id	sid	tid	token	lemma	pos
ejpam-3907	1	1	european	european	PROPN
ejpam-3907	1	2	journal	journal	PROPN
ejpam-3907	1	3	of	of	ADP
ejpam-3907	1	4	pure	pure	ADJ
ejpam-3907	1	5	and	and	CCONJ
ejpam-3907	1	6	applied	apply	VERB
ejpam-3907	1	7	mathematics	mathematic	NOUN
ejpam-3907	1	8	vol	vol	NOUN
ejpam-3907	1	9	.	.	PUNCT
ejpam-3907	2	1	14	14	NUM
ejpam-3907	2	2	,	,	PUNCT
ejpam-3907	2	3	no	no	INTJ
ejpam-3907	2	4	.	.	NOUN
ejpam-3907	2	5	3	3	NUM
ejpam-3907	2	6	,	,	PUNCT
ejpam-3907	2	7	2021	2021	NUM
ejpam-3907	2	8	,	,	PUNCT
ejpam-3907	2	9	685	685	NUM
ejpam-3907	2	10	-	-	SYM
ejpam-3907	2	11	694	694	NUM
ejpam-3907	2	12	issn	issn	PROPN
ejpam-3907	2	13	1307	1307	NUM
ejpam-3907	2	14	-	-	SYM
ejpam-3907	2	15	5543	5543	NUM
ejpam-3907	2	16	–	–	PUNCT
ejpam-3907	2	17	ejpam.com	ejpam.com	X
ejpam-3907	2	18	published	publish	VERB
ejpam-3907	2	19	by	by	ADP
ejpam-3907	2	20	new	new	PROPN
ejpam-3907	2	21	york	york	PROPN
ejpam-3907	2	22	business	business	PROPN
ejpam-3907	2	23	global	global	PROPN
ejpam-3907	2	24	cyclic	cyclic	PROPN
ejpam-3907	2	25	codes	code	NOUN
ejpam-3907	2	26	from	from	ADP
ejpam-3907	2	27	a	a	DET
ejpam-3907	2	28	sequence	sequence	NOUN
ejpam-3907	2	29	over	over	ADP
ejpam-3907	2	30	finite	finite	ADJ
ejpam-3907	2	31	fields	field	NOUN
ejpam-3907	2	32	nopendri1,3,∗	nopendri1,3,∗	PROPN
ejpam-3907	2	33	,	,	PUNCT
ejpam-3907	2	34	intan	intan	PROPN
ejpam-3907	2	35	muchtadi	muchtadi	PROPN
ejpam-3907	2	36	alamsyah1	alamsyah1	PROPN
ejpam-3907	2	37	,	,	PUNCT
ejpam-3907	2	38	djoko	djoko	PROPN
ejpam-3907	2	39	suprijanto2	suprijanto2	PROPN
ejpam-3907	2	40	,	,	PUNCT
ejpam-3907	2	41	aleams	aleam	NOUN
ejpam-3907	2	42	barra1	barra1	VERB
ejpam-3907	3	1	1	1	NUM
ejpam-3907	3	2	algebra	algebra	NOUN
ejpam-3907	3	3	research	research	NOUN
ejpam-3907	3	4	group	group	NOUN
ejpam-3907	3	5	,	,	PUNCT
ejpam-3907	3	6	faculty	faculty	NOUN
ejpam-3907	3	7	of	of	ADP
ejpam-3907	3	8	mathematics	mathematic	NOUN
ejpam-3907	3	9	and	and	CCONJ
ejpam-3907	3	10	natural	natural	ADJ
ejpam-3907	3	11	sciences	science	NOUN
ejpam-3907	3	12	,	,	PUNCT
ejpam-3907	3	13	institut	institut	PROPN
ejpam-3907	3	14	teknologi	teknologi	PROPN
ejpam-3907	3	15	bandung	bandung	PROPN
ejpam-3907	3	16	,	,	PUNCT
ejpam-3907	3	17	bandung	bandung	PROPN
ejpam-3907	3	18	,	,	PUNCT
ejpam-3907	3	19	indonesia	indonesia	PROPN
ejpam-3907	3	20	2	2	NUM
ejpam-3907	3	21	combinatorial	combinatorial	NOUN
ejpam-3907	3	22	mathematics	mathematics	PROPN
ejpam-3907	3	23	research	research	NOUN
ejpam-3907	3	24	group	group	NOUN
ejpam-3907	3	25	,	,	PUNCT
ejpam-3907	3	26	faculty	faculty	NOUN
ejpam-3907	3	27	of	of	ADP
ejpam-3907	3	28	mathematics	mathematic	NOUN
ejpam-3907	3	29	and	and	CCONJ
ejpam-3907	3	30	natural	natural	ADJ
ejpam-3907	3	31	sciences	science	NOUN
ejpam-3907	3	32	,	,	PUNCT
ejpam-3907	3	33	institut	institut	PROPN
ejpam-3907	3	34	teknologi	teknologi	PROPN
ejpam-3907	3	35	bandung	bandung	PROPN
ejpam-3907	3	36	,	,	PUNCT
ejpam-3907	3	37	bandung	bandung	PROPN
ejpam-3907	3	38	,	,	PUNCT
ejpam-3907	3	39	indonesia	indonesia	PROPN
ejpam-3907	3	40	3	3	NUM
ejpam-3907	3	41	cybernetics	cybernetics	PROPN
ejpam-3907	3	42	research	research	NOUN
ejpam-3907	3	43	group	group	NOUN
ejpam-3907	3	44	,	,	PUNCT
ejpam-3907	3	45	school	school	NOUN
ejpam-3907	3	46	of	of	ADP
ejpam-3907	3	47	industrial	industrial	ADJ
ejpam-3907	3	48	and	and	CCONJ
ejpam-3907	3	49	system	system	NOUN
ejpam-3907	3	50	engineering	engineering	NOUN
ejpam-3907	3	51	,	,	PUNCT
ejpam-3907	3	52	telkom	telkom	PROPN
ejpam-3907	3	53	university	university	PROPN
ejpam-3907	3	54	,	,	PUNCT
ejpam-3907	3	55	bandung	bandung	PROPN
ejpam-3907	3	56	,	,	PUNCT
ejpam-3907	3	57	indonesia	indonesia	PROPN
ejpam-3907	3	58	abstract	abstract	NOUN
ejpam-3907	3	59	.	.	PUNCT
ejpam-3907	4	1	a	a	DET
ejpam-3907	4	2	cyclic	cyclic	ADJ
ejpam-3907	4	3	code	code	NOUN
ejpam-3907	4	4	has	have	AUX
ejpam-3907	4	5	been	be	AUX
ejpam-3907	4	6	one	one	NUM
ejpam-3907	4	7	of	of	ADP
ejpam-3907	4	8	the	the	DET
ejpam-3907	4	9	most	most	ADV
ejpam-3907	4	10	active	active	ADJ
ejpam-3907	4	11	research	research	NOUN
ejpam-3907	4	12	topics	topic	NOUN
ejpam-3907	4	13	in	in	ADP
ejpam-3907	4	14	coding	code	VERB
ejpam-3907	4	15	theory	theory	NOUN
ejpam-3907	4	16	due	due	ADP
ejpam-3907	4	17	to	to	ADP
ejpam-3907	4	18	its	its	PRON
ejpam-3907	4	19	applications	application	NOUN
ejpam-3907	4	20	in	in	ADP
ejpam-3907	4	21	many	many	ADJ
ejpam-3907	4	22	areas	area	NOUN
ejpam-3907	4	23	,	,	PUNCT
ejpam-3907	4	24	such	such	ADJ
ejpam-3907	4	25	as	as	ADP
ejpam-3907	4	26	data	datum	NOUN
ejpam-3907	4	27	storage	storage	NOUN
ejpam-3907	4	28	systems	system	NOUN
ejpam-3907	4	29	and	and	CCONJ
ejpam-3907	4	30	communication	communication	NOUN
ejpam-3907	4	31	,	,	PUNCT
ejpam-3907	4	32	as	as	SCONJ
ejpam-3907	4	33	they	they	PRON
ejpam-3907	4	34	have	have	VERB
ejpam-3907	4	35	efficient	efficient	ADJ
ejpam-3907	4	36	encoding	encode	VERB
ejpam-3907	4	37	and	and	CCONJ
ejpam-3907	4	38	decoding	decode	VERB
ejpam-3907	4	39	algorithms	algorithm	NOUN
ejpam-3907	4	40	.	.	PUNCT
ejpam-3907	5	1	this	this	DET
ejpam-3907	5	2	paper	paper	NOUN
ejpam-3907	5	3	explains	explain	VERB
ejpam-3907	5	4	the	the	DET
ejpam-3907	5	5	construction	construction	NOUN
ejpam-3907	5	6	of	of	ADP
ejpam-3907	5	7	a	a	DET
ejpam-3907	5	8	family	family	NOUN
ejpam-3907	5	9	of	of	ADP
ejpam-3907	5	10	cyclic	cyclic	ADJ
ejpam-3907	5	11	codes	code	NOUN
ejpam-3907	5	12	from	from	ADP
ejpam-3907	5	13	sequences	sequence	NOUN
ejpam-3907	5	14	generated	generate	VERB
ejpam-3907	5	15	by	by	ADP
ejpam-3907	5	16	a	a	DET
ejpam-3907	5	17	trace	trace	NOUN
ejpam-3907	5	18	of	of	ADP
ejpam-3907	5	19	a	a	DET
ejpam-3907	5	20	monomial	monomial	NOUN
ejpam-3907	5	21	over	over	ADP
ejpam-3907	5	22	finite	finite	ADJ
ejpam-3907	5	23	fields	field	NOUN
ejpam-3907	5	24	of	of	ADP
ejpam-3907	5	25	odd	odd	ADJ
ejpam-3907	5	26	characteristics	characteristic	NOUN
ejpam-3907	5	27	.	.	PUNCT
ejpam-3907	6	1	the	the	DET
ejpam-3907	6	2	parameter	parameter	NOUN
ejpam-3907	6	3	and	and	CCONJ
ejpam-3907	6	4	some	some	DET
ejpam-3907	6	5	examples	example	NOUN
ejpam-3907	6	6	of	of	ADP
ejpam-3907	6	7	the	the	DET
ejpam-3907	6	8	codes	code	NOUN
ejpam-3907	6	9	are	be	AUX
ejpam-3907	6	10	presented	present	VERB
ejpam-3907	6	11	in	in	ADP
ejpam-3907	6	12	this	this	DET
ejpam-3907	6	13	paper	paper	NOUN
ejpam-3907	6	14	.	.	PUNCT
ejpam-3907	7	1	2020	2020	NUM
ejpam-3907	7	2	mathematics	mathematic	NOUN
ejpam-3907	7	3	subject	subject	NOUN
ejpam-3907	7	4	classifications	classification	NOUN
ejpam-3907	7	5	:	:	PUNCT
ejpam-3907	7	6	94b15	94b15	NUM
ejpam-3907	7	7	,	,	PUNCT
ejpam-3907	7	8	94b65	94b65	NUM
ejpam-3907	7	9	,	,	PUNCT
ejpam-3907	7	10	94a55	94a55	NUM
ejpam-3907	7	11	key	key	ADJ
ejpam-3907	7	12	words	word	NOUN
ejpam-3907	7	13	and	and	CCONJ
ejpam-3907	7	14	phrases	phrase	NOUN
ejpam-3907	7	15	:	:	PUNCT
ejpam-3907	7	16	cyclic	cyclic	ADJ
ejpam-3907	7	17	codes	code	NOUN
ejpam-3907	7	18	,	,	PUNCT
ejpam-3907	7	19	sequences	sequence	NOUN
ejpam-3907	7	20	,	,	PUNCT
ejpam-3907	7	21	linear	linear	ADJ
ejpam-3907	7	22	span	span	NOUN
ejpam-3907	7	23	,	,	PUNCT
ejpam-3907	7	24	cyclotomic	cyclotomic	ADJ
ejpam-3907	7	25	coset	coset	NOUN
ejpam-3907	7	26	,	,	PUNCT
ejpam-3907	7	27	minimal	minimal	ADJ
ejpam-3907	7	28	polynomials	polynomial	NOUN
ejpam-3907	7	29	1	1	NUM
ejpam-3907	7	30	.	.	PUNCT
ejpam-3907	8	1	introduction	introduction	NOUN
ejpam-3907	8	2	let	let	VERB
ejpam-3907	8	3	gf	gf	PROPN
ejpam-3907	8	4	(	(	PUNCT
ejpam-3907	8	5	q	q	X
ejpam-3907	8	6	)	)	PUNCT
ejpam-3907	8	7	be	be	AUX
ejpam-3907	8	8	finite	finite	ADJ
ejpam-3907	8	9	fields	field	NOUN
ejpam-3907	8	10	with	with	ADP
ejpam-3907	8	11	q	q	NOUN
ejpam-3907	8	12	=	=	PUNCT
ejpam-3907	8	13	pm	pm	NOUN
ejpam-3907	8	14	elements	element	NOUN
ejpam-3907	8	15	,	,	PUNCT
ejpam-3907	8	16	where	where	SCONJ
ejpam-3907	8	17	p	p	NOUN
ejpam-3907	8	18	is	be	AUX
ejpam-3907	8	19	prime	prime	ADJ
ejpam-3907	8	20	and	and	CCONJ
ejpam-3907	8	21	m	m	PRON
ejpam-3907	8	22	≥	≥	NOUN
ejpam-3907	8	23	1	1	NUM
ejpam-3907	8	24	.	.	X
ejpam-3907	9	1	consider	consider	VERB
ejpam-3907	9	2	(	(	PUNCT
ejpam-3907	9	3	gf	gf	X
ejpam-3907	9	4	(	(	PUNCT
ejpam-3907	9	5	q))n	q))n	VERB
ejpam-3907	9	6	as	as	ADP
ejpam-3907	9	7	a	a	DET
ejpam-3907	9	8	vector	vector	NOUN
ejpam-3907	9	9	space	space	NOUN
ejpam-3907	9	10	over	over	ADP
ejpam-3907	9	11	gf	gf	PROPN
ejpam-3907	9	12	(	(	PUNCT
ejpam-3907	9	13	q	q	NOUN
ejpam-3907	9	14	)	)	PUNCT
ejpam-3907	9	15	.	.	PUNCT
ejpam-3907	10	1	a	a	DET
ejpam-3907	10	2	q	q	ADJ
ejpam-3907	10	3	-	-	NOUN
ejpam-3907	10	4	ary	ary	NOUN
ejpam-3907	10	5	[	[	X
ejpam-3907	10	6	n	n	CCONJ
ejpam-3907	10	7	,	,	PUNCT
ejpam-3907	10	8	k	k	NOUN
ejpam-3907	10	9	,	,	PUNCT
ejpam-3907	10	10	d]-linear	d]-linear	ADJ
ejpam-3907	10	11	code	code	PROPN
ejpam-3907	10	12	c	c	PROPN
ejpam-3907	10	13	is	be	AUX
ejpam-3907	10	14	a	a	DET
ejpam-3907	10	15	k	k	ADJ
ejpam-3907	10	16	-	-	ADJ
ejpam-3907	10	17	dimensional	dimensional	ADJ
ejpam-3907	10	18	subspace	subspace	NOUN
ejpam-3907	10	19	of	of	ADP
ejpam-3907	10	20	(	(	PUNCT
ejpam-3907	10	21	gf	gf	X
ejpam-3907	10	22	(	(	PUNCT
ejpam-3907	10	23	q))n	q))n	VERB
ejpam-3907	10	24	with	with	ADP
ejpam-3907	10	25	the	the	DET
ejpam-3907	10	26	minimum	minimum	ADJ
ejpam-3907	10	27	nonzero	nonzero	PROPN
ejpam-3907	10	28	weight	weight	PROPN
ejpam-3907	10	29	d.	d.	PROPN
ejpam-3907	10	30	a	a	DET
ejpam-3907	10	31	linear	linear	PROPN
ejpam-3907	10	32	code	code	NOUN
ejpam-3907	10	33	c	c	NOUN
ejpam-3907	10	34	over	over	ADP
ejpam-3907	10	35	the	the	DET
ejpam-3907	10	36	finite	finite	ADJ
ejpam-3907	10	37	field	field	NOUN
ejpam-3907	10	38	gf	gf	X
ejpam-3907	10	39	(	(	PUNCT
ejpam-3907	10	40	q	q	X
ejpam-3907	10	41	)	)	PUNCT
ejpam-3907	10	42	is	be	AUX
ejpam-3907	10	43	said	say	VERB
ejpam-3907	10	44	to	to	PART
ejpam-3907	10	45	be	be	AUX
ejpam-3907	10	46	cyclic	cyclic	ADJ
ejpam-3907	10	47	if	if	SCONJ
ejpam-3907	10	48	any	any	DET
ejpam-3907	10	49	(	(	PUNCT
ejpam-3907	10	50	c0	c0	NOUN
ejpam-3907	10	51	,	,	PUNCT
ejpam-3907	10	52	c1	c1	PROPN
ejpam-3907	10	53	,	,	PUNCT
ejpam-3907	10	54	.	.	PUNCT
ejpam-3907	10	55	.	.	PUNCT
ejpam-3907	11	1	.	.	PUNCT
ejpam-3907	12	1	,	,	PUNCT
ejpam-3907	12	2	cn−1	cn−1	X
ejpam-3907	12	3	)	)	PUNCT
ejpam-3907	12	4	∈	∈	PROPN
ejpam-3907	12	5	c	c	NOUN
ejpam-3907	12	6	implies	imply	VERB
ejpam-3907	12	7	(	(	PUNCT
ejpam-3907	12	8	cn−1	cn−1	PROPN
ejpam-3907	12	9	,	,	PUNCT
ejpam-3907	12	10	c0	c0	NOUN
ejpam-3907	12	11	,	,	PUNCT
ejpam-3907	12	12	.	.	PUNCT
ejpam-3907	12	13	.	.	PUNCT
ejpam-3907	13	1	.	.	PUNCT
ejpam-3907	14	1	,	,	PUNCT
ejpam-3907	14	2	cn−2	cn−2	PROPN
ejpam-3907	14	3	)	)	PUNCT
ejpam-3907	14	4	∈	∈	PROPN
ejpam-3907	14	5	c.	c.	NOUN
ejpam-3907	14	6	a	a	DET
ejpam-3907	14	7	word	word	NOUN
ejpam-3907	15	1	c	c	NOUN
ejpam-3907	15	2	=	=	SYM
ejpam-3907	15	3	(	(	PUNCT
ejpam-3907	15	4	c0	c0	PROPN
ejpam-3907	15	5	,	,	PUNCT
ejpam-3907	15	6	c1	c1	PROPN
ejpam-3907	15	7	,	,	PUNCT
ejpam-3907	15	8	...	...	PUNCT
ejpam-3907	15	9	,	,	PUNCT
ejpam-3907	15	10	cn−1	cn−1	PROPN
ejpam-3907	15	11	)	)	PUNCT
ejpam-3907	15	12	in	in	ADP
ejpam-3907	15	13	c	c	NOUN
ejpam-3907	15	14	can	can	AUX
ejpam-3907	15	15	be	be	AUX
ejpam-3907	15	16	represented	represent	VERB
ejpam-3907	15	17	as	as	ADP
ejpam-3907	15	18	a	a	DET
ejpam-3907	15	19	polynomial	polynomial	ADJ
ejpam-3907	15	20	c(x	c(x	NOUN
ejpam-3907	15	21	)	)	PUNCT
ejpam-3907	15	22	=	=	SYM
ejpam-3907	15	23	c0	c0	NOUN
ejpam-3907	15	24	+	+	CCONJ
ejpam-3907	15	25	c1x	c1x	PROPN
ejpam-3907	15	26	+	+	X
ejpam-3907	15	27	...	...	PUNCT
ejpam-3907	16	1	+	+	CCONJ
ejpam-3907	16	2	cn−1x	cn−1x	NUM
ejpam-3907	16	3	n−1	n−1	PROPN
ejpam-3907	16	4	in	in	ADP
ejpam-3907	16	5	ring	ring	PROPN
ejpam-3907	16	6	rn	rn	PROPN
ejpam-3907	16	7	=	=	PRON
ejpam-3907	16	8	gf	gf	PROPN
ejpam-3907	16	9	(	(	PUNCT
ejpam-3907	16	10	q)[x]/〈xn	q)[x]/〈xn	PROPN
ejpam-3907	16	11	−	−	PROPN
ejpam-3907	16	12	1	1	NUM
ejpam-3907	16	13	〉	〉	NUM
ejpam-3907	16	14	.	.	PUNCT
ejpam-3907	17	1	so	so	ADV
ejpam-3907	17	2	that	that	SCONJ
ejpam-3907	17	3	c	c	PROPN
ejpam-3907	17	4	⊆	⊆	NUM
ejpam-3907	17	5	(	(	PUNCT
ejpam-3907	17	6	gf	gf	X
ejpam-3907	17	7	(	(	PUNCT
ejpam-3907	17	8	q))n	q))n	NOUN
ejpam-3907	17	9	can	can	AUX
ejpam-3907	17	10	be	be	AUX
ejpam-3907	17	11	identified	identify	VERB
ejpam-3907	17	12	by	by	ADP
ejpam-3907	17	13	a	a	DET
ejpam-3907	17	14	subset	subset	NOUN
ejpam-3907	17	15	of	of	ADP
ejpam-3907	17	16	rn	rn	PROPN
ejpam-3907	17	17	,	,	PUNCT
ejpam-3907	17	18	in	in	ADP
ejpam-3907	17	19	this	this	DET
ejpam-3907	17	20	case	case	NOUN
ejpam-3907	17	21	the	the	DET
ejpam-3907	17	22	cyclic	cyclic	PROPN
ejpam-3907	17	23	code	code	NOUN
ejpam-3907	17	24	is	be	AUX
ejpam-3907	17	25	an	an	DET
ejpam-3907	17	26	ideal	ideal	NOUN
ejpam-3907	17	27	of	of	ADP
ejpam-3907	17	28	rn	rn	PROPN
ejpam-3907	17	29	.	.	PUNCT
ejpam-3907	18	1	any	any	DET
ejpam-3907	18	2	ideal	ideal	NOUN
ejpam-3907	18	3	of	of	ADP
ejpam-3907	18	4	rn	rn	PROPN
ejpam-3907	18	5	is	be	AUX
ejpam-3907	18	6	principal	principal	ADJ
ejpam-3907	18	7	,	,	PUNCT
ejpam-3907	18	8	so	so	SCONJ
ejpam-3907	18	9	that	that	SCONJ
ejpam-3907	18	10	it	it	PRON
ejpam-3907	18	11	is	be	AUX
ejpam-3907	18	12	generated	generate	VERB
ejpam-3907	18	13	by	by	ADP
ejpam-3907	18	14	a	a	DET
ejpam-3907	18	15	polynomial	polynomial	ADJ
ejpam-3907	18	16	g(x	g(x	NOUN
ejpam-3907	18	17	)	)	PUNCT
ejpam-3907	18	18	,	,	PUNCT
ejpam-3907	18	19	where	where	SCONJ
ejpam-3907	18	20	g(x	g(x	NOUN
ejpam-3907	18	21	)	)	PUNCT
ejpam-3907	18	22	is	be	AUX
ejpam-3907	18	23	a	a	DET
ejpam-3907	18	24	divisor	divisor	NOUN
ejpam-3907	18	25	of	of	ADP
ejpam-3907	18	26	xn	xn	PROPN
ejpam-3907	19	1	−	−	PROPN
ejpam-3907	19	2	1	1	NUM
ejpam-3907	19	3	.	.	PUNCT
ejpam-3907	20	1	the	the	DET
ejpam-3907	20	2	polynomial	polynomial	ADJ
ejpam-3907	20	3	g	g	PROPN
ejpam-3907	20	4	is	be	AUX
ejpam-3907	20	5	called	call	VERB
ejpam-3907	20	6	generator	generator	NOUN
ejpam-3907	20	7	of	of	ADP
ejpam-3907	20	8	the	the	DET
ejpam-3907	20	9	cyclic	cyclic	PROPN
ejpam-3907	20	10	code	code	PROPN
ejpam-3907	20	11	c.	c.	NOUN
ejpam-3907	20	12	the	the	DET
ejpam-3907	20	13	dimension	dimension	NOUN
ejpam-3907	20	14	of	of	ADP
ejpam-3907	20	15	cyclic	cyclic	PROPN
ejpam-3907	20	16	code	code	NOUN
ejpam-3907	20	17	c	c	NOUN
ejpam-3907	20	18	can	can	AUX
ejpam-3907	20	19	be	be	AUX
ejpam-3907	20	20	determined	determine	VERB
ejpam-3907	20	21	from	from	ADP
ejpam-3907	20	22	degree	degree	NOUN
ejpam-3907	20	23	of	of	ADP
ejpam-3907	21	1	generator	generator	NOUN
ejpam-3907	21	2	polynomial	polynomial	PROPN
ejpam-3907	21	3	g.	g.	PROPN
ejpam-3907	22	1	the	the	DET
ejpam-3907	22	2	error	error	NOUN
ejpam-3907	22	3	-	-	PUNCT
ejpam-3907	22	4	correcting	correct	VERB
ejpam-3907	22	5	capability	capability	NOUN
ejpam-3907	22	6	of	of	ADP
ejpam-3907	22	7	cyclic	cyclic	ADJ
ejpam-3907	22	8	codes	code	NOUN
ejpam-3907	22	9	may	may	AUX
ejpam-3907	22	10	not	not	PART
ejpam-3907	22	11	be	be	AUX
ejpam-3907	22	12	as	as	ADV
ejpam-3907	22	13	good	good	ADJ
ejpam-3907	22	14	as	as	ADP
ejpam-3907	22	15	some	some	DET
ejpam-3907	22	16	other	other	ADJ
ejpam-3907	22	17	linear	linear	ADJ
ejpam-3907	22	18	codes	code	NOUN
ejpam-3907	22	19	in	in	ADP
ejpam-3907	22	20	general	general	ADJ
ejpam-3907	22	21	.	.	PUNCT
ejpam-3907	23	1	however	however	ADV
ejpam-3907	23	2	,	,	PUNCT
ejpam-3907	23	3	cyclic	cyclic	ADJ
ejpam-3907	23	4	codes	code	NOUN
ejpam-3907	23	5	are	be	AUX
ejpam-3907	23	6	widely	widely	ADV
ejpam-3907	23	7	used	use	VERB
ejpam-3907	23	8	in	in	ADP
ejpam-3907	23	9	many	many	ADJ
ejpam-3907	23	10	fields	field	NOUN
ejpam-3907	23	11	such	such	ADJ
ejpam-3907	23	12	as	as	ADP
ejpam-3907	23	13	data	data	NOUN
ejpam-3907	23	14	storage	storage	NOUN
ejpam-3907	23	15	∗corresponding	∗corresponde	VERB
ejpam-3907	23	16	author	author	NOUN
ejpam-3907	23	17	.	.	PUNCT
ejpam-3907	24	1	doi	doi	NOUN
ejpam-3907	24	2	:	:	PUNCT
ejpam-3907	24	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3907	https://doi.org/10.29020/nybg.ejpam.v14i3.3907	PROPN
ejpam-3907	24	4	email	email	NOUN
ejpam-3907	24	5	addresses	address	NOUN
ejpam-3907	24	6	:	:	PUNCT
ejpam-3907	25	1	nopendri301@s.itb.ac.id	nopendri301@s.itb.ac.id	NOUN
ejpam-3907	25	2	(	(	PUNCT
ejpam-3907	25	3	nopendri	nopendri	PROPN
ejpam-3907	25	4	)	)	PUNCT
ejpam-3907	25	5	,	,	PUNCT
ejpam-3907	25	6	ntan@math.itb.ac.id	ntan@math.itb.ac.id	PROPN
ejpam-3907	25	7	(	(	PUNCT
ejpam-3907	25	8	i.m.alamsyah	i.m.alamsyah	NOUN
ejpam-3907	25	9	)	)	PUNCT
ejpam-3907	25	10	,	,	PUNCT
ejpam-3907	25	11	djoko@math.itb.ac.id	djoko@math.itb.ac.id	PROPN
ejpam-3907	25	12	(	(	PUNCT
ejpam-3907	25	13	d.suprijanto),barra@math.itb.ac.id	d.suprijanto),barra@math.itb.ac.id	X
ejpam-3907	25	14	(	(	PUNCT
ejpam-3907	25	15	a.	a.	NOUN
ejpam-3907	25	16	barra	barra	PROPN
ejpam-3907	25	17	)	)	PUNCT
ejpam-3907	25	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3907	26	1	685	685	NUM
ejpam-3907	26	2	©	©	PROPN
ejpam-3907	26	3	2021	2021	NUM
ejpam-3907	26	4	ejpam	ejpam	VERB
ejpam-3907	26	5	all	all	DET
ejpam-3907	26	6	rights	right	NOUN
ejpam-3907	26	7	reserved	reserve	VERB
ejpam-3907	26	8	.	.	PUNCT
ejpam-3907	27	1	nopendri	nopendri	PROPN
ejpam-3907	27	2	et	et	PROPN
ejpam-3907	27	3	al	al	PROPN
ejpam-3907	27	4	.	.	PUNCT
ejpam-3907	27	5	/	/	SYM
ejpam-3907	27	6	eur	eur	PROPN
ejpam-3907	27	7	.	.	PUNCT
ejpam-3907	28	1	j.	j.	PROPN
ejpam-3907	28	2	pure	pure	PROPN
ejpam-3907	28	3	appl	appl	PROPN
ejpam-3907	28	4	.	.	PROPN
ejpam-3907	28	5	math	math	PROPN
ejpam-3907	28	6	,	,	PUNCT
ejpam-3907	28	7	14	14	NUM
ejpam-3907	28	8	(	(	PUNCT
ejpam-3907	28	9	3	3	NUM
ejpam-3907	28	10	)	)	PUNCT
ejpam-3907	28	11	(	(	PUNCT
ejpam-3907	28	12	2021	2021	NUM
ejpam-3907	28	13	)	)	PUNCT
ejpam-3907	28	14	,	,	PUNCT
ejpam-3907	28	15	685	685	NUM
ejpam-3907	28	16	-	-	SYM
ejpam-3907	28	17	694	694	NUM
ejpam-3907	28	18	686	686	NUM
ejpam-3907	28	19	and	and	CCONJ
ejpam-3907	28	20	communication	communication	NOUN
ejpam-3907	28	21	systems	system	NOUN
ejpam-3907	28	22	because	because	SCONJ
ejpam-3907	28	23	they	they	PRON
ejpam-3907	28	24	have	have	VERB
ejpam-3907	28	25	attractive	attractive	ADJ
ejpam-3907	28	26	algebraic	algebraic	ADJ
ejpam-3907	28	27	properties	property	NOUN
ejpam-3907	28	28	and	and	CCONJ
ejpam-3907	28	29	have	have	VERB
ejpam-3907	28	30	efficient	efficient	ADJ
ejpam-3907	28	31	algorithms	algorithm	NOUN
ejpam-3907	28	32	for	for	ADP
ejpam-3907	28	33	encoding	encode	VERB
ejpam-3907	28	34	and	and	CCONJ
ejpam-3907	28	35	decoding	decode	VERB
ejpam-3907	28	36	[	[	PUNCT
ejpam-3907	28	37	2	2	NUM
ejpam-3907	28	38	,	,	PUNCT
ejpam-3907	28	39	7	7	NUM
ejpam-3907	28	40	,	,	PUNCT
ejpam-3907	28	41	11	11	NUM
ejpam-3907	28	42	]	]	PUNCT
ejpam-3907	28	43	.	.	PUNCT
ejpam-3907	29	1	this	this	DET
ejpam-3907	29	2	code	code	NOUN
ejpam-3907	29	3	is	be	AUX
ejpam-3907	29	4	also	also	ADV
ejpam-3907	29	5	used	use	VERB
ejpam-3907	29	6	to	to	PART
ejpam-3907	29	7	construct	construct	VERB
ejpam-3907	29	8	impressive	impressive	ADJ
ejpam-3907	29	9	structures	structure	NOUN
ejpam-3907	29	10	such	such	ADJ
ejpam-3907	29	11	as	as	ADP
ejpam-3907	29	12	quantum	quantum	NOUN
ejpam-3907	29	13	codes	code	NOUN
ejpam-3907	29	14	[	[	X
ejpam-3907	29	15	18	18	NUM
ejpam-3907	29	16	]	]	PUNCT
ejpam-3907	29	17	,	,	PUNCT
ejpam-3907	29	18	frequency	frequency	NOUN
ejpam-3907	29	19	hopping	hop	VERB
ejpam-3907	29	20	sequences	sequence	NOUN
ejpam-3907	30	1	[	[	X
ejpam-3907	30	2	5	5	NUM
ejpam-3907	30	3	]	]	PUNCT
ejpam-3907	30	4	and	and	CCONJ
ejpam-3907	30	5	so	so	ADV
ejpam-3907	30	6	on	on	ADV
ejpam-3907	30	7	.	.	PUNCT
ejpam-3907	31	1	one	one	NUM
ejpam-3907	31	2	of	of	ADP
ejpam-3907	31	3	the	the	DET
ejpam-3907	31	4	main	main	ADJ
ejpam-3907	31	5	problems	problem	NOUN
ejpam-3907	31	6	in	in	ADP
ejpam-3907	31	7	coding	code	VERB
ejpam-3907	31	8	theory	theory	NOUN
ejpam-3907	31	9	research	research	NOUN
ejpam-3907	31	10	is	be	AUX
ejpam-3907	31	11	finding	find	VERB
ejpam-3907	31	12	the	the	DET
ejpam-3907	31	13	optimal	optimal	ADJ
ejpam-3907	31	14	code	code	NOUN
ejpam-3907	31	15	,	,	PUNCT
ejpam-3907	31	16	which	which	PRON
ejpam-3907	31	17	is	be	AUX
ejpam-3907	31	18	the	the	DET
ejpam-3907	31	19	code	code	NOUN
ejpam-3907	31	20	that	that	PRON
ejpam-3907	31	21	has	have	VERB
ejpam-3907	31	22	the	the	DET
ejpam-3907	31	23	largest	large	ADJ
ejpam-3907	31	24	minimum	minimum	ADJ
ejpam-3907	31	25	distance	distance	NOUN
ejpam-3907	31	26	d	d	PROPN
ejpam-3907	31	27	related	relate	VERB
ejpam-3907	31	28	to	to	ADP
ejpam-3907	31	29	the	the	DET
ejpam-3907	31	30	ability	ability	NOUN
ejpam-3907	31	31	to	to	PART
ejpam-3907	31	32	correct	correct	VERB
ejpam-3907	31	33	errors	error	NOUN
ejpam-3907	31	34	in	in	ADP
ejpam-3907	31	35	the	the	DET
ejpam-3907	31	36	information	information	NOUN
ejpam-3907	31	37	transfer	transfer	NOUN
ejpam-3907	31	38	or	or	CCONJ
ejpam-3907	31	39	meets	meet	VERB
ejpam-3907	31	40	some	some	DET
ejpam-3907	31	41	bounds	bound	NOUN
ejpam-3907	31	42	from	from	ADP
ejpam-3907	31	43	the	the	DET
ejpam-3907	31	44	best	well	ADV
ejpam-3907	31	45	known	know	VERB
ejpam-3907	31	46	linear	linear	PROPN
ejpam-3907	31	47	code	code	NOUN
ejpam-3907	31	48	according	accord	VERB
ejpam-3907	31	49	to	to	ADP
ejpam-3907	31	50	the	the	DET
ejpam-3907	31	51	tables	table	NOUN
ejpam-3907	31	52	[	[	X
ejpam-3907	31	53	8	8	NUM
ejpam-3907	31	54	]	]	PUNCT
ejpam-3907	31	55	.	.	PUNCT
ejpam-3907	32	1	the	the	DET
ejpam-3907	32	2	cyclic	cyclic	PROPN
ejpam-3907	32	3	code	code	NOUN
ejpam-3907	32	4	can	can	AUX
ejpam-3907	32	5	be	be	AUX
ejpam-3907	32	6	constructed	construct	VERB
ejpam-3907	32	7	from	from	ADP
ejpam-3907	32	8	a	a	DET
ejpam-3907	32	9	periodic	periodic	ADJ
ejpam-3907	32	10	sequence	sequence	NOUN
ejpam-3907	32	11	s	s	PART
ejpam-3907	32	12	[	[	X
ejpam-3907	32	13	3	3	NUM
ejpam-3907	32	14	,	,	PUNCT
ejpam-3907	32	15	6	6	NUM
ejpam-3907	32	16	]	]	PUNCT
ejpam-3907	32	17	.	.	PUNCT
ejpam-3907	33	1	these	these	DET
ejpam-3907	33	2	sequences	sequence	NOUN
ejpam-3907	33	3	are	be	AUX
ejpam-3907	33	4	generated	generate	VERB
ejpam-3907	33	5	from	from	ADP
ejpam-3907	33	6	a	a	DET
ejpam-3907	33	7	function	function	NOUN
ejpam-3907	33	8	over	over	ADP
ejpam-3907	33	9	a	a	DET
ejpam-3907	33	10	finite	finite	ADJ
ejpam-3907	33	11	field	field	NOUN
ejpam-3907	33	12	.	.	PUNCT
ejpam-3907	34	1	for	for	ADP
ejpam-3907	34	2	simplicity	simplicity	NOUN
ejpam-3907	34	3	,	,	PUNCT
ejpam-3907	34	4	we	we	PRON
ejpam-3907	34	5	call	call	VERB
ejpam-3907	34	6	this	this	DET
ejpam-3907	34	7	cyclic	cyclic	ADJ
ejpam-3907	34	8	code	code	NOUN
ejpam-3907	34	9	as	as	ADP
ejpam-3907	34	10	cs	cs	PROPN
ejpam-3907	34	11	.	.	PUNCT
ejpam-3907	34	12	the	the	DET
ejpam-3907	34	13	results	result	NOUN
ejpam-3907	34	14	of	of	ADP
ejpam-3907	34	15	ding	ding	NOUN
ejpam-3907	34	16	and	and	CCONJ
ejpam-3907	34	17	zhou	zhou	PROPN
ejpam-3907	34	18	’s	’s	PART
ejpam-3907	34	19	constructions	construction	NOUN
ejpam-3907	34	20	in	in	ADP
ejpam-3907	34	21	papers	paper	NOUN
ejpam-3907	34	22	[	[	X
ejpam-3907	34	23	3	3	X
ejpam-3907	34	24	]	]	PUNCT
ejpam-3907	34	25	and	and	CCONJ
ejpam-3907	34	26	[	[	X
ejpam-3907	34	27	6	6	NUM
ejpam-3907	34	28	]	]	PUNCT
ejpam-3907	34	29	are	be	AUX
ejpam-3907	34	30	interesting	interesting	ADJ
ejpam-3907	34	31	,	,	PUNCT
ejpam-3907	34	32	showing	show	VERB
ejpam-3907	34	33	that	that	SCONJ
ejpam-3907	34	34	the	the	DET
ejpam-3907	34	35	codes	code	NOUN
ejpam-3907	34	36	obtained	obtain	VERB
ejpam-3907	34	37	are	be	AUX
ejpam-3907	34	38	optimal	optimal	ADJ
ejpam-3907	34	39	.	.	PUNCT
ejpam-3907	35	1	several	several	ADJ
ejpam-3907	35	2	open	open	ADJ
ejpam-3907	35	3	problems	problem	NOUN
ejpam-3907	35	4	are	be	AUX
ejpam-3907	35	5	presented	present	VERB
ejpam-3907	35	6	in	in	ADP
ejpam-3907	35	7	these	these	DET
ejpam-3907	35	8	papers	paper	NOUN
ejpam-3907	35	9	[	[	X
ejpam-3907	35	10	3	3	NUM
ejpam-3907	35	11	,	,	PUNCT
ejpam-3907	35	12	6	6	NUM
ejpam-3907	35	13	]	]	PUNCT
ejpam-3907	35	14	.	.	PUNCT
ejpam-3907	36	1	some	some	DET
ejpam-3907	36	2	researchers	researcher	NOUN
ejpam-3907	36	3	have	have	AUX
ejpam-3907	36	4	solved	solve	VERB
ejpam-3907	36	5	the	the	DET
ejpam-3907	36	6	problems	problem	NOUN
ejpam-3907	36	7	,	,	PUNCT
ejpam-3907	36	8	see	see	VERB
ejpam-3907	36	9	[	[	X
ejpam-3907	36	10	12	12	NUM
ejpam-3907	36	11	,	,	PUNCT
ejpam-3907	36	12	14	14	NUM
ejpam-3907	36	13	,	,	PUNCT
ejpam-3907	36	14	16	16	NUM
ejpam-3907	36	15	,	,	PUNCT
ejpam-3907	36	16	17	17	NUM
ejpam-3907	36	17	]	]	PUNCT
ejpam-3907	36	18	.	.	PUNCT
ejpam-3907	37	1	finding	find	VERB
ejpam-3907	37	2	the	the	DET
ejpam-3907	37	3	dimension	dimension	NOUN
ejpam-3907	37	4	and	and	CCONJ
ejpam-3907	37	5	the	the	DET
ejpam-3907	37	6	generator	generator	NOUN
ejpam-3907	37	7	polynomial	polynomial	NOUN
ejpam-3907	37	8	of	of	ADP
ejpam-3907	37	9	cyclic	cyclic	PROPN
ejpam-3907	37	10	codes	code	NOUN
ejpam-3907	37	11	cs	cs	PROPN
ejpam-3907	37	12	from	from	ADP
ejpam-3907	37	13	monomial	monomial	ADJ
ejpam-3907	37	14	f(x	f(x	PROPN
ejpam-3907	37	15	)	)	PUNCT
ejpam-3907	38	1	=	=	PUNCT
ejpam-3907	38	2	xq	xq	PROPN
ejpam-3907	38	3	m−2	m−2	PROPN
ejpam-3907	38	4	∈	∈	PROPN
ejpam-3907	38	5	gf	gf	X
ejpam-3907	38	6	(	(	PUNCT
ejpam-3907	38	7	qm)[x	qm)[x	ADV
ejpam-3907	38	8	]	]	PUNCT
ejpam-3907	38	9	appear	appear	VERB
ejpam-3907	38	10	as	as	ADP
ejpam-3907	38	11	an	an	DET
ejpam-3907	38	12	open	open	ADJ
ejpam-3907	38	13	problem	problem	NOUN
ejpam-3907	38	14	in	in	ADP
ejpam-3907	38	15	[	[	X
ejpam-3907	38	16	3	3	NUM
ejpam-3907	38	17	]	]	PUNCT
ejpam-3907	38	18	,	,	PUNCT
ejpam-3907	38	19	and	and	CCONJ
ejpam-3907	38	20	solved	solve	VERB
ejpam-3907	38	21	by	by	ADP
ejpam-3907	38	22	[	[	X
ejpam-3907	38	23	17	17	NUM
ejpam-3907	38	24	]	]	PUNCT
ejpam-3907	38	25	then	then	ADV
ejpam-3907	38	26	.	.	PUNCT
ejpam-3907	39	1	however	however	ADV
ejpam-3907	39	2	,	,	PUNCT
ejpam-3907	39	3	differing	differ	VERB
ejpam-3907	39	4	sequences	sequence	NOUN
ejpam-3907	39	5	provide	provide	VERB
ejpam-3907	39	6	some	some	DET
ejpam-3907	39	7	different	different	ADJ
ejpam-3907	39	8	results	result	NOUN
ejpam-3907	39	9	.	.	PUNCT
ejpam-3907	40	1	in	in	ADP
ejpam-3907	40	2	this	this	DET
ejpam-3907	40	3	paper	paper	NOUN
ejpam-3907	40	4	,	,	PUNCT
ejpam-3907	40	5	we	we	PRON
ejpam-3907	40	6	discuss	discuss	VERB
ejpam-3907	40	7	the	the	DET
ejpam-3907	40	8	construction	construction	NOUN
ejpam-3907	40	9	of	of	ADP
ejpam-3907	40	10	the	the	DET
ejpam-3907	40	11	cyclic	cyclic	PROPN
ejpam-3907	40	12	code	code	NOUN
ejpam-3907	40	13	with	with	ADP
ejpam-3907	40	14	the	the	DET
ejpam-3907	40	15	new	new	ADJ
ejpam-3907	40	16	sequence	sequence	NOUN
ejpam-3907	40	17	,	,	PUNCT
ejpam-3907	40	18	and	and	CCONJ
ejpam-3907	40	19	we	we	PRON
ejpam-3907	40	20	say	say	VERB
ejpam-3907	40	21	that	that	SCONJ
ejpam-3907	40	22	“	"	PUNCT
ejpam-3907	40	23	sequence	sequence	NOUN
ejpam-3907	40	24	š	š	PROPN
ejpam-3907	40	25	”	"	PUNCT
ejpam-3907	40	26	,	,	PUNCT
ejpam-3907	40	27	from	from	ADP
ejpam-3907	40	28	the	the	DET
ejpam-3907	40	29	monomial	monomial	ADJ
ejpam-3907	40	30	f(x	f(x	PROPN
ejpam-3907	40	31	)	)	PUNCT
ejpam-3907	40	32	.	.	PUNCT
ejpam-3907	41	1	this	this	DET
ejpam-3907	41	2	construction	construction	NOUN
ejpam-3907	41	3	will	will	AUX
ejpam-3907	41	4	generate	generate	VERB
ejpam-3907	41	5	a	a	DET
ejpam-3907	41	6	new	new	ADJ
ejpam-3907	41	7	cyclic	cyclic	ADJ
ejpam-3907	41	8	code	code	NOUN
ejpam-3907	41	9	related	relate	VERB
ejpam-3907	41	10	to	to	ADP
ejpam-3907	41	11	the	the	DET
ejpam-3907	41	12	code	code	NOUN
ejpam-3907	41	13	from	from	ADP
ejpam-3907	41	14	the	the	DET
ejpam-3907	41	15	sequence	sequence	NOUN
ejpam-3907	41	16	s.	s.	PROPN
ejpam-3907	41	17	we	we	PRON
ejpam-3907	41	18	also	also	ADV
ejpam-3907	41	19	add	add	VERB
ejpam-3907	41	20	information	information	NOUN
ejpam-3907	41	21	about	about	ADP
ejpam-3907	41	22	the	the	DET
ejpam-3907	41	23	minimum	minimum	ADJ
ejpam-3907	41	24	distance	distance	NOUN
ejpam-3907	41	25	of	of	ADP
ejpam-3907	41	26	the	the	DET
ejpam-3907	41	27	code	code	NOUN
ejpam-3907	41	28	.	.	PUNCT
ejpam-3907	42	1	this	this	DET
ejpam-3907	42	2	paper	paper	NOUN
ejpam-3907	42	3	is	be	AUX
ejpam-3907	42	4	organized	organize	VERB
ejpam-3907	42	5	as	as	SCONJ
ejpam-3907	42	6	follows	follow	VERB
ejpam-3907	42	7	.	.	PUNCT
ejpam-3907	43	1	section	section	NOUN
ejpam-3907	43	2	2	2	NUM
ejpam-3907	43	3	introduces	introduce	VERB
ejpam-3907	43	4	some	some	DET
ejpam-3907	43	5	basic	basic	ADJ
ejpam-3907	43	6	notation	notation	NOUN
ejpam-3907	43	7	and	and	CCONJ
ejpam-3907	43	8	results	result	NOUN
ejpam-3907	43	9	about	about	ADP
ejpam-3907	43	10	q	q	ADJ
ejpam-3907	43	11	-	-	PUNCT
ejpam-3907	43	12	cyclotomic	cyclotomic	ADJ
ejpam-3907	43	13	cosets	coset	NOUN
ejpam-3907	43	14	and	and	CCONJ
ejpam-3907	43	15	sequences	sequence	NOUN
ejpam-3907	43	16	that	that	PRON
ejpam-3907	43	17	will	will	AUX
ejpam-3907	43	18	frequently	frequently	ADV
ejpam-3907	43	19	be	be	AUX
ejpam-3907	43	20	used	use	VERB
ejpam-3907	43	21	to	to	PART
ejpam-3907	43	22	prove	prove	VERB
ejpam-3907	43	23	our	our	PRON
ejpam-3907	43	24	main	main	ADJ
ejpam-3907	43	25	results	result	NOUN
ejpam-3907	43	26	in	in	ADP
ejpam-3907	43	27	the	the	DET
ejpam-3907	43	28	following	follow	VERB
ejpam-3907	43	29	sections	section	NOUN
ejpam-3907	43	30	.	.	PUNCT
ejpam-3907	44	1	the	the	DET
ejpam-3907	44	2	dimension	dimension	NOUN
ejpam-3907	44	3	and	and	CCONJ
ejpam-3907	44	4	the	the	DET
ejpam-3907	44	5	generator	generator	NOUN
ejpam-3907	44	6	polynomial	polynomial	NOUN
ejpam-3907	44	7	of	of	ADP
ejpam-3907	44	8	a	a	DET
ejpam-3907	44	9	class	class	NOUN
ejpam-3907	44	10	of	of	ADP
ejpam-3907	44	11	cyclic	cyclic	ADJ
ejpam-3907	44	12	codes	code	NOUN
ejpam-3907	44	13	defined	define	VERB
ejpam-3907	44	14	by	by	ADP
ejpam-3907	44	15	a	a	DET
ejpam-3907	44	16	sequence	sequence	NOUN
ejpam-3907	44	17	are	be	AUX
ejpam-3907	44	18	determined	determine	VERB
ejpam-3907	44	19	in	in	ADP
ejpam-3907	44	20	section	section	NOUN
ejpam-3907	44	21	3	3	NUM
ejpam-3907	44	22	.	.	PUNCT
ejpam-3907	45	1	the	the	DET
ejpam-3907	45	2	minimum	minimum	ADJ
ejpam-3907	45	3	distance	distance	NOUN
ejpam-3907	45	4	of	of	ADP
ejpam-3907	45	5	this	this	DET
ejpam-3907	45	6	cyclic	cyclic	ADJ
ejpam-3907	45	7	code	code	NOUN
ejpam-3907	45	8	is	be	AUX
ejpam-3907	45	9	also	also	ADV
ejpam-3907	45	10	provided	provide	VERB
ejpam-3907	45	11	in	in	ADP
ejpam-3907	45	12	that	that	DET
ejpam-3907	45	13	section	section	NOUN
ejpam-3907	45	14	.	.	PUNCT
ejpam-3907	46	1	in	in	ADP
ejpam-3907	46	2	section	section	NOUN
ejpam-3907	46	3	4	4	NUM
ejpam-3907	46	4	,	,	PUNCT
ejpam-3907	46	5	we	we	PRON
ejpam-3907	46	6	conclude	conclude	VERB
ejpam-3907	46	7	this	this	DET
ejpam-3907	46	8	paper	paper	NOUN
ejpam-3907	46	9	.	.	PUNCT
ejpam-3907	47	1	2	2	X
ejpam-3907	47	2	.	.	X
ejpam-3907	47	3	preliminaries	preliminary	NOUN
ejpam-3907	47	4	in	in	ADP
ejpam-3907	47	5	this	this	DET
ejpam-3907	47	6	section	section	NOUN
ejpam-3907	47	7	,	,	PUNCT
ejpam-3907	47	8	some	some	DET
ejpam-3907	47	9	basic	basic	ADJ
ejpam-3907	47	10	notations	notation	NOUN
ejpam-3907	47	11	and	and	CCONJ
ejpam-3907	47	12	results	result	NOUN
ejpam-3907	47	13	on	on	ADP
ejpam-3907	47	14	q	q	ADJ
ejpam-3907	47	15	-	-	PUNCT
ejpam-3907	47	16	cyclotomic	cyclotomic	ADJ
ejpam-3907	47	17	cosets	coset	NOUN
ejpam-3907	47	18	modulo	modulo	VERB
ejpam-3907	47	19	n	n	ADP
ejpam-3907	47	20	and	and	CCONJ
ejpam-3907	47	21	sequences	sequence	NOUN
ejpam-3907	47	22	used	use	VERB
ejpam-3907	47	23	to	to	PART
ejpam-3907	47	24	prove	prove	VERB
ejpam-3907	47	25	the	the	DET
ejpam-3907	47	26	main	main	ADJ
ejpam-3907	47	27	result	result	NOUN
ejpam-3907	47	28	are	be	AUX
ejpam-3907	47	29	introduced	introduce	VERB
ejpam-3907	47	30	.	.	PUNCT
ejpam-3907	48	1	definition	definition	NOUN
ejpam-3907	48	2	1	1	NUM
ejpam-3907	48	3	.	.	PUNCT
ejpam-3907	49	1	let	let	VERB
ejpam-3907	49	2	n	n	NOUN
ejpam-3907	49	3	=	=	PUNCT
ejpam-3907	49	4	qm−1	qm−1	NOUN
ejpam-3907	49	5	and	and	CCONJ
ejpam-3907	49	6	zn	zn	NOUN
ejpam-3907	49	7	=	=	SYM
ejpam-3907	49	8	{	{	PUNCT
ejpam-3907	49	9	0	0	NUM
ejpam-3907	49	10	,	,	PUNCT
ejpam-3907	49	11	1	1	NUM
ejpam-3907	49	12	,	,	PUNCT
ejpam-3907	49	13	2	2	NUM
ejpam-3907	49	14	,	,	PUNCT
ejpam-3907	49	15	.	.	PUNCT
ejpam-3907	49	16	.	.	PUNCT
ejpam-3907	50	1	.	.	PUNCT
ejpam-3907	51	1	,	,	PUNCT
ejpam-3907	51	2	n−1	n−1	PROPN
ejpam-3907	51	3	}	}	PUNCT
ejpam-3907	51	4	.	.	PUNCT
ejpam-3907	52	1	for	for	ADP
ejpam-3907	52	2	any	any	DET
ejpam-3907	52	3	integer	integer	NOUN
ejpam-3907	52	4	s	s	NOUN
ejpam-3907	52	5	,	,	PUNCT
ejpam-3907	52	6	0	0	NUM
ejpam-3907	52	7	≤	≤	NUM
ejpam-3907	52	8	s	s	PART
ejpam-3907	52	9	≤	≤	PROPN
ejpam-3907	52	10	n−1	n−1	PROPN
ejpam-3907	52	11	,	,	PUNCT
ejpam-3907	52	12	the	the	DET
ejpam-3907	52	13	q	q	ADJ
ejpam-3907	52	14	-	-	PUNCT
ejpam-3907	52	15	cyclotomic	cyclotomic	ADJ
ejpam-3907	52	16	coset	coset	NOUN
ejpam-3907	52	17	modulo	modulo	NOUN
ejpam-3907	52	18	n	n	ADP
ejpam-3907	52	19	containing	contain	VERB
ejpam-3907	52	20	s	s	PRON
ejpam-3907	52	21	is	be	AUX
ejpam-3907	52	22	defined	define	VERB
ejpam-3907	52	23	by	by	ADP
ejpam-3907	52	24	cs	cs	PROPN
ejpam-3907	52	25	=	=	PUNCT
ejpam-3907	52	26	{	{	PUNCT
ejpam-3907	52	27	s	s	PROPN
ejpam-3907	52	28	,	,	PUNCT
ejpam-3907	52	29	qs	qs	ADP
ejpam-3907	52	30	,	,	PUNCT
ejpam-3907	52	31	q2s	q2s	PROPN
ejpam-3907	52	32	,	,	PUNCT
ejpam-3907	52	33	.	.	PUNCT
ejpam-3907	52	34	.	.	PUNCT
ejpam-3907	53	1	.	.	PUNCT
ejpam-3907	54	1	,	,	PUNCT
ejpam-3907	54	2	qls−1s	qls−1s	NUM
ejpam-3907	54	3	}	}	PUNCT
ejpam-3907	54	4	⊂	⊂	PROPN
ejpam-3907	54	5	zn	zn	PROPN
ejpam-3907	54	6	where	where	SCONJ
ejpam-3907	54	7	ls	ls	ADJ
ejpam-3907	54	8	is	be	AUX
ejpam-3907	54	9	the	the	DET
ejpam-3907	54	10	least	least	ADV
ejpam-3907	54	11	positive	positive	ADJ
ejpam-3907	54	12	integer	integer	NOUN
ejpam-3907	54	13	such	such	ADJ
ejpam-3907	54	14	that	that	SCONJ
ejpam-3907	54	15	qls	qls	PROPN
ejpam-3907	54	16	≡	≡	PROPN
ejpam-3907	54	17	s	s	PROPN
ejpam-3907	54	18	(	(	PUNCT
ejpam-3907	54	19	mod	mod	PROPN
ejpam-3907	54	20	n	n	CCONJ
ejpam-3907	54	21	)	)	PUNCT
ejpam-3907	54	22	and	and	CCONJ
ejpam-3907	54	23	ls	ls	PROPN
ejpam-3907	54	24	is	be	AUX
ejpam-3907	54	25	called	call	VERB
ejpam-3907	54	26	the	the	DET
ejpam-3907	54	27	size	size	NOUN
ejpam-3907	54	28	of	of	ADP
ejpam-3907	54	29	cs	cs	PROPN
ejpam-3907	54	30	.	.	PROPN
ejpam-3907	54	31	lemma	lemma	PROPN
ejpam-3907	54	32	1	1	NUM
ejpam-3907	54	33	.	.	PUNCT
ejpam-3907	55	1	[	[	X
ejpam-3907	55	2	9	9	NUM
ejpam-3907	55	3	]	]	PUNCT
ejpam-3907	55	4	let	let	VERB
ejpam-3907	55	5	q	q	PART
ejpam-3907	55	6	be	be	AUX
ejpam-3907	55	7	a	a	DET
ejpam-3907	55	8	power	power	NOUN
ejpam-3907	55	9	of	of	ADP
ejpam-3907	55	10	a	a	DET
ejpam-3907	55	11	prime	prime	ADJ
ejpam-3907	55	12	p	p	NOUN
ejpam-3907	55	13	and	and	CCONJ
ejpam-3907	55	14	n	n	NOUN
ejpam-3907	55	15	=	=	SYM
ejpam-3907	55	16	qm−	qm−	NUM
ejpam-3907	55	17	1	1	X
ejpam-3907	55	18	.	.	X
ejpam-3907	56	1	for	for	ADP
ejpam-3907	56	2	any	any	DET
ejpam-3907	56	3	1	1	NUM
ejpam-3907	56	4	≤	≤	NUM
ejpam-3907	56	5	s	s	PART
ejpam-3907	56	6	≤	≤	NUM
ejpam-3907	56	7	n−	n−	NOUN
ejpam-3907	56	8	1	1	NUM
ejpam-3907	56	9	with	with	ADP
ejpam-3907	56	10	gcd(s	gcd(s	PROPN
ejpam-3907	56	11	,	,	PUNCT
ejpam-3907	56	12	n	n	CCONJ
ejpam-3907	56	13	)	)	PUNCT
ejpam-3907	56	14	=	=	SYM
ejpam-3907	56	15	1	1	NUM
ejpam-3907	56	16	the	the	DET
ejpam-3907	56	17	length	length	NOUN
ejpam-3907	56	18	ls	ls	ADJ
ejpam-3907	56	19	of	of	ADP
ejpam-3907	56	20	the	the	DET
ejpam-3907	56	21	q	q	ADJ
ejpam-3907	56	22	-	-	PUNCT
ejpam-3907	56	23	cyclotomic	cyclotomic	ADJ
ejpam-3907	56	24	coset	coset	NOUN
ejpam-3907	56	25	cs	cs	PROPN
ejpam-3907	56	26	is	be	AUX
ejpam-3907	56	27	equal	equal	ADJ
ejpam-3907	56	28	to	to	ADP
ejpam-3907	56	29	m.	m.	NOUN
ejpam-3907	56	30	definition	definition	NOUN
ejpam-3907	56	31	2	2	NUM
ejpam-3907	56	32	.	.	PUNCT
ejpam-3907	57	1	let	let	VERB
ejpam-3907	57	2	s∞	s∞	VERB
ejpam-3907	57	3	=	=	SYM
ejpam-3907	57	4	(	(	PUNCT
ejpam-3907	57	5	st	st	PROPN
ejpam-3907	57	6	)	)	PUNCT
ejpam-3907	57	7	∞	∞	PROPN
ejpam-3907	57	8	t=0	t=0	PROPN
ejpam-3907	57	9	be	be	VERB
ejpam-3907	57	10	a	a	DET
ejpam-3907	57	11	sequence	sequence	NOUN
ejpam-3907	57	12	over	over	ADP
ejpam-3907	57	13	gf	gf	PROPN
ejpam-3907	57	14	(	(	PUNCT
ejpam-3907	57	15	q	q	NOUN
ejpam-3907	57	16	)	)	PUNCT
ejpam-3907	57	17	.	.	PUNCT
ejpam-3907	58	1	a	a	DET
ejpam-3907	58	2	sequence	sequence	NOUN
ejpam-3907	58	3	s∞	s∞	NOUN
ejpam-3907	58	4	is	be	AUX
ejpam-3907	58	5	called	call	VERB
ejpam-3907	58	6	periodic	periodic	ADJ
ejpam-3907	58	7	with	with	ADP
ejpam-3907	58	8	period	period	NOUN
ejpam-3907	58	9	n	n	CCONJ
ejpam-3907	58	10	if	if	SCONJ
ejpam-3907	58	11	there	there	PRON
ejpam-3907	58	12	is	be	VERB
ejpam-3907	58	13	positive	positive	ADJ
ejpam-3907	58	14	integer	integer	NOUN
ejpam-3907	58	15	n	n	CCONJ
ejpam-3907	58	16	such	such	ADJ
ejpam-3907	58	17	that	that	DET
ejpam-3907	58	18	st	st	PROPN
ejpam-3907	58	19	=	=	NOUN
ejpam-3907	58	20	st+ln	st+ln	NOUN
ejpam-3907	58	21	for	for	ADP
ejpam-3907	58	22	every	every	DET
ejpam-3907	58	23	t	t	PROPN
ejpam-3907	58	24	,	,	PUNCT
ejpam-3907	58	25	l	l	PROPN
ejpam-3907	58	26	≥	≥	NOUN
ejpam-3907	58	27	0	0	NUM
ejpam-3907	58	28	.	.	PUNCT
ejpam-3907	59	1	nopendri	nopendri	PROPN
ejpam-3907	59	2	et	et	PROPN
ejpam-3907	59	3	al	al	PROPN
ejpam-3907	59	4	.	.	PUNCT
ejpam-3907	59	5	/	/	SYM
ejpam-3907	59	6	eur	eur	PROPN
ejpam-3907	59	7	.	.	PUNCT
ejpam-3907	60	1	j.	j.	PROPN
ejpam-3907	60	2	pure	pure	PROPN
ejpam-3907	60	3	appl	appl	PROPN
ejpam-3907	60	4	.	.	PROPN
ejpam-3907	60	5	math	math	PROPN
ejpam-3907	60	6	,	,	PUNCT
ejpam-3907	60	7	14	14	NUM
ejpam-3907	60	8	(	(	PUNCT
ejpam-3907	60	9	3	3	NUM
ejpam-3907	60	10	)	)	PUNCT
ejpam-3907	60	11	(	(	PUNCT
ejpam-3907	60	12	2021	2021	NUM
ejpam-3907	60	13	)	)	PUNCT
ejpam-3907	60	14	,	,	PUNCT
ejpam-3907	60	15	685	685	NUM
ejpam-3907	60	16	-	-	SYM
ejpam-3907	60	17	694	694	NUM
ejpam-3907	60	18	687	687	NUM
ejpam-3907	60	19	definition	definition	NOUN
ejpam-3907	60	20	3	3	NUM
ejpam-3907	60	21	.	.	PUNCT
ejpam-3907	61	1	the	the	DET
ejpam-3907	61	2	polynomial	polynomial	ADJ
ejpam-3907	61	3	c(x	c(x	NOUN
ejpam-3907	61	4	)	)	PUNCT
ejpam-3907	61	5	=	=	PUNCT
ejpam-3907	62	1	akx	akx	ADJ
ejpam-3907	62	2	k	k	X
ejpam-3907	63	1	+	+	PROPN
ejpam-3907	63	2	ak−1x	ak−1x	PROPN
ejpam-3907	63	3	k−1	k−1	PROPN
ejpam-3907	63	4	+	+	ADP
ejpam-3907	63	5	ak−2x	ak−2x	PROPN
ejpam-3907	63	6	k−2	k−2	PROPN
ejpam-3907	63	7	+	+	CCONJ
ejpam-3907	63	8	·	·	PUNCT
ejpam-3907	63	9	·	·	PUNCT
ejpam-3907	63	10	·	·	PUNCT
ejpam-3907	63	11	+	+	NOUN
ejpam-3907	63	12	a0	a0	NOUN
ejpam-3907	63	13	over	over	ADP
ejpam-3907	63	14	gf	gf	PROPN
ejpam-3907	63	15	(	(	PUNCT
ejpam-3907	63	16	q	q	NOUN
ejpam-3907	63	17	)	)	PUNCT
ejpam-3907	63	18	,	,	PUNCT
ejpam-3907	63	19	with	with	ADP
ejpam-3907	63	20	ak	ak	PROPN
ejpam-3907	63	21	=	=	SYM
ejpam-3907	63	22	1	1	NUM
ejpam-3907	63	23	,	,	PUNCT
ejpam-3907	63	24	is	be	AUX
ejpam-3907	63	25	called	call	VERB
ejpam-3907	63	26	characteristic	characteristic	ADJ
ejpam-3907	63	27	polynomial	polynomial	NOUN
ejpam-3907	63	28	of	of	ADP
ejpam-3907	63	29	s∞	s∞	PROPN
ejpam-3907	63	30	if	if	SCONJ
ejpam-3907	63	31	aksn+k	aksn+k	PROPN
ejpam-3907	63	32	+	+	CCONJ
ejpam-3907	63	33	ak−1sn+k−1	ak−1sn+k−1	X
ejpam-3907	63	34	+	+	CCONJ
ejpam-3907	63	35	ak−2sn+k−2	ak−2sn+k−2	NOUN
ejpam-3907	63	36	+	+	X
ejpam-3907	63	37	...	...	PUNCT
ejpam-3907	64	1	+	+	PUNCT
ejpam-3907	64	2	a0sn	a0sn	X
ejpam-3907	64	3	=	=	SYM
ejpam-3907	64	4	0	0	NUM
ejpam-3907	64	5	for	for	ADP
ejpam-3907	64	6	every	every	DET
ejpam-3907	64	7	n	n	NOUN
ejpam-3907	64	8	=	=	SYM
ejpam-3907	64	9	0	0	NUM
ejpam-3907	64	10	,	,	PUNCT
ejpam-3907	64	11	1	1	NUM
ejpam-3907	64	12	,	,	PUNCT
ejpam-3907	64	13	2	2	NUM
ejpam-3907	64	14	,	,	PUNCT
ejpam-3907	64	15	.	.	PUNCT
ejpam-3907	64	16	.	.	PUNCT
ejpam-3907	64	17	.	.	PUNCT
ejpam-3907	64	18	.	.	PUNCT
ejpam-3907	65	1	furthermore	furthermore	ADV
ejpam-3907	65	2	,	,	PUNCT
ejpam-3907	65	3	the	the	DET
ejpam-3907	65	4	polynomial	polynomial	ADJ
ejpam-3907	65	5	characteristic	characteristic	NOUN
ejpam-3907	65	6	of	of	ADP
ejpam-3907	65	7	the	the	DET
ejpam-3907	65	8	smallest	small	ADJ
ejpam-3907	65	9	degree	degree	NOUN
ejpam-3907	65	10	of	of	ADP
ejpam-3907	65	11	s∞	s∞	PROPN
ejpam-3907	65	12	is	be	AUX
ejpam-3907	65	13	called	call	VERB
ejpam-3907	65	14	minimal	minimal	ADJ
ejpam-3907	65	15	polynomial	polynomial	NOUN
ejpam-3907	65	16	of	of	ADP
ejpam-3907	65	17	s∞	s∞	PROPN
ejpam-3907	65	18	,	,	PUNCT
ejpam-3907	65	19	and	and	CCONJ
ejpam-3907	65	20	denoted	denote	VERB
ejpam-3907	65	21	by	by	ADP
ejpam-3907	65	22	ms(x	ms(x	NOUN
ejpam-3907	65	23	)	)	PUNCT
ejpam-3907	65	24	.	.	PUNCT
ejpam-3907	66	1	the	the	DET
ejpam-3907	66	2	minimal	minimal	ADJ
ejpam-3907	66	3	polynomial	polynomial	ADJ
ejpam-3907	66	4	ms(x	ms(x	NOUN
ejpam-3907	66	5	)	)	PUNCT
ejpam-3907	66	6	of	of	ADP
ejpam-3907	66	7	the	the	DET
ejpam-3907	66	8	sequence	sequence	NOUN
ejpam-3907	66	9	s∞	s∞	NOUN
ejpam-3907	66	10	is	be	AUX
ejpam-3907	66	11	unique	unique	ADJ
ejpam-3907	66	12	and	and	CCONJ
ejpam-3907	66	13	divides	divide	VERB
ejpam-3907	66	14	c(x	c(x	NOUN
ejpam-3907	66	15	)	)	PUNCT
ejpam-3907	66	16	.	.	PUNCT
ejpam-3907	67	1	the	the	DET
ejpam-3907	67	2	degree	degree	NOUN
ejpam-3907	67	3	of	of	ADP
ejpam-3907	67	4	ms(x	ms(x	NOUN
ejpam-3907	67	5	)	)	PUNCT
ejpam-3907	67	6	is	be	AUX
ejpam-3907	67	7	called	call	VERB
ejpam-3907	67	8	linear	linear	ADJ
ejpam-3907	67	9	span	span	NOUN
ejpam-3907	67	10	or	or	CCONJ
ejpam-3907	67	11	linear	linear	ADJ
ejpam-3907	67	12	complexity	complexity	NOUN
ejpam-3907	67	13	of	of	ADP
ejpam-3907	67	14	s∞	s∞	PROPN
ejpam-3907	67	15	and	and	CCONJ
ejpam-3907	67	16	is	be	AUX
ejpam-3907	67	17	denoted	denote	VERB
ejpam-3907	67	18	by	by	ADP
ejpam-3907	67	19	ls	ls	PROPN
ejpam-3907	67	20	.	.	PROPN
ejpam-3907	68	1	for	for	ADP
ejpam-3907	68	2	any	any	DET
ejpam-3907	68	3	sequence	sequence	NOUN
ejpam-3907	68	4	s∞	s∞	NOUN
ejpam-3907	68	5	,	,	PUNCT
ejpam-3907	68	6	we	we	PRON
ejpam-3907	68	7	can	can	AUX
ejpam-3907	68	8	determine	determine	VERB
ejpam-3907	68	9	the	the	DET
ejpam-3907	68	10	linear	linear	ADJ
ejpam-3907	68	11	span	span	NOUN
ejpam-3907	68	12	and	and	CCONJ
ejpam-3907	68	13	minimal	minimal	ADJ
ejpam-3907	68	14	polynomial	polynomial	NOUN
ejpam-3907	68	15	of	of	ADP
ejpam-3907	68	16	s∞	s∞	PROPN
ejpam-3907	68	17	from	from	ADP
ejpam-3907	68	18	the	the	DET
ejpam-3907	68	19	following	follow	VERB
ejpam-3907	68	20	lemma	lemma	PROPN
ejpam-3907	68	21	[	[	X
ejpam-3907	68	22	4	4	NUM
ejpam-3907	68	23	,	,	PUNCT
ejpam-3907	68	24	theorem	theorem	VERB
ejpam-3907	68	25	5.3	5.3	NUM
ejpam-3907	68	26	]	]	PUNCT
ejpam-3907	68	27	.	.	PUNCT
ejpam-3907	69	1	lemma	lemma	PROPN
ejpam-3907	69	2	2	2	X
ejpam-3907	69	3	.	.	PUNCT
ejpam-3907	70	1	let	let	VERB
ejpam-3907	70	2	s∞	s∞	VERB
ejpam-3907	70	3	=	=	SYM
ejpam-3907	70	4	(	(	PUNCT
ejpam-3907	70	5	st	st	PROPN
ejpam-3907	70	6	)	)	PUNCT
ejpam-3907	70	7	∞	∞	PROPN
ejpam-3907	70	8	t=0	t=0	PROPN
ejpam-3907	70	9	be	be	VERB
ejpam-3907	70	10	a	a	DET
ejpam-3907	70	11	sequence	sequence	NOUN
ejpam-3907	70	12	with	with	ADP
ejpam-3907	70	13	period	period	NOUN
ejpam-3907	70	14	l	l	NOUN
ejpam-3907	70	15	over	over	ADP
ejpam-3907	70	16	gf	gf	PROPN
ejpam-3907	70	17	(	(	PUNCT
ejpam-3907	70	18	q	q	NOUN
ejpam-3907	70	19	)	)	PUNCT
ejpam-3907	70	20	.	.	PUNCT
ejpam-3907	71	1	defined	define	VERB
ejpam-3907	71	2	sl(x	sl(x	PROPN
ejpam-3907	71	3	)	)	PUNCT
ejpam-3907	72	1	=	=	NOUN
ejpam-3907	72	2	∑l−1	∑l−1	PRON
ejpam-3907	72	3	t=0	t=0	PROPN
ejpam-3907	72	4	stx	stx	PROPN
ejpam-3907	72	5	t	t	PROPN
ejpam-3907	72	6	∈	∈	PROPN
ejpam-3907	72	7	gf	gf	X
ejpam-3907	72	8	(	(	PUNCT
ejpam-3907	72	9	q)[x	q)[x	NOUN
ejpam-3907	72	10	]	]	PUNCT
ejpam-3907	72	11	.	.	PUNCT
ejpam-3907	73	1	then	then	ADV
ejpam-3907	73	2	the	the	DET
ejpam-3907	73	3	minimial	minimial	ADJ
ejpam-3907	73	4	polynomial	polynomial	ADJ
ejpam-3907	73	5	ms(x	ms(x	NOUN
ejpam-3907	73	6	)	)	PUNCT
ejpam-3907	73	7	of	of	ADP
ejpam-3907	73	8	s∞	s∞	PROPN
ejpam-3907	73	9	is	be	AUX
ejpam-3907	73	10	given	give	VERB
ejpam-3907	73	11	by	by	ADP
ejpam-3907	73	12	xl	xl	PROPN
ejpam-3907	73	13	−	−	PROPN
ejpam-3907	73	14	1	1	NUM
ejpam-3907	73	15	gcd(sl(x	gcd(sl(x	PROPN
ejpam-3907	73	16	)	)	PUNCT
ejpam-3907	73	17	,	,	PUNCT
ejpam-3907	73	18	xl	xl	PROPN
ejpam-3907	73	19	−	−	PROPN
ejpam-3907	73	20	1	1	NUM
ejpam-3907	73	21	)	)	PUNCT
ejpam-3907	73	22	and	and	CCONJ
ejpam-3907	73	23	the	the	DET
ejpam-3907	73	24	linear	linear	ADJ
ejpam-3907	73	25	span	span	NOUN
ejpam-3907	73	26	ls	ls	PROPN
ejpam-3907	73	27	is	be	AUX
ejpam-3907	73	28	given	give	VERB
ejpam-3907	73	29	by	by	ADP
ejpam-3907	73	30	l−	l−	PROPN
ejpam-3907	73	31	deg	deg	PROPN
ejpam-3907	73	32	(	(	PUNCT
ejpam-3907	73	33	gcd(sl(x	gcd(sl(x	PROPN
ejpam-3907	73	34	)	)	PUNCT
ejpam-3907	73	35	,	,	PUNCT
ejpam-3907	73	36	xl	xl	PROPN
ejpam-3907	73	37	−	−	PROPN
ejpam-3907	73	38	1	1	NUM
ejpam-3907	73	39	)	)	PUNCT
ejpam-3907	73	40	)	)	PUNCT
ejpam-3907	73	41	.	.	PUNCT
ejpam-3907	74	1	another	another	DET
ejpam-3907	74	2	way	way	NOUN
ejpam-3907	74	3	is	be	AUX
ejpam-3907	74	4	given	give	VERB
ejpam-3907	74	5	in	in	ADP
ejpam-3907	74	6	the	the	DET
ejpam-3907	74	7	following	follow	VERB
ejpam-3907	74	8	lemma	lemma	PROPN
ejpam-3907	75	1	[	[	X
ejpam-3907	75	2	1	1	NUM
ejpam-3907	75	3	]	]	PUNCT
ejpam-3907	75	4	,	,	PUNCT
ejpam-3907	75	5	which	which	PRON
ejpam-3907	75	6	is	be	AUX
ejpam-3907	75	7	very	very	ADV
ejpam-3907	75	8	important	important	ADJ
ejpam-3907	75	9	for	for	ADP
ejpam-3907	75	10	proof	proof	NOUN
ejpam-3907	75	11	of	of	ADP
ejpam-3907	75	12	our	our	PRON
ejpam-3907	75	13	main	main	ADJ
ejpam-3907	75	14	result	result	NOUN
ejpam-3907	75	15	.	.	PUNCT
ejpam-3907	76	1	lemma	lemma	PROPN
ejpam-3907	76	2	3	3	X
ejpam-3907	76	3	.	.	PUNCT
ejpam-3907	77	1	any	any	DET
ejpam-3907	77	2	sequence	sequence	NOUN
ejpam-3907	77	3	s∞	s∞	NOUN
ejpam-3907	77	4	over	over	ADP
ejpam-3907	77	5	gf	gf	X
ejpam-3907	77	6	(	(	PUNCT
ejpam-3907	77	7	q	q	NOUN
ejpam-3907	77	8	)	)	PUNCT
ejpam-3907	77	9	of	of	ADP
ejpam-3907	77	10	period	period	NOUN
ejpam-3907	77	11	qm	qm	PROPN
ejpam-3907	77	12	−	−	PROPN
ejpam-3907	77	13	1	1	NUM
ejpam-3907	77	14	has	have	VERB
ejpam-3907	77	15	a	a	DET
ejpam-3907	77	16	unique	unique	ADJ
ejpam-3907	77	17	powers	power	NOUN
ejpam-3907	77	18	-	-	PUNCT
ejpam-3907	77	19	of	of	ADP
ejpam-3907	77	20	-	-	PUNCT
ejpam-3907	77	21	α	α	NOUN
ejpam-3907	77	22	representation	representation	NOUN
ejpam-3907	77	23	of	of	ADP
ejpam-3907	77	24	the	the	DET
ejpam-3907	77	25	form	form	NOUN
ejpam-3907	77	26	st	st	PROPN
ejpam-3907	77	27	=	=	PUNCT
ejpam-3907	77	28	qm−2∑	qm−2∑	ADV
ejpam-3907	77	29	i=0	i=0	PROPN
ejpam-3907	77	30	ciα	ciα	PROPN
ejpam-3907	77	31	it	it	PRON
ejpam-3907	77	32	,	,	PUNCT
ejpam-3907	77	33	for	for	ADP
ejpam-3907	77	34	all	all	DET
ejpam-3907	77	35	t	t	PROPN
ejpam-3907	77	36	≥	≥	NOUN
ejpam-3907	77	37	0	0	NUM
ejpam-3907	77	38	,	,	PUNCT
ejpam-3907	77	39	where	where	SCONJ
ejpam-3907	77	40	ci	ci	PROPN
ejpam-3907	77	41	∈	∈	PROPN
ejpam-3907	77	42	gf	gf	X
ejpam-3907	77	43	(	(	PUNCT
ejpam-3907	77	44	qm	qm	PROPN
ejpam-3907	77	45	)	)	PUNCT
ejpam-3907	77	46	and	and	CCONJ
ejpam-3907	77	47	α	α	PROPN
ejpam-3907	77	48	is	be	AUX
ejpam-3907	77	49	a	a	DET
ejpam-3907	77	50	primitive	primitive	ADJ
ejpam-3907	77	51	element	element	NOUN
ejpam-3907	77	52	in	in	ADP
ejpam-3907	77	53	gf	gf	PROPN
ejpam-3907	77	54	(	(	PUNCT
ejpam-3907	77	55	qm	qm	PROPN
ejpam-3907	77	56	)	)	PUNCT
ejpam-3907	77	57	.	.	PUNCT
ejpam-3907	78	1	suppose	suppose	VERB
ejpam-3907	78	2	that	that	SCONJ
ejpam-3907	78	3	i	i	PRON
ejpam-3907	78	4	=	=	X
ejpam-3907	78	5	{	{	PUNCT
ejpam-3907	78	6	i|ci	i|ci	PROPN
ejpam-3907	78	7	6=	6=	NUM
ejpam-3907	78	8	0	0	NUM
ejpam-3907	78	9	}	}	PUNCT
ejpam-3907	78	10	,	,	PUNCT
ejpam-3907	78	11	then	then	ADV
ejpam-3907	78	12	the	the	DET
ejpam-3907	78	13	minimal	minimal	ADJ
ejpam-3907	78	14	polynomial	polynomial	NOUN
ejpam-3907	78	15	of	of	ADP
ejpam-3907	78	16	s∞	s∞	PROPN
ejpam-3907	78	17	is	be	AUX
ejpam-3907	78	18	ms(x	ms(x	NOUN
ejpam-3907	78	19	)	)	PUNCT
ejpam-3907	78	20	=	=	SYM
ejpam-3907	78	21	∏	∏	PROPN
ejpam-3907	78	22	i∈i	i∈i	NOUN
ejpam-3907	78	23	(	(	PUNCT
ejpam-3907	78	24	x−	x−	PROPN
ejpam-3907	78	25	αi	αi	PROPN
ejpam-3907	78	26	)	)	PUNCT
ejpam-3907	78	27	,	,	PUNCT
ejpam-3907	78	28	(	(	PUNCT
ejpam-3907	78	29	1	1	X
ejpam-3907	78	30	)	)	PUNCT
ejpam-3907	78	31	and	and	CCONJ
ejpam-3907	78	32	the	the	DET
ejpam-3907	78	33	linear	linear	ADJ
ejpam-3907	78	34	span	span	NOUN
ejpam-3907	78	35	of	of	ADP
ejpam-3907	78	36	s∞	s∞	PROPN
ejpam-3907	78	37	is	be	AUX
ejpam-3907	78	38	ls	ls	ADJ
ejpam-3907	78	39	=	=	X
ejpam-3907	78	40	|i|	|i|	PROPN
ejpam-3907	78	41	.	.	PUNCT
ejpam-3907	79	1	it	it	PRON
ejpam-3907	79	2	should	should	AUX
ejpam-3907	79	3	be	be	AUX
ejpam-3907	79	4	noticed	notice	VERB
ejpam-3907	79	5	that	that	SCONJ
ejpam-3907	79	6	in	in	ADP
ejpam-3907	79	7	some	some	DET
ejpam-3907	79	8	references	reference	NOUN
ejpam-3907	79	9	,	,	PUNCT
ejpam-3907	79	10	the	the	DET
ejpam-3907	79	11	reciprocal	reciprocal	NOUN
ejpam-3907	79	12	of	of	ADP
ejpam-3907	79	13	ms(x	ms(x	NOUN
ejpam-3907	79	14	)	)	PUNCT
ejpam-3907	79	15	is	be	AUX
ejpam-3907	79	16	the	the	DET
ejpam-3907	79	17	minimal	minimal	ADJ
ejpam-3907	79	18	polynomial	polynomial	NOUN
ejpam-3907	79	19	of	of	ADP
ejpam-3907	79	20	the	the	DET
ejpam-3907	79	21	sequence	sequence	NOUN
ejpam-3907	79	22	s∞.	s∞.	NOUN
ejpam-3907	79	23	3	3	X
ejpam-3907	79	24	.	.	PUNCT
ejpam-3907	79	25	cyclic	cyclic	ADJ
ejpam-3907	79	26	codes	code	NOUN
ejpam-3907	79	27	from	from	ADP
ejpam-3907	79	28	the	the	DET
ejpam-3907	79	29	monomial	monomial	ADJ
ejpam-3907	79	30	f(x	f(x	PROPN
ejpam-3907	79	31	)	)	PUNCT
ejpam-3907	79	32	=	=	PUNCT
ejpam-3907	80	1	xqm−2	xqm−2	X
ejpam-3907	80	2	in	in	ADP
ejpam-3907	80	3	this	this	DET
ejpam-3907	80	4	section	section	NOUN
ejpam-3907	80	5	,	,	PUNCT
ejpam-3907	80	6	we	we	PRON
ejpam-3907	80	7	study	study	VERB
ejpam-3907	80	8	a	a	DET
ejpam-3907	80	9	particular	particular	ADJ
ejpam-3907	80	10	type	type	NOUN
ejpam-3907	80	11	of	of	ADP
ejpam-3907	80	12	sequences	sequence	NOUN
ejpam-3907	80	13	š∞	š∞	PROPN
ejpam-3907	80	14	defined	define	VERB
ejpam-3907	80	15	by	by	ADP
ejpam-3907	80	16	št	št	PROPN
ejpam-3907	80	17	=	=	PROPN
ejpam-3907	80	18	trm1	trm1	PROPN
ejpam-3907	80	19	(	(	PUNCT
ejpam-3907	80	20	f(αt	f(αt	PROPN
ejpam-3907	80	21	+	+	PROPN
ejpam-3907	80	22	1)−	1)−	NUM
ejpam-3907	80	23	f(αt	f(αt	NOUN
ejpam-3907	80	24	)	)	PUNCT
ejpam-3907	80	25	)	)	PUNCT
ejpam-3907	80	26	,	,	PUNCT
ejpam-3907	80	27	t	t	PROPN
ejpam-3907	80	28	≥	≥	NUM
ejpam-3907	80	29	0	0	NUM
ejpam-3907	80	30	,	,	PUNCT
ejpam-3907	80	31	(	(	PUNCT
ejpam-3907	80	32	2	2	X
ejpam-3907	80	33	)	)	PUNCT
ejpam-3907	80	34	nopendri	nopendri	PROPN
ejpam-3907	80	35	et	et	PROPN
ejpam-3907	80	36	al	al	PROPN
ejpam-3907	80	37	.	.	PUNCT
ejpam-3907	80	38	/	/	SYM
ejpam-3907	80	39	eur	eur	PROPN
ejpam-3907	80	40	.	.	PUNCT
ejpam-3907	81	1	j.	j.	PROPN
ejpam-3907	81	2	pure	pure	PROPN
ejpam-3907	81	3	appl	appl	PROPN
ejpam-3907	81	4	.	.	PROPN
ejpam-3907	81	5	math	math	PROPN
ejpam-3907	81	6	,	,	PUNCT
ejpam-3907	81	7	14	14	NUM
ejpam-3907	81	8	(	(	PUNCT
ejpam-3907	81	9	3	3	NUM
ejpam-3907	81	10	)	)	PUNCT
ejpam-3907	81	11	(	(	PUNCT
ejpam-3907	81	12	2021	2021	NUM
ejpam-3907	81	13	)	)	PUNCT
ejpam-3907	81	14	,	,	PUNCT
ejpam-3907	81	15	685	685	NUM
ejpam-3907	81	16	-	-	SYM
ejpam-3907	81	17	694	694	NUM
ejpam-3907	81	18	688	688	NUM
ejpam-3907	81	19	where	where	SCONJ
ejpam-3907	81	20	f(x	f(x	NOUN
ejpam-3907	81	21	)	)	PUNCT
ejpam-3907	81	22	=	=	PUNCT
ejpam-3907	82	1	xq	xq	PROPN
ejpam-3907	82	2	m−2	m−2	PROPN
ejpam-3907	82	3	,	,	PUNCT
ejpam-3907	82	4	(	(	PUNCT
ejpam-3907	82	5	3	3	X
ejpam-3907	82	6	)	)	PUNCT
ejpam-3907	82	7	is	be	AUX
ejpam-3907	82	8	a	a	DET
ejpam-3907	82	9	function	function	NOUN
ejpam-3907	82	10	in	in	ADP
ejpam-3907	82	11	gf	gf	PROPN
ejpam-3907	82	12	(	(	PUNCT
ejpam-3907	82	13	qm)[x	qm)[x	NOUN
ejpam-3907	82	14	]	]	PUNCT
ejpam-3907	82	15	,	,	PUNCT
ejpam-3907	82	16	m	m	VERB
ejpam-3907	82	17	is	be	AUX
ejpam-3907	82	18	a	a	DET
ejpam-3907	82	19	positive	positive	ADJ
ejpam-3907	82	20	integer	integer	NOUN
ejpam-3907	82	21	,	,	PUNCT
ejpam-3907	82	22	trm1	trm1	PROPN
ejpam-3907	82	23	is	be	AUX
ejpam-3907	82	24	the	the	DET
ejpam-3907	82	25	trace	trace	NOUN
ejpam-3907	82	26	function	function	NOUN
ejpam-3907	82	27	from	from	ADP
ejpam-3907	82	28	gf	gf	PROPN
ejpam-3907	82	29	(	(	PUNCT
ejpam-3907	82	30	qm	qm	PROPN
ejpam-3907	82	31	)	)	PUNCT
ejpam-3907	82	32	to	to	ADP
ejpam-3907	82	33	gf	gf	PROPN
ejpam-3907	82	34	(	(	PUNCT
ejpam-3907	82	35	q	q	NOUN
ejpam-3907	82	36	)	)	PUNCT
ejpam-3907	82	37	and	and	CCONJ
ejpam-3907	82	38	α	α	PRON
ejpam-3907	82	39	is	be	AUX
ejpam-3907	82	40	a	a	DET
ejpam-3907	82	41	primitive	primitive	ADJ
ejpam-3907	82	42	element	element	NOUN
ejpam-3907	82	43	of	of	ADP
ejpam-3907	82	44	gf	gf	PROPN
ejpam-3907	82	45	(	(	PUNCT
ejpam-3907	82	46	qm)∗.	qm)∗.	X
ejpam-3907	82	47	the	the	DET
ejpam-3907	82	48	objective	objective	NOUN
ejpam-3907	82	49	of	of	ADP
ejpam-3907	82	50	this	this	DET
ejpam-3907	82	51	part	part	NOUN
ejpam-3907	82	52	is	be	AUX
ejpam-3907	82	53	to	to	PART
ejpam-3907	82	54	construct	construct	VERB
ejpam-3907	82	55	a	a	DET
ejpam-3907	82	56	class	class	NOUN
ejpam-3907	82	57	of	of	ADP
ejpam-3907	82	58	cyclic	cyclic	PROPN
ejpam-3907	82	59	code	code	NOUN
ejpam-3907	82	60	from	from	ADP
ejpam-3907	82	61	this	this	DET
ejpam-3907	82	62	sequence	sequence	NOUN
ejpam-3907	82	63	with	with	ADP
ejpam-3907	82	64	explicit	explicit	ADJ
ejpam-3907	82	65	monomial	monomial	ADJ
ejpam-3907	82	66	f	f	PROPN
ejpam-3907	82	67	.	.	PUNCT
ejpam-3907	83	1	we	we	PRON
ejpam-3907	83	2	call	call	VERB
ejpam-3907	83	3	the	the	DET
ejpam-3907	83	4	cyclic	cyclic	ADJ
ejpam-3907	83	5	code	code	NOUN
ejpam-3907	83	6	cš	cš	NOUN
ejpam-3907	83	7	with	with	ADP
ejpam-3907	83	8	the	the	DET
ejpam-3907	83	9	generator	generator	NOUN
ejpam-3907	83	10	polynomial	polynomial	NOUN
ejpam-3907	83	11	from	from	ADP
ejpam-3907	83	12	the	the	DET
ejpam-3907	83	13	minimal	minimal	ADJ
ejpam-3907	83	14	polynomial	polynomial	NOUN
ejpam-3907	83	15	of	of	ADP
ejpam-3907	83	16	the	the	DET
ejpam-3907	83	17	sequence	sequence	NOUN
ejpam-3907	83	18	š∞	š∞	PROPN
ejpam-3907	84	1	=	=	SYM
ejpam-3907	84	2	(	(	PUNCT
ejpam-3907	84	3	št	št	PROPN
ejpam-3907	84	4	)	)	PUNCT
ejpam-3907	84	5	∞	∞	NUM
ejpam-3907	84	6	t=0	t=0	PROPN
ejpam-3907	84	7	.	.	PUNCT
ejpam-3907	85	1	let	let	VERB
ejpam-3907	85	2	n	n	NOUN
ejpam-3907	85	3	=	=	SYM
ejpam-3907	85	4	qm	qm	PROPN
ejpam-3907	85	5	−	−	PROPN
ejpam-3907	85	6	1	1	NUM
ejpam-3907	85	7	and	and	CCONJ
ejpam-3907	85	8	e	e	NOUN
ejpam-3907	85	9	=	=	NOUN
ejpam-3907	85	10	qm	qm	PROPN
ejpam-3907	85	11	−	−	PROPN
ejpam-3907	85	12	2	2	NUM
ejpam-3907	85	13	.	.	PUNCT
ejpam-3907	85	14	by	by	ADP
ejpam-3907	85	15	lemma	lemma	PROPN
ejpam-3907	85	16	3	3	NUM
ejpam-3907	85	17	and	and	CCONJ
ejpam-3907	85	18	(	(	PUNCT
ejpam-3907	85	19	2	2	NUM
ejpam-3907	85	20	)	)	PUNCT
ejpam-3907	85	21	,	,	PUNCT
ejpam-3907	85	22	to	to	PART
ejpam-3907	85	23	get	get	VERB
ejpam-3907	85	24	the	the	DET
ejpam-3907	85	25	parameters	parameter	NOUN
ejpam-3907	85	26	of	of	ADP
ejpam-3907	85	27	the	the	DET
ejpam-3907	85	28	corresponding	corresponding	ADJ
ejpam-3907	85	29	cyclic	cyclic	ADJ
ejpam-3907	85	30	codes	code	NOUN
ejpam-3907	85	31	is	be	AUX
ejpam-3907	85	32	to	to	PART
ejpam-3907	85	33	compute	compute	VERB
ejpam-3907	85	34	the	the	DET
ejpam-3907	85	35	powers	power	NOUN
ejpam-3907	85	36	-	-	PUNCT
ejpam-3907	85	37	of	of	ADP
ejpam-3907	85	38	-	-	PUNCT
ejpam-3907	85	39	α	α	NOUN
ejpam-3907	85	40	representation	representation	NOUN
ejpam-3907	85	41	of	of	ADP
ejpam-3907	85	42	trm1	trm1	PROPN
ejpam-3907	85	43	(	(	PUNCT
ejpam-3907	85	44	f(αt	f(αt	PROPN
ejpam-3907	85	45	+	+	PROPN
ejpam-3907	85	46	1)−	1)−	NUM
ejpam-3907	85	47	f(αt	f(αt	NOUN
ejpam-3907	85	48	)	)	PUNCT
ejpam-3907	85	49	)	)	PUNCT
ejpam-3907	85	50	as	as	SCONJ
ejpam-3907	85	51	follows	follow	VERB
ejpam-3907	85	52	:	:	PUNCT
ejpam-3907	85	53	št	št	PROPN
ejpam-3907	85	54	=	=	PUNCT
ejpam-3907	85	55	trm1	trm1	PROPN
ejpam-3907	85	56	(	(	PUNCT
ejpam-3907	85	57	f(αt	f(αt	PROPN
ejpam-3907	85	58	+	+	PROPN
ejpam-3907	85	59	1)−	1)−	NUM
ejpam-3907	85	60	f(αt	f(αt	NOUN
ejpam-3907	85	61	)	)	PUNCT
ejpam-3907	85	62	)	)	PUNCT
ejpam-3907	86	1	=	=	SYM
ejpam-3907	86	2	trm1	trm1	PROPN
ejpam-3907	86	3	(	(	PUNCT
ejpam-3907	86	4	(	(	PUNCT
ejpam-3907	86	5	αt	αt	NOUN
ejpam-3907	86	6	+	+	NOUN
ejpam-3907	86	7	1)e	1)e	NUM
ejpam-3907	86	8	−	−	NOUN
ejpam-3907	86	9	(	(	PUNCT
ejpam-3907	86	10	αt)e	αt)e	PROPN
ejpam-3907	86	11	)	)	PUNCT
ejpam-3907	86	12	=	=	SYM
ejpam-3907	86	13	trm1	trm1	PROPN
ejpam-3907	86	14	(	(	PUNCT
ejpam-3907	86	15	e∑	e∑	NOUN
ejpam-3907	86	16	i=0	i=0	PROPN
ejpam-3907	86	17	(	(	PUNCT
ejpam-3907	86	18	e	e	X
ejpam-3907	86	19	i	i	PROPN
ejpam-3907	86	20	)	)	PUNCT
ejpam-3907	86	21	αit	αit	VERB
ejpam-3907	86	22	−	−	PROPN
ejpam-3907	86	23	αet	αet	NOUN
ejpam-3907	86	24	)	)	PUNCT
ejpam-3907	87	1	=	=	PUNCT
ejpam-3907	87	2	qm−2∑	qm−2∑	ADV
ejpam-3907	87	3	i=0	i=0	PROPN
ejpam-3907	87	4	(	(	PUNCT
ejpam-3907	87	5	e	e	X
ejpam-3907	87	6	i	i	PROPN
ejpam-3907	87	7	)	)	PUNCT
ejpam-3907	87	8	m−1∑	m−1∑	PROPN
ejpam-3907	87	9	j=0	j=0	PROPN
ejpam-3907	87	10	αqjit	αqjit	ADJ
ejpam-3907	87	11	−	−	PROPN
ejpam-3907	87	12	m−1∑	m−1∑	NUM
ejpam-3907	87	13	j=0	j=0	PROPN
ejpam-3907	87	14	αqjet	αqjet	NOUN
ejpam-3907	87	15	=	=	SYM
ejpam-3907	87	16	qm−2∑	qm−2∑	ADV
ejpam-3907	87	17	i=0	i=0	PROPN
ejpam-3907	87	18	,	,	PUNCT
ejpam-3907	87	19	i	i	PRON
ejpam-3907	87	20	6∈ce	6∈ce	NUM
ejpam-3907	87	21	(	(	PUNCT
ejpam-3907	87	22	e	e	NOUN
ejpam-3907	87	23	i	i	NOUN
ejpam-3907	87	24	)	)	PUNCT
ejpam-3907	87	25	m−1∑	m−1∑	PROPN
ejpam-3907	87	26	j=0	j=0	PROPN
ejpam-3907	87	27	αqjit	αqjit	NOUN
ejpam-3907	87	28	=	=	PUNCT
ejpam-3907	87	29	qm−2∑	qm−2∑	PUNCT
ejpam-3907	87	30	i=0	i=0	PROPN
ejpam-3907	87	31	,	,	PUNCT
ejpam-3907	87	32	i	i	PRON
ejpam-3907	87	33	6∈ce	6∈ce	NUM
ejpam-3907	87	34	m−1∑	m−1∑	VERB
ejpam-3907	87	35	j=0	j=0	PROPN
ejpam-3907	87	36	(	(	PUNCT
ejpam-3907	87	37	e	e	X
ejpam-3907	87	38	qji	qji	PROPN
ejpam-3907	87	39	mod	mod	PROPN
ejpam-3907	87	40	n	n	CCONJ
ejpam-3907	87	41	)	)	PUNCT
ejpam-3907	87	42	mod	mod	PROPN
ejpam-3907	88	1	p	p	X
ejpam-3907	88	2	αit	αit	PROPN
ejpam-3907	88	3	=	=	SYM
ejpam-3907	88	4	qm−2∑	qm−2∑	ADV
ejpam-3907	88	5	i=0	i=0	PROPN
ejpam-3907	88	6	,	,	PUNCT
ejpam-3907	88	7	i	i	PRON
ejpam-3907	88	8	6∈ce	6∈ce	NUM
ejpam-3907	88	9	ke	ke	NOUN
ejpam-3907	88	10	,	,	PUNCT
ejpam-3907	88	11	q	q	NOUN
ejpam-3907	88	12	,	,	PUNCT
ejpam-3907	88	13	m(i)αit	m(i)αit	NOUN
ejpam-3907	88	14	,	,	PUNCT
ejpam-3907	88	15	(	(	PUNCT
ejpam-3907	88	16	4	4	X
ejpam-3907	88	17	)	)	PUNCT
ejpam-3907	89	1	where	where	SCONJ
ejpam-3907	89	2	ke	ke	NOUN
ejpam-3907	89	3	,	,	PUNCT
ejpam-3907	89	4	q	q	NOUN
ejpam-3907	89	5	,	,	PUNCT
ejpam-3907	89	6	m(i	m(i	NOUN
ejpam-3907	89	7	)	)	PUNCT
ejpam-3907	89	8	=	=	SYM
ejpam-3907	89	9	m−1∑	m−1∑	X
ejpam-3907	89	10	j=0	j=0	PROPN
ejpam-3907	89	11	(	(	PUNCT
ejpam-3907	89	12	e	e	X
ejpam-3907	89	13	qji	qji	ADJ
ejpam-3907	89	14	mod	mod	PROPN
ejpam-3907	89	15	n	n	CCONJ
ejpam-3907	89	16	)	)	PUNCT
ejpam-3907	89	17	mod	mod	PROPN
ejpam-3907	89	18	p	p	PROPN
ejpam-3907	89	19	and	and	CCONJ
ejpam-3907	89	20	ce	ce	PROPN
ejpam-3907	89	21	is	be	AUX
ejpam-3907	89	22	the	the	DET
ejpam-3907	89	23	q	q	ADJ
ejpam-3907	89	24	-	-	PUNCT
ejpam-3907	89	25	cyclotomic	cyclotomic	ADJ
ejpam-3907	89	26	coset	coset	NOUN
ejpam-3907	89	27	containing	contain	VERB
ejpam-3907	89	28	e	e	NOUN
ejpam-3907	89	29	modulo	modulo	NOUN
ejpam-3907	89	30	n.	n.	NOUN
ejpam-3907	89	31	from	from	ADP
ejpam-3907	89	32	(	(	PUNCT
ejpam-3907	89	33	4	4	NUM
ejpam-3907	89	34	)	)	PUNCT
ejpam-3907	89	35	,	,	PUNCT
ejpam-3907	89	36	define	define	VERB
ejpam-3907	89	37	supp(ke	supp(ke	ADJ
ejpam-3907	89	38	,	,	PUNCT
ejpam-3907	89	39	q	q	NOUN
ejpam-3907	89	40	,	,	PUNCT
ejpam-3907	89	41	m	m	NOUN
ejpam-3907	89	42	)	)	PUNCT
ejpam-3907	90	1	=	=	PRON
ejpam-3907	90	2	{	{	PUNCT
ejpam-3907	90	3	i	i	NOUN
ejpam-3907	90	4	∈	∈	PROPN
ejpam-3907	90	5	zn	zn	X
ejpam-3907	90	6	:	:	PUNCT
ejpam-3907	91	1	ke	ke	NOUN
ejpam-3907	91	2	,	,	PUNCT
ejpam-3907	91	3	q	q	NOUN
ejpam-3907	91	4	,	,	PUNCT
ejpam-3907	91	5	m(i	m(i	NOUN
ejpam-3907	91	6	)	)	PUNCT
ejpam-3907	91	7	6=	6=	ADP
ejpam-3907	91	8	0	0	NUM
ejpam-3907	91	9	,	,	PUNCT
ejpam-3907	91	10	i	i	PRON
ejpam-3907	91	11	6∈	6∈	PROPN
ejpam-3907	91	12	ce	ce	PROPN
ejpam-3907	91	13	}	}	PUNCT
ejpam-3907	91	14	.	.	PUNCT
ejpam-3907	92	1	(	(	PUNCT
ejpam-3907	92	2	5	5	X
ejpam-3907	92	3	)	)	PUNCT
ejpam-3907	92	4	now	now	ADV
ejpam-3907	92	5	,	,	PUNCT
ejpam-3907	92	6	we	we	PRON
ejpam-3907	92	7	need	need	VERB
ejpam-3907	92	8	to	to	PART
ejpam-3907	92	9	count	count	VERB
ejpam-3907	92	10	the	the	DET
ejpam-3907	92	11	supp(ke	supp(ke	NOUN
ejpam-3907	92	12	,	,	PUNCT
ejpam-3907	92	13	q	q	NOUN
ejpam-3907	92	14	,	,	PUNCT
ejpam-3907	92	15	m	m	NOUN
ejpam-3907	92	16	)	)	PUNCT
ejpam-3907	92	17	.	.	PUNCT
ejpam-3907	93	1	to	to	PART
ejpam-3907	93	2	do	do	VERB
ejpam-3907	93	3	this	this	PRON
ejpam-3907	93	4	,	,	PUNCT
ejpam-3907	93	5	we	we	PRON
ejpam-3907	93	6	have	have	VERB
ejpam-3907	93	7	to	to	PART
ejpam-3907	93	8	simplify	simplify	VERB
ejpam-3907	93	9	(	(	PUNCT
ejpam-3907	93	10	4	4	NUM
ejpam-3907	93	11	)	)	PUNCT
ejpam-3907	93	12	.	.	PUNCT
ejpam-3907	94	1	note	note	VERB
ejpam-3907	94	2	that	that	SCONJ
ejpam-3907	94	3	the	the	DET
ejpam-3907	94	4	following	follow	VERB
ejpam-3907	94	5	lemma	lemma	PROPN
ejpam-3907	94	6	is	be	AUX
ejpam-3907	94	7	well	well	ADV
ejpam-3907	94	8	-	-	PUNCT
ejpam-3907	94	9	known	know	VERB
ejpam-3907	94	10	.	.	PUNCT
ejpam-3907	95	1	lemma	lemma	PROPN
ejpam-3907	95	2	4	4	NUM
ejpam-3907	95	3	.	.	PUNCT
ejpam-3907	96	1	[	[	X
ejpam-3907	96	2	15	15	NUM
ejpam-3907	96	3	]	]	X
ejpam-3907	96	4	let	let	VERB
ejpam-3907	96	5	n	n	INTJ
ejpam-3907	96	6	>	>	X
ejpam-3907	96	7	m	m	PROPN
ejpam-3907	96	8	>	>	X
ejpam-3907	96	9	0	0	PROPN
ejpam-3907	96	10	,	,	PUNCT
ejpam-3907	96	11	then	then	ADV
ejpam-3907	96	12	(	(	PUNCT
ejpam-3907	96	13	n	n	CCONJ
ejpam-3907	96	14	−	−	PROPN
ejpam-3907	96	15	1	1	NUM
ejpam-3907	96	16	m	m	NOUN
ejpam-3907	96	17	)	)	PUNCT
ejpam-3907	97	1	=	=	SYM
ejpam-3907	97	2	n	n	CCONJ
ejpam-3907	97	3	−m	−m	NOUN
ejpam-3907	97	4	n	n	CCONJ
ejpam-3907	97	5	(	(	PUNCT
ejpam-3907	97	6	n	n	NOUN
ejpam-3907	97	7	m	m	PROPN
ejpam-3907	97	8	)	)	PUNCT
ejpam-3907	97	9	.	.	PUNCT
ejpam-3907	98	1	nopendri	nopendri	PROPN
ejpam-3907	98	2	et	et	PROPN
ejpam-3907	98	3	al	al	PROPN
ejpam-3907	98	4	.	.	PUNCT
ejpam-3907	98	5	/	/	SYM
ejpam-3907	98	6	eur	eur	PROPN
ejpam-3907	98	7	.	.	PUNCT
ejpam-3907	99	1	j.	j.	PROPN
ejpam-3907	99	2	pure	pure	PROPN
ejpam-3907	99	3	appl	appl	PROPN
ejpam-3907	99	4	.	.	PROPN
ejpam-3907	99	5	math	math	PROPN
ejpam-3907	99	6	,	,	PUNCT
ejpam-3907	99	7	14	14	NUM
ejpam-3907	99	8	(	(	PUNCT
ejpam-3907	99	9	3	3	NUM
ejpam-3907	99	10	)	)	PUNCT
ejpam-3907	99	11	(	(	PUNCT
ejpam-3907	99	12	2021	2021	NUM
ejpam-3907	99	13	)	)	PUNCT
ejpam-3907	99	14	,	,	PUNCT
ejpam-3907	99	15	685	685	NUM
ejpam-3907	99	16	-	-	SYM
ejpam-3907	99	17	694	694	NUM
ejpam-3907	99	18	689	689	NUM
ejpam-3907	99	19	let	let	VERB
ejpam-3907	99	20	kij	kij	PROPN
ejpam-3907	99	21	=	=	PROPN
ejpam-3907	99	22	qji	qji	ADJ
ejpam-3907	99	23	mod	mod	PROPN
ejpam-3907	99	24	n	n	CCONJ
ejpam-3907	99	25	,	,	PUNCT
ejpam-3907	99	26	from	from	ADP
ejpam-3907	99	27	the	the	DET
ejpam-3907	99	28	lemma	lemma	PROPN
ejpam-3907	99	29	4	4	NUM
ejpam-3907	99	30	and	and	CCONJ
ejpam-3907	99	31	note	note	VERB
ejpam-3907	99	32	that	that	SCONJ
ejpam-3907	99	33	the	the	DET
ejpam-3907	99	34	multiplicative	multiplicative	ADJ
ejpam-3907	99	35	inverse	inverse	NOUN
ejpam-3907	99	36	of	of	ADP
ejpam-3907	99	37	e+	e+	PUNCT
ejpam-3907	99	38	1	1	NUM
ejpam-3907	99	39	is	be	AUX
ejpam-3907	99	40	p−	p−	NOUN
ejpam-3907	99	41	1	1	NUM
ejpam-3907	99	42	in	in	ADP
ejpam-3907	99	43	modulo	modulo	NOUN
ejpam-3907	99	44	p	p	X
ejpam-3907	99	45	,	,	PUNCT
ejpam-3907	99	46	then	then	ADV
ejpam-3907	99	47	ke	ke	PROPN
ejpam-3907	99	48	,	,	PUNCT
ejpam-3907	99	49	q	q	NOUN
ejpam-3907	99	50	,	,	PUNCT
ejpam-3907	99	51	m(i	m(i	NOUN
ejpam-3907	99	52	)	)	PUNCT
ejpam-3907	99	53	≡	≡	PROPN
ejpam-3907	99	54	m−1∑	m−1∑	PROPN
ejpam-3907	100	1	j=0	j=0	PROPN
ejpam-3907	100	2	(	(	PUNCT
ejpam-3907	100	3	e	e	NOUN
ejpam-3907	100	4	kij	kij	PROPN
ejpam-3907	100	5	)	)	PUNCT
ejpam-3907	100	6	≡	≡	PROPN
ejpam-3907	100	7	m−1∑	m−1∑	PROPN
ejpam-3907	100	8	j=0	j=0	PROPN
ejpam-3907	100	9	e+	e+	VERB
ejpam-3907	100	10	1−	1−	NUM
ejpam-3907	100	11	kij	kij	PROPN
ejpam-3907	100	12	e+	e+	VERB
ejpam-3907	100	13	1	1	NUM
ejpam-3907	100	14	(	(	PUNCT
ejpam-3907	100	15	e+	e+	NUM
ejpam-3907	100	16	1	1	NUM
ejpam-3907	100	17	kij	kij	PROPN
ejpam-3907	100	18	)	)	PUNCT
ejpam-3907	100	19	≡	≡	PROPN
ejpam-3907	100	20	m−1∑	m−1∑	PROPN
ejpam-3907	100	21	j=0	j=0	PROPN
ejpam-3907	100	22	(	(	PUNCT
ejpam-3907	100	23	1	1	NUM
ejpam-3907	100	24	+	+	CCONJ
ejpam-3907	100	25	kij	kij	NOUN
ejpam-3907	100	26	)	)	PUNCT
ejpam-3907	100	27	(	(	PUNCT
ejpam-3907	100	28	e+	e+	NUM
ejpam-3907	100	29	1	1	NUM
ejpam-3907	100	30	kij	kij	PROPN
ejpam-3907	100	31	)	)	PUNCT
ejpam-3907	101	1	mod	mod	PROPN
ejpam-3907	101	2	p.	p.	NOUN
ejpam-3907	101	3	(	(	PUNCT
ejpam-3907	101	4	6	6	NUM
ejpam-3907	101	5	)	)	PUNCT
ejpam-3907	101	6	the	the	DET
ejpam-3907	101	7	last	last	ADJ
ejpam-3907	101	8	part	part	NOUN
ejpam-3907	101	9	of	of	ADP
ejpam-3907	101	10	(	(	PUNCT
ejpam-3907	101	11	6	6	NUM
ejpam-3907	101	12	)	)	PUNCT
ejpam-3907	101	13	always	always	ADV
ejpam-3907	101	14	has	have	VERB
ejpam-3907	101	15	the	the	DET
ejpam-3907	101	16	same	same	ADJ
ejpam-3907	101	17	form	form	NOUN
ejpam-3907	101	18	for	for	ADP
ejpam-3907	101	19	any	any	DET
ejpam-3907	101	20	j	j	PROPN
ejpam-3907	101	21	as	as	ADP
ejpam-3907	101	22	the	the	DET
ejpam-3907	101	23	following	follow	VERB
ejpam-3907	101	24	lemma	lemma	PROPN
ejpam-3907	101	25	.	.	PUNCT
ejpam-3907	102	1	lemma	lemma	PROPN
ejpam-3907	102	2	5	5	NUM
ejpam-3907	102	3	.	.	PUNCT
ejpam-3907	103	1	for	for	ADP
ejpam-3907	103	2	any	any	DET
ejpam-3907	103	3	i	i	PROPN
ejpam-3907	103	4	∈	∈	PROPN
ejpam-3907	103	5	zn	zn	PROPN
ejpam-3907	103	6	,	,	PUNCT
ejpam-3907	103	7	(	(	PUNCT
ejpam-3907	103	8	e+	e+	NUM
ejpam-3907	103	9	1	1	NUM
ejpam-3907	103	10	qi	qi	PROPN
ejpam-3907	103	11	mod	mod	PROPN
ejpam-3907	103	12	n	n	PROPN
ejpam-3907	103	13	)	)	PUNCT
ejpam-3907	103	14	=	=	PUNCT
ejpam-3907	103	15	(	(	PUNCT
ejpam-3907	103	16	e+	e+	NUM
ejpam-3907	103	17	1	1	NUM
ejpam-3907	103	18	i	i	PRON
ejpam-3907	103	19	mod	mod	NOUN
ejpam-3907	103	20	n	n	CCONJ
ejpam-3907	103	21	)	)	PUNCT
ejpam-3907	103	22	.	.	PUNCT
ejpam-3907	104	1	proof	proof	NOUN
ejpam-3907	104	2	.	.	PUNCT
ejpam-3907	105	1	let	let	VERB
ejpam-3907	105	2	i	i	PRON
ejpam-3907	105	3	=	=	SYM
ejpam-3907	105	4	∑m−1	∑m−1	NOUN
ejpam-3907	105	5	j=0	j=0	VERB
ejpam-3907	105	6	ijq	ijq	PROPN
ejpam-3907	105	7	j	j	PROPN
ejpam-3907	105	8	,	,	PUNCT
ejpam-3907	105	9	then	then	ADV
ejpam-3907	105	10	qi	qi	PROPN
ejpam-3907	105	11	mod	mod	PROPN
ejpam-3907	105	12	n	n	PROPN
ejpam-3907	105	13	=	=	PROPN
ejpam-3907	105	14	im−1	im−1	PROPN
ejpam-3907	105	15	+	+	CCONJ
ejpam-3907	105	16	i0q+	i0q+	PROPN
ejpam-3907	105	17	·	·	PUNCT
ejpam-3907	105	18	·	·	PUNCT
ejpam-3907	105	19	·	·	PUNCT
ejpam-3907	106	1	+	+	NUM
ejpam-3907	107	1	im−2q	im−2q	PROPN
ejpam-3907	107	2	m−1	m−1	PROPN
ejpam-3907	107	3	.	.	PUNCT
ejpam-3907	108	1	combaining	combaine	VERB
ejpam-3907	108	2	the	the	DET
ejpam-3907	108	3	fact	fact	NOUN
ejpam-3907	108	4	e+	e+	PUNCT
ejpam-3907	108	5	1	1	NUM
ejpam-3907	108	6	=	=	SYM
ejpam-3907	108	7	∑m−1	∑m−1	X
ejpam-3907	108	8	j=0	j=0	PROPN
ejpam-3907	108	9	(	(	PUNCT
ejpam-3907	108	10	q	q	PROPN
ejpam-3907	108	11	−	−	PROPN
ejpam-3907	108	12	1)qj	1)qj	PROPN
ejpam-3907	108	13	and	and	CCONJ
ejpam-3907	108	14	lucas	lucas	PROPN
ejpam-3907	108	15	’s	’s	PART
ejpam-3907	108	16	theorem	theorem	NOUN
ejpam-3907	108	17	[	[	X
ejpam-3907	108	18	13	13	NUM
ejpam-3907	108	19	]	]	PUNCT
ejpam-3907	108	20	we	we	PRON
ejpam-3907	108	21	have	have	VERB
ejpam-3907	108	22	(	(	PUNCT
ejpam-3907	108	23	e+	e+	NUM
ejpam-3907	108	24	1	1	NUM
ejpam-3907	108	25	qi	qi	PROPN
ejpam-3907	108	26	mod	mod	PROPN
ejpam-3907	108	27	n	n	CCONJ
ejpam-3907	108	28	)	)	PUNCT
ejpam-3907	108	29	≡	≡	PROPN
ejpam-3907	108	30	(	(	PUNCT
ejpam-3907	108	31	q	q	PROPN
ejpam-3907	108	32	−	−	PROPN
ejpam-3907	108	33	1	1	NUM
ejpam-3907	108	34	im−2	im−2	ADV
ejpam-3907	108	35	)	)	PUNCT
ejpam-3907	108	36	.	.	PUNCT
ejpam-3907	108	37	.	.	PUNCT
ejpam-3907	108	38	.	.	PUNCT
ejpam-3907	109	1	(	(	PUNCT
ejpam-3907	109	2	q	q	X
ejpam-3907	109	3	−	−	PROPN
ejpam-3907	109	4	1	1	NUM
ejpam-3907	109	5	i0	i0	PROPN
ejpam-3907	109	6	)	)	PUNCT
ejpam-3907	109	7	(	(	PUNCT
ejpam-3907	109	8	q	q	NOUN
ejpam-3907	109	9	−	−	PROPN
ejpam-3907	109	10	1	1	NUM
ejpam-3907	109	11	im−1	im−1	PROPN
ejpam-3907	109	12	)	)	PUNCT
ejpam-3907	109	13	≡	≡	PROPN
ejpam-3907	110	1	(	(	PUNCT
ejpam-3907	110	2	q	q	NOUN
ejpam-3907	110	3	−	−	PROPN
ejpam-3907	110	4	1	1	NUM
ejpam-3907	110	5	im−1	im−1	PROPN
ejpam-3907	110	6	)	)	PUNCT
ejpam-3907	110	7	.	.	PUNCT
ejpam-3907	110	8	.	.	PUNCT
ejpam-3907	110	9	.	.	PUNCT
ejpam-3907	111	1	(	(	PUNCT
ejpam-3907	111	2	q	q	NOUN
ejpam-3907	111	3	−	−	PROPN
ejpam-3907	111	4	1	1	NUM
ejpam-3907	111	5	i1	i1	PROPN
ejpam-3907	111	6	)	)	PUNCT
ejpam-3907	111	7	(	(	PUNCT
ejpam-3907	111	8	q	q	NOUN
ejpam-3907	111	9	−	−	PROPN
ejpam-3907	111	10	1	1	NUM
ejpam-3907	111	11	i0	i0	PROPN
ejpam-3907	111	12	)	)	PUNCT
ejpam-3907	111	13	≡	≡	PROPN
ejpam-3907	111	14	(	(	PUNCT
ejpam-3907	111	15	e+	e+	NUM
ejpam-3907	111	16	1	1	NUM
ejpam-3907	111	17	i	i	NOUN
ejpam-3907	111	18	)	)	PUNCT
ejpam-3907	112	1	mod	mod	PROPN
ejpam-3907	113	1	p.	p.	NOUN
ejpam-3907	113	2	this	this	DET
ejpam-3907	113	3	yields	yield	NOUN
ejpam-3907	113	4	,	,	PUNCT
ejpam-3907	113	5	for	for	ADP
ejpam-3907	113	6	kij	kij	PROPN
ejpam-3907	113	7	=	=	PROPN
ejpam-3907	113	8	qji	qji	ADJ
ejpam-3907	113	9	mod	mod	PROPN
ejpam-3907	113	10	n	n	CCONJ
ejpam-3907	113	11	,	,	PUNCT
ejpam-3907	113	12	(	(	PUNCT
ejpam-3907	113	13	where	where	SCONJ
ejpam-3907	113	14	j	j	PROPN
ejpam-3907	113	15	∈	∈	PROPN
ejpam-3907	113	16	zm	zm	PROPN
ejpam-3907	113	17	)	)	PUNCT
ejpam-3907	113	18	,	,	PUNCT
ejpam-3907	113	19	(	(	PUNCT
ejpam-3907	113	20	e+	e+	NUM
ejpam-3907	113	21	1	1	NUM
ejpam-3907	113	22	kij	kij	NOUN
ejpam-3907	113	23	)	)	PUNCT
ejpam-3907	113	24	≡	≡	PROPN
ejpam-3907	113	25	(	(	PUNCT
ejpam-3907	113	26	e+	e+	NUM
ejpam-3907	113	27	1	1	NUM
ejpam-3907	113	28	i	i	NOUN
ejpam-3907	113	29	)	)	PUNCT
ejpam-3907	113	30	mod	mod	PROPN
ejpam-3907	114	1	p.	p.	PROPN
ejpam-3907	114	2	hence	hence	ADV
ejpam-3907	114	3	,	,	PUNCT
ejpam-3907	114	4	the	the	DET
ejpam-3907	114	5	equation	equation	NOUN
ejpam-3907	114	6	(	(	PUNCT
ejpam-3907	114	7	6	6	NUM
ejpam-3907	114	8	)	)	PUNCT
ejpam-3907	114	9	equivalent	equivalent	NOUN
ejpam-3907	114	10	to	to	ADP
ejpam-3907	114	11	ke	ke	PROPN
ejpam-3907	114	12	,	,	PUNCT
ejpam-3907	114	13	q	q	NOUN
ejpam-3907	114	14	,	,	PUNCT
ejpam-3907	114	15	m(i	m(i	NOUN
ejpam-3907	114	16	)	)	PUNCT
ejpam-3907	114	17	≡	≡	PROPN
ejpam-3907	114	18	(	(	PUNCT
ejpam-3907	114	19	e+	e+	NUM
ejpam-3907	114	20	1	1	NUM
ejpam-3907	114	21	i	i	NOUN
ejpam-3907	114	22	)	)	PUNCT
ejpam-3907	114	23	m−1∑	m−1∑	PROPN
ejpam-3907	114	24	j=0	j=0	PROPN
ejpam-3907	114	25	(	(	PUNCT
ejpam-3907	114	26	1	1	NUM
ejpam-3907	114	27	+	+	CCONJ
ejpam-3907	114	28	kij	kij	PROPN
ejpam-3907	114	29	)	)	PUNCT
ejpam-3907	114	30	≡	≡	PROPN
ejpam-3907	114	31	(	(	PUNCT
ejpam-3907	114	32	e+	e+	NUM
ejpam-3907	114	33	1	1	NUM
ejpam-3907	114	34	i	i	NOUN
ejpam-3907	114	35	)	)	PUNCT
ejpam-3907	114	36	m+	m+	PROPN
ejpam-3907	114	37	m−1∑	m−1∑	NUM
ejpam-3907	114	38	j=0	j=0	PROPN
ejpam-3907	114	39	kij	kij	PROPN
ejpam-3907	114	40			PROPN
ejpam-3907	114	41	mod	mod	PROPN
ejpam-3907	114	42	p.	p.	NOUN
ejpam-3907	114	43	the	the	DET
ejpam-3907	114	44	following	follow	VERB
ejpam-3907	114	45	lemma	lemma	PROPN
ejpam-3907	114	46	assures	assure	VERB
ejpam-3907	114	47	that	that	SCONJ
ejpam-3907	114	48	the	the	PRON
ejpam-3907	114	49	(	(	PUNCT
ejpam-3907	114	50	e+	e+	NUM
ejpam-3907	114	51	1	1	NUM
ejpam-3907	114	52	i	i	NOUN
ejpam-3907	114	53	)	)	PUNCT
ejpam-3907	114	54	is	be	AUX
ejpam-3907	114	55	not	not	PART
ejpam-3907	114	56	divided	divide	VERB
ejpam-3907	114	57	by	by	ADP
ejpam-3907	114	58	p.	p.	PROPN
ejpam-3907	114	59	nopendri	nopendri	PROPN
ejpam-3907	115	1	et	et	PROPN
ejpam-3907	115	2	al	al	PROPN
ejpam-3907	115	3	.	.	PUNCT
ejpam-3907	115	4	/	/	SYM
ejpam-3907	115	5	eur	eur	PROPN
ejpam-3907	115	6	.	.	PUNCT
ejpam-3907	116	1	j.	j.	PROPN
ejpam-3907	116	2	pure	pure	PROPN
ejpam-3907	116	3	appl	appl	PROPN
ejpam-3907	116	4	.	.	PROPN
ejpam-3907	116	5	math	math	PROPN
ejpam-3907	116	6	,	,	PUNCT
ejpam-3907	116	7	14	14	NUM
ejpam-3907	116	8	(	(	PUNCT
ejpam-3907	116	9	3	3	NUM
ejpam-3907	116	10	)	)	PUNCT
ejpam-3907	116	11	(	(	PUNCT
ejpam-3907	116	12	2021	2021	NUM
ejpam-3907	116	13	)	)	PUNCT
ejpam-3907	116	14	,	,	PUNCT
ejpam-3907	116	15	685	685	NUM
ejpam-3907	116	16	-	-	SYM
ejpam-3907	116	17	694	694	NUM
ejpam-3907	116	18	690	690	NUM
ejpam-3907	116	19	lemma	lemma	PROPN
ejpam-3907	116	20	6	6	NUM
ejpam-3907	116	21	.	.	PUNCT
ejpam-3907	117	1	let	let	VERB
ejpam-3907	117	2	a	a	PRON
ejpam-3907	117	3	be	be	AUX
ejpam-3907	117	4	a	a	DET
ejpam-3907	117	5	positive	positive	ADJ
ejpam-3907	117	6	integer	integer	NOUN
ejpam-3907	117	7	and	and	CCONJ
ejpam-3907	117	8	k	k	PROPN
ejpam-3907	117	9	be	be	AUX
ejpam-3907	117	10	a	a	DET
ejpam-3907	117	11	nonnegative	nonnegative	ADJ
ejpam-3907	117	12	integer	integer	NOUN
ejpam-3907	117	13	.	.	PUNCT
ejpam-3907	118	1	for	for	ADP
ejpam-3907	118	2	p	p	DET
ejpam-3907	118	3	prime	prime	NOUN
ejpam-3907	118	4	then	then	ADV
ejpam-3907	118	5	(	(	PUNCT
ejpam-3907	118	6	pa	pa	PROPN
ejpam-3907	118	7	−	−	PROPN
ejpam-3907	118	8	1	1	NUM
ejpam-3907	118	9	k	k	PROPN
ejpam-3907	118	10	)	)	PUNCT
ejpam-3907	118	11	6≡	6≡	NUM
ejpam-3907	118	12	0	0	NUM
ejpam-3907	118	13	mod	mod	ADJ
ejpam-3907	118	14	p.	p.	NOUN
ejpam-3907	118	15	proof	proof	NOUN
ejpam-3907	118	16	.	.	PUNCT
ejpam-3907	119	1	(	(	PUNCT
ejpam-3907	119	2	pa	pa	NOUN
ejpam-3907	119	3	−	−	PROPN
ejpam-3907	119	4	1	1	NUM
ejpam-3907	119	5	k	k	PROPN
ejpam-3907	119	6	)	)	PUNCT
ejpam-3907	119	7	≡	≡	PROPN
ejpam-3907	119	8	(	(	PUNCT
ejpam-3907	119	9	pa	pa	PROPN
ejpam-3907	119	10	−	−	PROPN
ejpam-3907	119	11	1	1	NUM
ejpam-3907	119	12	)	)	PUNCT
ejpam-3907	119	13	!	!	PUNCT
ejpam-3907	120	1	k!(pa	k!(pa	NOUN
ejpam-3907	120	2	−	−	PROPN
ejpam-3907	120	3	1−	1−	NUM
ejpam-3907	120	4	k	k	NOUN
ejpam-3907	120	5	)	)	PUNCT
ejpam-3907	120	6	!	!	PUNCT
ejpam-3907	121	1	≡	≡	PROPN
ejpam-3907	121	2	(	(	PUNCT
ejpam-3907	121	3	pa	pa	PROPN
ejpam-3907	121	4	−	−	PROPN
ejpam-3907	121	5	1)(pa	1)(pa	NUM
ejpam-3907	121	6	−	−	NUM
ejpam-3907	121	7	2	2	NUM
ejpam-3907	121	8	)	)	PUNCT
ejpam-3907	121	9	·	·	PUNCT
ejpam-3907	121	10	·	·	PUNCT
ejpam-3907	121	11	·	·	PUNCT
ejpam-3907	122	1	(	(	PUNCT
ejpam-3907	122	2	pa	pa	PROPN
ejpam-3907	122	3	−	−	PROPN
ejpam-3907	122	4	k	k	PROPN
ejpam-3907	122	5	)	)	PUNCT
ejpam-3907	122	6	k	k	NOUN
ejpam-3907	122	7	!	!	PUNCT
ejpam-3907	122	8	≡	≡	PROPN
ejpam-3907	122	9	pak	pak	PROPN
ejpam-3907	122	10	−	−	PROPN
ejpam-3907	123	1	(	(	PUNCT
ejpam-3907	123	2	k∑	k∑	NOUN
ejpam-3907	123	3	i=1	i=1	PROPN
ejpam-3907	124	1	i	i	PROPN
ejpam-3907	124	2	)	)	PUNCT
ejpam-3907	125	1	p(k−1)a	p(k−1)a	PROPN
ejpam-3907	126	1	k	k	X
ejpam-3907	126	2	!	!	PUNCT
ejpam-3907	127	1	+	+	CCONJ
ejpam-3907	127	2	(	(	PUNCT
ejpam-3907	127	3	∑	∑	ADV
ejpam-3907	127	4	i	i	PRON
ejpam-3907	127	5	6	6	NUM
ejpam-3907	127	6	=	=	SYM
ejpam-3907	127	7	j	j	PROPN
ejpam-3907	127	8	,	,	PUNCT
ejpam-3907	127	9	i	i	PRON
ejpam-3907	127	10	,	,	PUNCT
ejpam-3907	127	11	j∈[k	j∈[k	PROPN
ejpam-3907	127	12	]	]	X
ejpam-3907	127	13	i.j	i.j	PROPN
ejpam-3907	127	14	)	)	PUNCT
ejpam-3907	127	15	p(k−2)a	p(k−2)a	PROPN
ejpam-3907	127	16	−	−	PROPN
ejpam-3907	127	17	·	·	PUNCT
ejpam-3907	127	18	·	·	PUNCT
ejpam-3907	127	19	·	·	PUNCT
ejpam-3907	127	20	+	+	CCONJ
ejpam-3907	127	21	(	(	PUNCT
ejpam-3907	127	22	−1)kk	−1)kk	PROPN
ejpam-3907	127	23	!	!	PUNCT
ejpam-3907	128	1	k	k	X
ejpam-3907	128	2	!	!	PUNCT
ejpam-3907	129	1	≡	≡	PROPN
ejpam-3907	129	2	(	(	PUNCT
ejpam-3907	129	3	−1)k	−1)k	PROPN
ejpam-3907	129	4	mod	mod	PROPN
ejpam-3907	129	5	p.	p.	PROPN
ejpam-3907	129	6	let	let	VERB
ejpam-3907	129	7	sq(i	sq(i	VERB
ejpam-3907	129	8	)	)	PUNCT
ejpam-3907	129	9	=	=	SYM
ejpam-3907	129	10	m−1∑	m−1∑	PROPN
ejpam-3907	129	11	j=0	j=0	PROPN
ejpam-3907	129	12	kij	kij	PROPN
ejpam-3907	129	13	,	,	PUNCT
ejpam-3907	129	14	then	then	ADV
ejpam-3907	129	15	(	(	PUNCT
ejpam-3907	129	16	5	5	X
ejpam-3907	129	17	)	)	PUNCT
ejpam-3907	129	18	becomes	become	VERB
ejpam-3907	129	19	supp(ke	supp(ke	ADJ
ejpam-3907	129	20	,	,	PUNCT
ejpam-3907	129	21	q	q	NOUN
ejpam-3907	129	22	,	,	PUNCT
ejpam-3907	129	23	m	m	NOUN
ejpam-3907	129	24	)	)	PUNCT
ejpam-3907	130	1	=	=	PRON
ejpam-3907	130	2	{	{	PUNCT
ejpam-3907	130	3	i	i	NOUN
ejpam-3907	130	4	∈	∈	PROPN
ejpam-3907	130	5	zn	zn	X
ejpam-3907	130	6	:	:	PUNCT
ejpam-3907	130	7	sq(i	sq(i	X
ejpam-3907	130	8	)	)	PUNCT
ejpam-3907	131	1	+	+	VERB
ejpam-3907	131	2	m	m	NOUN
ejpam-3907	131	3	6≡	6≡	NUM
ejpam-3907	131	4	0	0	NUM
ejpam-3907	131	5	mod	mod	ADJ
ejpam-3907	131	6	p}\{i	p}\{i	PROPN
ejpam-3907	131	7	∈	∈	NOUN
ejpam-3907	131	8	ce	ce	PROPN
ejpam-3907	131	9	}	}	PUNCT
ejpam-3907	131	10	.	.	PUNCT
ejpam-3907	132	1	(	(	PUNCT
ejpam-3907	132	2	7	7	X
ejpam-3907	132	3	)	)	PUNCT
ejpam-3907	132	4	let	let	VERB
ejpam-3907	132	5	a	a	PRON
ejpam-3907	132	6	=	=	PUNCT
ejpam-3907	132	7	{	{	PUNCT
ejpam-3907	132	8	i	i	NOUN
ejpam-3907	132	9	∈	∈	PROPN
ejpam-3907	132	10	zn	zn	X
ejpam-3907	132	11	:	:	PUNCT
ejpam-3907	132	12	sq(i	sq(i	X
ejpam-3907	132	13	)	)	PUNCT
ejpam-3907	133	1	+	+	VERB
ejpam-3907	133	2	m	m	NOUN
ejpam-3907	133	3	6≡	6≡	NUM
ejpam-3907	133	4	0	0	NUM
ejpam-3907	133	5	mod	mod	PROPN
ejpam-3907	133	6	p	p	X
ejpam-3907	133	7	}	}	PUNCT
ejpam-3907	133	8	and	and	CCONJ
ejpam-3907	133	9	b	b	X
ejpam-3907	133	10	=	=	PRON
ejpam-3907	133	11	{	{	PUNCT
ejpam-3907	133	12	i	i	NOUN
ejpam-3907	133	13	∈	∈	PROPN
ejpam-3907	133	14	ce	ce	PROPN
ejpam-3907	133	15	}	}	PUNCT
ejpam-3907	133	16	.	.	PUNCT
ejpam-3907	134	1	so	so	ADV
ejpam-3907	134	2	,	,	PUNCT
ejpam-3907	134	3	(	(	PUNCT
ejpam-3907	134	4	7	7	X
ejpam-3907	134	5	)	)	PUNCT
ejpam-3907	134	6	becomes	become	VERB
ejpam-3907	134	7	supp(ke	supp(ke	ADJ
ejpam-3907	134	8	,	,	PUNCT
ejpam-3907	134	9	q	q	NOUN
ejpam-3907	134	10	,	,	PUNCT
ejpam-3907	134	11	m	m	NOUN
ejpam-3907	134	12	)	)	PUNCT
ejpam-3907	134	13	=	=	SYM
ejpam-3907	134	14	a\b	a\b	NOUN
ejpam-3907	134	15	.	.	PUNCT
ejpam-3907	135	1	to	to	PART
ejpam-3907	135	2	get	get	VERB
ejpam-3907	135	3	the	the	DET
ejpam-3907	135	4	cardinality	cardinality	NOUN
ejpam-3907	135	5	of	of	ADP
ejpam-3907	135	6	a	a	PRON
ejpam-3907	135	7	we	we	PRON
ejpam-3907	135	8	need	need	VERB
ejpam-3907	135	9	to	to	PART
ejpam-3907	135	10	prove	prove	VERB
ejpam-3907	135	11	the	the	DET
ejpam-3907	135	12	following	follow	VERB
ejpam-3907	135	13	lemmas	lemmas	NOUN
ejpam-3907	135	14	.	.	PUNCT
ejpam-3907	136	1	let	let	VERB
ejpam-3907	136	2	λ1	λ1	ADJ
ejpam-3907	136	3	=	=	SYM
ejpam-3907	136	4	n	n	CCONJ
ejpam-3907	136	5	q−1	q−1	PROPN
ejpam-3907	136	6	and	and	CCONJ
ejpam-3907	136	7	λ2	λ2	NOUN
ejpam-3907	136	8	=	=	PUNCT
ejpam-3907	136	9	q	q	NOUN
ejpam-3907	137	1	−	−	NOUN
ejpam-3907	137	2	1	1	NUM
ejpam-3907	137	3	,	,	PUNCT
ejpam-3907	137	4	then	then	ADV
ejpam-3907	137	5	λ1	λ1	ADJ
ejpam-3907	137	6	=	=	SYM
ejpam-3907	137	7	1	1	NUM
ejpam-3907	137	8	+	+	CCONJ
ejpam-3907	137	9	q	q	NOUN
ejpam-3907	137	10	+	+	NUM
ejpam-3907	137	11	q2	q2	NOUN
ejpam-3907	137	12	+	+	X
ejpam-3907	137	13	·	·	PUNCT
ejpam-3907	137	14	·	·	PUNCT
ejpam-3907	137	15	·	·	PUNCT
ejpam-3907	138	1	+	+	NUM
ejpam-3907	138	2	qm−1	qm−1	NOUN
ejpam-3907	138	3	and	and	CCONJ
ejpam-3907	138	4	λ1λ2	λ1λ2	NOUN
ejpam-3907	138	5	=	=	PUNCT
ejpam-3907	138	6	n.	n.	PROPN
ejpam-3907	138	7	lemma	lemma	PROPN
ejpam-3907	138	8	7	7	X
ejpam-3907	138	9	.	.	PUNCT
ejpam-3907	138	10	let	let	VERB
ejpam-3907	138	11	a	a	DET
ejpam-3907	138	12	∈	∈	PROPN
ejpam-3907	138	13	zn	zn	X
ejpam-3907	138	14	and	and	CCONJ
ejpam-3907	138	15	j	j	PROPN
ejpam-3907	138	16	∈	∈	PROPN
ejpam-3907	138	17	{	{	PUNCT
ejpam-3907	138	18	0	0	NUM
ejpam-3907	138	19	,	,	PUNCT
ejpam-3907	138	20	1	1	NUM
ejpam-3907	138	21	,	,	PUNCT
ejpam-3907	138	22	2	2	NUM
ejpam-3907	138	23	,	,	PUNCT
ejpam-3907	138	24	.	.	PUNCT
ejpam-3907	138	25	.	.	PUNCT
ejpam-3907	138	26	.	.	PUNCT
ejpam-3907	139	1	,	,	PUNCT
ejpam-3907	139	2	m	m	VERB
ejpam-3907	139	3	−	−	NOUN
ejpam-3907	139	4	1	1	NUM
ejpam-3907	139	5	}	}	PUNCT
ejpam-3907	139	6	such	such	ADJ
ejpam-3907	139	7	that	that	SCONJ
ejpam-3907	139	8	aqj	aqj	PROPN
ejpam-3907	139	9	≥	≥	X
ejpam-3907	139	10	n	n	PROPN
ejpam-3907	139	11	and	and	CCONJ
ejpam-3907	139	12	aqj	aqj	NOUN
ejpam-3907	139	13	=	=	SYM
ejpam-3907	139	14	γn	γn	PROPN
ejpam-3907	139	15	+	+	CCONJ
ejpam-3907	139	16	δ	δ	PROPN
ejpam-3907	139	17	,	,	PUNCT
ejpam-3907	139	18	for	for	ADP
ejpam-3907	139	19	some	some	DET
ejpam-3907	139	20	δ	δ	PROPN
ejpam-3907	139	21	∈	∈	PROPN
ejpam-3907	139	22	zn	zn	X
ejpam-3907	139	23	.	.	PUNCT
ejpam-3907	140	1	then	then	ADV
ejpam-3907	140	2	aqj	aqj	PROPN
ejpam-3907	140	3	≡	≡	PROPN
ejpam-3907	140	4	aqj	aqj	PROPN
ejpam-3907	140	5	−	−	PROPN
ejpam-3907	140	6	γλ2(1	γλ2(1	NOUN
ejpam-3907	140	7	+	+	CCONJ
ejpam-3907	140	8	q	q	NOUN
ejpam-3907	140	9	+	+	NUM
ejpam-3907	140	10	q2	q2	NOUN
ejpam-3907	140	11	+	+	X
ejpam-3907	140	12	·	·	PUNCT
ejpam-3907	140	13	·	·	PUNCT
ejpam-3907	140	14	·	·	PUNCT
ejpam-3907	140	15	+	+	NUM
ejpam-3907	140	16	qm−1	qm−1	NOUN
ejpam-3907	140	17	)	)	PUNCT
ejpam-3907	140	18	mod	mod	PROPN
ejpam-3907	140	19	n	n	CCONJ
ejpam-3907	140	20	,	,	PUNCT
ejpam-3907	140	21	for	for	ADP
ejpam-3907	140	22	some	some	DET
ejpam-3907	140	23	γ	γ	NOUN
ejpam-3907	140	24	≥	≥	NOUN
ejpam-3907	140	25	0	0	NUM
ejpam-3907	140	26	.	.	PUNCT
ejpam-3907	140	27	proof	proof	NOUN
ejpam-3907	140	28	.	.	PUNCT
ejpam-3907	141	1	consider	consider	VERB
ejpam-3907	141	2	δ	δ	PROPN
ejpam-3907	141	3	∈	∈	PROPN
ejpam-3907	141	4	zn	zn	PROPN
ejpam-3907	141	5	,	,	PUNCT
ejpam-3907	141	6	that	that	PRON
ejpam-3907	141	7	is	be	AUX
ejpam-3907	141	8	δ	δ	PROPN
ejpam-3907	141	9	=	=	PUNCT
ejpam-3907	141	10	aqj	aqj	PROPN
ejpam-3907	142	1	−	−	PROPN
ejpam-3907	142	2	γn	γn	NOUN
ejpam-3907	142	3	=	=	PUNCT
ejpam-3907	142	4	aqj	aqj	PROPN
ejpam-3907	142	5	−	−	PROPN
ejpam-3907	142	6	γλ1λ2	γλ1λ2	PROPN
ejpam-3907	142	7	,	,	PUNCT
ejpam-3907	142	8	so	so	SCONJ
ejpam-3907	142	9	that	that	SCONJ
ejpam-3907	142	10	δ	δ	PROPN
ejpam-3907	142	11	≡	≡	PROPN
ejpam-3907	142	12	aqj	aqj	PROPN
ejpam-3907	142	13	−	−	PROPN
ejpam-3907	142	14	γλ2(1	γλ2(1	NOUN
ejpam-3907	142	15	+	+	CCONJ
ejpam-3907	142	16	q	q	NOUN
ejpam-3907	142	17	+	+	NUM
ejpam-3907	142	18	q2	q2	NOUN
ejpam-3907	142	19	+	+	X
ejpam-3907	142	20	·	·	PUNCT
ejpam-3907	142	21	·	·	PUNCT
ejpam-3907	142	22	·	·	PUNCT
ejpam-3907	142	23	+	+	NUM
ejpam-3907	142	24	qm−1	qm−1	NOUN
ejpam-3907	142	25	)	)	PUNCT
ejpam-3907	142	26	mod	mod	PROPN
ejpam-3907	142	27	n	n	CCONJ
ejpam-3907	142	28	,	,	PUNCT
ejpam-3907	142	29	for	for	ADP
ejpam-3907	142	30	some	some	DET
ejpam-3907	142	31	γ	γ	NOUN
ejpam-3907	142	32	≥	≥	NOUN
ejpam-3907	142	33	0	0	NUM
ejpam-3907	142	34	.	.	PUNCT
ejpam-3907	143	1	nopendri	nopendri	PROPN
ejpam-3907	143	2	et	et	PROPN
ejpam-3907	143	3	al	al	PROPN
ejpam-3907	143	4	.	.	PUNCT
ejpam-3907	143	5	/	/	SYM
ejpam-3907	143	6	eur	eur	PROPN
ejpam-3907	143	7	.	.	PUNCT
ejpam-3907	144	1	j.	j.	PROPN
ejpam-3907	144	2	pure	pure	PROPN
ejpam-3907	144	3	appl	appl	PROPN
ejpam-3907	144	4	.	.	PROPN
ejpam-3907	144	5	math	math	PROPN
ejpam-3907	144	6	,	,	PUNCT
ejpam-3907	144	7	14	14	NUM
ejpam-3907	144	8	(	(	PUNCT
ejpam-3907	144	9	3	3	NUM
ejpam-3907	144	10	)	)	PUNCT
ejpam-3907	144	11	(	(	PUNCT
ejpam-3907	144	12	2021	2021	NUM
ejpam-3907	144	13	)	)	PUNCT
ejpam-3907	144	14	,	,	PUNCT
ejpam-3907	144	15	685	685	NUM
ejpam-3907	144	16	-	-	SYM
ejpam-3907	144	17	694	694	NUM
ejpam-3907	144	18	691	691	NUM
ejpam-3907	144	19	lemma	lemma	PROPN
ejpam-3907	144	20	8	8	NUM
ejpam-3907	144	21	.	.	PUNCT
ejpam-3907	145	1	let	let	VERB
ejpam-3907	145	2	b	b	X
ejpam-3907	145	3	∈	∈	PROPN
ejpam-3907	145	4	zn	zn	PROPN
ejpam-3907	145	5	,	,	PUNCT
ejpam-3907	145	6	b	b	PROPN
ejpam-3907	145	7	6=	6=	PROPN
ejpam-3907	145	8	0	0	NUM
ejpam-3907	145	9	.	.	PUNCT
ejpam-3907	146	1	then	then	ADV
ejpam-3907	146	2	sq(b	sq(b	PUNCT
ejpam-3907	146	3	)	)	PUNCT
ejpam-3907	146	4	=	=	SYM
ejpam-3907	146	5	(	(	PUNCT
ejpam-3907	146	6	bq0	bq0	PROPN
ejpam-3907	146	7	mod	mod	PROPN
ejpam-3907	146	8	n	n	CCONJ
ejpam-3907	146	9	)	)	PUNCT
ejpam-3907	147	1	+	+	CCONJ
ejpam-3907	147	2	(	(	PUNCT
ejpam-3907	147	3	bq1	bq1	PROPN
ejpam-3907	147	4	mod	mod	PROPN
ejpam-3907	147	5	n	n	CCONJ
ejpam-3907	147	6	)	)	PUNCT
ejpam-3907	147	7	+	+	CCONJ
ejpam-3907	147	8	·	·	PUNCT
ejpam-3907	147	9	·	·	PUNCT
ejpam-3907	147	10	·	·	PUNCT
ejpam-3907	148	1	+	+	CCONJ
ejpam-3907	148	2	(	(	PUNCT
ejpam-3907	148	3	bqm−1	bqm−1	PROPN
ejpam-3907	148	4	mod	mod	PROPN
ejpam-3907	148	5	n	n	CCONJ
ejpam-3907	148	6	)	)	PUNCT
ejpam-3907	148	7	=	=	SYM
ejpam-3907	148	8	(	(	PUNCT
ejpam-3907	148	9	b−	b−	NOUN
ejpam-3907	148	10	γ′)(1	γ′)(1	ADP
ejpam-3907	148	11	+	+	CCONJ
ejpam-3907	148	12	q	q	NOUN
ejpam-3907	148	13	+	+	NUM
ejpam-3907	148	14	q2	q2	NOUN
ejpam-3907	148	15	+	+	X
ejpam-3907	148	16	·	·	PUNCT
ejpam-3907	148	17	·	·	PUNCT
ejpam-3907	148	18	·	·	PUNCT
ejpam-3907	148	19	+	+	NUM
ejpam-3907	148	20	qm−1	qm−1	NOUN
ejpam-3907	148	21	)	)	PUNCT
ejpam-3907	148	22	=	=	SYM
ejpam-3907	148	23	(	(	PUNCT
ejpam-3907	148	24	b−	b−	PROPN
ejpam-3907	148	25	γ′	γ′	PROPN
ejpam-3907	148	26	)	)	PUNCT
ejpam-3907	148	27	n	n	PRON
ejpam-3907	148	28	q	q	NOUN
ejpam-3907	148	29	−	−	PROPN
ejpam-3907	148	30	1	1	NUM
ejpam-3907	148	31	,	,	PUNCT
ejpam-3907	148	32	for	for	ADP
ejpam-3907	148	33	some	some	PRON
ejpam-3907	148	34	γ′	γ′	NOUN
ejpam-3907	148	35	<	<	X
ejpam-3907	148	36	b.	b.	PROPN
ejpam-3907	148	37	proof	proof	NOUN
ejpam-3907	148	38	.	.	PUNCT
ejpam-3907	149	1	suppose	suppose	VERB
ejpam-3907	149	2	j1	j1	PROPN
ejpam-3907	149	3	,	,	PUNCT
ejpam-3907	149	4	j2	j2	PROPN
ejpam-3907	149	5	,	,	PUNCT
ejpam-3907	149	6	·	·	PUNCT
ejpam-3907	149	7	·	·	PUNCT
ejpam-3907	149	8	·	·	PUNCT
ejpam-3907	149	9	,	,	PUNCT
ejpam-3907	149	10	jt	jt	PROPN
ejpam-3907	149	11	∈	∈	PROPN
ejpam-3907	149	12	{	{	PUNCT
ejpam-3907	149	13	0	0	NUM
ejpam-3907	149	14	,	,	PUNCT
ejpam-3907	149	15	1	1	NUM
ejpam-3907	149	16	,	,	PUNCT
ejpam-3907	149	17	2	2	NUM
ejpam-3907	149	18	,	,	PUNCT
ejpam-3907	149	19	·	·	PUNCT
ejpam-3907	149	20	·	·	PUNCT
ejpam-3907	149	21	·	·	PUNCT
ejpam-3907	149	22	,	,	PUNCT
ejpam-3907	149	23	m	m	VERB
ejpam-3907	149	24	−	−	NOUN
ejpam-3907	149	25	1	1	NUM
ejpam-3907	149	26	}	}	PUNCT
ejpam-3907	149	27	such	such	ADJ
ejpam-3907	149	28	that	that	DET
ejpam-3907	149	29	bqji	bqji	NOUN
ejpam-3907	149	30	≥	≥	PROPN
ejpam-3907	149	31	n	n	CCONJ
ejpam-3907	149	32	,	,	PUNCT
ejpam-3907	149	33	for	for	ADP
ejpam-3907	149	34	every	every	DET
ejpam-3907	149	35	i	i	NOUN
ejpam-3907	149	36	=	=	NOUN
ejpam-3907	149	37	1	1	NUM
ejpam-3907	149	38	,	,	PUNCT
ejpam-3907	149	39	2	2	NUM
ejpam-3907	149	40	,	,	PUNCT
ejpam-3907	149	41	·	·	PUNCT
ejpam-3907	149	42	·	·	PUNCT
ejpam-3907	149	43	·	·	PUNCT
ejpam-3907	149	44	,	,	PUNCT
ejpam-3907	149	45	t.	t.	NOUN
ejpam-3907	149	46	then	then	ADV
ejpam-3907	149	47	by	by	ADP
ejpam-3907	149	48	lemma	lemma	PROPN
ejpam-3907	149	49	7	7	NUM
ejpam-3907	149	50	,	,	PUNCT
ejpam-3907	149	51	we	we	PRON
ejpam-3907	149	52	have	have	AUX
ejpam-3907	149	53	bqji	bqji	VERB
ejpam-3907	149	54	≡	≡	PROPN
ejpam-3907	149	55	bqji	bqji	NOUN
ejpam-3907	149	56	−	−	PROPN
ejpam-3907	150	1	γiλ2(1	γiλ2(1	PROPN
ejpam-3907	150	2	+	+	CCONJ
ejpam-3907	150	3	q	q	NOUN
ejpam-3907	150	4	+	+	NUM
ejpam-3907	150	5	·	·	PUNCT
ejpam-3907	150	6	·	·	PUNCT
ejpam-3907	150	7	·	·	PUNCT
ejpam-3907	150	8	+	+	NUM
ejpam-3907	150	9	qm−1	qm−1	NOUN
ejpam-3907	150	10	)	)	PUNCT
ejpam-3907	150	11	mod	mod	PROPN
ejpam-3907	150	12	n	n	CCONJ
ejpam-3907	150	13	,	,	PUNCT
ejpam-3907	150	14	for	for	ADP
ejpam-3907	150	15	some	some	DET
ejpam-3907	150	16	γi	γi	NOUN
ejpam-3907	150	17	≥	≥	NOUN
ejpam-3907	150	18	0	0	NUM
ejpam-3907	150	19	and	and	CCONJ
ejpam-3907	150	20	for	for	ADP
ejpam-3907	150	21	all	all	DET
ejpam-3907	150	22	i	i	PRON
ejpam-3907	150	23	=	=	NOUN
ejpam-3907	150	24	1	1	NUM
ejpam-3907	150	25	,	,	PUNCT
ejpam-3907	150	26	2	2	NUM
ejpam-3907	150	27	,	,	PUNCT
ejpam-3907	150	28	·	·	PUNCT
ejpam-3907	150	29	·	·	PUNCT
ejpam-3907	150	30	·	·	PUNCT
ejpam-3907	150	31	,	,	PUNCT
ejpam-3907	150	32	t.	t.	NOUN
ejpam-3907	150	33	hence	hence	ADV
ejpam-3907	150	34	sq(b	sq(b	PUNCT
ejpam-3907	150	35	)	)	PUNCT
ejpam-3907	150	36	=	=	SYM
ejpam-3907	150	37	(	(	PUNCT
ejpam-3907	150	38	bq0	bq0	PROPN
ejpam-3907	150	39	mod	mod	PROPN
ejpam-3907	150	40	n	n	CCONJ
ejpam-3907	150	41	)	)	PUNCT
ejpam-3907	150	42	+	+	CCONJ
ejpam-3907	150	43	(	(	PUNCT
ejpam-3907	150	44	bq1	bq1	PROPN
ejpam-3907	150	45	mod	mod	PROPN
ejpam-3907	150	46	n	n	CCONJ
ejpam-3907	150	47	)	)	PUNCT
ejpam-3907	150	48	+	+	CCONJ
ejpam-3907	150	49	·	·	PUNCT
ejpam-3907	150	50	·	·	PUNCT
ejpam-3907	150	51	·	·	PUNCT
ejpam-3907	151	1	+	+	CCONJ
ejpam-3907	151	2	(	(	PUNCT
ejpam-3907	151	3	bqm−1	bqm−1	PROPN
ejpam-3907	151	4	mod	mod	PROPN
ejpam-3907	151	5	n	n	CCONJ
ejpam-3907	151	6	)	)	PUNCT
ejpam-3907	152	1	=	=	NOUN
ejpam-3907	152	2	b(q0	b(q0	NOUN
ejpam-3907	152	3	+	+	CCONJ
ejpam-3907	152	4	q1	q1	PROPN
ejpam-3907	152	5	+	+	CCONJ
ejpam-3907	152	6	q2	q2	NOUN
ejpam-3907	152	7	+	+	X
ejpam-3907	152	8	·	·	PUNCT
ejpam-3907	152	9	·	·	PUNCT
ejpam-3907	152	10	·	·	PUNCT
ejpam-3907	152	11	+	+	NUM
ejpam-3907	152	12	qm−1	qm−1	NOUN
ejpam-3907	152	13	)	)	PUNCT
ejpam-3907	152	14	−	−	PROPN
ejpam-3907	153	1	(	(	PUNCT
ejpam-3907	153	2	λ2	λ2	NOUN
ejpam-3907	153	3	t∑	t∑	X
ejpam-3907	153	4	i=0	i=0	PROPN
ejpam-3907	153	5	γi(q	γi(q	NUM
ejpam-3907	153	6	0	0	NUM
ejpam-3907	154	1	+	+	NUM
ejpam-3907	154	2	q1	q1	PROPN
ejpam-3907	154	3	+	+	CCONJ
ejpam-3907	154	4	q2	q2	NOUN
ejpam-3907	154	5	+	+	X
ejpam-3907	154	6	·	·	PUNCT
ejpam-3907	154	7	·	·	PUNCT
ejpam-3907	154	8	·	·	PUNCT
ejpam-3907	154	9	+	+	NUM
ejpam-3907	154	10	qm−1	qm−1	NOUN
ejpam-3907	154	11	)	)	PUNCT
ejpam-3907	154	12	)	)	PUNCT
ejpam-3907	155	1	=	=	PRON
ejpam-3907	155	2	(	(	PUNCT
ejpam-3907	155	3	b−	b−	NOUN
ejpam-3907	155	4	λ2	λ2	PROPN
ejpam-3907	155	5	t∑	t∑	PROPN
ejpam-3907	155	6	i=0	i=0	PROPN
ejpam-3907	155	7	γi	γi	NOUN
ejpam-3907	155	8	)	)	PUNCT
ejpam-3907	155	9	(	(	PUNCT
ejpam-3907	155	10	q0	q0	PROPN
ejpam-3907	155	11	+	+	NUM
ejpam-3907	155	12	q1	q1	PROPN
ejpam-3907	155	13	+	+	CCONJ
ejpam-3907	155	14	q2	q2	NOUN
ejpam-3907	155	15	+	+	X
ejpam-3907	155	16	·	·	PUNCT
ejpam-3907	155	17	·	·	PUNCT
ejpam-3907	155	18	·	·	PUNCT
ejpam-3907	156	1	+	+	NUM
ejpam-3907	156	2	qm−1	qm−1	NOUN
ejpam-3907	156	3	)	)	PUNCT
ejpam-3907	156	4	.	.	PUNCT
ejpam-3907	157	1	put	put	VERB
ejpam-3907	157	2	γ′	γ′	NOUN
ejpam-3907	157	3	=	=	PUNCT
ejpam-3907	158	1	λ2	λ2	NOUN
ejpam-3907	158	2	∑t	∑t	PROPN
ejpam-3907	158	3	i=1	i=1	PROPN
ejpam-3907	158	4	γi	γi	PROPN
ejpam-3907	158	5	.	.	PUNCT
ejpam-3907	158	6	lemma	lemma	PROPN
ejpam-3907	158	7	9	9	NUM
ejpam-3907	158	8	.	.	PUNCT
ejpam-3907	159	1	if	if	SCONJ
ejpam-3907	159	2	(	(	PUNCT
ejpam-3907	159	3	b−	b−	PROPN
ejpam-3907	159	4	γ′	γ′	NOUN
ejpam-3907	159	5	)	)	PUNCT
ejpam-3907	159	6	6=	6=	ADP
ejpam-3907	159	7	0	0	NUM
ejpam-3907	159	8	mod	mod	PROPN
ejpam-3907	159	9	p	p	X
ejpam-3907	159	10	,	,	PUNCT
ejpam-3907	159	11	then	then	ADV
ejpam-3907	159	12	(	(	PUNCT
ejpam-3907	159	13	b−	b−	NOUN
ejpam-3907	159	14	γ′)λ1	γ′)λ1	PUNCT
ejpam-3907	159	15	=	=	PUNCT
ejpam-3907	159	16	(	(	PUNCT
ejpam-3907	159	17	b−	b−	PROPN
ejpam-3907	159	18	γ′	γ′	PROPN
ejpam-3907	159	19	)	)	PUNCT
ejpam-3907	159	20	n	n	PRON
ejpam-3907	159	21	q	q	NOUN
ejpam-3907	159	22	−	−	PROPN
ejpam-3907	159	23	1	1	NUM
ejpam-3907	159	24	6=	6=	SYM
ejpam-3907	159	25	0	0	NUM
ejpam-3907	159	26	mod	mod	ADJ
ejpam-3907	159	27	p.	p.	NOUN
ejpam-3907	159	28	proof	proof	NOUN
ejpam-3907	159	29	.	.	PUNCT
ejpam-3907	160	1	since	since	SCONJ
ejpam-3907	160	2	λ1|n	λ1|n	PROPN
ejpam-3907	160	3	=	=	SYM
ejpam-3907	160	4	qm	qm	PROPN
ejpam-3907	160	5	−	−	PROPN
ejpam-3907	160	6	1	1	NUM
ejpam-3907	160	7	,	,	PUNCT
ejpam-3907	160	8	then	then	ADV
ejpam-3907	160	9	gcd(λ1	gcd(λ1	NOUN
ejpam-3907	160	10	,	,	PUNCT
ejpam-3907	160	11	p	p	NOUN
ejpam-3907	160	12	)	)	PUNCT
ejpam-3907	160	13	=	=	SYM
ejpam-3907	160	14	1	1	NUM
ejpam-3907	160	15	so	so	SCONJ
ejpam-3907	160	16	that	that	SCONJ
ejpam-3907	160	17	λ1	λ1	ADJ
ejpam-3907	160	18	mod	mod	NOUN
ejpam-3907	160	19	p	p	PROPN
ejpam-3907	160	20	is	be	AUX
ejpam-3907	160	21	a	a	DET
ejpam-3907	160	22	unit	unit	NOUN
ejpam-3907	160	23	in	in	ADP
ejpam-3907	160	24	zp	zp	PROPN
ejpam-3907	160	25	.	.	PUNCT
ejpam-3907	161	1	consequently	consequently	ADV
ejpam-3907	161	2	,	,	PUNCT
ejpam-3907	161	3	if	if	SCONJ
ejpam-3907	161	4	(	(	PUNCT
ejpam-3907	161	5	b−	b−	PROPN
ejpam-3907	161	6	γ′	γ′	PROPN
ejpam-3907	161	7	)	)	PUNCT
ejpam-3907	161	8	6≡	6≡	NUM
ejpam-3907	161	9	0	0	NUM
ejpam-3907	161	10	mod	mod	PROPN
ejpam-3907	161	11	p	p	NOUN
ejpam-3907	161	12	,	,	PUNCT
ejpam-3907	161	13	then	then	ADV
ejpam-3907	161	14	(	(	PUNCT
ejpam-3907	161	15	b−	b−	NOUN
ejpam-3907	161	16	γ′)λ1	γ′)λ1	PUNCT
ejpam-3907	161	17	≡	≡	PROPN
ejpam-3907	161	18	(	(	PUNCT
ejpam-3907	161	19	b−	b−	PROPN
ejpam-3907	161	20	γ′	γ′	PROPN
ejpam-3907	161	21	)	)	PUNCT
ejpam-3907	162	1	n	n	PROPN
ejpam-3907	162	2	q−1	q−1	PROPN
ejpam-3907	163	1	6≡	6≡	NUM
ejpam-3907	163	2	0	0	NUM
ejpam-3907	163	3	mod	mod	PROPN
ejpam-3907	163	4	p.	p.	NOUN
ejpam-3907	163	5	in	in	ADP
ejpam-3907	163	6	order	order	NOUN
ejpam-3907	163	7	to	to	PART
ejpam-3907	163	8	determine	determine	VERB
ejpam-3907	163	9	i	i	PRON
ejpam-3907	163	10	∈	∈	PROPN
ejpam-3907	163	11	zn	zn	PROPN
ejpam-3907	163	12	such	such	ADJ
ejpam-3907	163	13	that	that	PRON
ejpam-3907	163	14	sq(i	sq(i	VERB
ejpam-3907	163	15	)	)	PUNCT
ejpam-3907	163	16	6=	6=	ADP
ejpam-3907	163	17	0	0	NUM
ejpam-3907	163	18	mod	mod	PROPN
ejpam-3907	163	19	p	p	X
ejpam-3907	163	20	,	,	PUNCT
ejpam-3907	163	21	it	it	PRON
ejpam-3907	163	22	is	be	AUX
ejpam-3907	163	23	equivalent	equivalent	ADJ
ejpam-3907	163	24	to	to	PART
ejpam-3907	163	25	find	find	VERB
ejpam-3907	163	26	i	i	PRON
ejpam-3907	163	27	such	such	ADJ
ejpam-3907	163	28	that	that	SCONJ
ejpam-3907	163	29	i	i	PRON
ejpam-3907	163	30	−	−	VERB
ejpam-3907	163	31	γ′	γ′	NOUN
ejpam-3907	163	32	6≡	6≡	NUM
ejpam-3907	163	33	0	0	NUM
ejpam-3907	163	34	mod	mod	PROPN
ejpam-3907	163	35	p	p	NOUN
ejpam-3907	163	36	(	(	PUNCT
ejpam-3907	163	37	based	base	VERB
ejpam-3907	163	38	on	on	ADP
ejpam-3907	163	39	lemma	lemma	PROPN
ejpam-3907	163	40	8	8	NUM
ejpam-3907	163	41	and	and	CCONJ
ejpam-3907	163	42	lemma	lemma	PROPN
ejpam-3907	163	43	9	9	NUM
ejpam-3907	163	44	)	)	PUNCT
ejpam-3907	163	45	and	and	CCONJ
ejpam-3907	163	46	i	i	PRON
ejpam-3907	163	47	−	−	VERB
ejpam-3907	163	48	γ′	γ′	NOUN
ejpam-3907	163	49	6≡	6≡	NUM
ejpam-3907	163	50	0	0	NUM
ejpam-3907	163	51	mod	mod	PROPN
ejpam-3907	163	52	p	p	NOUN
ejpam-3907	164	1	if	if	SCONJ
ejpam-3907	165	1	and	and	CCONJ
ejpam-3907	165	2	only	only	ADV
ejpam-3907	165	3	if	if	SCONJ
ejpam-3907	165	4	gcd(i−	gcd(i−	PROPN
ejpam-3907	165	5	γ′	γ′	PROPN
ejpam-3907	165	6	,	,	PUNCT
ejpam-3907	165	7	qm	qm	PROPN
ejpam-3907	165	8	)	)	PUNCT
ejpam-3907	165	9	=	=	PUNCT
ejpam-3907	166	1	1	1	X
ejpam-3907	166	2	.	.	PUNCT
ejpam-3907	167	1	hence	hence	ADV
ejpam-3907	167	2	,	,	PUNCT
ejpam-3907	167	3	from	from	ADP
ejpam-3907	167	4	phi	phi	NOUN
ejpam-3907	167	5	euler	euler	NOUN
ejpam-3907	167	6	function	function	NOUN
ejpam-3907	167	7	we	we	PRON
ejpam-3907	167	8	have	have	VERB
ejpam-3907	167	9	#	#	SYM
ejpam-3907	167	10	a	a	DET
ejpam-3907	167	11	=	=	SYM
ejpam-3907	167	12	qm(1−	qm(1−	ADJ
ejpam-3907	167	13	1	1	NUM
ejpam-3907	167	14	p	p	NOUN
ejpam-3907	167	15	)	)	PUNCT
ejpam-3907	167	16	.	.	PUNCT
ejpam-3907	168	1	(	(	PUNCT
ejpam-3907	168	2	8)	8)	NUM
ejpam-3907	168	3	the	the	DET
ejpam-3907	168	4	biggest	big	ADJ
ejpam-3907	168	5	element	element	NOUN
ejpam-3907	168	6	in	in	ADP
ejpam-3907	168	7	zn	zn	PROPN
ejpam-3907	168	8	,	,	PUNCT
ejpam-3907	168	9	that	that	ADV
ejpam-3907	168	10	is	is	ADV
ejpam-3907	168	11	e	e	NOUN
ejpam-3907	168	12	=	=	SYM
ejpam-3907	168	13	qm	qm	PROPN
ejpam-3907	168	14	−	−	PROPN
ejpam-3907	168	15	2	2	NUM
ejpam-3907	168	16	,	,	PUNCT
ejpam-3907	168	17	contained	contain	VERB
ejpam-3907	168	18	in	in	ADP
ejpam-3907	168	19	a.	a.	NOUN
ejpam-3907	168	20	it	it	PRON
ejpam-3907	168	21	can	can	AUX
ejpam-3907	168	22	be	be	AUX
ejpam-3907	168	23	shown	show	VERB
ejpam-3907	168	24	by	by	ADP
ejpam-3907	168	25	the	the	DET
ejpam-3907	168	26	following	follow	VERB
ejpam-3907	168	27	lemma	lemma	PROPN
ejpam-3907	168	28	.	.	PUNCT
ejpam-3907	169	1	nopendri	nopendri	PROPN
ejpam-3907	169	2	et	et	PROPN
ejpam-3907	169	3	al	al	PROPN
ejpam-3907	169	4	.	.	PUNCT
ejpam-3907	169	5	/	/	SYM
ejpam-3907	169	6	eur	eur	PROPN
ejpam-3907	169	7	.	.	PUNCT
ejpam-3907	170	1	j.	j.	PROPN
ejpam-3907	170	2	pure	pure	PROPN
ejpam-3907	170	3	appl	appl	PROPN
ejpam-3907	170	4	.	.	PROPN
ejpam-3907	170	5	math	math	PROPN
ejpam-3907	170	6	,	,	PUNCT
ejpam-3907	170	7	14	14	NUM
ejpam-3907	170	8	(	(	PUNCT
ejpam-3907	170	9	3	3	NUM
ejpam-3907	170	10	)	)	PUNCT
ejpam-3907	170	11	(	(	PUNCT
ejpam-3907	170	12	2021	2021	NUM
ejpam-3907	170	13	)	)	PUNCT
ejpam-3907	170	14	,	,	PUNCT
ejpam-3907	170	15	685	685	NUM
ejpam-3907	170	16	-	-	SYM
ejpam-3907	170	17	694	694	NUM
ejpam-3907	170	18	692	692	NUM
ejpam-3907	170	19	lemma	lemma	PROPN
ejpam-3907	170	20	10	10	NUM
ejpam-3907	170	21	.	.	PUNCT
ejpam-3907	171	1	let	let	VERB
ejpam-3907	171	2	q	q	PART
ejpam-3907	171	3	be	be	AUX
ejpam-3907	171	4	a	a	DET
ejpam-3907	171	5	prime	prime	ADJ
ejpam-3907	171	6	power	power	NOUN
ejpam-3907	171	7	of	of	ADP
ejpam-3907	171	8	p.	p.	PROPN
ejpam-3907	171	9	defined	define	VERB
ejpam-3907	171	10	sq(i	sq(i	NOUN
ejpam-3907	171	11	)	)	PUNCT
ejpam-3907	171	12	=	=	SYM
ejpam-3907	171	13	m−1∑	m−1∑	PROPN
ejpam-3907	171	14	j=0	j=0	PROPN
ejpam-3907	171	15	kij	kij	PROPN
ejpam-3907	171	16	,	,	PUNCT
ejpam-3907	171	17	,	,	PUNCT
ejpam-3907	171	18	where	where	SCONJ
ejpam-3907	171	19	kij	kij	PROPN
ejpam-3907	171	20	=	=	PROPN
ejpam-3907	171	21	qji	qji	ADJ
ejpam-3907	171	22	mod	mod	PROPN
ejpam-3907	171	23	n	n	PROPN
ejpam-3907	171	24	and	and	CCONJ
ejpam-3907	171	25	n	n	CCONJ
ejpam-3907	171	26	=	=	NOUN
ejpam-3907	171	27	qm	qm	PROPN
ejpam-3907	171	28	−	−	PROPN
ejpam-3907	171	29	1	1	NUM
ejpam-3907	171	30	.	.	PUNCT
ejpam-3907	171	31	then	then	ADV
ejpam-3907	171	32	sq(e	sq(e	PUNCT
ejpam-3907	171	33	)	)	PUNCT
ejpam-3907	172	1	+	+	VERB
ejpam-3907	172	2	m	m	NOUN
ejpam-3907	172	3	6≡	6≡	NUM
ejpam-3907	172	4	0	0	NUM
ejpam-3907	172	5	mod	mod	PROPN
ejpam-3907	172	6	p	p	X
ejpam-3907	172	7	,	,	PUNCT
ejpam-3907	172	8	where	where	SCONJ
ejpam-3907	172	9	e	e	NOUN
ejpam-3907	172	10	=	=	NOUN
ejpam-3907	172	11	qm	qm	PROPN
ejpam-3907	172	12	−	−	NOUN
ejpam-3907	172	13	2	2	NUM
ejpam-3907	172	14	.	.	PUNCT
ejpam-3907	172	15	proof	proof	NOUN
ejpam-3907	172	16	.	.	PUNCT
ejpam-3907	173	1	sq(e	sq(e	X
ejpam-3907	173	2	)	)	PUNCT
ejpam-3907	174	1	+	+	NOUN
ejpam-3907	174	2	m	m	VERB
ejpam-3907	174	3	≡	≡	ADJ
ejpam-3907	174	4	(	(	PUNCT
ejpam-3907	174	5	e	e	PROPN
ejpam-3907	174	6	mod	mod	PROPN
ejpam-3907	174	7	n	n	CCONJ
ejpam-3907	174	8	)	)	PUNCT
ejpam-3907	175	1	+	+	CCONJ
ejpam-3907	175	2	(	(	PUNCT
ejpam-3907	175	3	qe	qe	PROPN
ejpam-3907	175	4	mod	mod	PROPN
ejpam-3907	175	5	n	n	CCONJ
ejpam-3907	175	6	)	)	PUNCT
ejpam-3907	175	7	+	+	CCONJ
ejpam-3907	175	8	·	·	PUNCT
ejpam-3907	175	9	·	·	PUNCT
ejpam-3907	175	10	·	·	PUNCT
ejpam-3907	176	1	+	+	PUNCT
ejpam-3907	176	2	(	(	PUNCT
ejpam-3907	176	3	qm−1e	qm−1e	PROPN
ejpam-3907	176	4	mod	mod	PROPN
ejpam-3907	176	5	n	n	CCONJ
ejpam-3907	176	6	)	)	PUNCT
ejpam-3907	177	1	+	+	NOUN
ejpam-3907	177	2	m	m	VERB
ejpam-3907	177	3	≡	≡	ADJ
ejpam-3907	177	4	(	(	PUNCT
ejpam-3907	177	5	n−	n−	NOUN
ejpam-3907	177	6	1	1	NUM
ejpam-3907	177	7	)	)	PUNCT
ejpam-3907	177	8	+	+	CCONJ
ejpam-3907	177	9	(	(	PUNCT
ejpam-3907	177	10	n−	n−	NOUN
ejpam-3907	177	11	q	q	NOUN
ejpam-3907	177	12	)	)	PUNCT
ejpam-3907	177	13	+	+	CCONJ
ejpam-3907	177	14	·	·	PUNCT
ejpam-3907	177	15	·	·	PUNCT
ejpam-3907	177	16	·	·	PUNCT
ejpam-3907	177	17	+	+	CCONJ
ejpam-3907	177	18	(	(	PUNCT
ejpam-3907	177	19	n−	n−	NOUN
ejpam-3907	177	20	qm−1	qm−1	NOUN
ejpam-3907	177	21	)	)	PUNCT
ejpam-3907	178	1	+	+	ADP
ejpam-3907	178	2	m	m	VERB
ejpam-3907	178	3	≡	≡	ADJ
ejpam-3907	178	4	mn+m−	mn+m−	PROPN
ejpam-3907	178	5	(	(	PUNCT
ejpam-3907	178	6	1	1	NUM
ejpam-3907	178	7	+	+	CCONJ
ejpam-3907	178	8	q	q	NOUN
ejpam-3907	178	9	+	+	NUM
ejpam-3907	178	10	q2	q2	NOUN
ejpam-3907	178	11	+	+	X
ejpam-3907	178	12	·	·	PUNCT
ejpam-3907	178	13	·	·	PUNCT
ejpam-3907	178	14	·	·	PUNCT
ejpam-3907	178	15	+	+	NUM
ejpam-3907	178	16	qm−1	qm−1	NOUN
ejpam-3907	178	17	)	)	PUNCT
ejpam-3907	179	1	≡	≡	PROPN
ejpam-3907	179	2	−1	−1	NOUN
ejpam-3907	179	3	mod	mod	PROPN
ejpam-3907	179	4	p.	p.	NOUN
ejpam-3907	179	5	from	from	ADP
ejpam-3907	179	6	lemma	lemma	PROPN
ejpam-3907	179	7	1	1	NUM
ejpam-3907	179	8	and	and	CCONJ
ejpam-3907	179	9	gcd(e	gcd(e	PROPN
ejpam-3907	179	10	,	,	PUNCT
ejpam-3907	179	11	n	n	CCONJ
ejpam-3907	179	12	)	)	PUNCT
ejpam-3907	179	13	=	=	SYM
ejpam-3907	179	14	1	1	NUM
ejpam-3907	179	15	we	we	PRON
ejpam-3907	179	16	have	have	AUX
ejpam-3907	179	17	|b|	|b|	PROPN
ejpam-3907	179	18	=	=	PUNCT
ejpam-3907	179	19	|ce|	|ce|	PROPN
ejpam-3907	179	20	=	=	PUNCT
ejpam-3907	179	21	m.	m.	NOUN
ejpam-3907	179	22	thus	thus	ADV
ejpam-3907	179	23	,	,	PUNCT
ejpam-3907	179	24	from	from	ADP
ejpam-3907	179	25	(	(	PUNCT
ejpam-3907	179	26	8)	8)	NUM
ejpam-3907	179	27	,	,	PUNCT
ejpam-3907	179	28	we	we	PRON
ejpam-3907	179	29	have	have	VERB
ejpam-3907	179	30	#	#	SYM
ejpam-3907	179	31	supp(ke	supp(ke	ADJ
ejpam-3907	179	32	,	,	PUNCT
ejpam-3907	179	33	q	q	NOUN
ejpam-3907	179	34	,	,	PUNCT
ejpam-3907	179	35	m	m	NOUN
ejpam-3907	179	36	)	)	PUNCT
ejpam-3907	179	37	=	=	PUNCT
ejpam-3907	179	38	qm(1−	qm(1−	ADJ
ejpam-3907	179	39	1	1	NUM
ejpam-3907	179	40	p	p	NOUN
ejpam-3907	179	41	)	)	PUNCT
ejpam-3907	179	42	−m	−m	NOUN
ejpam-3907	179	43	.	.	PUNCT
ejpam-3907	180	1	(	(	PUNCT
ejpam-3907	180	2	9	9	X
ejpam-3907	180	3	)	)	PUNCT
ejpam-3907	180	4	the	the	DET
ejpam-3907	180	5	following	follow	VERB
ejpam-3907	180	6	theorem	theorem	NOUN
ejpam-3907	180	7	gives	give	VERB
ejpam-3907	180	8	the	the	DET
ejpam-3907	180	9	minimal	minimal	ADJ
ejpam-3907	180	10	polynomial	polynomial	NOUN
ejpam-3907	180	11	of	of	ADP
ejpam-3907	180	12	the	the	DET
ejpam-3907	180	13	sequence	sequence	NOUN
ejpam-3907	180	14	š∞	š∞	PROPN
ejpam-3907	181	1	in	in	ADP
ejpam-3907	181	2	(	(	PUNCT
ejpam-3907	181	3	2	2	NUM
ejpam-3907	181	4	)	)	PUNCT
ejpam-3907	181	5	with	with	ADP
ejpam-3907	181	6	function	function	NOUN
ejpam-3907	181	7	(	(	PUNCT
ejpam-3907	181	8	3	3	NUM
ejpam-3907	181	9	)	)	PUNCT
ejpam-3907	181	10	.	.	PUNCT
ejpam-3907	182	1	theorem	theorem	NOUN
ejpam-3907	182	2	1	1	NUM
ejpam-3907	182	3	.	.	PUNCT
ejpam-3907	183	1	let	let	VERB
ejpam-3907	183	2	š∞	š∞	PRON
ejpam-3907	183	3	be	be	AUX
ejpam-3907	183	4	the	the	DET
ejpam-3907	183	5	sequence	sequence	NOUN
ejpam-3907	183	6	of	of	ADP
ejpam-3907	183	7	(	(	PUNCT
ejpam-3907	183	8	2	2	NUM
ejpam-3907	183	9	)	)	PUNCT
ejpam-3907	183	10	,	,	PUNCT
ejpam-3907	183	11	where	where	SCONJ
ejpam-3907	183	12	f(x	f(x	NOUN
ejpam-3907	183	13	)	)	PUNCT
ejpam-3907	184	1	=	=	PUNCT
ejpam-3907	184	2	xq	xq	PROPN
ejpam-3907	184	3	m−2	m−2	PROPN
ejpam-3907	184	4	,	,	PUNCT
ejpam-3907	184	5	then	then	ADV
ejpam-3907	184	6	the	the	DET
ejpam-3907	184	7	minimal	minimal	ADJ
ejpam-3907	184	8	polynomial	polynomial	NOUN
ejpam-3907	184	9	of	of	ADP
ejpam-3907	184	10	š∞	š∞	PROPN
ejpam-3907	184	11	is	be	AUX
ejpam-3907	184	12	given	give	VERB
ejpam-3907	184	13	by	by	ADP
ejpam-3907	184	14	mš(x	mš(x	NOUN
ejpam-3907	184	15	)	)	PUNCT
ejpam-3907	184	16	=	=	SYM
ejpam-3907	184	17	∏	∏	NUM
ejpam-3907	184	18	i∈zn	i∈zn	NOUN
ejpam-3907	184	19	,	,	PUNCT
ejpam-3907	184	20	sq(i)+m6≡0	sq(i)+m6≡0	PROPN
ejpam-3907	184	21	mod	mod	PROPN
ejpam-3907	184	22	p	p	X
ejpam-3907	184	23	,	,	PUNCT
ejpam-3907	184	24	i	i	PRON
ejpam-3907	184	25	6∈ce	6∈ce	NUM
ejpam-3907	184	26	(	(	PUNCT
ejpam-3907	184	27	x−	x−	PROPN
ejpam-3907	184	28	αi	αi	PROPN
ejpam-3907	184	29	)	)	PUNCT
ejpam-3907	184	30	,	,	PUNCT
ejpam-3907	184	31	(	(	PUNCT
ejpam-3907	184	32	10	10	NUM
ejpam-3907	184	33	)	)	PUNCT
ejpam-3907	184	34	and	and	CCONJ
ejpam-3907	184	35	the	the	DET
ejpam-3907	184	36	linier	linier	NOUN
ejpam-3907	184	37	span	span	NOUN
ejpam-3907	184	38	lš	lš	NOUN
ejpam-3907	184	39	of	of	ADP
ejpam-3907	184	40	š∞	š∞	PROPN
ejpam-3907	184	41	is	be	AUX
ejpam-3907	184	42	lš	lš	NOUN
ejpam-3907	184	43	=	=	PUNCT
ejpam-3907	184	44	qm(1−	qm(1−	ADJ
ejpam-3907	184	45	1	1	NUM
ejpam-3907	184	46	p	p	NOUN
ejpam-3907	184	47	)	)	PUNCT
ejpam-3907	184	48	−m	−m	NOUN
ejpam-3907	184	49	.	.	PUNCT
ejpam-3907	185	1	proof	proof	NOUN
ejpam-3907	185	2	.	.	PUNCT
ejpam-3907	186	1	this	this	DET
ejpam-3907	186	2	theorem	theorem	NOUN
ejpam-3907	186	3	follows	follow	VERB
ejpam-3907	186	4	from	from	ADP
ejpam-3907	186	5	lemma	lemma	PROPN
ejpam-3907	186	6	3	3	NUM
ejpam-3907	186	7	,	,	PUNCT
ejpam-3907	186	8	lemma	lemma	PROPN
ejpam-3907	186	9	10	10	NUM
ejpam-3907	186	10	,	,	PUNCT
ejpam-3907	186	11	eq	eq	NOUN
ejpam-3907	186	12	.	.	PUNCT
ejpam-3907	187	1	(	(	PUNCT
ejpam-3907	187	2	7	7	NUM
ejpam-3907	187	3	)	)	PUNCT
ejpam-3907	187	4	and	and	CCONJ
ejpam-3907	187	5	eq	eq	NOUN
ejpam-3907	187	6	.	.	PUNCT
ejpam-3907	188	1	(	(	PUNCT
ejpam-3907	188	2	9	9	NUM
ejpam-3907	188	3	)	)	PUNCT
ejpam-3907	188	4	.	.	PUNCT
ejpam-3907	189	1	the	the	PRON
ejpam-3907	189	2	polynomial	polynomial	ADJ
ejpam-3907	189	3	(	(	PUNCT
ejpam-3907	189	4	10	10	NUM
ejpam-3907	189	5	)	)	PUNCT
ejpam-3907	189	6	in	in	ADP
ejpam-3907	189	7	theorem	theorem	NOUN
ejpam-3907	189	8	1	1	NUM
ejpam-3907	189	9	can	can	AUX
ejpam-3907	189	10	be	be	AUX
ejpam-3907	189	11	used	use	VERB
ejpam-3907	189	12	to	to	PART
ejpam-3907	189	13	construct	construct	VERB
ejpam-3907	189	14	a	a	DET
ejpam-3907	189	15	class	class	NOUN
ejpam-3907	189	16	of	of	ADP
ejpam-3907	189	17	cyclic	cyclic	ADJ
ejpam-3907	189	18	codes	code	NOUN
ejpam-3907	189	19	as	as	ADP
ejpam-3907	189	20	the	the	DET
ejpam-3907	189	21	following	following	NOUN
ejpam-3907	189	22	.	.	PUNCT
ejpam-3907	190	1	theorem	theorem	NOUN
ejpam-3907	190	2	2	2	NUM
ejpam-3907	190	3	.	.	PUNCT
ejpam-3907	191	1	the	the	DET
ejpam-3907	191	2	cyclic	cyclic	PROPN
ejpam-3907	191	3	code	code	NOUN
ejpam-3907	191	4	cš	cš	NOUN
ejpam-3907	191	5	defined	define	VERB
ejpam-3907	191	6	by	by	ADP
ejpam-3907	191	7	sequence	sequence	NOUN
ejpam-3907	191	8	of	of	ADP
ejpam-3907	191	9	theorem	theorem	ADJ
ejpam-3907	191	10	1	1	NUM
ejpam-3907	191	11	has	have	VERB
ejpam-3907	191	12	parameters	parameter	NOUN
ejpam-3907	192	1	[	[	X
ejpam-3907	192	2	qm	qm	NOUN
ejpam-3907	192	3	−	−	PROPN
ejpam-3907	192	4	1	1	NUM
ejpam-3907	192	5	,	,	PUNCT
ejpam-3907	192	6	q	q	NOUN
ejpam-3907	193	1	m	m	NOUN
ejpam-3907	193	2	p	p	NOUN
ejpam-3907	193	3	−	−	PROPN
ejpam-3907	193	4	1	1	NUM
ejpam-3907	193	5	+	+	NOUN
ejpam-3907	193	6	m	m	NOUN
ejpam-3907	193	7	,	,	PUNCT
ejpam-3907	193	8	d	d	X
ejpam-3907	193	9	]	]	X
ejpam-3907	193	10	where	where	SCONJ
ejpam-3907	193	11	d	d	PROPN
ejpam-3907	193	12	≥	≥	X
ejpam-3907	193	13	q(p−1	q(p−1	SYM
ejpam-3907	193	14	)	)	PUNCT
ejpam-3907	193	15	p	p	NOUN
ejpam-3907	193	16	and	and	CCONJ
ejpam-3907	193	17	generator	generator	NOUN
ejpam-3907	193	18	polynomial	polynomial	ADJ
ejpam-3907	193	19	mš(x	mš(x	NOUN
ejpam-3907	193	20	)	)	PUNCT
ejpam-3907	193	21	of	of	ADP
ejpam-3907	193	22	(	(	PUNCT
ejpam-3907	193	23	10	10	NUM
ejpam-3907	193	24	)	)	PUNCT
ejpam-3907	193	25	.	.	PUNCT
ejpam-3907	194	1	proof	proof	NOUN
ejpam-3907	194	2	.	.	PUNCT
ejpam-3907	195	1	the	the	DET
ejpam-3907	195	2	dimension	dimension	NOUN
ejpam-3907	195	3	of	of	ADP
ejpam-3907	195	4	cš	cš	NOUN
ejpam-3907	195	5	follows	follow	VERB
ejpam-3907	195	6	from	from	ADP
ejpam-3907	195	7	theorem	theorem	ADJ
ejpam-3907	195	8	1	1	NUM
ejpam-3907	195	9	.	.	PUNCT
ejpam-3907	196	1	therefore	therefore	ADV
ejpam-3907	196	2	we	we	PRON
ejpam-3907	196	3	consider	consider	VERB
ejpam-3907	196	4	the	the	DET
ejpam-3907	196	5	lower	low	ADJ
ejpam-3907	196	6	bound	bind	VERB
ejpam-3907	196	7	of	of	ADP
ejpam-3907	196	8	minimum	minimum	ADJ
ejpam-3907	196	9	weight	weight	NOUN
ejpam-3907	196	10	d.	d.	PROPN
ejpam-3907	196	11	note	note	VERB
ejpam-3907	196	12	that	that	SCONJ
ejpam-3907	196	13	the	the	DET
ejpam-3907	196	14	weight	weight	NOUN
ejpam-3907	196	15	distribution	distribution	NOUN
ejpam-3907	196	16	of	of	ADP
ejpam-3907	196	17	the	the	DET
ejpam-3907	196	18	cyclic	cyclic	PROPN
ejpam-3907	196	19	code	code	NOUN
ejpam-3907	196	20	generated	generate	VERB
ejpam-3907	196	21	by	by	ADP
ejpam-3907	196	22	mš(x	mš(x	NOUN
ejpam-3907	196	23	)	)	PUNCT
ejpam-3907	196	24	is	be	AUX
ejpam-3907	196	25	the	the	DET
ejpam-3907	196	26	same	same	ADJ
ejpam-3907	196	27	as	as	ADP
ejpam-3907	196	28	that	that	PRON
ejpam-3907	196	29	generated	generate	VERB
ejpam-3907	196	30	by	by	ADP
ejpam-3907	196	31	the	the	DET
ejpam-3907	196	32	reciprocal	reciprocal	ADJ
ejpam-3907	196	33	polynomial	polynomial	NOUN
ejpam-3907	196	34	of	of	ADP
ejpam-3907	196	35	mš(x	mš(x	NOUN
ejpam-3907	196	36	)	)	PUNCT
ejpam-3907	196	37	.	.	PUNCT
ejpam-3907	197	1	references	reference	NOUN
ejpam-3907	197	2	693	693	NUM
ejpam-3907	197	3	furthermore	furthermore	ADV
ejpam-3907	197	4	,	,	PUNCT
ejpam-3907	197	5	the	the	DET
ejpam-3907	197	6	reciprocal	reciprocal	ADJ
ejpam-3907	197	7	polynomial	polynomial	NOUN
ejpam-3907	197	8	of	of	ADP
ejpam-3907	197	9	mš(x	mš(x	NOUN
ejpam-3907	197	10	)	)	PUNCT
ejpam-3907	197	11	has	have	VERB
ejpam-3907	197	12	zeros	zero	NOUN
ejpam-3907	197	13	αi	αi	VERB
ejpam-3907	197	14	where	where	SCONJ
ejpam-3907	197	15	i	i	PRON
ejpam-3907	197	16	∈	∈	VERB
ejpam-3907	197	17	h	h	NOUN
ejpam-3907	198	1	=	=	PRON
ejpam-3907	198	2	{	{	PUNCT
ejpam-3907	198	3	pj+1	pj+1	X
ejpam-3907	198	4	:	:	PUNCT
ejpam-3907	198	5	j	j	NOUN
ejpam-3907	198	6	=	=	SYM
ejpam-3907	198	7	1	1	NUM
ejpam-3907	198	8	,	,	PUNCT
ejpam-3907	198	9	2	2	NUM
ejpam-3907	198	10	,	,	PUNCT
ejpam-3907	198	11	.	.	PUNCT
ejpam-3907	198	12	.	.	PUNCT
ejpam-3907	198	13	.	.	PUNCT
ejpam-3907	199	1	,	,	PUNCT
ejpam-3907	199	2	q(p−1	q(p−1	PROPN
ejpam-3907	199	3	)	)	PUNCT
ejpam-3907	199	4	p	p	NOUN
ejpam-3907	199	5	−	−	PROPN
ejpam-3907	199	6	1	1	NUM
ejpam-3907	199	7	}	}	PUNCT
ejpam-3907	199	8	.	.	PUNCT
ejpam-3907	200	1	thus	thus	ADV
ejpam-3907	200	2	,	,	PUNCT
ejpam-3907	200	3	from	from	ADP
ejpam-3907	200	4	the	the	DET
ejpam-3907	200	5	hartmann	hartmann	PROPN
ejpam-3907	200	6	-	-	PUNCT
ejpam-3907	200	7	tzeng	tzeng	PROPN
ejpam-3907	200	8	bound	bind	VERB
ejpam-3907	200	9	[	[	PUNCT
ejpam-3907	200	10	10	10	NUM
ejpam-3907	200	11	,	,	PUNCT
ejpam-3907	200	12	theorem	theorem	VERB
ejpam-3907	200	13	1	1	NUM
ejpam-3907	200	14	]	]	PUNCT
ejpam-3907	200	15	,	,	PUNCT
ejpam-3907	200	16	we	we	PRON
ejpam-3907	200	17	have	have	VERB
ejpam-3907	200	18	d	d	X
ejpam-3907	200	19	≥	≥	X
ejpam-3907	200	20	q(p−1	q(p−1	PROPN
ejpam-3907	200	21	)	)	PUNCT
ejpam-3907	200	22	p	p	NOUN
ejpam-3907	200	23	.	.	PUNCT
ejpam-3907	201	1	example	example	NOUN
ejpam-3907	202	1	1	1	NUM
ejpam-3907	202	2	.	.	PUNCT
ejpam-3907	202	3	let	let	VERB
ejpam-3907	202	4	q	q	NOUN
ejpam-3907	203	1	=	=	SYM
ejpam-3907	203	2	3	3	NUM
ejpam-3907	203	3	,	,	PUNCT
ejpam-3907	203	4	m	m	VERB
ejpam-3907	203	5	=	=	NOUN
ejpam-3907	203	6	2	2	NUM
ejpam-3907	203	7	,	,	PUNCT
ejpam-3907	203	8	and	and	CCONJ
ejpam-3907	204	1	irreducible	irreducible	ADJ
ejpam-3907	204	2	polynomial	polynomial	NOUN
ejpam-3907	204	3	for	for	ADP
ejpam-3907	204	4	gf	gf	PROPN
ejpam-3907	204	5	(	(	PUNCT
ejpam-3907	204	6	32	32	NUM
ejpam-3907	204	7	)	)	PUNCT
ejpam-3907	204	8	is	be	AUX
ejpam-3907	204	9	x2	x2	PROPN
ejpam-3907	204	10	+	+	CCONJ
ejpam-3907	204	11	2x+	2x+	NUM
ejpam-3907	204	12	2	2	NUM
ejpam-3907	204	13	=	=	SYM
ejpam-3907	204	14	0	0	NUM
ejpam-3907	204	15	.	.	PUNCT
ejpam-3907	205	1	then	then	ADV
ejpam-3907	205	2	cš	cš	ADJ
ejpam-3907	205	3	is	be	AUX
ejpam-3907	205	4	a	a	DET
ejpam-3907	205	5	[	[	X
ejpam-3907	205	6	8	8	NUM
ejpam-3907	205	7	,	,	PUNCT
ejpam-3907	205	8	4	4	NUM
ejpam-3907	205	9	,	,	PUNCT
ejpam-3907	205	10	2	2	NUM
ejpam-3907	205	11	]	]	X
ejpam-3907	205	12	cyclic	cyclic	ADJ
ejpam-3907	205	13	code	code	NOUN
ejpam-3907	205	14	over	over	ADP
ejpam-3907	205	15	gf	gf	PROPN
ejpam-3907	205	16	(	(	PUNCT
ejpam-3907	205	17	3	3	NUM
ejpam-3907	205	18	)	)	PUNCT
ejpam-3907	205	19	with	with	ADP
ejpam-3907	205	20	the	the	DET
ejpam-3907	205	21	generator	generator	NOUN
ejpam-3907	205	22	polynomial	polynomial	ADJ
ejpam-3907	205	23	mš(x	mš(x	NOUN
ejpam-3907	205	24	)	)	PUNCT
ejpam-3907	205	25	=	=	SYM
ejpam-3907	205	26	x4	x4	PROPN
ejpam-3907	205	27	+2	+2	PROPN
ejpam-3907	205	28	.	.	PUNCT
ejpam-3907	206	1	it	it	PRON
ejpam-3907	206	2	is	be	AUX
ejpam-3907	206	3	known	know	VERB
ejpam-3907	206	4	that	that	SCONJ
ejpam-3907	206	5	for	for	ADP
ejpam-3907	206	6	optimal	optimal	ADJ
ejpam-3907	206	7	linear	linear	ADJ
ejpam-3907	206	8	codes	code	NOUN
ejpam-3907	206	9	of	of	ADP
ejpam-3907	206	10	length	length	NOUN
ejpam-3907	206	11	8	8	NUM
ejpam-3907	206	12	and	and	CCONJ
ejpam-3907	206	13	dimension	dimension	NOUN
ejpam-3907	206	14	4	4	NUM
ejpam-3907	206	15	over	over	ADP
ejpam-3907	206	16	gf	gf	X
ejpam-3907	206	17	(	(	PUNCT
ejpam-3907	206	18	3	3	NUM
ejpam-3907	206	19	)	)	PUNCT
ejpam-3907	206	20	,	,	PUNCT
ejpam-3907	206	21	the	the	DET
ejpam-3907	206	22	minimal	minimal	ADJ
ejpam-3907	206	23	distance	distance	NOUN
ejpam-3907	206	24	is	be	AUX
ejpam-3907	206	25	d	d	NOUN
ejpam-3907	206	26	=	=	SYM
ejpam-3907	206	27	4.its	4.it	NOUN
ejpam-3907	206	28	dual	dual	ADJ
ejpam-3907	206	29	is	be	AUX
ejpam-3907	206	30	a	a	DET
ejpam-3907	206	31	[	[	NOUN
ejpam-3907	206	32	8	8	NUM
ejpam-3907	206	33	,	,	PUNCT
ejpam-3907	206	34	4	4	NUM
ejpam-3907	206	35	,	,	PUNCT
ejpam-3907	206	36	2	2	NUM
ejpam-3907	206	37	]	]	X
ejpam-3907	206	38	cyclic	cyclic	PROPN
ejpam-3907	206	39	code	code	PROPN
ejpam-3907	206	40	.	.	PUNCT
ejpam-3907	207	1	example	example	NOUN
ejpam-3907	208	1	2	2	NUM
ejpam-3907	208	2	.	.	PUNCT
ejpam-3907	208	3	let	let	VERB
ejpam-3907	208	4	q	q	NOUN
ejpam-3907	209	1	=	=	SYM
ejpam-3907	209	2	3,m	3,m	NUM
ejpam-3907	209	3	=	=	SYM
ejpam-3907	209	4	3	3	NUM
ejpam-3907	209	5	,	,	PUNCT
ejpam-3907	209	6	and	and	CCONJ
ejpam-3907	209	7	α	α	PRON
ejpam-3907	209	8	be	be	VERB
ejpam-3907	209	9	a	a	DET
ejpam-3907	209	10	generator	generator	NOUN
ejpam-3907	209	11	of	of	ADP
ejpam-3907	209	12	gf	gf	PROPN
ejpam-3907	209	13	(	(	PUNCT
ejpam-3907	209	14	33)∗	33)∗	NOUN
ejpam-3907	209	15	with	with	ADP
ejpam-3907	209	16	α3	α3	NOUN
ejpam-3907	210	1	+	+	CCONJ
ejpam-3907	210	2	2α	2α	NOUN
ejpam-3907	210	3	+	+	CCONJ
ejpam-3907	210	4	1	1	NUM
ejpam-3907	210	5	=	=	SYM
ejpam-3907	210	6	0	0	NUM
ejpam-3907	210	7	.	.	PUNCT
ejpam-3907	211	1	then	then	ADV
ejpam-3907	211	2	cš	cš	ADJ
ejpam-3907	211	3	is	be	AUX
ejpam-3907	211	4	a	a	DET
ejpam-3907	211	5	[	[	X
ejpam-3907	211	6	26	26	NUM
ejpam-3907	211	7	,	,	PUNCT
ejpam-3907	211	8	11	11	NUM
ejpam-3907	211	9	,	,	PUNCT
ejpam-3907	211	10	6	6	NUM
ejpam-3907	211	11	]	]	X
ejpam-3907	211	12	cyclic	cyclic	ADJ
ejpam-3907	211	13	code	code	NOUN
ejpam-3907	211	14	over	over	ADP
ejpam-3907	211	15	gf	gf	PROPN
ejpam-3907	211	16	(	(	PUNCT
ejpam-3907	211	17	3	3	NUM
ejpam-3907	211	18	)	)	PUNCT
ejpam-3907	211	19	with	with	ADP
ejpam-3907	211	20	the	the	DET
ejpam-3907	211	21	generator	generator	NOUN
ejpam-3907	211	22	polynomial	polynomial	ADJ
ejpam-3907	211	23	mš(x	mš(x	NOUN
ejpam-3907	211	24	)	)	PUNCT
ejpam-3907	212	1	=	=	SYM
ejpam-3907	212	2	x15	x15	PROPN
ejpam-3907	213	1	+	+	NUM
ejpam-3907	213	2	x14	x14	PROPN
ejpam-3907	214	1	+	+	CCONJ
ejpam-3907	214	2	x12	x12	NUM
ejpam-3907	214	3	+	+	CCONJ
ejpam-3907	214	4	x11	x11	PRON
ejpam-3907	215	1	+	+	CCONJ
ejpam-3907	215	2	x10	x10	NOUN
ejpam-3907	215	3	+	+	NUM
ejpam-3907	215	4	x9	x9	NOUN
ejpam-3907	215	5	+	+	NUM
ejpam-3907	215	6	x8	x8	PROPN
ejpam-3907	215	7	+	+	CCONJ
ejpam-3907	215	8	x7	x7	NOUN
ejpam-3907	216	1	+	+	CCONJ
ejpam-3907	216	2	x6	x6	PROPN
ejpam-3907	216	3	+	+	CCONJ
ejpam-3907	216	4	x5	x5	PROPN
ejpam-3907	216	5	+	+	CCONJ
ejpam-3907	216	6	x4	x4	PROPN
ejpam-3907	217	1	+	+	CCONJ
ejpam-3907	217	2	x3	x3	ADJ
ejpam-3907	217	3	+	+	NOUN
ejpam-3907	217	4	1	1	X
ejpam-3907	217	5	.	.	X
ejpam-3907	218	1	it	it	PRON
ejpam-3907	218	2	is	be	AUX
ejpam-3907	218	3	known	know	VERB
ejpam-3907	218	4	that	that	SCONJ
ejpam-3907	218	5	for	for	ADP
ejpam-3907	218	6	optimal	optimal	ADJ
ejpam-3907	218	7	linear	linear	ADJ
ejpam-3907	218	8	codes	code	NOUN
ejpam-3907	218	9	of	of	ADP
ejpam-3907	218	10	length	length	NOUN
ejpam-3907	218	11	26	26	NUM
ejpam-3907	218	12	and	and	CCONJ
ejpam-3907	218	13	dimension	dimension	VERB
ejpam-3907	218	14	11	11	NUM
ejpam-3907	218	15	over	over	ADP
ejpam-3907	218	16	gf	gf	X
ejpam-3907	218	17	(	(	PUNCT
ejpam-3907	218	18	3	3	NUM
ejpam-3907	218	19	)	)	PUNCT
ejpam-3907	218	20	,	,	PUNCT
ejpam-3907	218	21	the	the	DET
ejpam-3907	218	22	minimal	minimal	ADJ
ejpam-3907	218	23	distance	distance	NOUN
ejpam-3907	218	24	satisfies	satisfy	VERB
ejpam-3907	218	25	9	9	NUM
ejpam-3907	218	26	≤	≤	NUM
ejpam-3907	218	27	d	d	NOUN
ejpam-3907	218	28	≤	≤	NUM
ejpam-3907	218	29	11	11	NUM
ejpam-3907	218	30	.	.	PUNCT
ejpam-3907	219	1	its	its	PRON
ejpam-3907	219	2	dual	dual	NOUN
ejpam-3907	219	3	is	be	AUX
ejpam-3907	219	4	a	a	DET
ejpam-3907	219	5	[	[	X
ejpam-3907	219	6	26	26	NUM
ejpam-3907	219	7	,	,	PUNCT
ejpam-3907	219	8	15,4	15,4	NUM
ejpam-3907	219	9	]	]	X
ejpam-3907	219	10	cyclic	cyclic	PROPN
ejpam-3907	219	11	code	code	PROPN
ejpam-3907	219	12	.	.	PUNCT
ejpam-3907	220	1	example	example	NOUN
ejpam-3907	221	1	3	3	X
ejpam-3907	221	2	.	.	PUNCT
ejpam-3907	221	3	let	let	VERB
ejpam-3907	221	4	q	q	NOUN
ejpam-3907	222	1	=	=	SYM
ejpam-3907	222	2	3,m	3,m	NUM
ejpam-3907	222	3	=	=	SYM
ejpam-3907	222	4	3	3	NUM
ejpam-3907	222	5	,	,	PUNCT
ejpam-3907	222	6	and	and	CCONJ
ejpam-3907	222	7	α	α	PRON
ejpam-3907	222	8	be	be	VERB
ejpam-3907	222	9	a	a	DET
ejpam-3907	222	10	generator	generator	NOUN
ejpam-3907	222	11	of	of	ADP
ejpam-3907	222	12	gf	gf	PROPN
ejpam-3907	222	13	(	(	PUNCT
ejpam-3907	222	14	33)∗	33)∗	NOUN
ejpam-3907	222	15	with	with	ADP
ejpam-3907	222	16	α3	α3	NOUN
ejpam-3907	222	17	+	+	CCONJ
ejpam-3907	222	18	2α2	2α2	NUM
ejpam-3907	222	19	+	+	CCONJ
ejpam-3907	222	20	1	1	NUM
ejpam-3907	222	21	=	=	SYM
ejpam-3907	222	22	0	0	NUM
ejpam-3907	222	23	.	.	PUNCT
ejpam-3907	223	1	then	then	ADV
ejpam-3907	223	2	cš	cš	ADJ
ejpam-3907	223	3	is	be	AUX
ejpam-3907	223	4	a	a	DET
ejpam-3907	223	5	[	[	X
ejpam-3907	223	6	26	26	NUM
ejpam-3907	223	7	,	,	PUNCT
ejpam-3907	223	8	11	11	NUM
ejpam-3907	223	9	,	,	PUNCT
ejpam-3907	223	10	6	6	NUM
ejpam-3907	223	11	]	]	X
ejpam-3907	223	12	cyclic	cyclic	ADJ
ejpam-3907	223	13	code	code	NOUN
ejpam-3907	223	14	over	over	ADP
ejpam-3907	223	15	gf	gf	PROPN
ejpam-3907	223	16	(	(	PUNCT
ejpam-3907	223	17	3	3	NUM
ejpam-3907	223	18	)	)	PUNCT
ejpam-3907	223	19	with	with	ADP
ejpam-3907	223	20	the	the	DET
ejpam-3907	223	21	generator	generator	NOUN
ejpam-3907	223	22	polynomial	polynomial	ADJ
ejpam-3907	223	23	mš(x	mš(x	NOUN
ejpam-3907	223	24	)	)	PUNCT
ejpam-3907	224	1	=	=	SYM
ejpam-3907	224	2	x15	x15	NUM
ejpam-3907	224	3	+	+	NUM
ejpam-3907	224	4	x12	x12	NUM
ejpam-3907	224	5	+	+	CCONJ
ejpam-3907	224	6	x11	x11	NOUN
ejpam-3907	225	1	+	+	CCONJ
ejpam-3907	225	2	x10	x10	NOUN
ejpam-3907	225	3	+	+	NUM
ejpam-3907	225	4	x9	x9	NOUN
ejpam-3907	225	5	+	+	NUM
ejpam-3907	225	6	x8	x8	PROPN
ejpam-3907	225	7	+	+	CCONJ
ejpam-3907	225	8	x7	x7	NOUN
ejpam-3907	226	1	+	+	CCONJ
ejpam-3907	226	2	x6	x6	PROPN
ejpam-3907	226	3	+	+	CCONJ
ejpam-3907	226	4	x5	x5	PROPN
ejpam-3907	226	5	+	+	CCONJ
ejpam-3907	226	6	x4	x4	PROPN
ejpam-3907	227	1	+	+	CCONJ
ejpam-3907	227	2	x3	x3	ADJ
ejpam-3907	227	3	+	+	CCONJ
ejpam-3907	227	4	x+	x+	ADJ
ejpam-3907	227	5	1	1	X
ejpam-3907	227	6	.	.	X
ejpam-3907	228	1	its	its	PRON
ejpam-3907	228	2	dual	dual	NOUN
ejpam-3907	228	3	is	be	AUX
ejpam-3907	228	4	a	a	DET
ejpam-3907	228	5	[	[	X
ejpam-3907	228	6	26	26	NUM
ejpam-3907	228	7	,	,	PUNCT
ejpam-3907	228	8	15,4	15,4	NUM
ejpam-3907	228	9	]	]	X
ejpam-3907	228	10	cyclic	cyclic	PROPN
ejpam-3907	228	11	code	code	NOUN
ejpam-3907	228	12	.	.	PUNCT
ejpam-3907	229	1	4	4	X
ejpam-3907	229	2	.	.	X
ejpam-3907	229	3	conclusion	conclusion	NOUN
ejpam-3907	229	4	we	we	PRON
ejpam-3907	229	5	have	have	AUX
ejpam-3907	229	6	given	give	VERB
ejpam-3907	229	7	the	the	DET
ejpam-3907	229	8	construction	construction	NOUN
ejpam-3907	229	9	of	of	ADP
ejpam-3907	229	10	a	a	DET
ejpam-3907	229	11	family	family	NOUN
ejpam-3907	229	12	of	of	ADP
ejpam-3907	229	13	cyclic	cyclic	PROPN
ejpam-3907	229	14	code	code	NOUN
ejpam-3907	229	15	from	from	ADP
ejpam-3907	229	16	periodic	periodic	ADJ
ejpam-3907	229	17	sequence	sequence	NOUN
ejpam-3907	229	18	š	š	NOUN
ejpam-3907	229	19	from	from	ADP
ejpam-3907	229	20	a	a	DET
ejpam-3907	229	21	monomial	monomial	ADJ
ejpam-3907	229	22	f(x	f(x	PROPN
ejpam-3907	229	23	)	)	PUNCT
ejpam-3907	230	1	=	=	PUNCT
ejpam-3907	230	2	xq	xq	X
ejpam-3907	231	1	m−2	m−2	PROPN
ejpam-3907	231	2	in	in	ADP
ejpam-3907	231	3	gf	gf	PROPN
ejpam-3907	231	4	(	(	PUNCT
ejpam-3907	231	5	qm	qm	PROPN
ejpam-3907	231	6	)	)	PUNCT
ejpam-3907	231	7	.	.	PUNCT
ejpam-3907	232	1	the	the	DET
ejpam-3907	232	2	lower	lower	ADV
ejpam-3907	232	3	bound	bind	VERB
ejpam-3907	232	4	of	of	ADP
ejpam-3907	232	5	the	the	DET
ejpam-3907	232	6	code	code	NOUN
ejpam-3907	232	7	is	be	AUX
ejpam-3907	232	8	presented	present	VERB
ejpam-3907	232	9	in	in	ADP
ejpam-3907	232	10	theorem	theorem	NOUN
ejpam-3907	232	11	2	2	NUM
ejpam-3907	232	12	.	.	PUNCT
ejpam-3907	233	1	in	in	ADP
ejpam-3907	233	2	general	general	ADJ
ejpam-3907	233	3	,	,	PUNCT
ejpam-3907	233	4	the	the	DET
ejpam-3907	233	5	code	code	NOUN
ejpam-3907	233	6	cš	cš	NOUN
ejpam-3907	233	7	has	have	AUX
ejpam-3907	233	8	parameter	parameter	NOUN
ejpam-3907	233	9	[	[	X
ejpam-3907	233	10	qm−	qm−	NUM
ejpam-3907	233	11	1	1	NUM
ejpam-3907	233	12	,	,	PUNCT
ejpam-3907	233	13	q	q	NOUN
ejpam-3907	234	1	m	m	NOUN
ejpam-3907	234	2	p	p	NOUN
ejpam-3907	234	3	−	−	PROPN
ejpam-3907	234	4	1	1	NUM
ejpam-3907	234	5	+	+	NOUN
ejpam-3907	234	6	m	m	NOUN
ejpam-3907	234	7	,	,	PUNCT
ejpam-3907	234	8	d	d	X
ejpam-3907	234	9	]	]	X
ejpam-3907	234	10	with	with	ADP
ejpam-3907	234	11	d	d	PROPN
ejpam-3907	234	12	≥	≥	X
ejpam-3907	234	13	q(p−1	q(p−1	PROPN
ejpam-3907	234	14	)	)	PUNCT
ejpam-3907	234	15	p	p	NOUN
ejpam-3907	234	16	.	.	PUNCT
ejpam-3907	235	1	three	three	NUM
ejpam-3907	235	2	examples	example	NOUN
ejpam-3907	235	3	are	be	AUX
ejpam-3907	235	4	presented	present	VERB
ejpam-3907	235	5	.	.	PUNCT
ejpam-3907	236	1	numerical	numerical	ADJ
ejpam-3907	236	2	examples	example	NOUN
ejpam-3907	236	3	show	show	VERB
ejpam-3907	236	4	that	that	SCONJ
ejpam-3907	236	5	for	for	ADP
ejpam-3907	236	6	the	the	DET
ejpam-3907	236	7	same	same	ADJ
ejpam-3907	236	8	length	length	NOUN
ejpam-3907	236	9	and	and	CCONJ
ejpam-3907	236	10	distance	distance	NOUN
ejpam-3907	236	11	,	,	PUNCT
ejpam-3907	236	12	the	the	DET
ejpam-3907	236	13	dual	dual	ADJ
ejpam-3907	236	14	of	of	ADP
ejpam-3907	236	15	cyclic	cyclic	ADJ
ejpam-3907	236	16	codes	code	NOUN
ejpam-3907	236	17	presented	present	VERB
ejpam-3907	236	18	in	in	ADP
ejpam-3907	236	19	this	this	DET
ejpam-3907	236	20	paper	paper	NOUN
ejpam-3907	236	21	has	have	VERB
ejpam-3907	236	22	a	a	DET
ejpam-3907	236	23	lower	low	ADJ
ejpam-3907	236	24	dimension	dimension	NOUN
ejpam-3907	236	25	than	than	ADP
ejpam-3907	236	26	in	in	ADP
ejpam-3907	236	27	[	[	X
ejpam-3907	236	28	3	3	NUM
ejpam-3907	236	29	,	,	PUNCT
ejpam-3907	236	30	1983	1983	NUM
ejpam-3907	236	31	]	]	PUNCT
ejpam-3907	236	32	and	and	CCONJ
ejpam-3907	236	33	[	[	X
ejpam-3907	236	34	17	17	NUM
ejpam-3907	236	35	,	,	PUNCT
ejpam-3907	236	36	page	page	NOUN
ejpam-3907	236	37	27	27	NUM
ejpam-3907	236	38	]	]	PUNCT
ejpam-3907	236	39	.	.	PUNCT
ejpam-3907	237	1	acknowledgements	acknowledgement	NOUN
ejpam-3907	237	2	the	the	DET
ejpam-3907	237	3	authors	author	NOUN
ejpam-3907	237	4	are	be	AUX
ejpam-3907	237	5	very	very	ADV
ejpam-3907	237	6	grateful	grateful	ADJ
ejpam-3907	237	7	to	to	ADP
ejpam-3907	237	8	the	the	DET
ejpam-3907	237	9	editors	editor	NOUN
ejpam-3907	237	10	and	and	CCONJ
ejpam-3907	237	11	the	the	DET
ejpam-3907	237	12	reviewers	reviewer	NOUN
ejpam-3907	237	13	for	for	ADP
ejpam-3907	237	14	their	their	PRON
ejpam-3907	237	15	comments	comment	NOUN
ejpam-3907	237	16	and	and	CCONJ
ejpam-3907	237	17	suggestions	suggestion	NOUN
ejpam-3907	237	18	to	to	PART
ejpam-3907	237	19	improve	improve	VERB
ejpam-3907	237	20	this	this	DET
ejpam-3907	237	21	paper	paper	NOUN
ejpam-3907	237	22	’s	’s	PART
ejpam-3907	237	23	quality	quality	NOUN
ejpam-3907	237	24	.	.	PUNCT
ejpam-3907	238	1	the	the	DET
ejpam-3907	238	2	authors	author	NOUN
ejpam-3907	238	3	also	also	ADV
ejpam-3907	238	4	thank	thank	VERB
ejpam-3907	238	5	irwansyah	irwansyah	NOUN
ejpam-3907	238	6	for	for	ADP
ejpam-3907	238	7	the	the	DET
ejpam-3907	238	8	valuable	valuable	ADJ
ejpam-3907	238	9	discussions	discussion	NOUN
ejpam-3907	238	10	.	.	PUNCT
ejpam-3907	239	1	this	this	DET
ejpam-3907	239	2	work	work	NOUN
ejpam-3907	239	3	was	be	AUX
ejpam-3907	239	4	supported	support	VERB
ejpam-3907	239	5	by	by	ADP
ejpam-3907	239	6	hibah	hibah	PROPN
ejpam-3907	239	7	riset	riset	PROPN
ejpam-3907	239	8	dasar	dasar	VERB
ejpam-3907	239	9	dikti	dikti	VERB
ejpam-3907	239	10	2019	2019	NUM
ejpam-3907	239	11	.	.	PUNCT
ejpam-3907	240	1	references	reference	NOUN
ejpam-3907	240	2	[	[	X
ejpam-3907	240	3	1	1	NUM
ejpam-3907	240	4	]	]	PUNCT
ejpam-3907	240	5	m	m	VERB
ejpam-3907	240	6	antweiler	antweiler	NOUN
ejpam-3907	240	7	and	and	CCONJ
ejpam-3907	240	8	l	l	NOUN
ejpam-3907	240	9	bömer	bömer	PROPN
ejpam-3907	240	10	.	.	PUNCT
ejpam-3907	240	11	complex	complex	ADJ
ejpam-3907	240	12	sequences	sequence	NOUN
ejpam-3907	240	13	over	over	ADP
ejpam-3907	240	14	gf	gf	PROPN
ejpam-3907	240	15	(	(	PUNCT
ejpam-3907	240	16	pm	pm	NOUN
ejpam-3907	240	17	)	)	PUNCT
ejpam-3907	240	18	with	with	ADP
ejpam-3907	240	19	a	a	DET
ejpam-3907	240	20	two	two	NUM
ejpam-3907	240	21	-	-	PUNCT
ejpam-3907	240	22	level	level	NOUN
ejpam-3907	240	23	autocorrelation	autocorrelation	NOUN
ejpam-3907	240	24	function	function	NOUN
ejpam-3907	240	25	and	and	CCONJ
ejpam-3907	240	26	a	a	DET
ejpam-3907	240	27	large	large	ADJ
ejpam-3907	240	28	linear	linear	ADJ
ejpam-3907	240	29	span	span	NOUN
ejpam-3907	240	30	.	.	PUNCT
ejpam-3907	241	1	ieee	ieee	PROPN
ejpam-3907	241	2	trans	trans	PROPN
ejpam-3907	241	3	.	.	PUNCT
ejpam-3907	242	1	inform	inform	NOUN
ejpam-3907	242	2	.	.	PUNCT
ejpam-3907	243	1	theory	theory	NOUN
ejpam-3907	243	2	,	,	PUNCT
ejpam-3907	243	3	38(1):120–130	38(1):120–130	PROPN
ejpam-3907	243	4	,	,	PUNCT
ejpam-3907	243	5	1992	1992	NUM
ejpam-3907	243	6	.	.	PUNCT
ejpam-3907	244	1	[	[	X
ejpam-3907	244	2	2	2	NUM
ejpam-3907	244	3	]	]	SYM
ejpam-3907	244	4	r	r	NOUN
ejpam-3907	244	5	t	t	PROPN
ejpam-3907	244	6	chien	chien	PROPN
ejpam-3907	244	7	.	.	PUNCT
ejpam-3907	245	1	cyclic	cyclic	ADJ
ejpam-3907	245	2	decoding	decoding	NOUN
ejpam-3907	245	3	procedures	procedure	NOUN
ejpam-3907	245	4	for	for	ADP
ejpam-3907	245	5	bose	bose	NOUN
ejpam-3907	245	6	-	-	PUNCT
ejpam-3907	245	7	chaudhuri	chaudhuri	PROPN
ejpam-3907	245	8	-	-	PUNCT
ejpam-3907	245	9	hocquenghem	hocquenghem	PROPN
ejpam-3907	245	10	codes	code	NOUN
ejpam-3907	245	11	.	.	PUNCT
ejpam-3907	246	1	ieee	ieee	PROPN
ejpam-3907	246	2	trans	trans	PROPN
ejpam-3907	246	3	.	.	PUNCT
ejpam-3907	247	1	inform	inform	NOUN
ejpam-3907	247	2	.	.	PUNCT
ejpam-3907	248	1	theory	theory	NOUN
ejpam-3907	248	2	,	,	PUNCT
ejpam-3907	248	3	10(4):357–363	10(4):357–363	PROPN
ejpam-3907	248	4	,	,	PUNCT
ejpam-3907	248	5	1964	1964	NUM
ejpam-3907	248	6	.	.	PUNCT
ejpam-3907	249	1	references	reference	NOUN
ejpam-3907	249	2	694	694	NUM
ejpam-3907	250	1	[	[	X
ejpam-3907	250	2	3	3	NUM
ejpam-3907	250	3	]	]	X
ejpam-3907	250	4	c	c	X
ejpam-3907	250	5	ding	ding	NOUN
ejpam-3907	250	6	.	.	PUNCT
ejpam-3907	251	1	cyclic	cyclic	ADJ
ejpam-3907	251	2	codes	code	NOUN
ejpam-3907	251	3	from	from	ADP
ejpam-3907	251	4	some	some	DET
ejpam-3907	251	5	monomials	monomial	NOUN
ejpam-3907	251	6	and	and	CCONJ
ejpam-3907	251	7	trinomials	trinomial	NOUN
ejpam-3907	251	8	.	.	PUNCT
ejpam-3907	252	1	siam	siam	PROPN
ejpam-3907	252	2	journal	journal	PROPN
ejpam-3907	252	3	on	on	ADP
ejpam-3907	252	4	discrete	discrete	ADJ
ejpam-3907	252	5	mathematics	mathematic	NOUN
ejpam-3907	252	6	,	,	PUNCT
ejpam-3907	252	7	27(4):1977–1994	27(4):1977–1994	NUM
ejpam-3907	252	8	,	,	PUNCT
ejpam-3907	252	9	2013	2013	NUM
ejpam-3907	252	10	.	.	PUNCT
ejpam-3907	253	1	[	[	X
ejpam-3907	253	2	4	4	NUM
ejpam-3907	253	3	]	]	X
ejpam-3907	253	4	c	c	X
ejpam-3907	253	5	ding	ding	NOUN
ejpam-3907	253	6	,	,	PUNCT
ejpam-3907	253	7	g	g	PROPN
ejpam-3907	253	8	xiao	xiao	PROPN
ejpam-3907	253	9	,	,	PUNCT
ejpam-3907	253	10	and	and	CCONJ
ejpam-3907	253	11	w	w	PROPN
ejpam-3907	253	12	shan	shan	PROPN
ejpam-3907	253	13	.	.	PUNCT
ejpam-3907	254	1	the	the	DET
ejpam-3907	254	2	stability	stability	NOUN
ejpam-3907	254	3	theory	theory	NOUN
ejpam-3907	254	4	of	of	ADP
ejpam-3907	254	5	stream	stream	NOUN
ejpam-3907	254	6	ciphers	cipher	NOUN
ejpam-3907	254	7	,	,	PUNCT
ejpam-3907	254	8	volume	volume	NOUN
ejpam-3907	254	9	561	561	NUM
ejpam-3907	254	10	of	of	ADP
ejpam-3907	254	11	lecture	lecture	NOUN
ejpam-3907	254	12	notes	note	NOUN
ejpam-3907	254	13	in	in	ADP
ejpam-3907	254	14	computer	computer	NOUN
ejpam-3907	254	15	science	science	NOUN
ejpam-3907	254	16	.	.	PUNCT
ejpam-3907	255	1	springer	springer	NOUN
ejpam-3907	255	2	-	-	PUNCT
ejpam-3907	255	3	verlag	verlag	PROPN
ejpam-3907	255	4	berlin	berlin	PROPN
ejpam-3907	255	5	heidelberg	heidelberg	PROPN
ejpam-3907	255	6	,	,	PUNCT
ejpam-3907	255	7	1st	1st	PROPN
ejpam-3907	255	8	edition	edition	NOUN
ejpam-3907	255	9	,	,	PUNCT
ejpam-3907	255	10	1991	1991	NUM
ejpam-3907	255	11	.	.	PUNCT
ejpam-3907	256	1	[	[	X
ejpam-3907	256	2	5	5	NUM
ejpam-3907	256	3	]	]	SYM
ejpam-3907	256	4	c	c	NOUN
ejpam-3907	256	5	ding	ding	NOUN
ejpam-3907	256	6	,	,	PUNCT
ejpam-3907	256	7	y	y	PROPN
ejpam-3907	256	8	yang	yang	PROPN
ejpam-3907	256	9	,	,	PUNCT
ejpam-3907	256	10	and	and	CCONJ
ejpam-3907	256	11	x	x	X
ejpam-3907	256	12	tang	tang	NOUN
ejpam-3907	256	13	.	.	PUNCT
ejpam-3907	257	1	optimal	optimal	ADJ
ejpam-3907	257	2	sets	set	NOUN
ejpam-3907	257	3	of	of	ADP
ejpam-3907	257	4	frequency	frequency	NOUN
ejpam-3907	257	5	hopping	hop	VERB
ejpam-3907	257	6	sequences	sequence	NOUN
ejpam-3907	257	7	from	from	ADP
ejpam-3907	257	8	linear	linear	ADJ
ejpam-3907	257	9	cyclic	cyclic	ADJ
ejpam-3907	257	10	codes	code	NOUN
ejpam-3907	257	11	.	.	PUNCT
ejpam-3907	258	1	ieee	ieee	PROPN
ejpam-3907	258	2	trans	trans	PROPN
ejpam-3907	258	3	.	.	PUNCT
ejpam-3907	259	1	inform	inform	NOUN
ejpam-3907	259	2	.	.	PUNCT
ejpam-3907	260	1	theory	theory	NOUN
ejpam-3907	260	2	,	,	PUNCT
ejpam-3907	260	3	56(7):3605–3612	56(7):3605–3612	NUM
ejpam-3907	260	4	,	,	PUNCT
ejpam-3907	260	5	2010	2010	NUM
ejpam-3907	260	6	.	.	PUNCT
ejpam-3907	261	1	[	[	X
ejpam-3907	261	2	6	6	NUM
ejpam-3907	261	3	]	]	SYM
ejpam-3907	261	4	c	c	X
ejpam-3907	261	5	ding	ding	NOUN
ejpam-3907	261	6	and	and	CCONJ
ejpam-3907	261	7	z	z	PROPN
ejpam-3907	261	8	zhou	zhou	PROPN
ejpam-3907	261	9	.	.	PUNCT
ejpam-3907	262	1	binary	binary	PROPN
ejpam-3907	262	2	cyclic	cyclic	PROPN
ejpam-3907	262	3	codes	code	NOUN
ejpam-3907	262	4	from	from	ADP
ejpam-3907	262	5	explicit	explicit	ADJ
ejpam-3907	262	6	polynomials	polynomial	NOUN
ejpam-3907	262	7	over	over	ADP
ejpam-3907	262	8	gf	gf	PROPN
ejpam-3907	262	9	(	(	PUNCT
ejpam-3907	262	10	2	2	NUM
ejpam-3907	262	11	m	m	NOUN
ejpam-3907	262	12	)	)	PUNCT
ejpam-3907	262	13	.	.	PUNCT
ejpam-3907	263	1	discrete	discrete	ADJ
ejpam-3907	263	2	mathematics	mathematic	NOUN
ejpam-3907	263	3	,	,	PUNCT
ejpam-3907	263	4	321:76–89	321:76–89	NUM
ejpam-3907	263	5	,	,	PUNCT
ejpam-3907	263	6	2014	2014	NUM
ejpam-3907	263	7	.	.	PUNCT
ejpam-3907	264	1	[	[	X
ejpam-3907	264	2	7	7	X
ejpam-3907	264	3	]	]	SYM
ejpam-3907	264	4	g	g	PROPN
ejpam-3907	264	5	d	d	PROPN
ejpam-3907	264	6	forney	forney	PROPN
ejpam-3907	264	7	.	.	PUNCT
ejpam-3907	265	1	on	on	ADP
ejpam-3907	265	2	decoding	decode	VERB
ejpam-3907	265	3	bch	bch	PROPN
ejpam-3907	265	4	codes	code	NOUN
ejpam-3907	265	5	.	.	PUNCT
ejpam-3907	266	1	ieee	ieee	PROPN
ejpam-3907	266	2	trans	trans	PROPN
ejpam-3907	266	3	.	.	PUNCT
ejpam-3907	267	1	inform	inform	NOUN
ejpam-3907	267	2	.	.	PUNCT
ejpam-3907	268	1	theory	theory	NOUN
ejpam-3907	268	2	,	,	PUNCT
ejpam-3907	268	3	11(4):549–557	11(4):549–557	NUM
ejpam-3907	268	4	,	,	PUNCT
ejpam-3907	268	5	1965	1965	NUM
ejpam-3907	268	6	.	.	PUNCT
ejpam-3907	269	1	[	[	X
ejpam-3907	269	2	8	8	NUM
ejpam-3907	269	3	]	]	PUNCT
ejpam-3907	269	4	m	m	AUX
ejpam-3907	269	5	grassl	grassl	VERB
ejpam-3907	269	6	.	.	PUNCT
ejpam-3907	270	1	bounds	bound	NOUN
ejpam-3907	270	2	on	on	ADP
ejpam-3907	270	3	the	the	DET
ejpam-3907	270	4	minimum	minimum	ADJ
ejpam-3907	270	5	distance	distance	NOUN
ejpam-3907	270	6	of	of	ADP
ejpam-3907	270	7	linear	linear	PROPN
ejpam-3907	270	8	codes	code	NOUN
ejpam-3907	270	9	and	and	CCONJ
ejpam-3907	270	10	quantum	quantum	NOUN
ejpam-3907	270	11	codes	code	NOUN
ejpam-3907	270	12	.	.	PUNCT
ejpam-3907	271	1	online	online	PROPN
ejpam-3907	271	2	available	available	ADJ
ejpam-3907	271	3	at	at	ADP
ejpam-3907	271	4	http://www.codetables.de	http://www.codetables.de	PROPN
ejpam-3907	271	5	,	,	PUNCT
ejpam-3907	271	6	2007	2007	NUM
ejpam-3907	271	7	.	.	PUNCT
ejpam-3907	272	1	accessed	access	VERB
ejpam-3907	272	2	on	on	ADP
ejpam-3907	272	3	2020	2020	NUM
ejpam-3907	272	4	-	-	SYM
ejpam-3907	272	5	12	12	NUM
ejpam-3907	272	6	-	-	SYM
ejpam-3907	272	7	20	20	NUM
ejpam-3907	272	8	.	.	PUNCT
ejpam-3907	273	1	[	[	X
ejpam-3907	273	2	9	9	NUM
ejpam-3907	273	3	]	]	X
ejpam-3907	273	4	k	k	PROPN
ejpam-3907	273	5	c	c	PROPN
ejpam-3907	273	6	gupta	gupta	PROPN
ejpam-3907	273	7	and	and	CCONJ
ejpam-3907	273	8	s	s	VERB
ejpam-3907	273	9	maitra	maitra	NOUN
ejpam-3907	273	10	.	.	PUNCT
ejpam-3907	274	1	primitive	primitive	ADJ
ejpam-3907	274	2	polynomials	polynomial	NOUN
ejpam-3907	274	3	over	over	ADP
ejpam-3907	274	4	gf	gf	PROPN
ejpam-3907	274	5	(	(	PUNCT
ejpam-3907	274	6	2	2	X
ejpam-3907	274	7	)	)	PUNCT
ejpam-3907	274	8	a	a	DET
ejpam-3907	274	9	cryptologic	cryptologic	ADJ
ejpam-3907	274	10	approach	approach	NOUN
ejpam-3907	274	11	.	.	PUNCT
ejpam-3907	275	1	in	in	ADP
ejpam-3907	275	2	information	information	NOUN
ejpam-3907	275	3	and	and	CCONJ
ejpam-3907	275	4	communications	communication	NOUN
ejpam-3907	275	5	security	security	NOUN
ejpam-3907	275	6	,	,	PUNCT
ejpam-3907	275	7	third	third	ADJ
ejpam-3907	275	8	international	international	ADJ
ejpam-3907	275	9	conference	conference	NOUN
ejpam-3907	275	10	,	,	PUNCT
ejpam-3907	275	11	icics	icic	NOUN
ejpam-3907	275	12	2001	2001	NUM
ejpam-3907	275	13	,	,	PUNCT
ejpam-3907	275	14	xian	xian	PROPN
ejpam-3907	275	15	,	,	PUNCT
ejpam-3907	275	16	china	china	PROPN
ejpam-3907	275	17	,	,	PUNCT
ejpam-3907	275	18	november	november	PROPN
ejpam-3907	275	19	13	13	NUM
ejpam-3907	275	20	-	-	SYM
ejpam-3907	275	21	16	16	NUM
ejpam-3907	275	22	,	,	PUNCT
ejpam-3907	275	23	2001	2001	NUM
ejpam-3907	275	24	,	,	PUNCT
ejpam-3907	275	25	pages	page	NOUN
ejpam-3907	275	26	23–34	23–34	NUM
ejpam-3907	275	27	,	,	PUNCT
ejpam-3907	275	28	2001	2001	NUM
ejpam-3907	275	29	.	.	PUNCT
ejpam-3907	276	1	[	[	X
ejpam-3907	276	2	10	10	NUM
ejpam-3907	276	3	]	]	X
ejpam-3907	276	4	c	c	NOUN
ejpam-3907	276	5	r	r	PROPN
ejpam-3907	276	6	p	p	PROPN
ejpam-3907	276	7	hartmann	hartmann	PROPN
ejpam-3907	276	8	and	and	CCONJ
ejpam-3907	276	9	k	k	PROPN
ejpam-3907	276	10	k	k	PROPN
ejpam-3907	276	11	tzeng	tzeng	PROPN
ejpam-3907	276	12	.	.	PUNCT
ejpam-3907	277	1	generalizations	generalization	NOUN
ejpam-3907	277	2	of	of	ADP
ejpam-3907	277	3	the	the	DET
ejpam-3907	277	4	bch	bch	PROPN
ejpam-3907	277	5	bound	bind	VERB
ejpam-3907	277	6	.	.	PUNCT
ejpam-3907	278	1	information	information	NOUN
ejpam-3907	278	2	and	and	CCONJ
ejpam-3907	278	3	control	control	NOUN
ejpam-3907	278	4	,	,	PUNCT
ejpam-3907	278	5	20(5):489–498	20(5):489–498	NUM
ejpam-3907	278	6	,	,	PUNCT
ejpam-3907	278	7	1972	1972	NUM
ejpam-3907	278	8	.	.	PUNCT
ejpam-3907	279	1	[	[	X
ejpam-3907	279	2	11	11	NUM
ejpam-3907	279	3	]	]	X
ejpam-3907	279	4	w	w	PROPN
ejpam-3907	279	5	c	c	PROPN
ejpam-3907	279	6	huffman	huffman	PROPN
ejpam-3907	279	7	and	and	CCONJ
ejpam-3907	279	8	v	v	ADP
ejpam-3907	279	9	pless	pless	NOUN
ejpam-3907	279	10	.	.	PUNCT
ejpam-3907	280	1	fundamentals	fundamental	NOUN
ejpam-3907	280	2	of	of	ADP
ejpam-3907	280	3	error	error	NOUN
ejpam-3907	280	4	-	-	PUNCT
ejpam-3907	280	5	correcting	correct	VERB
ejpam-3907	280	6	codes	code	NOUN
ejpam-3907	280	7	.	.	PUNCT
ejpam-3907	281	1	cambridge	cambridge	PROPN
ejpam-3907	281	2	university	university	PROPN
ejpam-3907	281	3	press	press	NOUN
ejpam-3907	281	4	,	,	PUNCT
ejpam-3907	281	5	2010	2010	NUM
ejpam-3907	281	6	.	.	PUNCT
ejpam-3907	282	1	[	[	X
ejpam-3907	282	2	12	12	NUM
ejpam-3907	282	3	]	]	X
ejpam-3907	282	4	l	l	NOUN
ejpam-3907	282	5	li	li	PROPN
ejpam-3907	282	6	,	,	PUNCT
ejpam-3907	282	7	s	s	PART
ejpam-3907	282	8	zhu	zhu	PROPN
ejpam-3907	282	9	,	,	PUNCT
ejpam-3907	282	10	l	l	PROPN
ejpam-3907	282	11	liu	liu	PROPN
ejpam-3907	282	12	,	,	PUNCT
ejpam-3907	282	13	and	and	CCONJ
ejpam-3907	282	14	x	x	PROPN
ejpam-3907	282	15	kai	kai	PROPN
ejpam-3907	282	16	.	.	PUNCT
ejpam-3907	283	1	some	some	DET
ejpam-3907	283	2	q	q	ADJ
ejpam-3907	283	3	-	-	PUNCT
ejpam-3907	283	4	ary	ary	ADJ
ejpam-3907	283	5	cyclic	cyclic	NOUN
ejpam-3907	283	6	codes	code	NOUN
ejpam-3907	283	7	from	from	ADP
ejpam-3907	283	8	explicit	explicit	ADJ
ejpam-3907	283	9	monomials	monomial	NOUN
ejpam-3907	283	10	over	over	ADP
ejpam-3907	283	11	fm	fm	PROPN
ejpam-3907	283	12	q	q	PROPN
ejpam-3907	283	13	.	.	PUNCT
ejpam-3907	284	1	problems	problem	NOUN
ejpam-3907	284	2	of	of	ADP
ejpam-3907	284	3	information	information	NOUN
ejpam-3907	284	4	transmission	transmission	NOUN
ejpam-3907	284	5	,	,	PUNCT
ejpam-3907	284	6	55(3):254–274	55(3):254–274	PROPN
ejpam-3907	284	7	,	,	PUNCT
ejpam-3907	284	8	2019	2019	NUM
ejpam-3907	284	9	.	.	PUNCT
ejpam-3907	285	1	[	[	X
ejpam-3907	285	2	13	13	NUM
ejpam-3907	285	3	]	]	SYM
ejpam-3907	285	4	e	e	X
ejpam-3907	285	5	lucas	lucas	NOUN
ejpam-3907	285	6	.	.	PUNCT
ejpam-3907	286	1	théorie	théorie	PROPN
ejpam-3907	286	2	des	des	PROPN
ejpam-3907	286	3	fonctions	fonctions	PROPN
ejpam-3907	286	4	numériques	numérique	NOUN
ejpam-3907	286	5	simplement	simplement	NOUN
ejpam-3907	286	6	périodiques	périodique	NOUN
ejpam-3907	286	7	.	.	PUNCT
ejpam-3907	286	8	am	be	AUX
ejpam-3907	286	9	.	.	PUNCT
ejpam-3907	287	1	j.	j.	PROPN
ejpam-3907	287	2	math	math	PROPN
ejpam-3907	287	3	,	,	PUNCT
ejpam-3907	287	4	1:229–231	1:229–231	NUM
ejpam-3907	287	5	,	,	PUNCT
ejpam-3907	287	6	1878	1878	NUM
ejpam-3907	287	7	.	.	PUNCT
ejpam-3907	288	1	[	[	X
ejpam-3907	288	2	14	14	NUM
ejpam-3907	288	3	]	]	X
ejpam-3907	288	4	z	z	NOUN
ejpam-3907	288	5	rajabi	rajabi	NOUN
ejpam-3907	288	6	and	and	CCONJ
ejpam-3907	288	7	k	k	PROPN
ejpam-3907	288	8	khashyarmanesh	khashyarmanesh	PROPN
ejpam-3907	288	9	.	.	PUNCT
ejpam-3907	289	1	some	some	DET
ejpam-3907	289	2	cyclic	cyclic	ADJ
ejpam-3907	289	3	codes	code	NOUN
ejpam-3907	289	4	from	from	ADP
ejpam-3907	289	5	some	some	DET
ejpam-3907	289	6	monomials	monomial	NOUN
ejpam-3907	289	7	.	.	PUNCT
ejpam-3907	290	1	appl	appl	PROPN
ejpam-3907	290	2	.	.	PUNCT
ejpam-3907	291	1	algebra	algebra	PROPN
ejpam-3907	291	2	eng	eng	PROPN
ejpam-3907	291	3	.	.	PROPN
ejpam-3907	291	4	,	,	PUNCT
ejpam-3907	291	5	commun	commun	PROPN
ejpam-3907	291	6	.	.	PUNCT
ejpam-3907	292	1	comput	comput	PROPN
ejpam-3907	292	2	.	.	PUNCT
ejpam-3907	292	3	,	,	PUNCT
ejpam-3907	292	4	28(6):469–495	28(6):469–495	NUM
ejpam-3907	292	5	,	,	PUNCT
ejpam-3907	292	6	2017	2017	NUM
ejpam-3907	292	7	.	.	PUNCT
ejpam-3907	293	1	[	[	X
ejpam-3907	293	2	15	15	NUM
ejpam-3907	293	3	]	]	X
ejpam-3907	293	4	k	k	PROPN
ejpam-3907	293	5	h	h	PROPN
ejpam-3907	293	6	rosen	rosen	PROPN
ejpam-3907	293	7	.	.	PUNCT
ejpam-3907	294	1	discrete	discrete	ADJ
ejpam-3907	294	2	mathematics	mathematic	NOUN
ejpam-3907	294	3	and	and	CCONJ
ejpam-3907	294	4	its	its	PRON
ejpam-3907	294	5	applications	application	NOUN
ejpam-3907	294	6	.	.	PUNCT
ejpam-3907	295	1	mcgraw	mcgraw	PROPN
ejpam-3907	295	2	-	-	PUNCT
ejpam-3907	295	3	hill	hill	PROPN
ejpam-3907	295	4	,	,	PUNCT
ejpam-3907	295	5	8th	8th	ADJ
ejpam-3907	295	6	edition	edition	NOUN
ejpam-3907	295	7	,	,	PUNCT
ejpam-3907	295	8	2019	2019	NUM
ejpam-3907	295	9	.	.	PUNCT
ejpam-3907	296	1	[	[	X
ejpam-3907	296	2	16	16	NUM
ejpam-3907	296	3	]	]	PUNCT
ejpam-3907	296	4	a	a	DET
ejpam-3907	296	5	syarifuddin	syarifuddin	NOUN
ejpam-3907	296	6	and	and	CCONJ
ejpam-3907	296	7	i	i	NOUN
ejpam-3907	296	8	muchtadi	muchtadi	NOUN
ejpam-3907	296	9	-	-	PUNCT
ejpam-3907	296	10	alamsyah	alamsyah	NOUN
ejpam-3907	296	11	.	.	PUNCT
ejpam-3907	297	1	construction	construction	NOUN
ejpam-3907	297	2	of	of	ADP
ejpam-3907	297	3	cyclic	cyclic	ADJ
ejpam-3907	297	4	codes	code	NOUN
ejpam-3907	297	5	over	over	ADP
ejpam-3907	297	6	ternary	ternary	ADJ
ejpam-3907	297	7	field	field	NOUN
ejpam-3907	297	8	from	from	ADP
ejpam-3907	297	9	periodic	periodic	ADJ
ejpam-3907	297	10	sequences	sequence	NOUN
ejpam-3907	297	11	.	.	PUNCT
ejpam-3907	298	1	southeast	southeast	ADJ
ejpam-3907	298	2	asian	asian	ADJ
ejpam-3907	298	3	bulletin	bulletin	NOUN
ejpam-3907	298	4	of	of	ADP
ejpam-3907	298	5	mathematics	mathematic	NOUN
ejpam-3907	298	6	,	,	PUNCT
ejpam-3907	298	7	42(5):773	42(5):773	NUM
ejpam-3907	298	8	–	–	PUNCT
ejpam-3907	298	9	780	780	NUM
ejpam-3907	298	10	,	,	PUNCT
ejpam-3907	298	11	2018	2018	NUM
ejpam-3907	298	12	.	.	PUNCT
ejpam-3907	299	1	[	[	X
ejpam-3907	299	2	17	17	NUM
ejpam-3907	299	3	]	]	X
ejpam-3907	299	4	c	c	PROPN
ejpam-3907	299	5	tang	tang	PROPN
ejpam-3907	299	6	,	,	PUNCT
ejpam-3907	299	7	y	y	PROPN
ejpam-3907	299	8	qi	qi	PROPN
ejpam-3907	299	9	,	,	PUNCT
ejpam-3907	299	10	and	and	CCONJ
ejpam-3907	299	11	m	m	PROPN
ejpam-3907	299	12	xu	xu	PROPN
ejpam-3907	299	13	.	.	PUNCT
ejpam-3907	300	1	a	a	DET
ejpam-3907	300	2	note	note	NOUN
ejpam-3907	300	3	on	on	ADP
ejpam-3907	300	4	cyclic	cyclic	ADJ
ejpam-3907	300	5	codes	code	NOUN
ejpam-3907	300	6	from	from	ADP
ejpam-3907	300	7	apn	apn	NOUN
ejpam-3907	300	8	functions	function	NOUN
ejpam-3907	300	9	.	.	PUNCT
ejpam-3907	301	1	appl	appl	PROPN
ejpam-3907	301	2	.	.	PUNCT
ejpam-3907	302	1	algebra	algebra	PROPN
ejpam-3907	302	2	eng	eng	PROPN
ejpam-3907	302	3	.	.	PROPN
ejpam-3907	302	4	,	,	PUNCT
ejpam-3907	302	5	commun	commun	PROPN
ejpam-3907	302	6	.	.	PUNCT
ejpam-3907	303	1	comput	comput	PROPN
ejpam-3907	303	2	.	.	PUNCT
ejpam-3907	303	3	,	,	PUNCT
ejpam-3907	303	4	25(1):21–37	25(1):21–37	NUM
ejpam-3907	303	5	,	,	PUNCT
ejpam-3907	303	6	2014	2014	NUM
ejpam-3907	303	7	.	.	PUNCT
ejpam-3907	304	1	[	[	X
ejpam-3907	304	2	18	18	NUM
ejpam-3907	304	3	]	]	PUNCT
ejpam-3907	304	4	a	a	DET
ejpam-3907	304	5	thangaraj	thangaraj	NOUN
ejpam-3907	304	6	and	and	CCONJ
ejpam-3907	304	7	s	s	PROPN
ejpam-3907	304	8	w	w	PROPN
ejpam-3907	304	9	mclaughlin	mclaughlin	PROPN
ejpam-3907	304	10	.	.	PUNCT
ejpam-3907	305	1	quantum	quantum	PROPN
ejpam-3907	305	2	codes	code	NOUN
ejpam-3907	305	3	from	from	ADP
ejpam-3907	305	4	cyclic	cyclic	ADJ
ejpam-3907	305	5	codes	code	NOUN
ejpam-3907	305	6	over	over	ADP
ejpam-3907	305	7	gf(4	gf(4	NOUN
ejpam-3907	305	8	m	m	NOUN
ejpam-3907	305	9	)	)	PUNCT
ejpam-3907	305	10	.	.	PUNCT
ejpam-3907	306	1	ieee	ieee	PROPN
ejpam-3907	306	2	trans	trans	PROPN
ejpam-3907	306	3	.	.	PUNCT
ejpam-3907	307	1	inform	inform	NOUN
ejpam-3907	307	2	.	.	PUNCT
ejpam-3907	308	1	theory	theory	NOUN
ejpam-3907	308	2	,	,	PUNCT
ejpam-3907	308	3	47(3):1176–1178	47(3):1176–1178	NUM
ejpam-3907	308	4	,	,	PUNCT
ejpam-3907	308	5	2001	2001	NUM
ejpam-3907	308	6	.	.	PUNCT