376	4	,	,	PUNCT
ejpam-3565	376	5	m5(ĝ5,3,ω̄6	m5(ĝ5,3,ω̄6	NOUN
ejpam-3565	376	6	,	,	PUNCT
ejpam-3565	376	7	x	x	NOUN
ejpam-3565	376	8	)	)	PUNCT
ejpam-3565	376	9	,	,	PUNCT
ejpam-3565	376	10	where	where	SCONJ
ejpam-3565	376	11	x	x	X
ejpam-3565	376	12	∈	∈	PROPN
ejpam-3565	376	13	{	{	PUNCT
ejpam-3565	376	14	0	0	NUM
ejpam-3565	376	15	,	,	PUNCT
ejpam-3565	376	16	1	1	NUM
ejpam-3565	376	17	,	,	PUNCT
ejpam-3565	376	18	ω	ω	NOUN
ejpam-3565	376	19	,	,	PUNCT
ejpam-3565	376	20	.	.	PUNCT
ejpam-3565	376	21	.	.	PUNCT
ejpam-3565	376	22	.	.	PUNCT
ejpam-3565	377	1	,	,	PUNCT
ejpam-3565	377	2	ω23	ω23	NOUN
ejpam-3565	377	3	}	}	PUNCT
ejpam-3565	377	4	,	,	PUNCT
ejpam-3565	377	5	m5(ĝ5,3,ω̄15	m5(ĝ5,3,ω̄15	NOUN
ejpam-3565	377	6	,	,	PUNCT
ejpam-3565	377	7	x	x	NOUN
ejpam-3565	377	8	)	)	PUNCT
ejpam-3565	377	9	,	,	PUNCT
ejpam-3565	377	10	where	where	SCONJ
ejpam-3565	377	11	x	x	X
ejpam-3565	377	12	∈	∈	PROPN
ejpam-3565	377	13	{	{	PUNCT
ejpam-3565	377	14	1	1	NUM
ejpam-3565	377	15	,	,	PUNCT
ejpam-3565	377	16	ω	ω	PROPN
ejpam-3565	377	17	,	,	PUNCT
ejpam-3565	377	18	.	.	PUNCT
ejpam-3565	377	19	.	.	PUNCT
ejpam-3565	377	20	.	.	PUNCT
ejpam-3565	378	1	,	,	PUNCT
ejpam-3565	378	2	ω11	ω11	ADV
ejpam-3565	378	3	}	}	PUNCT
ejpam-3565	378	4	m5(ĝ5,1,ω̄	m5(ĝ5,1,ω̄	PROPN
ejpam-3565	378	5	,	,	PUNCT
ejpam-3565	378	6	x	x	NOUN
ejpam-3565	378	7	)	)	PUNCT
ejpam-3565	378	8	,	,	PUNCT
ejpam-3565	378	9	where	where	SCONJ
ejpam-3565	378	10	x	x	X
ejpam-3565	378	11	∈	∈	PROPN
ejpam-3565	378	12	{	{	PUNCT
ejpam-3565	378	13	1	1	NUM
ejpam-3565	378	14	,	,	PUNCT
ejpam-3565	378	15	ω	ω	PROPN
ejpam-3565	378	16	,	,	PUNCT
ejpam-3565	378	17	.	.	PUNCT
ejpam-3565	378	18	.	.	PUNCT
ejpam-3565	378	19	.	.	PUNCT
ejpam-3565	379	1	,	,	PUNCT
ejpam-3565	379	2	ω11	ω11	AUX
ejpam-3565	379	3	}	}	PUNCT
ejpam-3565	379	4	133	133	NUM
ejpam-3565	379	5	2	2	NUM
ejpam-3565	379	6	m5(ĝ5,1,ω̄2	m5(ĝ5,1,ω̄2	NOUN
ejpam-3565	379	7	,	,	PUNCT
ejpam-3565	379	8	x	x	NOUN
ejpam-3565	379	9	)	)	PUNCT
ejpam-3565	379	10	,	,	PUNCT
ejpam-3565	379	11	where	where	SCONJ
ejpam-3565	379	12	x	x	X
ejpam-3565	379	13	∈	∈	PROPN
ejpam-3565	379	14	{	{	PUNCT
ejpam-3565	379	15	1	1	NUM
ejpam-3565	379	16	,	,	PUNCT
ejpam-3565	379	17	ω	ω	PROPN
ejpam-3565	379	18	,	,	PUNCT
ejpam-3565	379	19	.	.	PUNCT
ejpam-3565	379	20	.	.	PUNCT
ejpam-3565	379	21	.	.	PUNCT
ejpam-3565	380	1	,	,	PUNCT
ejpam-3565	380	2	ω11	ω11	AUX
ejpam-3565	380	3	}	}	PUNCT
ejpam-3565	380	4	m5(ĝ5,1,ω̄3	m5(ĝ5,1,ω̄3	PROPN
ejpam-3565	380	5	,	,	PUNCT
ejpam-3565	380	6	x	x	NOUN
ejpam-3565	380	7	)	)	PUNCT
ejpam-3565	380	8	,	,	PUNCT
ejpam-3565	380	9	where	where	SCONJ
ejpam-3565	380	10	x	x	X
ejpam-3565	380	11	∈	∈	PROPN
ejpam-3565	380	12	{	{	PUNCT
ejpam-3565	380	13	1	1	NUM
ejpam-3565	380	14	,	,	PUNCT
ejpam-3565	380	15	ω	ω	PROPN
ejpam-3565	380	16	,	,	PUNCT
ejpam-3565	380	17	.	.	PUNCT
ejpam-3565	380	18	.	.	PUNCT
ejpam-3565	380	19	.	.	PUNCT
ejpam-3565	381	1	,	,	PUNCT
ejpam-3565	381	2	ω5	ω5	PROPN
ejpam-3565	381	3	}	}	PUNCT
ejpam-3565	381	4	m5(ĝ5,2,0	m5(ĝ5,2,0	PROPN
ejpam-3565	381	5	,	,	PUNCT
ejpam-3565	381	6	x	x	NOUN
ejpam-3565	381	7	)	)	PUNCT
ejpam-3565	381	8	,	,	PUNCT
ejpam-3565	381	9	where	where	SCONJ
ejpam-3565	381	10	x	x	X
ejpam-3565	381	11	∈	∈	PROPN
ejpam-3565	381	12	{	{	PUNCT
ejpam-3565	381	13	1	1	NUM
ejpam-3565	381	14	,	,	PUNCT
ejpam-3565	381	15	ω	ω	PROPN
ejpam-3565	381	16	,	,	PUNCT
ejpam-3565	381	17	.	.	PUNCT
ejpam-3565	381	18	.	.	PUNCT
ejpam-3565	381	19	.	.	PUNCT
ejpam-3565	382	1	,	,	PUNCT
ejpam-3565	382	2	ω7	ω7	NOUN
ejpam-3565	382	3	}	}	PUNCT
ejpam-3565	382	4	m5(ĝ5,2,1	m5(ĝ5,2,1	PROPN
ejpam-3565	382	5	,	,	PUNCT
ejpam-3565	382	6	x	x	NOUN
ejpam-3565	382	7	)	)	PUNCT
ejpam-3565	382	8	,	,	PUNCT
ejpam-3565	383	1	where	where	SCONJ
ejpam-3565	383	2	x	x	X
ejpam-3565	383	3	∈	∈	PROPN
ejpam-3565	383	4	{	{	PUNCT
ejpam-3565	383	5	1	1	NUM
ejpam-3565	383	6	,	,	PUNCT
ejpam-3565	383	7	ω	ω	PROPN
ejpam-3565	383	8	,	,	PUNCT
ejpam-3565	383	9	.	.	PUNCT
ejpam-3565	383	10	.	.	PUNCT
ejpam-3565	383	11	.	.	PUNCT
ejpam-3565	383	12	,	,	PUNCT
ejpam-3565	383	13	ω7	ω7	NOUN
ejpam-3565	383	14	}	}	PUNCT
ejpam-3565	383	15	m5(ĝ5,2,ω̄2	m5(ĝ5,2,ω̄2	X
ejpam-3565	383	16	,	,	PUNCT
ejpam-3565	383	17	x	x	X
ejpam-3565	383	18	)	)	PUNCT
ejpam-3565	383	19	,	,	PUNCT
ejpam-3565	383	20	where	where	SCONJ
ejpam-3565	383	21	x	x	X
ejpam-3565	383	22	∈	∈	PROPN
ejpam-3565	383	23	{	{	PUNCT
ejpam-3565	383	24	0	0	NUM
ejpam-3565	383	25	,	,	PUNCT
ejpam-3565	383	26	1	1	NUM
ejpam-3565	383	27	,	,	PUNCT
ejpam-3565	383	28	ω	ω	NOUN
ejpam-3565	383	29	,	,	PUNCT
ejpam-3565	383	30	.	.	PUNCT
ejpam-3565	383	31	.	.	PUNCT
ejpam-3565	384	1	.	.	PUNCT
ejpam-3565	385	1	,	,	PUNCT
ejpam-3565	385	2	ω23	ω23	NOUN
ejpam-3565	385	3	}	}	PUNCT
ejpam-3565	385	4	m5(ĝ5,3,0	m5(ĝ5,3,0	ADV
ejpam-3565	385	5	,	,	PUNCT
ejpam-3565	385	6	x	x	NOUN
ejpam-3565	385	7	)	)	PUNCT
ejpam-3565	385	8	,	,	PUNCT
ejpam-3565	385	9	where	where	SCONJ
ejpam-3565	385	10	x	x	X
ejpam-3565	385	11	∈	∈	PROPN
ejpam-3565	385	12	{	{	PUNCT
ejpam-3565	385	13	1	1	NUM
ejpam-3565	385	14	,	,	PUNCT
ejpam-3565	385	15	ω	ω	PROPN
ejpam-3565	385	16	,	,	PUNCT
ejpam-3565	385	17	.	.	PUNCT
ejpam-3565	385	18	.	.	PUNCT
ejpam-3565	385	19	.	.	PUNCT
ejpam-3565	386	1	,	,	PUNCT
ejpam-3565	386	2	ω11	ω11	ADV
ejpam-3565	386	3	}	}	PUNCT
ejpam-3565	386	4	m5(ĝ5,3,1	m5(ĝ5,3,1	NOUN
ejpam-3565	386	5	,	,	PUNCT
ejpam-3565	386	6	x	x	NOUN
ejpam-3565	386	7	)	)	PUNCT
ejpam-3565	386	8	,	,	PUNCT
ejpam-3565	386	9	where	where	SCONJ
ejpam-3565	386	10	x	x	X
ejpam-3565	386	11	∈	∈	PROPN
ejpam-3565	386	12	{	{	PUNCT
ejpam-3565	386	13	0	0	NUM
ejpam-3565	386	14	,	,	PUNCT
ejpam-3565	386	15	1	1	NUM
ejpam-3565	386	16	,	,	PUNCT
ejpam-3565	386	17	ω	ω	NOUN
ejpam-3565	386	18	,	,	PUNCT
ejpam-3565	386	19	.	.	PUNCT
ejpam-3565	386	20	.	.	PUNCT
ejpam-3565	386	21	.	.	PUNCT
ejpam-3565	387	1	,	,	PUNCT
ejpam-3565	387	2	ω23	ω23	NOUN
ejpam-3565	387	3	}	}	PUNCT
ejpam-3565	387	4	m5(ĝ5,3,ω̄2	m5(ĝ5,3,ω̄2	PROPN
ejpam-3565	387	5	,	,	PUNCT
ejpam-3565	387	6	x	x	NOUN
ejpam-3565	387	7	)	)	PUNCT
ejpam-3565	387	8	,	,	PUNCT
ejpam-3565	387	9	where	where	SCONJ
ejpam-3565	387	10	x	x	X
ejpam-3565	387	11	∈	∈	PROPN
ejpam-3565	387	12	{	{	PUNCT
ejpam-3565	387	13	0	0	NUM
ejpam-3565	387	14	,	,	PUNCT
ejpam-3565	387	15	1	1	NUM
ejpam-3565	387	16	,	,	PUNCT
ejpam-3565	387	17	ω	ω	NOUN
ejpam-3565	387	18	,	,	PUNCT
ejpam-3565	387	19	.	.	PUNCT
ejpam-3565	387	20	.	.	PUNCT
ejpam-3565	388	1	.	.	PUNCT
ejpam-3565	389	1	,	,	PUNCT
ejpam-3565	389	2	ω23	ω23	NOUN
ejpam-3565	389	3	}	}	PUNCT
ejpam-3565	389	4	{	{	PUNCT
ejpam-3565	389	5	2,0,0	2,0,0	NOUN
ejpam-3565	389	6	}	}	PUNCT
ejpam-3565	389	7	m5(â5,1	m5(â5,1	PROPN
ejpam-3565	389	8	,	,	PUNCT
ejpam-3565	389	9	0	0	NUM
ejpam-3565	389	10	,	,	PUNCT
ejpam-3565	389	11	0	0	NUM
ejpam-3565	389	12	)	)	PUNCT
ejpam-3565	389	13	1	1	NUM
ejpam-3565	389	14	32	32	NUM
ejpam-3565	389	15	m5(â5,2	m5(â5,2	NOUN
ejpam-3565	389	16	,	,	PUNCT
ejpam-3565	389	17	0	0	NUM
ejpam-3565	389	18	,	,	PUNCT
ejpam-3565	389	19	0	0	NUM
ejpam-3565	389	20	)	)	PUNCT
ejpam-3565	389	21	1	1	NUM
ejpam-3565	389	22	24	24	NUM
ejpam-3565	389	23	m5(â5,3	m5(â5,3	PROPN
ejpam-3565	389	24	,	,	PUNCT
ejpam-3565	389	25	ω	ω	PROPN
ejpam-3565	389	26	21	21	NUM
ejpam-3565	389	27	,	,	PUNCT
ejpam-3565	389	28	ω3	ω3	NOUN
ejpam-3565	389	29	)	)	PUNCT
ejpam-3565	389	30	1	1	NUM
ejpam-3565	389	31	16	16	NUM
ejpam-3565	389	32	m5(â5,1	m5(â5,1	NOUN
ejpam-3565	389	33	,	,	PUNCT
ejpam-3565	389	34	0	0	NUM
ejpam-3565	389	35	,	,	PUNCT
ejpam-3565	389	36	z	z	NOUN
ejpam-3565	389	37	)	)	PUNCT
ejpam-3565	389	38	,	,	PUNCT
ejpam-3565	389	39	where	where	SCONJ
ejpam-3565	389	40	z	z	PROPN
ejpam-3565	389	41	∈	∈	PROPN
ejpam-3565	389	42	{	{	PUNCT
ejpam-3565	389	43	1	1	NUM
ejpam-3565	389	44	,	,	PUNCT
ejpam-3565	389	45	ω	ω	PROPN
ejpam-3565	389	46	,	,	PUNCT
ejpam-3565	389	47	.	.	PUNCT
ejpam-3565	389	48	.	.	PUNCT
ejpam-3565	389	49	.	.	PUNCT
ejpam-3565	390	1	,	,	PUNCT
ejpam-3565	390	2	ω5	ω5	PROPN
ejpam-3565	390	3	}	}	PUNCT
ejpam-3565	390	4	676	676	NUM
ejpam-3565	390	5	8	8	NUM
ejpam-3565	390	6	m5(â5,1	m5(â5,1	NOUN
ejpam-3565	390	7	,	,	PUNCT
ejpam-3565	390	8	y	y	PROPN
ejpam-3565	390	9	,	,	PUNCT
ejpam-3565	390	10	z	z	NOUN
ejpam-3565	390	11	)	)	PUNCT
ejpam-3565	390	12	,	,	PUNCT
ejpam-3565	390	13	where	where	SCONJ
ejpam-3565	390	14	y	y	PROPN
ejpam-3565	390	15	∈	∈	PROPN
ejpam-3565	390	16	{	{	PUNCT
ejpam-3565	390	17	1	1	NUM
ejpam-3565	390	18	,	,	PUNCT
ejpam-3565	390	19	ω	ω	PROPN
ejpam-3565	390	20	,	,	PUNCT
ejpam-3565	390	21	.	.	PUNCT
ejpam-3565	390	22	.	.	PUNCT
ejpam-3565	390	23	.	.	PUNCT
ejpam-3565	391	1	,	,	PUNCT
ejpam-3565	391	2	ω5	ω5	PROPN
ejpam-3565	391	3	}	}	PUNCT
ejpam-3565	391	4	,	,	PUNCT
ejpam-3565	391	5	z	z	PROPN
ejpam-3565	391	6	∈	∈	PROPN
ejpam-3565	391	7	t25	t25	NOUN
ejpam-3565	391	8	m5(â5,2	m5(â5,2	NOUN
ejpam-3565	391	9	,	,	PUNCT
ejpam-3565	391	10	0	0	NUM
ejpam-3565	391	11	,	,	PUNCT
ejpam-3565	391	12	z	z	NOUN
ejpam-3565	391	13	)	)	PUNCT
ejpam-3565	391	14	,	,	PUNCT
ejpam-3565	391	15	where	where	SCONJ
ejpam-3565	391	16	z	z	PROPN
ejpam-3565	391	17	∈	∈	PROPN
ejpam-3565	391	18	{	{	PUNCT
ejpam-3565	391	19	1	1	NUM
ejpam-3565	391	20	,	,	PUNCT
ejpam-3565	391	21	ω	ω	PROPN
ejpam-3565	391	22	,	,	PUNCT
ejpam-3565	391	23	.	.	PUNCT
ejpam-3565	391	24	.	.	PUNCT
ejpam-3565	391	25	.	.	PUNCT
ejpam-3565	392	1	,	,	PUNCT
ejpam-3565	392	2	ω7	ω7	NOUN
ejpam-3565	392	3	}	}	PUNCT
ejpam-3565	392	4	m5(â5,2	m5(â5,2	NOUN
ejpam-3565	392	5	,	,	PUNCT
ejpam-3565	392	6	y	y	PROPN
ejpam-3565	392	7	,	,	PUNCT
ejpam-3565	392	8	z	z	NOUN
ejpam-3565	392	9	)	)	PUNCT
ejpam-3565	392	10	,	,	PUNCT
ejpam-3565	392	11	where	where	SCONJ
ejpam-3565	392	12	y	y	PROPN
ejpam-3565	392	13	∈	∈	PROPN
ejpam-3565	392	14	{	{	PUNCT
ejpam-3565	392	15	1	1	NUM
ejpam-3565	392	16	,	,	PUNCT
ejpam-3565	392	17	ω	ω	PROPN
ejpam-3565	392	18	,	,	PUNCT
ejpam-3565	392	19	.	.	PUNCT
ejpam-3565	392	20	.	.	PUNCT
ejpam-3565	392	21	.	.	PUNCT
ejpam-3565	393	1	,	,	PUNCT
ejpam-3565	393	2	ω7	ω7	NOUN
ejpam-3565	393	3	}	}	PUNCT
ejpam-3565	393	4	,	,	PUNCT
ejpam-3565	393	5	z	z	PROPN
ejpam-3565	393	6	∈	∈	PROPN
ejpam-3565	393	7	t25	t25	PROPN
ejpam-3565	393	8	m5(â5,3	m5(â5,3	PROPN
ejpam-3565	393	9	,	,	PUNCT
ejpam-3565	393	10	y	y	PROPN
ejpam-3565	393	11	,	,	PUNCT
ejpam-3565	393	12	z	z	NOUN
ejpam-3565	393	13	)	)	PUNCT
ejpam-3565	393	14	,	,	PUNCT
ejpam-3565	393	15	where	where	SCONJ
ejpam-3565	393	16	y	y	PROPN
ejpam-3565	393	17	∈	∈	PROPN
ejpam-3565	393	18	j1	j1	PROPN
ejpam-3565	393	19	,	,	PUNCT
ejpam-3565	393	20	z	z	PROPN
ejpam-3565	393	21	∈	∈	PROPN
ejpam-3565	393	22	t25	t25	NOUN
ejpam-3565	393	23	,	,	PUNCT
ejpam-3565	393	24	m5(â5,3	m5(â5,3	PROPN
ejpam-3565	393	25	,	,	PUNCT
ejpam-3565	393	26	ω	ω	PROPN
ejpam-3565	393	27	21	21	NUM
ejpam-3565	393	28	,	,	PUNCT
ejpam-3565	393	29	z	z	NOUN
ejpam-3565	393	30	)	)	PUNCT
ejpam-3565	393	31	,	,	PUNCT
ejpam-3565	393	32	where	where	SCONJ
ejpam-3565	393	33	z	z	PROPN
ejpam-3565	393	34	∈	∈	PROPN
ejpam-3565	393	35	j2	j2	PROPN
ejpam-3565	393	36	6	6	NUM
ejpam-3565	393	37	.	.	PUNCT
ejpam-3565	394	1	conclusion	conclusion	NOUN
ejpam-3565	394	2	we	we	PRON
ejpam-3565	394	3	discussed	discuss	VERB
ejpam-3565	394	4	a	a	DET
ejpam-3565	394	5	method	method	NOUN
ejpam-3565	394	6	to	to	PART
ejpam-3565	394	7	construct	construct	VERB
ejpam-3565	394	8	self	self	NOUN
ejpam-3565	394	9	-	-	PUNCT
ejpam-3565	394	10	dual	dual	ADJ
ejpam-3565	394	11	codes	code	NOUN
ejpam-3565	394	12	over	over	ADP
ejpam-3565	394	13	gr(p3	gr(p3	PROPN
ejpam-3565	394	14	,	,	PUNCT
ejpam-3565	394	15	r	r	NOUN
ejpam-3565	394	16	)	)	PUNCT
ejpam-3565	394	17	from	from	ADP
ejpam-3565	394	18	a	a	DET
ejpam-3565	394	19	self	self	NOUN
ejpam-3565	394	20	-	-	PUNCT
ejpam-3565	394	21	dual	dual	ADJ
ejpam-3565	394	22	code	code	NOUN
ejpam-3565	394	23	over	over	ADP
ejpam-3565	394	24	fpr	fpr	NOUN
ejpam-3565	394	25	,	,	PUNCT
ejpam-3565	394	26	where	where	SCONJ
ejpam-3565	394	27	p	p	NOUN
ejpam-3565	394	28	is	be	AUX
ejpam-3565	394	29	an	an	DET
ejpam-3565	394	30	odd	odd	ADJ
ejpam-3565	394	31	prime	prime	NOUN
ejpam-3565	394	32	and	and	CCONJ
ejpam-3565	394	33	r	r	NOUN
ejpam-3565	394	34	is	be	AUX
ejpam-3565	394	35	a	a	DET
ejpam-3565	394	36	positive	positive	ADJ
ejpam-3565	394	37	integer	integer	NOUN
ejpam-3565	394	38	.	.	PUNCT
ejpam-3565	395	1	this	this	DET
ejpam-3565	395	2	construction	construction	NOUN
ejpam-3565	395	3	method	method	NOUN
ejpam-3565	395	4	led	lead	VERB
ejpam-3565	395	5	to	to	ADP
ejpam-3565	395	6	a	a	DET
ejpam-3565	395	7	mass	mass	ADJ
ejpam-3565	395	8	formula	formula	NOUN
ejpam-3565	395	9	and	and	CCONJ
ejpam-3565	395	10	classification	classification	NOUN
ejpam-3565	395	11	of	of	ADP
ejpam-3565	395	12	self	self	NOUN
ejpam-3565	395	13	-	-	PUNCT
ejpam-3565	395	14	dual	dual	ADJ
ejpam-3565	395	15	codes	code	NOUN
ejpam-3565	395	16	of	of	ADP
ejpam-3565	395	17	length	length	NOUN
ejpam-3565	395	18	4	4	NUM
ejpam-3565	395	19	over	over	ADP
ejpam-3565	395	20	gr(p3	gr(p3	PROPN
ejpam-3565	395	21	,	,	PUNCT
ejpam-3565	395	22	2	2	NUM
ejpam-3565	395	23	)	)	PUNCT
ejpam-3565	395	24	for	for	ADP
ejpam-3565	395	25	p	p	NOUN
ejpam-3565	395	26	=	=	SYM
ejpam-3565	395	27	3	3	NUM
ejpam-3565	395	28	,	,	PUNCT
ejpam-3565	395	29	5	5	NUM
ejpam-3565	395	30	.	.	PUNCT
ejpam-3565	396	1	in	in	ADP
ejpam-3565	396	2	this	this	DET
ejpam-3565	396	3	study	study	NOUN
ejpam-3565	396	4	,	,	PUNCT
ejpam-3565	396	5	we	we	PRON
ejpam-3565	396	6	only	only	ADV
ejpam-3565	396	7	dealt	deal	VERB
ejpam-3565	396	8	with	with	ADP
ejpam-3565	396	9	the	the	DET
ejpam-3565	396	10	case	case	NOUN
ejpam-3565	396	11	when	when	SCONJ
ejpam-3565	396	12	p	p	NOUN
ejpam-3565	396	13	is	be	AUX
ejpam-3565	396	14	an	an	DET
ejpam-3565	396	15	odd	odd	ADJ
ejpam-3565	396	16	prime	prime	NOUN
ejpam-3565	396	17	.	.	PUNCT
ejpam-3565	397	1	letting	let	VERB
ejpam-3565	397	2	p	p	X
ejpam-3565	397	3	=	=	NOUN
ejpam-3565	397	4	2	2	NUM
ejpam-3565	397	5	in	in	ADP
ejpam-3565	397	6	references	reference	NOUN
ejpam-3565	397	7	1715	1715	NUM
ejpam-3565	397	8	(	(	PUNCT
ejpam-3565	397	9	24	24	NUM
ejpam-3565	397	10	)	)	PUNCT
ejpam-3565	397	11	,	,	PUNCT
ejpam-3565	397	12	we	we	PRON
ejpam-3565	397	13	obtain	obtain	VERB
ejpam-3565	397	14	fij	fij	PROPN
ejpam-3565	398	1	+	+	CCONJ
ejpam-3565	398	2	ã30at	ã30at	NOUN
ejpam-3565	398	3	31	31	NUM
ejpam-3565	398	4	+	+	ADP
ejpam-3565	398	5	ã40at	ã40at	NUM
ejpam-3565	398	6	41	41	NUM
ejpam-3565	398	7	≡	≡	PROPN
ejpam-3565	398	8	0	0	PUNCT
ejpam-3565	399	1	(	(	PUNCT
ejpam-3565	399	2	mod	mod	NOUN
ejpam-3565	399	3	2	2	NUM
ejpam-3565	399	4	)	)	PUNCT
ejpam-3565	399	5	.	.	PUNCT
ejpam-3565	400	1	since	since	SCONJ
ejpam-3565	400	2	the	the	DET
ejpam-3565	400	3	diagonal	diagonal	ADJ
ejpam-3565	400	4	entries	entry	NOUN
ejpam-3565	400	5	of	of	ADP
ejpam-3565	400	6	x̃	x̃	PROPN
ejpam-3565	400	7	are	be	AUX
ejpam-3565	400	8	all	all	ADV
ejpam-3565	400	9	0	0	NUM
ejpam-3565	400	10	,	,	PUNCT
ejpam-3565	400	11	then	then	ADV
ejpam-3565	400	12	we	we	PRON
ejpam-3565	400	13	must	must	AUX
ejpam-3565	400	14	have	have	VERB
ejpam-3565	400	15	fii	fii	PROPN
ejpam-3565	400	16	≡	≡	PROPN
ejpam-3565	400	17	0	0	PUNCT
ejpam-3565	401	1	(	(	PUNCT
ejpam-3565	401	2	mod	mod	NOUN
ejpam-3565	401	3	2	2	NUM
ejpam-3565	401	4	)	)	PUNCT
ejpam-3565	401	5	for	for	ADP
ejpam-3565	401	6	each	each	DET
ejpam-3565	401	7	i.	i.	NOUN
ejpam-3565	401	8	hence	hence	ADV
ejpam-3565	401	9	,	,	PUNCT
ejpam-3565	401	10	from	from	ADP
ejpam-3565	401	11	(	(	PUNCT
ejpam-3565	401	12	20	20	NUM
ejpam-3565	401	13	)	)	PUNCT
ejpam-3565	401	14	,	,	PUNCT
ejpam-3565	401	15	the	the	DET
ejpam-3565	401	16	diagonal	diagonal	ADJ
ejpam-3565	401	17	entries	entry	NOUN
ejpam-3565	401	18	of	of	ADP
ejpam-3565	401	19	ik	ik	PROPN
ejpam-3565	401	20	+	+	CCONJ
ejpam-3565	401	21	a2a	a2a	PROPN
ejpam-3565	401	22	t	t	PROPN
ejpam-3565	401	23	2	2	NUM
ejpam-3565	401	24	+	+	CCONJ
ejpam-3565	401	25	a30a	a30a	PROPN
ejpam-3565	401	26	t	t	PROPN
ejpam-3565	401	27	30	30	NUM
ejpam-3565	401	28	+	+	CCONJ
ejpam-3565	401	29	a40a	a40a	X
ejpam-3565	401	30	t	t	PROPN
ejpam-3565	401	31	40	40	NUM
ejpam-3565	401	32	=	=	SYM
ejpam-3565	401	33	2(fij	2(fij	NUM
ejpam-3565	401	34	)	)	PUNCT
ejpam-3565	401	35	must	must	AUX
ejpam-3565	401	36	be	be	AUX
ejpam-3565	401	37	doubly	doubly	ADV
ejpam-3565	401	38	even	even	ADV
ejpam-3565	401	39	.	.	PUNCT
ejpam-3565	402	1	thus	thus	ADV
ejpam-3565	402	2	,	,	PUNCT
ejpam-3565	402	3	in	in	ADP
ejpam-3565	402	4	the	the	DET
ejpam-3565	402	5	case	case	NOUN
ejpam-3565	402	6	of	of	ADP
ejpam-3565	402	7	p	p	NOUN
ejpam-3565	402	8	=	=	SYM
ejpam-3565	402	9	2	2	NUM
ejpam-3565	402	10	,	,	PUNCT
ejpam-3565	402	11	the	the	DET
ejpam-3565	402	12	construction	construction	NOUN
ejpam-3565	402	13	algorithm	algorithm	NOUN
ejpam-3565	402	14	becomes	become	VERB
ejpam-3565	402	15	more	more	ADV
ejpam-3565	402	16	complicated	complicated	ADJ
ejpam-3565	402	17	because	because	SCONJ
ejpam-3565	402	18	we	we	PRON
ejpam-3565	402	19	need	need	VERB
ejpam-3565	402	20	an	an	DET
ejpam-3565	402	21	additional	additional	ADJ
ejpam-3565	402	22	property	property	NOUN
ejpam-3565	402	23	for	for	ADP
ejpam-3565	402	24	the	the	DET
ejpam-3565	402	25	self	self	NOUN
ejpam-3565	402	26	-	-	PUNCT
ejpam-3565	402	27	dual	dual	ADJ
ejpam-3565	402	28	codes	code	NOUN
ejpam-3565	402	29	over	over	ADP
ejpam-3565	402	30	f2r	f2r	PROPN
ejpam-3565	402	31	.	.	PUNCT
ejpam-3565	403	1	we	we	PRON
ejpam-3565	403	2	are	be	AUX
ejpam-3565	403	3	still	still	ADV
ejpam-3565	403	4	investigating	investigate	VERB
ejpam-3565	403	5	the	the	DET
ejpam-3565	403	6	mass	mass	ADJ
ejpam-3565	403	7	formula	formula	NOUN
ejpam-3565	403	8	for	for	ADP
ejpam-3565	403	9	self	self	NOUN
ejpam-3565	403	10	-	-	PUNCT
ejpam-3565	403	11	dual	dual	ADJ
ejpam-3565	403	12	codes	code	NOUN
ejpam-3565	403	13	over	over	ADP
ejpam-3565	403	14	gr(8	gr(8	NOUN
ejpam-3565	403	15	,	,	PUNCT
ejpam-3565	403	16	r	r	NOUN
ejpam-3565	403	17	)	)	PUNCT
ejpam-3565	403	18	.	.	PUNCT
ejpam-3565	404	1	acknowledgements	acknowledgement	NOUN
ejpam-3565	404	2	this	this	DET
ejpam-3565	404	3	research	research	NOUN
ejpam-3565	404	4	is	be	AUX
ejpam-3565	404	5	funded	fund	VERB
ejpam-3565	404	6	by	by	ADP
ejpam-3565	404	7	the	the	DET
ejpam-3565	404	8	department	department	PROPN
ejpam-3565	404	9	of	of	ADP
ejpam-3565	404	10	science	science	NOUN
ejpam-3565	404	11	and	and	CCONJ
ejpam-3565	404	12	technology	technology	NOUN
ejpam-3565	404	13	accelerated	accelerate	VERB
ejpam-3565	404	14	science	science	NOUN
ejpam-3565	404	15	and	and	CCONJ
ejpam-3565	404	16	technology	technology	NOUN
ejpam-3565	404	17	human	human	ADJ
ejpam-3565	404	18	resource	resource	NOUN
ejpam-3565	404	19	development	development	NOUN
ejpam-3565	404	20	program	program	NOUN
ejpam-3565	404	21	(	(	PUNCT
ejpam-3565	404	22	dost	dost	NOUN
ejpam-3565	404	23	-	-	PUNCT
ejpam-3565	404	24	asthrdp	asthrdp	ADJ
ejpam-3565	404	25	)	)	PUNCT
ejpam-3565	404	26	.	.	PUNCT
ejpam-3565	405	1	references	reference	NOUN
ejpam-3565	405	2	[	[	X
ejpam-3565	405	3	1	1	NUM
ejpam-3565	405	4	]	]	PUNCT
ejpam-3565	405	5	jm	jm	PROPN
ejpam-3565	405	6	balmaceda	balmaceda	PROPN
ejpam-3565	405	7	,	,	PUNCT
ejpam-3565	405	8	ra	ra	PROPN
ejpam-3565	405	9	betty	betty	PROPN
ejpam-3565	405	10	,	,	PUNCT
ejpam-3565	405	11	and	and	CCONJ
ejpam-3565	405	12	f	f	PROPN
ejpam-3565	405	13	nemenzo	nemenzo	NOUN
ejpam-3565	405	14	.	.	PUNCT
ejpam-3565	406	1	mass	mass	ADJ
ejpam-3565	406	2	formula	formula	NOUN
ejpam-3565	406	3	for	for	ADP
ejpam-3565	406	4	self	self	NOUN
ejpam-3565	406	5	-	-	PUNCT
ejpam-3565	406	6	dual	dual	ADJ
ejpam-3565	406	7	codes	code	NOUN
ejpam-3565	406	8	over	over	ADP
ejpam-3565	406	9	zp2	zp2	PROPN
ejpam-3565	406	10	.	.	PUNCT
ejpam-3565	407	1	discrete	discrete	ADJ
ejpam-3565	407	2	math	math	NOUN
ejpam-3565	407	3	.	.	PUNCT
ejpam-3565	407	4	,	,	PUNCT
ejpam-3565	407	5	308:2984–3002	308:2984–3002	NUM
ejpam-3565	407	6	,	,	PUNCT
ejpam-3565	407	7	2008	2008	NUM
ejpam-3565	407	8	.	.	PUNCT
ejpam-3565	408	1	[	[	X
ejpam-3565	408	2	2	2	NUM
ejpam-3565	408	3	]	]	PUNCT
ejpam-3565	408	4	w	w	PROPN
ejpam-3565	408	5	bosma	bosma	PROPN
ejpam-3565	408	6	,	,	PUNCT
ejpam-3565	408	7	j	j	PROPN
ejpam-3565	408	8	cannon	cannon	NOUN
ejpam-3565	408	9	,	,	PUNCT
ejpam-3565	408	10	and	and	CCONJ
ejpam-3565	408	11	c	c	PROPN
ejpam-3565	408	12	playoust	playoust	NOUN
ejpam-3565	408	13	.	.	PUNCT
ejpam-3565	409	1	the	the	DET
ejpam-3565	409	2	magma	magma	NOUN
ejpam-3565	409	3	algebra	algebra	NOUN
ejpam-3565	409	4	system	system	NOUN
ejpam-3565	409	5	.	.	PUNCT
ejpam-3565	410	1	i.	i.	PROPN
ejpam-3565	410	2	the	the	DET
ejpam-3565	410	3	user	user	NOUN
ejpam-3565	410	4	language	language	NOUN
ejpam-3565	410	5	.	.	PUNCT
ejpam-3565	411	1	j.	j.	PROPN
ejpam-3565	411	2	symbolic	symbolic	PROPN
ejpam-3565	411	3	comput	comput	PROPN
ejpam-3565	411	4	.	.	PUNCT
ejpam-3565	411	5	,	,	PUNCT
ejpam-3565	411	6	24(3	24(3	NUM
ejpam-3565	411	7	-	-	SYM
ejpam-3565	411	8	4):235–265	4):235–265	NUM
ejpam-3565	411	9	,	,	PUNCT
ejpam-3565	411	10	1997	1997	NUM
ejpam-3565	411	11	.	.	PUNCT
ejpam-3565	412	1	computational	computational	ADJ
ejpam-3565	412	2	algebra	algebra	NOUN
ejpam-3565	412	3	and	and	CCONJ
ejpam-3565	412	4	number	number	NOUN
ejpam-3565	412	5	theory	theory	NOUN
ejpam-3565	412	6	(	(	PUNCT
ejpam-3565	412	7	london	london	PROPN
ejpam-3565	412	8	,	,	PUNCT
ejpam-3565	412	9	1993	1993	NUM
ejpam-3565	412	10	)	)	PUNCT
ejpam-3565	412	11	.	.	PUNCT
ejpam-3565	413	1	[	[	X
ejpam-3565	413	2	3	3	NUM
ejpam-3565	413	3	]	]	SYM
ejpam-3565	413	4	w	w	ADJ
ejpam-3565	413	5	-	-	PUNCT
ejpam-3565	413	6	h	h	NOUN
ejpam-3565	413	7	choi	choi	NOUN
ejpam-3565	413	8	.	.	PUNCT
ejpam-3565	414	1	mass	mass	ADJ
ejpam-3565	414	2	formula	formula	NOUN
ejpam-3565	414	3	for	for	ADP
ejpam-3565	414	4	self	self	NOUN
ejpam-3565	414	5	-	-	PUNCT
ejpam-3565	414	6	dual	dual	ADJ
ejpam-3565	414	7	codes	code	NOUN
ejpam-3565	414	8	over	over	ADP
ejpam-3565	414	9	galois	galois	PROPN
ejpam-3565	414	10	rings	ring	NOUN
ejpam-3565	414	11	gr(p2	gr(p2	NOUN
ejpam-3565	414	12	,	,	PUNCT
ejpam-3565	414	13	2	2	NUM
ejpam-3565	414	14	)	)	PUNCT
ejpam-3565	414	15	.	.	PUNCT
ejpam-3565	415	1	korean	korean	PROPN
ejpam-3565	415	2	j.	j.	PROPN
ejpam-3565	415	3	math	math	PROPN
ejpam-3565	415	4	.	.	PROPN
ejpam-3565	415	5	,	,	PUNCT
ejpam-3565	415	6	24	24	NUM
ejpam-3565	415	7	(	(	PUNCT
ejpam-3565	415	8	4):751–764	4):751–764	NUM
ejpam-3565	415	9	,	,	PUNCT
ejpam-3565	415	10	2016	2016	NUM
ejpam-3565	415	11	.	.	PUNCT
ejpam-3565	416	1	[	[	X
ejpam-3565	416	2	4	4	NUM
ejpam-3565	416	3	]	]	SYM
ejpam-3565	416	4	w	w	ADJ
ejpam-3565	416	5	-	-	PUNCT
ejpam-3565	416	6	h	h	NOUN
ejpam-3565	416	7	choi	choi	NOUN
ejpam-3565	416	8	.	.	PUNCT
ejpam-3565	417	1	the	the	DET
ejpam-3565	417	2	classification	classification	NOUN
ejpam-3565	417	3	of	of	ADP
ejpam-3565	417	4	self	self	NOUN
ejpam-3565	417	5	-	-	PUNCT
ejpam-3565	417	6	dual	dual	ADJ
ejpam-3565	417	7	codes	code	NOUN
ejpam-3565	417	8	over	over	ADP
ejpam-3565	417	9	galois	galois	PROPN
ejpam-3565	417	10	rings	ring	NOUN
ejpam-3565	417	11	of	of	ADP
ejpam-3565	417	12	length	length	NOUN
ejpam-3565	417	13	4	4	NUM
ejpam-3565	417	14	.	.	PUNCT
ejpam-3565	417	15	bulletin	bulletin	NOUN
ejpam-3565	417	16	of	of	ADP
ejpam-3565	417	17	the	the	DET
ejpam-3565	417	18	korean	korean	PROPN
ejpam-3565	417	19	mathematical	mathematical	ADJ
ejpam-3565	417	20	society	society	NOUN
ejpam-3565	417	21	,	,	PUNCT
ejpam-3565	417	22	55:1371–1387	55:1371–1387	NOUN
ejpam-3565	417	23	,	,	PUNCT
ejpam-3565	417	24	2018	2018	NUM
ejpam-3565	417	25	.	.	PUNCT
ejpam-3565	418	1	[	[	X
ejpam-3565	418	2	5	5	X
ejpam-3565	418	3	]	]	PUNCT
ejpam-3565	418	4	p	p	NOUN
ejpam-3565	418	5	gaborit	gaborit	NOUN
ejpam-3565	418	6	.	.	PUNCT
ejpam-3565	419	1	mass	mass	ADJ
ejpam-3565	419	2	formulas	formula	NOUN
ejpam-3565	419	3	for	for	ADP
ejpam-3565	419	4	self	self	NOUN
ejpam-3565	419	5	-	-	PUNCT
ejpam-3565	419	6	dual	dual	ADJ
ejpam-3565	419	7	codes	code	NOUN
ejpam-3565	419	8	over	over	ADP
ejpam-3565	419	9	z4	z4	PROPN
ejpam-3565	419	10	and	and	CCONJ
ejpam-3565	419	11	fq	fq	PROPN
ejpam-3565	419	12	+	+	PROPN
ejpam-3565	419	13	ufq	ufq	PROPN
ejpam-3565	419	14	rings	ring	NOUN
ejpam-3565	419	15	.	.	PUNCT
ejpam-3565	420	1	ieee	ieee	PROPN
ejpam-3565	420	2	trans	trans	PROPN
ejpam-3565	420	3	.	.	PUNCT
ejpam-3565	421	1	inform	inform	NOUN
ejpam-3565	421	2	.	.	PUNCT
ejpam-3565	422	1	theory	theory	NOUN
ejpam-3565	422	2	,	,	PUNCT
ejpam-3565	422	3	42:1222–1228	42:1222–1228	PROPN
ejpam-3565	422	4	,	,	PUNCT
ejpam-3565	422	5	1996	1996	NUM
ejpam-3565	422	6	.	.	PUNCT
ejpam-3565	423	1	[	[	X
ejpam-3565	423	2	6	6	NUM
ejpam-3565	423	3	]	]	PUNCT
ejpam-3565	423	4	ar	ar	NOUN
ejpam-3565	423	5	hammons	hammon	NOUN
ejpam-3565	423	6	,	,	PUNCT
ejpam-3565	423	7	pv	pv	PROPN
ejpam-3565	423	8	kumar	kumar	PROPN
ejpam-3565	423	9	,	,	PUNCT
ejpam-3565	423	10	ar	ar	PROPN
ejpam-3565	423	11	calderbank	calderbank	PROPN
ejpam-3565	423	12	,	,	PUNCT
ejpam-3565	423	13	nja	nja	PROPN
ejpam-3565	423	14	sloane	sloane	NOUN
ejpam-3565	423	15	,	,	PUNCT
ejpam-3565	423	16	and	and	CCONJ
ejpam-3565	423	17	p	p	X
ejpam-3565	423	18	solé.	solé.	PROPN
ejpam-3565	423	19	the	the	DET
ejpam-3565	423	20	z4	z4	PROPN
ejpam-3565	423	21	-	-	PUNCT
ejpam-3565	423	22	linearity	linearity	NOUN
ejpam-3565	423	23	of	of	ADP
ejpam-3565	423	24	kerdock	kerdock	NOUN
ejpam-3565	423	25	,	,	PUNCT
ejpam-3565	423	26	preparata	preparata	NOUN
ejpam-3565	423	27	,	,	PUNCT
ejpam-3565	423	28	goethals	goethal	NOUN
ejpam-3565	423	29	,	,	PUNCT
ejpam-3565	423	30	and	and	CCONJ
ejpam-3565	423	31	related	related	ADJ
ejpam-3565	423	32	codes	code	NOUN
ejpam-3565	423	33	.	.	PUNCT
ejpam-3565	424	1	ieee	ieee	PROPN
ejpam-3565	424	2	trans	trans	PROPN
ejpam-3565	424	3	.	.	PUNCT
ejpam-3565	425	1	inform	inform	NOUN
ejpam-3565	425	2	.	.	PUNCT
ejpam-3565	426	1	theory	theory	NOUN
ejpam-3565	426	2	,	,	PUNCT
ejpam-3565	426	3	40	40	NUM
ejpam-3565	426	4	(	(	PUNCT
ejpam-3565	426	5	2):301–319	2):301–319	NUM
ejpam-3565	426	6	,	,	PUNCT
ejpam-3565	426	7	1994	1994	NUM
ejpam-3565	426	8	.	.	PUNCT
ejpam-3565	427	1	[	[	X
ejpam-3565	427	2	7	7	X
ejpam-3565	427	3	]	]	X
ejpam-3565	427	4	wc	wc	PROPN
ejpam-3565	427	5	huffman	huffman	PROPN
ejpam-3565	427	6	and	and	CCONJ
ejpam-3565	427	7	v	v	ADP
ejpam-3565	427	8	pless	pless	NOUN
ejpam-3565	427	9	.	.	PUNCT
ejpam-3565	428	1	fundamentals	fundamental	NOUN
ejpam-3565	428	2	of	of	ADP
ejpam-3565	428	3	error	error	NOUN
ejpam-3565	428	4	-	-	PUNCT
ejpam-3565	428	5	correcting	correct	VERB
ejpam-3565	428	6	codes	code	NOUN
ejpam-3565	428	7	.	.	PUNCT
ejpam-3565	429	1	cambridge	cambridge	PROPN
ejpam-3565	429	2	university	university	PROPN
ejpam-3565	429	3	press	press	PROPN
ejpam-3565	429	4	,	,	PUNCT
ejpam-3565	429	5	united	united	ADJ
ejpam-3565	429	6	kingdom	kingdom	PROPN
ejpam-3565	429	7	,	,	PUNCT
ejpam-3565	429	8	2004	2004	NUM
ejpam-3565	429	9	.	.	PUNCT
ejpam-3565	430	1	[	[	X
ejpam-3565	430	2	8	8	NUM
ejpam-3565	430	3	]	]	X
ejpam-3565	430	4	br	br	PROPN
ejpam-3565	430	5	mcdonald	mcdonald	PROPN
ejpam-3565	430	6	.	.	PUNCT
ejpam-3565	431	1	finite	finite	PROPN
ejpam-3565	431	2	rings	ring	NOUN
ejpam-3565	431	3	with	with	ADP
ejpam-3565	431	4	identity	identity	NOUN
ejpam-3565	431	5	.	.	PUNCT
ejpam-3565	432	1	marcel	marcel	PROPN
ejpam-3565	432	2	dekker	dekker	PROPN
ejpam-3565	432	3	,	,	PUNCT
ejpam-3565	432	4	inc	inc	PROPN
ejpam-3565	432	5	.	.	PROPN
ejpam-3565	432	6	,	,	PUNCT
ejpam-3565	432	7	new	new	PROPN
ejpam-3565	432	8	york	york	PROPN
ejpam-3565	432	9	,	,	PUNCT
ejpam-3565	432	10	1974	1974	NUM
ejpam-3565	432	11	.	.	PUNCT
ejpam-3565	433	1	[	[	X
ejpam-3565	433	2	9	9	NUM
ejpam-3565	433	3	]	]	X
ejpam-3565	433	4	k	k	PROPN
ejpam-3565	433	5	nagata	nagata	PROPN
ejpam-3565	433	6	,	,	PUNCT
ejpam-3565	433	7	f	f	PROPN
ejpam-3565	433	8	nemenzo	nemenzo	NOUN
ejpam-3565	433	9	,	,	PUNCT
ejpam-3565	433	10	and	and	CCONJ
ejpam-3565	433	11	h	h	PROPN
ejpam-3565	433	12	wada	wada	PROPN
ejpam-3565	433	13	.	.	PUNCT
ejpam-3565	434	1	constructive	constructive	ADJ
ejpam-3565	434	2	algorithm	algorithm	NOUN
ejpam-3565	434	3	of	of	ADP
ejpam-3565	434	4	self	self	NOUN
ejpam-3565	434	5	-	-	PUNCT
ejpam-3565	434	6	dual	dual	ADJ
ejpam-3565	434	7	errorcorrecting	errorcorrecte	VERB
ejpam-3565	434	8	codes	code	NOUN
ejpam-3565	434	9	.	.	PUNCT
ejpam-3565	435	1	in	in	ADP
ejpam-3565	435	2	11th	11th	ADJ
ejpam-3565	435	3	international	international	ADJ
ejpam-3565	435	4	workshop	workshop	NOUN
ejpam-3565	435	5	on	on	ADP
ejpam-3565	435	6	algebraic	algebraic	ADJ
ejpam-3565	435	7	and	and	CCONJ
ejpam-3565	435	8	combinatorial	combinatorial	ADJ
ejpam-3565	435	9	coding	code	VERB
ejpam-3565	435	10	theory	theory	NOUN
ejpam-3565	435	11	,	,	PUNCT
ejpam-3565	435	12	pages	page	NOUN
ejpam-3565	435	13	215–220	215–220	NUM
ejpam-3565	435	14	,	,	PUNCT
ejpam-3565	435	15	2008	2008	NUM
ejpam-3565	435	16	.	.	PUNCT
ejpam-3565	436	1	references	reference	NOUN
ejpam-3565	436	2	1716	1716	NUM
ejpam-3565	436	3	[	[	X
ejpam-3565	436	4	10	10	NUM
ejpam-3565	436	5	]	]	X
ejpam-3565	436	6	k	k	PROPN
ejpam-3565	436	7	nagata	nagata	PROPN
ejpam-3565	436	8	,	,	PUNCT
ejpam-3565	436	9	f	f	PROPN
ejpam-3565	436	10	nemenzo	nemenzo	NOUN
ejpam-3565	436	11	,	,	PUNCT
ejpam-3565	436	12	and	and	CCONJ
ejpam-3565	436	13	h	h	PROPN
ejpam-3565	436	14	wada	wada	PROPN
ejpam-3565	436	15	.	.	PUNCT
ejpam-3565	437	1	the	the	DET
ejpam-3565	437	2	number	number	NOUN
ejpam-3565	437	3	of	of	ADP
ejpam-3565	437	4	self	self	NOUN
ejpam-3565	437	5	-	-	PUNCT
ejpam-3565	437	6	dual	dual	ADJ
ejpam-3565	437	7	codes	code	NOUN
ejpam-3565	437	8	over	over	ADP
ejpam-3565	437	9	zp3	zp3	PROPN
ejpam-3565	437	10	.	.	PUNCT
ejpam-3565	438	1	des	des	PROPN
ejpam-3565	438	2	.	.	PROPN
ejpam-3565	438	3	codes	code	NOUN
ejpam-3565	438	4	cryptogr	cryptogr	NOUN
ejpam-3565	438	5	.	.	PUNCT
ejpam-3565	438	6	,	,	PUNCT
ejpam-3565	438	7	50:291–303	50:291–303	NUM
ejpam-3565	438	8	,	,	PUNCT
ejpam-3565	438	9	2009	2009	NUM
ejpam-3565	438	10	.	.	PUNCT
ejpam-3565	439	1	[	[	X
ejpam-3565	439	2	11	11	NUM
ejpam-3565	439	3	]	]	X
ejpam-3565	439	4	k	k	PROPN
ejpam-3565	439	5	nagata	nagata	PROPN
ejpam-3565	439	6	,	,	PUNCT
ejpam-3565	439	7	f	f	PROPN
ejpam-3565	439	8	nemenzo	nemenzo	NOUN
ejpam-3565	439	9	,	,	PUNCT
ejpam-3565	439	10	and	and	CCONJ
ejpam-3565	439	11	h	h	PROPN
ejpam-3565	439	12	wada	wada	PROPN
ejpam-3565	439	13	.	.	PUNCT
ejpam-3565	440	1	mass	mass	ADJ
ejpam-3565	440	2	formula	formula	NOUN
ejpam-3565	440	3	and	and	CCONJ
ejpam-3565	440	4	structure	structure	NOUN
ejpam-3565	440	5	of	of	ADP
ejpam-3565	440	6	self	self	NOUN
ejpam-3565	440	7	-	-	PUNCT
ejpam-3565	440	8	dual	dual	ADJ
ejpam-3565	440	9	codes	code	NOUN
ejpam-3565	440	10	over	over	ADP
ejpam-3565	440	11	z2s	z2s	PROPN
ejpam-3565	440	12	.	.	PUNCT
ejpam-3565	441	1	des	des	PROPN
ejpam-3565	441	2	.	.	PROPN
ejpam-3565	441	3	codes	code	NOUN
ejpam-3565	441	4	cryptogr	cryptogr	NOUN
ejpam-3565	441	5	.	.	PUNCT
ejpam-3565	441	6	,	,	PUNCT
ejpam-3565	442	1	67:293–316	67:293–316	NUM
ejpam-3565	442	2	,	,	PUNCT
ejpam-3565	442	3	2013	2013	NUM
ejpam-3565	442	4	.	.	PUNCT
ejpam-3565	443	1	[	[	X
ejpam-3565	443	2	12	12	NUM
ejpam-3565	443	3	]	]	PUNCT
ejpam-3565	443	4	gh	gh	PROPN
ejpam-3565	443	5	norton	norton	PROPN
ejpam-3565	443	6	and	and	CCONJ
ejpam-3565	443	7	a	a	DET
ejpam-3565	443	8	sălăgean	sălăgean	NOUN
ejpam-3565	443	9	.	.	PUNCT
ejpam-3565	444	1	on	on	ADP
ejpam-3565	444	2	the	the	DET
ejpam-3565	444	3	structure	structure	NOUN
ejpam-3565	444	4	of	of	ADP
ejpam-3565	444	5	linear	linear	PROPN
ejpam-3565	444	6	and	and	CCONJ
ejpam-3565	444	7	cyclic	cyclic	ADJ
ejpam-3565	444	8	codes	code	NOUN
ejpam-3565	444	9	over	over	ADP
ejpam-3565	444	10	a	a	DET
ejpam-3565	444	11	finite	finite	ADJ
ejpam-3565	444	12	chain	chain	NOUN
ejpam-3565	444	13	ring	ring	NOUN
ejpam-3565	444	14	.	.	PUNCT
ejpam-3565	445	1	aaecc	aaecc	PROPN
ejpam-3565	445	2	,	,	PUNCT
ejpam-3565	445	3	10(3):489–506	10(3):489–506	PROPN
ejpam-3565	445	4	,	,	PUNCT
ejpam-3565	445	5	2000	2000	NUM
ejpam-3565	445	6	.	.	PUNCT
ejpam-3565	446	1	[	[	X
ejpam-3565	446	2	13	13	NUM
ejpam-3565	446	3	]	]	X
ejpam-3565	446	4	yh	yh	PROPN
ejpam-3565	446	5	park	park	PROPN
ejpam-3565	446	6	.	.	PUNCT
ejpam-3565	447	1	the	the	DET
ejpam-3565	447	2	classification	classification	NOUN
ejpam-3565	447	3	of	of	ADP
ejpam-3565	447	4	self	self	NOUN
ejpam-3565	447	5	-	-	PUNCT
ejpam-3565	447	6	dual	dual	ADJ
ejpam-3565	447	7	modular	modular	ADJ
ejpam-3565	447	8	codes	code	NOUN
ejpam-3565	447	9	.	.	PUNCT
ejpam-3565	448	1	finite	finite	PROPN
ejpam-3565	448	2	fields	field	NOUN
ejpam-3565	448	3	and	and	CCONJ
ejpam-3565	448	4	their	their	PRON
ejpam-3565	448	5	applications	application	NOUN
ejpam-3565	448	6	,	,	PUNCT
ejpam-3565	448	7	17:442–460	17:442–460	NUM
ejpam-3565	448	8	,	,	PUNCT
ejpam-3565	448	9	2011	2011	NUM
ejpam-3565	448	10	.	.	PUNCT
ejpam-3565	449	1	[	[	X
ejpam-3565	449	2	14	14	NUM
ejpam-3565	449	3	]	]	SYM
ejpam-3565	449	4	v	v	X
ejpam-3565	449	5	pless	pless	NOUN
ejpam-3565	449	6	.	.	PUNCT
ejpam-3565	450	1	the	the	DET
ejpam-3565	450	2	number	number	NOUN
ejpam-3565	450	3	of	of	ADP
ejpam-3565	450	4	isotropic	isotropic	ADJ
ejpam-3565	450	5	subspaces	subspace	NOUN
ejpam-3565	450	6	in	in	ADP
ejpam-3565	450	7	a	a	DET
ejpam-3565	450	8	finite	finite	ADJ
ejpam-3565	450	9	geometry	geometry	NOUN
ejpam-3565	450	10	.	.	PUNCT
ejpam-3565	451	1	atti	atti	PROPN
ejpam-3565	451	2	.	.	PROPN
ejpam-3565	451	3	accad	accad	PROPN
ejpam-3565	451	4	.	.	PUNCT
ejpam-3565	452	1	naz	naz	PROPN
ejpam-3565	452	2	.	.	PUNCT
ejpam-3565	453	1	lincei	lincei	NOUN
ejpam-3565	453	2	rendic	rendic	NOUN
ejpam-3565	453	3	,	,	PUNCT
ejpam-3565	453	4	39:418–421	39:418–421	PROPN
ejpam-3565	453	5	,	,	PUNCT
ejpam-3565	453	6	1965	1965	NUM
ejpam-3565	453	7	.	.	PUNCT
ejpam-3565	454	1	[	[	X
ejpam-3565	454	2	15	15	NUM
ejpam-3565	454	3	]	]	X
ejpam-3565	454	4	jh	jh	PROPN
ejpam-3565	454	5	van	van	PROPN
ejpam-3565	454	6	lint	lint	PROPN
ejpam-3565	454	7	and	and	CCONJ
ejpam-3565	454	8	rm	rm	PROPN
ejpam-3565	454	9	wilson	wilson	PROPN
ejpam-3565	454	10	.	.	PUNCT
ejpam-3565	455	1	a	a	DET
ejpam-3565	455	2	course	course	NOUN
ejpam-3565	455	3	in	in	ADP
ejpam-3565	455	4	combinatorics	combinatoric	NOUN
ejpam-3565	455	5	.	.	PUNCT
ejpam-3565	456	1	cambridge	cambridge	PROPN
ejpam-3565	456	2	university	university	PROPN
ejpam-3565	456	3	press	press	PROPN
ejpam-3565	456	4	,	,	PUNCT
ejpam-3565	456	5	united	united	ADJ
ejpam-3565	456	6	kingdom	kingdom	PROPN
ejpam-3565	456	7	,	,	PUNCT
ejpam-3565	456	8	1993	1993	NUM
ejpam-3565	456	9	.	.	PUNCT
ejpam-3565	457	1	[	[	X
ejpam-3565	457	2	16	16	NUM
ejpam-3565	457	3	]	]	X
ejpam-3565	457	4	z	z	NOUN
ejpam-3565	457	5	-	-	PUNCT
ejpam-3565	457	6	x	x	SYM
ejpam-3565	457	7	wan	wan	PROPN
ejpam-3565	457	8	.	.	PROPN
ejpam-3565	457	9	finite	finite	PROPN
ejpam-3565	457	10	fields	field	NOUN
ejpam-3565	457	11	and	and	CCONJ
ejpam-3565	457	12	galois	galois	PROPN
ejpam-3565	457	13	rings	ring	NOUN
ejpam-3565	457	14	.	.	PUNCT
ejpam-3565	458	1	world	world	PROPN
ejpam-3565	458	2	scientific	scientific	PROPN
ejpam-3565	458	3	publishing	publishing	PROPN
ejpam-3565	458	4	co.	co.	PROPN
ejpam-3565	458	5	pte	pte	PROPN
ejpam-3565	458	6	.	.	PROPN
ejpam-3565	458	7	ltd	ltd	PROPN
ejpam-3565	458	8	.	.	PROPN
ejpam-3565	458	9	,	,	PUNCT
ejpam-3565	458	10	hackensack	hackensack	PROPN
ejpam-3565	458	11	,	,	PUNCT
ejpam-3565	458	12	nj	nj	PROPN
ejpam-3565	458	13	,	,	PUNCT
ejpam-3565	458	14	2012	2012	NUM
ejpam-3565	458	15	.	.	PUNCT