id	sid	tid	token	lemma	pos
cana-681	1	1	communications	communication	NOUN
cana-681	1	2	on	on	ADP
cana-681	1	3	applied	apply	VERB
cana-681	1	4	nonlinear	nonlinear	ADJ
cana-681	1	5	analysis	analysis	NOUN
cana-681	1	6	issn	issn	NOUN
cana-681	1	7	:	:	PUNCT
cana-681	1	8	1074	1074	NUM
cana-681	1	9	-	-	PUNCT
cana-681	1	10	133x	133x	NUM
cana-681	1	11	vol	vol	NOUN
cana-681	1	12	31	31	NUM
cana-681	1	13	no	no	NOUN
cana-681	1	14	.	.	PUNCT
cana-681	2	1	2s	2s	NUM
cana-681	2	2	(	(	PUNCT
cana-681	2	3	2024	2024	NUM
cana-681	2	4	)	)	PUNCT
cana-681	2	5	619	619	NUM
cana-681	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	2	7	eight	eight	NUM
cana-681	2	8	error	error	NOUN
cana-681	2	9	correction	correction	NOUN
cana-681	2	10	for	for	ADP
cana-681	2	11	(	(	PUNCT
cana-681	2	12	57,29,17	57,29,17	NUM
cana-681	2	13	)	)	PUNCT
cana-681	2	14	quadratic	quadratic	ADJ
cana-681	2	15	residue	residue	NOUN
cana-681	2	16	code	code	NOUN
cana-681	2	17	over	over	ADP
cana-681	2	18	binary	binary	ADJ
cana-681	2	19	field	field	PROPN
cana-681	2	20	p.	p.	PROPN
cana-681	2	21	shakila	shakila	PROPN
cana-681	2	22	banua	banua	NOUN
cana-681	2	23	,	,	PUNCT
cana-681	2	24	r.shobanab	r.shobanab	PROPN
cana-681	2	25	aassistant	aassistant	PROPN
cana-681	2	26	professor	professor	PROPN
cana-681	2	27	,	,	PUNCT
cana-681	2	28	department	department	NOUN
cana-681	2	29	of	of	ADP
cana-681	2	30	mathematics	mathematic	NOUN
cana-681	2	31	,	,	PUNCT
cana-681	2	32	vellalar	vellalar	ADJ
cana-681	2	33	college	college	NOUN
cana-681	2	34	for	for	ADP
cana-681	2	35	women	woman	NOUN
cana-681	2	36	,	,	PUNCT
cana-681	2	37	erode-638012	erode-638012	ADJ
cana-681	2	38	,	,	PUNCT
cana-681	2	39	tamilnadu	tamilnadu	ADJ
cana-681	2	40	,	,	PUNCT
cana-681	2	41	india	india	PROPN
cana-681	2	42	bresearch	bresearch	PROPN
cana-681	2	43	scholar	scholar	NOUN
cana-681	2	44	,	,	PUNCT
cana-681	2	45	department	department	NOUN
cana-681	2	46	of	of	ADP
cana-681	2	47	mathematics	mathematic	NOUN
cana-681	2	48	,	,	PUNCT
cana-681	2	49	vellalar	vellalar	ADJ
cana-681	2	50	college	college	NOUN
cana-681	2	51	for	for	ADP
cana-681	2	52	women	woman	NOUN
cana-681	2	53	,	,	PUNCT
cana-681	2	54	erode-638012	erode-638012	ADJ
cana-681	2	55	,	,	PUNCT
cana-681	2	56	tamilnadu	tamilnadu	NOUN
cana-681	2	57	,	,	PUNCT
cana-681	2	58	india	india	PROPN
cana-681	2	59	e	e	PROPN
cana-681	2	60	-	-	NOUN
cana-681	2	61	mail	mail	NOUN
cana-681	2	62	:	:	PUNCT
cana-681	2	63	a	a	DET
cana-681	2	64	shakimeeran10@gmail.com	shakimeeran10@gmail.com	PROPN
cana-681	2	65	,	,	PUNCT
cana-681	2	66	b	b	X
cana-681	2	67	shobanarj99@gmail.com	shobanarj99@gmail.com	PROPN
cana-681	2	68	article	article	NOUN
cana-681	2	69	history	history	NOUN
cana-681	2	70	:	:	PUNCT
cana-681	2	71	received	receive	VERB
cana-681	2	72	:	:	PUNCT
cana-681	2	73	26	26	NUM
cana-681	2	74	-	-	SYM
cana-681	2	75	03	03	NUM
cana-681	2	76	-	-	PUNCT
cana-681	2	77	2024	2024	NUM
cana-681	2	78	revised	revise	VERB
cana-681	2	79	:	:	PUNCT
cana-681	2	80	18	18	NUM
cana-681	2	81	-	-	SYM
cana-681	2	82	05	05	NUM
cana-681	2	83	-	-	PUNCT
cana-681	2	84	2024	2024	NUM
cana-681	2	85	accepted	accept	VERB
cana-681	2	86	:	:	PUNCT
cana-681	2	87	30	30	NUM
cana-681	2	88	-	-	SYM
cana-681	2	89	05	05	NUM
cana-681	2	90	-	-	PUNCT
cana-681	2	91	2024	2024	NUM
cana-681	2	92	abstract	abstract	NOUN
cana-681	2	93	:	:	PUNCT
cana-681	2	94	this	this	DET
cana-681	2	95	paper	paper	NOUN
cana-681	2	96	introduces	introduce	VERB
cana-681	2	97	novel	novel	ADJ
cana-681	2	98	parameters	parameter	NOUN
cana-681	2	99	and	and	CCONJ
cana-681	2	100	presents	present	VERB
cana-681	2	101	a	a	DET
cana-681	2	102	methodology	methodology	NOUN
cana-681	2	103	for	for	ADP
cana-681	2	104	identifying	identify	VERB
cana-681	2	105	the	the	DET
cana-681	2	106	necessary	necessary	ADJ
cana-681	2	107	syndrome	syndrome	NOUN
cana-681	2	108	indices	index	NOUN
cana-681	2	109	required	require	VERB
cana-681	2	110	to	to	PART
cana-681	2	111	compute	compute	VERB
cana-681	2	112	the	the	DET
cana-681	2	113	unknown	unknown	ADJ
cana-681	2	114	syndromes	syndrome	NOUN
cana-681	2	115	within	within	ADP
cana-681	2	116	the	the	DET
cana-681	2	117	context	context	NOUN
cana-681	2	118	of	of	ADP
cana-681	2	119	the	the	DET
cana-681	2	120	(	(	PUNCT
cana-681	2	121	57	57	NUM
cana-681	2	122	,	,	PUNCT
cana-681	2	123	29	29	NUM
cana-681	2	124	,	,	PUNCT
cana-681	2	125	17	17	NUM
cana-681	2	126	)	)	PUNCT
cana-681	2	127	quadratic	quadratic	ADJ
cana-681	2	128	residue	residue	NOUN
cana-681	2	129	code	code	NOUN
cana-681	2	130	.	.	PUNCT
cana-681	3	1	by	by	ADP
cana-681	3	2	determining	determine	VERB
cana-681	3	3	the	the	DET
cana-681	3	4	resulting	result	VERB
cana-681	3	5	index	index	NOUN
cana-681	3	6	sets	set	NOUN
cana-681	3	7	,	,	PUNCT
cana-681	3	8	the	the	DET
cana-681	3	9	unknown	unknown	ADJ
cana-681	3	10	syndromes	syndrome	NOUN
cana-681	3	11	can	can	AUX
cana-681	3	12	be	be	AUX
cana-681	3	13	computed	compute	VERB
cana-681	3	14	,	,	PUNCT
cana-681	3	15	subsequently	subsequently	ADV
cana-681	3	16	leading	lead	VERB
cana-681	3	17	to	to	ADP
cana-681	3	18	the	the	DET
cana-681	3	19	derivation	derivation	NOUN
cana-681	3	20	of	of	ADP
cana-681	3	21	the	the	DET
cana-681	3	22	corresponding	corresponding	ADJ
cana-681	3	23	error	error	NOUN
cana-681	3	24	-	-	PUNCT
cana-681	3	25	locator	locator	NOUN
cana-681	3	26	polynomial	polynomial	NOUN
cana-681	3	27	through	through	ADP
cana-681	3	28	the	the	DET
cana-681	3	29	application	application	NOUN
cana-681	3	30	of	of	ADP
cana-681	3	31	a	a	DET
cana-681	3	32	decoding	decode	VERB
cana-681	3	33	algorithm	algorithm	NOUN
cana-681	3	34	.	.	PUNCT
cana-681	4	1	keywords	keyword	NOUN
cana-681	4	2	:	:	PUNCT
cana-681	4	3	algebraic	algebraic	PROPN
cana-681	4	4	decoding	decode	VERB
cana-681	4	5	,	,	PUNCT
cana-681	4	6	quadratic	quadratic	ADJ
cana-681	4	7	residue	residue	NOUN
cana-681	4	8	code	code	NOUN
cana-681	4	9	,	,	PUNCT
cana-681	4	10	index	index	NOUN
cana-681	4	11	set	set	NOUN
cana-681	4	12	,	,	PUNCT
cana-681	4	13	syndromes	syndrome	NOUN
cana-681	4	14	.	.	PUNCT
cana-681	5	1	2020	2020	NUM
cana-681	5	2	subject	subject	ADJ
cana-681	5	3	classifications	classification	NOUN
cana-681	5	4	:	:	PUNCT
cana-681	5	5	94b15	94b15	NUM
cana-681	5	6	,	,	PUNCT
cana-681	5	7	94b35	94b35	NUM
cana-681	5	8	,	,	PUNCT
cana-681	5	9	94b60	94b60	NUM
cana-681	5	10	.	.	PUNCT
cana-681	6	1	1	1	NUM
cana-681	6	2	.	.	X
cana-681	6	3	introduction	introduction	NOUN
cana-681	6	4	in	in	ADP
cana-681	6	5	1958	1958	NUM
cana-681	6	6	,	,	PUNCT
cana-681	6	7	prange	prange	NOUN
cana-681	7	1	[	[	X
cana-681	7	2	11	11	NUM
cana-681	7	3	]	]	PUNCT
cana-681	7	4	pioneered	pioneer	VERB
cana-681	7	5	the	the	DET
cana-681	7	6	quadratic	quadratic	ADJ
cana-681	7	7	residue	residue	NOUN
cana-681	7	8	(	(	PUNCT
cana-681	7	9	qr	qr	NOUN
cana-681	7	10	)	)	PUNCT
cana-681	7	11	codes	code	NOUN
cana-681	7	12	.	.	PUNCT
cana-681	8	1	hamming	ham	VERB
cana-681	8	2	addressed	address	VERB
cana-681	8	3	the	the	DET
cana-681	8	4	issue	issue	NOUN
cana-681	8	5	of	of	ADP
cana-681	8	6	rectifying	rectify	VERB
cana-681	8	7	a	a	DET
cana-681	8	8	single	single	ADJ
cana-681	8	9	corrupted	corrupted	ADJ
cana-681	8	10	binary	binary	ADJ
cana-681	8	11	digit	digit	NOUN
cana-681	8	12	within	within	ADP
cana-681	8	13	any	any	DET
cana-681	8	14	sequence	sequence	NOUN
cana-681	8	15	of	of	ADP
cana-681	8	16	length	length	NOUN
cana-681	8	17	n	n	CCONJ
cana-681	8	18	during	during	ADP
cana-681	8	19	the	the	DET
cana-681	8	20	transmission	transmission	NOUN
cana-681	8	21	of	of	ADP
cana-681	8	22	binary	binary	ADJ
cana-681	8	23	data	datum	NOUN
cana-681	8	24	over	over	ADP
cana-681	8	25	a	a	DET
cana-681	8	26	noisy	noisy	ADJ
cana-681	8	27	channel	channel	NOUN
cana-681	8	28	.	.	PUNCT
cana-681	9	1	shapiro	shapiro	PROPN
cana-681	9	2	h.s	h.s	PROPN
cana-681	9	3	.	.	PROPN
cana-681	9	4	and	and	CCONJ
cana-681	9	5	slotnick	slotnick	PROPN
cana-681	9	6	d.l	d.l	PROPN
cana-681	9	7	.	.	PROPN
cana-681	9	8	researched	research	VERB
cana-681	9	9	the	the	DET
cana-681	9	10	equivalent	equivalent	ADJ
cana-681	9	11	problem	problem	NOUN
cana-681	9	12	for	for	ADP
cana-681	9	13	channels	channel	NOUN
cana-681	9	14	capable	capable	ADJ
cana-681	9	15	of	of	ADP
cana-681	9	16	corrupting	corrupt	VERB
cana-681	9	17	a	a	DET
cana-681	9	18	larger	large	ADJ
cana-681	9	19	number	number	NOUN
cana-681	9	20	of	of	ADP
cana-681	9	21	digits	digit	NOUN
cana-681	9	22	[	[	X
cana-681	9	23	13	13	NUM
cana-681	9	24	]	]	PUNCT
cana-681	9	25	.	.	PUNCT
cana-681	10	1	macwilliams	macwilliams	PROPN
cana-681	10	2	f.j	f.j	PROPN
cana-681	10	3	.	.	PROPN
cana-681	11	1	and	and	CCONJ
cana-681	11	2	sloane	sloane	NOUN
cana-681	11	3	n.j.a	n.j.a	NOUN
cana-681	11	4	.	.	PUNCT
cana-681	12	1	comprehensively	comprehensively	ADV
cana-681	12	2	elucidated	elucidate	VERB
cana-681	12	3	various	various	ADJ
cana-681	12	4	forms	form	NOUN
cana-681	12	5	of	of	ADP
cana-681	12	6	errorcorrecting	errorcorrecte	VERB
cana-681	12	7	codes	code	NOUN
cana-681	12	8	and	and	CCONJ
cana-681	12	9	decoding	decode	VERB
cana-681	12	10	algorithms	algorithm	NOUN
cana-681	12	11	[	[	X
cana-681	12	12	7	7	NUM
cana-681	12	13	]	]	PUNCT
cana-681	12	14	.	.	PUNCT
cana-681	13	1	m.	m.	PROPN
cana-681	13	2	elia	elia	PROPN
cana-681	13	3	achieved	achieve	VERB
cana-681	13	4	the	the	DET
cana-681	13	5	decoding	decoding	NOUN
cana-681	13	6	of	of	ADP
cana-681	13	7	the	the	DET
cana-681	13	8	(	(	PUNCT
cana-681	13	9	23,12,7	23,12,7	NOUN
cana-681	13	10	)	)	PUNCT
cana-681	13	11	golay	golay	NOUN
cana-681	13	12	code	code	NOUN
cana-681	13	13	by	by	ADP
cana-681	13	14	employing	employ	VERB
cana-681	13	15	the	the	DET
cana-681	13	16	algebraic	algebraic	ADJ
cana-681	13	17	decoding	decoding	NOUN
cana-681	13	18	method	method	NOUN
cana-681	13	19	for	for	ADP
cana-681	13	20	three	three	NUM
cana-681	13	21	-	-	PUNCT
cana-681	13	22	error	error	NOUN
cana-681	13	23	-	-	PUNCT
cana-681	13	24	correcting	correct	VERB
cana-681	13	25	bch	bch	NOUN
cana-681	13	26	codes	code	NOUN
cana-681	13	27	[	[	X
cana-681	13	28	2	2	NUM
cana-681	13	29	]	]	PUNCT
cana-681	13	30	.	.	PUNCT
cana-681	14	1	the	the	DET
cana-681	14	2	researchers	researcher	NOUN
cana-681	14	3	obtained	obtain	VERB
cana-681	14	4	the	the	DET
cana-681	14	5	results	result	NOUN
cana-681	14	6	of	of	ADP
cana-681	14	7	mathematical	mathematical	ADJ
cana-681	14	8	and	and	CCONJ
cana-681	14	9	analytical	analytical	ADJ
cana-681	14	10	computations	computation	NOUN
cana-681	14	11	for	for	ADP
cana-681	14	12	multiple	multiple	ADJ
cana-681	14	13	binary	binary	PROPN
cana-681	14	14	qr	qr	PROPN
cana-681	14	15	codes	code	NOUN
cana-681	14	16	[	[	X
cana-681	14	17	17	17	NUM
cana-681	14	18	]	]	PUNCT
cana-681	14	19	.	.	PUNCT
cana-681	15	1	additionally	additionally	ADV
cana-681	15	2	,	,	PUNCT
cana-681	15	3	they	they	PRON
cana-681	15	4	proposed	propose	VERB
cana-681	15	5	a	a	DET
cana-681	15	6	rapid	rapid	ADJ
cana-681	15	7	method	method	NOUN
cana-681	15	8	for	for	ADP
cana-681	15	9	identifying	identify	VERB
cana-681	15	10	primitive	primitive	ADJ
cana-681	15	11	polynomials	polynomial	NOUN
cana-681	15	12	over	over	ADP
cana-681	15	13	binary	binary	ADJ
cana-681	15	14	fields	field	NOUN
cana-681	15	15	in	in	ADP
cana-681	15	16	[	[	X
cana-681	15	17	8	8	NUM
cana-681	15	18	]	]	PUNCT
cana-681	15	19	.	.	PUNCT
cana-681	16	1	the	the	DET
cana-681	16	2	extended	extended	ADJ
cana-681	16	3	qr	qr	NOUN
cana-681	16	4	codes	code	NOUN
cana-681	16	5	of	of	ADP
cana-681	16	6	lengths	length	NOUN
cana-681	16	7	32	32	NUM
cana-681	16	8	and	and	CCONJ
cana-681	16	9	48	48	NUM
cana-681	16	10	exhibit	exhibit	NOUN
cana-681	16	11	non	non	ADJ
cana-681	16	12	-	-	ADJ
cana-681	16	13	linear	linear	ADJ
cana-681	16	14	binary	binary	ADJ
cana-681	16	15	patterns	pattern	NOUN
cana-681	16	16	with	with	ADP
cana-681	16	17	significantly	significantly	ADV
cana-681	16	18	higher	high	ADJ
cana-681	16	19	minimum	minimum	ADJ
cana-681	16	20	weights	weight	NOUN
cana-681	16	21	were	be	AUX
cana-681	16	22	discussed	discuss	VERB
cana-681	16	23	in	in	ADP
cana-681	16	24	[	[	X
cana-681	16	25	10	10	NUM
cana-681	16	26	]	]	PUNCT
cana-681	16	27	.	.	PUNCT
cana-681	17	1	in	in	ADP
cana-681	17	2	the	the	DET
cana-681	17	3	decoding	decode	VERB
cana-681	17	4	process	process	NOUN
cana-681	17	5	of	of	ADP
cana-681	17	6	the	the	DET
cana-681	17	7	(	(	PUNCT
cana-681	17	8	47,24,11	47,24,11	PROPN
cana-681	17	9	)	)	PUNCT
cana-681	17	10	qr	qr	NOUN
cana-681	17	11	code	code	PROPN
cana-681	17	12	,	,	PUNCT
cana-681	17	13	the	the	DET
cana-681	17	14	author	author	NOUN
cana-681	17	15	devised	devise	VERB
cana-681	17	16	two	two	NUM
cana-681	17	17	methodologies	methodology	NOUN
cana-681	17	18	to	to	PART
cana-681	17	19	ascertain	ascertain	VERB
cana-681	17	20	the	the	DET
cana-681	17	21	nonlinear	nonlinear	ADJ
cana-681	17	22	correlations	correlation	NOUN
cana-681	17	23	between	between	ADP
cana-681	17	24	known	known	ADJ
cana-681	17	25	and	and	CCONJ
cana-681	17	26	unknown	unknown	ADJ
cana-681	17	27	syndromes	syndrome	NOUN
cana-681	17	28	,	,	PUNCT
cana-681	17	29	effectively	effectively	ADV
cana-681	17	30	rectifying	rectify	VERB
cana-681	17	31	five	five	NUM
cana-681	17	32	errors	error	NOUN
cana-681	17	33	and	and	CCONJ
cana-681	17	34	diagnosing	diagnose	VERB
cana-681	17	35	six	six	NUM
cana-681	17	36	errors	error	NOUN
cana-681	17	37	[	[	X
cana-681	17	38	12	12	NUM
cana-681	17	39	]	]	PUNCT
cana-681	17	40	.	.	PUNCT
cana-681	18	1	the	the	DET
cana-681	18	2	qr	qr	PROPN
cana-681	18	3	code	code	NOUN
cana-681	18	4	was	be	AUX
cana-681	18	5	generated	generate	VERB
cana-681	18	6	using	use	VERB
cana-681	18	7	the	the	DET
cana-681	18	8	truong	truong	PROPN
cana-681	18	9	et	et	PROPN
cana-681	18	10	al	al	PROPN
cana-681	18	11	decoding	decode	VERB
cana-681	18	12	scheme	scheme	NOUN
cana-681	18	13	with	with	ADP
cana-681	18	14	parameters	parameter	NOUN
cana-681	18	15	(	(	PUNCT
cana-681	18	16	71,36,11	71,36,11	NUM
cana-681	18	17	)	)	PUNCT
cana-681	18	18	,	,	PUNCT
cana-681	18	19	(	(	PUNCT
cana-681	18	20	79,40,15	79,40,15	NUM
cana-681	18	21	)	)	PUNCT
cana-681	18	22	,	,	PUNCT
cana-681	18	23	and	and	CCONJ
cana-681	18	24	(	(	PUNCT
cana-681	18	25	97,49,15	97,49,15	NUM
cana-681	18	26	)	)	PUNCT
cana-681	18	27	,	,	PUNCT
cana-681	18	28	accompanied	accompany	VERB
cana-681	18	29	by	by	ADP
cana-681	18	30	comprehensive	comprehensive	ADJ
cana-681	18	31	computational	computational	ADJ
cana-681	18	32	modeling	modeling	NOUN
cana-681	18	33	[	[	X
cana-681	18	34	18	18	NUM
cana-681	18	35	]	]	PUNCT
cana-681	18	36	.	.	PUNCT
cana-681	19	1	furthermore	furthermore	ADV
cana-681	19	2	,	,	PUNCT
cana-681	19	3	chen	chen	PROPN
cana-681	19	4	et	et	PROPN
cana-681	19	5	al	al	PROPN
cana-681	19	6	.	.	PROPN
cana-681	19	7	demonstrated	demonstrate	VERB
cana-681	19	8	a	a	DET
cana-681	19	9	novel	novel	ADJ
cana-681	19	10	algebraic	algebraic	ADJ
cana-681	19	11	decoding	decode	VERB
cana-681	19	12	technique	technique	NOUN
cana-681	19	13	for	for	ADP
cana-681	19	14	the	the	DET
cana-681	19	15	(	(	PUNCT
cana-681	19	16	73,37,13	73,37,13	NUM
cana-681	19	17	)	)	PUNCT
cana-681	19	18	binary	binary	ADJ
cana-681	19	19	quadratic	quadratic	ADJ
cana-681	19	20	residue	residue	NOUN
cana-681	19	21	code	code	NOUN
cana-681	19	22	in	in	ADP
cana-681	19	23	[	[	X
cana-681	19	24	1	1	NUM
cana-681	19	25	]	]	PUNCT
cana-681	19	26	.	.	PUNCT
cana-681	20	1	lin	lin	PROPN
cana-681	20	2	et	et	PROPN
cana-681	20	3	al	al	PROPN
cana-681	20	4	.	.	PROPN
cana-681	20	5	developed	develop	VERB
cana-681	20	6	an	an	DET
cana-681	20	7	amended	amend	VERB
cana-681	20	8	decoding	decoding	NOUN
cana-681	20	9	method	method	NOUN
cana-681	20	10	specifically	specifically	ADV
cana-681	20	11	tailored	tailor	VERB
cana-681	20	12	for	for	ADP
cana-681	20	13	decoding	decode	VERB
cana-681	20	14	the	the	DET
cana-681	20	15	(	(	PUNCT
cana-681	20	16	48,24,12	48,24,12	NUM
cana-681	20	17	)	)	PUNCT
cana-681	20	18	extended	extend	VERB
cana-681	20	19	binary	binary	PROPN
cana-681	20	20	qr	qr	PROPN
cana-681	20	21	code	code	PROPN
cana-681	20	22	.	.	PUNCT
cana-681	21	1	this	this	DET
cana-681	21	2	method	method	NOUN
cana-681	21	3	enables	enable	VERB
cana-681	21	4	the	the	DET
cana-681	21	5	correction	correction	NOUN
cana-681	21	6	of	of	ADP
cana-681	21	7	up	up	ADP
cana-681	21	8	to	to	PART
cana-681	21	9	six	six	NUM
cana-681	21	10	errors	error	NOUN
cana-681	21	11	,	,	PUNCT
cana-681	21	12	leveraging	leverage	VERB
cana-681	21	13	the	the	DET
cana-681	21	14	reliability	reliability	NOUN
cana-681	21	15	-	-	PUNCT
cana-681	21	16	search	search	NOUN
cana-681	21	17	algorithm	algorithm	NOUN
cana-681	21	18	proposed	propose	VERB
cana-681	21	19	by	by	ADP
cana-681	21	20	dubney	dubney	PROPN
cana-681	21	21	et	et	PROPN
cana-681	21	22	al	al	PROPN
cana-681	21	23	.	.	PUNCT
cana-681	22	1	[	[	X
cana-681	22	2	16	16	NUM
cana-681	22	3	]	]	PUNCT
cana-681	22	4	.	.	PUNCT
cana-681	22	5	utilizing	utilize	VERB
cana-681	22	6	newton	newton	PROPN
cana-681	22	7	’s	’s	PART
cana-681	22	8	identities	identity	NOUN
cana-681	22	9	,	,	PUNCT
cana-681	22	10	the	the	DET
cana-681	22	11	coefficients	coefficient	NOUN
cana-681	22	12	of	of	ADP
cana-681	22	13	the	the	DET
cana-681	22	14	error	error	NOUN
cana-681	22	15	locator	locator	NOUN
cana-681	22	16	polynomial	polynomial	NOUN
cana-681	22	17	are	be	AUX
cana-681	22	18	determined	determine	VERB
cana-681	22	19	,	,	PUNCT
cana-681	22	20	facilitating	facilitate	VERB
cana-681	22	21	the	the	DET
cana-681	22	22	creation	creation	NOUN
cana-681	22	23	of	of	ADP
cana-681	22	24	a	a	DET
cana-681	22	25	decoding	decode	VERB
cana-681	22	26	method	method	NOUN
cana-681	22	27	aimed	aim	VERB
cana-681	22	28	at	at	ADP
cana-681	22	29	reducing	reduce	VERB
cana-681	22	30	decoding	decode	VERB
cana-681	22	31	time	time	NOUN
cana-681	22	32	[	[	X
cana-681	22	33	15	15	NUM
cana-681	22	34	]	]	PUNCT
cana-681	22	35	.	.	PUNCT
cana-681	23	1	additionally	additionally	ADV
cana-681	23	2	,	,	PUNCT
cana-681	23	3	various	various	ADJ
cana-681	23	4	enhanced	enhance	VERB
cana-681	23	5	communications	communication	NOUN
cana-681	23	6	on	on	ADP
cana-681	23	7	applied	apply	VERB
cana-681	23	8	nonlinear	nonlinear	ADJ
cana-681	23	9	analysis	analysis	NOUN
cana-681	23	10	issn	issn	NOUN
cana-681	23	11	:	:	PUNCT
cana-681	23	12	1074	1074	NUM
cana-681	23	13	-	-	PUNCT
cana-681	23	14	133x	133x	NUM
cana-681	23	15	vol	vol	NOUN
cana-681	23	16	31	31	NUM
cana-681	23	17	no	no	NOUN
cana-681	23	18	.	.	PUNCT
cana-681	24	1	2s	2s	NUM
cana-681	24	2	(	(	PUNCT
cana-681	24	3	2024	2024	NUM
cana-681	24	4	)	)	PUNCT
cana-681	24	5	620	620	NUM
cana-681	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	24	7	decoding	decode	VERB
cana-681	24	8	techniques	technique	NOUN
cana-681	24	9	for	for	ADP
cana-681	24	10	11	11	NUM
cana-681	24	11	qr	qr	NOUN
cana-681	24	12	codes	code	NOUN
cana-681	24	13	have	have	AUX
cana-681	24	14	been	be	AUX
cana-681	24	15	introduced	introduce	VERB
cana-681	24	16	through	through	ADP
cana-681	24	17	grobner	grobner	NOUN
cana-681	24	18	foundation	foundation	PROPN
cana-681	24	19	techniques	technique	NOUN
cana-681	24	20	[	[	X
cana-681	24	21	5	5	NUM
cana-681	24	22	]	]	PUNCT
cana-681	24	23	.	.	PUNCT
cana-681	25	1	ah.p	ah.p	PROPN
cana-681	25	2	.	.	PUNCT
cana-681	26	1	lee	lee	PROPN
cana-681	26	2	and	and	CCONJ
cana-681	26	3	h.c	h.c	PROPN
cana-681	26	4	.	.	PUNCT
cana-681	26	5	chang	chang	PROPN
cana-681	26	6	enhanced	enhance	VERB
cana-681	26	7	an	an	DET
cana-681	26	8	algebraic	algebraic	ADJ
cana-681	26	9	decoding	decode	VERB
cana-681	26	10	algorithm	algorithm	NOUN
cana-681	26	11	(	(	PUNCT
cana-681	26	12	ada	ada	PROPN
cana-681	26	13	)	)	PUNCT
cana-681	26	14	to	to	PART
cana-681	26	15	effectively	effectively	ADV
cana-681	26	16	decode	decode	VERB
cana-681	26	17	up	up	ADP
cana-681	26	18	to	to	PART
cana-681	26	19	five	five	NUM
cana-681	26	20	errors	error	NOUN
cana-681	26	21	in	in	ADP
cana-681	26	22	binary	binary	PROPN
cana-681	26	23	systematic	systematic	PROPN
cana-681	26	24	qr	qr	PROPN
cana-681	26	25	codes	code	NOUN
cana-681	26	26	[	[	X
cana-681	26	27	3	3	NUM
cana-681	26	28	]	]	PUNCT
cana-681	26	29	.	.	PUNCT
cana-681	27	1	additionally	additionally	ADV
cana-681	27	2	,	,	PUNCT
cana-681	27	3	the	the	DET
cana-681	27	4	author	author	NOUN
cana-681	27	5	proposed	propose	VERB
cana-681	27	6	a	a	DET
cana-681	27	7	hybrid	hybrid	ADJ
cana-681	27	8	algebraic	algebraic	ADJ
cana-681	27	9	decoding	decode	VERB
cana-681	27	10	algorithm	algorithm	NOUN
cana-681	27	11	tailored	tailor	VERB
cana-681	27	12	to	to	ADP
cana-681	27	13	the	the	DET
cana-681	27	14	specified	specified	ADJ
cana-681	27	15	parameters	parameter	NOUN
cana-681	27	16	.	.	PUNCT
cana-681	28	1	in	in	ADP
cana-681	28	2	cases	case	NOUN
cana-681	28	3	where	where	SCONJ
cana-681	28	4	the	the	DET
cana-681	28	5	total	total	ADJ
cana-681	28	6	number	number	NOUN
cana-681	28	7	of	of	ADP
cana-681	28	8	errors	error	NOUN
cana-681	28	9	v	v	NOUN
cana-681	28	10	is	be	AUX
cana-681	28	11	five	five	NUM
cana-681	28	12	or	or	CCONJ
cana-681	28	13	fewer	few	ADJ
cana-681	28	14	,	,	PUNCT
cana-681	28	15	the	the	DET
cana-681	28	16	laplace	laplace	NOUN
cana-681	28	17	formula	formula	NOUN
cana-681	28	18	was	be	AUX
cana-681	28	19	utilized	utilize	VERB
cana-681	28	20	to	to	PART
cana-681	28	21	derive	derive	VERB
cana-681	28	22	the	the	DET
cana-681	28	23	primary	primary	ADJ
cana-681	28	24	unknown	unknown	ADJ
cana-681	28	25	syndromes	syndrome	NOUN
cana-681	28	26	.	.	PUNCT
cana-681	29	1	when	when	SCONJ
cana-681	29	2	v	v	NOUN
cana-681	29	3	6	6	NUM
cana-681	29	4	and	and	CCONJ
cana-681	29	5	gaussian	gaussian	ADJ
cana-681	29	6	elimination	elimination	NOUN
cana-681	29	7	is	be	AUX
cana-681	29	8	utilized	utilize	VERB
cana-681	29	9	to	to	PART
cana-681	29	10	figure	figure	VERB
cana-681	29	11	out	out	ADP
cana-681	29	12	the	the	DET
cana-681	29	13	unknown	unknown	ADJ
cana-681	29	14	syndromes	syndrome	NOUN
cana-681	30	1	[	[	X
cana-681	30	2	6	6	NUM
cana-681	30	3	]	]	PUNCT
cana-681	30	4	.	.	PUNCT
cana-681	31	1	truong	truong	PROPN
cana-681	31	2	et	et	PROPN
cana-681	31	3	al	al	PROPN
cana-681	31	4	.	.	PROPN
cana-681	31	5	devised	devise	VERB
cana-681	31	6	a	a	DET
cana-681	31	7	method	method	NOUN
cana-681	31	8	to	to	PART
cana-681	31	9	compute	compute	VERB
cana-681	31	10	unknown	unknown	ADJ
cana-681	31	11	syndromes	syndrome	NOUN
cana-681	31	12	for	for	ADP
cana-681	31	13	the	the	DET
cana-681	31	14	(	(	PUNCT
cana-681	31	15	73,37,13	73,37,13	NUM
cana-681	31	16	)	)	PUNCT
cana-681	31	17	qr	qr	NOUN
cana-681	31	18	code	code	PROPN
cana-681	31	19	,	,	PUNCT
cana-681	31	20	with	with	ADP
cana-681	31	21	a	a	DET
cana-681	31	22	focus	focus	NOUN
cana-681	31	23	on	on	ADP
cana-681	31	24	enhancing	enhance	VERB
cana-681	31	25	decoding	decode	VERB
cana-681	31	26	performance	performance	NOUN
cana-681	31	27	using	use	VERB
cana-681	31	28	soft	soft	ADJ
cana-681	31	29	decisions	decision	NOUN
cana-681	31	30	.	.	PUNCT
cana-681	32	1	a	a	DET
cana-681	32	2	comprehensive	comprehensive	ADJ
cana-681	32	3	study	study	NOUN
cana-681	32	4	was	be	AUX
cana-681	32	5	conducted	conduct	VERB
cana-681	32	6	to	to	PART
cana-681	32	7	evaluate	evaluate	VERB
cana-681	32	8	error	error	NOUN
cana-681	32	9	-	-	PUNCT
cana-681	32	10	rate	rate	NOUN
cana-681	32	11	performance	performance	NOUN
cana-681	32	12	[	[	X
cana-681	32	13	4	4	NUM
cana-681	32	14	]	]	PUNCT
cana-681	32	15	.	.	PUNCT
cana-681	33	1	furthermore	furthermore	ADV
cana-681	33	2	,	,	PUNCT
cana-681	33	3	the	the	DET
cana-681	33	4	author	author	NOUN
cana-681	33	5	elaborated	elaborate	VERB
cana-681	33	6	on	on	ADP
cana-681	33	7	numerous	numerous	ADJ
cana-681	33	8	decoding	decode	VERB
cana-681	33	9	algorithm	algorithm	NOUN
cana-681	33	10	techniques	technique	NOUN
cana-681	33	11	and	and	CCONJ
cana-681	33	12	error	error	NOUN
cana-681	33	13	correction	correction	NOUN
cana-681	33	14	coding	code	VERB
cana-681	33	15	utilizing	utilize	VERB
cana-681	33	16	a	a	DET
cana-681	33	17	mathematical	mathematical	ADJ
cana-681	33	18	approach	approach	NOUN
cana-681	33	19	[	[	X
cana-681	33	20	14	14	NUM
cana-681	33	21	]	]	PUNCT
cana-681	33	22	.	.	PUNCT
cana-681	34	1	in	in	ADP
cana-681	34	2	a	a	DET
cana-681	34	3	separate	separate	ADJ
cana-681	34	4	study	study	NOUN
cana-681	34	5	,	,	PUNCT
cana-681	34	6	zhang	zhang	PROPN
cana-681	34	7	et	et	PROPN
cana-681	34	8	al	al	PROPN
cana-681	34	9	.	.	PROPN
cana-681	34	10	researched	research	VERB
cana-681	34	11	a	a	DET
cana-681	34	12	hard	hard	ADJ
cana-681	34	13	decision	decision	NOUN
cana-681	34	14	(	(	PUNCT
cana-681	34	15	hd	hd	NOUN
cana-681	34	16	)	)	PUNCT
cana-681	34	17	strategy	strategy	NOUN
cana-681	34	18	to	to	PART
cana-681	34	19	correct	correct	VERB
cana-681	34	20	up	up	ADP
cana-681	34	21	to	to	PART
cana-681	34	22	five	five	NUM
cana-681	34	23	errors	error	NOUN
cana-681	34	24	and	and	CCONJ
cana-681	34	25	decode	decode	VERB
cana-681	34	26	the	the	DET
cana-681	34	27	(	(	PUNCT
cana-681	34	28	47,24,11	47,24,11	NOUN
cana-681	34	29	)	)	PUNCT
cana-681	34	30	qr	qr	NOUN
cana-681	34	31	code	code	VERB
cana-681	34	32	more	more	ADV
cana-681	34	33	efficiently	efficiently	ADV
cana-681	35	1	[	[	X
cana-681	35	2	9	9	NUM
cana-681	35	3	]	]	PUNCT
cana-681	35	4	.	.	PUNCT
cana-681	36	1	through	through	ADP
cana-681	36	2	simulation	simulation	NOUN
cana-681	36	3	results	result	NOUN
cana-681	36	4	,	,	PUNCT
cana-681	36	5	zhang	zhang	PROPN
cana-681	36	6	et	et	PROPN
cana-681	36	7	al	al	PROPN
cana-681	36	8	.	.	PROPN
cana-681	36	9	demonstrated	demonstrate	VERB
cana-681	36	10	that	that	SCONJ
cana-681	36	11	the	the	DET
cana-681	36	12	new	new	ADJ
cana-681	36	13	hd	hd	NOUN
cana-681	36	14	algorithm	algorithm	NOUN
cana-681	36	15	reduces	reduce	VERB
cana-681	36	16	decoding	decode	VERB
cana-681	36	17	complexity	complexity	NOUN
cana-681	36	18	and	and	CCONJ
cana-681	36	19	conserves	conserve	VERB
cana-681	36	20	memory	memory	NOUN
cana-681	36	21	while	while	SCONJ
cana-681	36	22	maintaining	maintain	VERB
cana-681	36	23	the	the	DET
cana-681	36	24	same	same	ADJ
cana-681	36	25	error	error	NOUN
cana-681	36	26	-	-	PUNCT
cana-681	36	27	rate	rate	NOUN
cana-681	36	28	performance	performance	NOUN
cana-681	36	29	[	[	X
cana-681	36	30	19	19	NUM
cana-681	36	31	]	]	PUNCT
cana-681	36	32	.	.	PUNCT
cana-681	37	1	in	in	ADP
cana-681	37	2	this	this	DET
cana-681	37	3	paper	paper	NOUN
cana-681	37	4	,	,	PUNCT
cana-681	37	5	section	section	NOUN
cana-681	37	6	1	1	NUM
cana-681	37	7	contains	contain	VERB
cana-681	37	8	the	the	DET
cana-681	37	9	introduction	introduction	NOUN
cana-681	37	10	and	and	CCONJ
cana-681	37	11	section	section	NOUN
cana-681	37	12	2	2	NUM
cana-681	37	13	carry	carry	VERB
cana-681	37	14	preliminaries	preliminary	NOUN
cana-681	37	15	.	.	PUNCT
cana-681	38	1	in	in	ADP
cana-681	38	2	section	section	NOUN
cana-681	38	3	3	3	NUM
cana-681	38	4	,	,	PUNCT
cana-681	38	5	the	the	DET
cana-681	38	6	background	background	NOUN
cana-681	38	7	of	of	ADP
cana-681	38	8	the	the	DET
cana-681	38	9	qr	qr	PROPN
cana-681	38	10	code	code	NOUN
cana-681	38	11	is	be	AUX
cana-681	38	12	discussed	discuss	VERB
cana-681	38	13	.	.	PUNCT
cana-681	39	1	the	the	DET
cana-681	39	2	decoding	decode	VERB
cana-681	39	3	algorithm	algorithm	NOUN
cana-681	39	4	for	for	ADP
cana-681	39	5	the	the	DET
cana-681	39	6	(	(	PUNCT
cana-681	39	7	57,29,17	57,29,17	NUM
cana-681	39	8	)	)	PUNCT
cana-681	39	9	and	and	CCONJ
cana-681	39	10	the	the	DET
cana-681	39	11	unknown	unknown	ADJ
cana-681	39	12	syndromes	syndrome	NOUN
cana-681	39	13	are	be	AUX
cana-681	39	14	determined	determine	VERB
cana-681	39	15	in	in	ADP
cana-681	39	16	section	section	NOUN
cana-681	39	17	4	4	NUM
cana-681	39	18	.	.	PUNCT
cana-681	39	19	section	section	NOUN
cana-681	39	20	5	5	NUM
cana-681	39	21	contains	contain	VERB
cana-681	39	22	the	the	DET
cana-681	39	23	application	application	NOUN
cana-681	39	24	of	of	ADP
cana-681	39	25	the	the	DET
cana-681	39	26	algorithm	algorithm	NOUN
cana-681	39	27	and	and	CCONJ
cana-681	39	28	finally	finally	ADV
cana-681	39	29	,	,	PUNCT
cana-681	39	30	the	the	DET
cana-681	39	31	conclusion	conclusion	NOUN
cana-681	39	32	for	for	ADP
cana-681	39	33	this	this	DET
cana-681	39	34	paper	paper	NOUN
cana-681	39	35	is	be	AUX
cana-681	39	36	given	give	VERB
cana-681	39	37	in	in	ADP
cana-681	39	38	section	section	NOUN
cana-681	39	39	6	6	NUM
cana-681	39	40	.	.	NOUN
cana-681	39	41	2	2	NUM
cana-681	39	42	.	.	X
cana-681	39	43	preliminaries	preliminary	NOUN
cana-681	39	44	we	we	PRON
cana-681	39	45	will	will	AUX
cana-681	39	46	step	step	VERB
cana-681	39	47	over	over	ADP
cana-681	39	48	some	some	DET
cana-681	39	49	fundamental	fundamental	ADJ
cana-681	39	50	definitions	definition	NOUN
cana-681	39	51	in	in	ADP
cana-681	39	52	this	this	DET
cana-681	39	53	section	section	NOUN
cana-681	39	54	that	that	PRON
cana-681	39	55	are	be	AUX
cana-681	39	56	related	relate	VERB
cana-681	39	57	to	to	ADP
cana-681	39	58	our	our	PRON
cana-681	39	59	main	main	ADJ
cana-681	39	60	concept	concept	NOUN
cana-681	39	61	.	.	PUNCT
cana-681	40	1	definition	definition	NOUN
cana-681	40	2	2.1	2.1	NUM
cana-681	40	3	.	.	PUNCT
cana-681	41	1	[	[	X
cana-681	41	2	14	14	NUM
cana-681	41	3	]	]	X
cana-681	41	4	an	an	DET
cana-681	41	5	(	(	PUNCT
cana-681	41	6	𝑛	𝑛	PROPN
cana-681	41	7	,	,	PUNCT
cana-681	41	8	𝑘	𝑘	NOUN
cana-681	41	9	)	)	PUNCT
cana-681	41	10	block	block	NOUN
cana-681	41	11	code	code	PROPN
cana-681	41	12	𝐶	𝐶	PROPN
cana-681	41	13	is	be	AUX
cana-681	41	14	said	say	VERB
cana-681	41	15	to	to	PART
cana-681	41	16	be	be	AUX
cana-681	41	17	𝑐𝑦𝑐𝑙𝑖𝑐	𝑐𝑦𝑐𝑙𝑖𝑐	ADJ
cana-681	41	18	if	if	SCONJ
cana-681	41	19	it	it	PRON
cana-681	41	20	is	be	AUX
cana-681	41	21	linear	linear	ADJ
cana-681	41	22	and	and	CCONJ
cana-681	41	23	if	if	SCONJ
cana-681	41	24	every	every	DET
cana-681	41	25	codeword	codeword	NOUN
cana-681	41	26	𝑐	𝑐	NOUN
cana-681	41	27	=	=	SYM
cana-681	41	28	(	(	PUNCT
cana-681	41	29	𝑐0	𝑐0	NOUN
cana-681	41	30	,	,	PUNCT
cana-681	41	31	𝑐1	𝑐1	NOUN
cana-681	41	32	,	,	PUNCT
cana-681	41	33	…	…	PUNCT
cana-681	41	34	.	.	PUNCT
cana-681	42	1	𝑐𝑛−1	𝑐𝑛−1	NOUN
cana-681	42	2	)	)	PUNCT
cana-681	42	3	in	in	ADP
cana-681	42	4	𝐶	𝐶	PROPN
cana-681	42	5	,	,	PUNCT
cana-681	42	6	its	its	PRON
cana-681	42	7	right	right	ADJ
cana-681	42	8	cyclic	cyclic	ADJ
cana-681	42	9	shift	shift	NOUN
cana-681	42	10	𝑐	𝑐	NOUN
cana-681	42	11	,	,	PUNCT
cana-681	42	12	=	=	PRON
cana-681	42	13	(	(	PUNCT
cana-681	42	14	𝑐𝑛−1	𝑐𝑛−1	PROPN
cana-681	42	15	,	,	PUNCT
cana-681	42	16	𝑐0	𝑐0	PROPN
cana-681	42	17	,	,	PUNCT
cana-681	42	18	…	…	PUNCT
cana-681	42	19	,	,	PUNCT
cana-681	42	20	𝑐𝑛−2	𝑐𝑛−2	NOUN
cana-681	42	21	)	)	PUNCT
cana-681	42	22	is	be	AUX
cana-681	42	23	also	also	ADV
cana-681	42	24	in	in	ADP
cana-681	42	25	c.	c.	PROPN
cana-681	42	26	definition	definition	NOUN
cana-681	42	27	2.2	2.2	NUM
cana-681	42	28	.	.	PUNCT
cana-681	43	1	[	[	X
cana-681	43	2	7	7	X
cana-681	43	3	]	]	PUNCT
cana-681	43	4	let	let	VERB
cana-681	43	5	𝐺𝐹(𝑙)[𝑥	𝐺𝐹(𝑙)[𝑥	NOUN
cana-681	43	6	]	]	X
cana-681	43	7	/	/	SYM
cana-681	43	8	(	(	PUNCT
cana-681	43	9	𝑥𝑝	𝑥𝑝	ADV
cana-681	43	10	−	−	NOUN
cana-681	43	11	1	1	X
cana-681	43	12	)	)	PUNCT
cana-681	43	13	be	be	AUX
cana-681	43	14	a	a	DET
cana-681	43	15	ring	ring	NOUN
cana-681	43	16	,	,	PUNCT
cana-681	43	17	where	where	SCONJ
cana-681	43	18	a	a	DET
cana-681	43	19	prime	prime	ADJ
cana-681	43	20	number	number	NOUN
cana-681	43	21	is	be	AUX
cana-681	43	22	p	p	NOUN
cana-681	43	23	and	and	CCONJ
cana-681	43	24	the	the	DET
cana-681	43	25	quadratic	quadratic	ADJ
cana-681	43	26	residue	residue	NOUN
cana-681	43	27	of	of	ADP
cana-681	43	28	𝑝	𝑝	PROPN
cana-681	43	29	is	be	AUX
cana-681	43	30	𝑙	𝑙	NUM
cana-681	43	31	,	,	PUNCT
cana-681	43	32	(	(	PUNCT
cana-681	43	33	𝑥𝑝	𝑥𝑝	ADV
cana-681	43	34	−	−	NOUN
cana-681	43	35	1	1	X
cana-681	43	36	)	)	PUNCT
cana-681	43	37	=	=	SYM
cana-681	43	38	(	(	PUNCT
cana-681	44	1	𝑥	𝑥	NOUN
cana-681	44	2	−	−	PROPN
cana-681	44	3	1)𝑞(𝑥)𝑛(𝑥	1)𝑞(𝑥)𝑛(𝑥	NUM
cana-681	44	4	)	)	PUNCT
cana-681	44	5	.	.	PUNCT
cana-681	45	1	define	define	VERB
cana-681	45	2	the	the	DET
cana-681	45	3	set	set	NOUN
cana-681	45	4	of	of	ADP
cana-681	45	5	quadratic	quadratic	ADJ
cana-681	45	6	residues	residue	NOUN
cana-681	45	7	modulo	modulo	VERB
cana-681	45	8	𝑝	𝑝	NOUN
cana-681	45	9	by	by	ADP
cana-681	45	10	𝑄𝑝	𝑄𝑝	PROPN
cana-681	45	11	,	,	PUNCT
cana-681	45	12	and	and	CCONJ
cana-681	45	13	the	the	DET
cana-681	45	14	set	set	NOUN
cana-681	45	15	of	of	ADP
cana-681	45	16	quadratic	quadratic	ADJ
cana-681	45	17	non	non	NOUN
cana-681	45	18	-	-	NOUN
cana-681	45	19	residues	residue	NOUN
cana-681	45	20	by	by	ADP
cana-681	45	21	𝑁𝑝	𝑁𝑝	NOUN
cana-681	45	22	,	,	PUNCT
cana-681	45	23	𝑄	𝑄	PROPN
cana-681	45	24	,	,	PUNCT
cana-681	45	25	𝑄	𝑄	PROPN
cana-681	45	26	,	,	PUNCT
cana-681	45	27	,	,	PUNCT
cana-681	45	28	𝑁	𝑁	PROPN
cana-681	45	29	and	and	CCONJ
cana-681	45	30	𝑁′are	𝑁′are	VERB
cana-681	45	31	quadratic	quadratic	ADJ
cana-681	45	32	residue	residue	NOUN
cana-681	45	33	codes	code	NOUN
cana-681	45	34	,	,	PUNCT
cana-681	45	35	which	which	PRON
cana-681	45	36	are	be	AUX
cana-681	45	37	cyclic	cyclic	ADJ
cana-681	45	38	cod	cod	NOUN
cana-681	45	39	es	es	X
cana-681	45	40	(	(	PUNCT
cana-681	45	41	or	or	CCONJ
cana-681	45	42	ideals	ideal	NOUN
cana-681	45	43	)	)	PUNCT
cana-681	45	44	of	of	ADP
cana-681	45	45	the	the	DET
cana-681	45	46	ring	ring	NOUN
cana-681	45	47	with	with	ADP
cana-681	45	48	generator	generator	NOUN
cana-681	45	49	polynomials	polynomial	NOUN
cana-681	45	50	of	of	ADP
cana-681	45	51	𝑞(𝑥	𝑞(𝑥	PROPN
cana-681	45	52	)	)	PUNCT
cana-681	45	53	,	,	PUNCT
cana-681	45	54	(	(	PUNCT
cana-681	45	55	𝑥	𝑥	NOUN
cana-681	45	56	−	−	PROPN
cana-681	45	57	1)𝑞(𝑥	1)𝑞(𝑥	NUM
cana-681	45	58	)	)	PUNCT
cana-681	45	59	,	,	PUNCT
cana-681	45	60	𝑛(𝑥	𝑛(𝑥	PROPN
cana-681	45	61	)	)	PUNCT
cana-681	45	62	,	,	PUNCT
cana-681	45	63	(	(	PUNCT
cana-681	45	64	𝑥	𝑥	NOUN
cana-681	45	65	−	−	NUM
cana-681	45	66	1)𝑛(𝑥	1)𝑛(𝑥	NUM
cana-681	45	67	)	)	PUNCT
cana-681	45	68	,	,	PUNCT
cana-681	45	69	so	so	ADV
cana-681	45	70	forth	forth	ADV
cana-681	45	71	,	,	PUNCT
cana-681	45	72	where	where	SCONJ
cana-681	45	73	𝑞(𝑥	𝑞(𝑥	NOUN
cana-681	45	74	)	)	PUNCT
cana-681	46	1	=	=	SYM
cana-681	46	2	∏	∏	PROPN
cana-681	46	3	(	(	PUNCT
cana-681	46	4	𝑥	𝑥	NOUN
cana-681	46	5	−	−	X
cana-681	46	6	𝛼𝑖)𝑖∈𝑄𝑝	𝛼𝑖)𝑖∈𝑄𝑝	PROPN
cana-681	46	7	,	,	PUNCT
cana-681	46	8	𝑞(𝑥	𝑞(𝑥	PROPN
cana-681	46	9	)	)	PUNCT
cana-681	46	10	=	=	SYM
cana-681	46	11	∏	∏	PROPN
cana-681	46	12	(	(	PUNCT
cana-681	46	13	𝑥	𝑥	NOUN
cana-681	46	14	−	−	PROPN
cana-681	47	1	𝛼𝑖)𝑖∈𝑄𝑝	𝛼𝑖)𝑖∈𝑄𝑝	PROPN
cana-681	47	2	have	have	VERB
cana-681	47	3	coefficients	coefficient	NOUN
cana-681	47	4	from	from	ADP
cana-681	47	5	gf(l	gf(l	NOUN
cana-681	47	6	)	)	PUNCT
cana-681	47	7	.	.	PUNCT
cana-681	48	1	in	in	ADP
cana-681	48	2	a	a	DET
cana-681	48	3	field	field	NOUN
cana-681	48	4	that	that	PRON
cana-681	48	5	contains	contain	VERB
cana-681	48	6	gf(l	gf(l	NOUN
cana-681	48	7	)	)	PUNCT
cana-681	48	8	,	,	PUNCT
cana-681	48	9	α	α	PRON
cana-681	48	10	represents	represent	VERB
cana-681	48	11	a	a	DET
cana-681	48	12	primitive	primitive	ADJ
cana-681	48	13	𝑝𝑡ℎ	𝑝𝑡ℎ	NOUN
cana-681	48	14	root	root	NOUN
cana-681	48	15	of	of	ADP
cana-681	48	16	unity	unity	NOUN
cana-681	48	17	.	.	PUNCT
cana-681	49	1	definition	definition	NOUN
cana-681	49	2	2.3	2.3	NUM
cana-681	49	3	.	.	PUNCT
cana-681	50	1	[	[	X
cana-681	50	2	14	14	NUM
cana-681	50	3	]	]	X
cana-681	50	4	an	an	DET
cana-681	50	5	(	(	PUNCT
cana-681	50	6	n	n	X
cana-681	50	7	,	,	PUNCT
cana-681	50	8	k	k	NOUN
cana-681	50	9	)	)	PUNCT
cana-681	50	10	cyclic	cyclic	ADJ
cana-681	50	11	code	code	NOUN
cana-681	50	12	has	have	VERB
cana-681	50	13	a	a	DET
cana-681	50	14	unique	unique	ADJ
cana-681	50	15	minimal	minimal	ADJ
cana-681	50	16	monic	monic	ADJ
cana-681	50	17	polynomial	polynomial	NOUN
cana-681	50	18	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	50	19	)	)	PUNCT
cana-681	50	20	,	,	PUNCT
cana-681	50	21	which	which	PRON
cana-681	50	22	is	be	AUX
cana-681	50	23	the	the	DET
cana-681	50	24	generator	generator	NOUN
cana-681	50	25	of	of	ADP
cana-681	50	26	the	the	DET
cana-681	50	27	ideal	ideal	NOUN
cana-681	50	28	.	.	PUNCT
cana-681	51	1	this	this	PRON
cana-681	51	2	is	be	AUX
cana-681	51	3	called	call	VERB
cana-681	51	4	the	the	DET
cana-681	51	5	generator	generator	NOUN
cana-681	51	6	polynomial	polynomial	NOUN
cana-681	51	7	for	for	ADP
cana-681	51	8	the	the	DET
cana-681	51	9	code	code	NOUN
cana-681	51	10	.	.	PUNCT
cana-681	52	1	let	let	VERB
cana-681	52	2	the	the	DET
cana-681	52	3	degree	degree	NOUN
cana-681	52	4	of	of	ADP
cana-681	52	5	𝑔	𝑔	PROPN
cana-681	52	6	be	be	AUX
cana-681	52	7	𝑛	𝑛	PRON
cana-681	52	8	–	–	PUNCT
cana-681	52	9	𝑘	𝑘	NOUN
cana-681	52	10	,	,	PUNCT
cana-681	52	11	𝑔(𝑥	𝑔(𝑥	NUM
cana-681	52	12	)	)	PUNCT
cana-681	53	1	=	=	PUNCT
cana-681	53	2	𝑔0	𝑔0	NOUN
cana-681	53	3	+	+	CCONJ
cana-681	53	4	𝑔1𝑥	𝑔1𝑥	NOUN
cana-681	53	5	+	+	ADJ
cana-681	53	6	⋯+	⋯+	NOUN
cana-681	53	7	𝑔𝑛−𝑘𝑥	𝑔𝑛−𝑘𝑥	NOUN
cana-681	53	8	𝑛−𝑘.	𝑛−𝑘.	VERB
cana-681	53	9	communications	communication	NOUN
cana-681	53	10	on	on	ADP
cana-681	53	11	applied	apply	VERB
cana-681	53	12	nonlinear	nonlinear	ADJ
cana-681	53	13	analysis	analysis	NOUN
cana-681	53	14	issn	issn	NOUN
cana-681	53	15	:	:	PUNCT
cana-681	53	16	1074	1074	NUM
cana-681	53	17	-	-	PUNCT
cana-681	53	18	133x	133x	NUM
cana-681	53	19	vol	vol	NOUN
cana-681	53	20	31	31	NUM
cana-681	53	21	no	no	NOUN
cana-681	53	22	.	.	PUNCT
cana-681	54	1	2s	2s	NUM
cana-681	54	2	(	(	PUNCT
cana-681	54	3	2024	2024	NUM
cana-681	54	4	)	)	PUNCT
cana-681	54	5	621	621	NUM
cana-681	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	54	7	definition	definition	NOUN
cana-681	54	8	2.4	2.4	NUM
cana-681	54	9	.	.	PUNCT
cana-681	55	1	[	[	X
cana-681	55	2	14	14	NUM
cana-681	55	3	]	]	PUNCT
cana-681	55	4	an	an	DET
cana-681	55	5	irreducible	irreducible	ADJ
cana-681	55	6	polynomial	polynomial	ADJ
cana-681	55	7	𝑝(𝑥	𝑝(𝑥	NOUN
cana-681	55	8	)	)	PUNCT
cana-681	55	9	∈	∈	PROPN
cana-681	55	10	𝐺𝐹(𝑝)[𝑥	𝐺𝐹(𝑝)[𝑥	PROPN
cana-681	55	11	]	]	PUNCT
cana-681	55	12	of	of	ADP
cana-681	55	13	degree	degree	NOUN
cana-681	55	14	𝑚	𝑚	PROPN
cana-681	55	15	is	be	AUX
cana-681	55	16	said	say	VERB
cana-681	55	17	to	to	PART
cana-681	55	18	be	be	AUX
cana-681	55	19	primitive	primitive	ADJ
cana-681	55	20	if	if	SCONJ
cana-681	55	21	the	the	DET
cana-681	55	22	smallest	small	ADJ
cana-681	55	23	positive	positive	ADJ
cana-681	55	24	integers	integer	NOUN
cana-681	55	25	𝑛	𝑛	VERB
cana-681	55	26	for	for	ADP
cana-681	55	27	which	which	PRON
cana-681	55	28	𝑝(𝑥	𝑝(𝑥	NOUN
cana-681	55	29	)	)	PUNCT
cana-681	55	30	divides	divide	VERB
cana-681	55	31	𝑥𝑛	𝑥𝑛	PROPN
cana-681	55	32	−	−	PROPN
cana-681	55	33	1	1	NUM
cana-681	55	34	is	be	AUX
cana-681	55	35	𝑛	𝑛	NOUN
cana-681	55	36	=	=	ADJ
cana-681	55	37	𝑝𝑚	𝑝𝑚	ADP
cana-681	55	38	−	−	NOUN
cana-681	55	39	1	1	NUM
cana-681	55	40	.	.	PUNCT
cana-681	56	1	definition	definition	NOUN
cana-681	56	2	2.5	2.5	NUM
cana-681	56	3	.	.	PUNCT
cana-681	57	1	[	[	X
cana-681	57	2	14	14	NUM
cana-681	57	3	]	]	PUNCT
cana-681	57	4	a	a	DET
cana-681	57	5	sequence	sequence	NOUN
cana-681	57	6	generated	generate	VERB
cana-681	57	7	by	by	ADP
cana-681	57	8	a	a	DET
cana-681	57	9	connection	connection	NOUN
cana-681	57	10	polynomial	polynomial	ADJ
cana-681	57	11	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	57	12	)	)	PUNCT
cana-681	57	13	of	of	ADP
cana-681	57	14	degree	degree	NOUN
cana-681	57	15	𝑛	𝑛	PROPN
cana-681	57	16	is	be	AUX
cana-681	57	17	said	say	VERB
cana-681	57	18	to	to	PART
cana-681	57	19	be	be	AUX
cana-681	57	20	a	a	DET
cana-681	57	21	maximal	maximal	ADJ
cana-681	57	22	length	length	NOUN
cana-681	57	23	sequence	sequence	NOUN
cana-681	57	24	if	if	SCONJ
cana-681	57	25	the	the	DET
cana-681	57	26	period	period	NOUN
cana-681	57	27	of	of	ADP
cana-681	57	28	the	the	DET
cana-681	57	29	sequence	sequence	NOUN
cana-681	57	30	is	be	AUX
cana-681	57	31	2𝑛	2𝑛	PROPN
cana-681	58	1	−	−	PROPN
cana-681	58	2	1	1	X
cana-681	58	3	.	.	PUNCT
cana-681	58	4	definition	definition	NOUN
cana-681	58	5	2.6	2.6	NUM
cana-681	58	6	.	.	PUNCT
cana-681	59	1	[	[	X
cana-681	59	2	14	14	NUM
cana-681	59	3	]	]	PUNCT
cana-681	59	4	a	a	DET
cana-681	59	5	connection	connection	NOUN
cana-681	59	6	polynomial	polynomial	NOUN
cana-681	59	7	which	which	PRON
cana-681	59	8	produces	produce	VERB
cana-681	59	9	a	a	DET
cana-681	59	10	maximallength	maximallength	NOUN
cana-681	59	11	sequence	sequence	NOUN
cana-681	59	12	is	be	AUX
cana-681	59	13	a	a	DET
cana-681	59	14	primitive	primitive	ADJ
cana-681	59	15	polynomial	polynomial	NOUN
cana-681	59	16	.	.	PUNCT
cana-681	60	1	3	3	X
cana-681	60	2	.	.	X
cana-681	60	3	non	non	ADJ
cana-681	60	4	-	-	ADJ
cana-681	60	5	binary	binary	ADJ
cana-681	60	6	(	(	PUNCT
cana-681	60	7	57,29,17	57,29,17	NUM
cana-681	60	8	)	)	PUNCT
cana-681	60	9	qr	qr	NOUN
cana-681	60	10	code	code	VERB
cana-681	60	11	the	the	DET
cana-681	60	12	(	(	PUNCT
cana-681	60	13	n	n	X
cana-681	60	14	,	,	PUNCT
cana-681	60	15	k	k	NOUN
cana-681	60	16	,	,	PUNCT
cana-681	60	17	d	d	X
cana-681	60	18	)	)	PUNCT
cana-681	60	19	parameters	parameter	NOUN
cana-681	60	20	provide	provide	VERB
cana-681	60	21	essential	essential	ADJ
cana-681	60	22	information	information	NOUN
cana-681	60	23	about	about	ADP
cana-681	60	24	the	the	DET
cana-681	60	25	capabilities	capability	NOUN
cana-681	60	26	and	and	CCONJ
cana-681	60	27	performance	performance	NOUN
cana-681	60	28	of	of	ADP
cana-681	60	29	error	error	NOUN
cana-681	60	30	-	-	PUNCT
cana-681	60	31	correcting	correct	VERB
cana-681	60	32	codes	code	NOUN
cana-681	60	33	,	,	PUNCT
cana-681	60	34	guiding	guide	VERB
cana-681	60	35	their	their	PRON
cana-681	60	36	design	design	NOUN
cana-681	60	37	,	,	PUNCT
cana-681	60	38	implementation	implementation	NOUN
cana-681	60	39	,	,	PUNCT
cana-681	60	40	and	and	CCONJ
cana-681	60	41	usage	usage	NOUN
cana-681	60	42	in	in	ADP
cana-681	60	43	various	various	ADJ
cana-681	60	44	communication	communication	NOUN
cana-681	60	45	and	and	CCONJ
cana-681	60	46	storage	storage	NOUN
cana-681	60	47	systems	system	NOUN
cana-681	60	48	.	.	PUNCT
cana-681	61	1	let	let	AUX
cana-681	61	2	(	(	PUNCT
cana-681	61	3	𝑛	𝑛	PROPN
cana-681	61	4	,	,	PUNCT
cana-681	61	5	𝑛+1	𝑛+1	ADP
cana-681	61	6	2	2	NUM
cana-681	61	7	,	,	PUNCT
cana-681	61	8	𝑑	𝑑	NOUN
cana-681	61	9	)	)	PUNCT
cana-681	61	10	represent	represent	VERB
cana-681	61	11	a	a	DET
cana-681	61	12	binary	binary	PROPN
cana-681	61	13	qr	qr	PROPN
cana-681	61	14	code	code	PROPN
cana-681	61	15	with	with	ADP
cana-681	61	16	generator	generator	NOUN
cana-681	61	17	polynomial	polynomial	ADJ
cana-681	61	18	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	61	19	)	)	PUNCT
cana-681	61	20	over	over	ADP
cana-681	61	21	𝐺𝐹(2	𝐺𝐹(2	PROPN
cana-681	61	22	)	)	PUNCT
cana-681	61	23	.	.	PUNCT
cana-681	62	1	the	the	DET
cana-681	62	2	code	code	PROPN
cana-681	62	3	length	length	NOUN
cana-681	62	4	𝑛	𝑛	PROPN
cana-681	62	5	,	,	PUNCT
cana-681	62	6	should	should	AUX
cana-681	62	7	be	be	AUX
cana-681	62	8	a	a	DET
cana-681	62	9	prime	prime	ADJ
cana-681	62	10	number	number	NOUN
cana-681	62	11	of	of	ADP
cana-681	62	12	the	the	DET
cana-681	62	13	form	form	NOUN
cana-681	62	14	𝑛	𝑛	NOUN
cana-681	62	15	=	=	SYM
cana-681	62	16	8𝑙	8𝑙	NUM
cana-681	62	17	±	±	NUM
cana-681	62	18	1	1	NUM
cana-681	62	19	,	,	PUNCT
cana-681	62	20	where	where	SCONJ
cana-681	62	21	𝑚	𝑚	PROPN
cana-681	62	22	is	be	AUX
cana-681	62	23	the	the	DET
cana-681	62	24	smallest	small	ADJ
cana-681	62	25	positive	positive	ADJ
cana-681	62	26	integer	integer	NOUN
cana-681	62	27	such	such	ADJ
cana-681	62	28	that	that	SCONJ
cana-681	62	29	𝑛	𝑛	PROPN
cana-681	62	30	divides	divide	VERB
cana-681	62	31	2𝑚	2𝑚	NOUN
cana-681	62	32	−	−	NOUN
cana-681	62	33	1	1	NUM
cana-681	62	34	and	and	CCONJ
cana-681	62	35	1	1	NUM
cana-681	62	36	is	be	AUX
cana-681	62	37	an	an	DET
cana-681	62	38	arbitrary	arbitrary	ADJ
cana-681	62	39	positive	positive	ADJ
cana-681	62	40	integer	integer	NOUN
cana-681	62	41	.	.	PUNCT
cana-681	63	1	the	the	DET
cana-681	63	2	set	set	ADJ
cana-681	63	3	𝑄	𝑄	PROPN
cana-681	63	4	of	of	ADP
cana-681	63	5	quadratic	quadratic	ADJ
cana-681	63	6	residue	residue	NOUN
cana-681	63	7	modulo	modulo	NOUN
cana-681	63	8	𝑛	𝑛	PRON
cana-681	63	9	is	be	AUX
cana-681	63	10	the	the	DET
cana-681	63	11	set	set	NOUN
cana-681	63	12	of	of	ADP
cana-681	63	13	nonzero	nonzero	PROPN
cana-681	63	14	squares	square	NOUN
cana-681	63	15	modulo	modulo	VERB
cana-681	63	16	𝑛	𝑛	ADP
cana-681	63	17	that	that	PRON
cana-681	63	18	is	is	ADV
cana-681	63	19	,	,	PUNCT
cana-681	63	20	𝑄𝑛	𝑄𝑛	PROPN
cana-681	63	21	=	=	SYM
cana-681	63	22	{	{	PUNCT
cana-681	63	23	𝑗|𝑗	𝑗|𝑗	NOUN
cana-681	63	24	≡	≡	PROPN
cana-681	63	25	𝑥	𝑥	ADP
cana-681	63	26	2	2	NUM
cana-681	63	27	𝑚𝑜𝑑	𝑚𝑜𝑑	NOUN
cana-681	63	28	𝑛	𝑛	NOUN
cana-681	63	29	,	,	PUNCT
cana-681	63	30	1	1	NUM
cana-681	63	31	≤	≤	NUM
cana-681	63	32	𝑥	𝑥	PRON
cana-681	63	33	≤	≤	NUM
cana-681	63	34	𝑛	𝑛	PRON
cana-681	63	35	−	−	PROPN
cana-681	63	36	1	1	NUM
cana-681	63	37	}	}	PUNCT
cana-681	63	38	(	(	PUNCT
cana-681	63	39	1	1	X
cana-681	63	40	)	)	PUNCT
cana-681	63	41	for	for	ADP
cana-681	63	42	the	the	DET
cana-681	63	43	binary	binary	ADJ
cana-681	63	44	(	(	PUNCT
cana-681	63	45	57	57	NUM
cana-681	63	46	,	,	PUNCT
cana-681	63	47	29	29	NUM
cana-681	63	48	,	,	PUNCT
cana-681	63	49	17	17	NUM
cana-681	63	50	)	)	PUNCT
cana-681	63	51	qr	qr	NOUN
cana-681	63	52	code	code	PROPN
cana-681	63	53	,	,	PUNCT
cana-681	63	54	the	the	DET
cana-681	63	55	components	component	NOUN
cana-681	63	56	of	of	ADP
cana-681	63	57	codeword	codeword	NOUN
cana-681	63	58	are	be	AUX
cana-681	63	59	in	in	ADP
cana-681	63	60	finite	finite	ADJ
cana-681	63	61	field	field	NOUN
cana-681	63	62	gf	gf	X
cana-681	63	63	(	(	PUNCT
cana-681	63	64	228	228	NUM
cana-681	63	65	)	)	PUNCT
cana-681	63	66	and	and	CCONJ
cana-681	63	67	its	its	PRON
cana-681	63	68	quadratic	quadratic	ADJ
cana-681	63	69	residue	residue	NOUN
cana-681	63	70	set	set	NOUN
cana-681	63	71	is	be	AUX
cana-681	63	72	𝑄57	𝑄57	X
cana-681	64	1	=	=	PRON
cana-681	64	2	{	{	PUNCT
cana-681	64	3	1,4,6,7,9,11,16,19,21,24,25,28,30,31,36,39,41,42,43,45,49,51,54,55	1,4,6,7,9,11,16,19,21,24,25,28,30,31,36,39,41,42,43,45,49,51,54,55	NUM
cana-681	64	4	}	}	PUNCT
cana-681	64	5	(	(	PUNCT
cana-681	64	6	2	2	X
cana-681	64	7	)	)	PUNCT
cana-681	64	8	a	a	DET
cana-681	64	9	root	root	NOUN
cana-681	64	10	of	of	ADP
cana-681	64	11	the	the	DET
cana-681	64	12	primitive	primitive	ADJ
cana-681	64	13	polynomial	polynomial	ADJ
cana-681	64	14	𝑥28	𝑥28	NOUN
cana-681	64	15	+	+	CCONJ
cana-681	64	16	𝑥3	𝑥3	NOUN
cana-681	64	17	+	+	CCONJ
cana-681	64	18	1	1	NUM
cana-681	64	19	should	should	AUX
cana-681	64	20	be	be	AUX
cana-681	64	21	𝛼	𝛼	PRON
cana-681	64	22	∈	∈	NOUN
cana-681	64	23	𝐺𝐹(228	𝐺𝐹(228	NOUN
cana-681	64	24	)	)	PUNCT
cana-681	65	1	[	[	X
cana-681	65	2	1	1	NUM
cana-681	65	3	]	]	PUNCT
cana-681	65	4	.	.	PUNCT
cana-681	66	1	the	the	DET
cana-681	66	2	multiplicative	multiplicative	ADJ
cana-681	66	3	group	group	NOUN
cana-681	66	4	of	of	ADP
cana-681	66	5	nonzero	nonzero	PROPN
cana-681	66	6	elements	element	NOUN
cana-681	66	7	in	in	ADP
cana-681	66	8	the	the	DET
cana-681	66	9	finite	finite	ADJ
cana-681	66	10	field	field	NOUN
cana-681	66	11	𝐺𝐹(228	𝐺𝐹(228	NOUN
cana-681	66	12	)	)	PUNCT
cana-681	66	13	is	be	AUX
cana-681	66	14	thus	thus	ADV
cana-681	66	15	generated	generate	VERB
cana-681	66	16	by	by	ADP
cana-681	66	17	𝛼.	𝛼.	NOUN
cana-681	66	18	it	it	PRON
cana-681	66	19	follows	follow	VERB
cana-681	66	20	that	that	SCONJ
cana-681	66	21	a	a	DET
cana-681	66	22	primitive	primitive	ADJ
cana-681	66	23	57𝑡ℎ	57𝑡ℎ	NOUN
cana-681	66	24	root	root	NOUN
cana-681	66	25	of	of	ADP
cana-681	66	26	unity	unity	NOUN
cana-681	66	27	is	be	AUX
cana-681	66	28	𝛽	𝛽	NOUN
cana-681	66	29	=	=	PUNCT
cana-681	66	30	𝛼𝑢.	𝛼𝑢.	NOUN
cana-681	66	31	where	where	SCONJ
cana-681	66	32	𝑢	𝑢	X
cana-681	66	33	=	=	SYM
cana-681	66	34	(	(	PUNCT
cana-681	66	35	228	228	NUM
cana-681	66	36	−	−	PROPN
cana-681	66	37	1)/57	1)/57	PROPN
cana-681	66	38	=	=	SYM
cana-681	66	39	4	4	NUM
cana-681	66	40	,	,	PUNCT
cana-681	66	41	709	709	NUM
cana-681	66	42	.	.	PUNCT
cana-681	67	1	the	the	DET
cana-681	67	2	generator	generator	NOUN
cana-681	67	3	polynomial	polynomial	PROPN
cana-681	67	4	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	67	5	)	)	PUNCT
cana-681	67	6	is	be	AUX
cana-681	67	7	defined	define	VERB
cana-681	67	8	by	by	ADP
cana-681	67	9	,	,	PUNCT
cana-681	67	10	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	67	11	)	)	PUNCT
cana-681	68	1	=	=	SYM
cana-681	68	2	∏	∏	X
cana-681	68	3	(	(	PUNCT
cana-681	68	4	𝑥	𝑥	NOUN
cana-681	68	5	−	−	PROPN
cana-681	68	6	𝛽𝑖	𝛽𝑖	NOUN
cana-681	68	7	)	)	PUNCT
cana-681	68	8	𝑖∈𝑄57	𝑖∈𝑄57	PUNCT
cana-681	68	9	=	=	PUNCT
cana-681	68	10	𝑥28	𝑥28	NOUN
cana-681	68	11	+	+	CCONJ
cana-681	68	12	𝑥26	𝑥26	NOUN
cana-681	68	13	+	+	CCONJ
cana-681	68	14	𝑥24	𝑥24	NOUN
cana-681	68	15	+	+	CCONJ
cana-681	68	16	𝑥23	𝑥23	ADJ
cana-681	68	17	+	+	CCONJ
cana-681	68	18	𝑥22	𝑥22	NOUN
cana-681	68	19	+	+	CCONJ
cana-681	68	20	𝑥21	𝑥21	NOUN
cana-681	68	21	+	+	CCONJ
cana-681	68	22	𝑥19	𝑥19	NOUN
cana-681	68	23	+	+	CCONJ
cana-681	68	24	𝑥15	𝑥15	ADJ
cana-681	68	25	+	+	CCONJ
cana-681	68	26	𝑥14	𝑥14	ADJ
cana-681	68	27	+	+	CCONJ
cana-681	68	28	𝑥13	𝑥13	NOUN
cana-681	68	29	+	+	CCONJ
cana-681	68	30	𝑥12	𝑥12	VERB
cana-681	68	31	+	+	CCONJ
cana-681	68	32	𝑥7	𝑥7	ADJ
cana-681	68	33	+	+	CCONJ
cana-681	68	34	𝑥6	𝑥6	PROPN
cana-681	68	35	+	+	CCONJ
cana-681	68	36	𝑥5	𝑥5	PROPN
cana-681	68	37	+	+	CCONJ
cana-681	68	38	𝑥3	𝑥3	ADJ
cana-681	68	39	+	+	CCONJ
cana-681	68	40	𝑥2	𝑥2	NOUN
cana-681	68	41	+	+	CCONJ
cana-681	68	42	𝑥	𝑥	NOUN
cana-681	68	43	+	+	NOUN
cana-681	68	44	1	1	NUM
cana-681	68	45	where	where	SCONJ
cana-681	68	46	the	the	DET
cana-681	68	47	multiplicative	multiplicative	ADJ
cana-681	68	48	order	order	NOUN
cana-681	68	49	of	of	ADP
cana-681	68	50	the	the	DET
cana-681	68	51	integer	integer	NOUN
cana-681	68	52	2	2	NUM
cana-681	68	53	modulo	modulo	VERB
cana-681	68	54	the	the	DET
cana-681	68	55	code	code	NOUN
cana-681	68	56	length	length	NOUN
cana-681	68	57	𝑛	𝑛	PROPN
cana-681	69	1	=	=	SYM
cana-681	69	2	57	57	NUM
cana-681	69	3	is	be	AUX
cana-681	69	4	represented	represent	VERB
cana-681	69	5	by	by	ADP
cana-681	69	6	the	the	DET
cana-681	69	7	degree	degree	NOUN
cana-681	69	8	of	of	ADP
cana-681	69	9	g(x	g(x	NOUN
cana-681	69	10	)	)	PUNCT
cana-681	69	11	which	which	PRON
cana-681	69	12	is	be	AUX
cana-681	69	13	28	28	NUM
cana-681	69	14	.	.	PUNCT
cana-681	70	1	so	so	ADV
cana-681	70	2	,	,	PUNCT
cana-681	70	3	228	228	NUM
cana-681	70	4	≡	≡	PROPN
cana-681	70	5	1(𝑚𝑜𝑑	1(𝑚𝑜𝑑	NOUN
cana-681	70	6	57	57	NUM
cana-681	70	7	)	)	PUNCT
cana-681	70	8	and	and	CCONJ
cana-681	70	9	where	where	SCONJ
cana-681	70	10	𝑔(𝛽	𝑔(𝛽	ADJ
cana-681	70	11	)	)	PUNCT
cana-681	71	1	=	=	SYM
cana-681	71	2	0	0	X
cana-681	71	3	.	.	PUNCT
cana-681	72	1	an	an	DET
cana-681	72	2	error	error	NOUN
cana-681	72	3	pattern	pattern	NOUN
cana-681	72	4	is	be	AUX
cana-681	72	5	considered	consider	VERB
cana-681	72	6	correctable	correctable	ADJ
cana-681	72	7	for	for	ADP
cana-681	72	8	the	the	DET
cana-681	72	9	(	(	PUNCT
cana-681	72	10	57	57	NUM
cana-681	72	11	,	,	PUNCT
cana-681	72	12	29	29	NUM
cana-681	72	13	,	,	PUNCT
cana-681	72	14	17	17	NUM
cana-681	72	15	)	)	PUNCT
cana-681	72	16	qr	qr	NOUN
cana-681	72	17	code	code	NOUN
cana-681	72	18	if	if	SCONJ
cana-681	72	19	its	its	PRON
cana-681	72	20	weight	weight	NOUN
cana-681	72	21	is	be	AUX
cana-681	72	22	less	less	ADJ
cana-681	72	23	than	than	ADP
cana-681	72	24	or	or	CCONJ
cana-681	72	25	equal	equal	ADJ
cana-681	72	26	to	to	ADP
cana-681	72	27	the	the	DET
cana-681	72	28	error	error	NOUN
cana-681	72	29	-	-	PUNCT
cana-681	72	30	correcting	correct	VERB
cana-681	72	31	capacity	capacity	NOUN
cana-681	72	32	𝑡	𝑡	PROPN
cana-681	72	33	=	=	NOUN
cana-681	72	34	17−1	17−1	NUM
cana-681	72	35	2	2	NUM
cana-681	72	36	=	=	SYM
cana-681	72	37	8	8	NUM
cana-681	72	38	.	.	PUNCT
cana-681	73	1	let	let	VERB
cana-681	73	2	us	we	PRON
cana-681	73	3	now	now	ADV
cana-681	73	4	consider	consider	VERB
cana-681	73	5	a	a	DET
cana-681	73	6	noisy	noisy	ADJ
cana-681	73	7	channel	channel	NOUN
cana-681	73	8	and	and	CCONJ
cana-681	73	9	the	the	DET
cana-681	73	10	codeword	codeword	NOUN
cana-681	73	11	communications	communication	NOUN
cana-681	73	12	on	on	ADP
cana-681	73	13	applied	apply	VERB
cana-681	73	14	nonlinear	nonlinear	ADJ
cana-681	73	15	analysis	analysis	NOUN
cana-681	73	16	issn	issn	NOUN
cana-681	73	17	:	:	PUNCT
cana-681	73	18	1074	1074	NUM
cana-681	73	19	-	-	PUNCT
cana-681	73	20	133x	133x	NUM
cana-681	73	21	vol	vol	NOUN
cana-681	73	22	31	31	NUM
cana-681	73	23	no	no	NOUN
cana-681	73	24	.	.	PUNCT
cana-681	74	1	2s	2s	NUM
cana-681	74	2	(	(	PUNCT
cana-681	74	3	2024	2024	NUM
cana-681	74	4	)	)	PUNCT
cana-681	74	5	622	622	NUM
cana-681	75	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	75	2	𝑐(𝑥	𝑐(𝑥	ADJ
cana-681	75	3	)	)	PUNCT
cana-681	75	4	=	=	SYM
cana-681	75	5	𝑐0	𝑐0	NOUN
cana-681	75	6	+	+	CCONJ
cana-681	75	7	𝑐1𝑥	𝑐1𝑥	NOUN
cana-681	75	8	+	+	CCONJ
cana-681	75	9	𝑐2𝑥	𝑐2𝑥	NOUN
cana-681	75	10	2	2	NUM
cana-681	75	11	+	+	NOUN
cana-681	75	12	⋯+	⋯+	NOUN
cana-681	75	13	𝑐56𝑥	𝑐56𝑥	ADP
cana-681	75	14	56	56	NUM
cana-681	75	15	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	75	16	)	)	PUNCT
cana-681	75	17	=	=	SYM
cana-681	75	18	𝑒0	𝑒0	VERB
cana-681	75	19	+	+	CCONJ
cana-681	75	20	𝑒1𝑥	𝑒1𝑥	PROPN
cana-681	75	21	+	+	CCONJ
cana-681	75	22	𝑒2𝑥	𝑒2𝑥	NOUN
cana-681	75	23	2	2	NUM
cana-681	75	24	+	+	NOUN
cana-681	75	25	⋯+	⋯+	NOUN
cana-681	75	26	𝑒56𝑥	𝑒56𝑥	NOUN
cana-681	75	27	56	56	NUM
cana-681	75	28	𝑟(𝑥	𝑟(𝑥	PROPN
cana-681	75	29	)	)	PUNCT
cana-681	75	30	=	=	SYM
cana-681	75	31	𝑟0	𝑟0	NOUN
cana-681	75	32	+	+	CCONJ
cana-681	75	33	𝑟1𝑥	𝑟1𝑥	X
cana-681	75	34	+	+	CCONJ
cana-681	75	35	𝑟2𝑥	𝑟2𝑥	NUM
cana-681	75	36	2	2	NUM
cana-681	75	37	+	+	NOUN
cana-681	75	38	⋯+	⋯+	NOUN
cana-681	75	39	𝑟56𝑥	𝑟56𝑥	ADP
cana-681	75	40	56	56	NUM
cana-681	75	41	respectively	respectively	ADV
cana-681	75	42	,	,	PUNCT
cana-681	75	43	correspond	correspond	VERB
cana-681	75	44	to	to	ADP
cana-681	75	45	the	the	DET
cana-681	75	46	error	error	NOUN
cana-681	75	47	pattern	pattern	NOUN
cana-681	75	48	and	and	CCONJ
cana-681	75	49	the	the	DET
cana-681	75	50	received	receive	VERB
cana-681	75	51	vector	vector	NOUN
cana-681	75	52	.	.	PUNCT
cana-681	76	1	next	next	ADV
cana-681	76	2	,	,	PUNCT
cana-681	76	3	the	the	DET
cana-681	76	4	word	word	NOUN
cana-681	76	5	that	that	PRON
cana-681	76	6	was	be	AUX
cana-681	76	7	received	receive	VERB
cana-681	76	8	takes	take	VERB
cana-681	76	9	the	the	DET
cana-681	76	10	form	form	NOUN
cana-681	76	11	𝑟(𝑥	𝑟(𝑥	NOUN
cana-681	76	12	)	)	PUNCT
cana-681	77	1	=	=	SYM
cana-681	77	2	𝑐(𝑥	𝑐(𝑥	ADJ
cana-681	77	3	)	)	PUNCT
cana-681	77	4	+	+	NUM
cana-681	77	5	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	77	6	)	)	PUNCT
cana-681	77	7	.	.	PUNCT
cana-681	78	1	define	define	VERB
cana-681	78	2	𝑆𝑖	𝑆𝑖	PROPN
cana-681	78	3	=	=	PUNCT
cana-681	78	4	𝑟(𝛽	𝑟(𝛽	PROPN
cana-681	78	5	𝑖	𝑖	PART
cana-681	78	6	)	)	PUNCT
cana-681	78	7	=	=	SYM
cana-681	78	8	𝑒(𝛽𝑖	𝑒(𝛽𝑖	PROPN
cana-681	78	9	)	)	PUNCT
cana-681	78	10	,	,	PUNCT
cana-681	79	1	𝑖	𝑖	PROPN
cana-681	79	2	∈	∈	PROPN
cana-681	80	1	𝑄57	𝑄57	PROPN
cana-681	81	1	as	as	ADP
cana-681	81	2	the	the	DET
cana-681	81	3	set	set	NOUN
cana-681	81	4	of	of	ADP
cana-681	81	5	known	know	VERB
cana-681	81	6	syndromes	syndrome	NOUN
cana-681	81	7	that	that	PRON
cana-681	81	8	can	can	AUX
cana-681	81	9	be	be	AUX
cana-681	81	10	immediately	immediately	ADV
cana-681	81	11	computed	compute	VERB
cana-681	81	12	by	by	ADP
cana-681	81	13	evaluating	evaluate	VERB
cana-681	81	14	𝑟(𝑥	𝑟(𝑥	NOUN
cana-681	81	15	)	)	PUNCT
cana-681	81	16	at	at	ADP
cana-681	81	17	the	the	DET
cana-681	81	18	roots	root	NOUN
cana-681	81	19	of	of	ADP
cana-681	81	20	𝑔(𝑥	𝑔(𝑥	PROPN
cana-681	81	21	)	)	PUNCT
cana-681	82	1	.	.	PUNCT
cana-681	83	1	these	these	DET
cana-681	83	2	syndromes	syndrome	NOUN
cana-681	83	3	are	be	AUX
cana-681	83	4	referred	refer	VERB
cana-681	83	5	to	to	PART
cana-681	83	6	be	be	AUX
cana-681	83	7	unknown	unknown	ADJ
cana-681	83	8	syndromes	syndrome	NOUN
cana-681	83	9	if	if	SCONJ
cana-681	83	10	𝑖	𝑖	NOUN
cana-681	83	11	is	be	AUX
cana-681	83	12	absent	absent	ADJ
cana-681	83	13	from	from	ADP
cana-681	83	14	the	the	DET
cana-681	83	15	set	set	NOUN
cana-681	83	16	𝑄57	𝑄57	PROPN
cana-681	83	17	.	.	PUNCT
cana-681	84	1	it	it	PRON
cana-681	84	2	is	be	AUX
cana-681	84	3	said	say	VERB
cana-681	84	4	that	that	SCONJ
cana-681	84	5	the	the	DET
cana-681	84	6	syndrome	syndrome	NOUN
cana-681	84	7	𝑠𝑖	𝑠𝑖	NOUN
cana-681	84	8	is	be	AUX
cana-681	84	9	a	a	DET
cana-681	84	10	known	know	VERB
cana-681	84	11	syndrome	syndrome	NOUN
cana-681	84	12	if	if	SCONJ
cana-681	84	13	𝑖	𝑖	PROPN
cana-681	84	14	∈	∈	PROPN
cana-681	84	15	𝑄57	𝑄57	PROPN
cana-681	84	16	.	.	PUNCT
cana-681	85	1	if	if	SCONJ
cana-681	85	2	not	not	PART
cana-681	85	3	,	,	PUNCT
cana-681	85	4	it	it	PRON
cana-681	85	5	’s	’s	AUX
cana-681	85	6	referred	refer	VERB
cana-681	85	7	to	to	ADP
cana-681	85	8	as	as	ADP
cana-681	85	9	an	an	DET
cana-681	85	10	unidentified	unidentified	ADJ
cana-681	85	11	syndrome	syndrome	NOUN
cana-681	85	12	.	.	PUNCT
cana-681	86	1	the	the	DET
cana-681	86	2	unidentified	unidentified	ADJ
cana-681	86	3	syndromes	syndrome	NOUN
cana-681	86	4	are	be	AUX
cana-681	86	5	discovered	discover	VERB
cana-681	86	6	in	in	ADP
cana-681	86	7	(	(	PUNCT
cana-681	86	8	2	2	NUM
cana-681	86	9	)	)	PUNCT
cana-681	86	10	.	.	PUNCT
cana-681	87	1	there	there	PRON
cana-681	87	2	is	be	VERB
cana-681	87	3	a	a	DET
cana-681	87	4	relationship	relationship	NOUN
cana-681	87	5	between	between	ADP
cana-681	87	6	the	the	DET
cana-681	87	7	syndromes	syndrome	NOUN
cana-681	87	8	and	and	CCONJ
cana-681	87	9	the	the	DET
cana-681	87	10	qr	qr	PROPN
cana-681	87	11	code	code	NOUN
cana-681	87	12	,	,	PUNCT
cana-681	87	13	𝑆2𝑖	𝑆2𝑖	PROPN
cana-681	88	1	=	=	SYM
cana-681	88	2	𝑆𝑖	𝑆𝑖	PROPN
cana-681	88	3	2	2	NUM
cana-681	88	4	,	,	PUNCT
cana-681	88	5	with	with	ADP
cana-681	88	6	indices	index	NOUN
cana-681	88	7	modulo	modulo	VERB
cana-681	88	8	𝑛.	𝑛.	NOUN
cana-681	88	9	such	such	ADJ
cana-681	88	10	as	as	ADP
cana-681	88	11	,	,	PUNCT
cana-681	88	12	𝑆2	𝑆2	PROPN
cana-681	88	13	=	=	PUNCT
cana-681	88	14	𝑆1	𝑆1	NOUN
cana-681	88	15	2	2	NUM
cana-681	88	16	,	,	PUNCT
cana-681	88	17	𝑆4	𝑆4	PROPN
cana-681	88	18	=	=	SYM
cana-681	88	19	𝑆2	𝑆2	PROPN
cana-681	88	20	2	2	NUM
cana-681	88	21	=	=	NOUN
cana-681	88	22	𝑆1	𝑆1	NOUN
cana-681	88	23	4	4	NUM
cana-681	88	24	,	,	PUNCT
cana-681	88	25	𝑆8	𝑆8	ADJ
cana-681	88	26	=	=	PROPN
cana-681	88	27	𝑆4	𝑆4	PROPN
cana-681	88	28	2	2	NUM
cana-681	88	29	=	=	NOUN
cana-681	88	30	𝑆1	𝑆1	NOUN
cana-681	88	31	8	8	NUM
cana-681	88	32	,	,	PUNCT
cana-681	88	33	𝑆16	𝑆16	PROPN
cana-681	88	34	=	=	PUNCT
cana-681	88	35	𝑆8	𝑆8	ADJ
cana-681	88	36	2	2	NUM
cana-681	88	37	=	=	NOUN
cana-681	88	38	𝑆1	𝑆1	NOUN
cana-681	88	39	16	16	NUM
cana-681	88	40	,	,	PUNCT
cana-681	88	41	𝑆64	𝑆64	PROPN
cana-681	88	42	=	=	SYM
cana-681	88	43	𝑆32	𝑆32	PROPN
cana-681	88	44	2	2	NUM
cana-681	88	45	=	=	PUNCT
cana-681	88	46	𝑆1	𝑆1	NOUN
cana-681	88	47	64	64	NUM
cana-681	88	48	,	,	PUNCT
cana-681	88	49	𝑆128	𝑆128	PROPN
cana-681	88	50	=	=	SYM
cana-681	89	1	𝑆64	𝑆64	PROPN
cana-681	89	2	2	2	NUM
cana-681	89	3	=	=	NOUN
cana-681	89	4	𝑆1	𝑆1	NOUN
cana-681	89	5	128	128	NUM
cana-681	89	6	,	,	PUNCT
cana-681	89	7	𝑆256	𝑆256	PROPN
cana-681	89	8	=	=	SYM
cana-681	89	9	𝑆128	𝑆128	PROPN
cana-681	89	10	2	2	NUM
cana-681	89	11	=	=	NOUN
cana-681	89	12	𝑆1	𝑆1	NOUN
cana-681	89	13	256	256	NUM
cana-681	89	14	.	.	PUNCT
cana-681	90	1	the	the	DET
cana-681	90	2	error	error	NOUN
cana-681	90	3	locator	locator	NOUN
cana-681	90	4	patterns	pattern	NOUN
cana-681	90	5	is	be	AUX
cana-681	90	6	defined	define	VERB
cana-681	90	7	by	by	ADP
cana-681	90	8	,	,	PUNCT
cana-681	90	9	𝐿(𝑧	𝐿(𝑧	NUM
cana-681	90	10	)	)	PUNCT
cana-681	90	11	=	=	SYM
cana-681	90	12	∏	∏	PROPN
cana-681	90	13	(	(	PUNCT
cana-681	90	14	𝑧	𝑧	PRON
cana-681	90	15	−	−	NOUN
cana-681	90	16	𝑧𝑖	𝑧𝑖	NOUN
cana-681	90	17	)	)	PUNCT
cana-681	90	18	=	=	SYM
cana-681	90	19	𝑧	𝑧	PRON
cana-681	90	20	𝑣	𝑣	X
cana-681	90	21	+	+	PROPN
cana-681	90	22	∑	∑	PUNCT
cana-681	91	1	𝜎𝑗𝑧	𝜎𝑗𝑧	ADJ
cana-681	91	2	𝑣−𝑗𝑣	𝑣−𝑗𝑣	NOUN
cana-681	91	3	𝑗=1	𝑗=1	PUNCT
cana-681	91	4	𝑣	𝑣	X
cana-681	91	5	𝑖=1	𝑖=1	PROPN
cana-681	91	6	(	(	PUNCT
cana-681	91	7	3	3	X
cana-681	91	8	)	)	PUNCT
cana-681	91	9	𝜎1	𝜎1	NOUN
cana-681	91	10	=	=	PUNCT
cana-681	91	11	𝑧1	𝑧1	NOUN
cana-681	91	12	+	+	CCONJ
cana-681	91	13	𝑧2	𝑧2	PROPN
cana-681	91	14	+	+	NOUN
cana-681	91	15	⋯+	⋯+	NOUN
cana-681	91	16	𝑧𝑣	𝑧𝑣	NOUN
cana-681	91	17	𝜎2	𝜎2	NOUN
cana-681	91	18	=	=	PUNCT
cana-681	91	19	𝑧1𝑧2	𝑧1𝑧2	PROPN
cana-681	91	20	+	+	CCONJ
cana-681	91	21	𝑧1𝑧3	𝑧1𝑧3	ADJ
cana-681	91	22	…	…	SYM
cana-681	91	23	𝑧𝑣−1𝑧𝑣	𝑧𝑣−1𝑧𝑣	NOUN
cana-681	91	24	𝜎3	𝜎3	NOUN
cana-681	91	25	=	=	SYM
cana-681	91	26	𝑧2𝑧3	𝑧2𝑧3	PROPN
cana-681	91	27	+	+	CCONJ
cana-681	91	28	𝑧2𝑧4	𝑧2𝑧4	NOUN
cana-681	91	29	…	…	X
cana-681	91	30	𝑧2𝑣	𝑧2𝑣	NOUN
cana-681	91	31	.	.	PUNCT
cana-681	91	32	.	.	PUNCT
cana-681	91	33	.	.	PUNCT
cana-681	92	1	𝜎𝑣	𝜎𝑣	X
cana-681	92	2	=	=	SYM
cana-681	92	3	𝑧1𝑧2	𝑧1𝑧2	NOUN
cana-681	92	4	…	…	PUNCT
cana-681	92	5	𝑧𝑣	𝑧𝑣	PROPN
cana-681	92	6	thus	thus	ADV
cana-681	92	7	,	,	PUNCT
cana-681	92	8	by	by	ADP
cana-681	92	9	using	use	VERB
cana-681	92	10	the	the	DET
cana-681	92	11	chien	chien	PROPN
cana-681	92	12	search	search	NOUN
cana-681	92	13	algorithms	algorithm	NOUN
cana-681	92	14	to	to	PART
cana-681	92	15	locate	locate	VERB
cana-681	92	16	the	the	DET
cana-681	92	17	error	error	NOUN
cana-681	92	18	𝑧1𝑧2	𝑧1𝑧2	NOUN
cana-681	92	19	…	…	PROPN
cana-681	92	20	𝑧𝑣	𝑧𝑣	PROPN
cana-681	92	21	as	as	ADP
cana-681	92	22	roots	root	NOUN
cana-681	92	23	of	of	ADP
cana-681	92	24	polynomial	polynomial	ADJ
cana-681	92	25	𝐿(𝑧	𝐿(𝑧	NUM
cana-681	92	26	)	)	PUNCT
cana-681	92	27	in	in	ADP
cana-681	92	28	(	(	PUNCT
cana-681	92	29	3	3	NUM
cana-681	92	30	)	)	PUNCT
cana-681	92	31	,	,	PUNCT
cana-681	92	32	it	it	PRON
cana-681	92	33	is	be	AUX
cana-681	92	34	easy	easy	ADJ
cana-681	92	35	to	to	PART
cana-681	92	36	find	find	VERB
cana-681	92	37	the	the	DET
cana-681	92	38	elementary	elementary	ADJ
cana-681	92	39	symmetric	symmetric	ADJ
cana-681	92	40	functions	function	NOUN
cana-681	92	41	𝜎𝑖.the	𝜎𝑖.the	DET
cana-681	92	42	coefficients	coefficient	NOUN
cana-681	92	43	of	of	ADP
cana-681	92	44	𝐿(𝑧	𝐿(𝑧	NUM
cana-681	92	45	)	)	PUNCT
cana-681	92	46	are	be	AUX
cana-681	92	47	found	find	VERB
cana-681	92	48	using	use	VERB
cana-681	92	49	the	the	DET
cana-681	92	50	following	follow	VERB
cana-681	92	51	newton	newton	PROPN
cana-681	92	52	identities	identity	NOUN
cana-681	92	53	:	:	PUNCT
cana-681	93	1	𝑠1	𝑠1	PROPN
cana-681	93	2	+	+	CCONJ
cana-681	93	3	𝜎1	𝜎1	ADJ
cana-681	93	4	=	=	SYM
cana-681	93	5	0	0	NUM
cana-681	93	6	𝑠2	𝑠2	NOUN
cana-681	93	7	+	+	CCONJ
cana-681	93	8	𝜎1𝑠1	𝜎1𝑠1	NUM
cana-681	93	9	+	+	SYM
cana-681	93	10	2𝜎2	2𝜎2	NUM
cana-681	93	11	=	=	SYM
cana-681	93	12	0	0	NUM
cana-681	94	1	𝑠3	𝑠3	NOUN
cana-681	94	2	+	+	CCONJ
cana-681	94	3	𝜎1𝑠2	𝜎1𝑠2	X
cana-681	94	4	+	+	CCONJ
cana-681	94	5	𝜎2𝑠1	𝜎2𝑠1	X
cana-681	94	6	+	+	NUM
cana-681	94	7	3𝜎3	3𝜎3	NUM
cana-681	94	8	=	=	SYM
cana-681	94	9	0	0	NUM
cana-681	94	10	.	.	PUNCT
cana-681	94	11	.	.	PUNCT
cana-681	94	12	.	.	PUNCT
cana-681	95	1	𝑠𝑣	𝑠𝑣	NOUN
cana-681	96	1	+	+	CCONJ
cana-681	96	2	𝜎1𝑠𝑣−1	𝜎1𝑠𝑣−1	NUM
cana-681	97	1	+	+	ADJ
cana-681	97	2	…	…	PUNCT
cana-681	97	3	+	+	SYM
cana-681	97	4	𝜎𝑣−1𝑠1	𝜎𝑣−1𝑠1	NOUN
cana-681	97	5	+	+	CCONJ
cana-681	97	6	𝑣𝜎𝑣	𝑣𝜎𝑣	NOUN
cana-681	97	7	=	=	SYM
cana-681	97	8	0	0	NUM
cana-681	97	9	the	the	DET
cana-681	97	10	decoding	decode	VERB
cana-681	97	11	algorithm	algorithm	NOUN
cana-681	97	12	is	be	AUX
cana-681	97	13	used	use	VERB
cana-681	97	14	to	to	PART
cana-681	97	15	decode	decode	VERB
cana-681	97	16	the	the	DET
cana-681	97	17	qr	qr	PROPN
cana-681	97	18	code	code	NOUN
cana-681	97	19	up	up	ADP
cana-681	97	20	to	to	PART
cana-681	97	21	8	8	NUM
cana-681	97	22	errors	error	NOUN
cana-681	97	23	.	.	PUNCT
cana-681	98	1	the	the	DET
cana-681	98	2	𝑆1	𝑆1	NOUN
cana-681	98	3	,	,	PUNCT
cana-681	98	4	𝑆2	𝑆2	PROPN
cana-681	98	5	,	,	PUNCT
cana-681	98	6	…	…	PUNCT
cana-681	98	7	,	,	PUNCT
cana-681	98	8	𝑆16	𝑆16	PROPN
cana-681	98	9	syndromes	syndrome	NOUN
cana-681	98	10	are	be	AUX
cana-681	98	11	the	the	DET
cana-681	98	12	first	first	ADJ
cana-681	98	13	16	16	NUM
cana-681	98	14	in	in	ADP
cana-681	98	15	succession	succession	NOUN
cana-681	98	16	.	.	PUNCT
cana-681	99	1	however	however	ADV
cana-681	99	2	,	,	PUNCT
cana-681	99	3	only	only	ADV
cana-681	99	4	the	the	DET
cana-681	99	5	syndromes	syndrome	NOUN
cana-681	99	6	s1	s1	NOUN
cana-681	99	7	,	,	PUNCT
cana-681	99	8	s4	s4	PROPN
cana-681	99	9	,	,	PUNCT
cana-681	99	10	s6	s6	PROPN
cana-681	99	11	,	,	PUNCT
cana-681	99	12	s7	s7	NOUN
cana-681	99	13	,	,	PUNCT
cana-681	99	14	s9	s9	NOUN
cana-681	99	15	,	,	PUNCT
cana-681	99	16	s11	s11	PROPN
cana-681	99	17	,	,	PUNCT
cana-681	99	18	s16	s16	PROPN
cana-681	99	19	can	can	AUX
cana-681	99	20	be	be	AUX
cana-681	99	21	calculated	calculate	VERB
cana-681	99	22	directly	directly	ADV
cana-681	99	23	from	from	ADP
cana-681	99	24	𝑟(𝑥	𝑟(𝑥	PROPN
cana-681	99	25	)	)	PUNCT
cana-681	99	26	and	and	CCONJ
cana-681	99	27	the	the	DET
cana-681	99	28	others	other	NOUN
cana-681	99	29	s2	s2	PROPN
cana-681	99	30	,	,	PUNCT
cana-681	99	31	s3	s3	PROPN
cana-681	99	32	,	,	PUNCT
cana-681	99	33	s5	s5	PROPN
cana-681	99	34	,	,	PUNCT
cana-681	99	35	s8	s8	NOUN
cana-681	99	36	,	,	PUNCT
cana-681	99	37	s10	s10	PROPN
cana-681	99	38	,	,	PUNCT
cana-681	99	39	s12	s12	PROPN
cana-681	99	40	,	,	PUNCT
cana-681	99	41	s13	s13	NOUN
cana-681	99	42	,	,	PUNCT
cana-681	99	43	s14	s14	NOUN
cana-681	99	44	,	,	PUNCT
cana-681	99	45	s15	s15	PROPN
cana-681	99	46	are	be	AUX
cana-681	99	47	communications	communication	NOUN
cana-681	99	48	on	on	ADP
cana-681	99	49	applied	apply	VERB
cana-681	99	50	nonlinear	nonlinear	ADJ
cana-681	99	51	analysis	analysis	NOUN
cana-681	99	52	issn	issn	NOUN
cana-681	99	53	:	:	PUNCT
cana-681	99	54	1074	1074	NUM
cana-681	99	55	-	-	PUNCT
cana-681	99	56	133x	133x	NUM
cana-681	99	57	vol	vol	NOUN
cana-681	99	58	31	31	NUM
cana-681	99	59	no	no	NOUN
cana-681	99	60	.	.	PUNCT
cana-681	100	1	2s	2s	NUM
cana-681	100	2	(	(	PUNCT
cana-681	100	3	2024	2024	NUM
cana-681	100	4	)	)	PUNCT
cana-681	100	5	623	623	NUM
cana-681	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	100	7	not	not	PART
cana-681	100	8	determined	determine	VERB
cana-681	100	9	directly	directly	ADV
cana-681	100	10	from	from	ADP
cana-681	100	11	𝑟(𝑥	𝑟(𝑥	PROPN
cana-681	100	12	)	)	PUNCT
cana-681	100	13	,	,	PUNCT
cana-681	100	14	which	which	PRON
cana-681	100	15	can	can	AUX
cana-681	100	16	be	be	AUX
cana-681	100	17	expressed	express	VERB
cana-681	100	18	in	in	ADP
cana-681	100	19	powers	power	NOUN
cana-681	100	20	of	of	ADP
cana-681	100	21	s2	s2	PROPN
cana-681	100	22	and	and	CCONJ
cana-681	100	23	s15	s15	PROPN
cana-681	100	24	.	.	PROPN
cana-681	100	25	4	4	X
cana-681	100	26	.	.	X
cana-681	100	27	decoding	decode	VERB
cana-681	100	28	algorithm	algorithm	NOUN
cana-681	100	29	for	for	ADP
cana-681	100	30	(	(	PUNCT
cana-681	100	31	57	57	NUM
cana-681	100	32	,	,	PUNCT
cana-681	100	33	29	29	NUM
cana-681	100	34	,	,	PUNCT
cana-681	100	35	17	17	NUM
cana-681	100	36	)	)	PUNCT
cana-681	100	37	qr	qr	NOUN
cana-681	100	38	code	code	NOUN
cana-681	100	39	one	one	PRON
cana-681	100	40	can	can	AUX
cana-681	100	41	apply	apply	VERB
cana-681	100	42	the	the	DET
cana-681	100	43	decoding	decode	VERB
cana-681	100	44	algorithm	algorithm	NOUN
cana-681	100	45	to	to	ADP
cana-681	100	46	the	the	DET
cana-681	100	47	receive	receive	NOUN
cana-681	100	48	data	data	NOUN
cana-681	100	49	bits	bit	NOUN
cana-681	100	50	to	to	PART
cana-681	100	51	recover	recover	VERB
cana-681	100	52	the	the	DET
cana-681	100	53	original	original	ADJ
cana-681	100	54	error	error	NOUN
cana-681	100	55	.	.	PUNCT
cana-681	101	1	a	a	DET
cana-681	101	2	new	new	ADJ
cana-681	101	3	decoding	decode	VERB
cana-681	101	4	algorithm	algorithm	NOUN
cana-681	101	5	for	for	ADP
cana-681	101	6	the	the	DET
cana-681	101	7	code	code	NOUN
cana-681	101	8	is	be	AUX
cana-681	101	9	given	give	VERB
cana-681	101	10	below	below	ADV
cana-681	101	11	.	.	PUNCT
cana-681	102	1	step	step	NOUN
cana-681	102	2	1	1	NUM
cana-681	102	3	:	:	PUNCT
cana-681	102	4	the	the	DET
cana-681	102	5	first	first	ADJ
cana-681	102	6	16	16	NUM
cana-681	102	7	consecutive	consecutive	ADJ
cana-681	102	8	syndromes	syndrome	NOUN
cana-681	102	9	s1	s1	NOUN
cana-681	102	10	,	,	PUNCT
cana-681	102	11	s2	s2	VERB
cana-681	102	12	……	……	NOUN
cana-681	102	13	.	.	PUNCT
cana-681	102	14	,	,	PUNCT
cana-681	102	15	s16	s16	PROPN
cana-681	102	16	.	.	PUNCT
cana-681	103	1	step	step	NOUN
cana-681	103	2	2	2	NUM
cana-681	103	3	:	:	PUNCT
cana-681	103	4	obtain	obtain	VERB
cana-681	103	5	the	the	DET
cana-681	103	6	known	know	VERB
cana-681	103	7	syndromes	syndrome	NOUN
cana-681	103	8	s1	s1	NOUN
cana-681	103	9	,	,	PUNCT
cana-681	103	10	s4	s4	PROPN
cana-681	103	11	,	,	PUNCT
cana-681	103	12	s6	s6	PROPN
cana-681	103	13	,	,	PUNCT
cana-681	103	14	s7	s7	NOUN
cana-681	103	15	,	,	PUNCT
cana-681	103	16	s9	s9	NOUN
cana-681	103	17	,	,	PUNCT
cana-681	103	18	s11	s11	PROPN
cana-681	103	19	,	,	PUNCT
cana-681	103	20	s16	s16	NOUN
cana-681	103	21	.	.	PUNCT
cana-681	104	1	step	step	NOUN
cana-681	104	2	3	3	NUM
cana-681	104	3	:	:	PUNCT
cana-681	104	4	if	if	SCONJ
cana-681	104	5	odd	odd	ADJ
cana-681	104	6	syndromes	syndrome	NOUN
cana-681	104	7	are	be	AUX
cana-681	104	8	zero	zero	NUM
cana-681	104	9	,	,	PUNCT
cana-681	104	10	(	(	PUNCT
cana-681	104	11	i.e.	i.e.	X
cana-681	104	12	)	)	PUNCT
cana-681	104	13	s1	s1	NOUN
cana-681	104	14	=	=	SYM
cana-681	104	15	s7	s7	PROPN
cana-681	104	16	=	=	PROPN
cana-681	104	17	s9	s9	PROPN
cana-681	104	18	=	=	SYM
cana-681	104	19	s11	s11	PROPN
cana-681	104	20	=	=	SYM
cana-681	104	21	0	0	PROPN
cana-681	104	22	,	,	PUNCT
cana-681	104	23	assume	assume	VERB
cana-681	104	24	no	no	DET
cana-681	104	25	errors	error	NOUN
cana-681	104	26	occur	occur	VERB
cana-681	104	27	and	and	CCONJ
cana-681	104	28	stop	stop	VERB
cana-681	104	29	.	.	PUNCT
cana-681	105	1	step	step	NOUN
cana-681	105	2	4	4	NUM
cana-681	105	3	:	:	PUNCT
cana-681	105	4	choose	choose	VERB
cana-681	105	5	the	the	DET
cana-681	105	6	unknown	unknown	ADJ
cana-681	105	7	syndromes	syndrome	NOUN
cana-681	105	8	and	and	CCONJ
cana-681	105	9	set	set	VERB
cana-681	105	10	v	v	NOUN
cana-681	105	11	=	=	SYM
cana-681	105	12	1	1	NUM
cana-681	105	13	.	.	PUNCT
cana-681	105	14	step	step	NOUN
cana-681	105	15	5	5	NUM
cana-681	105	16	:	:	PUNCT
cana-681	105	17	choose	choose	VERB
cana-681	105	18	a	a	DET
cana-681	105	19	subset	subset	NOUN
cana-681	105	20	𝐼	𝐼	PROPN
cana-681	105	21	=	=	PROPN
cana-681	105	22	𝑖1	𝑖1	PROPN
cana-681	105	23	,	,	PUNCT
cana-681	105	24	𝑖2	𝑖2	PROPN
cana-681	105	25	,	,	PUNCT
cana-681	105	26	…	…	PUNCT
cana-681	105	27	,	,	PUNCT
cana-681	105	28	𝑖𝑣+1	𝑖𝑣+1	PRON
cana-681	105	29	⊂	⊂	NOUN
cana-681	105	30	𝑄.	𝑄.	NOUN
cana-681	105	31	step	step	NOUN
cana-681	105	32	6	6	NUM
cana-681	105	33	:	:	PUNCT
cana-681	105	34	choose	choose	VERB
cana-681	105	35	a	a	DET
cana-681	105	36	subset	subset	NOUN
cana-681	105	37	j	j	NOUN
cana-681	105	38	containing	contain	VERB
cana-681	105	39	v	v	ADP
cana-681	105	40	+	+	CCONJ
cana-681	105	41	1	1	NUM
cana-681	105	42	elements	element	NOUN
cana-681	105	43	from	from	ADP
cana-681	105	44	the	the	DET
cana-681	105	45	difference	difference	NOUN
cana-681	105	46	set	set	VERB
cana-681	105	47	in	in	ADP
cana-681	105	48	step	step	NOUN
cana-681	105	49	4	4	NUM
cana-681	105	50	.	.	PUNCT
cana-681	106	1	if	if	SCONJ
cana-681	106	2	all	all	DET
cana-681	106	3	the	the	DET
cana-681	106	4	possible	possible	ADJ
cana-681	106	5	sets	set	NOUN
cana-681	106	6	j	j	PROPN
cana-681	106	7	have	have	AUX
cana-681	106	8	been	be	AUX
cana-681	106	9	returning	return	VERB
cana-681	106	10	to	to	PART
cana-681	106	11	step	step	VERB
cana-681	106	12	2	2	NUM
cana-681	106	13	.	.	PUNCT
cana-681	106	14	step	step	NOUN
cana-681	106	15	7	7	NUM
cana-681	106	16	:	:	PUNCT
cana-681	106	17	if	if	SCONJ
cana-681	106	18	the	the	DET
cana-681	106	19	intersection	intersection	NOUN
cana-681	106	20	of	of	ADP
cana-681	106	21	the	the	DET
cana-681	106	22	multi	multi	ADJ
cana-681	106	23	-	-	ADJ
cana-681	106	24	set	set	ADJ
cana-681	106	25	𝐼⊕	𝐼⊕	PROPN
cana-681	106	26	𝐽	𝐽	PROPN
cana-681	106	27	is	be	AUX
cana-681	106	28	empty	empty	ADJ
cana-681	106	29	,	,	PUNCT
cana-681	106	30	return	return	VERB
cana-681	106	31	to	to	PART
cana-681	106	32	step	step	VERB
cana-681	106	33	4	4	NUM
cana-681	106	34	.	.	PUNCT
cana-681	107	1	step	step	NOUN
cana-681	107	2	8	8	NUM
cana-681	107	3	:	:	PUNCT
cana-681	107	4	computing	compute	VERB
cana-681	107	5	the	the	DET
cana-681	107	6	consecutive	consecutive	ADJ
cana-681	107	7	unknown	unknown	ADJ
cana-681	107	8	syndromes	syndrome	NOUN
cana-681	107	9	for	for	ADP
cana-681	107	10	possible	possible	ADJ
cana-681	107	11	pair	pair	NOUN
cana-681	107	12	𝑆2	𝑆2	ADJ
cana-681	107	13	𝑣	𝑣	ADP
cana-681	107	14	,	,	PUNCT
cana-681	107	15	𝑆15	𝑆15	NOUN
cana-681	107	16	𝑣	𝑣	X
cana-681	107	17	.	.	PUNCT
cana-681	108	1	step	step	NOUN
cana-681	108	2	9	9	NUM
cana-681	108	3	:	:	PUNCT
cana-681	108	4	if	if	SCONJ
cana-681	108	5	there	there	PRON
cana-681	108	6	exists	exist	VERB
cana-681	108	7	one	one	NUM
cana-681	108	8	monomial	monomial	NOUN
cana-681	108	9	of	of	ADP
cana-681	108	10	the	the	DET
cana-681	108	11	unknown	unknown	ADJ
cana-681	108	12	syndrome	syndrome	NOUN
cana-681	108	13	whose	whose	DET
cana-681	108	14	coefficient	coefficient	NOUN
cana-681	108	15	is	be	AUX
cana-681	108	16	1	1	NUM
cana-681	108	17	and	and	CCONJ
cana-681	108	18	whose	whose	DET
cana-681	108	19	power	power	NOUN
cana-681	108	20	is	be	AUX
cana-681	108	21	different	different	ADJ
cana-681	108	22	from	from	ADP
cana-681	108	23	that	that	PRON
cana-681	108	24	of	of	ADP
cana-681	108	25	other	other	ADJ
cana-681	108	26	monomials	monomial	NOUN
cana-681	108	27	,	,	PUNCT
cana-681	108	28	then	then	ADV
cana-681	108	29	stop	stop	VERB
cana-681	108	30	;	;	PUNCT
cana-681	108	31	otherwise	otherwise	ADV
cana-681	108	32	,	,	PUNCT
cana-681	108	33	return	return	VERB
cana-681	108	34	to	to	PART
cana-681	108	35	step	step	VERB
cana-681	108	36	4	4	NUM
cana-681	108	37	.	.	NOUN
cana-681	108	38	4.1	4.1	NUM
cana-681	108	39	determination	determination	NOUN
cana-681	108	40	of	of	ADP
cana-681	108	41	unknown	unknown	ADJ
cana-681	108	42	syndromes	syndrome	NOUN
cana-681	108	43	assume	assume	VERB
cana-681	108	44	that	that	SCONJ
cana-681	108	45	v	v	DET
cana-681	108	46	errors	error	NOUN
cana-681	108	47	occur	occur	VERB
cana-681	108	48	in	in	ADP
cana-681	108	49	the	the	DET
cana-681	108	50	received	receive	VERB
cana-681	108	51	word	word	NOUN
cana-681	108	52	.	.	PUNCT
cana-681	109	1	let	let	VERB
cana-681	109	2	i	i	PRON
cana-681	109	3	=	=	PROPN
cana-681	109	4	i1	i1	PROPN
cana-681	109	5	,	,	PUNCT
cana-681	109	6	i2	i2	PROPN
cana-681	109	7	,	,	PUNCT
cana-681	109	8	...	...	PUNCT
cana-681	109	9	iv+1	iv+1	PROPN
cana-681	109	10	and	and	CCONJ
cana-681	109	11	j	j	PROPN
cana-681	109	12	=	=	PROPN
cana-681	109	13	j1	j1	PROPN
cana-681	109	14	,	,	PUNCT
cana-681	109	15	j2	j2	PROPN
cana-681	109	16	,	,	PUNCT
cana-681	109	17	...	...	PUNCT
cana-681	110	1	jv+1	jv+1	PROPN
cana-681	110	2	denote	denote	VERB
cana-681	110	3	two	two	NUM
cana-681	110	4	subsets	subset	NOUN
cana-681	110	5	of	of	ADP
cana-681	110	6	0,1	0,1	NUM
cana-681	110	7	,	,	PUNCT
cana-681	110	8	2	2	NUM
cana-681	110	9	...	...	SYM
cana-681	110	10	56	56	NUM
cana-681	110	11	,	,	PUNCT
cana-681	110	12	respectively	respectively	ADV
cana-681	110	13	.	.	PUNCT
cana-681	111	1	next	next	ADV
cana-681	111	2	,	,	PUNCT
cana-681	111	3	consider	consider	VERB
cana-681	111	4	the	the	DET
cana-681	111	5	matrix	matrix	NOUN
cana-681	111	6	(	(	PUNCT
cana-681	111	7	i	i	PROPN
cana-681	111	8	,	,	PUNCT
cana-681	111	9	j	j	PROPN
cana-681	111	10	)	)	PUNCT
cana-681	111	11	of	of	ADP
cana-681	111	12	size	size	NOUN
cana-681	111	13	(	(	PUNCT
cana-681	111	14	v	v	NOUN
cana-681	111	15	+	+	NOUN
cana-681	111	16	1	1	NUM
cana-681	111	17	)	)	PUNCT
cana-681	111	18	×	×	NOUN
cana-681	111	19	(	(	PUNCT
cana-681	111	20	v	v	NOUN
cana-681	111	21	+	+	NOUN
cana-681	111	22	1	1	NUM
cana-681	111	23	)	)	PUNCT
cana-681	111	24	given	give	VERB
cana-681	111	25	by	by	ADP
cana-681	111	26	,	,	PUNCT
cana-681	111	27	𝑆(𝐼	𝑆(𝐼	ADJ
cana-681	111	28	,	,	PUNCT
cana-681	111	29	𝐽	𝐽	PROPN
cana-681	111	30	)	)	PUNCT
cana-681	111	31	=	=	PUNCT
cana-681	111	32	[	[	PUNCT
cana-681	112	1	𝑆𝑖1+𝑗1	𝑆𝑖1+𝑗1	PROPN
cana-681	112	2	⋯	⋯	VERB
cana-681	112	3	𝑆𝑖1+𝑗𝑣+1	𝑆𝑖1+𝑗𝑣+1	NOUN
cana-681	112	4	⋮	⋮	PROPN
cana-681	112	5	⋱	⋱	PUNCT
cana-681	112	6	⋮	⋮	PROPN
cana-681	112	7	𝑆𝑖𝑣+1+𝑗1	𝑆𝑖𝑣+1+𝑗1	PROPN
cana-681	112	8	⋯	⋯	VERB
cana-681	112	9	𝑆𝑖𝑣+1+𝑗𝑣+1	𝑆𝑖𝑣+1+𝑗𝑣+1	ADP
cana-681	112	10	]	]	PUNCT
cana-681	112	11	where	where	SCONJ
cana-681	112	12	the	the	DET
cana-681	112	13	summation	summation	NOUN
cana-681	112	14	of	of	ADP
cana-681	112	15	the	the	DET
cana-681	112	16	indices	index	NOUN
cana-681	112	17	of	of	ADP
cana-681	112	18	the	the	PRON
cana-681	112	19	is	be	AUX
cana-681	112	20	modulo	modulo	NOUN
cana-681	112	21	𝑛	𝑛	ADP
cana-681	112	22	and	and	CCONJ
cana-681	112	23	the	the	DET
cana-681	112	24	rank	rank	NOUN
cana-681	112	25	of	of	ADP
cana-681	112	26	𝑆(𝐼	𝑆(𝐼	PROPN
cana-681	112	27	,	,	PUNCT
cana-681	112	28	𝐽	𝐽	PROPN
cana-681	112	29	)	)	PUNCT
cana-681	112	30	is	be	AUX
cana-681	112	31	at	at	ADP
cana-681	112	32	most	most	ADJ
cana-681	112	33	𝑣	𝑣	ADP
cana-681	112	34	,	,	PUNCT
cana-681	112	35	which	which	PRON
cana-681	112	36	in	in	ADP
cana-681	112	37	turn	turn	NOUN
cana-681	112	38	implies	imply	VERB
cana-681	112	39	the	the	DET
cana-681	112	40	following	follow	VERB
cana-681	112	41	equation	equation	NOUN
cana-681	112	42	,	,	PUNCT
cana-681	112	43	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	112	44	𝑆(𝐼	𝑆(𝐼	PROPN
cana-681	112	45	,	,	PUNCT
cana-681	112	46	𝐽	𝐽	PROPN
cana-681	112	47	)	)	PUNCT
cana-681	113	1	=	=	SYM
cana-681	113	2	0	0	PUNCT
cana-681	113	3	(	(	PUNCT
cana-681	113	4	4	4	NUM
cana-681	113	5	)	)	PUNCT
cana-681	113	6	now	now	ADV
cana-681	113	7	,	,	PUNCT
cana-681	113	8	assuming	assume	VERB
cana-681	113	9	the	the	DET
cana-681	113	10	subsets	subset	NOUN
cana-681	113	11	𝐼and	𝐼and	PROPN
cana-681	113	12	𝐽	𝐽	PROPN
cana-681	113	13	for	for	ADP
cana-681	113	14	the	the	DET
cana-681	113	15	code	code	NOUN
cana-681	113	16	,	,	PUNCT
cana-681	113	17	𝐼	𝐼	PROPN
cana-681	113	18	⊕	⊕	PROPN
cana-681	113	19	𝐽	𝐽	PROPN
cana-681	113	20	=	=	PRON
cana-681	113	21	{	{	PUNCT
cana-681	113	22	(	(	PUNCT
cana-681	113	23	𝑖	𝑖	PROPN
cana-681	113	24	+	+	CCONJ
cana-681	113	25	𝑗	𝑗	NOUN
cana-681	113	26	)	)	PUNCT
cana-681	113	27	𝑚𝑜𝑑	𝑚𝑜𝑑	NOUN
cana-681	113	28	57|𝑖	57|𝑖	NUM
cana-681	113	29	∈	∈	PROPN
cana-681	113	30	𝐼	𝐼	PROPN
cana-681	113	31	,	,	PUNCT
cana-681	113	32	𝑗	𝑗	PROPN
cana-681	113	33	∈	∈	PROPN
cana-681	113	34	𝐽	𝐽	PROPN
cana-681	113	35	}	}	PUNCT
cana-681	113	36	example	example	NOUN
cana-681	113	37	:	:	PUNCT
cana-681	113	38	the	the	DET
cana-681	113	39	sum	sum	NOUN
cana-681	113	40	of	of	ADP
cana-681	113	41	two	two	NUM
cana-681	113	42	subsets	subset	NOUN
cana-681	113	43	𝐼and	𝐼and	PROPN
cana-681	113	44	𝐽	𝐽	PROPN
cana-681	113	45	are	be	AUX
cana-681	113	46	illustrated	illustrate	VERB
cana-681	113	47	below	below	ADV
cana-681	113	48	.	.	PUNCT
cana-681	114	1	if	if	SCONJ
cana-681	114	2	𝑣	𝑣	PRON
cana-681	114	3	=	=	SYM
cana-681	114	4	5	5	NUM
cana-681	114	5	,	,	PUNCT
cana-681	114	6	𝐼	𝐼	PROPN
cana-681	114	7	=	=	SYM
cana-681	114	8	{	{	PUNCT
cana-681	114	9	0,1,2,3,4	0,1,2,3,4	NUM
cana-681	114	10	}	}	PUNCT
cana-681	114	11	and	and	CCONJ
cana-681	114	12	𝐽	𝐽	NOUN
cana-681	114	13	=	=	PUNCT
cana-681	114	14	{	{	PUNCT
cana-681	114	15	1,2,3,4,5	1,2,3,4,5	NUM
cana-681	114	16	}	}	PUNCT
cana-681	114	17	,	,	PUNCT
cana-681	114	18	then	then	ADV
cana-681	114	19	𝐼	𝐼	PROPN
cana-681	114	20	⊕	⊕	PROPN
cana-681	114	21	𝐽	𝐽	PROPN
cana-681	114	22	=	=	PUNCT
cana-681	114	23	{	{	PUNCT
cana-681	114	24	0	0	NUM
cana-681	115	1	+	+	NUM
cana-681	115	2	1	1	NUM
cana-681	115	3	,	,	PUNCT
cana-681	115	4	0	0	NUM
cana-681	116	1	+	+	CCONJ
cana-681	116	2	2	2	NUM
cana-681	116	3	,	,	PUNCT
cana-681	116	4	0	0	NUM
cana-681	117	1	+	+	CCONJ
cana-681	117	2	3	3	NUM
cana-681	117	3	,	,	PUNCT
cana-681	117	4	0	0	NUM
cana-681	118	1	+	+	CCONJ
cana-681	118	2	4	4	NUM
cana-681	118	3	,	,	PUNCT
cana-681	118	4	0	0	NUM
cana-681	119	1	+	+	CCONJ
cana-681	119	2	5	5	NUM
cana-681	119	3	,	,	PUNCT
cana-681	119	4	1	1	NUM
cana-681	120	1	+	+	NUM
cana-681	120	2	1	1	NUM
cana-681	120	3	,	,	PUNCT
cana-681	120	4	1	1	NUM
cana-681	121	1	+	+	SYM
cana-681	121	2	2	2	NUM
cana-681	121	3	,	,	PUNCT
cana-681	121	4	1	1	NUM
cana-681	121	5	+	+	SYM
cana-681	121	6	3	3	NUM
cana-681	121	7	,	,	PUNCT
cana-681	121	8	1	1	NUM
cana-681	122	1	+	+	NUM
cana-681	122	2	4	4	NUM
cana-681	122	3	,	,	PUNCT
cana-681	122	4	1	1	NUM
cana-681	123	1	+	+	SYM
cana-681	123	2	5	5	NUM
cana-681	123	3	,	,	PUNCT
cana-681	123	4	2	2	NUM
cana-681	123	5	+	+	SYM
cana-681	123	6	1	1	NUM
cana-681	123	7	,	,	PUNCT
cana-681	123	8	2	2	NUM
cana-681	123	9	+	+	SYM
cana-681	123	10	2	2	NUM
cana-681	123	11	,	,	PUNCT
cana-681	123	12	2	2	NUM
cana-681	123	13	+	+	SYM
cana-681	123	14	3	3	NUM
cana-681	123	15	,	,	PUNCT
cana-681	123	16	2	2	NUM
cana-681	123	17	+	+	SYM
cana-681	123	18	4	4	NUM
cana-681	123	19	,	,	PUNCT
cana-681	123	20	2	2	NUM
cana-681	123	21	+	+	SYM
cana-681	123	22	5	5	NUM
cana-681	123	23	,	,	PUNCT
cana-681	123	24	3	3	NUM
cana-681	123	25	+	+	SYM
cana-681	123	26	1	1	NUM
cana-681	123	27	,	,	PUNCT
cana-681	123	28	3	3	NUM
cana-681	123	29	+	+	SYM
cana-681	123	30	2	2	NUM
cana-681	123	31	,	,	PUNCT
cana-681	123	32	3	3	NUM
cana-681	123	33	+	+	SYM
cana-681	123	34	3	3	NUM
cana-681	123	35	,	,	PUNCT
cana-681	123	36	3	3	NUM
cana-681	123	37	+	+	SYM
cana-681	123	38	4	4	NUM
cana-681	123	39	,	,	PUNCT
cana-681	123	40	3	3	NUM
cana-681	123	41	+	+	SYM
cana-681	123	42	5	5	NUM
cana-681	123	43	,	,	PUNCT
cana-681	123	44	4	4	NUM
cana-681	124	1	+	+	SYM
cana-681	124	2	1	1	NUM
cana-681	124	3	,	,	PUNCT
cana-681	124	4	4	4	NUM
cana-681	125	1	+	+	NUM
cana-681	125	2	2,+4	2,+4	NOUN
cana-681	125	3	+	+	CCONJ
cana-681	125	4	3	3	NUM
cana-681	125	5	,	,	PUNCT
cana-681	125	6	4	4	NUM
cana-681	125	7	+	+	SYM
cana-681	125	8	4	4	NUM
cana-681	125	9	,	,	PUNCT
cana-681	125	10	4	4	NUM
cana-681	125	11	+	+	SYM
cana-681	125	12	5	5	NUM
cana-681	125	13	communications	communication	NOUN
cana-681	125	14	on	on	ADP
cana-681	125	15	applied	apply	VERB
cana-681	125	16	nonlinear	nonlinear	ADJ
cana-681	125	17	analysis	analysis	NOUN
cana-681	125	18	issn	issn	NOUN
cana-681	125	19	:	:	PUNCT
cana-681	125	20	1074	1074	NUM
cana-681	125	21	-	-	PUNCT
cana-681	125	22	133x	133x	NUM
cana-681	125	23	vol	vol	NOUN
cana-681	125	24	31	31	NUM
cana-681	125	25	no	no	NOUN
cana-681	125	26	.	.	PUNCT
cana-681	126	1	2s	2s	NUM
cana-681	126	2	(	(	PUNCT
cana-681	126	3	2024	2024	NUM
cana-681	126	4	)	)	PUNCT
cana-681	126	5	624	624	NUM
cana-681	126	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	126	7	𝐼	𝐼	PROPN
cana-681	126	8	⊕	⊕	PROPN
cana-681	126	9	𝐽	𝐽	PROPN
cana-681	127	1	=	=	PUNCT
cana-681	127	2	{	{	PUNCT
cana-681	127	3	1	1	NUM
cana-681	127	4	,	,	PUNCT
cana-681	127	5	2	2	NUM
cana-681	127	6	,	,	PUNCT
cana-681	127	7	2	2	NUM
cana-681	127	8	,	,	PUNCT
cana-681	127	9	3	3	NUM
cana-681	127	10	,	,	PUNCT
cana-681	127	11	3	3	NUM
cana-681	127	12	,	,	PUNCT
cana-681	127	13	3	3	NUM
cana-681	127	14	,	,	PUNCT
cana-681	127	15	4	4	NUM
cana-681	127	16	,	,	PUNCT
cana-681	127	17	4	4	NUM
cana-681	127	18	,	,	PUNCT
cana-681	127	19	4	4	NUM
cana-681	127	20	,	,	PUNCT
cana-681	127	21	4	4	NUM
cana-681	127	22	,	,	PUNCT
cana-681	127	23	5	5	NUM
cana-681	127	24	,	,	PUNCT
cana-681	127	25	5	5	NUM
cana-681	127	26	,	,	PUNCT
cana-681	127	27	5	5	NUM
cana-681	127	28	,	,	PUNCT
cana-681	127	29	5	5	NUM
cana-681	127	30	,	,	PUNCT
cana-681	127	31	5	5	NUM
cana-681	127	32	,	,	PUNCT
cana-681	127	33	6	6	NUM
cana-681	127	34	,	,	PUNCT
cana-681	127	35	6	6	NUM
cana-681	127	36	,	,	PUNCT
cana-681	127	37	6	6	NUM
cana-681	127	38	,	,	PUNCT
cana-681	127	39	6	6	NUM
cana-681	127	40	,	,	PUNCT
cana-681	127	41	7	7	NUM
cana-681	127	42	,	,	PUNCT
cana-681	127	43	7	7	NUM
cana-681	127	44	,	,	PUNCT
cana-681	127	45	7	7	NUM
cana-681	127	46	,	,	PUNCT
cana-681	127	47	8	8	NUM
cana-681	127	48	,	,	PUNCT
cana-681	127	49	8	8	NUM
cana-681	127	50	,	,	PUNCT
cana-681	127	51	9	9	NUM
cana-681	127	52	}	}	PUNCT
cana-681	127	53	it	it	PRON
cana-681	127	54	was	be	AUX
cana-681	127	55	proposed	propose	VERB
cana-681	127	56	to	to	PART
cana-681	127	57	find	find	VERB
cana-681	127	58	the	the	DET
cana-681	127	59	corresponding	correspond	VERB
cana-681	127	60	subsets	subset	NOUN
cana-681	127	61	i	i	PRON
cana-681	127	62	and	and	CCONJ
cana-681	127	63	j.	j.	PROPN
cana-681	127	64	the	the	DET
cana-681	127	65	following	follow	VERB
cana-681	127	66	steps	step	NOUN
cana-681	127	67	are	be	AUX
cana-681	127	68	involved	involve	VERB
cana-681	127	69	in	in	ADP
cana-681	127	70	the	the	DET
cana-681	127	71	determination	determination	NOUN
cana-681	127	72	of	of	ADP
cana-681	127	73	unknown	unknown	ADJ
cana-681	127	74	syndromes	syndrome	NOUN
cana-681	127	75	,	,	PUNCT
cana-681	127	76	case	case	NOUN
cana-681	127	77	0	0	NUM
cana-681	127	78	:	:	PUNCT
cana-681	127	79	(	(	PUNCT
cana-681	127	80	zero	zero	NUM
cana-681	127	81	error	error	NOUN
cana-681	127	82	)	)	PUNCT
cana-681	127	83	no	no	DET
cana-681	127	84	error	error	NOUN
cana-681	127	85	in	in	ADP
cana-681	127	86	the	the	DET
cana-681	127	87	received	receive	VERB
cana-681	127	88	codeword	codeword	NOUN
cana-681	127	89	if	if	SCONJ
cana-681	127	90	𝑆1	𝑆1	NOUN
cana-681	127	91	=	=	SYM
cana-681	127	92	0	0	NUM
cana-681	127	93	;	;	PUNCT
cana-681	127	94	otherwise	otherwise	ADV
cana-681	127	95	go	go	VERB
cana-681	127	96	to	to	ADP
cana-681	127	97	case	case	NOUN
cana-681	127	98	1	1	NUM
cana-681	127	99	.	.	PUNCT
cana-681	127	100	case	case	NOUN
cana-681	127	101	1	1	NUM
cana-681	127	102	:	:	PUNCT
cana-681	127	103	(	(	PUNCT
cana-681	127	104	one	one	NUM
cana-681	127	105	error	error	NOUN
cana-681	127	106	)	)	PUNCT
cana-681	127	107	𝑆2	𝑆2	NOUN
cana-681	127	108	=	=	PUNCT
cana-681	127	109	𝑆1	𝑆1	NOUN
cana-681	127	110	2	2	NUM
cana-681	127	111	,	,	PUNCT
cana-681	127	112	𝑆15	𝑆15	NOUN
cana-681	127	113	=	=	PUNCT
cana-681	127	114	𝑆1	𝑆1	NOUN
cana-681	127	115	15	15	NUM
cana-681	127	116	case	case	NOUN
cana-681	127	117	2	2	NUM
cana-681	127	118	:	:	PUNCT
cana-681	127	119	(	(	PUNCT
cana-681	127	120	two	two	NUM
cana-681	127	121	errors	error	NOUN
cana-681	127	122	)	)	PUNCT
cana-681	127	123	let	let	VERB
cana-681	127	124	𝐼1	𝐼1	NOUN
cana-681	127	125	=	=	PUNCT
cana-681	127	126	{	{	PUNCT
cana-681	127	127	0,4,1	0,4,1	NOUN
cana-681	127	128	}	}	PUNCT
cana-681	127	129	,	,	PUNCT
cana-681	127	130	𝐽1	𝐽1	NOUN
cana-681	127	131	=	=	SYM
cana-681	127	132	{	{	PUNCT
cana-681	127	133	7,0,1	7,0,1	NOUN
cana-681	127	134	}	}	PUNCT
cana-681	127	135	,	,	PUNCT
cana-681	127	136	𝐼2	𝐼2	NOUN
cana-681	127	137	=	=	SYM
cana-681	127	138	{	{	PUNCT
cana-681	127	139	0,4,7	0,4,7	NOUN
cana-681	127	140	}	}	PUNCT
cana-681	127	141	,	,	PUNCT
cana-681	127	142	𝐽2	𝐽2	NOUN
cana-681	127	143	=	=	SYM
cana-681	127	144	{	{	PUNCT
cana-681	127	145	3,0,8	3,0,8	NUM
cana-681	127	146	}	}	PUNCT
cana-681	127	147	.	.	PUNCT
cana-681	128	1	the	the	DET
cana-681	128	2	matrices	matrix	NOUN
cana-681	128	3	are	be	AUX
cana-681	128	4	,	,	PUNCT
cana-681	128	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	128	6	,	,	PUNCT
cana-681	128	7	𝐽1	𝐽1	NOUN
cana-681	128	8	)	)	PUNCT
cana-681	128	9	=	=	PUNCT
cana-681	129	1	(	(	PUNCT
cana-681	129	2	𝑆7	𝑆7	PROPN
cana-681	129	3	𝑆0	𝑆0	PROPN
cana-681	129	4	𝑆1	𝑆1	PROPN
cana-681	129	5	𝑆11	𝑆11	PROPN
cana-681	129	6	𝑆4	𝑆4	PROPN
cana-681	129	7	𝑺𝟓	𝑺𝟓	PROPN
cana-681	129	8	𝑆4	𝑆4	PROPN
cana-681	129	9	𝑆1	𝑆1	PROPN
cana-681	129	10	𝑺𝟐	𝑺𝟐	PROPN
cana-681	129	11	)	)	PUNCT
cana-681	130	1	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	130	2	,	,	PUNCT
cana-681	130	3	𝐽2	𝐽2	NOUN
cana-681	130	4	)	)	PUNCT
cana-681	131	1	=	=	SYM
cana-681	131	2	(	(	PUNCT
cana-681	131	3	𝑆3	𝑆3	INTJ
cana-681	131	4	𝑆0	𝑆0	PROPN
cana-681	131	5	𝑆8	𝑆8	PROPN
cana-681	131	6	𝑆7	𝑆7	PROPN
cana-681	131	7	𝑆4	𝑆4	PROPN
cana-681	131	8	s12	s12	PROPN
cana-681	131	9	𝑆10	𝑆10	PROPN
cana-681	131	10	𝑆7	𝑆7	PROPN
cana-681	131	11	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	131	12	)	)	PUNCT
cana-681	132	1	the	the	DET
cana-681	132	2	corresponding	corresponding	ADJ
cana-681	132	3	monomial	monomial	NOUN
cana-681	132	4	in	in	ADP
cana-681	132	5	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	132	6	(	(	PUNCT
cana-681	132	7	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	132	8	,	,	PUNCT
cana-681	132	9	𝐽1	𝐽1	NOUN
cana-681	132	10	)	)	PUNCT
cana-681	132	11	)	)	PUNCT
cana-681	132	12	(	(	PUNCT
cana-681	132	13	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	132	14	(	(	PUNCT
cana-681	132	15	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	132	16	,	,	PUNCT
cana-681	132	17	𝐽2	𝐽2	NOUN
cana-681	132	18	)	)	PUNCT
cana-681	132	19	)	)	PUNCT
cana-681	132	20	)	)	PUNCT
cana-681	132	21	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	132	22	𝑆2	𝑆2	NOUN
cana-681	132	23	1	1	NUM
cana-681	132	24	,	,	PUNCT
cana-681	132	25	𝑆15	𝑆15	NOUN
cana-681	132	26	1	1	NUM
cana-681	132	27	.	.	PUNCT
cana-681	132	28	case	case	NOUN
cana-681	132	29	3	3	NUM
cana-681	132	30	:	:	PUNCT
cana-681	132	31	(	(	PUNCT
cana-681	132	32	three	three	NUM
cana-681	132	33	errors	error	NOUN
cana-681	132	34	)	)	PUNCT
cana-681	132	35	let	let	VERB
cana-681	132	36	𝐼1	𝐼1	NOUN
cana-681	132	37	=	=	SYM
cana-681	132	38	{	{	PUNCT
cana-681	132	39	7,0,1,2	7,0,1,2	NUM
cana-681	132	40	}	}	PUNCT
cana-681	132	41	,	,	PUNCT
cana-681	132	42	𝐽1	𝐽1	NOUN
cana-681	132	43	=	=	SYM
cana-681	132	44	{	{	PUNCT
cana-681	132	45	9,2,1,0	9,2,1,0	NUM
cana-681	132	46	}	}	PUNCT
cana-681	132	47	,	,	PUNCT
cana-681	132	48	𝐼2	𝐼2	NOUN
cana-681	132	49	=	=	SYM
cana-681	132	50	{	{	PUNCT
cana-681	132	51	11,7,8,10	11,7,8,10	NUM
cana-681	132	52	}	}	PUNCT
cana-681	132	53	,	,	PUNCT
cana-681	132	54	𝐽2	𝐽2	NOUN
cana-681	132	55	=	=	SYM
cana-681	132	56	{	{	PUNCT
cana-681	132	57	9,8,7,5	9,8,7,5	NUM
cana-681	132	58	}	}	PUNCT
cana-681	132	59	.	.	PUNCT
cana-681	133	1	the	the	DET
cana-681	133	2	matrices	matrix	NOUN
cana-681	133	3	are	be	AUX
cana-681	133	4	,	,	PUNCT
cana-681	133	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	133	6	,	,	PUNCT
cana-681	133	7	𝐽1	𝐽1	NOUN
cana-681	133	8	)	)	PUNCT
cana-681	133	9	=	=	SYM
cana-681	134	1	(	(	PUNCT
cana-681	134	2	𝑆16	𝑆16	PROPN
cana-681	134	3	𝑆9	𝑆9	PROPN
cana-681	134	4	𝑺𝟖	𝑺𝟖	PROPN
cana-681	134	5	𝑆7	𝑆7	PROPN
cana-681	134	6	𝑆9	𝑆9	PROPN
cana-681	134	7	𝑺𝟐	𝑺𝟐	PROPN
cana-681	134	8	𝑆1	𝑆1	NOUN
cana-681	134	9	𝑆0	𝑆0	PROPN
cana-681	134	10	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	134	11	𝑺𝟑	𝑺𝟑	PROPN
cana-681	134	12	𝑺𝟐	𝑺𝟐	PROPN
cana-681	134	13	𝑆1	𝑆1	PROPN
cana-681	134	14	𝑆11	𝑆11	PROPN
cana-681	134	15	𝑆4	𝑆4	PROPN
cana-681	134	16	𝑺𝟑	𝑺𝟑	PROPN
cana-681	134	17	𝑺𝟐	𝑺𝟐	PROPN
cana-681	134	18	)	)	PUNCT
cana-681	135	1	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	135	2	,	,	PUNCT
cana-681	135	3	𝐽2	𝐽2	NOUN
cana-681	135	4	)	)	PUNCT
cana-681	136	1	=	=	PUNCT
cana-681	136	2	(	(	PUNCT
cana-681	136	3	𝑺𝟐𝟎	𝑺𝟐𝟎	NUM
cana-681	136	4	𝑆19	𝑆19	PROPN
cana-681	136	5	𝑺𝟏𝟖	𝑺𝟏𝟖	NOUN
cana-681	136	6	𝑆16	𝑆16	PROPN
cana-681	136	7	𝑆16	𝑆16	PROPN
cana-681	137	1	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	137	2	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	138	1	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	138	2	𝑺𝟏𝟕	𝑺𝟏𝟕	NUM
cana-681	138	3	𝑆16	𝑆16	PROPN
cana-681	138	4	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	138	5	𝑺𝟏𝟑	𝑺𝟏𝟑	VERB
cana-681	139	1	𝑆19	𝑆19	PROPN
cana-681	139	2	𝑺𝟏𝟖	𝑺𝟏𝟖	PUNCT
cana-681	140	1	𝑺𝟏𝟕	𝑺𝟏𝟕	PROPN
cana-681	140	2	𝑺𝟏𝟓	𝑺𝟏𝟓	NUM
cana-681	140	3	)	)	PUNCT
cana-681	141	1	the	the	DET
cana-681	141	2	corresponding	corresponding	ADJ
cana-681	141	3	monomial	monomial	NOUN
cana-681	141	4	in	in	ADP
cana-681	141	5	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	141	6	(	(	PUNCT
cana-681	141	7	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	141	8	,	,	PUNCT
cana-681	141	9	𝐽1	𝐽1	NOUN
cana-681	141	10	)	)	PUNCT
cana-681	141	11	)	)	PUNCT
cana-681	141	12	(	(	PUNCT
cana-681	141	13	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	141	14	(	(	PUNCT
cana-681	141	15	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	141	16	,	,	PUNCT
cana-681	141	17	𝐽2	𝐽2	NOUN
cana-681	141	18	)	)	PUNCT
cana-681	141	19	)	)	PUNCT
cana-681	141	20	)	)	PUNCT
cana-681	141	21	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	141	22	𝑆2	𝑆2	NOUN
cana-681	141	23	3	3	NUM
cana-681	141	24	,	,	PUNCT
cana-681	141	25	𝑆15	𝑆15	NOUN
cana-681	141	26	3	3	NUM
cana-681	141	27	.	.	PUNCT
cana-681	141	28	case	case	NOUN
cana-681	141	29	4	4	NUM
cana-681	141	30	:	:	PUNCT
cana-681	141	31	(	(	PUNCT
cana-681	141	32	four	four	NUM
cana-681	141	33	errors	error	NOUN
cana-681	141	34	)	)	PUNCT
cana-681	141	35	let	let	VERB
cana-681	141	36	𝐼1	𝐼1	NOUN
cana-681	141	37	=	=	PUNCT
cana-681	141	38	{	{	PUNCT
cana-681	141	39	0,2,1,4,3	0,2,1,4,3	NUM
cana-681	141	40	}	}	PUNCT
cana-681	141	41	,	,	PUNCT
cana-681	141	42	𝐽1	𝐽1	NOUN
cana-681	141	43	=	=	SYM
cana-681	141	44	{	{	PUNCT
cana-681	141	45	2,0,1,6,9	2,0,1,6,9	NUM
cana-681	141	46	}	}	PUNCT
cana-681	141	47	,	,	PUNCT
cana-681	141	48	𝐼2	𝐼2	NOUN
cana-681	141	49	=	=	SYM
cana-681	141	50	{	{	PUNCT
cana-681	141	51	0,9,1,15,4	0,9,1,15,4	NOUN
cana-681	141	52	}	}	PUNCT
cana-681	141	53	,	,	PUNCT
cana-681	141	54	𝐽2	𝐽2	NOUN
cana-681	141	55	=	=	SYM
cana-681	141	56	{	{	PUNCT
cana-681	141	57	15,6,14,0,11	15,6,14,0,11	NUM
cana-681	141	58	}	}	PUNCT
cana-681	141	59	.	.	PUNCT
cana-681	142	1	the	the	DET
cana-681	142	2	matrices	matrix	NOUN
cana-681	142	3	are	be	AUX
cana-681	142	4	,	,	PUNCT
cana-681	142	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	142	6	,	,	PUNCT
cana-681	142	7	𝐽1	𝐽1	NOUN
cana-681	142	8	)	)	PUNCT
cana-681	142	9	=	=	PUNCT
cana-681	143	1	(	(	PUNCT
cana-681	143	2	𝑺𝟐	𝑺𝟐	NOUN
cana-681	143	3	𝑆0	𝑆0	PROPN
cana-681	143	4	𝑆1	𝑆1	VERB
cana-681	143	5	𝑆6	𝑆6	PROPN
cana-681	143	6	𝑆9	𝑆9	PROPN
cana-681	143	7	𝑆4	𝑆4	PROPN
cana-681	143	8	𝑺𝟐	𝑺𝟐	PROPN
cana-681	143	9	𝑺𝟐	𝑺𝟐	PROPN
cana-681	144	1	𝑺𝟖	𝑺𝟖	PROPN
cana-681	144	2	𝑆11	𝑆11	PROPN
cana-681	144	3	𝑺𝟐	𝑺𝟐	PROPN
cana-681	144	4	𝑆1	𝑆1	PROPN
cana-681	144	5	𝑺𝟐	𝑺𝟐	PROPN
cana-681	144	6	𝑆7	𝑆7	PROPN
cana-681	144	7	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	144	8	𝑆6	𝑆6	PROPN
cana-681	144	9	𝑆4	𝑆4	PROPN
cana-681	144	10	𝑺𝟓	𝑺𝟓	PROPN
cana-681	145	1	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	145	2	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	145	3	𝑺𝟓	𝑺𝟓	NOUN
cana-681	145	4	𝑺𝟑	𝑺𝟑	NOUN
cana-681	145	5	𝑆4	𝑆4	PROPN
cana-681	145	6	𝑆9	𝑆9	PROPN
cana-681	145	7	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	145	8	)	)	PUNCT
cana-681	145	9	communications	communication	NOUN
cana-681	145	10	on	on	ADP
cana-681	145	11	applied	apply	VERB
cana-681	145	12	nonlinear	nonlinear	ADJ
cana-681	145	13	analysis	analysis	NOUN
cana-681	145	14	issn	issn	NOUN
cana-681	145	15	:	:	PUNCT
cana-681	145	16	1074	1074	NUM
cana-681	145	17	-	-	PUNCT
cana-681	145	18	133x	133x	NUM
cana-681	145	19	vol	vol	NOUN
cana-681	145	20	31	31	NUM
cana-681	145	21	no	no	NOUN
cana-681	145	22	.	.	PUNCT
cana-681	146	1	2s	2s	NUM
cana-681	146	2	(	(	PUNCT
cana-681	146	3	2024	2024	NUM
cana-681	146	4	)	)	PUNCT
cana-681	146	5	625	625	NUM
cana-681	146	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	146	7	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	146	8	,	,	PUNCT
cana-681	146	9	𝐽2	𝐽2	NOUN
cana-681	146	10	)	)	PUNCT
cana-681	146	11	=	=	SYM
cana-681	147	1	(	(	PUNCT
cana-681	147	2	𝑺𝟏𝟓	𝑺𝟏𝟓	NOUN
cana-681	147	3	𝑆6	𝑆6	NOUN
cana-681	147	4	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	147	5	𝑆0	𝑆0	X
cana-681	148	1	𝑆11	𝑆11	VERB
cana-681	148	2	𝑆24	𝑆24	PROPN
cana-681	148	3	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	148	4	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	148	5	𝑆9	𝑆9	ADJ
cana-681	148	6	𝑺𝟐𝟎	𝑺𝟐𝟎	PROPN
cana-681	148	7	𝑆16	𝑆16	PROPN
cana-681	148	8	𝑆7	𝑆7	NOUN
cana-681	148	9	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	148	10	𝑆1	𝑆1	VERB
cana-681	148	11	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	148	12	𝑆30	𝑆30	PROPN
cana-681	148	13	𝑆21	𝑆21	PROPN
cana-681	148	14	𝑺𝟐𝟗	𝑺𝟐𝟗	ADP
cana-681	148	15	𝑺𝟏𝟓	𝑺𝟏𝟓	NOUN
cana-681	148	16	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	149	1	𝑆19	𝑆19	PROPN
cana-681	149	2	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	149	3	𝑆18	𝑆18	PROPN
cana-681	149	4	𝑆4	𝑆4	PROPN
cana-681	149	5	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	149	6	)	)	PUNCT
cana-681	149	7	the	the	DET
cana-681	149	8	corresponding	corresponding	ADJ
cana-681	149	9	monomial	monomial	NOUN
cana-681	149	10	in	in	ADP
cana-681	149	11	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	149	12	(	(	PUNCT
cana-681	149	13	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	149	14	,	,	PUNCT
cana-681	149	15	𝐽1	𝐽1	NOUN
cana-681	149	16	)	)	PUNCT
cana-681	149	17	)	)	PUNCT
cana-681	149	18	(	(	PUNCT
cana-681	149	19	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	149	20	(	(	PUNCT
cana-681	149	21	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	149	22	,	,	PUNCT
cana-681	149	23	𝐽2	𝐽2	NOUN
cana-681	149	24	)	)	PUNCT
cana-681	149	25	)	)	PUNCT
cana-681	149	26	)	)	PUNCT
cana-681	149	27	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	149	28	𝑆2	𝑆2	NOUN
cana-681	149	29	5	5	NUM
cana-681	149	30	,	,	PUNCT
cana-681	149	31	𝑆15	𝑆15	NOUN
cana-681	149	32	5	5	NUM
cana-681	149	33	.	.	PUNCT
cana-681	150	1	case	case	NOUN
cana-681	150	2	5	5	NUM
cana-681	150	3	:	:	PUNCT
cana-681	150	4	(	(	PUNCT
cana-681	150	5	five	five	NUM
cana-681	150	6	errors	error	NOUN
cana-681	150	7	)	)	PUNCT
cana-681	150	8	let	let	VERB
cana-681	150	9	𝐼1	𝐼1	NOUN
cana-681	150	10	=	=	PUNCT
cana-681	150	11	{	{	PUNCT
cana-681	150	12	1,0,12,2,20,40	1,0,12,2,20,40	NUM
cana-681	150	13	}	}	PUNCT
cana-681	150	14	,	,	PUNCT
cana-681	150	15	𝐽1	𝐽1	NOUN
cana-681	150	16	=	=	SYM
cana-681	150	17	{	{	PUNCT
cana-681	150	18	1,2,13,0,5,3	1,2,13,0,5,3	NUM
cana-681	150	19	}	}	PUNCT
cana-681	150	20	,	,	PUNCT
cana-681	150	21	𝐼2	𝐼2	NOUN
cana-681	150	22	=	=	SYM
cana-681	150	23	{	{	PUNCT
cana-681	150	24	15,6,2,45,32,1	15,6,2,45,32,1	NUM
cana-681	150	25	}	}	PUNCT
cana-681	150	26	,	,	PUNCT
cana-681	150	27	𝐽2	𝐽2	NOUN
cana-681	150	28	=	=	SYM
cana-681	150	29	{	{	PUNCT
cana-681	150	30	0,9,13,20,29,55	0,9,13,20,29,55	PUNCT
cana-681	150	31	}	}	PUNCT
cana-681	150	32	.	.	PUNCT
cana-681	151	1	the	the	DET
cana-681	151	2	matrices	matrix	NOUN
cana-681	151	3	are	be	AUX
cana-681	151	4	,	,	PUNCT
cana-681	151	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	151	6	,	,	PUNCT
cana-681	151	7	𝐽1	𝐽1	NOUN
cana-681	151	8	)	)	PUNCT
cana-681	151	9	=	=	PUNCT
cana-681	152	1	(	(	PUNCT
cana-681	152	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	152	3	𝑺𝟑	𝑺𝟑	NOUN
cana-681	152	4	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	152	5	𝑆1	𝑆1	NOUN
cana-681	152	6	𝑆6	𝑆6	PROPN
cana-681	153	1	𝑆4	𝑆4	PROPN
cana-681	153	2	𝑆1	𝑆1	VERB
cana-681	153	3	𝑺𝟐	𝑺𝟐	PROPN
cana-681	153	4	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	153	5	𝑆0	𝑆0	NOUN
cana-681	153	6	𝑺𝟓	𝑺𝟓	ADV
cana-681	153	7	𝑺𝟑	𝑺𝟑	NOUN
cana-681	153	8	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	153	9	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	153	10	𝑆25	𝑆25	PROPN
cana-681	153	11	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	153	12	𝑺𝟏𝟕	𝑺𝟏𝟕	PROPN
cana-681	153	13	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	153	14	𝑺𝟑	𝑺𝟑	NOUN
cana-681	153	15	𝑆4	𝑆4	PROPN
cana-681	153	16	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	153	17	𝑺𝟐	𝑺𝟐	PROPN
cana-681	153	18	𝑆7	𝑆7	PROPN
cana-681	153	19	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	153	20	𝑆21	𝑆21	PROPN
cana-681	153	21	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	154	1	𝑺𝟑𝟑	𝑺𝟑𝟑	PROPN
cana-681	154	2	𝑺𝟐𝟎	𝑺𝟐𝟎	PROPN
cana-681	154	3	𝑆25	𝑆25	AUX
cana-681	154	4	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	154	5	𝑆41	𝑆41	PROPN
cana-681	154	6	𝑆42	𝑆42	PROPN
cana-681	154	7	𝑆53	𝑆53	PROPN
cana-681	155	1	𝑺𝟒𝟎	𝑺𝟒𝟎	PROPN
cana-681	156	1	𝑆45	𝑆45	PROPN
cana-681	156	2	𝑆43	𝑆43	PROPN
cana-681	156	3	)	)	PUNCT
cana-681	156	4	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	156	5	,	,	PUNCT
cana-681	156	6	𝐽2	𝐽2	NOUN
cana-681	156	7	)	)	PUNCT
cana-681	157	1	=	=	SYM
cana-681	157	2	(	(	PUNCT
cana-681	157	3	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	157	4	𝑆24	𝑆24	PROPN
cana-681	158	1	𝑆28	𝑆28	PROPN
cana-681	158	2	𝑺𝟑𝟓	𝑺𝟑𝟓	PROPN
cana-681	159	1	𝑺𝟒𝟒	𝑺𝟒𝟒	PROPN
cana-681	159	2	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	159	3	𝑆6	𝑆6	X
cana-681	159	4	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	160	1	𝑆19	𝑆19	PROPN
cana-681	160	2	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	160	3	𝑺𝟑𝟓	𝑺𝟑𝟓	PROPN
cana-681	160	4	𝑺𝟒	𝑺𝟒	NOUN
cana-681	160	5	𝑺𝟐	𝑺𝟐	PROPN
cana-681	161	1	𝑆11	𝑆11	PROPN
cana-681	161	2	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	161	3	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	162	1	𝑆31	𝑆31	PROPN
cana-681	162	2	𝑆57	𝑆57	PROPN
cana-681	162	3	𝑆45	𝑆45	PROPN
cana-681	162	4	𝑆54	𝑆54	PROPN
cana-681	162	5	𝑆1	𝑆1	VERB
cana-681	162	6	𝑺𝟖	𝑺𝟖	PROPN
cana-681	163	1	𝑺𝟏𝟕	𝑺𝟏𝟕	PROPN
cana-681	163	2	𝑆43	𝑆43	PROPN
cana-681	163	3	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	163	4	𝑆41	𝑆41	VERB
cana-681	163	5	𝑆45	𝑆45	PROPN
cana-681	163	6	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	163	7	𝑆4	𝑆4	PROPN
cana-681	163	8	𝑆30	𝑆30	PROPN
cana-681	163	9	𝑆1	𝑆1	VERB
cana-681	163	10	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	163	11	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	164	1	𝑆21	𝑆21	PROPN
cana-681	164	2	𝑆30	𝑆30	PROPN
cana-681	164	3	𝑺𝟓𝟔	𝑺𝟓𝟔	PROPN
cana-681	164	4	)	)	PUNCT
cana-681	165	1	the	the	DET
cana-681	165	2	corresponding	corresponding	ADJ
cana-681	165	3	monomial	monomial	NOUN
cana-681	165	4	in	in	ADP
cana-681	165	5	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	165	6	(	(	PUNCT
cana-681	165	7	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	165	8	,	,	PUNCT
cana-681	165	9	𝐽1	𝐽1	NOUN
cana-681	165	10	)	)	PUNCT
cana-681	165	11	)	)	PUNCT
cana-681	165	12	(	(	PUNCT
cana-681	165	13	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	165	14	(	(	PUNCT
cana-681	165	15	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	165	16	,	,	PUNCT
cana-681	165	17	𝐽2	𝐽2	NOUN
cana-681	165	18	)	)	PUNCT
cana-681	165	19	)	)	PUNCT
cana-681	165	20	)	)	PUNCT
cana-681	165	21	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	165	22	𝑆2	𝑆2	NOUN
cana-681	165	23	4	4	NUM
cana-681	165	24	,	,	PUNCT
cana-681	165	25	𝑆15	𝑆15	NOUN
cana-681	165	26	3	3	NUM
cana-681	165	27	.	.	PUNCT
cana-681	165	28	case	case	NOUN
cana-681	165	29	6	6	NUM
cana-681	165	30	:	:	PUNCT
cana-681	165	31	(	(	PUNCT
cana-681	165	32	six	six	NUM
cana-681	165	33	errors	error	NOUN
cana-681	165	34	)	)	PUNCT
cana-681	165	35	let	let	VERB
cana-681	165	36	𝐼1	𝐼1	NOUN
cana-681	165	37	=	=	PUNCT
cana-681	165	38	{	{	PUNCT
cana-681	165	39	2,0,1,50,47,21,12	2,0,1,50,47,21,12	NUM
cana-681	165	40	}	}	PUNCT
cana-681	165	41	,	,	PUNCT
cana-681	165	42	𝐽1	𝐽1	NOUN
cana-681	165	43	=	=	SYM
cana-681	165	44	{	{	PUNCT
cana-681	165	45	0,2,1,19,16,4,50	0,2,1,19,16,4,50	NOUN
cana-681	165	46	}	}	PUNCT
cana-681	165	47	,	,	PUNCT
cana-681	165	48	𝐼2	𝐼2	NOUN
cana-681	165	49	=	=	SYM
cana-681	165	50	{	{	PUNCT
cana-681	165	51	13,1,0,11,39,51,4	13,1,0,11,39,51,4	ADV
cana-681	165	52	}	}	PUNCT
cana-681	165	53	,	,	PUNCT
cana-681	165	54	𝐽2	𝐽2	NOUN
cana-681	165	55	=	=	SYM
cana-681	165	56	{	{	PUNCT
cana-681	165	57	2,14,15,8,45,7,18	2,14,15,8,45,7,18	NUM
cana-681	165	58	}	}	PUNCT
cana-681	165	59	.	.	PUNCT
cana-681	166	1	the	the	DET
cana-681	166	2	matrices	matrix	NOUN
cana-681	166	3	are	be	AUX
cana-681	166	4	,	,	PUNCT
cana-681	166	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	166	6	,	,	PUNCT
cana-681	166	7	𝐽1	𝐽1	NOUN
cana-681	166	8	)	)	PUNCT
cana-681	166	9	=	=	PUNCT
cana-681	167	1	(	(	PUNCT
cana-681	167	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	167	3	𝑆4	𝑆4	PROPN
cana-681	167	4	𝑆3	𝑆3	PROPN
cana-681	168	1	𝑆21	𝑆21	PROPN
cana-681	168	2	𝑺𝟏𝟖	𝑺𝟏𝟖	PROPN
cana-681	168	3	𝑆6	𝑆6	PROPN
cana-681	168	4	𝑆52	𝑆52	PROPN
cana-681	168	5	𝑆0	𝑆0	PROPN
cana-681	168	6	𝑺𝟐	𝑺𝟐	PROPN
cana-681	168	7	𝑆1	𝑆1	NOUN
cana-681	168	8	𝑆19	𝑆19	PROPN
cana-681	168	9	𝑆16	𝑆16	PROPN
cana-681	168	10	𝑆4	𝑆4	PROPN
cana-681	168	11	𝑺𝟓𝟎	𝑺𝟓𝟎	PROPN
cana-681	168	12	𝑆1	𝑆1	VERB
cana-681	168	13	𝑺𝟑	𝑺𝟑	NOUN
cana-681	168	14	𝑺𝟐	𝑺𝟐	PROPN
cana-681	168	15	𝑺𝟐𝟎	𝑺𝟐𝟎	PROPN
cana-681	168	16	𝑆17	𝑆17	PROPN
cana-681	168	17	𝑺𝟓	𝑺𝟓	NOUN
cana-681	168	18	𝑆51	𝑆51	PROPN
cana-681	168	19	𝑺𝟓𝟎	𝑺𝟓𝟎	NOUN
cana-681	168	20	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	168	21	𝑆51	𝑆51	PROPN
cana-681	169	1	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	169	2	𝑆9	𝑆9	INTJ
cana-681	169	3	𝑆54	𝑆54	PROPN
cana-681	169	4	𝑆43	𝑆43	PROPN
cana-681	169	5	𝑺𝟒𝟕	𝑺𝟒𝟕	PROPN
cana-681	170	1	𝑆49	𝑆49	PROPN
cana-681	170	2	𝑺𝟒𝟖	𝑺𝟒𝟖	PROPN
cana-681	170	3	𝑆9	𝑆9	NOUN
cana-681	170	4	𝑆6	𝑆6	INTJ
cana-681	170	5	𝑆51	𝑆51	PROPN
cana-681	171	1	𝑺𝟒𝟎	𝑺𝟒𝟎	PROPN
cana-681	171	2	𝑆21	𝑆21	PROPN
cana-681	172	1	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	172	2	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	173	1	𝑺𝟒𝟎	𝑺𝟒𝟎	PROPN
cana-681	174	1	𝑺𝟑𝟕	𝑺𝟑𝟕	PROPN
cana-681	174	2	𝑆25	𝑆25	PROPN
cana-681	174	3	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	174	4	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	174	5	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	175	1	𝑺𝟏𝟑	𝑺𝟏𝟑	VERB
cana-681	175	2	𝑆31	𝑆31	PROPN
cana-681	175	3	𝑆28	𝑆28	PROPN
cana-681	175	4	𝑆16	𝑆16	PROPN
cana-681	175	5	𝑺𝟓	𝑺𝟓	NOUN
cana-681	175	6	)	)	PUNCT
cana-681	176	1	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	176	2	,	,	PUNCT
cana-681	176	3	𝐽2	𝐽2	NOUN
cana-681	176	4	)	)	PUNCT
cana-681	176	5	=	=	SYM
cana-681	177	1	(	(	PUNCT
cana-681	177	2	𝑺𝟏𝟓	𝑺𝟏𝟓	NOUN
cana-681	177	3	𝑺𝟐𝟕	𝑺𝟐𝟕	VERB
cana-681	177	4	𝑆28	𝑆28	PROPN
cana-681	177	5	𝑆21	𝑆21	PROPN
cana-681	177	6	𝑆1	𝑆1	VERB
cana-681	177	7	𝑺𝟐𝟎	𝑺𝟐𝟎	PROPN
cana-681	177	8	𝑆31	𝑆31	ADJ
cana-681	177	9	𝑺𝟑	𝑺𝟑	NOUN
cana-681	178	1	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	178	2	𝑆16	𝑆16	PROPN
cana-681	178	3	𝑆9	𝑆9	PROPN
cana-681	178	4	𝑺𝟒𝟔	𝑺𝟒𝟔	PROPN
cana-681	178	5	𝑺𝟖	𝑺𝟖	PROPN
cana-681	179	1	𝑆19	𝑆19	PROPN
cana-681	179	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	179	3	𝑆4	𝑆4	PROPN
cana-681	180	1	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	180	2	𝑺𝟖	𝑺𝟖	PUNCT
cana-681	181	1	𝑆45	𝑆45	PROPN
cana-681	181	2	𝑆7	𝑆7	PROPN
cana-681	181	3	𝑺𝟏𝟖	𝑺𝟏𝟖	X
cana-681	182	1	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	182	2	𝑆25	𝑆25	VERB
cana-681	182	3	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	182	4	𝑆19	𝑆19	PROPN
cana-681	182	5	𝑺𝟓𝟔	𝑺𝟓𝟔	NUM
cana-681	182	6	𝑺𝟏𝟖	𝑺𝟏𝟖	NOUN
cana-681	183	1	𝑆29	𝑆29	PRON
cana-681	183	2	𝑆41	𝑆41	VERB
cana-681	183	3	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	183	4	𝑆54	𝑆54	PROPN
cana-681	183	5	𝑺𝟒𝟕	𝑺𝟒𝟕	PROPN
cana-681	183	6	𝑺𝟐𝟕	𝑺𝟐𝟕	VERB
cana-681	183	7	𝑺𝟒𝟔	𝑺𝟒𝟔	PROPN
cana-681	183	8	𝑆57	𝑆57	PROPN
cana-681	183	9	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	183	10	𝑺𝟖	𝑺𝟖	PROPN
cana-681	184	1	𝑆9	𝑆9	DET
cana-681	184	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	184	3	𝑆39	𝑆39	PROPN
cana-681	184	4	𝑺𝟏	𝑺𝟏	PROPN
cana-681	184	5	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	184	6	𝑆6	𝑆6	PROPN
cana-681	184	7	𝑺𝟏𝟖	𝑺𝟏𝟖	PUNCT
cana-681	185	1	𝑆19	𝑆19	PROPN
cana-681	185	2	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	185	3	𝑆49	𝑆49	PROPN
cana-681	185	4	𝑆11	𝑆11	PROPN
cana-681	185	5	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	185	6	)	)	PUNCT
cana-681	185	7	communications	communication	NOUN
cana-681	185	8	on	on	ADP
cana-681	185	9	applied	apply	VERB
cana-681	185	10	nonlinear	nonlinear	ADJ
cana-681	185	11	analysis	analysis	NOUN
cana-681	185	12	issn	issn	NOUN
cana-681	185	13	:	:	PUNCT
cana-681	185	14	1074	1074	NUM
cana-681	185	15	-	-	PUNCT
cana-681	185	16	133x	133x	NUM
cana-681	185	17	vol	vol	NOUN
cana-681	185	18	31	31	NUM
cana-681	185	19	no	no	NOUN
cana-681	185	20	.	.	PUNCT
cana-681	186	1	2s	2s	NUM
cana-681	186	2	(	(	PUNCT
cana-681	186	3	2024	2024	NUM
cana-681	186	4	)	)	PUNCT
cana-681	186	5	626	626	NUM
cana-681	186	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	186	7	the	the	DET
cana-681	186	8	corresponding	corresponding	ADJ
cana-681	186	9	monomial	monomial	NOUN
cana-681	186	10	in	in	ADP
cana-681	186	11	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	186	12	(	(	PUNCT
cana-681	186	13	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	186	14	,	,	PUNCT
cana-681	186	15	𝐽1	𝐽1	NOUN
cana-681	186	16	)	)	PUNCT
cana-681	186	17	)	)	PUNCT
cana-681	186	18	(	(	PUNCT
cana-681	186	19	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	186	20	(	(	PUNCT
cana-681	186	21	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	186	22	,	,	PUNCT
cana-681	186	23	𝐽2	𝐽2	NOUN
cana-681	186	24	)	)	PUNCT
cana-681	186	25	)	)	PUNCT
cana-681	186	26	)	)	PUNCT
cana-681	186	27	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	187	1	𝑆2	𝑆2	NOUN
cana-681	187	2	3	3	NUM
cana-681	187	3	,	,	PUNCT
cana-681	187	4	𝑆15	𝑆15	NOUN
cana-681	187	5	3	3	NUM
cana-681	187	6	.	.	PUNCT
cana-681	188	1	case	case	NOUN
cana-681	188	2	7	7	NUM
cana-681	188	3	:	:	PUNCT
cana-681	188	4	(	(	PUNCT
cana-681	188	5	seven	seven	NUM
cana-681	188	6	errors	error	NOUN
cana-681	188	7	)	)	PUNCT
cana-681	188	8	let	let	VERB
cana-681	188	9	𝐼1	𝐼1	NOUN
cana-681	188	10	=	=	PUNCT
cana-681	188	11	{	{	PUNCT
cana-681	188	12	21,41,2,5,0,1,30,7	21,41,2,5,0,1,30,7	NUM
cana-681	188	13	}	}	PUNCT
cana-681	188	14	,	,	PUNCT
cana-681	188	15	𝐽1	𝐽1	NOUN
cana-681	188	16	=	=	SYM
cana-681	188	17	{	{	PUNCT
cana-681	188	18	4,6,0,30,2,1,11,21	4,6,0,30,2,1,11,21	NUM
cana-681	188	19	}	}	PUNCT
cana-681	188	20	,	,	PUNCT
cana-681	188	21	𝐼2	𝐼2	NOUN
cana-681	188	22	=	=	SYM
cana-681	188	23	{	{	PUNCT
cana-681	188	24	1,0,13,11,28,39,55,16	1,0,13,11,28,39,55,16	NUM
cana-681	188	25	}	}	PUNCT
cana-681	188	26	,	,	PUNCT
cana-681	188	27	𝐽2	𝐽2	NOUN
cana-681	188	28	=	=	SYM
cana-681	188	29	{	{	PUNCT
cana-681	188	30	14,15,2,4,24,45,39,0	14,15,2,4,24,45,39,0	NUM
cana-681	188	31	}	}	PUNCT
cana-681	188	32	.	.	PUNCT
cana-681	189	1	the	the	DET
cana-681	189	2	matrices	matrix	NOUN
cana-681	189	3	are	be	AUX
cana-681	189	4	,	,	PUNCT
cana-681	189	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	189	6	,	,	PUNCT
cana-681	189	7	𝐽1	𝐽1	NOUN
cana-681	189	8	)	)	PUNCT
cana-681	189	9	=	=	PUNCT
cana-681	190	1	(	(	PUNCT
cana-681	190	2	𝑆25	𝑆25	PROPN
cana-681	190	3	𝑺𝟐𝟕	𝑺𝟐𝟕	PROPN
cana-681	190	4	𝑆21	𝑆21	PROPN
cana-681	190	5	𝑆51	𝑆51	PROPN
cana-681	190	6	𝑆23	𝑆23	PROPN
cana-681	190	7	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	191	1	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	192	1	𝑆42	𝑆42	PROPN
cana-681	192	2	𝑆45	𝑆45	PROPN
cana-681	192	3	𝑺𝟒𝟕	𝑺𝟒𝟕	PROPN
cana-681	192	4	𝑆41	𝑆41	PROPN
cana-681	192	5	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	193	1	𝑆43	𝑆43	PROPN
cana-681	193	2	𝑆42	𝑆42	PROPN
cana-681	193	3	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	193	4	𝑺𝟓	𝑺𝟓	NOUN
cana-681	193	5	𝑆6	𝑆6	PROPN
cana-681	194	1	𝑺𝟖	𝑺𝟖	PROPN
cana-681	194	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	194	3	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	194	4	𝑆4	𝑆4	PROPN
cana-681	194	5	𝑺𝟑	𝑺𝟑	NOUN
cana-681	195	1	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	195	2	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	195	3	𝑆9	𝑆9	PROPN
cana-681	195	4	𝑆11	𝑆11	PROPN
cana-681	195	5	𝑺𝟓	𝑺𝟓	PROPN
cana-681	195	6	𝑺𝟑𝟓	𝑺𝟑𝟓	PROPN
cana-681	195	7	𝑆7	𝑆7	PROPN
cana-681	195	8	𝑆6	𝑆6	X
cana-681	195	9	𝑆16	𝑆16	PROPN
cana-681	195	10	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	195	11	𝑆4	𝑆4	PROPN
cana-681	195	12	𝑆6	𝑆6	PROPN
cana-681	195	13	𝑆0	𝑆0	PROPN
cana-681	195	14	𝑆30	𝑆30	PROPN
cana-681	195	15	𝑺𝟐	𝑺𝟐	PROPN
cana-681	195	16	𝑆1	𝑆1	PROPN
cana-681	195	17	𝑆11	𝑆11	PROPN
cana-681	195	18	𝑆21	𝑆21	PROPN
cana-681	195	19	𝑺𝟓	𝑺𝟓	NOUN
cana-681	195	20	𝑆7	𝑆7	PROPN
cana-681	195	21	𝑆1	𝑆1	PROPN
cana-681	195	22	𝑆31	𝑆31	PROPN
cana-681	195	23	𝑺𝟑	𝑺𝟑	NOUN
cana-681	195	24	𝑺𝟐	𝑺𝟐	PROPN
cana-681	195	25	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	195	26	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	196	1	𝑺𝟑𝟒	𝑺𝟑𝟒	PROPN
cana-681	196	2	𝑆36	𝑆36	PROPN
cana-681	196	3	𝑆30	𝑆30	PROPN
cana-681	196	4	𝑺𝟑	𝑺𝟑	NOUN
cana-681	196	5	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	196	6	𝑆31	𝑆31	PROPN
cana-681	196	7	𝑆41	𝑆41	PROPN
cana-681	197	1	𝑆51	𝑆51	PROPN
cana-681	197	2	𝑆11	𝑆11	PROPN
cana-681	197	3	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	197	4	𝑆7	𝑆7	NOUN
cana-681	198	1	𝑺𝟑𝟕	𝑺𝟑𝟕	PROPN
cana-681	198	2	𝑆9	𝑆9	NOUN
cana-681	198	3	𝑺𝟖	𝑺𝟖	PROPN
cana-681	198	4	𝑺𝟏𝟖	𝑺𝟏𝟖	PUNCT
cana-681	199	1	𝑆28	𝑆28	PROPN
cana-681	199	2	)	)	PUNCT
cana-681	199	3	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	199	4	,	,	PUNCT
cana-681	199	5	𝐽2	𝐽2	NOUN
cana-681	199	6	)	)	PUNCT
cana-681	199	7	=	=	SYM
cana-681	200	1	(	(	PUNCT
cana-681	200	2	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	200	3	𝑆16	𝑆16	PROPN
cana-681	200	4	𝑺𝟑	𝑺𝟑	NOUN
cana-681	200	5	𝑺𝟓	𝑺𝟓	ADV
cana-681	200	6	𝑆25	𝑆25	PROPN
cana-681	200	7	𝑺𝟒𝟔	𝑺𝟒𝟔	PROPN
cana-681	200	8	𝑺𝟒𝟎	𝑺𝟒𝟎	PROPN
cana-681	200	9	𝑆1	𝑆1	NOUN
cana-681	200	10	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	201	1	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	201	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	201	3	𝑆4	𝑆4	PROPN
cana-681	202	1	𝑆24	𝑆24	PROPN
cana-681	202	2	𝑆45	𝑆45	PROPN
cana-681	202	3	𝑆39	𝑆39	ADJ
cana-681	202	4	𝑆0	𝑆0	NOUN
cana-681	202	5	𝑺𝟐𝟕	𝑺𝟐𝟕	VERB
cana-681	202	6	𝑆28	𝑆28	PROPN
cana-681	202	7	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	203	1	𝑺𝟏𝟕	𝑺𝟏𝟕	PROPN
cana-681	203	2	𝑺𝟑𝟕	𝑺𝟑𝟕	PROPN
cana-681	203	3	𝑆1	𝑆1	VERB
cana-681	203	4	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	203	5	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	203	6	𝑆25	𝑆25	PROPN
cana-681	203	7	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	203	8	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	203	9	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	203	10	𝑺𝟑𝟓	𝑺𝟑𝟓	PROPN
cana-681	203	11	𝑺𝟓𝟔	𝑺𝟓𝟔	NOUN
cana-681	203	12	𝑺𝟓𝟎	𝑺𝟓𝟎	NOUN
cana-681	203	13	𝑆11	𝑆11	PROPN
cana-681	203	14	𝑆42	𝑆42	PROPN
cana-681	203	15	𝑆43	𝑆43	PROPN
cana-681	203	16	𝑆30	𝑆30	PROPN
cana-681	203	17	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	203	18	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	203	19	𝑆16	𝑆16	PROPN
cana-681	204	1	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	204	2	𝑆28	𝑆28	PROPN
cana-681	204	3	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	204	4	𝑆54	𝑆54	PROPN
cana-681	205	1	𝑺𝟒𝟏	𝑺𝟒𝟏	PROPN
cana-681	205	2	𝑆43	𝑆43	PROPN
cana-681	205	3	𝑆6	𝑆6	NOUN
cana-681	205	4	𝑆28	𝑆28	PROPN
cana-681	205	5	𝑆21	𝑆21	PROPN
cana-681	206	1	𝑆39	𝑆39	PROPN
cana-681	206	2	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	207	1	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	207	2	𝑺𝟓𝟕	𝑺𝟓𝟕	PROPN
cana-681	207	3	𝑺𝟐	𝑺𝟐	PROPN
cana-681	207	4	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	208	1	𝑆43	𝑆43	PROPN
cana-681	208	2	𝑺𝟑𝟕	𝑺𝟑𝟕	PROPN
cana-681	208	3	𝑆55	𝑆55	PROPN
cana-681	208	4	𝑆30	𝑆30	PROPN
cana-681	208	5	𝑆31	𝑆31	PROPN
cana-681	208	6	𝑺𝟏𝟖	𝑺𝟏𝟖	PROPN
cana-681	208	7	𝑆20	𝑆20	PROPN
cana-681	208	8	𝑺𝟒𝟎	𝑺𝟒𝟎	PROPN
cana-681	208	9	𝑆4	𝑆4	PROPN
cana-681	208	10	𝑆55	𝑆55	PROPN
cana-681	208	11	𝑆16	𝑆16	PROPN
cana-681	208	12	)	)	PUNCT
cana-681	208	13	the	the	DET
cana-681	208	14	corresponding	corresponding	ADJ
cana-681	208	15	monomial	monomial	NOUN
cana-681	208	16	in	in	ADP
cana-681	208	17	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	208	18	(	(	PUNCT
cana-681	208	19	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	208	20	,	,	PUNCT
cana-681	208	21	𝐽1	𝐽1	NOUN
cana-681	208	22	)	)	PUNCT
cana-681	208	23	)	)	PUNCT
cana-681	208	24	(	(	PUNCT
cana-681	208	25	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	208	26	(	(	PUNCT
cana-681	208	27	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	208	28	,	,	PUNCT
cana-681	208	29	𝐽2	𝐽2	NOUN
cana-681	208	30	)	)	PUNCT
cana-681	208	31	)	)	PUNCT
cana-681	208	32	)	)	PUNCT
cana-681	209	1	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	209	2	𝑆2	𝑆2	NOUN
cana-681	209	3	3	3	NUM
cana-681	209	4	,	,	PUNCT
cana-681	209	5	𝑆15	𝑆15	NOUN
cana-681	209	6	4	4	NUM
cana-681	209	7	.	.	PUNCT
cana-681	210	1	case	case	NOUN
cana-681	210	2	8	8	NUM
cana-681	210	3	:	:	PUNCT
cana-681	210	4	(	(	PUNCT
cana-681	210	5	eight	eight	NUM
cana-681	210	6	errors	error	NOUN
cana-681	210	7	)	)	PUNCT
cana-681	210	8	let	let	VERB
cana-681	210	9	𝐼1	𝐼1	NOUN
cana-681	210	10	=	=	SYM
cana-681	210	11	{	{	PUNCT
cana-681	210	12	51,0,2,1,8,49,11,21,3	51,0,2,1,8,49,11,21,3	NUM
cana-681	210	13	}	}	PUNCT
cana-681	210	14	,	,	PUNCT
cana-681	210	15	𝐽1	𝐽1	NOUN
cana-681	210	16	=	=	SYM
cana-681	210	17	{	{	PUNCT
cana-681	210	18	8,2,0,1,51,4,55,5,3	8,2,0,1,51,4,55,5,3	NOUN
cana-681	210	19	}	}	PUNCT
cana-681	210	20	,	,	PUNCT
cana-681	210	21	𝐼2	𝐼2	NOUN
cana-681	210	22	=	=	SYM
cana-681	210	23	{	{	PUNCT
cana-681	210	24	0,1,13,51,28,4,16,9,31	0,1,13,51,28,4,16,9,31	NUM
cana-681	210	25	}	}	PUNCT
cana-681	210	26	,	,	PUNCT
cana-681	210	27	𝐽2	𝐽2	NOUN
cana-681	210	28	=	=	SYM
cana-681	210	29	{	{	PUNCT
cana-681	210	30	15,14,2,21,11,13,6,1,3	15,14,2,21,11,13,6,1,3	NOUN
cana-681	210	31	}	}	PUNCT
cana-681	210	32	.	.	PUNCT
cana-681	211	1	the	the	DET
cana-681	211	2	matrices	matrix	NOUN
cana-681	211	3	are	be	AUX
cana-681	211	4	,	,	PUNCT
cana-681	211	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	211	6	,	,	PUNCT
cana-681	211	7	𝐽1	𝐽1	NOUN
cana-681	211	8	)	)	PUNCT
cana-681	211	9	=	=	SYM
cana-681	211	10	(	(	PUNCT
cana-681	211	11	𝑺𝟐	𝑺𝟐	NOUN
cana-681	211	12	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	211	13	𝑆51	𝑆51	PROPN
cana-681	211	14	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	212	1	𝑆45	𝑆45	PROPN
cana-681	212	2	𝑆55	𝑆55	PROPN
cana-681	213	1	𝑆49	𝑆49	PROPN
cana-681	213	2	𝑺𝟓𝟔	𝑺𝟓𝟔	PROPN
cana-681	213	3	𝑆54	𝑆54	PROPN
cana-681	213	4	𝑺𝟖	𝑺𝟖	PROPN
cana-681	214	1	𝑺𝟐	𝑺𝟐	PROPN
cana-681	214	2	𝑆0	𝑆0	PROPN
cana-681	214	3	𝑆1	𝑆1	VERB
cana-681	214	4	𝑆51	𝑆51	PROPN
cana-681	214	5	𝑆4	𝑆4	PROPN
cana-681	214	6	𝑆55	𝑆55	PROPN
cana-681	215	1	𝑺𝟓	𝑺𝟓	NOUN
cana-681	215	2	𝑺𝟑	𝑺𝟑	NOUN
cana-681	215	3	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	215	4	𝑆4	𝑆4	PROPN
cana-681	215	5	𝑺𝟐	𝑺𝟐	NOUN
cana-681	215	6	𝑺𝟑	𝑺𝟑	NOUN
cana-681	215	7	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	215	8	𝑆6	𝑆6	PROPN
cana-681	215	9	𝑆57	𝑆57	PROPN
cana-681	215	10	𝑆7	𝑆7	PROPN
cana-681	216	1	𝑺𝟓	𝑺𝟓	ADV
cana-681	216	2	𝑆9	𝑆9	PROPN
cana-681	216	3	𝑺𝟑	𝑺𝟑	NOUN
cana-681	216	4	𝑆1	𝑆1	VERB
cana-681	216	5	𝑺𝟐	𝑺𝟐	PROPN
cana-681	216	6	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	216	7	𝑺𝟓	𝑺𝟓	NOUN
cana-681	217	1	𝑺𝟓𝟔	𝑺𝟓𝟔	PROPN
cana-681	217	2	𝑆6	𝑆6	ADP
cana-681	217	3	𝑆4	𝑆4	PROPN
cana-681	217	4	𝑆9	𝑆9	PROPN
cana-681	218	1	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	218	2	𝑺𝟖	𝑺𝟖	PROPN
cana-681	219	1	𝑆9	𝑆9	DET
cana-681	219	2	𝑺𝟐	𝑺𝟐	PROPN
cana-681	219	3	𝑆12	𝑆12	PROPN
cana-681	219	4	𝑆6	𝑆6	NOUN
cana-681	220	1	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	220	2	𝑆11	𝑆11	PROPN
cana-681	220	3	𝑆16	𝑆16	PROPN
cana-681	220	4	𝑆51	𝑆51	PROPN
cana-681	220	5	𝑆49	𝑆49	PROPN
cana-681	220	6	𝑺𝟓𝟎	𝑺𝟓𝟎	NOUN
cana-681	220	7	𝑆43	𝑆43	PROPN
cana-681	220	8	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	220	9	𝑺𝟒𝟕	𝑺𝟒𝟕	PROPN
cana-681	221	1	𝑆54	𝑆54	PROPN
cana-681	221	2	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	221	3	𝑆57	𝑆57	PROPN
cana-681	222	1	𝑺𝟏𝟑	𝑺𝟏𝟑	PROPN
cana-681	222	2	𝑆11	𝑆11	PROPN
cana-681	222	3	𝑆12	𝑆12	PROPN
cana-681	222	4	𝑆5	𝑆5	NOUN
cana-681	222	5	𝑆15	𝑆15	NOUN
cana-681	222	6	𝑆9	𝑆9	NOUN
cana-681	223	1	𝑆16	𝑆16	PROPN
cana-681	223	2	𝑆14	𝑆14	PROPN
cana-681	223	3	𝑺𝟐𝟗	𝑺𝟐𝟗	PROPN
cana-681	224	1	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	224	2	𝑆21	𝑆21	PROPN
cana-681	224	3	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	225	1	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	225	2	𝑆25	𝑆25	VERB
cana-681	225	3	𝑆19	𝑆19	PROPN
cana-681	226	1	𝑺𝟐𝟔	𝑺𝟐𝟔	PROPN
cana-681	226	2	𝑆24	𝑆24	PROPN
cana-681	226	3	𝑆11	𝑆11	PROPN
cana-681	226	4	𝑺𝟓	𝑺𝟓	NOUN
cana-681	226	5	𝑺𝟑	𝑺𝟑	NOUN
cana-681	227	1	𝑺𝟑𝟒	𝑺𝟑𝟒	PROPN
cana-681	227	2	𝑆54	𝑆54	PROPN
cana-681	227	3	𝑆7	𝑆7	NOUN
cana-681	227	4	𝑆1	𝑆1	NOUN
cana-681	227	5	𝑺𝟖	𝑺𝟖	PROPN
cana-681	227	6	𝑆6	𝑆6	PROPN
cana-681	227	7	)	)	PUNCT
cana-681	227	8	communications	communication	NOUN
cana-681	227	9	on	on	ADP
cana-681	227	10	applied	apply	VERB
cana-681	227	11	nonlinear	nonlinear	ADJ
cana-681	227	12	analysis	analysis	NOUN
cana-681	227	13	issn	issn	NOUN
cana-681	227	14	:	:	PUNCT
cana-681	227	15	1074	1074	NUM
cana-681	227	16	-	-	PUNCT
cana-681	227	17	133x	133x	NUM
cana-681	227	18	vol	vol	NOUN
cana-681	227	19	31	31	NUM
cana-681	227	20	no	no	NOUN
cana-681	227	21	.	.	PUNCT
cana-681	228	1	2s	2s	NUM
cana-681	228	2	(	(	PUNCT
cana-681	228	3	2024	2024	NUM
cana-681	228	4	)	)	PUNCT
cana-681	228	5	627	627	NUM
cana-681	228	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	228	7	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	228	8	,	,	PUNCT
cana-681	228	9	𝐽2	𝐽2	NOUN
cana-681	228	10	)	)	PUNCT
cana-681	228	11	=	=	SYM
cana-681	229	1	(	(	PUNCT
cana-681	229	2	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	229	3	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	229	4	𝑺𝟐	𝑺𝟐	NOUN
cana-681	229	5	𝑆21	𝑆21	PROPN
cana-681	229	6	𝑆11	𝑆11	PROPN
cana-681	230	1	𝑺𝟏𝟑	𝑺𝟏𝟑	NOUN
cana-681	230	2	𝑆6	𝑆6	NOUN
cana-681	230	3	𝑆1	𝑆1	NOUN
cana-681	230	4	𝑺𝟑	𝑺𝟑	NOUN
cana-681	230	5	𝑆16	𝑆16	PROPN
cana-681	230	6	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	230	7	𝑺𝟑	𝑺𝟑	NOUN
cana-681	231	1	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	231	2	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	231	3	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	231	4	𝑆7	𝑆7	PROPN
cana-681	231	5	𝑺𝟐	𝑺𝟐	PROPN
cana-681	231	6	𝑆4	𝑆4	PROPN
cana-681	231	7	𝑆28	𝑆28	PROPN
cana-681	231	8	𝑺𝟐𝟕	𝑺𝟐𝟕	VERB
cana-681	231	9	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	231	10	𝑺𝟑𝟒	𝑺𝟑𝟒	ADJ
cana-681	231	11	𝑆24	𝑆24	NOUN
cana-681	231	12	𝑺𝟐𝟔	𝑺𝟐𝟔	NUM
cana-681	231	13	𝑆19	𝑆19	PROPN
cana-681	231	14	𝑺𝟏𝟒	𝑺𝟏𝟒	PROPN
cana-681	232	1	𝑆16	𝑆16	PROPN
cana-681	232	2	𝑆9	𝑆9	INTJ
cana-681	232	3	𝑺𝟖	𝑺𝟖	PROPN
cana-681	233	1	𝑺𝟓𝟑	𝑺𝟓𝟑	PROPN
cana-681	233	2	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	233	3	𝑺𝟓	𝑺𝟓	ADV
cana-681	233	4	𝑆7	𝑆7	ADJ
cana-681	233	5	𝑆57	𝑆57	PROPN
cana-681	233	6	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	233	7	𝑆54	𝑆54	PROPN
cana-681	234	1	𝑆43	𝑆43	PROPN
cana-681	234	2	𝑆42	𝑆42	PROPN
cana-681	234	3	𝑆30	𝑆30	PROPN
cana-681	234	4	𝑆49	𝑆49	PROPN
cana-681	234	5	𝑆39	𝑆39	VERB
cana-681	234	6	𝑆41	𝑆41	PROPN
cana-681	235	1	𝑺𝟑𝟒	𝑺𝟑𝟒	PROPN
cana-681	235	2	𝑺𝟐𝟗	𝑺𝟐𝟗	PROPN
cana-681	235	3	𝑆31	𝑆31	NOUN
cana-681	235	4	𝑆19	𝑆19	PROPN
cana-681	235	5	𝑺𝟏𝟖	𝑺𝟏𝟖	ADJ
cana-681	235	6	𝑆6	𝑆6	PROPN
cana-681	235	7	𝑆25	𝑆25	PROPN
cana-681	235	8	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	235	9	𝑺𝟏𝟕	𝑺𝟏𝟕	PROPN
cana-681	235	10	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	235	11	𝑺𝟓	𝑺𝟓	NOUN
cana-681	235	12	𝑆7	𝑆7	ADJ
cana-681	235	13	𝑆31	𝑆31	PROPN
cana-681	235	14	𝑆30	𝑆30	PROPN
cana-681	235	15	𝑺𝟏𝟖	𝑺𝟏𝟖	PUNCT
cana-681	236	1	𝑺𝟑𝟕	𝑺𝟑𝟕	PROPN
cana-681	236	2	𝑺𝟐𝟕	𝑺𝟐𝟕	PROPN
cana-681	236	3	𝑺𝟐𝟗	𝑺𝟐𝟗	PROPN
cana-681	236	4	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	237	1	𝑺𝟏𝟕	𝑺𝟏𝟕	NOUN
cana-681	238	1	𝑆19	𝑆19	NUM
cana-681	238	2	𝑆24	𝑆24	PROPN
cana-681	238	3	𝑺𝟐𝟑	𝑺𝟐𝟑	PROPN
cana-681	238	4	𝑆11	𝑆11	PROPN
cana-681	238	5	𝑆30	𝑆30	PROPN
cana-681	238	6	𝑺𝟐𝟎	𝑺𝟐𝟎	PROPN
cana-681	238	7	𝑺𝟐𝟐	𝑺𝟐𝟐	PROPN
cana-681	238	8	𝑺𝟏𝟓	𝑺𝟏𝟓	PROPN
cana-681	239	1	𝑺𝟏𝟎	𝑺𝟏𝟎	PROPN
cana-681	239	2	𝑺𝟏𝟐	𝑺𝟏𝟐	PROPN
cana-681	239	3	𝑆46	𝑆46	PUNCT
cana-681	240	1	𝑆45	𝑆45	PROPN
cana-681	240	2	𝑺𝟑𝟑	𝑺𝟑𝟑	PROPN
cana-681	240	3	𝑺𝟓𝟐	𝑺𝟓𝟐	PROPN
cana-681	240	4	𝑆42	𝑆42	PROPN
cana-681	241	1	𝑺𝟒𝟒	𝑺𝟒𝟒	PROPN
cana-681	242	1	𝑆37	𝑆37	PROPN
cana-681	242	2	𝑺𝟑𝟐	𝑺𝟑𝟐	PROPN
cana-681	242	3	𝑺𝟑𝟒	𝑺𝟑𝟒	PROPN
cana-681	242	4	)	)	PUNCT
cana-681	242	5	the	the	DET
cana-681	242	6	corresponding	corresponding	ADJ
cana-681	242	7	monomial	monomial	NOUN
cana-681	242	8	in	in	ADP
cana-681	242	9	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	242	10	(	(	PUNCT
cana-681	242	11	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	242	12	,	,	PUNCT
cana-681	242	13	𝐽1	𝐽1	NOUN
cana-681	242	14	)	)	PUNCT
cana-681	242	15	)	)	PUNCT
cana-681	242	16	(	(	PUNCT
cana-681	242	17	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	242	18	(	(	PUNCT
cana-681	242	19	𝑆(𝐼2	𝑆(𝐼2	PROPN
cana-681	242	20	,	,	PUNCT
cana-681	242	21	𝐽2	𝐽2	NOUN
cana-681	242	22	)	)	PUNCT
cana-681	242	23	)	)	PUNCT
cana-681	242	24	)	)	PUNCT
cana-681	243	1	𝑖𝑠	𝑖𝑠	CCONJ
cana-681	243	2	𝑆2	𝑆2	NOUN
cana-681	243	3	5	5	NUM
cana-681	243	4	,	,	PUNCT
cana-681	243	5	𝑆15	𝑆15	NOUN
cana-681	243	6	4	4	NUM
cana-681	243	7	.	.	PUNCT
cana-681	244	1	the	the	DET
cana-681	244	2	above	above	ADJ
cana-681	244	3	conviction	conviction	NOUN
cana-681	244	4	is	be	AUX
cana-681	244	5	described	describe	VERB
cana-681	244	6	in	in	ADP
cana-681	244	7	the	the	DET
cana-681	244	8	following	follow	VERB
cana-681	244	9	flowchart	flowchart	NOUN
cana-681	244	10	:	:	PUNCT
cana-681	244	11	5	5	X
cana-681	244	12	.	.	X
cana-681	244	13	application	application	NOUN
cana-681	244	14	for	for	ADP
cana-681	244	15	the	the	DET
cana-681	244	16	algorithm	algorithm	NOUN
cana-681	244	17	the	the	DET
cana-681	244	18	algorithm	algorithm	NOUN
cana-681	244	19	has	have	AUX
cana-681	244	20	been	be	AUX
cana-681	244	21	successfully	successfully	ADV
cana-681	244	22	implemented	implement	VERB
cana-681	244	23	to	to	ADP
cana-681	244	24	the	the	DET
cana-681	244	25	provided	provide	VERB
cana-681	244	26	example	example	NOUN
cana-681	244	27	,	,	PUNCT
cana-681	244	28	resulting	result	VERB
cana-681	244	29	in	in	ADP
cana-681	244	30	enhanced	enhanced	ADJ
cana-681	244	31	performance	performance	NOUN
cana-681	244	32	and	and	CCONJ
cana-681	244	33	efficiency	efficiency	NOUN
cana-681	244	34	.	.	PUNCT
cana-681	245	1	let	let	VERB
cana-681	245	2	(	(	PUNCT
cana-681	245	3	17,9,5	17,9,5	X
cana-681	245	4	)	)	PUNCT
cana-681	245	5	qr	qr	NOUN
cana-681	245	6	code	code	NOUN
cana-681	245	7	over	over	ADP
cana-681	245	8	𝐺𝐹(28	𝐺𝐹(28	NUM
cana-681	245	9	)	)	PUNCT
cana-681	245	10	generated	generate	VERB
cana-681	245	11	by	by	ADP
cana-681	245	12	the	the	DET
cana-681	245	13	primitive	primitive	ADJ
cana-681	245	14	communications	communication	NOUN
cana-681	245	15	on	on	ADP
cana-681	245	16	applied	apply	VERB
cana-681	245	17	nonlinear	nonlinear	ADJ
cana-681	245	18	analysis	analysis	NOUN
cana-681	245	19	issn	issn	NOUN
cana-681	245	20	:	:	PUNCT
cana-681	245	21	1074	1074	NUM
cana-681	245	22	-	-	PUNCT
cana-681	245	23	133x	133x	NUM
cana-681	245	24	vol	vol	NOUN
cana-681	245	25	31	31	NUM
cana-681	245	26	no	no	NOUN
cana-681	245	27	.	.	PUNCT
cana-681	246	1	2s	2s	NUM
cana-681	246	2	(	(	PUNCT
cana-681	246	3	2024	2024	NUM
cana-681	246	4	)	)	PUNCT
cana-681	246	5	628	628	NUM
cana-681	246	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	246	7	polynomial	polynomial	ADJ
cana-681	246	8	𝑥8	𝑥8	PROPN
cana-681	246	9	+	+	CCONJ
cana-681	246	10	𝑥6	𝑥6	NOUN
cana-681	246	11	+	+	CCONJ
cana-681	246	12	𝑥5	𝑥5	PROPN
cana-681	246	13	+	+	CCONJ
cana-681	246	14	𝑥	𝑥	NOUN
cana-681	246	15	+	+	NOUN
cana-681	246	16	1	1	X
cana-681	246	17	.	.	PUNCT
cana-681	247	1	the	the	DET
cana-681	247	2	set	set	NOUN
cana-681	247	3	𝑄17	𝑄17	NOUN
cana-681	247	4	=	=	SYM
cana-681	247	5	{	{	PUNCT
cana-681	247	6	1	1	NUM
cana-681	247	7	,	,	PUNCT
cana-681	247	8	2	2	NUM
cana-681	247	9	,	,	PUNCT
cana-681	247	10	4	4	NUM
cana-681	247	11	,	,	PUNCT
cana-681	247	12	8	8	NUM
cana-681	247	13	,	,	PUNCT
cana-681	247	14	9	9	NUM
cana-681	247	15	,	,	PUNCT
cana-681	247	16	13	13	NUM
cana-681	247	17	,	,	PUNCT
cana-681	247	18	15	15	NUM
cana-681	247	19	,	,	PUNCT
cana-681	247	20	16	16	NUM
cana-681	247	21	}	}	PUNCT
cana-681	247	22	.	.	PUNCT
cana-681	248	1	therefore	therefore	ADV
cana-681	248	2	𝛽	𝛽	X
cana-681	248	3	=	=	PRON
cana-681	248	4	𝛼𝑢	𝛼𝑢	PROPN
cana-681	248	5	is	be	AUX
cana-681	248	6	a	a	DET
cana-681	248	7	primitive	primitive	ADJ
cana-681	248	8	17𝑡ℎ	17𝑡ℎ	ADJ
cana-681	248	9	root	root	NOUN
cana-681	248	10	of	of	ADP
cana-681	248	11	unity	unity	NOUN
cana-681	248	12	and	and	CCONJ
cana-681	248	13	𝑢	𝑢	NOUN
cana-681	248	14	=	=	PUNCT
cana-681	248	15	(	(	PUNCT
cana-681	248	16	28	28	NUM
cana-681	248	17	−	−	PROPN
cana-681	248	18	1)/17	1)/17	NUM
cana-681	248	19	=	=	SYM
cana-681	248	20	15	15	NUM
cana-681	248	21	.	.	PUNCT
cana-681	249	1	this	this	DET
cana-681	249	2	code	code	NOUN
cana-681	249	3	can	can	AUX
cana-681	249	4	correct	correct	VERB
cana-681	249	5	upto	upto	VERB
cana-681	249	6	two	two	NUM
cana-681	249	7	errors	error	NOUN
cana-681	249	8	.	.	PUNCT
cana-681	250	1	for	for	ADP
cana-681	250	2	two	two	NUM
cana-681	250	3	error	error	NOUN
cana-681	250	4	cases	case	NOUN
cana-681	250	5	,	,	PUNCT
cana-681	250	6	0	0	NUM
cana-681	250	7	≤	≤	NUM
cana-681	250	8	𝑣	𝑣	DET
cana-681	250	9	≤	≤	ADJ
cana-681	250	10	2	2	NUM
cana-681	250	11	.	.	PUNCT
cana-681	251	1	for	for	ADP
cana-681	251	2	𝑣	𝑣	NOUN
cana-681	251	3	=	=	SYM
cana-681	251	4	1	1	NUM
cana-681	251	5	,	,	PUNCT
cana-681	251	6	𝐼1	𝐼1	NOUN
cana-681	251	7	=	=	SYM
cana-681	251	8	{	{	PUNCT
cana-681	251	9	1,4	1,4	NUM
cana-681	251	10	}	}	PUNCT
cana-681	251	11	,	,	PUNCT
cana-681	251	12	𝐽1	𝐽1	NOUN
cana-681	251	13	=	=	SYM
cana-681	251	14	{	{	PUNCT
cana-681	251	15	2,1	2,1	NUM
cana-681	251	16	}	}	PUNCT
cana-681	251	17	.	.	PUNCT
cana-681	252	1	the	the	DET
cana-681	252	2	matrices	matrix	NOUN
cana-681	252	3	are	be	AUX
cana-681	252	4	,	,	PUNCT
cana-681	252	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	252	6	,	,	PUNCT
cana-681	252	7	𝐽1	𝐽1	NOUN
cana-681	252	8	)	)	PUNCT
cana-681	252	9	=	=	PUNCT
cana-681	253	1	(	(	PUNCT
cana-681	253	2	𝑺𝟑	𝑺𝟑	NOUN
cana-681	253	3	𝑆2	𝑆2	VERB
cana-681	253	4	𝑆6	𝑆6	PROPN
cana-681	253	5	𝑆5	𝑆5	PROPN
cana-681	253	6	)	)	PUNCT
cana-681	253	7	the	the	DET
cana-681	253	8	corresponding	corresponding	ADJ
cana-681	253	9	monomial	monomial	NOUN
cana-681	253	10	in	in	ADP
cana-681	253	11	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	253	12	(	(	PUNCT
cana-681	253	13	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	253	14	,	,	PUNCT
cana-681	253	15	𝐽1	𝐽1	NOUN
cana-681	253	16	)	)	PUNCT
cana-681	253	17	)	)	PUNCT
cana-681	254	1	𝑖𝑠	𝑖𝑠	ADV
cana-681	254	2	𝑆3	𝑆3	INTJ
cana-681	254	3	1	1	NUM
cana-681	254	4	.	.	PUNCT
cana-681	255	1	for	for	ADP
cana-681	255	2	𝑣	𝑣	NOUN
cana-681	255	3	=	=	SYM
cana-681	255	4	2	2	NUM
cana-681	255	5	,	,	PUNCT
cana-681	255	6	𝐼1	𝐼1	NOUN
cana-681	255	7	=	=	SYM
cana-681	255	8	{	{	PUNCT
cana-681	255	9	2,1,8	2,1,8	NUM
cana-681	255	10	}	}	PUNCT
cana-681	255	11	,	,	PUNCT
cana-681	255	12	𝐽1	𝐽1	NOUN
cana-681	255	13	=	=	SYM
cana-681	255	14	{	{	PUNCT
cana-681	255	15	4,2,1	4,2,1	NOUN
cana-681	255	16	}	}	PUNCT
cana-681	255	17	.	.	PUNCT
cana-681	256	1	the	the	DET
cana-681	256	2	matrices	matrix	NOUN
cana-681	256	3	are	be	AUX
cana-681	256	4	,	,	PUNCT
cana-681	256	5	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	256	6	,	,	PUNCT
cana-681	256	7	𝐽1	𝐽1	NOUN
cana-681	256	8	)	)	PUNCT
cana-681	256	9	=	=	SYM
cana-681	257	1	(	(	PUNCT
cana-681	257	2	𝑆6	𝑆6	X
cana-681	257	3	𝑆4	𝑆4	PROPN
cana-681	257	4	𝑺𝟑	𝑺𝟑	PROPN
cana-681	257	5	𝑆5	𝑆5	PROPN
cana-681	257	6	𝑺𝟑	𝑺𝟑	NOUN
cana-681	257	7	𝑆2	𝑆2	PROPN
cana-681	257	8	𝑆12	𝑆12	PROPN
cana-681	257	9	𝑆10	𝑆10	PROPN
cana-681	257	10	𝑆9	𝑆9	PROPN
cana-681	257	11	)	)	PUNCT
cana-681	257	12	the	the	DET
cana-681	257	13	corresponding	corresponding	ADJ
cana-681	257	14	monomial	monomial	NOUN
cana-681	257	15	in	in	ADP
cana-681	257	16	𝑑𝑒𝑡	𝑑𝑒𝑡	NOUN
cana-681	257	17	(	(	PUNCT
cana-681	257	18	𝑆(𝐼1	𝑆(𝐼1	PROPN
cana-681	257	19	,	,	PUNCT
cana-681	257	20	𝐽1	𝐽1	NOUN
cana-681	257	21	)	)	PUNCT
cana-681	257	22	)	)	PUNCT
cana-681	257	23	𝑖𝑠	𝑖𝑠	ADV
cana-681	258	1	𝑆3	𝑆3	PROPN
cana-681	258	2	2	2	X
cana-681	258	3	.	.	X
cana-681	258	4	assume	assume	VERB
cana-681	258	5	the	the	DET
cana-681	258	6	message	message	NOUN
cana-681	258	7	polynomial	polynomial	ADJ
cana-681	258	8	𝐼(𝑥	𝐼(𝑥	PROPN
cana-681	258	9	)	)	PUNCT
cana-681	258	10	=	=	PUNCT
cana-681	258	11	𝑥5	𝑥5	PROPN
cana-681	258	12	+	+	CCONJ
cana-681	259	1	𝑥	𝑥	X
cana-681	259	2	+	+	NUM
cana-681	259	3	1	1	NUM
cana-681	259	4	and	and	CCONJ
cana-681	259	5	the	the	DET
cana-681	259	6	code	code	NOUN
cana-681	259	7	polynomial	polynomial	ADJ
cana-681	259	8	c(x	c(x	NOUN
cana-681	259	9	)	)	PUNCT
cana-681	260	1	=	=	SYM
cana-681	260	2	x16	x16	NOUN
cana-681	261	1	+	+	CCONJ
cana-681	261	2	x15	x15	PROPN
cana-681	261	3	+	+	CCONJ
cana-681	261	4	x13	x13	NOUN
cana-681	261	5	+	+	NUM
cana-681	261	6	x9	x9	NOUN
cana-681	261	7	+	+	CCONJ
cana-681	261	8	x8	x8	PROPN
cana-681	261	9	+	+	CCONJ
cana-681	261	10	x4	x4	PROPN
cana-681	262	1	+	+	CCONJ
cana-681	262	2	x2	x2	PROPN
cana-681	263	1	+	+	CCONJ
cana-681	263	2	x1	x1	PROPN
cana-681	264	1	+	+	PUNCT
cana-681	264	2	x	x	SYM
cana-681	264	3	+	+	NUM
cana-681	264	4	1	1	NUM
cana-681	264	5	.	.	X
cana-681	264	6	two	two	NUM
cana-681	264	7	error	error	NOUN
cana-681	264	8	cases	case	NOUN
cana-681	264	9	are	be	AUX
cana-681	264	10	given	give	VERB
cana-681	264	11	below	below	ADP
cana-681	264	12	.	.	PUNCT
cana-681	265	1	case	case	NOUN
cana-681	265	2	1	1	NUM
cana-681	265	3	:	:	PUNCT
cana-681	265	4	for	for	ADP
cana-681	265	5	one	one	NUM
cana-681	265	6	error	error	NOUN
cana-681	265	7	,	,	PUNCT
cana-681	265	8	assume	assume	VERB
cana-681	265	9	the	the	DET
cana-681	265	10	error	error	NOUN
cana-681	265	11	polynomial	polynomial	ADJ
cana-681	265	12	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	265	13	)	)	PUNCT
cana-681	265	14	=	=	SYM
cana-681	265	15	𝑥3	𝑥3	NOUN
cana-681	265	16	and	and	CCONJ
cana-681	265	17	the	the	DET
cana-681	265	18	received	receive	VERB
cana-681	265	19	polynomial	polynomial	NOUN
cana-681	265	20	is	be	AUX
cana-681	265	21	,	,	PUNCT
cana-681	265	22	r(x	r(x	PROPN
cana-681	265	23	)	)	PUNCT
cana-681	265	24	=	=	SYM
cana-681	266	1	x16	x16	NOUN
cana-681	267	1	+	+	CCONJ
cana-681	267	2	x15	x15	PROPN
cana-681	267	3	+	+	CCONJ
cana-681	267	4	x13	x13	NOUN
cana-681	267	5	+	+	NUM
cana-681	267	6	x9	x9	NOUN
cana-681	267	7	+	+	CCONJ
cana-681	267	8	x8	x8	PROPN
cana-681	267	9	+	+	CCONJ
cana-681	267	10	x5	x5	PROPN
cana-681	268	1	+	+	CCONJ
cana-681	268	2	x3	x3	ADJ
cana-681	268	3	+	+	CCONJ
cana-681	268	4	x	x	SYM
cana-681	268	5	+	+	NUM
cana-681	268	6	1	1	X
cana-681	268	7	.	.	X
cana-681	268	8	unknown	unknown	ADJ
cana-681	268	9	syndrome	syndrome	NOUN
cana-681	268	10	for	for	ADP
cana-681	268	11	one	one	NUM
cana-681	268	12	error	error	NOUN
cana-681	268	13	𝑆3	𝑆3	NOUN
cana-681	268	14	1	1	NUM
cana-681	268	15	=	=	SYM
cana-681	268	16	𝛼14	𝛼14	NOUN
cana-681	268	17	.	.	PUNCT
cana-681	269	1	the	the	DET
cana-681	269	2	error	error	NOUN
cana-681	269	3	locator	locator	NOUN
cana-681	269	4	polynomial	polynomial	NOUN
cana-681	269	5	𝐿(𝑧	𝐿(𝑧	NUM
cana-681	269	6	)	)	PUNCT
cana-681	269	7	=	=	SYM
cana-681	269	8	1	1	NUM
cana-681	269	9	+	+	CCONJ
cana-681	269	10	𝛼18𝑥.	𝛼18𝑥.	VERB
cana-681	269	11	the	the	DET
cana-681	269	12	root	root	NOUN
cana-681	269	13	of	of	ADP
cana-681	269	14	the	the	DET
cana-681	269	15	σ(x	σ(x	NOUN
cana-681	269	16	)	)	PUNCT
cana-681	269	17	is	be	AUX
cana-681	269	18	𝑥1	𝑥1	NOUN
cana-681	269	19	=	=	PROPN
cana-681	269	20	𝛼	𝛼	PROPN
cana-681	269	21	7	7	NUM
cana-681	269	22	and	and	CCONJ
cana-681	269	23	the	the	DET
cana-681	269	24	error	error	NOUN
cana-681	269	25	polynomial	polynomial	ADJ
cana-681	269	26	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	269	27	)	)	PUNCT
cana-681	269	28	=	=	SYM
cana-681	269	29	𝑥3	𝑥3	NOUN
cana-681	269	30	.	.	PUNCT
cana-681	270	1	case	case	NOUN
cana-681	270	2	2	2	NUM
cana-681	270	3	:	:	PUNCT
cana-681	270	4	for	for	ADP
cana-681	270	5	two	two	NUM
cana-681	270	6	error	error	NOUN
cana-681	270	7	,	,	PUNCT
cana-681	270	8	assume	assume	VERB
cana-681	270	9	the	the	DET
cana-681	270	10	error	error	NOUN
cana-681	270	11	polynomial	polynomial	ADJ
cana-681	270	12	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	270	13	)	)	PUNCT
cana-681	270	14	=	=	SYM
cana-681	271	1	𝑥3+𝑥2	𝑥3+𝑥2	PROPN
cana-681	271	2	and	and	CCONJ
cana-681	271	3	the	the	DET
cana-681	271	4	received	receive	VERB
cana-681	271	5	polynomial	polynomial	NOUN
cana-681	271	6	is	be	AUX
cana-681	271	7	,	,	PUNCT
cana-681	271	8	r(x	r(x	PROPN
cana-681	271	9	)	)	PUNCT
cana-681	271	10	=	=	SYM
cana-681	272	1	x16	x16	NOUN
cana-681	273	1	+	+	CCONJ
cana-681	273	2	x15	x15	PROPN
cana-681	273	3	+	+	CCONJ
cana-681	273	4	x13	x13	NOUN
cana-681	273	5	+	+	NUM
cana-681	273	6	x9	x9	NOUN
cana-681	273	7	+	+	CCONJ
cana-681	273	8	x8	x8	PROPN
cana-681	273	9	+	+	CCONJ
cana-681	273	10	x5	x5	PROPN
cana-681	274	1	+	+	CCONJ
cana-681	274	2	x3	x3	ADJ
cana-681	274	3	+	+	CCONJ
cana-681	274	4	x	x	SYM
cana-681	274	5	+	+	NUM
cana-681	274	6	1	1	X
cana-681	274	7	.	.	X
cana-681	274	8	unknown	unknown	ADJ
cana-681	274	9	syndrome	syndrome	NOUN
cana-681	274	10	for	for	ADP
cana-681	274	11	two	two	NUM
cana-681	274	12	error	error	NOUN
cana-681	274	13	𝑆3	𝑆3	NOUN
cana-681	274	14	2	2	NUM
cana-681	274	15	=	=	NOUN
cana-681	274	16	𝛼16	𝛼16	ADJ
cana-681	274	17	.	.	PUNCT
cana-681	275	1	the	the	DET
cana-681	275	2	error	error	NOUN
cana-681	275	3	locator	locator	NOUN
cana-681	275	4	polynomial	polynomial	NOUN
cana-681	275	5	𝐿(𝑧	𝐿(𝑧	NUM
cana-681	275	6	)	)	PUNCT
cana-681	275	7	=	=	SYM
cana-681	275	8	1	1	NUM
cana-681	275	9	+	+	CCONJ
cana-681	275	10	𝛼12𝑥.	𝛼12𝑥.	VERB
cana-681	275	11	the	the	DET
cana-681	275	12	root	root	NOUN
cana-681	275	13	of	of	ADP
cana-681	275	14	the	the	DET
cana-681	275	15	σ(x	σ(x	NOUN
cana-681	275	16	)	)	PUNCT
cana-681	275	17	is	be	AUX
cana-681	275	18	𝑥1	𝑥1	NOUN
cana-681	275	19	=	=	NOUN
cana-681	275	20	𝛼	𝛼	NOUN
cana-681	275	21	8	8	NUM
cana-681	275	22	and	and	CCONJ
cana-681	275	23	the	the	DET
cana-681	275	24	error	error	NOUN
cana-681	275	25	polynomial	polynomial	ADJ
cana-681	275	26	𝑒(𝑥	𝑒(𝑥	NOUN
cana-681	275	27	)	)	PUNCT
cana-681	275	28	=	=	PUNCT
cana-681	276	1	𝑥3+𝑥2	𝑥3+𝑥2	PROPN
cana-681	276	2	.	.	PROPN
cana-681	276	3	6	6	NUM
cana-681	276	4	.	.	PUNCT
cana-681	276	5	conclusion	conclusion	NOUN
cana-681	276	6	in	in	ADP
cana-681	276	7	this	this	DET
cana-681	276	8	manuscript	manuscript	NOUN
cana-681	276	9	,	,	PUNCT
cana-681	276	10	we	we	PRON
cana-681	276	11	present	present	VERB
cana-681	276	12	an	an	DET
cana-681	276	13	original	original	ADJ
cana-681	276	14	non	non	ADJ
cana-681	276	15	-	-	ADJ
cana-681	276	16	binary	binary	ADJ
cana-681	276	17	quadratic	quadratic	ADJ
cana-681	276	18	residue	residue	NOUN
cana-681	276	19	code	code	NOUN
cana-681	276	20	characterized	characterize	VERB
cana-681	276	21	by	by	ADP
cana-681	276	22	parameters	parameter	NOUN
cana-681	276	23	(	(	PUNCT
cana-681	276	24	57	57	NUM
cana-681	276	25	,	,	PUNCT
cana-681	276	26	29	29	NUM
cana-681	276	27	,	,	PUNCT
cana-681	276	28	17	17	NUM
cana-681	276	29	)	)	PUNCT
cana-681	276	30	,	,	PUNCT
cana-681	276	31	operating	operate	VERB
cana-681	276	32	within	within	ADP
cana-681	276	33	a	a	DET
cana-681	276	34	binary	binary	ADJ
cana-681	276	35	field	field	NOUN
cana-681	276	36	.	.	PUNCT
cana-681	277	1	our	our	PRON
cana-681	277	2	approach	approach	NOUN
cana-681	277	3	involves	involve	VERB
cana-681	277	4	the	the	DET
cana-681	277	5	adaptation	adaptation	NOUN
cana-681	277	6	of	of	ADP
cana-681	277	7	methods	method	NOUN
cana-681	277	8	analogous	analogous	ADJ
cana-681	277	9	to	to	ADP
cana-681	277	10	those	those	PRON
cana-681	277	11	employed	employ	VERB
cana-681	277	12	in	in	ADP
cana-681	277	13	discerning	discern	VERB
cana-681	277	14	unknown	unknown	ADJ
cana-681	277	15	syndromes	syndrome	NOUN
cana-681	277	16	within	within	ADP
cana-681	277	17	binary	binary	ADJ
cana-681	277	18	quadratic	quadratic	ADJ
cana-681	277	19	residue	residue	NOUN
cana-681	277	20	codes	code	NOUN
cana-681	277	21	,	,	PUNCT
cana-681	277	22	tailored	tailor	VERB
cana-681	277	23	for	for	ADP
cana-681	277	24	this	this	DET
cana-681	277	25	non	non	ADJ
cana-681	277	26	-	-	ADJ
cana-681	277	27	binary	binary	ADJ
cana-681	277	28	code	code	NOUN
cana-681	277	29	of	of	ADP
cana-681	277	30	length	length	NOUN
cana-681	277	31	57	57	NUM
cana-681	277	32	.	.	PUNCT
cana-681	278	1	by	by	ADP
cana-681	278	2	meticulously	meticulously	ADV
cana-681	278	3	selecting	select	VERB
cana-681	278	4	suitable	suitable	ADJ
cana-681	278	5	subsets	subset	NOUN
cana-681	278	6	and	and	CCONJ
cana-681	278	7	index	index	NOUN
cana-681	278	8	sets	set	NOUN
cana-681	278	9	,	,	PUNCT
cana-681	278	10	we	we	PRON
cana-681	278	11	effectively	effectively	ADV
cana-681	278	12	tackle	tackle	VERB
cana-681	278	13	eight	eight	NUM
cana-681	278	14	instances	instance	NOUN
cana-681	278	15	of	of	ADP
cana-681	278	16	errors	error	NOUN
cana-681	278	17	,	,	PUNCT
cana-681	278	18	subsequently	subsequently	ADV
cana-681	278	19	resolving	resolve	VERB
cana-681	278	20	them	they	PRON
cana-681	278	21	with	with	ADP
cana-681	278	22	the	the	DET
cana-681	278	23	aid	aid	NOUN
cana-681	278	24	of	of	ADP
cana-681	278	25	a	a	DET
cana-681	278	26	pioneering	pioneering	ADJ
cana-681	278	27	decoding	decode	VERB
cana-681	278	28	algorithm	algorithm	NOUN
cana-681	278	29	.	.	PUNCT
cana-681	279	1	furthermore	furthermore	ADV
cana-681	279	2	,	,	PUNCT
cana-681	279	3	we	we	PRON
cana-681	279	4	develop	develop	VERB
cana-681	279	5	into	into	ADP
cana-681	279	6	the	the	DET
cana-681	279	7	practical	practical	ADJ
cana-681	279	8	application	application	NOUN
cana-681	279	9	of	of	ADP
cana-681	279	10	this	this	DET
cana-681	279	11	algorithm	algorithm	NOUN
cana-681	279	12	within	within	ADP
cana-681	279	13	our	our	PRON
cana-681	279	14	study	study	NOUN
cana-681	279	15	.	.	PUNCT
cana-681	280	1	communications	communication	NOUN
cana-681	280	2	on	on	ADP
cana-681	280	3	applied	apply	VERB
cana-681	280	4	nonlinear	nonlinear	ADJ
cana-681	280	5	analysis	analysis	NOUN
cana-681	280	6	issn	issn	NOUN
cana-681	280	7	:	:	PUNCT
cana-681	280	8	1074	1074	NUM
cana-681	280	9	-	-	PUNCT
cana-681	280	10	133x	133x	NUM
cana-681	280	11	vol	vol	NOUN
cana-681	280	12	31	31	NUM
cana-681	280	13	no	no	NOUN
cana-681	280	14	.	.	PUNCT
cana-681	281	1	2s	2s	NUM
cana-681	281	2	(	(	PUNCT
cana-681	281	3	2024	2024	NUM
cana-681	281	4	)	)	PUNCT
cana-681	281	5	629	629	NUM
cana-681	281	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-681	281	7	references	reference	NOUN
cana-681	281	8	:	:	PUNCT
cana-681	282	1	[	[	X
cana-681	282	2	1	1	X
cana-681	282	3	]	]	X
cana-681	282	4	chen	chen	PROPN
cana-681	282	5	x	x	X
cana-681	282	6	,	,	PUNCT
cana-681	282	7	i	i	PROPN
cana-681	282	8	s	s	VERB
cana-681	282	9	reed	reed	NOUN
cana-681	282	10	,	,	PUNCT
cana-681	282	11	t	t	PROPN
cana-681	282	12	k	k	PROPN
cana-681	282	13	truong	truong	PROPN
cana-681	282	14	,	,	PUNCT
cana-681	282	15	decoding	decode	VERB
cana-681	282	16	the	the	DET
cana-681	282	17	(	(	PUNCT
cana-681	282	18	73	73	NUM
cana-681	282	19	,	,	PUNCT
cana-681	282	20	37	37	NUM
cana-681	282	21	,	,	PUNCT
cana-681	282	22	13	13	NUM
cana-681	282	23	)	)	PUNCT
cana-681	282	24	quadratic	quadratic	ADJ
cana-681	282	25	residue	residue	NOUN
cana-681	282	26	code	code	NOUN
cana-681	282	27	,	,	PUNCT
cana-681	282	28	ieee	ieee	NOUN
cana-681	282	29	proceedings	proceeding	NOUN
cana-681	282	30	computers	computer	NOUN
cana-681	282	31	and	and	CCONJ
cana-681	282	32	digital	digital	ADJ
cana-681	282	33	techniques	technique	NOUN
cana-681	282	34	,	,	PUNCT
cana-681	282	35	141(5	141(5	NUM
cana-681	282	36	)	)	PUNCT
cana-681	282	37	,	,	PUNCT
cana-681	282	38	september	september	PROPN
cana-681	282	39	1994	1994	NUM
cana-681	282	40	.	.	PUNCT
cana-681	283	1	[	[	X
cana-681	283	2	2	2	X
cana-681	283	3	]	]	X
cana-681	283	4	elia	elia	PROPN
cana-681	283	5	m	m	PROPN
cana-681	283	6	,	,	PUNCT
cana-681	283	7	algebraic	algebraic	PROPN
cana-681	283	8	decoding	decode	VERB
cana-681	283	9	of	of	ADP
cana-681	283	10	the	the	DET
cana-681	283	11	(	(	PUNCT
cana-681	283	12	23,12,7	23,12,7	NOUN
cana-681	283	13	)	)	PUNCT
cana-681	283	14	golay	golay	NOUN
cana-681	283	15	codes	code	NOUN
cana-681	283	16	,	,	PUNCT
cana-681	283	17	ieee	ieee	NOUN
cana-681	283	18	trans.inf.theory	trans.inf.theory	NOUN
cana-681	283	19	,	,	PUNCT
cana-681	283	20	33(1	33(1	NUM
cana-681	283	21	)	)	PUNCT
cana-681	283	22	,	,	PUNCT
cana-681	283	23	jan	jan	PROPN
cana-681	283	24	1987	1987	NUM
cana-681	283	25	.	.	PUNCT
cana-681	284	1	[	[	X
cana-681	284	2	3	3	NUM
cana-681	284	3	]	]	PUNCT
cana-681	284	4	hung	hung	PROPN
cana-681	284	5	peng	peng	PROPN
cana-681	284	6	lee	lee	PROPN
cana-681	284	7	,	,	PUNCT
cana-681	284	8	hsin	hsin	PROPN
cana-681	284	9	chiu	chiu	PROPN
cana-681	284	10	chang	chang	PROPN
cana-681	284	11	,	,	PUNCT
cana-681	284	12	modified	modify	VERB
cana-681	284	13	algebraic	algebraic	ADJ
cana-681	284	14	decoding	decoding	NOUN
cana-681	284	15	of	of	ADP
cana-681	284	16	the	the	DET
cana-681	284	17	binary	binary	NOUN
cana-681	284	18	(	(	PUNCT
cana-681	284	19	47	47	NUM
cana-681	284	20	,	,	PUNCT
cana-681	284	21	24	24	NUM
cana-681	284	22	,	,	PUNCT
cana-681	284	23	11	11	NUM
cana-681	284	24	)	)	PUNCT
cana-681	284	25	quadratic	quadratic	ADJ
cana-681	284	26	residue	residue	NOUN
cana-681	284	27	code	code	NOUN
cana-681	284	28	,	,	PUNCT
cana-681	284	29	2011	2011	NUM
cana-681	284	30	international	international	ADJ
cana-681	284	31	conference	conference	NOUN
cana-681	284	32	on	on	ADP
cana-681	284	33	consumer	consumer	NOUN
cana-681	284	34	electronics	electronic	NOUN
cana-681	284	35	,	,	PUNCT
cana-681	284	36	communications	communication	NOUN
cana-681	284	37	and	and	CCONJ
cana-681	284	38	networks	network	NOUN
cana-681	284	39	(	(	PUNCT
cana-681	284	40	cecnet	cecnet	NOUN
cana-681	284	41	)	)	PUNCT
cana-681	284	42	,	,	PUNCT
cana-681	284	43	16	16	NUM
cana-681	284	44	may	may	PROPN
cana-681	284	45	2011	2011	NUM
cana-681	284	46	.	.	PUNCT
cana-681	285	1	[	[	X
cana-681	285	2	4	4	NUM
cana-681	285	3	]	]	SYM
cana-681	285	4	li	li	PROPN
cana-681	285	5	y	y	PROPN
cana-681	285	6	,	,	PUNCT
cana-681	285	7	h	h	PROPN
cana-681	285	8	liu	liu	PROPN
cana-681	285	9	,	,	PUNCT
cana-681	285	10	q	q	PROPN
cana-681	285	11	chen	chen	PROPN
cana-681	285	12	and	and	CCONJ
cana-681	285	13	t	t	PROPN
cana-681	285	14	k	k	PROPN
cana-681	285	15	truong	truong	PROPN
cana-681	285	16	,	,	PUNCT
cana-681	285	17	algebraic	algebraic	ADJ
cana-681	285	18	and	and	CCONJ
cana-681	285	19	linear	linear	PROPN
cana-681	285	20	programming	programming	NOUN
cana-681	285	21	decoding	decoding	NOUN
cana-681	285	22	of	of	ADP
cana-681	285	23	the	the	DET
cana-681	285	24	(	(	PUNCT
cana-681	285	25	73	73	NUM
cana-681	285	26	,	,	PUNCT
cana-681	285	27	37	37	NUM
cana-681	285	28	,	,	PUNCT
cana-681	285	29	13	13	NUM
cana-681	285	30	)	)	PUNCT
cana-681	285	31	quadratic	quadratic	ADJ
cana-681	285	32	residue	residue	NOUN
cana-681	285	33	code	code	NOUN
cana-681	285	34	,	,	PUNCT
cana-681	285	35	ieee	ieee	PROPN
cana-681	285	36	international	international	ADJ
cana-681	285	37	conference	conference	NOUN
cana-681	285	38	on	on	ADP
cana-681	285	39	communications	communication	NOUN
cana-681	285	40	(	(	PUNCT
cana-681	285	41	icc	icc	PROPN
cana-681	285	42	)	)	PUNCT
cana-681	285	43	,	,	PUNCT
cana-681	285	44	sydney	sydney	PROPN
cana-681	285	45	,	,	PUNCT
cana-681	285	46	nsw	nsw	PROPN
cana-681	285	47	,	,	PUNCT
cana-681	285	48	australia	australia	PROPN
cana-681	285	49	,	,	PUNCT
cana-681	285	50	2014	2014	NUM
cana-681	285	51	.	.	PUNCT
cana-681	286	1	[	[	X
cana-681	286	2	5	5	X
cana-681	286	3	]	]	PUNCT
cana-681	286	4	lin	lin	PROPN
cana-681	286	5	t	t	PROPN
cana-681	286	6	c	c	PROPN
cana-681	286	7	,	,	PUNCT
cana-681	286	8	h	h	PROPN
cana-681	286	9	p	p	PROPN
cana-681	286	10	lee	lee	PROPN
cana-681	286	11	,	,	PUNCT
cana-681	286	12	h	h	PROPN
cana-681	286	13	c	c	PROPN
cana-681	286	14	chang	chang	PROPN
cana-681	286	15	,	,	PUNCT
cana-681	286	16	s	s	PART
cana-681	286	17	i	i	PROPN
cana-681	286	18	chu	chu	PROPN
cana-681	286	19	and	and	CCONJ
cana-681	286	20	t	t	PROPN
cana-681	286	21	k	k	PROPN
cana-681	286	22	truong	truong	PROPN
cana-681	286	23	,	,	PUNCT
cana-681	286	24	high	high	ADJ
cana-681	286	25	speed	speed	NOUN
cana-681	286	26	decoding	decoding	NOUN
cana-681	286	27	of	of	ADP
cana-681	286	28	the	the	DET
cana-681	286	29	binary	binary	ADJ
cana-681	286	30	(	(	PUNCT
cana-681	286	31	47,24,11	47,24,11	X
cana-681	286	32	)	)	PUNCT
cana-681	286	33	quadratic	quadratic	ADJ
cana-681	286	34	residue	residue	NOUN
cana-681	286	35	code	code	NOUN
cana-681	286	36	,	,	PUNCT
cana-681	286	37	information	information	NOUN
cana-681	286	38	sciences	science	NOUN
cana-681	286	39	,	,	PUNCT
cana-681	286	40	2010	2010	NUM
cana-681	286	41	.	.	PUNCT
cana-681	287	1	[	[	X
cana-681	287	2	6	6	NUM
cana-681	287	3	]	]	X
cana-681	287	4	lin	lin	PROPN
cana-681	287	5	wang	wang	PROPN
cana-681	287	6	,	,	PUNCT
cana-681	287	7	young	young	PROPN
cana-681	287	8	li	li	PROPN
cana-681	287	9	,	,	PUNCT
cana-681	287	10	trieu	trieu	PROPN
cana-681	287	11	kien	kien	PROPN
cana-681	287	12	,	,	PUNCT
cana-681	287	13	tsung	tsung	PROPN
cana-681	287	14	ching	ching	PROPN
cana-681	287	15	,	,	PUNCT
cana-681	287	16	on	on	ADP
cana-681	287	17	decoding	decode	VERB
cana-681	287	18	of	of	ADP
cana-681	287	19	the	the	DET
cana-681	287	20	(	(	PUNCT
cana-681	287	21	89,45,17	89,45,17	NUM
cana-681	287	22	)	)	PUNCT
cana-681	287	23	quadratic	quadratic	ADJ
cana-681	287	24	residue	residue	NOUN
cana-681	287	25	code	code	NOUN
cana-681	287	26	,	,	PUNCT
cana-681	287	27	ieee	ieee	NOUN
cana-681	287	28	transactions	transaction	NOUN
cana-681	287	29	on	on	ADP
cana-681	287	30	communication	communication	NOUN
cana-681	287	31	,	,	PUNCT
cana-681	287	32	61(3	61(3	NUM
cana-681	287	33	)	)	PUNCT
cana-681	287	34	,	,	PUNCT
cana-681	287	35	march	march	PROPN
cana-681	287	36	2013	2013	NUM
cana-681	287	37	.	.	PUNCT
cana-681	288	1	[	[	X
cana-681	288	2	7	7	X
cana-681	288	3	]	]	PUNCT
cana-681	288	4	macwiilliams	macwiilliam	NOUN
cana-681	288	5	f	f	PROPN
cana-681	288	6	j	j	PROPN
cana-681	288	7	and	and	CCONJ
cana-681	288	8	n	n	PRON
cana-681	288	9	j	j	PROPN
cana-681	288	10	a	a	DET
cana-681	288	11	sloane	sloane	NOUN
cana-681	288	12	,	,	PUNCT
cana-681	288	13	the	the	DET
cana-681	288	14	theory	theory	NOUN
cana-681	288	15	of	of	ADP
cana-681	288	16	error	error	NOUN
cana-681	288	17	-	-	PUNCT
cana-681	288	18	correcting	correct	VERB
cana-681	288	19	codes	code	NOUN
cana-681	288	20	(	(	PUNCT
cana-681	288	21	first	first	ADJ
cana-681	288	22	edition	edition	NOUN
cana-681	288	23	)	)	PUNCT
cana-681	288	24	,	,	PUNCT
cana-681	288	25	bell	bell	NOUN
cana-681	288	26	laboratories	laboratory	NOUN
cana-681	288	27	,	,	PUNCT
cana-681	288	28	murray	murray	PROPN
cana-681	288	29	hill	hill	PROPN
cana-681	288	30	,	,	PUNCT
cana-681	288	31	u.s.a	u.s.a	PROPN
cana-681	288	32	,	,	PUNCT
cana-681	288	33	1977	1977	NUM
cana-681	288	34	.	.	PUNCT
cana-681	289	1	[	[	X
cana-681	289	2	8	8	NUM
cana-681	289	3	]	]	X
cana-681	289	4	mita	mita	NOUN
cana-681	289	5	a	a	X
cana-681	289	6	,	,	PUNCT
cana-681	289	7	on	on	ADP
cana-681	289	8	the	the	DET
cana-681	289	9	construction	construction	NOUN
cana-681	289	10	of	of	ADP
cana-681	289	11	m	m	NOUN
cana-681	289	12	-	-	NOUN
cana-681	289	13	sequences	sequence	NOUN
cana-681	289	14	via	via	ADP
cana-681	289	15	primitive	primitive	ADJ
cana-681	289	16	polynomials	polynomial	NOUN
cana-681	289	17	with	with	ADP
cana-681	289	18	a	a	DET
cana-681	289	19	fast	fast	ADJ
cana-681	289	20	identification	identification	NOUN
cana-681	289	21	method	method	NOUN
cana-681	289	22	,	,	PUNCT
cana-681	289	23	international	international	ADJ
cana-681	289	24	journal	journal	NOUN
cana-681	289	25	of	of	ADP
cana-681	289	26	electrical	electrical	ADJ
cana-681	289	27	,	,	PUNCT
cana-681	289	28	computer	computer	NOUN
cana-681	289	29	,	,	PUNCT
cana-681	289	30	energetic	energetic	ADJ
cana-681	289	31	,	,	PUNCT
cana-681	289	32	electronic	electronic	ADJ
cana-681	289	33	and	and	CCONJ
cana-681	289	34	communication	communication	NOUN
cana-681	289	35	engineering	engineering	NOUN
cana-681	289	36	,	,	PUNCT
cana-681	289	37	25	25	NUM
cana-681	289	38	september	september	PROPN
cana-681	289	39	2008	2008	NUM
cana-681	289	40	.	.	PUNCT
cana-681	290	1	[	[	X
cana-681	290	2	9	9	NUM
cana-681	290	3	]	]	PUNCT
cana-681	290	4	pengwei	pengwei	PROPN
cana-681	290	5	zhang	zhang	PROPN
cana-681	290	6	,	,	PUNCT
cana-681	290	7	yong	yong	PROPN
cana-681	290	8	li	li	PROPN
cana-681	290	9	,	,	PUNCT
cana-681	290	10	hsin	hsin	PROPN
cana-681	290	11	chiu	chiu	PROPN
cana-681	290	12	chang	chang	PROPN
cana-681	290	13	,	,	PUNCT
cana-681	290	14	hongqing	hongqe	VERB
cana-681	290	15	liu	liu	PROPN
cana-681	290	16	,	,	PUNCT
cana-681	290	17	trieu	trieu	PROPN
cana-681	290	18	-	-	PUNCT
cana-681	290	19	kien	kien	PROPN
cana-681	290	20	truong	truong	PROPN
cana-681	290	21	,	,	PUNCT
cana-681	290	22	fast	fast	ADJ
cana-681	290	23	decoding	decoding	NOUN
cana-681	290	24	of	of	ADP
cana-681	290	25	the	the	DET
cana-681	290	26	(	(	PUNCT
cana-681	290	27	47	47	NUM
cana-681	290	28	,	,	PUNCT
cana-681	290	29	24	24	NUM
cana-681	290	30	,	,	PUNCT
cana-681	290	31	11	11	NUM
cana-681	290	32	)	)	PUNCT
cana-681	290	33	quadratic	quadratic	ADJ
cana-681	290	34	residue	residue	NOUN
cana-681	290	35	code	code	NOUN
cana-681	290	36	without	without	ADP
cana-681	290	37	determining	determine	VERB
cana-681	290	38	the	the	DET
cana-681	290	39	unknown	unknown	ADJ
cana-681	290	40	syndromes	syndrome	NOUN
cana-681	290	41	,	,	PUNCT
cana-681	290	42	ieee	ieee	NOUN
cana-681	290	43	communications	communication	NOUN
cana-681	290	44	letters	letter	NOUN
cana-681	290	45	,	,	PUNCT
cana-681	290	46	19(8	19(8	NUM
cana-681	290	47	)	)	PUNCT
cana-681	290	48	,	,	PUNCT
cana-681	290	49	august	august	PROPN
cana-681	290	50	2015	2015	NUM
cana-681	290	51	.	.	PUNCT
cana-681	291	1	[	[	X
cana-681	291	2	10	10	NUM
cana-681	291	3	]	]	X
cana-681	291	4	pless	pless	PROPN
cana-681	291	5	v	v	PROPN
cana-681	291	6	s	s	PROPN
cana-681	291	7	,	,	PUNCT
cana-681	291	8	zhongqiang	zhongqiang	PROPN
cana-681	291	9	qian	qian	PROPN
cana-681	291	10	,	,	PUNCT
cana-681	291	11	cyclic	cyclic	ADJ
cana-681	291	12	codes	code	NOUN
cana-681	291	13	and	and	CCONJ
cana-681	291	14	quadratic	quadratic	ADJ
cana-681	291	15	residue	residue	NOUN
cana-681	291	16	codes	code	NOUN
cana-681	291	17	over	over	ADP
cana-681	291	18	z4	z4	PROPN
cana-681	291	19	,	,	PUNCT
cana-681	291	20	ieee	ieee	NOUN
cana-681	291	21	transactions	transaction	NOUN
cana-681	291	22	on	on	ADP
cana-681	291	23	information	information	NOUN
cana-681	291	24	theory	theory	NOUN
cana-681	291	25	,	,	PUNCT
cana-681	291	26	42(5	42(5	NUM
cana-681	291	27	)	)	PUNCT
cana-681	291	28	,	,	PUNCT
cana-681	291	29	september	september	PROPN
cana-681	291	30	1996	1996	NUM
cana-681	291	31	.	.	PUNCT
cana-681	292	1	[	[	X
cana-681	292	2	11	11	NUM
cana-681	292	3	]	]	PUNCT
cana-681	292	4	prange	prange	NOUN
cana-681	292	5	,	,	PUNCT
cana-681	292	6	some	some	DET
cana-681	292	7	cyclic	cyclic	NOUN
cana-681	292	8	error	error	NOUN
cana-681	292	9	-	-	PUNCT
cana-681	292	10	correcting	correct	VERB
cana-681	292	11	codes	code	NOUN
cana-681	292	12	with	with	ADP
cana-681	292	13	simple	simple	ADJ
cana-681	292	14	decoding	decode	VERB
cana-681	292	15	algorithms	algorithm	NOUN
cana-681	292	16	,	,	PUNCT
cana-681	292	17	air	air	NOUN
cana-681	292	18	force	force	PROPN
cana-681	292	19	cambridge	cambridge	PROPN
cana-681	292	20	research	research	PROPN
cana-681	292	21	center	center	PROPN
cana-681	292	22	tn	tn	PROPN
cana-681	292	23	,	,	PUNCT
cana-681	292	24	1958	1958	NUM
cana-681	292	25	.	.	PUNCT
cana-681	293	1	[	[	X
cana-681	293	2	12	12	NUM
cana-681	293	3	]	]	PUNCT
cana-681	293	4	ruhua	ruhua	NOUN
cana-681	293	5	he	he	PRON
cana-681	293	6	,	,	PUNCT
cana-681	293	7	irving	irving	PROPN
cana-681	293	8	s.	s.	PROPN
cana-681	293	9	reed	reed	PROPN
cana-681	293	10	,	,	PUNCT
cana-681	293	11	trieu	trieu	PROPN
cana-681	293	12	-	-	PUNCT
cana-681	293	13	kien	kien	PROPN
cana-681	293	14	truong	truong	PROPN
cana-681	293	15	,	,	PUNCT
cana-681	293	16	xuemin	xuemin	PROPN
cana-681	293	17	chen	chen	PROPN
cana-681	293	18	,	,	PUNCT
cana-681	293	19	decoding	decode	VERB
cana-681	293	20	the	the	DET
cana-681	293	21	(	(	PUNCT
cana-681	293	22	47,24,11	47,24,11	NOUN
cana-681	293	23	)	)	PUNCT
cana-681	293	24	quadratic	quadratic	ADJ
cana-681	293	25	residue	residue	NOUN
cana-681	293	26	code	code	NOUN
cana-681	293	27	,	,	PUNCT
cana-681	293	28	ieee	ieee	NOUN
cana-681	293	29	transactions	transaction	NOUN
cana-681	293	30	on	on	ADP
cana-681	293	31	communications	communication	NOUN
cana-681	293	32	,	,	PUNCT
cana-681	293	33	47(3	47(3	NUM
cana-681	293	34	)	)	PUNCT
cana-681	293	35	,	,	PUNCT
cana-681	293	36	march	march	PROPN
cana-681	293	37	2001	2001	NUM
cana-681	293	38	.	.	PUNCT
cana-681	294	1	[	[	X
cana-681	294	2	13	13	NUM
cana-681	294	3	]	]	X
cana-681	294	4	shapiro	shapiro	PROPN
cana-681	294	5	h.s	h.s	PROPN
cana-681	294	6	,	,	PUNCT
cana-681	294	7	d.l.slotnick	d.l.slotnick	NOUN
cana-681	294	8	,	,	PUNCT
cana-681	294	9	on	on	ADP
cana-681	294	10	the	the	DET
cana-681	294	11	mathematical	mathematical	ADJ
cana-681	294	12	theory	theory	NOUN
cana-681	294	13	of	of	ADP
cana-681	294	14	error	error	NOUN
cana-681	294	15	-	-	PUNCT
cana-681	294	16	correcting	correct	VERB
cana-681	294	17	codes	code	NOUN
cana-681	294	18	,	,	PUNCT
cana-681	294	19	ibm	ibm	PROPN
cana-681	294	20	journal	journal	NOUN
cana-681	294	21	of	of	ADP
cana-681	294	22	research	research	NOUN
cana-681	294	23	and	and	CCONJ
cana-681	294	24	development	development	NOUN
cana-681	294	25	,	,	PUNCT
cana-681	294	26	3(1	3(1	NUM
cana-681	294	27	)	)	PUNCT
cana-681	294	28	,	,	PUNCT
cana-681	294	29	january	january	PROPN
cana-681	294	30	1959	1959	NUM
cana-681	294	31	.	.	PUNCT
cana-681	295	1	[	[	X
cana-681	295	2	14	14	NUM
cana-681	295	3	]	]	X
cana-681	295	4	todd	todd	PROPN
cana-681	295	5	k.moon	k.moon	PROPN
cana-681	295	6	,	,	PUNCT
cana-681	295	7	error	error	NOUN
cana-681	295	8	correction	correction	NOUN
cana-681	295	9	coding	code	VERB
cana-681	295	10	:	:	PUNCT
cana-681	295	11	mathematical	mathematical	ADJ
cana-681	295	12	methods	method	NOUN
cana-681	295	13	and	and	CCONJ
cana-681	295	14	algorithms	algorithm	NOUN
cana-681	295	15	,	,	PUNCT
cana-681	295	16	john	john	PROPN
cana-681	295	17	wiley	wiley	PROPN
cana-681	295	18	and	and	CCONJ
cana-681	295	19	sons	sons	PROPN
cana-681	295	20	inc	inc	PROPN
cana-681	295	21	,	,	PUNCT
cana-681	295	22	usa	usa	PROPN
cana-681	295	23	,	,	PUNCT
cana-681	295	24	2014	2014	NUM
cana-681	295	25	.	.	PUNCT
cana-681	296	1	[	[	X
cana-681	296	2	15	15	NUM
cana-681	296	3	]	]	X
cana-681	296	4	tsung	tsung	PROPN
cana-681	296	5	-	-	PUNCT
cana-681	296	6	ching	ching	PROPN
cana-681	296	7	lin	lin	PROPN
cana-681	296	8	,	,	PUNCT
cana-681	296	9	trieu	trieu	PROPN
cana-681	296	10	-	-	PUNCT
cana-681	296	11	kien	kien	PROPN
cana-681	296	12	truong	truong	PROPN
cana-681	296	13	,	,	PUNCT
cana-681	296	14	hung	hung	PROPN
cana-681	296	15	-	-	PUNCT
cana-681	296	16	peng	peng	PROPN
cana-681	296	17	lee	lee	PROPN
cana-681	296	18	,	,	PUNCT
cana-681	296	19	hsin	hsin	PROPN
cana-681	296	20	-	-	PUNCT
cana-681	296	21	chiu	chiu	PROPN
cana-681	296	22	chang	chang	PROPN
cana-681	296	23	,	,	PUNCT
cana-681	296	24	algebraic	algebraic	PROPN
cana-681	296	25	decoding	decode	VERB
cana-681	296	26	of	of	ADP
cana-681	296	27	the	the	DET
cana-681	296	28	(	(	PUNCT
cana-681	296	29	41	41	NUM
cana-681	296	30	,	,	PUNCT
cana-681	296	31	21	21	NUM
cana-681	296	32	,	,	PUNCT
cana-681	296	33	9	9	NUM
cana-681	296	34	)	)	PUNCT
cana-681	296	35	quadratic	quadratic	ADJ
cana-681	296	36	residue	residue	NOUN
cana-681	296	37	codes	code	NOUN
cana-681	296	38	,	,	PUNCT
cana-681	296	39	information	information	NOUN
cana-681	296	40	sciences	science	NOUN
cana-681	296	41	,	,	PUNCT
cana-681	296	42	179(19	179(19	NUM
cana-681	296	43	)	)	PUNCT
cana-681	296	44	,	,	PUNCT
cana-681	296	45	9	9	NUM
cana-681	296	46	september	september	PROPN
cana-681	296	47	2009	2009	NUM
cana-681	296	48	.	.	PUNCT
cana-681	297	1	[	[	X
cana-681	297	2	16	16	NUM
cana-681	297	3	]	]	X
cana-681	297	4	wen	wen	PROPN
cana-681	297	5	-	-	PROPN
cana-681	297	6	ku	ku	PROPN
cana-681	297	7	su	su	PROPN
cana-681	297	8	,	,	PUNCT
cana-681	297	9	pei	pei	PROPN
cana-681	297	10	-	-	PUNCT
cana-681	297	11	yu	yu	PROPN
cana-681	297	12	shih	shih	PROPN
cana-681	297	13	,	,	PUNCT
cana-681	297	14	tsung	tsung	PROPN
cana-681	297	15	-	-	PUNCT
cana-681	297	16	ching	ching	PROPN
cana-681	297	17	lin	lin	PROPN
cana-681	297	18	,	,	PUNCT
cana-681	297	19	and	and	CCONJ
cana-681	297	20	trieu	trieu	PROPN
cana-681	297	21	-	-	PUNCT
cana-681	297	22	kien	kien	PROPN
cana-681	297	23	truong	truong	PROPN
cana-681	297	24	,	,	PUNCT
cana-681	297	25	decoding	decode	VERB
cana-681	297	26	of	of	ADP
cana-681	297	27	the	the	DET
cana-681	297	28	(	(	PUNCT
cana-681	297	29	48,24	48,24	NUM
cana-681	297	30	,	,	PUNCT
cana-681	297	31	12	12	NUM
cana-681	297	32	)	)	PUNCT
cana-681	297	33	extended	extend	VERB
cana-681	297	34	quadratic	quadratic	ADJ
cana-681	297	35	residue	residue	NOUN
cana-681	297	36	code	code	NOUN
cana-681	297	37	up	up	ADP
cana-681	297	38	to	to	PART
cana-681	297	39	six	six	NUM
cana-681	297	40	errors	error	NOUN
cana-681	297	41	,	,	PUNCT
cana-681	297	42	international	international	ADJ
cana-681	297	43	conference	conference	NOUN
cana-681	297	44	on	on	ADP
cana-681	297	45	communications	communication	NOUN
cana-681	297	46	,	,	PUNCT
cana-681	297	47	circuits	circuit	NOUN
cana-681	297	48	and	and	CCONJ
cana-681	297	49	systems	system	NOUN
cana-681	297	50	,	,	PUNCT
cana-681	297	51	2008	2008	NUM
cana-681	297	52	.	.	PUNCT
cana-681	298	1	[	[	X
cana-681	298	2	17	17	NUM
cana-681	298	3	]	]	X
cana-681	298	4	xuemin	xuemin	PROPN
cana-681	298	5	chen	chen	PROPN
cana-681	298	6	,	,	PUNCT
cana-681	298	7	i.s	i.s	PROPN
cana-681	298	8	.	.	PROPN
cana-681	298	9	reed	reed	PROPN
cana-681	298	10	,	,	PUNCT
cana-681	298	11	t.k	t.k	PROPN
cana-681	298	12	.	.	PROPN
cana-681	298	13	truong	truong	PROPN
cana-681	298	14	,	,	PUNCT
cana-681	298	15	a	a	DET
cana-681	298	16	performance	performance	NOUN
cana-681	298	17	comparison	comparison	NOUN
cana-681	298	18	of	of	ADP
cana-681	298	19	the	the	DET
cana-681	298	20	binary	binary	ADJ
cana-681	298	21	quadratic	quadratic	ADJ
cana-681	298	22	residue	residue	NOUN
cana-681	298	23	codes	code	NOUN
cana-681	298	24	with	with	ADP
cana-681	298	25	the	the	DET
cana-681	298	26	1/2	1/2	NUM
cana-681	298	27	-	-	PUNCT
cana-681	298	28	rate	rate	NOUN
cana-681	298	29	convolutional	convolutional	ADJ
cana-681	298	30	codes	code	NOUN
cana-681	298	31	,	,	PUNCT
cana-681	298	32	ieee	ieee	NOUN
cana-681	298	33	transactions	transaction	NOUN
cana-681	298	34	on	on	ADP
cana-681	298	35	information	information	NOUN
cana-681	298	36	theory	theory	NOUN
cana-681	298	37	,	,	PUNCT
cana-681	298	38	40(1	40(1	NOUN
cana-681	298	39	)	)	PUNCT
cana-681	298	40	,	,	PUNCT
cana-681	298	41	january	january	PROPN
cana-681	298	42	1994	1994	NUM
cana-681	298	43	.	.	PUNCT
cana-681	299	1	[	[	X
cana-681	299	2	18	18	NUM
cana-681	299	3	]	]	PUNCT
cana-681	299	4	yaotsu	yaotsu	PROPN
cana-681	299	5	chang	chang	PROPN
cana-681	299	6	,	,	PUNCT
cana-681	299	7	trieu	trieu	PROPN
cana-681	299	8	-	-	PUNCT
cana-681	299	9	kien	kien	PROPN
cana-681	299	10	truong	truong	PROPN
cana-681	299	11	,	,	PUNCT
cana-681	299	12	algebraic	algebraic	PROPN
cana-681	299	13	decoding	decode	VERB
cana-681	299	14	of	of	ADP
cana-681	299	15	(	(	PUNCT
cana-681	299	16	71	71	NUM
cana-681	299	17	,	,	PUNCT
cana-681	299	18	36	36	NUM
cana-681	299	19	,	,	PUNCT
cana-681	299	20	11	11	NUM
cana-681	299	21	)	)	PUNCT
cana-681	299	22	,	,	PUNCT
cana-681	299	23	(	(	PUNCT
cana-681	299	24	79,40	79,40	VERB
cana-681	299	25	,	,	PUNCT
cana-681	299	26	15	15	NUM
cana-681	299	27	)	)	PUNCT
cana-681	299	28	,	,	PUNCT
cana-681	299	29	and	and	CCONJ
cana-681	299	30	(	(	PUNCT
cana-681	299	31	97	97	NUM
cana-681	299	32	,	,	PUNCT
cana-681	299	33	49	49	NUM
cana-681	299	34	,	,	PUNCT
cana-681	299	35	15	15	NUM
cana-681	299	36	)	)	PUNCT
cana-681	299	37	quadratic	quadratic	ADJ
cana-681	299	38	residue	residue	NOUN
cana-681	299	39	codes	code	NOUN
cana-681	299	40	,	,	PUNCT
cana-681	299	41	ieee	ieee	NOUN
cana-681	299	42	transaction	transaction	NOUN
cana-681	299	43	on	on	ADP
cana-681	299	44	communication	communication	NOUN
cana-681	299	45	,	,	PUNCT
cana-681	299	46	51(9	51(9	PROPN
cana-681	299	47	)	)	PUNCT
cana-681	299	48	,	,	PUNCT
cana-681	299	49	september	september	PROPN
cana-681	299	50	2003	2003	NUM
cana-681	299	51	.	.	PUNCT
cana-681	300	1	[	[	X
cana-681	300	2	19	19	NUM
cana-681	300	3	]	]	PUNCT
cana-681	300	4	zhang.p	zhang.p	NUM
cana-681	300	5	,	,	PUNCT
cana-681	300	6	y.	y.	PROPN
cana-681	300	7	li	li	PROPN
cana-681	300	8	,	,	PUNCT
cana-681	300	9	h.c	h.c	PROPN
cana-681	300	10	.	.	PROPN
cana-681	300	11	chang	chang	PROPN
cana-681	300	12	,	,	PUNCT
cana-681	300	13	h.	h.	PROPN
cana-681	300	14	liu	liu	PROPN
cana-681	300	15	and	and	CCONJ
cana-681	300	16	t.k	t.k	PROPN
cana-681	300	17	.	.	PROPN
cana-681	300	18	truong	truong	PROPN
cana-681	300	19	,	,	PUNCT
cana-681	300	20	fast	fast	ADJ
cana-681	300	21	decoding	decoding	NOUN
cana-681	300	22	of	of	ADP
cana-681	300	23	the	the	DET
cana-681	300	24	(	(	PUNCT
cana-681	300	25	47	47	NUM
cana-681	300	26	,	,	PUNCT
cana-681	300	27	24	24	NUM
cana-681	300	28	,	,	PUNCT
cana-681	300	29	11	11	NUM
cana-681	300	30	)	)	PUNCT
cana-681	300	31	quadratic	quadratic	ADJ
cana-681	300	32	residue	residue	NOUN
cana-681	300	33	code	code	NOUN
cana-681	300	34	without	without	ADP
cana-681	300	35	determining	determine	VERB
cana-681	300	36	the	the	DET
cana-681	300	37	unknown	unknown	ADJ
cana-681	300	38	syndromes	syndrome	NOUN
cana-681	300	39	,	,	PUNCT
cana-681	300	40	ieee	ieee	NOUN
cana-681	300	41	communications	communication	NOUN
cana-681	300	42	letters	letter	NOUN
cana-681	300	43	,	,	PUNCT
cana-681	300	44	19(8	19(8	NUM
cana-681	300	45	)	)	PUNCT
cana-681	300	46	,	,	PUNCT
cana-681	300	47	august	august	PROPN
cana-681	300	48	2015	2015	NUM
cana-681	300	49	.	.	PUNCT