id	sid	tid	token	lemma	pos
ejpam-1609	1	1	12_salturk.dvi	12_salturk.dvi	NUM
ejpam-1609	1	2	european	european	PROPN
ejpam-1609	1	3	journal	journal	PROPN
ejpam-1609	1	4	of	of	ADP
ejpam-1609	1	5	pure	pure	ADJ
ejpam-1609	1	6	and	and	CCONJ
ejpam-1609	1	7	applied	apply	VERB
ejpam-1609	1	8	mathematics	mathematic	NOUN
ejpam-1609	1	9	vol	vol	NOUN
ejpam-1609	1	10	.	.	PROPN
ejpam-1609	1	11	5	5	NUM
ejpam-1609	1	12	,	,	PUNCT
ejpam-1609	1	13	no	no	INTJ
ejpam-1609	1	14	.	.	NOUN
ejpam-1609	1	15	2	2	NUM
ejpam-1609	1	16	,	,	PUNCT
ejpam-1609	1	17	2012	2012	NUM
ejpam-1609	1	18	,	,	PUNCT
ejpam-1609	1	19	250	250	NUM
ejpam-1609	1	20	-	-	SYM
ejpam-1609	1	21	259	259	NUM
ejpam-1609	1	22	issn	issn	PROPN
ejpam-1609	1	23	1307	1307	NUM
ejpam-1609	1	24	-	-	SYM
ejpam-1609	1	25	5543	5543	NUM
ejpam-1609	1	26	–	–	PUNCT
ejpam-1609	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1609	1	28	generalized	generalized	ADJ
ejpam-1609	1	29	gaussian	gaussian	ADJ
ejpam-1609	1	30	numbers	number	NOUN
ejpam-1609	1	31	related	relate	VERB
ejpam-1609	1	32	to	to	ADP
ejpam-1609	1	33	linear	linear	ADJ
ejpam-1609	1	34	codes	code	NOUN
ejpam-1609	1	35	over	over	ADP
ejpam-1609	1	36	galois	galois	PROPN
ejpam-1609	1	37	rings	ring	NOUN
ejpam-1609	1	38	esengül	esengül	PROPN
ejpam-1609	1	39	saltürk∗	saltürk∗	PROPN
ejpam-1609	1	40	,	,	PUNCT
ejpam-1609	1	41	i̇rfan	i̇rfan	PROPN
ejpam-1609	1	42	şiap	şiap	PROPN
ejpam-1609	1	43	department	department	PROPN
ejpam-1609	1	44	of	of	ADP
ejpam-1609	1	45	mathematics	mathematics	PROPN
ejpam-1609	1	46	,	,	PUNCT
ejpam-1609	1	47	yildiz	yildiz	PROPN
ejpam-1609	1	48	technical	technical	PROPN
ejpam-1609	1	49	university	university	PROPN
ejpam-1609	1	50	,	,	PUNCT
ejpam-1609	1	51	istanbul	istanbul	PROPN
ejpam-1609	1	52	,	,	PUNCT
ejpam-1609	1	53	turkey	turkey	PROPN
ejpam-1609	1	54	abstract	abstract	NOUN
ejpam-1609	1	55	.	.	PUNCT
ejpam-1609	2	1	in	in	ADP
ejpam-1609	2	2	this	this	DET
ejpam-1609	2	3	paper	paper	NOUN
ejpam-1609	2	4	,	,	PUNCT
ejpam-1609	2	5	we	we	PRON
ejpam-1609	2	6	define	define	VERB
ejpam-1609	2	7	a	a	DET
ejpam-1609	2	8	family	family	NOUN
ejpam-1609	2	9	of	of	ADP
ejpam-1609	2	10	generalized	generalized	ADJ
ejpam-1609	2	11	gaussian	gaussian	ADJ
ejpam-1609	2	12	numbers	number	NOUN
ejpam-1609	2	13	that	that	PRON
ejpam-1609	2	14	gives	give	VERB
ejpam-1609	2	15	the	the	DET
ejpam-1609	2	16	number	number	NOUN
ejpam-1609	2	17	of	of	ADP
ejpam-1609	2	18	linear	linear	PROPN
ejpam-1609	2	19	codes	code	NOUN
ejpam-1609	2	20	over	over	ADP
ejpam-1609	2	21	galois	galois	PROPN
ejpam-1609	2	22	rings	ring	NOUN
ejpam-1609	2	23	directly	directly	ADV
ejpam-1609	2	24	.	.	PUNCT
ejpam-1609	3	1	also	also	ADV
ejpam-1609	3	2	,	,	PUNCT
ejpam-1609	3	3	we	we	PRON
ejpam-1609	3	4	study	study	VERB
ejpam-1609	3	5	some	some	PRON
ejpam-1609	3	6	of	of	ADP
ejpam-1609	3	7	their	their	PRON
ejpam-1609	3	8	properties	property	NOUN
ejpam-1609	3	9	and	and	CCONJ
ejpam-1609	3	10	obtain	obtain	VERB
ejpam-1609	3	11	some	some	DET
ejpam-1609	3	12	relations	relation	NOUN
ejpam-1609	3	13	between	between	ADP
ejpam-1609	3	14	them	they	PRON
ejpam-1609	3	15	.	.	PUNCT
ejpam-1609	4	1	2010	2010	NUM
ejpam-1609	4	2	mathematics	mathematic	NOUN
ejpam-1609	4	3	subject	subject	NOUN
ejpam-1609	4	4	classifications	classification	NOUN
ejpam-1609	4	5	:	:	PUNCT
ejpam-1609	4	6	11t71	11t71	NUM
ejpam-1609	4	7	,	,	PUNCT
ejpam-1609	4	8	94b05	94b05	NUM
ejpam-1609	4	9	,	,	PUNCT
ejpam-1609	4	10	05a10	05a10	NOUN
ejpam-1609	4	11	key	key	ADJ
ejpam-1609	4	12	words	word	NOUN
ejpam-1609	4	13	and	and	CCONJ
ejpam-1609	4	14	phrases	phrase	NOUN
ejpam-1609	4	15	:	:	PUNCT
ejpam-1609	4	16	gaussian	gaussian	ADJ
ejpam-1609	4	17	binomial	binomial	ADJ
ejpam-1609	4	18	coefficients	coefficient	NOUN
ejpam-1609	4	19	,	,	PUNCT
ejpam-1609	4	20	linear	linear	ADJ
ejpam-1609	4	21	codes	code	NOUN
ejpam-1609	4	22	over	over	ADP
ejpam-1609	4	23	rings	ring	NOUN
ejpam-1609	4	24	1	1	NUM
ejpam-1609	4	25	.	.	PUNCT
ejpam-1609	5	1	introduction	introduction	NOUN
ejpam-1609	5	2	binomial	binomial	ADJ
ejpam-1609	5	3	coefficients	coefficient	NOUN
ejpam-1609	5	4	and	and	CCONJ
ejpam-1609	5	5	gaussian	gaussian	ADJ
ejpam-1609	5	6	binomial	binomial	ADJ
ejpam-1609	5	7	coefficients	coefficient	NOUN
ejpam-1609	5	8	are	be	AUX
ejpam-1609	5	9	two	two	NUM
ejpam-1609	5	10	fundamental	fundamental	ADJ
ejpam-1609	5	11	classes	class	NOUN
ejpam-1609	5	12	of	of	ADP
ejpam-1609	5	13	numbers	number	NOUN
ejpam-1609	5	14	arising	arise	VERB
ejpam-1609	5	15	in	in	ADP
ejpam-1609	5	16	enumerative	enumerative	ADJ
ejpam-1609	5	17	combinatorics	combinatoric	NOUN
ejpam-1609	5	18	.	.	PUNCT
ejpam-1609	6	1	binomial	binomial	ADJ
ejpam-1609	6	2	coefficients	coefficient	NOUN
ejpam-1609	6	3	give	give	VERB
ejpam-1609	6	4	the	the	DET
ejpam-1609	6	5	number	number	NOUN
ejpam-1609	6	6	of	of	ADP
ejpam-1609	6	7	subsets	subset	NOUN
ejpam-1609	6	8	of	of	ADP
ejpam-1609	6	9	a	a	DET
ejpam-1609	6	10	finite	finite	ADJ
ejpam-1609	6	11	set	set	NOUN
ejpam-1609	6	12	.	.	PUNCT
ejpam-1609	7	1	on	on	ADP
ejpam-1609	7	2	the	the	DET
ejpam-1609	7	3	other	other	ADJ
ejpam-1609	7	4	hand	hand	NOUN
ejpam-1609	7	5	,	,	PUNCT
ejpam-1609	7	6	gaussian	gaussian	ADJ
ejpam-1609	7	7	binomial	binomial	ADJ
ejpam-1609	7	8	coefficients	coefficient	NOUN
ejpam-1609	7	9	give	give	VERB
ejpam-1609	7	10	the	the	DET
ejpam-1609	7	11	number	number	NOUN
ejpam-1609	7	12	of	of	ADP
ejpam-1609	7	13	linear	linear	PROPN
ejpam-1609	7	14	codes	code	NOUN
ejpam-1609	7	15	over	over	ADP
ejpam-1609	7	16	finite	finite	ADJ
ejpam-1609	7	17	fields	field	NOUN
ejpam-1609	7	18	of	of	ADP
ejpam-1609	7	19	a	a	DET
ejpam-1609	7	20	particular	particular	ADJ
ejpam-1609	7	21	dimension	dimension	NOUN
ejpam-1609	7	22	.	.	PUNCT
ejpam-1609	8	1	since	since	SCONJ
ejpam-1609	8	2	the	the	DET
ejpam-1609	8	3	theory	theory	NOUN
ejpam-1609	8	4	of	of	ADP
ejpam-1609	8	5	linear	linear	PROPN
ejpam-1609	8	6	codes	code	NOUN
ejpam-1609	8	7	over	over	ADP
ejpam-1609	8	8	fields	field	NOUN
ejpam-1609	8	9	has	have	AUX
ejpam-1609	8	10	been	be	AUX
ejpam-1609	8	11	extended	extend	VERB
ejpam-1609	8	12	linear	linear	NOUN
ejpam-1609	8	13	codes	code	NOUN
ejpam-1609	8	14	over	over	ADP
ejpam-1609	8	15	rings	ring	NOUN
ejpam-1609	8	16	recently	recently	ADV
ejpam-1609	8	17	,	,	PUNCT
ejpam-1609	8	18	the	the	DET
ejpam-1609	8	19	problems	problem	NOUN
ejpam-1609	8	20	that	that	PRON
ejpam-1609	8	21	had	have	AUX
ejpam-1609	8	22	found	find	VERB
ejpam-1609	8	23	answers	answer	NOUN
ejpam-1609	8	24	for	for	ADP
ejpam-1609	8	25	field	field	NOUN
ejpam-1609	8	26	cases	case	NOUN
ejpam-1609	8	27	remain	remain	VERB
ejpam-1609	8	28	open	open	ADJ
ejpam-1609	8	29	for	for	ADP
ejpam-1609	8	30	the	the	DET
ejpam-1609	8	31	ring	ring	NOUN
ejpam-1609	8	32	cases	case	NOUN
ejpam-1609	8	33	.	.	PUNCT
ejpam-1609	9	1	one	one	NUM
ejpam-1609	9	2	of	of	ADP
ejpam-1609	9	3	such	such	ADJ
ejpam-1609	9	4	problems	problem	NOUN
ejpam-1609	9	5	is	be	AUX
ejpam-1609	9	6	establishing	establish	VERB
ejpam-1609	9	7	a	a	DET
ejpam-1609	9	8	formula	formula	NOUN
ejpam-1609	9	9	for	for	ADP
ejpam-1609	9	10	the	the	DET
ejpam-1609	9	11	number	number	NOUN
ejpam-1609	9	12	of	of	ADP
ejpam-1609	9	13	linear	linear	ADJ
ejpam-1609	9	14	codes	code	NOUN
ejpam-1609	9	15	of	of	ADP
ejpam-1609	9	16	a	a	DET
ejpam-1609	9	17	particular	particular	ADJ
ejpam-1609	9	18	type	type	NOUN
ejpam-1609	9	19	similar	similar	ADJ
ejpam-1609	9	20	to	to	ADP
ejpam-1609	9	21	gaussian	gaussian	ADJ
ejpam-1609	9	22	number	number	NOUN
ejpam-1609	9	23	formula	formula	NOUN
ejpam-1609	9	24	.	.	PUNCT
ejpam-1609	10	1	in	in	ADP
ejpam-1609	10	2	this	this	DET
ejpam-1609	10	3	paper	paper	NOUN
ejpam-1609	10	4	,	,	PUNCT
ejpam-1609	10	5	the	the	DET
ejpam-1609	10	6	authors	author	NOUN
ejpam-1609	10	7	provide	provide	VERB
ejpam-1609	10	8	such	such	DET
ejpam-1609	10	9	a	a	DET
ejpam-1609	10	10	formula	formula	NOUN
ejpam-1609	10	11	that	that	PRON
ejpam-1609	10	12	directly	directly	ADV
ejpam-1609	10	13	gives	give	VERB
ejpam-1609	10	14	the	the	DET
ejpam-1609	10	15	number	number	NOUN
ejpam-1609	10	16	of	of	ADP
ejpam-1609	10	17	linear	linear	PROPN
ejpam-1609	10	18	codes	code	NOUN
ejpam-1609	10	19	over	over	ADP
ejpam-1609	10	20	galois	galois	PROPN
ejpam-1609	10	21	rings	ring	NOUN
ejpam-1609	10	22	of	of	ADP
ejpam-1609	10	23	a	a	DET
ejpam-1609	10	24	particular	particular	ADJ
ejpam-1609	10	25	type	type	NOUN
ejpam-1609	10	26	.	.	PUNCT
ejpam-1609	11	1	linear	linear	ADJ
ejpam-1609	11	2	codes	code	NOUN
ejpam-1609	11	3	over	over	ADP
ejpam-1609	11	4	finite	finite	ADJ
ejpam-1609	11	5	rings	ring	NOUN
ejpam-1609	11	6	have	have	AUX
ejpam-1609	11	7	been	be	AUX
ejpam-1609	11	8	a	a	DET
ejpam-1609	11	9	very	very	ADV
ejpam-1609	11	10	important	important	ADJ
ejpam-1609	11	11	field	field	NOUN
ejpam-1609	11	12	of	of	ADP
ejpam-1609	11	13	coding	code	VERB
ejpam-1609	11	14	theory	theory	NOUN
ejpam-1609	11	15	due	due	ADP
ejpam-1609	11	16	to	to	ADP
ejpam-1609	11	17	hammons	hammon	NOUN
ejpam-1609	11	18	et	et	NOUN
ejpam-1609	11	19	al	al	PROPN
ejpam-1609	12	1	[	[	X
ejpam-1609	12	2	4	4	NUM
ejpam-1609	12	3	]	]	PUNCT
ejpam-1609	12	4	.	.	PUNCT
ejpam-1609	13	1	the	the	DET
ejpam-1609	13	2	enumeration	enumeration	NOUN
ejpam-1609	13	3	problems	problem	NOUN
ejpam-1609	13	4	over	over	ADP
ejpam-1609	13	5	rings	ring	NOUN
ejpam-1609	13	6	are	be	AUX
ejpam-1609	13	7	studied	study	VERB
ejpam-1609	13	8	by	by	ADP
ejpam-1609	13	9	many	many	ADJ
ejpam-1609	13	10	researchers	researcher	NOUN
ejpam-1609	13	11	.	.	PUNCT
ejpam-1609	14	1	some	some	PRON
ejpam-1609	14	2	of	of	ADP
ejpam-1609	14	3	them	they	PRON
ejpam-1609	14	4	are	be	AUX
ejpam-1609	14	5	[	[	X
ejpam-1609	14	6	1	1	NUM
ejpam-1609	14	7	,	,	PUNCT
ejpam-1609	14	8	2	2	NUM
ejpam-1609	14	9	,	,	PUNCT
ejpam-1609	14	10	3	3	NUM
ejpam-1609	14	11	,	,	PUNCT
ejpam-1609	14	12	5	5	NUM
ejpam-1609	14	13	,	,	PUNCT
ejpam-1609	14	14	10	10	NUM
ejpam-1609	14	15	,	,	PUNCT
ejpam-1609	14	16	11	11	NUM
ejpam-1609	14	17	,	,	PUNCT
ejpam-1609	14	18	14	14	NUM
ejpam-1609	14	19	]	]	PUNCT
ejpam-1609	14	20	.	.	PUNCT
ejpam-1609	15	1	the	the	DET
ejpam-1609	15	2	enumeration	enumeration	NOUN
ejpam-1609	15	3	in	in	ADP
ejpam-1609	15	4	all	all	PRON
ejpam-1609	15	5	of	of	ADP
ejpam-1609	15	6	these	these	DET
ejpam-1609	15	7	works	work	NOUN
ejpam-1609	15	8	are	be	AUX
ejpam-1609	15	9	based	base	VERB
ejpam-1609	15	10	on	on	ADP
ejpam-1609	15	11	recursive	recursive	ADJ
ejpam-1609	15	12	formulae	formulae	NOUN
ejpam-1609	15	13	.	.	PUNCT
ejpam-1609	16	1	in	in	ADP
ejpam-1609	16	2	this	this	DET
ejpam-1609	16	3	work	work	NOUN
ejpam-1609	16	4	,	,	PUNCT
ejpam-1609	16	5	we	we	PRON
ejpam-1609	16	6	give	give	VERB
ejpam-1609	16	7	a	a	DET
ejpam-1609	16	8	direct	direct	ADJ
ejpam-1609	16	9	calculation	calculation	NOUN
ejpam-1609	16	10	of	of	ADP
ejpam-1609	16	11	the	the	DET
ejpam-1609	16	12	number	number	NOUN
ejpam-1609	16	13	of	of	ADP
ejpam-1609	16	14	linear	linear	PROPN
ejpam-1609	16	15	codes	code	NOUN
ejpam-1609	16	16	over	over	ADP
ejpam-1609	16	17	an	an	DET
ejpam-1609	16	18	important	important	ADJ
ejpam-1609	16	19	family	family	NOUN
ejpam-1609	16	20	of	of	ADP
ejpam-1609	16	21	finite	finite	PROPN
ejpam-1609	16	22	rings	ring	NOUN
ejpam-1609	16	23	which	which	PRON
ejpam-1609	16	24	is	be	AUX
ejpam-1609	16	25	galois	galois	PROPN
ejpam-1609	16	26	rings	ring	NOUN
ejpam-1609	16	27	.	.	PUNCT
ejpam-1609	17	1	as	as	ADP
ejpam-1609	17	2	a	a	DET
ejpam-1609	17	3	result	result	NOUN
ejpam-1609	17	4	of	of	ADP
ejpam-1609	17	5	this	this	PRON
ejpam-1609	17	6	,	,	PUNCT
ejpam-1609	17	7	we	we	PRON
ejpam-1609	17	8	define	define	VERB
ejpam-1609	17	9	generalized	generalized	ADJ
ejpam-1609	17	10	gaussian	gaussian	ADJ
ejpam-1609	17	11	numbers	number	NOUN
ejpam-1609	17	12	as	as	ADP
ejpam-1609	17	13	a	a	DET
ejpam-1609	17	14	further	further	ADJ
ejpam-1609	17	15	generalization	generalization	NOUN
ejpam-1609	17	16	of	of	ADP
ejpam-1609	17	17	the	the	DET
ejpam-1609	17	18	previous	previous	ADJ
ejpam-1609	17	19	works	work	NOUN
ejpam-1609	17	20	[	[	X
ejpam-1609	17	21	10	10	NUM
ejpam-1609	17	22	,	,	PUNCT
ejpam-1609	17	23	11	11	NUM
ejpam-1609	17	24	]	]	PUNCT
ejpam-1609	17	25	and	and	CCONJ
ejpam-1609	17	26	give	give	VERB
ejpam-1609	17	27	some	some	PRON
ejpam-1609	17	28	of	of	ADP
ejpam-1609	17	29	their	their	PRON
ejpam-1609	17	30	properties	property	NOUN
ejpam-1609	17	31	similar	similar	ADJ
ejpam-1609	17	32	to	to	ADP
ejpam-1609	17	33	gaussian	gaussian	VERB
ejpam-1609	17	34	binomial	binomial	ADJ
ejpam-1609	17	35	coefficients	coefficient	NOUN
ejpam-1609	17	36	.	.	PUNCT
ejpam-1609	18	1	finally	finally	ADV
ejpam-1609	18	2	,	,	PUNCT
ejpam-1609	18	3	some	some	DET
ejpam-1609	18	4	number	number	NOUN
ejpam-1609	18	5	sequences	sequence	NOUN
ejpam-1609	18	6	are	be	AUX
ejpam-1609	18	7	also	also	ADV
ejpam-1609	18	8	∗corresponding	∗corresponde	VERB
ejpam-1609	18	9	author	author	NOUN
ejpam-1609	18	10	.	.	PUNCT
ejpam-1609	19	1	email	email	NOUN
ejpam-1609	19	2	addresses	address	NOUN
ejpam-1609	19	3	:	:	PUNCT
ejpam-1609	19	4	esalturk�yildiz.edu.tr	esalturk�yildiz.edu.tr	PROPN
ejpam-1609	19	5	(	(	PUNCT
ejpam-1609	19	6	e.	e.	PROPN
ejpam-1609	19	7	saltürk	saltürk	PROPN
ejpam-1609	19	8	)	)	PUNCT
ejpam-1609	19	9	,	,	PUNCT
ejpam-1609	19	10	isiap�yildiz.edu.tr	isiap�yildiz.edu.tr	PROPN
ejpam-1609	19	11	(	(	PUNCT
ejpam-1609	19	12	̇i	̇i	ADJ
ejpam-1609	19	13	.	.	PUNCT
ejpam-1609	20	1	şiap	şiap	PROPN
ejpam-1609	20	2	)	)	PUNCT
ejpam-1609	20	3	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1609	21	1	250	250	NUM
ejpam-1609	21	2	c	c	X
ejpam-1609	21	3	©	©	PROPN
ejpam-1609	21	4	2012	2012	NUM
ejpam-1609	21	5	ejpam	ejpam	VERB
ejpam-1609	21	6	all	all	DET
ejpam-1609	21	7	rights	right	NOUN
ejpam-1609	21	8	reserved	reserve	VERB
ejpam-1609	21	9	.	.	PUNCT
ejpam-1609	22	1	e.	e.	PROPN
ejpam-1609	22	2	saltürk	saltürk	PROPN
ejpam-1609	22	3	,	,	PUNCT
ejpam-1609	22	4	i̇.	i̇.	PROPN
ejpam-1609	22	5	şiap	şiap	PROPN
ejpam-1609	22	6	/	/	SYM
ejpam-1609	22	7	eur	eur	PROPN
ejpam-1609	22	8	.	.	PUNCT
ejpam-1609	23	1	j.	j.	PROPN
ejpam-1609	23	2	pure	pure	PROPN
ejpam-1609	23	3	appl	appl	PROPN
ejpam-1609	23	4	.	.	PROPN
ejpam-1609	23	5	math	math	PROPN
ejpam-1609	23	6	,	,	PUNCT
ejpam-1609	23	7	5	5	NUM
ejpam-1609	23	8	(	(	PUNCT
ejpam-1609	23	9	2012	2012	NUM
ejpam-1609	23	10	)	)	PUNCT
ejpam-1609	23	11	,	,	PUNCT
ejpam-1609	23	12	250	250	NUM
ejpam-1609	23	13	-	-	SYM
ejpam-1609	23	14	259	259	NUM
ejpam-1609	23	15	251	251	NUM
ejpam-1609	23	16	presented	present	VERB
ejpam-1609	23	17	.	.	PUNCT
ejpam-1609	24	1	in	in	ADP
ejpam-1609	24	2	the	the	DET
ejpam-1609	24	3	sequel	sequel	NOUN
ejpam-1609	24	4	,	,	PUNCT
ejpam-1609	24	5	we	we	PRON
ejpam-1609	24	6	present	present	VERB
ejpam-1609	24	7	some	some	DET
ejpam-1609	24	8	well	well	ADV
ejpam-1609	24	9	known	know	VERB
ejpam-1609	24	10	concepts	concept	NOUN
ejpam-1609	24	11	and	and	CCONJ
ejpam-1609	24	12	results	result	NOUN
ejpam-1609	24	13	in	in	ADP
ejpam-1609	24	14	both	both	DET
ejpam-1609	24	15	coding	code	VERB
ejpam-1609	24	16	theory	theory	NOUN
ejpam-1609	24	17	and	and	CCONJ
ejpam-1609	24	18	algebra	algebra	NOUN
ejpam-1609	24	19	.	.	PUNCT
ejpam-1609	25	1	fq	fq	PROPN
ejpam-1609	25	2	will	will	AUX
ejpam-1609	25	3	denote	denote	VERB
ejpam-1609	25	4	the	the	DET
ejpam-1609	25	5	finite	finite	ADJ
ejpam-1609	25	6	field	field	NOUN
ejpam-1609	25	7	with	with	ADP
ejpam-1609	25	8	q	q	NOUN
ejpam-1609	25	9	elements	element	NOUN
ejpam-1609	25	10	where	where	SCONJ
ejpam-1609	25	11	q	q	NOUN
ejpam-1609	25	12	is	be	AUX
ejpam-1609	25	13	a	a	DET
ejpam-1609	25	14	prime	prime	ADJ
ejpam-1609	25	15	power	power	NOUN
ejpam-1609	25	16	.	.	PUNCT
ejpam-1609	26	1	a	a	DET
ejpam-1609	26	2	linear	linear	ADJ
ejpam-1609	26	3	code	code	NOUN
ejpam-1609	26	4	c	c	NOUN
ejpam-1609	26	5	of	of	ADP
ejpam-1609	26	6	length	length	NOUN
ejpam-1609	26	7	n	n	CCONJ
ejpam-1609	26	8	over	over	ADP
ejpam-1609	26	9	fq	fq	PROPN
ejpam-1609	26	10	is	be	AUX
ejpam-1609	26	11	a	a	DET
ejpam-1609	26	12	subspace	subspace	NOUN
ejpam-1609	26	13	of	of	ADP
ejpam-1609	26	14	fn	fn	PROPN
ejpam-1609	26	15	q	q	PROPN
ejpam-1609	26	16	.	.	PUNCT
ejpam-1609	27	1	definition	definition	NOUN
ejpam-1609	27	2	1	1	NUM
ejpam-1609	27	3	.	.	PUNCT
ejpam-1609	28	1	[	[	X
ejpam-1609	28	2	8	8	NUM
ejpam-1609	28	3	]	]	PUNCT
ejpam-1609	28	4	for	for	ADP
ejpam-1609	28	5	positive	positive	ADJ
ejpam-1609	28	6	integers	integer	NOUN
ejpam-1609	28	7	b	b	ADP
ejpam-1609	28	8	6=	6=	ADP
ejpam-1609	28	9	1	1	NUM
ejpam-1609	28	10	and	and	CCONJ
ejpam-1609	28	11	n	n	CCONJ
ejpam-1609	28	12	,	,	PUNCT
ejpam-1609	28	13	and	and	CCONJ
ejpam-1609	28	14	all	all	DET
ejpam-1609	28	15	nonnegative	nonnegative	ADJ
ejpam-1609	28	16	integers	integer	NOUN
ejpam-1609	28	17	k	k	NOUN
ejpam-1609	28	18	,	,	PUNCT
ejpam-1609	28	19	the	the	DET
ejpam-1609	28	20	b	b	PROPN
ejpam-1609	28	21	-	-	PUNCT
ejpam-1609	28	22	ary	ary	ADJ
ejpam-1609	28	23	gaussian	gaussian	ADJ
ejpam-1609	28	24	binomial	binomial	ADJ
ejpam-1609	28	25	coefficients	coefficient	NOUN
ejpam-1609	28	26	�	�	PROPN
ejpam-1609	28	27	n	n	CCONJ
ejpam-1609	28	28	k	k	PROPN
ejpam-1609	28	29	�	�	PROPN
ejpam-1609	28	30	b	b	PROPN
ejpam-1609	28	31	are	be	AUX
ejpam-1609	28	32	defined	define	VERB
ejpam-1609	28	33	by	by	ADP
ejpam-1609	28	34	�	�	PROPN
ejpam-1609	28	35	n	n	CCONJ
ejpam-1609	28	36	0	0	NUM
ejpam-1609	28	37	�	�	PROPN
ejpam-1609	28	38	b	b	PROPN
ejpam-1609	28	39	=	=	SYM
ejpam-1609	28	40	1	1	NUM
ejpam-1609	28	41	,	,	PUNCT
ejpam-1609	28	42	and	and	CCONJ
ejpam-1609	28	43	�	�	PROPN
ejpam-1609	28	44	n	n	CCONJ
ejpam-1609	28	45	k	k	PROPN
ejpam-1609	28	46	�	�	PROPN
ejpam-1609	28	47	b	b	PROPN
ejpam-1609	28	48	=	=	SYM
ejpam-1609	28	49	(	(	PUNCT
ejpam-1609	28	50	bn−	bn−	X
ejpam-1609	28	51	1)(bn−1	1)(bn−1	NUM
ejpam-1609	28	52	−	−	NUM
ejpam-1609	28	53	1	1	NUM
ejpam-1609	28	54	)	)	PUNCT
ejpam-1609	28	55	.	.	PUNCT
ejpam-1609	28	56	.	.	PUNCT
ejpam-1609	29	1	.	.	PUNCT
ejpam-1609	30	1	(	(	PUNCT
ejpam-1609	30	2	bn−k+1−	bn−k+1−	NOUN
ejpam-1609	30	3	1	1	NUM
ejpam-1609	30	4	)	)	PUNCT
ejpam-1609	30	5	(	(	PUNCT
ejpam-1609	30	6	bk	bk	VERB
ejpam-1609	30	7	−	−	PROPN
ejpam-1609	30	8	1)(bk−1−	1)(bk−1−	PROPN
ejpam-1609	30	9	1	1	NUM
ejpam-1609	30	10	)	)	PUNCT
ejpam-1609	30	11	.	.	PUNCT
ejpam-1609	30	12	.	.	PUNCT
ejpam-1609	30	13	.	.	PUNCT
ejpam-1609	31	1	(	(	PUNCT
ejpam-1609	31	2	b−	b−	NOUN
ejpam-1609	31	3	1	1	NUM
ejpam-1609	31	4	)	)	PUNCT
ejpam-1609	31	5	,	,	PUNCT
ejpam-1609	31	6	k	k	X
ejpam-1609	31	7	=	=	SYM
ejpam-1609	31	8	1,2	1,2	NUM
ejpam-1609	31	9	,	,	PUNCT
ejpam-1609	31	10	.	.	PUNCT
ejpam-1609	31	11	.	.	PUNCT
ejpam-1609	31	12	.	.	PUNCT
ejpam-1609	32	1	theorem	theorem	VERB
ejpam-1609	32	2	1	1	NUM
ejpam-1609	32	3	.	.	PUNCT
ejpam-1609	33	1	[	[	X
ejpam-1609	33	2	8	8	NUM
ejpam-1609	33	3	]	]	X
ejpam-1609	33	4	the	the	DET
ejpam-1609	33	5	number	number	NOUN
ejpam-1609	33	6	of	of	ADP
ejpam-1609	33	7	distinct	distinct	ADJ
ejpam-1609	33	8	(	(	PUNCT
ejpam-1609	33	9	although	although	SCONJ
ejpam-1609	33	10	not	not	PART
ejpam-1609	33	11	necessarily	necessarily	ADV
ejpam-1609	33	12	inequivalent	inequivalent	VERB
ejpam-1609	33	13	)	)	PUNCT
ejpam-1609	34	1	[	[	X
ejpam-1609	34	2	n	n	CCONJ
ejpam-1609	34	3	,	,	PUNCT
ejpam-1609	34	4	k]-codes	k]-code	NOUN
ejpam-1609	34	5	over	over	ADP
ejpam-1609	34	6	fq	fq	PROPN
ejpam-1609	34	7	is	be	AUX
ejpam-1609	34	8	the	the	DET
ejpam-1609	34	9	q	q	ADJ
ejpam-1609	34	10	-	-	PUNCT
ejpam-1609	34	11	ary	ary	ADJ
ejpam-1609	34	12	gaussian	gaussian	ADJ
ejpam-1609	34	13	binomial	binomial	ADJ
ejpam-1609	34	14	coefficient	coefficient	NOUN
ejpam-1609	34	15	�	�	PROPN
ejpam-1609	34	16	n	n	CCONJ
ejpam-1609	34	17	k	k	PROPN
ejpam-1609	34	18	�	�	PROPN
ejpam-1609	34	19	q	q	PROPN
ejpam-1609	34	20	where	where	SCONJ
ejpam-1609	34	21	q	q	NOUN
ejpam-1609	34	22	is	be	AUX
ejpam-1609	34	23	a	a	DET
ejpam-1609	34	24	prime	prime	NOUN
ejpam-1609	34	25	.	.	PUNCT
ejpam-1609	35	1	for	for	ADP
ejpam-1609	35	2	the	the	DET
ejpam-1609	35	3	proof	proof	NOUN
ejpam-1609	35	4	of	of	ADP
ejpam-1609	35	5	this	this	DET
ejpam-1609	35	6	theorem	theorem	NOUN
ejpam-1609	35	7	and	and	CCONJ
ejpam-1609	35	8	some	some	DET
ejpam-1609	35	9	more	more	ADJ
ejpam-1609	35	10	details	detail	NOUN
ejpam-1609	35	11	the	the	DET
ejpam-1609	35	12	reader	reader	NOUN
ejpam-1609	35	13	is	be	AUX
ejpam-1609	35	14	kindly	kindly	ADV
ejpam-1609	35	15	directed	direct	VERB
ejpam-1609	35	16	to	to	ADP
ejpam-1609	35	17	[	[	X
ejpam-1609	35	18	8	8	NUM
ejpam-1609	35	19	]	]	PUNCT
ejpam-1609	35	20	.	.	PUNCT
ejpam-1609	36	1	definition	definition	NOUN
ejpam-1609	36	2	2	2	NUM
ejpam-1609	36	3	.	.	PUNCT
ejpam-1609	37	1	[	[	X
ejpam-1609	37	2	13	13	NUM
ejpam-1609	37	3	]	]	PUNCT
ejpam-1609	37	4	a	a	DET
ejpam-1609	37	5	galois	galois	PROPN
ejpam-1609	37	6	ring	ring	NOUN
ejpam-1609	37	7	is	be	AUX
ejpam-1609	37	8	defined	define	VERB
ejpam-1609	37	9	to	to	PART
ejpam-1609	37	10	be	be	AUX
ejpam-1609	37	11	a	a	DET
ejpam-1609	37	12	finite	finite	ADJ
ejpam-1609	37	13	ring	ring	NOUN
ejpam-1609	37	14	with	with	ADP
ejpam-1609	37	15	identity	identity	NOUN
ejpam-1609	37	16	1	1	NUM
ejpam-1609	37	17	such	such	ADJ
ejpam-1609	37	18	that	that	SCONJ
ejpam-1609	37	19	the	the	DET
ejpam-1609	37	20	set	set	NOUN
ejpam-1609	37	21	of	of	ADP
ejpam-1609	37	22	its	its	PRON
ejpam-1609	37	23	zero	zero	NUM
ejpam-1609	37	24	divisors	divisor	NOUN
ejpam-1609	37	25	including	include	VERB
ejpam-1609	37	26	0	0	NUM
ejpam-1609	37	27	forms	form	NOUN
ejpam-1609	37	28	a	a	DET
ejpam-1609	37	29	principal	principal	ADJ
ejpam-1609	37	30	ideal	ideal	NOUN
ejpam-1609	37	31	(	(	PUNCT
ejpam-1609	37	32	p1	p1	NOUN
ejpam-1609	37	33	)	)	PUNCT
ejpam-1609	37	34	for	for	ADP
ejpam-1609	37	35	some	some	DET
ejpam-1609	37	36	prime	prime	NOUN
ejpam-1609	37	37	p	p	NOUN
ejpam-1609	37	38	where	where	SCONJ
ejpam-1609	37	39	p1	p1	NOUN
ejpam-1609	37	40	=	=	NOUN
ejpam-1609	37	41	1	1	NUM
ejpam-1609	37	42	+	+	NUM
ejpam-1609	37	43	1	1	NUM
ejpam-1609	37	44	+	+	NUM
ejpam-1609	37	45	·	·	PUNCT
ejpam-1609	37	46	·	·	PUNCT
ejpam-1609	37	47	·	·	PUNCT
ejpam-1609	38	1	+	+	CCONJ
ejpam-1609	38	2	1	1	X
ejpam-1609	38	3	︸	︸	X
ejpam-1609	38	4	︷︷	︷︷	VERB
ejpam-1609	38	5	︸	︸	ADP
ejpam-1609	39	1	p	p	NOUN
ejpam-1609	39	2	.	.	PUNCT
ejpam-1609	40	1	it	it	PRON
ejpam-1609	40	2	is	be	AUX
ejpam-1609	40	3	well	well	ADV
ejpam-1609	40	4	known	know	VERB
ejpam-1609	40	5	that	that	SCONJ
ejpam-1609	40	6	the	the	DET
ejpam-1609	40	7	characteristic	characteristic	ADJ
ejpam-1609	40	8	a	a	DET
ejpam-1609	40	9	finite	finite	PROPN
ejpam-1609	40	10	galois	galois	PROPN
ejpam-1609	40	11	ring	ring	NOUN
ejpam-1609	40	12	is	be	AUX
ejpam-1609	40	13	a	a	DET
ejpam-1609	40	14	prime	prime	ADJ
ejpam-1609	40	15	power	power	NOUN
ejpam-1609	40	16	number	number	NOUN
ejpam-1609	40	17	.	.	PUNCT
ejpam-1609	41	1	a	a	DET
ejpam-1609	41	2	finite	finite	ADJ
ejpam-1609	41	3	galois	galois	PROPN
ejpam-1609	41	4	ring	ring	NOUN
ejpam-1609	41	5	of	of	ADP
ejpam-1609	41	6	characteristic	characteristic	ADJ
ejpam-1609	41	7	pm	pm	NOUN
ejpam-1609	41	8	and	and	CCONJ
ejpam-1609	41	9	cardinality	cardinality	NOUN
ejpam-1609	41	10	pmt	pmt	PROPN
ejpam-1609	41	11	where	where	SCONJ
ejpam-1609	41	12	p	p	NOUN
ejpam-1609	41	13	is	be	AUX
ejpam-1609	41	14	a	a	DET
ejpam-1609	41	15	prime	prime	ADJ
ejpam-1609	41	16	number	number	NOUN
ejpam-1609	41	17	and	and	CCONJ
ejpam-1609	41	18	m	m	PROPN
ejpam-1609	41	19	,	,	PUNCT
ejpam-1609	41	20	t	t	PROPN
ejpam-1609	41	21	are	be	AUX
ejpam-1609	41	22	positive	positive	ADJ
ejpam-1609	41	23	integers	integer	NOUN
ejpam-1609	41	24	is	be	AUX
ejpam-1609	41	25	denoted	denote	VERB
ejpam-1609	41	26	by	by	ADP
ejpam-1609	41	27	r	r	NOUN
ejpam-1609	41	28	=	=	SYM
ejpam-1609	41	29	gr(pm	gr(pm	PROPN
ejpam-1609	41	30	,	,	PUNCT
ejpam-1609	41	31	t	t	PROPN
ejpam-1609	41	32	)	)	PUNCT
ejpam-1609	41	33	.	.	PUNCT
ejpam-1609	42	1	besides	besides	SCONJ
ejpam-1609	42	2	some	some	DET
ejpam-1609	42	3	further	further	ADJ
ejpam-1609	42	4	remarks	remark	NOUN
ejpam-1609	42	5	which	which	PRON
ejpam-1609	42	6	will	will	AUX
ejpam-1609	42	7	be	be	AUX
ejpam-1609	42	8	given	give	VERB
ejpam-1609	42	9	in	in	ADP
ejpam-1609	42	10	the	the	DET
ejpam-1609	42	11	next	next	ADJ
ejpam-1609	42	12	section	section	NOUN
ejpam-1609	42	13	,	,	PUNCT
ejpam-1609	42	14	more	more	ADV
ejpam-1609	42	15	detailed	detailed	ADJ
ejpam-1609	42	16	and	and	CCONJ
ejpam-1609	42	17	further	further	ADJ
ejpam-1609	42	18	information	information	NOUN
ejpam-1609	42	19	regarding	regard	VERB
ejpam-1609	42	20	galois	galois	PROPN
ejpam-1609	42	21	rings	ring	NOUN
ejpam-1609	42	22	can	can	AUX
ejpam-1609	42	23	be	be	AUX
ejpam-1609	42	24	found	find	VERB
ejpam-1609	42	25	in	in	ADP
ejpam-1609	42	26	[	[	X
ejpam-1609	42	27	9	9	NUM
ejpam-1609	42	28	,	,	PUNCT
ejpam-1609	42	29	13	13	NUM
ejpam-1609	42	30	]	]	PUNCT
ejpam-1609	42	31	.	.	PUNCT
ejpam-1609	43	1	definition	definition	NOUN
ejpam-1609	43	2	3	3	NUM
ejpam-1609	43	3	.	.	PUNCT
ejpam-1609	43	4	an	an	DET
ejpam-1609	43	5	r	r	NOUN
ejpam-1609	43	6	submodule	submodule	NOUN
ejpam-1609	43	7	of	of	ADP
ejpam-1609	43	8	rn	rn	PROPN
ejpam-1609	43	9	is	be	AUX
ejpam-1609	43	10	called	call	VERB
ejpam-1609	43	11	an	an	DET
ejpam-1609	43	12	r	r	NOUN
ejpam-1609	43	13	-	-	PUNCT
ejpam-1609	43	14	linear	linear	NOUN
ejpam-1609	43	15	code	code	NOUN
ejpam-1609	43	16	.	.	PUNCT
ejpam-1609	44	1	theorem	theorem	NOUN
ejpam-1609	44	2	2	2	NUM
ejpam-1609	44	3	.	.	PUNCT
ejpam-1609	45	1	[	[	X
ejpam-1609	45	2	6	6	NUM
ejpam-1609	45	3	]	]	PUNCT
ejpam-1609	45	4	a	a	DET
ejpam-1609	45	5	generator	generator	NOUN
ejpam-1609	45	6	matrix	matrix	NOUN
ejpam-1609	45	7	of	of	ADP
ejpam-1609	45	8	an	an	DET
ejpam-1609	45	9	gr(pm	gr(pm	NOUN
ejpam-1609	45	10	,	,	PUNCT
ejpam-1609	45	11	t)-linear	t)-linear	PUNCT
ejpam-1609	45	12	code	code	PROPN
ejpam-1609	45	13	c	c	PROPN
ejpam-1609	45	14	is	be	AUX
ejpam-1609	45	15	equivalent	equivalent	ADJ
ejpam-1609	45	16	to	to	ADP
ejpam-1609	45	17	a	a	DET
ejpam-1609	45	18	linear	linear	ADJ
ejpam-1609	45	19	code	code	NOUN
ejpam-1609	45	20	generated	generate	VERB
ejpam-1609	45	21	by	by	ADP
ejpam-1609	45	22			NOUN
ejpam-1609	45	23			NOUN
ejpam-1609	45	24			NOUN
ejpam-1609	45	25			NOUN
ejpam-1609	45	26			NOUN
ejpam-1609	45	27			NOUN
ejpam-1609	45	28	ik1	ik1	VERB
ejpam-1609	45	29	a11	a11	PROPN
ejpam-1609	45	30	a12	a12	PROPN
ejpam-1609	45	31	·	·	PUNCT
ejpam-1609	45	32	·	·	PUNCT
ejpam-1609	45	33	·	·	PUNCT
ejpam-1609	45	34	a1	a1	PROPN
ejpam-1609	45	35	m	m	NOUN
ejpam-1609	45	36	0	0	NUM
ejpam-1609	45	37	pik2	pik2	NOUN
ejpam-1609	45	38	pa22	pa22	PROPN
ejpam-1609	45	39	·	·	PUNCT
ejpam-1609	45	40	·	·	PUNCT
ejpam-1609	45	41	·	·	PUNCT
ejpam-1609	46	1	pa2	pa2	PROPN
ejpam-1609	46	2	m	m	PROPN
ejpam-1609	46	3	...	...	PUNCT
ejpam-1609	46	4	...	...	PUNCT
ejpam-1609	46	5	...	...	PUNCT
ejpam-1609	46	6	...	...	PUNCT
ejpam-1609	47	1	...	...	PUNCT
ejpam-1609	48	1	0	0	NUM
ejpam-1609	48	2	0	0	NUM
ejpam-1609	48	3	·	·	PUNCT
ejpam-1609	48	4	·	·	PUNCT
ejpam-1609	48	5	·	·	PUNCT
ejpam-1609	49	1	pm−1	pm−1	NOUN
ejpam-1609	49	2	ikm−1	ikm−1	PROPN
ejpam-1609	49	3	pm−1amm	pm−1amm	PROPN
ejpam-1609	49	4			PROPN
ejpam-1609	49	5			NOUN
ejpam-1609	49	6			VERB
ejpam-1609	49	7			NOUN
ejpam-1609	49	8			NOUN
ejpam-1609	49	9			PUNCT
ejpam-1609	50	1	(	(	PUNCT
ejpam-1609	50	2	1	1	X
ejpam-1609	50	3	)	)	PUNCT
ejpam-1609	50	4	where	where	SCONJ
ejpam-1609	50	5	ai	ai	VERB
ejpam-1609	50	6	j	j	PROPN
ejpam-1609	50	7	’s	’s	PART
ejpam-1609	50	8	denote	denote	VERB
ejpam-1609	50	9	matrices	matrix	NOUN
ejpam-1609	50	10	whose	whose	DET
ejpam-1609	50	11	entries	entry	NOUN
ejpam-1609	50	12	are	be	AUX
ejpam-1609	50	13	from	from	ADP
ejpam-1609	50	14	r	r	NOUN
ejpam-1609	50	15	and	and	CCONJ
ejpam-1609	50	16	ik1	ik1	ADV
ejpam-1609	50	17	,	,	PUNCT
ejpam-1609	50	18	ik2	ik2	PROPN
ejpam-1609	50	19	,	,	PUNCT
ejpam-1609	50	20	.	.	PUNCT
ejpam-1609	50	21	.	.	PUNCT
ejpam-1609	50	22	.	.	PUNCT
ejpam-1609	51	1	,	,	PUNCT
ejpam-1609	51	2	ikm	ikm	PROPN
ejpam-1609	51	3	are	be	AUX
ejpam-1609	51	4	identity	identity	NOUN
ejpam-1609	51	5	matrices	matrix	NOUN
ejpam-1609	51	6	of	of	ADP
ejpam-1609	51	7	sizes	size	NOUN
ejpam-1609	51	8	k1	k1	NOUN
ejpam-1609	51	9	,	,	PUNCT
ejpam-1609	51	10	k2	k2	NOUN
ejpam-1609	51	11	,	,	PUNCT
ejpam-1609	51	12	.	.	PUNCT
ejpam-1609	51	13	.	.	PUNCT
ejpam-1609	52	1	.	.	PUNCT
ejpam-1609	53	1	,	,	PUNCT
ejpam-1609	53	2	km	km	VERB
ejpam-1609	53	3	respectively	respectively	ADV
ejpam-1609	53	4	.	.	PUNCT
ejpam-1609	54	1	a	a	DET
ejpam-1609	54	2	linear	linear	PROPN
ejpam-1609	54	3	code	code	NOUN
ejpam-1609	54	4	c	c	NOUN
ejpam-1609	54	5	generated	generate	VERB
ejpam-1609	54	6	by	by	ADP
ejpam-1609	54	7	a	a	DET
ejpam-1609	54	8	matrix	matrix	NOUN
ejpam-1609	54	9	(	(	PUNCT
ejpam-1609	54	10	1	1	X
ejpam-1609	54	11	)	)	PUNCT
ejpam-1609	54	12	is	be	AUX
ejpam-1609	54	13	called	call	VERB
ejpam-1609	54	14	a	a	DET
ejpam-1609	54	15	(	(	PUNCT
ejpam-1609	54	16	k1	k1	NOUN
ejpam-1609	54	17	,	,	PUNCT
ejpam-1609	54	18	k2	k2	NOUN
ejpam-1609	54	19	,	,	PUNCT
ejpam-1609	54	20	.	.	PUNCT
ejpam-1609	54	21	.	.	PUNCT
ejpam-1609	55	1	.	.	PUNCT
ejpam-1609	56	1	,	,	PUNCT
ejpam-1609	56	2	km)-type	km)-type	PROPN
ejpam-1609	56	3	code	code	PROPN
ejpam-1609	56	4	.	.	PUNCT
ejpam-1609	57	1	e.	e.	PROPN
ejpam-1609	57	2	saltürk	saltürk	PROPN
ejpam-1609	57	3	,	,	PUNCT
ejpam-1609	57	4	i̇.	i̇.	PROPN
ejpam-1609	57	5	şiap	şiap	PROPN
ejpam-1609	57	6	/	/	SYM
ejpam-1609	57	7	eur	eur	PROPN
ejpam-1609	57	8	.	.	PUNCT
ejpam-1609	58	1	j.	j.	PROPN
ejpam-1609	58	2	pure	pure	PROPN
ejpam-1609	58	3	appl	appl	PROPN
ejpam-1609	58	4	.	.	PROPN
ejpam-1609	58	5	math	math	PROPN
ejpam-1609	58	6	,	,	PUNCT
ejpam-1609	58	7	5	5	NUM
ejpam-1609	58	8	(	(	PUNCT
ejpam-1609	58	9	2012	2012	NUM
ejpam-1609	58	10	)	)	PUNCT
ejpam-1609	58	11	,	,	PUNCT
ejpam-1609	58	12	250	250	NUM
ejpam-1609	58	13	-	-	SYM
ejpam-1609	58	14	259	259	NUM
ejpam-1609	58	15	252	252	NUM
ejpam-1609	58	16	2	2	NUM
ejpam-1609	58	17	.	.	PUNCT
ejpam-1609	59	1	codes	code	NOUN
ejpam-1609	59	2	over	over	ADP
ejpam-1609	59	3	galois	galois	PROPN
ejpam-1609	59	4	rings	ring	NOUN
ejpam-1609	59	5	a	a	DET
ejpam-1609	59	6	definition	definition	NOUN
ejpam-1609	59	7	in	in	ADP
ejpam-1609	59	8	a	a	DET
ejpam-1609	59	9	closed	closed	ADJ
ejpam-1609	59	10	form	form	NOUN
ejpam-1609	59	11	for	for	ADP
ejpam-1609	59	12	galois	galois	PROPN
ejpam-1609	59	13	rings	ring	NOUN
ejpam-1609	59	14	is	be	AUX
ejpam-1609	59	15	given	give	VERB
ejpam-1609	59	16	in	in	ADP
ejpam-1609	59	17	the	the	DET
ejpam-1609	59	18	previous	previous	ADJ
ejpam-1609	59	19	section	section	NOUN
ejpam-1609	59	20	(	(	PUNCT
ejpam-1609	59	21	definition	definition	NOUN
ejpam-1609	59	22	2	2	NUM
ejpam-1609	59	23	)	)	PUNCT
ejpam-1609	59	24	.	.	PUNCT
ejpam-1609	60	1	here	here	ADV
ejpam-1609	60	2	,	,	PUNCT
ejpam-1609	60	3	first	first	ADV
ejpam-1609	60	4	we	we	PRON
ejpam-1609	60	5	give	give	VERB
ejpam-1609	60	6	an	an	DET
ejpam-1609	60	7	alternative	alternative	ADJ
ejpam-1609	60	8	description	description	NOUN
ejpam-1609	60	9	of	of	ADP
ejpam-1609	60	10	a	a	DET
ejpam-1609	60	11	galois	galois	PROPN
ejpam-1609	60	12	ring	ring	NOUN
ejpam-1609	60	13	which	which	PRON
ejpam-1609	60	14	is	be	AUX
ejpam-1609	60	15	constructive	constructive	ADJ
ejpam-1609	60	16	and	and	CCONJ
ejpam-1609	60	17	it	it	PRON
ejpam-1609	60	18	will	will	AUX
ejpam-1609	60	19	be	be	AUX
ejpam-1609	60	20	referred	refer	VERB
ejpam-1609	60	21	frequently	frequently	ADV
ejpam-1609	60	22	.	.	PUNCT
ejpam-1609	61	1	define	define	VERB
ejpam-1609	61	2	the	the	DET
ejpam-1609	61	3	following	follow	VERB
ejpam-1609	61	4	map	map	NOUN
ejpam-1609	61	5	[	[	X
ejpam-1609	61	6	13	13	NUM
ejpam-1609	61	7	]	]	PUNCT
ejpam-1609	61	8	from	from	ADP
ejpam-1609	61	9	polynomial	polynomial	ADJ
ejpam-1609	61	10	ring	ring	NOUN
ejpam-1609	61	11	zpm[x	zpm[x	NOUN
ejpam-1609	61	12	]	]	PUNCT
ejpam-1609	61	13	over	over	ADP
ejpam-1609	61	14	zpm	zpm	PROPN
ejpam-1609	61	15	to	to	ADP
ejpam-1609	61	16	the	the	DET
ejpam-1609	61	17	polynomial	polynomial	ADJ
ejpam-1609	61	18	fp[x	fp[x	PROPN
ejpam-1609	61	19	]	]	PUNCT
ejpam-1609	61	20	over	over	ADP
ejpam-1609	61	21	fp	fp	ADJ
ejpam-1609	61	22	:	:	PUNCT
ejpam-1609	61	23	−	−	PROPN
ejpam-1609	61	24	:	:	PUNCT
ejpam-1609	61	25	zpm[x]→	zpm[x]→	PROPN
ejpam-1609	61	26	fp[x	fp[x	PROPN
ejpam-1609	61	27	]	]	SYM
ejpam-1609	61	28	a0	a0	PROPN
ejpam-1609	61	29	+	+	CCONJ
ejpam-1609	61	30	a1	a1	NOUN
ejpam-1609	61	31	x	x	X
ejpam-1609	61	32	+	+	CCONJ
ejpam-1609	61	33	.	.	PUNCT
ejpam-1609	61	34	.	.	PUNCT
ejpam-1609	62	1	.+	.+	NOUN
ejpam-1609	62	2	an	an	DET
ejpam-1609	62	3	xn	xn	PROPN
ejpam-1609	62	4	7→	7→	NUM
ejpam-1609	62	5	ā0	ā0	NOUN
ejpam-1609	63	1	+	+	NUM
ejpam-1609	63	2	ā1	ā1	NOUN
ejpam-1609	63	3	x	x	X
ejpam-1609	64	1	+	+	CCONJ
ejpam-1609	64	2	.	.	PUNCT
ejpam-1609	64	3	.	.	PUNCT
ejpam-1609	65	1	.+	.+	NOUN
ejpam-1609	65	2	ān	ān	NOUN
ejpam-1609	65	3	xn	xn	INTJ
ejpam-1609	65	4	where	where	SCONJ
ejpam-1609	65	5	x	x	PRON
ejpam-1609	65	6	is	be	AUX
ejpam-1609	65	7	an	an	DET
ejpam-1609	65	8	indeterminate	indeterminate	NOUN
ejpam-1609	65	9	over	over	ADP
ejpam-1609	65	10	zpm	zpm	PROPN
ejpam-1609	65	11	and	and	CCONJ
ejpam-1609	65	12	also	also	ADV
ejpam-1609	65	13	over	over	ADP
ejpam-1609	65	14	fp	fp	NOUN
ejpam-1609	65	15	,	,	PUNCT
ejpam-1609	65	16	āi	āi	PROPN
ejpam-1609	65	17	∈	∈	PROPN
ejpam-1609	65	18	zp	zp	NOUN
ejpam-1609	65	19	is	be	AUX
ejpam-1609	65	20	the	the	DET
ejpam-1609	65	21	residue	residue	NOUN
ejpam-1609	65	22	of	of	ADP
ejpam-1609	65	23	ai	ai	PROPN
ejpam-1609	65	24	∈	∈	PROPN
ejpam-1609	65	25	zpm	zpm	PROPN
ejpam-1609	65	26	and	and	CCONJ
ejpam-1609	65	27	i	i	NOUN
ejpam-1609	65	28	=	=	NOUN
ejpam-1609	65	29	0,1	0,1	NUM
ejpam-1609	65	30	,	,	PUNCT
ejpam-1609	65	31	.	.	PUNCT
ejpam-1609	65	32	.	.	PUNCT
ejpam-1609	66	1	.	.	PUNCT
ejpam-1609	67	1	,	,	PUNCT
ejpam-1609	67	2	n.	n.	NOUN
ejpam-1609	67	3	definition	definition	NOUN
ejpam-1609	67	4	4	4	NUM
ejpam-1609	67	5	.	.	PUNCT
ejpam-1609	68	1	[	[	X
ejpam-1609	68	2	9	9	NUM
ejpam-1609	68	3	]	]	PUNCT
ejpam-1609	68	4	let	let	VERB
ejpam-1609	68	5	f	f	PROPN
ejpam-1609	68	6	(	(	PUNCT
ejpam-1609	68	7	x	x	X
ejpam-1609	68	8	)	)	PUNCT
ejpam-1609	68	9	=	=	SYM
ejpam-1609	68	10	a0	a0	PROPN
ejpam-1609	68	11	+	+	CCONJ
ejpam-1609	68	12	a1	a1	NOUN
ejpam-1609	68	13	x	x	X
ejpam-1609	68	14	+	+	CCONJ
ejpam-1609	68	15	.	.	PUNCT
ejpam-1609	68	16	.	.	PUNCT
ejpam-1609	68	17	.	.	PUNCT
ejpam-1609	69	1	+	+	CCONJ
ejpam-1609	69	2	an	an	DET
ejpam-1609	69	3	xn	xn	NOUN
ejpam-1609	69	4	be	be	VERB
ejpam-1609	69	5	monic	monic	ADJ
ejpam-1609	69	6	polynomial	polynomial	ADJ
ejpam-1609	69	7	of	of	ADP
ejpam-1609	69	8	degree	degree	NOUN
ejpam-1609	69	9	d	d	X
ejpam-1609	69	10	¾	¾	NOUN
ejpam-1609	69	11	1	1	NUM
ejpam-1609	69	12	in	in	ADP
ejpam-1609	69	13	zpm[x	zpm[x	NOUN
ejpam-1609	69	14	]	]	PUNCT
ejpam-1609	69	15	.	.	PUNCT
ejpam-1609	70	1	if	if	SCONJ
ejpam-1609	70	2	f̄	f̄	PROPN
ejpam-1609	70	3	(	(	PUNCT
ejpam-1609	70	4	x	x	NOUN
ejpam-1609	70	5	)	)	PUNCT
ejpam-1609	70	6	=	=	SYM
ejpam-1609	70	7	ā0	ā0	NOUN
ejpam-1609	70	8	+	+	NUM
ejpam-1609	70	9	ā1	ā1	NOUN
ejpam-1609	70	10	x	x	X
ejpam-1609	71	1	+	+	CCONJ
ejpam-1609	71	2	.	.	PUNCT
ejpam-1609	71	3	.	.	PUNCT
ejpam-1609	71	4	.	.	PUNCT
ejpam-1609	72	1	+	+	CCONJ
ejpam-1609	72	2	ān	ān	NOUN
ejpam-1609	72	3	xn	xn	PROPN
ejpam-1609	72	4	is	be	AUX
ejpam-1609	72	5	irreducible	irreducible	ADJ
ejpam-1609	72	6	in	in	ADP
ejpam-1609	72	7	fp[x	fp[x	PROPN
ejpam-1609	72	8	]	]	PUNCT
ejpam-1609	72	9	,	,	PUNCT
ejpam-1609	72	10	f	f	PROPN
ejpam-1609	72	11	(	(	PUNCT
ejpam-1609	72	12	x	x	X
ejpam-1609	72	13	)	)	PUNCT
ejpam-1609	72	14	is	be	AUX
ejpam-1609	72	15	called	call	VERB
ejpam-1609	72	16	a	a	DET
ejpam-1609	72	17	monic	monic	ADJ
ejpam-1609	72	18	basic	basic	ADJ
ejpam-1609	72	19	irreducible	irreducible	ADJ
ejpam-1609	72	20	polynomial	polynomial	NOUN
ejpam-1609	72	21	in	in	ADP
ejpam-1609	72	22	zpm[x	zpm[x	NOUN
ejpam-1609	72	23	]	]	PUNCT
ejpam-1609	72	24	.	.	PUNCT
ejpam-1609	73	1	let	let	VERB
ejpam-1609	73	2	r	r	NOUN
ejpam-1609	73	3	=	=	SYM
ejpam-1609	73	4	zpm[ξ	zpm[ξ	PROPN
ejpam-1609	73	5	]	]	PUNCT
ejpam-1609	73	6	where	where	SCONJ
ejpam-1609	73	7	p	p	NOUN
ejpam-1609	73	8	is	be	AUX
ejpam-1609	73	9	a	a	DET
ejpam-1609	73	10	prime	prime	NOUN
ejpam-1609	73	11	and	and	CCONJ
ejpam-1609	73	12	m	m	NOUN
ejpam-1609	73	13	is	be	AUX
ejpam-1609	73	14	an	an	DET
ejpam-1609	73	15	integer	integer	NOUN
ejpam-1609	73	16	.	.	PUNCT
ejpam-1609	74	1	a	a	DET
ejpam-1609	74	2	galois	galois	PROPN
ejpam-1609	74	3	ring	ring	NOUN
ejpam-1609	74	4	of	of	ADP
ejpam-1609	74	5	characteristic	characteristic	ADJ
ejpam-1609	74	6	pm	pm	NOUN
ejpam-1609	74	7	and	and	CCONJ
ejpam-1609	74	8	cardinality	cardinality	PROPN
ejpam-1609	74	9	pmr	pmr	PROPN
ejpam-1609	74	10	is	be	AUX
ejpam-1609	74	11	a	a	DET
ejpam-1609	74	12	ring	ring	NOUN
ejpam-1609	74	13	isomorphic	isomorphic	ADJ
ejpam-1609	74	14	to	to	ADP
ejpam-1609	74	15	r	r	NOUN
ejpam-1609	74	16	,	,	PUNCT
ejpam-1609	74	17	where	where	SCONJ
ejpam-1609	74	18	ξ	ξ	PROPN
ejpam-1609	74	19	is	be	AUX
ejpam-1609	74	20	a	a	DET
ejpam-1609	74	21	primitive	primitive	ADJ
ejpam-1609	74	22	root	root	NOUN
ejpam-1609	74	23	of	of	ADP
ejpam-1609	74	24	a	a	DET
ejpam-1609	74	25	basic	basic	ADJ
ejpam-1609	74	26	irreducible	irreducible	ADJ
ejpam-1609	74	27	polynomial	polynomial	ADJ
ejpam-1609	74	28	f	f	X
ejpam-1609	74	29	(	(	PUNCT
ejpam-1609	74	30	x	x	NOUN
ejpam-1609	74	31	)	)	PUNCT
ejpam-1609	74	32	of	of	ADP
ejpam-1609	74	33	degree	degree	NOUN
ejpam-1609	74	34	n.	n.	NOUN
ejpam-1609	74	35	obviously	obviously	ADV
ejpam-1609	74	36	,	,	PUNCT
ejpam-1609	74	37	r	r	NOUN
ejpam-1609	74	38	=	=	SYM
ejpam-1609	74	39	zpm[x]/	zpm[x]/	NOUN
ejpam-1609	74	40	〈	〈	PROPN
ejpam-1609	74	41	f	f	X
ejpam-1609	74	42	(	(	PUNCT
ejpam-1609	74	43	x	x	NOUN
ejpam-1609	74	44	)	)	PUNCT
ejpam-1609	74	45	〉	〉	NOUN
ejpam-1609	74	46	and	and	CCONJ
ejpam-1609	74	47	r	r	NOUN
ejpam-1609	74	48	=	=	SYM
ejpam-1609	74	49	gr(pm	gr(pm	PROPN
ejpam-1609	74	50	,	,	PUNCT
ejpam-1609	74	51	d	d	NOUN
ejpam-1609	74	52	)	)	PUNCT
ejpam-1609	74	53	,	,	PUNCT
ejpam-1609	74	54	where	where	SCONJ
ejpam-1609	74	55	〈	〈	PROPN
ejpam-1609	74	56	f	f	X
ejpam-1609	74	57	(	(	PUNCT
ejpam-1609	74	58	x	x	NOUN
ejpam-1609	74	59	)	)	PUNCT
ejpam-1609	74	60	〉	〉	NOUN
ejpam-1609	74	61	means	mean	VERB
ejpam-1609	74	62	the	the	DET
ejpam-1609	74	63	ideal	ideal	NOUN
ejpam-1609	74	64	generated	generate	VERB
ejpam-1609	74	65	by	by	ADP
ejpam-1609	74	66	f	f	PROPN
ejpam-1609	74	67	(	(	PUNCT
ejpam-1609	74	68	x	x	NOUN
ejpam-1609	74	69	)	)	PUNCT
ejpam-1609	74	70	and	and	CCONJ
ejpam-1609	74	71	d	d	PROPN
ejpam-1609	74	72	is	be	AUX
ejpam-1609	74	73	the	the	DET
ejpam-1609	74	74	degree	degree	NOUN
ejpam-1609	74	75	of	of	ADP
ejpam-1609	74	76	f	f	PROPN
ejpam-1609	74	77	(	(	PUNCT
ejpam-1609	74	78	x	x	NOUN
ejpam-1609	74	79	)	)	PUNCT
ejpam-1609	74	80	.	.	PUNCT
ejpam-1609	75	1	in	in	ADP
ejpam-1609	75	2	the	the	DET
ejpam-1609	75	3	remaining	remain	VERB
ejpam-1609	75	4	part	part	NOUN
ejpam-1609	75	5	of	of	ADP
ejpam-1609	75	6	the	the	DET
ejpam-1609	75	7	paper	paper	NOUN
ejpam-1609	75	8	,	,	PUNCT
ejpam-1609	75	9	r	r	NOUN
ejpam-1609	75	10	will	will	AUX
ejpam-1609	75	11	be	be	AUX
ejpam-1609	75	12	always	always	ADV
ejpam-1609	75	13	referred	refer	VERB
ejpam-1609	75	14	as	as	ADP
ejpam-1609	75	15	the	the	DET
ejpam-1609	75	16	ring	ring	NOUN
ejpam-1609	75	17	gr(pm	gr(pm	NOUN
ejpam-1609	75	18	,	,	PUNCT
ejpam-1609	75	19	d	d	NOUN
ejpam-1609	75	20	)	)	PUNCT
ejpam-1609	75	21	.	.	PUNCT
ejpam-1609	76	1	although	although	SCONJ
ejpam-1609	76	2	r	r	NOUN
ejpam-1609	76	3	is	be	AUX
ejpam-1609	76	4	not	not	PART
ejpam-1609	76	5	a	a	DET
ejpam-1609	76	6	vector	vector	NOUN
ejpam-1609	76	7	space	space	NOUN
ejpam-1609	76	8	,	,	PUNCT
ejpam-1609	76	9	we	we	PRON
ejpam-1609	76	10	will	will	AUX
ejpam-1609	76	11	nevertheless	nevertheless	ADV
ejpam-1609	76	12	call	call	VERB
ejpam-1609	76	13	its	its	PRON
ejpam-1609	76	14	elements	element	NOUN
ejpam-1609	76	15	as	as	ADP
ejpam-1609	76	16	“	"	PUNCT
ejpam-1609	76	17	vectors	vector	NOUN
ejpam-1609	76	18	”	"	PUNCT
ejpam-1609	76	19	.	.	PUNCT
ejpam-1609	77	1	the	the	DET
ejpam-1609	77	2	galois	galois	PROPN
ejpam-1609	77	3	ring	ring	NOUN
ejpam-1609	77	4	r	r	NOUN
ejpam-1609	77	5	has	have	VERB
ejpam-1609	77	6	elements	element	NOUN
ejpam-1609	77	7	of	of	ADP
ejpam-1609	77	8	orders	order	NOUN
ejpam-1609	77	9	(	(	PUNCT
ejpam-1609	77	10	pm)d	pm)d	PROPN
ejpam-1609	77	11	,	,	PUNCT
ejpam-1609	77	12	(	(	PUNCT
ejpam-1609	77	13	pm−1)d	pm−1)d	NUM
ejpam-1609	77	14	,	,	PUNCT
ejpam-1609	77	15	(	(	PUNCT
ejpam-1609	77	16	pm−2)d	pm−2)d	NOUN
ejpam-1609	77	17	,	,	PUNCT
ejpam-1609	77	18	.	.	PUNCT
ejpam-1609	77	19	.	.	PUNCT
ejpam-1609	78	1	.	.	PUNCT
ejpam-1609	79	1	,	,	PUNCT
ejpam-1609	79	2	pd	pd	PROPN
ejpam-1609	79	3	and	and	CCONJ
ejpam-1609	79	4	the	the	DET
ejpam-1609	79	5	element	element	NOUN
ejpam-1609	79	6	zero	zero	NUM
ejpam-1609	79	7	is	be	AUX
ejpam-1609	79	8	of	of	ADP
ejpam-1609	79	9	order	order	NOUN
ejpam-1609	79	10	1	1	X
ejpam-1609	79	11	.	.	PUNCT
ejpam-1609	80	1	here	here	ADV
ejpam-1609	80	2	,	,	PUNCT
ejpam-1609	80	3	we	we	PRON
ejpam-1609	80	4	give	give	VERB
ejpam-1609	80	5	a	a	DET
ejpam-1609	80	6	formula	formula	NOUN
ejpam-1609	80	7	for	for	ADP
ejpam-1609	80	8	the	the	DET
ejpam-1609	80	9	number	number	NOUN
ejpam-1609	80	10	of	of	ADP
ejpam-1609	80	11	distinct	distinct	ADJ
ejpam-1609	80	12	(	(	PUNCT
ejpam-1609	80	13	not	not	PART
ejpam-1609	80	14	necessarily	necessarily	ADV
ejpam-1609	80	15	inequivalent	inequivalent	ADJ
ejpam-1609	80	16	)	)	PUNCT
ejpam-1609	80	17	linear	linear	ADJ
ejpam-1609	80	18	codes	code	NOUN
ejpam-1609	80	19	over	over	ADP
ejpam-1609	80	20	r.	r.	PROPN
ejpam-1609	80	21	we	we	PRON
ejpam-1609	80	22	do	do	VERB
ejpam-1609	80	23	the	the	DET
ejpam-1609	80	24	enumeration	enumeration	NOUN
ejpam-1609	80	25	by	by	ADP
ejpam-1609	80	26	constructing	construct	VERB
ejpam-1609	80	27	the	the	DET
ejpam-1609	80	28	generator	generator	NOUN
ejpam-1609	80	29	matrices	matrix	NOUN
ejpam-1609	80	30	of	of	ADP
ejpam-1609	80	31	those	those	DET
ejpam-1609	80	32	codes	code	NOUN
ejpam-1609	80	33	.	.	PUNCT
ejpam-1609	81	1	theorem	theorem	NOUN
ejpam-1609	81	2	3	3	NUM
ejpam-1609	81	3	.	.	PUNCT
ejpam-1609	82	1	the	the	DET
ejpam-1609	82	2	number	number	NOUN
ejpam-1609	82	3	of	of	ADP
ejpam-1609	82	4	distinct	distinct	ADJ
ejpam-1609	82	5	(	(	PUNCT
ejpam-1609	82	6	not	not	PART
ejpam-1609	82	7	necessarily	necessarily	ADV
ejpam-1609	82	8	inequivalent	inequivalent	ADJ
ejpam-1609	82	9	)	)	PUNCT
ejpam-1609	82	10	linear	linear	ADJ
ejpam-1609	82	11	codes	code	NOUN
ejpam-1609	82	12	over	over	ADP
ejpam-1609	82	13	r	r	NOUN
ejpam-1609	82	14	is	be	AUX
ejpam-1609	82	15	nr	nr	PRON
ejpam-1609	82	16	k1,k2,	k1,k2,	NOUN
ejpam-1609	82	17	...	...	PUNCT
ejpam-1609	82	18	,ks	,ks	PUNCT
ejpam-1609	82	19	(	(	PUNCT
ejpam-1609	82	20	n	n	CCONJ
ejpam-1609	82	21	)	)	PUNCT
ejpam-1609	82	22	=	=	SYM
ejpam-1609	82	23	�	�	PROPN
ejpam-1609	82	24	n	n	CCONJ
ejpam-1609	82	25	k1	k1	NOUN
ejpam-1609	82	26	,	,	PUNCT
ejpam-1609	82	27	k2	k2	NOUN
ejpam-1609	82	28	,	,	PUNCT
ejpam-1609	82	29	.	.	PUNCT
ejpam-1609	82	30	.	.	PUNCT
ejpam-1609	83	1	.	.	PUNCT
ejpam-1609	84	1	,	,	PUNCT
ejpam-1609	84	2	ks	ks	X
ejpam-1609	84	3	�	�	PROPN
ejpam-1609	84	4	r	r	NOUN
ejpam-1609	84	5	=	=	PUNCT
ejpam-1609	84	6	a	a	DET
ejpam-1609	84	7	b	b	NOUN
ejpam-1609	84	8	,	,	PUNCT
ejpam-1609	84	9	(	(	PUNCT
ejpam-1609	84	10	2	2	X
ejpam-1609	84	11	)	)	PUNCT
ejpam-1609	84	12	where	where	SCONJ
ejpam-1609	84	13	a=	a=	ADJ
ejpam-1609	84	14	∏m	∏m	X
ejpam-1609	84	15	t=1	t=1	PROPN
ejpam-1609	84	16	∏kt−1	∏kt−1	PROPN
ejpam-1609	84	17	i=0	i=0	PROPN
ejpam-1609	84	18	(	(	PUNCT
ejpam-1609	84	19	(	(	PUNCT
ejpam-1609	84	20	p	p	PROPN
ejpam-1609	84	21	m−(t−1	m−(t−1	PROPN
ejpam-1609	84	22	)	)	PUNCT
ejpam-1609	84	23	)	)	PUNCT
ejpam-1609	85	1	dn	dn	ADP
ejpam-1609	85	2	−	−	PROPN
ejpam-1609	85	3	(	(	PUNCT
ejpam-1609	85	4	pm−1−(t−1	pm−1−(t−1	NOUN
ejpam-1609	85	5	)	)	PUNCT
ejpam-1609	85	6	)	)	PUNCT
ejpam-1609	86	1	dn	dn	PROPN
ejpam-1609	86	2	·	·	PUNCT
ejpam-1609	86	3	d	d	X
ejpam-1609	86	4	∑t−1	∑t−1	PROPN
ejpam-1609	86	5	j=0	j=0	PROPN
ejpam-1609	86	6	k	k	PROPN
ejpam-1609	86	7	j	j	PROPN
ejpam-1609	86	8	·	·	SYM
ejpam-1609	86	9	pdi	pdi	PROPN
ejpam-1609	86	10	)	)	PUNCT
ejpam-1609	86	11	,	,	PUNCT
ejpam-1609	86	12	and	and	CCONJ
ejpam-1609	86	13	b	b	X
ejpam-1609	86	14	=	=	SYM
ejpam-1609	86	15	m∏	m∏	PROPN
ejpam-1609	86	16	s=1	s=1	X
ejpam-1609	87	1	ks−1∏	ks−1∏	PROPN
ejpam-1609	87	2	r=0	r=0	PROPN
ejpam-1609	87	3			NOUN
ejpam-1609	87	4			NOUN
ejpam-1609	87	5			NOUN
ejpam-1609	87	6	s∏	s∏	PROPN
ejpam-1609	87	7	z=1	z=1	PUNCT
ejpam-1609	87	8	(	(	PUNCT
ejpam-1609	87	9	pm−(s−1))dkz	pm−(s−1))dkz	PROPN
ejpam-1609	87	10	m∏	m∏	PROPN
ejpam-1609	87	11	j	j	PROPN
ejpam-1609	88	1	=	=	NOUN
ejpam-1609	88	2	s+1	s+1	PROPN
ejpam-1609	88	3	(	(	PUNCT
ejpam-1609	88	4	pm−	pm−	PROPN
ejpam-1609	88	5	(	(	PUNCT
ejpam-1609	88	6	j−1))dk	j−1))dk	PROPN
ejpam-1609	88	7	j	j	PROPN
ejpam-1609	88	8	−	−	PROPN
ejpam-1609	88	9	(	(	PUNCT
ejpam-1609	88	10	s∏	s∏	PROPN
ejpam-1609	88	11	z=1	z=1	X
ejpam-1609	88	12	(	(	PUNCT
ejpam-1609	88	13	pm−s)dkz)(pm−(s+1))dks+1	pm−s)dkz)(pm−(s+1))dks+1	PROPN
ejpam-1609	88	14	·	·	PUNCT
ejpam-1609	88	15	m∏	m∏	PROPN
ejpam-1609	88	16	t	t	PROPN
ejpam-1609	88	17	=	=	SYM
ejpam-1609	88	18	s+2	s+2	PROPN
ejpam-1609	88	19	(	(	PUNCT
ejpam-1609	88	20	pm−(t−1))dkt	pm−(t−1))dkt	PROPN
ejpam-1609	88	21	·	·	PUNCT
ejpam-1609	88	22	pr	pr	X
ejpam-1609	88	23	!	!	PUNCT
ejpam-1609	89	1	proof	proof	NOUN
ejpam-1609	89	2	.	.	PUNCT
ejpam-1609	90	1	in	in	ADP
ejpam-1609	90	2	order	order	NOUN
ejpam-1609	90	3	to	to	PART
ejpam-1609	90	4	enumerate	enumerate	VERB
ejpam-1609	90	5	linear	linear	ADJ
ejpam-1609	90	6	codes	code	NOUN
ejpam-1609	90	7	of	of	ADP
ejpam-1609	90	8	length	length	NOUN
ejpam-1609	90	9	n	n	NOUN
ejpam-1609	90	10	and	and	CCONJ
ejpam-1609	90	11	type	type	NOUN
ejpam-1609	90	12	(	(	PUNCT
ejpam-1609	90	13	k1	k1	NOUN
ejpam-1609	90	14	,	,	PUNCT
ejpam-1609	90	15	k2	k2	NOUN
ejpam-1609	90	16	,	,	PUNCT
ejpam-1609	90	17	.	.	PUNCT
ejpam-1609	90	18	.	.	PUNCT
ejpam-1609	90	19	.	.	PUNCT
ejpam-1609	91	1	,	,	PUNCT
ejpam-1609	91	2	km	km	NOUN
ejpam-1609	91	3	)	)	PUNCT
ejpam-1609	91	4	over	over	ADP
ejpam-1609	91	5	r	r	NOUN
ejpam-1609	91	6	,	,	PUNCT
ejpam-1609	91	7	we	we	PRON
ejpam-1609	91	8	construct	construct	VERB
ejpam-1609	91	9	their	their	PRON
ejpam-1609	91	10	generator	generator	NOUN
ejpam-1609	91	11	matrices	matrix	NOUN
ejpam-1609	91	12	by	by	ADP
ejpam-1609	91	13	choosing	choose	VERB
ejpam-1609	91	14	ordered	order	VERB
ejpam-1609	91	15	ki	ki	PROPN
ejpam-1609	91	16	r	r	VERB
ejpam-1609	91	17	-	-	PUNCT
ejpam-1609	91	18	linearly	linearly	ADV
ejpam-1609	91	19	independent	independent	ADJ
ejpam-1609	91	20	elements	element	NOUN
ejpam-1609	91	21	of	of	ADP
ejpam-1609	91	22	order	order	NOUN
ejpam-1609	91	23	(	(	PUNCT
ejpam-1609	91	24	pm−i+1)d	pm−i+1)d	NOUN
ejpam-1609	91	25	,	,	PUNCT
ejpam-1609	91	26	i	i	PRON
ejpam-1609	91	27	∈	∈	PROPN
ejpam-1609	91	28	{	{	PUNCT
ejpam-1609	91	29	1,2	1,2	NUM
ejpam-1609	91	30	,	,	PUNCT
ejpam-1609	91	31	.	.	PUNCT
ejpam-1609	91	32	.	.	PUNCT
ejpam-1609	92	1	.	.	PUNCT
ejpam-1609	93	1	,	,	PUNCT
ejpam-1609	93	2	m	m	VERB
ejpam-1609	93	3	}	}	PUNCT
ejpam-1609	93	4	respectively	respectively	ADV
ejpam-1609	93	5	.	.	PUNCT
ejpam-1609	94	1	let	let	VERB
ejpam-1609	94	2	s	s	PRON
ejpam-1609	94	3	=	=	PUNCT
ejpam-1609	94	4	(	(	PUNCT
ejpam-1609	94	5	v	v	NOUN
ejpam-1609	94	6	(	(	PUNCT
ejpam-1609	94	7	pm)d	pm)d	NOUN
ejpam-1609	94	8	1	1	NUM
ejpam-1609	94	9	,	,	PUNCT
ejpam-1609	94	10	v	v	NOUN
ejpam-1609	94	11	(	(	PUNCT
ejpam-1609	94	12	pm)d	pm)d	NOUN
ejpam-1609	94	13	2	2	NUM
ejpam-1609	94	14	,	,	PUNCT
ejpam-1609	94	15	.	.	PUNCT
ejpam-1609	94	16	.	.	PUNCT
ejpam-1609	95	1	.	.	PUNCT
ejpam-1609	96	1	,	,	PUNCT
ejpam-1609	96	2	v	v	X
ejpam-1609	96	3	(	(	PUNCT
ejpam-1609	96	4	pm)d	pm)d	ADJ
ejpam-1609	96	5	k1	k1	NOUN
ejpam-1609	96	6	,	,	PUNCT
ejpam-1609	96	7	v	v	NOUN
ejpam-1609	96	8	(	(	PUNCT
ejpam-1609	96	9	pm−1)d	pm−1)d	NUM
ejpam-1609	96	10	1	1	NUM
ejpam-1609	96	11	,	,	PUNCT
ejpam-1609	96	12	.	.	PUNCT
ejpam-1609	96	13	.	.	PUNCT
ejpam-1609	96	14	.	.	PUNCT
ejpam-1609	97	1	,	,	PUNCT
ejpam-1609	97	2	v	v	X
ejpam-1609	97	3	(	(	PUNCT
ejpam-1609	97	4	pm−1)d	pm−1)d	NOUN
ejpam-1609	97	5	k2	k2	PROPN
ejpam-1609	97	6	,	,	PUNCT
ejpam-1609	97	7	.	.	PUNCT
ejpam-1609	97	8	.	.	PUNCT
ejpam-1609	98	1	.	.	PUNCT
ejpam-1609	99	1	,	,	PUNCT
ejpam-1609	99	2	v	v	X
ejpam-1609	99	3	(	(	PUNCT
ejpam-1609	99	4	p2)d	p2)d	NOUN
ejpam-1609	99	5	1	1	NUM
ejpam-1609	99	6	,	,	PUNCT
ejpam-1609	99	7	.	.	PUNCT
ejpam-1609	99	8	.	.	PUNCT
ejpam-1609	99	9	.	.	PUNCT
ejpam-1609	100	1	,	,	PUNCT
ejpam-1609	100	2	v	v	X
ejpam-1609	100	3	(	(	PUNCT
ejpam-1609	100	4	p2)d	p2)d	PROPN
ejpam-1609	100	5	km−1	km−1	PROPN
ejpam-1609	100	6	,	,	PUNCT
ejpam-1609	100	7	v	v	NOUN
ejpam-1609	100	8	(	(	PUNCT
ejpam-1609	100	9	p)d	p)d	NOUN
ejpam-1609	100	10	1	1	NUM
ejpam-1609	100	11	,	,	PUNCT
ejpam-1609	100	12	.	.	PUNCT
ejpam-1609	100	13	.	.	PUNCT
ejpam-1609	100	14	.	.	PUNCT
ejpam-1609	101	1	,	,	PUNCT
ejpam-1609	101	2	v	v	X
ejpam-1609	101	3	(	(	PUNCT
ejpam-1609	101	4	p)d	p)d	ADJ
ejpam-1609	101	5	km	km	NOUN
ejpam-1609	101	6	)	)	PUNCT
ejpam-1609	101	7	e.	e.	PROPN
ejpam-1609	101	8	saltürk	saltürk	PROPN
ejpam-1609	101	9	,	,	PUNCT
ejpam-1609	101	10	i̇.	i̇.	PROPN
ejpam-1609	101	11	şiap	şiap	PROPN
ejpam-1609	101	12	/	/	SYM
ejpam-1609	101	13	eur	eur	PROPN
ejpam-1609	101	14	.	.	PUNCT
ejpam-1609	102	1	j.	j.	PROPN
ejpam-1609	102	2	pure	pure	PROPN
ejpam-1609	102	3	appl	appl	PROPN
ejpam-1609	102	4	.	.	PROPN
ejpam-1609	102	5	math	math	PROPN
ejpam-1609	102	6	,	,	PUNCT
ejpam-1609	102	7	5	5	NUM
ejpam-1609	102	8	(	(	PUNCT
ejpam-1609	102	9	2012	2012	NUM
ejpam-1609	102	10	)	)	PUNCT
ejpam-1609	102	11	,	,	PUNCT
ejpam-1609	102	12	250	250	NUM
ejpam-1609	102	13	-	-	SYM
ejpam-1609	102	14	259	259	NUM
ejpam-1609	102	15	253	253	NUM
ejpam-1609	102	16	be	be	AUX
ejpam-1609	102	17	the	the	DET
ejpam-1609	102	18	ordered	order	VERB
ejpam-1609	102	19	set	set	NOUN
ejpam-1609	102	20	of	of	ADP
ejpam-1609	102	21	such	such	ADJ
ejpam-1609	102	22	elements	element	NOUN
ejpam-1609	102	23	where	where	SCONJ
ejpam-1609	102	24	v	v	NOUN
ejpam-1609	102	25	(	(	PUNCT
ejpam-1609	102	26	j)d	j)d	X
ejpam-1609	103	1	i	i	PRON
ejpam-1609	103	2	denote	denote	VERB
ejpam-1609	103	3	the	the	DET
ejpam-1609	103	4	i	i	PROPN
ejpam-1609	103	5	th	th	X
ejpam-1609	103	6	element	element	NOUN
ejpam-1609	103	7	of	of	ADP
ejpam-1609	103	8	order	order	NOUN
ejpam-1609	103	9	(	(	PUNCT
ejpam-1609	103	10	j)d	j)d	NOUN
ejpam-1609	103	11	,	,	PUNCT
ejpam-1609	103	12	p	p	PROPN
ejpam-1609	103	13	≤	≤	PROPN
ejpam-1609	103	14	j	j	PROPN
ejpam-1609	103	15	≤	≤	PROPN
ejpam-1609	103	16	pm	pm	NOUN
ejpam-1609	103	17	,	,	PUNCT
ejpam-1609	103	18	1≤	1≤	INTJ
ejpam-1609	104	1	i	i	NOUN
ejpam-1609	104	2	≤	≤	PUNCT
ejpam-1609	104	3	kw	kw	INTJ
ejpam-1609	104	4	and	and	CCONJ
ejpam-1609	104	5	w	w	NOUN
ejpam-1609	104	6	=	=	SYM
ejpam-1609	104	7	1,2	1,2	NUM
ejpam-1609	104	8	,	,	PUNCT
ejpam-1609	104	9	.	.	PUNCT
ejpam-1609	104	10	.	.	PUNCT
ejpam-1609	104	11	.	.	PUNCT
ejpam-1609	105	1	,	,	PUNCT
ejpam-1609	105	2	m.	m.	NOUN
ejpam-1609	105	3	there	there	PRON
ejpam-1609	105	4	are	be	VERB
ejpam-1609	105	5	(	(	PUNCT
ejpam-1609	105	6	(	(	PUNCT
ejpam-1609	105	7	pm)d	pm)d	NOUN
ejpam-1609	105	8	)	)	PUNCT
ejpam-1609	105	9	n	n	PRON
ejpam-1609	105	10	elements	element	NOUN
ejpam-1609	105	11	in	in	ADP
ejpam-1609	105	12	rn	rn	PROPN
ejpam-1609	105	13	.	.	PUNCT
ejpam-1609	106	1	in	in	ADP
ejpam-1609	106	2	order	order	NOUN
ejpam-1609	106	3	to	to	PART
ejpam-1609	106	4	choose	choose	VERB
ejpam-1609	106	5	the	the	DET
ejpam-1609	106	6	first	first	ADJ
ejpam-1609	106	7	free	free	ADJ
ejpam-1609	106	8	vector	vector	NOUN
ejpam-1609	106	9	,	,	PUNCT
ejpam-1609	106	10	v	v	PROPN
ejpam-1609	106	11	(	(	PUNCT
ejpam-1609	106	12	pm)d	pm)d	NOUN
ejpam-1609	106	13	1	1	NUM
ejpam-1609	106	14	,	,	PUNCT
ejpam-1609	106	15	we	we	PRON
ejpam-1609	106	16	subtract	subtract	VERB
ejpam-1609	106	17	the	the	DET
ejpam-1609	106	18	number	number	NOUN
ejpam-1609	106	19	of	of	ADP
ejpam-1609	106	20	elements	element	NOUN
ejpam-1609	106	21	which	which	PRON
ejpam-1609	106	22	are	be	AUX
ejpam-1609	106	23	not	not	PART
ejpam-1609	106	24	of	of	ADP
ejpam-1609	106	25	order	order	NOUN
ejpam-1609	106	26	(	(	PUNCT
ejpam-1609	106	27	pm)d	pm)d	ADJ
ejpam-1609	106	28	from	from	ADP
ejpam-1609	106	29	the	the	DET
ejpam-1609	106	30	whole	whole	ADJ
ejpam-1609	106	31	group	group	NOUN
ejpam-1609	106	32	rn	rn	PROPN
ejpam-1609	106	33	.	.	PUNCT
ejpam-1609	107	1	the	the	DET
ejpam-1609	107	2	elements	element	NOUN
ejpam-1609	107	3	of	of	ADP
ejpam-1609	107	4	order	order	NOUN
ejpam-1609	107	5	(	(	PUNCT
ejpam-1609	107	6	pm)d	pm)d	VERB
ejpam-1609	107	7	have	have	AUX
ejpam-1609	107	8	at	at	ADV
ejpam-1609	107	9	least	least	ADV
ejpam-1609	107	10	one	one	NUM
ejpam-1609	107	11	unit	unit	NOUN
ejpam-1609	107	12	element	element	NOUN
ejpam-1609	107	13	of	of	ADP
ejpam-1609	107	14	r	r	NOUN
ejpam-1609	107	15	in	in	ADP
ejpam-1609	107	16	any	any	PRON
ejpam-1609	107	17	of	of	ADP
ejpam-1609	107	18	n	n	PRON
ejpam-1609	107	19	components	component	NOUN
ejpam-1609	107	20	.	.	PUNCT
ejpam-1609	108	1	the	the	DET
ejpam-1609	108	2	number	number	NOUN
ejpam-1609	108	3	of	of	ADP
ejpam-1609	108	4	the	the	DET
ejpam-1609	108	5	unit	unit	NOUN
ejpam-1609	108	6	elements	element	NOUN
ejpam-1609	108	7	of	of	ADP
ejpam-1609	108	8	r	r	NOUN
ejpam-1609	108	9	is	be	AUX
ejpam-1609	108	10	(	(	PUNCT
ejpam-1609	108	11	pm)d	pm)d	ADV
ejpam-1609	108	12	−	−	PROPN
ejpam-1609	108	13	(	(	PUNCT
ejpam-1609	108	14	pm−1)d	pm−1)d	NUM
ejpam-1609	108	15	since	since	SCONJ
ejpam-1609	108	16	the	the	DET
ejpam-1609	108	17	number	number	NOUN
ejpam-1609	108	18	of	of	ADP
ejpam-1609	108	19	elements	element	NOUN
ejpam-1609	108	20	which	which	PRON
ejpam-1609	108	21	are	be	AUX
ejpam-1609	108	22	not	not	PART
ejpam-1609	108	23	of	of	ADP
ejpam-1609	108	24	order	order	NOUN
ejpam-1609	108	25	(	(	PUNCT
ejpam-1609	108	26	pm)d	pm)d	ADJ
ejpam-1609	108	27	in	in	ADP
ejpam-1609	108	28	r	r	NOUN
ejpam-1609	108	29	is	be	AUX
ejpam-1609	108	30	(	(	PUNCT
ejpam-1609	108	31	pm−1)d	pm−1)d	X
ejpam-1609	108	32	.	.	PUNCT
ejpam-1609	109	1	since	since	SCONJ
ejpam-1609	109	2	there	there	PRON
ejpam-1609	109	3	are	be	VERB
ejpam-1609	109	4	n	n	PRON
ejpam-1609	109	5	choices	choice	NOUN
ejpam-1609	109	6	for	for	ADP
ejpam-1609	109	7	a	a	DET
ejpam-1609	109	8	unit	unit	NOUN
ejpam-1609	109	9	in	in	ADP
ejpam-1609	109	10	order	order	NOUN
ejpam-1609	109	11	to	to	PART
ejpam-1609	109	12	get	get	VERB
ejpam-1609	109	13	an	an	DET
ejpam-1609	109	14	element	element	NOUN
ejpam-1609	109	15	of	of	ADP
ejpam-1609	109	16	order	order	NOUN
ejpam-1609	109	17	(	(	PUNCT
ejpam-1609	109	18	pm−1)d	pm−1)d	NUM
ejpam-1609	109	19	,	,	PUNCT
ejpam-1609	109	20	we	we	PRON
ejpam-1609	109	21	obtain	obtain	VERB
ejpam-1609	109	22	the	the	DET
ejpam-1609	109	23	number	number	NOUN
ejpam-1609	109	24	(	(	PUNCT
ejpam-1609	109	25	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	109	26	)	)	PUNCT
ejpam-1609	109	27	n	n	CCONJ
ejpam-1609	109	28	as	as	ADP
ejpam-1609	109	29	the	the	DET
ejpam-1609	109	30	number	number	NOUN
ejpam-1609	109	31	of	of	ADP
ejpam-1609	109	32	elements	element	NOUN
ejpam-1609	109	33	of	of	ADP
ejpam-1609	109	34	rn	rn	PROPN
ejpam-1609	109	35	which	which	PRON
ejpam-1609	109	36	are	be	AUX
ejpam-1609	109	37	not	not	PART
ejpam-1609	109	38	of	of	ADP
ejpam-1609	109	39	order	order	NOUN
ejpam-1609	109	40	(	(	PUNCT
ejpam-1609	109	41	pm)d	pm)d	NOUN
ejpam-1609	109	42	.	.	PUNCT
ejpam-1609	110	1	we	we	PRON
ejpam-1609	110	2	have	have	VERB
ejpam-1609	110	3	(	(	PUNCT
ejpam-1609	110	4	(	(	PUNCT
ejpam-1609	110	5	pm)d)n−	pm)d)n−	PROPN
ejpam-1609	110	6	(	(	PUNCT
ejpam-1609	110	7	(	(	PUNCT
ejpam-1609	110	8	pm−1)d)n	pm−1)d)n	NOUN
ejpam-1609	110	9	possibilities	possibility	NOUN
ejpam-1609	110	10	.	.	PUNCT
ejpam-1609	111	1	for	for	ADP
ejpam-1609	111	2	the	the	DET
ejpam-1609	111	3	second	second	ADJ
ejpam-1609	111	4	vector	vector	NOUN
ejpam-1609	111	5	,	,	PUNCT
ejpam-1609	111	6	v	v	NOUN
ejpam-1609	111	7	(	(	PUNCT
ejpam-1609	111	8	pm)d	pm)d	NOUN
ejpam-1609	111	9	2	2	NUM
ejpam-1609	111	10	,	,	PUNCT
ejpam-1609	111	11	we	we	PRON
ejpam-1609	111	12	can	can	AUX
ejpam-1609	111	13	take	take	VERB
ejpam-1609	111	14	all	all	DET
ejpam-1609	111	15	vectors	vector	NOUN
ejpam-1609	111	16	of	of	ADP
ejpam-1609	111	17	order	order	NOUN
ejpam-1609	111	18	pm	pm	NOUN
ejpam-1609	111	19	except	except	SCONJ
ejpam-1609	111	20	the	the	DET
ejpam-1609	111	21	vectors	vector	NOUN
ejpam-1609	111	22	which	which	PRON
ejpam-1609	111	23	are	be	AUX
ejpam-1609	111	24	linearly	linearly	ADV
ejpam-1609	111	25	dependent	dependent	ADJ
ejpam-1609	111	26	with	with	ADP
ejpam-1609	111	27	the	the	DET
ejpam-1609	111	28	first	first	ADV
ejpam-1609	111	29	taken	take	VERB
ejpam-1609	111	30	into	into	ADP
ejpam-1609	111	31	account	account	NOUN
ejpam-1609	111	32	.	.	PUNCT
ejpam-1609	112	1	hence	hence	ADV
ejpam-1609	112	2	,	,	PUNCT
ejpam-1609	112	3	we	we	PRON
ejpam-1609	112	4	choose	choose	VERB
ejpam-1609	112	5	the	the	DET
ejpam-1609	112	6	second	second	ADJ
ejpam-1609	112	7	one	one	NUM
ejpam-1609	112	8	such	such	ADJ
ejpam-1609	112	9	that	that	SCONJ
ejpam-1609	112	10	〈	〈	PROPN
ejpam-1609	112	11	v(p	v(p	NOUN
ejpam-1609	112	12	m)d	m)d	ADJ
ejpam-1609	112	13	1	1	NUM
ejpam-1609	112	14	,	,	PUNCT
ejpam-1609	112	15	v	v	NOUN
ejpam-1609	112	16	(	(	PUNCT
ejpam-1609	112	17	pm)d	pm)d	NOUN
ejpam-1609	112	18	2	2	NUM
ejpam-1609	112	19	〉	〉	NOUN
ejpam-1609	112	20	=	=	SYM
ejpam-1609	112	21	c2	c2	PROPN
ejpam-1609	112	22	and	and	CCONJ
ejpam-1609	112	23	|c2|=	|c2|=	PROPN
ejpam-1609	112	24	(	(	PUNCT
ejpam-1609	112	25	(	(	PUNCT
ejpam-1609	112	26	p	p	NOUN
ejpam-1609	112	27	m)d)2	m)d)2	NOUN
ejpam-1609	112	28	.	.	PUNCT
ejpam-1609	113	1	the	the	DET
ejpam-1609	113	2	set	set	NOUN
ejpam-1609	113	3	of	of	ADP
ejpam-1609	113	4	vectors	vector	NOUN
ejpam-1609	113	5	that	that	PRON
ejpam-1609	113	6	can	can	AUX
ejpam-1609	113	7	not	not	PART
ejpam-1609	113	8	be	be	AUX
ejpam-1609	113	9	taken	take	VERB
ejpam-1609	113	10	for	for	ADP
ejpam-1609	113	11	the	the	DET
ejpam-1609	113	12	second	second	ADJ
ejpam-1609	113	13	vector	vector	NOUN
ejpam-1609	113	14	is	be	AUX
ejpam-1609	113	15	the	the	DET
ejpam-1609	113	16	following	follow	VERB
ejpam-1609	113	17	:	:	PUNCT
ejpam-1609	113	18	k2	k2	X
ejpam-1609	113	19	=	=	SYM
ejpam-1609	113	20	{	{	PUNCT
ejpam-1609	113	21	α1v1	α1v1	X
ejpam-1609	113	22	(	(	PUNCT
ejpam-1609	113	23	pm)d	pm)d	ADJ
ejpam-1609	113	24	+	+	NOUN
ejpam-1609	113	25	w|w	w|w	NOUN
ejpam-1609	113	26	is	be	AUX
ejpam-1609	113	27	not	not	PART
ejpam-1609	113	28	of	of	ADP
ejpam-1609	113	29	order	order	NOUN
ejpam-1609	113	30	(	(	PUNCT
ejpam-1609	113	31	pm)d	pm)d	ADJ
ejpam-1609	113	32	and	and	CCONJ
ejpam-1609	113	33	α1	α1	PROPN
ejpam-1609	113	34	∈	∈	PROPN
ejpam-1609	113	35	zp[ξ	zp[ξ	PROPN
ejpam-1609	113	36	]	]	PUNCT
ejpam-1609	113	37	}	}	PUNCT
ejpam-1609	113	38	.	.	PUNCT
ejpam-1609	114	1	since	since	SCONJ
ejpam-1609	114	2	|k2|=	|k2|=	PROPN
ejpam-1609	114	3	(	(	PUNCT
ejpam-1609	114	4	(	(	PUNCT
ejpam-1609	114	5	p	p	NOUN
ejpam-1609	114	6	m−1)d)npd	m−1)d)npd	NOUN
ejpam-1609	114	7	,	,	PUNCT
ejpam-1609	114	8	we	we	PRON
ejpam-1609	114	9	have	have	VERB
ejpam-1609	114	10	(	(	PUNCT
ejpam-1609	114	11	(	(	PUNCT
ejpam-1609	114	12	(	(	PUNCT
ejpam-1609	114	13	pm)d)n−	pm)d)n−	PROPN
ejpam-1609	114	14	(	(	PUNCT
ejpam-1609	114	15	(	(	PUNCT
ejpam-1609	114	16	pm−1)d)npd	pm−1)d)npd	NOUN
ejpam-1609	114	17	)	)	PUNCT
ejpam-1609	114	18	possibilities	possibility	NOUN
ejpam-1609	114	19	for	for	ADP
ejpam-1609	114	20	the	the	DET
ejpam-1609	114	21	second	second	ADJ
ejpam-1609	114	22	vector	vector	NOUN
ejpam-1609	114	23	.	.	PUNCT
ejpam-1609	115	1	next	next	ADV
ejpam-1609	115	2	,	,	PUNCT
ejpam-1609	115	3	we	we	PRON
ejpam-1609	115	4	choose	choose	VERB
ejpam-1609	115	5	v	v	NUM
ejpam-1609	115	6	(	(	PUNCT
ejpam-1609	115	7	pm)d	pm)d	NOUN
ejpam-1609	115	8	3	3	NUM
ejpam-1609	115	9	from	from	ADP
ejpam-1609	115	10	rn	rn	ADP
ejpam-1609	115	11	such	such	ADJ
ejpam-1609	115	12	that	that	SCONJ
ejpam-1609	115	13	c3	c3	PROPN
ejpam-1609	115	14	=	=	PUNCT
ejpam-1609	115	15	〈	〈	PROPN
ejpam-1609	115	16	c2	c2	PROPN
ejpam-1609	115	17	∪	∪	X
ejpam-1609	115	18	{	{	PUNCT
ejpam-1609	115	19	v	v	NOUN
ejpam-1609	115	20	(	(	PUNCT
ejpam-1609	115	21	pm)d	pm)d	NOUN
ejpam-1609	115	22	3	3	NUM
ejpam-1609	115	23	}	}	PUNCT
ejpam-1609	115	24	〉	〉	NOUN
ejpam-1609	115	25	and	and	CCONJ
ejpam-1609	115	26	|c3|	|c3|	NOUN
ejpam-1609	115	27	=	=	SYM
ejpam-1609	115	28	(	(	PUNCT
ejpam-1609	115	29	(	(	PUNCT
ejpam-1609	115	30	p	p	PROPN
ejpam-1609	115	31	m)d)3	m)d)3	NOUN
ejpam-1609	115	32	.	.	PUNCT
ejpam-1609	116	1	while	while	SCONJ
ejpam-1609	116	2	making	make	VERB
ejpam-1609	116	3	this	this	DET
ejpam-1609	116	4	choice	choice	NOUN
ejpam-1609	116	5	,	,	PUNCT
ejpam-1609	116	6	again	again	ADV
ejpam-1609	116	7	we	we	PRON
ejpam-1609	116	8	exclude	exclude	VERB
ejpam-1609	116	9	the	the	DET
ejpam-1609	116	10	set	set	NOUN
ejpam-1609	116	11	k3	k3	VERB
ejpam-1609	116	12	=	=	SYM
ejpam-1609	116	13	{	{	PUNCT
ejpam-1609	116	14	α1v1	α1v1	X
ejpam-1609	116	15	(	(	PUNCT
ejpam-1609	116	16	pm)d	pm)d	NUM
ejpam-1609	116	17	+	+	NOUN
ejpam-1609	116	18	α2v2	α2v2	ADJ
ejpam-1609	116	19	(	(	PUNCT
ejpam-1609	116	20	pm)d	pm)d	PROPN
ejpam-1609	116	21	+	+	NOUN
ejpam-1609	116	22	w|o(w	w|o(w	PROPN
ejpam-1609	116	23	)	)	PUNCT
ejpam-1609	116	24	6=	6=	ADP
ejpam-1609	116	25	pm	pm	NOUN
ejpam-1609	116	26	and	and	CCONJ
ejpam-1609	116	27	α1,α2	α1,α2	PROPN
ejpam-1609	116	28	∈	∈	PROPN
ejpam-1609	117	1	zp[ξ	zp[ξ	PROPN
ejpam-1609	117	2	]	]	PUNCT
ejpam-1609	117	3	}	}	PUNCT
ejpam-1609	117	4	.	.	PUNCT
ejpam-1609	118	1	hence	hence	ADV
ejpam-1609	118	2	,	,	PUNCT
ejpam-1609	118	3	we	we	PRON
ejpam-1609	118	4	have	have	VERB
ejpam-1609	118	5	(	(	PUNCT
ejpam-1609	118	6	(	(	PUNCT
ejpam-1609	118	7	(	(	PUNCT
ejpam-1609	118	8	pm)d)n−	pm)d)n−	NOUN
ejpam-1609	118	9	(	(	PUNCT
ejpam-1609	118	10	(	(	PUNCT
ejpam-1609	118	11	pm−1)d)np2d	pm−1)d)np2d	NOUN
ejpam-1609	118	12	)	)	PUNCT
ejpam-1609	118	13	ways	way	NOUN
ejpam-1609	118	14	to	to	PART
ejpam-1609	118	15	choose	choose	VERB
ejpam-1609	118	16	v	v	PROPN
ejpam-1609	118	17	(	(	PUNCT
ejpam-1609	118	18	pm)d	pm)d	NOUN
ejpam-1609	118	19	3	3	NUM
ejpam-1609	118	20	since	since	SCONJ
ejpam-1609	118	21	|k3|	|k3|	NOUN
ejpam-1609	118	22	=	=	SYM
ejpam-1609	118	23	(	(	PUNCT
ejpam-1609	118	24	(	(	PUNCT
ejpam-1609	118	25	p	p	NOUN
ejpam-1609	118	26	m−1)d)n(pd)2	m−1)d)n(pd)2	NOUN
ejpam-1609	118	27	possibilities	possibility	NOUN
ejpam-1609	118	28	.	.	PUNCT
ejpam-1609	119	1	the	the	DET
ejpam-1609	119	2	same	same	ADJ
ejpam-1609	119	3	calculation	calculation	NOUN
ejpam-1609	119	4	for	for	ADP
ejpam-1609	119	5	the	the	DET
ejpam-1609	119	6	remaining	remain	VERB
ejpam-1609	119	7	k1	k1	NOUN
ejpam-1609	119	8	−	−	PROPN
ejpam-1609	119	9	3	3	NUM
ejpam-1609	119	10	vectors	vector	NOUN
ejpam-1609	119	11	yields	yield	VERB
ejpam-1609	119	12	the	the	DET
ejpam-1609	119	13	following	follow	VERB
ejpam-1609	119	14	number	number	NOUN
ejpam-1609	119	15	(	(	PUNCT
ejpam-1609	119	16	by	by	ADP
ejpam-1609	119	17	considering	consider	VERB
ejpam-1609	119	18	all	all	DET
ejpam-1609	119	19	possibilities	possibility	NOUN
ejpam-1609	119	20	)	)	PUNCT
ejpam-1609	119	21	(	(	PUNCT
ejpam-1609	119	22	pmdn−	pmdn−	NOUN
ejpam-1609	119	23	p(m−1)dn)(pmdn−	p(m−1)dn)(pmdn−	NOUN
ejpam-1609	119	24	p(m−1)dnpd)(pmdn−	p(m−1)dnpd)(pmdn−	PROPN
ejpam-1609	119	25	p(m−1)dnp2d	p(m−1)dnp2d	PROPN
ejpam-1609	119	26	)	)	PUNCT
ejpam-1609	119	27	.	.	PUNCT
ejpam-1609	119	28	.	.	PUNCT
ejpam-1609	119	29	.	.	PUNCT
ejpam-1609	120	1	(	(	PUNCT
ejpam-1609	120	2	(	(	PUNCT
ejpam-1609	120	3	pm)n−	pm)n−	X
ejpam-1609	120	4	(	(	PUNCT
ejpam-1609	120	5	pm−1)npd(k1−1	pm−1)npd(k1−1	PROPN
ejpam-1609	120	6	)	)	PUNCT
ejpam-1609	120	7	)	)	PUNCT
ejpam-1609	121	1	=	=	PUNCT
ejpam-1609	121	2	k1−1∏	k1−1∏	PROPN
ejpam-1609	121	3	j=0	j=0	PROPN
ejpam-1609	121	4	pmdn−	pmdn−	VERB
ejpam-1609	121	5	p(m−1)dnpd	p(m−1)dnpd	PROPN
ejpam-1609	121	6	j.	j.	PROPN
ejpam-1609	121	7	now	now	ADV
ejpam-1609	121	8	,	,	PUNCT
ejpam-1609	121	9	we	we	PRON
ejpam-1609	121	10	choose	choose	VERB
ejpam-1609	121	11	k2	k2	ADJ
ejpam-1609	121	12	elements	element	NOUN
ejpam-1609	121	13	of	of	ADP
ejpam-1609	121	14	order	order	NOUN
ejpam-1609	121	15	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	121	16	and	and	CCONJ
ejpam-1609	121	17	the	the	DET
ejpam-1609	121	18	first	first	ADJ
ejpam-1609	121	19	one	one	NUM
ejpam-1609	121	20	is	be	AUX
ejpam-1609	121	21	v	v	NOUN
ejpam-1609	121	22	(	(	PUNCT
ejpam-1609	121	23	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	121	24	)	)	PUNCT
ejpam-1609	121	25	1	1	NUM
ejpam-1609	122	1	such	such	ADJ
ejpam-1609	122	2	that	that	DET
ejpam-1609	122	3	ck1	ck1	PROPN
ejpam-1609	122	4	+	+	ADJ
ejpam-1609	122	5	1	1	NUM
ejpam-1609	122	6	=	=	SYM
ejpam-1609	122	7	〈	〈	NOUN
ejpam-1609	122	8	ck1	ck1	NOUN
ejpam-1609	122	9	∪	∪	X
ejpam-1609	122	10	{	{	PUNCT
ejpam-1609	122	11	v(p	v(p	NOUN
ejpam-1609	122	12	(	(	PUNCT
ejpam-1609	122	13	m−1)d	m−1)d	NOUN
ejpam-1609	122	14	)	)	PUNCT
ejpam-1609	122	15	1	1	NUM
ejpam-1609	122	16	}	}	PUNCT
ejpam-1609	122	17	〉	〉	NOUN
ejpam-1609	122	18	and	and	CCONJ
ejpam-1609	122	19	|ck1	|ck1	NUM
ejpam-1609	122	20	+	+	NOUN
ejpam-1609	122	21	1|	1|	NUM
ejpam-1609	122	22	=	=	SYM
ejpam-1609	122	23	(	(	PUNCT
ejpam-1609	122	24	p	p	PROPN
ejpam-1609	122	25	md	md	PROPN
ejpam-1609	122	26	)	)	PUNCT
ejpam-1609	122	27	k1	k1	PROPN
ejpam-1609	122	28	.(p(m−1)d	.(p(m−1)d	PUNCT
ejpam-1609	122	29	)	)	PUNCT
ejpam-1609	122	30	1	1	X
ejpam-1609	122	31	.	.	PUNCT
ejpam-1609	123	1	here	here	ADV
ejpam-1609	123	2	,	,	PUNCT
ejpam-1609	123	3	we	we	PRON
ejpam-1609	123	4	have	have	VERB
ejpam-1609	123	5	to	to	PART
ejpam-1609	123	6	take	take	VERB
ejpam-1609	123	7	into	into	ADP
ejpam-1609	123	8	e.	e.	PROPN
ejpam-1609	123	9	saltürk	saltürk	PROPN
ejpam-1609	123	10	,	,	PUNCT
ejpam-1609	123	11	i̇.	i̇.	PROPN
ejpam-1609	123	12	şiap	şiap	PROPN
ejpam-1609	123	13	/	/	SYM
ejpam-1609	123	14	eur	eur	PROPN
ejpam-1609	123	15	.	.	PUNCT
ejpam-1609	124	1	j.	j.	PROPN
ejpam-1609	124	2	pure	pure	PROPN
ejpam-1609	124	3	appl	appl	PROPN
ejpam-1609	124	4	.	.	PROPN
ejpam-1609	124	5	math	math	PROPN
ejpam-1609	124	6	,	,	PUNCT
ejpam-1609	124	7	5	5	NUM
ejpam-1609	124	8	(	(	PUNCT
ejpam-1609	124	9	2012	2012	NUM
ejpam-1609	124	10	)	)	PUNCT
ejpam-1609	124	11	,	,	PUNCT
ejpam-1609	124	12	250	250	NUM
ejpam-1609	124	13	-	-	SYM
ejpam-1609	124	14	259	259	NUM
ejpam-1609	124	15	254	254	NUM
ejpam-1609	124	16	account	account	NOUN
ejpam-1609	124	17	the	the	DET
ejpam-1609	124	18	k1	k1	NOUN
ejpam-1609	124	19	elements	element	NOUN
ejpam-1609	124	20	which	which	PRON
ejpam-1609	124	21	have	have	AUX
ejpam-1609	124	22	been	be	AUX
ejpam-1609	124	23	already	already	ADV
ejpam-1609	124	24	considered	consider	VERB
ejpam-1609	124	25	of	of	ADP
ejpam-1609	124	26	order	order	NOUN
ejpam-1609	124	27	pm	pm	NOUN
ejpam-1609	124	28	that	that	PRON
ejpam-1609	124	29	will	will	AUX
ejpam-1609	124	30	contribute	contribute	VERB
ejpam-1609	124	31	to	to	ADP
ejpam-1609	124	32	the	the	DET
ejpam-1609	124	33	set	set	NOUN
ejpam-1609	124	34	of	of	ADP
ejpam-1609	124	35	elements	element	NOUN
ejpam-1609	124	36	of	of	ADP
ejpam-1609	124	37	order	order	NOUN
ejpam-1609	124	38	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	124	39	.	.	PUNCT
ejpam-1609	125	1	we	we	PRON
ejpam-1609	125	2	consider	consider	VERB
ejpam-1609	125	3	the	the	DET
ejpam-1609	125	4	elements	element	NOUN
ejpam-1609	125	5	of	of	ADP
ejpam-1609	125	6	the	the	DET
ejpam-1609	125	7	following	follow	VERB
ejpam-1609	125	8	set	set	NOUN
ejpam-1609	125	9	:	:	PUNCT
ejpam-1609	125	10	kk1	kk1	X
ejpam-1609	125	11	+	+	ADJ
ejpam-1609	125	12	1	1	NUM
ejpam-1609	125	13	=	=	NOUN
ejpam-1609	125	14	{	{	PUNCT
ejpam-1609	125	15	α1v1	α1v1	X
ejpam-1609	125	16	pmd	pmd	X
ejpam-1609	125	17	+	+	PROPN
ejpam-1609	125	18	α2v2	α2v2	X
ejpam-1609	125	19	pmd	pmd	NOUN
ejpam-1609	125	20	+	+	X
ejpam-1609	125	21	.	.	PUNCT
ejpam-1609	125	22	.	.	PUNCT
ejpam-1609	126	1	.+αk1	.+αk1	PUNCT
ejpam-1609	127	1	vk1	vk1	NOUN
ejpam-1609	127	2	pmd	pmd	PROPN
ejpam-1609	127	3	+	+	PROPN
ejpam-1609	127	4	w|w	w|w	NOUN
ejpam-1609	127	5	is	be	AUX
ejpam-1609	127	6	of	of	ADP
ejpam-1609	127	7	order	order	NOUN
ejpam-1609	127	8	less	less	ADV
ejpam-1609	127	9	or	or	CCONJ
ejpam-1609	127	10	equal	equal	ADJ
ejpam-1609	127	11	to	to	ADP
ejpam-1609	127	12	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	127	13	and	and	CCONJ
ejpam-1609	127	14	αi	αi	NOUN
ejpam-1609	127	15	∈	∈	PROPN
ejpam-1609	128	1	zp[ξ	zp[ξ	PROPN
ejpam-1609	128	2	]	]	PUNCT
ejpam-1609	128	3	,	,	PUNCT
ejpam-1609	128	4	i	i	NOUN
ejpam-1609	128	5	=	=	NOUN
ejpam-1609	128	6	1,2	1,2	NUM
ejpam-1609	128	7	,	,	PUNCT
ejpam-1609	128	8	.	.	PUNCT
ejpam-1609	128	9	.	.	PUNCT
ejpam-1609	128	10	.	.	PUNCT
ejpam-1609	129	1	,	,	PUNCT
ejpam-1609	129	2	k1	k1	PROPN
ejpam-1609	129	3	}	}	PUNCT
ejpam-1609	129	4	which	which	PRON
ejpam-1609	129	5	has	have	VERB
ejpam-1609	129	6	elements	element	NOUN
ejpam-1609	129	7	of	of	ADP
ejpam-1609	129	8	order	order	NOUN
ejpam-1609	129	9	less	less	ADV
ejpam-1609	129	10	or	or	CCONJ
ejpam-1609	129	11	equal	equal	ADJ
ejpam-1609	129	12	to	to	ADP
ejpam-1609	129	13	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	129	14	.	.	PUNCT
ejpam-1609	130	1	since	since	SCONJ
ejpam-1609	130	2	|kk1	|kk1	PROPN
ejpam-1609	130	3	+	+	PROPN
ejpam-1609	130	4	1|	1|	NUM
ejpam-1609	130	5	=	=	SYM
ejpam-1609	130	6	(	(	PUNCT
ejpam-1609	130	7	p	p	X
ejpam-1609	130	8	(	(	PUNCT
ejpam-1609	130	9	m−2)d)npdk1	m−2)d)npdk1	X
ejpam-1609	130	10	and	and	CCONJ
ejpam-1609	130	11	there	there	PRON
ejpam-1609	130	12	are	be	VERB
ejpam-1609	130	13	p(m−1)dn	p(m−1)dn	X
ejpam-1609	130	14	elements	element	NOUN
ejpam-1609	130	15	of	of	ADP
ejpam-1609	130	16	order	order	NOUN
ejpam-1609	130	17	≤	≤	X
ejpam-1609	130	18	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	130	19	in	in	ADP
ejpam-1609	130	20	r	r	NOUN
ejpam-1609	130	21	,	,	PUNCT
ejpam-1609	130	22	we	we	PRON
ejpam-1609	130	23	have	have	VERB
ejpam-1609	130	24	v	v	NUM
ejpam-1609	130	25	(	(	PUNCT
ejpam-1609	130	26	p(m−1)dn	p(m−1)dn	NOUN
ejpam-1609	130	27	)	)	PUNCT
ejpam-1609	130	28	1	1	NUM
ejpam-1609	130	29	is	be	AUX
ejpam-1609	130	30	(	(	PUNCT
ejpam-1609	130	31	p(m−1)dn	p(m−1)dn	NOUN
ejpam-1609	130	32	−	−	PROPN
ejpam-1609	130	33	p(m−2)dnpdk1	p(m−2)dnpdk1	NOUN
ejpam-1609	130	34	)	)	PUNCT
ejpam-1609	130	35	possibilities	possibility	NOUN
ejpam-1609	130	36	.	.	PUNCT
ejpam-1609	131	1	the	the	DET
ejpam-1609	131	2	same	same	ADJ
ejpam-1609	131	3	calculation	calculation	NOUN
ejpam-1609	131	4	for	for	ADP
ejpam-1609	131	5	the	the	DET
ejpam-1609	131	6	remaining	remain	VERB
ejpam-1609	131	7	k2	k2	ADJ
ejpam-1609	131	8	−	−	PROPN
ejpam-1609	131	9	1	1	NUM
ejpam-1609	131	10	vectors	vector	NOUN
ejpam-1609	131	11	yields	yield	VERB
ejpam-1609	131	12	the	the	DET
ejpam-1609	131	13	number	number	NOUN
ejpam-1609	131	14	{	{	PUNCT
ejpam-1609	131	15	(	(	PUNCT
ejpam-1609	131	16	p(m−1)d)n	p(m−1)d)n	NUM
ejpam-1609	131	17	−	−	PROPN
ejpam-1609	131	18	(	(	PUNCT
ejpam-1609	131	19	p(m−2)d	p(m−2)d	PROPN
ejpam-1609	131	20	)	)	PUNCT
ejpam-1609	131	21	npdk1}{(p(m−1)d	npdk1}{(p(m−1)d	NOUN
ejpam-1609	131	22	)	)	PUNCT
ejpam-1609	131	23	n−	n−	NOUN
ejpam-1609	131	24	(	(	PUNCT
ejpam-1609	131	25	p(m−2)d)npdk1	p(m−2)d)npdk1	VERB
ejpam-1609	131	26	pd}{(p(m−1)d	pd}{(p(m−1)d	NOUN
ejpam-1609	131	27	)	)	PUNCT
ejpam-1609	131	28	n−	n−	PROPN
ejpam-1609	131	29	(	(	PUNCT
ejpam-1609	131	30	p(m−2)d)npdk1	p(m−2)d)npdk1	VERB
ejpam-1609	131	31	p2d	p2d	NUM
ejpam-1609	131	32	}	}	PUNCT
ejpam-1609	131	33	.	.	PUNCT
ejpam-1609	131	34	.	.	PUNCT
ejpam-1609	131	35	.	.	PUNCT
ejpam-1609	132	1	{	{	PUNCT
ejpam-1609	132	2	(	(	PUNCT
ejpam-1609	132	3	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	132	4	)	)	PUNCT
ejpam-1609	132	5	n−	n−	PROPN
ejpam-1609	132	6	(	(	PUNCT
ejpam-1609	132	7	p(m−2)d)npdk1	p(m−2)d)npdk1	VERB
ejpam-1609	132	8	pd(k2−1)}=	pd(k2−1)}=	ADJ
ejpam-1609	132	9	k2−1∏	k2−1∏	PROPN
ejpam-1609	132	10	j=0	j=0	PROPN
ejpam-1609	132	11	{	{	PUNCT
ejpam-1609	132	12	(	(	PUNCT
ejpam-1609	132	13	p(m−1)d	p(m−1)d	NOUN
ejpam-1609	132	14	)	)	PUNCT
ejpam-1609	132	15	n	n	CCONJ
ejpam-1609	132	16	−	−	PROPN
ejpam-1609	132	17	(	(	PUNCT
ejpam-1609	132	18	p(m−2)d	p(m−2)d	PROPN
ejpam-1609	132	19	)	)	PUNCT
ejpam-1609	132	20	n	n	CCONJ
ejpam-1609	132	21	pdk1	pdk1	PROPN
ejpam-1609	132	22	pd	pd	PROPN
ejpam-1609	132	23	j	j	PROPN
ejpam-1609	132	24	}	}	PUNCT
ejpam-1609	132	25	.	.	PUNCT
ejpam-1609	133	1	inductively	inductively	ADV
ejpam-1609	133	2	,	,	PUNCT
ejpam-1609	133	3	if	if	SCONJ
ejpam-1609	133	4	the	the	DET
ejpam-1609	133	5	remaining	remain	VERB
ejpam-1609	133	6	ki	ki	PROPN
ejpam-1609	133	7	,	,	PUNCT
ejpam-1609	133	8	(	(	PUNCT
ejpam-1609	133	9	i	i	NOUN
ejpam-1609	133	10	=	=	NOUN
ejpam-1609	133	11	3,4	3,4	NUM
ejpam-1609	133	12	,	,	PUNCT
ejpam-1609	133	13	.	.	PUNCT
ejpam-1609	133	14	.	.	PUNCT
ejpam-1609	133	15	.	.	PUNCT
ejpam-1609	134	1	,	,	PUNCT
ejpam-1609	134	2	m	m	PROPN
ejpam-1609	134	3	)	)	PUNCT
ejpam-1609	134	4	,	,	PUNCT
ejpam-1609	134	5	linearly	linearly	ADV
ejpam-1609	134	6	independent	independent	ADJ
ejpam-1609	134	7	vectors	vector	NOUN
ejpam-1609	134	8	of	of	ADP
ejpam-1609	134	9	orders	order	NOUN
ejpam-1609	134	10	(	(	PUNCT
ejpam-1609	134	11	pm−i+1)d	pm−i+1)d	NOUN
ejpam-1609	134	12	are	be	AUX
ejpam-1609	134	13	chosen	choose	VERB
ejpam-1609	134	14	in	in	ADP
ejpam-1609	134	15	a	a	DET
ejpam-1609	134	16	similar	similar	ADJ
ejpam-1609	134	17	way	way	NOUN
ejpam-1609	134	18	,	,	PUNCT
ejpam-1609	134	19	the	the	DET
ejpam-1609	134	20	we	we	PRON
ejpam-1609	134	21	get	get	VERB
ejpam-1609	134	22	a=	a=	ADJ
ejpam-1609	134	23	m∏	m∏	NOUN
ejpam-1609	134	24	t=1	t=1	PROPN
ejpam-1609	134	25	kt−1∏	kt−1∏	PROPN
ejpam-1609	134	26	i=0	i=0	PROPN
ejpam-1609	134	27	(	(	PUNCT
ejpam-1609	134	28	(	(	PUNCT
ejpam-1609	134	29	p(m−(t−1))d	p(m−(t−1))d	NOUN
ejpam-1609	134	30	)	)	PUNCT
ejpam-1609	134	31	n	n	CCONJ
ejpam-1609	134	32	−	−	PROPN
ejpam-1609	134	33	(	(	PUNCT
ejpam-1609	134	34	p(m−1−(t−1))d	p(m−1−(t−1))d	NOUN
ejpam-1609	134	35	)	)	PUNCT
ejpam-1609	134	36	n	n	CCONJ
ejpam-1609	134	37	p	p	PROPN
ejpam-1609	134	38	∑t−1	∑t−1	PROPN
ejpam-1609	134	39	j=0	j=0	VERB
ejpam-1609	134	40	dk	dk	PROPN
ejpam-1609	134	41	j	j	PROPN
ejpam-1609	134	42	pd	pd	PROPN
ejpam-1609	134	43	i	i	PROPN
ejpam-1609	134	44	)	)	PUNCT
ejpam-1609	134	45	.	.	PUNCT
ejpam-1609	135	1	possibilities	possibility	NOUN
ejpam-1609	135	2	.	.	PUNCT
ejpam-1609	136	1	analogously	analogously	ADV
ejpam-1609	136	2	,	,	PUNCT
ejpam-1609	136	3	the	the	DET
ejpam-1609	136	4	term	term	NOUN
ejpam-1609	136	5	b	b	NOUN
ejpam-1609	136	6	=	=	SYM
ejpam-1609	136	7	m∏	m∏	PROPN
ejpam-1609	136	8	s=1	s=1	X
ejpam-1609	137	1	ks−1∏	ks−1∏	PROPN
ejpam-1609	137	2	r=0	r=0	PROPN
ejpam-1609	137	3			NOUN
ejpam-1609	137	4			NOUN
ejpam-1609	137	5			NOUN
ejpam-1609	137	6	s∏	s∏	PROPN
ejpam-1609	137	7	z=1	z=1	PUNCT
ejpam-1609	137	8	(	(	PUNCT
ejpam-1609	137	9	pm−(s−1))dkz	pm−(s−1))dkz	PROPN
ejpam-1609	137	10	m∏	m∏	PROPN
ejpam-1609	137	11	j	j	PROPN
ejpam-1609	138	1	=	=	NOUN
ejpam-1609	138	2	s+1	s+1	PROPN
ejpam-1609	138	3	(	(	PUNCT
ejpam-1609	138	4	pm−	pm−	PROPN
ejpam-1609	138	5	(	(	PUNCT
ejpam-1609	138	6	j−1))dk	j−1))dk	PROPN
ejpam-1609	138	7	j	j	PROPN
ejpam-1609	138	8	−	−	PROPN
ejpam-1609	138	9	(	(	PUNCT
ejpam-1609	138	10	s∏	s∏	PROPN
ejpam-1609	138	11	z=1	z=1	X
ejpam-1609	138	12	(	(	PUNCT
ejpam-1609	138	13	pm−s)dkz)(pm−(s+1))dks+1	pm−s)dkz)(pm−(s+1))dks+1	PROPN
ejpam-1609	138	14	·	·	PUNCT
ejpam-1609	138	15	m∏	m∏	PROPN
ejpam-1609	138	16	t	t	PROPN
ejpam-1609	138	17	=	=	SYM
ejpam-1609	138	18	s+2	s+2	PROPN
ejpam-1609	138	19	(	(	PUNCT
ejpam-1609	138	20	pm−(t−1))dkt	pm−(t−1))dkt	PROPN
ejpam-1609	138	21	.pr	.pr	PUNCT
ejpam-1609	138	22	!	!	PUNCT
ejpam-1609	139	1	describes	describe	VERB
ejpam-1609	139	2	the	the	DET
ejpam-1609	139	3	number	number	NOUN
ejpam-1609	139	4	of	of	ADP
ejpam-1609	139	5	bases	basis	NOUN
ejpam-1609	139	6	determining	determine	VERB
ejpam-1609	139	7	linear	linear	ADJ
ejpam-1609	139	8	codes	code	NOUN
ejpam-1609	139	9	of	of	ADP
ejpam-1609	139	10	length	length	NOUN
ejpam-1609	139	11	n	n	NOUN
ejpam-1609	139	12	and	and	CCONJ
ejpam-1609	139	13	type	type	NOUN
ejpam-1609	139	14	(	(	PUNCT
ejpam-1609	139	15	k1	k1	NOUN
ejpam-1609	139	16	,	,	PUNCT
ejpam-1609	139	17	k2	k2	NOUN
ejpam-1609	139	18	,	,	PUNCT
ejpam-1609	139	19	.	.	PUNCT
ejpam-1609	139	20	.	.	PUNCT
ejpam-1609	140	1	.	.	PUNCT
ejpam-1609	141	1	,	,	PUNCT
ejpam-1609	141	2	km	km	PROPN
ejpam-1609	141	3	)	)	PUNCT
ejpam-1609	141	4	over	over	ADP
ejpam-1609	141	5	r.	r.	PROPN
ejpam-1609	141	6	here	here	ADV
ejpam-1609	141	7	,	,	PUNCT
ejpam-1609	141	8	the	the	DET
ejpam-1609	141	9	choices	choice	NOUN
ejpam-1609	141	10	are	be	AUX
ejpam-1609	141	11	taken	take	VERB
ejpam-1609	141	12	from	from	ADP
ejpam-1609	141	13	inside	inside	ADP
ejpam-1609	141	14	a	a	DET
ejpam-1609	141	15	linear	linear	ADJ
ejpam-1609	141	16	code	code	NOUN
ejpam-1609	141	17	of	of	ADP
ejpam-1609	141	18	length	length	NOUN
ejpam-1609	141	19	n	n	NOUN
ejpam-1609	141	20	and	and	CCONJ
ejpam-1609	141	21	type	type	NOUN
ejpam-1609	141	22	(	(	PUNCT
ejpam-1609	141	23	k1	k1	NOUN
ejpam-1609	141	24	,	,	PUNCT
ejpam-1609	141	25	k2	k2	NOUN
ejpam-1609	141	26	,	,	PUNCT
ejpam-1609	141	27	.	.	PUNCT
ejpam-1609	141	28	.	.	PUNCT
ejpam-1609	142	1	.	.	PUNCT
ejpam-1609	143	1	,	,	PUNCT
ejpam-1609	143	2	km	km	PROPN
ejpam-1609	143	3	)	)	PUNCT
ejpam-1609	143	4	.	.	PUNCT
ejpam-1609	144	1	such	such	DET
ejpam-1609	144	2	a	a	DET
ejpam-1609	144	3	code	code	NOUN
ejpam-1609	144	4	has	have	VERB
ejpam-1609	144	5	(	(	PUNCT
ejpam-1609	144	6	pmd	pmd	PROPN
ejpam-1609	144	7	)	)	PUNCT
ejpam-1609	144	8	k1	k1	NOUN
ejpam-1609	144	9	.(p(m−1)d	.(p(m−1)d	PUNCT
ejpam-1609	144	10	)	)	PUNCT
ejpam-1609	144	11	k2	k2	PROPN
ejpam-1609	144	12	.	.	PUNCT
ejpam-1609	144	13	.	.	PUNCT
ejpam-1609	144	14	.	.	PUNCT
ejpam-1609	145	1	(	(	PUNCT
ejpam-1609	145	2	p2d	p2d	NOUN
ejpam-1609	145	3	)	)	PUNCT
ejpam-1609	145	4	km−1(p)dkm	km−1(p)dkm	PROPN
ejpam-1609	145	5	vectors	vector	NOUN
ejpam-1609	145	6	.	.	PUNCT
ejpam-1609	146	1	hence	hence	ADV
ejpam-1609	146	2	the	the	DET
ejpam-1609	146	3	following	follow	VERB
ejpam-1609	146	4	ratio	ratio	NOUN
ejpam-1609	146	5	gives	give	VERB
ejpam-1609	146	6	the	the	DET
ejpam-1609	146	7	result	result	NOUN
ejpam-1609	146	8	n	n	NOUN
ejpam-1609	146	9	=	=	PUNCT
ejpam-1609	146	10	a	a	DET
ejpam-1609	146	11	b	b	NOUN
ejpam-1609	146	12	.	.	PUNCT
ejpam-1609	147	1	now	now	ADV
ejpam-1609	147	2	we	we	PRON
ejpam-1609	147	3	give	give	VERB
ejpam-1609	147	4	a	a	DET
ejpam-1609	147	5	corollary	corollary	NOUN
ejpam-1609	147	6	for	for	ADP
ejpam-1609	147	7	counting	count	VERB
ejpam-1609	147	8	the	the	DET
ejpam-1609	147	9	linear	linear	ADJ
ejpam-1609	147	10	codes	code	NOUN
ejpam-1609	147	11	over	over	ADP
ejpam-1609	147	12	the	the	DET
ejpam-1609	147	13	first	first	ADJ
ejpam-1609	147	14	non	non	ADJ
ejpam-1609	147	15	trivial	trivial	ADJ
ejpam-1609	147	16	galois	galois	PROPN
ejpam-1609	147	17	ring	ring	NOUN
ejpam-1609	147	18	z4[ξ	z4[ξ	PROPN
ejpam-1609	147	19	]	]	PUNCT
ejpam-1609	147	20	of	of	ADP
ejpam-1609	147	21	16	16	NUM
ejpam-1609	147	22	elements	element	NOUN
ejpam-1609	147	23	.	.	PUNCT
ejpam-1609	148	1	e.	e.	PROPN
ejpam-1609	148	2	saltürk	saltürk	PROPN
ejpam-1609	148	3	,	,	PUNCT
ejpam-1609	148	4	i̇.	i̇.	PROPN
ejpam-1609	148	5	şiap	şiap	PROPN
ejpam-1609	148	6	/	/	SYM
ejpam-1609	148	7	eur	eur	PROPN
ejpam-1609	148	8	.	.	PUNCT
ejpam-1609	149	1	j.	j.	PROPN
ejpam-1609	149	2	pure	pure	PROPN
ejpam-1609	149	3	appl	appl	PROPN
ejpam-1609	149	4	.	.	PROPN
ejpam-1609	149	5	math	math	PROPN
ejpam-1609	149	6	,	,	PUNCT
ejpam-1609	149	7	5	5	NUM
ejpam-1609	149	8	(	(	PUNCT
ejpam-1609	149	9	2012	2012	NUM
ejpam-1609	149	10	)	)	PUNCT
ejpam-1609	149	11	,	,	PUNCT
ejpam-1609	149	12	250	250	NUM
ejpam-1609	149	13	-	-	SYM
ejpam-1609	149	14	259	259	NUM
ejpam-1609	149	15	255	255	NUM
ejpam-1609	149	16	corollary	corollary	ADJ
ejpam-1609	149	17	1	1	NUM
ejpam-1609	149	18	.	.	PUNCT
ejpam-1609	150	1	the	the	DET
ejpam-1609	150	2	number	number	NOUN
ejpam-1609	150	3	of	of	ADP
ejpam-1609	150	4	distinct	distinct	ADJ
ejpam-1609	150	5	linear	linear	NOUN
ejpam-1609	150	6	codes	code	NOUN
ejpam-1609	150	7	of	of	ADP
ejpam-1609	150	8	type	type	NOUN
ejpam-1609	150	9	(	(	PUNCT
ejpam-1609	150	10	k1	k1	NOUN
ejpam-1609	150	11	,	,	PUNCT
ejpam-1609	150	12	k2	k2	NOUN
ejpam-1609	150	13	)	)	PUNCT
ejpam-1609	150	14	over	over	ADP
ejpam-1609	150	15	z4[ξ	z4[ξ	PROPN
ejpam-1609	150	16	]	]	PUNCT
ejpam-1609	150	17	is	be	AUX
ejpam-1609	150	18	�	�	PROPN
ejpam-1609	150	19	n	n	CCONJ
ejpam-1609	150	20	k1	k1	NOUN
ejpam-1609	150	21	,	,	PUNCT
ejpam-1609	150	22	k2	k2	PROPN
ejpam-1609	150	23	�	�	PROPN
ejpam-1609	150	24	z4[ξ	z4[ξ	PROPN
ejpam-1609	150	25	]	]	X
ejpam-1609	151	1	=	=	PUNCT
ejpam-1609	151	2	nr	nr	PROPN
ejpam-1609	151	3	k1,k2	k1,k2	PROPN
ejpam-1609	151	4	(	(	PUNCT
ejpam-1609	151	5	n	n	CCONJ
ejpam-1609	151	6	)	)	PUNCT
ejpam-1609	151	7	=	=	SYM
ejpam-1609	151	8	∏k1−1	∏k1−1	NOUN
ejpam-1609	151	9	i=0	i=0	PROPN
ejpam-1609	151	10	(	(	PUNCT
ejpam-1609	151	11	16n−	16n−	NUM
ejpam-1609	151	12	4n+i	4n+i	NUM
ejpam-1609	151	13	)	)	PUNCT
ejpam-1609	151	14	∏k2−1	∏k2−1	DET
ejpam-1609	151	15	j=0	j=0	PROPN
ejpam-1609	151	16	(	(	PUNCT
ejpam-1609	151	17	4	4	NUM
ejpam-1609	151	18	n−	n−	NOUN
ejpam-1609	151	19	4k1	4k1	NUM
ejpam-1609	151	20	+	+	SYM
ejpam-1609	151	21	j	j	NOUN
ejpam-1609	151	22	)	)	PUNCT
ejpam-1609	151	23	∏k1−1	∏k1−1	NOUN
ejpam-1609	151	24	t=0	t=0	X
ejpam-1609	151	25	(	(	PUNCT
ejpam-1609	151	26	16k1.4k2	16k1.4k2	NUM
ejpam-1609	151	27	−	−	PROPN
ejpam-1609	151	28	4k1+k2+t	4k1+k2+t	PROPN
ejpam-1609	151	29	)	)	PUNCT
ejpam-1609	151	30	∏k2−1	∏k2−1	NUM
ejpam-1609	152	1	l=0	l=0	PROPN
ejpam-1609	152	2	(	(	PUNCT
ejpam-1609	152	3	4	4	NUM
ejpam-1609	152	4	k1+k2	k1+k2	PROPN
ejpam-1609	152	5	−	−	PROPN
ejpam-1609	152	6	4k1+l	4k1+l	NUM
ejpam-1609	152	7	)	)	PUNCT
ejpam-1609	152	8	where	where	SCONJ
ejpam-1609	152	9	ξ	ξ	PROPN
ejpam-1609	152	10	is	be	AUX
ejpam-1609	152	11	a	a	DET
ejpam-1609	152	12	root	root	NOUN
ejpam-1609	152	13	of	of	ADP
ejpam-1609	152	14	the	the	DET
ejpam-1609	152	15	basic	basic	ADJ
ejpam-1609	152	16	irreducible	irreducible	ADJ
ejpam-1609	152	17	polynomial	polynomial	ADJ
ejpam-1609	152	18	1	1	NUM
ejpam-1609	152	19	+	+	NOUN
ejpam-1609	152	20	x	x	PUNCT
ejpam-1609	152	21	+	+	CCONJ
ejpam-1609	152	22	x2	x2	PROPN
ejpam-1609	152	23	∈	∈	PROPN
ejpam-1609	152	24	z4[x	z4[x	PROPN
ejpam-1609	152	25	]	]	PUNCT
ejpam-1609	152	26	.	.	PUNCT
ejpam-1609	153	1	example	example	NOUN
ejpam-1609	154	1	1	1	NUM
ejpam-1609	154	2	.	.	PUNCT
ejpam-1609	154	3	the	the	DET
ejpam-1609	154	4	number	number	NOUN
ejpam-1609	154	5	of	of	ADP
ejpam-1609	154	6	distinct	distinct	ADJ
ejpam-1609	154	7	linear	linear	NOUN
ejpam-1609	154	8	codes	code	NOUN
ejpam-1609	154	9	of	of	ADP
ejpam-1609	154	10	length	length	NOUN
ejpam-1609	154	11	3	3	NUM
ejpam-1609	154	12	and	and	CCONJ
ejpam-1609	154	13	type	type	NOUN
ejpam-1609	154	14	(	(	PUNCT
ejpam-1609	154	15	k1	k1	NOUN
ejpam-1609	154	16	,	,	PUNCT
ejpam-1609	154	17	k2	k2	NOUN
ejpam-1609	154	18	)	)	PUNCT
ejpam-1609	154	19	=	=	PUNCT
ejpam-1609	154	20	(	(	PUNCT
ejpam-1609	154	21	2,1	2,1	NUM
ejpam-1609	154	22	)	)	PUNCT
ejpam-1609	154	23	over	over	ADP
ejpam-1609	154	24	z4[ξ	z4[ξ	PROPN
ejpam-1609	154	25	]	]	PUNCT
ejpam-1609	154	26	is	be	AUX
ejpam-1609	154	27	(	(	PUNCT
ejpam-1609	154	28	163−	163−	NUM
ejpam-1609	154	29	43)(163−	43)(163−	NUM
ejpam-1609	154	30	44)(43−	44)(43−	NUM
ejpam-1609	154	31	42	42	NUM
ejpam-1609	154	32	)	)	PUNCT
ejpam-1609	154	33	(	(	PUNCT
ejpam-1609	154	34	1624−	1624−	NUM
ejpam-1609	154	35	424)(1624−	424)(1624−	NUM
ejpam-1609	154	36	4242)(4241−	4242)(4241−	NUM
ejpam-1609	154	37	42	42	NUM
ejpam-1609	154	38	)	)	PUNCT
ejpam-1609	154	39	=	=	SYM
ejpam-1609	155	1	21	21	NUM
ejpam-1609	155	2	.	.	PUNCT
ejpam-1609	156	1	these	these	DET
ejpam-1609	156	2	linear	linear	ADJ
ejpam-1609	156	3	codes	code	NOUN
ejpam-1609	156	4	are	be	AUX
ejpam-1609	156	5	given	give	VERB
ejpam-1609	156	6	by	by	ADP
ejpam-1609	156	7	the	the	DET
ejpam-1609	156	8	following	follow	VERB
ejpam-1609	156	9	generator	generator	NOUN
ejpam-1609	156	10	matrices	matrix	NOUN
ejpam-1609	156	11	:	:	PUNCT
ejpam-1609	156	12			VERB
ejpam-1609	156	13			NOUN
ejpam-1609	156	14			NOUN
ejpam-1609	156	15	1	1	NUM
ejpam-1609	156	16	0	0	NUM
ejpam-1609	156	17	x	x	SYM
ejpam-1609	156	18	0	0	NUM
ejpam-1609	156	19	1	1	NUM
ejpam-1609	156	20	x	x	SYM
ejpam-1609	156	21	0	0	NUM
ejpam-1609	156	22	0	0	NUM
ejpam-1609	156	23	2	2	NUM
ejpam-1609	156	24			NOUN
ejpam-1609	156	25			NOUN
ejpam-1609	156	26			PUNCT
ejpam-1609	157	1			PROPN
ejpam-1609	157	2			NOUN
ejpam-1609	157	3			NOUN
ejpam-1609	157	4	1	1	NUM
ejpam-1609	157	5	x	x	SYM
ejpam-1609	157	6	0	0	NUM
ejpam-1609	157	7	0	0	NUM
ejpam-1609	157	8	2	2	NUM
ejpam-1609	157	9	0	0	NUM
ejpam-1609	157	10	0	0	NUM
ejpam-1609	157	11	0	0	NUM
ejpam-1609	157	12	1	1	NUM
ejpam-1609	157	13			NOUN
ejpam-1609	157	14			NOUN
ejpam-1609	157	15			PUNCT
ejpam-1609	158	1			PROPN
ejpam-1609	158	2			NOUN
ejpam-1609	158	3			NOUN
ejpam-1609	158	4	2	2	NUM
ejpam-1609	158	5	0	0	NUM
ejpam-1609	158	6	0	0	NUM
ejpam-1609	158	7	0	0	NUM
ejpam-1609	158	8	1	1	NUM
ejpam-1609	158	9	0	0	NUM
ejpam-1609	158	10	0	0	NUM
ejpam-1609	158	11	0	0	NUM
ejpam-1609	158	12	1	1	NUM
ejpam-1609	158	13			NOUN
ejpam-1609	158	14			NOUN
ejpam-1609	158	15			PUNCT
ejpam-1609	159	1	where	where	SCONJ
ejpam-1609	159	2	x	x	SYM
ejpam-1609	159	3	∈	∈	PROPN
ejpam-1609	159	4	{	{	PUNCT
ejpam-1609	159	5	0,1,ξ	0,1,ξ	NOUN
ejpam-1609	159	6	,	,	PUNCT
ejpam-1609	159	7	1	1	NUM
ejpam-1609	159	8	+	+	SYM
ejpam-1609	159	9	ξ	ξ	NOUN
ejpam-1609	159	10	}	}	PUNCT
ejpam-1609	159	11	and	and	CCONJ
ejpam-1609	159	12	ξ	ξ	PROPN
ejpam-1609	159	13	is	be	AUX
ejpam-1609	159	14	a	a	DET
ejpam-1609	159	15	root	root	NOUN
ejpam-1609	159	16	of	of	ADP
ejpam-1609	159	17	the	the	DET
ejpam-1609	159	18	polynomial	polynomial	ADJ
ejpam-1609	159	19	1	1	NUM
ejpam-1609	159	20	+	+	NOUN
ejpam-1609	159	21	x	x	SYM
ejpam-1609	160	1	+	+	CCONJ
ejpam-1609	160	2	x2	x2	PROPN
ejpam-1609	160	3	.	.	PUNCT
ejpam-1609	161	1	definition	definition	NOUN
ejpam-1609	161	2	5	5	NUM
ejpam-1609	161	3	.	.	PUNCT
ejpam-1609	162	1	let	let	VERB
ejpam-1609	162	2	r	r	PRON
ejpam-1609	162	3	be	be	AUX
ejpam-1609	162	4	a	a	DET
ejpam-1609	162	5	galois	galois	PROPN
ejpam-1609	162	6	ring	ring	NOUN
ejpam-1609	162	7	.	.	PUNCT
ejpam-1609	163	1	an	an	DET
ejpam-1609	163	2	additive	additive	ADJ
ejpam-1609	163	3	code	code	NOUN
ejpam-1609	163	4	of	of	ADP
ejpam-1609	163	5	length	length	NOUN
ejpam-1609	163	6	n	n	CCONJ
ejpam-1609	163	7	over	over	ADP
ejpam-1609	163	8	r	r	NOUN
ejpam-1609	163	9	is	be	AUX
ejpam-1609	163	10	subgroup	subgroup	NOUN
ejpam-1609	163	11	of	of	ADP
ejpam-1609	163	12	rn	rn	PROPN
ejpam-1609	163	13	.	.	PUNCT
ejpam-1609	164	1	here	here	ADV
ejpam-1609	164	2	we	we	PRON
ejpam-1609	164	3	emphasize	emphasize	VERB
ejpam-1609	164	4	that	that	SCONJ
ejpam-1609	164	5	an	an	DET
ejpam-1609	164	6	additive	additive	ADJ
ejpam-1609	164	7	code	code	NOUN
ejpam-1609	164	8	is	be	AUX
ejpam-1609	164	9	actually	actually	ADV
ejpam-1609	164	10	a	a	DET
ejpam-1609	164	11	zsubmodule	zsubmodule	NOUN
ejpam-1609	164	12	of	of	ADP
ejpam-1609	164	13	rn	rn	PROPN
ejpam-1609	164	14	.	.	PROPN
ejpam-1609	165	1	on	on	ADP
ejpam-1609	165	2	the	the	DET
ejpam-1609	165	3	other	other	ADJ
ejpam-1609	165	4	hand	hand	NOUN
ejpam-1609	165	5	,	,	PUNCT
ejpam-1609	165	6	a	a	DET
ejpam-1609	165	7	linear	linear	ADJ
ejpam-1609	165	8	code	code	NOUN
ejpam-1609	165	9	is	be	AUX
ejpam-1609	165	10	an	an	DET
ejpam-1609	165	11	rsubmodule	rsubmodule	NOUN
ejpam-1609	165	12	of	of	ADP
ejpam-1609	165	13	rn	rn	PROPN
ejpam-1609	165	14	.	.	PUNCT
ejpam-1609	166	1	now	now	ADV
ejpam-1609	166	2	we	we	PRON
ejpam-1609	166	3	give	give	VERB
ejpam-1609	166	4	the	the	DET
ejpam-1609	166	5	number	number	NOUN
ejpam-1609	166	6	of	of	ADP
ejpam-1609	166	7	additive	additive	ADJ
ejpam-1609	166	8	codes	code	NOUN
ejpam-1609	166	9	of	of	ADP
ejpam-1609	166	10	a	a	DET
ejpam-1609	166	11	particular	particular	ADJ
ejpam-1609	166	12	type	type	NOUN
ejpam-1609	166	13	over	over	ADP
ejpam-1609	166	14	galois	galois	PROPN
ejpam-1609	166	15	rings	ring	NOUN
ejpam-1609	166	16	.	.	PUNCT
ejpam-1609	167	1	theorem	theorem	VERB
ejpam-1609	167	2	4	4	NUM
ejpam-1609	167	3	.	.	PUNCT
ejpam-1609	168	1	the	the	DET
ejpam-1609	168	2	number	number	NOUN
ejpam-1609	168	3	of	of	ADP
ejpam-1609	168	4	distinct	distinct	ADJ
ejpam-1609	168	5	(	(	PUNCT
ejpam-1609	168	6	not	not	PART
ejpam-1609	168	7	necessarily	necessarily	ADV
ejpam-1609	168	8	inequivalent	inequivalent	ADJ
ejpam-1609	168	9	)	)	PUNCT
ejpam-1609	168	10	additive	additive	ADJ
ejpam-1609	168	11	codes	code	NOUN
ejpam-1609	168	12	over	over	ADP
ejpam-1609	168	13	r	r	NOUN
ejpam-1609	168	14	is	be	AUX
ejpam-1609	168	15	n+r	n+r	PROPN
ejpam-1609	168	16	k1,k2,	k1,k2,	NOUN
ejpam-1609	168	17	...	...	PUNCT
ejpam-1609	168	18	,ks	,ks	PUNCT
ejpam-1609	168	19	(	(	PUNCT
ejpam-1609	168	20	n	n	CCONJ
ejpam-1609	168	21	)	)	PUNCT
ejpam-1609	168	22	=	=	SYM
ejpam-1609	168	23	�	�	PROPN
ejpam-1609	168	24	n	n	CCONJ
ejpam-1609	168	25	k1	k1	NOUN
ejpam-1609	168	26	,	,	PUNCT
ejpam-1609	168	27	k2	k2	NOUN
ejpam-1609	168	28	,	,	PUNCT
ejpam-1609	168	29	.	.	PUNCT
ejpam-1609	168	30	.	.	PUNCT
ejpam-1609	168	31	.	.	PUNCT
ejpam-1609	169	1	,	,	PUNCT
ejpam-1609	169	2	ks	ks	PROPN
ejpam-1609	169	3	�	�	PROPN
ejpam-1609	169	4	+	+	NOUN
ejpam-1609	169	5	r	r	NOUN
ejpam-1609	169	6	=	=	PUNCT
ejpam-1609	169	7	a	a	DET
ejpam-1609	169	8	b	b	NOUN
ejpam-1609	169	9	,	,	PUNCT
ejpam-1609	169	10	(	(	PUNCT
ejpam-1609	169	11	3	3	X
ejpam-1609	169	12	)	)	PUNCT
ejpam-1609	169	13	where	where	SCONJ
ejpam-1609	169	14	a=	a=	ADV
ejpam-1609	169	15	∏m	∏m	X
ejpam-1609	169	16	t=1	t=1	PROPN
ejpam-1609	169	17	∏kt−1	∏kt−1	PROPN
ejpam-1609	169	18	i=0	i=0	PROPN
ejpam-1609	169	19	(	(	PUNCT
ejpam-1609	169	20	(	(	PUNCT
ejpam-1609	169	21	p	p	PROPN
ejpam-1609	169	22	m−(t−1	m−(t−1	PROPN
ejpam-1609	169	23	)	)	PUNCT
ejpam-1609	169	24	)	)	PUNCT
ejpam-1609	170	1	dn	dn	ADP
ejpam-1609	170	2	−	−	PROPN
ejpam-1609	170	3	(	(	PUNCT
ejpam-1609	170	4	pm−1−(t−1	pm−1−(t−1	NOUN
ejpam-1609	170	5	)	)	PUNCT
ejpam-1609	170	6	)	)	PUNCT
ejpam-1609	171	1	dn	dn	PROPN
ejpam-1609	171	2	.p	.p	PROPN
ejpam-1609	171	3	∑t−1	∑t−1	PROPN
ejpam-1609	171	4	j=0	j=0	PROPN
ejpam-1609	171	5	k	k	PROPN
ejpam-1609	171	6	j	j	PROPN
ejpam-1609	171	7	.pi	.pi	PROPN
ejpam-1609	171	8	)	)	PUNCT
ejpam-1609	171	9	,	,	PUNCT
ejpam-1609	171	10	and	and	CCONJ
ejpam-1609	171	11	b	b	X
ejpam-1609	171	12	=	=	SYM
ejpam-1609	171	13	m∏	m∏	PROPN
ejpam-1609	171	14	s=1	s=1	X
ejpam-1609	172	1	ks−1∏	ks−1∏	PROPN
ejpam-1609	172	2	r=0	r=0	PROPN
ejpam-1609	172	3			NOUN
ejpam-1609	172	4			NOUN
ejpam-1609	172	5			NOUN
ejpam-1609	172	6	s∏	s∏	PROPN
ejpam-1609	172	7	z=1	z=1	PUNCT
ejpam-1609	172	8	(	(	PUNCT
ejpam-1609	172	9	pm−(s−1))kz	pm−(s−1))kz	PROPN
ejpam-1609	172	10	m∏	m∏	PROPN
ejpam-1609	172	11	j	j	PROPN
ejpam-1609	173	1	=	=	NOUN
ejpam-1609	173	2	s+1	s+1	PROPN
ejpam-1609	173	3	(	(	PUNCT
ejpam-1609	173	4	pm−	pm−	PROPN
ejpam-1609	173	5	(	(	PUNCT
ejpam-1609	173	6	j−1))k	j−1))k	PROPN
ejpam-1609	173	7	j	j	PROPN
ejpam-1609	173	8	−	−	PROPN
ejpam-1609	173	9	(	(	PUNCT
ejpam-1609	173	10	s∏	s∏	PROPN
ejpam-1609	173	11	z=1	z=1	PROPN
ejpam-1609	173	12	(	(	PUNCT
ejpam-1609	173	13	pm−s)kz)(pm−(s+1))ks+1	pm−s)kz)(pm−(s+1))ks+1	NOUN
ejpam-1609	173	14	·	·	PUNCT
ejpam-1609	173	15	m∏	m∏	PROPN
ejpam-1609	173	16	t	t	PROPN
ejpam-1609	173	17	=	=	SYM
ejpam-1609	173	18	s+2	s+2	PROPN
ejpam-1609	173	19	(	(	PUNCT
ejpam-1609	173	20	pm−(t−1))kt	pm−(t−1))kt	NOUN
ejpam-1609	173	21	·	·	PUNCT
ejpam-1609	173	22	pr	pr	X
ejpam-1609	173	23	!	!	PUNCT
ejpam-1609	174	1	proof	proof	NOUN
ejpam-1609	174	2	.	.	PUNCT
ejpam-1609	175	1	we	we	PRON
ejpam-1609	175	2	prove	prove	VERB
ejpam-1609	175	3	the	the	DET
ejpam-1609	175	4	theorem	theorem	NOUN
ejpam-1609	175	5	similar	similar	ADJ
ejpam-1609	175	6	to	to	ADP
ejpam-1609	175	7	the	the	DET
ejpam-1609	175	8	proof	proof	NOUN
ejpam-1609	175	9	of	of	ADP
ejpam-1609	175	10	the	the	DET
ejpam-1609	175	11	theorem	theorem	NOUN
ejpam-1609	175	12	3	3	X
ejpam-1609	175	13	.	.	PUNCT
ejpam-1609	176	1	here	here	ADV
ejpam-1609	176	2	,	,	PUNCT
ejpam-1609	176	3	we	we	PRON
ejpam-1609	176	4	will	will	AUX
ejpam-1609	176	5	take	take	VERB
ejpam-1609	176	6	the	the	DET
ejpam-1609	176	7	additive	additive	ADJ
ejpam-1609	176	8	orders	order	NOUN
ejpam-1609	176	9	of	of	ADP
ejpam-1609	176	10	the	the	DET
ejpam-1609	176	11	elements	element	NOUN
ejpam-1609	176	12	of	of	ADP
ejpam-1609	176	13	zpm[ξ	zpm[ξ	NOUN
ejpam-1609	176	14	]	]	PUNCT
ejpam-1609	176	15	.	.	PUNCT
ejpam-1609	177	1	corollary	corollary	ADJ
ejpam-1609	177	2	2	2	NUM
ejpam-1609	177	3	.	.	PUNCT
ejpam-1609	178	1	the	the	DET
ejpam-1609	178	2	number	number	NOUN
ejpam-1609	178	3	of	of	ADP
ejpam-1609	178	4	distinct	distinct	ADJ
ejpam-1609	178	5	additive	additive	ADJ
ejpam-1609	178	6	codes	code	NOUN
ejpam-1609	178	7	of	of	ADP
ejpam-1609	178	8	type	type	NOUN
ejpam-1609	178	9	(	(	PUNCT
ejpam-1609	178	10	k1	k1	NOUN
ejpam-1609	178	11	,	,	PUNCT
ejpam-1609	178	12	k2	k2	NOUN
ejpam-1609	178	13	)	)	PUNCT
ejpam-1609	178	14	over	over	ADP
ejpam-1609	178	15	z4[ξ	z4[ξ	PROPN
ejpam-1609	178	16	]	]	PUNCT
ejpam-1609	178	17	is	be	AUX
ejpam-1609	178	18	�	�	PROPN
ejpam-1609	178	19	n	n	CCONJ
ejpam-1609	178	20	k1	k1	NOUN
ejpam-1609	178	21	,	,	PUNCT
ejpam-1609	178	22	k2	k2	PROPN
ejpam-1609	178	23	�	�	PROPN
ejpam-1609	178	24	+	+	NUM
ejpam-1609	178	25	z4[ξ	z4[ξ	NOUN
ejpam-1609	178	26	]	]	X
ejpam-1609	179	1	=	=	SYM
ejpam-1609	179	2	n+r	n+r	PROPN
ejpam-1609	179	3	k1,k2	k1,k2	PROPN
ejpam-1609	179	4	(	(	PUNCT
ejpam-1609	179	5	n	n	CCONJ
ejpam-1609	179	6	)	)	PUNCT
ejpam-1609	179	7	=	=	SYM
ejpam-1609	180	1	∏k1−1	∏k1−1	NOUN
ejpam-1609	180	2	i=0	i=0	PROPN
ejpam-1609	180	3	(	(	PUNCT
ejpam-1609	180	4	16n−	16n−	NUM
ejpam-1609	180	5	4n2i	4n2i	NOUN
ejpam-1609	180	6	)	)	PUNCT
ejpam-1609	181	1	∏k2−1	∏k2−1	DET
ejpam-1609	181	2	j=0	j=0	PROPN
ejpam-1609	181	3	(	(	PUNCT
ejpam-1609	181	4	4	4	NUM
ejpam-1609	181	5	n−	n−	NOUN
ejpam-1609	181	6	2k1	2k1	NUM
ejpam-1609	181	7	+	+	SYM
ejpam-1609	181	8	j	j	NOUN
ejpam-1609	181	9	)	)	PUNCT
ejpam-1609	181	10	∏k1−1	∏k1−1	NOUN
ejpam-1609	181	11	t=0	t=0	X
ejpam-1609	181	12	(	(	PUNCT
ejpam-1609	181	13	4	4	NUM
ejpam-1609	181	14	k1	k1	X
ejpam-1609	181	15	·	·	PUNCT
ejpam-1609	181	16	2k2	2k2	NUM
ejpam-1609	181	17	−	−	NUM
ejpam-1609	181	18	2k1+k2+t	2k1+k2+t	NUM
ejpam-1609	181	19	)	)	PUNCT
ejpam-1609	182	1	∏k2−1	∏k2−1	NUM
ejpam-1609	182	2	l=0	l=0	PROPN
ejpam-1609	182	3	(	(	PUNCT
ejpam-1609	182	4	2	2	NUM
ejpam-1609	182	5	k1+k2	k1+k2	PROPN
ejpam-1609	182	6	−	−	PROPN
ejpam-1609	182	7	2k1+l	2k1+l	PROPN
ejpam-1609	182	8	)	)	PUNCT
ejpam-1609	182	9	where	where	SCONJ
ejpam-1609	182	10	ξ	ξ	PROPN
ejpam-1609	182	11	is	be	AUX
ejpam-1609	182	12	a	a	DET
ejpam-1609	182	13	root	root	NOUN
ejpam-1609	182	14	of	of	ADP
ejpam-1609	182	15	the	the	DET
ejpam-1609	182	16	polynomial	polynomial	ADJ
ejpam-1609	182	17	1	1	NUM
ejpam-1609	182	18	+	+	NOUN
ejpam-1609	182	19	x	x	SYM
ejpam-1609	182	20	+	+	CCONJ
ejpam-1609	182	21	x2	x2	PROPN
ejpam-1609	182	22	.	.	PUNCT
ejpam-1609	183	1	e.	e.	PROPN
ejpam-1609	183	2	saltürk	saltürk	PROPN
ejpam-1609	183	3	,	,	PUNCT
ejpam-1609	183	4	i̇.	i̇.	PROPN
ejpam-1609	183	5	şiap	şiap	PROPN
ejpam-1609	183	6	/	/	SYM
ejpam-1609	183	7	eur	eur	PROPN
ejpam-1609	183	8	.	.	PUNCT
ejpam-1609	184	1	j.	j.	PROPN
ejpam-1609	184	2	pure	pure	PROPN
ejpam-1609	184	3	appl	appl	PROPN
ejpam-1609	184	4	.	.	PROPN
ejpam-1609	184	5	math	math	PROPN
ejpam-1609	184	6	,	,	PUNCT
ejpam-1609	184	7	5	5	NUM
ejpam-1609	184	8	(	(	PUNCT
ejpam-1609	184	9	2012	2012	NUM
ejpam-1609	184	10	)	)	PUNCT
ejpam-1609	184	11	,	,	PUNCT
ejpam-1609	184	12	250	250	NUM
ejpam-1609	184	13	-	-	SYM
ejpam-1609	184	14	259	259	NUM
ejpam-1609	184	15	256	256	NUM
ejpam-1609	184	16	3	3	NUM
ejpam-1609	184	17	.	.	PUNCT
ejpam-1609	184	18	generalized	generalize	VERB
ejpam-1609	184	19	gaussian	gaussian	ADJ
ejpam-1609	184	20	numbers	number	NOUN
ejpam-1609	184	21	in	in	ADP
ejpam-1609	184	22	this	this	DET
ejpam-1609	184	23	section	section	NOUN
ejpam-1609	184	24	,	,	PUNCT
ejpam-1609	184	25	we	we	PRON
ejpam-1609	184	26	are	be	AUX
ejpam-1609	184	27	interested	interested	ADJ
ejpam-1609	184	28	in	in	ADP
ejpam-1609	184	29	the	the	DET
ejpam-1609	184	30	properties	property	NOUN
ejpam-1609	184	31	of	of	ADP
ejpam-1609	184	32	the	the	DET
ejpam-1609	184	33	numbers	number	NOUN
ejpam-1609	184	34	nr	nr	PRON
ejpam-1609	184	35	k1,k2,	k1,k2,	PROPN
ejpam-1609	184	36	...	...	PUNCT
ejpam-1609	184	37	,km	,km	PUNCT
ejpam-1609	184	38	(	(	PUNCT
ejpam-1609	184	39	n	n	CCONJ
ejpam-1609	184	40	)	)	PUNCT
ejpam-1609	184	41	.	.	PUNCT
ejpam-1609	185	1	since	since	SCONJ
ejpam-1609	185	2	they	they	PRON
ejpam-1609	185	3	resemble	resemble	VERB
ejpam-1609	185	4	in	in	ADP
ejpam-1609	185	5	some	some	DET
ejpam-1609	185	6	sense	sense	NOUN
ejpam-1609	185	7	the	the	DET
ejpam-1609	185	8	gaussian	gaussian	ADJ
ejpam-1609	185	9	numbers	number	NOUN
ejpam-1609	185	10	we	we	PRON
ejpam-1609	185	11	call	call	VERB
ejpam-1609	185	12	these	these	DET
ejpam-1609	185	13	numbers	number	NOUN
ejpam-1609	185	14	generalized	generalize	VERB
ejpam-1609	185	15	gaussian	gaussian	ADJ
ejpam-1609	185	16	numbers	number	NOUN
ejpam-1609	185	17	.	.	PUNCT
ejpam-1609	186	1	hence	hence	ADV
ejpam-1609	186	2	,	,	PUNCT
ejpam-1609	186	3	we	we	PRON
ejpam-1609	186	4	study	study	VERB
ejpam-1609	186	5	some	some	DET
ejpam-1609	186	6	properties	property	NOUN
ejpam-1609	186	7	of	of	ADP
ejpam-1609	186	8	these	these	DET
ejpam-1609	186	9	numbers	number	NOUN
ejpam-1609	186	10	.	.	PUNCT
ejpam-1609	187	1	some	some	PRON
ejpam-1609	187	2	of	of	ADP
ejpam-1609	187	3	the	the	DET
ejpam-1609	187	4	well	well	ADV
ejpam-1609	187	5	known	know	VERB
ejpam-1609	187	6	properties	property	NOUN
ejpam-1609	187	7	of	of	ADP
ejpam-1609	187	8	the	the	DET
ejpam-1609	187	9	classical	classical	ADJ
ejpam-1609	187	10	gaussian	gaussian	ADJ
ejpam-1609	187	11	binomial	binomial	ADJ
ejpam-1609	187	12	coefficients	coefficient	NOUN
ejpam-1609	187	13	are	be	AUX
ejpam-1609	187	14	as	as	SCONJ
ejpam-1609	187	15	follows	follow	VERB
ejpam-1609	187	16	:	:	PUNCT
ejpam-1609	187	17	theorem	theorem	NOUN
ejpam-1609	187	18	5	5	NUM
ejpam-1609	187	19	.	.	PUNCT
ejpam-1609	187	20	assume	assume	VERB
ejpam-1609	187	21	the	the	DET
ejpam-1609	187	22	notations	notation	NOUN
ejpam-1609	187	23	in	in	ADP
ejpam-1609	187	24	definition	definition	NOUN
ejpam-1609	187	25	1	1	NUM
ejpam-1609	187	26	.	.	PUNCT
ejpam-1609	188	1	then	then	ADV
ejpam-1609	188	2	,	,	PUNCT
ejpam-1609	188	3	(	(	PUNCT
ejpam-1609	188	4	i	i	NOUN
ejpam-1609	188	5	)	)	PUNCT
ejpam-1609	188	6	�	�	PROPN
ejpam-1609	188	7	n	n	CCONJ
ejpam-1609	188	8	k	k	PROPN
ejpam-1609	188	9	�	�	PROPN
ejpam-1609	188	10	q	q	PROPN
ejpam-1609	188	11	=	=	PUNCT
ejpam-1609	188	12	�	�	PROPN
ejpam-1609	188	13	n	n	CCONJ
ejpam-1609	188	14	n−	n−	PROPN
ejpam-1609	188	15	k	k	PROPN
ejpam-1609	188	16	�	�	PROPN
ejpam-1609	188	17	q	q	PROPN
ejpam-1609	188	18	,	,	PUNCT
ejpam-1609	188	19	(	(	PUNCT
ejpam-1609	188	20	ii	ii	NOUN
ejpam-1609	188	21	)	)	PUNCT
ejpam-1609	188	22	�	�	PROPN
ejpam-1609	188	23	n	n	CCONJ
ejpam-1609	188	24	0	0	NUM
ejpam-1609	188	25	�	�	PROPN
ejpam-1609	188	26	q	q	NOUN
ejpam-1609	188	27	=	=	SYM
ejpam-1609	188	28	�	�	PROPN
ejpam-1609	188	29	n	n	CCONJ
ejpam-1609	188	30	n	n	PRON
ejpam-1609	188	31	�	�	PROPN
ejpam-1609	188	32	q	q	NOUN
ejpam-1609	188	33	=	=	SYM
ejpam-1609	188	34	1	1	NUM
ejpam-1609	188	35	,	,	PUNCT
ejpam-1609	188	36	(	(	PUNCT
ejpam-1609	188	37	iii	iii	X
ejpam-1609	188	38	)	)	PUNCT
ejpam-1609	188	39	�	�	PROPN
ejpam-1609	188	40	n	n	CCONJ
ejpam-1609	188	41	k	k	PROPN
ejpam-1609	188	42	�	�	PROPN
ejpam-1609	188	43	q	q	PROPN
ejpam-1609	188	44	=	=	PUNCT
ejpam-1609	188	45	�	�	PROPN
ejpam-1609	188	46	n−	n−	PROPN
ejpam-1609	188	47	1	1	NUM
ejpam-1609	188	48	k−	k−	PROPN
ejpam-1609	188	49	1	1	NUM
ejpam-1609	188	50	�	�	PROPN
ejpam-1609	188	51	q	q	PROPN
ejpam-1609	189	1	+	+	CCONJ
ejpam-1609	189	2	qk	qk	ADP
ejpam-1609	189	3	�	�	PROPN
ejpam-1609	189	4	n−	n−	PROPN
ejpam-1609	189	5	1	1	NUM
ejpam-1609	189	6	k	k	PROPN
ejpam-1609	189	7	�	�	PROPN
ejpam-1609	189	8	q	q	PROPN
ejpam-1609	189	9	,	,	PUNCT
ejpam-1609	189	10	(	(	PUNCT
ejpam-1609	189	11	iv	iv	X
ejpam-1609	189	12	)	)	PUNCT
ejpam-1609	189	13	�	�	PROPN
ejpam-1609	189	14	n	n	CCONJ
ejpam-1609	189	15	k	k	PROPN
ejpam-1609	189	16	�	�	PROPN
ejpam-1609	189	17	q	q	PROPN
ejpam-1609	189	18	=	=	PUNCT
ejpam-1609	189	19	�	�	PROPN
ejpam-1609	189	20	n−	n−	NOUN
ejpam-1609	189	21	1	1	NUM
ejpam-1609	189	22	k	k	PROPN
ejpam-1609	189	23	�	�	PROPN
ejpam-1609	189	24	q	q	PROPN
ejpam-1609	189	25	+	+	NUM
ejpam-1609	189	26	qn−k	qn−k	PROPN
ejpam-1609	189	27	�	�	PROPN
ejpam-1609	189	28	n−	n−	PROPN
ejpam-1609	189	29	1	1	NUM
ejpam-1609	189	30	k−	k−	PROPN
ejpam-1609	189	31	1	1	NUM
ejpam-1609	189	32	�	�	PROPN
ejpam-1609	189	33	q	q	PROPN
ejpam-1609	189	34	,	,	PUNCT
ejpam-1609	189	35	(	(	PUNCT
ejpam-1609	189	36	v	v	NOUN
ejpam-1609	189	37	)	)	PUNCT
ejpam-1609	189	38	limq→1	limq→1	PROPN
ejpam-1609	189	39	�	�	PROPN
ejpam-1609	189	40	n	n	CCONJ
ejpam-1609	189	41	k	k	PROPN
ejpam-1609	189	42	�	�	PROPN
ejpam-1609	189	43	q	q	PROPN
ejpam-1609	189	44	=	=	PUNCT
ejpam-1609	189	45	�	�	PROPN
ejpam-1609	189	46	n	n	CCONJ
ejpam-1609	189	47	k	k	PROPN
ejpam-1609	189	48	�	�	PROPN
ejpam-1609	189	49	(	(	PUNCT
ejpam-1609	189	50	binomial	binomial	ADJ
ejpam-1609	189	51	coefficient	coefficient	NOUN
ejpam-1609	189	52	)	)	PUNCT
ejpam-1609	189	53	.	.	PUNCT
ejpam-1609	190	1	now	now	ADV
ejpam-1609	190	2	we	we	PRON
ejpam-1609	190	3	present	present	VERB
ejpam-1609	190	4	some	some	DET
ejpam-1609	190	5	properties	property	NOUN
ejpam-1609	190	6	of	of	ADP
ejpam-1609	190	7	generalized	generalized	ADJ
ejpam-1609	190	8	gaussian	gaussian	ADJ
ejpam-1609	190	9	numbers	number	NOUN
ejpam-1609	190	10	in	in	ADP
ejpam-1609	190	11	the	the	DET
ejpam-1609	190	12	following	following	NOUN
ejpam-1609	190	13	theorem	theorem	NOUN
ejpam-1609	190	14	:	:	PUNCT
ejpam-1609	190	15	theorem	theorem	NOUN
ejpam-1609	190	16	6	6	NUM
ejpam-1609	190	17	.	.	PUNCT
ejpam-1609	191	1	let	let	VERB
ejpam-1609	191	2	n	n	PRON
ejpam-1609	191	3	be	be	AUX
ejpam-1609	191	4	a	a	DET
ejpam-1609	191	5	positive	positive	ADJ
ejpam-1609	191	6	integer	integer	NOUN
ejpam-1609	191	7	,	,	PUNCT
ejpam-1609	191	8	r=	r=	ADJ
ejpam-1609	191	9	zpm	zpm	NOUN
ejpam-1609	191	10	,	,	PUNCT
ejpam-1609	191	11	(	(	PUNCT
ejpam-1609	191	12	k	k	PROPN
ejpam-1609	191	13	≤	≤	PROPN
ejpam-1609	191	14	n	n	CCONJ
ejpam-1609	191	15	)	)	PUNCT
ejpam-1609	191	16	and	and	CCONJ
ejpam-1609	191	17	(	(	PUNCT
ejpam-1609	191	18	ki	ki	PROPN
ejpam-1609	191	19	≤	≤	PROPN
ejpam-1609	191	20	n	n	CCONJ
ejpam-1609	191	21	)	)	PUNCT
ejpam-1609	191	22	.	.	PUNCT
ejpam-1609	192	1	then	then	ADV
ejpam-1609	192	2	,	,	PUNCT
ejpam-1609	192	3	(	(	PUNCT
ejpam-1609	192	4	i	i	NOUN
ejpam-1609	192	5	)	)	PUNCT
ejpam-1609	192	6	if	if	SCONJ
ejpam-1609	192	7	∑m	∑m	PROPN
ejpam-1609	192	8	i=1	i=1	PROPN
ejpam-1609	192	9	ki	ki	PROPN
ejpam-1609	192	10	=	=	SYM
ejpam-1609	192	11	n	n	CCONJ
ejpam-1609	192	12	,	,	PUNCT
ejpam-1609	192	13	then	then	ADV
ejpam-1609	192	14	�	�	PROPN
ejpam-1609	192	15	n	n	CCONJ
ejpam-1609	192	16	k1	k1	NOUN
ejpam-1609	192	17	,	,	PUNCT
ejpam-1609	192	18	k2	k2	NOUN
ejpam-1609	192	19	,	,	PUNCT
ejpam-1609	192	20	.	.	PUNCT
ejpam-1609	192	21	.	.	PUNCT
ejpam-1609	192	22	.	.	PUNCT
ejpam-1609	193	1	,	,	PUNCT
ejpam-1609	193	2	km	km	PROPN
ejpam-1609	193	3	�	�	PROPN
ejpam-1609	193	4	r	r	NOUN
ejpam-1609	193	5	=	=	SYM
ejpam-1609	193	6	�	�	PROPN
ejpam-1609	193	7	n	n	CCONJ
ejpam-1609	193	8	km	km	PROPN
ejpam-1609	193	9	,	,	PUNCT
ejpam-1609	193	10	km−1	km−1	PROPN
ejpam-1609	193	11	,	,	PUNCT
ejpam-1609	193	12	.	.	PUNCT
ejpam-1609	193	13	.	.	PUNCT
ejpam-1609	194	1	.	.	PUNCT
ejpam-1609	195	1	,	,	PUNCT
ejpam-1609	195	2	k1	k1	PROPN
ejpam-1609	195	3	�	�	PROPN
ejpam-1609	195	4	r	r	PROPN
ejpam-1609	195	5	,	,	PUNCT
ejpam-1609	195	6	(	(	PUNCT
ejpam-1609	195	7	ii	ii	NOUN
ejpam-1609	195	8	)	)	PUNCT
ejpam-1609	195	9	�	�	PROPN
ejpam-1609	195	10	n	n	CCONJ
ejpam-1609	195	11	k1	k1	NOUN
ejpam-1609	195	12	,	,	PUNCT
ejpam-1609	195	13	k2	k2	NOUN
ejpam-1609	195	14	,	,	PUNCT
ejpam-1609	195	15	.	.	PUNCT
ejpam-1609	195	16	.	.	PUNCT
ejpam-1609	195	17	.	.	PUNCT
ejpam-1609	196	1	,	,	PUNCT
ejpam-1609	196	2	km	km	PROPN
ejpam-1609	196	3	�	�	PROPN
ejpam-1609	196	4	r	r	NOUN
ejpam-1609	196	5	=	=	SYM
ejpam-1609	196	6	�	�	PROPN
ejpam-1609	196	7	n	n	CCONJ
ejpam-1609	196	8	n−	n−	PROPN
ejpam-1609	196	9	∑m	∑m	PROPN
ejpam-1609	196	10	i=1	i=1	PRON
ejpam-1609	197	1	ki	ki	PROPN
ejpam-1609	197	2	,	,	PUNCT
ejpam-1609	197	3	km	km	PROPN
ejpam-1609	197	4	,	,	PUNCT
ejpam-1609	197	5	km−1	km−1	PROPN
ejpam-1609	197	6	,	,	PUNCT
ejpam-1609	197	7	.	.	PUNCT
ejpam-1609	197	8	.	.	PUNCT
ejpam-1609	198	1	.	.	PUNCT
ejpam-1609	199	1	,	,	PUNCT
ejpam-1609	199	2	k2	k2	PROPN
ejpam-1609	199	3	�	�	PROPN
ejpam-1609	199	4	r	r	PROPN
ejpam-1609	199	5	,	,	PUNCT
ejpam-1609	199	6	(	(	PUNCT
ejpam-1609	199	7	iii	iii	X
ejpam-1609	199	8	)	)	PUNCT
ejpam-1609	199	9	�	�	PROPN
ejpam-1609	199	10	n+	n+	PUNCT
ejpam-1609	199	11	1	1	NUM
ejpam-1609	199	12	n−	n−	PROPN
ejpam-1609	199	13	(	(	PUNCT
ejpam-1609	199	14	k−	k−	PROPN
ejpam-1609	199	15	1	1	NUM
ejpam-1609	199	16	)	)	PUNCT
ejpam-1609	199	17	,	,	PUNCT
ejpam-1609	199	18	k	k	NOUN
ejpam-1609	199	19	,	,	PUNCT
ejpam-1609	199	20	.	.	PUNCT
ejpam-1609	199	21	.	.	PUNCT
ejpam-1609	200	1	.	.	PUNCT
ejpam-1609	201	1	,	,	PUNCT
ejpam-1609	201	2	0	0	NUM
ejpam-1609	201	3	�	�	PROPN
ejpam-1609	201	4	r	r	NOUN
ejpam-1609	201	5	=	=	SYM
ejpam-1609	201	6	�	�	PROPN
ejpam-1609	201	7	n	n	PRON
ejpam-1609	201	8	n−	n−	PROPN
ejpam-1609	201	9	(	(	PUNCT
ejpam-1609	201	10	k−	k−	PROPN
ejpam-1609	201	11	1	1	NUM
ejpam-1609	201	12	)	)	PUNCT
ejpam-1609	201	13	,	,	PUNCT
ejpam-1609	201	14	k−	k−	PROPN
ejpam-1609	201	15	1,0,0	1,0,0	NUM
ejpam-1609	201	16	.	.	PUNCT
ejpam-1609	201	17	.	.	PUNCT
ejpam-1609	201	18	.	.	PUNCT
ejpam-1609	202	1	,	,	PUNCT
ejpam-1609	202	2	0	0	NUM
ejpam-1609	202	3	�	�	PROPN
ejpam-1609	202	4	r	r	PROPN
ejpam-1609	202	5	+	+	PROPN
ejpam-1609	202	6	pk	pk	NOUN
ejpam-1609	202	7	�	�	PROPN
ejpam-1609	202	8	n	n	CCONJ
ejpam-1609	202	9	n−	n−	PROPN
ejpam-1609	202	10	k	k	PROPN
ejpam-1609	202	11	,	,	PUNCT
ejpam-1609	202	12	k	k	NOUN
ejpam-1609	202	13	,	,	PUNCT
ejpam-1609	202	14	0,0	0,0	NUM
ejpam-1609	202	15	.	.	PUNCT
ejpam-1609	202	16	.	.	PUNCT
ejpam-1609	202	17	.	.	PUNCT
ejpam-1609	203	1	,	,	PUNCT
ejpam-1609	203	2	0	0	NUM
ejpam-1609	203	3	�	�	PROPN
ejpam-1609	203	4	r	r	NOUN
ejpam-1609	203	5	,	,	PUNCT
ejpam-1609	203	6	(	(	PUNCT
ejpam-1609	203	7	iv	iv	X
ejpam-1609	203	8	)	)	PUNCT
ejpam-1609	203	9	(	(	PUNCT
ejpam-1609	203	10	p−	p−	NOUN
ejpam-1609	203	11	1	1	NUM
ejpam-1609	203	12	)	)	PUNCT
ejpam-1609	203	13	�	�	PROPN
ejpam-1609	203	14	n	n	NUM
ejpam-1609	203	15	0,0	0,0	NOUN
ejpam-1609	203	16	,	,	PUNCT
ejpam-1609	203	17	.	.	PUNCT
ejpam-1609	203	18	.	.	PUNCT
ejpam-1609	203	19	.	.	PUNCT
ejpam-1609	204	1	,	,	PUNCT
ejpam-1609	204	2	k	k	X
ejpam-1609	204	3	,	,	PUNCT
ejpam-1609	204	4	1	1	NUM
ejpam-1609	204	5	�	�	NOUN
ejpam-1609	204	6	r	r	NOUN
ejpam-1609	204	7	=	=	PUNCT
ejpam-1609	204	8	(	(	PUNCT
ejpam-1609	204	9	pn	pn	NOUN
ejpam-1609	204	10	−	−	NOUN
ejpam-1609	204	11	1	1	NUM
ejpam-1609	204	12	)	)	PUNCT
ejpam-1609	204	13	�	�	PROPN
ejpam-1609	204	14	n−	n−	NOUN
ejpam-1609	204	15	1	1	NUM
ejpam-1609	204	16	0,0	0,0	NOUN
ejpam-1609	204	17	,	,	PUNCT
ejpam-1609	204	18	.	.	PUNCT
ejpam-1609	204	19	.	.	PUNCT
ejpam-1609	205	1	.	.	PUNCT
ejpam-1609	206	1	,	,	PUNCT
ejpam-1609	206	2	k	k	X
ejpam-1609	206	3	,	,	PUNCT
ejpam-1609	206	4	0	0	NUM
ejpam-1609	206	5	�	�	PROPN
ejpam-1609	206	6	r	r	NOUN
ejpam-1609	206	7	,	,	PUNCT
ejpam-1609	206	8	(	(	PUNCT
ejpam-1609	206	9	v	v	NOUN
ejpam-1609	206	10	)	)	PUNCT
ejpam-1609	206	11	�	�	PROPN
ejpam-1609	206	12	n	n	CCONJ
ejpam-1609	206	13	n	n	CCONJ
ejpam-1609	206	14	,	,	PUNCT
ejpam-1609	206	15	0,0	0,0	NOUN
ejpam-1609	206	16	,	,	PUNCT
ejpam-1609	206	17	.	.	PUNCT
ejpam-1609	206	18	.	.	PUNCT
ejpam-1609	207	1	.	.	PUNCT
ejpam-1609	208	1	,	,	PUNCT
ejpam-1609	208	2	0	0	NUM
ejpam-1609	208	3	�	�	PROPN
ejpam-1609	208	4	r	r	NOUN
ejpam-1609	208	5	=	=	SYM
ejpam-1609	208	6	�	�	PROPN
ejpam-1609	208	7	n	n	ADP
ejpam-1609	208	8	0	0	NUM
ejpam-1609	208	9	,	,	PUNCT
ejpam-1609	208	10	n	n	CCONJ
ejpam-1609	208	11	,	,	PUNCT
ejpam-1609	208	12	0	0	NUM
ejpam-1609	208	13	,	,	PUNCT
ejpam-1609	208	14	.	.	PUNCT
ejpam-1609	208	15	.	.	PUNCT
ejpam-1609	209	1	.	.	PUNCT
ejpam-1609	210	1	,	,	PUNCT
ejpam-1609	210	2	0	0	NUM
ejpam-1609	210	3	�	�	PROPN
ejpam-1609	210	4	r	r	NOUN
ejpam-1609	210	5	=	=	NOUN
ejpam-1609	210	6	.	.	PUNCT
ejpam-1609	210	7	.	.	PUNCT
ejpam-1609	210	8	.	.	PUNCT
ejpam-1609	211	1	=	=	PUNCT
ejpam-1609	211	2	�	�	PROPN
ejpam-1609	211	3	n	n	NUM
ejpam-1609	211	4	0,0,0	0,0,0	NOUN
ejpam-1609	211	5	,	,	PUNCT
ejpam-1609	211	6	.	.	PUNCT
ejpam-1609	211	7	.	.	PUNCT
ejpam-1609	212	1	.	.	PUNCT
ejpam-1609	213	1	,	,	PUNCT
ejpam-1609	213	2	n	n	X
ejpam-1609	213	3	�	�	PROPN
ejpam-1609	213	4	r	r	NOUN
ejpam-1609	213	5	=	=	SYM
ejpam-1609	213	6	1	1	X
ejpam-1609	213	7	.	.	PUNCT
ejpam-1609	213	8	e.	e.	PROPN
ejpam-1609	213	9	saltürk	saltürk	PROPN
ejpam-1609	213	10	,	,	PUNCT
ejpam-1609	213	11	i̇.	i̇.	PROPN
ejpam-1609	213	12	şiap	şiap	PROPN
ejpam-1609	213	13	/	/	SYM
ejpam-1609	213	14	eur	eur	PROPN
ejpam-1609	213	15	.	.	PUNCT
ejpam-1609	214	1	j.	j.	PROPN
ejpam-1609	214	2	pure	pure	PROPN
ejpam-1609	214	3	appl	appl	PROPN
ejpam-1609	214	4	.	.	PROPN
ejpam-1609	214	5	math	math	PROPN
ejpam-1609	214	6	,	,	PUNCT
ejpam-1609	214	7	5	5	NUM
ejpam-1609	214	8	(	(	PUNCT
ejpam-1609	214	9	2012	2012	NUM
ejpam-1609	214	10	)	)	PUNCT
ejpam-1609	214	11	,	,	PUNCT
ejpam-1609	214	12	250	250	NUM
ejpam-1609	214	13	-	-	SYM
ejpam-1609	214	14	259	259	NUM
ejpam-1609	214	15	257	257	NUM
ejpam-1609	214	16	(	(	PUNCT
ejpam-1609	214	17	vi	vi	NOUN
ejpam-1609	214	18	)	)	PUNCT
ejpam-1609	214	19	the	the	DET
ejpam-1609	214	20	followings	following	NOUN
ejpam-1609	214	21	hold	hold	VERB
ejpam-1609	214	22	:	:	PUNCT
ejpam-1609	214	23	(	(	PUNCT
ejpam-1609	214	24	vi).(1	vi).(1	NOUN
ejpam-1609	214	25	)	)	PUNCT
ejpam-1609	214	26	.	.	PUNCT
ejpam-1609	215	1	�	�	PROPN
ejpam-1609	215	2	n	n	CCONJ
ejpam-1609	215	3	k	k	PROPN
ejpam-1609	215	4	,	,	PUNCT
ejpam-1609	215	5	0,0	0,0	NOUN
ejpam-1609	215	6	,	,	PUNCT
ejpam-1609	215	7	.	.	PUNCT
ejpam-1609	215	8	.	.	PUNCT
ejpam-1609	215	9	.	.	PUNCT
ejpam-1609	216	1	,	,	PUNCT
ejpam-1609	216	2	0	0	NUM
ejpam-1609	216	3	�	�	PROPN
ejpam-1609	216	4	r	r	NOUN
ejpam-1609	216	5	=	=	SYM
ejpam-1609	216	6	�	�	PROPN
ejpam-1609	216	7	n	n	CCONJ
ejpam-1609	216	8	n−	n−	PROPN
ejpam-1609	216	9	k	k	PROPN
ejpam-1609	216	10	,	,	PUNCT
ejpam-1609	216	11	0,0	0,0	NOUN
ejpam-1609	216	12	,	,	PUNCT
ejpam-1609	216	13	.	.	PUNCT
ejpam-1609	216	14	.	.	PUNCT
ejpam-1609	216	15	.	.	PUNCT
ejpam-1609	217	1	,	,	PUNCT
ejpam-1609	217	2	0	0	NUM
ejpam-1609	217	3	�	�	PROPN
ejpam-1609	217	4	r	r	NOUN
ejpam-1609	217	5	,	,	PUNCT
ejpam-1609	217	6	(	(	PUNCT
ejpam-1609	217	7	vi).(2	vi).(2	ADJ
ejpam-1609	217	8	)	)	PUNCT
ejpam-1609	217	9	.	.	PUNCT
ejpam-1609	218	1	�	�	PROPN
ejpam-1609	218	2	n	n	CCONJ
ejpam-1609	218	3	0	0	NUM
ejpam-1609	218	4	,	,	PUNCT
ejpam-1609	218	5	k	k	NOUN
ejpam-1609	218	6	,	,	PUNCT
ejpam-1609	218	7	0	0	NUM
ejpam-1609	218	8	,	,	PUNCT
ejpam-1609	218	9	.	.	PUNCT
ejpam-1609	218	10	.	.	PUNCT
ejpam-1609	219	1	.	.	PUNCT
ejpam-1609	220	1	,	,	PUNCT
ejpam-1609	220	2	0	0	NUM
ejpam-1609	220	3	�	�	PROPN
ejpam-1609	220	4	r	r	NOUN
ejpam-1609	220	5	=	=	SYM
ejpam-1609	220	6	�	�	PROPN
ejpam-1609	220	7	n	n	ADP
ejpam-1609	220	8	0	0	NUM
ejpam-1609	220	9	,	,	PUNCT
ejpam-1609	220	10	n−	n−	PROPN
ejpam-1609	220	11	k	k	PROPN
ejpam-1609	220	12	,	,	PUNCT
ejpam-1609	220	13	0	0	NUM
ejpam-1609	220	14	,	,	PUNCT
ejpam-1609	220	15	.	.	PUNCT
ejpam-1609	220	16	.	.	PUNCT
ejpam-1609	221	1	.	.	PUNCT
ejpam-1609	222	1	,	,	PUNCT
ejpam-1609	222	2	0	0	NUM
ejpam-1609	222	3	�	�	PROPN
ejpam-1609	222	4	r	r	NOUN
ejpam-1609	222	5	,	,	PUNCT
ejpam-1609	222	6	.	.	PUNCT
ejpam-1609	222	7	.	.	PUNCT
ejpam-1609	222	8	.	.	PUNCT
ejpam-1609	222	9	.	.	PUNCT
ejpam-1609	222	10	.	.	PUNCT
ejpam-1609	222	11	.	.	PUNCT
ejpam-1609	222	12	.	.	PUNCT
ejpam-1609	222	13	.	.	PUNCT
ejpam-1609	222	14	.	.	PUNCT
ejpam-1609	222	15	.	.	PUNCT
ejpam-1609	222	16	.	.	PUNCT
ejpam-1609	222	17	.	.	PUNCT
ejpam-1609	222	18	.	.	PUNCT
ejpam-1609	222	19	.	.	PUNCT
ejpam-1609	222	20	.	.	PUNCT
ejpam-1609	222	21	.	.	PUNCT
ejpam-1609	222	22	.	.	PUNCT
ejpam-1609	222	23	.	.	PUNCT
ejpam-1609	222	24	.	.	PUNCT
ejpam-1609	222	25	.	.	PUNCT
ejpam-1609	222	26	.	.	PUNCT
ejpam-1609	223	1	(	(	PUNCT
ejpam-1609	223	2	iv).(m	iv).(m	NUM
ejpam-1609	223	3	)	)	PUNCT
ejpam-1609	223	4	.	.	PUNCT
ejpam-1609	224	1	�	�	PROPN
ejpam-1609	224	2	n	n	NUM
ejpam-1609	224	3	0,0,0	0,0,0	NOUN
ejpam-1609	224	4	,	,	PUNCT
ejpam-1609	224	5	.	.	PUNCT
ejpam-1609	224	6	.	.	PUNCT
ejpam-1609	225	1	.	.	PUNCT
ejpam-1609	226	1	,	,	PUNCT
ejpam-1609	226	2	k	k	PROPN
ejpam-1609	226	3	�	�	PROPN
ejpam-1609	226	4	r	r	NOUN
ejpam-1609	226	5	=	=	SYM
ejpam-1609	226	6	�	�	PROPN
ejpam-1609	226	7	n	n	NUM
ejpam-1609	226	8	0,0,0	0,0,0	NOUN
ejpam-1609	226	9	,	,	PUNCT
ejpam-1609	226	10	.	.	PUNCT
ejpam-1609	226	11	.	.	PUNCT
ejpam-1609	227	1	.	.	PUNCT
ejpam-1609	228	1	,	,	PUNCT
ejpam-1609	228	2	n−	n−	NOUN
ejpam-1609	228	3	k	k	PROPN
ejpam-1609	228	4	�	�	PROPN
ejpam-1609	228	5	r	r	NOUN
ejpam-1609	228	6	.	.	PUNCT
ejpam-1609	229	1	(	(	PUNCT
ejpam-1609	229	2	vii	vii	PROPN
ejpam-1609	229	3	)	)	PUNCT
ejpam-1609	229	4	for	for	ADP
ejpam-1609	229	5	m=	m=	ADJ
ejpam-1609	229	6	2,3	2,3	NUM
ejpam-1609	229	7	,	,	PUNCT
ejpam-1609	229	8	.	.	PUNCT
ejpam-1609	229	9	.	.	PUNCT
ejpam-1609	230	1	.	.	PUNCT
ejpam-1609	231	1	,	,	PUNCT
ejpam-1609	231	2	we	we	PRON
ejpam-1609	231	3	have	have	VERB
ejpam-1609	231	4	�	�	PROPN
ejpam-1609	231	5	n	n	ADP
ejpam-1609	231	6	0	0	NUM
ejpam-1609	231	7	,	,	PUNCT
ejpam-1609	231	8	k1	k1	NOUN
ejpam-1609	231	9	,	,	PUNCT
ejpam-1609	231	10	k2	k2	NOUN
ejpam-1609	231	11	,	,	PUNCT
ejpam-1609	231	12	.	.	PUNCT
ejpam-1609	231	13	.	.	PUNCT
ejpam-1609	232	1	.	.	PUNCT
ejpam-1609	233	1	,	,	PUNCT
ejpam-1609	233	2	km−1	km−1	PROPN
ejpam-1609	233	3	�	�	PROPN
ejpam-1609	233	4	zpm	zpm	PROPN
ejpam-1609	233	5	=	=	SYM
ejpam-1609	233	6	�	�	PROPN
ejpam-1609	233	7	n	n	CCONJ
ejpam-1609	233	8	k1	k1	NOUN
ejpam-1609	233	9	,	,	PUNCT
ejpam-1609	233	10	k2	k2	NOUN
ejpam-1609	233	11	,	,	PUNCT
ejpam-1609	233	12	.	.	PUNCT
ejpam-1609	233	13	.	.	PUNCT
ejpam-1609	234	1	.	.	PUNCT
ejpam-1609	235	1	,	,	PUNCT
ejpam-1609	235	2	km−1	km−1	PROPN
ejpam-1609	235	3	�	�	PROPN
ejpam-1609	235	4	z	z	PROPN
ejpam-1609	235	5	pm−1	pm−1	PROPN
ejpam-1609	235	6	.	.	PUNCT
ejpam-1609	236	1	(	(	PUNCT
ejpam-1609	236	2	viii	viii	NOUN
ejpam-1609	236	3	)	)	PUNCT
ejpam-1609	236	4	�	�	PROPN
ejpam-1609	236	5	n	n	CCONJ
ejpam-1609	236	6	k	k	PROPN
ejpam-1609	236	7	,	,	PUNCT
ejpam-1609	236	8	0,0	0,0	NOUN
ejpam-1609	236	9	,	,	PUNCT
ejpam-1609	236	10	.	.	PUNCT
ejpam-1609	236	11	.	.	PUNCT
ejpam-1609	236	12	.	.	PUNCT
ejpam-1609	237	1	,	,	PUNCT
ejpam-1609	237	2	0	0	NUM
ejpam-1609	237	3	�	�	PROPN
ejpam-1609	237	4	r	r	NOUN
ejpam-1609	237	5	=	=	PUNCT
ejpam-1609	237	6	(	(	PUNCT
ejpam-1609	237	7	pk)n−k	pk)n−k	PROPN
ejpam-1609	237	8	�	�	PROPN
ejpam-1609	237	9	n	n	ADP
ejpam-1609	237	10	0	0	NUM
ejpam-1609	237	11	,	,	PUNCT
ejpam-1609	237	12	k	k	NOUN
ejpam-1609	237	13	,	,	PUNCT
ejpam-1609	237	14	0	0	NUM
ejpam-1609	237	15	,	,	PUNCT
ejpam-1609	237	16	.	.	PUNCT
ejpam-1609	237	17	.	.	PUNCT
ejpam-1609	237	18	.	.	PUNCT
ejpam-1609	238	1	,	,	PUNCT
ejpam-1609	238	2	0	0	NUM
ejpam-1609	238	3	�	�	PROPN
ejpam-1609	238	4	r	r	NOUN
ejpam-1609	238	5	=	=	PUNCT
ejpam-1609	238	6	(	(	PUNCT
ejpam-1609	238	7	(	(	PUNCT
ejpam-1609	238	8	pk)n−k)2	pk)n−k)2	PROPN
ejpam-1609	238	9	�	�	PROPN
ejpam-1609	238	10	n	n	CCONJ
ejpam-1609	238	11	0,0	0,0	NOUN
ejpam-1609	238	12	,	,	PUNCT
ejpam-1609	238	13	k	k	NOUN
ejpam-1609	238	14	,	,	PUNCT
ejpam-1609	238	15	.	.	PUNCT
ejpam-1609	238	16	.	.	PUNCT
ejpam-1609	238	17	.	.	PUNCT
ejpam-1609	239	1	,	,	PUNCT
ejpam-1609	239	2	0	0	NUM
ejpam-1609	239	3	�	�	PROPN
ejpam-1609	239	4	r	r	NOUN
ejpam-1609	239	5	=	=	PUNCT
ejpam-1609	239	6	(	(	PUNCT
ejpam-1609	239	7	(	(	PUNCT
ejpam-1609	239	8	pk)n−k)3	pk)n−k)3	PROPN
ejpam-1609	239	9	�	�	PROPN
ejpam-1609	239	10	n	n	ADP
ejpam-1609	239	11	0,0,0	0,0,0	NOUN
ejpam-1609	239	12	,	,	PUNCT
ejpam-1609	239	13	k	k	NOUN
ejpam-1609	239	14	,	,	PUNCT
ejpam-1609	239	15	0	0	NUM
ejpam-1609	239	16	,	,	PUNCT
ejpam-1609	239	17	.	.	PUNCT
ejpam-1609	239	18	.	.	PUNCT
ejpam-1609	239	19	.	.	PUNCT
ejpam-1609	240	1	,	,	PUNCT
ejpam-1609	240	2	0	0	NUM
ejpam-1609	240	3	�	�	PROPN
ejpam-1609	240	4	r	r	NOUN
ejpam-1609	240	5	=	=	PUNCT
ejpam-1609	240	6	·	·	PUNCT
ejpam-1609	240	7	·	·	PUNCT
ejpam-1609	240	8	·	·	PUNCT
ejpam-1609	240	9	=	=	SYM
ejpam-1609	240	10	(	(	PUNCT
ejpam-1609	240	11	(	(	PUNCT
ejpam-1609	240	12	pk)n−k)m−1	pk)n−k)m−1	X
ejpam-1609	240	13	�	�	PROPN
ejpam-1609	240	14	n	n	NUM
ejpam-1609	240	15	0,0,0	0,0,0	NOUN
ejpam-1609	240	16	,	,	PUNCT
ejpam-1609	240	17	.	.	PUNCT
ejpam-1609	240	18	.	.	PUNCT
ejpam-1609	240	19	.	.	PUNCT
ejpam-1609	241	1	,	,	PUNCT
ejpam-1609	241	2	0	0	NUM
ejpam-1609	241	3	,	,	PUNCT
ejpam-1609	241	4	k	k	PROPN
ejpam-1609	241	5	�	�	PROPN
ejpam-1609	241	6	r	r	NOUN
ejpam-1609	241	7	.	.	PUNCT
ejpam-1609	242	1	proof	proof	NOUN
ejpam-1609	242	2	.	.	PUNCT
ejpam-1609	243	1	the	the	DET
ejpam-1609	243	2	proof	proof	NOUN
ejpam-1609	243	3	follows	follow	VERB
ejpam-1609	243	4	by	by	ADP
ejpam-1609	243	5	applying	apply	VERB
ejpam-1609	243	6	the	the	DET
ejpam-1609	243	7	definitions	definition	NOUN
ejpam-1609	243	8	carefully	carefully	ADV
ejpam-1609	243	9	.	.	PUNCT
ejpam-1609	244	1	the	the	DET
ejpam-1609	244	2	properties	property	NOUN
ejpam-1609	244	3	given	give	VERB
ejpam-1609	244	4	above	above	ADP
ejpam-1609	244	5	are	be	AUX
ejpam-1609	244	6	generalizations	generalization	NOUN
ejpam-1609	244	7	of	of	ADP
ejpam-1609	244	8	the	the	DET
ejpam-1609	244	9	given	give	VERB
ejpam-1609	244	10	properties	property	NOUN
ejpam-1609	244	11	in	in	ADP
ejpam-1609	244	12	[	[	X
ejpam-1609	244	13	10	10	NUM
ejpam-1609	244	14	]	]	PUNCT
ejpam-1609	244	15	.	.	PUNCT
ejpam-1609	245	1	also	also	ADV
ejpam-1609	245	2	very	very	ADV
ejpam-1609	245	3	recently	recently	ADV
ejpam-1609	245	4	some	some	DET
ejpam-1609	245	5	similar	similar	ADJ
ejpam-1609	245	6	studies	study	NOUN
ejpam-1609	245	7	are	be	AUX
ejpam-1609	245	8	also	also	ADV
ejpam-1609	245	9	done	do	VERB
ejpam-1609	245	10	over	over	ADP
ejpam-1609	245	11	different	different	ADJ
ejpam-1609	245	12	rings	ring	NOUN
ejpam-1609	245	13	in	in	ADP
ejpam-1609	245	14	[	[	X
ejpam-1609	245	15	11	11	NUM
ejpam-1609	245	16	]	]	PUNCT
ejpam-1609	245	17	.	.	PUNCT
ejpam-1609	246	1	in	in	ADP
ejpam-1609	246	2	a	a	DET
ejpam-1609	246	3	similar	similar	ADJ
ejpam-1609	246	4	approach	approach	NOUN
ejpam-1609	246	5	to	to	ADP
ejpam-1609	246	6	those	those	DET
ejpam-1609	246	7	works	work	NOUN
ejpam-1609	246	8	,	,	PUNCT
ejpam-1609	246	9	there	there	PRON
ejpam-1609	246	10	may	may	AUX
ejpam-1609	246	11	be	be	AUX
ejpam-1609	246	12	obtained	obtain	VERB
ejpam-1609	246	13	some	some	DET
ejpam-1609	246	14	new	new	ADJ
ejpam-1609	246	15	and	and	CCONJ
ejpam-1609	246	16	existing	exist	VERB
ejpam-1609	246	17	number	number	NOUN
ejpam-1609	246	18	sequences	sequence	NOUN
ejpam-1609	246	19	.	.	PUNCT
ejpam-1609	247	1	here	here	ADV
ejpam-1609	247	2	we	we	PRON
ejpam-1609	247	3	only	only	ADV
ejpam-1609	247	4	give	give	VERB
ejpam-1609	247	5	a	a	DET
ejpam-1609	247	6	few	few	ADJ
ejpam-1609	247	7	examples	example	NOUN
ejpam-1609	247	8	of	of	ADP
ejpam-1609	247	9	number	number	NOUN
ejpam-1609	247	10	sequences	sequence	NOUN
ejpam-1609	247	11	.	.	PUNCT
ejpam-1609	248	1	table	table	NOUN
ejpam-1609	248	2	1	1	NUM
ejpam-1609	248	3	:	:	PUNCT
ejpam-1609	248	4	number	number	NOUN
ejpam-1609	248	5	of	of	ADP
ejpam-1609	248	6	linear	linear	PROPN
ejpam-1609	248	7	odes	ode	NOUN
ejpam-1609	248	8	over	over	ADP
ejpam-1609	248	9	z4[ξ	z4[ξ	NOUN
ejpam-1609	248	10	]	]	PUNCT
ejpam-1609	248	11	for	for	ADP
ejpam-1609	248	12	n=	n=	ADJ
ejpam-1609	248	13	2	2	NUM
ejpam-1609	248	14	,	,	PUNCT
ejpam-1609	248	15	n	n	NOUN
ejpam-1609	248	16	=	=	SYM
ejpam-1609	248	17	3	3	NUM
ejpam-1609	248	18	and	and	CCONJ
ejpam-1609	248	19	n=	n=	ADJ
ejpam-1609	248	20	4	4	NUM
ejpam-1609	248	21	.	.	PUNCT
ejpam-1609	248	22	n	n	PROPN
ejpam-1609	248	23	(	(	PUNCT
ejpam-1609	248	24	length	length	NOUN
ejpam-1609	248	25	)	)	PUNCT
ejpam-1609	248	26	(	(	PUNCT
ejpam-1609	248	27	k1	k1	NOUN
ejpam-1609	248	28	,	,	PUNCT
ejpam-1609	248	29	k2	k2	ADJ
ejpam-1609	248	30	)	)	PUNCT
ejpam-1609	248	31	number	number	NOUN
ejpam-1609	248	32	n	n	CCONJ
ejpam-1609	248	33	(	(	PUNCT
ejpam-1609	248	34	length	length	NOUN
ejpam-1609	248	35	)	)	PUNCT
ejpam-1609	248	36	(	(	PUNCT
ejpam-1609	248	37	k1	k1	NOUN
ejpam-1609	248	38	,	,	PUNCT
ejpam-1609	248	39	k2	k2	ADJ
ejpam-1609	248	40	)	)	PUNCT
ejpam-1609	248	41	number	number	NOUN
ejpam-1609	248	42	(	(	PUNCT
ejpam-1609	248	43	0,1	0,1	NOUN
ejpam-1609	248	44	)	)	PUNCT
ejpam-1609	248	45	5	5	NUM
ejpam-1609	248	46	(	(	PUNCT
ejpam-1609	248	47	0,1	0,1	NUM
ejpam-1609	248	48	)	)	PUNCT
ejpam-1609	248	49	85	85	NUM
ejpam-1609	248	50	(	(	PUNCT
ejpam-1609	248	51	0,2	0,2	NUM
ejpam-1609	248	52	)	)	PUNCT
ejpam-1609	248	53	1	1	NUM
ejpam-1609	248	54	(	(	PUNCT
ejpam-1609	248	55	0,2	0,2	NUM
ejpam-1609	248	56	)	)	PUNCT
ejpam-1609	248	57	357	357	NUM
ejpam-1609	248	58	n=2	n=2	X
ejpam-1609	248	59	(	(	PUNCT
ejpam-1609	248	60	1,0	1,0	NUM
ejpam-1609	248	61	)	)	PUNCT
ejpam-1609	248	62	20	20	NUM
ejpam-1609	248	63	n	n	NOUN
ejpam-1609	248	64	(	(	PUNCT
ejpam-1609	248	65	0,3	0,3	NUM
ejpam-1609	248	66	)	)	PUNCT
ejpam-1609	248	67	85	85	NUM
ejpam-1609	248	68	(	(	PUNCT
ejpam-1609	248	69	1,1	1,1	NUM
ejpam-1609	248	70	)	)	PUNCT
ejpam-1609	248	71	5	5	NUM
ejpam-1609	248	72	(	(	PUNCT
ejpam-1609	248	73	0,4	0,4	NOUN
ejpam-1609	248	74	)	)	PUNCT
ejpam-1609	248	75	31	31	NUM
ejpam-1609	248	76	(	(	PUNCT
ejpam-1609	248	77	2,0	2,0	NUM
ejpam-1609	248	78	)	)	PUNCT
ejpam-1609	248	79	1	1	NUM
ejpam-1609	248	80	(	(	PUNCT
ejpam-1609	248	81	1,0	1,0	NUM
ejpam-1609	248	82	)	)	PUNCT
ejpam-1609	248	83	5440	5440	NUM
ejpam-1609	248	84	(	(	PUNCT
ejpam-1609	248	85	0,1	0,1	NUM
ejpam-1609	248	86	)	)	PUNCT
ejpam-1609	248	87	21	21	NUM
ejpam-1609	248	88	(	(	PUNCT
ejpam-1609	248	89	1,1	1,1	NUM
ejpam-1609	248	90	)	)	PUNCT
ejpam-1609	248	91	28560	28560	NUM
ejpam-1609	248	92	(	(	PUNCT
ejpam-1609	248	93	0,2	0,2	NUM
ejpam-1609	248	94	)	)	PUNCT
ejpam-1609	248	95	21	21	NUM
ejpam-1609	248	96	n=4	n=4	X
ejpam-1609	248	97	(	(	PUNCT
ejpam-1609	248	98	1,2	1,2	NUM
ejpam-1609	248	99	)	)	PUNCT
ejpam-1609	248	100	7140	7140	NUM
ejpam-1609	248	101	(	(	PUNCT
ejpam-1609	248	102	0,3	0,3	NUM
ejpam-1609	248	103	)	)	PUNCT
ejpam-1609	248	104	1	1	NUM
ejpam-1609	248	105	(	(	PUNCT
ejpam-1609	248	106	1,3	1,3	NUM
ejpam-1609	248	107	)	)	PUNCT
ejpam-1609	248	108	85	85	NUM
ejpam-1609	248	109	(	(	PUNCT
ejpam-1609	248	110	1,0	1,0	NUM
ejpam-1609	248	111	)	)	PUNCT
ejpam-1609	248	112	336	336	NUM
ejpam-1609	248	113	(	(	PUNCT
ejpam-1609	248	114	2,0	2,0	NUM
ejpam-1609	248	115	)	)	PUNCT
ejpam-1609	248	116	91392	91392	NUM
ejpam-1609	248	117	(	(	PUNCT
ejpam-1609	248	118	1,1	1,1	NUM
ejpam-1609	248	119	)	)	PUNCT
ejpam-1609	248	120	420	420	NUM
ejpam-1609	248	121	(	(	PUNCT
ejpam-1609	248	122	2,1	2,1	NUM
ejpam-1609	248	123	)	)	PUNCT
ejpam-1609	248	124	85680	85680	NUM
ejpam-1609	248	125	n=3	n=3	SYM
ejpam-1609	248	126	(	(	PUNCT
ejpam-1609	248	127	1,2	1,2	NUM
ejpam-1609	248	128	)	)	PUNCT
ejpam-1609	248	129	21	21	NUM
ejpam-1609	248	130	(	(	PUNCT
ejpam-1609	248	131	2,2	2,2	NUM
ejpam-1609	248	132	)	)	PUNCT
ejpam-1609	248	133	357	357	NUM
ejpam-1609	248	134	(	(	PUNCT
ejpam-1609	248	135	2,0	2,0	NUM
ejpam-1609	248	136	)	)	PUNCT
ejpam-1609	248	137	336	336	NUM
ejpam-1609	248	138	(	(	PUNCT
ejpam-1609	248	139	3,0	3,0	NUM
ejpam-1609	248	140	)	)	PUNCT
ejpam-1609	248	141	5440	5440	NUM
ejpam-1609	248	142	(	(	PUNCT
ejpam-1609	248	143	2,1	2,1	NUM
ejpam-1609	248	144	)	)	PUNCT
ejpam-1609	248	145	21	21	NUM
ejpam-1609	248	146	(	(	PUNCT
ejpam-1609	248	147	3,1	3,1	NUM
ejpam-1609	248	148	)	)	PUNCT
ejpam-1609	248	149	85	85	NUM
ejpam-1609	248	150	(	(	PUNCT
ejpam-1609	248	151	3,0	3,0	NUM
ejpam-1609	248	152	)	)	PUNCT
ejpam-1609	248	153	1	1	NUM
ejpam-1609	248	154	(	(	PUNCT
ejpam-1609	248	155	4,0	4,0	NUM
ejpam-1609	248	156	)	)	PUNCT
ejpam-1609	248	157	1	1	NUM
ejpam-1609	248	158	references	reference	NOUN
ejpam-1609	248	159	258	258	NUM
ejpam-1609	248	160	table	table	NOUN
ejpam-1609	248	161	1	1	NUM
ejpam-1609	248	162	is	be	AUX
ejpam-1609	248	163	given	give	VERB
ejpam-1609	248	164	as	as	ADP
ejpam-1609	248	165	a	a	DET
ejpam-1609	248	166	special	special	ADJ
ejpam-1609	248	167	example	example	NOUN
ejpam-1609	248	168	of	of	ADP
ejpam-1609	248	169	theorem	theorem	NOUN
ejpam-1609	248	170	6	6	NUM
ejpam-1609	248	171	for	for	ADP
ejpam-1609	248	172	pm	pm	NOUN
ejpam-1609	248	173	=	=	SYM
ejpam-1609	248	174	4	4	X
ejpam-1609	248	175	.	.	PUNCT
ejpam-1609	249	1	here	here	ADV
ejpam-1609	249	2	,	,	PUNCT
ejpam-1609	249	3	for	for	ADP
ejpam-1609	249	4	k1	k1	NOUN
ejpam-1609	249	5	=	=	SYM
ejpam-1609	249	6	0	0	NUM
ejpam-1609	249	7	,	,	PUNCT
ejpam-1609	249	8	k2	k2	NOUN
ejpam-1609	249	9	=	=	SYM
ejpam-1609	249	10	1	1	NUM
ejpam-1609	249	11	,	,	PUNCT
ejpam-1609	249	12	for	for	ADP
ejpam-1609	249	13	the	the	DET
ejpam-1609	249	14	values	value	NOUN
ejpam-1609	249	15	of	of	ADP
ejpam-1609	249	16	n	n	CCONJ
ejpam-1609	249	17	,	,	PUNCT
ejpam-1609	249	18	we	we	PRON
ejpam-1609	249	19	obtain	obtain	VERB
ejpam-1609	249	20	a	a	DET
ejpam-1609	249	21	sequence	sequence	NOUN
ejpam-1609	249	22	:	:	PUNCT
ejpam-1609	249	23	5,21,85,341,1365	5,21,85,341,1365	NUM
ejpam-1609	249	24	,	,	PUNCT
ejpam-1609	249	25	.	.	PUNCT
ejpam-1609	249	26	.	.	PUNCT
ejpam-1609	250	1	..	..	PUNCT
ejpam-1609	251	1	this	this	DET
ejpam-1609	251	2	sequence	sequence	NOUN
ejpam-1609	251	3	exists	exist	VERB
ejpam-1609	251	4	in	in	ADP
ejpam-1609	251	5	oeis	oeis	PROPN
ejpam-1609	251	6	[	[	X
ejpam-1609	251	7	12	12	NUM
ejpam-1609	251	8	]	]	PUNCT
ejpam-1609	251	9	by	by	ADP
ejpam-1609	251	10	reference	reference	NOUN
ejpam-1609	251	11	number	number	NOUN
ejpam-1609	251	12	a002450	a002450	NOUN
ejpam-1609	251	13	and	and	CCONJ
ejpam-1609	251	14	it	it	PRON
ejpam-1609	251	15	is	be	AUX
ejpam-1609	251	16	given	give	VERB
ejpam-1609	251	17	by	by	ADP
ejpam-1609	251	18	the	the	DET
ejpam-1609	251	19	formula	formula	NOUN
ejpam-1609	251	20	4n−1	4n−1	NUM
ejpam-1609	251	21	3	3	NUM
ejpam-1609	251	22	.	.	PUNCT
ejpam-1609	252	1	for	for	ADP
ejpam-1609	252	2	k1	k1	NOUN
ejpam-1609	252	3	=	=	SYM
ejpam-1609	252	4	1	1	NUM
ejpam-1609	252	5	,	,	PUNCT
ejpam-1609	252	6	k2	k2	NOUN
ejpam-1609	252	7	=	=	SYM
ejpam-1609	252	8	0	0	NUM
ejpam-1609	252	9	,	,	PUNCT
ejpam-1609	252	10	we	we	PRON
ejpam-1609	252	11	obtain	obtain	VERB
ejpam-1609	252	12	a	a	DET
ejpam-1609	252	13	sequence	sequence	NOUN
ejpam-1609	252	14	:	:	PUNCT
ejpam-1609	252	15	20,336,5440	20,336,5440	NUM
ejpam-1609	252	16	,	,	PUNCT
ejpam-1609	252	17	.	.	PUNCT
ejpam-1609	252	18	.	.	PUNCT
ejpam-1609	253	1	.	.	PUNCT
ejpam-1609	254	1	which	which	PRON
ejpam-1609	254	2	exists	exist	VERB
ejpam-1609	254	3	as	as	ADP
ejpam-1609	254	4	a166984	a166984	PROPN
ejpam-1609	254	5	in	in	ADP
ejpam-1609	254	6	oeis	oeis	PROPN
ejpam-1609	255	1	[	[	X
ejpam-1609	255	2	12	12	NUM
ejpam-1609	255	3	]	]	PUNCT
ejpam-1609	255	4	.	.	PUNCT
ejpam-1609	256	1	moreover	moreover	ADV
ejpam-1609	256	2	some	some	DET
ejpam-1609	256	3	new	new	ADJ
ejpam-1609	256	4	number	number	NOUN
ejpam-1609	256	5	sequences	sequence	NOUN
ejpam-1609	256	6	may	may	AUX
ejpam-1609	256	7	be	be	AUX
ejpam-1609	256	8	obtained	obtain	VERB
ejpam-1609	256	9	by	by	ADP
ejpam-1609	256	10	further	far	ADV
ejpam-1609	256	11	examining	examine	VERB
ejpam-1609	256	12	the	the	DET
ejpam-1609	256	13	numbers	number	NOUN
ejpam-1609	256	14	obtained	obtain	VERB
ejpam-1609	256	15	by	by	ADP
ejpam-1609	256	16	fixing	fix	VERB
ejpam-1609	256	17	(	(	PUNCT
ejpam-1609	256	18	k1	k1	NOUN
ejpam-1609	256	19	,	,	PUNCT
ejpam-1609	256	20	k2	k2	NOUN
ejpam-1609	256	21	)	)	PUNCT
ejpam-1609	256	22	and	and	CCONJ
ejpam-1609	256	23	changing	change	VERB
ejpam-1609	256	24	n.	n.	NOUN
ejpam-1609	256	25	for	for	ADP
ejpam-1609	256	26	instance	instance	NOUN
ejpam-1609	256	27	,	,	PUNCT
ejpam-1609	256	28	if	if	SCONJ
ejpam-1609	256	29	we	we	PRON
ejpam-1609	256	30	take	take	VERB
ejpam-1609	256	31	k1	k1	NOUN
ejpam-1609	256	32	=	=	SYM
ejpam-1609	256	33	1	1	NUM
ejpam-1609	256	34	,	,	PUNCT
ejpam-1609	256	35	k2	k2	NOUN
ejpam-1609	256	36	=	=	SYM
ejpam-1609	256	37	1	1	NUM
ejpam-1609	256	38	,	,	PUNCT
ejpam-1609	256	39	then	then	ADV
ejpam-1609	256	40	sequence	sequence	NOUN
ejpam-1609	256	41	:	:	PUNCT
ejpam-1609	256	42	5,420,28560,1855040	5,420,28560,1855040	NUM
ejpam-1609	256	43	.	.	PUNCT
ejpam-1609	256	44	.	.	PUNCT
ejpam-1609	256	45	.	.	PUNCT
ejpam-1609	257	1	does	do	AUX
ejpam-1609	257	2	not	not	PART
ejpam-1609	257	3	exist	exist	VERB
ejpam-1609	257	4	in	in	ADP
ejpam-1609	257	5	the	the	DET
ejpam-1609	257	6	literature	literature	NOUN
ejpam-1609	257	7	[	[	X
ejpam-1609	257	8	12	12	NUM
ejpam-1609	257	9	]	]	PUNCT
ejpam-1609	257	10	.	.	PUNCT
ejpam-1609	258	1	4	4	X
ejpam-1609	258	2	.	.	X
ejpam-1609	258	3	conclusion	conclusion	NOUN
ejpam-1609	258	4	in	in	ADP
ejpam-1609	258	5	this	this	DET
ejpam-1609	258	6	paper	paper	NOUN
ejpam-1609	258	7	,	,	PUNCT
ejpam-1609	258	8	we	we	PRON
ejpam-1609	258	9	have	have	AUX
ejpam-1609	258	10	developed	develop	VERB
ejpam-1609	258	11	and	and	CCONJ
ejpam-1609	258	12	proved	prove	VERB
ejpam-1609	258	13	a	a	DET
ejpam-1609	258	14	direct	direct	ADJ
ejpam-1609	258	15	formula	formula	NOUN
ejpam-1609	258	16	for	for	ADP
ejpam-1609	258	17	the	the	DET
ejpam-1609	258	18	number	number	NOUN
ejpam-1609	258	19	of	of	ADP
ejpam-1609	258	20	linear	linear	PROPN
ejpam-1609	258	21	codes	code	NOUN
ejpam-1609	258	22	over	over	ADP
ejpam-1609	258	23	the	the	DET
ejpam-1609	258	24	galois	galois	PROPN
ejpam-1609	258	25	ring	ring	NOUN
ejpam-1609	258	26	zpm[ξ	zpm[ξ	PROPN
ejpam-1609	258	27	]	]	PUNCT
ejpam-1609	258	28	.	.	PUNCT
ejpam-1609	259	1	as	as	ADP
ejpam-1609	259	2	an	an	DET
ejpam-1609	259	3	application	application	NOUN
ejpam-1609	259	4	of	of	ADP
ejpam-1609	259	5	this	this	DET
ejpam-1609	259	6	formula	formula	NOUN
ejpam-1609	259	7	,	,	PUNCT
ejpam-1609	259	8	we	we	PRON
ejpam-1609	259	9	generalize	generalize	VERB
ejpam-1609	259	10	the	the	DET
ejpam-1609	259	11	properties	property	NOUN
ejpam-1609	259	12	given	give	VERB
ejpam-1609	259	13	in	in	ADP
ejpam-1609	259	14	[	[	X
ejpam-1609	259	15	10	10	NUM
ejpam-1609	259	16	]	]	PUNCT
ejpam-1609	259	17	and	and	CCONJ
ejpam-1609	259	18	name	name	VERB
ejpam-1609	259	19	them	they	PRON
ejpam-1609	259	20	generalized	generalized	ADJ
ejpam-1609	259	21	gaussian	gaussian	ADJ
ejpam-1609	259	22	numbers	number	NOUN
ejpam-1609	259	23	.	.	PUNCT
ejpam-1609	260	1	a	a	DET
ejpam-1609	260	2	new	new	ADJ
ejpam-1609	260	3	number	number	NOUN
ejpam-1609	260	4	sequence	sequence	NOUN
ejpam-1609	260	5	is	be	AUX
ejpam-1609	260	6	also	also	ADV
ejpam-1609	260	7	presented	present	VERB
ejpam-1609	260	8	.	.	PUNCT
ejpam-1609	261	1	it	it	PRON
ejpam-1609	261	2	is	be	AUX
ejpam-1609	261	3	believed	believe	VERB
ejpam-1609	261	4	that	that	SCONJ
ejpam-1609	261	5	the	the	DET
ejpam-1609	261	6	properties	property	NOUN
ejpam-1609	261	7	of	of	ADP
ejpam-1609	261	8	generalized	generalized	ADJ
ejpam-1609	261	9	gaussian	gaussian	ADJ
ejpam-1609	261	10	numbers	number	NOUN
ejpam-1609	261	11	can	can	AUX
ejpam-1609	261	12	be	be	AUX
ejpam-1609	261	13	further	far	ADV
ejpam-1609	261	14	explored	explore	VERB
ejpam-1609	261	15	.	.	PUNCT
ejpam-1609	262	1	also	also	ADV
ejpam-1609	262	2	some	some	PRON
ejpam-1609	262	3	more	more	ADV
ejpam-1609	262	4	new	new	ADJ
ejpam-1609	262	5	sequences	sequence	NOUN
ejpam-1609	262	6	can	can	AUX
ejpam-1609	262	7	be	be	AUX
ejpam-1609	262	8	obtained	obtain	VERB
ejpam-1609	262	9	from	from	ADP
ejpam-1609	262	10	these	these	DET
ejpam-1609	262	11	numbers	number	NOUN
ejpam-1609	262	12	.	.	PUNCT
ejpam-1609	263	1	acknowledgements	acknowledgement	NOUN
ejpam-1609	263	2	we	we	PRON
ejpam-1609	263	3	would	would	AUX
ejpam-1609	263	4	like	like	VERB
ejpam-1609	263	5	to	to	PART
ejpam-1609	263	6	thank	thank	VERB
ejpam-1609	263	7	the	the	DET
ejpam-1609	263	8	referees	referee	NOUN
ejpam-1609	263	9	for	for	ADP
ejpam-1609	263	10	their	their	PRON
ejpam-1609	263	11	remarks	remark	NOUN
ejpam-1609	263	12	and	and	CCONJ
ejpam-1609	263	13	suggestions	suggestion	NOUN
ejpam-1609	263	14	.	.	PUNCT
ejpam-1609	264	1	this	this	DET
ejpam-1609	264	2	research	research	NOUN
ejpam-1609	264	3	is	be	AUX
ejpam-1609	264	4	supported	support	VERB
ejpam-1609	264	5	by	by	ADP
ejpam-1609	264	6	yildiz	yildiz	PROPN
ejpam-1609	264	7	technical	technical	PROPN
ejpam-1609	264	8	university	university	PROPN
ejpam-1609	264	9	research	research	NOUN
ejpam-1609	264	10	support	support	NOUN
ejpam-1609	264	11	unit	unit	NOUN
ejpam-1609	264	12	(	(	PUNCT
ejpam-1609	264	13	2011	2011	NUM
ejpam-1609	264	14	-	-	SYM
ejpam-1609	264	15	03	03	NUM
ejpam-1609	264	16	-	-	PUNCT
ejpam-1609	264	17	dop01	dop01	NOUN
ejpam-1609	264	18	)	)	PUNCT
ejpam-1609	264	19	.	.	PUNCT
ejpam-1609	265	1	references	reference	NOUN
ejpam-1609	265	2	[	[	X
ejpam-1609	265	3	1	1	NUM
ejpam-1609	265	4	]	]	X
ejpam-1609	265	5	g.	g.	NOUN
ejpam-1609	265	6	calugareanu	calugareanu	PROPN
ejpam-1609	265	7	.	.	PUNCT
ejpam-1609	266	1	the	the	DET
ejpam-1609	266	2	total	total	ADJ
ejpam-1609	266	3	number	number	NOUN
ejpam-1609	266	4	of	of	ADP
ejpam-1609	266	5	subgroups	subgroup	NOUN
ejpam-1609	266	6	of	of	ADP
ejpam-1609	266	7	a	a	DET
ejpam-1609	266	8	finite	finite	ADJ
ejpam-1609	266	9	abelian	abelian	PROPN
ejpam-1609	266	10	group	group	PROPN
ejpam-1609	266	11	.	.	PUNCT
ejpam-1609	267	1	scientiae	scientiae	PROPN
ejpam-1609	267	2	mathematicae	mathematicae	PROPN
ejpam-1609	267	3	japonicae	japonicae	PROPN
ejpam-1609	267	4	,	,	PUNCT
ejpam-1609	267	5	60:157	60:157	NUM
ejpam-1609	267	6	-	-	SYM
ejpam-1609	267	7	167	167	NUM
ejpam-1609	267	8	,	,	PUNCT
ejpam-1609	267	9	2004	2004	NUM
ejpam-1609	267	10	.	.	PUNCT
ejpam-1609	268	1	[	[	X
ejpam-1609	268	2	2	2	X
ejpam-1609	268	3	]	]	PUNCT
ejpam-1609	268	4	s.	s.	PROPN
ejpam-1609	268	5	delsarte	delsarte	PROPN
ejpam-1609	268	6	.	.	PUNCT
ejpam-1609	269	1	fonctions	fonction	NOUN
ejpam-1609	269	2	de	de	X
ejpam-1609	269	3	möbius	möbius	PROPN
ejpam-1609	269	4	sur	sur	PROPN
ejpam-1609	269	5	les	les	X
ejpam-1609	269	6	groupes	groupe	NOUN
ejpam-1609	269	7	abeliens	abelien	NOUN
ejpam-1609	269	8	finis	finis	NOUN
ejpam-1609	269	9	,	,	PUNCT
ejpam-1609	269	10	annals	annal	NOUN
ejpam-1609	269	11	of	of	ADP
ejpam-1609	269	12	math	math	NOUN
ejpam-1609	269	13	.	.	PUNCT
ejpam-1609	270	1	49:600609	49:600609	NOUN
ejpam-1609	270	2	,	,	PUNCT
ejpam-1609	270	3	1948	1948	NUM
ejpam-1609	270	4	.	.	PUNCT
ejpam-1609	271	1	[	[	X
ejpam-1609	271	2	3	3	NUM
ejpam-1609	271	3	]	]	X
ejpam-1609	271	4	p.e	p.e	PROPN
ejpam-1609	271	5	.	.	PROPN
ejpam-1609	271	6	djubjuk	djubjuk	PROPN
ejpam-1609	271	7	.	.	PUNCT
ejpam-1609	272	1	on	on	ADP
ejpam-1609	272	2	the	the	DET
ejpam-1609	272	3	number	number	NOUN
ejpam-1609	272	4	of	of	ADP
ejpam-1609	272	5	subgroups	subgroup	NOUN
ejpam-1609	272	6	of	of	ADP
ejpam-1609	272	7	a	a	DET
ejpam-1609	272	8	finite	finite	ADJ
ejpam-1609	272	9	abelian	abelian	PROPN
ejpam-1609	272	10	group	group	PROPN
ejpam-1609	272	11	,	,	PUNCT
ejpam-1609	272	12	izv	izv	PROPN
ejpam-1609	272	13	.	.	PROPN
ejpam-1609	272	14	akad	akad	PROPN
ejpam-1609	272	15	.	.	PUNCT
ejpam-1609	273	1	nauk	nauk	PROPN
ejpam-1609	273	2	sssr	sssr	PROPN
ejpam-1609	273	3	ser	ser	PROPN
ejpam-1609	273	4	.	.	PROPN
ejpam-1609	274	1	mat	mat	PROPN
ejpam-1609	274	2	.	.	PROPN
ejpam-1609	274	3	,	,	PUNCT
ejpam-1609	274	4	12:351	12:351	NUM
ejpam-1609	274	5	-	-	SYM
ejpam-1609	274	6	378	378	NUM
ejpam-1609	274	7	,	,	PUNCT
ejpam-1609	274	8	1948	1948	NUM
ejpam-1609	274	9	.	.	PUNCT
ejpam-1609	275	1	[	[	X
ejpam-1609	275	2	4	4	NUM
ejpam-1609	275	3	]	]	X
ejpam-1609	275	4	a.r	a.r	PROPN
ejpam-1609	275	5	.	.	PROPN
ejpam-1609	275	6	hammons	hammons	PROPN
ejpam-1609	275	7	,	,	PUNCT
ejpam-1609	275	8	p.v	p.v	PROPN
ejpam-1609	275	9	.	.	PROPN
ejpam-1609	275	10	kumar	kumar	PROPN
ejpam-1609	275	11	,	,	PUNCT
ejpam-1609	275	12	a.r	a.r	PROPN
ejpam-1609	275	13	.	.	PROPN
ejpam-1609	275	14	calderbank	calderbank	PROPN
ejpam-1609	275	15	,	,	PUNCT
ejpam-1609	275	16	n.j.a	n.j.a	PROPN
ejpam-1609	275	17	.	.	PROPN
ejpam-1609	275	18	sloane	sloane	NOUN
ejpam-1609	275	19	and	and	CCONJ
ejpam-1609	275	20	p.	p.	PROPN
ejpam-1609	275	21	sole	sole	NOUN
ejpam-1609	275	22	.	.	PUNCT
ejpam-1609	276	1	the	the	DET
ejpam-1609	276	2	z4	z4	PROPN
ejpam-1609	276	3	-	-	PUNCT
ejpam-1609	276	4	linearity	linearity	NOUN
ejpam-1609	276	5	of	of	ADP
ejpam-1609	276	6	kerdock	kerdock	NOUN
ejpam-1609	276	7	,	,	PUNCT
ejpam-1609	276	8	preparata	preparata	NOUN
ejpam-1609	276	9	,	,	PUNCT
ejpam-1609	276	10	goethals	goethal	NOUN
ejpam-1609	276	11	and	and	CCONJ
ejpam-1609	276	12	related	related	ADJ
ejpam-1609	276	13	codes	code	NOUN
ejpam-1609	276	14	.	.	PUNCT
ejpam-1609	277	1	ieee	ieee	NOUN
ejpam-1609	277	2	transactions	transaction	NOUN
ejpam-1609	277	3	on	on	ADP
ejpam-1609	277	4	information	information	NOUN
ejpam-1609	277	5	theory	theory	NOUN
ejpam-1609	277	6	,	,	PUNCT
ejpam-1609	277	7	40:301	40:301	NUM
ejpam-1609	277	8	-	-	SYM
ejpam-1609	277	9	319	319	NUM
ejpam-1609	277	10	,	,	PUNCT
ejpam-1609	277	11	1994	1994	NUM
ejpam-1609	277	12	.	.	PUNCT
ejpam-1609	278	1	[	[	X
ejpam-1609	278	2	5	5	X
ejpam-1609	278	3	]	]	PUNCT
ejpam-1609	278	4	t.	t.	PROPN
ejpam-1609	278	5	honold	honold	PROPN
ejpam-1609	278	6	and	and	CCONJ
ejpam-1609	278	7	i.	i.	PROPN
ejpam-1609	278	8	landjev	landjev	PROPN
ejpam-1609	278	9	.	.	PUNCT
ejpam-1609	279	1	linear	linear	PROPN
ejpam-1609	279	2	codes	code	NOUN
ejpam-1609	279	3	over	over	ADP
ejpam-1609	279	4	finite	finite	ADJ
ejpam-1609	279	5	chain	chain	NOUN
ejpam-1609	279	6	rings	ring	NOUN
ejpam-1609	279	7	,	,	PUNCT
ejpam-1609	279	8	the	the	DET
ejpam-1609	279	9	electronic	electronic	ADJ
ejpam-1609	279	10	journal	journal	NOUN
ejpam-1609	279	11	of	of	ADP
ejpam-1609	279	12	combinatorics	combinatoric	NOUN
ejpam-1609	279	13	7	7	NUM
ejpam-1609	279	14	,	,	PUNCT
ejpam-1609	279	15	2000	2000	NUM
ejpam-1609	279	16	.	.	PUNCT
ejpam-1609	280	1	[	[	X
ejpam-1609	280	2	6	6	NUM
ejpam-1609	280	3	]	]	PUNCT
ejpam-1609	280	4	w.c	w.c	PROPN
ejpam-1609	280	5	.	.	PROPN
ejpam-1609	280	6	huffman	huffman	PROPN
ejpam-1609	280	7	.	.	PUNCT
ejpam-1609	281	1	decompositions	decomposition	NOUN
ejpam-1609	281	2	and	and	CCONJ
ejpam-1609	281	3	extremal	extremal	ADJ
ejpam-1609	281	4	type	type	NOUN
ejpam-1609	281	5	ii	ii	PROPN
ejpam-1609	281	6	codes	code	NOUN
ejpam-1609	281	7	over	over	ADP
ejpam-1609	281	8	z4	z4	PROPN
ejpam-1609	281	9	.	.	PUNCT
ejpam-1609	282	1	ieee	ieee	PROPN
ejpam-1609	282	2	trans	trans	PROPN
ejpam-1609	282	3	.	.	PROPN
ejpam-1609	282	4	inf	inf	PROPN
ejpam-1609	282	5	.	.	PUNCT
ejpam-1609	282	6	theory	theory	PROPN
ejpam-1609	282	7	44:800	44:800	PROPN
ejpam-1609	282	8	-	-	SYM
ejpam-1609	282	9	809	809	NUM
ejpam-1609	282	10	,	,	PUNCT
ejpam-1609	282	11	1998	1998	NUM
ejpam-1609	282	12	.	.	PUNCT
ejpam-1609	283	1	[	[	X
ejpam-1609	283	2	7	7	X
ejpam-1609	283	3	]	]	X
ejpam-1609	283	4	m.	m.	NOUN
ejpam-1609	283	5	ozen	ozen	NOUN
ejpam-1609	283	6	and	and	CCONJ
ejpam-1609	283	7	i.	i.	PROPN
ejpam-1609	283	8	siap	siap	PROPN
ejpam-1609	283	9	.	.	PUNCT
ejpam-1609	284	1	codes	code	NOUN
ejpam-1609	284	2	over	over	ADP
ejpam-1609	284	3	galois	galois	PROPN
ejpam-1609	284	4	rings	ring	NOUN
ejpam-1609	284	5	with	with	ADP
ejpam-1609	284	6	respect	respect	NOUN
ejpam-1609	284	7	to	to	ADP
ejpam-1609	284	8	the	the	DET
ejpam-1609	284	9	rosenbloom	rosenbloom	NOUN
ejpam-1609	284	10	-	-	PUNCT
ejpam-1609	284	11	tsfasman	tsfasman	NOUN
ejpam-1609	284	12	metric	metric	NOUN
ejpam-1609	284	13	.	.	PUNCT
ejpam-1609	285	1	special	special	ADJ
ejpam-1609	285	2	issue	issue	NOUN
ejpam-1609	285	3	for	for	ADP
ejpam-1609	285	4	icmsaoš05	icmsaoš05	PROPN
ejpam-1609	285	5	first	first	PROPN
ejpam-1609	285	6	international	international	ADJ
ejpam-1609	285	7	conference	conference	NOUN
ejpam-1609	285	8	on	on	ADP
ejpam-1609	285	9	modeling	modeling	NOUN
ejpam-1609	285	10	,	,	PUNCT
ejpam-1609	285	11	simulation	simulation	NOUN
ejpam-1609	285	12	and	and	CCONJ
ejpam-1609	285	13	applied	apply	VERB
ejpam-1609	285	14	optimization	optimization	NOUN
ejpam-1609	285	15	,	,	PUNCT
ejpam-1609	285	16	the	the	DET
ejpam-1609	285	17	franklin	franklin	PROPN
ejpam-1609	285	18	institute	institute	PROPN
ejpam-1609	285	19	journal	journal	PROPN
ejpam-1609	285	20	,	,	PUNCT
ejpam-1609	285	21	5:790	5:790	NUM
ejpam-1609	285	22	-	-	SYM
ejpam-1609	285	23	799	799	NUM
ejpam-1609	285	24	,	,	PUNCT
ejpam-1609	285	25	2007	2007	NUM
ejpam-1609	285	26	.	.	PUNCT
ejpam-1609	286	1	references	reference	NOUN
ejpam-1609	286	2	259	259	NUM
ejpam-1609	287	1	[	[	X
ejpam-1609	287	2	8	8	NUM
ejpam-1609	287	3	]	]	X
ejpam-1609	287	4	f.j	f.j	PROPN
ejpam-1609	287	5	.	.	PROPN
ejpam-1609	287	6	macwilliams	macwilliam	NOUN
ejpam-1609	287	7	and	and	CCONJ
ejpam-1609	287	8	n.j.a	n.j.a	PROPN
ejpam-1609	287	9	sloane	sloane	NOUN
ejpam-1609	287	10	.	.	PUNCT
ejpam-1609	288	1	the	the	DET
ejpam-1609	288	2	theory	theory	NOUN
ejpam-1609	288	3	of	of	ADP
ejpam-1609	288	4	error	error	NOUN
ejpam-1609	288	5	correcting	correct	VERB
ejpam-1609	288	6	codes	code	NOUN
ejpam-1609	288	7	.	.	PUNCT
ejpam-1609	289	1	north	north	NOUN
ejpam-1609	289	2	-	-	PUNCT
ejpam-1609	289	3	holland	holland	PROPN
ejpam-1609	289	4	pub	pub	NOUN
ejpam-1609	289	5	.	.	PUNCT
ejpam-1609	290	1	co.	co.	PROPN
ejpam-1609	290	2	,	,	PUNCT
ejpam-1609	290	3	1977	1977	NUM
ejpam-1609	290	4	.	.	PUNCT
ejpam-1609	291	1	[	[	X
ejpam-1609	291	2	9	9	NUM
ejpam-1609	291	3	]	]	X
ejpam-1609	291	4	b.r	b.r	PROPN
ejpam-1609	291	5	.	.	PROPN
ejpam-1609	291	6	mcdonald	mcdonald	PROPN
ejpam-1609	291	7	,	,	PUNCT
ejpam-1609	291	8	finite	finite	PROPN
ejpam-1609	291	9	rings	ring	NOUN
ejpam-1609	291	10	with	with	ADP
ejpam-1609	291	11	identity	identity	NOUN
ejpam-1609	291	12	,	,	PUNCT
ejpam-1609	291	13	pure	pure	ADJ
ejpam-1609	291	14	and	and	CCONJ
ejpam-1609	291	15	applied	applied	ADJ
ejpam-1609	291	16	mathematics	mathematic	NOUN
ejpam-1609	291	17	.	.	PUNCT
ejpam-1609	292	1	marcel	marcel	PROPN
ejpam-1609	292	2	dekker	dekker	PROPN
ejpam-1609	292	3	.	.	PUNCT
ejpam-1609	293	1	1974	1974	NUM
ejpam-1609	293	2	.	.	PUNCT
ejpam-1609	294	1	[	[	X
ejpam-1609	294	2	10	10	NUM
ejpam-1609	294	3	]	]	X
ejpam-1609	294	4	e.	e.	PROPN
ejpam-1609	294	5	saltürk	saltürk	PROPN
ejpam-1609	294	6	and	and	CCONJ
ejpam-1609	294	7	i̇.	i̇.	PROPN
ejpam-1609	294	8	şiap	şiap	PROPN
ejpam-1609	294	9	.	.	PUNCT
ejpam-1609	295	1	on	on	ADP
ejpam-1609	295	2	the	the	DET
ejpam-1609	295	3	number	number	NOUN
ejpam-1609	295	4	of	of	ADP
ejpam-1609	295	5	linear	linear	PROPN
ejpam-1609	295	6	codes	code	NOUN
ejpam-1609	295	7	over	over	ADP
ejpam-1609	295	8	zpm	zpm	PROPN
ejpam-1609	295	9	,	,	PUNCT
ejpam-1609	295	10	submitted	submit	VERB
ejpam-1609	295	11	.	.	PUNCT
ejpam-1609	296	1	[	[	X
ejpam-1609	296	2	11	11	NUM
ejpam-1609	296	3	]	]	X
ejpam-1609	296	4	e.	e.	PROPN
ejpam-1609	296	5	saltürk	saltürk	PROPN
ejpam-1609	296	6	and	and	CCONJ
ejpam-1609	296	7	i̇.	i̇.	PROPN
ejpam-1609	296	8	şiap	şiap	PROPN
ejpam-1609	296	9	.	.	PUNCT
ejpam-1609	297	1	the	the	DET
ejpam-1609	297	2	total	total	ADJ
ejpam-1609	297	3	number	number	NOUN
ejpam-1609	297	4	of	of	ADP
ejpam-1609	297	5	linear	linear	PROPN
ejpam-1609	297	6	codes	code	NOUN
ejpam-1609	297	7	over	over	ADP
ejpam-1609	297	8	fq	fq	PROPN
ejpam-1609	297	9	+	+	CCONJ
ejpam-1609	297	10	ufq	ufq	PROPN
ejpam-1609	297	11	,	,	PUNCT
ejpam-1609	297	12	submitted	submit	VERB
ejpam-1609	297	13	.	.	PUNCT
ejpam-1609	298	1	[	[	X
ejpam-1609	298	2	12	12	NUM
ejpam-1609	298	3	]	]	X
ejpam-1609	298	4	n.j.a	n.j.a	ADJ
ejpam-1609	298	5	.	.	PUNCT
ejpam-1609	298	6	sloane	sloane	NOUN
ejpam-1609	298	7	.	.	PUNCT
ejpam-1609	299	1	on	on	ADP
ejpam-1609	299	2	-	-	PUNCT
ejpam-1609	299	3	line	line	NOUN
ejpam-1609	299	4	encyclopedia	encyclopedia	NOUN
ejpam-1609	299	5	of	of	ADP
ejpam-1609	299	6	integer	integer	NOUN
ejpam-1609	299	7	sequences	sequence	NOUN
ejpam-1609	299	8	.	.	PUNCT
ejpam-1609	300	1	published	publish	VERB
ejpam-1609	300	2	electronically	electronically	ADV
ejpam-1609	300	3	at	at	ADP
ejpam-1609	300	4	http://www.resear	http://www.resear	PROPN
ejpam-1609	300	5	h.att	h.att	PROPN
ejpam-1609	300	6	.	.	PUNCT
ejpam-1609	301	1	om	om	PROPN
ejpam-1609	301	2	/	/	SYM
ejpam-1609	301	3	njas	njas	ADJ
ejpam-1609	301	4	/	/	SYM
ejpam-1609	301	5	sequen	sequen	NOUN
ejpam-1609	301	6	es	es	NOUN
ejpam-1609	301	7	.	.	PUNCT
ejpam-1609	302	1	[	[	X
ejpam-1609	302	2	13	13	NUM
ejpam-1609	302	3	]	]	X
ejpam-1609	302	4	z.x	z.x	PROPN
ejpam-1609	302	5	.	.	PROPN
ejpam-1609	302	6	wan	wan	PROPN
ejpam-1609	302	7	.	.	PUNCT
ejpam-1609	302	8	quaternary	quaternary	ADJ
ejpam-1609	302	9	codes	code	NOUN
ejpam-1609	302	10	.	.	PUNCT
ejpam-1609	303	1	series	series	NOUN
ejpam-1609	303	2	on	on	ADP
ejpam-1609	303	3	applied	applied	ADJ
ejpam-1609	303	4	mathematics	mathematic	NOUN
ejpam-1609	303	5	,	,	PUNCT
ejpam-1609	303	6	world	world	NOUN
ejpam-1609	303	7	scientific	scientific	PROPN
ejpam-1609	303	8	publisher	publisher	PROPN
ejpam-1609	303	9	co.	co.	PROPN
ejpam-1609	303	10	,	,	PUNCT
ejpam-1609	303	11	singapore	singapore	PROPN
ejpam-1609	303	12	,	,	PUNCT
ejpam-1609	303	13	1997	1997	NUM
ejpam-1609	303	14	.	.	PUNCT
ejpam-1609	304	1	[	[	X
ejpam-1609	304	2	14	14	NUM
ejpam-1609	304	3	]	]	X
ejpam-1609	304	4	y.	y.	PROPN
ejpam-1609	304	5	yeh	yeh	PROPN
ejpam-1609	304	6	.	.	PUNCT
ejpam-1609	305	1	on	on	ADP
ejpam-1609	305	2	prime	prime	ADJ
ejpam-1609	305	3	power	power	NOUN
ejpam-1609	305	4	abelian	abelian	NOUN
ejpam-1609	305	5	groups	group	NOUN
ejpam-1609	305	6	.	.	PUNCT
ejpam-1609	306	1	bull	bull	NOUN
ejpam-1609	306	2	.	.	PUNCT
ejpam-1609	307	1	ams	am	NOUN
ejpam-1609	307	2	,	,	PUNCT
ejpam-1609	307	3	54:323	54:323	NUM
ejpam-1609	307	4	-	-	SYM
ejpam-1609	307	5	327	327	NUM
ejpam-1609	307	6	,	,	PUNCT
ejpam-1609	307	7	1948	1948	NUM
ejpam-1609	307	8	.	.	PUNCT