id	sid	tid	token	lemma	pos
ejpam-6414	1	1	european	european	PROPN
ejpam-6414	1	2	journal	journal	PROPN
ejpam-6414	1	3	of	of	ADP
ejpam-6414	1	4	pure	pure	ADJ
ejpam-6414	1	5	and	and	CCONJ
ejpam-6414	1	6	applied	applied	ADJ
ejpam-6414	1	7	mathematics	mathematic	NOUN
ejpam-6414	1	8	2025	2025	NUM
ejpam-6414	1	9	,	,	PUNCT
ejpam-6414	1	10	vol	vol	NOUN
ejpam-6414	1	11	.	.	PROPN
ejpam-6414	1	12	18	18	NUM
ejpam-6414	1	13	,	,	PUNCT
ejpam-6414	1	14	issue	issue	NOUN
ejpam-6414	1	15	3	3	NUM
ejpam-6414	1	16	,	,	PUNCT
ejpam-6414	1	17	article	article	NOUN
ejpam-6414	1	18	number	number	NOUN
ejpam-6414	1	19	6414	6414	NUM
ejpam-6414	1	20	issn	issn	PROPN
ejpam-6414	1	21	1307	1307	NUM
ejpam-6414	1	22	-	-	SYM
ejpam-6414	1	23	5543	5543	NUM
ejpam-6414	1	24	–	–	PUNCT
ejpam-6414	1	25	ejpam.com	ejpam.com	X
ejpam-6414	1	26	published	publish	VERB
ejpam-6414	1	27	by	by	ADP
ejpam-6414	1	28	new	new	PROPN
ejpam-6414	1	29	york	york	PROPN
ejpam-6414	1	30	business	business	PROPN
ejpam-6414	1	31	global	global	ADJ
ejpam-6414	1	32	structural	structural	ADJ
ejpam-6414	1	33	insights	insight	NOUN
ejpam-6414	1	34	and	and	CCONJ
ejpam-6414	1	35	decoding	decode	VERB
ejpam-6414	1	36	strategies	strategy	NOUN
ejpam-6414	1	37	for	for	ADP
ejpam-6414	1	38	bch	bch	PROPN
ejpam-6414	1	39	codes	code	NOUN
ejpam-6414	1	40	over	over	ADP
ejpam-6414	1	41	quasi	quasi	ADJ
ejpam-6414	1	42	-	-	ADJ
ejpam-6414	1	43	galois	galois	ADJ
ejpam-6414	1	44	rings	ring	NOUN
ejpam-6414	1	45	muhammad	muhammad	PROPN
ejpam-6414	1	46	sajjad1,∗	sajjad1,∗	PROPN
ejpam-6414	1	47	,	,	PUNCT
ejpam-6414	1	48	muhammad	muhammad	PROPN
ejpam-6414	1	49	shoaib	shoaib	PROPN
ejpam-6414	1	50	abid2	abid2	PROPN
ejpam-6414	1	51	,	,	PUNCT
ejpam-6414	1	52	maha	maha	PROPN
ejpam-6414	1	53	alammari3	alammari3	PROPN
ejpam-6414	1	54	,	,	PUNCT
ejpam-6414	1	55	robinson	robinson	PROPN
ejpam-6414	1	56	-	-	PUNCT
ejpam-6414	1	57	julian	julian	PROPN
ejpam-6414	1	58	serna4	serna4	PROPN
ejpam-6414	1	59	1	1	NUM
ejpam-6414	1	60	nutech	nutech	NOUN
ejpam-6414	1	61	school	school	NOUN
ejpam-6414	1	62	of	of	ADP
ejpam-6414	1	63	applied	apply	VERB
ejpam-6414	1	64	science	science	NOUN
ejpam-6414	1	65	and	and	CCONJ
ejpam-6414	1	66	humanities	humanity	NOUN
ejpam-6414	1	67	,	,	PUNCT
ejpam-6414	1	68	national	national	ADJ
ejpam-6414	1	69	university	university	PROPN
ejpam-6414	1	70	of	of	ADP
ejpam-6414	1	71	technology	technology	NOUN
ejpam-6414	1	72	,	,	PUNCT
ejpam-6414	1	73	islamabad	islamabad	PROPN
ejpam-6414	1	74	,	,	PUNCT
ejpam-6414	1	75	44000	44000	NUM
ejpam-6414	1	76	,	,	PUNCT
ejpam-6414	1	77	pakistan	pakistan	PROPN
ejpam-6414	1	78	2	2	NUM
ejpam-6414	1	79	department	department	NOUN
ejpam-6414	1	80	of	of	ADP
ejpam-6414	1	81	mathematics	mathematic	NOUN
ejpam-6414	1	82	,	,	PUNCT
ejpam-6414	1	83	quaid	quaid	PROPN
ejpam-6414	1	84	-	-	PUNCT
ejpam-6414	1	85	i	i	PROPN
ejpam-6414	1	86	-	-	PUNCT
ejpam-6414	1	87	azam	azam	PROPN
ejpam-6414	1	88	university	university	PROPN
ejpam-6414	1	89	,	,	PUNCT
ejpam-6414	1	90	islamabad	islamabad	PROPN
ejpam-6414	1	91	,	,	PUNCT
ejpam-6414	1	92	pakistan	pakistan	PROPN
ejpam-6414	1	93	3	3	NUM
ejpam-6414	1	94	department	department	NOUN
ejpam-6414	1	95	of	of	ADP
ejpam-6414	1	96	mathematics	mathematics	PROPN
ejpam-6414	1	97	,	,	PUNCT
ejpam-6414	1	98	college	college	NOUN
ejpam-6414	1	99	of	of	ADP
ejpam-6414	1	100	science	science	NOUN
ejpam-6414	1	101	,	,	PUNCT
ejpam-6414	1	102	king	king	PROPN
ejpam-6414	1	103	saud	saud	PROPN
ejpam-6414	1	104	university	university	PROPN
ejpam-6414	1	105	,	,	PUNCT
ejpam-6414	1	106	p.o	p.o	PROPN
ejpam-6414	1	107	.	.	PROPN
ejpam-6414	1	108	box	box	PROPN
ejpam-6414	1	109	22452	22452	NUM
ejpam-6414	1	110	riyadh	riyadh	PROPN
ejpam-6414	1	111	11495	11495	NUM
ejpam-6414	1	112	,	,	PUNCT
ejpam-6414	1	113	saudi	saudi	PROPN
ejpam-6414	1	114	arabia	arabia	PROPN
ejpam-6414	1	115	4	4	NUM
ejpam-6414	1	116	escuela	escuela	NOUN
ejpam-6414	1	117	de	de	X
ejpam-6414	1	118	matemáticas	matemáticas	PROPN
ejpam-6414	1	119	y	y	PROPN
ejpam-6414	1	120	estad́ıstica	estad́ıstica	PROPN
ejpam-6414	1	121	,	,	PUNCT
ejpam-6414	1	122	universidad	universidad	PROPN
ejpam-6414	1	123	pedagógica	pedagógica	PROPN
ejpam-6414	1	124	y	y	PROPN
ejpam-6414	1	125	tecnológica	tecnológica	PROPN
ejpam-6414	1	126	de	de	PROPN
ejpam-6414	1	127	colombia	colombia	PROPN
ejpam-6414	1	128	,	,	PUNCT
ejpam-6414	1	129	tunja	tunja	NUM
ejpam-6414	1	130	,	,	PUNCT
ejpam-6414	1	131	colombia	colombia	PROPN
ejpam-6414	1	132	abstract	abstract	NOUN
ejpam-6414	1	133	.	.	PUNCT
ejpam-6414	2	1	robust	robust	ADJ
ejpam-6414	2	2	data	datum	NOUN
ejpam-6414	2	3	disclosure	disclosure	NOUN
ejpam-6414	2	4	constitutes	constitute	VERB
ejpam-6414	2	5	an	an	DET
ejpam-6414	2	6	essential	essential	ADJ
ejpam-6414	2	7	problem	problem	NOUN
ejpam-6414	2	8	for	for	ADP
ejpam-6414	2	9	contemporary	contemporary	ADJ
ejpam-6414	2	10	system	system	NOUN
ejpam-6414	2	11	communication	communication	NOUN
ejpam-6414	2	12	,	,	PUNCT
ejpam-6414	2	13	and	and	CCONJ
ejpam-6414	2	14	the	the	DET
ejpam-6414	2	15	theory	theory	NOUN
ejpam-6414	2	16	of	of	ADP
ejpam-6414	2	17	coding	coding	NOUN
ejpam-6414	2	18	becomes	become	VERB
ejpam-6414	2	19	the	the	DET
ejpam-6414	2	20	key	key	NOUN
ejpam-6414	2	21	to	to	ADP
ejpam-6414	2	22	maintaining	maintain	VERB
ejpam-6414	2	23	data	datum	NOUN
ejpam-6414	2	24	integrity	integrity	NOUN
ejpam-6414	2	25	.	.	PUNCT
ejpam-6414	3	1	this	this	DET
ejpam-6414	3	2	paper	paper	NOUN
ejpam-6414	3	3	discusses	discuss	VERB
ejpam-6414	3	4	constructions	construction	NOUN
ejpam-6414	3	5	and	and	CCONJ
ejpam-6414	3	6	decoding	decode	VERB
ejpam-6414	3	7	of	of	ADP
ejpam-6414	3	8	bose	bose	NOUN
ejpam-6414	3	9	–	–	PUNCT
ejpam-6414	3	10	chaudhuri	chaudhuri	PROPN
ejpam-6414	3	11	–	–	PUNCT
ejpam-6414	3	12	hocquenghem	hocquenghem	PROPN
ejpam-6414	3	13	(	(	PUNCT
ejpam-6414	3	14	bch	bch	PROPN
ejpam-6414	3	15	)	)	PUNCT
ejpam-6414	3	16	codes	code	NOUN
ejpam-6414	3	17	over	over	ADP
ejpam-6414	3	18	quasigalois	quasigalois	PROPN
ejpam-6414	3	19	rings	ring	NOUN
ejpam-6414	3	20	(	(	PUNCT
ejpam-6414	3	21	qgrs	qgrs	PROPN
ejpam-6414	3	22	)	)	PUNCT
ejpam-6414	3	23	–	–	PUNCT
ejpam-6414	3	24	generalization	generalization	NOUN
ejpam-6414	3	25	of	of	ADP
ejpam-6414	3	26	classical	classical	ADJ
ejpam-6414	3	27	galois	galois	PROPN
ejpam-6414	3	28	rings	ring	NOUN
ejpam-6414	3	29	.	.	PUNCT
ejpam-6414	4	1	the	the	DET
ejpam-6414	4	2	qgrs	qgrs	NOUN
ejpam-6414	4	3	provide	provide	VERB
ejpam-6414	4	4	richer	rich	ADJ
ejpam-6414	4	5	algebraic	algebraic	ADJ
ejpam-6414	4	6	structures	structure	NOUN
ejpam-6414	4	7	that	that	PRON
ejpam-6414	4	8	lead	lead	VERB
ejpam-6414	4	9	to	to	ADP
ejpam-6414	4	10	improved	improve	VERB
ejpam-6414	4	11	error	error	NOUN
ejpam-6414	4	12	correction	correction	NOUN
ejpam-6414	4	13	capabilities	capability	NOUN
ejpam-6414	4	14	,	,	PUNCT
ejpam-6414	4	15	greater	great	ADJ
ejpam-6414	4	16	code	code	NOUN
ejpam-6414	4	17	rates	rate	NOUN
ejpam-6414	4	18	,	,	PUNCT
ejpam-6414	4	19	and	and	CCONJ
ejpam-6414	4	20	more	more	ADJ
ejpam-6414	4	21	codewords	codeword	NOUN
ejpam-6414	4	22	than	than	ADP
ejpam-6414	4	23	their	their	PRON
ejpam-6414	4	24	galois	galois	PROPN
ejpam-6414	4	25	counterparts	counterpart	NOUN
ejpam-6414	4	26	.	.	PUNCT
ejpam-6414	5	1	we	we	PRON
ejpam-6414	5	2	provide	provide	VERB
ejpam-6414	5	3	an	an	DET
ejpam-6414	5	4	all	all	PRON
ejpam-6414	5	5	-	-	PUNCT
ejpam-6414	5	6	round	round	NOUN
ejpam-6414	5	7	theory	theory	NOUN
ejpam-6414	5	8	of	of	ADP
ejpam-6414	5	9	construction	construction	NOUN
ejpam-6414	5	10	for	for	ADP
ejpam-6414	5	11	bch	bch	PROPN
ejpam-6414	5	12	codes	code	NOUN
ejpam-6414	5	13	over	over	ADP
ejpam-6414	5	14	qgrs	qgrs	PROPN
ejpam-6414	5	15	,	,	PUNCT
ejpam-6414	5	16	describe	describe	VERB
ejpam-6414	5	17	them	they	PRON
ejpam-6414	5	18	in	in	ADP
ejpam-6414	5	19	their	their	PRON
ejpam-6414	5	20	construction	construction	NOUN
ejpam-6414	5	21	process	process	NOUN
ejpam-6414	5	22	,	,	PUNCT
ejpam-6414	5	23	and	and	CCONJ
ejpam-6414	5	24	walk	walk	VERB
ejpam-6414	5	25	through	through	ADP
ejpam-6414	5	26	an	an	DET
ejpam-6414	5	27	efficient	efficient	ADJ
ejpam-6414	5	28	decoding	decoding	NOUN
ejpam-6414	5	29	technique	technique	NOUN
ejpam-6414	5	30	.	.	PUNCT
ejpam-6414	6	1	our	our	PRON
ejpam-6414	6	2	findings	finding	NOUN
ejpam-6414	6	3	demonstrate	demonstrate	VERB
ejpam-6414	6	4	the	the	DET
ejpam-6414	6	5	ability	ability	NOUN
ejpam-6414	6	6	of	of	ADP
ejpam-6414	6	7	bch	bch	PROPN
ejpam-6414	6	8	codes	code	NOUN
ejpam-6414	6	9	under	under	ADP
ejpam-6414	6	10	qgr	qgr	NOUN
ejpam-6414	6	11	to	to	PART
ejpam-6414	6	12	provide	provide	VERB
ejpam-6414	6	13	high	high	ADJ
ejpam-6414	6	14	reliability	reliability	NOUN
ejpam-6414	6	15	and	and	CCONJ
ejpam-6414	6	16	performance	performance	NOUN
ejpam-6414	6	17	for	for	ADP
ejpam-6414	6	18	the	the	DET
ejpam-6414	6	19	communication	communication	NOUN
ejpam-6414	6	20	systems	system	NOUN
ejpam-6414	6	21	,	,	PUNCT
ejpam-6414	6	22	which	which	PRON
ejpam-6414	6	23	will	will	AUX
ejpam-6414	6	24	make	make	VERB
ejpam-6414	6	25	them	they	PRON
ejpam-6414	6	26	a	a	DET
ejpam-6414	6	27	candidate	candidate	NOUN
ejpam-6414	6	28	for	for	ADP
ejpam-6414	6	29	future	future	ADJ
ejpam-6414	6	30	use	use	NOUN
ejpam-6414	6	31	in	in	ADP
ejpam-6414	6	32	data	data	NOUN
ejpam-6414	6	33	transmission	transmission	NOUN
ejpam-6414	6	34	and	and	CCONJ
ejpam-6414	6	35	storage	storage	NOUN
ejpam-6414	6	36	.	.	PUNCT
ejpam-6414	7	1	2020	2020	NUM
ejpam-6414	7	2	mathematics	mathematic	NOUN
ejpam-6414	7	3	subject	subject	NOUN
ejpam-6414	7	4	classifications	classification	NOUN
ejpam-6414	7	5	:	:	PUNCT
ejpam-6414	7	6	94b75	94b75	NUM
ejpam-6414	7	7	,	,	PUNCT
ejpam-6414	7	8	11t71	11t71	NUM
ejpam-6414	7	9	,	,	PUNCT
ejpam-6414	7	10	94a24	94a24	NUM
ejpam-6414	7	11	,	,	PUNCT
ejpam-6414	7	12	68p30	68p30	NUM
ejpam-6414	7	13	,	,	PUNCT
ejpam-6414	7	14	14g50	14g50	NUM
ejpam-6414	7	15	,	,	PUNCT
ejpam-6414	7	16	94a05	94a05	NUM
ejpam-6414	7	17	key	key	ADJ
ejpam-6414	7	18	words	word	NOUN
ejpam-6414	7	19	and	and	CCONJ
ejpam-6414	7	20	phrases	phrase	NOUN
ejpam-6414	7	21	:	:	PUNCT
ejpam-6414	7	22	quasi	quasi	ADJ
ejpam-6414	7	23	-	-	ADJ
ejpam-6414	7	24	galois	galois	PROPN
ejpam-6414	7	25	rings	ring	NOUN
ejpam-6414	7	26	,	,	PUNCT
ejpam-6414	7	27	bch	bch	PROPN
ejpam-6414	7	28	codes	code	NOUN
ejpam-6414	7	29	,	,	PUNCT
ejpam-6414	7	30	error	error	NOUN
ejpam-6414	7	31	correction	correction	NOUN
ejpam-6414	7	32	,	,	PUNCT
ejpam-6414	7	33	code	code	NOUN
ejpam-6414	7	34	rate	rate	NOUN
ejpam-6414	7	35	,	,	PUNCT
ejpam-6414	7	36	ringbased	ringbase	VERB
ejpam-6414	7	37	coding	coding	NOUN
ejpam-6414	7	38	theory	theory	NOUN
ejpam-6414	7	39	,	,	PUNCT
ejpam-6414	7	40	cyclic	cyclic	ADJ
ejpam-6414	7	41	subgroups	subgroup	NOUN
ejpam-6414	7	42	1	1	NUM
ejpam-6414	7	43	.	.	X
ejpam-6414	8	1	introduction	introduction	NOUN
ejpam-6414	8	2	it	it	PRON
ejpam-6414	8	3	relates	relate	VERB
ejpam-6414	8	4	to	to	ADP
ejpam-6414	8	5	how	how	SCONJ
ejpam-6414	8	6	information	information	NOUN
ejpam-6414	8	7	that	that	PRON
ejpam-6414	8	8	is	be	AUX
ejpam-6414	8	9	to	to	PART
ejpam-6414	8	10	be	be	AUX
ejpam-6414	8	11	transmitted	transmit	VERB
ejpam-6414	8	12	is	be	AUX
ejpam-6414	8	13	put	put	VERB
ejpam-6414	8	14	into	into	ADP
ejpam-6414	8	15	another	another	DET
ejpam-6414	8	16	form	form	NOUN
ejpam-6414	8	17	that	that	PRON
ejpam-6414	8	18	can	can	AUX
ejpam-6414	8	19	easily	easily	ADV
ejpam-6414	8	20	be	be	AUX
ejpam-6414	8	21	transmitted	transmit	VERB
ejpam-6414	8	22	through	through	ADP
ejpam-6414	8	23	a	a	DET
ejpam-6414	8	24	channel	channel	NOUN
ejpam-6414	8	25	,	,	PUNCT
ejpam-6414	8	26	which	which	PRON
ejpam-6414	8	27	is	be	AUX
ejpam-6414	8	28	usually	usually	ADV
ejpam-6414	8	29	a	a	DET
ejpam-6414	8	30	wire	wire	NOUN
ejpam-6414	8	31	or	or	CCONJ
ejpam-6414	8	32	broadcasting	broadcasting	NOUN
ejpam-6414	8	33	system	system	NOUN
ejpam-6414	8	34	.	.	PUNCT
ejpam-6414	9	1	this	this	PRON
ejpam-6414	9	2	entails	entail	VERB
ejpam-6414	9	3	the	the	DET
ejpam-6414	9	4	use	use	NOUN
ejpam-6414	9	5	of	of	ADP
ejpam-6414	9	6	different	different	ADJ
ejpam-6414	9	7	codes	code	NOUN
ejpam-6414	9	8	to	to	PART
ejpam-6414	9	9	reduce	reduce	VERB
ejpam-6414	9	10	errors	error	NOUN
ejpam-6414	9	11	that	that	PRON
ejpam-6414	9	12	may	may	AUX
ejpam-6414	9	13	be	be	AUX
ejpam-6414	9	14	occasioned	occasion	VERB
ejpam-6414	9	15	by	by	ADP
ejpam-6414	9	16	the	the	DET
ejpam-6414	9	17	transmission	transmission	NOUN
ejpam-6414	9	18	medium	medium	NOUN
ejpam-6414	9	19	,	,	PUNCT
ejpam-6414	9	20	such	such	ADJ
ejpam-6414	9	21	as	as	ADP
ejpam-6414	9	22	noise	noise	NOUN
ejpam-6414	9	23	,	,	PUNCT
ejpam-6414	9	24	interference	interference	NOUN
ejpam-6414	9	25	or	or	CCONJ
ejpam-6414	9	26	loss	loss	NOUN
ejpam-6414	9	27	of	of	ADP
ejpam-6414	9	28	signal	signal	ADJ
ejpam-6414	9	29	strength	strength	NOUN
ejpam-6414	9	30	.	.	PUNCT
ejpam-6414	10	1	the	the	DET
ejpam-6414	10	2	∗corresponding	∗corresponde	VERB
ejpam-6414	10	3	author	author	NOUN
ejpam-6414	10	4	.	.	PUNCT
ejpam-6414	11	1	doi	doi	NOUN
ejpam-6414	11	2	:	:	PUNCT
ejpam-6414	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6414	https://doi.org/10.29020/nybg.ejpam.v18i3.6414	PRON
ejpam-6414	11	4	email	email	NOUN
ejpam-6414	11	5	addresses	address	NOUN
ejpam-6414	11	6	:	:	PUNCT
ejpam-6414	11	7	muhammad.sajjad@nutech.edu.pk	muhammad.sajjad@nutech.edu.pk	PROPN
ejpam-6414	11	8	(	(	PUNCT
ejpam-6414	11	9	m.	m.	PROPN
ejpam-6414	11	10	sajjad	sajjad	PROPN
ejpam-6414	11	11	)	)	PUNCT
ejpam-6414	11	12	,	,	PUNCT
ejpam-6414	11	13	janjuashoaib814@gmail.com	janjuashoaib814@gmail.com	X
ejpam-6414	11	14	(	(	PUNCT
ejpam-6414	11	15	m.	m.	PROPN
ejpam-6414	11	16	s.	s.	PROPN
ejpam-6414	11	17	abid	abid	PROPN
ejpam-6414	11	18	)	)	PUNCT
ejpam-6414	11	19	,	,	PUNCT
ejpam-6414	11	20	malammari@ksu.edu.sa	malammari@ksu.edu.sa	PROPN
ejpam-6414	11	21	(	(	PUNCT
ejpam-6414	11	22	m.	m.	NOUN
ejpam-6414	11	23	alammari	alammari	PROPN
ejpam-6414	11	24	)	)	PUNCT
ejpam-6414	11	25	,	,	PUNCT
ejpam-6414	11	26	robinson.serna@uptc.edu.co	robinson.serna@uptc.edu.co	ADP
ejpam-6414	11	27	(	(	PUNCT
ejpam-6414	11	28	r.	r.	PROPN
ejpam-6414	11	29	j.	j.	PROPN
ejpam-6414	11	30	serna	serna	PROPN
ejpam-6414	11	31	)	)	PUNCT
ejpam-6414	11	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6414	11	33	1	1	NUM
ejpam-6414	11	34	copyright	copyright	NOUN
ejpam-6414	11	35	:	:	PUNCT
ejpam-6414	12	1	©	©	PROPN
ejpam-6414	12	2	2025	2025	NUM
ejpam-6414	12	3	the	the	DET
ejpam-6414	12	4	author(s	author(s	NOUN
ejpam-6414	12	5	)	)	PUNCT
ejpam-6414	12	6	.	.	PUNCT
ejpam-6414	13	1	(	(	PUNCT
ejpam-6414	13	2	cc	cc	NOUN
ejpam-6414	13	3	by	by	ADP
ejpam-6414	13	4	-	-	PUNCT
ejpam-6414	13	5	nc	nc	PROPN
ejpam-6414	13	6	4.0	4.0	NUM
ejpam-6414	13	7	)	)	PUNCT
ejpam-6414	13	8	muhammad	muhammad	PROPN
ejpam-6414	13	9	sajjad	sajjad	PROPN
ejpam-6414	13	10	et	et	PROPN
ejpam-6414	13	11	al	al	PROPN
ejpam-6414	13	12	.	.	PUNCT
ejpam-6414	13	13	/	/	SYM
ejpam-6414	13	14	eur	eur	PROPN
ejpam-6414	13	15	.	.	PUNCT
ejpam-6414	14	1	j.	j.	PROPN
ejpam-6414	14	2	pure	pure	PROPN
ejpam-6414	14	3	appl	appl	PROPN
ejpam-6414	14	4	.	.	PROPN
ejpam-6414	14	5	math	math	PROPN
ejpam-6414	14	6	,	,	PUNCT
ejpam-6414	14	7	18	18	NUM
ejpam-6414	14	8	(	(	PUNCT
ejpam-6414	14	9	3	3	NUM
ejpam-6414	14	10	)	)	PUNCT
ejpam-6414	14	11	(	(	PUNCT
ejpam-6414	14	12	2025	2025	NUM
ejpam-6414	14	13	)	)	PUNCT
ejpam-6414	14	14	,	,	PUNCT
ejpam-6414	14	15	6414	6414	NUM
ejpam-6414	14	16	2	2	NUM
ejpam-6414	14	17	of	of	ADP
ejpam-6414	14	18	22	22	NUM
ejpam-6414	14	19	principles	principle	NOUN
ejpam-6414	14	20	of	of	ADP
ejpam-6414	14	21	error	error	NOUN
ejpam-6414	14	22	-	-	PUNCT
ejpam-6414	14	23	detecting	detect	VERB
ejpam-6414	14	24	and	and	CCONJ
ejpam-6414	14	25	error	error	NOUN
ejpam-6414	14	26	-	-	PUNCT
ejpam-6414	14	27	correcting	correct	VERB
ejpam-6414	14	28	codes	code	NOUN
ejpam-6414	14	29	are	be	AUX
ejpam-6414	14	30	very	very	ADV
ejpam-6414	14	31	essential	essential	ADJ
ejpam-6414	14	32	to	to	PART
ejpam-6414	14	33	ensure	ensure	VERB
ejpam-6414	14	34	high	high	ADJ
ejpam-6414	14	35	data	datum	NOUN
ejpam-6414	14	36	reliability	reliability	NOUN
ejpam-6414	14	37	,	,	PUNCT
ejpam-6414	14	38	and	and	CCONJ
ejpam-6414	14	39	this	this	PRON
ejpam-6414	14	40	involves	involve	VERB
ejpam-6414	14	41	the	the	DET
ejpam-6414	14	42	hamming	hamming	NOUN
ejpam-6414	14	43	codes	code	NOUN
ejpam-6414	14	44	,	,	PUNCT
ejpam-6414	14	45	reed	reed	PROPN
ejpam-6414	14	46	-	-	PUNCT
ejpam-6414	14	47	solomon	solomon	PROPN
ejpam-6414	14	48	codes	code	NOUN
ejpam-6414	14	49	,	,	PUNCT
ejpam-6414	14	50	and	and	CCONJ
ejpam-6414	14	51	bch	bch	PROPN
ejpam-6414	14	52	codes	code	NOUN
ejpam-6414	14	53	.	.	PUNCT
ejpam-6414	15	1	these	these	DET
ejpam-6414	15	2	techniques	technique	NOUN
ejpam-6414	15	3	enhance	enhance	VERB
ejpam-6414	15	4	the	the	DET
ejpam-6414	15	5	dependability	dependability	NOUN
ejpam-6414	15	6	of	of	ADP
ejpam-6414	15	7	the	the	DET
ejpam-6414	15	8	original	original	ADJ
ejpam-6414	15	9	data	datum	NOUN
ejpam-6414	15	10	in	in	ADP
ejpam-6414	15	11	that	that	SCONJ
ejpam-6414	15	12	the	the	DET
ejpam-6414	15	13	receiver	receiver	NOUN
ejpam-6414	15	14	checks	check	NOUN
ejpam-6414	15	15	and	and	CCONJ
ejpam-6414	15	16	rectifies	rectify	VERB
ejpam-6414	15	17	errors	error	NOUN
ejpam-6414	15	18	without	without	ADP
ejpam-6414	15	19	having	have	VERB
ejpam-6414	15	20	to	to	PART
ejpam-6414	15	21	ask	ask	VERB
ejpam-6414	15	22	for	for	ADP
ejpam-6414	15	23	retransmission	retransmission	NOUN
ejpam-6414	15	24	.	.	PUNCT
ejpam-6414	16	1	as	as	SCONJ
ejpam-6414	16	2	inferred	infer	VERB
ejpam-6414	16	3	from	from	ADP
ejpam-6414	16	4	the	the	DET
ejpam-6414	16	5	above	above	ADJ
ejpam-6414	16	6	observations	observation	NOUN
ejpam-6414	16	7	,	,	PUNCT
ejpam-6414	16	8	this	this	DET
ejpam-6414	16	9	paper	paper	NOUN
ejpam-6414	16	10	aims	aim	VERB
ejpam-6414	16	11	at	at	ADP
ejpam-6414	16	12	showing	show	VERB
ejpam-6414	16	13	that	that	SCONJ
ejpam-6414	16	14	the	the	DET
ejpam-6414	16	15	selection	selection	NOUN
ejpam-6414	16	16	of	of	ADP
ejpam-6414	16	17	a	a	DET
ejpam-6414	16	18	particular	particular	ADJ
ejpam-6414	16	19	scheme	scheme	NOUN
ejpam-6414	16	20	to	to	PART
ejpam-6414	16	21	be	be	AUX
ejpam-6414	16	22	used	use	VERB
ejpam-6414	16	23	can	can	AUX
ejpam-6414	16	24	greatly	greatly	ADV
ejpam-6414	16	25	affect	affect	VERB
ejpam-6414	16	26	the	the	DET
ejpam-6414	16	27	dependability	dependability	NOUN
ejpam-6414	16	28	and	and	CCONJ
ejpam-6414	16	29	efficiency	efficiency	NOUN
ejpam-6414	16	30	of	of	ADP
ejpam-6414	16	31	the	the	DET
ejpam-6414	16	32	communication	communication	NOUN
ejpam-6414	16	33	system	system	NOUN
ejpam-6414	16	34	with	with	ADP
ejpam-6414	16	35	respect	respect	NOUN
ejpam-6414	16	36	to	to	ADP
ejpam-6414	16	37	the	the	DET
ejpam-6414	16	38	rb	rb	NOUN
ejpam-6414	16	39	/	/	SYM
ejpam-6414	16	40	sss	sss	NOUN
ejpam-6414	16	41	trade	trade	NOUN
ejpam-6414	16	42	-	-	PUNCT
ejpam-6414	16	43	off	off	NOUN
ejpam-6414	16	44	.	.	PUNCT
ejpam-6414	17	1	hence	hence	ADV
ejpam-6414	17	2	,	,	PUNCT
ejpam-6414	17	3	the	the	DET
ejpam-6414	17	4	coding	code	VERB
ejpam-6414	17	5	theory	theory	NOUN
ejpam-6414	17	6	is	be	AUX
ejpam-6414	17	7	a	a	DET
ejpam-6414	17	8	very	very	ADV
ejpam-6414	17	9	enabling	enabling	ADJ
ejpam-6414	17	10	tool	tool	NOUN
ejpam-6414	17	11	for	for	ADP
ejpam-6414	17	12	a	a	DET
ejpam-6414	17	13	plethora	plethora	NOUN
ejpam-6414	17	14	of	of	ADP
ejpam-6414	17	15	utilization	utilization	NOUN
ejpam-6414	17	16	opportunities	opportunity	NOUN
ejpam-6414	17	17	in	in	ADP
ejpam-6414	17	18	the	the	DET
ejpam-6414	17	19	digital	digital	ADJ
ejpam-6414	17	20	world	world	NOUN
ejpam-6414	17	21	,	,	PUNCT
ejpam-6414	17	22	such	such	ADJ
ejpam-6414	17	23	as	as	ADP
ejpam-6414	17	24	in	in	ADP
ejpam-6414	17	25	digital	digital	ADJ
ejpam-6414	17	26	communication	communication	NOUN
ejpam-6414	17	27	,	,	PUNCT
ejpam-6414	17	28	data	datum	NOUN
ejpam-6414	17	29	storage	storage	NOUN
ejpam-6414	17	30	,	,	PUNCT
ejpam-6414	17	31	deep	deep	ADJ
ejpam-6414	17	32	-	-	PUNCT
ejpam-6414	17	33	space	space	NOUN
ejpam-6414	17	34	signals	signal	NOUN
ejpam-6414	17	35	and	and	CCONJ
ejpam-6414	17	36	even	even	ADV
ejpam-6414	17	37	in	in	ADP
ejpam-6414	17	38	the	the	DET
ejpam-6414	17	39	new	new	ADJ
ejpam-6414	17	40	fashion	fashion	NOUN
ejpam-6414	17	41	wireless	wireless	NOUN
ejpam-6414	17	42	networks	network	NOUN
ejpam-6414	17	43	[	[	X
ejpam-6414	17	44	1	1	NUM
ejpam-6414	17	45	]	]	PUNCT
ejpam-6414	17	46	.	.	PUNCT
ejpam-6414	18	1	this	this	DET
ejpam-6414	18	2	section	section	NOUN
ejpam-6414	18	3	is	be	AUX
ejpam-6414	18	4	devoted	devote	VERB
ejpam-6414	18	5	to	to	ADP
ejpam-6414	18	6	the	the	DET
ejpam-6414	18	7	discussion	discussion	NOUN
ejpam-6414	18	8	of	of	ADP
ejpam-6414	18	9	major	major	ADJ
ejpam-6414	18	10	achievements	achievement	NOUN
ejpam-6414	18	11	and	and	CCONJ
ejpam-6414	18	12	the	the	DET
ejpam-6414	18	13	state	state	NOUN
ejpam-6414	18	14	of	of	ADP
ejpam-6414	18	15	the	the	DET
ejpam-6414	18	16	progress	progress	NOUN
ejpam-6414	18	17	as	as	ADV
ejpam-6414	18	18	well	well	ADV
ejpam-6414	18	19	as	as	ADP
ejpam-6414	18	20	the	the	DET
ejpam-6414	18	21	results	result	NOUN
ejpam-6414	18	22	of	of	ADP
ejpam-6414	18	23	recent	recent	ADJ
ejpam-6414	18	24	decades	decade	NOUN
ejpam-6414	18	25	in	in	ADP
ejpam-6414	18	26	the	the	DET
ejpam-6414	18	27	study	study	NOUN
ejpam-6414	18	28	of	of	ADP
ejpam-6414	18	29	bch	bch	PROPN
ejpam-6414	18	30	codes	code	NOUN
ejpam-6414	18	31	over	over	ADP
ejpam-6414	18	32	different	different	ADJ
ejpam-6414	18	33	algebraic	algebraic	ADJ
ejpam-6414	18	34	structures	structure	NOUN
ejpam-6414	18	35	.	.	PUNCT
ejpam-6414	19	1	the	the	DET
ejpam-6414	19	2	first	first	ADJ
ejpam-6414	19	3	step	step	NOUN
ejpam-6414	19	4	was	be	AUX
ejpam-6414	19	5	defined	define	VERB
ejpam-6414	19	6	by	by	ADP
ejpam-6414	19	7	assmus	assmus	NOUN
ejpam-6414	19	8	and	and	CCONJ
ejpam-6414	19	9	mattson	mattson	NOUN
ejpam-6414	19	10	in	in	ADP
ejpam-6414	19	11	[	[	X
ejpam-6414	19	12	1	1	NUM
ejpam-6414	19	13	]	]	PUNCT
ejpam-6414	19	14	who	who	PRON
ejpam-6414	19	15	gave	give	VERB
ejpam-6414	19	16	an	an	DET
ejpam-6414	19	17	axiomatic	axiomatic	ADJ
ejpam-6414	19	18	approach	approach	NOUN
ejpam-6414	19	19	to	to	ADP
ejpam-6414	19	20	error	error	NOUN
ejpam-6414	19	21	-	-	PUNCT
ejpam-6414	19	22	correcting	correct	VERB
ejpam-6414	19	23	codes	code	NOUN
ejpam-6414	19	24	and	and	CCONJ
ejpam-6414	19	25	stated	state	VERB
ejpam-6414	19	26	fundamental	fundamental	ADJ
ejpam-6414	19	27	theorems	theorem	NOUN
ejpam-6414	19	28	of	of	ADP
ejpam-6414	19	29	modern	modern	ADJ
ejpam-6414	19	30	coding	coding	NOUN
ejpam-6414	19	31	theory	theory	NOUN
ejpam-6414	19	32	.	.	PUNCT
ejpam-6414	20	1	their	their	PRON
ejpam-6414	20	2	work	work	NOUN
ejpam-6414	20	3	provided	provide	VERB
ejpam-6414	20	4	what	what	PRON
ejpam-6414	20	5	is	be	AUX
ejpam-6414	20	6	now	now	ADV
ejpam-6414	20	7	acknowledged	acknowledge	VERB
ejpam-6414	20	8	as	as	ADP
ejpam-6414	20	9	the	the	DET
ejpam-6414	20	10	first	first	ADJ
ejpam-6414	20	11	formal	formal	ADJ
ejpam-6414	20	12	mathematical	mathematical	ADJ
ejpam-6414	20	13	definitions	definition	NOUN
ejpam-6414	20	14	for	for	ADP
ejpam-6414	20	15	making	make	VERB
ejpam-6414	20	16	and	and	CCONJ
ejpam-6414	20	17	deciphering	decipher	VERB
ejpam-6414	20	18	codes	code	NOUN
ejpam-6414	20	19	that	that	PRON
ejpam-6414	20	20	are	be	AUX
ejpam-6414	20	21	still	still	ADV
ejpam-6414	20	22	in	in	ADP
ejpam-6414	20	23	use	use	NOUN
ejpam-6414	20	24	today	today	NOUN
ejpam-6414	20	25	.	.	PUNCT
ejpam-6414	21	1	augot	augot	PROPN
ejpam-6414	21	2	,	,	PUNCT
ejpam-6414	21	3	betti	betti	PROPN
ejpam-6414	21	4	,	,	PUNCT
ejpam-6414	21	5	and	and	CCONJ
ejpam-6414	21	6	orsini	orsini	PROPN
ejpam-6414	22	1	[	[	X
ejpam-6414	22	2	2	2	NUM
ejpam-6414	22	3	]	]	PUNCT
ejpam-6414	22	4	also	also	ADV
ejpam-6414	22	5	elaborated	elaborate	VERB
ejpam-6414	22	6	on	on	ADP
ejpam-6414	22	7	linear	linear	ADJ
ejpam-6414	22	8	and	and	CCONJ
ejpam-6414	22	9	cyclic	cyclic	ADJ
ejpam-6414	22	10	codes	code	NOUN
ejpam-6414	22	11	and	and	CCONJ
ejpam-6414	22	12	their	their	PRON
ejpam-6414	22	13	importance	importance	NOUN
ejpam-6414	22	14	in	in	ADP
ejpam-6414	22	15	the	the	DET
ejpam-6414	22	16	real	real	ADJ
ejpam-6414	22	17	world	world	NOUN
ejpam-6414	22	18	,	,	PUNCT
ejpam-6414	22	19	in	in	ADP
ejpam-6414	22	20	fields	field	NOUN
ejpam-6414	22	21	like	like	ADP
ejpam-6414	22	22	cryptography	cryptography	NOUN
ejpam-6414	22	23	and	and	CCONJ
ejpam-6414	22	24	data	datum	NOUN
ejpam-6414	22	25	transmission	transmission	NOUN
ejpam-6414	22	26	.	.	PUNCT
ejpam-6414	23	1	a	a	DET
ejpam-6414	23	2	thorough	thorough	ADJ
ejpam-6414	23	3	introduction	introduction	NOUN
ejpam-6414	23	4	is	be	AUX
ejpam-6414	23	5	given	give	VERB
ejpam-6414	23	6	to	to	ADP
ejpam-6414	23	7	their	their	PRON
ejpam-6414	23	8	basic	basic	ADJ
ejpam-6414	23	9	algebraic	algebraic	ADJ
ejpam-6414	23	10	properties	property	NOUN
ejpam-6414	23	11	and	and	CCONJ
ejpam-6414	23	12	the	the	DET
ejpam-6414	23	13	encoding	encoding	NOUN
ejpam-6414	23	14	methods	method	NOUN
ejpam-6414	23	15	that	that	PRON
ejpam-6414	23	16	are	be	AUX
ejpam-6414	23	17	crucial	crucial	ADJ
ejpam-6414	23	18	in	in	ADP
ejpam-6414	23	19	enhancing	enhance	VERB
ejpam-6414	23	20	the	the	DET
ejpam-6414	23	21	code	code	NOUN
ejpam-6414	23	22	’s	’s	PART
ejpam-6414	23	23	performance	performance	NOUN
ejpam-6414	23	24	.	.	PUNCT
ejpam-6414	24	1	blake	blake	NOUN
ejpam-6414	25	1	[	[	X
ejpam-6414	25	2	3	3	NUM
ejpam-6414	25	3	]	]	PUNCT
ejpam-6414	25	4	studied	study	VERB
ejpam-6414	25	5	codes	code	NOUN
ejpam-6414	25	6	over	over	ADP
ejpam-6414	25	7	certain	certain	ADJ
ejpam-6414	25	8	rings	ring	NOUN
ejpam-6414	25	9	,	,	PUNCT
ejpam-6414	25	10	thus	thus	ADV
ejpam-6414	25	11	enriching	enrich	VERB
ejpam-6414	25	12	and	and	CCONJ
ejpam-6414	25	13	developing	develop	VERB
ejpam-6414	25	14	theoretical	theoretical	ADJ
ejpam-6414	25	15	fundamentals	fundamental	NOUN
ejpam-6414	25	16	of	of	ADP
ejpam-6414	25	17	coding	code	VERB
ejpam-6414	25	18	theory	theory	NOUN
ejpam-6414	25	19	for	for	ADP
ejpam-6414	25	20	various	various	ADJ
ejpam-6414	25	21	algebraic	algebraic	ADJ
ejpam-6414	25	22	structures	structure	NOUN
ejpam-6414	25	23	except	except	SCONJ
ejpam-6414	25	24	for	for	ADP
ejpam-6414	25	25	fields	field	NOUN
ejpam-6414	25	26	.	.	PUNCT
ejpam-6414	26	1	his	his	PRON
ejpam-6414	26	2	work	work	NOUN
ejpam-6414	26	3	laid	lay	VERB
ejpam-6414	26	4	the	the	DET
ejpam-6414	26	5	foundation	foundation	NOUN
ejpam-6414	26	6	for	for	ADP
ejpam-6414	26	7	studying	study	VERB
ejpam-6414	26	8	bch	bch	PROPN
ejpam-6414	26	9	codes	code	NOUN
ejpam-6414	26	10	over	over	ADP
ejpam-6414	26	11	non	non	ADJ
ejpam-6414	26	12	-	-	ADJ
ejpam-6414	26	13	field	field	ADJ
ejpam-6414	26	14	rings	ring	NOUN
ejpam-6414	26	15	such	such	ADJ
ejpam-6414	26	16	as	as	ADP
ejpam-6414	26	17	the	the	DET
ejpam-6414	26	18	integer	integer	NOUN
ejpam-6414	26	19	residue	residue	NOUN
ejpam-6414	26	20	rings	ring	NOUN
ejpam-6414	26	21	[	[	X
ejpam-6414	26	22	4	4	NUM
ejpam-6414	26	23	,	,	PUNCT
ejpam-6414	26	24	5	5	NUM
ejpam-6414	26	25	]	]	PUNCT
ejpam-6414	26	26	and	and	CCONJ
ejpam-6414	26	27	modular	modular	ADJ
ejpam-6414	26	28	rings	ring	NOUN
ejpam-6414	26	29	[	[	X
ejpam-6414	26	30	6	6	NUM
ejpam-6414	26	31	,	,	PUNCT
ejpam-6414	26	32	7	7	NUM
ejpam-6414	26	33	]	]	PUNCT
ejpam-6414	26	34	which	which	PRON
ejpam-6414	26	35	are	be	AUX
ejpam-6414	26	36	vital	vital	ADJ
ejpam-6414	26	37	in	in	ADP
ejpam-6414	26	38	studying	study	VERB
ejpam-6414	26	39	bch	bch	PROPN
ejpam-6414	26	40	codes	code	NOUN
ejpam-6414	26	41	over	over	ADP
ejpam-6414	26	42	qgrs	qgrs	PROPN
ejpam-6414	26	43	.	.	PUNCT
ejpam-6414	27	1	shah	shah	PROPN
ejpam-6414	27	2	et	et	PROPN
ejpam-6414	27	3	al	al	PROPN
ejpam-6414	27	4	.	.	PUNCT
ejpam-6414	28	1	[	[	X
ejpam-6414	28	2	8	8	NUM
ejpam-6414	28	3	]	]	PUNCT
ejpam-6414	28	4	discussed	discuss	VERB
ejpam-6414	28	5	constructions	construction	NOUN
ejpam-6414	28	6	of	of	ADP
ejpam-6414	28	7	codes	code	NOUN
ejpam-6414	28	8	by	by	ADP
ejpam-6414	28	9	the	the	DET
ejpam-6414	28	10	semigroup	semigroup	PROPN
ejpam-6414	28	11	rings	ring	NOUN
ejpam-6414	28	12	,	,	PUNCT
ejpam-6414	28	13	which	which	PRON
ejpam-6414	28	14	discussed	discuss	VERB
ejpam-6414	28	15	new	new	ADJ
ejpam-6414	28	16	way	way	NOUN
ejpam-6414	28	17	of	of	ADP
ejpam-6414	28	18	code	code	NOUN
ejpam-6414	28	19	construction	construction	NOUN
ejpam-6414	28	20	and	and	CCONJ
ejpam-6414	28	21	encoding	encoding	NOUN
ejpam-6414	28	22	techniques	technique	NOUN
ejpam-6414	28	23	.	.	PUNCT
ejpam-6414	29	1	their	their	PRON
ejpam-6414	29	2	work	work	NOUN
ejpam-6414	29	3	helps	help	VERB
ejpam-6414	29	4	to	to	PART
ejpam-6414	29	5	increase	increase	VERB
ejpam-6414	29	6	the	the	DET
ejpam-6414	29	7	area	area	NOUN
ejpam-6414	29	8	of	of	ADP
ejpam-6414	29	9	algebraic	algebraic	ADJ
ejpam-6414	29	10	applications	application	NOUN
ejpam-6414	29	11	of	of	ADP
ejpam-6414	29	12	bch	bch	PROPN
ejpam-6414	29	13	codes	code	NOUN
ejpam-6414	29	14	and	and	CCONJ
ejpam-6414	29	15	construct	construct	VERB
ejpam-6414	29	16	them	they	PRON
ejpam-6414	29	17	over	over	ADP
ejpam-6414	29	18	qgr	qgr	NOUN
ejpam-6414	29	19	,	,	PUNCT
ejpam-6414	29	20	enhancing	enhance	VERB
ejpam-6414	29	21	the	the	DET
ejpam-6414	29	22	usability	usability	NOUN
ejpam-6414	29	23	and	and	CCONJ
ejpam-6414	29	24	reliability	reliability	NOUN
ejpam-6414	29	25	of	of	ADP
ejpam-6414	29	26	error	error	NOUN
ejpam-6414	29	27	-	-	PUNCT
ejpam-6414	29	28	correcting	correct	VERB
ejpam-6414	29	29	codes	code	NOUN
ejpam-6414	29	30	.	.	PUNCT
ejpam-6414	30	1	for	for	ADP
ejpam-6414	30	2	achieving	achieve	VERB
ejpam-6414	30	3	efficient	efficient	ADJ
ejpam-6414	30	4	error	error	NOUN
ejpam-6414	30	5	correction	correction	NOUN
ejpam-6414	30	6	in	in	ADP
ejpam-6414	30	7	finite	finite	ADJ
ejpam-6414	30	8	field	field	NOUN
ejpam-6414	30	9	applications	application	NOUN
ejpam-6414	30	10	,	,	PUNCT
ejpam-6414	30	11	kim	kim	PROPN
ejpam-6414	30	12	,	,	PUNCT
ejpam-6414	30	13	lee	lee	PROPN
ejpam-6414	30	14	and	and	CCONJ
ejpam-6414	30	15	yoo	yoo	PROPN
ejpam-6414	31	1	[	[	X
ejpam-6414	31	2	9	9	NUM
ejpam-6414	31	3	]	]	PUNCT
ejpam-6414	31	4	introduced	introduce	VERB
ejpam-6414	31	5	an	an	DET
ejpam-6414	31	6	infinite	infinite	ADJ
ejpam-6414	31	7	family	family	NOUN
ejpam-6414	31	8	of	of	ADP
ejpam-6414	31	9	griesmer	griesmer	NOUN
ejpam-6414	31	10	quasi	quasi	ADJ
ejpam-6414	31	11	-	-	ADJ
ejpam-6414	31	12	cyclic	cyclic	ADJ
ejpam-6414	31	13	self	self	NOUN
ejpam-6414	31	14	-	-	PUNCT
ejpam-6414	31	15	orthogonal	orthogonal	ADJ
ejpam-6414	31	16	codes	code	NOUN
ejpam-6414	31	17	.	.	PUNCT
ejpam-6414	32	1	their	their	PRON
ejpam-6414	32	2	work	work	NOUN
ejpam-6414	32	3	shows	show	VERB
ejpam-6414	32	4	that	that	SCONJ
ejpam-6414	32	5	bch	bch	PROPN
ejpam-6414	32	6	codes	code	NOUN
ejpam-6414	32	7	are	be	AUX
ejpam-6414	32	8	far	far	ADV
ejpam-6414	32	9	better	well	ADV
ejpam-6414	32	10	compared	compare	VERB
ejpam-6414	32	11	to	to	ADP
ejpam-6414	32	12	qgrs	qgrs	NOUN
ejpam-6414	32	13	in	in	ADP
ejpam-6414	32	14	improving	improve	VERB
ejpam-6414	32	15	the	the	DET
ejpam-6414	32	16	coding	code	VERB
ejpam-6414	32	17	efficiency	efficiency	NOUN
ejpam-6414	32	18	and	and	CCONJ
ejpam-6414	32	19	resilience	resilience	NOUN
ejpam-6414	32	20	in	in	ADP
ejpam-6414	32	21	actual	actual	ADJ
ejpam-6414	32	22	applications	application	NOUN
ejpam-6414	32	23	.	.	PUNCT
ejpam-6414	33	1	zullo	zullo	PROPN
ejpam-6414	34	1	[	[	X
ejpam-6414	34	2	10	10	NUM
ejpam-6414	34	3	]	]	PUNCT
ejpam-6414	34	4	also	also	ADV
ejpam-6414	34	5	discussed	discuss	VERB
ejpam-6414	34	6	multi	multi	ADJ
ejpam-6414	34	7	-	-	ADJ
ejpam-6414	34	8	orbit	orbit	ADJ
ejpam-6414	34	9	cyclic	cyclic	ADJ
ejpam-6414	34	10	subspace	subspace	NOUN
ejpam-6414	34	11	codes	code	NOUN
ejpam-6414	34	12	and	and	CCONJ
ejpam-6414	34	13	linear	linear	ADJ
ejpam-6414	34	14	sets	set	NOUN
ejpam-6414	34	15	,	,	PUNCT
ejpam-6414	34	16	which	which	PRON
ejpam-6414	34	17	give	give	VERB
ejpam-6414	34	18	more	more	ADJ
ejpam-6414	34	19	of	of	ADP
ejpam-6414	34	20	the	the	DET
ejpam-6414	34	21	algebraic	algebraic	ADJ
ejpam-6414	34	22	properties	property	NOUN
ejpam-6414	34	23	and	and	CCONJ
ejpam-6414	34	24	the	the	DET
ejpam-6414	34	25	structures	structure	NOUN
ejpam-6414	34	26	of	of	ADP
ejpam-6414	34	27	cyclic	cyclic	ADJ
ejpam-6414	34	28	codes	code	NOUN
ejpam-6414	34	29	.	.	PUNCT
ejpam-6414	35	1	it	it	PRON
ejpam-6414	35	2	is	be	AUX
ejpam-6414	35	3	necessary	necessary	ADJ
ejpam-6414	35	4	to	to	PART
ejpam-6414	35	5	state	state	VERB
ejpam-6414	35	6	that	that	SCONJ
ejpam-6414	35	7	this	this	DET
ejpam-6414	35	8	research	research	NOUN
ejpam-6414	35	9	advances	advance	VERB
ejpam-6414	35	10	the	the	DET
ejpam-6414	35	11	knowledge	knowledge	NOUN
ejpam-6414	35	12	of	of	ADP
ejpam-6414	35	13	the	the	DET
ejpam-6414	35	14	theoretical	theoretical	ADJ
ejpam-6414	35	15	background	background	NOUN
ejpam-6414	35	16	and	and	CCONJ
ejpam-6414	35	17	real	real	ADJ
ejpam-6414	35	18	-	-	PUNCT
ejpam-6414	35	19	world	world	NOUN
ejpam-6414	35	20	applications	application	NOUN
ejpam-6414	35	21	of	of	ADP
ejpam-6414	35	22	bch	bch	PROPN
ejpam-6414	35	23	codes	code	NOUN
ejpam-6414	35	24	over	over	ADP
ejpam-6414	35	25	various	various	ADJ
ejpam-6414	35	26	algebraic	algebraic	ADJ
ejpam-6414	35	27	structures	structure	NOUN
ejpam-6414	35	28	.	.	PUNCT
ejpam-6414	36	1	andrade	andrade	PROPN
ejpam-6414	36	2	and	and	CCONJ
ejpam-6414	36	3	palazzo	palazzo	NOUN
ejpam-6414	37	1	[	[	X
ejpam-6414	37	2	3	3	X
ejpam-6414	37	3	]	]	PUNCT
ejpam-6414	37	4	studied	study	VERB
ejpam-6414	37	5	the	the	DET
ejpam-6414	37	6	construction	construction	NOUN
ejpam-6414	37	7	and	and	CCONJ
ejpam-6414	37	8	decoding	decoding	NOUN
ejpam-6414	37	9	of	of	ADP
ejpam-6414	37	10	bch	bch	PROPN
ejpam-6414	37	11	codes	code	NOUN
ejpam-6414	37	12	over	over	ADP
ejpam-6414	37	13	finite	finite	PROPN
ejpam-6414	37	14	commutative	commutative	ADJ
ejpam-6414	37	15	rings	ring	NOUN
ejpam-6414	37	16	that	that	PRON
ejpam-6414	37	17	constituted	constitute	VERB
ejpam-6414	37	18	the	the	DET
ejpam-6414	37	19	first	first	ADJ
ejpam-6414	37	20	step	step	NOUN
ejpam-6414	37	21	towards	towards	ADP
ejpam-6414	37	22	constructing	construct	VERB
ejpam-6414	37	23	the	the	DET
ejpam-6414	37	24	bch	bch	PROPN
ejpam-6414	37	25	code	code	PROPN
ejpam-6414	37	26	over	over	ADP
ejpam-6414	37	27	rings	ring	NOUN
ejpam-6414	37	28	other	other	ADJ
ejpam-6414	37	29	than	than	ADP
ejpam-6414	37	30	the	the	DET
ejpam-6414	37	31	galois	galois	PROPN
ejpam-6414	37	32	fields	field	NOUN
ejpam-6414	37	33	.	.	PUNCT
ejpam-6414	38	1	their	their	PRON
ejpam-6414	38	2	study	study	NOUN
ejpam-6414	38	3	stresses	stress	VERB
ejpam-6414	38	4	the	the	DET
ejpam-6414	38	5	ability	ability	NOUN
ejpam-6414	38	6	to	to	PART
ejpam-6414	38	7	apply	apply	VERB
ejpam-6414	38	8	bch	bch	NOUN
ejpam-6414	38	9	codes	code	NOUN
ejpam-6414	38	10	in	in	ADP
ejpam-6414	38	11	various	various	ADJ
ejpam-6414	38	12	algebraic	algebraic	ADJ
ejpam-6414	38	13	settings	setting	NOUN
ejpam-6414	38	14	,	,	PUNCT
ejpam-6414	38	15	including	include	VERB
ejpam-6414	38	16	possible	possible	ADJ
ejpam-6414	38	17	over	over	ADP
ejpam-6414	38	18	qgrs	qgrs	PROPN
ejpam-6414	38	19	.	.	PUNCT
ejpam-6414	39	1	shankar	shankar	PROPN
ejpam-6414	40	1	[	[	X
ejpam-6414	40	2	11	11	NUM
ejpam-6414	40	3	]	]	PUNCT
ejpam-6414	40	4	surveyed	survey	VERB
ejpam-6414	40	5	bch	bch	PROPN
ejpam-6414	40	6	codes	code	NOUN
ejpam-6414	40	7	over	over	ADP
ejpam-6414	40	8	an	an	DET
ejpam-6414	40	9	arbitrary	arbitrary	ADJ
ejpam-6414	40	10	integer	integer	NOUN
ejpam-6414	40	11	ring	ring	NOUN
ejpam-6414	40	12	,	,	PUNCT
ejpam-6414	40	13	extending	extend	VERB
ejpam-6414	40	14	the	the	DET
ejpam-6414	40	15	theory	theory	NOUN
ejpam-6414	40	16	of	of	ADP
ejpam-6414	40	17	bch	bch	PROPN
ejpam-6414	40	18	codes	code	NOUN
ejpam-6414	40	19	to	to	ADP
ejpam-6414	40	20	other	other	ADJ
ejpam-6414	40	21	algebraic	algebraic	ADJ
ejpam-6414	40	22	structures	structure	NOUN
ejpam-6414	40	23	.	.	PUNCT
ejpam-6414	41	1	the	the	DET
ejpam-6414	41	2	contribution	contribution	NOUN
ejpam-6414	41	3	of	of	ADP
ejpam-6414	41	4	this	this	DET
ejpam-6414	41	5	research	research	NOUN
ejpam-6414	41	6	is	be	AUX
ejpam-6414	41	7	useful	useful	ADJ
ejpam-6414	41	8	in	in	ADP
ejpam-6414	41	9	improving	improve	VERB
ejpam-6414	41	10	the	the	DET
ejpam-6414	41	11	reliability	reliability	NOUN
ejpam-6414	41	12	and	and	CCONJ
ejpam-6414	41	13	usability	usability	NOUN
ejpam-6414	41	14	of	of	ADP
ejpam-6414	41	15	bch	bch	PROPN
ejpam-6414	41	16	codes	code	NOUN
ejpam-6414	41	17	in	in	ADP
ejpam-6414	41	18	various	various	ADJ
ejpam-6414	41	19	communication	communication	NOUN
ejpam-6414	41	20	and	and	CCONJ
ejpam-6414	41	21	storage	storage	NOUN
ejpam-6414	41	22	systems	system	NOUN
ejpam-6414	41	23	.	.	PUNCT
ejpam-6414	42	1	interlando	interlando	PROPN
ejpam-6414	42	2	and	and	CCONJ
ejpam-6414	42	3	palazzo	palazzo	NOUN
ejpam-6414	43	1	[	[	X
ejpam-6414	43	2	12	12	NUM
ejpam-6414	43	3	]	]	PUNCT
ejpam-6414	43	4	have	have	AUX
ejpam-6414	43	5	given	give	VERB
ejpam-6414	43	6	a	a	DET
ejpam-6414	43	7	structural	structural	ADJ
ejpam-6414	43	8	description	description	NOUN
ejpam-6414	43	9	of	of	ADP
ejpam-6414	43	10	cyclic	cyclic	PROPN
ejpam-6414	43	11	code	code	NOUN
ejpam-6414	43	12	over	over	ADP
ejpam-6414	43	13	zm	zm	PROPN
ejpam-6414	43	14	,	,	PUNCT
ejpam-6414	43	15	and	and	CCONJ
ejpam-6414	43	16	the	the	DET
ejpam-6414	43	17	decoding	decode	VERB
ejpam-6414	43	18	process	process	NOUN
ejpam-6414	43	19	in	in	ADP
ejpam-6414	43	20	detail	detail	NOUN
ejpam-6414	43	21	.	.	PUNCT
ejpam-6414	44	1	their	their	PRON
ejpam-6414	44	2	research	research	NOUN
ejpam-6414	44	3	provides	provide	VERB
ejpam-6414	44	4	significant	significant	ADJ
ejpam-6414	44	5	information	information	NOUN
ejpam-6414	44	6	regarding	regard	VERB
ejpam-6414	44	7	the	the	DET
ejpam-6414	44	8	enhancement	enhancement	NOUN
ejpam-6414	44	9	of	of	ADP
ejpam-6414	44	10	the	the	DET
ejpam-6414	44	11	bch	bch	PROPN
ejpam-6414	44	12	codes	code	NOUN
ejpam-6414	44	13	applied	apply	VERB
ejpam-6414	44	14	to	to	ADP
ejpam-6414	44	15	the	the	DET
ejpam-6414	44	16	modular	modular	ADJ
ejpam-6414	44	17	rings	ring	NOUN
ejpam-6414	44	18	and	and	CCONJ
ejpam-6414	44	19	other	other	ADJ
ejpam-6414	44	20	non	non	ADJ
ejpam-6414	44	21	-	-	ADJ
ejpam-6414	44	22	field	field	ADJ
ejpam-6414	44	23	structures	structure	NOUN
ejpam-6414	44	24	,	,	PUNCT
ejpam-6414	45	1	muhammad	muhammad	PROPN
ejpam-6414	45	2	sajjad	sajjad	PROPN
ejpam-6414	45	3	et	et	PROPN
ejpam-6414	45	4	al	al	PROPN
ejpam-6414	45	5	.	.	PUNCT
ejpam-6414	45	6	/	/	SYM
ejpam-6414	45	7	eur	eur	PROPN
ejpam-6414	45	8	.	.	PUNCT
ejpam-6414	46	1	j.	j.	PROPN
ejpam-6414	46	2	pure	pure	PROPN
ejpam-6414	46	3	appl	appl	PROPN
ejpam-6414	46	4	.	.	PROPN
ejpam-6414	46	5	math	math	PROPN
ejpam-6414	46	6	,	,	PUNCT
ejpam-6414	46	7	18	18	NUM
ejpam-6414	46	8	(	(	PUNCT
ejpam-6414	46	9	3	3	NUM
ejpam-6414	46	10	)	)	PUNCT
ejpam-6414	46	11	(	(	PUNCT
ejpam-6414	46	12	2025	2025	NUM
ejpam-6414	46	13	)	)	PUNCT
ejpam-6414	46	14	,	,	PUNCT
ejpam-6414	46	15	6414	6414	NUM
ejpam-6414	46	16	3	3	NUM
ejpam-6414	46	17	of	of	ADP
ejpam-6414	46	18	22	22	NUM
ejpam-6414	46	19	as	as	ADV
ejpam-6414	46	20	well	well	ADV
ejpam-6414	46	21	as	as	ADP
ejpam-6414	46	22	the	the	DET
ejpam-6414	46	23	possible	possible	ADJ
ejpam-6414	46	24	use	use	NOUN
ejpam-6414	46	25	in	in	ADP
ejpam-6414	46	26	the	the	DET
ejpam-6414	46	27	qgrs	qgrs	NOUN
ejpam-6414	46	28	.	.	PUNCT
ejpam-6414	47	1	sajjad	sajjad	PROPN
ejpam-6414	47	2	et	et	PROPN
ejpam-6414	47	3	al	al	PROPN
ejpam-6414	47	4	.	.	PROPN
ejpam-6414	47	5	’s	’s	PART
ejpam-6414	48	1	[	[	X
ejpam-6414	48	2	13–17	13–17	NUM
ejpam-6414	48	3	]	]	PUNCT
ejpam-6414	48	4	recent	recent	ADJ
ejpam-6414	48	5	works	work	NOUN
ejpam-6414	48	6	have	have	AUX
ejpam-6414	48	7	involved	involve	VERB
ejpam-6414	48	8	decoding	decode	VERB
ejpam-6414	48	9	algorithms	algorithm	NOUN
ejpam-6414	48	10	that	that	PRON
ejpam-6414	48	11	are	be	AUX
ejpam-6414	48	12	designed	design	VERB
ejpam-6414	48	13	to	to	PART
ejpam-6414	48	14	work	work	VERB
ejpam-6414	48	15	on	on	ADP
ejpam-6414	48	16	certain	certain	ADJ
ejpam-6414	48	17	algebraic	algebraic	ADJ
ejpam-6414	48	18	structures	structure	NOUN
ejpam-6414	48	19	,	,	PUNCT
ejpam-6414	48	20	including	include	VERB
ejpam-6414	48	21	gaussian	gaussian	ADJ
ejpam-6414	48	22	fields	field	NOUN
ejpam-6414	48	23	,	,	PUNCT
ejpam-6414	48	24	eisenstein	eisenstein	NOUN
ejpam-6414	48	25	fields	field	NOUN
ejpam-6414	48	26	,	,	PUNCT
ejpam-6414	48	27	quaternion	quaternion	NOUN
ejpam-6414	48	28	integers	integer	NOUN
ejpam-6414	48	29	,	,	PUNCT
ejpam-6414	48	30	and	and	CCONJ
ejpam-6414	48	31	octonion	octonion	NOUN
ejpam-6414	48	32	integers	integer	NOUN
ejpam-6414	48	33	.	.	PUNCT
ejpam-6414	49	1	these	these	DET
ejpam-6414	49	2	studies	study	NOUN
ejpam-6414	49	3	have	have	AUX
ejpam-6414	49	4	substantially	substantially	ADV
ejpam-6414	49	5	contributed	contribute	VERB
ejpam-6414	49	6	to	to	ADP
ejpam-6414	49	7	the	the	DET
ejpam-6414	49	8	improvement	improvement	NOUN
ejpam-6414	49	9	of	of	ADP
ejpam-6414	49	10	the	the	DET
ejpam-6414	49	11	error	error	NOUN
ejpam-6414	49	12	correction	correction	NOUN
ejpam-6414	49	13	capability	capability	NOUN
ejpam-6414	49	14	of	of	ADP
ejpam-6414	49	15	bch	bch	PROPN
ejpam-6414	49	16	codes	code	NOUN
ejpam-6414	49	17	as	as	ADP
ejpam-6414	49	18	applicable	applicable	ADJ
ejpam-6414	49	19	to	to	ADP
ejpam-6414	49	20	today	today	NOUN
ejpam-6414	49	21	’s	’s	PART
ejpam-6414	49	22	communication	communication	NOUN
ejpam-6414	49	23	systems	system	NOUN
ejpam-6414	49	24	.	.	PUNCT
ejpam-6414	50	1	lee	lee	PROPN
ejpam-6414	50	2	,	,	PUNCT
ejpam-6414	50	3	li	li	PROPN
ejpam-6414	50	4	,	,	PUNCT
ejpam-6414	50	5	wu	wu	PROPN
ejpam-6414	50	6	and	and	CCONJ
ejpam-6414	50	7	zeng	zeng	PROPN
ejpam-6414	51	1	[	[	X
ejpam-6414	51	2	18	18	NUM
ejpam-6414	51	3	]	]	PUNCT
ejpam-6414	51	4	continued	continue	VERB
ejpam-6414	51	5	with	with	ADP
ejpam-6414	51	6	the	the	DET
ejpam-6414	51	7	investigation	investigation	NOUN
ejpam-6414	51	8	of	of	ADP
ejpam-6414	51	9	the	the	DET
ejpam-6414	51	10	hulls	hull	NOUN
ejpam-6414	51	11	of	of	ADP
ejpam-6414	51	12	primitive	primitive	ADJ
ejpam-6414	51	13	binary	binary	ADJ
ejpam-6414	51	14	and	and	CCONJ
ejpam-6414	51	15	ternary	ternary	ADJ
ejpam-6414	51	16	bch	bch	PROPN
ejpam-6414	51	17	codes	code	NOUN
ejpam-6414	51	18	with	with	ADP
ejpam-6414	51	19	respect	respect	NOUN
ejpam-6414	51	20	to	to	ADP
ejpam-6414	51	21	particular	particular	ADJ
ejpam-6414	51	22	structures	structure	NOUN
ejpam-6414	51	23	that	that	PRON
ejpam-6414	51	24	can	can	AUX
ejpam-6414	51	25	improve	improve	VERB
ejpam-6414	51	26	code	code	NOUN
ejpam-6414	51	27	performance	performance	NOUN
ejpam-6414	51	28	indicators	indicator	NOUN
ejpam-6414	51	29	.	.	PUNCT
ejpam-6414	52	1	their	their	PRON
ejpam-6414	52	2	paper	paper	NOUN
ejpam-6414	52	3	offers	offer	VERB
ejpam-6414	52	4	useful	useful	ADJ
ejpam-6414	52	5	information	information	NOUN
ejpam-6414	52	6	about	about	ADP
ejpam-6414	52	7	the	the	DET
ejpam-6414	52	8	enhancement	enhancement	NOUN
ejpam-6414	52	9	of	of	ADP
ejpam-6414	52	10	bch	bch	PROPN
ejpam-6414	52	11	codes	code	NOUN
ejpam-6414	52	12	in	in	ADP
ejpam-6414	52	13	terms	term	NOUN
ejpam-6414	52	14	of	of	ADP
ejpam-6414	52	15	performance	performance	NOUN
ejpam-6414	52	16	for	for	ADP
ejpam-6414	52	17	error	error	NOUN
ejpam-6414	52	18	correction	correction	NOUN
ejpam-6414	52	19	and	and	CCONJ
ejpam-6414	52	20	information	information	NOUN
ejpam-6414	52	21	reliability	reliability	NOUN
ejpam-6414	52	22	in	in	ADP
ejpam-6414	52	23	implementation	implementation	NOUN
ejpam-6414	52	24	.	.	PUNCT
ejpam-6414	53	1	in	in	ADP
ejpam-6414	53	2	a	a	DET
ejpam-6414	53	3	work	work	NOUN
ejpam-6414	53	4	devoted	devote	VERB
ejpam-6414	53	5	to	to	ADP
ejpam-6414	53	6	the	the	DET
ejpam-6414	53	7	description	description	NOUN
ejpam-6414	53	8	of	of	ADP
ejpam-6414	53	9	specific	specific	ADJ
ejpam-6414	53	10	properties	property	NOUN
ejpam-6414	53	11	and	and	CCONJ
ejpam-6414	53	12	decoding	decode	VERB
ejpam-6414	53	13	of	of	ADP
ejpam-6414	53	14	specific	specific	ADJ
ejpam-6414	53	15	binary	binary	ADJ
ejpam-6414	53	16	bch	bch	PROPN
ejpam-6414	53	17	codes	code	NOUN
ejpam-6414	53	18	of	of	ADP
ejpam-6414	53	19	length	length	NOUN
ejpam-6414	53	20	n	n	PROPN
ejpam-6414	53	21	=	=	SYM
ejpam-6414	53	22	2m+1	2m+1	PROPN
ejpam-6414	53	23	,	,	PUNCT
ejpam-6414	53	24	liu	liu	PROPN
ejpam-6414	53	25	li	li	PROPN
ejpam-6414	53	26	fu	fu	PROPN
ejpam-6414	53	27	lu	lu	PROPN
ejpam-6414	53	28	and	and	CCONJ
ejpam-6414	53	29	rao	rao	NOUN
ejpam-6414	53	30	[	[	X
ejpam-6414	53	31	19	19	NUM
ejpam-6414	53	32	]	]	PUNCT
ejpam-6414	53	33	,	,	PUNCT
ejpam-6414	53	34	this	this	DET
ejpam-6414	53	35	research	research	NOUN
ejpam-6414	53	36	with	with	ADP
ejpam-6414	53	37	the	the	DET
ejpam-6414	53	38	collection	collection	NOUN
ejpam-6414	53	39	of	of	ADP
ejpam-6414	53	40	bch	bch	PROPN
ejpam-6414	53	41	codes	code	NOUN
ejpam-6414	53	42	which	which	PRON
ejpam-6414	53	43	can	can	AUX
ejpam-6414	53	44	be	be	AUX
ejpam-6414	53	45	used	use	VERB
ejpam-6414	53	46	for	for	ADP
ejpam-6414	53	47	different	different	ADJ
ejpam-6414	53	48	communication	communication	NOUN
ejpam-6414	53	49	schemes	scheme	NOUN
ejpam-6414	53	50	and	and	CCONJ
ejpam-6414	53	51	data	data	NOUN
ejpam-6414	53	52	-	-	PUNCT
ejpam-6414	53	53	storing	store	VERB
ejpam-6414	53	54	methods	method	NOUN
ejpam-6414	53	55	.	.	PUNCT
ejpam-6414	54	1	further	far	ADV
ejpam-6414	54	2	,	,	PUNCT
ejpam-6414	54	3	new	new	ADJ
ejpam-6414	54	4	studies	study	NOUN
ejpam-6414	54	5	by	by	ADP
ejpam-6414	54	6	different	different	ADJ
ejpam-6414	54	7	authors	author	NOUN
ejpam-6414	54	8	[	[	X
ejpam-6414	54	9	20	20	NUM
ejpam-6414	54	10	,	,	PUNCT
ejpam-6414	54	11	21	21	NUM
ejpam-6414	54	12	]	]	PUNCT
ejpam-6414	54	13	have	have	AUX
ejpam-6414	54	14	explored	explore	VERB
ejpam-6414	54	15	details	detail	NOUN
ejpam-6414	54	16	of	of	ADP
ejpam-6414	54	17	bch	bch	PROPN
ejpam-6414	54	18	codes	code	NOUN
ejpam-6414	54	19	with	with	ADP
ejpam-6414	54	20	the	the	DET
ejpam-6414	54	21	parameters	parameter	NOUN
ejpam-6414	54	22	and	and	CCONJ
ejpam-6414	54	23	families	family	NOUN
ejpam-6414	54	24	of	of	ADP
ejpam-6414	54	25	negacyclic	negacyclic	ADJ
ejpam-6414	54	26	and	and	CCONJ
ejpam-6414	54	27	constacyclic	constacyclic	ADJ
ejpam-6414	54	28	bch	bch	PROPN
ejpam-6414	54	29	codes	code	NOUN
ejpam-6414	54	30	besides	besides	SCONJ
ejpam-6414	54	31	using	use	VERB
ejpam-6414	54	32	them	they	PRON
ejpam-6414	54	33	in	in	ADP
ejpam-6414	54	34	cryptography	cryptography	NOUN
ejpam-6414	54	35	and	and	CCONJ
ejpam-6414	54	36	communication	communication	NOUN
ejpam-6414	54	37	.	.	PUNCT
ejpam-6414	55	1	these	these	DET
ejpam-6414	55	2	works	work	VERB
ejpam-6414	55	3	present	present	VERB
ejpam-6414	55	4	the	the	DET
ejpam-6414	55	5	continued	continue	VERB
ejpam-6414	55	6	research	research	NOUN
ejpam-6414	55	7	on	on	ADP
ejpam-6414	55	8	the	the	DET
ejpam-6414	55	9	improvements	improvement	NOUN
ejpam-6414	55	10	of	of	ADP
ejpam-6414	55	11	the	the	DET
ejpam-6414	55	12	additive	additive	ADJ
ejpam-6414	55	13	bch	bch	PROPN
ejpam-6414	55	14	codes	code	NOUN
ejpam-6414	55	15	in	in	ADP
ejpam-6414	55	16	terms	term	NOUN
ejpam-6414	55	17	of	of	ADP
ejpam-6414	55	18	redundancy	redundancy	NOUN
ejpam-6414	55	19	and	and	CCONJ
ejpam-6414	55	20	code	code	NOUN
ejpam-6414	55	21	length	length	NOUN
ejpam-6414	55	22	in	in	ADP
ejpam-6414	55	23	various	various	ADJ
ejpam-6414	55	24	algebraic	algebraic	ADJ
ejpam-6414	55	25	structures	structure	NOUN
ejpam-6414	55	26	.	.	PUNCT
ejpam-6414	56	1	several	several	ADJ
ejpam-6414	56	2	studies	study	NOUN
ejpam-6414	56	3	have	have	AUX
ejpam-6414	56	4	contributed	contribute	VERB
ejpam-6414	56	5	significantly	significantly	ADV
ejpam-6414	56	6	to	to	ADP
ejpam-6414	56	7	the	the	DET
ejpam-6414	56	8	advancement	advancement	NOUN
ejpam-6414	56	9	of	of	ADP
ejpam-6414	56	10	bch	bch	PROPN
ejpam-6414	56	11	codes	code	NOUN
ejpam-6414	56	12	and	and	CCONJ
ejpam-6414	56	13	their	their	PRON
ejpam-6414	56	14	decoding	decode	VERB
ejpam-6414	56	15	strategies	strategy	NOUN
ejpam-6414	56	16	.	.	PUNCT
ejpam-6414	57	1	asif	asif	NOUN
ejpam-6414	57	2	and	and	CCONJ
ejpam-6414	57	3	shah	shah	NOUN
ejpam-6414	58	1	[	[	X
ejpam-6414	58	2	22	22	NUM
ejpam-6414	58	3	]	]	PUNCT
ejpam-6414	58	4	explored	explore	VERB
ejpam-6414	58	5	a	a	DET
ejpam-6414	58	6	computational	computational	ADJ
ejpam-6414	58	7	approach	approach	NOUN
ejpam-6414	58	8	to	to	ADP
ejpam-6414	58	9	bch	bch	PROPN
ejpam-6414	58	10	codes	code	NOUN
ejpam-6414	58	11	and	and	CCONJ
ejpam-6414	58	12	demonstrated	demonstrate	VERB
ejpam-6414	58	13	their	their	PRON
ejpam-6414	58	14	effectiveness	effectiveness	NOUN
ejpam-6414	58	15	in	in	ADP
ejpam-6414	58	16	image	image	NOUN
ejpam-6414	58	17	encryption	encryption	NOUN
ejpam-6414	58	18	applications	application	NOUN
ejpam-6414	58	19	,	,	PUNCT
ejpam-6414	58	20	showcasing	showcase	VERB
ejpam-6414	58	21	the	the	DET
ejpam-6414	58	22	practical	practical	ADJ
ejpam-6414	58	23	utility	utility	NOUN
ejpam-6414	58	24	of	of	ADP
ejpam-6414	58	25	algebraic	algebraic	PROPN
ejpam-6414	58	26	coding	code	VERB
ejpam-6414	58	27	in	in	ADP
ejpam-6414	58	28	data	datum	NOUN
ejpam-6414	58	29	security	security	NOUN
ejpam-6414	58	30	.	.	PUNCT
ejpam-6414	59	1	shah	shah	NOUN
ejpam-6414	59	2	and	and	CCONJ
ejpam-6414	59	3	andrade	andrade	PROPN
ejpam-6414	60	1	[	[	X
ejpam-6414	60	2	23	23	NUM
ejpam-6414	60	3	]	]	PUNCT
ejpam-6414	60	4	proposed	propose	VERB
ejpam-6414	60	5	a	a	DET
ejpam-6414	60	6	decoding	decode	VERB
ejpam-6414	60	7	method	method	NOUN
ejpam-6414	60	8	aimed	aim	VERB
ejpam-6414	60	9	at	at	ADP
ejpam-6414	60	10	enhancing	enhance	VERB
ejpam-6414	60	11	both	both	DET
ejpam-6414	60	12	the	the	DET
ejpam-6414	60	13	code	code	NOUN
ejpam-6414	60	14	rate	rate	NOUN
ejpam-6414	60	15	and	and	CCONJ
ejpam-6414	60	16	error	error	NOUN
ejpam-6414	60	17	correction	correction	NOUN
ejpam-6414	60	18	capabilities	capability	NOUN
ejpam-6414	60	19	,	,	PUNCT
ejpam-6414	60	20	thereby	thereby	ADV
ejpam-6414	60	21	improving	improve	VERB
ejpam-6414	60	22	the	the	DET
ejpam-6414	60	23	overall	overall	ADJ
ejpam-6414	60	24	performance	performance	NOUN
ejpam-6414	60	25	of	of	ADP
ejpam-6414	60	26	bch	bch	PROPN
ejpam-6414	60	27	codes	code	NOUN
ejpam-6414	60	28	.	.	PUNCT
ejpam-6414	61	1	further	far	ADV
ejpam-6414	61	2	,	,	PUNCT
ejpam-6414	61	3	shah	shah	PROPN
ejpam-6414	61	4	,	,	PUNCT
ejpam-6414	61	5	qamar	qamar	PROPN
ejpam-6414	61	6	,	,	PUNCT
ejpam-6414	61	7	and	and	CCONJ
ejpam-6414	61	8	de	de	X
ejpam-6414	61	9	andrade	andrade	PROPN
ejpam-6414	62	1	[	[	X
ejpam-6414	62	2	24	24	NUM
ejpam-6414	62	3	]	]	PUNCT
ejpam-6414	62	4	investigated	investigate	VERB
ejpam-6414	62	5	the	the	DET
ejpam-6414	62	6	construction	construction	NOUN
ejpam-6414	62	7	and	and	CCONJ
ejpam-6414	62	8	decoding	decoding	NOUN
ejpam-6414	62	9	of	of	ADP
ejpam-6414	62	10	bch	bch	PROPN
ejpam-6414	62	11	codes	code	NOUN
ejpam-6414	62	12	over	over	ADP
ejpam-6414	62	13	a	a	DET
ejpam-6414	62	14	chain	chain	NOUN
ejpam-6414	62	15	of	of	ADP
ejpam-6414	62	16	commutative	commutative	ADJ
ejpam-6414	62	17	rings	ring	NOUN
ejpam-6414	62	18	,	,	PUNCT
ejpam-6414	62	19	providing	provide	VERB
ejpam-6414	62	20	an	an	DET
ejpam-6414	62	21	algebraic	algebraic	ADJ
ejpam-6414	62	22	foundation	foundation	NOUN
ejpam-6414	62	23	for	for	ADP
ejpam-6414	62	24	extending	extend	VERB
ejpam-6414	62	25	classical	classical	ADJ
ejpam-6414	62	26	code	code	NOUN
ejpam-6414	62	27	structures	structure	NOUN
ejpam-6414	62	28	.	.	PUNCT
ejpam-6414	63	1	additionally	additionally	ADV
ejpam-6414	63	2	,	,	PUNCT
ejpam-6414	63	3	shah	shah	NOUN
ejpam-6414	63	4	,	,	PUNCT
ejpam-6414	63	5	khan	khan	PROPN
ejpam-6414	63	6	,	,	PUNCT
ejpam-6414	63	7	and	and	CCONJ
ejpam-6414	63	8	andrade	andrade	NOUN
ejpam-6414	64	1	[	[	X
ejpam-6414	64	2	25	25	NUM
ejpam-6414	64	3	]	]	PUNCT
ejpam-6414	64	4	introduced	introduce	VERB
ejpam-6414	64	5	a	a	DET
ejpam-6414	64	6	novel	novel	NOUN
ejpam-6414	64	7	decoding	decoding	NOUN
ejpam-6414	64	8	technique	technique	NOUN
ejpam-6414	64	9	by	by	ADP
ejpam-6414	64	10	embedding	embed	VERB
ejpam-6414	64	11	an	an	DET
ejpam-6414	64	12	n	n	CCONJ
ejpam-6414	64	13	-	-	PUNCT
ejpam-6414	64	14	length	length	NOUN
ejpam-6414	64	15	binary	binary	PROPN
ejpam-6414	64	16	bch	bch	PROPN
ejpam-6414	64	17	code	code	PROPN
ejpam-6414	64	18	within	within	ADP
ejpam-6414	64	19	a	a	DET
ejpam-6414	64	20	n(n+1	n(n+1	ADJ
ejpam-6414	64	21	)	)	PUNCT
ejpam-6414	64	22	-length	-length	PROPN
ejpam-6414	64	23	cyclic	cyclic	PROPN
ejpam-6414	64	24	code	code	NOUN
ejpam-6414	64	25	,	,	PUNCT
ejpam-6414	64	26	allowing	allow	VERB
ejpam-6414	64	27	for	for	ADP
ejpam-6414	64	28	improved	improved	ADJ
ejpam-6414	64	29	decoding	decoding	NOUN
ejpam-6414	64	30	accuracy	accuracy	NOUN
ejpam-6414	64	31	.	.	PUNCT
ejpam-6414	65	1	these	these	DET
ejpam-6414	65	2	foundational	foundational	ADJ
ejpam-6414	65	3	works	work	NOUN
ejpam-6414	65	4	underscore	underscore	VERB
ejpam-6414	65	5	the	the	DET
ejpam-6414	65	6	importance	importance	NOUN
ejpam-6414	65	7	of	of	ADP
ejpam-6414	65	8	algebraic	algebraic	ADJ
ejpam-6414	65	9	generalizations	generalization	NOUN
ejpam-6414	65	10	and	and	CCONJ
ejpam-6414	65	11	decoding	decode	VERB
ejpam-6414	65	12	efficiency	efficiency	NOUN
ejpam-6414	65	13	in	in	ADP
ejpam-6414	65	14	enhancing	enhance	VERB
ejpam-6414	65	15	the	the	DET
ejpam-6414	65	16	reliability	reliability	NOUN
ejpam-6414	65	17	of	of	ADP
ejpam-6414	65	18	bch	bch	PROPN
ejpam-6414	65	19	codes	code	NOUN
ejpam-6414	65	20	for	for	ADP
ejpam-6414	65	21	modern	modern	ADJ
ejpam-6414	65	22	communication	communication	NOUN
ejpam-6414	65	23	systems	system	NOUN
ejpam-6414	65	24	.	.	PUNCT
ejpam-6414	66	1	furthermore	furthermore	ADV
ejpam-6414	66	2	,	,	PUNCT
ejpam-6414	66	3	cyclic	cyclic	ADJ
ejpam-6414	66	4	codes	code	NOUN
ejpam-6414	66	5	were	be	AUX
ejpam-6414	66	6	compared	compare	VERB
ejpam-6414	66	7	by	by	ADP
ejpam-6414	66	8	shah	shah	NOUN
ejpam-6414	66	9	and	and	CCONJ
ejpam-6414	66	10	de	de	X
ejpam-6414	66	11	andrade	andrade	PROPN
ejpam-6414	67	1	[	[	X
ejpam-6414	67	2	26	26	NUM
ejpam-6414	67	3	]	]	PUNCT
ejpam-6414	67	4	with	with	ADP
ejpam-6414	67	5	the	the	DET
ejpam-6414	67	6	help	help	NOUN
ejpam-6414	67	7	of	of	ADP
ejpam-6414	67	8	b[x	b[x	NOUN
ejpam-6414	67	9	]	]	X
ejpam-6414	67	10	,	,	PUNCT
ejpam-6414	67	11	b	b	X
ejpam-6414	67	12	[	[	PUNCT
ejpam-6414	67	13	x	x	X
ejpam-6414	67	14	,	,	PUNCT
ejpam-6414	67	15	1	1	NUM
ejpam-6414	67	16	pk	pk	NOUN
ejpam-6414	67	17	z0	z0	PROPN
ejpam-6414	67	18	]	]	PUNCT
ejpam-6414	67	19	,	,	PUNCT
ejpam-6414	67	20	and	and	CCONJ
ejpam-6414	67	21	b	b	X
ejpam-6414	67	22	[	[	PUNCT
ejpam-6414	67	23	x	x	X
ejpam-6414	67	24	,	,	PUNCT
ejpam-6414	67	25	1	1	NUM
ejpam-6414	67	26	kpz0	kpz0	X
ejpam-6414	67	27	]	]	PUNCT
ejpam-6414	67	28	pointing	point	VERB
ejpam-6414	67	29	to	to	ADP
ejpam-6414	67	30	further	further	ADJ
ejpam-6414	67	31	developments	development	NOUN
ejpam-6414	67	32	in	in	ADP
ejpam-6414	67	33	constructing	construct	VERB
ejpam-6414	67	34	methods	method	NOUN
ejpam-6414	67	35	as	as	ADV
ejpam-6414	67	36	well	well	ADV
ejpam-6414	67	37	as	as	ADP
ejpam-6414	67	38	decoding	decode	VERB
ejpam-6414	67	39	rules	rule	NOUN
ejpam-6414	67	40	.	.	PUNCT
ejpam-6414	68	1	their	their	PRON
ejpam-6414	68	2	work	work	NOUN
ejpam-6414	68	3	offers	offer	VERB
ejpam-6414	68	4	understanding	understanding	NOUN
ejpam-6414	68	5	on	on	ADP
ejpam-6414	68	6	how	how	SCONJ
ejpam-6414	68	7	to	to	PART
ejpam-6414	68	8	implement	implement	VERB
ejpam-6414	68	9	bch	bch	PROPN
ejpam-6414	68	10	code	code	NOUN
ejpam-6414	68	11	for	for	ADP
ejpam-6414	68	12	certain	certain	ADJ
ejpam-6414	68	13	algebraic	algebraic	ADJ
ejpam-6414	68	14	structures	structure	NOUN
ejpam-6414	68	15	,	,	PUNCT
ejpam-6414	68	16	focusing	focus	VERB
ejpam-6414	68	17	on	on	ADP
ejpam-6414	68	18	enhanced	enhance	VERB
ejpam-6414	68	19	error	error	NOUN
ejpam-6414	68	20	correction	correction	NOUN
ejpam-6414	68	21	and	and	CCONJ
ejpam-6414	68	22	speed	speed	NOUN
ejpam-6414	68	23	.	.	PUNCT
ejpam-6414	69	1	zhu	zhu	PROPN
ejpam-6414	69	2	,	,	PUNCT
ejpam-6414	69	3	li	li	PROPN
ejpam-6414	69	4	,	,	PUNCT
ejpam-6414	69	5	and	and	CCONJ
ejpam-6414	69	6	zhu	zhu	X
ejpam-6414	70	1	[	[	X
ejpam-6414	70	2	27	27	NUM
ejpam-6414	70	3	]	]	PUNCT
ejpam-6414	70	4	identified	identify	VERB
ejpam-6414	70	5	parameters	parameter	NOUN
ejpam-6414	70	6	of	of	ADP
ejpam-6414	70	7	two	two	NUM
ejpam-6414	70	8	classes	class	NOUN
ejpam-6414	70	9	of	of	ADP
ejpam-6414	70	10	negacyclic	negacyclic	ADJ
ejpam-6414	70	11	bch	bch	PROPN
ejpam-6414	70	12	codes	code	NOUN
ejpam-6414	70	13	,	,	PUNCT
ejpam-6414	70	14	their	their	PRON
ejpam-6414	70	15	structure	structure	NOUN
ejpam-6414	70	16	,	,	PUNCT
ejpam-6414	70	17	and	and	CCONJ
ejpam-6414	70	18	decoding	decode	VERB
ejpam-6414	70	19	.	.	PUNCT
ejpam-6414	71	1	thus	thus	ADV
ejpam-6414	71	2	,	,	PUNCT
ejpam-6414	71	3	the	the	DET
ejpam-6414	71	4	results	result	NOUN
ejpam-6414	71	5	of	of	ADP
ejpam-6414	71	6	this	this	DET
ejpam-6414	71	7	research	research	NOUN
ejpam-6414	71	8	can	can	AUX
ejpam-6414	71	9	be	be	AUX
ejpam-6414	71	10	used	use	VERB
ejpam-6414	71	11	to	to	PART
ejpam-6414	71	12	improve	improve	VERB
ejpam-6414	71	13	the	the	DET
ejpam-6414	71	14	efficiency	efficiency	NOUN
ejpam-6414	71	15	and	and	CCONJ
ejpam-6414	71	16	practical	practical	ADJ
ejpam-6414	71	17	use	use	NOUN
ejpam-6414	71	18	of	of	ADP
ejpam-6414	71	19	bch	bch	PROPN
ejpam-6414	71	20	codes	code	NOUN
ejpam-6414	71	21	in	in	ADP
ejpam-6414	71	22	the	the	DET
ejpam-6414	71	23	field	field	NOUN
ejpam-6414	71	24	of	of	ADP
ejpam-6414	71	25	cryptography	cryptography	NOUN
ejpam-6414	71	26	and	and	CCONJ
ejpam-6414	71	27	in	in	ADP
ejpam-6414	71	28	digital	digital	ADJ
ejpam-6414	71	29	communication	communication	NOUN
ejpam-6414	71	30	systems	system	NOUN
ejpam-6414	71	31	.	.	PUNCT
ejpam-6414	72	1	wang	wang	PROPN
ejpam-6414	72	2	,	,	PUNCT
ejpam-6414	72	3	sun	sun	NOUN
ejpam-6414	72	4	and	and	CCONJ
ejpam-6414	72	5	ding	ding	NOUN
ejpam-6414	72	6	[	[	X
ejpam-6414	72	7	28	28	NUM
ejpam-6414	72	8	]	]	PUNCT
ejpam-6414	72	9	proposed	propose	VERB
ejpam-6414	72	10	two	two	NUM
ejpam-6414	72	11	families	family	NOUN
ejpam-6414	72	12	of	of	ADP
ejpam-6414	72	13	negacyclic	negacyclic	ADJ
ejpam-6414	72	14	bch	bch	PROPN
ejpam-6414	72	15	codes	code	NOUN
ejpam-6414	72	16	that	that	PRON
ejpam-6414	72	17	were	be	AUX
ejpam-6414	72	18	proved	prove	VERB
ejpam-6414	72	19	to	to	PART
ejpam-6414	72	20	be	be	AUX
ejpam-6414	72	21	more	more	ADV
ejpam-6414	72	22	powerful	powerful	ADJ
ejpam-6414	72	23	in	in	ADP
ejpam-6414	72	24	correcting	correct	VERB
ejpam-6414	72	25	more	more	ADJ
ejpam-6414	72	26	errors	error	NOUN
ejpam-6414	72	27	and	and	CCONJ
ejpam-6414	72	28	more	more	ADV
ejpam-6414	72	29	reliable	reliable	ADJ
ejpam-6414	72	30	in	in	ADP
ejpam-6414	72	31	data	data	NOUN
ejpam-6414	72	32	transmission	transmission	NOUN
ejpam-6414	72	33	.	.	PUNCT
ejpam-6414	73	1	citing	cite	VERB
ejpam-6414	73	2	their	their	PRON
ejpam-6414	73	3	discoveries	discovery	NOUN
ejpam-6414	73	4	,	,	PUNCT
ejpam-6414	73	5	they	they	PRON
ejpam-6414	73	6	emphasize	emphasize	VERB
ejpam-6414	73	7	that	that	SCONJ
ejpam-6414	73	8	bch	bch	PROPN
ejpam-6414	73	9	codes	code	NOUN
ejpam-6414	73	10	are	be	AUX
ejpam-6414	73	11	applicable	applicable	ADJ
ejpam-6414	73	12	in	in	ADP
ejpam-6414	73	13	any	any	DET
ejpam-6414	73	14	algebraic	algebraic	ADJ
ejpam-6414	73	15	structure	structure	NOUN
ejpam-6414	73	16	,	,	PUNCT
ejpam-6414	73	17	which	which	PRON
ejpam-6414	73	18	makes	make	VERB
ejpam-6414	73	19	them	they	PRON
ejpam-6414	73	20	useful	useful	ADJ
ejpam-6414	73	21	in	in	ADP
ejpam-6414	73	22	today	today	NOUN
ejpam-6414	73	23	’s	’s	PART
ejpam-6414	73	24	communication	communication	NOUN
ejpam-6414	73	25	networks	network	NOUN
ejpam-6414	73	26	.	.	PUNCT
ejpam-6414	74	1	moreover	moreover	ADV
ejpam-6414	74	2	,	,	PUNCT
ejpam-6414	74	3	the	the	DET
ejpam-6414	74	4	research	research	NOUN
ejpam-6414	74	5	of	of	ADP
ejpam-6414	74	6	pang	pang	NOUN
ejpam-6414	74	7	,	,	PUNCT
ejpam-6414	74	8	zhu	zhu	PROPN
ejpam-6414	74	9	,	,	PUNCT
ejpam-6414	74	10	yang	yang	PROPN
ejpam-6414	74	11	,	,	PUNCT
ejpam-6414	74	12	gao	gao	PROPN
ejpam-6414	74	13	,	,	PUNCT
ejpam-6414	74	14	zhou	zhou	PROPN
ejpam-6414	74	15	,	,	PUNCT
ejpam-6414	74	16	kai	kai	PROPN
ejpam-6414	74	17	,	,	PUNCT
ejpam-6414	74	18	and	and	CCONJ
ejpam-6414	74	19	others	other	NOUN
ejpam-6414	75	1	[	[	X
ejpam-6414	75	2	29	29	NUM
ejpam-6414	75	3	,	,	PUNCT
ejpam-6414	75	4	30	30	NUM
ejpam-6414	75	5	]	]	PUNCT
ejpam-6414	75	6	focuses	focus	VERB
ejpam-6414	75	7	on	on	ADP
ejpam-6414	75	8	bch	bch	PROPN
ejpam-6414	75	9	codes	code	NOUN
ejpam-6414	75	10	with	with	ADP
ejpam-6414	75	11	a	a	DET
ejpam-6414	75	12	larger	large	ADJ
ejpam-6414	75	13	hull	hull	NOUN
ejpam-6414	75	14	dimenmuhammad	dimenmuhammad	X
ejpam-6414	75	15	sajjad	sajjad	PROPN
ejpam-6414	75	16	et	et	PROPN
ejpam-6414	75	17	al	al	PROPN
ejpam-6414	75	18	.	.	PUNCT
ejpam-6414	75	19	/	/	SYM
ejpam-6414	75	20	eur	eur	PROPN
ejpam-6414	75	21	.	.	PUNCT
ejpam-6414	76	1	j.	j.	PROPN
ejpam-6414	76	2	pure	pure	PROPN
ejpam-6414	76	3	appl	appl	PROPN
ejpam-6414	76	4	.	.	PROPN
ejpam-6414	76	5	math	math	PROPN
ejpam-6414	76	6	,	,	PUNCT
ejpam-6414	76	7	18	18	NUM
ejpam-6414	76	8	(	(	PUNCT
ejpam-6414	76	9	3	3	NUM
ejpam-6414	76	10	)	)	PUNCT
ejpam-6414	76	11	(	(	PUNCT
ejpam-6414	76	12	2025	2025	NUM
ejpam-6414	76	13	)	)	PUNCT
ejpam-6414	76	14	,	,	PUNCT
ejpam-6414	76	15	6414	6414	NUM
ejpam-6414	76	16	4	4	NUM
ejpam-6414	76	17	of	of	ADP
ejpam-6414	76	18	22	22	NUM
ejpam-6414	76	19	sionality	sionality	NOUN
ejpam-6414	76	20	and	and	CCONJ
ejpam-6414	76	21	ternary	ternary	ADJ
ejpam-6414	76	22	lcd	lcd	NOUN
ejpam-6414	76	23	consta	consta	PROPN
ejpam-6414	76	24	-	-	PUNCT
ejpam-6414	76	25	cyclic	cyclic	ADJ
ejpam-6414	76	26	bch	bch	PROPN
ejpam-6414	76	27	codes	code	NOUN
ejpam-6414	76	28	.	.	PUNCT
ejpam-6414	77	1	these	these	PRON
ejpam-6414	77	2	have	have	AUX
ejpam-6414	77	3	included	include	VERB
ejpam-6414	77	4	broadening	broadening	NOUN
ejpam-6414	77	5	of	of	ADP
ejpam-6414	77	6	the	the	DET
ejpam-6414	77	7	theoretical	theoretical	ADJ
ejpam-6414	77	8	as	as	ADV
ejpam-6414	77	9	well	well	ADV
ejpam-6414	77	10	as	as	ADP
ejpam-6414	77	11	practical	practical	ADJ
ejpam-6414	77	12	applications	application	NOUN
ejpam-6414	77	13	of	of	ADP
ejpam-6414	77	14	the	the	DET
ejpam-6414	77	15	bch	bch	PROPN
ejpam-6414	77	16	codes	code	NOUN
ejpam-6414	77	17	and	and	CCONJ
ejpam-6414	77	18	,	,	PUNCT
ejpam-6414	77	19	in	in	ADP
ejpam-6414	77	20	addition	addition	NOUN
ejpam-6414	77	21	,	,	PUNCT
ejpam-6414	77	22	the	the	DET
ejpam-6414	77	23	improvements	improvement	NOUN
ejpam-6414	77	24	of	of	ADP
ejpam-6414	77	25	the	the	DET
ejpam-6414	77	26	performance	performance	NOUN
ejpam-6414	77	27	characteristics	characteristic	NOUN
ejpam-6414	77	28	of	of	ADP
ejpam-6414	77	29	bch	bch	PROPN
ejpam-6414	77	30	codes	code	NOUN
ejpam-6414	77	31	in	in	ADP
ejpam-6414	77	32	extended	extended	ADJ
ejpam-6414	77	33	communication	communication	NOUN
ejpam-6414	77	34	networks	network	NOUN
ejpam-6414	77	35	.	.	PUNCT
ejpam-6414	78	1	an	an	DET
ejpam-6414	78	2	ever	ever	ADV
ejpam-6414	78	3	-	-	PUNCT
ejpam-6414	78	4	evolving	evolve	VERB
ejpam-6414	78	5	communication	communication	NOUN
ejpam-6414	78	6	technology	technology	NOUN
ejpam-6414	78	7	means	mean	VERB
ejpam-6414	78	8	that	that	SCONJ
ejpam-6414	78	9	there	there	PRON
ejpam-6414	78	10	is	be	VERB
ejpam-6414	78	11	a	a	DET
ejpam-6414	78	12	constant	constant	ADJ
ejpam-6414	78	13	need	need	NOUN
ejpam-6414	78	14	for	for	ADP
ejpam-6414	78	15	enhanced	enhanced	ADJ
ejpam-6414	78	16	methods	method	NOUN
ejpam-6414	78	17	of	of	ADP
ejpam-6414	78	18	error	error	NOUN
ejpam-6414	78	19	correction	correction	NOUN
ejpam-6414	78	20	for	for	ADP
ejpam-6414	78	21	the	the	DET
ejpam-6414	78	22	effective	effective	ADJ
ejpam-6414	78	23	transfer	transfer	NOUN
ejpam-6414	78	24	of	of	ADP
ejpam-6414	78	25	data	datum	NOUN
ejpam-6414	78	26	.	.	PUNCT
ejpam-6414	79	1	bch	bch	PROPN
ejpam-6414	79	2	(	(	PUNCT
ejpam-6414	79	3	bosechaudhuri	bosechaudhuri	PROPN
ejpam-6414	79	4	-	-	PUNCT
ejpam-6414	79	5	hocquenghem	hocquenghem	NOUN
ejpam-6414	79	6	)	)	PUNCT
ejpam-6414	79	7	codes	code	NOUN
ejpam-6414	79	8	have	have	AUX
ejpam-6414	79	9	always	always	ADV
ejpam-6414	79	10	been	be	AUX
ejpam-6414	79	11	acknowledged	acknowledge	VERB
ejpam-6414	79	12	for	for	ADP
ejpam-6414	79	13	their	their	PRON
ejpam-6414	79	14	suitability	suitability	NOUN
ejpam-6414	79	15	for	for	ADP
ejpam-6414	79	16	error	error	NOUN
ejpam-6414	79	17	correction	correction	NOUN
ejpam-6414	79	18	because	because	SCONJ
ejpam-6414	79	19	of	of	ADP
ejpam-6414	79	20	the	the	DET
ejpam-6414	79	21	clear	clear	ADJ
ejpam-6414	79	22	algebraic	algebraic	ADJ
ejpam-6414	79	23	structure	structure	NOUN
ejpam-6414	79	24	of	of	ADP
ejpam-6414	79	25	the	the	DET
ejpam-6414	79	26	code	code	NOUN
ejpam-6414	79	27	and	and	CCONJ
ejpam-6414	79	28	the	the	DET
ejpam-6414	79	29	availability	availability	NOUN
ejpam-6414	79	30	of	of	ADP
ejpam-6414	79	31	efficient	efficient	ADJ
ejpam-6414	79	32	decoding	decoding	NOUN
ejpam-6414	79	33	procedures	procedure	NOUN
ejpam-6414	79	34	.	.	PUNCT
ejpam-6414	80	1	however	however	ADV
ejpam-6414	80	2	,	,	PUNCT
ejpam-6414	80	3	the	the	DET
ejpam-6414	80	4	desire	desire	NOUN
ejpam-6414	80	5	to	to	PART
ejpam-6414	80	6	make	make	VERB
ejpam-6414	80	7	coding	code	VERB
ejpam-6414	80	8	more	more	ADV
ejpam-6414	80	9	efficient	efficient	ADJ
ejpam-6414	80	10	has	have	AUX
ejpam-6414	80	11	resulted	result	VERB
ejpam-6414	80	12	in	in	ADP
ejpam-6414	80	13	the	the	DET
ejpam-6414	80	14	consideration	consideration	NOUN
ejpam-6414	80	15	of	of	ADP
ejpam-6414	80	16	what	what	PRON
ejpam-6414	80	17	is	be	AUX
ejpam-6414	80	18	called	call	VERB
ejpam-6414	80	19	codes	code	NOUN
ejpam-6414	80	20	over	over	ADP
ejpam-6414	80	21	other	other	ADJ
ejpam-6414	80	22	algebraic	algebraic	ADJ
ejpam-6414	80	23	structures	structure	NOUN
ejpam-6414	80	24	like	like	ADP
ejpam-6414	80	25	the	the	DET
ejpam-6414	80	26	integer	integer	NOUN
ejpam-6414	80	27	residue	residue	NOUN
ejpam-6414	80	28	rings	ring	NOUN
ejpam-6414	80	29	and	and	CCONJ
ejpam-6414	80	30	finite	finite	PROPN
ejpam-6414	80	31	commutative	commutative	ADJ
ejpam-6414	80	32	rings	ring	NOUN
ejpam-6414	80	33	[	[	X
ejpam-6414	80	34	1	1	NUM
ejpam-6414	80	35	,	,	PUNCT
ejpam-6414	80	36	31	31	NUM
ejpam-6414	80	37	]	]	PUNCT
ejpam-6414	80	38	.	.	PUNCT
ejpam-6414	81	1	therefore	therefore	ADV
ejpam-6414	81	2	,	,	PUNCT
ejpam-6414	81	3	the	the	DET
ejpam-6414	81	4	theory	theory	NOUN
ejpam-6414	81	5	of	of	ADP
ejpam-6414	81	6	quasi	quasi	ADJ
ejpam-6414	81	7	-	-	ADJ
ejpam-6414	81	8	galois	galois	ADJ
ejpam-6414	81	9	rings	ring	NOUN
ejpam-6414	81	10	(	(	PUNCT
ejpam-6414	81	11	qgrs	qgrs	PROPN
ejpam-6414	81	12	)	)	PUNCT
ejpam-6414	81	13	is	be	AUX
ejpam-6414	81	14	a	a	DET
ejpam-6414	81	15	natural	natural	ADJ
ejpam-6414	81	16	and	and	CCONJ
ejpam-6414	81	17	quite	quite	DET
ejpam-6414	81	18	a	a	DET
ejpam-6414	81	19	powerful	powerful	ADJ
ejpam-6414	81	20	generalization	generalization	NOUN
ejpam-6414	81	21	of	of	ADP
ejpam-6414	81	22	the	the	DET
ejpam-6414	81	23	theory	theory	NOUN
ejpam-6414	81	24	of	of	ADP
ejpam-6414	81	25	galois	galois	PROPN
ejpam-6414	81	26	rings	ring	NOUN
ejpam-6414	81	27	that	that	PRON
ejpam-6414	81	28	could	could	AUX
ejpam-6414	81	29	be	be	AUX
ejpam-6414	81	30	useful	useful	ADJ
ejpam-6414	81	31	for	for	ADP
ejpam-6414	81	32	improving	improve	VERB
ejpam-6414	81	33	the	the	DET
ejpam-6414	81	34	bch	bch	PROPN
ejpam-6414	81	35	codes	code	NOUN
ejpam-6414	81	36	[	[	X
ejpam-6414	81	37	1	1	NUM
ejpam-6414	81	38	]	]	PUNCT
ejpam-6414	81	39	.	.	PUNCT
ejpam-6414	82	1	compared	compare	VERB
ejpam-6414	82	2	to	to	ADP
ejpam-6414	82	3	the	the	DET
ejpam-6414	82	4	previous	previous	ADJ
ejpam-6414	82	5	galois	galois	PROPN
ejpam-6414	82	6	rings	ring	NOUN
ejpam-6414	82	7	,	,	PUNCT
ejpam-6414	82	8	qgrs	qgrs	PROPN
ejpam-6414	82	9	have	have	VERB
ejpam-6414	82	10	additional	additional	ADJ
ejpam-6414	82	11	algebraic	algebraic	ADJ
ejpam-6414	82	12	characteristics	characteristic	NOUN
ejpam-6414	82	13	that	that	PRON
ejpam-6414	82	14	make	make	VERB
ejpam-6414	82	15	it	it	PRON
ejpam-6414	82	16	possible	possible	ADJ
ejpam-6414	82	17	to	to	PART
ejpam-6414	82	18	build	build	VERB
ejpam-6414	82	19	bch	bch	NOUN
ejpam-6414	82	20	codes	code	NOUN
ejpam-6414	82	21	with	with	ADP
ejpam-6414	82	22	higher	high	ADJ
ejpam-6414	82	23	error	error	NOUN
ejpam-6414	82	24	-	-	PUNCT
ejpam-6414	82	25	correcting	correct	VERB
ejpam-6414	82	26	capability	capability	NOUN
ejpam-6414	82	27	and	and	CCONJ
ejpam-6414	82	28	code	code	NOUN
ejpam-6414	82	29	rate	rate	NOUN
ejpam-6414	82	30	.	.	PUNCT
ejpam-6414	83	1	these	these	DET
ejpam-6414	83	2	properties	property	NOUN
ejpam-6414	83	3	include	include	VERB
ejpam-6414	83	4	an	an	DET
ejpam-6414	83	5	increased	increase	VERB
ejpam-6414	83	6	number	number	NOUN
ejpam-6414	83	7	of	of	ADP
ejpam-6414	83	8	code	code	NOUN
ejpam-6414	83	9	words	word	NOUN
ejpam-6414	83	10	,	,	PUNCT
ejpam-6414	83	11	which	which	PRON
ejpam-6414	83	12	makes	make	VERB
ejpam-6414	83	13	the	the	DET
ejpam-6414	83	14	bch	bch	PROPN
ejpam-6414	83	15	codes	code	NOUN
ejpam-6414	83	16	over	over	ADP
ejpam-6414	83	17	qgrs	qgrs	PROPN
ejpam-6414	83	18	more	more	ADV
ejpam-6414	83	19	suitable	suitable	ADJ
ejpam-6414	83	20	for	for	ADP
ejpam-6414	83	21	modern	modern	ADJ
ejpam-6414	83	22	communication	communication	NOUN
ejpam-6414	83	23	systems	system	NOUN
ejpam-6414	83	24	,	,	PUNCT
ejpam-6414	83	25	and	and	CCONJ
ejpam-6414	83	26	an	an	DET
ejpam-6414	83	27	improved	improved	ADJ
ejpam-6414	83	28	code	code	NOUN
ejpam-6414	83	29	rate	rate	NOUN
ejpam-6414	83	30	.	.	PUNCT
ejpam-6414	84	1	new	new	ADJ
ejpam-6414	84	2	studies	study	NOUN
ejpam-6414	84	3	have	have	AUX
ejpam-6414	84	4	established	establish	VERB
ejpam-6414	84	5	that	that	SCONJ
ejpam-6414	84	6	it	it	PRON
ejpam-6414	84	7	is	be	AUX
ejpam-6414	84	8	possible	possible	ADJ
ejpam-6414	84	9	to	to	PART
ejpam-6414	84	10	construct	construct	VERB
ejpam-6414	84	11	and	and	CCONJ
ejpam-6414	84	12	decode	decode	PROPN
ejpam-6414	84	13	bch	bch	PROPN
ejpam-6414	84	14	codes	code	NOUN
ejpam-6414	84	15	over	over	ADP
ejpam-6414	84	16	qgrs	qgrs	PROPN
ejpam-6414	84	17	.	.	PUNCT
ejpam-6414	85	1	for	for	ADP
ejpam-6414	85	2	instance	instance	NOUN
ejpam-6414	85	3	,	,	PUNCT
ejpam-6414	85	4	while	while	SCONJ
ejpam-6414	85	5	applying	apply	VERB
ejpam-6414	85	6	andrade	andrade	NOUN
ejpam-6414	85	7	and	and	CCONJ
ejpam-6414	85	8	palazzo	palazzo	PROPN
ejpam-6414	85	9	’s	’s	PART
ejpam-6414	85	10	work	work	NOUN
ejpam-6414	85	11	on	on	ADP
ejpam-6414	85	12	bch	bch	PROPN
ejpam-6414	85	13	codes	code	NOUN
ejpam-6414	85	14	over	over	ADP
ejpam-6414	85	15	finite	finite	PROPN
ejpam-6414	85	16	commutative	commutative	ADJ
ejpam-6414	85	17	rings	ring	NOUN
ejpam-6414	85	18	,	,	PUNCT
ejpam-6414	85	19	there	there	PRON
ejpam-6414	85	20	has	have	AUX
ejpam-6414	85	21	been	be	AUX
ejpam-6414	85	22	a	a	DET
ejpam-6414	85	23	marked	mark	VERB
ejpam-6414	85	24	enhancement	enhancement	NOUN
ejpam-6414	85	25	in	in	ADP
ejpam-6414	85	26	the	the	DET
ejpam-6414	85	27	error	error	NOUN
ejpam-6414	85	28	correction	correction	NOUN
ejpam-6414	85	29	efficiency	efficiency	NOUN
ejpam-6414	85	30	[	[	X
ejpam-6414	85	31	1	1	NUM
ejpam-6414	85	32	]	]	PUNCT
ejpam-6414	85	33	.	.	PUNCT
ejpam-6414	86	1	likewise	likewise	ADV
ejpam-6414	86	2	,	,	PUNCT
ejpam-6414	86	3	shankar	shankar	PROPN
ejpam-6414	86	4	’s	’s	PART
ejpam-6414	86	5	work	work	NOUN
ejpam-6414	86	6	further	far	ADV
ejpam-6414	86	7	extending	extend	VERB
ejpam-6414	86	8	the	the	DET
ejpam-6414	86	9	bch	bch	PROPN
ejpam-6414	86	10	codes	code	NOUN
ejpam-6414	86	11	over	over	ADP
ejpam-6414	86	12	arbitrary	arbitrary	ADJ
ejpam-6414	86	13	integer	integer	NOUN
ejpam-6414	86	14	rings	ring	NOUN
ejpam-6414	86	15	has	have	AUX
ejpam-6414	86	16	added	add	VERB
ejpam-6414	86	17	more	more	ADJ
ejpam-6414	86	18	feathers	feather	NOUN
ejpam-6414	86	19	in	in	ADP
ejpam-6414	86	20	the	the	DET
ejpam-6414	86	21	hat	hat	NOUN
ejpam-6414	86	22	of	of	ADP
ejpam-6414	86	23	these	these	DET
ejpam-6414	86	24	codes	code	NOUN
ejpam-6414	86	25	in	in	ADP
ejpam-6414	86	26	numerous	numerous	ADJ
ejpam-6414	86	27	applications	application	NOUN
ejpam-6414	86	28	[	[	X
ejpam-6414	86	29	31	31	NUM
ejpam-6414	86	30	]	]	PUNCT
ejpam-6414	86	31	.	.	PUNCT
ejpam-6414	87	1	these	these	DET
ejpam-6414	87	2	works	work	NOUN
ejpam-6414	87	3	form	form	VERB
ejpam-6414	87	4	a	a	DET
ejpam-6414	87	5	base	base	NOUN
ejpam-6414	87	6	upon	upon	SCONJ
ejpam-6414	87	7	which	which	PRON
ejpam-6414	87	8	further	further	ADJ
ejpam-6414	87	9	research	research	NOUN
ejpam-6414	87	10	can	can	AUX
ejpam-6414	87	11	be	be	AUX
ejpam-6414	87	12	conducted	conduct	VERB
ejpam-6414	87	13	in	in	ADP
ejpam-6414	87	14	order	order	NOUN
ejpam-6414	87	15	to	to	PART
ejpam-6414	87	16	better	well	ADV
ejpam-6414	87	17	understand	understand	VERB
ejpam-6414	87	18	the	the	DET
ejpam-6414	87	19	characteristics	characteristic	NOUN
ejpam-6414	87	20	of	of	ADP
ejpam-6414	87	21	qgrs	qgrs	NOUN
ejpam-6414	87	22	and	and	CCONJ
ejpam-6414	87	23	the	the	DET
ejpam-6414	87	24	use	use	NOUN
ejpam-6414	87	25	of	of	ADP
ejpam-6414	87	26	these	these	DET
ejpam-6414	87	27	groups	group	NOUN
ejpam-6414	87	28	in	in	ADP
ejpam-6414	87	29	constructing	construct	VERB
ejpam-6414	87	30	bch	bch	NOUN
ejpam-6414	87	31	codes	code	NOUN
ejpam-6414	87	32	.	.	PUNCT
ejpam-6414	88	1	this	this	DET
ejpam-6414	88	2	article	article	NOUN
ejpam-6414	88	3	has	have	VERB
ejpam-6414	88	4	important	important	ADJ
ejpam-6414	88	5	contributions	contribution	NOUN
ejpam-6414	88	6	to	to	ADP
ejpam-6414	88	7	the	the	DET
ejpam-6414	88	8	domain	domain	NOUN
ejpam-6414	88	9	of	of	ADP
ejpam-6414	88	10	coding	code	VERB
ejpam-6414	88	11	theory	theory	NOUN
ejpam-6414	88	12	in	in	ADP
ejpam-6414	88	13	order	order	NOUN
ejpam-6414	88	14	to	to	PART
ejpam-6414	88	15	implement	implement	VERB
ejpam-6414	88	16	bch	bch	PROPN
ejpam-6414	88	17	codes	code	NOUN
ejpam-6414	88	18	over	over	ADP
ejpam-6414	88	19	quasi	quasi	ADJ
ejpam-6414	88	20	-	-	ADJ
ejpam-6414	88	21	galois	galois	ADJ
ejpam-6414	88	22	rings	ring	NOUN
ejpam-6414	88	23	(	(	PUNCT
ejpam-6414	88	24	qgrs	qgrs	PROPN
ejpam-6414	88	25	)	)	PUNCT
ejpam-6414	88	26	for	for	ADP
ejpam-6414	88	27	enhancing	enhance	VERB
ejpam-6414	88	28	the	the	DET
ejpam-6414	88	29	actual	actual	ADJ
ejpam-6414	88	30	communication	communication	NOUN
ejpam-6414	88	31	systems	system	NOUN
ejpam-6414	88	32	.	.	PUNCT
ejpam-6414	89	1	from	from	ADP
ejpam-6414	89	2	this	this	PRON
ejpam-6414	89	3	,	,	PUNCT
ejpam-6414	89	4	a	a	DET
ejpam-6414	89	5	comprehensive	comprehensive	ADJ
ejpam-6414	89	6	theoretical	theoretical	ADJ
ejpam-6414	89	7	background	background	NOUN
ejpam-6414	89	8	for	for	ADP
ejpam-6414	89	9	bch	bch	PROPN
ejpam-6414	89	10	codes	code	NOUN
ejpam-6414	89	11	over	over	ADP
ejpam-6414	89	12	qgrs	qgrs	PROPN
ejpam-6414	89	13	is	be	AUX
ejpam-6414	89	14	presented	present	VERB
ejpam-6414	89	15	to	to	PART
ejpam-6414	89	16	explain	explain	VERB
ejpam-6414	89	17	possible	possible	ADJ
ejpam-6414	89	18	higher	high	ADJ
ejpam-6414	89	19	code	code	NOUN
ejpam-6414	89	20	rates	rate	NOUN
ejpam-6414	89	21	and	and	CCONJ
ejpam-6414	89	22	a	a	DET
ejpam-6414	89	23	larger	large	ADJ
ejpam-6414	89	24	number	number	NOUN
ejpam-6414	89	25	of	of	ADP
ejpam-6414	89	26	code	code	NOUN
ejpam-6414	89	27	words	word	NOUN
ejpam-6414	89	28	compared	compare	VERB
ejpam-6414	89	29	to	to	ADP
ejpam-6414	89	30	the	the	DET
ejpam-6414	89	31	use	use	NOUN
ejpam-6414	89	32	of	of	ADP
ejpam-6414	89	33	galois	galois	PROPN
ejpam-6414	89	34	rings	ring	NOUN
ejpam-6414	89	35	.	.	PUNCT
ejpam-6414	90	1	thus	thus	ADV
ejpam-6414	90	2	,	,	PUNCT
ejpam-6414	90	3	the	the	DET
ejpam-6414	90	4	article	article	NOUN
ejpam-6414	90	5	demonstrates	demonstrate	VERB
ejpam-6414	90	6	the	the	DET
ejpam-6414	90	7	practical	practical	ADJ
ejpam-6414	90	8	applicability	applicability	NOUN
ejpam-6414	90	9	of	of	ADP
ejpam-6414	90	10	the	the	DET
ejpam-6414	90	11	qgr	qgr	NOUN
ejpam-6414	90	12	-	-	PUNCT
ejpam-6414	90	13	based	base	VERB
ejpam-6414	90	14	bch	bch	PROPN
ejpam-6414	90	15	codes	code	NOUN
ejpam-6414	90	16	as	as	ADP
ejpam-6414	90	17	a	a	DET
ejpam-6414	90	18	result	result	NOUN
ejpam-6414	90	19	of	of	ADP
ejpam-6414	90	20	presenting	present	VERB
ejpam-6414	90	21	novel	novel	ADJ
ejpam-6414	90	22	construction	construction	NOUN
ejpam-6414	90	23	methods	method	NOUN
ejpam-6414	90	24	and	and	CCONJ
ejpam-6414	90	25	efficient	efficient	ADJ
ejpam-6414	90	26	decoding	decode	VERB
ejpam-6414	90	27	strategies	strategy	NOUN
ejpam-6414	90	28	.	.	PUNCT
ejpam-6414	91	1	the	the	DET
ejpam-6414	91	2	enhanced	enhance	VERB
ejpam-6414	91	3	understanding	understanding	NOUN
ejpam-6414	91	4	of	of	ADP
ejpam-6414	91	5	these	these	DET
ejpam-6414	91	6	codes	code	NOUN
ejpam-6414	91	7	’	'	PUNCT
ejpam-6414	91	8	theoretical	theoretical	ADJ
ejpam-6414	91	9	and	and	CCONJ
ejpam-6414	91	10	practical	practical	ADJ
ejpam-6414	91	11	characteristics	characteristic	NOUN
ejpam-6414	91	12	underlines	underline	VERB
ejpam-6414	91	13	their	their	PRON
ejpam-6414	91	14	capability	capability	NOUN
ejpam-6414	91	15	to	to	PART
ejpam-6414	91	16	dramatically	dramatically	ADV
ejpam-6414	91	17	improve	improve	VERB
ejpam-6414	91	18	the	the	DET
ejpam-6414	91	19	effectiveness	effectiveness	NOUN
ejpam-6414	91	20	and	and	CCONJ
ejpam-6414	91	21	stability	stability	NOUN
ejpam-6414	91	22	of	of	ADP
ejpam-6414	91	23	today	today	NOUN
ejpam-6414	91	24	’s	’s	PART
ejpam-6414	91	25	communication	communication	NOUN
ejpam-6414	91	26	networks	network	NOUN
ejpam-6414	91	27	in	in	ADP
ejpam-6414	91	28	various	various	ADJ
ejpam-6414	91	29	applications	application	NOUN
ejpam-6414	91	30	.	.	PUNCT
ejpam-6414	92	1	thus	thus	ADV
ejpam-6414	92	2	,	,	PUNCT
ejpam-6414	92	3	this	this	DET
ejpam-6414	92	4	investigation	investigation	NOUN
ejpam-6414	92	5	is	be	AUX
ejpam-6414	92	6	expected	expect	VERB
ejpam-6414	92	7	to	to	PART
ejpam-6414	92	8	bring	bring	VERB
ejpam-6414	92	9	the	the	DET
ejpam-6414	92	10	bch	bch	PROPN
ejpam-6414	92	11	code	code	PROPN
ejpam-6414	92	12	over	over	ADP
ejpam-6414	92	13	qgrs	qgrs	PROPN
ejpam-6414	92	14	into	into	ADP
ejpam-6414	92	15	light	light	NOUN
ejpam-6414	92	16	as	as	ADP
ejpam-6414	92	17	potent	potent	ADJ
ejpam-6414	92	18	and	and	CCONJ
ejpam-6414	92	19	effective	effective	ADJ
ejpam-6414	92	20	candidates	candidate	NOUN
ejpam-6414	92	21	to	to	PART
ejpam-6414	92	22	be	be	AUX
ejpam-6414	92	23	incorporated	incorporate	VERB
ejpam-6414	92	24	in	in	ADP
ejpam-6414	92	25	the	the	DET
ejpam-6414	92	26	advanced	advanced	ADJ
ejpam-6414	92	27	communication	communication	NOUN
ejpam-6414	92	28	systems	system	NOUN
ejpam-6414	92	29	as	as	ADV
ejpam-6414	92	30	well	well	ADV
ejpam-6414	92	31	as	as	ADP
ejpam-6414	92	32	contribute	contribute	VERB
ejpam-6414	92	33	to	to	ADP
ejpam-6414	92	34	the	the	DET
ejpam-6414	92	35	continuous	continuous	ADJ
ejpam-6414	92	36	improvement	improvement	NOUN
ejpam-6414	92	37	of	of	ADP
ejpam-6414	92	38	coding	code	VERB
ejpam-6414	92	39	methods	method	NOUN
ejpam-6414	92	40	in	in	ADP
ejpam-6414	92	41	the	the	DET
ejpam-6414	92	42	modern	modern	ADJ
ejpam-6414	92	43	world	world	NOUN
ejpam-6414	92	44	.	.	PUNCT
ejpam-6414	93	1	2	2	X
ejpam-6414	93	2	.	.	X
ejpam-6414	93	3	preliminaries	preliminary	NOUN
ejpam-6414	93	4	this	this	DET
ejpam-6414	93	5	section	section	NOUN
ejpam-6414	93	6	consists	consist	VERB
ejpam-6414	93	7	of	of	ADP
ejpam-6414	93	8	basic	basic	ADJ
ejpam-6414	93	9	results	result	NOUN
ejpam-6414	93	10	that	that	PRON
ejpam-6414	93	11	are	be	AUX
ejpam-6414	93	12	useful	useful	ADJ
ejpam-6414	93	13	to	to	PART
ejpam-6414	93	14	understand	understand	VERB
ejpam-6414	93	15	the	the	DET
ejpam-6414	93	16	upcoming	upcoming	ADJ
ejpam-6414	93	17	sections	section	NOUN
ejpam-6414	93	18	[	[	X
ejpam-6414	93	19	12–14	12–14	NUM
ejpam-6414	93	20	,	,	PUNCT
ejpam-6414	93	21	18	18	NUM
ejpam-6414	93	22	,	,	PUNCT
ejpam-6414	93	23	19	19	NUM
ejpam-6414	93	24	,	,	PUNCT
ejpam-6414	93	25	26	26	NUM
ejpam-6414	93	26	]	]	PUNCT
ejpam-6414	93	27	.	.	PUNCT
ejpam-6414	94	1	muhammad	muhammad	PROPN
ejpam-6414	94	2	sajjad	sajjad	PROPN
ejpam-6414	94	3	et	et	PROPN
ejpam-6414	94	4	al	al	PROPN
ejpam-6414	94	5	.	.	PUNCT
ejpam-6414	94	6	/	/	SYM
ejpam-6414	94	7	eur	eur	PROPN
ejpam-6414	94	8	.	.	PUNCT
ejpam-6414	95	1	j.	j.	PROPN
ejpam-6414	95	2	pure	pure	PROPN
ejpam-6414	95	3	appl	appl	PROPN
ejpam-6414	95	4	.	.	PROPN
ejpam-6414	95	5	math	math	PROPN
ejpam-6414	95	6	,	,	PUNCT
ejpam-6414	95	7	18	18	NUM
ejpam-6414	95	8	(	(	PUNCT
ejpam-6414	95	9	3	3	NUM
ejpam-6414	95	10	)	)	PUNCT
ejpam-6414	95	11	(	(	PUNCT
ejpam-6414	95	12	2025	2025	NUM
ejpam-6414	95	13	)	)	PUNCT
ejpam-6414	95	14	,	,	PUNCT
ejpam-6414	95	15	6414	6414	NUM
ejpam-6414	95	16	5	5	NUM
ejpam-6414	95	17	of	of	ADP
ejpam-6414	95	18	22	22	NUM
ejpam-6414	95	19	2.1	2.1	NUM
ejpam-6414	95	20	.	.	PUNCT
ejpam-6414	96	1	quasi	quasi	ADJ
ejpam-6414	96	2	-	-	ADJ
ejpam-6414	96	3	galois	galois	ADJ
ejpam-6414	96	4	ring	ring	NOUN
ejpam-6414	96	5	let	let	VERB
ejpam-6414	96	6	a	a	DET
ejpam-6414	96	7	quasi	quasi	ADJ
ejpam-6414	96	8	-	-	ADJ
ejpam-6414	96	9	galois	galois	ADJ
ejpam-6414	96	10	ring	ring	NOUN
ejpam-6414	96	11	(	(	PUNCT
ejpam-6414	96	12	q	q	NOUN
ejpam-6414	96	13	-	-	PUNCT
ejpam-6414	96	14	gr	gr	NOUN
ejpam-6414	96	15	)	)	PUNCT
ejpam-6414	96	16	be	be	AUX
ejpam-6414	96	17	a	a	DET
ejpam-6414	96	18	local	local	ADJ
ejpam-6414	96	19	,	,	PUNCT
ejpam-6414	96	20	finite	finite	PROPN
ejpam-6414	96	21	,	,	PUNCT
ejpam-6414	96	22	commutative	commutative	ADJ
ejpam-6414	96	23	ring	ring	NOUN
ejpam-6414	96	24	with	with	ADP
ejpam-6414	96	25	cardinality	cardinality	NOUN
ejpam-6414	96	26	prs	prs	NOUN
ejpam-6414	96	27	and	and	CCONJ
ejpam-6414	96	28	characteristic	characteristic	ADJ
ejpam-6414	96	29	p	p	X
ejpam-6414	96	30	(	(	PUNCT
ejpam-6414	96	31	where	where	SCONJ
ejpam-6414	96	32	p	p	NOUN
ejpam-6414	96	33	is	be	AUX
ejpam-6414	96	34	a	a	DET
ejpam-6414	96	35	prime	prime	NOUN
ejpam-6414	96	36	and	and	CCONJ
ejpam-6414	96	37	n	n	CCONJ
ejpam-6414	96	38	,	,	PUNCT
ejpam-6414	96	39	s	s	VERB
ejpam-6414	96	40	are	be	AUX
ejpam-6414	96	41	any	any	DET
ejpam-6414	96	42	positive	positive	ADJ
ejpam-6414	96	43	integers	integer	NOUN
ejpam-6414	96	44	)	)	PUNCT
ejpam-6414	96	45	.	.	PUNCT
ejpam-6414	97	1	particularly	particularly	ADV
ejpam-6414	97	2	from	from	ADP
ejpam-6414	97	3	the	the	DET
ejpam-6414	97	4	perspective	perspective	NOUN
ejpam-6414	97	5	of	of	ADP
ejpam-6414	97	6	applications	application	NOUN
ejpam-6414	97	7	in	in	ADP
ejpam-6414	97	8	coding	code	VERB
ejpam-6414	97	9	theory	theory	NOUN
ejpam-6414	97	10	,	,	PUNCT
ejpam-6414	97	11	q	q	PROPN
ejpam-6414	97	12	-	-	PUNCT
ejpam-6414	97	13	grs	grs	PROPN
ejpam-6414	97	14	are	be	AUX
ejpam-6414	97	15	highly	highly	ADV
ejpam-6414	97	16	intriguing	intriguing	ADJ
ejpam-6414	97	17	because	because	SCONJ
ejpam-6414	97	18	they	they	PRON
ejpam-6414	97	19	possess	possess	VERB
ejpam-6414	97	20	the	the	DET
ejpam-6414	97	21	desirable	desirable	ADJ
ejpam-6414	97	22	attribute	attribute	NOUN
ejpam-6414	97	23	of	of	ADP
ejpam-6414	97	24	having	have	VERB
ejpam-6414	97	25	prime	prime	ADJ
ejpam-6414	97	26	characteristics	characteristic	NOUN
ejpam-6414	97	27	.	.	PUNCT
ejpam-6414	98	1	it	it	PRON
ejpam-6414	98	2	is	be	AUX
ejpam-6414	98	3	denoted	denote	VERB
ejpam-6414	98	4	by	by	ADP
ejpam-6414	98	5	and	and	CCONJ
ejpam-6414	98	6	defined	define	VERB
ejpam-6414	98	7	as	as	ADP
ejpam-6414	98	8	a(ps	a(ps	PROPN
ejpam-6414	98	9	,	,	PUNCT
ejpam-6414	98	10	n	n	CCONJ
ejpam-6414	98	11	)	)	PUNCT
ejpam-6414	98	12	=	=	AUX
ejpam-6414	98	13	fps	fps	VERB
ejpam-6414	99	1	[	[	X
ejpam-6414	99	2	x	x	X
ejpam-6414	99	3	]	]	X
ejpam-6414	99	4	⟨xn⟩	⟨xn⟩	NOUN
ejpam-6414	99	5	=	=	PUNCT
ejpam-6414	99	6	{	{	PUNCT
ejpam-6414	99	7	n−1∑	n−1∑	PROPN
ejpam-6414	99	8	i=0	i=0	PROPN
ejpam-6414	99	9	aiθ	aiθ	NOUN
ejpam-6414	100	1	i	i	PRON
ejpam-6414	100	2	:	:	PUNCT
ejpam-6414	100	3	ai	ai	VERB
ejpam-6414	100	4	∈	∈	PROPN
ejpam-6414	100	5	fps	fps	PROPN
ejpam-6414	100	6	}	}	PUNCT
ejpam-6414	100	7	(	(	PUNCT
ejpam-6414	100	8	1	1	X
ejpam-6414	100	9	)	)	PUNCT
ejpam-6414	100	10	where	where	SCONJ
ejpam-6414	100	11	θ	θ	PROPN
ejpam-6414	100	12	is	be	AUX
ejpam-6414	100	13	a	a	DET
ejpam-6414	100	14	formal	formal	ADJ
ejpam-6414	100	15	non	non	ADJ
ejpam-6414	100	16	-	-	ADJ
ejpam-6414	100	17	trivial	trivial	ADJ
ejpam-6414	100	18	root	root	NOUN
ejpam-6414	100	19	of	of	ADP
ejpam-6414	100	20	the	the	DET
ejpam-6414	100	21	polynomial	polynomial	ADJ
ejpam-6414	100	22	xn	xn	PROPN
ejpam-6414	100	23	∈	∈	PROPN
ejpam-6414	100	24	fps	fps	NOUN
ejpam-6414	100	25	[	[	X
ejpam-6414	100	26	x	x	X
ejpam-6414	100	27	]	]	X
ejpam-6414	100	28	,	,	PUNCT
ejpam-6414	100	29	i.e.	i.e.	X
ejpam-6414	100	30	,	,	PUNCT
ejpam-6414	100	31	θ	θ	PROPN
ejpam-6414	100	32	n	n	NOUN
ejpam-6414	100	33	=	=	SYM
ejpam-6414	100	34	0	0	NUM
ejpam-6414	100	35	.	.	X
ejpam-6414	100	36	2.2	2.2	NUM
ejpam-6414	100	37	.	.	PUNCT
ejpam-6414	100	38	units	unit	NOUN
ejpam-6414	100	39	in	in	ADP
ejpam-6414	100	40	q	q	NOUN
ejpam-6414	100	41	-	-	PUNCT
ejpam-6414	100	42	gr	gr	NOUN
ejpam-6414	100	43	if	if	SCONJ
ejpam-6414	100	44	a0	a0	PROPN
ejpam-6414	100	45	̸=	̸=	PROPN
ejpam-6414	100	46	0	0	NUM
ejpam-6414	100	47	in	in	ADP
ejpam-6414	100	48	the	the	DET
ejpam-6414	100	49	expression	expression	NOUN
ejpam-6414	100	50	,	,	PUNCT
ejpam-6414	100	51	n−1∑	n−1∑	PROPN
ejpam-6414	100	52	i=0	i=0	PROPN
ejpam-6414	100	53	aiθ	aiθ	VERB
ejpam-6414	100	54	i	i	PRON
ejpam-6414	100	55	,	,	PUNCT
ejpam-6414	100	56	ai	ai	VERB
ejpam-6414	100	57	∈	∈	PROPN
ejpam-6414	100	58	fps	fps	NOUN
ejpam-6414	100	59	,	,	PUNCT
ejpam-6414	100	60	then	then	ADV
ejpam-6414	100	61	the	the	DET
ejpam-6414	100	62	element	element	NOUN
ejpam-6414	100	63	is	be	AUX
ejpam-6414	100	64	a	a	DET
ejpam-6414	100	65	unit	unit	NOUN
ejpam-6414	100	66	in	in	ADP
ejpam-6414	100	67	a(ps	a(ps	PROPN
ejpam-6414	100	68	,	,	PUNCT
ejpam-6414	100	69	n	n	CCONJ
ejpam-6414	100	70	)	)	PUNCT
ejpam-6414	100	71	.	.	PUNCT
ejpam-6414	101	1	2.3	2.3	NUM
ejpam-6414	101	2	.	.	PUNCT
ejpam-6414	102	1	nilpotent	nilpotent	ADJ
ejpam-6414	102	2	elements	element	NOUN
ejpam-6414	102	3	in	in	ADP
ejpam-6414	102	4	q	q	NOUN
ejpam-6414	102	5	-	-	PUNCT
ejpam-6414	102	6	gr	gr	NOUN
ejpam-6414	102	7	if	if	SCONJ
ejpam-6414	102	8	a0	a0	PROPN
ejpam-6414	102	9	=	=	SYM
ejpam-6414	102	10	0	0	NUM
ejpam-6414	102	11	in	in	ADP
ejpam-6414	102	12	,	,	PUNCT
ejpam-6414	102	13	a(ps	a(ps	PROPN
ejpam-6414	102	14	,	,	PUNCT
ejpam-6414	102	15	n	n	CCONJ
ejpam-6414	102	16	)	)	PUNCT
ejpam-6414	102	17	=	=	VERB
ejpam-6414	102	18	fps	fps	VERB
ejpam-6414	103	1	[	[	X
ejpam-6414	103	2	x	x	X
ejpam-6414	103	3	]	]	X
ejpam-6414	103	4	⟨xn⟩	⟨xn⟩	NOUN
ejpam-6414	103	5	=	=	PUNCT
ejpam-6414	103	6	{	{	PUNCT
ejpam-6414	103	7	n−1∑	n−1∑	PROPN
ejpam-6414	103	8	i=0	i=0	PROPN
ejpam-6414	103	9	aiθ	aiθ	NOUN
ejpam-6414	104	1	i	i	PRON
ejpam-6414	104	2	:	:	PUNCT
ejpam-6414	104	3	ai	ai	VERB
ejpam-6414	104	4	∈	∈	PROPN
ejpam-6414	104	5	fps	fps	PROPN
ejpam-6414	104	6	}	}	PUNCT
ejpam-6414	104	7	,	,	PUNCT
ejpam-6414	104	8	then	then	ADV
ejpam-6414	104	9	the	the	DET
ejpam-6414	104	10	element	element	NOUN
ejpam-6414	104	11	is	be	AUX
ejpam-6414	104	12	nilpotent	nilpotent	ADJ
ejpam-6414	104	13	.	.	PUNCT
ejpam-6414	105	1	if	if	SCONJ
ejpam-6414	105	2	a0	a0	PROPN
ejpam-6414	105	3	=	=	SYM
ejpam-6414	105	4	1	1	NUM
ejpam-6414	105	5	,	,	PUNCT
ejpam-6414	105	6	then	then	ADV
ejpam-6414	105	7	it	it	PRON
ejpam-6414	105	8	corresponds	correspond	VERB
ejpam-6414	105	9	to	to	ADP
ejpam-6414	105	10	a	a	DET
ejpam-6414	105	11	principal	principal	ADJ
ejpam-6414	105	12	unit	unit	NOUN
ejpam-6414	105	13	element	element	NOUN
ejpam-6414	105	14	.	.	PUNCT
ejpam-6414	106	1	proposition	proposition	NOUN
ejpam-6414	106	2	2.1	2.1	NUM
ejpam-6414	106	3	.	.	PUNCT
ejpam-6414	107	1	let	let	AUX
ejpam-6414	107	2	a(ps	a(ps	NOUN
ejpam-6414	107	3	,	,	PUNCT
ejpam-6414	107	4	n	n	CCONJ
ejpam-6414	107	5	)	)	PUNCT
ejpam-6414	107	6	be	be	AUX
ejpam-6414	107	7	a	a	DET
ejpam-6414	107	8	q	q	NOUN
ejpam-6414	107	9	-	-	PUNCT
ejpam-6414	107	10	gr	gr	NOUN
ejpam-6414	107	11	.	.	PUNCT
ejpam-6414	108	1	then	then	ADV
ejpam-6414	108	2	the	the	DET
ejpam-6414	108	3	group	group	NOUN
ejpam-6414	108	4	of	of	ADP
ejpam-6414	108	5	units	unit	NOUN
ejpam-6414	108	6	in	in	ADP
ejpam-6414	108	7	a(ps	a(ps	PROPN
ejpam-6414	108	8	,	,	PUNCT
ejpam-6414	108	9	n	n	CCONJ
ejpam-6414	108	10	)	)	PUNCT
ejpam-6414	108	11	is	be	AUX
ejpam-6414	108	12	isomorphic	isomorphic	ADJ
ejpam-6414	108	13	to	to	ADP
ejpam-6414	108	14	the	the	DET
ejpam-6414	108	15	direct	direct	ADJ
ejpam-6414	108	16	product	product	NOUN
ejpam-6414	108	17	of	of	ADP
ejpam-6414	108	18	two	two	NUM
ejpam-6414	108	19	groups	group	NOUN
ejpam-6414	108	20	,	,	PUNCT
ejpam-6414	108	21	u(a(ps	u(a(ps	NOUN
ejpam-6414	108	22	,	,	PUNCT
ejpam-6414	108	23	n	n	CCONJ
ejpam-6414	108	24	)	)	PUNCT
ejpam-6414	108	25	)	)	PUNCT
ejpam-6414	109	1	∼=	∼=	PROPN
ejpam-6414	109	2	g1	g1	PROPN
ejpam-6414	109	3	×g2	×g2	PROPN
ejpam-6414	109	4	,	,	PUNCT
ejpam-6414	109	5	where	where	SCONJ
ejpam-6414	109	6	g1	g1	PROPN
ejpam-6414	109	7	is	be	AUX
ejpam-6414	109	8	a	a	DET
ejpam-6414	109	9	cyclic	cyclic	ADJ
ejpam-6414	109	10	group	group	NOUN
ejpam-6414	109	11	of	of	ADP
ejpam-6414	109	12	order	order	NOUN
ejpam-6414	109	13	ps−1	ps−1	PROPN
ejpam-6414	109	14	,	,	PUNCT
ejpam-6414	109	15	and	and	CCONJ
ejpam-6414	109	16	g2	g2	PROPN
ejpam-6414	109	17	is	be	AUX
ejpam-6414	109	18	an	an	DET
ejpam-6414	109	19	abelian	abelian	ADJ
ejpam-6414	109	20	p	p	NOUN
ejpam-6414	109	21	-	-	PUNCT
ejpam-6414	109	22	group	group	NOUN
ejpam-6414	109	23	of	of	ADP
ejpam-6414	109	24	order	order	NOUN
ejpam-6414	109	25	ps(n−1	ps(n−1	NOUN
ejpam-6414	109	26	)	)	PUNCT
ejpam-6414	109	27	.	.	PUNCT
ejpam-6414	110	1	particularly	particularly	ADV
ejpam-6414	110	2	,	,	PUNCT
ejpam-6414	110	3	if	if	SCONJ
ejpam-6414	110	4	s	s	VERB
ejpam-6414	110	5	=	=	SYM
ejpam-6414	110	6	1	1	NUM
ejpam-6414	110	7	and	and	CCONJ
ejpam-6414	110	8	n	n	CCONJ
ejpam-6414	110	9	=	=	SYM
ejpam-6414	110	10	2	2	NUM
ejpam-6414	110	11	,	,	PUNCT
ejpam-6414	110	12	then	then	ADV
ejpam-6414	110	13	g2	g2	PROPN
ejpam-6414	110	14	is	be	AUX
ejpam-6414	110	15	a	a	DET
ejpam-6414	110	16	cyclic	cyclic	ADJ
ejpam-6414	110	17	group	group	NOUN
ejpam-6414	110	18	of	of	ADP
ejpam-6414	110	19	order	order	NOUN
ejpam-6414	111	1	p.	p.	NOUN
ejpam-6414	111	2	while	while	SCONJ
ejpam-6414	111	3	for	for	ADP
ejpam-6414	111	4	p	p	NOUN
ejpam-6414	111	5	=	=	SYM
ejpam-6414	111	6	2	2	NUM
ejpam-6414	111	7	,	,	PUNCT
ejpam-6414	111	8	s	s	PART
ejpam-6414	111	9	=	=	SYM
ejpam-6414	111	10	1	1	NUM
ejpam-6414	111	11	,	,	PUNCT
ejpam-6414	111	12	n	n	NOUN
ejpam-6414	111	13	=	=	SYM
ejpam-6414	111	14	3	3	NUM
ejpam-6414	111	15	,	,	PUNCT
ejpam-6414	111	16	we	we	PRON
ejpam-6414	111	17	have	have	VERB
ejpam-6414	111	18	g2	g2	PROPN
ejpam-6414	111	19	∼=	∼=	PROPN
ejpam-6414	111	20	c4	c4	NOUN
ejpam-6414	111	21	.	.	PUNCT
ejpam-6414	112	1	2.4	2.4	NUM
ejpam-6414	112	2	.	.	PUNCT
ejpam-6414	112	3	ideal	ideal	ADJ
ejpam-6414	112	4	structure	structure	NOUN
ejpam-6414	112	5	of	of	ADP
ejpam-6414	112	6	q	q	NOUN
ejpam-6414	112	7	-	-	PUNCT
ejpam-6414	112	8	gr	gr	NOUN
ejpam-6414	112	9	since	since	SCONJ
ejpam-6414	112	10	q	q	NOUN
ejpam-6414	112	11	-	-	PUNCT
ejpam-6414	112	12	gr	gr	NOUN
ejpam-6414	112	13	is	be	AUX
ejpam-6414	112	14	a	a	DET
ejpam-6414	112	15	local	local	ADJ
ejpam-6414	112	16	ring	ring	NOUN
ejpam-6414	112	17	,	,	PUNCT
ejpam-6414	112	18	it	it	PRON
ejpam-6414	112	19	contains	contain	VERB
ejpam-6414	112	20	a	a	DET
ejpam-6414	112	21	unique	unique	ADJ
ejpam-6414	112	22	maximal	maximal	ADJ
ejpam-6414	112	23	ideal	ideal	NOUN
ejpam-6414	112	24	,	,	PUNCT
ejpam-6414	112	25	and	and	CCONJ
ejpam-6414	112	26	the	the	DET
ejpam-6414	112	27	ring	ring	NOUN
ejpam-6414	112	28	is	be	AUX
ejpam-6414	112	29	given	give	VERB
ejpam-6414	112	30	by	by	ADP
ejpam-6414	112	31	:	:	PUNCT
ejpam-6414	112	32	a(ps	a(ps	PROPN
ejpam-6414	112	33	,	,	PUNCT
ejpam-6414	112	34	n	n	CCONJ
ejpam-6414	112	35	)	)	PUNCT
ejpam-6414	112	36	=	=	AUX
ejpam-6414	112	37	fps	fps	VERB
ejpam-6414	113	1	[	[	X
ejpam-6414	113	2	x	x	X
ejpam-6414	113	3	]	]	X
ejpam-6414	113	4	⟨xn⟩	⟨xn⟩	NOUN
ejpam-6414	113	5	=	=	PUNCT
ejpam-6414	113	6	{	{	PUNCT
ejpam-6414	113	7	n−1∑	n−1∑	PROPN
ejpam-6414	113	8	i=0	i=0	PROPN
ejpam-6414	113	9	aiθ	aiθ	NOUN
ejpam-6414	114	1	i	i	PRON
ejpam-6414	114	2	:	:	PUNCT
ejpam-6414	114	3	ai	ai	VERB
ejpam-6414	114	4	∈	∈	PROPN
ejpam-6414	114	5	fps	fps	PROPN
ejpam-6414	114	6	}	}	PUNCT
ejpam-6414	114	7	,	,	PUNCT
ejpam-6414	114	8	θn	θn	ADJ
ejpam-6414	114	9	=	=	NOUN
ejpam-6414	114	10	0	0	PROPN
ejpam-6414	114	11	.	.	PUNCT
ejpam-6414	115	1	every	every	DET
ejpam-6414	115	2	proper	proper	ADJ
ejpam-6414	115	3	ideal	ideal	NOUN
ejpam-6414	115	4	in	in	ADP
ejpam-6414	115	5	q	q	NOUN
ejpam-6414	115	6	-	-	PUNCT
ejpam-6414	115	7	gr	gr	NOUN
ejpam-6414	115	8	is	be	AUX
ejpam-6414	115	9	of	of	ADP
ejpam-6414	115	10	the	the	DET
ejpam-6414	115	11	form	form	NOUN
ejpam-6414	115	12	:	:	PUNCT
ejpam-6414	115	13	jk	jk	NOUN
ejpam-6414	115	14	=	=	SYM
ejpam-6414	115	15	θka(ps	θka(ps	NOUN
ejpam-6414	115	16	,	,	PUNCT
ejpam-6414	115	17	n	n	CCONJ
ejpam-6414	115	18	)	)	PUNCT
ejpam-6414	115	19	,	,	PUNCT
ejpam-6414	115	20	1	1	NUM
ejpam-6414	115	21	≤	≤	NUM
ejpam-6414	115	22	k	k	X
ejpam-6414	115	23	≤	≤	PROPN
ejpam-6414	115	24	n−	n−	PROPN
ejpam-6414	115	25	1	1	NUM
ejpam-6414	115	26	.	.	PUNCT
ejpam-6414	116	1	muhammad	muhammad	PROPN
ejpam-6414	116	2	sajjad	sajjad	PROPN
ejpam-6414	116	3	et	et	PROPN
ejpam-6414	116	4	al	al	PROPN
ejpam-6414	116	5	.	.	PUNCT
ejpam-6414	116	6	/	/	SYM
ejpam-6414	116	7	eur	eur	PROPN
ejpam-6414	116	8	.	.	PUNCT
ejpam-6414	117	1	j.	j.	PROPN
ejpam-6414	117	2	pure	pure	PROPN
ejpam-6414	117	3	appl	appl	PROPN
ejpam-6414	117	4	.	.	PROPN
ejpam-6414	117	5	math	math	PROPN
ejpam-6414	117	6	,	,	PUNCT
ejpam-6414	117	7	18	18	NUM
ejpam-6414	117	8	(	(	PUNCT
ejpam-6414	117	9	3	3	NUM
ejpam-6414	117	10	)	)	PUNCT
ejpam-6414	117	11	(	(	PUNCT
ejpam-6414	117	12	2025	2025	NUM
ejpam-6414	117	13	)	)	PUNCT
ejpam-6414	117	14	,	,	PUNCT
ejpam-6414	117	15	6414	6414	NUM
ejpam-6414	117	16	6	6	NUM
ejpam-6414	117	17	of	of	ADP
ejpam-6414	117	18	22	22	NUM
ejpam-6414	117	19	3	3	NUM
ejpam-6414	117	20	.	.	PUNCT
ejpam-6414	117	21	bch	bch	PROPN
ejpam-6414	117	22	code	code	PROPN
ejpam-6414	117	23	construction	construction	NOUN
ejpam-6414	117	24	over	over	ADP
ejpam-6414	117	25	qgr	qgr	NOUN
ejpam-6414	117	26	before	before	ADP
ejpam-6414	117	27	designing	design	VERB
ejpam-6414	117	28	bch	bch	PROPN
ejpam-6414	117	29	codes	code	NOUN
ejpam-6414	117	30	over	over	ADP
ejpam-6414	117	31	q	q	NOUN
ejpam-6414	117	32	-	-	PUNCT
ejpam-6414	117	33	grs	grs	PROPN
ejpam-6414	117	34	,	,	PUNCT
ejpam-6414	117	35	it	it	PRON
ejpam-6414	117	36	is	be	AUX
ejpam-6414	117	37	necessary	necessary	ADJ
ejpam-6414	117	38	to	to	PART
ejpam-6414	117	39	specify	specify	VERB
ejpam-6414	117	40	the	the	DET
ejpam-6414	117	41	galois	galois	PROPN
ejpam-6414	117	42	extension	extension	NOUN
ejpam-6414	117	43	of	of	ADP
ejpam-6414	117	44	q	q	NOUN
ejpam-6414	117	45	-	-	PUNCT
ejpam-6414	117	46	grs	grs	NOUN
ejpam-6414	117	47	in	in	ADP
ejpam-6414	117	48	order	order	NOUN
ejpam-6414	117	49	to	to	PART
ejpam-6414	117	50	factorize	factorize	VERB
ejpam-6414	117	51	xn	xn	PUNCT
ejpam-6414	118	1	−	−	PROPN
ejpam-6414	118	2	1	1	NUM
ejpam-6414	118	3	over	over	ADP
ejpam-6414	118	4	the	the	DET
ejpam-6414	118	5	group	group	NOUN
ejpam-6414	118	6	of	of	ADP
ejpam-6414	118	7	units	unit	NOUN
ejpam-6414	118	8	of	of	ADP
ejpam-6414	118	9	the	the	DET
ejpam-6414	118	10	applicable	applicable	ADJ
ejpam-6414	118	11	extension	extension	NOUN
ejpam-6414	118	12	ring	ring	NOUN
ejpam-6414	118	13	of	of	ADP
ejpam-6414	118	14	the	the	DET
ejpam-6414	118	15	known	know	VERB
ejpam-6414	118	16	local	local	ADJ
ejpam-6414	118	17	ring	ring	NOUN
ejpam-6414	118	18	(	(	PUNCT
ejpam-6414	118	19	qgr	qgr	NOUN
ejpam-6414	118	20	)	)	PUNCT
ejpam-6414	119	1	and	and	CCONJ
ejpam-6414	119	2	then	then	ADV
ejpam-6414	119	3	construct	construct	VERB
ejpam-6414	119	4	the	the	DET
ejpam-6414	119	5	generator	generator	NOUN
ejpam-6414	119	6	polynomial	polynomial	NOUN
ejpam-6414	119	7	for	for	ADP
ejpam-6414	119	8	the	the	DET
ejpam-6414	119	9	bch	bch	PROPN
ejpam-6414	119	10	code	code	PROPN
ejpam-6414	119	11	.	.	PUNCT
ejpam-6414	120	1	3.1	3.1	NUM
ejpam-6414	120	2	.	.	PUNCT
ejpam-6414	121	1	galois	galois	PROPN
ejpam-6414	121	2	extension	extension	NOUN
ejpam-6414	121	3	of	of	ADP
ejpam-6414	121	4	q	q	NOUN
ejpam-6414	121	5	-	-	PUNCT
ejpam-6414	121	6	gr	gr	NOUN
ejpam-6414	121	7	a(ps	a(ps	PROPN
ejpam-6414	121	8	,	,	PUNCT
ejpam-6414	121	9	n	n	CCONJ
ejpam-6414	121	10	)	)	PUNCT
ejpam-6414	121	11	let	let	AUX
ejpam-6414	121	12	a(ps	a(ps	NOUN
ejpam-6414	121	13	,	,	PUNCT
ejpam-6414	121	14	n	n	CCONJ
ejpam-6414	121	15	)	)	PUNCT
ejpam-6414	121	16	be	be	AUX
ejpam-6414	121	17	a	a	DET
ejpam-6414	121	18	class	class	NOUN
ejpam-6414	121	19	of	of	ADP
ejpam-6414	121	20	local	local	ADJ
ejpam-6414	121	21	finite	finite	NOUN
ejpam-6414	121	22	rings	ring	NOUN
ejpam-6414	121	23	with	with	ADP
ejpam-6414	121	24	a	a	DET
ejpam-6414	121	25	unique	unique	ADJ
ejpam-6414	121	26	maximal	maximal	ADJ
ejpam-6414	121	27	ideal	ideal	NOUN
ejpam-6414	121	28	m(ps	m(ps	PROPN
ejpam-6414	121	29	,	,	PUNCT
ejpam-6414	121	30	n	n	CCONJ
ejpam-6414	121	31	)	)	PUNCT
ejpam-6414	121	32	,	,	PUNCT
ejpam-6414	121	33	and	and	CCONJ
ejpam-6414	121	34	let	let	VERB
ejpam-6414	121	35	the	the	DET
ejpam-6414	121	36	residue	residue	NOUN
ejpam-6414	121	37	field	field	NOUN
ejpam-6414	121	38	be	be	VERB
ejpam-6414	121	39	:	:	PUNCT
ejpam-6414	121	40	k	k	X
ejpam-6414	121	41	=	=	SYM
ejpam-6414	121	42	a(ps	a(ps	PROPN
ejpam-6414	121	43	,	,	PUNCT
ejpam-6414	121	44	n)/m(ps	n)/m(ps	NOUN
ejpam-6414	121	45	,	,	PUNCT
ejpam-6414	121	46	n	n	CCONJ
ejpam-6414	121	47	)	)	PUNCT
ejpam-6414	121	48	∼=	∼=	PROPN
ejpam-6414	121	49	fps	fps	NOUN
ejpam-6414	121	50	.	.	PUNCT
ejpam-6414	122	1	consider	consider	VERB
ejpam-6414	122	2	the	the	DET
ejpam-6414	122	3	natural	natural	ADJ
ejpam-6414	122	4	projection	projection	NOUN
ejpam-6414	122	5	map	map	NOUN
ejpam-6414	122	6	,	,	PUNCT
ejpam-6414	122	7	π	π	X
ejpam-6414	122	8	:	:	PUNCT
ejpam-6414	122	9	a(ps	a(ps	NOUN
ejpam-6414	122	10	,	,	PUNCT
ejpam-6414	122	11	n)[x	n)[x	NOUN
ejpam-6414	122	12	]	]	PUNCT
ejpam-6414	122	13	→	→	SYM
ejpam-6414	122	14	k[x	k[x	PROPN
ejpam-6414	122	15	]	]	X
ejpam-6414	122	16	,	,	PUNCT
ejpam-6414	122	17	where	where	SCONJ
ejpam-6414	122	18	a(ps	a(ps	NOUN
ejpam-6414	122	19	,	,	PUNCT
ejpam-6414	122	20	n)[x	n)[x	NOUN
ejpam-6414	122	21	]	]	PUNCT
ejpam-6414	122	22	denotes	denote	VERB
ejpam-6414	122	23	the	the	DET
ejpam-6414	122	24	ring	ring	NOUN
ejpam-6414	122	25	of	of	ADP
ejpam-6414	122	26	polynomials	polynomial	NOUN
ejpam-6414	122	27	in	in	ADP
ejpam-6414	122	28	the	the	DET
ejpam-6414	122	29	variable	variable	NOUN
ejpam-6414	122	30	x	x	PUNCT
ejpam-6414	122	31	with	with	ADP
ejpam-6414	122	32	coefficients	coefficient	NOUN
ejpam-6414	122	33	from	from	ADP
ejpam-6414	122	34	a(ps	a(ps	PROPN
ejpam-6414	122	35	,	,	PUNCT
ejpam-6414	122	36	n	n	CCONJ
ejpam-6414	122	37	)	)	PUNCT
ejpam-6414	122	38	,	,	PUNCT
ejpam-6414	122	39	and	and	CCONJ
ejpam-6414	122	40	is	be	AUX
ejpam-6414	122	41	defined	define	VERB
ejpam-6414	122	42	by	by	ADP
ejpam-6414	122	43	:	:	PUNCT
ejpam-6414	122	44	π(a(x	π(a(x	NOUN
ejpam-6414	122	45	)	)	PUNCT
ejpam-6414	122	46	)	)	PUNCT
ejpam-6414	123	1	=	=	SYM
ejpam-6414	123	2	a(x	a(x	NOUN
ejpam-6414	123	3	)	)	PUNCT
ejpam-6414	123	4	.	.	PUNCT
ejpam-6414	124	1	if	if	SCONJ
ejpam-6414	124	2	f(x	f(x	PROPN
ejpam-6414	124	3	)	)	PUNCT
ejpam-6414	124	4	is	be	AUX
ejpam-6414	124	5	a	a	DET
ejpam-6414	124	6	monic	monic	ADJ
ejpam-6414	124	7	polynomial	polynomial	NOUN
ejpam-6414	124	8	of	of	ADP
ejpam-6414	124	9	degree	degree	NOUN
ejpam-6414	124	10	m	m	VERB
ejpam-6414	124	11	such	such	ADJ
ejpam-6414	124	12	that	that	SCONJ
ejpam-6414	124	13	π(f(x	π(f(x	NOUN
ejpam-6414	124	14	)	)	PUNCT
ejpam-6414	124	15	)	)	PUNCT
ejpam-6414	124	16	is	be	AUX
ejpam-6414	124	17	irreducible	irreducible	ADJ
ejpam-6414	124	18	over	over	ADP
ejpam-6414	124	19	the	the	DET
ejpam-6414	124	20	residue	residue	NOUN
ejpam-6414	124	21	field	field	NOUN
ejpam-6414	125	1	k	k	NOUN
ejpam-6414	125	2	,	,	PUNCT
ejpam-6414	125	3	then	then	ADV
ejpam-6414	125	4	f(x	f(x	PROPN
ejpam-6414	125	5	)	)	PUNCT
ejpam-6414	125	6	is	be	AUX
ejpam-6414	125	7	irreducible	irreducible	ADJ
ejpam-6414	125	8	over	over	ADP
ejpam-6414	125	9	a(ps	a(ps	PROPN
ejpam-6414	125	10	,	,	PUNCT
ejpam-6414	125	11	n	n	CCONJ
ejpam-6414	125	12	)	)	PUNCT
ejpam-6414	125	13	.	.	PUNCT
ejpam-6414	126	1	the	the	DET
ejpam-6414	126	2	ring	ring	NOUN
ejpam-6414	126	3	r	r	NOUN
ejpam-6414	126	4	=	=	SYM
ejpam-6414	126	5	a(ps	a(ps	NOUN
ejpam-6414	126	6	,	,	PUNCT
ejpam-6414	126	7	n)[x	n)[x	NOUN
ejpam-6414	126	8	]	]	PUNCT
ejpam-6414	126	9	⟨f(x)⟩	⟨f(x)⟩	PRON
ejpam-6414	126	10	is	be	AUX
ejpam-6414	126	11	called	call	VERB
ejpam-6414	126	12	the	the	DET
ejpam-6414	126	13	galois	galois	PROPN
ejpam-6414	126	14	extension	extension	NOUN
ejpam-6414	126	15	of	of	ADP
ejpam-6414	126	16	the	the	DET
ejpam-6414	126	17	q	q	NOUN
ejpam-6414	126	18	-	-	PUNCT
ejpam-6414	126	19	gr	gr	NOUN
ejpam-6414	126	20	a(ps	a(ps	PROPN
ejpam-6414	126	21	,	,	PUNCT
ejpam-6414	126	22	n	n	CCONJ
ejpam-6414	126	23	)	)	PUNCT
ejpam-6414	126	24	,	,	PUNCT
ejpam-6414	126	25	and	and	CCONJ
ejpam-6414	126	26	consists	consist	VERB
ejpam-6414	126	27	of	of	ADP
ejpam-6414	126	28	the	the	DET
ejpam-6414	126	29	collection	collection	NOUN
ejpam-6414	126	30	of	of	ADP
ejpam-6414	126	31	residue	residue	NOUN
ejpam-6414	126	32	class	class	NOUN
ejpam-6414	126	33	polynomials	polynomial	NOUN
ejpam-6414	126	34	in	in	ADP
ejpam-6414	126	35	the	the	DET
ejpam-6414	126	36	variable	variable	NOUN
ejpam-6414	126	37	x	x	NOUN
ejpam-6414	126	38	over	over	ADP
ejpam-6414	126	39	a(ps	a(ps	PROPN
ejpam-6414	126	40	,	,	PUNCT
ejpam-6414	126	41	n	n	CCONJ
ejpam-6414	126	42	)	)	PUNCT
ejpam-6414	126	43	,	,	PUNCT
ejpam-6414	126	44	modulo	modulo	VERB
ejpam-6414	126	45	the	the	DET
ejpam-6414	126	46	polynomial	polynomial	ADJ
ejpam-6414	126	47	f(x	f(x	PROPN
ejpam-6414	126	48	)	)	PUNCT
ejpam-6414	126	49	.	.	PUNCT
ejpam-6414	127	1	the	the	DET
ejpam-6414	127	2	elements	element	NOUN
ejpam-6414	127	3	of	of	ADP
ejpam-6414	127	4	r	r	NOUN
ejpam-6414	127	5	are	be	AUX
ejpam-6414	127	6	of	of	ADP
ejpam-6414	127	7	the	the	DET
ejpam-6414	127	8	form	form	NOUN
ejpam-6414	127	9	:	:	PUNCT
ejpam-6414	127	10	r	r	NOUN
ejpam-6414	127	11	=	=	PUNCT
ejpam-6414	127	12	{	{	PUNCT
ejpam-6414	127	13	m−1∑	m−1∑	PROPN
ejpam-6414	127	14	i=0	i=0	PROPN
ejpam-6414	127	15	ciα	ciα	PROPN
ejpam-6414	128	1	i	i	PRON
ejpam-6414	128	2	:	:	PUNCT
ejpam-6414	128	3	ci	ci	PROPN
ejpam-6414	128	4	∈	∈	PROPN
ejpam-6414	128	5	a(ps	a(ps	PROPN
ejpam-6414	128	6	,	,	PUNCT
ejpam-6414	128	7	n	n	CCONJ
ejpam-6414	128	8	)	)	PUNCT
ejpam-6414	128	9	}	}	PUNCT
ejpam-6414	128	10	,	,	PUNCT
ejpam-6414	128	11	where	where	SCONJ
ejpam-6414	128	12	α	α	NOUN
ejpam-6414	128	13	is	be	AUX
ejpam-6414	128	14	a	a	DET
ejpam-6414	128	15	root	root	NOUN
ejpam-6414	128	16	of	of	ADP
ejpam-6414	128	17	f(x	f(x	PROPN
ejpam-6414	128	18	)	)	PUNCT
ejpam-6414	128	19	,	,	PUNCT
ejpam-6414	128	20	i.e.	i.e.	X
ejpam-6414	128	21	,	,	PUNCT
ejpam-6414	128	22	f(α	f(α	NOUN
ejpam-6414	128	23	)	)	PUNCT
ejpam-6414	128	24	=	=	SYM
ejpam-6414	129	1	0	0	X
ejpam-6414	129	2	.	.	PUNCT
ejpam-6414	130	1	let	let	VERB
ejpam-6414	130	2	r∗	r∗	PROPN
ejpam-6414	130	3	be	be	AUX
ejpam-6414	130	4	the	the	DET
ejpam-6414	130	5	multiplicative	multiplicative	ADJ
ejpam-6414	130	6	abelian	abelian	ADJ
ejpam-6414	130	7	group	group	NOUN
ejpam-6414	130	8	of	of	ADP
ejpam-6414	130	9	the	the	DET
ejpam-6414	130	10	units	unit	NOUN
ejpam-6414	130	11	of	of	ADP
ejpam-6414	130	12	r	r	NOUN
ejpam-6414	130	13	,	,	PUNCT
ejpam-6414	130	14	which	which	PRON
ejpam-6414	130	15	can	can	AUX
ejpam-6414	130	16	be	be	AUX
ejpam-6414	130	17	expressed	express	VERB
ejpam-6414	130	18	as	as	ADP
ejpam-6414	130	19	the	the	DET
ejpam-6414	130	20	direct	direct	ADJ
ejpam-6414	130	21	product	product	NOUN
ejpam-6414	130	22	of	of	ADP
ejpam-6414	130	23	subgroups	subgroup	NOUN
ejpam-6414	130	24	.	.	PUNCT
ejpam-6414	131	1	a	a	DET
ejpam-6414	131	2	cyclic	cyclic	ADJ
ejpam-6414	131	3	subgroup	subgroup	NOUN
ejpam-6414	131	4	of	of	ADP
ejpam-6414	131	5	r∗	r∗	PROPN
ejpam-6414	131	6	is	be	AUX
ejpam-6414	131	7	denoted	denote	VERB
ejpam-6414	131	8	by	by	ADP
ejpam-6414	131	9	gs	gs	X
ejpam-6414	131	10	.	.	PUNCT
ejpam-6414	132	1	the	the	DET
ejpam-6414	132	2	unit	unit	NOUN
ejpam-6414	132	3	elements	element	NOUN
ejpam-6414	132	4	of	of	ADP
ejpam-6414	132	5	r	r	NOUN
ejpam-6414	132	6	can	can	AUX
ejpam-6414	132	7	be	be	AUX
ejpam-6414	132	8	described	describe	VERB
ejpam-6414	132	9	as	as	ADP
ejpam-6414	132	10	:	:	PUNCT
ejpam-6414	132	11	r∗	r∗	PROPN
ejpam-6414	132	12	=	=	PUNCT
ejpam-6414	132	13	{	{	PUNCT
ejpam-6414	132	14	x	x	PUNCT
ejpam-6414	132	15	=	=	SYM
ejpam-6414	132	16	c0	c0	PROPN
ejpam-6414	132	17	+	+	CCONJ
ejpam-6414	132	18	c1α+	c1α+	PROPN
ejpam-6414	132	19	·	·	PUNCT
ejpam-6414	132	20	·	·	PUNCT
ejpam-6414	132	21	·	·	PUNCT
ejpam-6414	133	1	+	+	NUM
ejpam-6414	133	2	cm−1α	cm−1α	X
ejpam-6414	133	3	m−1	m−1	PROPN
ejpam-6414	133	4	∈	∈	PROPN
ejpam-6414	133	5	r	r	NOUN
ejpam-6414	133	6	:	:	PUNCT
ejpam-6414	133	7	∃ci	∃ci	NOUN
ejpam-6414	133	8	∈	∈	PROPN
ejpam-6414	133	9	u(a(ps	u(a(ps	NOUN
ejpam-6414	133	10	,	,	PUNCT
ejpam-6414	133	11	n	n	CCONJ
ejpam-6414	133	12	)	)	PUNCT
ejpam-6414	133	13	)	)	PUNCT
ejpam-6414	133	14	for	for	ADP
ejpam-6414	133	15	i	i	PROPN
ejpam-6414	133	16	=	=	SYM
ejpam-6414	133	17	0	0	NUM
ejpam-6414	133	18	,	,	PUNCT
ejpam-6414	133	19	1	1	NUM
ejpam-6414	133	20	,	,	PUNCT
ejpam-6414	133	21	.	.	PUNCT
ejpam-6414	133	22	.	.	PUNCT
ejpam-6414	133	23	.	.	PUNCT
ejpam-6414	134	1	,	,	PUNCT
ejpam-6414	134	2	m−	m−	PROPN
ejpam-6414	134	3	1	1	NUM
ejpam-6414	134	4	}	}	PUNCT
ejpam-6414	134	5	,	,	PUNCT
ejpam-6414	134	6	where	where	SCONJ
ejpam-6414	134	7	u(a(ps	u(a(ps	NOUN
ejpam-6414	134	8	,	,	PUNCT
ejpam-6414	134	9	n	n	CCONJ
ejpam-6414	134	10	)	)	PUNCT
ejpam-6414	134	11	)	)	PUNCT
ejpam-6414	134	12	indicates	indicate	VERB
ejpam-6414	134	13	the	the	DET
ejpam-6414	134	14	group	group	NOUN
ejpam-6414	134	15	of	of	ADP
ejpam-6414	134	16	units	unit	NOUN
ejpam-6414	134	17	of	of	ADP
ejpam-6414	134	18	the	the	DET
ejpam-6414	134	19	q	q	NOUN
ejpam-6414	134	20	-	-	PUNCT
ejpam-6414	134	21	gr	gr	NOUN
ejpam-6414	134	22	a(ps	a(ps	PROPN
ejpam-6414	134	23	,	,	PUNCT
ejpam-6414	134	24	n	n	CCONJ
ejpam-6414	134	25	)	)	PUNCT
ejpam-6414	134	26	.	.	PUNCT
ejpam-6414	135	1	on	on	ADP
ejpam-6414	135	2	the	the	DET
ejpam-6414	135	3	other	other	ADJ
ejpam-6414	135	4	hand	hand	NOUN
ejpam-6414	135	5	,	,	PUNCT
ejpam-6414	135	6	the	the	DET
ejpam-6414	135	7	nilradical	nilradical	ADJ
ejpam-6414	135	8	of	of	ADP
ejpam-6414	135	9	r	r	NOUN
ejpam-6414	135	10	,	,	PUNCT
ejpam-6414	135	11	denoted	denote	VERB
ejpam-6414	135	12	by	by	ADP
ejpam-6414	135	13	nil(r	nil(r	PROPN
ejpam-6414	135	14	)	)	PUNCT
ejpam-6414	135	15	,	,	PUNCT
ejpam-6414	135	16	is	be	AUX
ejpam-6414	135	17	defined	define	VERB
ejpam-6414	135	18	as	as	ADP
ejpam-6414	135	19	:	:	PUNCT
ejpam-6414	135	20	nil(r	nil(r	NUM
ejpam-6414	135	21	)	)	PUNCT
ejpam-6414	135	22	=	=	PRON
ejpam-6414	135	23	{	{	PUNCT
ejpam-6414	135	24	c0	c0	NOUN
ejpam-6414	135	25	+	+	CCONJ
ejpam-6414	135	26	c1α+	c1α+	PROPN
ejpam-6414	135	27	·	·	PUNCT
ejpam-6414	135	28	·	·	PUNCT
ejpam-6414	135	29	·	·	PUNCT
ejpam-6414	136	1	+	+	NUM
ejpam-6414	136	2	cm−1α	cm−1α	X
ejpam-6414	136	3	m−1	m−1	PROPN
ejpam-6414	136	4	:	:	PUNCT
ejpam-6414	136	5	ci	ci	PROPN
ejpam-6414	136	6	∈	∈	PROPN
ejpam-6414	136	7	nil(a(ps	nil(a(ps	NOUN
ejpam-6414	136	8	,	,	PUNCT
ejpam-6414	136	9	n	n	CCONJ
ejpam-6414	136	10	)	)	PUNCT
ejpam-6414	136	11	)	)	PUNCT
ejpam-6414	136	12	}	}	PUNCT
ejpam-6414	136	13	.	.	PUNCT
ejpam-6414	137	1	similarly	similarly	ADV
ejpam-6414	137	2	,	,	PUNCT
ejpam-6414	137	3	the	the	DET
ejpam-6414	137	4	extension	extension	NOUN
ejpam-6414	137	5	of	of	ADP
ejpam-6414	137	6	the	the	DET
ejpam-6414	137	7	residue	residue	NOUN
ejpam-6414	137	8	field	field	NOUN
ejpam-6414	137	9	k	k	PROPN
ejpam-6414	137	10	of	of	ADP
ejpam-6414	137	11	a(ps	a(ps	PROPN
ejpam-6414	137	12	,	,	PUNCT
ejpam-6414	137	13	n	n	CCONJ
ejpam-6414	137	14	)	)	PUNCT
ejpam-6414	137	15	is	be	AUX
ejpam-6414	137	16	:	:	PUNCT
ejpam-6414	137	17	k	k	X
ejpam-6414	137	18	′	′	NUM
ejpam-6414	138	1	=	=	PUNCT
ejpam-6414	138	2	(	(	PUNCT
ejpam-6414	138	3	a(ps	a(ps	PROPN
ejpam-6414	138	4	,	,	PUNCT
ejpam-6414	138	5	n)/m(ps	n)/m(ps	PROPN
ejpam-6414	138	6	,	,	PUNCT
ejpam-6414	138	7	n))[x	n))[x	X
ejpam-6414	138	8	]	]	PUNCT
ejpam-6414	138	9	⟨π(f(x))⟩	⟨π(f(x))⟩	NOUN
ejpam-6414	138	10	=	=	SYM
ejpam-6414	138	11	k[x	k[x	PROPN
ejpam-6414	138	12	]	]	X
ejpam-6414	138	13	⟨π(f(x))⟩	⟨π(f(x))⟩	PUNCT
ejpam-6414	138	14	,	,	PUNCT
ejpam-6414	138	15	which	which	PRON
ejpam-6414	138	16	has	have	VERB
ejpam-6414	138	17	cardinality	cardinality	NOUN
ejpam-6414	138	18	pms	pm	NOUN
ejpam-6414	138	19	.	.	PUNCT
ejpam-6414	139	1	the	the	DET
ejpam-6414	139	2	multiplicative	multiplicative	ADJ
ejpam-6414	139	3	group	group	NOUN
ejpam-6414	139	4	of	of	ADP
ejpam-6414	139	5	units	unit	NOUN
ejpam-6414	139	6	in	in	ADP
ejpam-6414	139	7	k	k	PROPN
ejpam-6414	139	8	′	′	NUM
ejpam-6414	139	9	is	be	AUX
ejpam-6414	139	10	denoted	denote	VERB
ejpam-6414	139	11	by	by	ADP
ejpam-6414	139	12	k	k	PROPN
ejpam-6414	139	13	′∗.	′∗.	PROPN
ejpam-6414	139	14	muhammad	muhammad	PROPN
ejpam-6414	139	15	sajjad	sajjad	PROPN
ejpam-6414	139	16	et	et	PROPN
ejpam-6414	139	17	al	al	PROPN
ejpam-6414	139	18	.	.	PUNCT
ejpam-6414	139	19	/	/	SYM
ejpam-6414	139	20	eur	eur	PROPN
ejpam-6414	139	21	.	.	PUNCT
ejpam-6414	140	1	j.	j.	PROPN
ejpam-6414	140	2	pure	pure	PROPN
ejpam-6414	140	3	appl	appl	PROPN
ejpam-6414	140	4	.	.	PROPN
ejpam-6414	140	5	math	math	PROPN
ejpam-6414	140	6	,	,	PUNCT
ejpam-6414	140	7	18	18	NUM
ejpam-6414	140	8	(	(	PUNCT
ejpam-6414	140	9	3	3	NUM
ejpam-6414	140	10	)	)	PUNCT
ejpam-6414	140	11	(	(	PUNCT
ejpam-6414	140	12	2025	2025	NUM
ejpam-6414	140	13	)	)	PUNCT
ejpam-6414	140	14	,	,	PUNCT
ejpam-6414	140	15	6414	6414	NUM
ejpam-6414	140	16	7	7	NUM
ejpam-6414	140	17	of	of	ADP
ejpam-6414	140	18	22	22	NUM
ejpam-6414	140	19	3.2	3.2	NUM
ejpam-6414	140	20	.	.	PUNCT
ejpam-6414	141	1	generator	generator	NOUN
ejpam-6414	141	2	polynomial	polynomial	PROPN
ejpam-6414	141	3	of	of	ADP
ejpam-6414	141	4	bch	bch	PROPN
ejpam-6414	141	5	codes	code	NOUN
ejpam-6414	141	6	using	use	VERB
ejpam-6414	141	7	maximal	maximal	ADJ
ejpam-6414	141	8	cyclic	cyclic	ADJ
ejpam-6414	141	9	subgroup	subgroup	NOUN
ejpam-6414	141	10	of	of	ADP
ejpam-6414	141	11	group	group	NOUN
ejpam-6414	141	12	units	unit	NOUN
ejpam-6414	141	13	of	of	ADP
ejpam-6414	141	14	q	q	NOUN
ejpam-6414	141	15	-	-	PUNCT
ejpam-6414	141	16	gr	gr	ADP
ejpam-6414	141	17	the	the	DET
ejpam-6414	141	18	generator	generator	NOUN
ejpam-6414	141	19	polynomial	polynomial	NOUN
ejpam-6414	141	20	of	of	ADP
ejpam-6414	141	21	a	a	DET
ejpam-6414	141	22	bch	bch	PROPN
ejpam-6414	141	23	code	code	NOUN
ejpam-6414	141	24	of	of	ADP
ejpam-6414	141	25	length	length	NOUN
ejpam-6414	141	26	n	n	NUM
ejpam-6414	141	27	is	be	AUX
ejpam-6414	141	28	defined	define	VERB
ejpam-6414	141	29	as	as	ADP
ejpam-6414	141	30	g(x	g(x	NOUN
ejpam-6414	141	31	)	)	PUNCT
ejpam-6414	141	32	=	=	SYM
ejpam-6414	141	33	lcm{mi(x	lcm{mi(x	PROPN
ejpam-6414	141	34	)	)	PUNCT
ejpam-6414	141	35	:	:	PUNCT
ejpam-6414	142	1	i	i	PRON
ejpam-6414	142	2	=	=	SYM
ejpam-6414	142	3	c	c	X
ejpam-6414	142	4	,	,	PUNCT
ejpam-6414	142	5	c+	c+	VERB
ejpam-6414	142	6	1	1	NUM
ejpam-6414	142	7	,	,	PUNCT
ejpam-6414	142	8	.	.	PUNCT
ejpam-6414	142	9	.	.	PUNCT
ejpam-6414	143	1	.	.	PUNCT
ejpam-6414	144	1	,	,	PUNCT
ejpam-6414	144	2	c+	c+	VERB
ejpam-6414	144	3	d−	d−	PROPN
ejpam-6414	144	4	2	2	NUM
ejpam-6414	144	5	}	}	PUNCT
ejpam-6414	144	6	,	,	PUNCT
ejpam-6414	144	7	where	where	SCONJ
ejpam-6414	144	8	mi(x	mi(x	NOUN
ejpam-6414	144	9	)	)	PUNCT
ejpam-6414	144	10	are	be	AUX
ejpam-6414	144	11	the	the	DET
ejpam-6414	144	12	minimal	minimal	ADJ
ejpam-6414	144	13	polynomials	polynomial	NOUN
ejpam-6414	144	14	corresponding	correspond	VERB
ejpam-6414	144	15	to	to	ADP
ejpam-6414	144	16	each	each	DET
ejpam-6414	144	17	ψi	ψi	NOUN
ejpam-6414	144	18	,	,	PUNCT
ejpam-6414	144	19	for	for	ADP
ejpam-6414	144	20	i	i	PROPN
ejpam-6414	144	21	=	=	SYM
ejpam-6414	144	22	1	1	NUM
ejpam-6414	144	23	,	,	PUNCT
ejpam-6414	144	24	2	2	NUM
ejpam-6414	144	25	,	,	PUNCT
ejpam-6414	144	26	.	.	PUNCT
ejpam-6414	144	27	.	.	PUNCT
ejpam-6414	145	1	.	.	PUNCT
ejpam-6414	146	1	,	,	PUNCT
ejpam-6414	146	2	d−	d−	PROPN
ejpam-6414	146	3	1	1	NUM
ejpam-6414	146	4	.	.	PUNCT
ejpam-6414	147	1	the	the	DET
ejpam-6414	147	2	parity	parity	NOUN
ejpam-6414	147	3	-	-	PUNCT
ejpam-6414	147	4	check	check	NOUN
ejpam-6414	147	5	matrix	matrix	NOUN
ejpam-6414	147	6	h	h	NOUN
ejpam-6414	147	7	of	of	ADP
ejpam-6414	147	8	the	the	DET
ejpam-6414	147	9	bch	bch	PROPN
ejpam-6414	147	10	code	code	PROPN
ejpam-6414	147	11	with	with	ADP
ejpam-6414	147	12	the	the	DET
ejpam-6414	147	13	generator	generator	NOUN
ejpam-6414	147	14	polynomial	polynomial	ADJ
ejpam-6414	147	15	g(x	g(x	PROPN
ejpam-6414	147	16	)	)	PUNCT
ejpam-6414	147	17	is	be	AUX
ejpam-6414	147	18	given	give	VERB
ejpam-6414	147	19	by	by	ADP
ejpam-6414	147	20	:	:	PUNCT
ejpam-6414	147	21	h	h	PROPN
ejpam-6414	147	22	=	=	SYM
ejpam-6414	147	23	1	1	PROPN
ejpam-6414	147	24	ψc	ψc	VERB
ejpam-6414	147	25	ψ2c	ψ2c	PROPN
ejpam-6414	147	26	·	·	PUNCT
ejpam-6414	147	27	·	·	PUNCT
ejpam-6414	147	28	·	·	PUNCT
ejpam-6414	147	29	ψ(n−1)c	ψ(n−1)c	NOUN
ejpam-6414	147	30	...	...	PUNCT
ejpam-6414	147	31	...	...	PUNCT
ejpam-6414	147	32	...	...	PUNCT
ejpam-6414	147	33	.	.	PUNCT
ejpam-6414	147	34	.	.	PUNCT
ejpam-6414	147	35	.	.	PUNCT
ejpam-6414	148	1	...	...	PUNCT
ejpam-6414	149	1	1	1	NUM
ejpam-6414	149	2	ψc+d−2	ψc+d−2	NOUN
ejpam-6414	149	3	ψ2(c+d−2	ψ2(c+d−2	NOUN
ejpam-6414	149	4	)	)	PUNCT
ejpam-6414	149	5	·	·	PUNCT
ejpam-6414	149	6	·	·	PUNCT
ejpam-6414	149	7	·	·	PUNCT
ejpam-6414	149	8	ψ(n−1)(c+d−2	ψ(n−1)(c+d−2	X
ejpam-6414	149	9	)	)	PUNCT
ejpam-6414	149	10			PROPN
ejpam-6414	149	11	.	.	PUNCT
ejpam-6414	150	1	equivalently	equivalently	ADV
ejpam-6414	150	2	,	,	PUNCT
ejpam-6414	150	3	the	the	DET
ejpam-6414	150	4	code	code	NOUN
ejpam-6414	150	5	c	c	PROPN
ejpam-6414	150	6	is	be	AUX
ejpam-6414	150	7	the	the	DET
ejpam-6414	150	8	null	null	ADJ
ejpam-6414	150	9	space	space	NOUN
ejpam-6414	150	10	of	of	ADP
ejpam-6414	150	11	the	the	DET
ejpam-6414	150	12	matrix	matrix	NOUN
ejpam-6414	150	13	h.	h.	NOUN
ejpam-6414	151	1	the	the	DET
ejpam-6414	151	2	following	follow	VERB
ejpam-6414	151	3	steps	step	NOUN
ejpam-6414	151	4	are	be	AUX
ejpam-6414	151	5	used	use	VERB
ejpam-6414	151	6	to	to	PART
ejpam-6414	151	7	construct	construct	VERB
ejpam-6414	151	8	the	the	DET
ejpam-6414	151	9	generator	generator	NOUN
ejpam-6414	151	10	polynomial	polynomial	NOUN
ejpam-6414	151	11	of	of	ADP
ejpam-6414	151	12	an	an	DET
ejpam-6414	151	13	n	n	CCONJ
ejpam-6414	151	14	-	-	PUNCT
ejpam-6414	151	15	length	length	NOUN
ejpam-6414	151	16	bch	bch	PROPN
ejpam-6414	151	17	code	code	NOUN
ejpam-6414	151	18	over	over	ADP
ejpam-6414	151	19	a	a	DET
ejpam-6414	151	20	galois	galois	PROPN
ejpam-6414	151	21	ring	ring	NOUN
ejpam-6414	151	22	:	:	PUNCT
ejpam-6414	151	23	(	(	PUNCT
ejpam-6414	151	24	i	i	NOUN
ejpam-6414	151	25	)	)	PUNCT
ejpam-6414	151	26	create	create	VERB
ejpam-6414	151	27	the	the	DET
ejpam-6414	151	28	maximal	maximal	ADJ
ejpam-6414	151	29	cyclic	cyclic	ADJ
ejpam-6414	151	30	subgroup	subgroup	NOUN
ejpam-6414	151	31	of	of	ADP
ejpam-6414	151	32	the	the	DET
ejpam-6414	151	33	group	group	NOUN
ejpam-6414	151	34	of	of	ADP
ejpam-6414	151	35	units	unit	NOUN
ejpam-6414	151	36	of	of	ADP
ejpam-6414	151	37	order	order	NOUN
ejpam-6414	151	38	n.	n.	NOUN
ejpam-6414	151	39	(	(	PUNCT
ejpam-6414	151	40	ii	ii	NOUN
ejpam-6414	151	41	)	)	PUNCT
ejpam-6414	151	42	compute	compute	VERB
ejpam-6414	151	43	the	the	DET
ejpam-6414	151	44	minimal	minimal	ADJ
ejpam-6414	151	45	polynomials	polynomial	NOUN
ejpam-6414	151	46	for	for	ADP
ejpam-6414	151	47	each	each	DET
ejpam-6414	151	48	design	design	NOUN
ejpam-6414	151	49	distance	distance	NOUN
ejpam-6414	151	50	.	.	PUNCT
ejpam-6414	152	1	(	(	PUNCT
ejpam-6414	152	2	iii	iii	NOUN
ejpam-6414	152	3	)	)	PUNCT
ejpam-6414	152	4	find	find	VERB
ejpam-6414	152	5	the	the	DET
ejpam-6414	152	6	least	least	ADV
ejpam-6414	152	7	common	common	ADJ
ejpam-6414	152	8	multiple	multiple	NOUN
ejpam-6414	152	9	of	of	ADP
ejpam-6414	152	10	all	all	DET
ejpam-6414	152	11	the	the	DET
ejpam-6414	152	12	minimal	minimal	ADJ
ejpam-6414	152	13	polynomials	polynomial	NOUN
ejpam-6414	152	14	.	.	PUNCT
ejpam-6414	153	1	the	the	DET
ejpam-6414	153	2	pseudocode	pseudocode	NOUN
ejpam-6414	153	3	for	for	ADP
ejpam-6414	153	4	construction	construction	NOUN
ejpam-6414	153	5	of	of	ADP
ejpam-6414	153	6	bch	bch	PROPN
ejpam-6414	153	7	codes	code	NOUN
ejpam-6414	153	8	over	over	ADP
ejpam-6414	153	9	the	the	DET
ejpam-6414	153	10	quasi	quasi	ADJ
ejpam-6414	153	11	-	-	ADJ
ejpam-6414	153	12	galois	galois	ADJ
ejpam-6414	153	13	ring	ring	NOUN
ejpam-6414	153	14	is	be	AUX
ejpam-6414	153	15	given	give	VERB
ejpam-6414	153	16	in	in	ADP
ejpam-6414	153	17	algorithm	algorithm	NOUN
ejpam-6414	153	18	1	1	NUM
ejpam-6414	153	19	.	.	PUNCT
ejpam-6414	153	20	example	example	NOUN
ejpam-6414	153	21	3.1	3.1	NUM
ejpam-6414	153	22	:	:	PUNCT
ejpam-6414	153	23	bch	bch	PROPN
ejpam-6414	153	24	codes	code	NOUN
ejpam-6414	153	25	over	over	ADP
ejpam-6414	153	26	a(2	a(2	PROPN
ejpam-6414	153	27	,	,	PUNCT
ejpam-6414	153	28	2	2	NUM
ejpam-6414	153	29	)	)	PUNCT
ejpam-6414	153	30	let	let	VERB
ejpam-6414	153	31	a(2	a(2	PROPN
ejpam-6414	153	32	,	,	PUNCT
ejpam-6414	153	33	2	2	NUM
ejpam-6414	153	34	)	)	PUNCT
ejpam-6414	153	35	be	be	AUX
ejpam-6414	153	36	a	a	DET
ejpam-6414	153	37	quasi	quasi	ADJ
ejpam-6414	153	38	-	-	ADJ
ejpam-6414	153	39	galois	galois	ADJ
ejpam-6414	153	40	ring	ring	NOUN
ejpam-6414	153	41	(	(	PUNCT
ejpam-6414	153	42	qgrs	qgrs	PROPN
ejpam-6414	153	43	)	)	PUNCT
ejpam-6414	153	44	,	,	PUNCT
ejpam-6414	153	45	defined	define	VERB
ejpam-6414	153	46	as	as	ADP
ejpam-6414	153	47	:	:	PUNCT
ejpam-6414	153	48	a(2	a(2	ADJ
ejpam-6414	153	49	,	,	PUNCT
ejpam-6414	153	50	2	2	NUM
ejpam-6414	153	51	)	)	PUNCT
ejpam-6414	154	1	=	=	SYM
ejpam-6414	154	2	f2[y	f2[y	PROPN
ejpam-6414	154	3	]	]	PUNCT
ejpam-6414	154	4	⟨y2⟩	⟨y2⟩	NOUN
ejpam-6414	155	1	=	=	X
ejpam-6414	155	2	{	{	PUNCT
ejpam-6414	155	3	1∑	1∑	PROPN
ejpam-6414	155	4	i=0	i=0	PROPN
ejpam-6414	155	5	aiθ	aiθ	PROPN
ejpam-6414	155	6	i	i	PRON
ejpam-6414	155	7	:	:	PUNCT
ejpam-6414	156	1	ai	ai	VERB
ejpam-6414	156	2	∈	∈	PROPN
ejpam-6414	156	3	f2	f2	PROPN
ejpam-6414	156	4	,	,	PUNCT
ejpam-6414	156	5	θ	θ	PROPN
ejpam-6414	156	6	2	2	NUM
ejpam-6414	156	7	=	=	SYM
ejpam-6414	156	8	0	0	NUM
ejpam-6414	156	9	mod	mod	NOUN
ejpam-6414	156	10	2	2	NUM
ejpam-6414	156	11	}	}	PUNCT
ejpam-6414	156	12	=	=	SYM
ejpam-6414	156	13	{	{	PUNCT
ejpam-6414	156	14	a0	a0	NOUN
ejpam-6414	156	15	+	+	CCONJ
ejpam-6414	156	16	a1θ	a1θ	PROPN
ejpam-6414	156	17	:	:	PUNCT
ejpam-6414	156	18	a0	a0	PROPN
ejpam-6414	156	19	,	,	PUNCT
ejpam-6414	156	20	a1	a1	NOUN
ejpam-6414	156	21	∈	∈	PROPN
ejpam-6414	156	22	f2	f2	NOUN
ejpam-6414	156	23	=	=	SYM
ejpam-6414	156	24	{	{	PUNCT
ejpam-6414	156	25	0	0	NUM
ejpam-6414	156	26	,	,	PUNCT
ejpam-6414	156	27	1	1	NUM
ejpam-6414	156	28	}	}	PUNCT
ejpam-6414	156	29	}	}	PUNCT
ejpam-6414	156	30	=	=	SYM
ejpam-6414	156	31	{	{	PUNCT
ejpam-6414	156	32	0	0	NUM
ejpam-6414	156	33	,	,	PUNCT
ejpam-6414	156	34	1	1	NUM
ejpam-6414	156	35	,	,	PUNCT
ejpam-6414	156	36	θ	θ	PROPN
ejpam-6414	156	37	,	,	PUNCT
ejpam-6414	156	38	1+θ	1+θ	NUM
ejpam-6414	156	39	}	}	PUNCT
ejpam-6414	156	40	.	.	PUNCT
ejpam-6414	157	1	the	the	DET
ejpam-6414	157	2	group	group	NOUN
ejpam-6414	157	3	of	of	ADP
ejpam-6414	157	4	units	unit	NOUN
ejpam-6414	157	5	in	in	ADP
ejpam-6414	157	6	a(2	a(2	PROPN
ejpam-6414	157	7	,	,	PUNCT
ejpam-6414	157	8	2	2	NUM
ejpam-6414	157	9	)	)	PUNCT
ejpam-6414	157	10	is	be	AUX
ejpam-6414	157	11	:	:	PUNCT
ejpam-6414	157	12	u(a(2	u(a(2	ADP
ejpam-6414	157	13	,	,	PUNCT
ejpam-6414	157	14	2	2	NUM
ejpam-6414	157	15	)	)	PUNCT
ejpam-6414	157	16	)	)	PUNCT
ejpam-6414	158	1	=	=	PRON
ejpam-6414	158	2	{	{	PUNCT
ejpam-6414	158	3	1	1	NUM
ejpam-6414	158	4	,	,	PUNCT
ejpam-6414	158	5	1	1	NUM
ejpam-6414	158	6	+	+	NUM
ejpam-6414	158	7	θ	θ	NOUN
ejpam-6414	158	8	}	}	PUNCT
ejpam-6414	158	9	.	.	PUNCT
ejpam-6414	159	1	basic	basic	ADJ
ejpam-6414	159	2	irreducible	irreducible	ADJ
ejpam-6414	159	3	polynomial	polynomial	NOUN
ejpam-6414	159	4	in	in	ADP
ejpam-6414	159	5	a(2	a(2	PROPN
ejpam-6414	159	6	,	,	PUNCT
ejpam-6414	159	7	2)[x	2)[x	PROPN
ejpam-6414	159	8	]	]	PUNCT
ejpam-6414	159	9	:	:	PUNCT
ejpam-6414	159	10	the	the	DET
ejpam-6414	159	11	residue	residue	NOUN
ejpam-6414	159	12	field	field	NOUN
ejpam-6414	159	13	of	of	ADP
ejpam-6414	159	14	a(2	a(2	PROPN
ejpam-6414	159	15	,	,	PUNCT
ejpam-6414	159	16	2	2	NUM
ejpam-6414	159	17	)	)	PUNCT
ejpam-6414	159	18	is	be	AUX
ejpam-6414	159	19	f2	f2	ADJ
ejpam-6414	159	20	,	,	PUNCT
ejpam-6414	159	21	and	and	CCONJ
ejpam-6414	159	22	the	the	DET
ejpam-6414	159	23	natural	natural	ADJ
ejpam-6414	159	24	projection	projection	NOUN
ejpam-6414	159	25	is	be	AUX
ejpam-6414	159	26	:	:	PUNCT
ejpam-6414	159	27	π	π	X
ejpam-6414	159	28	:	:	PUNCT
ejpam-6414	160	1	a(2	a(2	ADJ
ejpam-6414	160	2	,	,	PUNCT
ejpam-6414	160	3	2)[x	2)[x	PROPN
ejpam-6414	160	4	]	]	PUNCT
ejpam-6414	160	5	→	→	SYM
ejpam-6414	160	6	f2[x	f2[x	ADV
ejpam-6414	160	7	]	]	PUNCT
ejpam-6414	160	8	.	.	PUNCT
ejpam-6414	161	1	case	case	NOUN
ejpam-6414	161	2	1	1	NUM
ejpam-6414	161	3	:	:	PUNCT
ejpam-6414	161	4	let	let	VERB
ejpam-6414	161	5	f(x	f(x	PROPN
ejpam-6414	161	6	)	)	PUNCT
ejpam-6414	161	7	∈	∈	PROPN
ejpam-6414	161	8	a(2	a(2	PROPN
ejpam-6414	161	9	,	,	PUNCT
ejpam-6414	161	10	2)[x	2)[x	PROPN
ejpam-6414	161	11	]	]	PUNCT
ejpam-6414	161	12	be	be	AUX
ejpam-6414	161	13	a	a	DET
ejpam-6414	161	14	monic	monic	ADJ
ejpam-6414	161	15	polynomial	polynomial	NOUN
ejpam-6414	161	16	of	of	ADP
ejpam-6414	161	17	degree	degree	NOUN
ejpam-6414	161	18	2	2	NUM
ejpam-6414	161	19	of	of	ADP
ejpam-6414	161	20	the	the	DET
ejpam-6414	161	21	form	form	NOUN
ejpam-6414	161	22	:	:	PUNCT
ejpam-6414	161	23	f(x	f(x	PROPN
ejpam-6414	161	24	)	)	PUNCT
ejpam-6414	162	1	=	=	SYM
ejpam-6414	162	2	a0	a0	NOUN
ejpam-6414	162	3	+	+	CCONJ
ejpam-6414	162	4	a1x+	a1x+	NOUN
ejpam-6414	162	5	x2	x2	PROPN
ejpam-6414	162	6	,	,	PUNCT
ejpam-6414	162	7	where	where	SCONJ
ejpam-6414	162	8	a0	a0	NOUN
ejpam-6414	162	9	,	,	PUNCT
ejpam-6414	162	10	a1	a1	NOUN
ejpam-6414	162	11	∈	∈	PROPN
ejpam-6414	162	12	a(2	a(2	PROPN
ejpam-6414	162	13	,	,	PUNCT
ejpam-6414	162	14	2	2	NUM
ejpam-6414	162	15	)	)	PUNCT
ejpam-6414	162	16	.	.	PUNCT
ejpam-6414	163	1	muhammad	muhammad	PROPN
ejpam-6414	163	2	sajjad	sajjad	PROPN
ejpam-6414	163	3	et	et	PROPN
ejpam-6414	163	4	al	al	PROPN
ejpam-6414	163	5	.	.	PUNCT
ejpam-6414	163	6	/	/	SYM
ejpam-6414	163	7	eur	eur	PROPN
ejpam-6414	163	8	.	.	PUNCT
ejpam-6414	164	1	j.	j.	PROPN
ejpam-6414	164	2	pure	pure	PROPN
ejpam-6414	164	3	appl	appl	PROPN
ejpam-6414	164	4	.	.	PROPN
ejpam-6414	164	5	math	math	PROPN
ejpam-6414	164	6	,	,	PUNCT
ejpam-6414	164	7	18	18	NUM
ejpam-6414	164	8	(	(	PUNCT
ejpam-6414	164	9	3	3	NUM
ejpam-6414	164	10	)	)	PUNCT
ejpam-6414	164	11	(	(	PUNCT
ejpam-6414	164	12	2025	2025	NUM
ejpam-6414	164	13	)	)	PUNCT
ejpam-6414	164	14	,	,	PUNCT
ejpam-6414	164	15	6414	6414	NUM
ejpam-6414	164	16	8	8	NUM
ejpam-6414	164	17	of	of	ADP
ejpam-6414	164	18	22	22	NUM
ejpam-6414	164	19	choose	choose	NOUN
ejpam-6414	164	20	a0	a0	NOUN
ejpam-6414	164	21	=	=	SYM
ejpam-6414	164	22	1	1	NUM
ejpam-6414	164	23	,	,	PUNCT
ejpam-6414	164	24	a1	a1	NOUN
ejpam-6414	164	25	=	=	SYM
ejpam-6414	164	26	1	1	NUM
ejpam-6414	164	27	+	+	NUM
ejpam-6414	164	28	θ	θ	PROPN
ejpam-6414	164	29	,	,	PUNCT
ejpam-6414	164	30	then	then	ADV
ejpam-6414	164	31	:	:	PUNCT
ejpam-6414	164	32	f(x	f(x	PROPN
ejpam-6414	164	33	)	)	PUNCT
ejpam-6414	165	1	=	=	SYM
ejpam-6414	166	1	x2	x2	PROPN
ejpam-6414	167	1	+	+	CCONJ
ejpam-6414	167	2	(	(	PUNCT
ejpam-6414	167	3	1	1	NUM
ejpam-6414	167	4	+	+	SYM
ejpam-6414	167	5	θ)x+	θ)x+	NUM
ejpam-6414	167	6	1	1	NUM
ejpam-6414	167	7	.	.	PUNCT
ejpam-6414	168	1	now	now	ADV
ejpam-6414	168	2	we	we	PRON
ejpam-6414	168	3	check	check	VERB
ejpam-6414	168	4	if	if	SCONJ
ejpam-6414	168	5	f(x	f(x	PROPN
ejpam-6414	168	6	)	)	PUNCT
ejpam-6414	168	7	is	be	AUX
ejpam-6414	168	8	irreducible	irreducible	ADJ
ejpam-6414	168	9	over	over	ADP
ejpam-6414	168	10	a(2	a(2	PROPN
ejpam-6414	168	11	,	,	PUNCT
ejpam-6414	168	12	2	2	NUM
ejpam-6414	168	13	)	)	PUNCT
ejpam-6414	168	14	.	.	PUNCT
ejpam-6414	169	1	its	its	PRON
ejpam-6414	169	2	image	image	NOUN
ejpam-6414	169	3	under	under	ADP
ejpam-6414	169	4	projection	projection	NOUN
ejpam-6414	169	5	is	be	AUX
ejpam-6414	169	6	:	:	PUNCT
ejpam-6414	169	7	π(f(x	π(f(x	NOUN
ejpam-6414	169	8	)	)	PUNCT
ejpam-6414	169	9	)	)	PUNCT
ejpam-6414	170	1	=	=	SYM
ejpam-6414	171	1	x2	x2	PROPN
ejpam-6414	172	1	+	+	CCONJ
ejpam-6414	172	2	x+	x+	PROPN
ejpam-6414	172	3	1	1	NUM
ejpam-6414	172	4	,	,	PUNCT
ejpam-6414	172	5	which	which	PRON
ejpam-6414	172	6	is	be	AUX
ejpam-6414	172	7	a	a	DET
ejpam-6414	172	8	monic	monic	ADJ
ejpam-6414	172	9	irreducible	irreducible	ADJ
ejpam-6414	172	10	polynomial	polynomial	NOUN
ejpam-6414	172	11	over	over	ADP
ejpam-6414	172	12	f2	f2	PROPN
ejpam-6414	172	13	.	.	PUNCT
ejpam-6414	173	1	we	we	PRON
ejpam-6414	173	2	now	now	ADV
ejpam-6414	173	3	evaluate	evaluate	VERB
ejpam-6414	173	4	f(x	f(x	PROPN
ejpam-6414	173	5	)	)	PUNCT
ejpam-6414	173	6	at	at	ADP
ejpam-6414	173	7	all	all	DET
ejpam-6414	173	8	possible	possible	ADJ
ejpam-6414	173	9	elements	element	NOUN
ejpam-6414	173	10	of	of	ADP
ejpam-6414	173	11	a(2	a(2	PROPN
ejpam-6414	173	12	,	,	PUNCT
ejpam-6414	173	13	2	2	NUM
ejpam-6414	173	14	):	):	PUNCT
ejpam-6414	173	15	f(0	f(0	NOUN
ejpam-6414	173	16	)	)	PUNCT
ejpam-6414	173	17	=	=	SYM
ejpam-6414	174	1	1	1	NUM
ejpam-6414	174	2	̸=	̸=	PROPN
ejpam-6414	174	3	0	0	NUM
ejpam-6414	174	4	,	,	PUNCT
ejpam-6414	174	5	f(1	f(1	PROPN
ejpam-6414	174	6	)	)	PUNCT
ejpam-6414	174	7	=	=	SYM
ejpam-6414	174	8	1	1	NUM
ejpam-6414	174	9	+	+	CCONJ
ejpam-6414	174	10	(	(	PUNCT
ejpam-6414	174	11	1	1	NUM
ejpam-6414	174	12	+	+	NUM
ejpam-6414	174	13	θ	θ	NOUN
ejpam-6414	174	14	)	)	PUNCT
ejpam-6414	174	15	+	+	CCONJ
ejpam-6414	174	16	1	1	NUM
ejpam-6414	174	17	=	=	SYM
ejpam-6414	174	18	1	1	NUM
ejpam-6414	174	19	+	+	NUM
ejpam-6414	174	20	θ	θ	PROPN
ejpam-6414	174	21	̸=	̸=	PROPN
ejpam-6414	174	22	0	0	NUM
ejpam-6414	174	23	,	,	PUNCT
ejpam-6414	174	24	muhammad	muhammad	PROPN
ejpam-6414	174	25	sajjad	sajjad	PROPN
ejpam-6414	174	26	et	et	PROPN
ejpam-6414	174	27	al	al	PROPN
ejpam-6414	174	28	.	.	PUNCT
ejpam-6414	174	29	/	/	SYM
ejpam-6414	174	30	eur	eur	PROPN
ejpam-6414	174	31	.	.	PUNCT
ejpam-6414	175	1	j.	j.	PROPN
ejpam-6414	175	2	pure	pure	PROPN
ejpam-6414	175	3	appl	appl	PROPN
ejpam-6414	175	4	.	.	PROPN
ejpam-6414	175	5	math	math	PROPN
ejpam-6414	175	6	,	,	PUNCT
ejpam-6414	175	7	18	18	NUM
ejpam-6414	175	8	(	(	PUNCT
ejpam-6414	175	9	3	3	NUM
ejpam-6414	175	10	)	)	PUNCT
ejpam-6414	175	11	(	(	PUNCT
ejpam-6414	175	12	2025	2025	NUM
ejpam-6414	175	13	)	)	PUNCT
ejpam-6414	175	14	,	,	PUNCT
ejpam-6414	175	15	6414	6414	NUM
ejpam-6414	175	16	9	9	NUM
ejpam-6414	175	17	of	of	ADP
ejpam-6414	175	18	22	22	NUM
ejpam-6414	175	19	f(θ	f(θ	NOUN
ejpam-6414	175	20	)	)	PUNCT
ejpam-6414	175	21	=	=	PUNCT
ejpam-6414	175	22	θ2	θ2	PROPN
ejpam-6414	175	23	+	+	CCONJ
ejpam-6414	175	24	(	(	PUNCT
ejpam-6414	175	25	1	1	NUM
ejpam-6414	175	26	+	+	CCONJ
ejpam-6414	175	27	θ)θ	θ)θ	NOUN
ejpam-6414	176	1	+	+	SYM
ejpam-6414	176	2	1	1	NUM
ejpam-6414	176	3	=	=	SYM
ejpam-6414	176	4	0	0	NUM
ejpam-6414	176	5	+	+	NUM
ejpam-6414	176	6	θ	θ	NOUN
ejpam-6414	176	7	+	+	CCONJ
ejpam-6414	176	8	1	1	NUM
ejpam-6414	176	9	+	+	SYM
ejpam-6414	176	10	1	1	NUM
ejpam-6414	176	11	=	=	SYM
ejpam-6414	176	12	θ	θ	X
ejpam-6414	176	13	̸=	̸=	PROPN
ejpam-6414	176	14	0	0	NUM
ejpam-6414	176	15	,	,	PUNCT
ejpam-6414	176	16	f(1	f(1	PROPN
ejpam-6414	176	17	+	+	PUNCT
ejpam-6414	176	18	θ	θ	X
ejpam-6414	176	19	)	)	PUNCT
ejpam-6414	176	20	=	=	SYM
ejpam-6414	176	21	(	(	PUNCT
ejpam-6414	176	22	1	1	NUM
ejpam-6414	176	23	+	+	NUM
ejpam-6414	176	24	θ)2	θ)2	NOUN
ejpam-6414	176	25	+	+	CCONJ
ejpam-6414	176	26	(	(	PUNCT
ejpam-6414	176	27	1	1	NUM
ejpam-6414	176	28	+	+	NUM
ejpam-6414	176	29	θ)2	θ)2	NOUN
ejpam-6414	176	30	+	+	CCONJ
ejpam-6414	176	31	1	1	NUM
ejpam-6414	176	32	=	=	SYM
ejpam-6414	176	33	1	1	NUM
ejpam-6414	176	34	+	+	NUM
ejpam-6414	176	35	θ	θ	NOUN
ejpam-6414	176	36	+	+	CCONJ
ejpam-6414	176	37	1	1	NUM
ejpam-6414	176	38	+	+	NUM
ejpam-6414	176	39	θ	θ	NOUN
ejpam-6414	176	40	+	+	CCONJ
ejpam-6414	176	41	1	1	NUM
ejpam-6414	176	42	=	=	SYM
ejpam-6414	176	43	1	1	NUM
ejpam-6414	176	44	̸=	̸=	PROPN
ejpam-6414	176	45	0	0	NUM
ejpam-6414	176	46	.	.	PUNCT
ejpam-6414	177	1	thus	thus	ADV
ejpam-6414	177	2	,	,	PUNCT
ejpam-6414	177	3	f(x	f(x	PROPN
ejpam-6414	177	4	)	)	PUNCT
ejpam-6414	177	5	is	be	AUX
ejpam-6414	177	6	irreducible	irreducible	ADJ
ejpam-6414	177	7	over	over	ADP
ejpam-6414	177	8	a(2	a(2	PROPN
ejpam-6414	177	9	,	,	PUNCT
ejpam-6414	177	10	2	2	NUM
ejpam-6414	177	11	)	)	PUNCT
ejpam-6414	177	12	and	and	CCONJ
ejpam-6414	177	13	hence	hence	ADV
ejpam-6414	177	14	is	be	AUX
ejpam-6414	177	15	a	a	DET
ejpam-6414	177	16	basic	basic	ADJ
ejpam-6414	177	17	irreducible	irreducible	ADJ
ejpam-6414	177	18	polynomial	polynomial	ADJ
ejpam-6414	177	19	.	.	PUNCT
ejpam-6414	178	1	extension	extension	NOUN
ejpam-6414	178	2	of	of	ADP
ejpam-6414	178	3	a(2	a(2	PROPN
ejpam-6414	178	4	,	,	PUNCT
ejpam-6414	178	5	2	2	NUM
ejpam-6414	178	6	)	)	PUNCT
ejpam-6414	178	7	with	with	ADP
ejpam-6414	178	8	respect	respect	NOUN
ejpam-6414	178	9	to	to	ADP
ejpam-6414	178	10	f(x	f(x	PROPN
ejpam-6414	178	11	):	):	PUNCT
ejpam-6414	178	12	the	the	DET
ejpam-6414	178	13	galois	galois	PROPN
ejpam-6414	178	14	extension	extension	NOUN
ejpam-6414	178	15	of	of	ADP
ejpam-6414	178	16	a(2	a(2	PROPN
ejpam-6414	178	17	,	,	PUNCT
ejpam-6414	178	18	2	2	NUM
ejpam-6414	178	19	)	)	PUNCT
ejpam-6414	178	20	by	by	ADP
ejpam-6414	178	21	the	the	DET
ejpam-6414	178	22	basic	basic	ADJ
ejpam-6414	178	23	irreducible	irreducible	ADJ
ejpam-6414	178	24	polynomial	polynomial	ADJ
ejpam-6414	178	25	f(x	f(x	PROPN
ejpam-6414	178	26	)	)	PUNCT
ejpam-6414	178	27	is	be	AUX
ejpam-6414	178	28	defined	define	VERB
ejpam-6414	178	29	as	as	ADP
ejpam-6414	178	30	:	:	PUNCT
ejpam-6414	178	31	r	r	NOUN
ejpam-6414	178	32	=	=	SYM
ejpam-6414	178	33	a(2	a(2	PROPN
ejpam-6414	178	34	,	,	PUNCT
ejpam-6414	178	35	2)[x	2)[x	PROPN
ejpam-6414	178	36	]	]	PUNCT
ejpam-6414	178	37	⟨f(x)⟩	⟨f(x)⟩	X
ejpam-6414	179	1	=	=	PUNCT
ejpam-6414	179	2	{	{	PUNCT
ejpam-6414	179	3	1∑	1∑	PROPN
ejpam-6414	179	4	i=0	i=0	PROPN
ejpam-6414	179	5	ciα	ciα	PROPN
ejpam-6414	180	1	i	i	PRON
ejpam-6414	180	2	:	:	PUNCT
ejpam-6414	180	3	ci	ci	PROPN
ejpam-6414	180	4	∈	∈	PROPN
ejpam-6414	180	5	a(2	a(2	PROPN
ejpam-6414	180	6	,	,	PUNCT
ejpam-6414	180	7	2	2	NUM
ejpam-6414	180	8	)	)	PUNCT
ejpam-6414	180	9	}	}	PUNCT
ejpam-6414	180	10	,	,	PUNCT
ejpam-6414	180	11	where	where	SCONJ
ejpam-6414	180	12	f(x	f(x	NOUN
ejpam-6414	180	13	)	)	PUNCT
ejpam-6414	180	14	=	=	SYM
ejpam-6414	181	1	x2	x2	PROPN
ejpam-6414	182	1	+	+	CCONJ
ejpam-6414	182	2	(	(	PUNCT
ejpam-6414	182	3	1	1	NUM
ejpam-6414	182	4	+	+	SYM
ejpam-6414	182	5	θ)x+	θ)x+	SYM
ejpam-6414	182	6	1	1	NUM
ejpam-6414	182	7	and	and	CCONJ
ejpam-6414	182	8	f(α	f(α	NOUN
ejpam-6414	182	9	)	)	PUNCT
ejpam-6414	182	10	=	=	NOUN
ejpam-6414	182	11	0	0	X
ejpam-6414	182	12	.	.	PUNCT
ejpam-6414	182	13	maximal	maximal	ADJ
ejpam-6414	182	14	cyclic	cyclic	ADJ
ejpam-6414	182	15	subgroup	subgroup	NOUN
ejpam-6414	182	16	of	of	ADP
ejpam-6414	182	17	r∗	r∗	PROPN
ejpam-6414	182	18	:	:	PUNCT
ejpam-6414	182	19	given	give	VERB
ejpam-6414	182	20	that	that	SCONJ
ejpam-6414	182	21	α	α	NOUN
ejpam-6414	182	22	satisfies	satisfie	NOUN
ejpam-6414	182	23	:	:	PUNCT
ejpam-6414	182	24	α2	α2	PROPN
ejpam-6414	182	25	=	=	SYM
ejpam-6414	182	26	(	(	PUNCT
ejpam-6414	182	27	1	1	NUM
ejpam-6414	182	28	+	+	NUM
ejpam-6414	182	29	θ)α+	θ)α+	NOUN
ejpam-6414	182	30	1	1	NUM
ejpam-6414	182	31	,	,	PUNCT
ejpam-6414	182	32	we	we	PRON
ejpam-6414	182	33	compute	compute	VERB
ejpam-6414	182	34	the	the	DET
ejpam-6414	182	35	successive	successive	ADJ
ejpam-6414	182	36	powers	power	NOUN
ejpam-6414	182	37	:	:	PUNCT
ejpam-6414	182	38	α3	α3	PROPN
ejpam-6414	182	39	=	=	SYM
ejpam-6414	182	40	(	(	PUNCT
ejpam-6414	182	41	1	1	NUM
ejpam-6414	182	42	+	+	NUM
ejpam-6414	182	43	θ)α2	θ)α2	PROPN
ejpam-6414	182	44	+	+	CCONJ
ejpam-6414	182	45	α	α	NOUN
ejpam-6414	182	46	=	=	SYM
ejpam-6414	182	47	(	(	PUNCT
ejpam-6414	182	48	1	1	NUM
ejpam-6414	183	1	+	+	NUM
ejpam-6414	183	2	θ)((1	θ)((1	PROPN
ejpam-6414	183	3	+	+	CCONJ
ejpam-6414	183	4	θ)α+	θ)α+	NOUN
ejpam-6414	183	5	1	1	NUM
ejpam-6414	183	6	)	)	PUNCT
ejpam-6414	184	1	+	+	CCONJ
ejpam-6414	184	2	α	α	NOUN
ejpam-6414	184	3	=	=	SYM
ejpam-6414	184	4	(	(	PUNCT
ejpam-6414	184	5	1	1	NUM
ejpam-6414	184	6	+	+	CCONJ
ejpam-6414	184	7	θ)2α+	θ)2α+	ADJ
ejpam-6414	184	8	(	(	PUNCT
ejpam-6414	184	9	1	1	NUM
ejpam-6414	184	10	+	+	NUM
ejpam-6414	184	11	θ	θ	NOUN
ejpam-6414	184	12	)	)	PUNCT
ejpam-6414	184	13	+	+	NOUN
ejpam-6414	184	14	α	α	NOUN
ejpam-6414	184	15	=	=	SYM
ejpam-6414	184	16	α+	α+	PUNCT
ejpam-6414	184	17	1	1	NUM
ejpam-6414	184	18	+	+	NUM
ejpam-6414	184	19	θ	θ	NOUN
ejpam-6414	184	20	+	+	CCONJ
ejpam-6414	184	21	α	α	NOUN
ejpam-6414	184	22	=	=	SYM
ejpam-6414	184	23	1	1	NUM
ejpam-6414	184	24	+	+	NUM
ejpam-6414	184	25	θ	θ	PROPN
ejpam-6414	184	26	,	,	PUNCT
ejpam-6414	184	27	α4	α4	NOUN
ejpam-6414	184	28	=	=	SYM
ejpam-6414	184	29	α	α	PROPN
ejpam-6414	184	30	·	·	PUNCT
ejpam-6414	184	31	α3	α3	NOUN
ejpam-6414	184	32	=	=	SYM
ejpam-6414	184	33	α(1	α(1	PROPN
ejpam-6414	184	34	+	+	PROPN
ejpam-6414	184	35	θ	θ	X
ejpam-6414	184	36	)	)	PUNCT
ejpam-6414	184	37	=	=	SYM
ejpam-6414	184	38	(	(	PUNCT
ejpam-6414	184	39	1	1	NUM
ejpam-6414	184	40	+	+	CCONJ
ejpam-6414	184	41	θ)α	θ)α	NOUN
ejpam-6414	184	42	,	,	PUNCT
ejpam-6414	184	43	α5	α5	NOUN
ejpam-6414	184	44	=	=	SYM
ejpam-6414	184	45	α	α	PROPN
ejpam-6414	184	46	·	·	PUNCT
ejpam-6414	184	47	α4	α4	NOUN
ejpam-6414	184	48	=	=	SYM
ejpam-6414	184	49	α	α	NOUN
ejpam-6414	184	50	·	·	PUNCT
ejpam-6414	184	51	(	(	PUNCT
ejpam-6414	184	52	1	1	NUM
ejpam-6414	184	53	+	+	NUM
ejpam-6414	184	54	θ)α	θ)α	NOUN
ejpam-6414	184	55	=	=	SYM
ejpam-6414	184	56	(	(	PUNCT
ejpam-6414	184	57	1	1	NUM
ejpam-6414	184	58	+	+	NUM
ejpam-6414	184	59	θ)α2	θ)α2	PROPN
ejpam-6414	184	60	=	=	SYM
ejpam-6414	184	61	(	(	PUNCT
ejpam-6414	184	62	1	1	NUM
ejpam-6414	184	63	+	+	NUM
ejpam-6414	184	64	θ)((1	θ)((1	PROPN
ejpam-6414	184	65	+	+	CCONJ
ejpam-6414	184	66	θ)α+	θ)α+	NOUN
ejpam-6414	184	67	1	1	NUM
ejpam-6414	184	68	)	)	PUNCT
ejpam-6414	184	69	=	=	NOUN
ejpam-6414	184	70	α+	α+	PUNCT
ejpam-6414	184	71	1	1	NUM
ejpam-6414	184	72	,	,	PUNCT
ejpam-6414	184	73	α6	α6	NOUN
ejpam-6414	184	74	=	=	SYM
ejpam-6414	184	75	α	α	PROPN
ejpam-6414	184	76	·	·	PUNCT
ejpam-6414	184	77	α5	α5	NOUN
ejpam-6414	184	78	=	=	PUNCT
ejpam-6414	184	79	α(α+	α(α+	NUM
ejpam-6414	184	80	1	1	NUM
ejpam-6414	184	81	)	)	PUNCT
ejpam-6414	184	82	=	=	VERB
ejpam-6414	185	1	α2	α2	ADJ
ejpam-6414	185	2	+	+	CCONJ
ejpam-6414	185	3	α	α	NOUN
ejpam-6414	185	4	=	=	SYM
ejpam-6414	185	5	(	(	PUNCT
ejpam-6414	185	6	1	1	NUM
ejpam-6414	185	7	+	+	NUM
ejpam-6414	185	8	θ)α+	θ)α+	NOUN
ejpam-6414	185	9	1	1	NUM
ejpam-6414	185	10	+	+	CCONJ
ejpam-6414	185	11	α	α	NOUN
ejpam-6414	185	12	=	=	SYM
ejpam-6414	185	13	1	1	NUM
ejpam-6414	185	14	.	.	PUNCT
ejpam-6414	186	1	so	so	ADV
ejpam-6414	186	2	,	,	PUNCT
ejpam-6414	186	3	the	the	DET
ejpam-6414	186	4	order	order	NOUN
ejpam-6414	186	5	of	of	ADP
ejpam-6414	186	6	α	α	PROPN
ejpam-6414	186	7	is	be	AUX
ejpam-6414	186	8	6	6	NUM
ejpam-6414	186	9	.	.	PUNCT
ejpam-6414	187	1	the	the	DET
ejpam-6414	187	2	maximal	maximal	ADJ
ejpam-6414	187	3	cyclic	cyclic	PROPN
ejpam-6414	187	4	subgroup	subgroup	PROPN
ejpam-6414	187	5	g3	g3	PROPN
ejpam-6414	187	6	⊂	⊂	PROPN
ejpam-6414	187	7	r∗	r∗	PROPN
ejpam-6414	187	8	generated	generate	VERB
ejpam-6414	187	9	by	by	ADP
ejpam-6414	187	10	γ	γ	PROPN
ejpam-6414	187	11	=	=	SYM
ejpam-6414	187	12	α2	α2	PROPN
ejpam-6414	187	13	is	be	AUX
ejpam-6414	187	14	:	:	PUNCT
ejpam-6414	187	15	g3	g3	PROPN
ejpam-6414	187	16	=	=	SYM
ejpam-6414	187	17	{	{	PUNCT
ejpam-6414	187	18	γ	γ	X
ejpam-6414	187	19	,	,	PUNCT
ejpam-6414	187	20	γ2	γ2	ADJ
ejpam-6414	187	21	,	,	PUNCT
ejpam-6414	187	22	γ3	γ3	NOUN
ejpam-6414	187	23	=	=	NOUN
ejpam-6414	187	24	1	1	NUM
ejpam-6414	187	25	}	}	PUNCT
ejpam-6414	187	26	=	=	PRON
ejpam-6414	187	27	{	{	PUNCT
ejpam-6414	187	28	1	1	NUM
ejpam-6414	187	29	+	+	CCONJ
ejpam-6414	187	30	(	(	PUNCT
ejpam-6414	187	31	1	1	NUM
ejpam-6414	187	32	+	+	NUM
ejpam-6414	187	33	θ)α	θ)α	NOUN
ejpam-6414	187	34	,	,	PUNCT
ejpam-6414	187	35	(	(	PUNCT
ejpam-6414	187	36	1	1	NUM
ejpam-6414	187	37	+	+	NUM
ejpam-6414	187	38	θ)α	θ)α	NOUN
ejpam-6414	187	39	,	,	PUNCT
ejpam-6414	187	40	1	1	NUM
ejpam-6414	187	41	}	}	PUNCT
ejpam-6414	187	42	.	.	PUNCT
ejpam-6414	188	1	generator	generator	NOUN
ejpam-6414	188	2	polynomial	polynomial	PROPN
ejpam-6414	188	3	of	of	ADP
ejpam-6414	188	4	bch	bch	PROPN
ejpam-6414	188	5	code	code	PROPN
ejpam-6414	188	6	over	over	ADP
ejpam-6414	188	7	a(2	a(2	PROPN
ejpam-6414	188	8	,	,	PUNCT
ejpam-6414	188	9	2	2	NUM
ejpam-6414	188	10	):	):	PUNCT
ejpam-6414	188	11	since	since	SCONJ
ejpam-6414	188	12	γ	γ	X
ejpam-6414	188	13	is	be	AUX
ejpam-6414	188	14	a	a	DET
ejpam-6414	188	15	primitive	primitive	ADJ
ejpam-6414	188	16	cube	cube	NOUN
ejpam-6414	188	17	root	root	NOUN
ejpam-6414	188	18	of	of	ADP
ejpam-6414	188	19	unity	unity	NOUN
ejpam-6414	188	20	in	in	ADP
ejpam-6414	188	21	g3	g3	NOUN
ejpam-6414	188	22	,	,	PUNCT
ejpam-6414	188	23	and	and	CCONJ
ejpam-6414	188	24	taking	take	VERB
ejpam-6414	188	25	design	design	NOUN
ejpam-6414	188	26	distance	distance	NOUN
ejpam-6414	188	27	d	d	NOUN
ejpam-6414	188	28	=	=	SYM
ejpam-6414	188	29	3	3	NUM
ejpam-6414	188	30	,	,	PUNCT
ejpam-6414	188	31	we	we	PRON
ejpam-6414	188	32	need	need	VERB
ejpam-6414	188	33	the	the	DET
ejpam-6414	188	34	minimal	minimal	ADJ
ejpam-6414	188	35	polynomials	polynomial	NOUN
ejpam-6414	188	36	of	of	ADP
ejpam-6414	188	37	γi	γi	NOUN
ejpam-6414	188	38	for	for	ADP
ejpam-6414	188	39	i	i	PRON
ejpam-6414	188	40	=	=	NOUN
ejpam-6414	188	41	1	1	NUM
ejpam-6414	188	42	,	,	PUNCT
ejpam-6414	188	43	2	2	NUM
ejpam-6414	188	44	.	.	PUNCT
ejpam-6414	188	45	both	both	DET
ejpam-6414	188	46	γ	γ	PROPN
ejpam-6414	188	47	and	and	CCONJ
ejpam-6414	188	48	γ2	γ2	PROPN
ejpam-6414	188	49	share	share	VERB
ejpam-6414	188	50	the	the	DET
ejpam-6414	188	51	same	same	ADJ
ejpam-6414	188	52	minimal	minimal	ADJ
ejpam-6414	188	53	polynomial	polynomial	ADJ
ejpam-6414	188	54	:	:	PUNCT
ejpam-6414	188	55	m1(x	m1(x	NOUN
ejpam-6414	188	56	)	)	PUNCT
ejpam-6414	188	57	=	=	SYM
ejpam-6414	188	58	(	(	PUNCT
ejpam-6414	188	59	x−	x−	PROPN
ejpam-6414	188	60	γ)(x−	γ)(x−	PROPN
ejpam-6414	188	61	γ2	γ2	PROPN
ejpam-6414	188	62	)	)	PUNCT
ejpam-6414	189	1	=	=	SYM
ejpam-6414	190	1	x2	x2	PROPN
ejpam-6414	191	1	+	+	CCONJ
ejpam-6414	191	2	x+	x+	ADJ
ejpam-6414	191	3	1	1	X
ejpam-6414	191	4	.	.	PUNCT
ejpam-6414	192	1	hence	hence	ADV
ejpam-6414	192	2	,	,	PUNCT
ejpam-6414	192	3	the	the	DET
ejpam-6414	192	4	generator	generator	NOUN
ejpam-6414	192	5	polynomial	polynomial	NOUN
ejpam-6414	192	6	is	be	AUX
ejpam-6414	192	7	:	:	PUNCT
ejpam-6414	192	8	g(x	g(x	X
ejpam-6414	192	9	)	)	PUNCT
ejpam-6414	193	1	=	=	PUNCT
ejpam-6414	193	2	lcm(m1(x),m2(x	lcm(m1(x),m2(x	ADJ
ejpam-6414	193	3	)	)	PUNCT
ejpam-6414	193	4	)	)	PUNCT
ejpam-6414	194	1	=	=	PUNCT
ejpam-6414	194	2	m1(x	m1(x	X
ejpam-6414	194	3	)	)	PUNCT
ejpam-6414	194	4	=	=	SYM
ejpam-6414	195	1	x2	x2	PROPN
ejpam-6414	196	1	+	+	CCONJ
ejpam-6414	196	2	x+	x+	PROPN
ejpam-6414	196	3	1	1	X
ejpam-6414	196	4	.	.	X
ejpam-6414	196	5	for	for	ADP
ejpam-6414	196	6	r	r	NOUN
ejpam-6414	196	7	=	=	SYM
ejpam-6414	196	8	2	2	NUM
ejpam-6414	196	9	,	,	PUNCT
ejpam-6414	196	10	q	q	NOUN
ejpam-6414	196	11	=	=	SYM
ejpam-6414	196	12	2	2	NUM
ejpam-6414	196	13	,	,	PUNCT
ejpam-6414	196	14	and	and	CCONJ
ejpam-6414	196	15	m	m	PROPN
ejpam-6414	196	16	=	=	SYM
ejpam-6414	196	17	2	2	NUM
ejpam-6414	196	18	,	,	PUNCT
ejpam-6414	196	19	the	the	DET
ejpam-6414	196	20	length	length	NOUN
ejpam-6414	196	21	of	of	ADP
ejpam-6414	196	22	the	the	DET
ejpam-6414	196	23	narrow	narrow	ADJ
ejpam-6414	196	24	-	-	PUNCT
ejpam-6414	196	25	sense	sense	NOUN
ejpam-6414	196	26	primitive	primitive	ADJ
ejpam-6414	196	27	bch	bch	PROPN
ejpam-6414	196	28	code	code	NOUN
ejpam-6414	196	29	is	be	AUX
ejpam-6414	196	30	:	:	PUNCT
ejpam-6414	196	31	n	n	PROPN
ejpam-6414	196	32	=	=	SYM
ejpam-6414	196	33	qm	qm	PROPN
ejpam-6414	196	34	−	−	PROPN
ejpam-6414	196	35	1	1	NUM
ejpam-6414	197	1	=	=	SYM
ejpam-6414	197	2	22	22	NUM
ejpam-6414	197	3	−	−	NOUN
ejpam-6414	197	4	1	1	NUM
ejpam-6414	197	5	=	=	SYM
ejpam-6414	197	6	3	3	X
ejpam-6414	197	7	.	.	PUNCT
ejpam-6414	198	1	the	the	DET
ejpam-6414	198	2	cyclic	cyclic	PROPN
ejpam-6414	198	3	code	code	PROPN
ejpam-6414	198	4	c	c	NOUN
ejpam-6414	198	5	generated	generate	VERB
ejpam-6414	198	6	by	by	ADP
ejpam-6414	198	7	g(x	g(x	PROPN
ejpam-6414	198	8	)	)	PUNCT
ejpam-6414	198	9	over	over	ADP
ejpam-6414	198	10	g3	g3	PROPN
ejpam-6414	199	1	⊂	⊂	PROPN
ejpam-6414	199	2	r∗	r∗	PROPN
ejpam-6414	199	3	⊂	⊂	PROPN
ejpam-6414	199	4	a(2	a(2	PROPN
ejpam-6414	199	5	,	,	PUNCT
ejpam-6414	199	6	2	2	NUM
ejpam-6414	199	7	)	)	PUNCT
ejpam-6414	199	8	has	have	AUX
ejpam-6414	199	9	dimension	dimension	NOUN
ejpam-6414	199	10	1	1	NUM
ejpam-6414	199	11	.	.	PUNCT
ejpam-6414	200	1	thus	thus	ADV
ejpam-6414	200	2	,	,	PUNCT
ejpam-6414	200	3	the	the	DET
ejpam-6414	200	4	bch	bch	PROPN
ejpam-6414	200	5	code	code	PROPN
ejpam-6414	200	6	c	c	PROPN
ejpam-6414	200	7	is	be	AUX
ejpam-6414	200	8	a	a	DET
ejpam-6414	200	9	:	:	PUNCT
ejpam-6414	200	10	[	[	X
ejpam-6414	200	11	3	3	NUM
ejpam-6414	200	12	,	,	PUNCT
ejpam-6414	200	13	1	1	NUM
ejpam-6414	200	14	,	,	PUNCT
ejpam-6414	200	15	3	3	NUM
ejpam-6414	200	16	]	]	X
ejpam-6414	200	17	primitive	primitive	ADJ
ejpam-6414	200	18	narrow	narrow	ADJ
ejpam-6414	200	19	-	-	PUNCT
ejpam-6414	200	20	sense	sense	NOUN
ejpam-6414	200	21	bch	bch	PROPN
ejpam-6414	200	22	code	code	NOUN
ejpam-6414	200	23	over	over	ADP
ejpam-6414	200	24	the	the	DET
ejpam-6414	200	25	maximal	maximal	ADJ
ejpam-6414	200	26	cyclic	cyclic	ADJ
ejpam-6414	200	27	subgroup	subgroup	NOUN
ejpam-6414	200	28	of	of	ADP
ejpam-6414	200	29	the	the	DET
ejpam-6414	200	30	group	group	NOUN
ejpam-6414	200	31	of	of	ADP
ejpam-6414	200	32	units	unit	NOUN
ejpam-6414	200	33	in	in	ADP
ejpam-6414	200	34	a(2	a(2	PROPN
ejpam-6414	200	35	,	,	PUNCT
ejpam-6414	200	36	2	2	NUM
ejpam-6414	200	37	)	)	PUNCT
ejpam-6414	200	38	.	.	PUNCT
ejpam-6414	201	1	muhammad	muhammad	PROPN
ejpam-6414	201	2	sajjad	sajjad	PROPN
ejpam-6414	201	3	et	et	PROPN
ejpam-6414	201	4	al	al	PROPN
ejpam-6414	201	5	.	.	PUNCT
ejpam-6414	201	6	/	/	SYM
ejpam-6414	201	7	eur	eur	PROPN
ejpam-6414	201	8	.	.	PUNCT
ejpam-6414	202	1	j.	j.	PROPN
ejpam-6414	202	2	pure	pure	PROPN
ejpam-6414	202	3	appl	appl	PROPN
ejpam-6414	202	4	.	.	PROPN
ejpam-6414	202	5	math	math	PROPN
ejpam-6414	202	6	,	,	PUNCT
ejpam-6414	202	7	18	18	NUM
ejpam-6414	202	8	(	(	PUNCT
ejpam-6414	202	9	3	3	NUM
ejpam-6414	202	10	)	)	PUNCT
ejpam-6414	202	11	(	(	PUNCT
ejpam-6414	202	12	2025	2025	NUM
ejpam-6414	202	13	)	)	PUNCT
ejpam-6414	202	14	,	,	PUNCT
ejpam-6414	202	15	6414	6414	NUM
ejpam-6414	202	16	10	10	NUM
ejpam-6414	202	17	of	of	ADP
ejpam-6414	202	18	22	22	NUM
ejpam-6414	202	19	case	case	NOUN
ejpam-6414	202	20	2	2	NUM
ejpam-6414	202	21	:	:	PUNCT
ejpam-6414	202	22	bch	bch	PROPN
ejpam-6414	202	23	codes	code	NOUN
ejpam-6414	202	24	over	over	ADP
ejpam-6414	202	25	a(2	a(2	PROPN
ejpam-6414	202	26	,	,	PUNCT
ejpam-6414	202	27	2	2	NUM
ejpam-6414	202	28	)	)	PUNCT
ejpam-6414	202	29	with	with	ADP
ejpam-6414	202	30	degree	degree	NOUN
ejpam-6414	202	31	3	3	NUM
ejpam-6414	202	32	extension	extension	NOUN
ejpam-6414	202	33	let	let	VERB
ejpam-6414	202	34	f(x	f(x	PROPN
ejpam-6414	202	35	)	)	PUNCT
ejpam-6414	202	36	∈	∈	PROPN
ejpam-6414	202	37	a(2	a(2	PROPN
ejpam-6414	202	38	,	,	PUNCT
ejpam-6414	202	39	2)[x	2)[x	PROPN
ejpam-6414	202	40	]	]	PUNCT
ejpam-6414	202	41	be	be	AUX
ejpam-6414	202	42	a	a	DET
ejpam-6414	202	43	monic	monic	ADJ
ejpam-6414	202	44	polynomial	polynomial	NOUN
ejpam-6414	202	45	of	of	ADP
ejpam-6414	202	46	degree	degree	NOUN
ejpam-6414	202	47	3	3	NUM
ejpam-6414	202	48	,	,	PUNCT
ejpam-6414	202	49	of	of	ADP
ejpam-6414	202	50	the	the	DET
ejpam-6414	202	51	form	form	NOUN
ejpam-6414	202	52	:	:	PUNCT
ejpam-6414	202	53	f(x	f(x	PROPN
ejpam-6414	202	54	)	)	PUNCT
ejpam-6414	203	1	=	=	SYM
ejpam-6414	203	2	a0	a0	NOUN
ejpam-6414	203	3	+	+	CCONJ
ejpam-6414	203	4	a1x+	a1x+	NOUN
ejpam-6414	203	5	x3	x3	PROPN
ejpam-6414	203	6	,	,	PUNCT
ejpam-6414	203	7	where	where	SCONJ
ejpam-6414	203	8	a0	a0	NOUN
ejpam-6414	203	9	,	,	PUNCT
ejpam-6414	203	10	a1	a1	NOUN
ejpam-6414	203	11	∈	∈	PROPN
ejpam-6414	203	12	a(2	a(2	PROPN
ejpam-6414	203	13	,	,	PUNCT
ejpam-6414	203	14	2	2	NUM
ejpam-6414	203	15	)	)	PUNCT
ejpam-6414	203	16	.	.	PUNCT
ejpam-6414	204	1	choose	choose	VERB
ejpam-6414	204	2	a0	a0	PROPN
ejpam-6414	204	3	=	=	SYM
ejpam-6414	204	4	1	1	NUM
ejpam-6414	204	5	,	,	PUNCT
ejpam-6414	204	6	a1	a1	NOUN
ejpam-6414	204	7	=	=	SYM
ejpam-6414	204	8	1	1	NUM
ejpam-6414	204	9	+	+	NUM
ejpam-6414	204	10	θ	θ	PROPN
ejpam-6414	204	11	,	,	PUNCT
ejpam-6414	204	12	then	then	ADV
ejpam-6414	204	13	:	:	PUNCT
ejpam-6414	204	14	f(x	f(x	PROPN
ejpam-6414	204	15	)	)	PUNCT
ejpam-6414	204	16	=	=	PUNCT
ejpam-6414	205	1	x3	x3	VERB
ejpam-6414	205	2	+	+	CCONJ
ejpam-6414	205	3	(	(	PUNCT
ejpam-6414	205	4	1	1	NUM
ejpam-6414	205	5	+	+	SYM
ejpam-6414	205	6	θ)x+	θ)x+	NUM
ejpam-6414	205	7	1	1	NUM
ejpam-6414	205	8	.	.	PUNCT
ejpam-6414	206	1	under	under	ADP
ejpam-6414	206	2	the	the	DET
ejpam-6414	206	3	natural	natural	ADJ
ejpam-6414	206	4	projection	projection	NOUN
ejpam-6414	206	5	π	π	NOUN
ejpam-6414	206	6	:	:	PUNCT
ejpam-6414	206	7	a(2	a(2	ADJ
ejpam-6414	206	8	,	,	PUNCT
ejpam-6414	206	9	2)[x	2)[x	PROPN
ejpam-6414	206	10	]	]	PUNCT
ejpam-6414	206	11	→	→	SYM
ejpam-6414	206	12	f2[x	f2[x	ADV
ejpam-6414	206	13	]	]	PUNCT
ejpam-6414	206	14	,	,	PUNCT
ejpam-6414	206	15	we	we	PRON
ejpam-6414	206	16	get	get	VERB
ejpam-6414	206	17	:	:	PUNCT
ejpam-6414	206	18	π(f(x	π(f(x	NOUN
ejpam-6414	206	19	)	)	PUNCT
ejpam-6414	206	20	)	)	PUNCT
ejpam-6414	206	21	=	=	PUNCT
ejpam-6414	207	1	x3	x3	VERB
ejpam-6414	207	2	+	+	CCONJ
ejpam-6414	207	3	x+	x+	ADJ
ejpam-6414	207	4	1	1	NUM
ejpam-6414	207	5	,	,	PUNCT
ejpam-6414	207	6	which	which	PRON
ejpam-6414	207	7	is	be	AUX
ejpam-6414	207	8	a	a	DET
ejpam-6414	207	9	monic	monic	ADJ
ejpam-6414	207	10	irreducible	irreducible	ADJ
ejpam-6414	207	11	polynomial	polynomial	NOUN
ejpam-6414	207	12	over	over	ADP
ejpam-6414	207	13	f2	f2	PROPN
ejpam-6414	207	14	.	.	PUNCT
ejpam-6414	208	1	we	we	PRON
ejpam-6414	208	2	now	now	ADV
ejpam-6414	208	3	verify	verify	VERB
ejpam-6414	208	4	the	the	DET
ejpam-6414	208	5	irreducibility	irreducibility	NOUN
ejpam-6414	208	6	of	of	ADP
ejpam-6414	208	7	f(x	f(x	PROPN
ejpam-6414	208	8	)	)	PUNCT
ejpam-6414	208	9	over	over	ADP
ejpam-6414	208	10	a(2	a(2	PROPN
ejpam-6414	208	11	,	,	PUNCT
ejpam-6414	208	12	2	2	NUM
ejpam-6414	208	13	)	)	PUNCT
ejpam-6414	208	14	by	by	ADP
ejpam-6414	208	15	evaluating	evaluate	VERB
ejpam-6414	208	16	:	:	PUNCT
ejpam-6414	208	17	f(0	f(0	NOUN
ejpam-6414	208	18	)	)	PUNCT
ejpam-6414	208	19	=	=	SYM
ejpam-6414	208	20	1	1	NUM
ejpam-6414	208	21	̸=	̸=	PROPN
ejpam-6414	208	22	0	0	NUM
ejpam-6414	208	23	,	,	PUNCT
ejpam-6414	208	24	f(1	f(1	PROPN
ejpam-6414	208	25	)	)	PUNCT
ejpam-6414	208	26	=	=	SYM
ejpam-6414	209	1	1	1	NUM
ejpam-6414	209	2	+	+	CCONJ
ejpam-6414	209	3	(	(	PUNCT
ejpam-6414	209	4	1	1	NUM
ejpam-6414	209	5	+	+	NUM
ejpam-6414	209	6	θ	θ	NOUN
ejpam-6414	209	7	)	)	PUNCT
ejpam-6414	210	1	+	+	CCONJ
ejpam-6414	210	2	1	1	NUM
ejpam-6414	210	3	=	=	SYM
ejpam-6414	210	4	1	1	NUM
ejpam-6414	210	5	+	+	NUM
ejpam-6414	210	6	θ	θ	PROPN
ejpam-6414	210	7	̸=	̸=	PROPN
ejpam-6414	210	8	0	0	NUM
ejpam-6414	210	9	,	,	PUNCT
ejpam-6414	210	10	f(θ	f(θ	NOUN
ejpam-6414	210	11	)	)	PUNCT
ejpam-6414	210	12	=	=	SYM
ejpam-6414	210	13	θ3	θ3	NOUN
ejpam-6414	210	14	+	+	CCONJ
ejpam-6414	210	15	(	(	PUNCT
ejpam-6414	210	16	1	1	NUM
ejpam-6414	210	17	+	+	CCONJ
ejpam-6414	210	18	θ)θ	θ)θ	NOUN
ejpam-6414	210	19	+	+	SYM
ejpam-6414	210	20	1	1	NUM
ejpam-6414	210	21	=	=	SYM
ejpam-6414	210	22	0	0	NUM
ejpam-6414	210	23	+	+	NUM
ejpam-6414	210	24	θ	θ	NOUN
ejpam-6414	211	1	+	+	CCONJ
ejpam-6414	211	2	1	1	NUM
ejpam-6414	211	3	+	+	SYM
ejpam-6414	211	4	1	1	NUM
ejpam-6414	211	5	=	=	SYM
ejpam-6414	211	6	θ	θ	X
ejpam-6414	211	7	̸=	̸=	PROPN
ejpam-6414	211	8	0	0	NUM
ejpam-6414	211	9	,	,	PUNCT
ejpam-6414	211	10	f(1	f(1	PROPN
ejpam-6414	211	11	+	+	PUNCT
ejpam-6414	211	12	θ	θ	X
ejpam-6414	211	13	)	)	PUNCT
ejpam-6414	211	14	=	=	SYM
ejpam-6414	212	1	(	(	PUNCT
ejpam-6414	212	2	1	1	NUM
ejpam-6414	212	3	+	+	CCONJ
ejpam-6414	212	4	θ)3	θ)3	NOUN
ejpam-6414	212	5	+	+	CCONJ
ejpam-6414	212	6	(	(	PUNCT
ejpam-6414	212	7	1	1	NUM
ejpam-6414	212	8	+	+	NUM
ejpam-6414	212	9	θ)2	θ)2	NOUN
ejpam-6414	212	10	+	+	CCONJ
ejpam-6414	212	11	1	1	NUM
ejpam-6414	212	12	=	=	SYM
ejpam-6414	212	13	1	1	NUM
ejpam-6414	212	14	+	+	NUM
ejpam-6414	212	15	θ	θ	PROPN
ejpam-6414	212	16	̸=	̸=	PROPN
ejpam-6414	212	17	0	0	NUM
ejpam-6414	212	18	.	.	PUNCT
ejpam-6414	213	1	hence	hence	ADV
ejpam-6414	213	2	,	,	PUNCT
ejpam-6414	213	3	f(x	f(x	PROPN
ejpam-6414	213	4	)	)	PUNCT
ejpam-6414	213	5	is	be	AUX
ejpam-6414	213	6	a	a	DET
ejpam-6414	213	7	basic	basic	ADJ
ejpam-6414	213	8	irreducible	irreducible	ADJ
ejpam-6414	213	9	polynomial	polynomial	NOUN
ejpam-6414	213	10	in	in	ADP
ejpam-6414	213	11	a(2	a(2	PROPN
ejpam-6414	213	12	,	,	PUNCT
ejpam-6414	213	13	2)[x	2)[x	PROPN
ejpam-6414	213	14	]	]	PUNCT
ejpam-6414	213	15	.	.	PUNCT
ejpam-6414	214	1	extension	extension	NOUN
ejpam-6414	214	2	of	of	ADP
ejpam-6414	214	3	a(2	a(2	PROPN
ejpam-6414	214	4	,	,	PUNCT
ejpam-6414	214	5	2	2	NUM
ejpam-6414	214	6	)	)	PUNCT
ejpam-6414	214	7	with	with	ADP
ejpam-6414	214	8	respect	respect	NOUN
ejpam-6414	214	9	to	to	ADP
ejpam-6414	214	10	f(x	f(x	PROPN
ejpam-6414	214	11	):	):	PUNCT
ejpam-6414	214	12	define	define	VERB
ejpam-6414	214	13	the	the	DET
ejpam-6414	214	14	extension	extension	NOUN
ejpam-6414	214	15	ring	ring	NOUN
ejpam-6414	214	16	as	as	ADP
ejpam-6414	214	17	:	:	PUNCT
ejpam-6414	214	18	r	r	NOUN
ejpam-6414	214	19	=	=	SYM
ejpam-6414	214	20	a(2	a(2	PROPN
ejpam-6414	214	21	,	,	PUNCT
ejpam-6414	214	22	2)[x	2)[x	PROPN
ejpam-6414	214	23	]	]	PUNCT
ejpam-6414	214	24	⟨f(x)⟩	⟨f(x)⟩	X
ejpam-6414	214	25	=	=	SYM
ejpam-6414	214	26	{	{	PUNCT
ejpam-6414	214	27	2∑	2∑	NUM
ejpam-6414	214	28	i=0	i=0	PROPN
ejpam-6414	214	29	ciα	ciα	PROPN
ejpam-6414	215	1	i	i	PRON
ejpam-6414	215	2	:	:	PUNCT
ejpam-6414	215	3	ci	ci	PROPN
ejpam-6414	215	4	∈	∈	PROPN
ejpam-6414	215	5	a(2	a(2	PROPN
ejpam-6414	215	6	,	,	PUNCT
ejpam-6414	215	7	2	2	NUM
ejpam-6414	215	8	)	)	PUNCT
ejpam-6414	215	9	}	}	PUNCT
ejpam-6414	215	10	,	,	PUNCT
ejpam-6414	215	11	where	where	SCONJ
ejpam-6414	215	12	α	α	NOUN
ejpam-6414	215	13	is	be	AUX
ejpam-6414	215	14	a	a	DET
ejpam-6414	215	15	root	root	NOUN
ejpam-6414	215	16	of	of	ADP
ejpam-6414	215	17	f(x	f(x	PROPN
ejpam-6414	215	18	)	)	PUNCT
ejpam-6414	215	19	,	,	PUNCT
ejpam-6414	215	20	i.e.	i.e.	X
ejpam-6414	215	21	,	,	PUNCT
ejpam-6414	215	22	f(α	f(α	NOUN
ejpam-6414	215	23	)	)	PUNCT
ejpam-6414	215	24	=	=	SYM
ejpam-6414	215	25	0	0	NUM
ejpam-6414	215	26	,	,	PUNCT
ejpam-6414	215	27	implying	implying	ADJ
ejpam-6414	215	28	:	:	PUNCT
ejpam-6414	215	29	α3	α3	NOUN
ejpam-6414	215	30	=	=	SYM
ejpam-6414	215	31	(	(	PUNCT
ejpam-6414	215	32	1	1	NUM
ejpam-6414	215	33	+	+	NUM
ejpam-6414	215	34	θ)α+	θ)α+	NOUN
ejpam-6414	215	35	1	1	NUM
ejpam-6414	215	36	.	.	PUNCT
ejpam-6414	215	37	maximal	maximal	ADJ
ejpam-6414	215	38	cyclic	cyclic	ADJ
ejpam-6414	215	39	subgroup	subgroup	NOUN
ejpam-6414	215	40	of	of	ADP
ejpam-6414	215	41	r∗	r∗	PROPN
ejpam-6414	215	42	:	:	PUNCT
ejpam-6414	215	43	since	since	SCONJ
ejpam-6414	215	44	f(x	f(x	PROPN
ejpam-6414	215	45	)	)	PUNCT
ejpam-6414	215	46	=	=	PUNCT
ejpam-6414	216	1	x3	x3	VERB
ejpam-6414	216	2	+	+	CCONJ
ejpam-6414	216	3	(	(	PUNCT
ejpam-6414	216	4	1	1	NUM
ejpam-6414	216	5	+	+	NOUN
ejpam-6414	216	6	θ)x+	θ)x+	NOUN
ejpam-6414	216	7	1	1	NUM
ejpam-6414	216	8	is	be	AUX
ejpam-6414	216	9	basic	basic	ADJ
ejpam-6414	216	10	irreducible	irreducible	ADJ
ejpam-6414	216	11	and	and	CCONJ
ejpam-6414	216	12	α	α	NOUN
ejpam-6414	216	13	is	be	AUX
ejpam-6414	216	14	its	its	PRON
ejpam-6414	216	15	root	root	NOUN
ejpam-6414	216	16	,	,	PUNCT
ejpam-6414	216	17	the	the	DET
ejpam-6414	216	18	multiplicative	multiplicative	ADJ
ejpam-6414	216	19	group	group	NOUN
ejpam-6414	216	20	r∗	r∗	PROPN
ejpam-6414	216	21	has	have	VERB
ejpam-6414	216	22	a	a	DET
ejpam-6414	216	23	cyclic	cyclic	ADJ
ejpam-6414	216	24	subgroup	subgroup	NOUN
ejpam-6414	216	25	g7	g7	PROPN
ejpam-6414	216	26	of	of	ADP
ejpam-6414	216	27	order	order	NOUN
ejpam-6414	216	28	7	7	NUM
ejpam-6414	216	29	generated	generate	VERB
ejpam-6414	216	30	by	by	ADP
ejpam-6414	216	31	γ	γ	X
ejpam-6414	216	32	=	=	SYM
ejpam-6414	216	33	α2	α2	PROPN
ejpam-6414	216	34	.	.	PUNCT
ejpam-6414	217	1	then	then	ADV
ejpam-6414	217	2	:	:	PUNCT
ejpam-6414	217	3	g7	g7	PROPN
ejpam-6414	217	4	=	=	SYM
ejpam-6414	217	5	{	{	PUNCT
ejpam-6414	217	6	γ	γ	X
ejpam-6414	217	7	,	,	PUNCT
ejpam-6414	217	8	γ2	γ2	PROPN
ejpam-6414	217	9	,	,	PUNCT
ejpam-6414	217	10	.	.	PUNCT
ejpam-6414	217	11	.	.	PUNCT
ejpam-6414	217	12	.	.	PUNCT
ejpam-6414	218	1	,	,	PUNCT
ejpam-6414	218	2	γ7	γ7	PROPN
ejpam-6414	218	3	=	=	NOUN
ejpam-6414	218	4	1	1	NUM
ejpam-6414	218	5	}	}	PUNCT
ejpam-6414	218	6	=	=	SYM
ejpam-6414	218	7	{	{	PUNCT
ejpam-6414	218	8	α2	α2	ADJ
ejpam-6414	218	9	,	,	PUNCT
ejpam-6414	218	10	α+	α+	X
ejpam-6414	218	11	(	(	PUNCT
ejpam-6414	218	12	1	1	NUM
ejpam-6414	218	13	+	+	NUM
ejpam-6414	218	14	θ)α2	θ)α2	PROPN
ejpam-6414	218	15	,	,	PUNCT
ejpam-6414	218	16	.	.	PUNCT
ejpam-6414	218	17	.	.	PUNCT
ejpam-6414	219	1	.	.	PUNCT
ejpam-6414	220	1	,	,	PUNCT
ejpam-6414	220	2	1	1	X
ejpam-6414	220	3	}	}	PUNCT
ejpam-6414	220	4	.	.	PUNCT
ejpam-6414	221	1	this	this	PRON
ejpam-6414	221	2	is	be	AUX
ejpam-6414	221	3	isomorphic	isomorphic	ADJ
ejpam-6414	221	4	to	to	ADP
ejpam-6414	221	5	the	the	DET
ejpam-6414	221	6	residue	residue	NOUN
ejpam-6414	221	7	field	field	NOUN
ejpam-6414	221	8	:	:	PUNCT
ejpam-6414	221	9	k	k	X
ejpam-6414	221	10	=	=	PUNCT
ejpam-6414	221	11	f2[x	f2[x	NOUN
ejpam-6414	221	12	]	]	X
ejpam-6414	221	13	⟨π(f(x))⟩	⟨π(f(x))⟩	VERB
ejpam-6414	221	14	=	=	SYM
ejpam-6414	221	15	f2[x	f2[x	NOUN
ejpam-6414	221	16	]	]	X
ejpam-6414	222	1	⟨x3	⟨x3	PROPN
ejpam-6414	222	2	+	+	CCONJ
ejpam-6414	222	3	x+	x+	ADJ
ejpam-6414	222	4	1⟩	1⟩	NUM
ejpam-6414	222	5	.	.	PUNCT
ejpam-6414	223	1	muhammad	muhammad	PROPN
ejpam-6414	223	2	sajjad	sajjad	PROPN
ejpam-6414	223	3	et	et	PROPN
ejpam-6414	223	4	al	al	PROPN
ejpam-6414	223	5	.	.	PUNCT
ejpam-6414	223	6	/	/	SYM
ejpam-6414	223	7	eur	eur	PROPN
ejpam-6414	223	8	.	.	PUNCT
ejpam-6414	224	1	j.	j.	PROPN
ejpam-6414	224	2	pure	pure	PROPN
ejpam-6414	224	3	appl	appl	PROPN
ejpam-6414	224	4	.	.	PROPN
ejpam-6414	224	5	math	math	PROPN
ejpam-6414	224	6	,	,	PUNCT
ejpam-6414	224	7	18	18	NUM
ejpam-6414	224	8	(	(	PUNCT
ejpam-6414	224	9	3	3	NUM
ejpam-6414	224	10	)	)	PUNCT
ejpam-6414	224	11	(	(	PUNCT
ejpam-6414	224	12	2025	2025	NUM
ejpam-6414	224	13	)	)	PUNCT
ejpam-6414	224	14	,	,	PUNCT
ejpam-6414	224	15	6414	6414	NUM
ejpam-6414	224	16	11	11	NUM
ejpam-6414	224	17	of	of	ADP
ejpam-6414	224	18	22	22	NUM
ejpam-6414	224	19	table	table	NOUN
ejpam-6414	224	20	1	1	NUM
ejpam-6414	224	21	:	:	PUNCT
ejpam-6414	224	22	multiplicative	multiplicative	ADJ
ejpam-6414	224	23	group	group	NOUN
ejpam-6414	224	24	of	of	ADP
ejpam-6414	224	25	order	order	NOUN
ejpam-6414	224	26	14	14	NUM
ejpam-6414	224	27	exp	exp	NOUN
ejpam-6414	224	28	.	.	PUNCT
ejpam-6414	225	1	polynomial	polynomial	ADJ
ejpam-6414	225	2	exp	exp	NOUN
ejpam-6414	225	3	.	.	PUNCT
ejpam-6414	226	1	polynomial	polynomial	ADJ
ejpam-6414	226	2	1	1	NUM
ejpam-6414	226	3	α	α	NOUN
ejpam-6414	226	4	8	8	NUM
ejpam-6414	226	5	α+	α+	NOUN
ejpam-6414	226	6	uα2	uα2	ADJ
ejpam-6414	226	7	2	2	NUM
ejpam-6414	226	8	α2	α2	ADJ
ejpam-6414	226	9	9	9	NUM
ejpam-6414	226	10	α2	α2	ADJ
ejpam-6414	226	11	+	+	NUM
ejpam-6414	226	12	uα+	uα+	PROPN
ejpam-6414	226	13	u	u	NOUN
ejpam-6414	226	14	3	3	NUM
ejpam-6414	226	15	(	(	PUNCT
ejpam-6414	226	16	1	1	NUM
ejpam-6414	226	17	+	+	NUM
ejpam-6414	226	18	u)α+	u)α+	ADJ
ejpam-6414	226	19	1	1	NUM
ejpam-6414	226	20	10	10	NUM
ejpam-6414	226	21	α2u+	α2u+	ADJ
ejpam-6414	226	22	α+	α+	PUNCT
ejpam-6414	226	23	1	1	NUM
ejpam-6414	226	24	4	4	NUM
ejpam-6414	226	25	α+	α+	NOUN
ejpam-6414	226	26	(	(	PUNCT
ejpam-6414	226	27	1	1	NUM
ejpam-6414	226	28	+	+	CCONJ
ejpam-6414	226	29	u)α2	u)α2	PROPN
ejpam-6414	226	30	11	11	NUM
ejpam-6414	226	31	α2	α2	ADJ
ejpam-6414	226	32	+	+	CCONJ
ejpam-6414	226	33	(	(	PUNCT
ejpam-6414	226	34	1	1	NUM
ejpam-6414	226	35	+	+	NUM
ejpam-6414	226	36	u)α+	u)α+	ADJ
ejpam-6414	226	37	u	u	NOUN
ejpam-6414	226	38	5	5	NUM
ejpam-6414	226	39	α2	α2	ADJ
ejpam-6414	226	40	+	+	CCONJ
ejpam-6414	226	41	α+	α+	PUNCT
ejpam-6414	226	42	(	(	PUNCT
ejpam-6414	226	43	1	1	NUM
ejpam-6414	226	44	+	+	NUM
ejpam-6414	226	45	u	u	NOUN
ejpam-6414	226	46	)	)	PUNCT
ejpam-6414	226	47	12	12	NUM
ejpam-6414	226	48	1	1	NUM
ejpam-6414	226	49	+	+	CCONJ
ejpam-6414	226	50	α+	α+	PUNCT
ejpam-6414	226	51	(	(	PUNCT
ejpam-6414	226	52	1	1	NUM
ejpam-6414	226	53	+	+	CCONJ
ejpam-6414	226	54	u)α2	u)α2	PROPN
ejpam-6414	226	55	6	6	NUM
ejpam-6414	226	56	α2	α2	ADJ
ejpam-6414	226	57	+	+	CCONJ
ejpam-6414	226	58	1	1	NUM
ejpam-6414	226	59	13	13	NUM
ejpam-6414	226	60	α2	α2	ADJ
ejpam-6414	226	61	+	+	CCONJ
ejpam-6414	226	62	u+	u+	NUM
ejpam-6414	226	63	1	1	NUM
ejpam-6414	226	64	7	7	NUM
ejpam-6414	226	65	αu+	αu+	NOUN
ejpam-6414	226	66	1	1	NUM
ejpam-6414	226	67	14	14	NUM
ejpam-6414	226	68	1	1	NUM
ejpam-6414	226	69	generator	generator	NOUN
ejpam-6414	226	70	polynomial	polynomial	NOUN
ejpam-6414	226	71	of	of	ADP
ejpam-6414	226	72	bch	bch	PROPN
ejpam-6414	226	73	code	code	PROPN
ejpam-6414	226	74	over	over	ADP
ejpam-6414	226	75	a(2	a(2	PROPN
ejpam-6414	226	76	,	,	PUNCT
ejpam-6414	226	77	2	2	NUM
ejpam-6414	226	78	):	):	PUNCT
ejpam-6414	226	79	since	since	SCONJ
ejpam-6414	226	80	γ	γ	PROPN
ejpam-6414	226	81	=	=	SYM
ejpam-6414	226	82	α2	α2	PROPN
ejpam-6414	226	83	is	be	AUX
ejpam-6414	226	84	a	a	DET
ejpam-6414	226	85	primitive	primitive	ADJ
ejpam-6414	226	86	cube	cube	NOUN
ejpam-6414	226	87	root	root	NOUN
ejpam-6414	226	88	of	of	ADP
ejpam-6414	226	89	unity	unity	NOUN
ejpam-6414	226	90	in	in	ADP
ejpam-6414	226	91	g7	g7	PROPN
ejpam-6414	226	92	,	,	PUNCT
ejpam-6414	226	93	and	and	CCONJ
ejpam-6414	226	94	for	for	ADP
ejpam-6414	226	95	design	design	NOUN
ejpam-6414	226	96	distance	distance	NOUN
ejpam-6414	226	97	d	d	NOUN
ejpam-6414	226	98	=	=	SYM
ejpam-6414	226	99	3	3	NUM
ejpam-6414	226	100	,	,	PUNCT
ejpam-6414	226	101	we	we	PRON
ejpam-6414	226	102	need	need	VERB
ejpam-6414	226	103	the	the	DET
ejpam-6414	226	104	minimal	minimal	ADJ
ejpam-6414	226	105	polynomials	polynomial	NOUN
ejpam-6414	226	106	of	of	ADP
ejpam-6414	226	107	γi	γi	NOUN
ejpam-6414	226	108	for	for	ADP
ejpam-6414	226	109	i	i	PRON
ejpam-6414	226	110	=	=	NOUN
ejpam-6414	226	111	1	1	NUM
ejpam-6414	226	112	,	,	PUNCT
ejpam-6414	226	113	2	2	NUM
ejpam-6414	226	114	.	.	X
ejpam-6414	227	1	let	let	AUX
ejpam-6414	227	2	m1(x	m1(x	PRON
ejpam-6414	227	3	)	)	PUNCT
ejpam-6414	227	4	be	be	AUX
ejpam-6414	227	5	the	the	DET
ejpam-6414	227	6	minimal	minimal	ADJ
ejpam-6414	227	7	polynomial	polynomial	NOUN
ejpam-6414	227	8	of	of	ADP
ejpam-6414	227	9	γ	γ	PROPN
ejpam-6414	227	10	.	.	PROPN
ejpam-6414	228	1	then	then	ADV
ejpam-6414	228	2	γ	γ	PROPN
ejpam-6414	228	3	,	,	PUNCT
ejpam-6414	228	4	γ2	γ2	PROPN
ejpam-6414	228	5	,	,	PUNCT
ejpam-6414	228	6	γ4	γ4	NOUN
ejpam-6414	228	7	have	have	VERB
ejpam-6414	228	8	the	the	DET
ejpam-6414	228	9	same	same	ADJ
ejpam-6414	228	10	minimal	minimal	ADJ
ejpam-6414	228	11	polynomial	polynomial	ADJ
ejpam-6414	228	12	:	:	PUNCT
ejpam-6414	228	13	m1(x	m1(x	NOUN
ejpam-6414	228	14	)	)	PUNCT
ejpam-6414	228	15	=	=	SYM
ejpam-6414	228	16	(	(	PUNCT
ejpam-6414	228	17	x−	x−	PROPN
ejpam-6414	228	18	γ)(x−	γ)(x−	PROPN
ejpam-6414	228	19	γ2)(x−	γ2)(x−	PROPN
ejpam-6414	228	20	γ4	γ4	PROPN
ejpam-6414	228	21	)	)	PUNCT
ejpam-6414	228	22	=	=	SYM
ejpam-6414	229	1	x3	x3	VERB
ejpam-6414	229	2	+	+	CCONJ
ejpam-6414	229	3	x+	x+	ADJ
ejpam-6414	229	4	1	1	X
ejpam-6414	229	5	.	.	PUNCT
ejpam-6414	230	1	hence	hence	ADV
ejpam-6414	230	2	,	,	PUNCT
ejpam-6414	230	3	the	the	DET
ejpam-6414	230	4	generator	generator	NOUN
ejpam-6414	230	5	polynomial	polynomial	NOUN
ejpam-6414	230	6	is	be	AUX
ejpam-6414	230	7	:	:	PUNCT
ejpam-6414	230	8	g(x	g(x	X
ejpam-6414	230	9	)	)	PUNCT
ejpam-6414	230	10	=	=	SYM
ejpam-6414	230	11	lcm{m1(x),m2(x	lcm{m1(x),m2(x	NOUN
ejpam-6414	230	12	)	)	PUNCT
ejpam-6414	230	13	}	}	PUNCT
ejpam-6414	230	14	=	=	SYM
ejpam-6414	230	15	m1(x	m1(x	NOUN
ejpam-6414	230	16	)	)	PUNCT
ejpam-6414	230	17	=	=	SYM
ejpam-6414	231	1	x3	x3	VERB
ejpam-6414	231	2	+	+	CCONJ
ejpam-6414	231	3	x+	x+	ADJ
ejpam-6414	231	4	1	1	X
ejpam-6414	231	5	.	.	PUNCT
ejpam-6414	231	6	given	give	VERB
ejpam-6414	231	7	r	r	NOUN
ejpam-6414	231	8	=	=	SYM
ejpam-6414	231	9	3	3	NUM
ejpam-6414	231	10	,	,	PUNCT
ejpam-6414	231	11	q	q	NOUN
ejpam-6414	231	12	=	=	SYM
ejpam-6414	231	13	2	2	NUM
ejpam-6414	231	14	,	,	PUNCT
ejpam-6414	231	15	m	m	VERB
ejpam-6414	231	16	=	=	NOUN
ejpam-6414	231	17	3	3	NUM
ejpam-6414	231	18	,	,	PUNCT
ejpam-6414	231	19	and	and	CCONJ
ejpam-6414	231	20	c	c	NOUN
ejpam-6414	231	21	=	=	SYM
ejpam-6414	231	22	1	1	NUM
ejpam-6414	231	23	(	(	PUNCT
ejpam-6414	231	24	narrow	narrow	ADJ
ejpam-6414	231	25	-	-	PUNCT
ejpam-6414	231	26	sense	sense	NOUN
ejpam-6414	231	27	bch	bch	PROPN
ejpam-6414	231	28	code	code	PROPN
ejpam-6414	231	29	)	)	PUNCT
ejpam-6414	231	30	,	,	PUNCT
ejpam-6414	231	31	the	the	DET
ejpam-6414	231	32	code	code	NOUN
ejpam-6414	231	33	length	length	NOUN
ejpam-6414	231	34	is	be	AUX
ejpam-6414	231	35	:	:	PUNCT
ejpam-6414	231	36	n	n	PROPN
ejpam-6414	231	37	=	=	SYM
ejpam-6414	231	38	qm	qm	PROPN
ejpam-6414	231	39	−	−	PROPN
ejpam-6414	231	40	1	1	NUM
ejpam-6414	231	41	=	=	SYM
ejpam-6414	231	42	23	23	NUM
ejpam-6414	231	43	−	−	NOUN
ejpam-6414	231	44	1	1	NUM
ejpam-6414	231	45	=	=	SYM
ejpam-6414	231	46	7	7	NUM
ejpam-6414	231	47	.	.	PUNCT
ejpam-6414	232	1	the	the	DET
ejpam-6414	232	2	cyclic	cyclic	PROPN
ejpam-6414	232	3	code	code	PROPN
ejpam-6414	232	4	c	c	NOUN
ejpam-6414	232	5	generated	generate	VERB
ejpam-6414	232	6	by	by	ADP
ejpam-6414	232	7	g(x	g(x	PROPN
ejpam-6414	232	8	)	)	PUNCT
ejpam-6414	232	9	over	over	ADP
ejpam-6414	232	10	g7	g7	PROPN
ejpam-6414	232	11	⊂	⊂	PROPN
ejpam-6414	232	12	r∗	r∗	PROPN
ejpam-6414	232	13	⊂	⊂	PROPN
ejpam-6414	232	14	a(2	a(2	PROPN
ejpam-6414	232	15	,	,	PUNCT
ejpam-6414	232	16	2	2	NUM
ejpam-6414	232	17	)	)	PUNCT
ejpam-6414	232	18	has	have	AUX
ejpam-6414	232	19	dimension	dimension	NOUN
ejpam-6414	232	20	4	4	NUM
ejpam-6414	232	21	.	.	PUNCT
ejpam-6414	233	1	thus	thus	ADV
ejpam-6414	233	2	,	,	PUNCT
ejpam-6414	233	3	c	c	PROPN
ejpam-6414	233	4	is	be	AUX
ejpam-6414	233	5	a	a	DET
ejpam-6414	233	6	:	:	PUNCT
ejpam-6414	233	7	[	[	X
ejpam-6414	233	8	7	7	NUM
ejpam-6414	233	9	,	,	PUNCT
ejpam-6414	233	10	4	4	NUM
ejpam-6414	233	11	,	,	PUNCT
ejpam-6414	233	12	3	3	NUM
ejpam-6414	233	13	]	]	X
ejpam-6414	233	14	primitive	primitive	ADJ
ejpam-6414	233	15	narrow	narrow	ADJ
ejpam-6414	233	16	-	-	PUNCT
ejpam-6414	233	17	sense	sense	NOUN
ejpam-6414	233	18	bch	bch	PROPN
ejpam-6414	233	19	code	code	NOUN
ejpam-6414	233	20	over	over	ADP
ejpam-6414	233	21	the	the	DET
ejpam-6414	233	22	maximal	maximal	ADJ
ejpam-6414	233	23	cyclic	cyclic	ADJ
ejpam-6414	233	24	subgroup	subgroup	NOUN
ejpam-6414	233	25	of	of	ADP
ejpam-6414	233	26	units	unit	NOUN
ejpam-6414	233	27	in	in	ADP
ejpam-6414	233	28	a(2	a(2	PROPN
ejpam-6414	233	29	,	,	PUNCT
ejpam-6414	233	30	2	2	NUM
ejpam-6414	233	31	)	)	PUNCT
ejpam-6414	233	32	.	.	PUNCT
ejpam-6414	234	1	case	case	NOUN
ejpam-6414	234	2	3	3	NUM
ejpam-6414	234	3	:	:	PUNCT
ejpam-6414	234	4	bch	bch	PROPN
ejpam-6414	234	5	codes	code	NOUN
ejpam-6414	234	6	over	over	ADP
ejpam-6414	234	7	a(2	a(2	PROPN
ejpam-6414	234	8	,	,	PUNCT
ejpam-6414	234	9	2	2	NUM
ejpam-6414	234	10	)	)	PUNCT
ejpam-6414	234	11	with	with	ADP
ejpam-6414	234	12	degree	degree	NOUN
ejpam-6414	234	13	4	4	NUM
ejpam-6414	234	14	extension	extension	NOUN
ejpam-6414	234	15	let	let	VERB
ejpam-6414	234	16	f(x	f(x	PROPN
ejpam-6414	234	17	)	)	PUNCT
ejpam-6414	234	18	∈	∈	PROPN
ejpam-6414	234	19	a(2	a(2	PROPN
ejpam-6414	234	20	,	,	PUNCT
ejpam-6414	234	21	2)[x	2)[x	PROPN
ejpam-6414	234	22	]	]	PUNCT
ejpam-6414	234	23	be	be	AUX
ejpam-6414	234	24	a	a	DET
ejpam-6414	234	25	monic	monic	ADJ
ejpam-6414	234	26	polynomial	polynomial	NOUN
ejpam-6414	234	27	of	of	ADP
ejpam-6414	234	28	degree	degree	NOUN
ejpam-6414	234	29	4	4	NUM
ejpam-6414	234	30	:	:	PUNCT
ejpam-6414	234	31	f(x	f(x	PROPN
ejpam-6414	234	32	)	)	PUNCT
ejpam-6414	235	1	=	=	SYM
ejpam-6414	235	2	a0	a0	NOUN
ejpam-6414	235	3	+	+	CCONJ
ejpam-6414	235	4	a1x+	a1x+	NOUN
ejpam-6414	235	5	x4	x4	PROPN
ejpam-6414	235	6	,	,	PUNCT
ejpam-6414	235	7	where	where	SCONJ
ejpam-6414	235	8	a0	a0	NOUN
ejpam-6414	235	9	,	,	PUNCT
ejpam-6414	235	10	a1	a1	NOUN
ejpam-6414	235	11	∈	∈	PROPN
ejpam-6414	235	12	a(2	a(2	PROPN
ejpam-6414	235	13	,	,	PUNCT
ejpam-6414	235	14	2	2	NUM
ejpam-6414	235	15	)	)	PUNCT
ejpam-6414	235	16	.	.	PUNCT
ejpam-6414	236	1	choose	choose	VERB
ejpam-6414	236	2	a0	a0	PROPN
ejpam-6414	236	3	=	=	SYM
ejpam-6414	236	4	1	1	NUM
ejpam-6414	236	5	,	,	PUNCT
ejpam-6414	236	6	a1	a1	NOUN
ejpam-6414	236	7	=	=	SYM
ejpam-6414	236	8	1	1	NUM
ejpam-6414	236	9	+	+	NUM
ejpam-6414	236	10	θ	θ	PROPN
ejpam-6414	236	11	,	,	PUNCT
ejpam-6414	236	12	then	then	ADV
ejpam-6414	236	13	:	:	PUNCT
ejpam-6414	236	14	f(x	f(x	PROPN
ejpam-6414	236	15	)	)	PUNCT
ejpam-6414	236	16	=	=	PUNCT
ejpam-6414	237	1	x4	x4	PROPN
ejpam-6414	238	1	+	+	CCONJ
ejpam-6414	238	2	(	(	PUNCT
ejpam-6414	238	3	1	1	NUM
ejpam-6414	238	4	+	+	SYM
ejpam-6414	238	5	θ)x+	θ)x+	NUM
ejpam-6414	238	6	1	1	NUM
ejpam-6414	238	7	.	.	PUNCT
ejpam-6414	239	1	the	the	DET
ejpam-6414	239	2	projection	projection	NOUN
ejpam-6414	239	3	map	map	NOUN
ejpam-6414	239	4	π	π	X
ejpam-6414	239	5	:	:	PUNCT
ejpam-6414	239	6	a(2	a(2	ADJ
ejpam-6414	239	7	,	,	PUNCT
ejpam-6414	239	8	2)[x	2)[x	PROPN
ejpam-6414	239	9	]	]	PUNCT
ejpam-6414	239	10	→	→	SYM
ejpam-6414	239	11	f2[x	f2[x	ADV
ejpam-6414	239	12	]	]	PUNCT
ejpam-6414	239	13	gives	give	VERB
ejpam-6414	239	14	:	:	PUNCT
ejpam-6414	239	15	π(f(x	π(f(x	PROPN
ejpam-6414	239	16	)	)	PUNCT
ejpam-6414	239	17	)	)	PUNCT
ejpam-6414	240	1	=	=	PUNCT
ejpam-6414	240	2	x4	x4	PROPN
ejpam-6414	241	1	+	+	CCONJ
ejpam-6414	241	2	x+	x+	PROPN
ejpam-6414	241	3	1	1	NUM
ejpam-6414	241	4	,	,	PUNCT
ejpam-6414	241	5	which	which	PRON
ejpam-6414	241	6	is	be	AUX
ejpam-6414	241	7	a	a	DET
ejpam-6414	241	8	monic	monic	ADJ
ejpam-6414	241	9	irreducible	irreducible	ADJ
ejpam-6414	241	10	polynomial	polynomial	NOUN
ejpam-6414	241	11	over	over	ADP
ejpam-6414	241	12	f2	f2	PROPN
ejpam-6414	241	13	.	.	PUNCT
ejpam-6414	242	1	we	we	PRON
ejpam-6414	242	2	now	now	ADV
ejpam-6414	242	3	verify	verify	VERB
ejpam-6414	242	4	irreducibility	irreducibility	NOUN
ejpam-6414	242	5	over	over	ADP
ejpam-6414	242	6	a(2	a(2	PROPN
ejpam-6414	242	7	,	,	PUNCT
ejpam-6414	242	8	2	2	NUM
ejpam-6414	242	9	):	):	PUNCT
ejpam-6414	242	10	muhammad	muhammad	PROPN
ejpam-6414	242	11	sajjad	sajjad	PROPN
ejpam-6414	242	12	et	et	PROPN
ejpam-6414	242	13	al	al	PROPN
ejpam-6414	242	14	.	.	PUNCT
ejpam-6414	242	15	/	/	SYM
ejpam-6414	242	16	eur	eur	PROPN
ejpam-6414	242	17	.	.	PUNCT
ejpam-6414	243	1	j.	j.	PROPN
ejpam-6414	243	2	pure	pure	PROPN
ejpam-6414	243	3	appl	appl	PROPN
ejpam-6414	243	4	.	.	PROPN
ejpam-6414	243	5	math	math	PROPN
ejpam-6414	243	6	,	,	PUNCT
ejpam-6414	243	7	18	18	NUM
ejpam-6414	243	8	(	(	PUNCT
ejpam-6414	243	9	3	3	NUM
ejpam-6414	243	10	)	)	PUNCT
ejpam-6414	243	11	(	(	PUNCT
ejpam-6414	243	12	2025	2025	NUM
ejpam-6414	243	13	)	)	PUNCT
ejpam-6414	243	14	,	,	PUNCT
ejpam-6414	243	15	6414	6414	NUM
ejpam-6414	243	16	12	12	NUM
ejpam-6414	243	17	of	of	ADP
ejpam-6414	243	18	22	22	NUM
ejpam-6414	243	19	f(0	f(0	NOUN
ejpam-6414	243	20	)	)	PUNCT
ejpam-6414	243	21	=	=	SYM
ejpam-6414	244	1	1	1	NUM
ejpam-6414	244	2	̸=	̸=	PROPN
ejpam-6414	244	3	0	0	NUM
ejpam-6414	244	4	,	,	PUNCT
ejpam-6414	244	5	f(1	f(1	PROPN
ejpam-6414	244	6	)	)	PUNCT
ejpam-6414	244	7	=	=	SYM
ejpam-6414	244	8	1	1	NUM
ejpam-6414	244	9	+	+	CCONJ
ejpam-6414	244	10	(	(	PUNCT
ejpam-6414	244	11	1	1	NUM
ejpam-6414	244	12	+	+	NUM
ejpam-6414	244	13	θ	θ	NOUN
ejpam-6414	244	14	)	)	PUNCT
ejpam-6414	244	15	+	+	CCONJ
ejpam-6414	244	16	1	1	NUM
ejpam-6414	244	17	=	=	SYM
ejpam-6414	244	18	1	1	NUM
ejpam-6414	244	19	+	+	NUM
ejpam-6414	244	20	θ	θ	PROPN
ejpam-6414	244	21	̸=	̸=	PROPN
ejpam-6414	244	22	0	0	NUM
ejpam-6414	244	23	,	,	PUNCT
ejpam-6414	244	24	f(θ	f(θ	PROPN
ejpam-6414	244	25	)	)	PUNCT
ejpam-6414	244	26	=	=	SYM
ejpam-6414	244	27	θ4	θ4	NOUN
ejpam-6414	244	28	+	+	CCONJ
ejpam-6414	244	29	(	(	PUNCT
ejpam-6414	244	30	1	1	NUM
ejpam-6414	244	31	+	+	CCONJ
ejpam-6414	244	32	θ)θ	θ)θ	NOUN
ejpam-6414	244	33	+	+	SYM
ejpam-6414	244	34	1	1	NUM
ejpam-6414	244	35	=	=	SYM
ejpam-6414	244	36	θ	θ	PROPN
ejpam-6414	244	37	+	+	NUM
ejpam-6414	244	38	θ	θ	X
ejpam-6414	244	39	+	+	CCONJ
ejpam-6414	244	40	1	1	NUM
ejpam-6414	244	41	=	=	SYM
ejpam-6414	244	42	1	1	NUM
ejpam-6414	244	43	̸=	̸=	PROPN
ejpam-6414	244	44	0	0	NUM
ejpam-6414	244	45	,	,	PUNCT
ejpam-6414	244	46	f(1	f(1	PROPN
ejpam-6414	244	47	+	+	PUNCT
ejpam-6414	244	48	θ	θ	X
ejpam-6414	244	49	)	)	PUNCT
ejpam-6414	244	50	=	=	SYM
ejpam-6414	244	51	(	(	PUNCT
ejpam-6414	244	52	1	1	NUM
ejpam-6414	244	53	+	+	NUM
ejpam-6414	244	54	θ)4	θ)4	NOUN
ejpam-6414	244	55	+	+	CCONJ
ejpam-6414	244	56	(	(	PUNCT
ejpam-6414	244	57	1	1	NUM
ejpam-6414	244	58	+	+	NUM
ejpam-6414	244	59	θ)2	θ)2	NOUN
ejpam-6414	244	60	+	+	CCONJ
ejpam-6414	244	61	1	1	NUM
ejpam-6414	244	62	=	=	SYM
ejpam-6414	244	63	1	1	NUM
ejpam-6414	244	64	+	+	NUM
ejpam-6414	244	65	θ	θ	PROPN
ejpam-6414	244	66	̸=	̸=	PROPN
ejpam-6414	244	67	0	0	NUM
ejpam-6414	244	68	.	.	PUNCT
ejpam-6414	245	1	thus	thus	ADV
ejpam-6414	245	2	,	,	PUNCT
ejpam-6414	245	3	f(x	f(x	PROPN
ejpam-6414	245	4	)	)	PUNCT
ejpam-6414	245	5	is	be	AUX
ejpam-6414	245	6	a	a	DET
ejpam-6414	245	7	basic	basic	ADJ
ejpam-6414	245	8	irreducible	irreducible	ADJ
ejpam-6414	245	9	polynomial	polynomial	NOUN
ejpam-6414	245	10	in	in	ADP
ejpam-6414	245	11	a(2	a(2	PROPN
ejpam-6414	245	12	,	,	PUNCT
ejpam-6414	245	13	2)[x	2)[x	PROPN
ejpam-6414	245	14	]	]	PUNCT
ejpam-6414	245	15	.	.	PUNCT
ejpam-6414	246	1	extension	extension	NOUN
ejpam-6414	246	2	of	of	ADP
ejpam-6414	246	3	a(2	a(2	PROPN
ejpam-6414	246	4	,	,	PUNCT
ejpam-6414	246	5	2	2	NUM
ejpam-6414	246	6	)	)	PUNCT
ejpam-6414	246	7	with	with	ADP
ejpam-6414	246	8	respect	respect	NOUN
ejpam-6414	246	9	to	to	ADP
ejpam-6414	246	10	f(x	f(x	PROPN
ejpam-6414	246	11	):	):	PUNCT
ejpam-6414	246	12	we	we	PRON
ejpam-6414	246	13	define	define	VERB
ejpam-6414	246	14	the	the	DET
ejpam-6414	246	15	galois	galois	PROPN
ejpam-6414	246	16	extension	extension	NOUN
ejpam-6414	246	17	ring	ring	NOUN
ejpam-6414	246	18	:	:	PUNCT
ejpam-6414	246	19	r	r	NOUN
ejpam-6414	246	20	=	=	SYM
ejpam-6414	246	21	a(2	a(2	PROPN
ejpam-6414	246	22	,	,	PUNCT
ejpam-6414	246	23	2)[x	2)[x	PROPN
ejpam-6414	246	24	]	]	PUNCT
ejpam-6414	246	25	⟨f(x)⟩	⟨f(x)⟩	X
ejpam-6414	246	26	=	=	SYM
ejpam-6414	246	27	{	{	PUNCT
ejpam-6414	246	28	3∑	3∑	NUM
ejpam-6414	246	29	i=0	i=0	PROPN
ejpam-6414	246	30	ciα	ciα	PROPN
ejpam-6414	247	1	i	i	PRON
ejpam-6414	247	2	:	:	PUNCT
ejpam-6414	247	3	ci	ci	PROPN
ejpam-6414	247	4	∈	∈	PROPN
ejpam-6414	247	5	a(2	a(2	PROPN
ejpam-6414	247	6	,	,	PUNCT
ejpam-6414	247	7	2	2	NUM
ejpam-6414	247	8	)	)	PUNCT
ejpam-6414	247	9	}	}	PUNCT
ejpam-6414	247	10	,	,	PUNCT
ejpam-6414	247	11	where	where	SCONJ
ejpam-6414	247	12	f(x	f(x	NOUN
ejpam-6414	247	13	)	)	PUNCT
ejpam-6414	247	14	=	=	PUNCT
ejpam-6414	248	1	x4	x4	PROPN
ejpam-6414	249	1	+	+	CCONJ
ejpam-6414	249	2	(	(	PUNCT
ejpam-6414	249	3	1	1	NUM
ejpam-6414	249	4	+	+	SYM
ejpam-6414	249	5	θ)x+	θ)x+	SYM
ejpam-6414	249	6	1	1	NUM
ejpam-6414	249	7	and	and	CCONJ
ejpam-6414	249	8	f(α	f(α	NOUN
ejpam-6414	249	9	)	)	PUNCT
ejpam-6414	249	10	=	=	SYM
ejpam-6414	249	11	0	0	NUM
ejpam-6414	249	12	,	,	PUNCT
ejpam-6414	249	13	hence	hence	ADV
ejpam-6414	249	14	:	:	PUNCT
ejpam-6414	249	15	α4	α4	NOUN
ejpam-6414	249	16	=	=	SYM
ejpam-6414	249	17	(	(	PUNCT
ejpam-6414	249	18	1	1	NUM
ejpam-6414	249	19	+	+	NUM
ejpam-6414	249	20	θ)α+	θ)α+	NOUN
ejpam-6414	249	21	1	1	NUM
ejpam-6414	249	22	.	.	PUNCT
ejpam-6414	249	23	maximal	maximal	ADJ
ejpam-6414	249	24	cyclic	cyclic	ADJ
ejpam-6414	249	25	subgroup	subgroup	NOUN
ejpam-6414	249	26	of	of	ADP
ejpam-6414	249	27	r∗	r∗	PROPN
ejpam-6414	249	28	:	:	PUNCT
ejpam-6414	249	29	the	the	DET
ejpam-6414	249	30	multiplicative	multiplicative	PROPN
ejpam-6414	249	31	group	group	NOUN
ejpam-6414	249	32	r∗	r∗	PROPN
ejpam-6414	249	33	has	have	VERB
ejpam-6414	249	34	a	a	DET
ejpam-6414	249	35	cyclic	cyclic	ADJ
ejpam-6414	249	36	subgroup	subgroup	NOUN
ejpam-6414	249	37	g15	g15	NOUN
ejpam-6414	249	38	of	of	ADP
ejpam-6414	249	39	order	order	NOUN
ejpam-6414	249	40	15	15	NUM
ejpam-6414	249	41	generated	generate	VERB
ejpam-6414	249	42	by	by	ADP
ejpam-6414	249	43	γ	γ	X
ejpam-6414	249	44	=	=	SYM
ejpam-6414	249	45	α2	α2	PROPN
ejpam-6414	249	46	.	.	PUNCT
ejpam-6414	250	1	this	this	DET
ejpam-6414	250	2	subgroup	subgroup	NOUN
ejpam-6414	250	3	is	be	AUX
ejpam-6414	250	4	isomorphic	isomorphic	ADJ
ejpam-6414	250	5	to	to	ADP
ejpam-6414	250	6	the	the	DET
ejpam-6414	250	7	residue	residue	NOUN
ejpam-6414	250	8	field	field	NOUN
ejpam-6414	250	9	:	:	PUNCT
ejpam-6414	250	10	k	k	X
ejpam-6414	250	11	=	=	PUNCT
ejpam-6414	250	12	f2[x	f2[x	NOUN
ejpam-6414	250	13	]	]	X
ejpam-6414	250	14	⟨π(f(x))⟩	⟨π(f(x))⟩	VERB
ejpam-6414	250	15	=	=	SYM
ejpam-6414	250	16	f2[x	f2[x	NOUN
ejpam-6414	250	17	]	]	X
ejpam-6414	250	18	⟨x4	⟨x4	PROPN
ejpam-6414	251	1	+	+	CCONJ
ejpam-6414	251	2	x+	x+	X
ejpam-6414	251	3	1⟩	1⟩	NUM
ejpam-6414	251	4	.	.	PUNCT
ejpam-6414	252	1	table	table	NOUN
ejpam-6414	252	2	2	2	NUM
ejpam-6414	252	3	:	:	PUNCT
ejpam-6414	252	4	cyclic	cyclic	ADJ
ejpam-6414	252	5	group	group	NOUN
ejpam-6414	252	6	of	of	ADP
ejpam-6414	252	7	order	order	NOUN
ejpam-6414	252	8	30	30	NUM
ejpam-6414	252	9	exp	exp	NOUN
ejpam-6414	252	10	.	.	PUNCT
ejpam-6414	253	1	polynomial	polynomial	ADJ
ejpam-6414	253	2	exp	exp	PROPN
ejpam-6414	253	3	.	.	PUNCT
ejpam-6414	254	1	polynomial	polynomial	ADJ
ejpam-6414	254	2	1	1	NUM
ejpam-6414	254	3	α	α	NOUN
ejpam-6414	254	4	16	16	NUM
ejpam-6414	255	1	(	(	PUNCT
ejpam-6414	255	2	1	1	NUM
ejpam-6414	255	3	+	+	CCONJ
ejpam-6414	255	4	u)α	u)α	NOUN
ejpam-6414	255	5	2	2	NUM
ejpam-6414	255	6	α2	α2	ADJ
ejpam-6414	255	7	17	17	NUM
ejpam-6414	255	8	(	(	PUNCT
ejpam-6414	255	9	1	1	NUM
ejpam-6414	255	10	+	+	CCONJ
ejpam-6414	255	11	u)α2	u)α2	PROPN
ejpam-6414	255	12	3	3	NUM
ejpam-6414	255	13	α3	α3	NOUN
ejpam-6414	255	14	18	18	NUM
ejpam-6414	255	15	(	(	PUNCT
ejpam-6414	255	16	1	1	NUM
ejpam-6414	255	17	+	+	X
ejpam-6414	255	18	u)α3	u)α3	PROPN
ejpam-6414	255	19	4	4	NUM
ejpam-6414	255	20	1	1	NUM
ejpam-6414	255	21	+	+	CCONJ
ejpam-6414	255	22	(	(	PUNCT
ejpam-6414	255	23	1	1	NUM
ejpam-6414	255	24	+	+	CCONJ
ejpam-6414	255	25	uα	uα	NOUN
ejpam-6414	255	26	)	)	PUNCT
ejpam-6414	255	27	19	19	NUM
ejpam-6414	255	28	(	(	PUNCT
ejpam-6414	255	29	1	1	NUM
ejpam-6414	255	30	+	+	NUM
ejpam-6414	255	31	u	u	NOUN
ejpam-6414	255	32	)	)	PUNCT
ejpam-6414	256	1	+	+	CCONJ
ejpam-6414	256	2	α	α	PROPN
ejpam-6414	256	3	5	5	NUM
ejpam-6414	256	4	α+	α+	NOUN
ejpam-6414	256	5	(	(	PUNCT
ejpam-6414	256	6	1	1	NUM
ejpam-6414	256	7	+	+	CCONJ
ejpam-6414	256	8	uα2	uα2	ADJ
ejpam-6414	256	9	)	)	PUNCT
ejpam-6414	256	10	20	20	NUM
ejpam-6414	256	11	(	(	PUNCT
ejpam-6414	256	12	1	1	NUM
ejpam-6414	256	13	+	+	NUM
ejpam-6414	256	14	u)α+	u)α+	ADJ
ejpam-6414	256	15	α2	α2	ADJ
ejpam-6414	256	16	6	6	NUM
ejpam-6414	256	17	α2	α2	ADJ
ejpam-6414	256	18	+	+	CCONJ
ejpam-6414	256	19	(	(	PUNCT
ejpam-6414	256	20	1	1	X
ejpam-6414	256	21	+	+	X
ejpam-6414	256	22	u)α3	u)α3	PROPN
ejpam-6414	256	23	21	21	NUM
ejpam-6414	256	24	(	(	PUNCT
ejpam-6414	256	25	1	1	NUM
ejpam-6414	256	26	+	+	CCONJ
ejpam-6414	256	27	u)α2	u)α2	PROPN
ejpam-6414	257	1	+	+	CCONJ
ejpam-6414	257	2	α3	α3	NOUN
ejpam-6414	257	3	7	7	NUM
ejpam-6414	257	4	α3	α3	NOUN
ejpam-6414	257	5	+	+	CCONJ
ejpam-6414	257	6	α+	α+	PUNCT
ejpam-6414	257	7	1	1	NUM
ejpam-6414	257	8	+	+	NUM
ejpam-6414	257	9	u	u	NOUN
ejpam-6414	257	10	22	22	NUM
ejpam-6414	257	11	1	1	NUM
ejpam-6414	257	12	+	+	CCONJ
ejpam-6414	257	13	(	(	PUNCT
ejpam-6414	257	14	1	1	NUM
ejpam-6414	257	15	+	+	NUM
ejpam-6414	257	16	u)α+	u)α+	ADJ
ejpam-6414	257	17	(	(	PUNCT
ejpam-6414	257	18	1	1	NUM
ejpam-6414	257	19	+	+	CCONJ
ejpam-6414	257	20	u)α3	u)α3	PROPN
ejpam-6414	257	21	8	8	NUM
ejpam-6414	257	22	α2	α2	ADJ
ejpam-6414	257	23	+	+	CCONJ
ejpam-6414	257	24	1	1	NUM
ejpam-6414	257	25	23	23	NUM
ejpam-6414	257	26	(	(	PUNCT
ejpam-6414	257	27	1	1	NUM
ejpam-6414	257	28	+	+	NUM
ejpam-6414	257	29	u	u	NOUN
ejpam-6414	257	30	)	)	PUNCT
ejpam-6414	258	1	+	+	CCONJ
ejpam-6414	258	2	(	(	PUNCT
ejpam-6414	258	3	1	1	X
ejpam-6414	258	4	+	+	CCONJ
ejpam-6414	258	5	u)α2	u)α2	PROPN
ejpam-6414	258	6	9	9	NUM
ejpam-6414	258	7	α3	α3	NOUN
ejpam-6414	259	1	+	+	CCONJ
ejpam-6414	259	2	α	α	PROPN
ejpam-6414	259	3	24	24	NUM
ejpam-6414	259	4	(	(	PUNCT
ejpam-6414	259	5	1	1	NUM
ejpam-6414	259	6	+	+	NUM
ejpam-6414	259	7	u)α+	u)α+	ADJ
ejpam-6414	259	8	(	(	PUNCT
ejpam-6414	259	9	1	1	NUM
ejpam-6414	259	10	+	+	X
ejpam-6414	259	11	u)α3	u)α3	PROPN
ejpam-6414	259	12	10	10	NUM
ejpam-6414	259	13	α2	α2	ADJ
ejpam-6414	260	1	+	+	CCONJ
ejpam-6414	261	1	(	(	PUNCT
ejpam-6414	261	2	1	1	NUM
ejpam-6414	261	3	+	+	NUM
ejpam-6414	261	4	u)α+	u)α+	ADJ
ejpam-6414	261	5	1	1	NUM
ejpam-6414	261	6	25	25	NUM
ejpam-6414	261	7	(	(	PUNCT
ejpam-6414	261	8	1	1	NUM
ejpam-6414	261	9	+	+	NUM
ejpam-6414	261	10	u	u	NOUN
ejpam-6414	261	11	)	)	PUNCT
ejpam-6414	261	12	+	+	CCONJ
ejpam-6414	261	13	α+	α+	PUNCT
ejpam-6414	261	14	(	(	PUNCT
ejpam-6414	261	15	1	1	NUM
ejpam-6414	261	16	+	+	CCONJ
ejpam-6414	261	17	u)α2	u)α2	PROPN
ejpam-6414	261	18	11	11	NUM
ejpam-6414	261	19	α3	α3	NOUN
ejpam-6414	261	20	+	+	CCONJ
ejpam-6414	261	21	(	(	PUNCT
ejpam-6414	261	22	1	1	NUM
ejpam-6414	261	23	+	+	CCONJ
ejpam-6414	261	24	u)α2	u)α2	PROPN
ejpam-6414	261	25	+	+	CCONJ
ejpam-6414	261	26	α	α	NOUN
ejpam-6414	261	27	26	26	NUM
ejpam-6414	261	28	(	(	PUNCT
ejpam-6414	261	29	1	1	NUM
ejpam-6414	261	30	+	+	NUM
ejpam-6414	261	31	u)α+	u)α+	ADJ
ejpam-6414	261	32	α2	α2	NOUN
ejpam-6414	261	33	+	+	CCONJ
ejpam-6414	261	34	(	(	PUNCT
ejpam-6414	261	35	1	1	X
ejpam-6414	261	36	+	+	X
ejpam-6414	261	37	u)α3	u)α3	PROPN
ejpam-6414	261	38	12	12	NUM
ejpam-6414	261	39	(	(	PUNCT
ejpam-6414	261	40	1	1	NUM
ejpam-6414	261	41	+	+	X
ejpam-6414	261	42	u)α3	u)α3	PROPN
ejpam-6414	261	43	+	+	CCONJ
ejpam-6414	261	44	α2	α2	ADJ
ejpam-6414	261	45	+	+	CCONJ
ejpam-6414	261	46	(	(	PUNCT
ejpam-6414	261	47	1	1	NUM
ejpam-6414	261	48	+	+	NUM
ejpam-6414	261	49	u)α+	u)α+	ADJ
ejpam-6414	261	50	1	1	NUM
ejpam-6414	261	51	27	27	NUM
ejpam-6414	261	52	(	(	PUNCT
ejpam-6414	261	53	1	1	NUM
ejpam-6414	261	54	+	+	NUM
ejpam-6414	261	55	u	u	NOUN
ejpam-6414	261	56	)	)	PUNCT
ejpam-6414	262	1	+	+	CCONJ
ejpam-6414	262	2	α+	α+	PUNCT
ejpam-6414	262	3	(	(	PUNCT
ejpam-6414	262	4	1	1	NUM
ejpam-6414	262	5	+	+	CCONJ
ejpam-6414	262	6	u)α2	u)α2	PROPN
ejpam-6414	262	7	+	+	CCONJ
ejpam-6414	262	8	α3	α3	NOUN
ejpam-6414	262	9	13	13	NUM
ejpam-6414	262	10	α3	α3	NOUN
ejpam-6414	262	11	+	+	CCONJ
ejpam-6414	262	12	(	(	PUNCT
ejpam-6414	262	13	1	1	NUM
ejpam-6414	262	14	+	+	CCONJ
ejpam-6414	262	15	u)α2	u)α2	PROPN
ejpam-6414	262	16	+	+	CCONJ
ejpam-6414	262	17	(	(	PUNCT
ejpam-6414	262	18	1	1	NUM
ejpam-6414	262	19	+	+	NUM
ejpam-6414	262	20	u	u	NOUN
ejpam-6414	262	21	)	)	PUNCT
ejpam-6414	262	22	28	28	NUM
ejpam-6414	262	23	1	1	NUM
ejpam-6414	263	1	+	+	CCONJ
ejpam-6414	263	2	α2	α2	ADJ
ejpam-6414	263	3	+	+	CCONJ
ejpam-6414	263	4	(	(	PUNCT
ejpam-6414	263	5	1	1	X
ejpam-6414	263	6	+	+	X
ejpam-6414	263	7	u)α3	u)α3	PROPN
ejpam-6414	263	8	14	14	NUM
ejpam-6414	263	9	(	(	PUNCT
ejpam-6414	263	10	1	1	NUM
ejpam-6414	264	1	+	+	X
ejpam-6414	264	2	u)α3	u)α3	PROPN
ejpam-6414	264	3	+	+	CCONJ
ejpam-6414	264	4	1	1	NUM
ejpam-6414	264	5	29	29	NUM
ejpam-6414	264	6	(	(	PUNCT
ejpam-6414	264	7	1	1	NUM
ejpam-6414	264	8	+	+	NUM
ejpam-6414	264	9	u	u	NOUN
ejpam-6414	264	10	)	)	PUNCT
ejpam-6414	265	1	+	+	CCONJ
ejpam-6414	265	2	α3	α3	NOUN
ejpam-6414	265	3	15	15	NUM
ejpam-6414	265	4	1	1	NUM
ejpam-6414	265	5	+	+	NUM
ejpam-6414	265	6	u	u	NOUN
ejpam-6414	265	7	30	30	NUM
ejpam-6414	265	8	1	1	NUM
ejpam-6414	265	9	muhammad	muhammad	PROPN
ejpam-6414	265	10	sajjad	sajjad	PROPN
ejpam-6414	265	11	et	et	PROPN
ejpam-6414	265	12	al	al	PROPN
ejpam-6414	265	13	.	.	PUNCT
ejpam-6414	265	14	/	/	SYM
ejpam-6414	265	15	eur	eur	PROPN
ejpam-6414	265	16	.	.	PUNCT
ejpam-6414	266	1	j.	j.	PROPN
ejpam-6414	266	2	pure	pure	PROPN
ejpam-6414	266	3	appl	appl	PROPN
ejpam-6414	266	4	.	.	PROPN
ejpam-6414	266	5	math	math	PROPN
ejpam-6414	266	6	,	,	PUNCT
ejpam-6414	266	7	18	18	NUM
ejpam-6414	266	8	(	(	PUNCT
ejpam-6414	266	9	3	3	NUM
ejpam-6414	266	10	)	)	PUNCT
ejpam-6414	266	11	(	(	PUNCT
ejpam-6414	266	12	2025	2025	NUM
ejpam-6414	266	13	)	)	PUNCT
ejpam-6414	266	14	,	,	PUNCT
ejpam-6414	266	15	6414	6414	NUM
ejpam-6414	266	16	13	13	NUM
ejpam-6414	266	17	of	of	ADP
ejpam-6414	266	18	22	22	NUM
ejpam-6414	266	19	generator	generator	NOUN
ejpam-6414	266	20	polynomial	polynomial	NOUN
ejpam-6414	266	21	of	of	ADP
ejpam-6414	266	22	bch	bch	PROPN
ejpam-6414	266	23	code	code	PROPN
ejpam-6414	266	24	over	over	ADP
ejpam-6414	266	25	a(2	a(2	PROPN
ejpam-6414	266	26	,	,	PUNCT
ejpam-6414	266	27	2	2	NUM
ejpam-6414	266	28	):	):	PUNCT
ejpam-6414	266	29	since	since	SCONJ
ejpam-6414	266	30	γ	γ	PROPN
ejpam-6414	266	31	=	=	SYM
ejpam-6414	266	32	α2	α2	PROPN
ejpam-6414	266	33	is	be	AUX
ejpam-6414	266	34	a	a	DET
ejpam-6414	266	35	primitive	primitive	ADJ
ejpam-6414	266	36	cube	cube	NOUN
ejpam-6414	266	37	root	root	NOUN
ejpam-6414	266	38	of	of	ADP
ejpam-6414	266	39	unity	unity	NOUN
ejpam-6414	266	40	in	in	ADP
ejpam-6414	266	41	g15	g15	PROPN
ejpam-6414	266	42	,	,	PUNCT
ejpam-6414	266	43	for	for	ADP
ejpam-6414	266	44	design	design	NOUN
ejpam-6414	266	45	distance	distance	NOUN
ejpam-6414	266	46	d	d	NOUN
ejpam-6414	266	47	=	=	SYM
ejpam-6414	266	48	3	3	NUM
ejpam-6414	266	49	,	,	PUNCT
ejpam-6414	266	50	we	we	PRON
ejpam-6414	266	51	need	need	VERB
ejpam-6414	266	52	the	the	DET
ejpam-6414	266	53	minimal	minimal	ADJ
ejpam-6414	266	54	polynomials	polynomial	NOUN
ejpam-6414	266	55	of	of	ADP
ejpam-6414	266	56	γi	γi	NOUN
ejpam-6414	266	57	,	,	PUNCT
ejpam-6414	266	58	i	i	PRON
ejpam-6414	266	59	=	=	NOUN
ejpam-6414	266	60	1	1	NUM
ejpam-6414	266	61	,	,	PUNCT
ejpam-6414	266	62	2	2	NUM
ejpam-6414	266	63	.	.	X
ejpam-6414	267	1	let	let	AUX
ejpam-6414	267	2	m1(x	m1(x	PRON
ejpam-6414	267	3	)	)	PUNCT
ejpam-6414	267	4	be	be	AUX
ejpam-6414	267	5	the	the	DET
ejpam-6414	267	6	minimal	minimal	ADJ
ejpam-6414	267	7	polynomial	polynomial	NOUN
ejpam-6414	267	8	of	of	ADP
ejpam-6414	267	9	γ	γ	PROPN
ejpam-6414	267	10	.	.	PROPN
ejpam-6414	268	1	then	then	ADV
ejpam-6414	268	2	γ	γ	PROPN
ejpam-6414	268	3	,	,	PUNCT
ejpam-6414	268	4	γ2	γ2	PROPN
ejpam-6414	268	5	,	,	PUNCT
ejpam-6414	268	6	γ4	γ4	PROPN
ejpam-6414	268	7	,	,	PUNCT
ejpam-6414	268	8	γ8	γ8	NOUN
ejpam-6414	268	9	all	all	DET
ejpam-6414	268	10	share	share	VERB
ejpam-6414	268	11	the	the	DET
ejpam-6414	268	12	same	same	ADJ
ejpam-6414	268	13	minimal	minimal	ADJ
ejpam-6414	268	14	polynomial	polynomial	ADJ
ejpam-6414	268	15	:	:	PUNCT
ejpam-6414	268	16	m1(x	m1(x	NOUN
ejpam-6414	268	17	)	)	PUNCT
ejpam-6414	268	18	=	=	SYM
ejpam-6414	268	19	(	(	PUNCT
ejpam-6414	268	20	x−	x−	PROPN
ejpam-6414	268	21	γ)(x−	γ)(x−	PROPN
ejpam-6414	268	22	γ2)(x−	γ2)(x−	PROPN
ejpam-6414	268	23	γ4)(x−	γ4)(x−	PUNCT
ejpam-6414	269	1	γ8	γ8	NOUN
ejpam-6414	269	2	)	)	PUNCT
ejpam-6414	269	3	=	=	PUNCT
ejpam-6414	270	1	x4	x4	PROPN
ejpam-6414	271	1	+	+	CCONJ
ejpam-6414	271	2	x+	x+	ADJ
ejpam-6414	271	3	1	1	X
ejpam-6414	271	4	.	.	X
ejpam-6414	271	5	therefore	therefore	ADV
ejpam-6414	271	6	,	,	PUNCT
ejpam-6414	271	7	the	the	DET
ejpam-6414	271	8	generator	generator	NOUN
ejpam-6414	271	9	polynomial	polynomial	NOUN
ejpam-6414	271	10	is	be	AUX
ejpam-6414	271	11	:	:	PUNCT
ejpam-6414	271	12	g(x	g(x	X
ejpam-6414	271	13	)	)	PUNCT
ejpam-6414	271	14	=	=	SYM
ejpam-6414	271	15	lcm{m1(x),m2(x	lcm{m1(x),m2(x	NOUN
ejpam-6414	271	16	)	)	PUNCT
ejpam-6414	271	17	}	}	PUNCT
ejpam-6414	271	18	=	=	SYM
ejpam-6414	271	19	m1(x	m1(x	NOUN
ejpam-6414	271	20	)	)	PUNCT
ejpam-6414	271	21	=	=	SYM
ejpam-6414	272	1	x4	x4	PROPN
ejpam-6414	273	1	+	+	CCONJ
ejpam-6414	273	2	x+	x+	PROPN
ejpam-6414	273	3	1	1	X
ejpam-6414	273	4	.	.	PUNCT
ejpam-6414	273	5	given	give	VERB
ejpam-6414	273	6	r	r	NOUN
ejpam-6414	273	7	=	=	SYM
ejpam-6414	273	8	4	4	NUM
ejpam-6414	273	9	,	,	PUNCT
ejpam-6414	273	10	q	q	NOUN
ejpam-6414	273	11	=	=	SYM
ejpam-6414	273	12	2	2	NUM
ejpam-6414	273	13	,	,	PUNCT
ejpam-6414	273	14	m	m	VERB
ejpam-6414	273	15	=	=	NOUN
ejpam-6414	273	16	4	4	NUM
ejpam-6414	273	17	,	,	PUNCT
ejpam-6414	273	18	and	and	CCONJ
ejpam-6414	273	19	c	c	NOUN
ejpam-6414	273	20	=	=	SYM
ejpam-6414	273	21	1	1	NUM
ejpam-6414	273	22	,	,	PUNCT
ejpam-6414	273	23	the	the	DET
ejpam-6414	273	24	code	code	NOUN
ejpam-6414	273	25	length	length	NOUN
ejpam-6414	273	26	is	be	AUX
ejpam-6414	273	27	:	:	PUNCT
ejpam-6414	273	28	n	n	PROPN
ejpam-6414	273	29	=	=	SYM
ejpam-6414	273	30	qm	qm	PROPN
ejpam-6414	273	31	−	−	PROPN
ejpam-6414	273	32	1	1	NUM
ejpam-6414	273	33	=	=	SYM
ejpam-6414	273	34	24	24	NUM
ejpam-6414	273	35	−	−	NOUN
ejpam-6414	273	36	1	1	NUM
ejpam-6414	273	37	=	=	SYM
ejpam-6414	273	38	15	15	NUM
ejpam-6414	273	39	.	.	PUNCT
ejpam-6414	274	1	the	the	DET
ejpam-6414	274	2	cyclic	cyclic	PROPN
ejpam-6414	274	3	code	code	PROPN
ejpam-6414	274	4	c	c	NOUN
ejpam-6414	274	5	generated	generate	VERB
ejpam-6414	274	6	by	by	ADP
ejpam-6414	274	7	g(x	g(x	PROPN
ejpam-6414	274	8	)	)	PUNCT
ejpam-6414	274	9	over	over	ADP
ejpam-6414	274	10	g15	g15	PROPN
ejpam-6414	274	11	⊂	⊂	PROPN
ejpam-6414	274	12	r∗	r∗	PROPN
ejpam-6414	274	13	⊂	⊂	PROPN
ejpam-6414	274	14	a(2	a(2	PROPN
ejpam-6414	274	15	,	,	PUNCT
ejpam-6414	274	16	2	2	NUM
ejpam-6414	274	17	)	)	PUNCT
ejpam-6414	274	18	has	have	AUX
ejpam-6414	274	19	dimension	dimension	NOUN
ejpam-6414	274	20	11	11	NUM
ejpam-6414	274	21	.	.	PUNCT
ejpam-6414	275	1	hence	hence	ADV
ejpam-6414	275	2	,	,	PUNCT
ejpam-6414	275	3	c	c	PROPN
ejpam-6414	275	4	is	be	AUX
ejpam-6414	275	5	a	a	DET
ejpam-6414	275	6	:	:	PUNCT
ejpam-6414	275	7	[	[	X
ejpam-6414	275	8	15	15	NUM
ejpam-6414	275	9	,	,	PUNCT
ejpam-6414	275	10	11	11	NUM
ejpam-6414	275	11	,	,	PUNCT
ejpam-6414	275	12	3	3	NUM
ejpam-6414	275	13	]	]	X
ejpam-6414	275	14	primitive	primitive	ADJ
ejpam-6414	275	15	narrow	narrow	ADJ
ejpam-6414	275	16	-	-	PUNCT
ejpam-6414	275	17	sense	sense	NOUN
ejpam-6414	275	18	bch	bch	PROPN
ejpam-6414	275	19	code	code	NOUN
ejpam-6414	275	20	over	over	ADP
ejpam-6414	275	21	the	the	DET
ejpam-6414	275	22	maximal	maximal	ADJ
ejpam-6414	275	23	cyclic	cyclic	ADJ
ejpam-6414	275	24	subgroup	subgroup	NOUN
ejpam-6414	275	25	of	of	ADP
ejpam-6414	275	26	units	unit	NOUN
ejpam-6414	275	27	in	in	ADP
ejpam-6414	275	28	a(2	a(2	PROPN
ejpam-6414	275	29	,	,	PUNCT
ejpam-6414	275	30	2	2	NUM
ejpam-6414	275	31	)	)	PUNCT
ejpam-6414	275	32	.	.	PUNCT
ejpam-6414	276	1	4	4	X
ejpam-6414	276	2	.	.	X
ejpam-6414	276	3	decoding	decode	VERB
ejpam-6414	276	4	of	of	ADP
ejpam-6414	276	5	bch	bch	PROPN
ejpam-6414	276	6	codes	code	NOUN
ejpam-6414	276	7	over	over	ADP
ejpam-6414	276	8	qgrs	qgrs	NOUN
ejpam-6414	276	9	and	and	CCONJ
ejpam-6414	276	10	their	their	PRON
ejpam-6414	276	11	significance	significance	NOUN
ejpam-6414	276	12	[	[	X
ejpam-6414	276	13	13	13	NUM
ejpam-6414	276	14	,	,	PUNCT
ejpam-6414	276	15	14	14	NUM
ejpam-6414	276	16	,	,	PUNCT
ejpam-6414	276	17	16	16	NUM
ejpam-6414	276	18	]	]	SYM
ejpam-6414	276	19	4.1	4.1	NUM
ejpam-6414	276	20	.	.	PUNCT
ejpam-6414	277	1	decoding	decode	VERB
ejpam-6414	277	2	of	of	ADP
ejpam-6414	277	3	bch	bch	PROPN
ejpam-6414	277	4	codes	code	NOUN
ejpam-6414	277	5	using	use	VERB
ejpam-6414	277	6	advanced	advanced	ADJ
ejpam-6414	277	7	modified	modify	VERB
ejpam-6414	277	8	berlekamp	berlekamp	NOUN
ejpam-6414	277	9	–	–	PUNCT
ejpam-6414	277	10	massey	massey	ADJ
ejpam-6414	277	11	algorithm	algorithm	NOUN
ejpam-6414	277	12	let	let	VERB
ejpam-6414	277	13	c	c	NOUN
ejpam-6414	277	14	be	be	AUX
ejpam-6414	277	15	a	a	DET
ejpam-6414	277	16	bch	bch	PROPN
ejpam-6414	277	17	code	code	NOUN
ejpam-6414	277	18	with	with	ADP
ejpam-6414	277	19	length	length	NOUN
ejpam-6414	277	20	n	n	CCONJ
ejpam-6414	277	21	,	,	PUNCT
ejpam-6414	277	22	designed	design	VERB
ejpam-6414	277	23	distance	distance	NOUN
ejpam-6414	277	24	d	d	NOUN
ejpam-6414	277	25	,	,	PUNCT
ejpam-6414	277	26	and	and	CCONJ
ejpam-6414	277	27	received	receive	VERB
ejpam-6414	277	28	vector	vector	NOUN
ejpam-6414	277	29	r.	r.	NOUN
ejpam-6414	277	30	let	let	VERB
ejpam-6414	277	31	s	s	PRON
ejpam-6414	277	32	denote	denote	VERB
ejpam-6414	277	33	the	the	DET
ejpam-6414	277	34	syndrome	syndrome	NOUN
ejpam-6414	277	35	vector	vector	NOUN
ejpam-6414	277	36	,	,	PUNCT
ejpam-6414	277	37	computed	compute	VERB
ejpam-6414	277	38	as	as	ADP
ejpam-6414	277	39	the	the	DET
ejpam-6414	277	40	multiplication	multiplication	NOUN
ejpam-6414	277	41	of	of	ADP
ejpam-6414	277	42	the	the	DET
ejpam-6414	277	43	parity	parity	NOUN
ejpam-6414	277	44	-	-	PUNCT
ejpam-6414	277	45	check	check	NOUN
ejpam-6414	277	46	matrix	matrix	NOUN
ejpam-6414	277	47	h	h	NOUN
ejpam-6414	277	48	and	and	CCONJ
ejpam-6414	277	49	the	the	DET
ejpam-6414	277	50	transpose	transpose	NOUN
ejpam-6414	277	51	of	of	ADP
ejpam-6414	277	52	the	the	DET
ejpam-6414	277	53	received	receive	VERB
ejpam-6414	277	54	vector	vector	NOUN
ejpam-6414	277	55	:	:	PUNCT
ejpam-6414	277	56	s	s	X
ejpam-6414	277	57	=	=	SYM
ejpam-6414	277	58	hrt	hrt	PROPN
ejpam-6414	277	59	.	.	PROPN
ejpam-6414	277	60	apply	apply	VERB
ejpam-6414	277	61	the	the	DET
ejpam-6414	277	62	advanced	advanced	ADJ
ejpam-6414	277	63	modified	modify	VERB
ejpam-6414	277	64	berlekamp	berlekamp	NOUN
ejpam-6414	277	65	–	–	PUNCT
ejpam-6414	277	66	massey	massey	NOUN
ejpam-6414	277	67	algorithm	algorithm	NOUN
ejpam-6414	277	68	(	(	PUNCT
ejpam-6414	277	69	ambma	ambma	PROPN
ejpam-6414	277	70	)	)	PUNCT
ejpam-6414	277	71	to	to	PART
ejpam-6414	277	72	find	find	VERB
ejpam-6414	277	73	the	the	DET
ejpam-6414	277	74	error	error	NOUN
ejpam-6414	277	75	-	-	PUNCT
ejpam-6414	277	76	locator	locator	NOUN
ejpam-6414	277	77	polynomial	polynomial	NOUN
ejpam-6414	277	78	δn(x	δn(x	X
ejpam-6414	277	79	)	)	PUNCT
ejpam-6414	277	80	under	under	ADP
ejpam-6414	277	81	the	the	DET
ejpam-6414	277	82	following	follow	VERB
ejpam-6414	277	83	initial	initial	ADJ
ejpam-6414	277	84	conditions	condition	NOUN
ejpam-6414	277	85	:	:	PUNCT
ejpam-6414	277	86	d−1	d−1	PROPN
ejpam-6414	277	87	=	=	SYM
ejpam-6414	277	88	1	1	NUM
ejpam-6414	277	89	,	,	PUNCT
ejpam-6414	277	90	δ−1(x	δ−1(x	NOUN
ejpam-6414	277	91	)	)	PUNCT
ejpam-6414	277	92	=	=	SYM
ejpam-6414	277	93	1	1	NUM
ejpam-6414	277	94	,	,	PUNCT
ejpam-6414	277	95	l−1	l−1	PROPN
ejpam-6414	277	96	=	=	SYM
ejpam-6414	277	97	0	0	NUM
ejpam-6414	277	98	,	,	PUNCT
ejpam-6414	277	99	l0	l0	PROPN
ejpam-6414	277	100	=	=	SYM
ejpam-6414	277	101	0	0	NUM
ejpam-6414	277	102	,	,	PUNCT
ejpam-6414	277	103	δ0(x	δ0(x	NOUN
ejpam-6414	277	104	)	)	PUNCT
ejpam-6414	277	105	=	=	SYM
ejpam-6414	277	106	1	1	NUM
ejpam-6414	277	107	,	,	PUNCT
ejpam-6414	277	108	d0	d0	NOUN
ejpam-6414	277	109	=	=	SYM
ejpam-6414	277	110	first	first	ADJ
ejpam-6414	277	111	non	non	ADJ
ejpam-6414	277	112	-	-	ADJ
ejpam-6414	277	113	zero	zero	NUM
ejpam-6414	277	114	syndrome	syndrome	NOUN
ejpam-6414	277	115	.	.	PUNCT
ejpam-6414	278	1	let	let	VERB
ejpam-6414	278	2	dn	dn	PART
ejpam-6414	278	3	represent	represent	VERB
ejpam-6414	278	4	the	the	DET
ejpam-6414	278	5	discrepancy	discrepancy	NOUN
ejpam-6414	278	6	at	at	ADP
ejpam-6414	278	7	iteration	iteration	NOUN
ejpam-6414	278	8	n.	n.	NOUN
ejpam-6414	278	9	if	if	SCONJ
ejpam-6414	278	10	dn	dn	PROPN
ejpam-6414	278	11	=	=	SYM
ejpam-6414	278	12	0	0	NUM
ejpam-6414	278	13	or	or	CCONJ
ejpam-6414	278	14	is	be	AUX
ejpam-6414	278	15	a	a	DET
ejpam-6414	278	16	zero	zero	NUM
ejpam-6414	278	17	divisor	divisor	NOUN
ejpam-6414	278	18	,	,	PUNCT
ejpam-6414	278	19	then	then	ADV
ejpam-6414	278	20	:	:	PUNCT
ejpam-6414	278	21	δn(x	δn(x	X
ejpam-6414	278	22	)	)	PUNCT
ejpam-6414	278	23	=	=	SYM
ejpam-6414	278	24	δn+1(x	δn+1(x	NOUN
ejpam-6414	278	25	)	)	PUNCT
ejpam-6414	278	26	,	,	PUNCT
ejpam-6414	278	27	ln	ln	NOUN
ejpam-6414	278	28	=	=	PUNCT
ejpam-6414	278	29	ln+1	ln+1	PROPN
ejpam-6414	278	30	.	.	PUNCT
ejpam-6414	279	1	if	if	SCONJ
ejpam-6414	279	2	dn	dn	PROPN
ejpam-6414	279	3	is	be	AUX
ejpam-6414	279	4	a	a	DET
ejpam-6414	279	5	nonzero	nonzero	ADJ
ejpam-6414	279	6	unit	unit	NOUN
ejpam-6414	279	7	element	element	NOUN
ejpam-6414	279	8	,	,	PUNCT
ejpam-6414	279	9	choose	choose	VERB
ejpam-6414	279	10	m	m	PRON
ejpam-6414	279	11	≤	≤	ADJ
ejpam-6414	279	12	n−	n−	NOUN
ejpam-6414	279	13	1	1	NUM
ejpam-6414	279	14	such	such	ADJ
ejpam-6414	279	15	that	that	SCONJ
ejpam-6414	279	16	n−	n−	NOUN
ejpam-6414	279	17	lm	lm	INTJ
ejpam-6414	279	18	is	be	AUX
ejpam-6414	279	19	the	the	DET
ejpam-6414	279	20	largest	large	ADJ
ejpam-6414	279	21	or	or	CCONJ
ejpam-6414	279	22	equal	equal	ADJ
ejpam-6414	279	23	to	to	ADP
ejpam-6414	279	24	the	the	DET
ejpam-6414	279	25	last	last	ADJ
ejpam-6414	279	26	column	column	NOUN
ejpam-6414	279	27	index	index	NOUN
ejpam-6414	279	28	satisfying	satisfy	VERB
ejpam-6414	279	29	the	the	DET
ejpam-6414	279	30	update	update	NOUN
ejpam-6414	279	31	condition	condition	NOUN
ejpam-6414	279	32	.	.	PUNCT
ejpam-6414	280	1	from	from	ADP
ejpam-6414	280	2	dn	dn	NOUN
ejpam-6414	280	3	−	−	PROPN
ejpam-6414	280	4	ydm	ydm	NOUN
ejpam-6414	280	5	=	=	SYM
ejpam-6414	280	6	0	0	NUM
ejpam-6414	280	7	,	,	PUNCT
ejpam-6414	280	8	compute	compute	NOUN
ejpam-6414	280	9	y	y	PROPN
ejpam-6414	280	10	,	,	PUNCT
ejpam-6414	280	11	and	and	CCONJ
ejpam-6414	280	12	update	update	VERB
ejpam-6414	280	13	the	the	DET
ejpam-6414	280	14	error	error	NOUN
ejpam-6414	280	15	-	-	PUNCT
ejpam-6414	280	16	locator	locator	NOUN
ejpam-6414	280	17	polynomial	polynomial	NOUN
ejpam-6414	280	18	as	as	ADP
ejpam-6414	280	19	:	:	PUNCT
ejpam-6414	280	20	δn+1(x	δn+1(x	NOUN
ejpam-6414	280	21	)	)	PUNCT
ejpam-6414	280	22	=	=	SYM
ejpam-6414	280	23	δn(x)−	δn(x)−	PROPN
ejpam-6414	280	24	yxn−mδm(x	yxn−mδm(x	PROPN
ejpam-6414	280	25	)	)	PUNCT
ejpam-6414	280	26	.	.	PUNCT
ejpam-6414	281	1	muhammad	muhammad	PROPN
ejpam-6414	281	2	sajjad	sajjad	PROPN
ejpam-6414	281	3	et	et	PROPN
ejpam-6414	281	4	al	al	PROPN
ejpam-6414	281	5	.	.	PUNCT
ejpam-6414	281	6	/	/	SYM
ejpam-6414	281	7	eur	eur	PROPN
ejpam-6414	281	8	.	.	PUNCT
ejpam-6414	282	1	j.	j.	PROPN
ejpam-6414	282	2	pure	pure	PROPN
ejpam-6414	282	3	appl	appl	PROPN
ejpam-6414	282	4	.	.	PROPN
ejpam-6414	282	5	math	math	PROPN
ejpam-6414	282	6	,	,	PUNCT
ejpam-6414	282	7	18	18	NUM
ejpam-6414	282	8	(	(	PUNCT
ejpam-6414	282	9	3	3	NUM
ejpam-6414	282	10	)	)	PUNCT
ejpam-6414	282	11	(	(	PUNCT
ejpam-6414	282	12	2025	2025	NUM
ejpam-6414	282	13	)	)	PUNCT
ejpam-6414	282	14	,	,	PUNCT
ejpam-6414	282	15	6414	6414	NUM
ejpam-6414	282	16	14	14	NUM
ejpam-6414	282	17	of	of	ADP
ejpam-6414	282	18	22	22	NUM
ejpam-6414	282	19	the	the	DET
ejpam-6414	282	20	next	next	ADJ
ejpam-6414	282	21	discrepancy	discrepancy	NOUN
ejpam-6414	282	22	is	be	AUX
ejpam-6414	282	23	given	give	VERB
ejpam-6414	282	24	by	by	ADP
ejpam-6414	282	25	:	:	PUNCT
ejpam-6414	282	26	dn+1	dn+1	X
ejpam-6414	282	27	=	=	SYM
ejpam-6414	282	28	sn+2	sn+2	PROPN
ejpam-6414	282	29	+	+	CCONJ
ejpam-6414	282	30	δ	δ	PROPN
ejpam-6414	282	31	(	(	PUNCT
ejpam-6414	282	32	n+1	n+1	PROPN
ejpam-6414	282	33	)	)	PUNCT
ejpam-6414	282	34	1	1	NUM
ejpam-6414	282	35	sn+1	sn+1	NOUN
ejpam-6414	282	36	+	+	NUM
ejpam-6414	282	37	δ	δ	PROPN
ejpam-6414	282	38	(	(	PUNCT
ejpam-6414	282	39	n+1	n+1	PROPN
ejpam-6414	282	40	)	)	PUNCT
ejpam-6414	282	41	2	2	NUM
ejpam-6414	282	42	sn	sn	NOUN
ejpam-6414	282	43	+	+	CCONJ
ejpam-6414	282	44	·	·	PUNCT
ejpam-6414	282	45	·	·	PUNCT
ejpam-6414	282	46	·	·	PUNCT
ejpam-6414	282	47	+	+	NUM
ejpam-6414	282	48	δ	δ	PROPN
ejpam-6414	282	49	(	(	PUNCT
ejpam-6414	282	50	n+1	n+1	PROPN
ejpam-6414	282	51	)	)	PUNCT
ejpam-6414	282	52	ln+1	ln+1	X
ejpam-6414	282	53	sn+2−ln+1	sn+2−ln+1	NOUN
ejpam-6414	282	54	.	.	PUNCT
ejpam-6414	283	1	next	next	ADV
ejpam-6414	283	2	,	,	PUNCT
ejpam-6414	283	3	compute	compute	VERB
ejpam-6414	283	4	the	the	DET
ejpam-6414	283	5	reciprocal	reciprocal	ADJ
ejpam-6414	283	6	polynomial	polynomial	ADJ
ejpam-6414	283	7	g(x	g(x	NOUN
ejpam-6414	283	8	)	)	PUNCT
ejpam-6414	283	9	of	of	ADP
ejpam-6414	283	10	δn(x	δn(x	NOUN
ejpam-6414	283	11	)	)	PUNCT
ejpam-6414	283	12	,	,	PUNCT
ejpam-6414	283	13	and	and	CCONJ
ejpam-6414	283	14	find	find	VERB
ejpam-6414	283	15	its	its	PRON
ejpam-6414	283	16	roots	root	NOUN
ejpam-6414	283	17	in	in	ADP
ejpam-6414	283	18	the	the	DET
ejpam-6414	283	19	form	form	NOUN
ejpam-6414	283	20	xu	xu	INTJ
ejpam-6414	283	21	.	.	PUNCT
ejpam-6414	284	1	these	these	DET
ejpam-6414	284	2	roots	root	NOUN
ejpam-6414	284	3	correspond	correspond	VERB
ejpam-6414	284	4	to	to	ADP
ejpam-6414	284	5	the	the	DET
ejpam-6414	284	6	error	error	NOUN
ejpam-6414	284	7	locations	location	NOUN
ejpam-6414	284	8	.	.	PUNCT
ejpam-6414	285	1	choose	choose	VERB
ejpam-6414	285	2	elements	element	NOUN
ejpam-6414	285	3	zu	zu	NOUN
ejpam-6414	285	4	such	such	ADJ
ejpam-6414	285	5	that	that	SCONJ
ejpam-6414	285	6	(	(	PUNCT
ejpam-6414	285	7	zu−xu	zu−xu	NUM
ejpam-6414	285	8	)	)	PUNCT
ejpam-6414	285	9	are	be	AUX
ejpam-6414	285	10	either	either	DET
ejpam-6414	285	11	zero	zero	NUM
ejpam-6414	285	12	or	or	CCONJ
ejpam-6414	285	13	zero	zero	NUM
ejpam-6414	285	14	divisors	divisor	NOUN
ejpam-6414	285	15	,	,	PUNCT
ejpam-6414	285	16	where	where	SCONJ
ejpam-6414	285	17	1	1	NUM
ejpam-6414	285	18	≤	≤	NUM
ejpam-6414	285	19	u	u	NOUN
ejpam-6414	285	20	≤	≤	ADJ
ejpam-6414	285	21	n−	n−	PROPN
ejpam-6414	285	22	1	1	NUM
ejpam-6414	285	23	and	and	CCONJ
ejpam-6414	285	24	xu	xu	PROPN
ejpam-6414	286	1	=	=	SYM
ejpam-6414	286	2	αu	αu	PROPN
ejpam-6414	286	3	.	.	PUNCT
ejpam-6414	286	4	now	now	ADV
ejpam-6414	286	5	construct	construct	VERB
ejpam-6414	286	6	the	the	DET
ejpam-6414	286	7	error	error	NOUN
ejpam-6414	286	8	-	-	PUNCT
ejpam-6414	286	9	locator	locator	NOUN
ejpam-6414	286	10	polynomial	polynomial	NOUN
ejpam-6414	286	11	using	use	VERB
ejpam-6414	286	12	the	the	DET
ejpam-6414	286	13	elementary	elementary	ADJ
ejpam-6414	286	14	symmetric	symmetric	ADJ
ejpam-6414	286	15	function	function	NOUN
ejpam-6414	286	16	:	:	PUNCT
ejpam-6414	286	17	(	(	PUNCT
ejpam-6414	286	18	x−	x−	PROPN
ejpam-6414	286	19	z1)(x−	z1)(x−	PROPN
ejpam-6414	286	20	z2	z2	PROPN
ejpam-6414	286	21	)	)	PUNCT
ejpam-6414	286	22	·	·	PUNCT
ejpam-6414	286	23	·	·	PUNCT
ejpam-6414	286	24	·	·	PUNCT
ejpam-6414	287	1	(	(	PUNCT
ejpam-6414	287	2	x−	x−	PROPN
ejpam-6414	287	3	zv	zv	PROPN
ejpam-6414	287	4	)	)	PUNCT
ejpam-6414	287	5	=	=	PUNCT
ejpam-6414	287	6	δ0x	δ0x	X
ejpam-6414	287	7	v	v	X
ejpam-6414	287	8	+	+	CCONJ
ejpam-6414	287	9	δ1x	δ1x	X
ejpam-6414	287	10	v−1	v−1	X
ejpam-6414	287	11	+	+	X
ejpam-6414	287	12	·	·	PUNCT
ejpam-6414	287	13	·	·	PUNCT
ejpam-6414	287	14	·	·	PUNCT
ejpam-6414	287	15	+	+	NUM
ejpam-6414	287	16	δv	δv	NOUN
ejpam-6414	287	17	,	,	PUNCT
ejpam-6414	287	18	where	where	SCONJ
ejpam-6414	287	19	z1	z1	ADJ
ejpam-6414	287	20	,	,	PUNCT
ejpam-6414	287	21	z2	z2	PROPN
ejpam-6414	287	22	,	,	PUNCT
ejpam-6414	287	23	.	.	PUNCT
ejpam-6414	287	24	.	.	PUNCT
ejpam-6414	287	25	.	.	PUNCT
ejpam-6414	288	1	,	,	PUNCT
ejpam-6414	288	2	zv	zv	PROPN
ejpam-6414	288	3	represent	represent	VERB
ejpam-6414	288	4	the	the	DET
ejpam-6414	288	5	v	v	NOUN
ejpam-6414	288	6	error	error	NOUN
ejpam-6414	288	7	locations	location	NOUN
ejpam-6414	288	8	.	.	PUNCT
ejpam-6414	289	1	using	use	VERB
ejpam-6414	289	2	forney	forney	PROPN
ejpam-6414	289	3	’s	’s	PART
ejpam-6414	289	4	algorithm	algorithm	NOUN
ejpam-6414	290	1	[	[	X
ejpam-6414	290	2	13	13	NUM
ejpam-6414	290	3	,	,	PUNCT
ejpam-6414	290	4	14	14	NUM
ejpam-6414	290	5	,	,	PUNCT
ejpam-6414	290	6	16	16	NUM
ejpam-6414	290	7	]	]	PUNCT
ejpam-6414	290	8	,	,	PUNCT
ejpam-6414	290	9	compute	compute	VERB
ejpam-6414	290	10	the	the	DET
ejpam-6414	290	11	error	error	NOUN
ejpam-6414	290	12	magnitudes	magnitude	VERB
ejpam-6414	290	13	yj	yj	INTJ
ejpam-6414	290	14	as	as	ADP
ejpam-6414	290	15	:	:	PUNCT
ejpam-6414	290	16	yj	yj	PROPN
ejpam-6414	290	17	=	=	PUNCT
ejpam-6414	290	18	v−1∑	v−1∑	NUM
ejpam-6414	290	19	l=0	l=0	PROPN
ejpam-6414	290	20	δj	δj	NOUN
ejpam-6414	290	21	,	,	PUNCT
ejpam-6414	290	22	usv−l	usv−l	ADV
ejpam-6414	290	23	v−1∑	v−1∑	NUM
ejpam-6414	290	24	l=0	l=0	PROPN
ejpam-6414	290	25	δj	δj	ADP
ejpam-6414	290	26	,	,	PUNCT
ejpam-6414	290	27	uz	uz	NOUN
ejpam-6414	290	28	v−l	v−l	NOUN
ejpam-6414	290	29	j	j	PROPN
ejpam-6414	290	30	,	,	PUNCT
ejpam-6414	290	31	where	where	SCONJ
ejpam-6414	290	32	the	the	DET
ejpam-6414	290	33	recurrence	recurrence	NOUN
ejpam-6414	290	34	relation	relation	NOUN
ejpam-6414	290	35	for	for	ADP
ejpam-6414	290	36	δj	δj	NOUN
ejpam-6414	290	37	,	,	PUNCT
ejpam-6414	290	38	u	u	NOUN
ejpam-6414	290	39	is	be	AUX
ejpam-6414	290	40	:	:	PUNCT
ejpam-6414	290	41	δ0	δ0	NOUN
ejpam-6414	290	42	=	=	PUNCT
ejpam-6414	290	43	δj,0	δj,0	PROPN
ejpam-6414	290	44	=	=	SYM
ejpam-6414	290	45	1	1	NUM
ejpam-6414	290	46	,	,	PUNCT
ejpam-6414	290	47	δj	δj	NOUN
ejpam-6414	290	48	,	,	PUNCT
ejpam-6414	290	49	u	u	NOUN
ejpam-6414	290	50	=	=	SYM
ejpam-6414	290	51	δu	δu	ADP
ejpam-6414	290	52	+	+	CCONJ
ejpam-6414	290	53	xj	xj	PROPN
ejpam-6414	290	54	·	·	PUNCT
ejpam-6414	290	55	δj	δj	ADP
ejpam-6414	290	56	,	,	PUNCT
ejpam-6414	290	57	u−1	u−1	PROPN
ejpam-6414	290	58	,	,	PUNCT
ejpam-6414	290	59	u	u	NOUN
ejpam-6414	290	60	=	=	PROPN
ejpam-6414	290	61	1	1	NUM
ejpam-6414	290	62	,	,	PUNCT
ejpam-6414	290	63	2	2	NUM
ejpam-6414	290	64	,	,	PUNCT
ejpam-6414	290	65	.	.	PUNCT
ejpam-6414	290	66	.	.	PUNCT
ejpam-6414	291	1	.	.	PUNCT
ejpam-6414	292	1	,	,	PUNCT
ejpam-6414	292	2	v	v	ADP
ejpam-6414	292	3	−	−	PROPN
ejpam-6414	292	4	1	1	NUM
ejpam-6414	292	5	,	,	PUNCT
ejpam-6414	292	6	j	j	PROPN
ejpam-6414	292	7	=	=	SYM
ejpam-6414	292	8	1	1	NUM
ejpam-6414	292	9	,	,	PUNCT
ejpam-6414	292	10	2	2	NUM
ejpam-6414	292	11	,	,	PUNCT
ejpam-6414	292	12	.	.	PUNCT
ejpam-6414	292	13	.	.	PUNCT
ejpam-6414	293	1	.	.	PUNCT
ejpam-6414	294	1	,	,	PUNCT
ejpam-6414	294	2	v.	v.	CCONJ
ejpam-6414	294	3	the	the	DET
ejpam-6414	294	4	final	final	ADJ
ejpam-6414	294	5	error	error	NOUN
ejpam-6414	294	6	vector	vector	NOUN
ejpam-6414	294	7	e	e	NOUN
ejpam-6414	294	8	is	be	AUX
ejpam-6414	294	9	obtained	obtain	VERB
ejpam-6414	294	10	,	,	PUNCT
ejpam-6414	294	11	and	and	CCONJ
ejpam-6414	294	12	the	the	DET
ejpam-6414	294	13	corrected	correct	VERB
ejpam-6414	294	14	codeword	codeword	NOUN
ejpam-6414	294	15	is	be	AUX
ejpam-6414	294	16	:	:	PUNCT
ejpam-6414	295	1	c	c	X
ejpam-6414	295	2	=	=	SYM
ejpam-6414	296	1	r	r	NOUN
ejpam-6414	296	2	−	−	PROPN
ejpam-6414	296	3	e.	e.	PROPN
ejpam-6414	296	4	the	the	DET
ejpam-6414	296	5	pseudocode	pseudocode	PROPN
ejpam-6414	296	6	for	for	ADP
ejpam-6414	296	7	the	the	DET
ejpam-6414	296	8	decoding	decoding	NOUN
ejpam-6414	296	9	of	of	ADP
ejpam-6414	296	10	bch	bch	PROPN
ejpam-6414	296	11	codes	code	NOUN
ejpam-6414	296	12	over	over	ADP
ejpam-6414	296	13	the	the	DET
ejpam-6414	296	14	quasi	quasi	ADJ
ejpam-6414	296	15	-	-	ADJ
ejpam-6414	296	16	galois	galois	ADJ
ejpam-6414	296	17	ring	ring	NOUN
ejpam-6414	296	18	using	use	VERB
ejpam-6414	296	19	ambma	ambma	PROPN
ejpam-6414	296	20	is	be	AUX
ejpam-6414	296	21	given	give	VERB
ejpam-6414	296	22	in	in	ADP
ejpam-6414	296	23	algorithm	algorithm	NOUN
ejpam-6414	296	24	2	2	NUM
ejpam-6414	296	25	.	.	PUNCT
ejpam-6414	296	26	example	example	NOUN
ejpam-6414	296	27	4.1	4.1	NUM
ejpam-6414	296	28	let	let	VERB
ejpam-6414	296	29	(	(	PUNCT
ejpam-6414	296	30	7	7	NUM
ejpam-6414	296	31	,	,	PUNCT
ejpam-6414	296	32	4	4	NUM
ejpam-6414	296	33	,	,	PUNCT
ejpam-6414	296	34	3	3	NUM
ejpam-6414	296	35	)	)	PUNCT
ejpam-6414	296	36	be	be	AUX
ejpam-6414	296	37	a	a	DET
ejpam-6414	296	38	bch	bch	PROPN
ejpam-6414	296	39	code	code	NOUN
ejpam-6414	296	40	over	over	ADP
ejpam-6414	296	41	the	the	DET
ejpam-6414	296	42	qgrs	qgrs	NOUN
ejpam-6414	296	43	a(2	a(2	PROPN
ejpam-6414	296	44	,	,	PUNCT
ejpam-6414	296	45	2	2	NUM
ejpam-6414	296	46	)	)	PUNCT
ejpam-6414	296	47	as	as	SCONJ
ejpam-6414	296	48	described	describe	VERB
ejpam-6414	296	49	in	in	ADP
ejpam-6414	296	50	section	section	NOUN
ejpam-6414	296	51	4	4	NUM
ejpam-6414	296	52	,	,	PUNCT
ejpam-6414	296	53	and	and	CCONJ
ejpam-6414	296	54	let	let	VERB
ejpam-6414	296	55	the	the	DET
ejpam-6414	296	56	received	received	ADJ
ejpam-6414	296	57	vector	vector	NOUN
ejpam-6414	296	58	be	be	AUX
ejpam-6414	296	59	r	r	NOUN
ejpam-6414	296	60	=	=	SYM
ejpam-6414	296	61	(	(	PUNCT
ejpam-6414	296	62	0	0	NUM
ejpam-6414	296	63	,	,	PUNCT
ejpam-6414	296	64	0	0	NUM
ejpam-6414	296	65	,	,	PUNCT
ejpam-6414	296	66	0	0	NUM
ejpam-6414	296	67	,	,	PUNCT
ejpam-6414	296	68	.	.	PUNCT
ejpam-6414	296	69	.	.	PUNCT
ejpam-6414	296	70	.	.	PUNCT
ejpam-6414	297	1	,	,	PUNCT
ejpam-6414	297	2	α2u+	α2u+	INTJ
ejpam-6414	297	3	α+	α+	PUNCT
ejpam-6414	297	4	1)1×7	1)1×7	PROPN
ejpam-6414	297	5	.	.	PUNCT
ejpam-6414	298	1	compute	compute	VERB
ejpam-6414	298	2	the	the	DET
ejpam-6414	298	3	syndrome	syndrome	NOUN
ejpam-6414	298	4	vector	vector	NOUN
ejpam-6414	298	5	s	s	NOUN
ejpam-6414	298	6	as	as	ADP
ejpam-6414	298	7	:	:	PUNCT
ejpam-6414	298	8	s	s	X
ejpam-6414	298	9	=	=	X
ejpam-6414	298	10	hrt	hrt	PROPN
ejpam-6414	298	11	=	=	SYM
ejpam-6414	298	12	(	(	PUNCT
ejpam-6414	298	13	1	1	NUM
ejpam-6414	298	14	γ	γ	X
ejpam-6414	298	15	γ2	γ2	NOUN
ejpam-6414	298	16	·	·	PUNCT
ejpam-6414	298	17	·	·	PUNCT
ejpam-6414	298	18	·	·	PUNCT
ejpam-6414	299	1	γ6	γ6	VERB
ejpam-6414	299	2	1	1	NUM
ejpam-6414	299	3	γ2	γ2	PROPN
ejpam-6414	299	4	γ4	γ4	PROPN
ejpam-6414	299	5	·	·	PUNCT
ejpam-6414	299	6	·	·	PUNCT
ejpam-6414	299	7	·	·	PUNCT
ejpam-6414	299	8	γ12	γ12	NUM
ejpam-6414	299	9	)	)	PUNCT
ejpam-6414	299	10			ADJ
ejpam-6414	299	11	0	0	NUM
ejpam-6414	299	12	0	0	NUM
ejpam-6414	299	13	0	0	NUM
ejpam-6414	299	14	...	...	PUNCT
ejpam-6414	300	1	α2u+	α2u+	INTJ
ejpam-6414	300	2	α+	α+	PUNCT
ejpam-6414	300	3	1	1	NUM
ejpam-6414	300	4			NOUN
ejpam-6414	300	5	=	=	PRON
ejpam-6414	300	6	(	(	PUNCT
ejpam-6414	300	7	γ11	γ11	PROPN
ejpam-6414	300	8	γ12	γ12	NOUN
ejpam-6414	300	9	)	)	PUNCT
ejpam-6414	300	10	=	=	PUNCT
ejpam-6414	301	1	(	(	PUNCT
ejpam-6414	301	2	γ4	γ4	NOUN
ejpam-6414	301	3	γ3	γ3	NOUN
ejpam-6414	301	4	)	)	PUNCT
ejpam-6414	302	1	=	=	PUNCT
ejpam-6414	302	2	(	(	PUNCT
ejpam-6414	302	3	α+	α+	X
ejpam-6414	302	4	uα2	uα2	ADV
ejpam-6414	302	5	α2	α2	ADJ
ejpam-6414	302	6	+	+	CCONJ
ejpam-6414	302	7	1	1	X
ejpam-6414	302	8	)	)	PUNCT
ejpam-6414	302	9	=	=	SYM
ejpam-6414	303	1	(	(	PUNCT
ejpam-6414	303	2	s1	s1	PROPN
ejpam-6414	303	3	s2	s2	PROPN
ejpam-6414	303	4	)	)	PUNCT
ejpam-6414	303	5	.	.	PUNCT
ejpam-6414	304	1	apply	apply	VERB
ejpam-6414	304	2	the	the	DET
ejpam-6414	304	3	ambma	ambma	NOUN
ejpam-6414	304	4	to	to	PART
ejpam-6414	304	5	determine	determine	VERB
ejpam-6414	304	6	δn(x	δn(x	X
ejpam-6414	304	7	)	)	PUNCT
ejpam-6414	304	8	using	use	VERB
ejpam-6414	304	9	the	the	DET
ejpam-6414	304	10	iteration	iteration	NOUN
ejpam-6414	304	11	steps	step	NOUN
ejpam-6414	304	12	shown	show	VERB
ejpam-6414	304	13	in	in	ADP
ejpam-6414	304	14	table	table	NOUN
ejpam-6414	304	15	3	3	NUM
ejpam-6414	304	16	.	.	PUNCT
ejpam-6414	305	1	muhammad	muhammad	PROPN
ejpam-6414	305	2	sajjad	sajjad	PROPN
ejpam-6414	305	3	et	et	PROPN
ejpam-6414	305	4	al	al	PROPN
ejpam-6414	305	5	.	.	PUNCT
ejpam-6414	305	6	/	/	SYM
ejpam-6414	305	7	eur	eur	PROPN
ejpam-6414	305	8	.	.	PUNCT
ejpam-6414	306	1	j.	j.	PROPN
ejpam-6414	306	2	pure	pure	PROPN
ejpam-6414	306	3	appl	appl	PROPN
ejpam-6414	306	4	.	.	PROPN
ejpam-6414	306	5	math	math	PROPN
ejpam-6414	306	6	,	,	PUNCT
ejpam-6414	306	7	18	18	NUM
ejpam-6414	306	8	(	(	PUNCT
ejpam-6414	306	9	3	3	NUM
ejpam-6414	306	10	)	)	PUNCT
ejpam-6414	306	11	(	(	PUNCT
ejpam-6414	306	12	2025	2025	NUM
ejpam-6414	306	13	)	)	PUNCT
ejpam-6414	306	14	,	,	PUNCT
ejpam-6414	306	15	6414	6414	NUM
ejpam-6414	306	16	15	15	NUM
ejpam-6414	306	17	of	of	ADP
ejpam-6414	306	18	22	22	NUM
ejpam-6414	306	19	table	table	NOUN
ejpam-6414	306	20	3	3	NUM
ejpam-6414	306	21	:	:	PUNCT
ejpam-6414	306	22	ambma	ambma	ADJ
ejpam-6414	306	23	for	for	ADP
ejpam-6414	306	24	finding	find	VERB
ejpam-6414	306	25	the	the	DET
ejpam-6414	306	26	linear	linear	ADJ
ejpam-6414	306	27	polynomial	polynomial	ADJ
ejpam-6414	306	28	iterations	iteration	NOUN
ejpam-6414	306	29	δn(x	δn(x	X
ejpam-6414	306	30	)	)	PUNCT
ejpam-6414	306	31	dn	dn	ADP
ejpam-6414	306	32	ln	ln	ADV
ejpam-6414	306	33	n	n	CCONJ
ejpam-6414	306	34	−	−	PROPN
ejpam-6414	306	35	ln	ln	ADJ
ejpam-6414	306	36	−1	−1	NOUN
ejpam-6414	306	37	1	1	NUM
ejpam-6414	306	38	1	1	NUM
ejpam-6414	306	39	0	0	NUM
ejpam-6414	306	40	−1	−1	NOUN
ejpam-6414	306	41	0	0	NUM
ejpam-6414	306	42	1	1	NUM
ejpam-6414	306	43	α+	α+	NOUN
ejpam-6414	306	44	uα2	uα2	NOUN
ejpam-6414	306	45	0	0	NUM
ejpam-6414	306	46	0	0	NUM
ejpam-6414	306	47	1	1	NUM
ejpam-6414	306	48	1	1	NUM
ejpam-6414	306	49	+	+	CCONJ
ejpam-6414	306	50	γ4x	γ4x	PUNCT
ejpam-6414	306	51	1	1	NUM
ejpam-6414	306	52	1	1	NUM
ejpam-6414	306	53	0	0	NUM
ejpam-6414	306	54	2	2	NUM
ejpam-6414	306	55	1	1	NUM
ejpam-6414	306	56	+	+	NUM
ejpam-6414	306	57	γ6x	γ6x	NOUN
ejpam-6414	306	58	thus	thus	ADV
ejpam-6414	306	59	,	,	PUNCT
ejpam-6414	306	60	it	it	PRON
ejpam-6414	306	61	follows	follow	VERB
ejpam-6414	306	62	that	that	SCONJ
ejpam-6414	306	63	:	:	PUNCT
ejpam-6414	306	64	δ2(x	δ2(x	X
ejpam-6414	306	65	)	)	PUNCT
ejpam-6414	306	66	=	=	SYM
ejpam-6414	306	67	1	1	NUM
ejpam-6414	306	68	+	+	NUM
ejpam-6414	306	69	γ6x	γ6x	NOUN
ejpam-6414	306	70	,	,	PUNCT
ejpam-6414	306	71	and	and	CCONJ
ejpam-6414	306	72	the	the	DET
ejpam-6414	306	73	reciprocal	reciprocal	ADJ
ejpam-6414	306	74	function	function	NOUN
ejpam-6414	306	75	is	be	AUX
ejpam-6414	306	76	g(x	g(x	NOUN
ejpam-6414	306	77	)	)	PUNCT
ejpam-6414	307	1	=	=	SYM
ejpam-6414	307	2	γ6	γ6	PROPN
ejpam-6414	307	3	+	+	CCONJ
ejpam-6414	307	4	x.	x.	NOUN
ejpam-6414	308	1	the	the	DET
ejpam-6414	308	2	root	root	NOUN
ejpam-6414	308	3	of	of	ADP
ejpam-6414	308	4	g(x	g(x	NOUN
ejpam-6414	308	5	)	)	PUNCT
ejpam-6414	308	6	is	be	AUX
ejpam-6414	308	7	γ6	γ6	PROPN
ejpam-6414	308	8	,	,	PUNCT
ejpam-6414	308	9	which	which	PRON
ejpam-6414	308	10	indicates	indicate	VERB
ejpam-6414	308	11	the	the	DET
ejpam-6414	308	12	error	error	NOUN
ejpam-6414	308	13	is	be	AUX
ejpam-6414	308	14	located	locate	VERB
ejpam-6414	308	15	at	at	ADP
ejpam-6414	308	16	position	position	NOUN
ejpam-6414	308	17	7	7	NUM
ejpam-6414	308	18	in	in	ADP
ejpam-6414	308	19	the	the	DET
ejpam-6414	308	20	received	receive	VERB
ejpam-6414	308	21	muhammad	muhammad	PROPN
ejpam-6414	308	22	sajjad	sajjad	PROPN
ejpam-6414	308	23	et	et	PROPN
ejpam-6414	308	24	al	al	PROPN
ejpam-6414	308	25	.	.	PUNCT
ejpam-6414	308	26	/	/	SYM
ejpam-6414	308	27	eur	eur	PROPN
ejpam-6414	308	28	.	.	PUNCT
ejpam-6414	309	1	j.	j.	PROPN
ejpam-6414	309	2	pure	pure	PROPN
ejpam-6414	309	3	appl	appl	PROPN
ejpam-6414	309	4	.	.	PROPN
ejpam-6414	309	5	math	math	PROPN
ejpam-6414	309	6	,	,	PUNCT
ejpam-6414	309	7	18	18	NUM
ejpam-6414	309	8	(	(	PUNCT
ejpam-6414	309	9	3	3	NUM
ejpam-6414	309	10	)	)	PUNCT
ejpam-6414	309	11	(	(	PUNCT
ejpam-6414	309	12	2025	2025	NUM
ejpam-6414	309	13	)	)	PUNCT
ejpam-6414	309	14	,	,	PUNCT
ejpam-6414	309	15	6414	6414	NUM
ejpam-6414	309	16	16	16	NUM
ejpam-6414	309	17	of	of	ADP
ejpam-6414	309	18	22	22	NUM
ejpam-6414	309	19	vector	vector	NOUN
ejpam-6414	309	20	r.	r.	NOUN
ejpam-6414	309	21	the	the	DET
ejpam-6414	309	22	error	error	NOUN
ejpam-6414	309	23	-	-	PUNCT
ejpam-6414	309	24	locator	locator	NOUN
ejpam-6414	309	25	polynomial	polynomial	NOUN
ejpam-6414	309	26	δ0x	δ0x	PROPN
ejpam-6414	309	27	v	v	X
ejpam-6414	309	28	+	+	CCONJ
ejpam-6414	309	29	δ1	δ1	NOUN
ejpam-6414	309	30	=	=	SYM
ejpam-6414	309	31	x−	x−	PROPN
ejpam-6414	309	32	γ6	γ6	PROPN
ejpam-6414	309	33	is	be	AUX
ejpam-6414	309	34	a	a	DET
ejpam-6414	309	35	symmetric	symmetric	ADJ
ejpam-6414	309	36	function	function	NOUN
ejpam-6414	309	37	for	for	ADP
ejpam-6414	309	38	v	v	NOUN
ejpam-6414	309	39	=	=	SYM
ejpam-6414	309	40	1	1	NUM
ejpam-6414	309	41	.	.	X
ejpam-6414	309	42	compute	compute	VERB
ejpam-6414	309	43	the	the	DET
ejpam-6414	309	44	error	error	NOUN
ejpam-6414	309	45	magnitude	magnitude	NOUN
ejpam-6414	309	46	using	use	VERB
ejpam-6414	309	47	forney	forney	PROPN
ejpam-6414	309	48	’s	’s	PART
ejpam-6414	309	49	formula	formula	NOUN
ejpam-6414	309	50	,	,	PUNCT
ejpam-6414	309	51	y1	y1	NOUN
ejpam-6414	309	52	=	=	PUNCT
ejpam-6414	309	53	δ1,0s1	δ1,0s1	NOUN
ejpam-6414	309	54	δ1,0x1	δ1,0x1	NOUN
ejpam-6414	309	55	=	=	SYM
ejpam-6414	309	56	s1	s1	NOUN
ejpam-6414	309	57	z1	z1	PROPN
ejpam-6414	309	58	=	=	SYM
ejpam-6414	309	59	γ4	γ4	PROPN
ejpam-6414	309	60	γ6	γ6	NOUN
ejpam-6414	309	61	=	=	PUNCT
ejpam-6414	309	62	γ5	γ5	PROPN
ejpam-6414	309	63	=	=	SYM
ejpam-6414	309	64	α2u+	α2u+	PROPN
ejpam-6414	309	65	α+	α+	PRON
ejpam-6414	309	66	1	1	NUM
ejpam-6414	309	67	,	,	PUNCT
ejpam-6414	309	68	where	where	SCONJ
ejpam-6414	309	69	δ0	δ0	NOUN
ejpam-6414	309	70	=	=	SYM
ejpam-6414	309	71	1	1	NUM
ejpam-6414	309	72	,	,	PUNCT
ejpam-6414	309	73	δ1	δ1	NOUN
ejpam-6414	309	74	=	=	PUNCT
ejpam-6414	309	75	−α2u−	−α2u−	X
ejpam-6414	309	76	α−	α−	ADP
ejpam-6414	309	77	1	1	NUM
ejpam-6414	309	78	,	,	PUNCT
ejpam-6414	309	79	and	and	CCONJ
ejpam-6414	309	80	v	v	X
ejpam-6414	309	81	=	=	SYM
ejpam-6414	309	82	1	1	NUM
ejpam-6414	309	83	.	.	PUNCT
ejpam-6414	310	1	therefore	therefore	ADV
ejpam-6414	310	2	,	,	PUNCT
ejpam-6414	310	3	the	the	DET
ejpam-6414	310	4	error	error	NOUN
ejpam-6414	310	5	vector	vector	NOUN
ejpam-6414	310	6	is	be	AUX
ejpam-6414	310	7	:	:	PUNCT
ejpam-6414	310	8	e	e	X
ejpam-6414	310	9	=	=	SYM
ejpam-6414	310	10	(	(	PUNCT
ejpam-6414	310	11	0	0	NUM
ejpam-6414	310	12	,	,	PUNCT
ejpam-6414	310	13	0	0	NUM
ejpam-6414	310	14	,	,	PUNCT
ejpam-6414	310	15	0	0	NUM
ejpam-6414	310	16	,	,	PUNCT
ejpam-6414	310	17	.	.	PUNCT
ejpam-6414	310	18	.	.	PUNCT
ejpam-6414	310	19	.	.	PUNCT
ejpam-6414	311	1	,	,	PUNCT
ejpam-6414	311	2	α2u+	α2u+	INTJ
ejpam-6414	311	3	α+	α+	PRON
ejpam-6414	311	4	1	1	NUM
ejpam-6414	311	5	)	)	PUNCT
ejpam-6414	311	6	,	,	PUNCT
ejpam-6414	311	7	and	and	CCONJ
ejpam-6414	311	8	the	the	DET
ejpam-6414	311	9	corrected	correct	VERB
ejpam-6414	311	10	codeword	codeword	NOUN
ejpam-6414	311	11	is	be	AUX
ejpam-6414	311	12	:	:	PUNCT
ejpam-6414	312	1	c	c	X
ejpam-6414	312	2	=	=	SYM
ejpam-6414	313	1	r	r	NOUN
ejpam-6414	313	2	−	−	NOUN
ejpam-6414	313	3	e	e	NOUN
ejpam-6414	313	4	=	=	PUNCT
ejpam-6414	313	5	(	(	PUNCT
ejpam-6414	313	6	0	0	NUM
ejpam-6414	313	7	,	,	PUNCT
ejpam-6414	313	8	0	0	NUM
ejpam-6414	313	9	,	,	PUNCT
ejpam-6414	313	10	0	0	NUM
ejpam-6414	313	11	,	,	PUNCT
ejpam-6414	313	12	.	.	PUNCT
ejpam-6414	313	13	.	.	PUNCT
ejpam-6414	313	14	.	.	PUNCT
ejpam-6414	314	1	,	,	PUNCT
ejpam-6414	314	2	0	0	NUM
ejpam-6414	314	3	)	)	PUNCT
ejpam-6414	314	4	.	.	PUNCT
ejpam-6414	315	1	example	example	NOUN
ejpam-6414	315	2	4.2	4.2	NUM
ejpam-6414	315	3	let	let	VERB
ejpam-6414	315	4	(	(	PUNCT
ejpam-6414	315	5	15	15	NUM
ejpam-6414	315	6	,	,	PUNCT
ejpam-6414	315	7	11	11	NUM
ejpam-6414	315	8	,	,	PUNCT
ejpam-6414	315	9	3	3	NUM
ejpam-6414	315	10	)	)	PUNCT
ejpam-6414	315	11	be	be	AUX
ejpam-6414	315	12	a	a	DET
ejpam-6414	315	13	bch	bch	PROPN
ejpam-6414	315	14	code	code	NOUN
ejpam-6414	315	15	over	over	ADP
ejpam-6414	315	16	the	the	DET
ejpam-6414	315	17	qgrs	qgrs	NOUN
ejpam-6414	315	18	a(2	a(2	PROPN
ejpam-6414	315	19	,	,	PUNCT
ejpam-6414	315	20	2	2	NUM
ejpam-6414	315	21	)	)	PUNCT
ejpam-6414	315	22	as	as	SCONJ
ejpam-6414	315	23	described	describe	VERB
ejpam-6414	315	24	in	in	ADP
ejpam-6414	315	25	section	section	NOUN
ejpam-6414	315	26	4	4	NUM
ejpam-6414	315	27	,	,	PUNCT
ejpam-6414	315	28	and	and	CCONJ
ejpam-6414	315	29	let	let	VERB
ejpam-6414	315	30	the	the	DET
ejpam-6414	315	31	received	received	ADJ
ejpam-6414	315	32	vector	vector	NOUN
ejpam-6414	315	33	be	be	AUX
ejpam-6414	315	34	r	r	NOUN
ejpam-6414	315	35	=	=	SYM
ejpam-6414	315	36	(	(	PUNCT
ejpam-6414	315	37	0	0	NUM
ejpam-6414	315	38	,	,	PUNCT
ejpam-6414	315	39	(	(	PUNCT
ejpam-6414	315	40	1	1	NUM
ejpam-6414	315	41	+	+	CCONJ
ejpam-6414	315	42	u)α	u)α	NOUN
ejpam-6414	315	43	,	,	PUNCT
ejpam-6414	315	44	0	0	NUM
ejpam-6414	315	45	,	,	PUNCT
ejpam-6414	315	46	0	0	NUM
ejpam-6414	315	47	,	,	PUNCT
ejpam-6414	315	48	.	.	PUNCT
ejpam-6414	315	49	.	.	PUNCT
ejpam-6414	316	1	.	.	PUNCT
ejpam-6414	317	1	,	,	PUNCT
ejpam-6414	317	2	0)1×15	0)1×15	NOUN
ejpam-6414	317	3	.	.	PUNCT
ejpam-6414	318	1	compute	compute	VERB
ejpam-6414	318	2	the	the	DET
ejpam-6414	318	3	syndrome	syndrome	NOUN
ejpam-6414	318	4	vector	vector	NOUN
ejpam-6414	318	5	s	s	NOUN
ejpam-6414	318	6	as	as	ADP
ejpam-6414	318	7	:	:	PUNCT
ejpam-6414	318	8	s	s	X
ejpam-6414	318	9	=	=	X
ejpam-6414	318	10	hrt	hrt	PROPN
ejpam-6414	318	11	=	=	SYM
ejpam-6414	318	12	(	(	PUNCT
ejpam-6414	318	13	1	1	NUM
ejpam-6414	318	14	γ	γ	X
ejpam-6414	318	15	γ2	γ2	NOUN
ejpam-6414	318	16	·	·	PUNCT
ejpam-6414	318	17	·	·	PUNCT
ejpam-6414	318	18	·	·	PUNCT
ejpam-6414	319	1	γ14	γ14	ADJ
ejpam-6414	319	2	1	1	NUM
ejpam-6414	319	3	γ2	γ2	NOUN
ejpam-6414	319	4	γ4	γ4	NOUN
ejpam-6414	319	5	·	·	PUNCT
ejpam-6414	319	6	·	·	PUNCT
ejpam-6414	319	7	·	·	PUNCT
ejpam-6414	319	8	γ28	γ28	X
ejpam-6414	319	9	)	)	PUNCT
ejpam-6414	319	10			ADJ
ejpam-6414	319	11	0	0	PUNCT
ejpam-6414	320	1	(	(	PUNCT
ejpam-6414	320	2	1	1	NUM
ejpam-6414	320	3	+	+	CCONJ
ejpam-6414	320	4	u)α	u)α	NOUN
ejpam-6414	320	5	0	0	NUM
ejpam-6414	320	6	...	...	SYM
ejpam-6414	320	7	0	0	NUM
ejpam-6414	321	1			PRON
ejpam-6414	321	2	=	=	PRON
ejpam-6414	322	1	(	(	PUNCT
ejpam-6414	322	2	(	(	PUNCT
ejpam-6414	322	3	1	1	NUM
ejpam-6414	322	4	+	+	NUM
ejpam-6414	322	5	u)α3	u)α3	PROPN
ejpam-6414	322	6	(	(	PUNCT
ejpam-6414	322	7	1	1	NUM
ejpam-6414	322	8	+	+	CCONJ
ejpam-6414	322	9	u)α+	u)α+	ADJ
ejpam-6414	322	10	α2	α2	ADJ
ejpam-6414	322	11	)	)	PUNCT
ejpam-6414	322	12	=	=	PUNCT
ejpam-6414	323	1	(	(	PUNCT
ejpam-6414	323	2	s1	s1	PROPN
ejpam-6414	323	3	s2	s2	PROPN
ejpam-6414	323	4	)	)	PUNCT
ejpam-6414	323	5	=	=	PUNCT
ejpam-6414	324	1	(	(	PUNCT
ejpam-6414	324	2	γ9	γ9	NOUN
ejpam-6414	324	3	γ10	γ10	PROPN
ejpam-6414	324	4	)	)	PUNCT
ejpam-6414	324	5	.	.	PUNCT
ejpam-6414	325	1	apply	apply	VERB
ejpam-6414	325	2	the	the	DET
ejpam-6414	325	3	ambma	ambma	NOUN
ejpam-6414	325	4	to	to	PART
ejpam-6414	325	5	determine	determine	VERB
ejpam-6414	325	6	δn(x	δn(x	X
ejpam-6414	325	7	)	)	PUNCT
ejpam-6414	325	8	using	use	VERB
ejpam-6414	325	9	the	the	DET
ejpam-6414	325	10	iteration	iteration	NOUN
ejpam-6414	325	11	steps	step	NOUN
ejpam-6414	325	12	shown	show	VERB
ejpam-6414	325	13	in	in	ADP
ejpam-6414	325	14	table	table	NOUN
ejpam-6414	325	15	4	4	NUM
ejpam-6414	325	16	.	.	PUNCT
ejpam-6414	325	17	table	table	NOUN
ejpam-6414	325	18	4	4	NUM
ejpam-6414	325	19	:	:	PUNCT
ejpam-6414	325	20	ambma	ambma	VERB
ejpam-6414	325	21	for	for	ADP
ejpam-6414	325	22	finding	find	VERB
ejpam-6414	325	23	the	the	DET
ejpam-6414	325	24	polynomial	polynomial	ADJ
ejpam-6414	325	25	iterations	iteration	NOUN
ejpam-6414	325	26	δn(x	δn(x	X
ejpam-6414	325	27	)	)	PUNCT
ejpam-6414	325	28	dn	dn	ADP
ejpam-6414	325	29	ln	ln	ADV
ejpam-6414	325	30	n	n	CCONJ
ejpam-6414	325	31	−	−	PROPN
ejpam-6414	325	32	ln	ln	ADJ
ejpam-6414	325	33	−1	−1	NOUN
ejpam-6414	325	34	1	1	NUM
ejpam-6414	325	35	1	1	NUM
ejpam-6414	325	36	0	0	NUM
ejpam-6414	325	37	−1	−1	NOUN
ejpam-6414	325	38	0	0	NUM
ejpam-6414	325	39	1	1	NUM
ejpam-6414	325	40	(	(	PUNCT
ejpam-6414	325	41	1	1	NUM
ejpam-6414	325	42	+	+	X
ejpam-6414	325	43	u)α3	u)α3	PROPN
ejpam-6414	325	44	0	0	NUM
ejpam-6414	325	45	0	0	NUM
ejpam-6414	325	46	1	1	NUM
ejpam-6414	325	47	1	1	NUM
ejpam-6414	325	48	+	+	CCONJ
ejpam-6414	325	49	γ9x	γ9x	X
ejpam-6414	325	50	(	(	PUNCT
ejpam-6414	325	51	1	1	NUM
ejpam-6414	325	52	+	+	NUM
ejpam-6414	325	53	u)α+	u)α+	ADJ
ejpam-6414	325	54	(	(	PUNCT
ejpam-6414	325	55	1	1	NUM
ejpam-6414	325	56	+	+	CCONJ
ejpam-6414	325	57	u)α3	u)α3	PROPN
ejpam-6414	325	58	1	1	NUM
ejpam-6414	325	59	0	0	NUM
ejpam-6414	325	60	2	2	NUM
ejpam-6414	325	61	1	1	NUM
ejpam-6414	325	62	+	+	CCONJ
ejpam-6414	325	63	γx	γx	NOUN
ejpam-6414	325	64	hence	hence	ADV
ejpam-6414	325	65	,	,	PUNCT
ejpam-6414	325	66	we	we	PRON
ejpam-6414	325	67	find	find	VERB
ejpam-6414	325	68	:	:	PUNCT
ejpam-6414	325	69	δ2(x	δ2(x	X
ejpam-6414	325	70	)	)	PUNCT
ejpam-6414	325	71	=	=	SYM
ejpam-6414	325	72	1	1	NUM
ejpam-6414	325	73	+	+	CCONJ
ejpam-6414	325	74	γx	γx	NOUN
ejpam-6414	325	75	,	,	PUNCT
ejpam-6414	325	76	and	and	CCONJ
ejpam-6414	325	77	the	the	DET
ejpam-6414	325	78	reciprocal	reciprocal	ADJ
ejpam-6414	325	79	function	function	NOUN
ejpam-6414	325	80	is	be	AUX
ejpam-6414	325	81	g(x	g(x	NOUN
ejpam-6414	325	82	)	)	PUNCT
ejpam-6414	326	1	=	=	SYM
ejpam-6414	326	2	γ	γ	X
ejpam-6414	326	3	+	+	PROPN
ejpam-6414	326	4	x.	x.	PROPN
ejpam-6414	326	5	muhammad	muhammad	PROPN
ejpam-6414	326	6	sajjad	sajjad	PROPN
ejpam-6414	326	7	et	et	PROPN
ejpam-6414	326	8	al	al	PROPN
ejpam-6414	326	9	.	.	PUNCT
ejpam-6414	326	10	/	/	SYM
ejpam-6414	326	11	eur	eur	PROPN
ejpam-6414	326	12	.	.	PUNCT
ejpam-6414	327	1	j.	j.	PROPN
ejpam-6414	327	2	pure	pure	PROPN
ejpam-6414	327	3	appl	appl	PROPN
ejpam-6414	327	4	.	.	PROPN
ejpam-6414	327	5	math	math	PROPN
ejpam-6414	327	6	,	,	PUNCT
ejpam-6414	327	7	18	18	NUM
ejpam-6414	327	8	(	(	PUNCT
ejpam-6414	327	9	3	3	NUM
ejpam-6414	327	10	)	)	PUNCT
ejpam-6414	327	11	(	(	PUNCT
ejpam-6414	327	12	2025	2025	NUM
ejpam-6414	327	13	)	)	PUNCT
ejpam-6414	327	14	,	,	PUNCT
ejpam-6414	327	15	6414	6414	NUM
ejpam-6414	327	16	17	17	NUM
ejpam-6414	327	17	of	of	ADP
ejpam-6414	327	18	22	22	NUM
ejpam-6414	327	19	the	the	DET
ejpam-6414	327	20	root	root	NOUN
ejpam-6414	327	21	of	of	ADP
ejpam-6414	327	22	g(x	g(x	NOUN
ejpam-6414	327	23	)	)	PUNCT
ejpam-6414	327	24	is	be	AUX
ejpam-6414	327	25	γ	γ	X
ejpam-6414	327	26	,	,	PUNCT
ejpam-6414	327	27	indicating	indicate	VERB
ejpam-6414	327	28	that	that	SCONJ
ejpam-6414	327	29	the	the	DET
ejpam-6414	327	30	error	error	NOUN
ejpam-6414	327	31	occurred	occur	VERB
ejpam-6414	327	32	at	at	ADP
ejpam-6414	327	33	a	a	DET
ejpam-6414	327	34	position	position	NOUN
ejpam-6414	327	35	2	2	NUM
ejpam-6414	327	36	in	in	ADP
ejpam-6414	327	37	the	the	DET
ejpam-6414	327	38	received	receive	VERB
ejpam-6414	327	39	vector	vector	NOUN
ejpam-6414	327	40	r.	r.	NOUN
ejpam-6414	327	41	the	the	DET
ejpam-6414	327	42	symmetric	symmetric	ADJ
ejpam-6414	327	43	form	form	NOUN
ejpam-6414	327	44	of	of	ADP
ejpam-6414	327	45	the	the	DET
ejpam-6414	327	46	error	error	NOUN
ejpam-6414	327	47	-	-	PUNCT
ejpam-6414	327	48	locator	locator	NOUN
ejpam-6414	327	49	polynomial	polynomial	NOUN
ejpam-6414	327	50	is	be	AUX
ejpam-6414	327	51	:	:	PUNCT
ejpam-6414	327	52	δ0x	δ0x	PROPN
ejpam-6414	327	53	v	v	X
ejpam-6414	327	54	+	+	CCONJ
ejpam-6414	327	55	δ1	δ1	NOUN
ejpam-6414	327	56	=	=	SYM
ejpam-6414	327	57	x−	x−	PROPN
ejpam-6414	327	58	γ	γ	PROPN
ejpam-6414	327	59	,	,	PUNCT
ejpam-6414	327	60	where	where	SCONJ
ejpam-6414	327	61	v	v	NOUN
ejpam-6414	327	62	=	=	SYM
ejpam-6414	327	63	1	1	NUM
ejpam-6414	327	64	.	.	PUNCT
ejpam-6414	327	65	using	use	VERB
ejpam-6414	327	66	forney	forney	PROPN
ejpam-6414	327	67	’s	’s	PART
ejpam-6414	327	68	formula	formula	NOUN
ejpam-6414	327	69	,	,	PUNCT
ejpam-6414	327	70	compute	compute	VERB
ejpam-6414	327	71	the	the	DET
ejpam-6414	327	72	error	error	NOUN
ejpam-6414	327	73	magnitude	magnitude	NOUN
ejpam-6414	327	74	y1	y1	NOUN
ejpam-6414	327	75	=	=	PUNCT
ejpam-6414	327	76	δ1,0s1	δ1,0s1	NOUN
ejpam-6414	327	77	δ1,0x1	δ1,0x1	NOUN
ejpam-6414	327	78	=	=	SYM
ejpam-6414	327	79	s1	s1	NOUN
ejpam-6414	327	80	z1	z1	NOUN
ejpam-6414	327	81	=	=	SYM
ejpam-6414	327	82	γ9	γ9	NOUN
ejpam-6414	327	83	γ	γ	NOUN
ejpam-6414	327	84	=	=	SYM
ejpam-6414	327	85	γ8	γ8	NOUN
ejpam-6414	327	86	=	=	PUNCT
ejpam-6414	327	87	α16	α16	NOUN
ejpam-6414	327	88	=	=	SYM
ejpam-6414	327	89	(	(	PUNCT
ejpam-6414	327	90	1	1	NUM
ejpam-6414	327	91	+	+	CCONJ
ejpam-6414	327	92	u)α	u)α	NOUN
ejpam-6414	327	93	,	,	PUNCT
ejpam-6414	327	94	where	where	SCONJ
ejpam-6414	327	95	δ0	δ0	NOUN
ejpam-6414	327	96	=	=	SYM
ejpam-6414	327	97	1	1	NUM
ejpam-6414	327	98	,	,	PUNCT
ejpam-6414	327	99	δ1	δ1	NOUN
ejpam-6414	327	100	=	=	PUNCT
ejpam-6414	328	1	−(1	−(1	NOUN
ejpam-6414	328	2	+	+	CCONJ
ejpam-6414	328	3	u)α	u)α	NOUN
ejpam-6414	328	4	,	,	PUNCT
ejpam-6414	328	5	and	and	CCONJ
ejpam-6414	328	6	v	v	X
ejpam-6414	328	7	=	=	SYM
ejpam-6414	328	8	1	1	NUM
ejpam-6414	328	9	.	.	PUNCT
ejpam-6414	329	1	therefore	therefore	ADV
ejpam-6414	329	2	,	,	PUNCT
ejpam-6414	329	3	the	the	DET
ejpam-6414	329	4	error	error	NOUN
ejpam-6414	329	5	vector	vector	NOUN
ejpam-6414	329	6	is	be	AUX
ejpam-6414	329	7	e	e	NOUN
ejpam-6414	329	8	=	=	X
ejpam-6414	329	9	(	(	PUNCT
ejpam-6414	329	10	0	0	NUM
ejpam-6414	329	11	,	,	PUNCT
ejpam-6414	329	12	(	(	PUNCT
ejpam-6414	329	13	1	1	NUM
ejpam-6414	329	14	+	+	CCONJ
ejpam-6414	329	15	u)α	u)α	NOUN
ejpam-6414	329	16	,	,	PUNCT
ejpam-6414	329	17	0	0	NUM
ejpam-6414	329	18	,	,	PUNCT
ejpam-6414	329	19	0	0	NUM
ejpam-6414	329	20	,	,	PUNCT
ejpam-6414	329	21	.	.	PUNCT
ejpam-6414	329	22	.	.	PUNCT
ejpam-6414	330	1	.	.	PUNCT
ejpam-6414	331	1	,	,	PUNCT
ejpam-6414	331	2	0	0	NUM
ejpam-6414	331	3	)	)	PUNCT
ejpam-6414	331	4	,	,	PUNCT
ejpam-6414	331	5	and	and	CCONJ
ejpam-6414	331	6	the	the	DET
ejpam-6414	331	7	corrected	correct	VERB
ejpam-6414	331	8	codeword	codeword	NOUN
ejpam-6414	331	9	is	be	AUX
ejpam-6414	331	10	:	:	PUNCT
ejpam-6414	331	11	c	c	X
ejpam-6414	331	12	=	=	SYM
ejpam-6414	332	1	r	r	NOUN
ejpam-6414	332	2	−	−	NOUN
ejpam-6414	332	3	e	e	NOUN
ejpam-6414	332	4	=	=	PUNCT
ejpam-6414	332	5	(	(	PUNCT
ejpam-6414	332	6	0	0	NUM
ejpam-6414	332	7	,	,	PUNCT
ejpam-6414	332	8	0	0	NUM
ejpam-6414	332	9	,	,	PUNCT
ejpam-6414	332	10	0	0	NUM
ejpam-6414	332	11	,	,	PUNCT
ejpam-6414	332	12	.	.	PUNCT
ejpam-6414	332	13	.	.	PUNCT
ejpam-6414	332	14	.	.	PUNCT
ejpam-6414	333	1	,	,	PUNCT
ejpam-6414	333	2	0	0	NUM
ejpam-6414	333	3	)	)	PUNCT
ejpam-6414	333	4	.	.	PUNCT
ejpam-6414	334	1	4.2	4.2	NUM
ejpam-6414	334	2	.	.	PUNCT
ejpam-6414	334	3	significance	significance	NOUN
ejpam-6414	334	4	of	of	ADP
ejpam-6414	334	5	quasi	quasi	ADJ
ejpam-6414	334	6	-	-	ADJ
ejpam-6414	334	7	galois	galois	ADJ
ejpam-6414	334	8	ring	ring	NOUN
ejpam-6414	334	9	-	-	PUNCT
ejpam-6414	334	10	based	base	VERB
ejpam-6414	334	11	bch	bch	PROPN
ejpam-6414	334	12	code	code	NOUN
ejpam-6414	334	13	construction	construction	NOUN
ejpam-6414	334	14	and	and	CCONJ
ejpam-6414	334	15	decoding	decode	VERB
ejpam-6414	334	16	in	in	ADP
ejpam-6414	334	17	modern	modern	ADJ
ejpam-6414	334	18	data	datum	NOUN
ejpam-6414	334	19	transmission	transmission	NOUN
ejpam-6414	334	20	the	the	DET
ejpam-6414	334	21	use	use	NOUN
ejpam-6414	334	22	of	of	ADP
ejpam-6414	334	23	quasi	quasi	ADJ
ejpam-6414	334	24	-	-	ADJ
ejpam-6414	334	25	galois	galois	ADJ
ejpam-6414	334	26	rings	ring	NOUN
ejpam-6414	334	27	(	(	PUNCT
ejpam-6414	334	28	qgrs	qgrs	PROPN
ejpam-6414	334	29	)	)	PUNCT
ejpam-6414	334	30	in	in	ADP
ejpam-6414	334	31	the	the	DET
ejpam-6414	334	32	construction	construction	NOUN
ejpam-6414	334	33	and	and	CCONJ
ejpam-6414	334	34	decoding	decoding	NOUN
ejpam-6414	334	35	of	of	ADP
ejpam-6414	334	36	bch	bch	PROPN
ejpam-6414	334	37	codes	code	NOUN
ejpam-6414	334	38	marks	mark	VERB
ejpam-6414	334	39	a	a	DET
ejpam-6414	334	40	significant	significant	ADJ
ejpam-6414	334	41	advancement	advancement	NOUN
ejpam-6414	334	42	in	in	ADP
ejpam-6414	334	43	the	the	DET
ejpam-6414	334	44	field	field	NOUN
ejpam-6414	334	45	of	of	ADP
ejpam-6414	334	46	error	error	NOUN
ejpam-6414	334	47	-	-	PUNCT
ejpam-6414	334	48	correcting	correct	VERB
ejpam-6414	334	49	codes	code	NOUN
ejpam-6414	334	50	,	,	PUNCT
ejpam-6414	334	51	particularly	particularly	ADV
ejpam-6414	334	52	for	for	ADP
ejpam-6414	334	53	modern	modern	ADJ
ejpam-6414	334	54	data	datum	NOUN
ejpam-6414	334	55	transmission	transmission	NOUN
ejpam-6414	334	56	applications	application	NOUN
ejpam-6414	334	57	.	.	PUNCT
ejpam-6414	335	1	qgrs	qgrs	PROPN
ejpam-6414	335	2	extend	extend	VERB
ejpam-6414	335	3	the	the	DET
ejpam-6414	335	4	algebraic	algebraic	ADJ
ejpam-6414	335	5	framework	framework	NOUN
ejpam-6414	335	6	of	of	ADP
ejpam-6414	335	7	classical	classical	ADJ
ejpam-6414	335	8	galois	galois	PROPN
ejpam-6414	335	9	rings	ring	NOUN
ejpam-6414	335	10	,	,	PUNCT
ejpam-6414	335	11	enabling	enable	VERB
ejpam-6414	335	12	richer	rich	ADJ
ejpam-6414	335	13	structural	structural	ADJ
ejpam-6414	335	14	properties	property	NOUN
ejpam-6414	335	15	that	that	PRON
ejpam-6414	335	16	lead	lead	VERB
ejpam-6414	335	17	to	to	ADP
ejpam-6414	335	18	greater	great	ADJ
ejpam-6414	335	19	design	design	NOUN
ejpam-6414	335	20	flexibility	flexibility	NOUN
ejpam-6414	335	21	.	.	PUNCT
ejpam-6414	336	1	this	this	PRON
ejpam-6414	336	2	allows	allow	VERB
ejpam-6414	336	3	for	for	ADP
ejpam-6414	336	4	bch	bch	PROPN
ejpam-6414	336	5	codes	code	NOUN
ejpam-6414	336	6	with	with	ADP
ejpam-6414	336	7	improved	improve	VERB
ejpam-6414	336	8	minimum	minimum	ADJ
ejpam-6414	336	9	distances	distance	NOUN
ejpam-6414	336	10	,	,	PUNCT
ejpam-6414	336	11	larger	large	ADJ
ejpam-6414	336	12	codeword	codeword	NOUN
ejpam-6414	336	13	sets	set	NOUN
ejpam-6414	336	14	,	,	PUNCT
ejpam-6414	336	15	and	and	CCONJ
ejpam-6414	336	16	higher	high	ADJ
ejpam-6414	336	17	code	code	NOUN
ejpam-6414	336	18	rates	rate	NOUN
ejpam-6414	336	19	—	—	PUNCT
ejpam-6414	336	20	key	key	ADJ
ejpam-6414	336	21	features	feature	NOUN
ejpam-6414	336	22	for	for	ADP
ejpam-6414	336	23	ensuring	ensure	VERB
ejpam-6414	336	24	data	datum	NOUN
ejpam-6414	336	25	integrity	integrity	NOUN
ejpam-6414	336	26	in	in	ADP
ejpam-6414	336	27	bandwidth	bandwidth	ADJ
ejpam-6414	336	28	-	-	PUNCT
ejpam-6414	336	29	intensive	intensive	ADJ
ejpam-6414	336	30	and	and	CCONJ
ejpam-6414	336	31	noise	noise	NOUN
ejpam-6414	336	32	-	-	PUNCT
ejpam-6414	336	33	prone	prone	ADJ
ejpam-6414	336	34	communication	communication	NOUN
ejpam-6414	336	35	environments	environment	NOUN
ejpam-6414	336	36	such	such	ADJ
ejpam-6414	336	37	as	as	ADP
ejpam-6414	336	38	satellite	satellite	NOUN
ejpam-6414	336	39	systems	system	NOUN
ejpam-6414	336	40	,	,	PUNCT
ejpam-6414	336	41	mobile	mobile	ADJ
ejpam-6414	336	42	networks	network	NOUN
ejpam-6414	336	43	,	,	PUNCT
ejpam-6414	336	44	and	and	CCONJ
ejpam-6414	336	45	high	high	ADJ
ejpam-6414	336	46	-	-	PUNCT
ejpam-6414	336	47	density	density	NOUN
ejpam-6414	336	48	data	datum	NOUN
ejpam-6414	336	49	storage	storage	NOUN
ejpam-6414	336	50	devices	device	NOUN
ejpam-6414	336	51	.	.	PUNCT
ejpam-6414	337	1	moreover	moreover	ADV
ejpam-6414	337	2	,	,	PUNCT
ejpam-6414	337	3	the	the	DET
ejpam-6414	337	4	decoding	decode	VERB
ejpam-6414	337	5	strategies	strategy	NOUN
ejpam-6414	337	6	developed	develop	VERB
ejpam-6414	337	7	for	for	ADP
ejpam-6414	337	8	bch	bch	PROPN
ejpam-6414	337	9	codes	code	NOUN
ejpam-6414	337	10	over	over	ADP
ejpam-6414	337	11	qgrs	qgrs	PROPN
ejpam-6414	337	12	enhance	enhance	VERB
ejpam-6414	337	13	the	the	DET
ejpam-6414	337	14	reliability	reliability	NOUN
ejpam-6414	337	15	and	and	CCONJ
ejpam-6414	337	16	speed	speed	NOUN
ejpam-6414	337	17	of	of	ADP
ejpam-6414	337	18	error	error	NOUN
ejpam-6414	337	19	correction	correction	NOUN
ejpam-6414	337	20	.	.	PUNCT
ejpam-6414	338	1	these	these	DET
ejpam-6414	338	2	methods	method	NOUN
ejpam-6414	338	3	exploit	exploit	VERB
ejpam-6414	338	4	the	the	DET
ejpam-6414	338	5	algebraic	algebraic	ADJ
ejpam-6414	338	6	depth	depth	NOUN
ejpam-6414	338	7	of	of	ADP
ejpam-6414	338	8	qgrs	qgrs	NOUN
ejpam-6414	338	9	to	to	PART
ejpam-6414	338	10	support	support	VERB
ejpam-6414	338	11	efficient	efficient	ADJ
ejpam-6414	338	12	syndrome	syndrome	NOUN
ejpam-6414	338	13	computation	computation	NOUN
ejpam-6414	338	14	and	and	CCONJ
ejpam-6414	338	15	error	error	NOUN
ejpam-6414	338	16	location	location	NOUN
ejpam-6414	338	17	,	,	PUNCT
ejpam-6414	338	18	making	make	VERB
ejpam-6414	338	19	them	they	PRON
ejpam-6414	338	20	suitable	suitable	ADJ
ejpam-6414	338	21	for	for	ADP
ejpam-6414	338	22	real	real	ADJ
ejpam-6414	338	23	-	-	PUNCT
ejpam-6414	338	24	time	time	NOUN
ejpam-6414	338	25	and	and	CCONJ
ejpam-6414	338	26	low	low	ADJ
ejpam-6414	338	27	-	-	PUNCT
ejpam-6414	338	28	latency	latency	NOUN
ejpam-6414	338	29	systems	system	NOUN
ejpam-6414	338	30	.	.	PUNCT
ejpam-6414	339	1	as	as	SCONJ
ejpam-6414	339	2	data	datum	NOUN
ejpam-6414	339	3	communication	communication	NOUN
ejpam-6414	339	4	continues	continue	VERB
ejpam-6414	339	5	to	to	PART
ejpam-6414	339	6	evolve	evolve	VERB
ejpam-6414	339	7	,	,	PUNCT
ejpam-6414	339	8	especially	especially	ADV
ejpam-6414	339	9	with	with	ADP
ejpam-6414	339	10	emerging	emerge	VERB
ejpam-6414	339	11	technologies	technology	NOUN
ejpam-6414	339	12	requiring	require	VERB
ejpam-6414	339	13	robust	robust	ADJ
ejpam-6414	339	14	and	and	CCONJ
ejpam-6414	339	15	scalable	scalable	ADJ
ejpam-6414	339	16	coding	code	VERB
ejpam-6414	339	17	schemes	scheme	NOUN
ejpam-6414	339	18	,	,	PUNCT
ejpam-6414	339	19	qgr	qgr	NOUN
ejpam-6414	339	20	-	-	PUNCT
ejpam-6414	339	21	based	base	VERB
ejpam-6414	339	22	bch	bch	PROPN
ejpam-6414	339	23	codes	code	NOUN
ejpam-6414	339	24	offer	offer	VERB
ejpam-6414	339	25	a	a	DET
ejpam-6414	339	26	future	future	ADJ
ejpam-6414	339	27	-	-	PUNCT
ejpam-6414	339	28	ready	ready	ADJ
ejpam-6414	339	29	solution	solution	NOUN
ejpam-6414	339	30	by	by	ADP
ejpam-6414	339	31	balancing	balance	VERB
ejpam-6414	339	32	strong	strong	ADJ
ejpam-6414	339	33	theoretical	theoretical	ADJ
ejpam-6414	339	34	foundations	foundation	NOUN
ejpam-6414	339	35	with	with	ADP
ejpam-6414	339	36	practical	practical	ADJ
ejpam-6414	339	37	performance	performance	NOUN
ejpam-6414	339	38	benefits	benefit	NOUN
ejpam-6414	339	39	.	.	PUNCT
ejpam-6414	340	1	5	5	X
ejpam-6414	340	2	.	.	X
ejpam-6414	340	3	comparison	comparison	NOUN
ejpam-6414	340	4	and	and	CCONJ
ejpam-6414	340	5	discussion	discussion	NOUN
ejpam-6414	340	6	this	this	DET
ejpam-6414	340	7	section	section	NOUN
ejpam-6414	340	8	provides	provide	VERB
ejpam-6414	340	9	a	a	DET
ejpam-6414	340	10	comparative	comparative	ADJ
ejpam-6414	340	11	analysis	analysis	NOUN
ejpam-6414	340	12	of	of	ADP
ejpam-6414	340	13	bch	bch	PROPN
ejpam-6414	340	14	codes	code	NOUN
ejpam-6414	340	15	over	over	ADP
ejpam-6414	340	16	galois	galois	PROPN
ejpam-6414	340	17	rings	ring	NOUN
ejpam-6414	340	18	[	[	X
ejpam-6414	340	19	3	3	NUM
ejpam-6414	340	20	]	]	PUNCT
ejpam-6414	340	21	and	and	CCONJ
ejpam-6414	340	22	quasi	quasi	ADJ
ejpam-6414	340	23	-	-	ADJ
ejpam-6414	340	24	galois	galois	ADJ
ejpam-6414	340	25	rings	ring	NOUN
ejpam-6414	340	26	(	(	PUNCT
ejpam-6414	340	27	qgrs	qgrs	PROPN
ejpam-6414	340	28	)	)	PUNCT
ejpam-6414	340	29	.	.	PUNCT
ejpam-6414	341	1	let	let	VERB
ejpam-6414	341	2	the	the	DET
ejpam-6414	341	3	parameters	parameter	NOUN
ejpam-6414	341	4	be	be	AUX
ejpam-6414	341	5	as	as	SCONJ
ejpam-6414	341	6	follows	follow	VERB
ejpam-6414	341	7	:	:	PUNCT
ejpam-6414	341	8	code	code	NOUN
ejpam-6414	341	9	length	length	NOUN
ejpam-6414	341	10	n	n	CCONJ
ejpam-6414	341	11	,	,	PUNCT
ejpam-6414	341	12	designed	design	VERB
ejpam-6414	341	13	distance	distance	NOUN
ejpam-6414	341	14	d	d	NOUN
ejpam-6414	341	15	,	,	PUNCT
ejpam-6414	341	16	dimensions	dimension	NOUN
ejpam-6414	341	17	k1	k1	NOUN
ejpam-6414	341	18	and	and	CCONJ
ejpam-6414	341	19	k2	k2	NOUN
ejpam-6414	341	20	,	,	PUNCT
ejpam-6414	341	21	code	code	NOUN
ejpam-6414	341	22	rates	rate	NOUN
ejpam-6414	341	23	r1	r1	NOUN
ejpam-6414	341	24	and	and	CCONJ
ejpam-6414	341	25	r2	r2	NOUN
ejpam-6414	341	26	,	,	PUNCT
ejpam-6414	341	27	and	and	CCONJ
ejpam-6414	341	28	the	the	DET
ejpam-6414	341	29	number	number	NOUN
ejpam-6414	341	30	of	of	ADP
ejpam-6414	341	31	codewords	codeword	NOUN
ejpam-6414	341	32	qk	qk	PROPN
ejpam-6414	341	33	for	for	ADP
ejpam-6414	341	34	bch	bch	PROPN
ejpam-6414	341	35	codes	code	NOUN
ejpam-6414	341	36	defined	define	VERB
ejpam-6414	341	37	over	over	ADP
ejpam-6414	341	38	galois	galois	PROPN
ejpam-6414	341	39	rings	ring	NOUN
ejpam-6414	341	40	gr(pn	gr(pn	PROPN
ejpam-6414	341	41	,	,	PUNCT
ejpam-6414	341	42	s	s	PART
ejpam-6414	341	43	)	)	PUNCT
ejpam-6414	341	44	and	and	CCONJ
ejpam-6414	341	45	quasi	quasi	ADJ
ejpam-6414	341	46	-	-	ADJ
ejpam-6414	341	47	galois	galois	ADJ
ejpam-6414	341	48	rings	ring	NOUN
ejpam-6414	341	49	a(ps	a(ps	PROPN
ejpam-6414	341	50	,	,	PUNCT
ejpam-6414	341	51	n	n	CCONJ
ejpam-6414	341	52	)	)	PUNCT
ejpam-6414	341	53	.	.	PUNCT
ejpam-6414	342	1	comparative	comparative	ADJ
ejpam-6414	342	2	results	result	NOUN
ejpam-6414	342	3	using	use	VERB
ejpam-6414	342	4	the	the	DET
ejpam-6414	342	5	examples	example	NOUN
ejpam-6414	342	6	gr(2	gr(2	NOUN
ejpam-6414	342	7	,	,	PUNCT
ejpam-6414	342	8	2	2	NUM
ejpam-6414	342	9	)	)	PUNCT
ejpam-6414	342	10	and	and	CCONJ
ejpam-6414	342	11	a(2	a(2	PROPN
ejpam-6414	342	12	,	,	PUNCT
ejpam-6414	342	13	2	2	NUM
ejpam-6414	342	14	)	)	PUNCT
ejpam-6414	342	15	are	be	AUX
ejpam-6414	342	16	summarized	summarize	VERB
ejpam-6414	342	17	in	in	ADP
ejpam-6414	342	18	tables	table	NOUN
ejpam-6414	342	19	5	5	NUM
ejpam-6414	342	20	muhammad	muhammad	PROPN
ejpam-6414	342	21	sajjad	sajjad	PROPN
ejpam-6414	342	22	et	et	PROPN
ejpam-6414	342	23	al	al	PROPN
ejpam-6414	342	24	.	.	PUNCT
ejpam-6414	342	25	/	/	SYM
ejpam-6414	342	26	eur	eur	PROPN
ejpam-6414	342	27	.	.	PUNCT
ejpam-6414	343	1	j.	j.	PROPN
ejpam-6414	343	2	pure	pure	PROPN
ejpam-6414	343	3	appl	appl	PROPN
ejpam-6414	343	4	.	.	PROPN
ejpam-6414	343	5	math	math	PROPN
ejpam-6414	343	6	,	,	PUNCT
ejpam-6414	343	7	18	18	NUM
ejpam-6414	343	8	(	(	PUNCT
ejpam-6414	343	9	3	3	NUM
ejpam-6414	343	10	)	)	PUNCT
ejpam-6414	343	11	(	(	PUNCT
ejpam-6414	343	12	2025	2025	NUM
ejpam-6414	343	13	)	)	PUNCT
ejpam-6414	343	14	,	,	PUNCT
ejpam-6414	343	15	6414	6414	NUM
ejpam-6414	343	16	18	18	NUM
ejpam-6414	343	17	of	of	ADP
ejpam-6414	343	18	22	22	NUM
ejpam-6414	343	19	table	table	NOUN
ejpam-6414	343	20	5	5	NUM
ejpam-6414	343	21	:	:	PUNCT
ejpam-6414	343	22	code	code	NOUN
ejpam-6414	343	23	analysis	analysis	NOUN
ejpam-6414	343	24	of	of	ADP
ejpam-6414	343	25	bch	bch	PROPN
ejpam-6414	343	26	codes	code	NOUN
ejpam-6414	343	27	over	over	ADP
ejpam-6414	343	28	galois	galois	PROPN
ejpam-6414	343	29	rings	ring	NOUN
ejpam-6414	343	30	gr(2	gr(2	PROPN
ejpam-6414	343	31	,	,	PUNCT
ejpam-6414	343	32	2	2	NUM
ejpam-6414	343	33	)	)	PUNCT
ejpam-6414	343	34	characteristic	characteristic	NOUN
ejpam-6414	344	1	n	n	NOUN
ejpam-6414	344	2	d	d	PROPN
ejpam-6414	344	3	k	k	PROPN
ejpam-6414	344	4	2k	2k	PROPN
ejpam-6414	344	5	r1	r1	NOUN
ejpam-6414	344	6	2	2	NUM
ejpam-6414	344	7	3	3	NUM
ejpam-6414	344	8	3	3	NUM
ejpam-6414	344	9	1	1	NUM
ejpam-6414	344	10	21	21	NUM
ejpam-6414	344	11	0.3333	0.3333	NUM
ejpam-6414	344	12	table	table	NOUN
ejpam-6414	344	13	6	6	NUM
ejpam-6414	344	14	:	:	PUNCT
ejpam-6414	344	15	code	code	NOUN
ejpam-6414	344	16	analysis	analysis	NOUN
ejpam-6414	344	17	of	of	ADP
ejpam-6414	344	18	bch	bch	PROPN
ejpam-6414	344	19	codes	code	NOUN
ejpam-6414	344	20	over	over	ADP
ejpam-6414	344	21	quasi	quasi	ADJ
ejpam-6414	344	22	-	-	ADJ
ejpam-6414	344	23	galois	galois	ADJ
ejpam-6414	344	24	rings	ring	NOUN
ejpam-6414	344	25	a(2	a(2	PROPN
ejpam-6414	344	26	,	,	PUNCT
ejpam-6414	344	27	2	2	X
ejpam-6414	344	28	)	)	PUNCT
ejpam-6414	344	29	characteristic	characteristic	NOUN
ejpam-6414	344	30	n	n	NOUN
ejpam-6414	344	31	d	d	X
ejpam-6414	344	32	k	k	PROPN
ejpam-6414	344	33	2k	2k	PROPN
ejpam-6414	344	34	r2	r2	PROPN
ejpam-6414	344	35	2	2	NUM
ejpam-6414	344	36	15	15	NUM
ejpam-6414	344	37	3	3	NUM
ejpam-6414	344	38	11	11	NUM
ejpam-6414	344	39	244	244	NUM
ejpam-6414	344	40	0.7333	0.7333	NUM
ejpam-6414	344	41	2	2	NUM
ejpam-6414	344	42	15	15	NUM
ejpam-6414	344	43	5	5	NUM
ejpam-6414	344	44	7	7	NUM
ejpam-6414	344	45	228	228	NUM
ejpam-6414	344	46	0.4647	0.4647	NUM
ejpam-6414	344	47	2	2	NUM
ejpam-6414	344	48	15	15	NUM
ejpam-6414	344	49	7	7	NUM
ejpam-6414	344	50	5	5	NUM
ejpam-6414	344	51	220	220	NUM
ejpam-6414	344	52	0.3333	0.3333	NUM
ejpam-6414	344	53	2	2	NUM
ejpam-6414	344	54	15	15	NUM
ejpam-6414	344	55	9	9	NUM
ejpam-6414	344	56	1	1	NUM
ejpam-6414	344	57	24	24	NUM
ejpam-6414	344	58	0.0667	0.0667	NUM
ejpam-6414	344	59	2	2	NUM
ejpam-6414	344	60	15	15	NUM
ejpam-6414	344	61	11	11	NUM
ejpam-6414	344	62	1	1	NUM
ejpam-6414	344	63	24	24	NUM
ejpam-6414	344	64	0.0667	0.0667	NUM
ejpam-6414	344	65	2	2	NUM
ejpam-6414	344	66	15	15	NUM
ejpam-6414	344	67	13	13	NUM
ejpam-6414	344	68	1	1	NUM
ejpam-6414	344	69	24	24	NUM
ejpam-6414	344	70	0.0667	0.0667	NUM
ejpam-6414	344	71	figure	figure	NOUN
ejpam-6414	344	72	1	1	NUM
ejpam-6414	344	73	:	:	PUNCT
ejpam-6414	344	74	designed	design	VERB
ejpam-6414	344	75	distances	distance	NOUN
ejpam-6414	344	76	vs.	vs.	ADP
ejpam-6414	344	77	code	code	NOUN
ejpam-6414	344	78	rates	rate	NOUN
ejpam-6414	344	79	of	of	ADP
ejpam-6414	344	80	bch	bch	PROPN
ejpam-6414	344	81	codes	code	NOUN
ejpam-6414	344	82	over	over	ADP
ejpam-6414	344	83	gr(2	gr(2	PROPN
ejpam-6414	344	84	,	,	PUNCT
ejpam-6414	344	85	2	2	NUM
ejpam-6414	344	86	)	)	PUNCT
ejpam-6414	344	87	and	and	CCONJ
ejpam-6414	344	88	a(2	a(2	PROPN
ejpam-6414	344	89	,	,	PUNCT
ejpam-6414	344	90	2	2	NUM
ejpam-6414	344	91	)	)	PUNCT
ejpam-6414	344	92	and	and	CCONJ
ejpam-6414	344	93	6	6	NUM
ejpam-6414	344	94	.	.	PUNCT
ejpam-6414	345	1	furthermore	furthermore	ADV
ejpam-6414	345	2	,	,	PUNCT
ejpam-6414	345	3	graphical	graphical	ADJ
ejpam-6414	345	4	comparisons	comparison	NOUN
ejpam-6414	345	5	of	of	ADP
ejpam-6414	345	6	the	the	DET
ejpam-6414	345	7	designed	design	VERB
ejpam-6414	345	8	distances	distance	NOUN
ejpam-6414	345	9	,	,	PUNCT
ejpam-6414	345	10	code	code	NOUN
ejpam-6414	345	11	rates	rate	NOUN
ejpam-6414	345	12	,	,	PUNCT
ejpam-6414	345	13	and	and	CCONJ
ejpam-6414	345	14	dimensions	dimension	NOUN
ejpam-6414	345	15	are	be	AUX
ejpam-6414	345	16	shown	show	VERB
ejpam-6414	345	17	in	in	ADP
ejpam-6414	345	18	figures	figure	NOUN
ejpam-6414	345	19	1	1	NUM
ejpam-6414	345	20	and	and	CCONJ
ejpam-6414	345	21	2	2	NUM
ejpam-6414	345	22	.	.	X
ejpam-6414	345	23	from	from	ADP
ejpam-6414	345	24	the	the	DET
ejpam-6414	345	25	analysis	analysis	NOUN
ejpam-6414	345	26	above	above	ADV
ejpam-6414	345	27	,	,	PUNCT
ejpam-6414	345	28	we	we	PRON
ejpam-6414	345	29	observe	observe	VERB
ejpam-6414	345	30	the	the	DET
ejpam-6414	345	31	following	following	NOUN
ejpam-6414	345	32	:	:	PUNCT
ejpam-6414	345	33	•	•	NOUN
ejpam-6414	345	34	in	in	ADP
ejpam-6414	345	35	the	the	DET
ejpam-6414	345	36	case	case	NOUN
ejpam-6414	345	37	of	of	ADP
ejpam-6414	345	38	the	the	DET
ejpam-6414	345	39	galois	galois	PROPN
ejpam-6414	345	40	ring	ring	NOUN
ejpam-6414	345	41	gr(2	gr(2	PROPN
ejpam-6414	345	42	,	,	PUNCT
ejpam-6414	345	43	2	2	NUM
ejpam-6414	345	44	)	)	PUNCT
ejpam-6414	345	45	,	,	PUNCT
ejpam-6414	345	46	only	only	ADV
ejpam-6414	345	47	one	one	NUM
ejpam-6414	345	48	possibility	possibility	NOUN
ejpam-6414	345	49	exists	exist	VERB
ejpam-6414	345	50	for	for	ADP
ejpam-6414	345	51	constructing	construct	VERB
ejpam-6414	345	52	bch	bch	NOUN
ejpam-6414	345	53	codes	code	NOUN
ejpam-6414	345	54	,	,	PUNCT
ejpam-6414	345	55	whereas	whereas	SCONJ
ejpam-6414	345	56	six	six	NUM
ejpam-6414	345	57	distinct	distinct	ADJ
ejpam-6414	345	58	possibilities	possibility	NOUN
ejpam-6414	345	59	are	be	AUX
ejpam-6414	345	60	available	available	ADJ
ejpam-6414	345	61	for	for	ADP
ejpam-6414	345	62	a(2	a(2	PROPN
ejpam-6414	345	63	,	,	PUNCT
ejpam-6414	345	64	2	2	NUM
ejpam-6414	345	65	)	)	PUNCT
ejpam-6414	345	66	.	.	PUNCT
ejpam-6414	346	1	•	•	NUM
ejpam-6414	346	2	the	the	DET
ejpam-6414	346	3	maximum	maximum	PROPN
ejpam-6414	346	4	code	code	NOUN
ejpam-6414	346	5	length	length	NOUN
ejpam-6414	346	6	achievable	achievable	ADJ
ejpam-6414	346	7	over	over	ADP
ejpam-6414	346	8	gr(2	gr(2	PROPN
ejpam-6414	346	9	,	,	PUNCT
ejpam-6414	346	10	2	2	NUM
ejpam-6414	346	11	)	)	PUNCT
ejpam-6414	346	12	is	be	AUX
ejpam-6414	346	13	3	3	NUM
ejpam-6414	346	14	,	,	PUNCT
ejpam-6414	346	15	while	while	SCONJ
ejpam-6414	346	16	for	for	ADP
ejpam-6414	346	17	a(2	a(2	PROPN
ejpam-6414	346	18	,	,	PUNCT
ejpam-6414	346	19	2	2	X
ejpam-6414	346	20	)	)	PUNCT
ejpam-6414	346	21	it	it	PRON
ejpam-6414	346	22	is	be	AUX
ejpam-6414	346	23	15	15	NUM
ejpam-6414	346	24	.	.	NOUN
ejpam-6414	347	1	•	•	NUM
ejpam-6414	347	2	designed	design	VERB
ejpam-6414	347	3	distance	distance	NOUN
ejpam-6414	347	4	values	value	NOUN
ejpam-6414	347	5	for	for	ADP
ejpam-6414	347	6	bch	bch	PROPN
ejpam-6414	347	7	codes	code	NOUN
ejpam-6414	347	8	over	over	ADP
ejpam-6414	347	9	a(2	a(2	PROPN
ejpam-6414	347	10	,	,	PUNCT
ejpam-6414	347	11	2	2	NUM
ejpam-6414	347	12	)	)	PUNCT
ejpam-6414	347	13	range	range	NOUN
ejpam-6414	347	14	from	from	ADP
ejpam-6414	347	15	3	3	NUM
ejpam-6414	347	16	to	to	ADP
ejpam-6414	347	17	13	13	NUM
ejpam-6414	347	18	,	,	PUNCT
ejpam-6414	347	19	whereas	whereas	SCONJ
ejpam-6414	347	20	for	for	ADP
ejpam-6414	347	21	gr(2	gr(2	NOUN
ejpam-6414	347	22	,	,	PUNCT
ejpam-6414	347	23	2	2	NUM
ejpam-6414	347	24	)	)	PUNCT
ejpam-6414	347	25	it	it	PRON
ejpam-6414	347	26	is	be	AUX
ejpam-6414	347	27	only	only	ADV
ejpam-6414	347	28	3	3	NUM
ejpam-6414	347	29	.	.	PUNCT
ejpam-6414	348	1	this	this	PRON
ejpam-6414	348	2	indicates	indicate	VERB
ejpam-6414	348	3	that	that	SCONJ
ejpam-6414	348	4	bch	bch	PROPN
ejpam-6414	348	5	codes	code	NOUN
ejpam-6414	348	6	over	over	ADP
ejpam-6414	348	7	quasi	quasi	ADJ
ejpam-6414	348	8	-	-	ADJ
ejpam-6414	348	9	galois	galois	ADJ
ejpam-6414	348	10	rings	ring	NOUN
ejpam-6414	348	11	offer	offer	VERB
ejpam-6414	348	12	superior	superior	ADJ
ejpam-6414	348	13	error	error	NOUN
ejpam-6414	348	14	-	-	PUNCT
ejpam-6414	348	15	correction	correction	NOUN
ejpam-6414	348	16	capabilities	capability	NOUN
ejpam-6414	348	17	.	.	PUNCT
ejpam-6414	349	1	muhammad	muhammad	PROPN
ejpam-6414	349	2	sajjad	sajjad	PROPN
ejpam-6414	349	3	et	et	PROPN
ejpam-6414	349	4	al	al	PROPN
ejpam-6414	349	5	.	.	PUNCT
ejpam-6414	349	6	/	/	SYM
ejpam-6414	349	7	eur	eur	PROPN
ejpam-6414	349	8	.	.	PUNCT
ejpam-6414	350	1	j.	j.	PROPN
ejpam-6414	350	2	pure	pure	PROPN
ejpam-6414	350	3	appl	appl	PROPN
ejpam-6414	350	4	.	.	PROPN
ejpam-6414	350	5	math	math	PROPN
ejpam-6414	350	6	,	,	PUNCT
ejpam-6414	350	7	18	18	NUM
ejpam-6414	350	8	(	(	PUNCT
ejpam-6414	350	9	3	3	NUM
ejpam-6414	350	10	)	)	PUNCT
ejpam-6414	350	11	(	(	PUNCT
ejpam-6414	350	12	2025	2025	NUM
ejpam-6414	350	13	)	)	PUNCT
ejpam-6414	350	14	,	,	PUNCT
ejpam-6414	350	15	6414	6414	NUM
ejpam-6414	350	16	19	19	NUM
ejpam-6414	350	17	of	of	ADP
ejpam-6414	350	18	22	22	NUM
ejpam-6414	350	19	figure	figure	NOUN
ejpam-6414	350	20	2	2	NUM
ejpam-6414	350	21	:	:	PUNCT
ejpam-6414	350	22	designed	design	VERB
ejpam-6414	350	23	distances	distance	NOUN
ejpam-6414	350	24	vs.	vs.	ADP
ejpam-6414	350	25	dimensions	dimension	NOUN
ejpam-6414	350	26	of	of	ADP
ejpam-6414	350	27	bch	bch	PROPN
ejpam-6414	350	28	codes	code	NOUN
ejpam-6414	350	29	over	over	ADP
ejpam-6414	350	30	gr(2	gr(2	PROPN
ejpam-6414	350	31	,	,	PUNCT
ejpam-6414	350	32	2	2	NUM
ejpam-6414	350	33	)	)	PUNCT
ejpam-6414	350	34	and	and	CCONJ
ejpam-6414	350	35	a(2	a(2	PROPN
ejpam-6414	350	36	,	,	PUNCT
ejpam-6414	350	37	2	2	NUM
ejpam-6414	350	38	)	)	PUNCT
ejpam-6414	350	39	•	•	NOUN
ejpam-6414	350	40	furthermore	furthermore	ADV
ejpam-6414	350	41	,	,	PUNCT
ejpam-6414	350	42	the	the	DET
ejpam-6414	350	43	number	number	NOUN
ejpam-6414	350	44	of	of	ADP
ejpam-6414	350	45	codewords	codeword	NOUN
ejpam-6414	350	46	over	over	ADP
ejpam-6414	350	47	a(2	a(2	PROPN
ejpam-6414	350	48	,	,	PUNCT
ejpam-6414	350	49	2	2	NUM
ejpam-6414	350	50	)	)	PUNCT
ejpam-6414	350	51	is	be	AUX
ejpam-6414	350	52	significantly	significantly	ADV
ejpam-6414	350	53	larger	large	ADJ
ejpam-6414	350	54	than	than	ADP
ejpam-6414	350	55	that	that	PRON
ejpam-6414	350	56	of	of	ADP
ejpam-6414	350	57	bch	bch	PROPN
ejpam-6414	350	58	codes	code	NOUN
ejpam-6414	350	59	over	over	ADP
ejpam-6414	350	60	gr(2	gr(2	PROPN
ejpam-6414	350	61	,	,	PUNCT
ejpam-6414	350	62	2	2	NUM
ejpam-6414	350	63	)	)	PUNCT
ejpam-6414	350	64	,	,	PUNCT
ejpam-6414	350	65	enhancing	enhance	VERB
ejpam-6414	350	66	their	their	PRON
ejpam-6414	350	67	usefulness	usefulness	NOUN
ejpam-6414	350	68	in	in	ADP
ejpam-6414	350	69	applications	application	NOUN
ejpam-6414	350	70	requiring	require	VERB
ejpam-6414	350	71	higher	high	ADJ
ejpam-6414	350	72	data	datum	NOUN
ejpam-6414	350	73	capacity	capacity	NOUN
ejpam-6414	350	74	and	and	CCONJ
ejpam-6414	350	75	reliability	reliability	NOUN
ejpam-6414	350	76	.	.	PUNCT
ejpam-6414	351	1	6	6	X
ejpam-6414	351	2	.	.	X
ejpam-6414	351	3	conclusions	conclusion	NOUN
ejpam-6414	351	4	and	and	CCONJ
ejpam-6414	351	5	future	future	ADJ
ejpam-6414	351	6	directions	direction	NOUN
ejpam-6414	351	7	the	the	DET
ejpam-6414	351	8	study	study	NOUN
ejpam-6414	351	9	of	of	ADP
ejpam-6414	351	10	bch	bch	PROPN
ejpam-6414	351	11	codes	code	NOUN
ejpam-6414	351	12	over	over	ADP
ejpam-6414	351	13	quasi	quasi	ADJ
ejpam-6414	351	14	-	-	ADJ
ejpam-6414	351	15	galois	galois	ADJ
ejpam-6414	351	16	rings	ring	NOUN
ejpam-6414	351	17	(	(	PUNCT
ejpam-6414	351	18	qgrs	qgrs	PROPN
ejpam-6414	351	19	)	)	PUNCT
ejpam-6414	351	20	,	,	PUNCT
ejpam-6414	351	21	as	as	SCONJ
ejpam-6414	351	22	presented	present	VERB
ejpam-6414	351	23	in	in	ADP
ejpam-6414	351	24	this	this	DET
ejpam-6414	351	25	article	article	NOUN
ejpam-6414	351	26	,	,	PUNCT
ejpam-6414	351	27	demonstrates	demonstrate	VERB
ejpam-6414	351	28	their	their	PRON
ejpam-6414	351	29	strong	strong	ADJ
ejpam-6414	351	30	potential	potential	NOUN
ejpam-6414	351	31	in	in	ADP
ejpam-6414	351	32	enhancing	enhance	VERB
ejpam-6414	351	33	modern	modern	ADJ
ejpam-6414	351	34	communication	communication	NOUN
ejpam-6414	351	35	systems	system	NOUN
ejpam-6414	351	36	.	.	PUNCT
ejpam-6414	352	1	through	through	ADP
ejpam-6414	352	2	a	a	DET
ejpam-6414	352	3	comprehensive	comprehensive	ADJ
ejpam-6414	352	4	analysis	analysis	NOUN
ejpam-6414	352	5	of	of	ADP
ejpam-6414	352	6	the	the	DET
ejpam-6414	352	7	underlying	underlie	VERB
ejpam-6414	352	8	theoretical	theoretical	ADJ
ejpam-6414	352	9	foundations	foundation	NOUN
ejpam-6414	352	10	,	,	PUNCT
ejpam-6414	352	11	construction	construction	NOUN
ejpam-6414	352	12	methodologies	methodology	NOUN
ejpam-6414	352	13	,	,	PUNCT
ejpam-6414	352	14	and	and	CCONJ
ejpam-6414	352	15	decoding	decode	VERB
ejpam-6414	352	16	algorithms	algorithm	NOUN
ejpam-6414	352	17	,	,	PUNCT
ejpam-6414	352	18	it	it	PRON
ejpam-6414	352	19	is	be	AUX
ejpam-6414	352	20	evident	evident	ADJ
ejpam-6414	352	21	that	that	SCONJ
ejpam-6414	352	22	the	the	DET
ejpam-6414	352	23	extended	extended	ADJ
ejpam-6414	352	24	algebraic	algebraic	ADJ
ejpam-6414	352	25	structure	structure	NOUN
ejpam-6414	352	26	and	and	CCONJ
ejpam-6414	352	27	intrinsic	intrinsic	ADJ
ejpam-6414	352	28	properties	property	NOUN
ejpam-6414	352	29	of	of	ADP
ejpam-6414	352	30	qgrs	qgrs	NOUN
ejpam-6414	352	31	contribute	contribute	VERB
ejpam-6414	352	32	significantly	significantly	ADV
ejpam-6414	352	33	to	to	ADP
ejpam-6414	352	34	improving	improve	VERB
ejpam-6414	352	35	both	both	DET
ejpam-6414	352	36	code	code	NOUN
ejpam-6414	352	37	rates	rate	NOUN
ejpam-6414	352	38	and	and	CCONJ
ejpam-6414	352	39	the	the	DET
ejpam-6414	352	40	total	total	ADJ
ejpam-6414	352	41	number	number	NOUN
ejpam-6414	352	42	of	of	ADP
ejpam-6414	352	43	codewords	codeword	NOUN
ejpam-6414	352	44	.	.	PUNCT
ejpam-6414	353	1	these	these	DET
ejpam-6414	353	2	enhanced	enhance	VERB
ejpam-6414	353	3	attributes	attribute	NOUN
ejpam-6414	353	4	translate	translate	VERB
ejpam-6414	353	5	into	into	ADP
ejpam-6414	353	6	superior	superior	ADJ
ejpam-6414	353	7	error	error	NOUN
ejpam-6414	353	8	correction	correction	NOUN
ejpam-6414	353	9	capabilities	capability	NOUN
ejpam-6414	353	10	,	,	PUNCT
ejpam-6414	353	11	making	make	VERB
ejpam-6414	353	12	qgr	qgr	NOUN
ejpam-6414	353	13	-	-	PUNCT
ejpam-6414	353	14	based	base	VERB
ejpam-6414	353	15	bch	bch	PROPN
ejpam-6414	353	16	codes	code	NOUN
ejpam-6414	353	17	promising	promise	VERB
ejpam-6414	353	18	candidates	candidate	NOUN
ejpam-6414	353	19	for	for	ADP
ejpam-6414	353	20	contemporary	contemporary	ADJ
ejpam-6414	353	21	and	and	CCONJ
ejpam-6414	353	22	next	next	ADJ
ejpam-6414	353	23	-	-	PUNCT
ejpam-6414	353	24	generation	generation	NOUN
ejpam-6414	353	25	communication	communication	NOUN
ejpam-6414	353	26	technologies	technology	NOUN
ejpam-6414	353	27	.	.	PUNCT
ejpam-6414	354	1	the	the	DET
ejpam-6414	354	2	ability	ability	NOUN
ejpam-6414	354	3	to	to	PART
ejpam-6414	354	4	construct	construct	VERB
ejpam-6414	354	5	longer	long	ADJ
ejpam-6414	354	6	codes	code	NOUN
ejpam-6414	354	7	with	with	ADP
ejpam-6414	354	8	greater	great	ADJ
ejpam-6414	354	9	flexibility	flexibility	NOUN
ejpam-6414	354	10	and	and	CCONJ
ejpam-6414	354	11	efficiency	efficiency	NOUN
ejpam-6414	354	12	over	over	ADP
ejpam-6414	354	13	qgrs	qgrs	PROPN
ejpam-6414	354	14	,	,	PUNCT
ejpam-6414	354	15	as	as	ADP
ejpam-6414	354	16	compared	compare	VERB
ejpam-6414	354	17	to	to	ADP
ejpam-6414	354	18	classical	classical	ADJ
ejpam-6414	354	19	galois	galois	PROPN
ejpam-6414	354	20	rings	ring	NOUN
ejpam-6414	354	21	,	,	PUNCT
ejpam-6414	354	22	further	far	ADV
ejpam-6414	354	23	substantiates	substantiate	VERB
ejpam-6414	354	24	their	their	PRON
ejpam-6414	354	25	relevance	relevance	NOUN
ejpam-6414	354	26	.	.	PUNCT
ejpam-6414	355	1	future	future	ADJ
ejpam-6414	355	2	research	research	NOUN
ejpam-6414	355	3	can	can	AUX
ejpam-6414	355	4	be	be	AUX
ejpam-6414	355	5	directed	direct	VERB
ejpam-6414	355	6	toward	toward	ADP
ejpam-6414	355	7	refining	refine	VERB
ejpam-6414	355	8	the	the	DET
ejpam-6414	355	9	construction	construction	NOUN
ejpam-6414	355	10	and	and	CCONJ
ejpam-6414	355	11	decoding	decode	VERB
ejpam-6414	355	12	processes	process	NOUN
ejpam-6414	355	13	of	of	ADP
ejpam-6414	355	14	bch	bch	PROPN
ejpam-6414	355	15	codes	code	NOUN
ejpam-6414	355	16	over	over	ADP
ejpam-6414	355	17	qgrs	qgrs	PROPN
ejpam-6414	355	18	,	,	PUNCT
ejpam-6414	355	19	with	with	ADP
ejpam-6414	355	20	a	a	DET
ejpam-6414	355	21	focus	focus	NOUN
ejpam-6414	355	22	on	on	ADP
ejpam-6414	355	23	optimizing	optimize	VERB
ejpam-6414	355	24	algorithmic	algorithmic	ADJ
ejpam-6414	355	25	complexity	complexity	NOUN
ejpam-6414	355	26	and	and	CCONJ
ejpam-6414	355	27	implementation	implementation	NOUN
ejpam-6414	355	28	feasibility	feasibility	NOUN
ejpam-6414	355	29	.	.	PUNCT
ejpam-6414	356	1	additionally	additionally	ADV
ejpam-6414	356	2	,	,	PUNCT
ejpam-6414	356	3	exploring	explore	VERB
ejpam-6414	356	4	the	the	DET
ejpam-6414	356	5	practical	practical	ADJ
ejpam-6414	356	6	deployment	deployment	NOUN
ejpam-6414	356	7	of	of	ADP
ejpam-6414	356	8	qgr	qgr	NOUN
ejpam-6414	356	9	-	-	PUNCT
ejpam-6414	356	10	based	base	VERB
ejpam-6414	356	11	codes	code	NOUN
ejpam-6414	356	12	in	in	ADP
ejpam-6414	356	13	real	real	ADJ
ejpam-6414	356	14	-	-	PUNCT
ejpam-6414	356	15	world	world	NOUN
ejpam-6414	356	16	communication	communication	NOUN
ejpam-6414	356	17	systems	system	NOUN
ejpam-6414	356	18	could	could	AUX
ejpam-6414	356	19	provide	provide	VERB
ejpam-6414	356	20	valuable	valuable	ADJ
ejpam-6414	356	21	insights	insight	NOUN
ejpam-6414	356	22	into	into	ADP
ejpam-6414	356	23	their	their	PRON
ejpam-6414	356	24	performance	performance	NOUN
ejpam-6414	356	25	under	under	ADP
ejpam-6414	356	26	practical	practical	ADJ
ejpam-6414	356	27	constraints	constraint	NOUN
ejpam-6414	356	28	.	.	PUNCT
ejpam-6414	357	1	another	another	DET
ejpam-6414	357	2	promising	promising	ADJ
ejpam-6414	357	3	direction	direction	NOUN
ejpam-6414	357	4	involves	involve	VERB
ejpam-6414	357	5	the	the	DET
ejpam-6414	357	6	integration	integration	NOUN
ejpam-6414	357	7	of	of	ADP
ejpam-6414	357	8	bch	bch	PROPN
ejpam-6414	357	9	codes	code	NOUN
ejpam-6414	357	10	over	over	ADP
ejpam-6414	357	11	qgrs	qgrs	NOUN
ejpam-6414	357	12	with	with	ADP
ejpam-6414	357	13	higher	high	ADJ
ejpam-6414	357	14	layers	layer	NOUN
ejpam-6414	357	15	of	of	ADP
ejpam-6414	357	16	coding	code	VERB
ejpam-6414	357	17	and	and	CCONJ
ejpam-6414	357	18	modern	modern	ADJ
ejpam-6414	357	19	cryptographic	cryptographic	ADJ
ejpam-6414	357	20	protocols	protocol	NOUN
ejpam-6414	357	21	.	.	PUNCT
ejpam-6414	358	1	such	such	ADJ
ejpam-6414	358	2	hybrid	hybrid	ADJ
ejpam-6414	358	3	approaches	approach	NOUN
ejpam-6414	358	4	may	may	AUX
ejpam-6414	358	5	lead	lead	VERB
ejpam-6414	358	6	to	to	ADP
ejpam-6414	358	7	more	more	ADV
ejpam-6414	358	8	robust	robust	ADJ
ejpam-6414	358	9	and	and	CCONJ
ejpam-6414	358	10	secure	secure	ADJ
ejpam-6414	358	11	communication	communication	NOUN
ejpam-6414	358	12	architectures	architecture	NOUN
ejpam-6414	358	13	.	.	PUNCT
ejpam-6414	359	1	therefore	therefore	ADV
ejpam-6414	359	2	,	,	PUNCT
ejpam-6414	359	3	building	build	VERB
ejpam-6414	359	4	upon	upon	SCONJ
ejpam-6414	359	5	the	the	DET
ejpam-6414	359	6	findings	finding	NOUN
ejpam-6414	359	7	of	of	ADP
ejpam-6414	359	8	this	this	DET
ejpam-6414	359	9	article	article	NOUN
ejpam-6414	359	10	,	,	PUNCT
ejpam-6414	359	11	the	the	DET
ejpam-6414	359	12	continued	continue	VERB
ejpam-6414	359	13	development	development	NOUN
ejpam-6414	359	14	of	of	ADP
ejpam-6414	359	15	bch	bch	PROPN
ejpam-6414	359	16	codes	code	NOUN
ejpam-6414	359	17	over	over	ADP
ejpam-6414	359	18	quasi	quasi	ADJ
ejpam-6414	359	19	-	-	ADJ
ejpam-6414	359	20	galois	galois	ADJ
ejpam-6414	359	21	rings	ring	NOUN
ejpam-6414	359	22	can	can	AUX
ejpam-6414	359	23	significantly	significantly	ADV
ejpam-6414	359	24	contribute	contribute	VERB
ejpam-6414	359	25	to	to	ADP
ejpam-6414	359	26	the	the	DET
ejpam-6414	359	27	advancement	advancement	NOUN
ejpam-6414	359	28	of	of	ADP
ejpam-6414	359	29	reliable	reliable	ADJ
ejpam-6414	359	30	and	and	CCONJ
ejpam-6414	359	31	efficient	efficient	ADJ
ejpam-6414	359	32	communication	communication	NOUN
ejpam-6414	359	33	networks	network	NOUN
ejpam-6414	359	34	.	.	PUNCT
ejpam-6414	360	1	muhammad	muhammad	PROPN
ejpam-6414	360	2	sajjad	sajjad	PROPN
ejpam-6414	360	3	et	et	PROPN
ejpam-6414	360	4	al	al	PROPN
ejpam-6414	360	5	.	.	PUNCT
ejpam-6414	360	6	/	/	SYM
ejpam-6414	360	7	eur	eur	PROPN
ejpam-6414	360	8	.	.	PUNCT
ejpam-6414	361	1	j.	j.	PROPN
ejpam-6414	361	2	pure	pure	PROPN
ejpam-6414	361	3	appl	appl	PROPN
ejpam-6414	361	4	.	.	PROPN
ejpam-6414	361	5	math	math	PROPN
ejpam-6414	361	6	,	,	PUNCT
ejpam-6414	361	7	18	18	NUM
ejpam-6414	361	8	(	(	PUNCT
ejpam-6414	361	9	3	3	NUM
ejpam-6414	361	10	)	)	PUNCT
ejpam-6414	361	11	(	(	PUNCT
ejpam-6414	361	12	2025	2025	NUM
ejpam-6414	361	13	)	)	PUNCT
ejpam-6414	361	14	,	,	PUNCT
ejpam-6414	361	15	6414	6414	NUM
ejpam-6414	361	16	20	20	NUM
ejpam-6414	361	17	of	of	ADP
ejpam-6414	361	18	22	22	NUM
ejpam-6414	361	19	acknowledgements	acknowledgement	NOUN
ejpam-6414	361	20	this	this	DET
ejpam-6414	361	21	research	research	NOUN
ejpam-6414	361	22	is	be	AUX
ejpam-6414	361	23	supported	support	VERB
ejpam-6414	361	24	by	by	ADP
ejpam-6414	361	25	universidad	universidad	PROPN
ejpam-6414	361	26	pedagógica	pedagógica	PROPN
ejpam-6414	361	27	y	y	PROPN
ejpam-6414	361	28	tecnológica	tecnológica	PROPN
ejpam-6414	361	29	de	de	PROPN
ejpam-6414	361	30	colombia	colombia	PROPN
ejpam-6414	361	31	(	(	PUNCT
ejpam-6414	361	32	sgi	sgi	PROPN
ejpam-6414	361	33	3725	3725	NUM
ejpam-6414	361	34	)	)	PUNCT
ejpam-6414	361	35	and	and	CCONJ
ejpam-6414	361	36	minciencias	minciencia	NOUN
ejpam-6414	361	37	(	(	PUNCT
ejpam-6414	361	38	conv	conv	ADJ
ejpam-6414	361	39	.	.	PROPN
ejpam-6414	361	40	934	934	NUM
ejpam-6414	361	41	)	)	PUNCT
ejpam-6414	361	42	.	.	PUNCT
ejpam-6414	362	1	data	datum	NOUN
ejpam-6414	362	2	availability	availability	NOUN
ejpam-6414	362	3	all	all	DET
ejpam-6414	362	4	the	the	DET
ejpam-6414	362	5	data	datum	NOUN
ejpam-6414	362	6	is	be	AUX
ejpam-6414	362	7	given	give	VERB
ejpam-6414	362	8	in	in	ADP
ejpam-6414	362	9	this	this	DET
ejpam-6414	362	10	study	study	NOUN
ejpam-6414	362	11	.	.	PUNCT
ejpam-6414	363	1	tribute	tribute	NOUN
ejpam-6414	363	2	we	we	PRON
ejpam-6414	363	3	would	would	AUX
ejpam-6414	363	4	like	like	VERB
ejpam-6414	363	5	to	to	PART
ejpam-6414	363	6	express	express	VERB
ejpam-6414	363	7	our	our	PRON
ejpam-6414	363	8	heartfelt	heartfelt	ADJ
ejpam-6414	363	9	gratitude	gratitude	NOUN
ejpam-6414	363	10	to	to	ADP
ejpam-6414	363	11	our	our	PRON
ejpam-6414	363	12	beloved	beloved	ADJ
ejpam-6414	363	13	supervisor	supervisor	NOUN
ejpam-6414	363	14	,	,	PUNCT
ejpam-6414	363	15	professor	professor	PROPN
ejpam-6414	363	16	dr	dr	PROPN
ejpam-6414	363	17	.	.	PROPN
ejpam-6414	363	18	tariq	tariq	PROPN
ejpam-6414	363	19	shah	shah	PROPN
ejpam-6414	363	20	(	(	PUNCT
ejpam-6414	363	21	late	late	ADJ
ejpam-6414	363	22	)	)	PUNCT
ejpam-6414	363	23	,	,	PUNCT
ejpam-6414	363	24	whose	whose	DET
ejpam-6414	363	25	exceptional	exceptional	ADJ
ejpam-6414	363	26	guidance	guidance	NOUN
ejpam-6414	363	27	,	,	PUNCT
ejpam-6414	363	28	profound	profound	ADJ
ejpam-6414	363	29	expertise	expertise	NOUN
ejpam-6414	363	30	,	,	PUNCT
ejpam-6414	363	31	and	and	CCONJ
ejpam-6414	363	32	steadfast	steadfast	ADJ
ejpam-6414	363	33	support	support	NOUN
ejpam-6414	363	34	were	be	AUX
ejpam-6414	363	35	instrumental	instrumental	ADJ
ejpam-6414	363	36	in	in	ADP
ejpam-6414	363	37	shaping	shape	VERB
ejpam-6414	363	38	our	our	PRON
ejpam-6414	363	39	academic	academic	ADJ
ejpam-6414	363	40	journey	journey	NOUN
ejpam-6414	363	41	.	.	PUNCT
ejpam-6414	364	1	his	his	PRON
ejpam-6414	364	2	mentorship	mentorship	NOUN
ejpam-6414	364	3	not	not	PART
ejpam-6414	364	4	only	only	ADV
ejpam-6414	364	5	nurtured	nurture	VERB
ejpam-6414	364	6	our	our	PRON
ejpam-6414	364	7	growth	growth	NOUN
ejpam-6414	364	8	as	as	SCONJ
ejpam-6414	364	9	researchers	researcher	NOUN
ejpam-6414	364	10	in	in	ADP
ejpam-6414	364	11	algebra	algebra	NOUN
ejpam-6414	364	12	,	,	PUNCT
ejpam-6414	364	13	number	number	NOUN
ejpam-6414	364	14	theory	theory	NOUN
ejpam-6414	364	15	,	,	PUNCT
ejpam-6414	364	16	coding	code	VERB
ejpam-6414	364	17	theory	theory	NOUN
ejpam-6414	364	18	,	,	PUNCT
ejpam-6414	364	19	and	and	CCONJ
ejpam-6414	364	20	cryptography	cryptography	NOUN
ejpam-6414	364	21	but	but	CCONJ
ejpam-6414	364	22	also	also	ADV
ejpam-6414	364	23	profoundly	profoundly	ADV
ejpam-6414	364	24	influenced	influence	VERB
ejpam-6414	364	25	our	our	PRON
ejpam-6414	364	26	personal	personal	ADJ
ejpam-6414	364	27	and	and	CCONJ
ejpam-6414	364	28	professional	professional	ADJ
ejpam-6414	364	29	development	development	NOUN
ejpam-6414	364	30	.	.	PUNCT
ejpam-6414	365	1	his	his	PRON
ejpam-6414	365	2	legacy	legacy	NOUN
ejpam-6414	365	3	of	of	ADP
ejpam-6414	365	4	wisdom	wisdom	NOUN
ejpam-6414	365	5	,	,	PUNCT
ejpam-6414	365	6	integrity	integrity	NOUN
ejpam-6414	365	7	,	,	PUNCT
ejpam-6414	365	8	and	and	CCONJ
ejpam-6414	365	9	inspiration	inspiration	NOUN
ejpam-6414	365	10	continues	continue	VERB
ejpam-6414	365	11	to	to	PART
ejpam-6414	365	12	guide	guide	VERB
ejpam-6414	365	13	us	we	PRON
ejpam-6414	365	14	.	.	PUNCT
ejpam-6414	366	1	may	may	AUX
ejpam-6414	366	2	his	his	PRON
ejpam-6414	366	3	soul	soul	NOUN
ejpam-6414	366	4	rest	rest	VERB
ejpam-6414	366	5	in	in	ADP
ejpam-6414	366	6	eternal	eternal	ADJ
ejpam-6414	366	7	peace	peace	NOUN
ejpam-6414	366	8	.	.	PUNCT
ejpam-6414	367	1	figure	figure	VERB
ejpam-6414	367	2	3	3	NUM
ejpam-6414	367	3	:	:	PUNCT
ejpam-6414	367	4	prof	prof	PROPN
ejpam-6414	367	5	.	.	PUNCT
ejpam-6414	368	1	dr	dr	PROPN
ejpam-6414	368	2	.	.	PROPN
ejpam-6414	368	3	tariq	tariq	PROPN
ejpam-6414	368	4	shah	shah	PROPN
ejpam-6414	368	5	references	reference	NOUN
ejpam-6414	368	6	[	[	X
ejpam-6414	368	7	1	1	NUM
ejpam-6414	368	8	]	]	PUNCT
ejpam-6414	368	9	e.	e.	PROPN
ejpam-6414	368	10	f.	f.	PROPN
ejpam-6414	368	11	jr	jr	PROPN
ejpam-6414	368	12	.	.	PROPN
ejpam-6414	368	13	assmus	assmus	PROPN
ejpam-6414	368	14	and	and	CCONJ
ejpam-6414	368	15	h.	h.	PROPN
ejpam-6414	368	16	f.	f.	PROPN
ejpam-6414	368	17	mattson	mattson	PROPN
ejpam-6414	368	18	.	.	PUNCT
ejpam-6414	369	1	error	error	NOUN
ejpam-6414	369	2	-	-	PUNCT
ejpam-6414	369	3	correcting	correct	VERB
ejpam-6414	369	4	codes	code	NOUN
ejpam-6414	369	5	:	:	PUNCT
ejpam-6414	369	6	an	an	DET
ejpam-6414	369	7	axiomatic	axiomatic	ADJ
ejpam-6414	369	8	approach	approach	NOUN
ejpam-6414	369	9	.	.	PUNCT
ejpam-6414	370	1	information	information	NOUN
ejpam-6414	370	2	and	and	CCONJ
ejpam-6414	370	3	control	control	NOUN
ejpam-6414	370	4	,	,	PUNCT
ejpam-6414	370	5	6(4):315–330	6(4):315–330	NUM
ejpam-6414	370	6	,	,	PUNCT
ejpam-6414	370	7	1963	1963	NUM
ejpam-6414	370	8	.	.	PUNCT
ejpam-6414	371	1	muhammad	muhammad	PROPN
ejpam-6414	371	2	sajjad	sajjad	PROPN
ejpam-6414	371	3	et	et	PROPN
ejpam-6414	371	4	al	al	PROPN
ejpam-6414	371	5	.	.	PUNCT
ejpam-6414	371	6	/	/	SYM
ejpam-6414	371	7	eur	eur	PROPN
ejpam-6414	371	8	.	.	PUNCT
ejpam-6414	372	1	j.	j.	PROPN
ejpam-6414	372	2	pure	pure	PROPN
ejpam-6414	372	3	appl	appl	PROPN
ejpam-6414	372	4	.	.	PROPN
ejpam-6414	372	5	math	math	PROPN
ejpam-6414	372	6	,	,	PUNCT
ejpam-6414	372	7	18	18	NUM
ejpam-6414	372	8	(	(	PUNCT
ejpam-6414	372	9	3	3	NUM
ejpam-6414	372	10	)	)	PUNCT
ejpam-6414	372	11	(	(	PUNCT
ejpam-6414	372	12	2025	2025	NUM
ejpam-6414	372	13	)	)	PUNCT
ejpam-6414	372	14	,	,	PUNCT
ejpam-6414	372	15	6414	6414	NUM
ejpam-6414	372	16	21	21	NUM
ejpam-6414	372	17	of	of	ADP
ejpam-6414	372	18	22	22	NUM
ejpam-6414	372	19	[	[	X
ejpam-6414	372	20	2	2	NUM
ejpam-6414	372	21	]	]	X
ejpam-6414	372	22	d.	d.	PROPN
ejpam-6414	372	23	augot	augot	PROPN
ejpam-6414	372	24	,	,	PUNCT
ejpam-6414	372	25	e.	e.	PROPN
ejpam-6414	372	26	betti	betti	PROPN
ejpam-6414	372	27	,	,	PUNCT
ejpam-6414	372	28	and	and	CCONJ
ejpam-6414	372	29	e.	e.	PROPN
ejpam-6414	372	30	orsini	orsini	PROPN
ejpam-6414	372	31	.	.	PUNCT
ejpam-6414	373	1	an	an	DET
ejpam-6414	373	2	introduction	introduction	NOUN
ejpam-6414	373	3	to	to	ADP
ejpam-6414	373	4	linear	linear	ADJ
ejpam-6414	373	5	and	and	CCONJ
ejpam-6414	373	6	cyclic	cyclic	ADJ
ejpam-6414	373	7	codes	code	NOUN
ejpam-6414	373	8	.	.	PUNCT
ejpam-6414	374	1	in	in	ADP
ejpam-6414	374	2	gröbner	gröbner	NOUN
ejpam-6414	374	3	bases	basis	NOUN
ejpam-6414	374	4	,	,	PUNCT
ejpam-6414	374	5	coding	coding	NOUN
ejpam-6414	374	6	,	,	PUNCT
ejpam-6414	374	7	and	and	CCONJ
ejpam-6414	374	8	cryptography	cryptography	NOUN
ejpam-6414	374	9	,	,	PUNCT
ejpam-6414	374	10	pages	page	NOUN
ejpam-6414	374	11	47–68	47–68	NUM
ejpam-6414	374	12	.	.	PUNCT
ejpam-6414	374	13	springer	springer	NOUN
ejpam-6414	374	14	,	,	PUNCT
ejpam-6414	374	15	2009	2009	NUM
ejpam-6414	374	16	.	.	PUNCT
ejpam-6414	375	1	[	[	X
ejpam-6414	375	2	3	3	X
ejpam-6414	375	3	]	]	PUNCT
ejpam-6414	375	4	a.	a.	NOUN
ejpam-6414	375	5	a.	a.	PROPN
ejpam-6414	375	6	de	de	PROPN
ejpam-6414	375	7	andrade	andrade	PROPN
ejpam-6414	375	8	and	and	CCONJ
ejpam-6414	375	9	r.	r.	PROPN
ejpam-6414	375	10	jr	jr	PROPN
ejpam-6414	375	11	.	.	PROPN
ejpam-6414	375	12	palazzo	palazzo	PROPN
ejpam-6414	375	13	.	.	PUNCT
ejpam-6414	376	1	construction	construction	NOUN
ejpam-6414	376	2	and	and	CCONJ
ejpam-6414	376	3	decoding	decoding	NOUN
ejpam-6414	376	4	of	of	ADP
ejpam-6414	376	5	bch	bch	PROPN
ejpam-6414	376	6	codes	code	NOUN
ejpam-6414	376	7	over	over	ADP
ejpam-6414	376	8	finite	finite	PROPN
ejpam-6414	376	9	commutative	commutative	ADJ
ejpam-6414	376	10	rings	ring	NOUN
ejpam-6414	376	11	.	.	PUNCT
ejpam-6414	377	1	linear	linear	PROPN
ejpam-6414	377	2	algebra	algebra	PROPN
ejpam-6414	377	3	and	and	CCONJ
ejpam-6414	377	4	its	its	PRON
ejpam-6414	377	5	applications	application	NOUN
ejpam-6414	377	6	,	,	PUNCT
ejpam-6414	377	7	286(1–3):69–85	286(1–3):69–85	NUM
ejpam-6414	377	8	,	,	PUNCT
ejpam-6414	377	9	1999	1999	NUM
ejpam-6414	377	10	.	.	PUNCT
ejpam-6414	378	1	[	[	X
ejpam-6414	378	2	4	4	NUM
ejpam-6414	378	3	]	]	X
ejpam-6414	378	4	i.	i.	PROPN
ejpam-6414	378	5	f.	f.	PROPN
ejpam-6414	378	6	blake	blake	PROPN
ejpam-6414	378	7	.	.	PUNCT
ejpam-6414	379	1	codes	code	NOUN
ejpam-6414	379	2	over	over	ADP
ejpam-6414	379	3	certain	certain	ADJ
ejpam-6414	379	4	rings	ring	NOUN
ejpam-6414	379	5	.	.	PUNCT
ejpam-6414	380	1	information	information	NOUN
ejpam-6414	380	2	and	and	CCONJ
ejpam-6414	380	3	control	control	NOUN
ejpam-6414	380	4	,	,	PUNCT
ejpam-6414	380	5	20(4):396–404	20(4):396–404	PROPN
ejpam-6414	380	6	,	,	PUNCT
ejpam-6414	380	7	1972	1972	NUM
ejpam-6414	380	8	.	.	PUNCT
ejpam-6414	381	1	[	[	X
ejpam-6414	381	2	5	5	NUM
ejpam-6414	381	3	]	]	PUNCT
ejpam-6414	381	4	i.	i.	PROPN
ejpam-6414	381	5	f.	f.	PROPN
ejpam-6414	381	6	blake	blake	PROPN
ejpam-6414	381	7	.	.	PUNCT
ejpam-6414	382	1	codes	code	NOUN
ejpam-6414	382	2	over	over	ADP
ejpam-6414	382	3	integer	integer	NOUN
ejpam-6414	382	4	residue	residue	NOUN
ejpam-6414	382	5	rings	ring	NOUN
ejpam-6414	382	6	.	.	PUNCT
ejpam-6414	383	1	information	information	NOUN
ejpam-6414	383	2	and	and	CCONJ
ejpam-6414	383	3	control	control	NOUN
ejpam-6414	383	4	,	,	PUNCT
ejpam-6414	383	5	29(4):295–300	29(4):295–300	NUM
ejpam-6414	383	6	,	,	PUNCT
ejpam-6414	383	7	1975	1975	NUM
ejpam-6414	383	8	.	.	PUNCT
ejpam-6414	384	1	[	[	X
ejpam-6414	384	2	6	6	NUM
ejpam-6414	384	3	]	]	PUNCT
ejpam-6414	384	4	e.	e.	PROPN
ejpam-6414	384	5	spiegel	spiegel	PROPN
ejpam-6414	384	6	.	.	PUNCT
ejpam-6414	385	1	codes	code	NOUN
ejpam-6414	385	2	over	over	ADP
ejpam-6414	385	3	zm	zm	PROPN
ejpam-6414	385	4	.	.	PUNCT
ejpam-6414	386	1	information	information	NOUN
ejpam-6414	386	2	and	and	CCONJ
ejpam-6414	386	3	control	control	NOUN
ejpam-6414	386	4	,	,	PUNCT
ejpam-6414	386	5	35(1):48–51	35(1):48–51	NUM
ejpam-6414	386	6	,	,	PUNCT
ejpam-6414	386	7	1977	1977	NUM
ejpam-6414	386	8	.	.	PUNCT
ejpam-6414	387	1	[	[	X
ejpam-6414	387	2	7	7	X
ejpam-6414	387	3	]	]	X
ejpam-6414	387	4	e.	e.	PROPN
ejpam-6414	387	5	spiegel	spiegel	PROPN
ejpam-6414	387	6	.	.	PUNCT
ejpam-6414	388	1	codes	code	NOUN
ejpam-6414	388	2	over	over	ADP
ejpam-6414	388	3	zm	zm	PROPN
ejpam-6414	388	4	,	,	PUNCT
ejpam-6414	388	5	revisited	revisit	VERB
ejpam-6414	388	6	.	.	PUNCT
ejpam-6414	389	1	information	information	NOUN
ejpam-6414	389	2	and	and	CCONJ
ejpam-6414	389	3	control	control	NOUN
ejpam-6414	389	4	,	,	PUNCT
ejpam-6414	389	5	37(1):100–104	37(1):100–104	PROPN
ejpam-6414	389	6	,	,	PUNCT
ejpam-6414	389	7	1978	1978	NUM
ejpam-6414	389	8	.	.	PUNCT
ejpam-6414	390	1	[	[	X
ejpam-6414	390	2	8	8	X
ejpam-6414	390	3	]	]	PUNCT
ejpam-6414	390	4	t.	t.	NOUN
ejpam-6414	390	5	shah	shah	PROPN
ejpam-6414	390	6	,	,	PUNCT
ejpam-6414	390	7	a.	a.	PROPN
ejpam-6414	390	8	khan	khan	PROPN
ejpam-6414	390	9	,	,	PUNCT
ejpam-6414	390	10	and	and	CCONJ
ejpam-6414	390	11	a.	a.	NOUN
ejpam-6414	390	12	a.	a.	PROPN
ejpam-6414	390	13	de	de	PROPN
ejpam-6414	390	14	andrade	andrade	PROPN
ejpam-6414	390	15	.	.	PUNCT
ejpam-6414	391	1	constructions	construction	NOUN
ejpam-6414	391	2	of	of	ADP
ejpam-6414	391	3	codes	code	NOUN
ejpam-6414	391	4	through	through	ADP
ejpam-6414	391	5	the	the	DET
ejpam-6414	391	6	semigroup	semigroup	PROPN
ejpam-6414	391	7	ring	ring	PROPN
ejpam-6414	391	8	b	b	PROPN
ejpam-6414	392	1	[	[	X
ejpam-6414	392	2	x	x	X
ejpam-6414	392	3	;	;	PUNCT
ejpam-6414	392	4	122z0	122z0	NUM
ejpam-6414	392	5	]	]	PUNCT
ejpam-6414	392	6	and	and	CCONJ
ejpam-6414	392	7	encoding	encoding	NOUN
ejpam-6414	392	8	.	.	PUNCT
ejpam-6414	393	1	computers	computer	NOUN
ejpam-6414	393	2	&	&	CCONJ
ejpam-6414	393	3	mathematics	mathematics	PROPN
ejpam-6414	393	4	with	with	ADP
ejpam-6414	393	5	applications	application	NOUN
ejpam-6414	393	6	,	,	PUNCT
ejpam-6414	393	7	62(4):1645–1654	62(4):1645–1654	NUM
ejpam-6414	393	8	,	,	PUNCT
ejpam-6414	393	9	2011	2011	NUM
ejpam-6414	393	10	.	.	PUNCT
ejpam-6414	394	1	[	[	X
ejpam-6414	394	2	9	9	NUM
ejpam-6414	394	3	]	]	PUNCT
ejpam-6414	394	4	b.	b.	PROPN
ejpam-6414	394	5	kim	kim	PROPN
ejpam-6414	394	6	,	,	PUNCT
ejpam-6414	394	7	y.	y.	PROPN
ejpam-6414	394	8	lee	lee	PROPN
ejpam-6414	394	9	,	,	PUNCT
ejpam-6414	394	10	and	and	CCONJ
ejpam-6414	394	11	j.	j.	PROPN
ejpam-6414	394	12	yoo	yoo	PROPN
ejpam-6414	394	13	.	.	PUNCT
ejpam-6414	395	1	an	an	DET
ejpam-6414	395	2	infinite	infinite	ADJ
ejpam-6414	395	3	family	family	NOUN
ejpam-6414	395	4	of	of	ADP
ejpam-6414	395	5	griesmer	griesmer	NOUN
ejpam-6414	395	6	quasi	quasi	ADJ
ejpam-6414	395	7	-	-	ADJ
ejpam-6414	395	8	cyclic	cyclic	ADJ
ejpam-6414	395	9	self	self	NOUN
ejpam-6414	395	10	-	-	PUNCT
ejpam-6414	395	11	orthogonal	orthogonal	ADJ
ejpam-6414	395	12	codes	code	NOUN
ejpam-6414	395	13	.	.	PUNCT
ejpam-6414	396	1	finite	finite	PROPN
ejpam-6414	396	2	fields	field	NOUN
ejpam-6414	396	3	and	and	CCONJ
ejpam-6414	396	4	their	their	PRON
ejpam-6414	396	5	applications	application	NOUN
ejpam-6414	396	6	,	,	PUNCT
ejpam-6414	396	7	76:101923	76:101923	NUM
ejpam-6414	396	8	,	,	PUNCT
ejpam-6414	396	9	2021	2021	NUM
ejpam-6414	396	10	.	.	PUNCT
ejpam-6414	397	1	[	[	X
ejpam-6414	397	2	10	10	NUM
ejpam-6414	397	3	]	]	X
ejpam-6414	397	4	f.	f.	PROPN
ejpam-6414	397	5	zullo	zullo	PROPN
ejpam-6414	397	6	.	.	PUNCT
ejpam-6414	398	1	multi	multi	ADJ
ejpam-6414	398	2	-	-	ADJ
ejpam-6414	398	3	orbit	orbit	ADJ
ejpam-6414	398	4	cyclic	cyclic	ADJ
ejpam-6414	398	5	subspace	subspace	NOUN
ejpam-6414	398	6	codes	code	NOUN
ejpam-6414	398	7	and	and	CCONJ
ejpam-6414	398	8	linear	linear	ADJ
ejpam-6414	398	9	sets	set	NOUN
ejpam-6414	398	10	.	.	PUNCT
ejpam-6414	399	1	finite	finite	PROPN
ejpam-6414	399	2	fields	field	NOUN
ejpam-6414	399	3	and	and	CCONJ
ejpam-6414	399	4	their	their	PRON
ejpam-6414	399	5	applications	application	NOUN
ejpam-6414	399	6	,	,	PUNCT
ejpam-6414	399	7	87:102153	87:102153	NUM
ejpam-6414	399	8	,	,	PUNCT
ejpam-6414	399	9	2023	2023	NUM
ejpam-6414	399	10	.	.	PUNCT
ejpam-6414	400	1	[	[	X
ejpam-6414	400	2	11	11	NUM
ejpam-6414	400	3	]	]	PUNCT
ejpam-6414	400	4	p.	p.	PROPN
ejpam-6414	400	5	shankar	shankar	PROPN
ejpam-6414	400	6	.	.	PUNCT
ejpam-6414	401	1	on	on	ADP
ejpam-6414	401	2	bch	bch	PROPN
ejpam-6414	401	3	codes	code	NOUN
ejpam-6414	401	4	over	over	ADP
ejpam-6414	401	5	arbitrary	arbitrary	ADJ
ejpam-6414	401	6	integer	integer	NOUN
ejpam-6414	401	7	rings	ring	NOUN
ejpam-6414	401	8	(	(	PUNCT
ejpam-6414	401	9	corresp	corresp	PROPN
ejpam-6414	401	10	.	.	PUNCT
ejpam-6414	401	11	)	)	PUNCT
ejpam-6414	401	12	.	.	PUNCT
ejpam-6414	402	1	ieee	ieee	NOUN
ejpam-6414	402	2	transactions	transaction	NOUN
ejpam-6414	402	3	on	on	ADP
ejpam-6414	402	4	information	information	NOUN
ejpam-6414	402	5	theory	theory	NOUN
ejpam-6414	402	6	,	,	PUNCT
ejpam-6414	402	7	25(4):480–483	25(4):480–483	PROPN
ejpam-6414	402	8	,	,	PUNCT
ejpam-6414	402	9	1979	1979	NUM
ejpam-6414	402	10	.	.	PUNCT
ejpam-6414	403	1	[	[	X
ejpam-6414	403	2	12	12	NUM
ejpam-6414	403	3	]	]	X
ejpam-6414	403	4	j.	j.	PROPN
ejpam-6414	403	5	c.	c.	PROPN
ejpam-6414	403	6	interlando	interlando	PROPN
ejpam-6414	403	7	and	and	CCONJ
ejpam-6414	403	8	r.	r.	PROPN
ejpam-6414	403	9	palazzo	palazzo	PROPN
ejpam-6414	403	10	jr	jr	PROPN
ejpam-6414	403	11	.	.	PUNCT
ejpam-6414	404	1	a	a	DET
ejpam-6414	404	2	note	note	NOUN
ejpam-6414	404	3	on	on	ADP
ejpam-6414	404	4	cyclic	cyclic	ADJ
ejpam-6414	404	5	codes	code	NOUN
ejpam-6414	404	6	over	over	ADP
ejpam-6414	404	7	zm	zm	PROPN
ejpam-6414	404	8	.	.	PUNCT
ejpam-6414	405	1	latin	latin	PROPN
ejpam-6414	405	2	amer	amer	PROPN
ejpam-6414	405	3	.	.	PUNCT
ejpam-6414	406	1	appl	appl	PROPN
ejpam-6414	406	2	.	.	PUNCT
ejpam-6414	407	1	res	re	NOUN
ejpam-6414	407	2	,	,	PUNCT
ejpam-6414	407	3	25:83–85	25:83–85	NUM
ejpam-6414	407	4	,	,	PUNCT
ejpam-6414	407	5	1995	1995	NUM
ejpam-6414	407	6	.	.	PUNCT
ejpam-6414	408	1	[	[	X
ejpam-6414	408	2	13	13	NUM
ejpam-6414	408	3	]	]	PUNCT
ejpam-6414	408	4	m.	m.	NOUN
ejpam-6414	408	5	sajjad	sajjad	PROPN
ejpam-6414	408	6	,	,	PUNCT
ejpam-6414	408	7	t.	t.	NOUN
ejpam-6414	408	8	shah	shah	PROPN
ejpam-6414	408	9	,	,	PUNCT
ejpam-6414	408	10	m.	m.	NOUN
ejpam-6414	408	11	alammari	alammari	PROPN
ejpam-6414	408	12	,	,	PUNCT
ejpam-6414	408	13	and	and	CCONJ
ejpam-6414	408	14	h.	h.	PROPN
ejpam-6414	408	15	alsaud	alsaud	PROPN
ejpam-6414	408	16	.	.	PUNCT
ejpam-6414	409	1	construction	construction	NOUN
ejpam-6414	409	2	and	and	CCONJ
ejpam-6414	409	3	decoding	decoding	NOUN
ejpam-6414	409	4	of	of	ADP
ejpam-6414	409	5	bch	bch	NOUN
ejpam-6414	409	6	-	-	PUNCT
ejpam-6414	409	7	codes	code	NOUN
ejpam-6414	409	8	over	over	ADP
ejpam-6414	409	9	the	the	DET
ejpam-6414	409	10	gaussian	gaussian	ADJ
ejpam-6414	409	11	field	field	NOUN
ejpam-6414	409	12	.	.	PUNCT
ejpam-6414	410	1	ieee	ieee	NOUN
ejpam-6414	410	2	access	access	NOUN
ejpam-6414	410	3	,	,	PUNCT
ejpam-6414	410	4	pages	page	NOUN
ejpam-6414	410	5	1–8	1–8	NUM
ejpam-6414	410	6	,	,	PUNCT
ejpam-6414	410	7	2023	2023	NUM
ejpam-6414	410	8	.	.	PUNCT
ejpam-6414	411	1	[	[	X
ejpam-6414	411	2	14	14	NUM
ejpam-6414	411	3	]	]	PUNCT
ejpam-6414	411	4	m.	m.	NOUN
ejpam-6414	411	5	sajjad	sajjad	PROPN
ejpam-6414	411	6	,	,	PUNCT
ejpam-6414	411	7	t.	t.	NOUN
ejpam-6414	411	8	shah	shah	PROPN
ejpam-6414	411	9	,	,	PUNCT
ejpam-6414	411	10	q.	q.	PROPN
ejpam-6414	411	11	xin	xin	PROPN
ejpam-6414	411	12	,	,	PUNCT
ejpam-6414	411	13	and	and	CCONJ
ejpam-6414	411	14	b.	b.	PROPN
ejpam-6414	411	15	almutairi	almutairi	PROPN
ejpam-6414	411	16	.	.	PUNCT
ejpam-6414	412	1	eisenstein	eisenstein	PROPN
ejpam-6414	412	2	field	field	PROPN
ejpam-6414	412	3	bch	bch	PROPN
ejpam-6414	412	4	codes	code	VERB
ejpam-6414	412	5	construction	construction	NOUN
ejpam-6414	412	6	and	and	CCONJ
ejpam-6414	412	7	decoding	decoding	NOUN
ejpam-6414	412	8	.	.	PUNCT
ejpam-6414	413	1	aims	aim	VERB
ejpam-6414	413	2	mathematics	mathematic	NOUN
ejpam-6414	413	3	,	,	PUNCT
ejpam-6414	413	4	8(12):29453–29473	8(12):29453–29473	NUM
ejpam-6414	413	5	,	,	PUNCT
ejpam-6414	413	6	2023	2023	NUM
ejpam-6414	413	7	.	.	PUNCT
ejpam-6414	414	1	[	[	X
ejpam-6414	414	2	15	15	NUM
ejpam-6414	414	3	]	]	X
ejpam-6414	414	4	m.	m.	NOUN
ejpam-6414	414	5	sajjad	sajjad	PROPN
ejpam-6414	414	6	,	,	PUNCT
ejpam-6414	414	7	t.	t.	NOUN
ejpam-6414	414	8	shah	shah	PROPN
ejpam-6414	414	9	,	,	PUNCT
ejpam-6414	414	10	m.	m.	NOUN
ejpam-6414	414	11	m.	m.	PROPN
ejpam-6414	414	12	hazzazi	hazzazi	PROPN
ejpam-6414	414	13	,	,	PUNCT
ejpam-6414	414	14	a.	a.	PROPN
ejpam-6414	414	15	r.	r.	PROPN
ejpam-6414	414	16	alharbi	alharbi	PROPN
ejpam-6414	414	17	,	,	PUNCT
ejpam-6414	414	18	and	and	CCONJ
ejpam-6414	414	19	i.	i.	PROPN
ejpam-6414	414	20	hussain	hussain	PROPN
ejpam-6414	414	21	.	.	PUNCT
ejpam-6414	415	1	quaternion	quaternion	NOUN
ejpam-6414	415	2	integers	integer	NOUN
ejpam-6414	415	3	based	base	VERB
ejpam-6414	415	4	higher	high	ADJ
ejpam-6414	415	5	length	length	NOUN
ejpam-6414	415	6	cyclic	cyclic	NOUN
ejpam-6414	415	7	codes	code	NOUN
ejpam-6414	415	8	and	and	CCONJ
ejpam-6414	415	9	their	their	PRON
ejpam-6414	415	10	decoding	decode	VERB
ejpam-6414	415	11	algorithm	algorithm	NOUN
ejpam-6414	415	12	.	.	PUNCT
ejpam-6414	416	1	computers	computer	NOUN
ejpam-6414	416	2	,	,	PUNCT
ejpam-6414	416	3	materials	material	NOUN
ejpam-6414	416	4	&	&	CCONJ
ejpam-6414	416	5	continua	continuum	NOUN
ejpam-6414	416	6	,	,	PUNCT
ejpam-6414	416	7	73(1):1–17	73(1):1–17	PROPN
ejpam-6414	416	8	,	,	PUNCT
ejpam-6414	416	9	2022	2022	NUM
ejpam-6414	416	10	.	.	PUNCT
ejpam-6414	417	1	[	[	X
ejpam-6414	417	2	16	16	NUM
ejpam-6414	417	3	]	]	PUNCT
ejpam-6414	417	4	m.	m.	NOUN
ejpam-6414	417	5	sajjad	sajjad	PROPN
ejpam-6414	417	6	and	and	CCONJ
ejpam-6414	417	7	t.	t.	PROPN
ejpam-6414	417	8	shah	shah	NOUN
ejpam-6414	417	9	.	.	PUNCT
ejpam-6414	418	1	decoding	decode	VERB
ejpam-6414	418	2	of	of	ADP
ejpam-6414	418	3	cyclic	cyclic	ADJ
ejpam-6414	418	4	codes	code	NOUN
ejpam-6414	418	5	over	over	ADP
ejpam-6414	418	6	quaternion	quaternion	NOUN
ejpam-6414	418	7	integers	integer	NOUN
ejpam-6414	418	8	by	by	ADP
ejpam-6414	418	9	modified	modified	ADJ
ejpam-6414	418	10	berlekamp	berlekamp	NOUN
ejpam-6414	418	11	–	–	PUNCT
ejpam-6414	418	12	massey	massey	NOUN
ejpam-6414	418	13	algorithm	algorithm	NOUN
ejpam-6414	418	14	.	.	PUNCT
ejpam-6414	419	1	computational	computational	ADJ
ejpam-6414	419	2	and	and	CCONJ
ejpam-6414	419	3	applied	applied	ADJ
ejpam-6414	419	4	mathematics	mathematic	NOUN
ejpam-6414	419	5	,	,	PUNCT
ejpam-6414	419	6	43(2):102	43(2):102	NUM
ejpam-6414	419	7	,	,	PUNCT
ejpam-6414	419	8	2024	2024	NUM
ejpam-6414	419	9	.	.	PUNCT
ejpam-6414	420	1	[	[	X
ejpam-6414	420	2	17	17	NUM
ejpam-6414	420	3	]	]	PUNCT
ejpam-6414	420	4	m.	m.	NOUN
ejpam-6414	420	5	sajjad	sajjad	PROPN
ejpam-6414	420	6	,	,	PUNCT
ejpam-6414	420	7	t.	t.	NOUN
ejpam-6414	420	8	shah	shah	PROPN
ejpam-6414	420	9	,	,	PUNCT
ejpam-6414	420	10	r.	r.	PROPN
ejpam-6414	420	11	j.	j.	PROPN
ejpam-6414	420	12	serna	serna	PROPN
ejpam-6414	420	13	,	,	PUNCT
ejpam-6414	420	14	z.	z.	PROPN
ejpam-6414	420	15	e.	e.	PROPN
ejpam-6414	420	16	suárez	suárez	PROPN
ejpam-6414	420	17	aguilar	aguilar	PROPN
ejpam-6414	420	18	,	,	PUNCT
ejpam-6414	420	19	and	and	CCONJ
ejpam-6414	420	20	o.	o.	PROPN
ejpam-6414	420	21	s.	s.	PROPN
ejpam-6414	420	22	delgado	delgado	PROPN
ejpam-6414	420	23	.	.	PUNCT
ejpam-6414	421	1	fundamental	fundamental	ADJ
ejpam-6414	421	2	results	result	NOUN
ejpam-6414	421	3	of	of	ADP
ejpam-6414	421	4	cyclic	cyclic	ADJ
ejpam-6414	421	5	codes	code	NOUN
ejpam-6414	421	6	over	over	ADP
ejpam-6414	421	7	octonion	octonion	NOUN
ejpam-6414	421	8	integers	integer	NOUN
ejpam-6414	421	9	and	and	CCONJ
ejpam-6414	421	10	their	their	PRON
ejpam-6414	421	11	decoding	decode	VERB
ejpam-6414	421	12	algorithm	algorithm	NOUN
ejpam-6414	421	13	.	.	PUNCT
ejpam-6414	422	1	computation	computation	NOUN
ejpam-6414	422	2	,	,	PUNCT
ejpam-6414	422	3	10(12):219	10(12):219	NUM
ejpam-6414	422	4	,	,	PUNCT
ejpam-6414	422	5	2022	2022	NUM
ejpam-6414	422	6	.	.	PUNCT
ejpam-6414	423	1	[	[	X
ejpam-6414	423	2	18	18	NUM
ejpam-6414	423	3	]	]	X
ejpam-6414	423	4	y.	y.	PROPN
ejpam-6414	423	5	lei	lei	PROPN
ejpam-6414	423	6	,	,	PUNCT
ejpam-6414	423	7	c.	c.	PROPN
ejpam-6414	423	8	li	li	PROPN
ejpam-6414	423	9	,	,	PUNCT
ejpam-6414	423	10	y.	y.	PROPN
ejpam-6414	423	11	wu	wu	PROPN
ejpam-6414	423	12	,	,	PUNCT
ejpam-6414	423	13	and	and	CCONJ
ejpam-6414	423	14	p.	p.	PROPN
ejpam-6414	423	15	zeng	zeng	PROPN
ejpam-6414	423	16	.	.	PUNCT
ejpam-6414	424	1	more	more	ADJ
ejpam-6414	424	2	results	result	NOUN
ejpam-6414	424	3	on	on	ADP
ejpam-6414	424	4	hulls	hull	NOUN
ejpam-6414	424	5	of	of	ADP
ejpam-6414	424	6	some	some	DET
ejpam-6414	424	7	primitive	primitive	ADJ
ejpam-6414	424	8	binary	binary	ADJ
ejpam-6414	424	9	and	and	CCONJ
ejpam-6414	424	10	ternary	ternary	ADJ
ejpam-6414	424	11	bch	bch	PROPN
ejpam-6414	424	12	codes	code	NOUN
ejpam-6414	424	13	.	.	PUNCT
ejpam-6414	425	1	finite	finite	PROPN
ejpam-6414	425	2	fields	field	NOUN
ejpam-6414	425	3	and	and	CCONJ
ejpam-6414	425	4	their	their	PRON
ejpam-6414	425	5	applications	application	NOUN
ejpam-6414	425	6	,	,	PUNCT
ejpam-6414	425	7	82:102066	82:102066	NUM
ejpam-6414	425	8	,	,	PUNCT
ejpam-6414	425	9	2022	2022	NUM
ejpam-6414	425	10	.	.	PUNCT
ejpam-6414	426	1	[	[	X
ejpam-6414	426	2	19	19	NUM
ejpam-6414	426	3	]	]	X
ejpam-6414	426	4	y.	y.	PROPN
ejpam-6414	426	5	liu	liu	PROPN
ejpam-6414	426	6	,	,	PUNCT
ejpam-6414	426	7	r.	r.	PROPN
ejpam-6414	426	8	li	li	PROPN
ejpam-6414	426	9	,	,	PUNCT
ejpam-6414	426	10	q.	q.	PROPN
ejpam-6414	426	11	fu	fu	PROPN
ejpam-6414	426	12	,	,	PUNCT
ejpam-6414	426	13	l.	l.	PROPN
ejpam-6414	426	14	lu	lu	PROPN
ejpam-6414	426	15	,	,	PUNCT
ejpam-6414	426	16	and	and	CCONJ
ejpam-6414	426	17	y.	y.	PROPN
ejpam-6414	426	18	rao	rao	PROPN
ejpam-6414	426	19	.	.	PUNCT
ejpam-6414	427	1	some	some	DET
ejpam-6414	427	2	binary	binary	PROPN
ejpam-6414	427	3	bch	bch	PROPN
ejpam-6414	427	4	codes	code	NOUN
ejpam-6414	427	5	with	with	ADP
ejpam-6414	427	6	length	length	NOUN
ejpam-6414	427	7	n=	n=	PROPN
ejpam-6414	427	8	2ˆm+	2ˆm+	PROPN
ejpam-6414	427	9	1	1	NUM
ejpam-6414	427	10	.	.	PUNCT
ejpam-6414	427	11	finite	finite	PROPN
ejpam-6414	427	12	fields	field	NOUN
ejpam-6414	427	13	and	and	CCONJ
ejpam-6414	427	14	their	their	PRON
ejpam-6414	427	15	applications	application	NOUN
ejpam-6414	427	16	,	,	PUNCT
ejpam-6414	427	17	55:109–133	55:109–133	NUM
ejpam-6414	427	18	,	,	PUNCT
ejpam-6414	427	19	2019	2019	NUM
ejpam-6414	427	20	.	.	PUNCT
ejpam-6414	428	1	[	[	X
ejpam-6414	428	2	20	20	NUM
ejpam-6414	428	3	]	]	PUNCT
ejpam-6414	428	4	s.	s.	PROPN
ejpam-6414	428	5	r.	r.	PROPN
ejpam-6414	428	6	nagpaul	nagpaul	PROPN
ejpam-6414	428	7	.	.	PUNCT
ejpam-6414	429	1	topics	topic	NOUN
ejpam-6414	429	2	in	in	ADP
ejpam-6414	429	3	applied	applied	ADJ
ejpam-6414	429	4	abstract	abstract	ADJ
ejpam-6414	429	5	algebra	algebra	NOUN
ejpam-6414	429	6	,	,	PUNCT
ejpam-6414	429	7	volume	volume	NOUN
ejpam-6414	429	8	15	15	NUM
ejpam-6414	429	9	.	.	PUNCT
ejpam-6414	430	1	american	american	PROPN
ejpam-6414	430	2	mathematical	mathematical	PROPN
ejpam-6414	430	3	society	society	NOUN
ejpam-6414	430	4	,	,	PUNCT
ejpam-6414	430	5	2005	2005	NUM
ejpam-6414	430	6	.	.	PUNCT
ejpam-6414	431	1	[	[	X
ejpam-6414	431	2	21	21	NUM
ejpam-6414	431	3	]	]	PUNCT
ejpam-6414	431	4	a.	a.	NOUN
ejpam-6414	431	5	a.	a.	PROPN
ejpam-6414	431	6	de	de	PROPN
ejpam-6414	431	7	andrade	andrade	PROPN
ejpam-6414	431	8	and	and	CCONJ
ejpam-6414	431	9	t.	t.	PROPN
ejpam-6414	431	10	shah	shah	PROPN
ejpam-6414	431	11	.	.	PUNCT
ejpam-6414	432	1	goppa	goppa	PROPN
ejpam-6414	432	2	codes	code	NOUN
ejpam-6414	432	3	through	through	ADP
ejpam-6414	432	4	polynomials	polynomial	NOUN
ejpam-6414	432	5	of	of	ADP
ejpam-6414	432	6	b	b	NOUN
ejpam-6414	432	7	[	[	X
ejpam-6414	432	8	x;(1/22̂	x;(1/22̂	X
ejpam-6414	432	9	)	)	PUNCT
ejpam-6414	432	10	z	z	NOUN
ejpam-6414	432	11	0	0	NUM
ejpam-6414	432	12	]	]	PUNCT
ejpam-6414	432	13	and	and	CCONJ
ejpam-6414	432	14	its	its	PRON
ejpam-6414	432	15	decoding	decode	VERB
ejpam-6414	432	16	principle	principle	NOUN
ejpam-6414	432	17	.	.	PUNCT
ejpam-6414	433	1	journal	journal	PROPN
ejpam-6414	433	2	of	of	ADP
ejpam-6414	433	3	advanced	advanced	ADJ
ejpam-6414	433	4	research	research	NOUN
ejpam-6414	433	5	in	in	ADP
ejpam-6414	433	6	applied	applied	ADJ
ejpam-6414	433	7	mathematics	mathematic	NOUN
ejpam-6414	433	8	,	,	PUNCT
ejpam-6414	433	9	pages	page	NOUN
ejpam-6414	433	10	12–20	12–20	NUM
ejpam-6414	433	11	,	,	PUNCT
ejpam-6414	433	12	2011	2011	NUM
ejpam-6414	433	13	.	.	PUNCT
ejpam-6414	434	1	[	[	X
ejpam-6414	434	2	22	22	NUM
ejpam-6414	434	3	]	]	PUNCT
ejpam-6414	434	4	m.	m.	NOUN
ejpam-6414	434	5	asif	asif	NOUN
ejpam-6414	434	6	and	and	CCONJ
ejpam-6414	434	7	t.	t.	NOUN
ejpam-6414	434	8	shah	shah	PROPN
ejpam-6414	434	9	.	.	PUNCT
ejpam-6414	435	1	bch	bch	PROPN
ejpam-6414	435	2	codes	code	NOUN
ejpam-6414	435	3	with	with	ADP
ejpam-6414	435	4	computational	computational	ADJ
ejpam-6414	435	5	approach	approach	NOUN
ejpam-6414	435	6	and	and	CCONJ
ejpam-6414	435	7	its	its	PRON
ejpam-6414	435	8	applications	application	NOUN
ejpam-6414	435	9	in	in	ADP
ejpam-6414	435	10	muhammad	muhammad	PROPN
ejpam-6414	435	11	sajjad	sajjad	PROPN
ejpam-6414	435	12	et	et	PROPN
ejpam-6414	435	13	al	al	PROPN
ejpam-6414	435	14	.	.	PUNCT
ejpam-6414	435	15	/	/	SYM
ejpam-6414	435	16	eur	eur	PROPN
ejpam-6414	435	17	.	.	PUNCT
ejpam-6414	436	1	j.	j.	PROPN
ejpam-6414	436	2	pure	pure	PROPN
ejpam-6414	436	3	appl	appl	PROPN
ejpam-6414	436	4	.	.	PROPN
ejpam-6414	436	5	math	math	PROPN
ejpam-6414	436	6	,	,	PUNCT
ejpam-6414	436	7	18	18	NUM
ejpam-6414	436	8	(	(	PUNCT
ejpam-6414	436	9	3	3	NUM
ejpam-6414	436	10	)	)	PUNCT
ejpam-6414	436	11	(	(	PUNCT
ejpam-6414	436	12	2025	2025	NUM
ejpam-6414	436	13	)	)	PUNCT
ejpam-6414	436	14	,	,	PUNCT
ejpam-6414	436	15	6414	6414	NUM
ejpam-6414	436	16	22	22	NUM
ejpam-6414	436	17	of	of	ADP
ejpam-6414	436	18	22	22	NUM
ejpam-6414	436	19	image	image	NOUN
ejpam-6414	436	20	encryption	encryption	NOUN
ejpam-6414	436	21	.	.	PUNCT
ejpam-6414	437	1	journal	journal	NOUN
ejpam-6414	437	2	of	of	ADP
ejpam-6414	437	3	intelligent	intelligent	ADJ
ejpam-6414	437	4	&	&	CCONJ
ejpam-6414	437	5	fuzzy	fuzzy	ADJ
ejpam-6414	437	6	systems	system	NOUN
ejpam-6414	437	7	,	,	PUNCT
ejpam-6414	437	8	37(3):3925–3939	37(3):3925–3939	NUM
ejpam-6414	437	9	,	,	PUNCT
ejpam-6414	437	10	2019	2019	NUM
ejpam-6414	437	11	.	.	PUNCT
ejpam-6414	438	1	[	[	X
ejpam-6414	438	2	23	23	NUM
ejpam-6414	438	3	]	]	PUNCT
ejpam-6414	438	4	t.	t.	NOUN
ejpam-6414	438	5	shah	shah	PROPN
ejpam-6414	438	6	and	and	CCONJ
ejpam-6414	438	7	a.	a.	NOUN
ejpam-6414	438	8	a.	a.	PROPN
ejpam-6414	438	9	d.	d.	PROPN
ejpam-6414	438	10	andrade	andrade	PROPN
ejpam-6414	438	11	.	.	PUNCT
ejpam-6414	439	1	a	a	DET
ejpam-6414	439	2	decoding	decode	VERB
ejpam-6414	439	3	procedure	procedure	NOUN
ejpam-6414	439	4	which	which	PRON
ejpam-6414	439	5	improves	improve	VERB
ejpam-6414	439	6	code	code	NOUN
ejpam-6414	439	7	rate	rate	NOUN
ejpam-6414	439	8	and	and	CCONJ
ejpam-6414	439	9	error	error	NOUN
ejpam-6414	439	10	corrections	correction	NOUN
ejpam-6414	439	11	.	.	PUNCT
ejpam-6414	440	1	jaram	jaram	PROPN
ejpam-6414	440	2	,	,	PUNCT
ejpam-6414	440	3	4(4):37–50	4(4):37–50	NUM
ejpam-6414	440	4	,	,	PUNCT
ejpam-6414	440	5	2012	2012	NUM
ejpam-6414	440	6	.	.	PUNCT
ejpam-6414	441	1	[	[	X
ejpam-6414	441	2	24	24	NUM
ejpam-6414	441	3	]	]	PUNCT
ejpam-6414	441	4	t.	t.	NOUN
ejpam-6414	441	5	shah	shah	PROPN
ejpam-6414	441	6	,	,	PUNCT
ejpam-6414	441	7	a.	a.	PROPN
ejpam-6414	441	8	qamar	qamar	PROPN
ejpam-6414	441	9	,	,	PUNCT
ejpam-6414	441	10	and	and	CCONJ
ejpam-6414	441	11	a.	a.	NOUN
ejpam-6414	441	12	a.	a.	PROPN
ejpam-6414	441	13	de	de	PROPN
ejpam-6414	441	14	andrade	andrade	PROPN
ejpam-6414	441	15	.	.	PUNCT
ejpam-6414	442	1	construction	construction	NOUN
ejpam-6414	442	2	and	and	CCONJ
ejpam-6414	442	3	decoding	decoding	NOUN
ejpam-6414	442	4	of	of	ADP
ejpam-6414	442	5	bch	bch	PROPN
ejpam-6414	442	6	codes	code	NOUN
ejpam-6414	442	7	over	over	ADP
ejpam-6414	442	8	chain	chain	NOUN
ejpam-6414	442	9	of	of	ADP
ejpam-6414	442	10	commutative	commutative	ADJ
ejpam-6414	442	11	rings	ring	NOUN
ejpam-6414	442	12	.	.	PUNCT
ejpam-6414	443	1	mathematical	mathematical	ADJ
ejpam-6414	443	2	sciences	sciences	PROPN
ejpam-6414	443	3	,	,	PUNCT
ejpam-6414	443	4	6(1):51	6(1):51	NUM
ejpam-6414	443	5	,	,	PUNCT
ejpam-6414	443	6	2012	2012	NUM
ejpam-6414	443	7	.	.	PUNCT
ejpam-6414	444	1	[	[	X
ejpam-6414	444	2	25	25	NUM
ejpam-6414	444	3	]	]	PUNCT
ejpam-6414	444	4	t.	t.	NOUN
ejpam-6414	444	5	shah	shah	PROPN
ejpam-6414	444	6	,	,	PUNCT
ejpam-6414	444	7	m.	m.	NOUN
ejpam-6414	444	8	khan	khan	PROPN
ejpam-6414	444	9	,	,	PUNCT
ejpam-6414	444	10	and	and	CCONJ
ejpam-6414	444	11	a.	a.	NOUN
ejpam-6414	444	12	a.	a.	PROPN
ejpam-6414	444	13	d.	d.	PROPN
ejpam-6414	444	14	andrade	andrade	PROPN
ejpam-6414	444	15	.	.	PUNCT
ejpam-6414	445	1	a	a	DET
ejpam-6414	445	2	decoding	decode	VERB
ejpam-6414	445	3	method	method	NOUN
ejpam-6414	445	4	of	of	ADP
ejpam-6414	445	5	an	an	DET
ejpam-6414	445	6	n	n	NUM
ejpam-6414	445	7	length	length	NOUN
ejpam-6414	445	8	binary	binary	PROPN
ejpam-6414	445	9	bch	bch	PROPN
ejpam-6414	445	10	code	code	PROPN
ejpam-6414	445	11	through	through	ADP
ejpam-6414	445	12	(	(	PUNCT
ejpam-6414	445	13	n	n	X
ejpam-6414	445	14	+	+	CCONJ
ejpam-6414	445	15	1)n	1)n	NUM
ejpam-6414	445	16	length	length	NOUN
ejpam-6414	445	17	binary	binary	PROPN
ejpam-6414	445	18	cyclic	cyclic	PROPN
ejpam-6414	445	19	code	code	PROPN
ejpam-6414	445	20	.	.	PUNCT
ejpam-6414	446	1	anais	anais	PROPN
ejpam-6414	446	2	da	da	PROPN
ejpam-6414	446	3	academia	academia	PROPN
ejpam-6414	446	4	brasileira	brasileira	PROPN
ejpam-6414	446	5	de	de	PROPN
ejpam-6414	446	6	ciências	ciências	PROPN
ejpam-6414	446	7	,	,	PUNCT
ejpam-6414	446	8	85(3):863–872	85(3):863–872	NUM
ejpam-6414	446	9	,	,	PUNCT
ejpam-6414	446	10	2013	2013	NUM
ejpam-6414	446	11	.	.	PUNCT
ejpam-6414	447	1	[	[	X
ejpam-6414	447	2	26	26	NUM
ejpam-6414	447	3	]	]	PUNCT
ejpam-6414	447	4	t.	t.	NOUN
ejpam-6414	447	5	shah	shah	PROPN
ejpam-6414	447	6	and	and	CCONJ
ejpam-6414	447	7	a.	a.	NOUN
ejpam-6414	447	8	a.	a.	PROPN
ejpam-6414	447	9	de	de	PROPN
ejpam-6414	447	10	andrade	andrade	PROPN
ejpam-6414	447	11	.	.	PUNCT
ejpam-6414	448	1	cyclic	cyclic	PROPN
ejpam-6414	448	2	codes	code	NOUN
ejpam-6414	448	3	through	through	ADP
ejpam-6414	448	4	b[x	b[x	PROPN
ejpam-6414	448	5	]	]	PUNCT
ejpam-6414	448	6	,	,	PUNCT
ejpam-6414	448	7	b	b	X
ejpam-6414	448	8	[	[	PUNCT
ejpam-6414	448	9	x	x	X
ejpam-6414	448	10	,	,	PUNCT
ejpam-6414	448	11	1	1	NUM
ejpam-6414	448	12	pk	pk	NOUN
ejpam-6414	448	13	z0	z0	PROPN
ejpam-6414	448	14	]	]	PUNCT
ejpam-6414	448	15	,	,	PUNCT
ejpam-6414	448	16	and	and	CCONJ
ejpam-6414	448	17	b	b	X
ejpam-6414	448	18	[	[	PUNCT
ejpam-6414	448	19	x	x	X
ejpam-6414	448	20	,	,	PUNCT
ejpam-6414	448	21	1	1	NUM
ejpam-6414	448	22	kpz0	kpz0	NOUN
ejpam-6414	448	23	]	]	PUNCT
ejpam-6414	448	24	,	,	PUNCT
ejpam-6414	448	25	and	and	CCONJ
ejpam-6414	448	26	:	:	PUNCT
ejpam-6414	448	27	a	a	DET
ejpam-6414	448	28	comparison	comparison	NOUN
ejpam-6414	448	29	.	.	PUNCT
ejpam-6414	449	1	journal	journal	NOUN
ejpam-6414	449	2	of	of	ADP
ejpam-6414	449	3	algebra	algebra	PROPN
ejpam-6414	449	4	and	and	CCONJ
ejpam-6414	449	5	its	its	PRON
ejpam-6414	449	6	applications	application	NOUN
ejpam-6414	449	7	,	,	PUNCT
ejpam-6414	449	8	11(04):1250078	11(04):1250078	NUM
ejpam-6414	449	9	,	,	PUNCT
ejpam-6414	449	10	2012	2012	NUM
ejpam-6414	449	11	.	.	PUNCT
ejpam-6414	450	1	[	[	X
ejpam-6414	450	2	27	27	NUM
ejpam-6414	450	3	]	]	X
ejpam-6414	450	4	h.	h.	PROPN
ejpam-6414	450	5	zhu	zhu	PROPN
ejpam-6414	450	6	,	,	PUNCT
ejpam-6414	450	7	j.	j.	PROPN
ejpam-6414	450	8	li	li	PROPN
ejpam-6414	450	9	,	,	PUNCT
ejpam-6414	450	10	and	and	CCONJ
ejpam-6414	450	11	s.	s.	PROPN
ejpam-6414	450	12	zhu	zhu	PROPN
ejpam-6414	450	13	.	.	PUNCT
ejpam-6414	451	1	parameters	parameter	NOUN
ejpam-6414	451	2	of	of	ADP
ejpam-6414	451	3	two	two	NUM
ejpam-6414	451	4	classes	class	NOUN
ejpam-6414	451	5	of	of	ADP
ejpam-6414	451	6	negacyclic	negacyclic	ADJ
ejpam-6414	451	7	bch	bch	PROPN
ejpam-6414	451	8	codes	code	NOUN
ejpam-6414	451	9	.	.	PUNCT
ejpam-6414	452	1	journal	journal	NOUN
ejpam-6414	452	2	of	of	ADP
ejpam-6414	452	3	applied	apply	VERB
ejpam-6414	452	4	mathematics	mathematic	NOUN
ejpam-6414	452	5	and	and	CCONJ
ejpam-6414	452	6	computing	computing	NOUN
ejpam-6414	452	7	,	,	PUNCT
ejpam-6414	452	8	69(6):4353–4380	69(6):4353–4380	NUM
ejpam-6414	452	9	,	,	PUNCT
ejpam-6414	452	10	2023	2023	NUM
ejpam-6414	452	11	.	.	PUNCT
ejpam-6414	453	1	[	[	X
ejpam-6414	453	2	28	28	NUM
ejpam-6414	453	3	]	]	PUNCT
ejpam-6414	453	4	x.	x.	PROPN
ejpam-6414	453	5	wang	wang	PROPN
ejpam-6414	453	6	,	,	PUNCT
ejpam-6414	453	7	z.	z.	PROPN
ejpam-6414	453	8	sun	sun	PROPN
ejpam-6414	453	9	,	,	PUNCT
ejpam-6414	453	10	and	and	CCONJ
ejpam-6414	453	11	c.	c.	PROPN
ejpam-6414	453	12	ding	ding	PROPN
ejpam-6414	453	13	.	.	PUNCT
ejpam-6414	454	1	two	two	NUM
ejpam-6414	454	2	families	family	NOUN
ejpam-6414	454	3	of	of	ADP
ejpam-6414	454	4	negacyclic	negacyclic	ADJ
ejpam-6414	454	5	bch	bch	PROPN
ejpam-6414	454	6	codes	code	NOUN
ejpam-6414	454	7	.	.	PUNCT
ejpam-6414	455	1	designs	design	NOUN
ejpam-6414	455	2	,	,	PUNCT
ejpam-6414	455	3	codes	code	NOUN
ejpam-6414	455	4	and	and	CCONJ
ejpam-6414	455	5	cryptography	cryptography	NOUN
ejpam-6414	455	6	,	,	PUNCT
ejpam-6414	455	7	91(7):2395–2420	91(7):2395–2420	NUM
ejpam-6414	455	8	,	,	PUNCT
ejpam-6414	455	9	2023	2023	NUM
ejpam-6414	455	10	.	.	PUNCT
ejpam-6414	456	1	[	[	X
ejpam-6414	456	2	29	29	NUM
ejpam-6414	456	3	]	]	X
ejpam-6414	456	4	b.	b.	PROPN
ejpam-6414	456	5	pang	pang	PROPN
ejpam-6414	456	6	,	,	PUNCT
ejpam-6414	456	7	s.	s.	PROPN
ejpam-6414	456	8	zhu	zhu	PROPN
ejpam-6414	456	9	,	,	PUNCT
ejpam-6414	456	10	t.	t.	PROPN
ejpam-6414	456	11	yang	yang	PROPN
ejpam-6414	456	12	,	,	PUNCT
ejpam-6414	456	13	and	and	CCONJ
ejpam-6414	456	14	j.	j.	PROPN
ejpam-6414	456	15	gao	gao	PROPN
ejpam-6414	456	16	.	.	PUNCT
ejpam-6414	457	1	bch	bch	PROPN
ejpam-6414	457	2	codes	code	NOUN
ejpam-6414	457	3	with	with	ADP
ejpam-6414	457	4	larger	large	ADJ
ejpam-6414	457	5	dimensional	dimensional	ADJ
ejpam-6414	457	6	hull	hull	NOUN
ejpam-6414	457	7	.	.	PUNCT
ejpam-6414	458	1	designs	design	NOUN
ejpam-6414	458	2	,	,	PUNCT
ejpam-6414	458	3	codes	code	NOUN
ejpam-6414	458	4	and	and	CCONJ
ejpam-6414	458	5	cryptography	cryptography	NOUN
ejpam-6414	458	6	,	,	PUNCT
ejpam-6414	458	7	91(12):3933–3951	91(12):3933–3951	NUM
ejpam-6414	458	8	,	,	PUNCT
ejpam-6414	458	9	2023	2023	NUM
ejpam-6414	458	10	.	.	PUNCT
ejpam-6414	459	1	[	[	X
ejpam-6414	459	2	30	30	NUM
ejpam-6414	459	3	]	]	X
ejpam-6414	459	4	y.	y.	PROPN
ejpam-6414	459	5	zhou	zhou	PROPN
ejpam-6414	459	6	,	,	PUNCT
ejpam-6414	459	7	x.	x.	PROPN
ejpam-6414	459	8	kai	kai	PROPN
ejpam-6414	459	9	,	,	PUNCT
ejpam-6414	459	10	and	and	CCONJ
ejpam-6414	459	11	s.	s.	PROPN
ejpam-6414	459	12	zhu	zhu	PROPN
ejpam-6414	459	13	.	.	PUNCT
ejpam-6414	460	1	two	two	NUM
ejpam-6414	460	2	classes	class	NOUN
ejpam-6414	460	3	of	of	ADP
ejpam-6414	460	4	ternary	ternary	ADJ
ejpam-6414	460	5	lcd	lcd	PROPN
ejpam-6414	460	6	constacyclic	constacyclic	PROPN
ejpam-6414	460	7	bch	bch	PROPN
ejpam-6414	460	8	codes	code	NOUN
ejpam-6414	460	9	.	.	PUNCT
ejpam-6414	461	1	cryptography	cryptography	NOUN
ejpam-6414	461	2	and	and	CCONJ
ejpam-6414	461	3	communications	communication	NOUN
ejpam-6414	461	4	,	,	PUNCT
ejpam-6414	461	5	15(5):905–919	15(5):905–919	NUM
ejpam-6414	461	6	,	,	PUNCT
ejpam-6414	461	7	2023	2023	NUM
ejpam-6414	461	8	.	.	PUNCT
ejpam-6414	462	1	[	[	X
ejpam-6414	462	2	31	31	NUM
ejpam-6414	462	3	]	]	PUNCT
ejpam-6414	462	4	r.	r.	PROPN
ejpam-6414	462	5	e.	e.	PROPN
ejpam-6414	462	6	blahut	blahut	PROPN
ejpam-6414	462	7	.	.	PUNCT
ejpam-6414	463	1	algebraic	algebraic	ADJ
ejpam-6414	463	2	codes	code	NOUN
ejpam-6414	463	3	for	for	ADP
ejpam-6414	463	4	data	data	NOUN
ejpam-6414	463	5	transmission	transmission	NOUN
ejpam-6414	463	6	.	.	PUNCT
ejpam-6414	464	1	cambridge	cambridge	PROPN
ejpam-6414	464	2	university	university	PROPN
ejpam-6414	464	3	press	press	NOUN
ejpam-6414	464	4	,	,	PUNCT
ejpam-6414	464	5	2003	2003	NUM
ejpam-6414	464	6	.	.	PUNCT