id	sid	tid	token	lemma	pos
ejpam-3419	1	1	european	european	PROPN
ejpam-3419	1	2	journal	journal	PROPN
ejpam-3419	1	3	of	of	ADP
ejpam-3419	1	4	pure	pure	ADJ
ejpam-3419	1	5	and	and	CCONJ
ejpam-3419	1	6	applied	apply	VERB
ejpam-3419	1	7	mathematics	mathematic	NOUN
ejpam-3419	1	8	vol	vol	NOUN
ejpam-3419	1	9	.	.	PROPN
ejpam-3419	2	1	12	12	NUM
ejpam-3419	2	2	,	,	PUNCT
ejpam-3419	2	3	no	no	INTJ
ejpam-3419	2	4	.	.	NOUN
ejpam-3419	2	5	2	2	NUM
ejpam-3419	2	6	,	,	PUNCT
ejpam-3419	2	7	2019	2019	NUM
ejpam-3419	2	8	,	,	PUNCT
ejpam-3419	2	9	668	668	NUM
ejpam-3419	2	10	-	-	SYM
ejpam-3419	2	11	679	679	NUM
ejpam-3419	2	12	issn	issn	PROPN
ejpam-3419	2	13	1307	1307	NUM
ejpam-3419	2	14	-	-	SYM
ejpam-3419	2	15	5543	5543	NUM
ejpam-3419	2	16	–	–	PUNCT
ejpam-3419	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3419	2	18	published	publish	VERB
ejpam-3419	2	19	by	by	ADP
ejpam-3419	2	20	new	new	PROPN
ejpam-3419	2	21	york	york	PROPN
ejpam-3419	2	22	business	business	PROPN
ejpam-3419	2	23	global	global	ADJ
ejpam-3419	2	24	counting	count	VERB
ejpam-3419	2	25	z2z4z8	z2z4z8	NOUN
ejpam-3419	2	26	-	-	PUNCT
ejpam-3419	2	27	additive	additive	ADJ
ejpam-3419	2	28	codes	code	NOUN
ejpam-3419	2	29	basri	basri	VERB
ejpam-3419	2	30	çalışkan1,∗	çalışkan1,∗	PROPN
ejpam-3419	2	31	,	,	PUNCT
ejpam-3419	2	32	kemal	kemal	NOUN
ejpam-3419	2	33	balıkçı2	balıkçı2	NOUN
ejpam-3419	2	34	1	1	NUM
ejpam-3419	2	35	department	department	NOUN
ejpam-3419	2	36	of	of	ADP
ejpam-3419	2	37	mathematics	mathematic	NOUN
ejpam-3419	2	38	,	,	PUNCT
ejpam-3419	2	39	faculty	faculty	NOUN
ejpam-3419	2	40	of	of	ADP
ejpam-3419	2	41	arts	art	NOUN
ejpam-3419	2	42	and	and	CCONJ
ejpam-3419	2	43	science	science	NOUN
ejpam-3419	2	44	,	,	PUNCT
ejpam-3419	2	45	osmaniye	osmaniye	PROPN
ejpam-3419	2	46	korkut	korkut	PROPN
ejpam-3419	2	47	ata	ata	PROPN
ejpam-3419	2	48	university	university	PROPN
ejpam-3419	2	49	,	,	PUNCT
ejpam-3419	2	50	osmaniye	osmaniye	PROPN
ejpam-3419	2	51	,	,	PUNCT
ejpam-3419	2	52	turkey	turkey	PROPN
ejpam-3419	2	53	2	2	NUM
ejpam-3419	2	54	department	department	NOUN
ejpam-3419	2	55	of	of	ADP
ejpam-3419	2	56	electrical	electrical	ADJ
ejpam-3419	2	57	and	and	CCONJ
ejpam-3419	2	58	electronic	electronic	ADJ
ejpam-3419	2	59	,	,	PUNCT
ejpam-3419	2	60	engineering	engineering	NOUN
ejpam-3419	2	61	faculty	faculty	NOUN
ejpam-3419	2	62	,	,	PUNCT
ejpam-3419	2	63	osmaniye	osmaniye	PROPN
ejpam-3419	2	64	korkut	korkut	PROPN
ejpam-3419	2	65	ata	ata	PROPN
ejpam-3419	2	66	university	university	PROPN
ejpam-3419	2	67	,	,	PUNCT
ejpam-3419	2	68	osmaniye	osmaniye	PROPN
ejpam-3419	2	69	,	,	PUNCT
ejpam-3419	2	70	turkey	turkey	NOUN
ejpam-3419	2	71	abstract	abstract	NOUN
ejpam-3419	2	72	.	.	PUNCT
ejpam-3419	3	1	in	in	ADP
ejpam-3419	3	2	algebraic	algebraic	ADJ
ejpam-3419	3	3	coding	code	VERB
ejpam-3419	3	4	theory	theory	NOUN
ejpam-3419	3	5	,	,	PUNCT
ejpam-3419	3	6	all	all	DET
ejpam-3419	3	7	linear	linear	ADJ
ejpam-3419	3	8	codes	code	NOUN
ejpam-3419	3	9	can	can	AUX
ejpam-3419	3	10	be	be	AUX
ejpam-3419	3	11	described	describe	VERB
ejpam-3419	3	12	by	by	ADP
ejpam-3419	3	13	generator	generator	NOUN
ejpam-3419	3	14	matrices	matrix	NOUN
ejpam-3419	3	15	.	.	PUNCT
ejpam-3419	4	1	any	any	DET
ejpam-3419	4	2	linear	linear	PROPN
ejpam-3419	4	3	code	code	NOUN
ejpam-3419	4	4	has	have	VERB
ejpam-3419	4	5	different	different	ADJ
ejpam-3419	4	6	generator	generator	NOUN
ejpam-3419	4	7	matrices	matrix	NOUN
ejpam-3419	4	8	.	.	PUNCT
ejpam-3419	5	1	it	it	PRON
ejpam-3419	5	2	is	be	AUX
ejpam-3419	5	3	important	important	ADJ
ejpam-3419	5	4	to	to	PART
ejpam-3419	5	5	find	find	VERB
ejpam-3419	5	6	the	the	DET
ejpam-3419	5	7	number	number	NOUN
ejpam-3419	5	8	of	of	ADP
ejpam-3419	5	9	the	the	DET
ejpam-3419	5	10	generator	generator	NOUN
ejpam-3419	5	11	matrices	matrix	NOUN
ejpam-3419	5	12	for	for	ADP
ejpam-3419	5	13	the	the	DET
ejpam-3419	5	14	construction	construction	NOUN
ejpam-3419	5	15	of	of	ADP
ejpam-3419	5	16	these	these	DET
ejpam-3419	5	17	codes	code	NOUN
ejpam-3419	5	18	.	.	PUNCT
ejpam-3419	6	1	in	in	ADP
ejpam-3419	6	2	this	this	DET
ejpam-3419	6	3	paper	paper	NOUN
ejpam-3419	6	4	,	,	PUNCT
ejpam-3419	6	5	we	we	PRON
ejpam-3419	6	6	study	study	VERB
ejpam-3419	6	7	z2z4z8	z2z4z8	NUM
ejpam-3419	6	8	-	-	PUNCT
ejpam-3419	6	9	additive	additive	ADJ
ejpam-3419	6	10	codes	code	NOUN
ejpam-3419	6	11	,	,	PUNCT
ejpam-3419	6	12	which	which	PRON
ejpam-3419	6	13	are	be	AUX
ejpam-3419	6	14	an	an	DET
ejpam-3419	6	15	extension	extension	NOUN
ejpam-3419	6	16	of	of	ADP
ejpam-3419	6	17	z2z4	z2z4	NOUN
ejpam-3419	6	18	-	-	ADJ
ejpam-3419	6	19	additive	additive	ADJ
ejpam-3419	6	20	codes	code	NOUN
ejpam-3419	6	21	.	.	PUNCT
ejpam-3419	7	1	we	we	PRON
ejpam-3419	7	2	count	count	VERB
ejpam-3419	7	3	the	the	DET
ejpam-3419	7	4	number	number	NOUN
ejpam-3419	7	5	of	of	ADP
ejpam-3419	7	6	arbitrary	arbitrary	ADJ
ejpam-3419	7	7	z2z4z8	z2z4z8	NUM
ejpam-3419	7	8	-	-	PUNCT
ejpam-3419	7	9	additive	additive	ADJ
ejpam-3419	7	10	codes	code	NOUN
ejpam-3419	7	11	.	.	PUNCT
ejpam-3419	8	1	then	then	ADV
ejpam-3419	8	2	we	we	PRON
ejpam-3419	8	3	investigate	investigate	VERB
ejpam-3419	8	4	connections	connection	NOUN
ejpam-3419	8	5	to	to	ADP
ejpam-3419	8	6	z2z4	z2z4	PROPN
ejpam-3419	8	7	and	and	CCONJ
ejpam-3419	8	8	z2z8	z2z8	NOUN
ejpam-3419	8	9	-	-	PUNCT
ejpam-3419	8	10	additive	additive	ADJ
ejpam-3419	8	11	codes	code	NOUN
ejpam-3419	8	12	with	with	ADP
ejpam-3419	8	13	z2z4z8	z2z4z8	NOUN
ejpam-3419	8	14	-	-	PUNCT
ejpam-3419	8	15	additive	additive	ADJ
ejpam-3419	8	16	codes	code	NOUN
ejpam-3419	8	17	,	,	PUNCT
ejpam-3419	8	18	and	and	CCONJ
ejpam-3419	8	19	give	give	VERB
ejpam-3419	8	20	some	some	DET
ejpam-3419	8	21	illustrative	illustrative	ADJ
ejpam-3419	8	22	examples	example	NOUN
ejpam-3419	8	23	.	.	PUNCT
ejpam-3419	9	1	2010	2010	NUM
ejpam-3419	9	2	mathematics	mathematic	NOUN
ejpam-3419	9	3	subject	subject	NOUN
ejpam-3419	9	4	classifications	classification	NOUN
ejpam-3419	9	5	:	:	PUNCT
ejpam-3419	9	6	94b15	94b15	NUM
ejpam-3419	9	7	,	,	PUNCT
ejpam-3419	9	8	94b60	94b60	NUM
ejpam-3419	9	9	key	key	ADJ
ejpam-3419	9	10	words	word	NOUN
ejpam-3419	9	11	and	and	CCONJ
ejpam-3419	9	12	phrases	phrase	NOUN
ejpam-3419	9	13	:	:	PUNCT
ejpam-3419	9	14	additive	additive	ADJ
ejpam-3419	9	15	codes	code	NOUN
ejpam-3419	9	16	,	,	PUNCT
ejpam-3419	9	17	z2z4z8	z2z4z8	NOUN
ejpam-3419	9	18	-	-	PUNCT
ejpam-3419	9	19	additive	additive	ADJ
ejpam-3419	9	20	codes	code	NOUN
ejpam-3419	9	21	,	,	PUNCT
ejpam-3419	9	22	gaussian	gaussian	ADJ
ejpam-3419	9	23	numbers	number	NOUN
ejpam-3419	9	24	.	.	PUNCT
ejpam-3419	10	1	1	1	X
ejpam-3419	10	2	.	.	X
ejpam-3419	10	3	introduction	introduction	NOUN
ejpam-3419	10	4	coding	code	VERB
ejpam-3419	10	5	theory	theory	NOUN
ejpam-3419	10	6	is	be	AUX
ejpam-3419	10	7	important	important	ADJ
ejpam-3419	10	8	in	in	ADP
ejpam-3419	10	9	modern	modern	ADJ
ejpam-3419	10	10	communication	communication	NOUN
ejpam-3419	10	11	systems	system	NOUN
ejpam-3419	10	12	and	and	CCONJ
ejpam-3419	10	13	has	have	AUX
ejpam-3419	10	14	become	become	VERB
ejpam-3419	10	15	applicable	applicable	ADJ
ejpam-3419	10	16	to	to	ADP
ejpam-3419	10	17	many	many	ADJ
ejpam-3419	10	18	areas	area	NOUN
ejpam-3419	10	19	such	such	ADJ
ejpam-3419	10	20	as	as	ADP
ejpam-3419	10	21	data	datum	NOUN
ejpam-3419	10	22	storage	storage	NOUN
ejpam-3419	10	23	devices	device	NOUN
ejpam-3419	10	24	,	,	PUNCT
ejpam-3419	10	25	mobile	mobile	ADJ
ejpam-3419	10	26	phones	phone	NOUN
ejpam-3419	10	27	and	and	CCONJ
ejpam-3419	10	28	the	the	DET
ejpam-3419	10	29	internet	internet	NOUN
ejpam-3419	10	30	.	.	PUNCT
ejpam-3419	11	1	one	one	NUM
ejpam-3419	11	2	of	of	ADP
ejpam-3419	11	3	the	the	DET
ejpam-3419	11	4	main	main	ADJ
ejpam-3419	11	5	problems	problem	NOUN
ejpam-3419	11	6	in	in	ADP
ejpam-3419	11	7	communication	communication	NOUN
ejpam-3419	11	8	is	be	AUX
ejpam-3419	11	9	”	"	PUNCT
ejpam-3419	11	10	how	how	SCONJ
ejpam-3419	11	11	accurately	accurately	ADV
ejpam-3419	11	12	can	can	AUX
ejpam-3419	11	13	the	the	DET
ejpam-3419	11	14	symbols	symbol	NOUN
ejpam-3419	11	15	of	of	ADP
ejpam-3419	11	16	communication	communication	NOUN
ejpam-3419	11	17	be	be	AUX
ejpam-3419	11	18	transmitted	transmit	VERB
ejpam-3419	11	19	?	?	PUNCT
ejpam-3419	11	20	”	"	PUNCT
ejpam-3419	11	21	.	.	PUNCT
ejpam-3419	12	1	this	this	DET
ejpam-3419	12	2	problem	problem	NOUN
ejpam-3419	12	3	is	be	AUX
ejpam-3419	12	4	concerned	concern	VERB
ejpam-3419	12	5	with	with	ADP
ejpam-3419	12	6	the	the	DET
ejpam-3419	12	7	accuracy	accuracy	NOUN
ejpam-3419	12	8	of	of	ADP
ejpam-3419	12	9	transference	transference	NOUN
ejpam-3419	12	10	from	from	ADP
ejpam-3419	12	11	sender	sender	NOUN
ejpam-3419	12	12	to	to	ADP
ejpam-3419	12	13	receiver	receiver	NOUN
ejpam-3419	12	14	of	of	ADP
ejpam-3419	12	15	sets	set	NOUN
ejpam-3419	12	16	of	of	ADP
ejpam-3419	12	17	symbols	symbol	NOUN
ejpam-3419	12	18	;	;	PUNCT
ejpam-3419	12	19	that	that	PRON
ejpam-3419	12	20	is	is	ADV
ejpam-3419	12	21	,	,	PUNCT
ejpam-3419	12	22	it	it	PRON
ejpam-3419	12	23	involves	involve	VERB
ejpam-3419	12	24	transmission	transmission	NOUN
ejpam-3419	12	25	of	of	ADP
ejpam-3419	12	26	finite	finite	ADJ
ejpam-3419	12	27	discrete	discrete	ADJ
ejpam-3419	12	28	symbols	symbol	NOUN
ejpam-3419	12	29	[	[	X
ejpam-3419	12	30	12	12	NUM
ejpam-3419	12	31	]	]	PUNCT
ejpam-3419	12	32	.	.	PUNCT
ejpam-3419	13	1	for	for	ADP
ejpam-3419	13	2	this	this	DET
ejpam-3419	13	3	purpose	purpose	NOUN
ejpam-3419	13	4	,	,	PUNCT
ejpam-3419	13	5	linear	linear	ADJ
ejpam-3419	13	6	codes	code	NOUN
ejpam-3419	13	7	are	be	AUX
ejpam-3419	13	8	widely	widely	ADV
ejpam-3419	13	9	used	use	VERB
ejpam-3419	13	10	in	in	ADP
ejpam-3419	13	11	coding	code	VERB
ejpam-3419	13	12	theory	theory	NOUN
ejpam-3419	13	13	.	.	PUNCT
ejpam-3419	14	1	a	a	DET
ejpam-3419	14	2	linear	linear	ADJ
ejpam-3419	14	3	code	code	NOUN
ejpam-3419	14	4	of	of	ADP
ejpam-3419	14	5	length	length	NOUN
ejpam-3419	14	6	n	n	CCONJ
ejpam-3419	14	7	over	over	ADP
ejpam-3419	14	8	fq	fq	PROPN
ejpam-3419	14	9	is	be	AUX
ejpam-3419	14	10	a	a	DET
ejpam-3419	14	11	subspace	subspace	NOUN
ejpam-3419	14	12	c	c	NOUN
ejpam-3419	14	13	of	of	ADP
ejpam-3419	14	14	the	the	DET
ejpam-3419	14	15	vector	vector	NOUN
ejpam-3419	14	16	space	space	NOUN
ejpam-3419	14	17	fnq	fnq	PROPN
ejpam-3419	14	18	where	where	SCONJ
ejpam-3419	14	19	fq	fq	PROPN
ejpam-3419	14	20	is	be	AUX
ejpam-3419	14	21	a	a	DET
ejpam-3419	14	22	finite	finite	ADJ
ejpam-3419	14	23	field	field	NOUN
ejpam-3419	14	24	of	of	ADP
ejpam-3419	14	25	size	size	NOUN
ejpam-3419	14	26	q	q	PROPN
ejpam-3419	14	27	which	which	PRON
ejpam-3419	14	28	is	be	AUX
ejpam-3419	14	29	prime	prime	ADJ
ejpam-3419	14	30	or	or	CCONJ
ejpam-3419	14	31	a	a	DET
ejpam-3419	14	32	power	power	NOUN
ejpam-3419	14	33	of	of	ADP
ejpam-3419	14	34	a	a	DET
ejpam-3419	14	35	prime	prime	NOUN
ejpam-3419	14	36	.	.	PUNCT
ejpam-3419	15	1	although	although	SCONJ
ejpam-3419	15	2	the	the	DET
ejpam-3419	15	3	finite	finite	NOUN
ejpam-3419	15	4	fields	field	NOUN
ejpam-3419	15	5	are	be	AUX
ejpam-3419	15	6	widely	widely	ADV
ejpam-3419	15	7	used	use	VERB
ejpam-3419	15	8	in	in	ADP
ejpam-3419	15	9	coding	code	VERB
ejpam-3419	15	10	theory	theory	NOUN
ejpam-3419	15	11	,	,	PUNCT
ejpam-3419	15	12	the	the	DET
ejpam-3419	15	13	studies	study	NOUN
ejpam-3419	15	14	of	of	ADP
ejpam-3419	15	15	the	the	DET
ejpam-3419	15	16	codes	code	NOUN
ejpam-3419	15	17	on	on	ADP
ejpam-3419	15	18	different	different	ADJ
ejpam-3419	15	19	rings	ring	NOUN
ejpam-3419	15	20	have	have	AUX
ejpam-3419	15	21	attracted	attract	VERB
ejpam-3419	15	22	the	the	DET
ejpam-3419	15	23	interest	interest	NOUN
ejpam-3419	15	24	of	of	ADP
ejpam-3419	15	25	the	the	DET
ejpam-3419	15	26	researchers	researcher	NOUN
ejpam-3419	15	27	[	[	X
ejpam-3419	15	28	9	9	NUM
ejpam-3419	15	29	]	]	PUNCT
ejpam-3419	15	30	.	.	PUNCT
ejpam-3419	16	1	let	let	VERB
ejpam-3419	16	2	zm	zm	PROPN
ejpam-3419	16	3	be	be	AUX
ejpam-3419	16	4	the	the	DET
ejpam-3419	16	5	ring	ring	NOUN
ejpam-3419	16	6	of	of	ADP
ejpam-3419	16	7	integers	integer	NOUN
ejpam-3419	16	8	modulo	modulo	PROPN
ejpam-3419	16	9	m.	m.	NOUN
ejpam-3419	16	10	znm	znm	NOUN
ejpam-3419	16	11	is	be	AUX
ejpam-3419	16	12	called	call	VERB
ejpam-3419	16	13	the	the	DET
ejpam-3419	16	14	set	set	NOUN
ejpam-3419	16	15	of	of	ADP
ejpam-3419	16	16	cartesian	cartesian	ADJ
ejpam-3419	16	17	product	product	NOUN
ejpam-3419	16	18	of	of	ADP
ejpam-3419	16	19	n	n	PROPN
ejpam-3419	16	20	copies	copy	NOUN
ejpam-3419	16	21	of	of	ADP
ejpam-3419	16	22	zm	zm	PROPN
ejpam-3419	16	23	.	.	PUNCT
ejpam-3419	17	1	any	any	DET
ejpam-3419	17	2	nonempty	nonempty	NOUN
ejpam-3419	17	3	subset	subset	VERB
ejpam-3419	17	4	c	c	NOUN
ejpam-3419	17	5	of	of	ADP
ejpam-3419	17	6	znm	znm	PROPN
ejpam-3419	17	7	is	be	AUX
ejpam-3419	17	8	a	a	DET
ejpam-3419	17	9	code	code	NOUN
ejpam-3419	17	10	and	and	CCONJ
ejpam-3419	17	11	a	a	DET
ejpam-3419	17	12	submodule	submodule	NOUN
ejpam-3419	17	13	of	of	ADP
ejpam-3419	17	14	a	a	DET
ejpam-3419	17	15	znm	znm	NOUN
ejpam-3419	17	16	is	be	AUX
ejpam-3419	17	17	called	call	VERB
ejpam-3419	17	18	a	a	DET
ejpam-3419	17	19	linear	linear	ADJ
ejpam-3419	17	20	code	code	NOUN
ejpam-3419	17	21	of	of	ADP
ejpam-3419	17	22	length	length	NOUN
ejpam-3419	17	23	n	n	PROPN
ejpam-3419	17	24	over	over	ADP
ejpam-3419	17	25	zm	zm	PROPN
ejpam-3419	17	26	.	.	PUNCT
ejpam-3419	18	1	specially	specially	ADV
ejpam-3419	18	2	,	,	PUNCT
ejpam-3419	18	3	for	for	ADP
ejpam-3419	18	4	m=2	m=2	PROPN
ejpam-3419	18	5	and	and	CCONJ
ejpam-3419	18	6	m	m	PROPN
ejpam-3419	18	7	=	=	ADJ
ejpam-3419	18	8	4	4	NUM
ejpam-3419	18	9	the	the	DET
ejpam-3419	18	10	codes	code	NOUN
ejpam-3419	18	11	are	be	AUX
ejpam-3419	18	12	called	call	VERB
ejpam-3419	18	13	binary	binary	ADJ
ejpam-3419	18	14	(	(	PUNCT
ejpam-3419	18	15	z2	z2	PROPN
ejpam-3419	18	16	)	)	PUNCT
ejpam-3419	18	17	and	and	CCONJ
ejpam-3419	18	18	quaternary	quaternary	ADJ
ejpam-3419	18	19	codes	code	NOUN
ejpam-3419	18	20	(	(	PUNCT
ejpam-3419	18	21	z4	z4	PROPN
ejpam-3419	18	22	)	)	PUNCT
ejpam-3419	18	23	,	,	PUNCT
ejpam-3419	18	24	respectively	respectively	ADV
ejpam-3419	18	25	.	.	PUNCT
ejpam-3419	19	1	it	it	PRON
ejpam-3419	19	2	was	be	AUX
ejpam-3419	19	3	shown	show	VERB
ejpam-3419	19	4	that	that	SCONJ
ejpam-3419	19	5	specific	specific	ADJ
ejpam-3419	19	6	∗corresponding	∗corresponde	VERB
ejpam-3419	19	7	author	author	NOUN
ejpam-3419	19	8	.	.	PUNCT
ejpam-3419	20	1	doi	doi	NOUN
ejpam-3419	20	2	:	:	PUNCT
ejpam-3419	20	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3427	https://doi.org/10.29020/nybg.ejpam.v12i2.3427	NOUN
ejpam-3419	20	4	email	email	NOUN
ejpam-3419	20	5	addresses	address	NOUN
ejpam-3419	20	6	:	:	PUNCT
ejpam-3419	20	7	bcaliskan@osmaniye.edu.tr	bcaliskan@osmaniye.edu.tr	PROPN
ejpam-3419	20	8	(	(	PUNCT
ejpam-3419	20	9	b.	b.	PROPN
ejpam-3419	20	10	çalışkan	çalışkan	PROPN
ejpam-3419	20	11	)	)	PUNCT
ejpam-3419	20	12	,	,	PUNCT
ejpam-3419	20	13	kbalikci@osmaniye.edu.tr	kbalikci@osmaniye.edu.tr	PROPN
ejpam-3419	20	14	(	(	PUNCT
ejpam-3419	20	15	k.	k.	PROPN
ejpam-3419	20	16	balıkçı	balıkçı	PROPN
ejpam-3419	20	17	)	)	PUNCT
ejpam-3419	20	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3419	21	1	668	668	NUM
ejpam-3419	21	2	c	c	NOUN
ejpam-3419	21	3	©	©	PROPN
ejpam-3419	21	4	2019	2019	NUM
ejpam-3419	21	5	ejpam	ejpam	NOUN
ejpam-3419	21	6	all	all	DET
ejpam-3419	21	7	rights	right	NOUN
ejpam-3419	21	8	reserved	reserve	VERB
ejpam-3419	21	9	.	.	PUNCT
ejpam-3419	22	1	b.	b.	PROPN
ejpam-3419	22	2	çalışkan	çalışkan	PROPN
ejpam-3419	22	3	,	,	PUNCT
ejpam-3419	22	4	k.	k.	PROPN
ejpam-3419	22	5	balıkçı	balıkçı	PROPN
ejpam-3419	22	6	/	/	SYM
ejpam-3419	22	7	eur	eur	PROPN
ejpam-3419	22	8	.	.	PUNCT
ejpam-3419	23	1	j.	j.	PROPN
ejpam-3419	23	2	pure	pure	PROPN
ejpam-3419	23	3	appl	appl	PROPN
ejpam-3419	23	4	.	.	PROPN
ejpam-3419	23	5	math	math	PROPN
ejpam-3419	23	6	,	,	PUNCT
ejpam-3419	23	7	12	12	NUM
ejpam-3419	23	8	(	(	PUNCT
ejpam-3419	23	9	2	2	NUM
ejpam-3419	23	10	)	)	PUNCT
ejpam-3419	23	11	(	(	PUNCT
ejpam-3419	23	12	2019	2019	NUM
ejpam-3419	23	13	)	)	PUNCT
ejpam-3419	23	14	,	,	PUNCT
ejpam-3419	23	15	668	668	NUM
ejpam-3419	23	16	-	-	SYM
ejpam-3419	23	17	679	679	NUM
ejpam-3419	23	18	669	669	NUM
ejpam-3419	23	19	good	good	ADJ
ejpam-3419	23	20	non	non	ADJ
ejpam-3419	23	21	-	-	ADJ
ejpam-3419	23	22	linear	linear	ADJ
ejpam-3419	23	23	binary	binary	ADJ
ejpam-3419	23	24	codes	code	NOUN
ejpam-3419	23	25	which	which	PRON
ejpam-3419	23	26	simplifies	simplifie	NOUN
ejpam-3419	23	27	encoding	encode	VERB
ejpam-3419	23	28	and	and	CCONJ
ejpam-3419	23	29	decoding	decoding	NOUN
ejpam-3419	23	30	can	can	AUX
ejpam-3419	23	31	be	be	AUX
ejpam-3419	23	32	seen	see	VERB
ejpam-3419	23	33	as	as	ADP
ejpam-3419	23	34	binary	binary	ADJ
ejpam-3419	23	35	images	image	NOUN
ejpam-3419	23	36	of	of	ADP
ejpam-3419	23	37	linear	linear	ADJ
ejpam-3419	23	38	codes	code	NOUN
ejpam-3419	23	39	over	over	ADP
ejpam-3419	23	40	z4	z4	PROPN
ejpam-3419	23	41	under	under	ADP
ejpam-3419	23	42	the	the	DET
ejpam-3419	23	43	gray	gray	ADJ
ejpam-3419	23	44	map	map	NOUN
ejpam-3419	23	45	[	[	X
ejpam-3419	23	46	9	9	NUM
ejpam-3419	23	47	]	]	PUNCT
ejpam-3419	23	48	.	.	PUNCT
ejpam-3419	24	1	additive	additive	ADJ
ejpam-3419	24	2	codes	code	NOUN
ejpam-3419	24	3	were	be	AUX
ejpam-3419	24	4	first	first	ADV
ejpam-3419	24	5	defined	define	VERB
ejpam-3419	24	6	by	by	ADP
ejpam-3419	24	7	delsarte	delsarte	NOUN
ejpam-3419	25	1	[	[	X
ejpam-3419	25	2	7	7	X
ejpam-3419	25	3	]	]	PUNCT
ejpam-3419	25	4	in	in	ADP
ejpam-3419	25	5	terms	term	NOUN
ejpam-3419	25	6	of	of	ADP
ejpam-3419	25	7	association	association	NOUN
ejpam-3419	25	8	schemes	scheme	NOUN
ejpam-3419	25	9	.	.	PUNCT
ejpam-3419	26	1	he	he	PRON
ejpam-3419	26	2	defined	define	VERB
ejpam-3419	26	3	additive	additive	ADJ
ejpam-3419	26	4	codes	code	NOUN
ejpam-3419	26	5	as	as	ADP
ejpam-3419	26	6	subgroups	subgroup	NOUN
ejpam-3419	26	7	of	of	ADP
ejpam-3419	26	8	the	the	DET
ejpam-3419	26	9	underlying	underlying	ADJ
ejpam-3419	26	10	abelian	abelian	ADJ
ejpam-3419	26	11	group	group	NOUN
ejpam-3419	26	12	in	in	ADP
ejpam-3419	26	13	a	a	DET
ejpam-3419	26	14	translation	translation	NOUN
ejpam-3419	26	15	association	association	NOUN
ejpam-3419	26	16	scheme	scheme	NOUN
ejpam-3419	26	17	.	.	PUNCT
ejpam-3419	27	1	according	accord	VERB
ejpam-3419	27	2	to	to	ADP
ejpam-3419	27	3	this	this	PRON
ejpam-3419	27	4	,	,	PUNCT
ejpam-3419	27	5	for	for	ADP
ejpam-3419	27	6	the	the	DET
ejpam-3419	27	7	binary	binary	ADJ
ejpam-3419	27	8	hamming	hamming	NOUN
ejpam-3419	27	9	scheme	scheme	NOUN
ejpam-3419	27	10	,	,	PUNCT
ejpam-3419	27	11	when	when	SCONJ
ejpam-3419	27	12	the	the	DET
ejpam-3419	27	13	underlying	underlying	ADJ
ejpam-3419	27	14	abelian	abelian	ADJ
ejpam-3419	27	15	group	group	NOUN
ejpam-3419	27	16	is	be	AUX
ejpam-3419	27	17	of	of	ADP
ejpam-3419	27	18	order	order	NOUN
ejpam-3419	27	19	2n	2n	NUM
ejpam-3419	27	20	,	,	PUNCT
ejpam-3419	27	21	the	the	DET
ejpam-3419	27	22	only	only	ADJ
ejpam-3419	27	23	structures	structure	NOUN
ejpam-3419	27	24	for	for	ADP
ejpam-3419	27	25	the	the	DET
ejpam-3419	27	26	abelian	abelian	ADJ
ejpam-3419	27	27	group	group	NOUN
ejpam-3419	27	28	are	be	AUX
ejpam-3419	27	29	those	those	PRON
ejpam-3419	27	30	of	of	ADP
ejpam-3419	27	31	the	the	DET
ejpam-3419	27	32	form	form	NOUN
ejpam-3419	27	33	zα2	zα2	NOUN
ejpam-3419	27	34	×	×	PROPN
ejpam-3419	27	35	zβ4	zβ4	NOUN
ejpam-3419	27	36	where	where	SCONJ
ejpam-3419	27	37	α	α	NOUN
ejpam-3419	27	38	and	and	CCONJ
ejpam-3419	27	39	β	β	X
ejpam-3419	27	40	are	be	AUX
ejpam-3419	27	41	positive	positive	ADJ
ejpam-3419	27	42	integers	integer	NOUN
ejpam-3419	27	43	(	(	PUNCT
ejpam-3419	27	44	n	n	NOUN
ejpam-3419	27	45	=	=	SYM
ejpam-3419	27	46	α	α	PROPN
ejpam-3419	27	47	+	+	CCONJ
ejpam-3419	27	48	2β	2β	NUM
ejpam-3419	27	49	)	)	PUNCT
ejpam-3419	27	50	.	.	PUNCT
ejpam-3419	28	1	later	later	ADV
ejpam-3419	28	2	,	,	PUNCT
ejpam-3419	28	3	translation	translation	NOUN
ejpam-3419	28	4	invariant	invariant	PROPN
ejpam-3419	28	5	propelinear	propelinear	NOUN
ejpam-3419	28	6	codes	code	NOUN
ejpam-3419	28	7	were	be	AUX
ejpam-3419	28	8	first	first	ADV
ejpam-3419	28	9	introduced	introduce	VERB
ejpam-3419	28	10	by	by	ADP
ejpam-3419	28	11	pujol	pujol	NOUN
ejpam-3419	28	12	et	et	PROPN
ejpam-3419	28	13	al.[11	al.[11	PROPN
ejpam-3419	28	14	]	]	PUNCT
ejpam-3419	28	15	.	.	PUNCT
ejpam-3419	29	1	they	they	PRON
ejpam-3419	29	2	showed	show	VERB
ejpam-3419	29	3	that	that	SCONJ
ejpam-3419	29	4	all	all	DET
ejpam-3419	29	5	these	these	DET
ejpam-3419	29	6	binary	binary	ADJ
ejpam-3419	29	7	codes	code	NOUN
ejpam-3419	29	8	are	be	AUX
ejpam-3419	29	9	group	group	NOUN
ejpam-3419	29	10	-	-	PUNCT
ejpam-3419	29	11	isomorphic	isomorphic	ADJ
ejpam-3419	29	12	to	to	ADP
ejpam-3419	29	13	subgroups	subgroup	NOUN
ejpam-3419	29	14	of	of	ADP
ejpam-3419	29	15	zα2	zα2	NOUN
ejpam-3419	29	16	×	×	PROPN
ejpam-3419	29	17	zβ4	zβ4	PROPN
ejpam-3419	29	18	×	×	NOUN
ejpam-3419	29	19	qσ	qσ	PROPN
ejpam-3419	29	20	8	8	NUM
ejpam-3419	29	21	,	,	PUNCT
ejpam-3419	29	22	being	be	AUX
ejpam-3419	29	23	q8	q8	PROPN
ejpam-3419	29	24	the	the	DET
ejpam-3419	29	25	non	non	ADJ
ejpam-3419	29	26	-	-	ADJ
ejpam-3419	29	27	abelian	abelian	ADJ
ejpam-3419	29	28	quaternion	quaternion	NOUN
ejpam-3419	29	29	group	group	NOUN
ejpam-3419	29	30	with	with	ADP
ejpam-3419	29	31	eight	eight	NUM
ejpam-3419	29	32	elements	element	NOUN
ejpam-3419	29	33	.	.	PUNCT
ejpam-3419	30	1	recently	recently	ADV
ejpam-3419	30	2	,	,	PUNCT
ejpam-3419	30	3	in	in	ADP
ejpam-3419	30	4	particular	particular	ADJ
ejpam-3419	30	5	,	,	PUNCT
ejpam-3419	30	6	z2z4	z2z4	ADJ
ejpam-3419	30	7	-	-	ADJ
ejpam-3419	30	8	additive	additive	ADJ
ejpam-3419	30	9	codes	code	NOUN
ejpam-3419	30	10	and	and	CCONJ
ejpam-3419	30	11	z2z4z8	z2z4z8	NOUN
ejpam-3419	30	12	-	-	PUNCT
ejpam-3419	30	13	additive	additive	ADJ
ejpam-3419	30	14	codes	code	NOUN
ejpam-3419	30	15	,	,	PUNCT
ejpam-3419	30	16	which	which	PRON
ejpam-3419	30	17	are	be	AUX
ejpam-3419	30	18	a	a	DET
ejpam-3419	30	19	generalization	generalization	NOUN
ejpam-3419	30	20	of	of	ADP
ejpam-3419	30	21	z2z4	z2z4	NOUN
ejpam-3419	30	22	-	-	ADJ
ejpam-3419	30	23	additive	additive	ADJ
ejpam-3419	30	24	codes	code	NOUN
ejpam-3419	30	25	,	,	PUNCT
ejpam-3419	30	26	have	have	AUX
ejpam-3419	30	27	been	be	AUX
ejpam-3419	30	28	extensively	extensively	ADV
ejpam-3419	30	29	studied	study	VERB
ejpam-3419	30	30	[	[	X
ejpam-3419	30	31	1–6	1–6	NUM
ejpam-3419	30	32	,	,	PUNCT
ejpam-3419	30	33	8	8	NUM
ejpam-3419	30	34	]	]	PUNCT
ejpam-3419	30	35	.	.	PUNCT
ejpam-3419	31	1	in	in	ADP
ejpam-3419	31	2	order	order	NOUN
ejpam-3419	31	3	to	to	PART
ejpam-3419	31	4	examine	examine	VERB
ejpam-3419	31	5	the	the	DET
ejpam-3419	31	6	z2z4z8	z2z4z8	NUM
ejpam-3419	31	7	-	-	PUNCT
ejpam-3419	31	8	additive	additive	ADJ
ejpam-3419	31	9	codes	code	NOUN
ejpam-3419	31	10	of	of	ADP
ejpam-3419	31	11	a	a	DET
ejpam-3419	31	12	given	give	VERB
ejpam-3419	31	13	length	length	NOUN
ejpam-3419	31	14	and	and	CCONJ
ejpam-3419	31	15	type	type	NOUN
ejpam-3419	31	16	,	,	PUNCT
ejpam-3419	31	17	it	it	PRON
ejpam-3419	31	18	is	be	AUX
ejpam-3419	31	19	necessary	necessary	ADJ
ejpam-3419	31	20	to	to	PART
ejpam-3419	31	21	construct	construct	VERB
ejpam-3419	31	22	the	the	DET
ejpam-3419	31	23	generator	generator	NOUN
ejpam-3419	31	24	matrices	matrix	NOUN
ejpam-3419	31	25	of	of	ADP
ejpam-3419	31	26	these	these	DET
ejpam-3419	31	27	codes	code	NOUN
ejpam-3419	31	28	and	and	CCONJ
ejpam-3419	31	29	to	to	PART
ejpam-3419	31	30	find	find	VERB
ejpam-3419	31	31	the	the	DET
ejpam-3419	31	32	number	number	NOUN
ejpam-3419	31	33	of	of	ADP
ejpam-3419	31	34	these	these	DET
ejpam-3419	31	35	generator	generator	NOUN
ejpam-3419	31	36	matrices	matrix	NOUN
ejpam-3419	31	37	.	.	PUNCT
ejpam-3419	32	1	in	in	ADP
ejpam-3419	32	2	fact	fact	NOUN
ejpam-3419	32	3	,	,	PUNCT
ejpam-3419	32	4	the	the	DET
ejpam-3419	32	5	counting	counting	NOUN
ejpam-3419	32	6	problem	problem	NOUN
ejpam-3419	32	7	is	be	AUX
ejpam-3419	32	8	the	the	DET
ejpam-3419	32	9	calculation	calculation	NOUN
ejpam-3419	32	10	of	of	ADP
ejpam-3419	32	11	the	the	DET
ejpam-3419	32	12	number	number	NOUN
ejpam-3419	32	13	of	of	ADP
ejpam-3419	32	14	subspaces	subspace	NOUN
ejpam-3419	32	15	created	create	VERB
ejpam-3419	32	16	by	by	ADP
ejpam-3419	32	17	the	the	DET
ejpam-3419	32	18	rows	row	NOUN
ejpam-3419	32	19	of	of	ADP
ejpam-3419	32	20	the	the	DET
ejpam-3419	32	21	generator	generator	NOUN
ejpam-3419	32	22	matrices	matrice	VERB
ejpam-3419	32	23	over	over	ADP
ejpam-3419	32	24	the	the	DET
ejpam-3419	32	25	finite	finite	ADJ
ejpam-3419	32	26	fields	field	NOUN
ejpam-3419	32	27	.	.	PUNCT
ejpam-3419	33	1	recently	recently	ADV
ejpam-3419	33	2	,	,	PUNCT
ejpam-3419	33	3	in	in	ADP
ejpam-3419	33	4	this	this	DET
ejpam-3419	33	5	regard	regard	NOUN
ejpam-3419	33	6	,	,	PUNCT
ejpam-3419	33	7	there	there	PRON
ejpam-3419	33	8	has	have	AUX
ejpam-3419	33	9	been	be	AUX
ejpam-3419	33	10	some	some	DET
ejpam-3419	33	11	researches	research	NOUN
ejpam-3419	33	12	of	of	ADP
ejpam-3419	33	13	particular	particular	ADJ
ejpam-3419	33	14	types	type	NOUN
ejpam-3419	33	15	over	over	ADP
ejpam-3419	33	16	the	the	DET
ejpam-3419	33	17	different	different	ADJ
ejpam-3419	33	18	rings	ring	NOUN
ejpam-3419	33	19	.	.	PUNCT
ejpam-3419	34	1	for	for	ADP
ejpam-3419	34	2	example	example	NOUN
ejpam-3419	34	3	,	,	PUNCT
ejpam-3419	34	4	while	while	SCONJ
ejpam-3419	34	5	dougherty	dougherty	PROPN
ejpam-3419	34	6	et	et	PROPN
ejpam-3419	34	7	al	al	PROPN
ejpam-3419	34	8	.	.	PUNCT
ejpam-3419	35	1	[	[	X
ejpam-3419	35	2	8	8	NUM
ejpam-3419	35	3	]	]	PUNCT
ejpam-3419	35	4	counted	count	VERB
ejpam-3419	35	5	the	the	DET
ejpam-3419	35	6	z2z4	z2z4	NOUN
ejpam-3419	35	7	-	-	ADJ
ejpam-3419	35	8	additive	additive	ADJ
ejpam-3419	35	9	codes	code	NOUN
ejpam-3419	35	10	,	,	PUNCT
ejpam-3419	35	11	aydogdu	aydogdu	ADV
ejpam-3419	35	12	et	et	PROPN
ejpam-3419	35	13	al	al	PROPN
ejpam-3419	35	14	.	.	PUNCT
ejpam-3419	36	1	[	[	X
ejpam-3419	36	2	3	3	NUM
ejpam-3419	36	3	]	]	PUNCT
ejpam-3419	36	4	performed	perform	VERB
ejpam-3419	36	5	the	the	DET
ejpam-3419	36	6	count	count	NOUN
ejpam-3419	36	7	of	of	ADP
ejpam-3419	36	8	the	the	DET
ejpam-3419	36	9	z2z8	z2z8	ADJ
ejpam-3419	36	10	-	-	PUNCT
ejpam-3419	36	11	additive	additive	ADJ
ejpam-3419	36	12	codes	code	NOUN
ejpam-3419	36	13	.	.	PUNCT
ejpam-3419	37	1	in	in	ADP
ejpam-3419	37	2	this	this	DET
ejpam-3419	37	3	paper	paper	NOUN
ejpam-3419	37	4	,	,	PUNCT
ejpam-3419	37	5	we	we	PRON
ejpam-3419	37	6	aim	aim	VERB
ejpam-3419	37	7	to	to	PART
ejpam-3419	37	8	focus	focus	VERB
ejpam-3419	37	9	on	on	ADP
ejpam-3419	37	10	the	the	DET
ejpam-3419	37	11	number	number	NOUN
ejpam-3419	37	12	of	of	ADP
ejpam-3419	37	13	matrices	matrix	NOUN
ejpam-3419	37	14	that	that	PRON
ejpam-3419	37	15	generate	generate	VERB
ejpam-3419	37	16	different	different	ADJ
ejpam-3419	37	17	(	(	PUNCT
ejpam-3419	37	18	not	not	PART
ejpam-3419	37	19	necessarily	necessarily	ADV
ejpam-3419	37	20	equivalent	equivalent	ADJ
ejpam-3419	37	21	)	)	PUNCT
ejpam-3419	37	22	z2z4z8	z2z4z8	NUM
ejpam-3419	37	23	-	-	PUNCT
ejpam-3419	37	24	additive	additive	ADJ
ejpam-3419	37	25	codes	code	NOUN
ejpam-3419	37	26	.	.	PUNCT
ejpam-3419	38	1	first	first	ADV
ejpam-3419	38	2	of	of	ADP
ejpam-3419	38	3	all	all	PRON
ejpam-3419	38	4	,	,	PUNCT
ejpam-3419	38	5	we	we	PRON
ejpam-3419	38	6	will	will	AUX
ejpam-3419	38	7	introduce	introduce	VERB
ejpam-3419	38	8	the	the	DET
ejpam-3419	38	9	structure	structure	NOUN
ejpam-3419	38	10	of	of	ADP
ejpam-3419	38	11	z2z4z8	z2z4z8	NOUN
ejpam-3419	38	12	-	-	PUNCT
ejpam-3419	38	13	additive	additive	ADJ
ejpam-3419	38	14	codes	code	NOUN
ejpam-3419	38	15	and	and	CCONJ
ejpam-3419	38	16	then	then	ADV
ejpam-3419	38	17	give	give	VERB
ejpam-3419	38	18	the	the	DET
ejpam-3419	38	19	basic	basic	ADJ
ejpam-3419	38	20	theorem	theorem	NOUN
ejpam-3419	38	21	of	of	ADP
ejpam-3419	38	22	our	our	PRON
ejpam-3419	38	23	article	article	NOUN
ejpam-3419	38	24	and	and	CCONJ
ejpam-3419	38	25	a	a	DET
ejpam-3419	38	26	simple	simple	ADJ
ejpam-3419	38	27	example	example	NOUN
ejpam-3419	38	28	.	.	PUNCT
ejpam-3419	39	1	in	in	ADP
ejpam-3419	39	2	addition	addition	NOUN
ejpam-3419	39	3	,	,	PUNCT
ejpam-3419	39	4	we	we	PRON
ejpam-3419	39	5	will	will	AUX
ejpam-3419	39	6	demonstrate	demonstrate	VERB
ejpam-3419	39	7	the	the	DET
ejpam-3419	39	8	relationship	relationship	NOUN
ejpam-3419	39	9	of	of	ADP
ejpam-3419	39	10	z2z4z8	z2z4z8	NOUN
ejpam-3419	39	11	-	-	PUNCT
ejpam-3419	39	12	additive	additive	ADJ
ejpam-3419	39	13	codes	code	NOUN
ejpam-3419	39	14	with	with	ADP
ejpam-3419	39	15	z2z4	z2z4	PROPN
ejpam-3419	39	16	and	and	CCONJ
ejpam-3419	39	17	z2z8	z2z8	NOUN
ejpam-3419	39	18	-	-	PUNCT
ejpam-3419	39	19	additive	additive	ADJ
ejpam-3419	39	20	codes	code	NOUN
ejpam-3419	39	21	.	.	PUNCT
ejpam-3419	40	1	2	2	X
ejpam-3419	40	2	.	.	X
ejpam-3419	40	3	preliminaries	preliminary	NOUN
ejpam-3419	40	4	in	in	ADP
ejpam-3419	40	5	this	this	DET
ejpam-3419	40	6	section	section	NOUN
ejpam-3419	40	7	,	,	PUNCT
ejpam-3419	40	8	we	we	PRON
ejpam-3419	40	9	briefly	briefly	ADV
ejpam-3419	40	10	introduce	introduce	VERB
ejpam-3419	40	11	the	the	DET
ejpam-3419	40	12	backgrounds	background	NOUN
ejpam-3419	40	13	of	of	ADP
ejpam-3419	40	14	our	our	PRON
ejpam-3419	40	15	proceeding	proceeding	NOUN
ejpam-3419	40	16	works	work	NOUN
ejpam-3419	40	17	.	.	PUNCT
ejpam-3419	41	1	2.1	2.1	NUM
ejpam-3419	41	2	.	.	PUNCT
ejpam-3419	42	1	z2z4z8	z2z4z8	X
ejpam-3419	42	2	-	-	PUNCT
ejpam-3419	42	3	additive	additive	ADJ
ejpam-3419	42	4	codes	code	NOUN
ejpam-3419	42	5	definition	definition	NOUN
ejpam-3419	42	6	1	1	NUM
ejpam-3419	42	7	.	.	PUNCT
ejpam-3419	43	1	let	let	VERB
ejpam-3419	43	2	z2	z2	PROPN
ejpam-3419	43	3	,	,	PUNCT
ejpam-3419	43	4	z4	z4	PROPN
ejpam-3419	43	5	and	and	CCONJ
ejpam-3419	43	6	z8	z8	NOUN
ejpam-3419	43	7	be	be	AUX
ejpam-3419	43	8	the	the	DET
ejpam-3419	43	9	rings	ring	NOUN
ejpam-3419	43	10	of	of	ADP
ejpam-3419	43	11	integers	integer	NOUN
ejpam-3419	43	12	modulo	modulo	VERB
ejpam-3419	43	13	2	2	NUM
ejpam-3419	43	14	,	,	PUNCT
ejpam-3419	43	15	4	4	NUM
ejpam-3419	43	16	and	and	CCONJ
ejpam-3419	43	17	8	8	NUM
ejpam-3419	43	18	,	,	PUNCT
ejpam-3419	43	19	respectively	respectively	ADV
ejpam-3419	43	20	.	.	PUNCT
ejpam-3419	44	1	then	then	ADV
ejpam-3419	44	2	,	,	PUNCT
ejpam-3419	44	3	c	c	PROPN
ejpam-3419	44	4	is	be	AUX
ejpam-3419	44	5	called	call	VERB
ejpam-3419	44	6	a	a	DET
ejpam-3419	44	7	z2z4z8	z2z4z8	NOUN
ejpam-3419	44	8	-	-	PUNCT
ejpam-3419	44	9	additive	additive	ADJ
ejpam-3419	44	10	code	code	NOUN
ejpam-3419	44	11	if	if	SCONJ
ejpam-3419	44	12	it	it	PRON
ejpam-3419	44	13	is	be	AUX
ejpam-3419	44	14	a	a	DET
ejpam-3419	44	15	subgroup	subgroup	NOUN
ejpam-3419	44	16	of	of	ADP
ejpam-3419	44	17	zα2	zα2	NOUN
ejpam-3419	44	18	×	×	PROPN
ejpam-3419	44	19	zβ4	zβ4	PROPN
ejpam-3419	44	20	×	×	PROPN
ejpam-3419	44	21	zθ8	zθ8	NOUN
ejpam-3419	44	22	where	where	SCONJ
ejpam-3419	44	23	α	α	X
ejpam-3419	44	24	,	,	PUNCT
ejpam-3419	44	25	β	β	NOUN
ejpam-3419	44	26	and	and	CCONJ
ejpam-3419	44	27	θ	θ	PROPN
ejpam-3419	44	28	are	be	AUX
ejpam-3419	44	29	positive	positive	ADJ
ejpam-3419	44	30	integers	integer	NOUN
ejpam-3419	44	31	[	[	X
ejpam-3419	44	32	2	2	NUM
ejpam-3419	44	33	]	]	PUNCT
ejpam-3419	44	34	.	.	PUNCT
ejpam-3419	45	1	according	accord	VERB
ejpam-3419	45	2	to	to	ADP
ejpam-3419	45	3	this	this	DET
ejpam-3419	45	4	definition	definition	NOUN
ejpam-3419	45	5	,	,	PUNCT
ejpam-3419	45	6	the	the	DET
ejpam-3419	45	7	first	first	ADJ
ejpam-3419	45	8	α	α	PROPN
ejpam-3419	45	9	coordinates	coordinate	NOUN
ejpam-3419	45	10	of	of	ADP
ejpam-3419	45	11	c	c	PROPN
ejpam-3419	45	12	consist	consist	NOUN
ejpam-3419	45	13	of	of	ADP
ejpam-3419	45	14	entries	entry	NOUN
ejpam-3419	45	15	from	from	ADP
ejpam-3419	45	16	z2	z2	PROPN
ejpam-3419	45	17	,	,	PUNCT
ejpam-3419	45	18	the	the	DET
ejpam-3419	45	19	next	next	ADJ
ejpam-3419	45	20	β	β	PROPN
ejpam-3419	45	21	coordinates	coordinate	NOUN
ejpam-3419	45	22	are	be	AUX
ejpam-3419	45	23	elements	element	NOUN
ejpam-3419	45	24	from	from	ADP
ejpam-3419	45	25	z4	z4	PROPN
ejpam-3419	45	26	and	and	CCONJ
ejpam-3419	45	27	remaining	remain	VERB
ejpam-3419	45	28	θ	θ	PROPN
ejpam-3419	45	29	coordinates	coordinate	NOUN
ejpam-3419	45	30	are	be	AUX
ejpam-3419	45	31	the	the	DET
ejpam-3419	45	32	elements	element	NOUN
ejpam-3419	45	33	of	of	ADP
ejpam-3419	45	34	the	the	DET
ejpam-3419	45	35	ring	ring	NOUN
ejpam-3419	45	36	z8	z8	PROPN
ejpam-3419	45	37	.	.	PUNCT
ejpam-3419	46	1	from	from	ADP
ejpam-3419	46	2	the	the	DET
ejpam-3419	46	3	fundamental	fundamental	ADJ
ejpam-3419	46	4	theorem	theorem	NOUN
ejpam-3419	46	5	of	of	ADP
ejpam-3419	46	6	finite	finite	ADJ
ejpam-3419	46	7	abelian	abelian	ADJ
ejpam-3419	46	8	groups	group	NOUN
ejpam-3419	46	9	,	,	PUNCT
ejpam-3419	46	10	such	such	DET
ejpam-3419	46	11	an	an	DET
ejpam-3419	46	12	additive	additive	ADJ
ejpam-3419	46	13	code	code	NOUN
ejpam-3419	46	14	c	c	NOUN
ejpam-3419	46	15	which	which	PRON
ejpam-3419	46	16	is	be	AUX
ejpam-3419	46	17	a	a	DET
ejpam-3419	46	18	subgroup	subgroup	NOUN
ejpam-3419	46	19	of	of	ADP
ejpam-3419	46	20	zα2	zα2	NOUN
ejpam-3419	46	21	×	×	PROPN
ejpam-3419	46	22	zβ4	zβ4	NOUN
ejpam-3419	46	23	×	×	PROPN
ejpam-3419	46	24	zθ8	zθ8	PROPN
ejpam-3419	46	25	is	be	AUX
ejpam-3419	46	26	group	group	NOUN
ejpam-3419	46	27	isomorphic	isomorphic	ADJ
ejpam-3419	46	28	to	to	ADP
ejpam-3419	46	29	the	the	DET
ejpam-3419	46	30	abelian	abelian	ADJ
ejpam-3419	46	31	structure	structure	NOUN
ejpam-3419	46	32	zk02	zk02	PROPN
ejpam-3419	46	33	×	×	NOUN
ejpam-3419	46	34	zk14	zk14	PROPN
ejpam-3419	46	35	×	×	PROPN
ejpam-3419	46	36	zk22	zk22	PROPN
ejpam-3419	46	37	×	×	NOUN
ejpam-3419	46	38	zk38	zk38	PROPN
ejpam-3419	46	39	×	×	NOUN
ejpam-3419	46	40	zk44	zk44	PROPN
ejpam-3419	46	41	×	×	NOUN
ejpam-3419	46	42	zk52	zk52	PROPN
ejpam-3419	46	43	.	.	PUNCT
ejpam-3419	47	1	by	by	ADP
ejpam-3419	47	2	this	this	DET
ejpam-3419	47	3	isomorphism	isomorphism	NOUN
ejpam-3419	47	4	,	,	PUNCT
ejpam-3419	47	5	such	such	DET
ejpam-3419	47	6	a	a	DET
ejpam-3419	47	7	z2z4z8	z2z4z8	NUM
ejpam-3419	47	8	-	-	PUNCT
ejpam-3419	47	9	additive	additive	ADJ
ejpam-3419	47	10	code	code	NOUN
ejpam-3419	47	11	is	be	AUX
ejpam-3419	47	12	classified	classify	VERB
ejpam-3419	47	13	as	as	ADP
ejpam-3419	47	14	of	of	ADP
ejpam-3419	47	15	type	type	NOUN
ejpam-3419	47	16	(	(	PUNCT
ejpam-3419	47	17	α	α	NOUN
ejpam-3419	47	18	,	,	PUNCT
ejpam-3419	47	19	β	β	X
ejpam-3419	47	20	,	,	PUNCT
ejpam-3419	47	21	θ	θ	PROPN
ejpam-3419	47	22	;	;	PUNCT
ejpam-3419	47	23	k0	k0	PROPN
ejpam-3419	47	24	,	,	PUNCT
ejpam-3419	47	25	k1	k1	PROPN
ejpam-3419	47	26	,	,	PUNCT
ejpam-3419	47	27	k2	k2	NOUN
ejpam-3419	47	28	,	,	PUNCT
ejpam-3419	47	29	k3	k3	PROPN
ejpam-3419	47	30	,	,	PUNCT
ejpam-3419	47	31	k4	k4	PROPN
ejpam-3419	47	32	,	,	PUNCT
ejpam-3419	47	33	k5	k5	PROPN
ejpam-3419	47	34	)	)	PUNCT
ejpam-3419	48	1	[	[	X
ejpam-3419	48	2	2	2	NUM
ejpam-3419	48	3	]	]	PUNCT
ejpam-3419	48	4	.	.	PUNCT
ejpam-3419	49	1	b.	b.	PROPN
ejpam-3419	49	2	çalışkan	çalışkan	PROPN
ejpam-3419	49	3	,	,	PUNCT
ejpam-3419	49	4	k.	k.	PROPN
ejpam-3419	49	5	balıkçı	balıkçı	PROPN
ejpam-3419	49	6	/	/	SYM
ejpam-3419	49	7	eur	eur	PROPN
ejpam-3419	49	8	.	.	PUNCT
ejpam-3419	50	1	j.	j.	PROPN
ejpam-3419	50	2	pure	pure	PROPN
ejpam-3419	50	3	appl	appl	PROPN
ejpam-3419	50	4	.	.	PROPN
ejpam-3419	50	5	math	math	PROPN
ejpam-3419	50	6	,	,	PUNCT
ejpam-3419	50	7	12	12	NUM
ejpam-3419	50	8	(	(	PUNCT
ejpam-3419	50	9	2	2	NUM
ejpam-3419	50	10	)	)	PUNCT
ejpam-3419	50	11	(	(	PUNCT
ejpam-3419	50	12	2019	2019	NUM
ejpam-3419	50	13	)	)	PUNCT
ejpam-3419	50	14	,	,	PUNCT
ejpam-3419	50	15	668	668	NUM
ejpam-3419	50	16	-	-	SYM
ejpam-3419	50	17	679	679	NUM
ejpam-3419	50	18	670	670	NUM
ejpam-3419	50	19	2.2	2.2	NUM
ejpam-3419	50	20	.	.	PUNCT
ejpam-3419	51	1	generator	generator	NOUN
ejpam-3419	51	2	and	and	CCONJ
ejpam-3419	51	3	parity	parity	NOUN
ejpam-3419	51	4	-	-	PUNCT
ejpam-3419	51	5	check	check	NOUN
ejpam-3419	51	6	matrices	matrix	NOUN
ejpam-3419	51	7	of	of	ADP
ejpam-3419	51	8	z2z4z8	z2z4z8	NOUN
ejpam-3419	51	9	-	-	PUNCT
ejpam-3419	51	10	additive	additive	ADJ
ejpam-3419	51	11	codes	code	NOUN
ejpam-3419	51	12	let	let	VERB
ejpam-3419	51	13	c	c	NOUN
ejpam-3419	51	14	be	be	AUX
ejpam-3419	51	15	a	a	DET
ejpam-3419	51	16	z2z4z8	z2z4z8	NOUN
ejpam-3419	51	17	-	-	PUNCT
ejpam-3419	51	18	additive	additive	ADJ
ejpam-3419	51	19	code	code	NOUN
ejpam-3419	51	20	of	of	ADP
ejpam-3419	51	21	type	type	NOUN
ejpam-3419	51	22	(	(	PUNCT
ejpam-3419	51	23	α	α	NOUN
ejpam-3419	51	24	,	,	PUNCT
ejpam-3419	51	25	β	β	X
ejpam-3419	51	26	,	,	PUNCT
ejpam-3419	51	27	θ	θ	PROPN
ejpam-3419	51	28	;	;	PUNCT
ejpam-3419	51	29	k0	k0	PROPN
ejpam-3419	51	30	,	,	PUNCT
ejpam-3419	51	31	k1	k1	PROPN
ejpam-3419	51	32	,	,	PUNCT
ejpam-3419	51	33	k2	k2	NOUN
ejpam-3419	51	34	,	,	PUNCT
ejpam-3419	51	35	k3	k3	PROPN
ejpam-3419	51	36	,	,	PUNCT
ejpam-3419	51	37	k4	k4	PROPN
ejpam-3419	51	38	,	,	PUNCT
ejpam-3419	51	39	k5	k5	PROPN
ejpam-3419	51	40	)	)	PUNCT
ejpam-3419	51	41	.	.	PUNCT
ejpam-3419	52	1	then	then	ADV
ejpam-3419	52	2	,	,	PUNCT
ejpam-3419	52	3	it	it	PRON
ejpam-3419	52	4	is	be	AUX
ejpam-3419	52	5	shown	show	VERB
ejpam-3419	52	6	that	that	SCONJ
ejpam-3419	52	7	c	c	PROPN
ejpam-3419	52	8	is	be	AUX
ejpam-3419	52	9	permutation	permutation	NOUN
ejpam-3419	52	10	equivalent	equivalent	ADJ
ejpam-3419	52	11	to	to	ADP
ejpam-3419	52	12	a	a	DET
ejpam-3419	52	13	z2z4z8	z2z4z8	NOUN
ejpam-3419	52	14	-	-	PUNCT
ejpam-3419	52	15	additive	additive	ADJ
ejpam-3419	52	16	code	code	NOUN
ejpam-3419	52	17	which	which	PRON
ejpam-3419	52	18	has	have	VERB
ejpam-3419	52	19	the	the	DET
ejpam-3419	52	20	following	follow	VERB
ejpam-3419	52	21	generator	generator	NOUN
ejpam-3419	52	22	matrix	matrix	NOUN
ejpam-3419	52	23	in	in	ADP
ejpam-3419	52	24	standard	standard	ADJ
ejpam-3419	52	25	form:	form:	PROPN
ejpam-3419	52	26	ik0	ik0	VERB
ejpam-3419	52	27	a01	a01	NOUN
ejpam-3419	52	28	0	0	PUNCT
ejpam-3419	52	29	0	0	NUM
ejpam-3419	52	30	2t1	2t1	NUM
ejpam-3419	52	31	0	0	NUM
ejpam-3419	52	32	0	0	SYM
ejpam-3419	52	33	0	0	NUM
ejpam-3419	53	1	4t2	4t2	NUM
ejpam-3419	53	2	0	0	NUM
ejpam-3419	54	1	s1	s1	PROPN
ejpam-3419	54	2	ik1	ik1	PROPN
ejpam-3419	54	3	b01	b01	PROPN
ejpam-3419	54	4	b02	b02	PROPN
ejpam-3419	54	5	0	0	PROPN
ejpam-3419	54	6	0	0	NUM
ejpam-3419	54	7	2t3	2t3	NUM
ejpam-3419	54	8	2t4	2t4	NUM
ejpam-3419	54	9	0	0	NUM
ejpam-3419	54	10	0	0	NUM
ejpam-3419	54	11	0	0	NUM
ejpam-3419	54	12	2ik2	2ik2	NUM
ejpam-3419	54	13	2b12	2b12	NOUN
ejpam-3419	54	14	0	0	NUM
ejpam-3419	54	15	0	0	NUM
ejpam-3419	54	16	0	0	NUM
ejpam-3419	54	17	4t5	4t5	NUM
ejpam-3419	54	18	0	0	NUM
ejpam-3419	54	19	s2	s2	NOUN
ejpam-3419	54	20	0	0	NUM
ejpam-3419	54	21	s01	s01	PROPN
ejpam-3419	54	22	s02	s02	PROPN
ejpam-3419	54	23	ik3	ik3	PROPN
ejpam-3419	54	24	a01	a01	PROPN
ejpam-3419	54	25	a02	a02	PROPN
ejpam-3419	54	26	a03	a03	PROPN
ejpam-3419	54	27	0	0	NUM
ejpam-3419	54	28	s3	s3	PROPN
ejpam-3419	54	29	0	0	NUM
ejpam-3419	54	30	0	0	NUM
ejpam-3419	54	31	2s12	2s12	NOUN
ejpam-3419	54	32	0	0	NUM
ejpam-3419	54	33	2ik4	2ik4	NUM
ejpam-3419	54	34	2a12	2a12	NUM
ejpam-3419	54	35	2a13	2a13	NUM
ejpam-3419	54	36	0	0	NUM
ejpam-3419	54	37	0	0	NUM
ejpam-3419	54	38	0	0	NUM
ejpam-3419	54	39	0	0	NUM
ejpam-3419	54	40	0	0	NUM
ejpam-3419	54	41	0	0	NUM
ejpam-3419	54	42	0	0	NUM
ejpam-3419	54	43	4ik5	4ik5	NUM
ejpam-3419	54	44	4a23	4a23	NOUN
ejpam-3419	54	45			ADP
ejpam-3419	54	46	(	(	PUNCT
ejpam-3419	54	47	1	1	X
ejpam-3419	54	48	)	)	PUNCT
ejpam-3419	54	49	where	where	SCONJ
ejpam-3419	54	50	a01	a01	NOUN
ejpam-3419	54	51	,	,	PUNCT
ejpam-3419	54	52	s1	s1	NOUN
ejpam-3419	54	53	,	,	PUNCT
ejpam-3419	54	54	s2	s2	PROPN
ejpam-3419	54	55	,	,	PUNCT
ejpam-3419	54	56	s3	s3	PROPN
ejpam-3419	54	57	are	be	AUX
ejpam-3419	54	58	matrices	matrix	NOUN
ejpam-3419	54	59	with	with	ADP
ejpam-3419	54	60	all	all	DET
ejpam-3419	54	61	entries	entry	NOUN
ejpam-3419	54	62	from	from	ADP
ejpam-3419	54	63	z2	z2	PROPN
ejpam-3419	54	64	and	and	CCONJ
ejpam-3419	54	65	b02	b02	PROPN
ejpam-3419	54	66	,	,	PUNCT
ejpam-3419	54	67	b12	b12	NOUN
ejpam-3419	54	68	,	,	PUNCT
ejpam-3419	54	69	s02	s02	PROPN
ejpam-3419	54	70	and	and	CCONJ
ejpam-3419	54	71	s12	s12	NOUN
ejpam-3419	54	72	are	be	AUX
ejpam-3419	54	73	matrices	matrix	NOUN
ejpam-3419	54	74	over	over	ADP
ejpam-3419	54	75	z4	z4	PROPN
ejpam-3419	54	76	.	.	PUNCT
ejpam-3419	55	1	also	also	ADV
ejpam-3419	55	2	,	,	PUNCT
ejpam-3419	55	3	t4	t4	PROPN
ejpam-3419	55	4	,	,	PUNCT
ejpam-3419	55	5	t5	t5	PROPN
ejpam-3419	55	6	and	and	CCONJ
ejpam-3419	55	7	ai3	ai3	NOUN
ejpam-3419	55	8	are	be	AUX
ejpam-3419	55	9	matrices	matrix	NOUN
ejpam-3419	55	10	over	over	ADP
ejpam-3419	55	11	z8	z8	NOUN
ejpam-3419	55	12	for	for	ADP
ejpam-3419	55	13	0	0	NUM
ejpam-3419	55	14	≤	≤	NUM
ejpam-3419	56	1	i	i	PRON
ejpam-3419	56	2	≤	≤	NOUN
ejpam-3419	56	3	2	2	NUM
ejpam-3419	56	4	.	.	PUNCT
ejpam-3419	57	1	all	all	DET
ejpam-3419	57	2	the	the	DET
ejpam-3419	57	3	entries	entry	NOUN
ejpam-3419	57	4	in	in	ADP
ejpam-3419	57	5	b01	b01	NOUN
ejpam-3419	57	6	,	,	PUNCT
ejpam-3419	57	7	s01	s01	NOUN
ejpam-3419	57	8	and	and	CCONJ
ejpam-3419	57	9	t1	t1	NOUN
ejpam-3419	57	10	are	be	AUX
ejpam-3419	57	11	in	in	ADP
ejpam-3419	57	12	{	{	PUNCT
ejpam-3419	57	13	0	0	NUM
ejpam-3419	57	14	,	,	PUNCT
ejpam-3419	57	15	1	1	NUM
ejpam-3419	57	16	}	}	SYM
ejpam-3419	57	17	⊆	⊆	NUM
ejpam-3419	57	18	z4	z4	NOUN
ejpam-3419	57	19	.	.	PUNCT
ejpam-3419	58	1	likewise	likewise	ADV
ejpam-3419	58	2	,	,	PUNCT
ejpam-3419	58	3	a01	a01	NOUN
ejpam-3419	58	4	and	and	CCONJ
ejpam-3419	58	5	t2	t2	NOUN
ejpam-3419	58	6	are	be	AUX
ejpam-3419	58	7	matrices	matrix	NOUN
ejpam-3419	58	8	over	over	ADP
ejpam-3419	58	9	z4	z4	PROPN
ejpam-3419	58	10	whose	whose	DET
ejpam-3419	58	11	all	all	DET
ejpam-3419	58	12	entries	entry	NOUN
ejpam-3419	58	13	are	be	AUX
ejpam-3419	58	14	from	from	ADP
ejpam-3419	58	15	{	{	PUNCT
ejpam-3419	58	16	0	0	NUM
ejpam-3419	58	17	,	,	PUNCT
ejpam-3419	58	18	1	1	NUM
ejpam-3419	58	19	}	}	PUNCT
ejpam-3419	58	20	.	.	PUNCT
ejpam-3419	59	1	t3	t3	PROPN
ejpam-3419	59	2	,	,	PUNCT
ejpam-3419	59	3	a12	a12	NOUN
ejpam-3419	59	4	and	and	CCONJ
ejpam-3419	59	5	a02	a02	PROPN
ejpam-3419	59	6	are	be	AUX
ejpam-3419	59	7	matrices	matrix	NOUN
ejpam-3419	59	8	over	over	ADP
ejpam-3419	59	9	z8	z8	NOUN
ejpam-3419	59	10	,	,	PUNCT
ejpam-3419	59	11	but	but	CCONJ
ejpam-3419	59	12	all	all	DET
ejpam-3419	59	13	values	value	NOUN
ejpam-3419	59	14	are	be	AUX
ejpam-3419	59	15	the	the	DET
ejpam-3419	59	16	elements	element	NOUN
ejpam-3419	59	17	of	of	ADP
ejpam-3419	59	18	the	the	DET
ejpam-3419	59	19	set	set	NOUN
ejpam-3419	59	20	{	{	PUNCT
ejpam-3419	59	21	0	0	NUM
ejpam-3419	59	22	,	,	PUNCT
ejpam-3419	59	23	1	1	NUM
ejpam-3419	59	24	,	,	PUNCT
ejpam-3419	59	25	2	2	NUM
ejpam-3419	59	26	,	,	PUNCT
ejpam-3419	59	27	3	3	NUM
ejpam-3419	59	28	}	}	PUNCT
ejpam-3419	59	29	.	.	PUNCT
ejpam-3419	60	1	also	also	ADV
ejpam-3419	60	2	,	,	PUNCT
ejpam-3419	60	3	c	c	PROPN
ejpam-3419	60	4	has	have	VERB
ejpam-3419	60	5	2k022k12k223k322k42k5	2k022k12k223k322k42k5	NUM
ejpam-3419	60	6	codewords	codeword	NOUN
ejpam-3419	60	7	[	[	X
ejpam-3419	60	8	2	2	NUM
ejpam-3419	60	9	]	]	PUNCT
ejpam-3419	60	10	.	.	PUNCT
ejpam-3419	61	1	in	in	ADP
ejpam-3419	61	2	(	(	PUNCT
ejpam-3419	61	3	1	1	NUM
ejpam-3419	61	4	)	)	PUNCT
ejpam-3419	61	5	,	,	PUNCT
ejpam-3419	61	6	k0	k0	PROPN
ejpam-3419	61	7	,	,	PUNCT
ejpam-3419	61	8	k2	k2	PROPN
ejpam-3419	61	9	and	and	CCONJ
ejpam-3419	61	10	k5	k5	PROPN
ejpam-3419	61	11	represent	represent	VERB
ejpam-3419	61	12	the	the	DET
ejpam-3419	61	13	number	number	NOUN
ejpam-3419	61	14	of	of	ADP
ejpam-3419	61	15	order	order	NOUN
ejpam-3419	61	16	2	2	NUM
ejpam-3419	61	17	generators	generator	NOUN
ejpam-3419	61	18	that	that	PRON
ejpam-3419	61	19	are	be	AUX
ejpam-3419	61	20	contributed	contribute	VERB
ejpam-3419	61	21	through	through	ADP
ejpam-3419	61	22	z2	z2	PROPN
ejpam-3419	61	23	,	,	PUNCT
ejpam-3419	61	24	z4	z4	PROPN
ejpam-3419	61	25	and	and	CCONJ
ejpam-3419	61	26	z8	z8	NOUN
ejpam-3419	61	27	parts	part	NOUN
ejpam-3419	61	28	,	,	PUNCT
ejpam-3419	61	29	respectively	respectively	ADV
ejpam-3419	61	30	.	.	PUNCT
ejpam-3419	62	1	also	also	ADV
ejpam-3419	62	2	,	,	PUNCT
ejpam-3419	62	3	k1	k1	PROPN
ejpam-3419	62	4	and	and	CCONJ
ejpam-3419	62	5	k4	k4	PROPN
ejpam-3419	62	6	represent	represent	VERB
ejpam-3419	62	7	the	the	DET
ejpam-3419	62	8	number	number	NOUN
ejpam-3419	62	9	of	of	ADP
ejpam-3419	62	10	order	order	NOUN
ejpam-3419	62	11	4	4	NUM
ejpam-3419	62	12	generators	generator	NOUN
ejpam-3419	62	13	that	that	PRON
ejpam-3419	62	14	are	be	AUX
ejpam-3419	62	15	contributed	contribute	VERB
ejpam-3419	62	16	through	through	ADP
ejpam-3419	62	17	z4	z4	PROPN
ejpam-3419	62	18	and	and	CCONJ
ejpam-3419	62	19	z8	z8	NOUN
ejpam-3419	62	20	parts	part	NOUN
ejpam-3419	62	21	,	,	PUNCT
ejpam-3419	62	22	respectively	respectively	ADV
ejpam-3419	62	23	.	.	PUNCT
ejpam-3419	63	1	k3	k3	PROPN
ejpam-3419	63	2	represents	represent	VERB
ejpam-3419	63	3	the	the	DET
ejpam-3419	63	4	number	number	NOUN
ejpam-3419	63	5	of	of	ADP
ejpam-3419	63	6	order	order	NOUN
ejpam-3419	63	7	8	8	NUM
ejpam-3419	63	8	generators	generator	NOUN
ejpam-3419	63	9	that	that	PRON
ejpam-3419	63	10	are	be	AUX
ejpam-3419	63	11	contributed	contribute	VERB
ejpam-3419	63	12	through	through	ADP
ejpam-3419	63	13	the	the	DET
ejpam-3419	63	14	z8	z8	NOUN
ejpam-3419	63	15	part	part	NOUN
ejpam-3419	63	16	.	.	PUNCT
ejpam-3419	64	1	note	note	VERB
ejpam-3419	64	2	that	that	SCONJ
ejpam-3419	64	3	,	,	PUNCT
ejpam-3419	64	4	the	the	DET
ejpam-3419	64	5	order	order	NOUN
ejpam-3419	64	6	2	2	NUM
ejpam-3419	64	7	elements	element	NOUN
ejpam-3419	64	8	from	from	ADP
ejpam-3419	64	9	the	the	DET
ejpam-3419	64	10	z4	z4	PROPN
ejpam-3419	64	11	and	and	CCONJ
ejpam-3419	64	12	z8	z8	NOUN
ejpam-3419	64	13	parts	part	NOUN
ejpam-3419	64	14	have	have	VERB
ejpam-3419	64	15	the	the	DET
ejpam-3419	64	16	first	first	ADJ
ejpam-3419	64	17	α	α	PROPN
ejpam-3419	64	18	coordinates	coordinate	NOUN
ejpam-3419	64	19	all	all	DET
ejpam-3419	64	20	zero	zero	NUM
ejpam-3419	65	1	[	[	X
ejpam-3419	65	2	2	2	NUM
ejpam-3419	65	3	]	]	PUNCT
ejpam-3419	65	4	.	.	PUNCT
ejpam-3419	66	1	the	the	DET
ejpam-3419	66	2	inner	inner	ADJ
ejpam-3419	66	3	product	product	NOUN
ejpam-3419	66	4	for	for	ADP
ejpam-3419	66	5	the	the	DET
ejpam-3419	66	6	elements	element	NOUN
ejpam-3419	66	7	u	u	NOUN
ejpam-3419	66	8	,	,	PUNCT
ejpam-3419	66	9	v	v	NOUN
ejpam-3419	66	10	∈	∈	NOUN
ejpam-3419	66	11	zα2	zα2	NOUN
ejpam-3419	66	12	×	×	PROPN
ejpam-3419	66	13	zβ4	zβ4	PROPN
ejpam-3419	66	14	×	×	PROPN
ejpam-3419	66	15	zθ8	zθ8	NOUN
ejpam-3419	66	16	as	as	SCONJ
ejpam-3419	66	17	follows	follow	VERB
ejpam-3419	66	18	〈	〈	PROPN
ejpam-3419	66	19	u	u	NOUN
ejpam-3419	66	20	·	·	PUNCT
ejpam-3419	66	21	v	v	NOUN
ejpam-3419	66	22	〉	〉	NOUN
ejpam-3419	66	23	=	=	SYM
ejpam-3419	66	24	4	4	NUM
ejpam-3419	66	25	(	(	PUNCT
ejpam-3419	66	26	α∑	α∑	PROPN
ejpam-3419	66	27	i=1	i=1	PROPN
ejpam-3419	66	28	uivi	uivi	PROPN
ejpam-3419	66	29	)	)	PUNCT
ejpam-3419	67	1	+	+	CCONJ
ejpam-3419	67	2	2	2	NUM
ejpam-3419	67	3			PROPN
ejpam-3419	67	4	α+β∑	α+β∑	PROPN
ejpam-3419	67	5	j	j	NOUN
ejpam-3419	67	6	=	=	NOUN
ejpam-3419	67	7	α+1	α+1	NUM
ejpam-3419	67	8	ujvj	ujvj	NOUN
ejpam-3419	67	9	+	+	NOUN
ejpam-3419	67	10	α+β+θ∑	α+β+θ∑	PROPN
ejpam-3419	67	11	k	k	PROPN
ejpam-3419	67	12	=	=	NOUN
ejpam-3419	67	13	α+β+1	α+β+1	ADJ
ejpam-3419	67	14	ukvk	ukvk	NOUN
ejpam-3419	67	15	.	.	PUNCT
ejpam-3419	68	1	definition	definition	NOUN
ejpam-3419	68	2	2	2	NUM
ejpam-3419	68	3	.	.	PUNCT
ejpam-3419	69	1	the	the	DET
ejpam-3419	69	2	set	set	NOUN
ejpam-3419	69	3	of	of	ADP
ejpam-3419	69	4	all	all	DET
ejpam-3419	69	5	vectors	vector	NOUN
ejpam-3419	69	6	which	which	PRON
ejpam-3419	69	7	are	be	AUX
ejpam-3419	69	8	orthogonal	orthogonal	ADJ
ejpam-3419	69	9	to	to	ADP
ejpam-3419	69	10	every	every	DET
ejpam-3419	69	11	vector	vector	NOUN
ejpam-3419	69	12	in	in	ADP
ejpam-3419	69	13	c	c	PROPN
ejpam-3419	69	14	is	be	AUX
ejpam-3419	69	15	called	call	VERB
ejpam-3419	69	16	the	the	DET
ejpam-3419	69	17	dual	dual	ADJ
ejpam-3419	69	18	code	code	NOUN
ejpam-3419	69	19	of	of	ADP
ejpam-3419	69	20	c	c	PROPN
ejpam-3419	69	21	,	,	PUNCT
ejpam-3419	69	22	and	and	CCONJ
ejpam-3419	69	23	denoted	denote	VERB
ejpam-3419	69	24	by	by	ADP
ejpam-3419	69	25	c⊥.	c⊥.	NOUN
ejpam-3419	69	26	the	the	DET
ejpam-3419	69	27	dual	dual	ADJ
ejpam-3419	69	28	code	code	NOUN
ejpam-3419	69	29	c⊥	c⊥	NOUN
ejpam-3419	69	30	can	can	AUX
ejpam-3419	69	31	be	be	AUX
ejpam-3419	69	32	defined	define	VERB
ejpam-3419	69	33	in	in	ADP
ejpam-3419	69	34	the	the	DET
ejpam-3419	69	35	usual	usual	ADJ
ejpam-3419	69	36	way	way	NOUN
ejpam-3419	69	37	with	with	ADP
ejpam-3419	69	38	respect	respect	NOUN
ejpam-3419	69	39	to	to	ADP
ejpam-3419	69	40	inner	inner	ADJ
ejpam-3419	69	41	product	product	NOUN
ejpam-3419	69	42	c⊥	c⊥	VERB
ejpam-3419	70	1	=	=	X
ejpam-3419	70	2	{	{	PUNCT
ejpam-3419	70	3	v	v	NUM
ejpam-3419	70	4	∈	∈	NOUN
ejpam-3419	70	5	zα2	zα2	NOUN
ejpam-3419	70	6	×	×	PROPN
ejpam-3419	70	7	zβ4	zβ4	PROPN
ejpam-3419	70	8	×	×	PROPN
ejpam-3419	70	9	zθ8|	zθ8|	X
ejpam-3419	71	1	〈	〈	PROPN
ejpam-3419	71	2	u	u	NOUN
ejpam-3419	71	3	·	·	PUNCT
ejpam-3419	71	4	v	v	NOUN
ejpam-3419	71	5	〉	〉	NOUN
ejpam-3419	71	6	=	=	SYM
ejpam-3419	71	7	0	0	NUM
ejpam-3419	71	8	for	for	ADP
ejpam-3419	71	9	all	all	DET
ejpam-3419	71	10	u	u	NOUN
ejpam-3419	71	11	∈	∈	PROPN
ejpam-3419	71	12	c	c	NOUN
ejpam-3419	71	13	}	}	PUNCT
ejpam-3419	71	14	.	.	PUNCT
ejpam-3419	72	1	a	a	DET
ejpam-3419	72	2	generator	generator	NOUN
ejpam-3419	72	3	matrix	matrix	NOUN
ejpam-3419	72	4	for	for	ADP
ejpam-3419	72	5	c⊥	c⊥	PROPN
ejpam-3419	72	6	is	be	AUX
ejpam-3419	72	7	called	call	VERB
ejpam-3419	72	8	a	a	DET
ejpam-3419	72	9	parity	parity	NOUN
ejpam-3419	72	10	-	-	PUNCT
ejpam-3419	72	11	check	check	NOUN
ejpam-3419	72	12	matrix	matrix	NOUN
ejpam-3419	72	13	of	of	ADP
ejpam-3419	72	14	c	c	NOUN
ejpam-3419	72	15	[	[	X
ejpam-3419	72	16	2	2	NUM
ejpam-3419	72	17	]	]	PUNCT
ejpam-3419	72	18	.	.	PUNCT
ejpam-3419	73	1	let	let	VERB
ejpam-3419	73	2	c	c	PRON
ejpam-3419	73	3	be	be	AUX
ejpam-3419	73	4	a	a	DET
ejpam-3419	73	5	z2z4z8	z2z4z8	NOUN
ejpam-3419	73	6	-	-	PUNCT
ejpam-3419	73	7	additive	additive	ADJ
ejpam-3419	73	8	code	code	NOUN
ejpam-3419	73	9	with	with	ADP
ejpam-3419	73	10	the	the	DET
ejpam-3419	73	11	generator	generator	NOUN
ejpam-3419	73	12	matrix	matrix	NOUN
ejpam-3419	73	13	(	(	PUNCT
ejpam-3419	73	14	1	1	NUM
ejpam-3419	73	15	)	)	PUNCT
ejpam-3419	73	16	,	,	PUNCT
ejpam-3419	73	17	then	then	ADV
ejpam-3419	73	18	we	we	PRON
ejpam-3419	73	19	have	have	VERB
ejpam-3419	73	20	the	the	DET
ejpam-3419	73	21	following	follow	VERB
ejpam-3419	73	22	parity	parity	NOUN
ejpam-3419	73	23	-	-	PUNCT
ejpam-3419	73	24	check	check	NOUN
ejpam-3419	73	25	matrix:	matrix:	NOUN
ejpam-3419	73	26	−at01	−at01	PROPN
ejpam-3419	73	27	iα−k0	iα−k0	PROPN
ejpam-3419	73	28	−2st1	−2st1	NOUN
ejpam-3419	73	29	0	0	NUM
ejpam-3419	73	30	0	0	NUM
ejpam-3419	73	31	−t	−t	NOUN
ejpam-3419	73	32	t1	t1	NOUN
ejpam-3419	73	33	0	0	PUNCT
ejpam-3419	74	1	bt	bt	PROPN
ejpam-3419	74	2	02	02	NUM
ejpam-3419	74	3	−bt	−bt	PROPN
ejpam-3419	74	4	12b	12b	PROPN
ejpam-3419	74	5	t	t	PROPN
ejpam-3419	74	6	01	01	NUM
ejpam-3419	74	7	bt	bt	PROPN
ejpam-3419	74	8	12	12	NUM
ejpam-3419	74	9	iβ−k1−k2	iβ−k1−k2	NOUN
ejpam-3419	74	10	0	0	NUM
ejpam-3419	74	11	0	0	NUM
ejpam-3419	74	12	−2bt	−2bt	NOUN
ejpam-3419	74	13	01	01	NUM
ejpam-3419	74	14	2ik2	2ik2	NUM
ejpam-3419	74	15	0	0	NUM
ejpam-3419	74	16	p	p	PRON
ejpam-3419	74	17	−t	−t	NOUN
ejpam-3419	74	18	t2	t2	PROPN
ejpam-3419	74	19	0	0	NUM
ejpam-3419	74	20	−t	−t	PROPN
ejpam-3419	74	21	t4	t4	PROPN
ejpam-3419	74	22	+	+	PROPN
ejpam-3419	75	1	t	t	PROPN
ejpam-3419	75	2	t3a	t3a	PROPN
ejpam-3419	75	3	t	t	PROPN
ejpam-3419	75	4	23	23	NUM
ejpam-3419	76	1	+	+	NUM
ejpam-3419	76	2	t	t	X
ejpam-3419	76	3	t5b	t5b	NOUN
ejpam-3419	76	4	t	t	PROPN
ejpam-3419	76	5	01	01	NUM
ejpam-3419	76	6	−t	−t	PROPN
ejpam-3419	76	7	t5	t5	PROPN
ejpam-3419	76	8	0	0	NUM
ejpam-3419	76	9	0	0	NUM
ejpam-3419	76	10	0	0	NUM
ejpam-3419	77	1	−2	−2	NOUN
ejpam-3419	77	2	t	t	X
ejpam-3419	77	3	t3	t3	NOUN
ejpam-3419	77	4	0	0	NUM
ejpam-3419	77	5	0	0	NUM
ejpam-3419	77	6	0	0	NUM
ejpam-3419	77	7	0	0	NUM
ejpam-3419	77	8	0	0	NUM
ejpam-3419	77	9	0	0	NUM
ejpam-3419	77	10	0	0	NUM
ejpam-3419	78	1			ADP
ejpam-3419	78	2	(	(	PUNCT
ejpam-3419	78	3	2	2	NUM
ejpam-3419	78	4	)	)	PUNCT
ejpam-3419	78	5	b.	b.	PROPN
ejpam-3419	78	6	çalışkan	çalışkan	PROPN
ejpam-3419	78	7	,	,	PUNCT
ejpam-3419	78	8	k.	k.	PROPN
ejpam-3419	78	9	balıkçı	balıkçı	PROPN
ejpam-3419	78	10	/	/	SYM
ejpam-3419	78	11	eur	eur	PROPN
ejpam-3419	78	12	.	.	PUNCT
ejpam-3419	79	1	j.	j.	PROPN
ejpam-3419	79	2	pure	pure	PROPN
ejpam-3419	79	3	appl	appl	PROPN
ejpam-3419	79	4	.	.	PROPN
ejpam-3419	79	5	math	math	PROPN
ejpam-3419	79	6	,	,	PUNCT
ejpam-3419	79	7	12	12	NUM
ejpam-3419	79	8	(	(	PUNCT
ejpam-3419	79	9	2	2	NUM
ejpam-3419	79	10	)	)	PUNCT
ejpam-3419	79	11	(	(	PUNCT
ejpam-3419	79	12	2019	2019	NUM
ejpam-3419	79	13	)	)	PUNCT
ejpam-3419	79	14	,	,	PUNCT
ejpam-3419	79	15	668	668	NUM
ejpam-3419	79	16	-	-	SYM
ejpam-3419	79	17	679	679	NUM
ejpam-3419	79	18	671	671	NUM
ejpam-3419	79	19	where	where	SCONJ
ejpam-3419	79	20	p	p	NOUN
ejpam-3419	79	21	is	be	AUX
ejpam-3419	79	22	the	the	DET
ejpam-3419	79	23	matrix	matrix	NOUN
ejpam-3419	79	24	:	:	PUNCT
ejpam-3419	79	25	p	p	X
ejpam-3419	79	26	=	=	PUNCT
ejpam-3419	79	27			NOUN
ejpam-3419	79	28	4s2	4s2	NUM
ejpam-3419	80	1	t	t	NOUN
ejpam-3419	80	2	−	−	NUM
ejpam-3419	80	3	2s3	2s3	NUM
ejpam-3419	81	1	t	t	PROPN
ejpam-3419	81	2	at01	at01	PROPN
ejpam-3419	81	3	−2s3	−2s3	NUM
ejpam-3419	81	4	t	t	PROPN
ejpam-3419	81	5	0	0	NUM
ejpam-3419	81	6	0	0	NUM
ejpam-3419	82	1	−2st01bt12	−2st01bt12	PROPN
ejpam-3419	83	1	−	−	PROPN
ejpam-3419	83	2	2st02	2st02	PROPN
ejpam-3419	83	3	+	+	CCONJ
ejpam-3419	83	4	2st12a	2st12a	PROPN
ejpam-3419	83	5	t	t	NOUN
ejpam-3419	83	6	01	01	NUM
ejpam-3419	83	7	−2st12	−2st12	NOUN
ejpam-3419	83	8	0	0	NUM
ejpam-3419	83	9	0	0	NUM
ejpam-3419	84	1	−4st01	−4st01	NOUN
ejpam-3419	84	2	0	0	NUM
ejpam-3419	84	3	0	0	NUM
ejpam-3419	84	4	0	0	NUM
ejpam-3419	85	1	−at03	−at03	NUM
ejpam-3419	86	1	+	+	ADJ
ejpam-3419	86	2	at13a	at13a	NOUN
ejpam-3419	86	3	t	t	NOUN
ejpam-3419	86	4	01	01	NUM
ejpam-3419	87	1	+	+	NOUN
ejpam-3419	87	2	at23a	at23a	ADJ
ejpam-3419	87	3	t	t	PROPN
ejpam-3419	87	4	02	02	NUM
ejpam-3419	87	5	−at23at12at01	−at23at12at01	VERB
ejpam-3419	87	6	+	+	X
ejpam-3419	87	7	2st01	2st01	NUM
ejpam-3419	87	8	t	t	NOUN
ejpam-3419	87	9	t	t	NOUN
ejpam-3419	87	10	5	5	NUM
ejpam-3419	87	11	−at13	−at13	ADV
ejpam-3419	87	12	+	+	NOUN
ejpam-3419	87	13	at23a	at23a	ADJ
ejpam-3419	87	14	t	t	PROPN
ejpam-3419	87	15	12	12	NUM
ejpam-3419	87	16	−at23	−at23	PROPN
ejpam-3419	87	17	iθ−k3−k4−k5	iθ−k3−k4−k5	X
ejpam-3419	87	18	−2at02	−2at02	PROPN
ejpam-3419	88	1	+	+	CCONJ
ejpam-3419	88	2	2at12a	2at12a	PROPN
ejpam-3419	88	3	t	t	NOUN
ejpam-3419	88	4	01	01	NUM
ejpam-3419	88	5	−2at12	−2at12	PROPN
ejpam-3419	88	6	2ik5	2ik5	NUM
ejpam-3419	88	7	0	0	NUM
ejpam-3419	88	8	−4at01	−4at01	PROPN
ejpam-3419	88	9	4ik4	4ik4	NUM
ejpam-3419	88	10	0	0	NUM
ejpam-3419	88	11	0	0	NUM
ejpam-3419	88	12			PROPN
ejpam-3419	88	13	·	·	PUNCT
ejpam-3419	88	14	(	(	PUNCT
ejpam-3419	88	15	3	3	X
ejpam-3419	88	16	)	)	PUNCT
ejpam-3419	88	17	so	so	ADV
ejpam-3419	88	18	,	,	PUNCT
ejpam-3419	88	19	the	the	DET
ejpam-3419	88	20	dual	dual	ADJ
ejpam-3419	88	21	code	code	NOUN
ejpam-3419	88	22	c⊥	c⊥	NOUN
ejpam-3419	88	23	is	be	AUX
ejpam-3419	88	24	of	of	ADP
ejpam-3419	88	25	type	type	NOUN
ejpam-3419	88	26	(	(	PUNCT
ejpam-3419	88	27	α	α	NOUN
ejpam-3419	88	28	,	,	PUNCT
ejpam-3419	88	29	β	β	X
ejpam-3419	88	30	,	,	PUNCT
ejpam-3419	88	31	θ;α−	θ;α−	PROPN
ejpam-3419	88	32	k0	k0	PROPN
ejpam-3419	88	33	,	,	PUNCT
ejpam-3419	88	34	β	β	NOUN
ejpam-3419	88	35	−	−	NOUN
ejpam-3419	88	36	k1	k1	PROPN
ejpam-3419	88	37	−	−	PROPN
ejpam-3419	88	38	k2	k2	PROPN
ejpam-3419	88	39	,	,	PUNCT
ejpam-3419	88	40	k2	k2	PROPN
ejpam-3419	88	41	,	,	PUNCT
ejpam-3419	88	42	θ	θ	PROPN
ejpam-3419	88	43	−	−	NOUN
ejpam-3419	88	44	k3	k3	VERB
ejpam-3419	88	45	−	−	PROPN
ejpam-3419	88	46	k4	k4	NOUN
ejpam-3419	88	47	−	−	PROPN
ejpam-3419	88	48	k5	k5	PROPN
ejpam-3419	88	49	,	,	PUNCT
ejpam-3419	88	50	k5	k5	PROPN
ejpam-3419	88	51	,	,	PUNCT
ejpam-3419	88	52	k4	k4	PROPN
ejpam-3419	88	53	)	)	PUNCT
ejpam-3419	88	54	.	.	PUNCT
ejpam-3419	89	1	3	3	X
ejpam-3419	89	2	.	.	X
ejpam-3419	89	3	the	the	DET
ejpam-3419	89	4	number	number	NOUN
ejpam-3419	89	5	of	of	ADP
ejpam-3419	89	6	generator	generator	NOUN
ejpam-3419	89	7	matrices	matrix	NOUN
ejpam-3419	89	8	for	for	ADP
ejpam-3419	89	9	z2z4z8	z2z4z8	NOUN
ejpam-3419	89	10	-	-	PUNCT
ejpam-3419	89	11	additive	additive	ADJ
ejpam-3419	89	12	codes	code	NOUN
ejpam-3419	89	13	in	in	ADP
ejpam-3419	89	14	this	this	DET
ejpam-3419	89	15	section	section	NOUN
ejpam-3419	89	16	,	,	PUNCT
ejpam-3419	89	17	we	we	PRON
ejpam-3419	89	18	shall	shall	AUX
ejpam-3419	89	19	count	count	VERB
ejpam-3419	89	20	the	the	DET
ejpam-3419	89	21	number	number	NOUN
ejpam-3419	89	22	of	of	ADP
ejpam-3419	89	23	arbitrary	arbitrary	ADJ
ejpam-3419	89	24	z2z4z8	z2z4z8	ADJ
ejpam-3419	89	25	-	-	PUNCT
ejpam-3419	89	26	additive	additive	ADJ
ejpam-3419	89	27	codes	code	NOUN
ejpam-3419	89	28	of	of	ADP
ejpam-3419	89	29	type	type	NOUN
ejpam-3419	89	30	(	(	PUNCT
ejpam-3419	89	31	α	α	NOUN
ejpam-3419	89	32	,	,	PUNCT
ejpam-3419	89	33	β	β	X
ejpam-3419	89	34	,	,	PUNCT
ejpam-3419	89	35	θ	θ	PROPN
ejpam-3419	89	36	;	;	PUNCT
ejpam-3419	89	37	k0	k0	PROPN
ejpam-3419	89	38	,	,	PUNCT
ejpam-3419	89	39	k1	k1	PROPN
ejpam-3419	89	40	,	,	PUNCT
ejpam-3419	89	41	k2	k2	NOUN
ejpam-3419	89	42	,	,	PUNCT
ejpam-3419	89	43	k3	k3	PROPN
ejpam-3419	89	44	,	,	PUNCT
ejpam-3419	89	45	k4	k4	PROPN
ejpam-3419	89	46	,	,	PUNCT
ejpam-3419	89	47	k5	k5	PROPN
ejpam-3419	89	48	)	)	PUNCT
ejpam-3419	89	49	.	.	PUNCT
ejpam-3419	90	1	for	for	ADP
ejpam-3419	90	2	this	this	DET
ejpam-3419	90	3	purpose	purpose	NOUN
ejpam-3419	90	4	,	,	PUNCT
ejpam-3419	90	5	we	we	PRON
ejpam-3419	90	6	will	will	AUX
ejpam-3419	90	7	give	give	VERB
ejpam-3419	90	8	two	two	NUM
ejpam-3419	90	9	lemmas	lemma	NOUN
ejpam-3419	90	10	and	and	CCONJ
ejpam-3419	90	11	the	the	DET
ejpam-3419	90	12	definition	definition	NOUN
ejpam-3419	90	13	of	of	ADP
ejpam-3419	90	14	gaussian	gaussian	ADJ
ejpam-3419	90	15	coefficient	coefficient	NOUN
ejpam-3419	90	16	.	.	PUNCT
ejpam-3419	91	1	we	we	PRON
ejpam-3419	91	2	will	will	AUX
ejpam-3419	91	3	also	also	ADV
ejpam-3419	91	4	present	present	VERB
ejpam-3419	91	5	our	our	PRON
ejpam-3419	91	6	main	main	ADJ
ejpam-3419	91	7	theorem	theorem	NOUN
ejpam-3419	91	8	and	and	CCONJ
ejpam-3419	91	9	give	give	VERB
ejpam-3419	91	10	some	some	DET
ejpam-3419	91	11	examples	example	NOUN
ejpam-3419	91	12	.	.	PUNCT
ejpam-3419	92	1	lemma	lemma	PROPN
ejpam-3419	92	2	1	1	NUM
ejpam-3419	92	3	.	.	PUNCT
ejpam-3419	93	1	the	the	DET
ejpam-3419	93	2	number	number	NOUN
ejpam-3419	93	3	of	of	ADP
ejpam-3419	93	4	ways	way	NOUN
ejpam-3419	93	5	of	of	ADP
ejpam-3419	93	6	choosing	choose	VERB
ejpam-3419	93	7	elements	element	NOUN
ejpam-3419	93	8	(	(	PUNCT
ejpam-3419	93	9	or	or	CCONJ
ejpam-3419	93	10	vectors	vector	NOUN
ejpam-3419	93	11	)	)	PUNCT
ejpam-3419	93	12	to	to	PART
ejpam-3419	93	13	generate	generate	VERB
ejpam-3419	93	14	a	a	DET
ejpam-3419	93	15	z2z4z8additive	z2z4z8additive	PROPN
ejpam-3419	93	16	code	code	NOUN
ejpam-3419	93	17	of	of	ADP
ejpam-3419	93	18	type	type	NOUN
ejpam-3419	93	19	(	(	PUNCT
ejpam-3419	93	20	α	α	NOUN
ejpam-3419	93	21	,	,	PUNCT
ejpam-3419	93	22	β	β	X
ejpam-3419	93	23	,	,	PUNCT
ejpam-3419	93	24	θ	θ	PROPN
ejpam-3419	93	25	;	;	PUNCT
ejpam-3419	93	26	k0	k0	PROPN
ejpam-3419	93	27	,	,	PUNCT
ejpam-3419	93	28	k1	k1	PROPN
ejpam-3419	93	29	,	,	PUNCT
ejpam-3419	93	30	k2	k2	NOUN
ejpam-3419	93	31	,	,	PUNCT
ejpam-3419	93	32	k3	k3	PROPN
ejpam-3419	93	33	,	,	PUNCT
ejpam-3419	93	34	k4	k4	PROPN
ejpam-3419	93	35	,	,	PUNCT
ejpam-3419	93	36	k5	k5	PROPN
ejpam-3419	93	37	)	)	PUNCT
ejpam-3419	93	38	is	be	AUX
ejpam-3419	93	39	∏6	∏6	PROPN
ejpam-3419	93	40	j=1nj	j=1nj	NOUN
ejpam-3419	93	41	,	,	PUNCT
ejpam-3419	93	42	where	where	SCONJ
ejpam-3419	93	43	n1	n1	PROPN
ejpam-3419	93	44	=	=	SYM
ejpam-3419	93	45	k0−1∏	k0−1∏	PROPN
ejpam-3419	93	46	i=0	i=0	PROPN
ejpam-3419	93	47	(	(	PUNCT
ejpam-3419	93	48	2α	2α	NOUN
ejpam-3419	93	49	−	−	PROPN
ejpam-3419	93	50	2i	2i	NUM
ejpam-3419	93	51	)	)	PUNCT
ejpam-3419	93	52	2β+θ	2β+θ	NUM
ejpam-3419	93	53	,	,	PUNCT
ejpam-3419	93	54	n2	n2	NOUN
ejpam-3419	93	55	=	=	PUNCT
ejpam-3419	93	56	k1−1∏	k1−1∏	PROPN
ejpam-3419	93	57	i=0	i=0	PROPN
ejpam-3419	93	58	(	(	PUNCT
ejpam-3419	93	59	4β	4β	NOUN
ejpam-3419	93	60	−	−	PROPN
ejpam-3419	93	61	2β+i	2β+i	NUM
ejpam-3419	93	62	)	)	PUNCT
ejpam-3419	93	63	2α+2θ	2α+2θ	NUM
ejpam-3419	93	64	,	,	PUNCT
ejpam-3419	93	65	n3	n3	NOUN
ejpam-3419	93	66	=	=	PUNCT
ejpam-3419	93	67	k2−1∏	k2−1∏	PROPN
ejpam-3419	93	68	i=0	i=0	PROPN
ejpam-3419	93	69	(	(	PUNCT
ejpam-3419	93	70	2β+θ	2β+θ	NUM
ejpam-3419	93	71	−	−	PROPN
ejpam-3419	93	72	2θ+k1+i	2θ+k1+i	NUM
ejpam-3419	93	73	)	)	PUNCT
ejpam-3419	93	74	,	,	PUNCT
ejpam-3419	93	75	n4	n4	PROPN
ejpam-3419	93	76	=	=	PROPN
ejpam-3419	93	77	k3−1∏	k3−1∏	PROPN
ejpam-3419	93	78	i=0	i=0	PROPN
ejpam-3419	93	79	(	(	PUNCT
ejpam-3419	93	80	8θ	8θ	NUM
ejpam-3419	93	81	−	−	NOUN
ejpam-3419	93	82	4θ2i	4θ2i	NOUN
ejpam-3419	93	83	)	)	PUNCT
ejpam-3419	93	84	2α+2β	2α+2β	NUM
ejpam-3419	93	85	,	,	PUNCT
ejpam-3419	94	1	n5	n5	PROPN
ejpam-3419	94	2	=	=	PUNCT
ejpam-3419	94	3	k4−1∏	k4−1∏	PROPN
ejpam-3419	94	4	i=0	i=0	PROPN
ejpam-3419	94	5	(	(	PUNCT
ejpam-3419	94	6	4θ	4θ	NOUN
ejpam-3419	94	7	−	−	PROPN
ejpam-3419	94	8	2θ+k3+i	2θ+k3+i	NUM
ejpam-3419	94	9	)	)	PUNCT
ejpam-3419	94	10	2α+2β	2α+2β	NUM
ejpam-3419	94	11	,	,	PUNCT
ejpam-3419	94	12	n6	n6	PROPN
ejpam-3419	94	13	=	=	PROPN
ejpam-3419	94	14	k5−1∏	k5−1∏	PROPN
ejpam-3419	94	15	i=0	i=0	PROPN
ejpam-3419	94	16	(	(	PUNCT
ejpam-3419	94	17	2θ	2θ	NUM
ejpam-3419	94	18	−	−	NOUN
ejpam-3419	94	19	2k3+k4+i	2k3+k4+i	NOUN
ejpam-3419	94	20	)	)	PUNCT
ejpam-3419	94	21	.	.	PUNCT
ejpam-3419	95	1	proof	proof	NOUN
ejpam-3419	95	2	.	.	PUNCT
ejpam-3419	96	1	recall	recall	VERB
ejpam-3419	96	2	the	the	DET
ejpam-3419	96	3	generating	generate	VERB
ejpam-3419	96	4	matrix	matrix	NOUN
ejpam-3419	96	5	given	give	VERB
ejpam-3419	96	6	in	in	ADP
ejpam-3419	96	7	(	(	PUNCT
ejpam-3419	96	8	1	1	NUM
ejpam-3419	96	9	)	)	PUNCT
ejpam-3419	96	10	,	,	PUNCT
ejpam-3419	96	11	we	we	PRON
ejpam-3419	96	12	will	will	AUX
ejpam-3419	96	13	examine	examine	VERB
ejpam-3419	96	14	six	six	NUM
ejpam-3419	96	15	major	major	ADJ
ejpam-3419	96	16	parts	part	NOUN
ejpam-3419	96	17	for	for	ADP
ejpam-3419	96	18	proof	proof	NOUN
ejpam-3419	96	19	.	.	PUNCT
ejpam-3419	97	1	in	in	ADP
ejpam-3419	97	2	zα2z	zα2z	PROPN
ejpam-3419	97	3	β	β	NOUN
ejpam-3419	97	4	4zθ8	4zθ8	NUM
ejpam-3419	97	5	,	,	PUNCT
ejpam-3419	97	6	because	because	SCONJ
ejpam-3419	97	7	of	of	ADP
ejpam-3419	97	8	the	the	DET
ejpam-3419	97	9	number	number	NOUN
ejpam-3419	97	10	of	of	ADP
ejpam-3419	97	11	all	all	DET
ejpam-3419	97	12	vectors	vector	NOUN
ejpam-3419	97	13	of	of	ADP
ejpam-3419	97	14	order	order	NOUN
ejpam-3419	97	15	2	2	NUM
ejpam-3419	97	16	is	be	AUX
ejpam-3419	97	17	2α2β2θ	2α2β2θ	NUM
ejpam-3419	97	18	,	,	PUNCT
ejpam-3419	97	19	we	we	PRON
ejpam-3419	97	20	can	can	AUX
ejpam-3419	97	21	choose	choose	VERB
ejpam-3419	97	22	first	first	ADJ
ejpam-3419	97	23	element	element	NOUN
ejpam-3419	97	24	of	of	ADP
ejpam-3419	97	25	order	order	NOUN
ejpam-3419	97	26	2	2	NUM
ejpam-3419	97	27	that	that	PRON
ejpam-3419	97	28	contributes	contribute	VERB
ejpam-3419	97	29	through	through	ADP
ejpam-3419	97	30	z2	z2	NUM
ejpam-3419	97	31	part	part	NOUN
ejpam-3419	97	32	in	in	ADP
ejpam-3419	97	33	(	(	PUNCT
ejpam-3419	97	34	2α	2α	NOUN
ejpam-3419	97	35	−	−	PROPN
ejpam-3419	97	36	1	1	X
ejpam-3419	97	37	)	)	PUNCT
ejpam-3419	97	38	2β2θ	2β2θ	NOUN
ejpam-3419	97	39	ways	way	NOUN
ejpam-3419	97	40	.	.	PUNCT
ejpam-3419	98	1	next	next	ADJ
ejpam-3419	98	2	,	,	PUNCT
ejpam-3419	98	3	(	(	PUNCT
ejpam-3419	98	4	2α	2α	NOUN
ejpam-3419	98	5	−	−	PROPN
ejpam-3419	98	6	2	2	X
ejpam-3419	98	7	)	)	PUNCT
ejpam-3419	98	8	2β2θ	2β2θ	NOUN
ejpam-3419	98	9	selections	selection	NOUN
ejpam-3419	98	10	can	can	AUX
ejpam-3419	98	11	be	be	AUX
ejpam-3419	98	12	made	make	VERB
ejpam-3419	98	13	for	for	ADP
ejpam-3419	98	14	the	the	DET
ejpam-3419	98	15	second	second	ADJ
ejpam-3419	98	16	element	element	NOUN
ejpam-3419	98	17	.	.	PUNCT
ejpam-3419	99	1	similarly	similarly	ADV
ejpam-3419	99	2	,	,	PUNCT
ejpam-3419	99	3	the	the	DET
ejpam-3419	99	4	last	last	ADJ
ejpam-3419	99	5	element	element	NOUN
ejpam-3419	99	6	can	can	AUX
ejpam-3419	99	7	be	be	AUX
ejpam-3419	99	8	selected	select	VERB
ejpam-3419	99	9	by	by	ADP
ejpam-3419	99	10	(	(	PUNCT
ejpam-3419	99	11	2α	2α	PROPN
ejpam-3419	99	12	−	−	PROPN
ejpam-3419	99	13	2k0−1	2k0−1	NUM
ejpam-3419	99	14	)	)	PUNCT
ejpam-3419	99	15	2β2θ	2β2θ	NOUN
ejpam-3419	99	16	ways	way	NOUN
ejpam-3419	99	17	.	.	PUNCT
ejpam-3419	100	1	thus	thus	ADV
ejpam-3419	100	2	,	,	PUNCT
ejpam-3419	100	3	the	the	DET
ejpam-3419	100	4	k0	k0	PROPN
ejpam-3419	100	5	elements	element	NOUN
ejpam-3419	100	6	of	of	ADP
ejpam-3419	100	7	order	order	NOUN
ejpam-3419	100	8	2	2	NUM
ejpam-3419	100	9	that	that	PRON
ejpam-3419	100	10	contribute	contribute	VERB
ejpam-3419	100	11	only	only	ADV
ejpam-3419	100	12	to	to	ADP
ejpam-3419	100	13	the	the	DET
ejpam-3419	100	14	binary	binary	ADJ
ejpam-3419	100	15	part	part	NOUN
ejpam-3419	100	16	are	be	AUX
ejpam-3419	100	17	selected	select	VERB
ejpam-3419	100	18	in	in	ADP
ejpam-3419	100	19	n1	n1	ADJ
ejpam-3419	100	20	different	different	ADJ
ejpam-3419	100	21	ways	way	NOUN
ejpam-3419	100	22	.	.	PUNCT
ejpam-3419	101	1	next	next	ADV
ejpam-3419	101	2	,	,	PUNCT
ejpam-3419	101	3	we	we	PRON
ejpam-3419	101	4	will	will	AUX
ejpam-3419	101	5	choose	choose	VERB
ejpam-3419	101	6	k1	k1	NOUN
ejpam-3419	101	7	vectors	vector	NOUN
ejpam-3419	101	8	of	of	ADP
ejpam-3419	101	9	order	order	NOUN
ejpam-3419	101	10	4	4	NUM
ejpam-3419	101	11	that	that	SCONJ
ejpam-3419	101	12	from	from	ADP
ejpam-3419	101	13	the	the	DET
ejpam-3419	101	14	z4	z4	PROPN
ejpam-3419	101	15	part	part	NOUN
ejpam-3419	101	16	.	.	PUNCT
ejpam-3419	102	1	however	however	ADV
ejpam-3419	102	2	,	,	PUNCT
ejpam-3419	102	3	in	in	ADP
ejpam-3419	102	4	those	those	DET
ejpam-3419	102	5	vectors	vector	NOUN
ejpam-3419	102	6	,	,	PUNCT
ejpam-3419	102	7	there	there	PRON
ejpam-3419	102	8	should	should	AUX
ejpam-3419	102	9	not	not	PART
ejpam-3419	102	10	be	be	AUX
ejpam-3419	102	11	vectors	vector	NOUN
ejpam-3419	102	12	of	of	ADP
ejpam-3419	102	13	order	order	NOUN
ejpam-3419	102	14	4	4	NUM
ejpam-3419	102	15	that	that	PRON
ejpam-3419	102	16	contribute	contribute	VERB
ejpam-3419	102	17	to	to	ADP
ejpam-3419	102	18	the	the	DET
ejpam-3419	102	19	z8	z8	NOUN
ejpam-3419	102	20	part	part	NOUN
ejpam-3419	102	21	.	.	PUNCT
ejpam-3419	103	1	there	there	PRON
ejpam-3419	103	2	are	be	VERB
ejpam-3419	103	3	b.	b.	PROPN
ejpam-3419	103	4	çalışkan	çalışkan	PROPN
ejpam-3419	103	5	,	,	PUNCT
ejpam-3419	103	6	k.	k.	PROPN
ejpam-3419	103	7	balıkçı	balıkçı	PROPN
ejpam-3419	103	8	/	/	SYM
ejpam-3419	103	9	eur	eur	PROPN
ejpam-3419	103	10	.	.	PUNCT
ejpam-3419	104	1	j.	j.	PROPN
ejpam-3419	104	2	pure	pure	PROPN
ejpam-3419	104	3	appl	appl	PROPN
ejpam-3419	104	4	.	.	PROPN
ejpam-3419	104	5	math	math	PROPN
ejpam-3419	104	6	,	,	PUNCT
ejpam-3419	104	7	12	12	NUM
ejpam-3419	104	8	(	(	PUNCT
ejpam-3419	104	9	2	2	NUM
ejpam-3419	104	10	)	)	PUNCT
ejpam-3419	104	11	(	(	PUNCT
ejpam-3419	104	12	2019	2019	NUM
ejpam-3419	104	13	)	)	PUNCT
ejpam-3419	104	14	,	,	PUNCT
ejpam-3419	104	15	668	668	NUM
ejpam-3419	104	16	-	-	SYM
ejpam-3419	104	17	679	679	NUM
ejpam-3419	104	18	672	672	NUM
ejpam-3419	104	19	2α4β4θ	2α4β4θ	NUM
ejpam-3419	104	20	vectors	vector	NOUN
ejpam-3419	104	21	of	of	ADP
ejpam-3419	104	22	order	order	NOUN
ejpam-3419	104	23	4	4	NUM
ejpam-3419	104	24	in	in	ADP
ejpam-3419	104	25	all	all	DET
ejpam-3419	104	26	space	space	NOUN
ejpam-3419	104	27	.	.	PUNCT
ejpam-3419	105	1	since	since	SCONJ
ejpam-3419	105	2	the	the	DET
ejpam-3419	105	3	number	number	NOUN
ejpam-3419	105	4	of	of	ADP
ejpam-3419	105	5	elements	element	NOUN
ejpam-3419	105	6	of	of	ADP
ejpam-3419	105	7	order	order	NOUN
ejpam-3419	105	8	4	4	NUM
ejpam-3419	105	9	in	in	ADP
ejpam-3419	105	10	the	the	DET
ejpam-3419	105	11	z4	z4	PROPN
ejpam-3419	105	12	part	part	NOUN
ejpam-3419	105	13	is	be	AUX
ejpam-3419	105	14	2α	2α	NOUN
ejpam-3419	105	15	(	(	PUNCT
ejpam-3419	105	16	4β	4β	NOUN
ejpam-3419	105	17	−	−	NOUN
ejpam-3419	105	18	2β	2β	NOUN
ejpam-3419	105	19	)	)	PUNCT
ejpam-3419	105	20	4θ	4θ	NOUN
ejpam-3419	105	21	,	,	PUNCT
ejpam-3419	105	22	the	the	DET
ejpam-3419	105	23	first	first	ADJ
ejpam-3419	105	24	element	element	NOUN
ejpam-3419	105	25	can	can	AUX
ejpam-3419	105	26	be	be	AUX
ejpam-3419	105	27	selected	select	VERB
ejpam-3419	105	28	in	in	ADP
ejpam-3419	105	29	2α	2α	NOUN
ejpam-3419	105	30	(	(	PUNCT
ejpam-3419	105	31	4β	4β	NOUN
ejpam-3419	105	32	−	−	NOUN
ejpam-3419	105	33	2β	2β	NOUN
ejpam-3419	105	34	·	·	PUNCT
ejpam-3419	105	35	1	1	X
ejpam-3419	105	36	)	)	PUNCT
ejpam-3419	105	37	4θ	4θ	NOUN
ejpam-3419	105	38	ways	way	NOUN
ejpam-3419	105	39	.	.	PUNCT
ejpam-3419	106	1	the	the	DET
ejpam-3419	106	2	number	number	NOUN
ejpam-3419	106	3	of	of	ADP
ejpam-3419	106	4	choosing	choose	VERB
ejpam-3419	106	5	for	for	ADP
ejpam-3419	106	6	the	the	DET
ejpam-3419	106	7	next	next	ADJ
ejpam-3419	106	8	element	element	NOUN
ejpam-3419	106	9	is	be	AUX
ejpam-3419	106	10	2α	2α	NOUN
ejpam-3419	106	11	(	(	PUNCT
ejpam-3419	106	12	4β	4β	NOUN
ejpam-3419	106	13	−	−	NOUN
ejpam-3419	106	14	2β	2β	NOUN
ejpam-3419	106	15	·	·	PUNCT
ejpam-3419	106	16	2	2	X
ejpam-3419	106	17	)	)	PUNCT
ejpam-3419	106	18	4θ	4θ	NOUN
ejpam-3419	106	19	and	and	CCONJ
ejpam-3419	106	20	2α	2α	NOUN
ejpam-3419	106	21	(	(	PUNCT
ejpam-3419	106	22	4β	4β	NOUN
ejpam-3419	106	23	−	−	PROPN
ejpam-3419	106	24	2β2k1−1	2β2k1−1	NUM
ejpam-3419	106	25	)	)	PUNCT
ejpam-3419	106	26	4θ	4θ	NOUN
ejpam-3419	106	27	for	for	ADP
ejpam-3419	106	28	the	the	DET
ejpam-3419	106	29	last	last	ADJ
ejpam-3419	106	30	element	element	NOUN
ejpam-3419	106	31	.	.	PUNCT
ejpam-3419	107	1	so	so	ADV
ejpam-3419	107	2	,	,	PUNCT
ejpam-3419	107	3	there	there	PRON
ejpam-3419	107	4	are	be	VERB
ejpam-3419	107	5	n2	n2	ADJ
ejpam-3419	107	6	different	different	ADJ
ejpam-3419	107	7	ways	way	NOUN
ejpam-3419	107	8	for	for	ADP
ejpam-3419	107	9	k1	k1	NOUN
ejpam-3419	107	10	elements	element	NOUN
ejpam-3419	107	11	of	of	ADP
ejpam-3419	107	12	order	order	NOUN
ejpam-3419	107	13	4	4	NUM
ejpam-3419	107	14	that	that	PRON
ejpam-3419	107	15	contribute	contribute	VERB
ejpam-3419	107	16	to	to	ADP
ejpam-3419	107	17	the	the	DET
ejpam-3419	107	18	z4	z4	PROPN
ejpam-3419	107	19	part	part	NOUN
ejpam-3419	107	20	.	.	PUNCT
ejpam-3419	108	1	next	next	ADV
ejpam-3419	108	2	,	,	PUNCT
ejpam-3419	108	3	we	we	PRON
ejpam-3419	108	4	need	need	VERB
ejpam-3419	108	5	to	to	PART
ejpam-3419	108	6	choose	choose	VERB
ejpam-3419	108	7	k2	k2	ADJ
ejpam-3419	108	8	vectors	vector	NOUN
ejpam-3419	108	9	of	of	ADP
ejpam-3419	108	10	order	order	NOUN
ejpam-3419	108	11	2	2	NUM
ejpam-3419	108	12	that	that	PRON
ejpam-3419	108	13	are	be	AUX
ejpam-3419	108	14	not	not	PART
ejpam-3419	108	15	in	in	ADP
ejpam-3419	108	16	the	the	DET
ejpam-3419	108	17	space	space	NOUN
ejpam-3419	108	18	generated	generate	VERB
ejpam-3419	108	19	by	by	ADP
ejpam-3419	108	20	k1	k1	NOUN
ejpam-3419	108	21	vectors	vector	NOUN
ejpam-3419	108	22	of	of	ADP
ejpam-3419	108	23	order	order	NOUN
ejpam-3419	108	24	4	4	NUM
ejpam-3419	108	25	.	.	PUNCT
ejpam-3419	109	1	this	this	PRON
ejpam-3419	109	2	imposes	impose	VERB
ejpam-3419	109	3	that	that	SCONJ
ejpam-3419	109	4	the	the	DET
ejpam-3419	109	5	first	first	ADJ
ejpam-3419	109	6	α	α	PROPN
ejpam-3419	109	7	entries	entry	NOUN
ejpam-3419	109	8	of	of	ADP
ejpam-3419	109	9	such	such	ADJ
ejpam-3419	109	10	elements	element	NOUN
ejpam-3419	109	11	to	to	PART
ejpam-3419	109	12	be	be	AUX
ejpam-3419	109	13	all	all	DET
ejpam-3419	109	14	zero	zero	NUM
ejpam-3419	109	15	.	.	PUNCT
ejpam-3419	110	1	thus	thus	ADV
ejpam-3419	110	2	,	,	PUNCT
ejpam-3419	110	3	in	in	ADP
ejpam-3419	110	4	order	order	NOUN
ejpam-3419	110	5	to	to	PART
ejpam-3419	110	6	pick	pick	VERB
ejpam-3419	110	7	such	such	DET
ejpam-3419	110	8	an	an	DET
ejpam-3419	110	9	element	element	NOUN
ejpam-3419	110	10	first	first	ADV
ejpam-3419	110	11	we	we	PRON
ejpam-3419	110	12	subtract	subtract	VERB
ejpam-3419	110	13	elements	element	NOUN
ejpam-3419	110	14	of	of	ADP
ejpam-3419	110	15	order	order	NOUN
ejpam-3419	110	16	2	2	NUM
ejpam-3419	110	17	that	that	PRON
ejpam-3419	110	18	are	be	AUX
ejpam-3419	110	19	obtained	obtain	VERB
ejpam-3419	110	20	through	through	ADP
ejpam-3419	110	21	already	already	ADV
ejpam-3419	110	22	chosen	choose	VERB
ejpam-3419	110	23	k1	k1	NOUN
ejpam-3419	110	24	elements	element	NOUN
ejpam-3419	110	25	for	for	ADP
ejpam-3419	110	26	the	the	DET
ejpam-3419	110	27	z4	z4	PROPN
ejpam-3419	110	28	part	part	NOUN
ejpam-3419	110	29	.	.	PUNCT
ejpam-3419	111	1	so	so	ADV
ejpam-3419	111	2	,	,	PUNCT
ejpam-3419	111	3	there	there	PRON
ejpam-3419	111	4	are	be	VERB
ejpam-3419	111	5	2β2θ	2β2θ	NUM
ejpam-3419	111	6	such	such	ADJ
ejpam-3419	111	7	vectors	vector	NOUN
ejpam-3419	111	8	in	in	ADP
ejpam-3419	111	9	the	the	DET
ejpam-3419	111	10	z4	z4	PROPN
ejpam-3419	111	11	part	part	NOUN
ejpam-3419	111	12	.	.	PUNCT
ejpam-3419	112	1	then	then	ADV
ejpam-3419	112	2	,	,	PUNCT
ejpam-3419	112	3	first	first	ADJ
ejpam-3419	112	4	element	element	NOUN
ejpam-3419	112	5	can	can	AUX
ejpam-3419	112	6	be	be	AUX
ejpam-3419	112	7	chosen	choose	VERB
ejpam-3419	112	8	in	in	ADP
ejpam-3419	112	9	2β2θ−2θ2k1	2β2θ−2θ2k1	NUM
ejpam-3419	112	10	ways	way	NOUN
ejpam-3419	112	11	,	,	PUNCT
ejpam-3419	112	12	next	next	ADJ
ejpam-3419	112	13	choice	choice	NOUN
ejpam-3419	112	14	comes	come	VERB
ejpam-3419	112	15	from	from	ADP
ejpam-3419	112	16	2β2θ	2β2θ	NOUN
ejpam-3419	112	17	−	−	PROPN
ejpam-3419	112	18	2	2	NUM
ejpam-3419	112	19	·	·	SYM
ejpam-3419	112	20	2θ2k1	2θ2k1	NUM
ejpam-3419	112	21	and	and	CCONJ
ejpam-3419	112	22	inductively	inductively	ADV
ejpam-3419	112	23	we	we	PRON
ejpam-3419	112	24	reach	reach	VERB
ejpam-3419	112	25	n3	n3	NOUN
ejpam-3419	112	26	.	.	PUNCT
ejpam-3419	113	1	now	now	ADV
ejpam-3419	113	2	,	,	PUNCT
ejpam-3419	113	3	there	there	PRON
ejpam-3419	113	4	are	be	VERB
ejpam-3419	113	5	2α4β8θ	2α4β8θ	NUM
ejpam-3419	113	6	vectors	vector	NOUN
ejpam-3419	113	7	in	in	ADP
ejpam-3419	113	8	total	total	NOUN
ejpam-3419	113	9	but	but	CCONJ
ejpam-3419	113	10	the	the	DET
ejpam-3419	113	11	number	number	NOUN
ejpam-3419	113	12	of	of	ADP
ejpam-3419	113	13	all	all	DET
ejpam-3419	113	14	vectors	vector	NOUN
ejpam-3419	113	15	of	of	ADP
ejpam-3419	113	16	order	order	NOUN
ejpam-3419	113	17	8	8	NUM
ejpam-3419	113	18	are	be	AUX
ejpam-3419	113	19	2α4β8θ	2α4β8θ	NUM
ejpam-3419	113	20	−	−	NOUN
ejpam-3419	113	21	2α4β4θ	2α4β4θ	NUM
ejpam-3419	113	22	.	.	PUNCT
ejpam-3419	114	1	so	so	ADV
ejpam-3419	114	2	,	,	PUNCT
ejpam-3419	114	3	we	we	PRON
ejpam-3419	114	4	choose	choose	VERB
ejpam-3419	114	5	the	the	DET
ejpam-3419	114	6	first	first	ADJ
ejpam-3419	114	7	one	one	NUM
ejpam-3419	114	8	of	of	ADP
ejpam-3419	114	9	order	order	NOUN
ejpam-3419	114	10	8	8	NUM
ejpam-3419	114	11	in	in	ADP
ejpam-3419	114	12	2α4β	2α4β	NUM
ejpam-3419	114	13	(	(	PUNCT
ejpam-3419	114	14	8θ	8θ	NUM
ejpam-3419	114	15	−	−	PROPN
ejpam-3419	114	16	4θ	4θ	NOUN
ejpam-3419	114	17	)	)	PUNCT
ejpam-3419	114	18	different	different	ADJ
ejpam-3419	114	19	ways	way	NOUN
ejpam-3419	114	20	.	.	PUNCT
ejpam-3419	115	1	then	then	ADV
ejpam-3419	115	2	we	we	PRON
ejpam-3419	115	3	choose	choose	VERB
ejpam-3419	115	4	the	the	DET
ejpam-3419	115	5	remaining	remain	VERB
ejpam-3419	115	6	k3−1	k3−1	PROPN
ejpam-3419	115	7	elements	element	NOUN
ejpam-3419	115	8	of	of	ADP
ejpam-3419	115	9	order	order	NOUN
ejpam-3419	115	10	8	8	NUM
ejpam-3419	115	11	in	in	ADP
ejpam-3419	115	12	a	a	DET
ejpam-3419	115	13	similar	similar	ADJ
ejpam-3419	115	14	way	way	NOUN
ejpam-3419	115	15	as	as	ADP
ejpam-3419	115	16	before	before	ADV
ejpam-3419	115	17	.	.	PUNCT
ejpam-3419	116	1	hence	hence	ADV
ejpam-3419	116	2	,	,	PUNCT
ejpam-3419	116	3	the	the	DET
ejpam-3419	116	4	last	last	ADJ
ejpam-3419	116	5	element	element	NOUN
ejpam-3419	116	6	can	can	AUX
ejpam-3419	116	7	be	be	AUX
ejpam-3419	116	8	chosen	choose	VERB
ejpam-3419	116	9	in	in	ADP
ejpam-3419	116	10	2α4β	2α4β	PROPN
ejpam-3419	116	11	(	(	PUNCT
ejpam-3419	116	12	8θ	8θ	NUM
ejpam-3419	116	13	−	−	PROPN
ejpam-3419	116	14	4θ2k3−1	4θ2k3−1	PROPN
ejpam-3419	116	15	)	)	PUNCT
ejpam-3419	116	16	ways	way	NOUN
ejpam-3419	116	17	.	.	PUNCT
ejpam-3419	117	1	so	so	ADV
ejpam-3419	117	2	,	,	PUNCT
ejpam-3419	117	3	we	we	PRON
ejpam-3419	117	4	obtain	obtain	VERB
ejpam-3419	117	5	n4	n4	PROPN
ejpam-3419	117	6	.	.	PUNCT
ejpam-3419	118	1	next	next	ADV
ejpam-3419	118	2	,	,	PUNCT
ejpam-3419	118	3	to	to	PART
ejpam-3419	118	4	choose	choose	VERB
ejpam-3419	118	5	vectors	vector	NOUN
ejpam-3419	118	6	of	of	ADP
ejpam-3419	118	7	order	order	NOUN
ejpam-3419	118	8	4	4	NUM
ejpam-3419	118	9	that	that	PRON
ejpam-3419	118	10	are	be	AUX
ejpam-3419	118	11	contributed	contribute	VERB
ejpam-3419	118	12	through	through	ADP
ejpam-3419	118	13	the	the	DET
ejpam-3419	118	14	z8	z8	NOUN
ejpam-3419	118	15	part	part	NOUN
ejpam-3419	118	16	.	.	PUNCT
ejpam-3419	119	1	there	there	PRON
ejpam-3419	119	2	are	be	VERB
ejpam-3419	119	3	2α4β	2α4β	NUM
ejpam-3419	119	4	(	(	PUNCT
ejpam-3419	119	5	4θ	4θ	NOUN
ejpam-3419	119	6	−	−	PROPN
ejpam-3419	119	7	2θ2k3	2θ2k3	NUM
ejpam-3419	119	8	)	)	PUNCT
ejpam-3419	119	9	selections	selection	NOUN
ejpam-3419	119	10	for	for	ADP
ejpam-3419	119	11	the	the	DET
ejpam-3419	119	12	first	first	ADJ
ejpam-3419	119	13	vector	vector	NOUN
ejpam-3419	119	14	.	.	PUNCT
ejpam-3419	120	1	note	note	VERB
ejpam-3419	120	2	that	that	SCONJ
ejpam-3419	120	3	,	,	PUNCT
ejpam-3419	120	4	the	the	DET
ejpam-3419	120	5	elements	element	NOUN
ejpam-3419	120	6	of	of	ADP
ejpam-3419	120	7	order	order	NOUN
ejpam-3419	120	8	4	4	NUM
ejpam-3419	120	9	that	that	PRON
ejpam-3419	120	10	are	be	AUX
ejpam-3419	120	11	formed	form	VERB
ejpam-3419	120	12	from	from	ADP
ejpam-3419	120	13	the	the	DET
ejpam-3419	120	14	k3	k3	ADJ
ejpam-3419	120	15	elements	element	NOUN
ejpam-3419	120	16	of	of	ADP
ejpam-3419	120	17	order	order	NOUN
ejpam-3419	120	18	8	8	NUM
ejpam-3419	120	19	by	by	ADP
ejpam-3419	120	20	taking	take	VERB
ejpam-3419	120	21	their	their	PRON
ejpam-3419	120	22	2	2	NUM
ejpam-3419	120	23	multiples	multiple	NOUN
ejpam-3419	120	24	need	need	VERB
ejpam-3419	120	25	to	to	PART
ejpam-3419	120	26	be	be	AUX
ejpam-3419	120	27	considered	consider	VERB
ejpam-3419	120	28	.	.	PUNCT
ejpam-3419	121	1	next	next	ADJ
ejpam-3419	121	2	,	,	PUNCT
ejpam-3419	121	3	2α4β	2α4β	NUM
ejpam-3419	121	4	(	(	PUNCT
ejpam-3419	121	5	4θ	4θ	NOUN
ejpam-3419	121	6	−	−	PROPN
ejpam-3419	121	7	2	2	NUM
ejpam-3419	121	8	·	·	SYM
ejpam-3419	121	9	2θ2k3	2θ2k3	NUM
ejpam-3419	121	10	)	)	PUNCT
ejpam-3419	121	11	selections	selection	NOUN
ejpam-3419	121	12	can	can	AUX
ejpam-3419	121	13	be	be	AUX
ejpam-3419	121	14	made	make	VERB
ejpam-3419	121	15	for	for	ADP
ejpam-3419	121	16	the	the	DET
ejpam-3419	121	17	second	second	ADJ
ejpam-3419	121	18	element	element	NOUN
ejpam-3419	121	19	.	.	PUNCT
ejpam-3419	122	1	similarly	similarly	ADV
ejpam-3419	122	2	,	,	PUNCT
ejpam-3419	122	3	the	the	DET
ejpam-3419	122	4	last	last	ADJ
ejpam-3419	122	5	element	element	NOUN
ejpam-3419	122	6	can	can	AUX
ejpam-3419	122	7	be	be	AUX
ejpam-3419	122	8	selected	select	VERB
ejpam-3419	122	9	by	by	ADP
ejpam-3419	122	10	2α4β	2α4β	NUM
ejpam-3419	122	11	(	(	PUNCT
ejpam-3419	122	12	4θ	4θ	NOUN
ejpam-3419	122	13	−	−	PROPN
ejpam-3419	122	14	2k4−1	2k4−1	PROPN
ejpam-3419	122	15	·	·	SYM
ejpam-3419	122	16	2θ2k3	2θ2k3	NUM
ejpam-3419	122	17	)	)	PUNCT
ejpam-3419	122	18	ways	way	NOUN
ejpam-3419	122	19	.	.	PUNCT
ejpam-3419	123	1	thus	thus	ADV
ejpam-3419	123	2	,	,	PUNCT
ejpam-3419	123	3	the	the	DET
ejpam-3419	123	4	k4	k4	ADJ
ejpam-3419	123	5	elements	element	NOUN
ejpam-3419	123	6	of	of	ADP
ejpam-3419	123	7	order	order	NOUN
ejpam-3419	123	8	4	4	NUM
ejpam-3419	123	9	that	that	PRON
ejpam-3419	123	10	contribute	contribute	VERB
ejpam-3419	123	11	only	only	ADV
ejpam-3419	123	12	to	to	ADP
ejpam-3419	123	13	the	the	DET
ejpam-3419	123	14	z8	z8	NOUN
ejpam-3419	123	15	part	part	NOUN
ejpam-3419	123	16	are	be	AUX
ejpam-3419	123	17	selected	select	VERB
ejpam-3419	123	18	in	in	ADP
ejpam-3419	123	19	n5	n5	PROPN
ejpam-3419	123	20	different	different	ADJ
ejpam-3419	123	21	ways	way	NOUN
ejpam-3419	123	22	.	.	PUNCT
ejpam-3419	124	1	finally	finally	ADV
ejpam-3419	124	2	,	,	PUNCT
ejpam-3419	124	3	we	we	PRON
ejpam-3419	124	4	need	need	VERB
ejpam-3419	124	5	to	to	PART
ejpam-3419	124	6	choose	choose	VERB
ejpam-3419	124	7	k5	k5	PROPN
ejpam-3419	124	8	vectors	vector	NOUN
ejpam-3419	124	9	of	of	ADP
ejpam-3419	124	10	order	order	NOUN
ejpam-3419	124	11	2	2	NUM
ejpam-3419	124	12	that	that	PRON
ejpam-3419	124	13	are	be	AUX
ejpam-3419	124	14	not	not	PART
ejpam-3419	124	15	generated	generate	VERB
ejpam-3419	124	16	by	by	ADP
ejpam-3419	124	17	k3	k3	ADJ
ejpam-3419	124	18	and	and	CCONJ
ejpam-3419	124	19	k4	k4	ADJ
ejpam-3419	124	20	vectors	vector	NOUN
ejpam-3419	124	21	of	of	ADP
ejpam-3419	124	22	order	order	NOUN
ejpam-3419	124	23	2	2	X
ejpam-3419	124	24	.	.	X
ejpam-3419	124	25	note	note	VERB
ejpam-3419	124	26	that	that	SCONJ
ejpam-3419	124	27	,	,	PUNCT
ejpam-3419	124	28	the	the	DET
ejpam-3419	124	29	first	first	ADJ
ejpam-3419	124	30	entries	entry	NOUN
ejpam-3419	124	31	of	of	ADP
ejpam-3419	124	32	such	such	ADJ
ejpam-3419	124	33	elements	element	NOUN
ejpam-3419	124	34	to	to	PART
ejpam-3419	124	35	be	be	AUX
ejpam-3419	124	36	all	all	DET
ejpam-3419	124	37	zero	zero	NUM
ejpam-3419	124	38	.	.	PUNCT
ejpam-3419	125	1	so	so	ADV
ejpam-3419	125	2	,	,	PUNCT
ejpam-3419	125	3	there	there	PRON
ejpam-3419	125	4	are	be	VERB
ejpam-3419	125	5	2θ	2θ	NUM
ejpam-3419	125	6	vectors	vector	NOUN
ejpam-3419	125	7	of	of	ADP
ejpam-3419	125	8	order	order	NOUN
ejpam-3419	125	9	2	2	X
ejpam-3419	125	10	.	.	PUNCT
ejpam-3419	126	1	in	in	ADP
ejpam-3419	126	2	order	order	NOUN
ejpam-3419	126	3	to	to	PART
ejpam-3419	126	4	pick	pick	VERB
ejpam-3419	126	5	such	such	DET
ejpam-3419	126	6	an	an	DET
ejpam-3419	126	7	element	element	NOUN
ejpam-3419	126	8	first	first	ADV
ejpam-3419	126	9	we	we	PRON
ejpam-3419	126	10	subtract	subtract	VERB
ejpam-3419	126	11	order	order	NOUN
ejpam-3419	126	12	2	2	NUM
ejpam-3419	126	13	elements	element	NOUN
ejpam-3419	126	14	that	that	PRON
ejpam-3419	126	15	are	be	AUX
ejpam-3419	126	16	obtained	obtain	VERB
ejpam-3419	126	17	through	through	ADP
ejpam-3419	126	18	already	already	ADV
ejpam-3419	126	19	chosen	choose	VERB
ejpam-3419	126	20	k3	k3	ADJ
ejpam-3419	126	21	and	and	CCONJ
ejpam-3419	126	22	k4	k4	ADJ
ejpam-3419	126	23	elements	element	NOUN
ejpam-3419	126	24	for	for	ADP
ejpam-3419	126	25	the	the	DET
ejpam-3419	126	26	z8	z8	NOUN
ejpam-3419	126	27	part	part	NOUN
ejpam-3419	126	28	.	.	PUNCT
ejpam-3419	127	1	so	so	ADV
ejpam-3419	127	2	,	,	PUNCT
ejpam-3419	127	3	we	we	PRON
ejpam-3419	127	4	have	have	VERB
ejpam-3419	127	5	2θ	2θ	NUM
ejpam-3419	127	6	−	−	PROPN
ejpam-3419	127	7	2k3+k4	2k3+k4	NUM
ejpam-3419	127	8	choices	choice	NOUN
ejpam-3419	127	9	.	.	PUNCT
ejpam-3419	128	1	the	the	DET
ejpam-3419	128	2	second	second	ADJ
ejpam-3419	128	3	element	element	NOUN
ejpam-3419	128	4	comes	come	VERB
ejpam-3419	128	5	from	from	ADP
ejpam-3419	128	6	2θ	2θ	NUM
ejpam-3419	128	7	−	−	PROPN
ejpam-3419	128	8	2	2	NUM
ejpam-3419	128	9	·	·	SYM
ejpam-3419	128	10	2k3+k4	2k3+k4	NUM
ejpam-3419	128	11	and	and	CCONJ
ejpam-3419	128	12	inductively	inductively	ADV
ejpam-3419	128	13	we	we	PRON
ejpam-3419	128	14	reach	reach	VERB
ejpam-3419	128	15	n6	n6	PROPN
ejpam-3419	128	16	.	.	PUNCT
ejpam-3419	129	1	lemma	lemma	PROPN
ejpam-3419	129	2	2	2	X
ejpam-3419	129	3	.	.	PUNCT
ejpam-3419	130	1	the	the	DET
ejpam-3419	130	2	number	number	NOUN
ejpam-3419	130	3	of	of	ADP
ejpam-3419	130	4	distinct	distinct	ADJ
ejpam-3419	130	5	generator	generator	NOUN
ejpam-3419	130	6	matrices	matrix	NOUN
ejpam-3419	130	7	of	of	ADP
ejpam-3419	130	8	a	a	DET
ejpam-3419	130	9	z2z4z8	z2z4z8	NOUN
ejpam-3419	130	10	-	-	PUNCT
ejpam-3419	130	11	additive	additive	ADJ
ejpam-3419	130	12	code	code	NOUN
ejpam-3419	130	13	of	of	ADP
ejpam-3419	130	14	type	type	NOUN
ejpam-3419	130	15	(	(	PUNCT
ejpam-3419	130	16	α	α	NOUN
ejpam-3419	130	17	,	,	PUNCT
ejpam-3419	130	18	β	β	X
ejpam-3419	130	19	,	,	PUNCT
ejpam-3419	130	20	θ	θ	PROPN
ejpam-3419	130	21	;	;	PUNCT
ejpam-3419	130	22	k0	k0	PROPN
ejpam-3419	130	23	,	,	PUNCT
ejpam-3419	130	24	k1	k1	PROPN
ejpam-3419	130	25	,	,	PUNCT
ejpam-3419	130	26	k2	k2	NOUN
ejpam-3419	130	27	,	,	PUNCT
ejpam-3419	130	28	k3	k3	PROPN
ejpam-3419	130	29	,	,	PUNCT
ejpam-3419	130	30	k4	k4	PROPN
ejpam-3419	130	31	,	,	PUNCT
ejpam-3419	130	32	k5	k5	PROPN
ejpam-3419	130	33	)	)	PUNCT
ejpam-3419	130	34	is	be	AUX
ejpam-3419	130	35	∏6	∏6	ADJ
ejpam-3419	130	36	j=1dj	j=1dj	ADJ
ejpam-3419	130	37	,	,	PUNCT
ejpam-3419	131	1	where	where	SCONJ
ejpam-3419	131	2	d1	d1	PROPN
ejpam-3419	131	3	=	=	SYM
ejpam-3419	131	4	2k0(k1+k2+k3+k4+k5	2k0(k1+k2+k3+k4+k5	NUM
ejpam-3419	131	5	)	)	PUNCT
ejpam-3419	131	6	k0−1∏	k0−1∏	PROPN
ejpam-3419	131	7	i=0	i=0	PROPN
ejpam-3419	131	8	(	(	PUNCT
ejpam-3419	131	9	2k0	2k0	NUM
ejpam-3419	131	10	−	−	NOUN
ejpam-3419	131	11	2i	2i	NOUN
ejpam-3419	131	12	)	)	PUNCT
ejpam-3419	131	13	,	,	PUNCT
ejpam-3419	131	14	d2	d2	PROPN
ejpam-3419	131	15	=	=	SYM
ejpam-3419	131	16	2k1(k0+k1+k2	2k1(k0+k1+k2	PROPN
ejpam-3419	131	17	+	+	NOUN
ejpam-3419	131	18	2k3	2k3	NUM
ejpam-3419	131	19	+	+	ADJ
ejpam-3419	131	20	2k4+k5	2k4+k5	NUM
ejpam-3419	131	21	)	)	PUNCT
ejpam-3419	131	22	k1−1∏	k1−1∏	PROPN
ejpam-3419	131	23	i=0	i=0	PROPN
ejpam-3419	131	24	(	(	PUNCT
ejpam-3419	131	25	2k1	2k1	NUM
ejpam-3419	131	26	−	−	NOUN
ejpam-3419	131	27	2i	2i	NUM
ejpam-3419	131	28	)	)	PUNCT
ejpam-3419	131	29	,	,	PUNCT
ejpam-3419	131	30	d3	d3	PROPN
ejpam-3419	131	31	=	=	PUNCT
ejpam-3419	131	32	2k2(k1	2k2(k1	NUM
ejpam-3419	131	33	+	+	PROPN
ejpam-3419	131	34	3k3	3k3	NUM
ejpam-3419	131	35	+	+	NOUN
ejpam-3419	131	36	2k4+k5	2k4+k5	NUM
ejpam-3419	131	37	)	)	PUNCT
ejpam-3419	132	1	k2−1∏	k2−1∏	PROPN
ejpam-3419	132	2	i=0	i=0	PROPN
ejpam-3419	132	3	(	(	PUNCT
ejpam-3419	132	4	2k2	2k2	NUM
ejpam-3419	132	5	−	−	PRON
ejpam-3419	132	6	2i	2i	NUM
ejpam-3419	132	7	)	)	PUNCT
ejpam-3419	132	8	,	,	PUNCT
ejpam-3419	132	9	d4	d4	PROPN
ejpam-3419	132	10	=	=	PROPN
ejpam-3419	133	1	2k3(k0	2k3(k0	NUM
ejpam-3419	133	2	+	+	NOUN
ejpam-3419	133	3	2k1+k2	2k1+k2	NUM
ejpam-3419	133	4	+	+	ADJ
ejpam-3419	133	5	2k3	2k3	NUM
ejpam-3419	133	6	+	+	ADJ
ejpam-3419	133	7	2k4+k5	2k4+k5	NUM
ejpam-3419	133	8	)	)	PUNCT
ejpam-3419	133	9	k3−1∏	k3−1∏	PROPN
ejpam-3419	133	10	i=0	i=0	PROPN
ejpam-3419	133	11	(	(	PUNCT
ejpam-3419	133	12	2k3	2k3	NUM
ejpam-3419	133	13	−	−	PROPN
ejpam-3419	133	14	2i	2i	NUM
ejpam-3419	133	15	)	)	PUNCT
ejpam-3419	133	16	,	,	PUNCT
ejpam-3419	133	17	b.	b.	PROPN
ejpam-3419	133	18	çalışkan	çalışkan	PROPN
ejpam-3419	133	19	,	,	PUNCT
ejpam-3419	133	20	k.	k.	PROPN
ejpam-3419	133	21	balıkçı	balıkçı	PROPN
ejpam-3419	133	22	/	/	SYM
ejpam-3419	133	23	eur	eur	PROPN
ejpam-3419	133	24	.	.	PUNCT
ejpam-3419	134	1	j.	j.	PROPN
ejpam-3419	134	2	pure	pure	PROPN
ejpam-3419	134	3	appl	appl	PROPN
ejpam-3419	134	4	.	.	PROPN
ejpam-3419	134	5	math	math	PROPN
ejpam-3419	134	6	,	,	PUNCT
ejpam-3419	134	7	12	12	NUM
ejpam-3419	134	8	(	(	PUNCT
ejpam-3419	134	9	2	2	NUM
ejpam-3419	134	10	)	)	PUNCT
ejpam-3419	134	11	(	(	PUNCT
ejpam-3419	134	12	2019	2019	NUM
ejpam-3419	134	13	)	)	PUNCT
ejpam-3419	134	14	,	,	PUNCT
ejpam-3419	134	15	668	668	NUM
ejpam-3419	134	16	-	-	SYM
ejpam-3419	134	17	679	679	NUM
ejpam-3419	134	18	673	673	NUM
ejpam-3419	134	19	d5	d5	NOUN
ejpam-3419	134	20	=	=	PUNCT
ejpam-3419	134	21	2k4(k0	2k4(k0	NUM
ejpam-3419	134	22	+	+	NOUN
ejpam-3419	134	23	2k1+k2	2k1+k2	NUM
ejpam-3419	134	24	+	+	SYM
ejpam-3419	134	25	2k3+k4+k5	2k3+k4+k5	NUM
ejpam-3419	134	26	)	)	PUNCT
ejpam-3419	134	27	k4−1∏	k4−1∏	PROPN
ejpam-3419	134	28	i=0	i=0	PROPN
ejpam-3419	134	29	(	(	PUNCT
ejpam-3419	134	30	2k4	2k4	NUM
ejpam-3419	134	31	−	−	PROPN
ejpam-3419	134	32	2i	2i	NOUN
ejpam-3419	134	33	)	)	PUNCT
ejpam-3419	134	34	,	,	PUNCT
ejpam-3419	134	35	d6	d6	NOUN
ejpam-3419	134	36	=	=	PUNCT
ejpam-3419	135	1	2k5(k3+k4	2k5(k3+k4	NUM
ejpam-3419	135	2	)	)	PUNCT
ejpam-3419	136	1	k5−1∏	k5−1∏	VERB
ejpam-3419	136	2	i=0	i=0	PROPN
ejpam-3419	136	3	(	(	PUNCT
ejpam-3419	136	4	2k5	2k5	NUM
ejpam-3419	136	5	−	−	PROPN
ejpam-3419	136	6	2i	2i	NUM
ejpam-3419	136	7	)	)	PUNCT
ejpam-3419	136	8	.	.	PUNCT
ejpam-3419	137	1	proof	proof	NOUN
ejpam-3419	137	2	.	.	PUNCT
ejpam-3419	138	1	as	as	SCONJ
ejpam-3419	138	2	we	we	PRON
ejpam-3419	138	3	did	do	VERB
ejpam-3419	138	4	in	in	ADP
ejpam-3419	138	5	lemma	lemma	PROPN
ejpam-3419	138	6	1	1	NUM
ejpam-3419	138	7	,	,	PUNCT
ejpam-3419	138	8	we	we	PRON
ejpam-3419	138	9	will	will	AUX
ejpam-3419	138	10	apply	apply	VERB
ejpam-3419	138	11	the	the	DET
ejpam-3419	138	12	same	same	ADJ
ejpam-3419	138	13	procedure	procedure	NOUN
ejpam-3419	138	14	in	in	ADP
ejpam-3419	138	15	a	a	DET
ejpam-3419	138	16	group	group	NOUN
ejpam-3419	138	17	of	of	ADP
ejpam-3419	138	18	the	the	DET
ejpam-3419	138	19	type	type	NOUN
ejpam-3419	138	20	(	(	PUNCT
ejpam-3419	138	21	k0	k0	PROPN
ejpam-3419	138	22	,	,	PUNCT
ejpam-3419	138	23	k1	k1	PROPN
ejpam-3419	138	24	,	,	PUNCT
ejpam-3419	138	25	k2	k2	NOUN
ejpam-3419	138	26	,	,	PUNCT
ejpam-3419	138	27	k3	k3	PROPN
ejpam-3419	138	28	,	,	PUNCT
ejpam-3419	138	29	k4	k4	PROPN
ejpam-3419	138	30	,	,	PUNCT
ejpam-3419	138	31	k5	k5	PROPN
ejpam-3419	138	32	)	)	PUNCT
ejpam-3419	138	33	.	.	PUNCT
ejpam-3419	139	1	in	in	ADP
ejpam-3419	139	2	order	order	NOUN
ejpam-3419	139	3	to	to	PART
ejpam-3419	139	4	choose	choose	VERB
ejpam-3419	139	5	first	first	ADJ
ejpam-3419	139	6	element	element	NOUN
ejpam-3419	139	7	of	of	ADP
ejpam-3419	139	8	order	order	NOUN
ejpam-3419	139	9	2	2	NUM
ejpam-3419	139	10	that	that	PRON
ejpam-3419	139	11	contributes	contribute	VERB
ejpam-3419	139	12	through	through	ADP
ejpam-3419	139	13	the	the	DET
ejpam-3419	139	14	z2	z2	PROPN
ejpam-3419	139	15	part	part	NOUN
ejpam-3419	139	16	,	,	PUNCT
ejpam-3419	139	17	we	we	PRON
ejpam-3419	139	18	subtract	subtract	VERB
ejpam-3419	139	19	all	all	DET
ejpam-3419	139	20	elements	element	NOUN
ejpam-3419	139	21	of	of	ADP
ejpam-3419	139	22	order	order	NOUN
ejpam-3419	139	23	2	2	NUM
ejpam-3419	139	24	in	in	ADP
ejpam-3419	139	25	the	the	DET
ejpam-3419	139	26	group	group	NOUN
ejpam-3419	139	27	from	from	ADP
ejpam-3419	139	28	the	the	DET
ejpam-3419	139	29	ones	one	NOUN
ejpam-3419	139	30	that	that	PRON
ejpam-3419	139	31	are	be	AUX
ejpam-3419	139	32	not	not	PART
ejpam-3419	139	33	coming	come	VERB
ejpam-3419	139	34	through	through	ADP
ejpam-3419	139	35	the	the	DET
ejpam-3419	139	36	z2	z2	PROPN
ejpam-3419	139	37	part	part	NOUN
ejpam-3419	139	38	,	,	PUNCT
ejpam-3419	139	39	i.e.	i.e.	X
ejpam-3419	139	40	2k0+k1+k2+k3+k4+k5	2k0+k1+k2+k3+k4+k5	ADJ
ejpam-3419	139	41	−	−	ADP
ejpam-3419	139	42	2k1+k2+k3+k4+k5	2k1+k2+k3+k4+k5	NUM
ejpam-3419	139	43	.	.	PUNCT
ejpam-3419	140	1	next	next	ADV
ejpam-3419	140	2	,	,	PUNCT
ejpam-3419	140	3	the	the	DET
ejpam-3419	140	4	second	second	ADJ
ejpam-3419	140	5	element	element	NOUN
ejpam-3419	140	6	can	can	AUX
ejpam-3419	140	7	be	be	AUX
ejpam-3419	140	8	chosen	choose	VERB
ejpam-3419	140	9	in	in	ADP
ejpam-3419	140	10	2k0+k1+k2+k3+k4+k5	2k0+k1+k2+k3+k4+k5	NUM
ejpam-3419	140	11	−	−	NUM
ejpam-3419	140	12	2	2	NUM
ejpam-3419	140	13	·	·	SYM
ejpam-3419	140	14	2k1+k2+k3+k4+k5	2k1+k2+k3+k4+k5	NUM
ejpam-3419	140	15	different	different	ADJ
ejpam-3419	140	16	ways	way	NOUN
ejpam-3419	140	17	and	and	CCONJ
ejpam-3419	140	18	inductively	inductively	ADV
ejpam-3419	140	19	we	we	PRON
ejpam-3419	140	20	reach	reach	VERB
ejpam-3419	140	21	at	at	ADP
ejpam-3419	140	22	d1	d1	PROPN
ejpam-3419	140	23	.	.	PUNCT
ejpam-3419	141	1	next	next	ADV
ejpam-3419	141	2	,	,	PUNCT
ejpam-3419	141	3	to	to	PART
ejpam-3419	141	4	choose	choose	VERB
ejpam-3419	141	5	an	an	DET
ejpam-3419	141	6	element	element	NOUN
ejpam-3419	141	7	of	of	ADP
ejpam-3419	141	8	order	order	NOUN
ejpam-3419	141	9	4	4	NUM
ejpam-3419	141	10	in	in	ADP
ejpam-3419	141	11	the	the	DET
ejpam-3419	141	12	group	group	NOUN
ejpam-3419	141	13	,	,	PUNCT
ejpam-3419	141	14	we	we	PRON
ejpam-3419	141	15	have	have	VERB
ejpam-3419	141	16	(	(	PUNCT
ejpam-3419	141	17	4k1	4k1	NUM
ejpam-3419	141	18	−	−	NOUN
ejpam-3419	141	19	2k1	2k1	NUM
ejpam-3419	141	20	)	)	PUNCT
ejpam-3419	141	21	2k0+k2	2k0+k2	NUM
ejpam-3419	142	1	+	+	NOUN
ejpam-3419	142	2	2k3	2k3	NUM
ejpam-3419	142	3	+	+	ADJ
ejpam-3419	142	4	2k4+k5	2k4+k5	NUM
ejpam-3419	142	5	choices	choice	NOUN
ejpam-3419	142	6	.	.	PUNCT
ejpam-3419	143	1	then	then	ADV
ejpam-3419	143	2	,	,	PUNCT
ejpam-3419	143	3	there	there	PRON
ejpam-3419	143	4	are	be	VERB
ejpam-3419	143	5	(	(	PUNCT
ejpam-3419	143	6	4k1	4k1	NUM
ejpam-3419	143	7	−	−	NUM
ejpam-3419	143	8	2	2	NUM
ejpam-3419	143	9	·	·	SYM
ejpam-3419	143	10	2k1	2k1	NUM
ejpam-3419	143	11	)	)	PUNCT
ejpam-3419	143	12	2k0+k2	2k0+k2	NUM
ejpam-3419	144	1	+	+	NOUN
ejpam-3419	144	2	2k3	2k3	NUM
ejpam-3419	144	3	+	+	ADJ
ejpam-3419	144	4	2k4+k5	2k4+k5	NUM
ejpam-3419	144	5	choices	choice	NOUN
ejpam-3419	144	6	for	for	ADP
ejpam-3419	144	7	second	second	ADJ
ejpam-3419	144	8	element	element	NOUN
ejpam-3419	144	9	of	of	ADP
ejpam-3419	144	10	order	order	NOUN
ejpam-3419	144	11	4	4	NUM
ejpam-3419	144	12	.	.	PUNCT
ejpam-3419	145	1	so	so	ADV
ejpam-3419	145	2	,	,	PUNCT
ejpam-3419	145	3	inductively	inductively	ADV
ejpam-3419	145	4	,	,	PUNCT
ejpam-3419	145	5	we	we	PRON
ejpam-3419	145	6	have	have	VERB
ejpam-3419	145	7	d2	d2	PROPN
ejpam-3419	145	8	.	.	PUNCT
ejpam-3419	146	1	now	now	ADV
ejpam-3419	146	2	,	,	PUNCT
ejpam-3419	146	3	to	to	PART
ejpam-3419	146	4	choose	choose	VERB
ejpam-3419	146	5	an	an	DET
ejpam-3419	146	6	element	element	NOUN
ejpam-3419	146	7	of	of	ADP
ejpam-3419	146	8	order	order	NOUN
ejpam-3419	146	9	2	2	NUM
ejpam-3419	146	10	in	in	ADP
ejpam-3419	146	11	the	the	DET
ejpam-3419	146	12	group	group	NOUN
ejpam-3419	146	13	that	that	PRON
ejpam-3419	146	14	only	only	ADV
ejpam-3419	146	15	contributes	contribute	VERB
ejpam-3419	146	16	through	through	ADP
ejpam-3419	146	17	the	the	DET
ejpam-3419	146	18	z4	z4	PROPN
ejpam-3419	146	19	part	part	NOUN
ejpam-3419	146	20	.	.	PUNCT
ejpam-3419	147	1	there	there	PRON
ejpam-3419	147	2	are	be	VERB
ejpam-3419	147	3	(	(	PUNCT
ejpam-3419	147	4	2k1+k2	2k1+k2	NUM
ejpam-3419	147	5	−	−	NOUN
ejpam-3419	147	6	2k1	2k1	NUM
ejpam-3419	147	7	)	)	PUNCT
ejpam-3419	148	1	23k3	23k3	NUM
ejpam-3419	148	2	+	+	NOUN
ejpam-3419	148	3	2k4+k5	2k4+k5	NUM
ejpam-3419	148	4	choices	choice	NOUN
ejpam-3419	148	5	for	for	ADP
ejpam-3419	148	6	the	the	DET
ejpam-3419	148	7	first	first	ADJ
ejpam-3419	148	8	element	element	NOUN
ejpam-3419	148	9	.	.	PUNCT
ejpam-3419	149	1	next	next	ADV
ejpam-3419	149	2	,	,	PUNCT
ejpam-3419	149	3	the	the	DET
ejpam-3419	149	4	second	second	ADJ
ejpam-3419	149	5	element	element	NOUN
ejpam-3419	149	6	can	can	AUX
ejpam-3419	149	7	be	be	AUX
ejpam-3419	149	8	chosen	choose	VERB
ejpam-3419	149	9	(	(	PUNCT
ejpam-3419	149	10	2k1+k2	2k1+k2	NUM
ejpam-3419	149	11	−	−	NOUN
ejpam-3419	149	12	2	2	NUM
ejpam-3419	149	13	·	·	SYM
ejpam-3419	149	14	2k1	2k1	NUM
ejpam-3419	149	15	)	)	PUNCT
ejpam-3419	150	1	23k3	23k3	NUM
ejpam-3419	150	2	+	+	ADJ
ejpam-3419	150	3	2k4+k5	2k4+k5	NUM
ejpam-3419	150	4	different	different	ADJ
ejpam-3419	150	5	ways	way	NOUN
ejpam-3419	150	6	and	and	CCONJ
ejpam-3419	150	7	inductively	inductively	ADV
ejpam-3419	150	8	we	we	PRON
ejpam-3419	150	9	reach	reach	VERB
ejpam-3419	150	10	at	at	ADP
ejpam-3419	150	11	d3	d3	PROPN
ejpam-3419	150	12	.	.	PUNCT
ejpam-3419	151	1	after	after	ADP
ejpam-3419	151	2	the	the	DET
ejpam-3419	151	3	z2	z2	PROPN
ejpam-3419	151	4	and	and	CCONJ
ejpam-3419	151	5	z4	z4	PROPN
ejpam-3419	151	6	parts	part	NOUN
ejpam-3419	151	7	,	,	PUNCT
ejpam-3419	151	8	we	we	PRON
ejpam-3419	151	9	now	now	ADV
ejpam-3419	151	10	calculate	calculate	VERB
ejpam-3419	151	11	the	the	DET
ejpam-3419	151	12	selections	selection	NOUN
ejpam-3419	151	13	for	for	ADP
ejpam-3419	151	14	the	the	DET
ejpam-3419	151	15	z8	z8	NOUN
ejpam-3419	151	16	part	part	NOUN
ejpam-3419	151	17	.	.	PUNCT
ejpam-3419	152	1	first	first	ADV
ejpam-3419	152	2	,	,	PUNCT
ejpam-3419	152	3	in	in	ADP
ejpam-3419	152	4	order	order	NOUN
ejpam-3419	152	5	to	to	PART
ejpam-3419	152	6	choose	choose	VERB
ejpam-3419	152	7	an	an	DET
ejpam-3419	152	8	element	element	NOUN
ejpam-3419	152	9	of	of	ADP
ejpam-3419	152	10	order	order	NOUN
ejpam-3419	152	11	8	8	NUM
ejpam-3419	152	12	in	in	ADP
ejpam-3419	152	13	the	the	DET
ejpam-3419	152	14	group	group	NOUN
ejpam-3419	152	15	,	,	PUNCT
ejpam-3419	152	16	we	we	PRON
ejpam-3419	152	17	have	have	VERB
ejpam-3419	152	18	(	(	PUNCT
ejpam-3419	152	19	8k3	8k3	NUM
ejpam-3419	152	20	−	−	PROPN
ejpam-3419	152	21	4k3	4k3	NUM
ejpam-3419	152	22	)	)	PUNCT
ejpam-3419	152	23	2k0	2k0	NUM
ejpam-3419	153	1	+	+	NOUN
ejpam-3419	153	2	2k1+k2	2k1+k2	NUM
ejpam-3419	153	3	+	+	ADJ
ejpam-3419	153	4	2k4+k5	2k4+k5	NUM
ejpam-3419	153	5	choices	choice	NOUN
ejpam-3419	153	6	.	.	PUNCT
ejpam-3419	154	1	next	next	ADV
ejpam-3419	154	2	,	,	PUNCT
ejpam-3419	154	3	we	we	PRON
ejpam-3419	154	4	can	can	AUX
ejpam-3419	154	5	choose	choose	VERB
ejpam-3419	154	6	second	second	ADJ
ejpam-3419	154	7	element	element	NOUN
ejpam-3419	154	8	in	in	ADP
ejpam-3419	154	9	(	(	PUNCT
ejpam-3419	154	10	8k3	8k3	NUM
ejpam-3419	154	11	−	−	PROPN
ejpam-3419	154	12	2	2	NUM
ejpam-3419	154	13	·	·	SYM
ejpam-3419	154	14	4k3	4k3	NUM
ejpam-3419	154	15	)	)	PUNCT
ejpam-3419	154	16	2k0	2k0	NUM
ejpam-3419	154	17	+	+	NOUN
ejpam-3419	154	18	2k1+k2	2k1+k2	NUM
ejpam-3419	154	19	+	+	ADJ
ejpam-3419	154	20	2k4+k5	2k4+k5	NUM
ejpam-3419	154	21	different	different	ADJ
ejpam-3419	154	22	ways	way	NOUN
ejpam-3419	154	23	.	.	PUNCT
ejpam-3419	155	1	similarly	similarly	ADV
ejpam-3419	155	2	,	,	PUNCT
ejpam-3419	155	3	if	if	SCONJ
ejpam-3419	155	4	we	we	PRON
ejpam-3419	155	5	continue	continue	VERB
ejpam-3419	155	6	,	,	PUNCT
ejpam-3419	155	7	we	we	PRON
ejpam-3419	155	8	reach	reach	VERB
ejpam-3419	155	9	at	at	ADP
ejpam-3419	155	10	d4	d4	PROPN
ejpam-3419	155	11	.	.	PUNCT
ejpam-3419	156	1	next	next	ADV
ejpam-3419	156	2	,	,	PUNCT
ejpam-3419	156	3	to	to	PART
ejpam-3419	156	4	choose	choose	VERB
ejpam-3419	156	5	an	an	DET
ejpam-3419	156	6	element	element	NOUN
ejpam-3419	156	7	of	of	ADP
ejpam-3419	156	8	order	order	NOUN
ejpam-3419	156	9	4	4	NUM
ejpam-3419	156	10	within	within	ADP
ejpam-3419	156	11	the	the	DET
ejpam-3419	156	12	group	group	NOUN
ejpam-3419	156	13	that	that	PRON
ejpam-3419	156	14	only	only	ADV
ejpam-3419	156	15	contributes	contribute	VERB
ejpam-3419	156	16	through	through	ADP
ejpam-3419	156	17	the	the	DET
ejpam-3419	156	18	z8	z8	NOUN
ejpam-3419	156	19	part	part	NOUN
ejpam-3419	156	20	.	.	PUNCT
ejpam-3419	157	1	we	we	PRON
ejpam-3419	157	2	have	have	VERB
ejpam-3419	157	3	(	(	PUNCT
ejpam-3419	157	4	4k4	4k4	NUM
ejpam-3419	157	5	−	−	NOUN
ejpam-3419	157	6	2k4	2k4	NUM
ejpam-3419	157	7	)	)	PUNCT
ejpam-3419	157	8	2k0	2k0	PUNCT
ejpam-3419	158	1	+	+	PROPN
ejpam-3419	158	2	2k1+k2	2k1+k2	NUM
ejpam-3419	158	3	+	+	ADJ
ejpam-3419	158	4	2k3+k5	2k3+k5	NUM
ejpam-3419	158	5	choices	choice	NOUN
ejpam-3419	158	6	.	.	PUNCT
ejpam-3419	159	1	therefore	therefore	ADV
ejpam-3419	159	2	,	,	PUNCT
ejpam-3419	159	3	there	there	PRON
ejpam-3419	159	4	are	be	VERB
ejpam-3419	159	5	(	(	PUNCT
ejpam-3419	159	6	4k4	4k4	NUM
ejpam-3419	159	7	−	−	NOUN
ejpam-3419	159	8	2	2	NUM
ejpam-3419	159	9	·	·	SYM
ejpam-3419	159	10	2k4	2k4	NUM
ejpam-3419	159	11	)	)	PUNCT
ejpam-3419	159	12	2k0	2k0	PUNCT
ejpam-3419	159	13	+	+	NOUN
ejpam-3419	159	14	2k1+k2	2k1+k2	NUM
ejpam-3419	159	15	+	+	ADJ
ejpam-3419	159	16	2k3+k5	2k3+k5	NUM
ejpam-3419	159	17	different	different	ADJ
ejpam-3419	159	18	choices	choice	NOUN
ejpam-3419	159	19	for	for	ADP
ejpam-3419	159	20	the	the	DET
ejpam-3419	159	21	second	second	ADJ
ejpam-3419	159	22	element	element	NOUN
ejpam-3419	159	23	.	.	PUNCT
ejpam-3419	160	1	so	so	ADV
ejpam-3419	160	2	,	,	PUNCT
ejpam-3419	160	3	inductively	inductively	ADV
ejpam-3419	160	4	,	,	PUNCT
ejpam-3419	160	5	the	the	DET
ejpam-3419	160	6	last	last	ADJ
ejpam-3419	160	7	element	element	NOUN
ejpam-3419	160	8	can	can	AUX
ejpam-3419	160	9	be	be	AUX
ejpam-3419	160	10	chosen	choose	VERB
ejpam-3419	160	11	in	in	ADP
ejpam-3419	160	12	(	(	PUNCT
ejpam-3419	160	13	4k4	4k4	NUM
ejpam-3419	160	14	−	−	PROPN
ejpam-3419	160	15	2k4−12k4	2k4−12k4	NUM
ejpam-3419	160	16	)	)	PUNCT
ejpam-3419	160	17	2k0	2k0	PUNCT
ejpam-3419	161	1	+	+	NOUN
ejpam-3419	161	2	2k1+k2	2k1+k2	NUM
ejpam-3419	161	3	+	+	ADJ
ejpam-3419	161	4	2k3+k5	2k3+k5	NUM
ejpam-3419	161	5	different	different	ADJ
ejpam-3419	161	6	ways	way	NOUN
ejpam-3419	161	7	.	.	PUNCT
ejpam-3419	162	1	as	as	ADP
ejpam-3419	162	2	a	a	DET
ejpam-3419	162	3	result	result	NOUN
ejpam-3419	162	4	,	,	PUNCT
ejpam-3419	162	5	we	we	PRON
ejpam-3419	162	6	reach	reach	VERB
ejpam-3419	162	7	at	at	ADP
ejpam-3419	162	8	d5	d5	NOUN
ejpam-3419	162	9	.	.	PUNCT
ejpam-3419	163	1	finally	finally	ADV
ejpam-3419	163	2	,	,	PUNCT
ejpam-3419	163	3	to	to	PART
ejpam-3419	163	4	choose	choose	VERB
ejpam-3419	163	5	an	an	DET
ejpam-3419	163	6	element	element	NOUN
ejpam-3419	163	7	of	of	ADP
ejpam-3419	163	8	order	order	NOUN
ejpam-3419	163	9	2	2	NUM
ejpam-3419	163	10	within	within	ADP
ejpam-3419	163	11	the	the	DET
ejpam-3419	163	12	group	group	NOUN
ejpam-3419	163	13	that	that	PRON
ejpam-3419	163	14	solely	solely	ADV
ejpam-3419	163	15	contributes	contribute	VERB
ejpam-3419	163	16	through	through	ADP
ejpam-3419	163	17	the	the	DET
ejpam-3419	163	18	z8	z8	NOUN
ejpam-3419	163	19	part	part	NOUN
ejpam-3419	163	20	.	.	PUNCT
ejpam-3419	164	1	for	for	ADP
ejpam-3419	164	2	this	this	PRON
ejpam-3419	164	3	,	,	PUNCT
ejpam-3419	164	4	there	there	PRON
ejpam-3419	164	5	are	be	VERB
ejpam-3419	164	6	2k3+k4+k5	2k3+k4+k5	ADJ
ejpam-3419	164	7	−	−	NOUN
ejpam-3419	164	8	2k3+k4	2k3+k4	NUM
ejpam-3419	164	9	choices	choice	NOUN
ejpam-3419	164	10	.	.	PUNCT
ejpam-3419	165	1	the	the	DET
ejpam-3419	165	2	second	second	ADJ
ejpam-3419	165	3	element	element	NOUN
ejpam-3419	165	4	can	can	AUX
ejpam-3419	165	5	be	be	AUX
ejpam-3419	165	6	chosen	choose	VERB
ejpam-3419	165	7	in	in	ADP
ejpam-3419	165	8	2k3+k4+k5	2k3+k4+k5	PROPN
ejpam-3419	165	9	−	−	PROPN
ejpam-3419	165	10	2	2	NUM
ejpam-3419	165	11	·	·	SYM
ejpam-3419	165	12	2k3+k4	2k3+k4	NUM
ejpam-3419	165	13	different	different	ADJ
ejpam-3419	165	14	ways	way	NOUN
ejpam-3419	165	15	.	.	PUNCT
ejpam-3419	166	1	so	so	ADV
ejpam-3419	166	2	,	,	PUNCT
ejpam-3419	166	3	the	the	DET
ejpam-3419	166	4	last	last	ADJ
ejpam-3419	166	5	element	element	NOUN
ejpam-3419	166	6	can	can	AUX
ejpam-3419	166	7	be	be	AUX
ejpam-3419	166	8	chosen	choose	VERB
ejpam-3419	166	9	in	in	ADP
ejpam-3419	166	10	2k3+k4+k5	2k3+k4+k5	PROPN
ejpam-3419	166	11	−	−	PROPN
ejpam-3419	166	12	2k5−12k3+k4	2k5−12k3+k4	NUM
ejpam-3419	166	13	different	different	ADJ
ejpam-3419	166	14	ways	way	NOUN
ejpam-3419	166	15	.	.	PUNCT
ejpam-3419	167	1	in	in	ADP
ejpam-3419	167	2	this	this	DET
ejpam-3419	167	3	way	way	NOUN
ejpam-3419	167	4	,	,	PUNCT
ejpam-3419	167	5	d6	d6	NOUN
ejpam-3419	167	6	is	be	AUX
ejpam-3419	167	7	obtained	obtain	VERB
ejpam-3419	167	8	and	and	CCONJ
ejpam-3419	167	9	the	the	DET
ejpam-3419	167	10	proof	proof	NOUN
ejpam-3419	167	11	is	be	AUX
ejpam-3419	167	12	completed	complete	VERB
ejpam-3419	167	13	.	.	PUNCT
ejpam-3419	168	1	definition	definition	NOUN
ejpam-3419	168	2	3	3	NUM
ejpam-3419	168	3	.	.	PUNCT
ejpam-3419	169	1	[	[	X
ejpam-3419	169	2	10	10	NUM
ejpam-3419	169	3	]	]	PUNCT
ejpam-3419	169	4	let	let	VERB
ejpam-3419	169	5	n	n	NOUN
ejpam-3419	169	6	and	and	CCONJ
ejpam-3419	169	7	q	q	AUX
ejpam-3419	169	8	be	be	AUX
ejpam-3419	169	9	two	two	NUM
ejpam-3419	169	10	positive	positive	ADJ
ejpam-3419	169	11	integers	integer	NOUN
ejpam-3419	169	12	[	[	X
ejpam-3419	169	13	n]q	n]q	X
ejpam-3419	169	14	=	=	SYM
ejpam-3419	169	15	1	1	NUM
ejpam-3419	169	16	+	+	CCONJ
ejpam-3419	169	17	q	q	NOUN
ejpam-3419	169	18	+	+	NUM
ejpam-3419	169	19	q2	q2	NOUN
ejpam-3419	169	20	+	+	X
ejpam-3419	169	21	.	.	PUNCT
ejpam-3419	169	22	.	.	PUNCT
ejpam-3419	170	1	.+	.+	NOUN
ejpam-3419	171	1	qn−1	qn−1	PROPN
ejpam-3419	171	2	=	=	PUNCT
ejpam-3419	171	3	qn	qn	NOUN
ejpam-3419	171	4	−	−	PROPN
ejpam-3419	171	5	1	1	NUM
ejpam-3419	171	6	q	q	NOUN
ejpam-3419	171	7	−	−	PROPN
ejpam-3419	171	8	1	1	NUM
ejpam-3419	171	9	and	and	CCONJ
ejpam-3419	171	10	the	the	DET
ejpam-3419	171	11	q	q	NOUN
ejpam-3419	171	12	-	-	PUNCT
ejpam-3419	171	13	factorial	factorial	NOUN
ejpam-3419	171	14	is	be	AUX
ejpam-3419	171	15	defined	define	VERB
ejpam-3419	171	16	as	as	ADP
ejpam-3419	171	17	[	[	X
ejpam-3419	171	18	n]q	n]q	X
ejpam-3419	171	19	!	!	PUNCT
ejpam-3419	171	20	=	=	PUNCT
ejpam-3419	172	1	[	[	X
ejpam-3419	172	2	n]q	n]q	X
ejpam-3419	172	3	·	·	PUNCT
ejpam-3419	173	1	[	[	X
ejpam-3419	173	2	n−	n−	NOUN
ejpam-3419	173	3	1]q	1]q	NUM
ejpam-3419	173	4	·	·	PUNCT
ejpam-3419	173	5	·	·	PUNCT
ejpam-3419	173	6	·	·	PUNCT
ejpam-3419	174	1	[	[	X
ejpam-3419	174	2	2]q	2]q	NUM
ejpam-3419	174	3	·	·	PUNCT
ejpam-3419	175	1	[	[	X
ejpam-3419	175	2	1]q	1]q	PROPN
ejpam-3419	175	3	b.	b.	PROPN
ejpam-3419	175	4	çalışkan	çalışkan	PROPN
ejpam-3419	175	5	,	,	PUNCT
ejpam-3419	175	6	k.	k.	PROPN
ejpam-3419	175	7	balıkçı	balıkçı	PROPN
ejpam-3419	175	8	/	/	SYM
ejpam-3419	175	9	eur	eur	PROPN
ejpam-3419	175	10	.	.	PUNCT
ejpam-3419	176	1	j.	j.	PROPN
ejpam-3419	176	2	pure	pure	PROPN
ejpam-3419	176	3	appl	appl	PROPN
ejpam-3419	176	4	.	.	PROPN
ejpam-3419	176	5	math	math	PROPN
ejpam-3419	176	6	,	,	PUNCT
ejpam-3419	176	7	12	12	NUM
ejpam-3419	176	8	(	(	PUNCT
ejpam-3419	176	9	2	2	NUM
ejpam-3419	176	10	)	)	PUNCT
ejpam-3419	176	11	(	(	PUNCT
ejpam-3419	176	12	2019	2019	NUM
ejpam-3419	176	13	)	)	PUNCT
ejpam-3419	176	14	,	,	PUNCT
ejpam-3419	176	15	668	668	NUM
ejpam-3419	176	16	-	-	SYM
ejpam-3419	176	17	679	679	NUM
ejpam-3419	176	18	674	674	NUM
ejpam-3419	176	19	and	and	CCONJ
ejpam-3419	176	20	a−1∏	a−1∏	PROPN
ejpam-3419	176	21	j=0	j=0	PROPN
ejpam-3419	176	22	(	(	PUNCT
ejpam-3419	176	23	2b	2b	NUM
ejpam-3419	176	24	−	−	NOUN
ejpam-3419	176	25	2j	2j	NUM
ejpam-3419	176	26	)	)	PUNCT
ejpam-3419	176	27	=	=	SYM
ejpam-3419	176	28	(	(	PUNCT
ejpam-3419	176	29	2b	2b	NUM
ejpam-3419	176	30	−	−	NOUN
ejpam-3419	176	31	1	1	NUM
ejpam-3419	176	32	)	)	PUNCT
ejpam-3419	176	33	(	(	PUNCT
ejpam-3419	176	34	2b	2b	NUM
ejpam-3419	176	35	−	−	NOUN
ejpam-3419	176	36	2	2	NUM
ejpam-3419	176	37	)	)	PUNCT
ejpam-3419	176	38	(	(	PUNCT
ejpam-3419	176	39	2b	2b	NUM
ejpam-3419	176	40	−	−	PROPN
ejpam-3419	176	41	22	22	NUM
ejpam-3419	176	42	)	)	PUNCT
ejpam-3419	176	43	·	·	PUNCT
ejpam-3419	176	44	·	·	PUNCT
ejpam-3419	176	45	·	·	PUNCT
ejpam-3419	176	46	(	(	PUNCT
ejpam-3419	176	47	2b	2b	NUM
ejpam-3419	176	48	−	−	PROPN
ejpam-3419	176	49	2a−2	2a−2	NUM
ejpam-3419	176	50	)	)	PUNCT
ejpam-3419	176	51	(	(	PUNCT
ejpam-3419	176	52	2b	2b	NUM
ejpam-3419	176	53	−	−	NOUN
ejpam-3419	176	54	2(a−1	2(a−1	NOUN
ejpam-3419	176	55	)	)	PUNCT
ejpam-3419	176	56	)	)	PUNCT
ejpam-3419	177	1	=	=	PUNCT
ejpam-3419	178	1	21	21	NUM
ejpam-3419	178	2	+	+	NOUN
ejpam-3419	178	3	2+	2+	NUM
ejpam-3419	178	4	...	...	PUNCT
ejpam-3419	178	5	+(a−1	+(a−1	NOUN
ejpam-3419	178	6	)	)	PUNCT
ejpam-3419	178	7	(	(	PUNCT
ejpam-3419	178	8	2b	2b	NUM
ejpam-3419	178	9	−	−	NOUN
ejpam-3419	178	10	1	1	NUM
ejpam-3419	178	11	)	)	PUNCT
ejpam-3419	178	12	(	(	PUNCT
ejpam-3419	178	13	2b−1	2b−1	NUM
ejpam-3419	178	14	−	−	PROPN
ejpam-3419	178	15	1	1	NUM
ejpam-3419	178	16	)	)	PUNCT
ejpam-3419	178	17	·	·	PUNCT
ejpam-3419	178	18	·	·	PUNCT
ejpam-3419	178	19	·	·	PUNCT
ejpam-3419	178	20	(	(	PUNCT
ejpam-3419	178	21	2b−(a−1	2b−(a−1	NUM
ejpam-3419	178	22	)	)	PUNCT
ejpam-3419	178	23	−	−	PROPN
ejpam-3419	178	24	1	1	NUM
ejpam-3419	178	25	)	)	PUNCT
ejpam-3419	178	26	=	=	SYM
ejpam-3419	178	27	2	2	NUM
ejpam-3419	178	28	(	(	PUNCT
ejpam-3419	178	29	a	a	DET
ejpam-3419	178	30	2	2	NUM
ejpam-3419	178	31	)	)	PUNCT
ejpam-3419	179	1	[	[	X
ejpam-3419	179	2	b]2	b]2	X
ejpam-3419	179	3	!	!	PUNCT
ejpam-3419	180	1	[	[	X
ejpam-3419	180	2	b−	b−	NOUN
ejpam-3419	180	3	a]2	a]2	PUNCT
ejpam-3419	180	4	!	!	PUNCT
ejpam-3419	180	5	·	·	PUNCT
ejpam-3419	180	6	definition	definition	NOUN
ejpam-3419	180	7	4	4	NUM
ejpam-3419	180	8	.	.	PUNCT
ejpam-3419	181	1	[	[	X
ejpam-3419	181	2	10	10	NUM
ejpam-3419	181	3	]	]	X
ejpam-3419	181	4	let	let	VERB
ejpam-3419	181	5	n	n	PRON
ejpam-3419	181	6	,	,	PUNCT
ejpam-3419	181	7	k	k	PROPN
ejpam-3419	181	8	and	and	CCONJ
ejpam-3419	181	9	q	q	PROPN
ejpam-3419	181	10	be	be	AUX
ejpam-3419	181	11	non	non	ADJ
ejpam-3419	181	12	-	-	ADJ
ejpam-3419	181	13	negative	negative	ADJ
ejpam-3419	181	14	integers	integer	NOUN
ejpam-3419	181	15	such	such	ADJ
ejpam-3419	181	16	that	that	SCONJ
ejpam-3419	181	17	k	k	PROPN
ejpam-3419	181	18	≤	≤	PROPN
ejpam-3419	181	19	n.	n.	NOUN
ejpam-3419	181	20	then	then	ADV
ejpam-3419	181	21	,	,	PUNCT
ejpam-3419	181	22	[	[	PUNCT
ejpam-3419	181	23	n	n	X
ejpam-3419	181	24	k	k	NOUN
ejpam-3419	181	25	]	]	X
ejpam-3419	181	26	q	q	X
ejpam-3419	182	1	=	=	PUNCT
ejpam-3419	182	2	[	[	X
ejpam-3419	182	3	n]q	n]q	X
ejpam-3419	182	4	!	!	PUNCT
ejpam-3419	183	1	[	[	X
ejpam-3419	183	2	k]q![n−	k]q![n−	ADJ
ejpam-3419	183	3	k]q	k]q	PROPN
ejpam-3419	183	4	!	!	PUNCT
ejpam-3419	183	5	·	·	PUNCT
ejpam-3419	184	1	here	here	ADV
ejpam-3419	184	2	,	,	PUNCT
ejpam-3419	184	3	[	[	X
ejpam-3419	184	4	0]q	0]q	NOUN
ejpam-3419	184	5	!	!	PUNCT
ejpam-3419	185	1	=	=	NOUN
ejpam-3419	185	2	1	1	NUM
ejpam-3419	185	3	and	and	CCONJ
ejpam-3419	185	4	if	if	SCONJ
ejpam-3419	185	5	k	k	PROPN
ejpam-3419	185	6	=	=	NOUN
ejpam-3419	185	7	0	0	PUNCT
ejpam-3419	186	1	then	then	ADV
ejpam-3419	186	2	the	the	DET
ejpam-3419	186	3	q	q	PUNCT
ejpam-3419	186	4	binomial	binomial	ADJ
ejpam-3419	186	5	coefficient	coefficient	NOUN
ejpam-3419	186	6	is	be	AUX
ejpam-3419	186	7	equal	equal	ADJ
ejpam-3419	186	8	to	to	ADP
ejpam-3419	186	9	1	1	NUM
ejpam-3419	186	10	.	.	PUNCT
ejpam-3419	187	1	also	also	ADV
ejpam-3419	187	2	we	we	PRON
ejpam-3419	187	3	have	have	VERB
ejpam-3419	187	4	an	an	DET
ejpam-3419	187	5	algebraic	algebraic	ADJ
ejpam-3419	187	6	expression	expression	NOUN
ejpam-3419	187	7	of	of	ADP
ejpam-3419	187	8	gaussian	gaussian	ADJ
ejpam-3419	187	9	coefficients	coefficient	NOUN
ejpam-3419	187	10	as	as	SCONJ
ejpam-3419	187	11	follows	follow	VERB
ejpam-3419	187	12	;	;	PUNCT
ejpam-3419	187	13	[	[	PUNCT
ejpam-3419	187	14	n	n	X
ejpam-3419	187	15	k1	k1	NOUN
ejpam-3419	187	16	,	,	PUNCT
ejpam-3419	187	17	k2	k2	NOUN
ejpam-3419	187	18	,	,	PUNCT
ejpam-3419	187	19	.	.	PUNCT
ejpam-3419	187	20	.	.	PUNCT
ejpam-3419	188	1	.	.	PUNCT
ejpam-3419	189	1	,	,	PUNCT
ejpam-3419	189	2	km	km	NOUN
ejpam-3419	189	3	]	]	PUNCT
ejpam-3419	189	4	2	2	NUM
ejpam-3419	189	5	=	=	SYM
ejpam-3419	189	6	[	[	PUNCT
ejpam-3419	189	7	n	n	CCONJ
ejpam-3419	189	8	k1	k1	X
ejpam-3419	189	9	]	]	PUNCT
ejpam-3419	189	10	2	2	NUM
ejpam-3419	189	11	·	·	PUNCT
ejpam-3419	189	12	[	[	PUNCT
ejpam-3419	189	13	n−	n−	NOUN
ejpam-3419	189	14	k1	k1	PROPN
ejpam-3419	189	15	k2	k2	PROPN
ejpam-3419	189	16	]	]	PUNCT
ejpam-3419	189	17	2	2	NUM
ejpam-3419	189	18	·	·	PUNCT
ejpam-3419	189	19	·	·	PUNCT
ejpam-3419	189	20	·	·	PUNCT
ejpam-3419	190	1	[	[	PUNCT
ejpam-3419	190	2	n−	n−	NOUN
ejpam-3419	190	3	∑m−1	∑m−1	NOUN
ejpam-3419	190	4	i=1	i=1	ADP
ejpam-3419	190	5	km	km	X
ejpam-3419	190	6	]	]	PUNCT
ejpam-3419	190	7	2	2	NUM
ejpam-3419	190	8	·	·	PUNCT
ejpam-3419	190	9	theorem	theorem	VERB
ejpam-3419	190	10	1	1	NUM
ejpam-3419	190	11	.	.	PUNCT
ejpam-3419	191	1	the	the	DET
ejpam-3419	191	2	number	number	NOUN
ejpam-3419	191	3	of	of	ADP
ejpam-3419	191	4	distinct	distinct	ADJ
ejpam-3419	191	5	z2z4z8	z2z4z8	NUM
ejpam-3419	191	6	-	-	PUNCT
ejpam-3419	191	7	additive	additive	ADJ
ejpam-3419	191	8	codes	code	NOUN
ejpam-3419	191	9	of	of	ADP
ejpam-3419	191	10	type	type	NOUN
ejpam-3419	191	11	(	(	PUNCT
ejpam-3419	191	12	α	α	NOUN
ejpam-3419	191	13	,	,	PUNCT
ejpam-3419	191	14	β	β	X
ejpam-3419	191	15	,	,	PUNCT
ejpam-3419	191	16	θ	θ	PROPN
ejpam-3419	191	17	;	;	PUNCT
ejpam-3419	191	18	k0	k0	PROPN
ejpam-3419	191	19	,	,	PUNCT
ejpam-3419	191	20	k1	k1	PROPN
ejpam-3419	191	21	,	,	PUNCT
ejpam-3419	191	22	k2	k2	NOUN
ejpam-3419	191	23	,	,	PUNCT
ejpam-3419	191	24	k3	k3	PROPN
ejpam-3419	191	25	,	,	PUNCT
ejpam-3419	191	26	k4	k4	PROPN
ejpam-3419	191	27	,	,	PUNCT
ejpam-3419	191	28	k5	k5	PROPN
ejpam-3419	191	29	)	)	PUNCT
ejpam-3419	191	30	is	be	AUX
ejpam-3419	191	31	n2×4×8	n2×4×8	NOUN
ejpam-3419	191	32	=	=	SYM
ejpam-3419	191	33	2δ	2δ	NUM
ejpam-3419	191	34	[	[	PUNCT
ejpam-3419	191	35	α	α	X
ejpam-3419	191	36	k0	k0	PROPN
ejpam-3419	191	37	]	]	PUNCT
ejpam-3419	191	38	2	2	NUM
ejpam-3419	191	39	[	[	PUNCT
ejpam-3419	191	40	β	β	X
ejpam-3419	191	41	k1	k1	PROPN
ejpam-3419	191	42	,	,	PUNCT
ejpam-3419	191	43	k2	k2	NOUN
ejpam-3419	191	44	]	]	PUNCT
ejpam-3419	191	45	2	2	NUM
ejpam-3419	191	46	[	[	PUNCT
ejpam-3419	191	47	θ	θ	X
ejpam-3419	191	48	k3	k3	PROPN
ejpam-3419	191	49	,	,	PUNCT
ejpam-3419	191	50	k4	k4	PROPN
ejpam-3419	191	51	,	,	PUNCT
ejpam-3419	191	52	k5	k5	PROPN
ejpam-3419	191	53	]	]	PUNCT
ejpam-3419	191	54	2	2	NUM
ejpam-3419	191	55	where	where	SCONJ
ejpam-3419	191	56	,	,	PUNCT
ejpam-3419	191	57	δ	δ	PROPN
ejpam-3419	191	58	=	=	PROPN
ejpam-3419	191	59	k0	k0	PROPN
ejpam-3419	192	1	[	[	X
ejpam-3419	192	2	(	(	PUNCT
ejpam-3419	192	3	β	β	X
ejpam-3419	192	4	−	−	NOUN
ejpam-3419	192	5	s	s	PART
ejpam-3419	192	6	)	)	PUNCT
ejpam-3419	192	7	+	+	CCONJ
ejpam-3419	192	8	(	(	PUNCT
ejpam-3419	192	9	θ	θ	PROPN
ejpam-3419	192	10	−	−	PROPN
ejpam-3419	192	11	t	t	PROPN
ejpam-3419	192	12	)	)	PUNCT
ejpam-3419	192	13	]	]	PUNCT
ejpam-3419	193	1	+	+	PUNCT
ejpam-3419	193	2	k1	k1	NOUN
ejpam-3419	193	3	[	[	X
ejpam-3419	193	4	(	(	PUNCT
ejpam-3419	193	5	α−	α−	ADP
ejpam-3419	193	6	k0	k0	PROPN
ejpam-3419	193	7	)	)	PUNCT
ejpam-3419	193	8	+	+	CCONJ
ejpam-3419	193	9	(	(	PUNCT
ejpam-3419	193	10	β	β	X
ejpam-3419	193	11	−	−	NOUN
ejpam-3419	193	12	s	s	PART
ejpam-3419	193	13	)	)	PUNCT
ejpam-3419	193	14	+	+	CCONJ
ejpam-3419	193	15	2	2	NUM
ejpam-3419	193	16	(	(	PUNCT
ejpam-3419	193	17	θ	θ	PROPN
ejpam-3419	193	18	−	−	PROPN
ejpam-3419	193	19	t	t	PROPN
ejpam-3419	193	20	)	)	PUNCT
ejpam-3419	193	21	+	+	CCONJ
ejpam-3419	193	22	k5	k5	PROPN
ejpam-3419	193	23	]	]	PUNCT
ejpam-3419	193	24	+	+	NOUN
ejpam-3419	193	25	k2	k2	X
ejpam-3419	193	26	[	[	X
ejpam-3419	193	27	(	(	PUNCT
ejpam-3419	193	28	θ	θ	PROPN
ejpam-3419	193	29	−	−	PROPN
ejpam-3419	193	30	t)−	t)−	PROPN
ejpam-3419	193	31	2k3	2k3	NUM
ejpam-3419	193	32	−	−	PROPN
ejpam-3419	193	33	k4	k4	NOUN
ejpam-3419	193	34	]	]	PUNCT
ejpam-3419	194	1	+	+	X
ejpam-3419	194	2	k3	k3	ADJ
ejpam-3419	194	3	[	[	X
ejpam-3419	194	4	(	(	PUNCT
ejpam-3419	194	5	α−	α−	ADP
ejpam-3419	194	6	k0	k0	PROPN
ejpam-3419	194	7	)	)	PUNCT
ejpam-3419	194	8	+	+	CCONJ
ejpam-3419	194	9	2	2	NUM
ejpam-3419	194	10	(	(	PUNCT
ejpam-3419	194	11	β	β	X
ejpam-3419	194	12	−	−	NOUN
ejpam-3419	194	13	s	s	PART
ejpam-3419	194	14	)	)	PUNCT
ejpam-3419	194	15	+	+	CCONJ
ejpam-3419	194	16	2	2	NUM
ejpam-3419	194	17	(	(	PUNCT
ejpam-3419	194	18	θ	θ	PROPN
ejpam-3419	194	19	−	−	PROPN
ejpam-3419	194	20	t	t	PROPN
ejpam-3419	194	21	)	)	PUNCT
ejpam-3419	194	22	+	+	CCONJ
ejpam-3419	194	23	k2	k2	PROPN
ejpam-3419	194	24	+	+	CCONJ
ejpam-3419	194	25	k5	k5	PROPN
ejpam-3419	194	26	]	]	PUNCT
ejpam-3419	195	1	+	+	NUM
ejpam-3419	195	2	k4	k4	ADJ
ejpam-3419	195	3	[	[	X
ejpam-3419	195	4	(	(	PUNCT
ejpam-3419	195	5	α−	α−	ADP
ejpam-3419	195	6	k0	k0	PROPN
ejpam-3419	195	7	)	)	PUNCT
ejpam-3419	195	8	+	+	CCONJ
ejpam-3419	195	9	2	2	NUM
ejpam-3419	195	10	(	(	PUNCT
ejpam-3419	195	11	β	β	X
ejpam-3419	195	12	−	−	NOUN
ejpam-3419	195	13	s	s	PART
ejpam-3419	195	14	)	)	PUNCT
ejpam-3419	195	15	+	+	CCONJ
ejpam-3419	195	16	(	(	PUNCT
ejpam-3419	195	17	θ	θ	PROPN
ejpam-3419	195	18	−	−	PROPN
ejpam-3419	195	19	t	t	PROPN
ejpam-3419	195	20	)	)	PUNCT
ejpam-3419	195	21	+	+	X
ejpam-3419	195	22	k2	k2	X
ejpam-3419	195	23	]	]	X
ejpam-3419	195	24	s	s	PART
ejpam-3419	195	25	=	=	X
ejpam-3419	195	26	k1	k1	PROPN
ejpam-3419	195	27	+	+	CCONJ
ejpam-3419	195	28	k2	k2	PROPN
ejpam-3419	195	29	and	and	CCONJ
ejpam-3419	195	30	t	t	NOUN
ejpam-3419	195	31	=	=	PUNCT
ejpam-3419	195	32	k3	k3	VERB
ejpam-3419	195	33	+	+	CCONJ
ejpam-3419	195	34	k4	k4	ADJ
ejpam-3419	195	35	+	+	CCONJ
ejpam-3419	195	36	k5	k5	PROPN
ejpam-3419	195	37	.	.	PUNCT
ejpam-3419	196	1	proof	proof	NOUN
ejpam-3419	196	2	.	.	PUNCT
ejpam-3419	197	1	in	in	ADP
ejpam-3419	197	2	order	order	NOUN
ejpam-3419	197	3	to	to	PART
ejpam-3419	197	4	prove	prove	VERB
ejpam-3419	197	5	this	this	DET
ejpam-3419	197	6	theorem	theorem	NOUN
ejpam-3419	197	7	we	we	PRON
ejpam-3419	197	8	count	count	VERB
ejpam-3419	197	9	ordered	order	VERB
ejpam-3419	197	10	generators	generator	NOUN
ejpam-3419	197	11	for	for	ADP
ejpam-3419	197	12	the	the	DET
ejpam-3419	197	13	code	code	NOUN
ejpam-3419	197	14	of	of	ADP
ejpam-3419	197	15	the	the	DET
ejpam-3419	197	16	type	type	NOUN
ejpam-3419	197	17	(	(	PUNCT
ejpam-3419	197	18	α	α	NOUN
ejpam-3419	197	19	,	,	PUNCT
ejpam-3419	197	20	β	β	X
ejpam-3419	197	21	,	,	PUNCT
ejpam-3419	197	22	θ	θ	PROPN
ejpam-3419	197	23	;	;	PUNCT
ejpam-3419	197	24	k0	k0	PROPN
ejpam-3419	197	25	,	,	PUNCT
ejpam-3419	197	26	k1	k1	PROPN
ejpam-3419	197	27	,	,	PUNCT
ejpam-3419	197	28	k2	k2	NOUN
ejpam-3419	197	29	,	,	PUNCT
ejpam-3419	197	30	k3	k3	PROPN
ejpam-3419	197	31	,	,	PUNCT
ejpam-3419	197	32	k4	k4	PROPN
ejpam-3419	197	33	,	,	PUNCT
ejpam-3419	197	34	k5	k5	PROPN
ejpam-3419	197	35	)	)	PUNCT
ejpam-3419	197	36	.	.	PUNCT
ejpam-3419	198	1	firstly	firstly	ADV
ejpam-3419	198	2	,	,	PUNCT
ejpam-3419	198	3	we	we	PRON
ejpam-3419	198	4	count	count	VERB
ejpam-3419	198	5	the	the	DET
ejpam-3419	198	6	ordered	order	VERB
ejpam-3419	198	7	generators	generator	NOUN
ejpam-3419	198	8	by	by	ADP
ejpam-3419	198	9	choosing	choose	VERB
ejpam-3419	198	10	them	they	PRON
ejpam-3419	198	11	from	from	ADP
ejpam-3419	198	12	the	the	DET
ejpam-3419	198	13	all	all	DET
ejpam-3419	198	14	space	space	NOUN
ejpam-3419	198	15	zα2	zα2	NOUN
ejpam-3419	198	16	×zβ4	×zβ4	PUNCT
ejpam-3419	198	17	×zθ8	×zθ8	X
ejpam-3419	198	18	which	which	PRON
ejpam-3419	198	19	gives	give	VERB
ejpam-3419	198	20	say	say	VERB
ejpam-3419	198	21	a.	a.	NOUN
ejpam-3419	198	22	let	let	VERB
ejpam-3419	198	23	the	the	DET
ejpam-3419	198	24	number	number	NOUN
ejpam-3419	198	25	of	of	ADP
ejpam-3419	198	26	codes	code	NOUN
ejpam-3419	198	27	of	of	ADP
ejpam-3419	198	28	type	type	NOUN
ejpam-3419	198	29	(	(	PUNCT
ejpam-3419	198	30	k0	k0	PROPN
ejpam-3419	198	31	,	,	PUNCT
ejpam-3419	198	32	k1	k1	PROPN
ejpam-3419	198	33	,	,	PUNCT
ejpam-3419	198	34	k2	k2	NOUN
ejpam-3419	198	35	,	,	PUNCT
ejpam-3419	198	36	k3	k3	PROPN
ejpam-3419	198	37	,	,	PUNCT
ejpam-3419	198	38	k4	k4	PROPN
ejpam-3419	198	39	,	,	PUNCT
ejpam-3419	198	40	k5	k5	PROPN
ejpam-3419	198	41	)	)	PUNCT
ejpam-3419	198	42	be	be	VERB
ejpam-3419	198	43	n2×4×8	n2×4×8	PROPN
ejpam-3419	198	44	.	.	PUNCT
ejpam-3419	199	1	secondly	secondly	ADV
ejpam-3419	199	2	,	,	PUNCT
ejpam-3419	199	3	we	we	PRON
ejpam-3419	199	4	choose	choose	VERB
ejpam-3419	199	5	the	the	DET
ejpam-3419	199	6	ordered	order	VERB
ejpam-3419	199	7	generators	generator	NOUN
ejpam-3419	199	8	from	from	ADP
ejpam-3419	199	9	these	these	DET
ejpam-3419	199	10	codes	code	NOUN
ejpam-3419	199	11	which	which	PRON
ejpam-3419	199	12	gives	give	VERB
ejpam-3419	199	13	say	say	INTJ
ejpam-3419	199	14	b.	b.	PROPN
ejpam-3419	200	1	so	so	ADV
ejpam-3419	200	2	,	,	PUNCT
ejpam-3419	200	3	we	we	PRON
ejpam-3419	200	4	have	have	VERB
ejpam-3419	200	5	the	the	DET
ejpam-3419	200	6	following	follow	VERB
ejpam-3419	200	7	equation	equation	NOUN
ejpam-3419	200	8	n2×4×8	n2×4×8	ADV
ejpam-3419	200	9	=	=	PUNCT
ejpam-3419	200	10	a	a	DET
ejpam-3419	200	11	b	b	PROPN
ejpam-3419	200	12	·	·	PUNCT
ejpam-3419	200	13	b.	b.	PROPN
ejpam-3419	200	14	çalışkan	çalışkan	PROPN
ejpam-3419	200	15	,	,	PUNCT
ejpam-3419	200	16	k.	k.	PROPN
ejpam-3419	200	17	balıkçı	balıkçı	PROPN
ejpam-3419	200	18	/	/	SYM
ejpam-3419	200	19	eur	eur	PROPN
ejpam-3419	200	20	.	.	PUNCT
ejpam-3419	201	1	j.	j.	PROPN
ejpam-3419	201	2	pure	pure	PROPN
ejpam-3419	201	3	appl	appl	PROPN
ejpam-3419	201	4	.	.	PROPN
ejpam-3419	201	5	math	math	PROPN
ejpam-3419	201	6	,	,	PUNCT
ejpam-3419	201	7	12	12	NUM
ejpam-3419	201	8	(	(	PUNCT
ejpam-3419	201	9	2	2	NUM
ejpam-3419	201	10	)	)	PUNCT
ejpam-3419	201	11	(	(	PUNCT
ejpam-3419	201	12	2019	2019	NUM
ejpam-3419	201	13	)	)	PUNCT
ejpam-3419	201	14	,	,	PUNCT
ejpam-3419	201	15	668	668	NUM
ejpam-3419	201	16	-	-	SYM
ejpam-3419	201	17	679	679	NUM
ejpam-3419	201	18	675	675	NUM
ejpam-3419	201	19	note	note	NOUN
ejpam-3419	201	20	that	that	SCONJ
ejpam-3419	201	21	,	,	PUNCT
ejpam-3419	201	22	lemma	lemma	PROPN
ejpam-3419	201	23	1	1	NUM
ejpam-3419	201	24	gives	give	VERB
ejpam-3419	201	25	the	the	DET
ejpam-3419	201	26	numerator	numerator	NOUN
ejpam-3419	201	27	a	a	PRON
ejpam-3419	201	28	and	and	CCONJ
ejpam-3419	201	29	lemma	lemma	PROPN
ejpam-3419	201	30	2	2	NUM
ejpam-3419	201	31	gives	give	VERB
ejpam-3419	201	32	the	the	DET
ejpam-3419	201	33	denominator	denominator	NOUN
ejpam-3419	201	34	b.	b.	PROPN
ejpam-3419	201	35	from	from	ADP
ejpam-3419	201	36	definition	definition	NOUN
ejpam-3419	201	37	3	3	NUM
ejpam-3419	201	38	,	,	PUNCT
ejpam-3419	201	39	we	we	PRON
ejpam-3419	201	40	have	have	VERB
ejpam-3419	201	41	,	,	PUNCT
ejpam-3419	201	42	n1	n1	PROPN
ejpam-3419	201	43	=	=	SYM
ejpam-3419	201	44	2	2	NUM
ejpam-3419	201	45	k0(β+θ)+	k0(β+θ)+	NOUN
ejpam-3419	201	46	(	(	PUNCT
ejpam-3419	201	47	k0	k0	PROPN
ejpam-3419	201	48	2	2	NUM
ejpam-3419	201	49	)	)	PUNCT
ejpam-3419	202	1	[	[	X
ejpam-3419	202	2	α]2	α]2	X
ejpam-3419	202	3	!	!	PUNCT
ejpam-3419	203	1	[	[	X
ejpam-3419	203	2	α−	α−	ADP
ejpam-3419	203	3	k0]2	k0]2	NOUN
ejpam-3419	203	4	!	!	PUNCT
ejpam-3419	204	1	,	,	PUNCT
ejpam-3419	204	2	n2	n2	NOUN
ejpam-3419	204	3	=	=	SYM
ejpam-3419	204	4	2	2	NUM
ejpam-3419	204	5	k1(α+β+2θ)+	k1(α+β+2θ)+	NOUN
ejpam-3419	204	6	(	(	PUNCT
ejpam-3419	204	7	k1	k1	PROPN
ejpam-3419	204	8	2	2	NUM
ejpam-3419	204	9	)	)	PUNCT
ejpam-3419	205	1	[	[	X
ejpam-3419	205	2	β]2	β]2	X
ejpam-3419	205	3	!	!	PUNCT
ejpam-3419	206	1	[	[	X
ejpam-3419	206	2	β	β	X
ejpam-3419	206	3	−	−	NOUN
ejpam-3419	206	4	k1]2	k1]2	ADJ
ejpam-3419	206	5	!	!	PUNCT
ejpam-3419	207	1	,	,	PUNCT
ejpam-3419	207	2	n3	n3	NOUN
ejpam-3419	207	3	=	=	NOUN
ejpam-3419	207	4	2	2	PROPN
ejpam-3419	207	5	k2(θ+k1)+	k2(θ+k1)+	PROPN
ejpam-3419	207	6	(	(	PUNCT
ejpam-3419	207	7	k2	k2	PROPN
ejpam-3419	207	8	2	2	NUM
ejpam-3419	207	9	)	)	PUNCT
ejpam-3419	208	1	[	[	X
ejpam-3419	208	2	β	β	X
ejpam-3419	208	3	−	−	NOUN
ejpam-3419	208	4	k1]2	k1]2	ADV
ejpam-3419	208	5	!	!	PUNCT
ejpam-3419	209	1	[	[	X
ejpam-3419	209	2	β	β	X
ejpam-3419	209	3	−	−	PROPN
ejpam-3419	209	4	k1	k1	NOUN
ejpam-3419	209	5	−	−	PROPN
ejpam-3419	209	6	k2]2	k2]2	PROPN
ejpam-3419	209	7	!	!	PUNCT
ejpam-3419	209	8	,	,	PUNCT
ejpam-3419	209	9	n4	n4	PROPN
ejpam-3419	209	10	=	=	PROPN
ejpam-3419	209	11	2	2	NUM
ejpam-3419	209	12	k3(α+2β+2θ)+	k3(α+2β+2θ)+	PROPN
ejpam-3419	209	13	(	(	PUNCT
ejpam-3419	209	14	k3	k3	VERB
ejpam-3419	209	15	2	2	NUM
ejpam-3419	209	16	)	)	PUNCT
ejpam-3419	210	1	[	[	X
ejpam-3419	210	2	θ]2	θ]2	NOUN
ejpam-3419	210	3	!	!	PUNCT
ejpam-3419	211	1	[	[	X
ejpam-3419	211	2	θ	θ	X
ejpam-3419	211	3	−	−	PROPN
ejpam-3419	211	4	k3]2	k3]2	PROPN
ejpam-3419	211	5	!	!	PUNCT
ejpam-3419	211	6	,	,	PUNCT
ejpam-3419	211	7	n5	n5	PROPN
ejpam-3419	211	8	=	=	SYM
ejpam-3419	211	9	2	2	NUM
ejpam-3419	211	10	k4(α+2β+θ+k3)+	k4(α+2β+θ+k3)+	PROPN
ejpam-3419	211	11	(	(	PUNCT
ejpam-3419	211	12	k4	k4	NOUN
ejpam-3419	211	13	2	2	NUM
ejpam-3419	211	14	)	)	PUNCT
ejpam-3419	212	1	[	[	X
ejpam-3419	212	2	θ	θ	X
ejpam-3419	212	3	−	−	PROPN
ejpam-3419	212	4	k3]2	k3]2	PROPN
ejpam-3419	212	5	!	!	PUNCT
ejpam-3419	213	1	[	[	X
ejpam-3419	213	2	θ	θ	X
ejpam-3419	213	3	−	−	NOUN
ejpam-3419	213	4	k3	k3	VERB
ejpam-3419	213	5	−	−	PROPN
ejpam-3419	213	6	k4]2	k4]2	NOUN
ejpam-3419	213	7	!	!	PUNCT
ejpam-3419	214	1	,	,	PUNCT
ejpam-3419	214	2	n6	n6	PROPN
ejpam-3419	214	3	=	=	NOUN
ejpam-3419	214	4	2	2	X
ejpam-3419	214	5	k5(k3+k4)+	k5(k3+k4)+	PROPN
ejpam-3419	214	6	(	(	PUNCT
ejpam-3419	214	7	k5	k5	PROPN
ejpam-3419	214	8	2	2	PROPN
ejpam-3419	214	9	)	)	PUNCT
ejpam-3419	215	1	[	[	X
ejpam-3419	215	2	θ	θ	X
ejpam-3419	215	3	−	−	NOUN
ejpam-3419	215	4	k3	k3	VERB
ejpam-3419	215	5	−	−	PROPN
ejpam-3419	215	6	k4]2	k4]2	NOUN
ejpam-3419	215	7	!	!	PUNCT
ejpam-3419	216	1	[	[	X
ejpam-3419	216	2	θ	θ	X
ejpam-3419	216	3	−	−	NOUN
ejpam-3419	216	4	k3	k3	VERB
ejpam-3419	216	5	−	−	PROPN
ejpam-3419	216	6	k4	k4	NOUN
ejpam-3419	216	7	−	−	PROPN
ejpam-3419	216	8	k5]2	k5]2	NOUN
ejpam-3419	216	9	!	!	PUNCT
ejpam-3419	216	10	.	.	PUNCT
ejpam-3419	217	1	also	also	ADV
ejpam-3419	217	2	,	,	PUNCT
ejpam-3419	217	3	from	from	ADP
ejpam-3419	217	4	definition	definition	NOUN
ejpam-3419	217	5	3	3	NUM
ejpam-3419	217	6	,	,	PUNCT
ejpam-3419	217	7	we	we	PRON
ejpam-3419	217	8	have	have	VERB
ejpam-3419	217	9	,	,	PUNCT
ejpam-3419	217	10	d1	d1	PROPN
ejpam-3419	217	11	=	=	SYM
ejpam-3419	217	12	2	2	NUM
ejpam-3419	217	13	k0(k1+k2+k3+k4+k5)+	k0(k1+k2+k3+k4+k5)+	PROPN
ejpam-3419	217	14	(	(	PUNCT
ejpam-3419	217	15	k0	k0	PROPN
ejpam-3419	217	16	2	2	NUM
ejpam-3419	217	17	)	)	PUNCT
ejpam-3419	218	1	[	[	X
ejpam-3419	218	2	k0]2	k0]2	X
ejpam-3419	218	3	!	!	PUNCT
ejpam-3419	218	4	,	,	PUNCT
ejpam-3419	218	5	d2	d2	PROPN
ejpam-3419	218	6	=	=	SYM
ejpam-3419	218	7	2	2	NUM
ejpam-3419	218	8	k1(k0+k1+k2	k1(k0+k1+k2	NOUN
ejpam-3419	218	9	+	+	NOUN
ejpam-3419	218	10	2k3	2k3	NUM
ejpam-3419	218	11	+	+	NOUN
ejpam-3419	218	12	2k4+k5)+	2k4+k5)+	NUM
ejpam-3419	218	13	(	(	PUNCT
ejpam-3419	218	14	k1	k1	NOUN
ejpam-3419	218	15	2	2	NUM
ejpam-3419	218	16	)	)	PUNCT
ejpam-3419	219	1	[	[	X
ejpam-3419	219	2	k1]2	k1]2	X
ejpam-3419	219	3	!	!	PUNCT
ejpam-3419	219	4	,	,	PUNCT
ejpam-3419	219	5	d3	d3	PROPN
ejpam-3419	219	6	=	=	SYM
ejpam-3419	219	7	2	2	NUM
ejpam-3419	219	8	k1+k2(3k3	k1+k2(3k3	NOUN
ejpam-3419	219	9	+	+	NOUN
ejpam-3419	219	10	2k4+k5)+	2k4+k5)+	NUM
ejpam-3419	219	11	(	(	PUNCT
ejpam-3419	219	12	k2	k2	NOUN
ejpam-3419	219	13	2	2	NUM
ejpam-3419	219	14	)	)	PUNCT
ejpam-3419	220	1	[	[	X
ejpam-3419	220	2	k2]2	k2]2	X
ejpam-3419	220	3	!	!	PUNCT
ejpam-3419	220	4	,	,	PUNCT
ejpam-3419	220	5	d4	d4	PROPN
ejpam-3419	220	6	=	=	NOUN
ejpam-3419	220	7	2	2	NUM
ejpam-3419	220	8	k3(k0	k3(k0	NOUN
ejpam-3419	220	9	+	+	NOUN
ejpam-3419	220	10	2k1+k2	2k1+k2	NUM
ejpam-3419	220	11	+	+	ADJ
ejpam-3419	220	12	2k3	2k3	NUM
ejpam-3419	220	13	+	+	NOUN
ejpam-3419	220	14	2k4+k5)+	2k4+k5)+	NUM
ejpam-3419	220	15	(	(	PUNCT
ejpam-3419	220	16	k3	k3	VERB
ejpam-3419	220	17	2	2	NUM
ejpam-3419	220	18	)	)	PUNCT
ejpam-3419	221	1	[	[	X
ejpam-3419	221	2	k3]2	k3]2	X
ejpam-3419	221	3	!	!	PUNCT
ejpam-3419	221	4	,	,	PUNCT
ejpam-3419	221	5	d5	d5	NOUN
ejpam-3419	221	6	=	=	NOUN
ejpam-3419	221	7	2	2	NUM
ejpam-3419	221	8	k4(k0	k4(k0	NOUN
ejpam-3419	221	9	+	+	PROPN
ejpam-3419	221	10	2k1+k2	2k1+k2	NUM
ejpam-3419	221	11	+	+	ADJ
ejpam-3419	221	12	2k3+k4+k5)+	2k3+k4+k5)+	NUM
ejpam-3419	221	13	(	(	PUNCT
ejpam-3419	221	14	k4	k4	NOUN
ejpam-3419	221	15	2	2	NUM
ejpam-3419	221	16	)	)	PUNCT
ejpam-3419	222	1	[	[	X
ejpam-3419	222	2	k4]2	k4]2	NOUN
ejpam-3419	222	3	!	!	PUNCT
ejpam-3419	222	4	,	,	PUNCT
ejpam-3419	222	5	d6	d6	NOUN
ejpam-3419	222	6	=	=	SYM
ejpam-3419	222	7	2	2	X
ejpam-3419	222	8	k5(k3+k4)+	k5(k3+k4)+	PROPN
ejpam-3419	222	9	(	(	PUNCT
ejpam-3419	222	10	k5	k5	PROPN
ejpam-3419	222	11	2	2	PROPN
ejpam-3419	222	12	)	)	PUNCT
ejpam-3419	223	1	[	[	X
ejpam-3419	223	2	k5]2	k5]2	X
ejpam-3419	223	3	!	!	PUNCT
ejpam-3419	223	4	·	·	PUNCT
ejpam-3419	224	1	then	then	ADV
ejpam-3419	224	2	,	,	PUNCT
ejpam-3419	224	3	n2×4×8	n2×4×8	ADV
ejpam-3419	224	4	=	=	PUNCT
ejpam-3419	224	5	a	a	DET
ejpam-3419	224	6	b	b	X
ejpam-3419	224	7	=	=	SYM
ejpam-3419	224	8	∏6	∏6	PROPN
ejpam-3419	224	9	j=1nj∏6	j=1nj∏6	PROPN
ejpam-3419	224	10	j=1dj	j=1dj	X
ejpam-3419	224	11	·	·	PUNCT
ejpam-3419	225	1	so	so	ADV
ejpam-3419	225	2	,	,	PUNCT
ejpam-3419	225	3	we	we	PRON
ejpam-3419	225	4	have	have	VERB
ejpam-3419	225	5	n2×4×8	n2×4×8	NOUN
ejpam-3419	225	6	=	=	SYM
ejpam-3419	225	7	2δ	2δ	NUM
ejpam-3419	225	8	[	[	PUNCT
ejpam-3419	225	9	α	α	X
ejpam-3419	225	10	k0	k0	PROPN
ejpam-3419	225	11	]	]	PUNCT
ejpam-3419	225	12	2	2	NUM
ejpam-3419	225	13	[	[	PUNCT
ejpam-3419	225	14	β	β	X
ejpam-3419	225	15	k1	k1	X
ejpam-3419	225	16	]	]	PUNCT
ejpam-3419	225	17	2	2	NUM
ejpam-3419	225	18	[	[	PUNCT
ejpam-3419	225	19	β	β	X
ejpam-3419	225	20	−	−	NOUN
ejpam-3419	225	21	k1	k1	PROPN
ejpam-3419	225	22	k2	k2	NOUN
ejpam-3419	225	23	]	]	PUNCT
ejpam-3419	225	24	2	2	NUM
ejpam-3419	225	25	[	[	PUNCT
ejpam-3419	225	26	θ	θ	NOUN
ejpam-3419	225	27	k3	k3	X
ejpam-3419	225	28	]	]	PUNCT
ejpam-3419	225	29	2	2	NUM
ejpam-3419	225	30	[	[	PUNCT
ejpam-3419	225	31	θ	θ	NOUN
ejpam-3419	225	32	−	−	NOUN
ejpam-3419	225	33	k3	k3	ADJ
ejpam-3419	225	34	k4	k4	NOUN
ejpam-3419	225	35	]	]	PUNCT
ejpam-3419	225	36	2	2	NUM
ejpam-3419	225	37	[	[	PUNCT
ejpam-3419	225	38	θ	θ	NOUN
ejpam-3419	225	39	−	−	NOUN
ejpam-3419	225	40	k3	k3	VERB
ejpam-3419	225	41	−	−	PROPN
ejpam-3419	225	42	k4	k4	PROPN
ejpam-3419	225	43	k5	k5	PROPN
ejpam-3419	225	44	]	]	PUNCT
ejpam-3419	225	45	2	2	X
ejpam-3419	225	46	.	.	PUNCT
ejpam-3419	225	47	b.	b.	PROPN
ejpam-3419	225	48	çalışkan	çalışkan	PROPN
ejpam-3419	225	49	,	,	PUNCT
ejpam-3419	225	50	k.	k.	PROPN
ejpam-3419	225	51	balıkçı	balıkçı	PROPN
ejpam-3419	225	52	/	/	SYM
ejpam-3419	225	53	eur	eur	PROPN
ejpam-3419	225	54	.	.	PUNCT
ejpam-3419	226	1	j.	j.	PROPN
ejpam-3419	226	2	pure	pure	PROPN
ejpam-3419	226	3	appl	appl	PROPN
ejpam-3419	226	4	.	.	PROPN
ejpam-3419	226	5	math	math	PROPN
ejpam-3419	226	6	,	,	PUNCT
ejpam-3419	226	7	12	12	NUM
ejpam-3419	226	8	(	(	PUNCT
ejpam-3419	226	9	2	2	NUM
ejpam-3419	226	10	)	)	PUNCT
ejpam-3419	226	11	(	(	PUNCT
ejpam-3419	226	12	2019	2019	NUM
ejpam-3419	226	13	)	)	PUNCT
ejpam-3419	226	14	,	,	PUNCT
ejpam-3419	226	15	668	668	NUM
ejpam-3419	226	16	-	-	SYM
ejpam-3419	226	17	679	679	NUM
ejpam-3419	226	18	676	676	NUM
ejpam-3419	226	19	hence	hence	ADV
ejpam-3419	226	20	the	the	DET
ejpam-3419	226	21	number	number	NOUN
ejpam-3419	226	22	of	of	ADP
ejpam-3419	226	23	distinct	distinct	ADJ
ejpam-3419	226	24	z2z4z8	z2z4z8	NUM
ejpam-3419	226	25	-	-	PUNCT
ejpam-3419	226	26	additive	additive	ADJ
ejpam-3419	226	27	codes	code	NOUN
ejpam-3419	226	28	of	of	ADP
ejpam-3419	226	29	type	type	NOUN
ejpam-3419	226	30	(	(	PUNCT
ejpam-3419	226	31	α	α	NOUN
ejpam-3419	226	32	,	,	PUNCT
ejpam-3419	226	33	β	β	X
ejpam-3419	226	34	,	,	PUNCT
ejpam-3419	226	35	θ	θ	PROPN
ejpam-3419	226	36	;	;	PUNCT
ejpam-3419	226	37	k0	k0	PROPN
ejpam-3419	226	38	,	,	PUNCT
ejpam-3419	226	39	k1	k1	PROPN
ejpam-3419	226	40	,	,	PUNCT
ejpam-3419	226	41	k2	k2	NOUN
ejpam-3419	226	42	,	,	PUNCT
ejpam-3419	226	43	k3	k3	PROPN
ejpam-3419	226	44	,	,	PUNCT
ejpam-3419	226	45	k4	k4	PROPN
ejpam-3419	226	46	,	,	PUNCT
ejpam-3419	226	47	k5	k5	PROPN
ejpam-3419	226	48	)	)	PUNCT
ejpam-3419	226	49	is	be	AUX
ejpam-3419	226	50	n2×4×8	n2×4×8	NOUN
ejpam-3419	226	51	=	=	SYM
ejpam-3419	226	52	2δ	2δ	NUM
ejpam-3419	226	53	[	[	PUNCT
ejpam-3419	226	54	α	α	X
ejpam-3419	226	55	k0	k0	PROPN
ejpam-3419	226	56	]	]	PUNCT
ejpam-3419	226	57	2	2	NUM
ejpam-3419	226	58	[	[	PUNCT
ejpam-3419	226	59	β	β	X
ejpam-3419	226	60	k1	k1	PROPN
ejpam-3419	226	61	,	,	PUNCT
ejpam-3419	226	62	k2	k2	NOUN
ejpam-3419	226	63	]	]	PUNCT
ejpam-3419	226	64	2	2	NUM
ejpam-3419	226	65	[	[	PUNCT
ejpam-3419	226	66	θ	θ	X
ejpam-3419	226	67	k3	k3	PROPN
ejpam-3419	226	68	,	,	PUNCT
ejpam-3419	226	69	k4	k4	PROPN
ejpam-3419	226	70	,	,	PUNCT
ejpam-3419	226	71	k5	k5	PROPN
ejpam-3419	226	72	]	]	PUNCT
ejpam-3419	226	73	2	2	NUM
ejpam-3419	226	74	where	where	SCONJ
ejpam-3419	226	75	,	,	PUNCT
ejpam-3419	226	76	δ	δ	PROPN
ejpam-3419	226	77	,	,	PUNCT
ejpam-3419	226	78	s	s	PART
ejpam-3419	226	79	and	and	CCONJ
ejpam-3419	226	80	t	t	PROPN
ejpam-3419	226	81	are	be	AUX
ejpam-3419	226	82	as	as	ADV
ejpam-3419	226	83	defined	define	VERB
ejpam-3419	226	84	above	above	ADP
ejpam-3419	226	85	.	.	PUNCT
ejpam-3419	226	86	example	example	NOUN
ejpam-3419	227	1	1	1	NUM
ejpam-3419	227	2	.	.	PUNCT
ejpam-3419	227	3	let	let	VERB
ejpam-3419	227	4	c	c	PRON
ejpam-3419	227	5	be	be	AUX
ejpam-3419	227	6	a	a	DET
ejpam-3419	227	7	z2z4z8	z2z4z8	NOUN
ejpam-3419	227	8	-	-	PUNCT
ejpam-3419	227	9	additive	additive	ADJ
ejpam-3419	227	10	code	code	NOUN
ejpam-3419	227	11	of	of	ADP
ejpam-3419	227	12	type	type	NOUN
ejpam-3419	227	13	(	(	PUNCT
ejpam-3419	227	14	2	2	NUM
ejpam-3419	227	15	,	,	PUNCT
ejpam-3419	227	16	1	1	NUM
ejpam-3419	227	17	,	,	PUNCT
ejpam-3419	227	18	1	1	NUM
ejpam-3419	227	19	,	,	PUNCT
ejpam-3419	227	20	1	1	NUM
ejpam-3419	227	21	,	,	PUNCT
ejpam-3419	227	22	1	1	NUM
ejpam-3419	227	23	,	,	PUNCT
ejpam-3419	227	24	0	0	NUM
ejpam-3419	227	25	,	,	PUNCT
ejpam-3419	227	26	1	1	NUM
ejpam-3419	227	27	,	,	PUNCT
ejpam-3419	227	28	0	0	NUM
ejpam-3419	227	29	,	,	PUNCT
ejpam-3419	227	30	0	0	NUM
ejpam-3419	227	31	)	)	PUNCT
ejpam-3419	227	32	,	,	PUNCT
ejpam-3419	227	33	then	then	ADV
ejpam-3419	227	34	all	all	DET
ejpam-3419	227	35	possible	possible	ADJ
ejpam-3419	227	36	generator	generator	NOUN
ejpam-3419	227	37	matrices	matrix	NOUN
ejpam-3419	227	38	are	be	AUX
ejpam-3419	227	39	12	12	NUM
ejpam-3419	227	40	matrices	matrix	NOUN
ejpam-3419	227	41	that	that	PRON
ejpam-3419	227	42	generate	generate	VERB
ejpam-3419	227	43	different	different	ADJ
ejpam-3419	227	44	codes	code	NOUN
ejpam-3419	227	45	.	.	PUNCT
ejpam-3419	228	1	here	here	ADV
ejpam-3419	228	2	α	α	X
ejpam-3419	228	3	=	=	SYM
ejpam-3419	228	4	2	2	NUM
ejpam-3419	228	5	,	,	PUNCT
ejpam-3419	228	6	β	β	X
ejpam-3419	228	7	=	=	SYM
ejpam-3419	228	8	θ	θ	X
ejpam-3419	228	9	=	=	SYM
ejpam-3419	228	10	1	1	NUM
ejpam-3419	228	11	,	,	PUNCT
ejpam-3419	228	12	k0	k0	PROPN
ejpam-3419	228	13	=	=	PROPN
ejpam-3419	228	14	k1	k1	PROPN
ejpam-3419	228	15	=	=	PUNCT
ejpam-3419	228	16	k3	k3	VERB
ejpam-3419	228	17	=	=	SYM
ejpam-3419	228	18	1	1	NUM
ejpam-3419	228	19	and	and	CCONJ
ejpam-3419	228	20	k2	k2	ADJ
ejpam-3419	228	21	=	=	SYM
ejpam-3419	228	22	k4	k4	PROPN
ejpam-3419	228	23	=	=	PROPN
ejpam-3419	228	24	k5	k5	PROPN
ejpam-3419	228	25	=	=	PROPN
ejpam-3419	228	26	0	0	PROPN
ejpam-3419	228	27	.	.	PUNCT
ejpam-3419	229	1	here	here	ADV
ejpam-3419	229	2	,	,	PUNCT
ejpam-3419	229	3	n1	n1	NOUN
ejpam-3419	229	4	,	,	PUNCT
ejpam-3419	229	5	n2	n2	NOUN
ejpam-3419	229	6	and	and	CCONJ
ejpam-3419	229	7	n4	n4	PROPN
ejpam-3419	229	8	are	be	AUX
ejpam-3419	229	9	calculated	calculate	VERB
ejpam-3419	229	10	as	as	ADP
ejpam-3419	229	11	12	12	NUM
ejpam-3419	229	12	,	,	PUNCT
ejpam-3419	229	13	32	32	NUM
ejpam-3419	229	14	and	and	CCONJ
ejpam-3419	229	15	64	64	NUM
ejpam-3419	229	16	,	,	PUNCT
ejpam-3419	229	17	respectively	respectively	ADV
ejpam-3419	229	18	.	.	PUNCT
ejpam-3419	230	1	also	also	ADV
ejpam-3419	230	2	,	,	PUNCT
ejpam-3419	230	3	d1	d1	PROPN
ejpam-3419	230	4	,	,	PUNCT
ejpam-3419	230	5	d2	d2	PROPN
ejpam-3419	230	6	and	and	CCONJ
ejpam-3419	230	7	d4	d4	PROPN
ejpam-3419	230	8	are	be	AUX
ejpam-3419	230	9	4	4	NUM
ejpam-3419	230	10	,	,	PUNCT
ejpam-3419	230	11	16	16	NUM
ejpam-3419	230	12	and	and	CCONJ
ejpam-3419	230	13	32	32	NUM
ejpam-3419	230	14	,	,	PUNCT
ejpam-3419	230	15	respectively	respectively	ADV
ejpam-3419	230	16	.	.	PUNCT
ejpam-3419	231	1	because	because	SCONJ
ejpam-3419	231	2	of	of	ADP
ejpam-3419	231	3	k2	k2	ADJ
ejpam-3419	231	4	=	=	SYM
ejpam-3419	231	5	k4	k4	PROPN
ejpam-3419	231	6	=	=	PROPN
ejpam-3419	231	7	k5	k5	PROPN
ejpam-3419	231	8	=	=	SYM
ejpam-3419	231	9	0	0	PROPN
ejpam-3419	231	10	,	,	PUNCT
ejpam-3419	231	11	n3	n3	NOUN
ejpam-3419	231	12	,	,	PUNCT
ejpam-3419	231	13	n5	n5	PROPN
ejpam-3419	231	14	,	,	PUNCT
ejpam-3419	231	15	n6	n6	PROPN
ejpam-3419	231	16	,	,	PUNCT
ejpam-3419	231	17	d3	d3	PROPN
ejpam-3419	231	18	,	,	PUNCT
ejpam-3419	231	19	d5	d5	NOUN
ejpam-3419	231	20	and	and	CCONJ
ejpam-3419	231	21	d6	d6	NOUN
ejpam-3419	231	22	do	do	AUX
ejpam-3419	231	23	not	not	PART
ejpam-3419	231	24	exist	exist	VERB
ejpam-3419	231	25	.	.	PUNCT
ejpam-3419	232	1	so	so	ADV
ejpam-3419	232	2	,	,	PUNCT
ejpam-3419	232	3	we	we	PRON
ejpam-3419	232	4	skip	skip	VERB
ejpam-3419	232	5	these	these	DET
ejpam-3419	232	6	terms	term	NOUN
ejpam-3419	232	7	,	,	PUNCT
ejpam-3419	232	8	hence	hence	ADV
ejpam-3419	232	9	n2×4×8	n2×4×8	NOUN
ejpam-3419	232	10	=	=	NOUN
ejpam-3419	232	11	n1n2n4	n1n2n4	NOUN
ejpam-3419	232	12	d1d2d4	d1d2d4	PROPN
ejpam-3419	232	13	=	=	NOUN
ejpam-3419	232	14	24576	24576	NUM
ejpam-3419	232	15	2048	2048	NUM
ejpam-3419	232	16	=	=	SYM
ejpam-3419	232	17	12	12	NUM
ejpam-3419	232	18	.	.	PUNCT
ejpam-3419	233	1	these	these	DET
ejpam-3419	233	2	12	12	NUM
ejpam-3419	233	3	generator	generator	NOUN
ejpam-3419	233	4	matrices	matrix	NOUN
ejpam-3419	233	5	can	can	AUX
ejpam-3419	233	6	be	be	AUX
ejpam-3419	233	7	obtained	obtain	VERB
ejpam-3419	233	8	as	as	ADP
ejpam-3419	233	9	follows	follow	VERB
ejpam-3419	233	10	:	:	PUNCT
ejpam-3419	233	11	•	•	NUM
ejpam-3419	233	12			NOUN
ejpam-3419	233	13	1	1	NUM
ejpam-3419	233	14	x	x	SYM
ejpam-3419	233	15	0	0	NUM
ejpam-3419	233	16	0	0	NUM
ejpam-3419	233	17	0	0	NUM
ejpam-3419	234	1	y	y	PROPN
ejpam-3419	234	2	1	1	NUM
ejpam-3419	234	3	0	0	NUM
ejpam-3419	234	4	0	0	NUM
ejpam-3419	235	1	z	z	NOUN
ejpam-3419	235	2	0	0	NUM
ejpam-3419	235	3	1	1	NUM
ejpam-3419	235	4			NOUN
ejpam-3419	235	5	here	here	ADV
ejpam-3419	235	6	,	,	PUNCT
ejpam-3419	235	7	we	we	PRON
ejpam-3419	235	8	have	have	VERB
ejpam-3419	235	9	8	8	NUM
ejpam-3419	235	10	possible	possible	ADJ
ejpam-3419	235	11	matrices	matrix	NOUN
ejpam-3419	235	12	,	,	PUNCT
ejpam-3419	235	13	•	•	ADP
ejpam-3419	235	14			NOUN
ejpam-3419	235	15	0	0	NUM
ejpam-3419	235	16	1	1	NUM
ejpam-3419	235	17	0	0	NUM
ejpam-3419	235	18	0	0	NUM
ejpam-3419	236	1	y	y	NOUN
ejpam-3419	236	2	0	0	NUM
ejpam-3419	236	3	1	1	NUM
ejpam-3419	236	4	0	0	NUM
ejpam-3419	236	5	z	z	NOUN
ejpam-3419	236	6	0	0	NUM
ejpam-3419	236	7	0	0	NUM
ejpam-3419	236	8	1	1	NUM
ejpam-3419	236	9			NOUN
ejpam-3419	236	10	here	here	ADV
ejpam-3419	236	11	,	,	PUNCT
ejpam-3419	236	12	we	we	PRON
ejpam-3419	236	13	have	have	VERB
ejpam-3419	236	14	4	4	NUM
ejpam-3419	236	15	possible	possible	ADJ
ejpam-3419	236	16	matrices	matrix	NOUN
ejpam-3419	236	17	,	,	PUNCT
ejpam-3419	236	18	where	where	SCONJ
ejpam-3419	236	19	x	x	X
ejpam-3419	236	20	,	,	PUNCT
ejpam-3419	236	21	y	y	PROPN
ejpam-3419	236	22	and	and	CCONJ
ejpam-3419	236	23	z	z	NOUN
ejpam-3419	236	24	are	be	AUX
ejpam-3419	236	25	either	either	PRON
ejpam-3419	236	26	0	0	NUM
ejpam-3419	236	27	or	or	CCONJ
ejpam-3419	236	28	1	1	NUM
ejpam-3419	236	29	.	.	PUNCT
ejpam-3419	236	30	from	from	ADP
ejpam-3419	236	31	theorem	theorem	ADJ
ejpam-3419	236	32	1	1	NUM
ejpam-3419	236	33	,	,	PUNCT
ejpam-3419	236	34	we	we	PRON
ejpam-3419	236	35	have	have	VERB
ejpam-3419	236	36	the	the	DET
ejpam-3419	236	37	following	follow	VERB
ejpam-3419	236	38	corollary	corollary	NOUN
ejpam-3419	236	39	.	.	PUNCT
ejpam-3419	237	1	corollary	corollary	ADJ
ejpam-3419	237	2	1	1	NUM
ejpam-3419	237	3	.	.	PUNCT
ejpam-3419	238	1	the	the	DET
ejpam-3419	238	2	dual	dual	ADJ
ejpam-3419	238	3	of	of	ADP
ejpam-3419	238	4	a	a	DET
ejpam-3419	238	5	z2z4z8	z2z4z8	NOUN
ejpam-3419	238	6	-	-	PUNCT
ejpam-3419	238	7	additive	additive	ADJ
ejpam-3419	238	8	code	code	NOUN
ejpam-3419	238	9	of	of	ADP
ejpam-3419	238	10	type	type	NOUN
ejpam-3419	238	11	(	(	PUNCT
ejpam-3419	238	12	α	α	NOUN
ejpam-3419	238	13	,	,	PUNCT
ejpam-3419	238	14	β	β	X
ejpam-3419	238	15	,	,	PUNCT
ejpam-3419	238	16	θ	θ	PROPN
ejpam-3419	238	17	;	;	PUNCT
ejpam-3419	238	18	k0	k0	PROPN
ejpam-3419	238	19	,	,	PUNCT
ejpam-3419	238	20	k1	k1	PROPN
ejpam-3419	238	21	,	,	PUNCT
ejpam-3419	238	22	k2	k2	NOUN
ejpam-3419	238	23	,	,	PUNCT
ejpam-3419	238	24	k3	k3	PROPN
ejpam-3419	238	25	,	,	PUNCT
ejpam-3419	238	26	k4	k4	PROPN
ejpam-3419	238	27	,	,	PUNCT
ejpam-3419	238	28	k5	k5	PROPN
ejpam-3419	238	29	)	)	PUNCT
ejpam-3419	238	30	is	be	AUX
ejpam-3419	238	31	of	of	ADP
ejpam-3419	238	32	type	type	NOUN
ejpam-3419	238	33	(	(	PUNCT
ejpam-3419	238	34	α	α	NOUN
ejpam-3419	238	35	,	,	PUNCT
ejpam-3419	238	36	β	β	X
ejpam-3419	238	37	,	,	PUNCT
ejpam-3419	238	38	θ;α−	θ;α−	PROPN
ejpam-3419	238	39	k0	k0	PROPN
ejpam-3419	238	40	,	,	PUNCT
ejpam-3419	239	1	β−	β−	PROPN
ejpam-3419	239	2	k1−	k1−	PROPN
ejpam-3419	239	3	k2	k2	PROPN
ejpam-3419	239	4	,	,	PUNCT
ejpam-3419	239	5	k2	k2	PROPN
ejpam-3419	239	6	,	,	PUNCT
ejpam-3419	239	7	θ−	θ−	PROPN
ejpam-3419	239	8	k3−	k3−	PROPN
ejpam-3419	239	9	k4−	k4−	PROPN
ejpam-3419	239	10	k5	k5	PROPN
ejpam-3419	239	11	,	,	PUNCT
ejpam-3419	239	12	k5	k5	PROPN
ejpam-3419	239	13	,	,	PUNCT
ejpam-3419	239	14	k4	k4	PROPN
ejpam-3419	239	15	)	)	PUNCT
ejpam-3419	239	16	and	and	CCONJ
ejpam-3419	239	17	the	the	DET
ejpam-3419	239	18	number	number	NOUN
ejpam-3419	239	19	of	of	ADP
ejpam-3419	239	20	generator	generator	NOUN
ejpam-3419	239	21	matrices	matrix	NOUN
ejpam-3419	239	22	of	of	ADP
ejpam-3419	239	23	this	this	DET
ejpam-3419	239	24	dual	dual	ADJ
ejpam-3419	239	25	code	code	NOUN
ejpam-3419	239	26	is	be	AUX
ejpam-3419	239	27	n2×4×8	n2×4×8	NOUN
ejpam-3419	239	28	=	=	SYM
ejpam-3419	239	29	2δ	2δ	NUM
ejpam-3419	239	30	[	[	PUNCT
ejpam-3419	239	31	α	α	NOUN
ejpam-3419	239	32	α−	α−	ADP
ejpam-3419	239	33	k0	k0	PROPN
ejpam-3419	239	34	]	]	PUNCT
ejpam-3419	239	35	2	2	NUM
ejpam-3419	239	36	[	[	PUNCT
ejpam-3419	239	37	β	β	X
ejpam-3419	239	38	β	β	X
ejpam-3419	239	39	−	−	PROPN
ejpam-3419	239	40	s	s	PROPN
ejpam-3419	239	41	,	,	PUNCT
ejpam-3419	239	42	k2	k2	ADJ
ejpam-3419	239	43	]	]	PUNCT
ejpam-3419	239	44	2	2	NUM
ejpam-3419	239	45	[	[	PUNCT
ejpam-3419	239	46	θ	θ	NOUN
ejpam-3419	239	47	θ	θ	PROPN
ejpam-3419	239	48	−	−	PROPN
ejpam-3419	239	49	t	t	PROPN
ejpam-3419	239	50	,	,	PUNCT
ejpam-3419	239	51	k5	k5	PROPN
ejpam-3419	239	52	,	,	PUNCT
ejpam-3419	239	53	k4	k4	NOUN
ejpam-3419	239	54	]	]	PUNCT
ejpam-3419	239	55	2	2	NUM
ejpam-3419	239	56	where	where	SCONJ
ejpam-3419	239	57	δ	δ	X
ejpam-3419	239	58	=	=	PRON
ejpam-3419	239	59	(	(	PUNCT
ejpam-3419	239	60	α−	α−	ADP
ejpam-3419	239	61	k0	k0	PROPN
ejpam-3419	239	62	)	)	PUNCT
ejpam-3419	239	63	(	(	PUNCT
ejpam-3419	239	64	k1	k1	NOUN
ejpam-3419	239	65	+	+	CCONJ
ejpam-3419	239	66	k3	k3	ADJ
ejpam-3419	239	67	)	)	PUNCT
ejpam-3419	240	1	+	+	CCONJ
ejpam-3419	240	2	(	(	PUNCT
ejpam-3419	240	3	β	β	X
ejpam-3419	240	4	−	−	NOUN
ejpam-3419	240	5	s	s	PART
ejpam-3419	240	6	)	)	PUNCT
ejpam-3419	240	7	(	(	PUNCT
ejpam-3419	240	8	k0	k0	PROPN
ejpam-3419	240	9	+	+	CCONJ
ejpam-3419	240	10	k1	k1	PROPN
ejpam-3419	240	11	+	+	CCONJ
ejpam-3419	240	12	2k3	2k3	NUM
ejpam-3419	240	13	+	+	CCONJ
ejpam-3419	240	14	k5	k5	PROPN
ejpam-3419	240	15	)	)	PUNCT
ejpam-3419	241	1	+	+	NOUN
ejpam-3419	241	2	k2	k2	X
ejpam-3419	241	3	(	(	PUNCT
ejpam-3419	241	4	k3	k3	VERB
ejpam-3419	241	5	−	−	PROPN
ejpam-3419	241	6	2	2	NUM
ejpam-3419	241	7	(	(	PUNCT
ejpam-3419	241	8	θ	θ	NOUN
ejpam-3419	241	9	−	−	PROPN
ejpam-3419	241	10	t)−	t)−	PROPN
ejpam-3419	241	11	k5	k5	PROPN
ejpam-3419	241	12	)	)	PUNCT
ejpam-3419	241	13	+	+	CCONJ
ejpam-3419	241	14	(	(	PUNCT
ejpam-3419	241	15	θ	θ	PROPN
ejpam-3419	241	16	−	−	PROPN
ejpam-3419	241	17	t	t	PROPN
ejpam-3419	241	18	)	)	PUNCT
ejpam-3419	241	19	(	(	PUNCT
ejpam-3419	241	20	k0	k0	PROPN
ejpam-3419	241	21	+	+	CCONJ
ejpam-3419	241	22	2k1	2k1	NUM
ejpam-3419	241	23	+	+	CCONJ
ejpam-3419	241	24	k2	k2	ADJ
ejpam-3419	241	25	+	+	CCONJ
ejpam-3419	241	26	2k3	2k3	PROPN
ejpam-3419	241	27	+	+	CCONJ
ejpam-3419	241	28	k4	k4	X
ejpam-3419	241	29	)	)	PUNCT
ejpam-3419	242	1	+	+	PROPN
ejpam-3419	242	2	k5	k5	PROPN
ejpam-3419	242	3	(	(	PUNCT
ejpam-3419	242	4	k0	k0	PROPN
ejpam-3419	242	5	+	+	CCONJ
ejpam-3419	242	6	2k1	2k1	NUM
ejpam-3419	242	7	+	+	CCONJ
ejpam-3419	242	8	k2	k2	X
ejpam-3419	242	9	+	+	CCONJ
ejpam-3419	242	10	k3	k3	ADJ
ejpam-3419	242	11	)	)	PUNCT
ejpam-3419	242	12	.	.	PUNCT
ejpam-3419	243	1	where	where	SCONJ
ejpam-3419	243	2	s	s	NOUN
ejpam-3419	243	3	=	=	SYM
ejpam-3419	243	4	k1	k1	PROPN
ejpam-3419	243	5	+	+	CCONJ
ejpam-3419	243	6	k2	k2	PROPN
ejpam-3419	243	7	and	and	CCONJ
ejpam-3419	243	8	t	t	NOUN
ejpam-3419	243	9	=	=	PUNCT
ejpam-3419	243	10	k3	k3	VERB
ejpam-3419	243	11	+	+	CCONJ
ejpam-3419	243	12	k4	k4	ADJ
ejpam-3419	243	13	+	+	CCONJ
ejpam-3419	243	14	k5	k5	PROPN
ejpam-3419	243	15	.	.	PUNCT
ejpam-3419	244	1	b.	b.	PROPN
ejpam-3419	244	2	çalışkan	çalışkan	PROPN
ejpam-3419	244	3	,	,	PUNCT
ejpam-3419	244	4	k.	k.	PROPN
ejpam-3419	244	5	balıkçı	balıkçı	PROPN
ejpam-3419	244	6	/	/	SYM
ejpam-3419	244	7	eur	eur	PROPN
ejpam-3419	244	8	.	.	PUNCT
ejpam-3419	245	1	j.	j.	PROPN
ejpam-3419	245	2	pure	pure	PROPN
ejpam-3419	245	3	appl	appl	PROPN
ejpam-3419	245	4	.	.	PROPN
ejpam-3419	245	5	math	math	PROPN
ejpam-3419	245	6	,	,	PUNCT
ejpam-3419	245	7	12	12	NUM
ejpam-3419	245	8	(	(	PUNCT
ejpam-3419	245	9	2	2	NUM
ejpam-3419	245	10	)	)	PUNCT
ejpam-3419	245	11	(	(	PUNCT
ejpam-3419	245	12	2019	2019	NUM
ejpam-3419	245	13	)	)	PUNCT
ejpam-3419	245	14	,	,	PUNCT
ejpam-3419	245	15	668	668	NUM
ejpam-3419	245	16	-	-	SYM
ejpam-3419	245	17	679	679	NUM
ejpam-3419	245	18	677	677	NUM
ejpam-3419	245	19	example	example	NOUN
ejpam-3419	245	20	2	2	NUM
ejpam-3419	245	21	.	.	PUNCT
ejpam-3419	246	1	let	let	VERB
ejpam-3419	246	2	us	we	PRON
ejpam-3419	246	3	show	show	VERB
ejpam-3419	246	4	that	that	SCONJ
ejpam-3419	246	5	for	for	ADP
ejpam-3419	246	6	the	the	DET
ejpam-3419	246	7	code	code	NOUN
ejpam-3419	246	8	in	in	ADP
ejpam-3419	246	9	the	the	DET
ejpam-3419	246	10	example	example	NOUN
ejpam-3419	246	11	1	1	NUM
ejpam-3419	246	12	,	,	PUNCT
ejpam-3419	246	13	the	the	DET
ejpam-3419	246	14	number	number	NOUN
ejpam-3419	246	15	of	of	ADP
ejpam-3419	246	16	generator	generator	NOUN
ejpam-3419	246	17	matrices	matrix	NOUN
ejpam-3419	246	18	of	of	ADP
ejpam-3419	246	19	the	the	DET
ejpam-3419	246	20	dual	dual	ADJ
ejpam-3419	246	21	code	code	NOUN
ejpam-3419	246	22	is	be	AUX
ejpam-3419	246	23	12	12	NUM
ejpam-3419	246	24	.	.	PUNCT
ejpam-3419	247	1	since	since	SCONJ
ejpam-3419	247	2	α	α	PROPN
ejpam-3419	247	3	−	−	PROPN
ejpam-3419	247	4	k0	k0	PROPN
ejpam-3419	247	5	=	=	PROPN
ejpam-3419	247	6	2	2	NUM
ejpam-3419	247	7	−	−	NUM
ejpam-3419	247	8	1	1	NUM
ejpam-3419	247	9	,	,	PUNCT
ejpam-3419	247	10	β	β	NOUN
ejpam-3419	247	11	−	−	NOUN
ejpam-3419	247	12	k1	k1	PROPN
ejpam-3419	247	13	−	−	PROPN
ejpam-3419	247	14	k2	k2	NOUN
ejpam-3419	247	15	=	=	NOUN
ejpam-3419	247	16	1	1	NUM
ejpam-3419	247	17	−	−	PROPN
ejpam-3419	247	18	1	1	NUM
ejpam-3419	247	19	−	−	NOUN
ejpam-3419	247	20	0	0	NUM
ejpam-3419	247	21	=	=	SYM
ejpam-3419	247	22	0	0	NUM
ejpam-3419	247	23	,	,	PUNCT
ejpam-3419	247	24	k2	k2	NOUN
ejpam-3419	247	25	=	=	SYM
ejpam-3419	247	26	0	0	NUM
ejpam-3419	247	27	,	,	PUNCT
ejpam-3419	247	28	θ	θ	NOUN
ejpam-3419	247	29	−	−	NOUN
ejpam-3419	247	30	k3	k3	VERB
ejpam-3419	247	31	−	−	PROPN
ejpam-3419	247	32	k4	k4	NOUN
ejpam-3419	247	33	−	−	PROPN
ejpam-3419	247	34	k5	k5	PROPN
ejpam-3419	247	35	=	=	PROPN
ejpam-3419	247	36	1−	1−	NUM
ejpam-3419	247	37	1−	1−	NUM
ejpam-3419	247	38	0−	0−	NUM
ejpam-3419	247	39	0	0	NUM
ejpam-3419	248	1	=	=	SYM
ejpam-3419	248	2	0	0	NUM
ejpam-3419	248	3	and	and	CCONJ
ejpam-3419	248	4	k5	k5	PROPN
ejpam-3419	248	5	=	=	PUNCT
ejpam-3419	248	6	k4	k4	PROPN
ejpam-3419	248	7	=	=	NOUN
ejpam-3419	248	8	0	0	NUM
ejpam-3419	248	9	;	;	PUNCT
ejpam-3419	248	10	the	the	DET
ejpam-3419	248	11	type	type	NOUN
ejpam-3419	248	12	of	of	ADP
ejpam-3419	248	13	the	the	DET
ejpam-3419	248	14	dual	dual	ADJ
ejpam-3419	248	15	code	code	NOUN
ejpam-3419	248	16	is	be	AUX
ejpam-3419	248	17	(	(	PUNCT
ejpam-3419	248	18	2	2	NUM
ejpam-3419	248	19	,	,	PUNCT
ejpam-3419	248	20	1	1	NUM
ejpam-3419	248	21	,	,	PUNCT
ejpam-3419	248	22	1	1	NUM
ejpam-3419	248	23	,	,	PUNCT
ejpam-3419	248	24	1	1	NUM
ejpam-3419	248	25	,	,	PUNCT
ejpam-3419	248	26	0	0	NUM
ejpam-3419	248	27	,	,	PUNCT
ejpam-3419	248	28	0	0	NUM
ejpam-3419	248	29	,	,	PUNCT
ejpam-3419	248	30	0	0	NUM
ejpam-3419	248	31	,	,	PUNCT
ejpam-3419	248	32	0	0	NUM
ejpam-3419	248	33	,	,	PUNCT
ejpam-3419	248	34	0	0	NUM
ejpam-3419	248	35	)	)	PUNCT
ejpam-3419	248	36	and	and	CCONJ
ejpam-3419	248	37	δ	δ	X
ejpam-3419	248	38	=	=	PUNCT
ejpam-3419	248	39	(	(	PUNCT
ejpam-3419	248	40	2−	2−	NUM
ejpam-3419	248	41	1)(1	1)(1	NUM
ejpam-3419	248	42	+	+	CCONJ
ejpam-3419	248	43	1	1	NUM
ejpam-3419	248	44	)	)	PUNCT
ejpam-3419	248	45	+	+	CCONJ
ejpam-3419	248	46	0	0	NUM
ejpam-3419	249	1	+	+	CCONJ
ejpam-3419	249	2	0	0	NUM
ejpam-3419	250	1	+	+	CCONJ
ejpam-3419	250	2	0	0	NUM
ejpam-3419	251	1	+	+	CCONJ
ejpam-3419	251	2	0	0	NUM
ejpam-3419	251	3	=	=	SYM
ejpam-3419	251	4	2	2	X
ejpam-3419	251	5	.	.	PUNCT
ejpam-3419	252	1	so	so	ADV
ejpam-3419	252	2	,	,	PUNCT
ejpam-3419	252	3	n2×4×8(2	n2×4×8(2	PROPN
ejpam-3419	252	4	,	,	PUNCT
ejpam-3419	252	5	1	1	NUM
ejpam-3419	252	6	,	,	PUNCT
ejpam-3419	252	7	1	1	NUM
ejpam-3419	252	8	,	,	PUNCT
ejpam-3419	252	9	1	1	NUM
ejpam-3419	252	10	,	,	PUNCT
ejpam-3419	252	11	0	0	NUM
ejpam-3419	252	12	,	,	PUNCT
ejpam-3419	252	13	0	0	NUM
ejpam-3419	252	14	,	,	PUNCT
ejpam-3419	252	15	0	0	NUM
ejpam-3419	252	16	,	,	PUNCT
ejpam-3419	252	17	0	0	NUM
ejpam-3419	252	18	,	,	PUNCT
ejpam-3419	252	19	0	0	NUM
ejpam-3419	252	20	)	)	PUNCT
ejpam-3419	252	21	=	=	SYM
ejpam-3419	253	1	22	22	NUM
ejpam-3419	253	2	[	[	PUNCT
ejpam-3419	253	3	2	2	NUM
ejpam-3419	253	4	2	2	NUM
ejpam-3419	253	5	]	]	SYM
ejpam-3419	253	6	2	2	NUM
ejpam-3419	253	7	[	[	PUNCT
ejpam-3419	253	8	1	1	NUM
ejpam-3419	253	9	0	0	NUM
ejpam-3419	253	10	,	,	PUNCT
ejpam-3419	253	11	0	0	NUM
ejpam-3419	253	12	]	]	SYM
ejpam-3419	253	13	2	2	NUM
ejpam-3419	253	14	[	[	PUNCT
ejpam-3419	253	15	1	1	NUM
ejpam-3419	253	16	0	0	NUM
ejpam-3419	253	17	,	,	PUNCT
ejpam-3419	253	18	0	0	NUM
ejpam-3419	253	19	,	,	PUNCT
ejpam-3419	253	20	0	0	NUM
ejpam-3419	253	21	]	]	SYM
ejpam-3419	253	22	2	2	NUM
ejpam-3419	253	23	=	=	SYM
ejpam-3419	253	24	12	12	NUM
ejpam-3419	253	25	.	.	NOUN
ejpam-3419	254	1	4	4	NUM
ejpam-3419	254	2	.	.	X
ejpam-3419	254	3	connections	connection	NOUN
ejpam-3419	254	4	to	to	ADP
ejpam-3419	254	5	z2z4	z2z4	PROPN
ejpam-3419	254	6	and	and	CCONJ
ejpam-3419	254	7	z2z8	z2z8	NOUN
ejpam-3419	254	8	-	-	PUNCT
ejpam-3419	254	9	additive	additive	ADJ
ejpam-3419	254	10	codes	code	NOUN
ejpam-3419	254	11	here	here	ADV
ejpam-3419	254	12	,	,	PUNCT
ejpam-3419	254	13	we	we	PRON
ejpam-3419	254	14	relate	relate	VERB
ejpam-3419	254	15	the	the	DET
ejpam-3419	254	16	number	number	NOUN
ejpam-3419	254	17	of	of	ADP
ejpam-3419	254	18	the	the	DET
ejpam-3419	254	19	z2z4z8	z2z4z8	NOUN
ejpam-3419	254	20	-	-	PUNCT
ejpam-3419	254	21	additive	additive	ADJ
ejpam-3419	254	22	codes	code	NOUN
ejpam-3419	254	23	with	with	ADP
ejpam-3419	254	24	the	the	DET
ejpam-3419	254	25	number	number	NOUN
ejpam-3419	254	26	of	of	ADP
ejpam-3419	254	27	additive	additive	ADJ
ejpam-3419	254	28	codes	code	NOUN
ejpam-3419	254	29	over	over	ADP
ejpam-3419	254	30	z2z4	z2z4	PROPN
ejpam-3419	254	31	and	and	CCONJ
ejpam-3419	254	32	z2z8	z2z8	PROPN
ejpam-3419	254	33	,	,	PUNCT
ejpam-3419	254	34	respectively	respectively	ADV
ejpam-3419	254	35	.	.	PUNCT
ejpam-3419	255	1	hence	hence	ADV
ejpam-3419	255	2	,	,	PUNCT
ejpam-3419	255	3	we	we	PRON
ejpam-3419	255	4	also	also	ADV
ejpam-3419	255	5	obtain	obtain	VERB
ejpam-3419	255	6	formulas	formula	NOUN
ejpam-3419	255	7	for	for	ADP
ejpam-3419	255	8	counting	count	VERB
ejpam-3419	255	9	the	the	DET
ejpam-3419	255	10	number	number	NOUN
ejpam-3419	255	11	of	of	ADP
ejpam-3419	255	12	matrices	matrix	NOUN
ejpam-3419	255	13	that	that	PRON
ejpam-3419	255	14	generate	generate	VERB
ejpam-3419	255	15	all	all	DET
ejpam-3419	255	16	these	these	DET
ejpam-3419	255	17	codes	code	NOUN
ejpam-3419	255	18	.	.	PUNCT
ejpam-3419	256	1	corollary	corollary	ADJ
ejpam-3419	256	2	2	2	NUM
ejpam-3419	256	3	.	.	PUNCT
ejpam-3419	257	1	let	let	VERB
ejpam-3419	257	2	c	c	PRON
ejpam-3419	257	3	be	be	AUX
ejpam-3419	257	4	a	a	DET
ejpam-3419	257	5	z2z4z8	z2z4z8	NOUN
ejpam-3419	257	6	-	-	PUNCT
ejpam-3419	257	7	additive	additive	ADJ
ejpam-3419	257	8	code	code	NOUN
ejpam-3419	257	9	of	of	ADP
ejpam-3419	257	10	type	type	NOUN
ejpam-3419	257	11	(	(	PUNCT
ejpam-3419	257	12	α	α	NOUN
ejpam-3419	257	13	,	,	PUNCT
ejpam-3419	257	14	β	β	X
ejpam-3419	257	15	,	,	PUNCT
ejpam-3419	257	16	θ	θ	PROPN
ejpam-3419	257	17	;	;	PUNCT
ejpam-3419	257	18	k0	k0	PROPN
ejpam-3419	257	19	,	,	PUNCT
ejpam-3419	257	20	k1	k1	PROPN
ejpam-3419	257	21	,	,	PUNCT
ejpam-3419	257	22	k2	k2	NOUN
ejpam-3419	257	23	,	,	PUNCT
ejpam-3419	257	24	k3	k3	PROPN
ejpam-3419	257	25	,	,	PUNCT
ejpam-3419	257	26	k4	k4	PROPN
ejpam-3419	257	27	,	,	PUNCT
ejpam-3419	257	28	k5	k5	PROPN
ejpam-3419	257	29	)	)	PUNCT
ejpam-3419	257	30	.	.	PUNCT
ejpam-3419	258	1	if	if	SCONJ
ejpam-3419	258	2	θ	θ	X
ejpam-3419	258	3	=	=	SYM
ejpam-3419	258	4	k3	k3	VERB
ejpam-3419	258	5	=	=	SYM
ejpam-3419	258	6	k4	k4	NOUN
ejpam-3419	258	7	=	=	PROPN
ejpam-3419	258	8	k5	k5	PROPN
ejpam-3419	258	9	=	=	SYM
ejpam-3419	258	10	0	0	PROPN
ejpam-3419	258	11	,	,	PUNCT
ejpam-3419	258	12	then	then	ADV
ejpam-3419	258	13	we	we	PRON
ejpam-3419	258	14	get	get	VERB
ejpam-3419	258	15	a	a	DET
ejpam-3419	258	16	z2z4	z2z4	ADJ
ejpam-3419	258	17	-	-	PUNCT
ejpam-3419	258	18	additive	additive	ADJ
ejpam-3419	258	19	code	code	NOUN
ejpam-3419	258	20	of	of	ADP
ejpam-3419	258	21	type	type	NOUN
ejpam-3419	258	22	(	(	PUNCT
ejpam-3419	258	23	α	α	NOUN
ejpam-3419	258	24	,	,	PUNCT
ejpam-3419	258	25	β	β	X
ejpam-3419	258	26	;	;	PUNCT
ejpam-3419	258	27	k0	k0	PROPN
ejpam-3419	258	28	,	,	PUNCT
ejpam-3419	258	29	k1	k1	PROPN
ejpam-3419	258	30	,	,	PUNCT
ejpam-3419	258	31	k2	k2	NOUN
ejpam-3419	258	32	)	)	PUNCT
ejpam-3419	258	33	.	.	PUNCT
ejpam-3419	259	1	the	the	DET
ejpam-3419	259	2	number	number	NOUN
ejpam-3419	259	3	of	of	ADP
ejpam-3419	259	4	these	these	DET
ejpam-3419	259	5	distinct	distinct	ADJ
ejpam-3419	259	6	codes	code	NOUN
ejpam-3419	259	7	is	be	AUX
ejpam-3419	259	8	as	as	SCONJ
ejpam-3419	259	9	follows	follow	VERB
ejpam-3419	259	10	n2×4×8(α	n2×4×8(α	NOUN
ejpam-3419	259	11	,	,	PUNCT
ejpam-3419	259	12	β	β	X
ejpam-3419	259	13	,	,	PUNCT
ejpam-3419	259	14	0	0	NUM
ejpam-3419	259	15	;	;	PUNCT
ejpam-3419	259	16	k0	k0	PROPN
ejpam-3419	259	17	,	,	PUNCT
ejpam-3419	259	18	k1	k1	PROPN
ejpam-3419	259	19	,	,	PUNCT
ejpam-3419	259	20	k2	k2	NOUN
ejpam-3419	259	21	,	,	PUNCT
ejpam-3419	259	22	0	0	NUM
ejpam-3419	259	23	,	,	PUNCT
ejpam-3419	259	24	0	0	NUM
ejpam-3419	259	25	,	,	PUNCT
ejpam-3419	259	26	0	0	NUM
ejpam-3419	259	27	)	)	PUNCT
ejpam-3419	259	28	=	=	SYM
ejpam-3419	259	29	2k0(β−k1−k2)+k1(α+β−k0−k1−k2	2k0(β−k1−k2)+k1(α+β−k0−k1−k2	NUM
ejpam-3419	259	30	)	)	PUNCT
ejpam-3419	259	31	[	[	PUNCT
ejpam-3419	259	32	α	α	PROPN
ejpam-3419	259	33	k0	k0	PROPN
ejpam-3419	259	34	]	]	PUNCT
ejpam-3419	259	35	2	2	NUM
ejpam-3419	259	36	[	[	PUNCT
ejpam-3419	259	37	β	β	X
ejpam-3419	259	38	k1	k1	PROPN
ejpam-3419	259	39	,	,	PUNCT
ejpam-3419	259	40	k2	k2	NOUN
ejpam-3419	259	41	]	]	PUNCT
ejpam-3419	259	42	2	2	NUM
ejpam-3419	259	43	=	=	SYM
ejpam-3419	259	44	n2×4(α	n2×4(α	PROPN
ejpam-3419	259	45	,	,	PUNCT
ejpam-3419	259	46	β	β	X
ejpam-3419	259	47	;	;	PUNCT
ejpam-3419	259	48	k0	k0	PROPN
ejpam-3419	259	49	,	,	PUNCT
ejpam-3419	259	50	k1	k1	PROPN
ejpam-3419	259	51	,	,	PUNCT
ejpam-3419	259	52	k2	k2	ADJ
ejpam-3419	259	53	)	)	PUNCT
ejpam-3419	259	54	proof	proof	NOUN
ejpam-3419	259	55	.	.	PUNCT
ejpam-3419	260	1	it	it	PRON
ejpam-3419	260	2	is	be	AUX
ejpam-3419	260	3	known	know	VERB
ejpam-3419	260	4	[	[	X
ejpam-3419	260	5	5	5	NUM
ejpam-3419	260	6	]	]	PUNCT
ejpam-3419	260	7	that	that	SCONJ
ejpam-3419	260	8	the	the	DET
ejpam-3419	260	9	generator	generator	NOUN
ejpam-3419	260	10	matrix	matrix	NOUN
ejpam-3419	260	11	for	for	ADP
ejpam-3419	260	12	a	a	DET
ejpam-3419	260	13	z2z4	z2z4	ADJ
ejpam-3419	260	14	-	-	ADJ
ejpam-3419	260	15	additive	additive	ADJ
ejpam-3419	260	16	code	code	NOUN
ejpam-3419	260	17	c	c	PROPN
ejpam-3419	260	18	of	of	ADP
ejpam-3419	260	19	type	type	NOUN
ejpam-3419	260	20	(	(	PUNCT
ejpam-3419	260	21	α	α	NOUN
ejpam-3419	260	22	,	,	PUNCT
ejpam-3419	260	23	β	β	X
ejpam-3419	260	24	;	;	PUNCT
ejpam-3419	260	25	γ	γ	X
ejpam-3419	260	26	,	,	PUNCT
ejpam-3419	260	27	δ	δ	PROPN
ejpam-3419	260	28	,	,	PUNCT
ejpam-3419	260	29	κ	κ	NOUN
ejpam-3419	260	30	)	)	PUNCT
ejpam-3419	260	31	has	have	VERB
ejpam-3419	260	32	the	the	DET
ejpam-3419	260	33	following	following	ADJ
ejpam-3419	260	34	standard	standard	NOUN
ejpam-3419	260	35	form	form	VERB
ejpam-3419	260	36	iκ	iκ	NOUN
ejpam-3419	260	37	tb	tb	ADP
ejpam-3419	260	38	2t2	2t2	NUM
ejpam-3419	260	39	0	0	NUM
ejpam-3419	260	40	0	0	NUM
ejpam-3419	260	41	0	0	NUM
ejpam-3419	260	42	0	0	NUM
ejpam-3419	260	43	2t1	2t1	NUM
ejpam-3419	260	44	2iγ−κ	2iγ−κ	NUM
ejpam-3419	260	45	0	0	NUM
ejpam-3419	260	46	0	0	NUM
ejpam-3419	261	1	sb	sb	PROPN
ejpam-3419	261	2	sq	sq	PROPN
ejpam-3419	261	3	r	r	NOUN
ejpam-3419	261	4	iδ	iδ	NOUN
ejpam-3419	261	5			PROPN
ejpam-3419	261	6	(	(	PUNCT
ejpam-3419	261	7	4	4	NUM
ejpam-3419	261	8	)	)	PUNCT
ejpam-3419	261	9	where	where	SCONJ
ejpam-3419	261	10	tb	tb	NOUN
ejpam-3419	261	11	,	,	PUNCT
ejpam-3419	261	12	sb	sb	PROPN
ejpam-3419	261	13	are	be	AUX
ejpam-3419	261	14	matrices	matrix	NOUN
ejpam-3419	261	15	over	over	ADP
ejpam-3419	261	16	z2	z2	PROPN
ejpam-3419	261	17	;	;	PUNCT
ejpam-3419	261	18	t1	t1	NOUN
ejpam-3419	261	19	,	,	PUNCT
ejpam-3419	261	20	t2	t2	NOUN
ejpam-3419	261	21	,	,	PUNCT
ejpam-3419	261	22	r	r	NOUN
ejpam-3419	261	23	are	be	AUX
ejpam-3419	261	24	matrices	matrix	NOUN
ejpam-3419	261	25	over	over	ADP
ejpam-3419	261	26	z4	z4	PROPN
ejpam-3419	261	27	with	with	ADP
ejpam-3419	261	28	all	all	DET
ejpam-3419	261	29	entries	entry	NOUN
ejpam-3419	261	30	in	in	ADP
ejpam-3419	261	31	{	{	PUNCT
ejpam-3419	261	32	0	0	NUM
ejpam-3419	261	33	,	,	PUNCT
ejpam-3419	261	34	1	1	NUM
ejpam-3419	261	35	}	}	PUNCT
ejpam-3419	261	36	∈	∈	PROPN
ejpam-3419	261	37	z4	z4	NOUN
ejpam-3419	261	38	and	and	CCONJ
ejpam-3419	261	39	sq	sq	PROPN
ejpam-3419	261	40	is	be	AUX
ejpam-3419	261	41	a	a	DET
ejpam-3419	261	42	matrix	matrix	NOUN
ejpam-3419	261	43	over	over	ADP
ejpam-3419	261	44	z4	z4	PROPN
ejpam-3419	261	45	.	.	PUNCT
ejpam-3419	262	1	also	also	ADV
ejpam-3419	262	2	,	,	PUNCT
ejpam-3419	262	3	from	from	ADP
ejpam-3419	262	4	[	[	X
ejpam-3419	262	5	13	13	NUM
ejpam-3419	262	6	]	]	PUNCT
ejpam-3419	262	7	,	,	PUNCT
ejpam-3419	262	8	we	we	PRON
ejpam-3419	262	9	know	know	VERB
ejpam-3419	262	10	that	that	SCONJ
ejpam-3419	262	11	the	the	DET
ejpam-3419	262	12	generator	generator	NOUN
ejpam-3419	262	13	matrix	matrix	NOUN
ejpam-3419	262	14	of	of	ADP
ejpam-3419	262	15	c	c	PROPN
ejpam-3419	262	16	of	of	ADP
ejpam-3419	262	17	type	type	NOUN
ejpam-3419	262	18	(	(	PUNCT
ejpam-3419	262	19	α	α	NOUN
ejpam-3419	262	20	,	,	PUNCT
ejpam-3419	262	21	β	β	X
ejpam-3419	262	22	;	;	PUNCT
ejpam-3419	262	23	k0	k0	PROPN
ejpam-3419	262	24	,	,	PUNCT
ejpam-3419	262	25	k1	k1	PROPN
ejpam-3419	262	26	,	,	PUNCT
ejpam-3419	262	27	k2	k2	NOUN
ejpam-3419	262	28	)	)	PUNCT
ejpam-3419	262	29	is	be	AUX
ejpam-3419	262	30	in	in	ADP
ejpam-3419	262	31	the	the	DET
ejpam-3419	262	32	form	form	NOUN
ejpam-3419	262	33	of	of	ADJ
ejpam-3419	262	34	ik0	ik0	VERB
ejpam-3419	262	35	a01	a01	NOUN
ejpam-3419	262	36	0	0	PUNCT
ejpam-3419	262	37	0	0	NUM
ejpam-3419	262	38	2t02	2t02	NOUN
ejpam-3419	262	39	0	0	NUM
ejpam-3419	263	1	s1	s1	PROPN
ejpam-3419	263	2	ik1	ik1	PROPN
ejpam-3419	263	3	a01	a01	NOUN
ejpam-3419	263	4	a02	a02	PROPN
ejpam-3419	263	5	0	0	PROPN
ejpam-3419	263	6	0	0	NUM
ejpam-3419	263	7	0	0	NUM
ejpam-3419	263	8	2ik2	2ik2	NUM
ejpam-3419	263	9	2a12	2a12	NUM
ejpam-3419	263	10			PROPN
ejpam-3419	263	11	(	(	PUNCT
ejpam-3419	263	12	5	5	NUM
ejpam-3419	263	13	)	)	PUNCT
ejpam-3419	263	14	which	which	PRON
ejpam-3419	263	15	is	be	AUX
ejpam-3419	263	16	permutation	permutation	NOUN
ejpam-3419	263	17	equivalent	equivalent	ADJ
ejpam-3419	263	18	to	to	ADP
ejpam-3419	263	19	a	a	DET
ejpam-3419	263	20	matrix	matrix	NOUN
ejpam-3419	263	21	of	of	ADP
ejpam-3419	263	22	the	the	DET
ejpam-3419	263	23	form	form	NOUN
ejpam-3419	263	24	(	(	PUNCT
ejpam-3419	263	25	4	4	NUM
ejpam-3419	263	26	)	)	PUNCT
ejpam-3419	263	27	.	.	PUNCT
ejpam-3419	264	1	so	so	ADV
ejpam-3419	264	2	,	,	PUNCT
ejpam-3419	264	3	from	from	ADP
ejpam-3419	264	4	the	the	DET
ejpam-3419	264	5	generator	generator	NOUN
ejpam-3419	264	6	matrices	matrix	NOUN
ejpam-3419	264	7	(	(	PUNCT
ejpam-3419	264	8	4	4	NUM
ejpam-3419	264	9	)	)	PUNCT
ejpam-3419	264	10	and	and	CCONJ
ejpam-3419	264	11	(	(	PUNCT
ejpam-3419	264	12	5	5	X
ejpam-3419	264	13	)	)	PUNCT
ejpam-3419	264	14	we	we	PRON
ejpam-3419	264	15	have	have	VERB
ejpam-3419	264	16	the	the	DET
ejpam-3419	264	17	equations	equation	NOUN
ejpam-3419	264	18	such	such	ADJ
ejpam-3419	264	19	that	that	PRON
ejpam-3419	264	20	κ	κ	PROPN
ejpam-3419	264	21	=	=	PROPN
ejpam-3419	264	22	k0	k0	PROPN
ejpam-3419	264	23	,	,	PUNCT
ejpam-3419	264	24	δ	δ	PROPN
ejpam-3419	264	25	=	=	SYM
ejpam-3419	264	26	k1	k1	PROPN
ejpam-3419	264	27	and	and	CCONJ
ejpam-3419	264	28	γ	γ	NOUN
ejpam-3419	264	29	−	−	PROPN
ejpam-3419	264	30	κ	κ	PROPN
ejpam-3419	264	31	=	=	SYM
ejpam-3419	264	32	k2	k2	PROPN
ejpam-3419	264	33	.	.	PUNCT
ejpam-3419	265	1	in	in	ADP
ejpam-3419	265	2	theorem	theorem	NOUN
ejpam-3419	265	3	1	1	NUM
ejpam-3419	265	4	,	,	PUNCT
ejpam-3419	265	5	it	it	PRON
ejpam-3419	265	6	is	be	AUX
ejpam-3419	265	7	clear	clear	ADJ
ejpam-3419	265	8	that	that	SCONJ
ejpam-3419	265	9	if	if	SCONJ
ejpam-3419	265	10	θ	θ	X
ejpam-3419	265	11	=	=	SYM
ejpam-3419	265	12	k3	k3	VERB
ejpam-3419	265	13	=	=	SYM
ejpam-3419	265	14	k4	k4	NOUN
ejpam-3419	265	15	=	=	PROPN
ejpam-3419	265	16	k5	k5	PROPN
ejpam-3419	265	17	=	=	SYM
ejpam-3419	265	18	0	0	PROPN
ejpam-3419	265	19	,	,	PUNCT
ejpam-3419	265	20	then	then	ADV
ejpam-3419	265	21	we	we	PRON
ejpam-3419	265	22	have	have	VERB
ejpam-3419	265	23	a	a	DET
ejpam-3419	265	24	z2z4z8	z2z4z8	NOUN
ejpam-3419	265	25	-	-	PUNCT
ejpam-3419	265	26	additive	additive	ADJ
ejpam-3419	265	27	code	code	NOUN
ejpam-3419	265	28	of	of	ADP
ejpam-3419	265	29	type	type	NOUN
ejpam-3419	265	30	(	(	PUNCT
ejpam-3419	265	31	α	α	NOUN
ejpam-3419	265	32	,	,	PUNCT
ejpam-3419	265	33	β	β	X
ejpam-3419	265	34	,	,	PUNCT
ejpam-3419	265	35	0	0	NUM
ejpam-3419	265	36	;	;	PUNCT
ejpam-3419	265	37	k0	k0	PROPN
ejpam-3419	265	38	,	,	PUNCT
ejpam-3419	265	39	k1	k1	PROPN
ejpam-3419	265	40	,	,	PUNCT
ejpam-3419	265	41	k2	k2	NOUN
ejpam-3419	265	42	,	,	PUNCT
ejpam-3419	265	43	0	0	NUM
ejpam-3419	265	44	,	,	PUNCT
ejpam-3419	265	45	0	0	NUM
ejpam-3419	265	46	,	,	PUNCT
ejpam-3419	265	47	0	0	NUM
ejpam-3419	265	48	)	)	PUNCT
ejpam-3419	265	49	.	.	PUNCT
ejpam-3419	266	1	also	also	ADV
ejpam-3419	266	2	,	,	PUNCT
ejpam-3419	266	3	the	the	DET
ejpam-3419	266	4	number	number	NOUN
ejpam-3419	266	5	of	of	ADP
ejpam-3419	266	6	these	these	DET
ejpam-3419	266	7	codes	code	NOUN
ejpam-3419	266	8	is	be	AUX
ejpam-3419	266	9	n2×4×8(α	n2×4×8(α	NOUN
ejpam-3419	266	10	,	,	PUNCT
ejpam-3419	266	11	β	β	X
ejpam-3419	266	12	,	,	PUNCT
ejpam-3419	266	13	0	0	NUM
ejpam-3419	266	14	;	;	PUNCT
ejpam-3419	266	15	k0	k0	PROPN
ejpam-3419	266	16	,	,	PUNCT
ejpam-3419	266	17	k1	k1	PROPN
ejpam-3419	266	18	,	,	PUNCT
ejpam-3419	266	19	k2	k2	NOUN
ejpam-3419	266	20	,	,	PUNCT
ejpam-3419	266	21	0	0	NUM
ejpam-3419	266	22	,	,	PUNCT
ejpam-3419	266	23	0	0	NUM
ejpam-3419	266	24	,	,	PUNCT
ejpam-3419	266	25	0	0	NUM
ejpam-3419	266	26	)	)	PUNCT
ejpam-3419	266	27	=	=	SYM
ejpam-3419	266	28	2k0(β−k1−k2)+k1(α+β−k0−k1−k2	2k0(β−k1−k2)+k1(α+β−k0−k1−k2	NUM
ejpam-3419	266	29	)	)	PUNCT
ejpam-3419	266	30	[	[	PUNCT
ejpam-3419	266	31	α	α	PROPN
ejpam-3419	266	32	k0	k0	PROPN
ejpam-3419	266	33	]	]	PUNCT
ejpam-3419	266	34	2	2	NUM
ejpam-3419	266	35	[	[	PUNCT
ejpam-3419	266	36	β	β	X
ejpam-3419	266	37	k1	k1	PROPN
ejpam-3419	266	38	,	,	PUNCT
ejpam-3419	266	39	k2	k2	NOUN
ejpam-3419	266	40	]	]	PUNCT
ejpam-3419	266	41	2	2	NUM
ejpam-3419	266	42	=	=	SYM
ejpam-3419	266	43	n2×4(α	n2×4(α	PROPN
ejpam-3419	266	44	,	,	PUNCT
ejpam-3419	266	45	β	β	X
ejpam-3419	266	46	;	;	PUNCT
ejpam-3419	266	47	k0	k0	PROPN
ejpam-3419	266	48	,	,	PUNCT
ejpam-3419	266	49	k1	k1	PROPN
ejpam-3419	266	50	,	,	PUNCT
ejpam-3419	266	51	k2	k2	NOUN
ejpam-3419	266	52	)	)	PUNCT
ejpam-3419	266	53	(	(	PUNCT
ejpam-3419	266	54	6	6	NUM
ejpam-3419	266	55	)	)	PUNCT
ejpam-3419	266	56	b.	b.	PROPN
ejpam-3419	266	57	çalışkan	çalışkan	PROPN
ejpam-3419	266	58	,	,	PUNCT
ejpam-3419	266	59	k.	k.	PROPN
ejpam-3419	266	60	balıkçı	balıkçı	PROPN
ejpam-3419	266	61	/	/	SYM
ejpam-3419	266	62	eur	eur	PROPN
ejpam-3419	266	63	.	.	PUNCT
ejpam-3419	267	1	j.	j.	PROPN
ejpam-3419	267	2	pure	pure	PROPN
ejpam-3419	267	3	appl	appl	PROPN
ejpam-3419	267	4	.	.	PROPN
ejpam-3419	267	5	math	math	PROPN
ejpam-3419	267	6	,	,	PUNCT
ejpam-3419	267	7	12	12	NUM
ejpam-3419	267	8	(	(	PUNCT
ejpam-3419	267	9	2	2	NUM
ejpam-3419	267	10	)	)	PUNCT
ejpam-3419	267	11	(	(	PUNCT
ejpam-3419	267	12	2019	2019	NUM
ejpam-3419	267	13	)	)	PUNCT
ejpam-3419	267	14	,	,	PUNCT
ejpam-3419	267	15	668	668	NUM
ejpam-3419	267	16	-	-	SYM
ejpam-3419	267	17	679	679	NUM
ejpam-3419	267	18	678	678	NUM
ejpam-3419	267	19	in	in	ADP
ejpam-3419	267	20	(	(	PUNCT
ejpam-3419	267	21	6	6	NUM
ejpam-3419	267	22	)	)	PUNCT
ejpam-3419	267	23	,	,	PUNCT
ejpam-3419	267	24	if	if	SCONJ
ejpam-3419	267	25	we	we	PRON
ejpam-3419	267	26	replace	replace	VERB
ejpam-3419	267	27	κ	κ	NOUN
ejpam-3419	267	28	=	=	PROPN
ejpam-3419	267	29	k0	k0	PROPN
ejpam-3419	267	30	,	,	PUNCT
ejpam-3419	267	31	δ	δ	PROPN
ejpam-3419	267	32	=	=	SYM
ejpam-3419	267	33	k1	k1	PROPN
ejpam-3419	267	34	and	and	CCONJ
ejpam-3419	267	35	γ	γ	NOUN
ejpam-3419	267	36	−	−	PROPN
ejpam-3419	267	37	κ	κ	PROPN
ejpam-3419	267	38	=	=	SYM
ejpam-3419	267	39	k2	k2	PROPN
ejpam-3419	267	40	,	,	PUNCT
ejpam-3419	267	41	then	then	ADV
ejpam-3419	267	42	it	it	PRON
ejpam-3419	267	43	is	be	AUX
ejpam-3419	267	44	obtained	obtain	VERB
ejpam-3419	267	45	the	the	DET
ejpam-3419	267	46	number	number	NOUN
ejpam-3419	267	47	of	of	ADP
ejpam-3419	267	48	z2z4	z2z4	NOUN
ejpam-3419	267	49	-	-	ADJ
ejpam-3419	267	50	additive	additive	ADJ
ejpam-3419	267	51	codes	code	NOUN
ejpam-3419	267	52	c	c	PROPN
ejpam-3419	267	53	of	of	ADP
ejpam-3419	267	54	type	type	NOUN
ejpam-3419	267	55	(	(	PUNCT
ejpam-3419	267	56	α	α	NOUN
ejpam-3419	267	57	,	,	PUNCT
ejpam-3419	267	58	β	β	X
ejpam-3419	267	59	;	;	PUNCT
ejpam-3419	267	60	γ	γ	X
ejpam-3419	267	61	,	,	PUNCT
ejpam-3419	267	62	δ	δ	PROPN
ejpam-3419	267	63	,	,	PUNCT
ejpam-3419	267	64	κ	κ	NOUN
ejpam-3419	267	65	)	)	PUNCT
ejpam-3419	267	66	as	as	ADP
ejpam-3419	267	67	in	in	ADP
ejpam-3419	267	68	[	[	X
ejpam-3419	267	69	8	8	NUM
ejpam-3419	267	70	]	]	PUNCT
ejpam-3419	267	71	,	,	PUNCT
ejpam-3419	267	72	(	(	PUNCT
ejpam-3419	267	73	theorem	theorem	VERB
ejpam-3419	267	74	3.3	3.3	NUM
ejpam-3419	267	75	)	)	PUNCT
ejpam-3419	267	76	.	.	PUNCT
ejpam-3419	268	1	corollary	corollary	ADJ
ejpam-3419	268	2	3	3	X
ejpam-3419	268	3	.	.	PUNCT
ejpam-3419	269	1	let	let	VERB
ejpam-3419	269	2	c	c	PRON
ejpam-3419	269	3	be	be	AUX
ejpam-3419	269	4	a	a	DET
ejpam-3419	269	5	z2z4z8	z2z4z8	NOUN
ejpam-3419	269	6	-	-	PUNCT
ejpam-3419	269	7	additive	additive	ADJ
ejpam-3419	269	8	code	code	NOUN
ejpam-3419	269	9	of	of	ADP
ejpam-3419	269	10	type	type	NOUN
ejpam-3419	269	11	(	(	PUNCT
ejpam-3419	269	12	α	α	NOUN
ejpam-3419	269	13	,	,	PUNCT
ejpam-3419	269	14	β	β	X
ejpam-3419	269	15	,	,	PUNCT
ejpam-3419	269	16	θ	θ	PROPN
ejpam-3419	269	17	;	;	PUNCT
ejpam-3419	269	18	k0	k0	PROPN
ejpam-3419	269	19	,	,	PUNCT
ejpam-3419	269	20	k1	k1	PROPN
ejpam-3419	269	21	,	,	PUNCT
ejpam-3419	269	22	k2	k2	NOUN
ejpam-3419	269	23	,	,	PUNCT
ejpam-3419	269	24	k3	k3	PROPN
ejpam-3419	269	25	,	,	PUNCT
ejpam-3419	269	26	k4	k4	PROPN
ejpam-3419	269	27	,	,	PUNCT
ejpam-3419	269	28	k5	k5	PROPN
ejpam-3419	269	29	)	)	PUNCT
ejpam-3419	269	30	.	.	PUNCT
ejpam-3419	270	1	if	if	SCONJ
ejpam-3419	270	2	β	β	NOUN
ejpam-3419	270	3	=	=	SYM
ejpam-3419	270	4	k1	k1	NOUN
ejpam-3419	270	5	=	=	SYM
ejpam-3419	270	6	k2	k2	PROPN
ejpam-3419	270	7	=	=	SYM
ejpam-3419	270	8	0	0	PROPN
ejpam-3419	270	9	,	,	PUNCT
ejpam-3419	270	10	then	then	ADV
ejpam-3419	270	11	we	we	PRON
ejpam-3419	270	12	get	get	VERB
ejpam-3419	270	13	a	a	DET
ejpam-3419	270	14	z2z8	z2z8	ADJ
ejpam-3419	270	15	-	-	PUNCT
ejpam-3419	270	16	additive	additive	ADJ
ejpam-3419	270	17	code	code	NOUN
ejpam-3419	270	18	of	of	ADP
ejpam-3419	270	19	type	type	NOUN
ejpam-3419	270	20	(	(	PUNCT
ejpam-3419	270	21	α	α	NOUN
ejpam-3419	270	22	,	,	PUNCT
ejpam-3419	270	23	θ	θ	PROPN
ejpam-3419	270	24	;	;	PUNCT
ejpam-3419	270	25	k0	k0	PROPN
ejpam-3419	270	26	,	,	PUNCT
ejpam-3419	270	27	k3	k3	PROPN
ejpam-3419	270	28	,	,	PUNCT
ejpam-3419	270	29	k4	k4	PROPN
ejpam-3419	270	30	,	,	PUNCT
ejpam-3419	270	31	k5	k5	PROPN
ejpam-3419	270	32	)	)	PUNCT
ejpam-3419	270	33	.	.	PUNCT
ejpam-3419	271	1	the	the	DET
ejpam-3419	271	2	number	number	NOUN
ejpam-3419	271	3	of	of	ADP
ejpam-3419	271	4	these	these	DET
ejpam-3419	271	5	distinct	distinct	ADJ
ejpam-3419	271	6	codes	code	NOUN
ejpam-3419	271	7	is	be	AUX
ejpam-3419	271	8	as	as	SCONJ
ejpam-3419	271	9	follows	follow	VERB
ejpam-3419	271	10	n2×4×8(α	n2×4×8(α	NOUN
ejpam-3419	271	11	,	,	PUNCT
ejpam-3419	271	12	0	0	NUM
ejpam-3419	271	13	,	,	PUNCT
ejpam-3419	271	14	θ	θ	PROPN
ejpam-3419	271	15	;	;	PUNCT
ejpam-3419	271	16	k0	k0	PROPN
ejpam-3419	271	17	,	,	PUNCT
ejpam-3419	271	18	0	0	NUM
ejpam-3419	271	19	,	,	PUNCT
ejpam-3419	271	20	0	0	NUM
ejpam-3419	271	21	,	,	PUNCT
ejpam-3419	271	22	k3	k3	PROPN
ejpam-3419	271	23	,	,	PUNCT
ejpam-3419	271	24	k4	k4	PROPN
ejpam-3419	271	25	,	,	PUNCT
ejpam-3419	271	26	k5	k5	PROPN
ejpam-3419	271	27	)	)	PUNCT
ejpam-3419	271	28	=	=	PUNCT
ejpam-3419	272	1	2k0(θ−k3−k4−k5)+k3[(α−k0)+2(θ−k3−k4−k5)+k5	2k0(θ−k3−k4−k5)+k3[(α−k0)+2(θ−k3−k4−k5)+k5	NUM
ejpam-3419	272	2	]	]	X
ejpam-3419	272	3	[	[	PUNCT
ejpam-3419	272	4	α	α	X
ejpam-3419	272	5	k0	k0	PROPN
ejpam-3419	272	6	]	]	PUNCT
ejpam-3419	272	7	2	2	NUM
ejpam-3419	272	8	[	[	PUNCT
ejpam-3419	272	9	θ	θ	X
ejpam-3419	272	10	k3	k3	PROPN
ejpam-3419	272	11	,	,	PUNCT
ejpam-3419	272	12	k4	k4	PROPN
ejpam-3419	272	13	,	,	PUNCT
ejpam-3419	272	14	k5	k5	PROPN
ejpam-3419	272	15	]	]	PUNCT
ejpam-3419	272	16	2	2	NUM
ejpam-3419	272	17	=	=	SYM
ejpam-3419	272	18	n2×8(α	n2×8(α	PROPN
ejpam-3419	272	19	,	,	PUNCT
ejpam-3419	272	20	θ	θ	PROPN
ejpam-3419	272	21	;	;	PUNCT
ejpam-3419	272	22	k0	k0	PROPN
ejpam-3419	272	23	,	,	PUNCT
ejpam-3419	272	24	k3	k3	PROPN
ejpam-3419	272	25	,	,	PUNCT
ejpam-3419	272	26	k4	k4	PROPN
ejpam-3419	272	27	,	,	PUNCT
ejpam-3419	272	28	k5	k5	PROPN
ejpam-3419	272	29	)	)	PUNCT
ejpam-3419	272	30	.	.	PUNCT
ejpam-3419	273	1	proof	proof	NOUN
ejpam-3419	273	2	.	.	PUNCT
ejpam-3419	274	1	in	in	ADP
ejpam-3419	274	2	theorem	theorem	NOUN
ejpam-3419	274	3	1	1	NUM
ejpam-3419	274	4	,	,	PUNCT
ejpam-3419	274	5	it	it	PRON
ejpam-3419	274	6	is	be	AUX
ejpam-3419	274	7	clear	clear	ADJ
ejpam-3419	274	8	that	that	SCONJ
ejpam-3419	274	9	if	if	SCONJ
ejpam-3419	274	10	β	β	X
ejpam-3419	274	11	=	=	SYM
ejpam-3419	274	12	k1	k1	NOUN
ejpam-3419	274	13	=	=	SYM
ejpam-3419	274	14	k2	k2	PROPN
ejpam-3419	274	15	=	=	SYM
ejpam-3419	274	16	0	0	PROPN
ejpam-3419	274	17	,	,	PUNCT
ejpam-3419	274	18	then	then	ADV
ejpam-3419	274	19	we	we	PRON
ejpam-3419	274	20	have	have	VERB
ejpam-3419	274	21	a	a	DET
ejpam-3419	274	22	z2z4z8additive	z2z4z8additive	PROPN
ejpam-3419	274	23	code	code	NOUN
ejpam-3419	274	24	of	of	ADP
ejpam-3419	274	25	type	type	NOUN
ejpam-3419	274	26	(	(	PUNCT
ejpam-3419	274	27	α	α	NOUN
ejpam-3419	274	28	,	,	PUNCT
ejpam-3419	274	29	0	0	NUM
ejpam-3419	274	30	,	,	PUNCT
ejpam-3419	274	31	θ	θ	PROPN
ejpam-3419	274	32	;	;	PUNCT
ejpam-3419	274	33	k0	k0	PROPN
ejpam-3419	274	34	,	,	PUNCT
ejpam-3419	274	35	0	0	NUM
ejpam-3419	274	36	,	,	PUNCT
ejpam-3419	274	37	0	0	NUM
ejpam-3419	274	38	,	,	PUNCT
ejpam-3419	274	39	k3	k3	PROPN
ejpam-3419	274	40	,	,	PUNCT
ejpam-3419	274	41	k4	k4	PROPN
ejpam-3419	274	42	,	,	PUNCT
ejpam-3419	274	43	k5	k5	PROPN
ejpam-3419	274	44	)	)	PUNCT
ejpam-3419	274	45	.	.	PUNCT
ejpam-3419	275	1	also	also	ADV
ejpam-3419	275	2	,	,	PUNCT
ejpam-3419	275	3	the	the	DET
ejpam-3419	275	4	number	number	NOUN
ejpam-3419	275	5	of	of	ADP
ejpam-3419	275	6	these	these	DET
ejpam-3419	275	7	codes	code	NOUN
ejpam-3419	275	8	is	be	AUX
ejpam-3419	275	9	n2×4×8(α	n2×4×8(α	NOUN
ejpam-3419	275	10	,	,	PUNCT
ejpam-3419	275	11	0	0	NUM
ejpam-3419	275	12	,	,	PUNCT
ejpam-3419	275	13	θ	θ	PROPN
ejpam-3419	275	14	;	;	PUNCT
ejpam-3419	275	15	k0	k0	PROPN
ejpam-3419	275	16	,	,	PUNCT
ejpam-3419	275	17	0	0	NUM
ejpam-3419	275	18	,	,	PUNCT
ejpam-3419	275	19	0	0	NUM
ejpam-3419	275	20	,	,	PUNCT
ejpam-3419	275	21	k3	k3	PROPN
ejpam-3419	275	22	,	,	PUNCT
ejpam-3419	275	23	k4	k4	PROPN
ejpam-3419	275	24	,	,	PUNCT
ejpam-3419	275	25	k5	k5	PROPN
ejpam-3419	275	26	)	)	PUNCT
ejpam-3419	275	27	=	=	PUNCT
ejpam-3419	276	1	2k0(θ−k3−k4−k5)+k3[(α−k0)+2(θ−k3−k4−k5)+k5	2k0(θ−k3−k4−k5)+k3[(α−k0)+2(θ−k3−k4−k5)+k5	NUM
ejpam-3419	276	2	]	]	X
ejpam-3419	276	3	[	[	PUNCT
ejpam-3419	276	4	α	α	X
ejpam-3419	276	5	k0	k0	PROPN
ejpam-3419	276	6	]	]	PUNCT
ejpam-3419	276	7	2	2	NUM
ejpam-3419	276	8	[	[	PUNCT
ejpam-3419	276	9	θ	θ	X
ejpam-3419	276	10	k3	k3	PROPN
ejpam-3419	276	11	,	,	PUNCT
ejpam-3419	276	12	k4	k4	PROPN
ejpam-3419	276	13	,	,	PUNCT
ejpam-3419	276	14	k5	k5	PROPN
ejpam-3419	276	15	]	]	PUNCT
ejpam-3419	276	16	2	2	NUM
ejpam-3419	276	17	=	=	SYM
ejpam-3419	276	18	n2×8(α	n2×8(α	PROPN
ejpam-3419	276	19	,	,	PUNCT
ejpam-3419	276	20	θ	θ	PROPN
ejpam-3419	276	21	;	;	PUNCT
ejpam-3419	276	22	k0	k0	PROPN
ejpam-3419	276	23	,	,	PUNCT
ejpam-3419	276	24	k3	k3	PROPN
ejpam-3419	276	25	,	,	PUNCT
ejpam-3419	276	26	k4	k4	PROPN
ejpam-3419	276	27	,	,	PUNCT
ejpam-3419	276	28	k5	k5	PROPN
ejpam-3419	276	29	)	)	PUNCT
ejpam-3419	276	30	.	.	PUNCT
ejpam-3419	277	1	(	(	PUNCT
ejpam-3419	277	2	7	7	X
ejpam-3419	277	3	)	)	PUNCT
ejpam-3419	277	4	in	in	ADP
ejpam-3419	277	5	(	(	PUNCT
ejpam-3419	277	6	7	7	NUM
ejpam-3419	277	7	)	)	PUNCT
ejpam-3419	277	8	,	,	PUNCT
ejpam-3419	277	9	if	if	SCONJ
ejpam-3419	277	10	we	we	PRON
ejpam-3419	277	11	replace	replace	VERB
ejpam-3419	277	12	both	both	CCONJ
ejpam-3419	277	13	k3	k3	ADJ
ejpam-3419	277	14	=	=	PROPN
ejpam-3419	277	15	k1	k1	NOUN
ejpam-3419	277	16	,	,	PUNCT
ejpam-3419	277	17	k4	k4	NOUN
ejpam-3419	277	18	=	=	SYM
ejpam-3419	277	19	k2	k2	PROPN
ejpam-3419	277	20	,	,	PUNCT
ejpam-3419	277	21	k5	k5	PROPN
ejpam-3419	277	22	=	=	PUNCT
ejpam-3419	277	23	k3	k3	PROPN
ejpam-3419	277	24	and	and	CCONJ
ejpam-3419	277	25	k1	k1	NOUN
ejpam-3419	277	26	+	+	CCONJ
ejpam-3419	277	27	k2	k2	ADJ
ejpam-3419	277	28	+	+	CCONJ
ejpam-3419	277	29	k3	k3	ADJ
ejpam-3419	277	30	=	=	PROPN
ejpam-3419	277	31	l	l	NOUN
ejpam-3419	277	32	,	,	PUNCT
ejpam-3419	277	33	then	then	ADV
ejpam-3419	277	34	it	it	PRON
ejpam-3419	277	35	is	be	AUX
ejpam-3419	277	36	obtained	obtain	VERB
ejpam-3419	277	37	the	the	DET
ejpam-3419	277	38	number	number	NOUN
ejpam-3419	277	39	of	of	ADP
ejpam-3419	277	40	z2z8	z2z8	ADJ
ejpam-3419	277	41	-	-	PUNCT
ejpam-3419	277	42	additive	additive	ADJ
ejpam-3419	277	43	codes	code	NOUN
ejpam-3419	277	44	of	of	ADP
ejpam-3419	277	45	type	type	NOUN
ejpam-3419	277	46	(	(	PUNCT
ejpam-3419	277	47	α	α	NOUN
ejpam-3419	277	48	,	,	PUNCT
ejpam-3419	277	49	θ	θ	PROPN
ejpam-3419	277	50	;	;	PUNCT
ejpam-3419	277	51	k0	k0	PROPN
ejpam-3419	277	52	,	,	PUNCT
ejpam-3419	277	53	k3	k3	PROPN
ejpam-3419	277	54	,	,	PUNCT
ejpam-3419	277	55	k4	k4	PROPN
ejpam-3419	277	56	,	,	PUNCT
ejpam-3419	277	57	k5	k5	PROPN
ejpam-3419	277	58	)	)	PUNCT
ejpam-3419	277	59	as	as	ADP
ejpam-3419	277	60	in	in	ADP
ejpam-3419	277	61	[	[	X
ejpam-3419	277	62	3	3	NUM
ejpam-3419	277	63	]	]	PUNCT
ejpam-3419	277	64	,	,	PUNCT
ejpam-3419	277	65	(	(	PUNCT
ejpam-3419	277	66	theorem	theorem	VERB
ejpam-3419	277	67	2.1	2.1	NUM
ejpam-3419	277	68	)	)	PUNCT
ejpam-3419	277	69	.	.	PUNCT
ejpam-3419	278	1	example	example	NOUN
ejpam-3419	279	1	3	3	NUM
ejpam-3419	279	2	.	.	X
ejpam-3419	280	1	n2×4(3	n2×4(3	PROPN
ejpam-3419	280	2	,	,	PUNCT
ejpam-3419	280	3	4	4	NUM
ejpam-3419	280	4	;	;	PUNCT
ejpam-3419	280	5	2	2	NUM
ejpam-3419	280	6	,	,	PUNCT
ejpam-3419	280	7	1	1	NUM
ejpam-3419	280	8	,	,	PUNCT
ejpam-3419	280	9	2	2	NUM
ejpam-3419	280	10	)	)	PUNCT
ejpam-3419	280	11	=	=	SYM
ejpam-3419	280	12	n2×4×8(3	n2×4×8(3	PROPN
ejpam-3419	280	13	,	,	PUNCT
ejpam-3419	280	14	4	4	NUM
ejpam-3419	280	15	,	,	PUNCT
ejpam-3419	280	16	0	0	NUM
ejpam-3419	280	17	;	;	PUNCT
ejpam-3419	280	18	2	2	NUM
ejpam-3419	280	19	,	,	PUNCT
ejpam-3419	280	20	1	1	NUM
ejpam-3419	280	21	,	,	PUNCT
ejpam-3419	280	22	2	2	NUM
ejpam-3419	280	23	,	,	PUNCT
ejpam-3419	280	24	0	0	NUM
ejpam-3419	280	25	,	,	PUNCT
ejpam-3419	280	26	0	0	NUM
ejpam-3419	280	27	,	,	PUNCT
ejpam-3419	280	28	0	0	NUM
ejpam-3419	280	29	)	)	PUNCT
ejpam-3419	280	30	=	=	SYM
ejpam-3419	280	31	11760	11760	NUM
ejpam-3419	280	32	n2×8(3	n2×8(3	PROPN
ejpam-3419	280	33	,	,	PUNCT
ejpam-3419	280	34	4	4	NUM
ejpam-3419	280	35	;	;	PUNCT
ejpam-3419	280	36	2	2	NUM
ejpam-3419	280	37	,	,	PUNCT
ejpam-3419	280	38	0	0	NUM
ejpam-3419	280	39	,	,	PUNCT
ejpam-3419	280	40	1	1	NUM
ejpam-3419	280	41	,	,	PUNCT
ejpam-3419	280	42	2	2	NUM
ejpam-3419	280	43	)	)	PUNCT
ejpam-3419	280	44	=	=	SYM
ejpam-3419	280	45	n2×4×8(3	n2×4×8(3	PROPN
ejpam-3419	280	46	,	,	PUNCT
ejpam-3419	280	47	0	0	NUM
ejpam-3419	280	48	,	,	PUNCT
ejpam-3419	280	49	4	4	NUM
ejpam-3419	280	50	;	;	PUNCT
ejpam-3419	280	51	2	2	NUM
ejpam-3419	280	52	,	,	PUNCT
ejpam-3419	280	53	0	0	NUM
ejpam-3419	280	54	,	,	PUNCT
ejpam-3419	280	55	0	0	NUM
ejpam-3419	280	56	,	,	PUNCT
ejpam-3419	280	57	0	0	NUM
ejpam-3419	280	58	,	,	PUNCT
ejpam-3419	280	59	1	1	NUM
ejpam-3419	280	60	,	,	PUNCT
ejpam-3419	280	61	2	2	NUM
ejpam-3419	280	62	)	)	PUNCT
ejpam-3419	280	63	=	=	SYM
ejpam-3419	280	64	11760	11760	NUM
ejpam-3419	280	65	5	5	NUM
ejpam-3419	280	66	.	.	PUNCT
ejpam-3419	281	1	conclusions	conclusion	NOUN
ejpam-3419	281	2	in	in	ADP
ejpam-3419	281	3	this	this	DET
ejpam-3419	281	4	work	work	NOUN
ejpam-3419	281	5	we	we	PRON
ejpam-3419	281	6	established	establish	VERB
ejpam-3419	281	7	a	a	DET
ejpam-3419	281	8	formula	formula	NOUN
ejpam-3419	281	9	that	that	PRON
ejpam-3419	281	10	gives	give	VERB
ejpam-3419	281	11	the	the	DET
ejpam-3419	281	12	number	number	NOUN
ejpam-3419	281	13	of	of	ADP
ejpam-3419	281	14	distinct	distinct	ADJ
ejpam-3419	281	15	z2z4z8	z2z4z8	NUM
ejpam-3419	281	16	-	-	PUNCT
ejpam-3419	281	17	additive	additive	ADJ
ejpam-3419	281	18	codes	code	NOUN
ejpam-3419	281	19	and	and	CCONJ
ejpam-3419	281	20	their	their	PRON
ejpam-3419	281	21	dual	dual	ADJ
ejpam-3419	281	22	codes	code	NOUN
ejpam-3419	281	23	.	.	PUNCT
ejpam-3419	282	1	also	also	ADV
ejpam-3419	282	2	,	,	PUNCT
ejpam-3419	282	3	we	we	PRON
ejpam-3419	282	4	showed	show	VERB
ejpam-3419	282	5	the	the	DET
ejpam-3419	282	6	relationships	relationship	NOUN
ejpam-3419	282	7	among	among	ADP
ejpam-3419	282	8	the	the	DET
ejpam-3419	282	9	numbers	number	NOUN
ejpam-3419	282	10	of	of	ADP
ejpam-3419	282	11	z2z4	z2z4	NOUN
ejpam-3419	282	12	,	,	PUNCT
ejpam-3419	282	13	z2z8	z2z8	PROPN
ejpam-3419	282	14	and	and	CCONJ
ejpam-3419	282	15	z2z4z8	z2z4z8	NUM
ejpam-3419	282	16	-	-	PUNCT
ejpam-3419	282	17	additive	additive	ADJ
ejpam-3419	282	18	codes	code	NOUN
ejpam-3419	282	19	.	.	PUNCT
ejpam-3419	283	1	also	also	ADV
ejpam-3419	283	2	,	,	PUNCT
ejpam-3419	283	3	we	we	PRON
ejpam-3419	283	4	gave	give	VERB
ejpam-3419	283	5	some	some	DET
ejpam-3419	283	6	examples	example	NOUN
ejpam-3419	283	7	that	that	PRON
ejpam-3419	283	8	show	show	VERB
ejpam-3419	283	9	the	the	DET
ejpam-3419	283	10	relationships	relationship	NOUN
ejpam-3419	283	11	.	.	PUNCT
ejpam-3419	284	1	moreover	moreover	ADV
ejpam-3419	284	2	,	,	PUNCT
ejpam-3419	284	3	it	it	PRON
ejpam-3419	284	4	is	be	AUX
ejpam-3419	284	5	clear	clear	ADJ
ejpam-3419	284	6	that	that	SCONJ
ejpam-3419	284	7	in	in	ADP
ejpam-3419	284	8	theorem	theorem	NOUN
ejpam-3419	284	9	1	1	NUM
ejpam-3419	284	10	,	,	PUNCT
ejpam-3419	284	11	if	if	SCONJ
ejpam-3419	284	12	the	the	DET
ejpam-3419	284	13	parameters	parameter	NOUN
ejpam-3419	284	14	of	of	ADP
ejpam-3419	284	15	z2z4z8	z2z4z8	NOUN
ejpam-3419	284	16	-	-	PUNCT
ejpam-3419	284	17	additive	additive	ADJ
ejpam-3419	284	18	codes	code	NOUN
ejpam-3419	284	19	of	of	ADP
ejpam-3419	284	20	type	type	NOUN
ejpam-3419	284	21	(	(	PUNCT
ejpam-3419	284	22	α	α	NOUN
ejpam-3419	284	23	,	,	PUNCT
ejpam-3419	284	24	β	β	X
ejpam-3419	284	25	,	,	PUNCT
ejpam-3419	284	26	θ	θ	PROPN
ejpam-3419	284	27	;	;	PUNCT
ejpam-3419	284	28	k0	k0	PROPN
ejpam-3419	284	29	,	,	PUNCT
ejpam-3419	284	30	k1	k1	PROPN
ejpam-3419	284	31	,	,	PUNCT
ejpam-3419	284	32	k2	k2	NOUN
ejpam-3419	284	33	,	,	PUNCT
ejpam-3419	284	34	k3	k3	PROPN
ejpam-3419	284	35	,	,	PUNCT
ejpam-3419	284	36	k4	k4	PROPN
ejpam-3419	284	37	,	,	PUNCT
ejpam-3419	284	38	k5	k5	PROPN
ejpam-3419	284	39	)	)	PUNCT
ejpam-3419	284	40	are	be	AUX
ejpam-3419	284	41	appropriated	appropriate	VERB
ejpam-3419	284	42	,	,	PUNCT
ejpam-3419	284	43	the	the	DET
ejpam-3419	284	44	numbers	number	NOUN
ejpam-3419	284	45	of	of	ADP
ejpam-3419	284	46	z2	z2	PROPN
ejpam-3419	284	47	,	,	PUNCT
ejpam-3419	284	48	z4	z4	PROPN
ejpam-3419	284	49	and	and	CCONJ
ejpam-3419	284	50	z8	z8	PROPN
ejpam-3419	284	51	linear	linear	PROPN
ejpam-3419	284	52	codes	code	NOUN
ejpam-3419	284	53	can	can	AUX
ejpam-3419	284	54	be	be	AUX
ejpam-3419	284	55	obtained	obtain	VERB
ejpam-3419	284	56	.	.	PUNCT
ejpam-3419	285	1	acknowledgements	acknowledgement	NOUN
ejpam-3419	285	2	we	we	PRON
ejpam-3419	285	3	would	would	AUX
ejpam-3419	285	4	like	like	VERB
ejpam-3419	285	5	to	to	PART
ejpam-3419	285	6	thank	thank	VERB
ejpam-3419	285	7	the	the	DET
ejpam-3419	285	8	referees	referee	NOUN
ejpam-3419	285	9	for	for	ADP
ejpam-3419	285	10	their	their	PRON
ejpam-3419	285	11	valuable	valuable	ADJ
ejpam-3419	285	12	remarks	remark	NOUN
ejpam-3419	285	13	.	.	PUNCT
ejpam-3419	286	1	references	reference	NOUN
ejpam-3419	286	2	679	679	NUM
ejpam-3419	286	3	references	reference	NOUN
ejpam-3419	286	4	[	[	X
ejpam-3419	286	5	1	1	NUM
ejpam-3419	286	6	]	]	PUNCT
ejpam-3419	286	7	t	t	NOUN
ejpam-3419	286	8	abualrub	abualrub	NOUN
ejpam-3419	286	9	,	,	PUNCT
ejpam-3419	286	10	i	i	PROPN
ejpam-3419	286	11	siap	siap	PROPN
ejpam-3419	286	12	,	,	PUNCT
ejpam-3419	286	13	and	and	CCONJ
ejpam-3419	286	14	n	n	PRON
ejpam-3419	286	15	aydin	aydin	NOUN
ejpam-3419	286	16	.	.	PUNCT
ejpam-3419	287	1	z2z4	z2z4	VERB
ejpam-3419	287	2	-	-	ADJ
ejpam-3419	287	3	additive	additive	ADJ
ejpam-3419	287	4	cyclic	cyclic	NOUN
ejpam-3419	287	5	codes	code	NOUN
ejpam-3419	287	6	.	.	PUNCT
ejpam-3419	288	1	ieee	ieee	PROPN
ejpam-3419	288	2	trans	trans	PROPN
ejpam-3419	288	3	.	.	PUNCT
ejpam-3419	289	1	inform	inform	NOUN
ejpam-3419	289	2	.	.	PUNCT
ejpam-3419	290	1	theory	theory	NOUN
ejpam-3419	290	2	,	,	PUNCT
ejpam-3419	290	3	60(3):15081514	60(3):15081514	NUM
ejpam-3419	290	4	,	,	PUNCT
ejpam-3419	290	5	2014	2014	NUM
ejpam-3419	290	6	.	.	PUNCT
ejpam-3419	291	1	[	[	X
ejpam-3419	291	2	2	2	X
ejpam-3419	291	3	]	]	X
ejpam-3419	291	4	i	i	PRON
ejpam-3419	291	5	aydogdu	aydogdu	ADV
ejpam-3419	291	6	and	and	CCONJ
ejpam-3419	291	7	f	f	PROPN
ejpam-3419	291	8	gursoy	gursoy	NOUN
ejpam-3419	291	9	.	.	PUNCT
ejpam-3419	292	1	z2z4z8	z2z4z8	X
ejpam-3419	292	2	-	-	PUNCT
ejpam-3419	292	3	cyclic	cyclic	ADJ
ejpam-3419	292	4	codes	code	NOUN
ejpam-3419	292	5	.	.	PUNCT
ejpam-3419	293	1	j.	j.	PROPN
ejpam-3419	293	2	appl	appl	PROPN
ejpam-3419	293	3	.	.	PROPN
ejpam-3419	293	4	math	math	PROPN
ejpam-3419	293	5	.	.	PUNCT
ejpam-3419	294	1	comput	comput	NOUN
ejpam-3419	294	2	.	.	PUNCT
ejpam-3419	294	3	,	,	PUNCT
ejpam-3419	294	4	60(12):327341	60(12):327341	PROPN
ejpam-3419	294	5	,	,	PUNCT
ejpam-3419	294	6	2019	2019	NUM
ejpam-3419	294	7	.	.	PUNCT
ejpam-3419	295	1	[	[	X
ejpam-3419	295	2	3	3	X
ejpam-3419	295	3	]	]	X
ejpam-3419	295	4	i	i	PRON
ejpam-3419	295	5	aydogdu	aydogdu	ADV
ejpam-3419	295	6	and	and	CCONJ
ejpam-3419	295	7	i	i	PROPN
ejpam-3419	295	8	siap	siap	PROPN
ejpam-3419	295	9	.	.	PUNCT
ejpam-3419	296	1	counting	count	VERB
ejpam-3419	296	2	the	the	DET
ejpam-3419	296	3	generator	generator	NOUN
ejpam-3419	296	4	matrices	matrix	NOUN
ejpam-3419	296	5	of	of	ADP
ejpam-3419	296	6	z2z8	z2z8	NOUN
ejpam-3419	296	7	-	-	NOUN
ejpam-3419	296	8	codes	code	NOUN
ejpam-3419	296	9	.	.	PUNCT
ejpam-3419	297	1	mathematical	mathematical	ADJ
ejpam-3419	297	2	sciences	science	NOUN
ejpam-3419	297	3	and	and	CCONJ
ejpam-3419	297	4	applications	application	NOUN
ejpam-3419	297	5	e	e	NOUN
ejpam-3419	297	6	-	-	NOUN
ejpam-3419	297	7	notes	note	NOUN
ejpam-3419	297	8	,	,	PUNCT
ejpam-3419	297	9	1(2):143–149	1(2):143–149	NUM
ejpam-3419	297	10	,	,	PUNCT
ejpam-3419	297	11	2013	2013	NUM
ejpam-3419	297	12	.	.	PUNCT
ejpam-3419	298	1	[	[	X
ejpam-3419	298	2	4	4	X
ejpam-3419	298	3	]	]	X
ejpam-3419	298	4	i	i	PRON
ejpam-3419	298	5	aydogdu	aydogdu	ADV
ejpam-3419	299	1	and	and	CCONJ
ejpam-3419	299	2	i	i	PROPN
ejpam-3419	299	3	siap	siap	PROPN
ejpam-3419	299	4	.	.	PUNCT
ejpam-3419	300	1	on	on	ADP
ejpam-3419	300	2	zprzps	zprzps	NOUN
ejpam-3419	300	3	-	-	PUNCT
ejpam-3419	300	4	additive	additive	ADJ
ejpam-3419	300	5	codes	code	NOUN
ejpam-3419	300	6	.	.	PUNCT
ejpam-3419	301	1	linear	linear	PROPN
ejpam-3419	301	2	multilinear	multilinear	PROPN
ejpam-3419	301	3	algebra	algebra	PROPN
ejpam-3419	301	4	,	,	PUNCT
ejpam-3419	301	5	63(10):20892102	63(10):20892102	NUM
ejpam-3419	301	6	,	,	PUNCT
ejpam-3419	301	7	2015	2015	NUM
ejpam-3419	301	8	.	.	PUNCT
ejpam-3419	302	1	[	[	X
ejpam-3419	302	2	5	5	NUM
ejpam-3419	302	3	]	]	X
ejpam-3419	302	4	j	j	PROPN
ejpam-3419	302	5	borges	borges	PROPN
ejpam-3419	302	6	,	,	PUNCT
ejpam-3419	302	7	c	c	PROPN
ejpam-3419	302	8	fernndez	fernndez	PROPN
ejpam-3419	302	9	-	-	PUNCT
ejpam-3419	302	10	crdoba	crdoba	NOUN
ejpam-3419	302	11	,	,	PUNCT
ejpam-3419	302	12	j	j	PROPN
ejpam-3419	302	13	pujol	pujol	NOUN
ejpam-3419	302	14	,	,	PUNCT
ejpam-3419	302	15	j	j	PROPN
ejpam-3419	302	16	rif	rif	PROPN
ejpam-3419	302	17	,	,	PUNCT
ejpam-3419	302	18	and	and	CCONJ
ejpam-3419	302	19	m	m	PROPN
ejpam-3419	302	20	villanueva	villanueva	PROPN
ejpam-3419	302	21	.	.	PUNCT
ejpam-3419	303	1	z2z4	z2z4	ADJ
ejpam-3419	303	2	-	-	ADJ
ejpam-3419	303	3	linear	linear	ADJ
ejpam-3419	303	4	codes	code	NOUN
ejpam-3419	303	5	:	:	PUNCT
ejpam-3419	303	6	generator	generator	NOUN
ejpam-3419	303	7	matrices	matrix	NOUN
ejpam-3419	303	8	and	and	CCONJ
ejpam-3419	303	9	duality	duality	NOUN
ejpam-3419	303	10	.	.	PUNCT
ejpam-3419	304	1	designs	design	NOUN
ejpam-3419	304	2	,	,	PUNCT
ejpam-3419	304	3	codes	code	NOUN
ejpam-3419	304	4	cryptogr	cryptogr	NOUN
ejpam-3419	304	5	.	.	PUNCT
ejpam-3419	304	6	,	,	PUNCT
ejpam-3419	305	1	54(2):167179	54(2):167179	NUM
ejpam-3419	305	2	,	,	PUNCT
ejpam-3419	305	3	2010	2010	NUM
ejpam-3419	305	4	.	.	PUNCT
ejpam-3419	306	1	[	[	X
ejpam-3419	306	2	6	6	NUM
ejpam-3419	306	3	]	]	X
ejpam-3419	306	4	j	j	PROPN
ejpam-3419	306	5	borges	borges	PROPN
ejpam-3419	306	6	,	,	PUNCT
ejpam-3419	306	7	c	c	PROPN
ejpam-3419	306	8	fernndez	fernndez	PROPN
ejpam-3419	306	9	-	-	PUNCT
ejpam-3419	306	10	crdoba	crdoba	NOUN
ejpam-3419	306	11	,	,	PUNCT
ejpam-3419	306	12	and	and	CCONJ
ejpam-3419	306	13	r	r	NOUN
ejpam-3419	306	14	ten	ten	NUM
ejpam-3419	306	15	-	-	PUNCT
ejpam-3419	306	16	valls	vall	NOUN
ejpam-3419	306	17	.	.	PUNCT
ejpam-3419	307	1	z2z4	z2z4	X
ejpam-3419	307	2	-	-	ADJ
ejpam-3419	307	3	additive	additive	ADJ
ejpam-3419	307	4	cyclic	cyclic	NOUN
ejpam-3419	307	5	codes	code	NOUN
ejpam-3419	307	6	,	,	PUNCT
ejpam-3419	307	7	generator	generator	NOUN
ejpam-3419	307	8	polynomials	polynomial	NOUN
ejpam-3419	307	9	and	and	CCONJ
ejpam-3419	307	10	dual	dual	ADJ
ejpam-3419	307	11	codes	code	NOUN
ejpam-3419	307	12	.	.	PUNCT
ejpam-3419	308	1	ieee	ieee	PROPN
ejpam-3419	308	2	trans	trans	PROPN
ejpam-3419	308	3	.	.	PUNCT
ejpam-3419	309	1	inform	inform	NOUN
ejpam-3419	309	2	.	.	PUNCT
ejpam-3419	310	1	theory	theory	NOUN
ejpam-3419	310	2	,	,	PUNCT
ejpam-3419	310	3	62(11):63486354	62(11):63486354	NUM
ejpam-3419	310	4	,	,	PUNCT
ejpam-3419	310	5	2016	2016	NUM
ejpam-3419	310	6	.	.	PUNCT
ejpam-3419	311	1	[	[	X
ejpam-3419	311	2	7	7	X
ejpam-3419	311	3	]	]	X
ejpam-3419	311	4	p	p	X
ejpam-3419	311	5	delsarte	delsarte	NOUN
ejpam-3419	311	6	.	.	PUNCT
ejpam-3419	312	1	an	an	DET
ejpam-3419	312	2	algebraic	algebraic	ADJ
ejpam-3419	312	3	approach	approach	NOUN
ejpam-3419	312	4	to	to	ADP
ejpam-3419	312	5	the	the	DET
ejpam-3419	312	6	association	association	NOUN
ejpam-3419	312	7	schemes	scheme	NOUN
ejpam-3419	312	8	of	of	ADP
ejpam-3419	312	9	coding	code	VERB
ejpam-3419	312	10	theory	theory	NOUN
ejpam-3419	312	11	.	.	PUNCT
ejpam-3419	313	1	philips	philips	PROPN
ejpam-3419	313	2	research	research	PROPN
ejpam-3419	313	3	rep.suppl	rep.suppl	PROPN
ejpam-3419	313	4	.	.	PROPN
ejpam-3419	313	5	,	,	PUNCT
ejpam-3419	313	6	10	10	NUM
ejpam-3419	313	7	,	,	PUNCT
ejpam-3419	313	8	1973	1973	NUM
ejpam-3419	314	1	.	.	PUNCT
ejpam-3419	315	1	[	[	X
ejpam-3419	315	2	8	8	NUM
ejpam-3419	315	3	]	]	X
ejpam-3419	315	4	s.t	s.t	PROPN
ejpam-3419	315	5	dougherty	dougherty	PROPN
ejpam-3419	315	6	and	and	CCONJ
ejpam-3419	315	7	e	e	NOUN
ejpam-3419	315	8	salturk	salturk	NOUN
ejpam-3419	315	9	.	.	PUNCT
ejpam-3419	316	1	counting	count	VERB
ejpam-3419	316	2	z2z4	z2z4	NOUN
ejpam-3419	316	3	-	-	PUNCT
ejpam-3419	316	4	additive	additive	ADJ
ejpam-3419	316	5	codes	code	NOUN
ejpam-3419	316	6	.	.	PUNCT
ejpam-3419	317	1	noncommutative	noncommutative	ADJ
ejpam-3419	317	2	rings	ring	NOUN
ejpam-3419	317	3	and	and	CCONJ
ejpam-3419	317	4	their	their	PRON
ejpam-3419	317	5	applications	application	NOUN
ejpam-3419	317	6	,	,	PUNCT
ejpam-3419	317	7	contemporary	contemporary	ADJ
ejpam-3419	317	8	mathematics	mathematic	NOUN
ejpam-3419	317	9	,	,	PUNCT
ejpam-3419	317	10	634:137–147	634:137–147	NUM
ejpam-3419	317	11	,	,	PUNCT
ejpam-3419	317	12	2015	2015	NUM
ejpam-3419	317	13	.	.	PUNCT
ejpam-3419	318	1	[	[	X
ejpam-3419	318	2	9	9	NUM
ejpam-3419	318	3	]	]	X
ejpam-3419	318	4	a.r	a.r	PROPN
ejpam-3419	318	5	hammons	hammon	NOUN
ejpam-3419	318	6	,	,	PUNCT
ejpam-3419	318	7	p.v	p.v	PROPN
ejpam-3419	318	8	kumar	kumar	PROPN
ejpam-3419	318	9	,	,	PUNCT
ejpam-3419	318	10	a.r	a.r	PROPN
ejpam-3419	318	11	calderbank	calderbank	PROPN
ejpam-3419	318	12	,	,	PUNCT
ejpam-3419	318	13	n.j.a	n.j.a	ADJ
ejpam-3419	318	14	sloane	sloane	NOUN
ejpam-3419	318	15	,	,	PUNCT
ejpam-3419	318	16	and	and	CCONJ
ejpam-3419	318	17	p	p	NOUN
ejpam-3419	318	18	sol	sol	NOUN
ejpam-3419	318	19	.	.	PUNCT
ejpam-3419	319	1	the	the	DET
ejpam-3419	319	2	z4linearity	z4linearity	PROPN
ejpam-3419	319	3	of	of	ADP
ejpam-3419	319	4	kerdock	kerdock	NOUN
ejpam-3419	319	5	,	,	PUNCT
ejpam-3419	319	6	preparata	preparata	NOUN
ejpam-3419	319	7	,	,	PUNCT
ejpam-3419	319	8	goethals	goethal	NOUN
ejpam-3419	319	9	and	and	CCONJ
ejpam-3419	319	10	related	related	ADJ
ejpam-3419	319	11	codes	code	NOUN
ejpam-3419	319	12	.	.	PUNCT
ejpam-3419	320	1	ieee	ieee	PROPN
ejpam-3419	320	2	trans	trans	PROPN
ejpam-3419	320	3	.	.	PUNCT
ejpam-3419	321	1	inform	inform	NOUN
ejpam-3419	321	2	.	.	PUNCT
ejpam-3419	322	1	theory	theory	NOUN
ejpam-3419	322	2	,	,	PUNCT
ejpam-3419	322	3	40:301319	40:301319	NUM
ejpam-3419	322	4	,	,	PUNCT
ejpam-3419	322	5	1994	1994	NUM
ejpam-3419	322	6	.	.	PUNCT
ejpam-3419	323	1	[	[	X
ejpam-3419	323	2	10	10	NUM
ejpam-3419	323	3	]	]	X
ejpam-3419	323	4	f.	f.	PROPN
ejpam-3419	323	5	j	j	PROPN
ejpam-3419	323	6	macwilliams	macwilliams	PROPN
ejpam-3419	323	7	and	and	CCONJ
ejpam-3419	323	8	n.j.a	n.j.a	PROPN
ejpam-3419	323	9	sloane	sloane	NOUN
ejpam-3419	323	10	.	.	PUNCT
ejpam-3419	324	1	the	the	DET
ejpam-3419	324	2	theory	theory	NOUN
ejpam-3419	324	3	of	of	ADP
ejpam-3419	324	4	error	error	NOUN
ejpam-3419	324	5	-	-	PUNCT
ejpam-3419	324	6	correcting	correct	VERB
ejpam-3419	324	7	codes	code	NOUN
ejpam-3419	324	8	.	.	PUNCT
ejpam-3419	325	1	northholland	northholland	ADJ
ejpam-3419	325	2	pub	pub	PROPN
ejpam-3419	325	3	.	.	PUNCT
ejpam-3419	326	1	co.	co.	PROPN
ejpam-3419	326	2	,	,	PUNCT
ejpam-3419	326	3	new	new	PROPN
ejpam-3419	326	4	york	york	PROPN
ejpam-3419	326	5	,	,	PUNCT
ejpam-3419	326	6	ny	ny	PROPN
ejpam-3419	326	7	,	,	PUNCT
ejpam-3419	326	8	1977	1977	NUM
ejpam-3419	326	9	.	.	PUNCT
ejpam-3419	327	1	[	[	X
ejpam-3419	327	2	11	11	NUM
ejpam-3419	327	3	]	]	X
ejpam-3419	327	4	j	j	PROPN
ejpam-3419	327	5	pujol	pujol	NOUN
ejpam-3419	327	6	and	and	CCONJ
ejpam-3419	327	7	j	j	PROPN
ejpam-3419	327	8	rif	rif	PROPN
ejpam-3419	327	9	.	.	PROPN
ejpam-3419	327	10	translation	translation	PROPN
ejpam-3419	327	11	invariant	invariant	PROPN
ejpam-3419	327	12	propelinear	propelinear	NOUN
ejpam-3419	327	13	codes	code	NOUN
ejpam-3419	327	14	.	.	PUNCT
ejpam-3419	328	1	ieee	ieee	PROPN
ejpam-3419	328	2	trans	trans	PROPN
ejpam-3419	328	3	.	.	PUNCT
ejpam-3419	329	1	inform	inform	NOUN
ejpam-3419	329	2	.	.	PUNCT
ejpam-3419	330	1	theory	theory	NOUN
ejpam-3419	330	2	,	,	PUNCT
ejpam-3419	330	3	43:590598	43:590598	NUM
ejpam-3419	330	4	,	,	PUNCT
ejpam-3419	330	5	1997	1997	NUM
ejpam-3419	330	6	.	.	PUNCT
ejpam-3419	331	1	[	[	X
ejpam-3419	331	2	12	12	NUM
ejpam-3419	331	3	]	]	X
ejpam-3419	331	4	c.e	c.e	PROPN
ejpam-3419	331	5	shannon	shannon	PROPN
ejpam-3419	331	6	and	and	CCONJ
ejpam-3419	331	7	w	w	PROPN
ejpam-3419	331	8	weaver	weaver	PROPN
ejpam-3419	331	9	.	.	PUNCT
ejpam-3419	332	1	the	the	DET
ejpam-3419	332	2	mathematical	mathematical	ADJ
ejpam-3419	332	3	theory	theory	NOUN
ejpam-3419	332	4	of	of	ADP
ejpam-3419	332	5	communication	communication	NOUN
ejpam-3419	332	6	.	.	PUNCT
ejpam-3419	333	1	the	the	DET
ejpam-3419	333	2	university	university	PROPN
ejpam-3419	333	3	of	of	ADP
ejpam-3419	333	4	illinois	illinois	PROPN
ejpam-3419	333	5	,	,	PUNCT
ejpam-3419	333	6	urbana	urbana	PROPN
ejpam-3419	333	7	,	,	PUNCT
ejpam-3419	333	8	1964	1964	NUM
ejpam-3419	333	9	.	.	PUNCT
ejpam-3419	334	1	[	[	X
ejpam-3419	334	2	13	13	NUM
ejpam-3419	334	3	]	]	X
ejpam-3419	334	4	i	i	PRON
ejpam-3419	334	5	siap	siap	PROPN
ejpam-3419	334	6	and	and	CCONJ
ejpam-3419	334	7	i	i	PRON
ejpam-3419	334	8	aydogdu	aydogdu	ADV
ejpam-3419	334	9	.	.	PUNCT
ejpam-3419	335	1	the	the	DET
ejpam-3419	335	2	structure	structure	NOUN
ejpam-3419	335	3	of	of	ADP
ejpam-3419	335	4	z2z2s	z2z2s	X
ejpam-3419	335	5	-	-	PUNCT
ejpam-3419	335	6	additive	additive	ADJ
ejpam-3419	335	7	codes	code	NOUN
ejpam-3419	335	8	:	:	PUNCT
ejpam-3419	335	9	bounds	bound	NOUN
ejpam-3419	335	10	on	on	ADP
ejpam-3419	335	11	the	the	DET
ejpam-3419	335	12	minimum	minimum	ADJ
ejpam-3419	335	13	distance	distance	NOUN
ejpam-3419	335	14	.	.	PUNCT
ejpam-3419	336	1	appl	appl	PROPN
ejpam-3419	336	2	.	.	PROPN
ejpam-3419	337	1	math	math	PROPN
ejpam-3419	337	2	.	.	PUNCT
ejpam-3419	338	1	inf	inf	PROPN
ejpam-3419	338	2	.	.	PUNCT
ejpam-3419	339	1	sci	sci	PROPN
ejpam-3419	339	2	.	.	PROPN
ejpam-3419	339	3	,	,	PUNCT
ejpam-3419	339	4	7(6):2271–2278	7(6):2271–2278	NUM
ejpam-3419	339	5	,	,	PUNCT
ejpam-3419	339	6	2013	2013	NUM
ejpam-3419	339	7	.	.	PUNCT