id	sid	tid	token	lemma	pos
cana-3963	1	1	communications	communication	NOUN
cana-3963	1	2	on	on	ADP
cana-3963	1	3	applied	apply	VERB
cana-3963	1	4	nonlinear	nonlinear	ADJ
cana-3963	1	5	analysis	analysis	NOUN
cana-3963	1	6	issn	issn	NOUN
cana-3963	1	7	:	:	PUNCT
cana-3963	1	8	1074	1074	NUM
cana-3963	1	9	-	-	PUNCT
cana-3963	1	10	133x	133x	NUM
cana-3963	1	11	vol	vol	NOUN
cana-3963	1	12	32	32	NUM
cana-3963	1	13	no	no	NOUN
cana-3963	1	14	.	.	PUNCT
cana-3963	2	1	9s	9s	NUM
cana-3963	2	2	(	(	PUNCT
cana-3963	2	3	2025	2025	NUM
cana-3963	2	4	)	)	PUNCT
cana-3963	2	5	542	542	NUM
cana-3963	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	2	7	new	new	ADJ
cana-3963	2	8	quantum	quantum	NOUN
cana-3963	2	9	codes	code	NOUN
cana-3963	2	10	using	use	VERB
cana-3963	2	11	monomial	monomial	ADJ
cana-3963	2	12	matrix	matrix	NOUN
cana-3963	2	13	over	over	ADP
cana-3963	2	14	hermitian	hermitian	ADJ
cana-3963	2	15	dualcontaining	dualcontaining	NOUN
cana-3963	2	16	matrix	matrix	NOUN
cana-3963	2	17	product	product	NOUN
cana-3963	2	18	codes	code	NOUN
cana-3963	2	19	shivender	shivender	PROPN
cana-3963	2	20	goswami1	goswami1	PROPN
cana-3963	2	21	,	,	PUNCT
cana-3963	2	22	manoj	manoj	PROPN
cana-3963	2	23	kumar2	kumar2	PROPN
cana-3963	2	24	*	*	PROPN
cana-3963	2	25	,	,	PUNCT
cana-3963	2	26	akash	akash	PROPN
cana-3963	2	27	rathor3	rathor3	PROPN
cana-3963	2	28	,	,	PUNCT
cana-3963	2	29	ankit	ankit	PROPN
cana-3963	2	30	chaudhary4	chaudhary4	PROPN
cana-3963	2	31	,	,	PUNCT
cana-3963	2	32	r.k	r.k	PROPN
cana-3963	2	33	.	.	PROPN
cana-3963	2	34	mishra5	mishra5	PROPN
cana-3963	2	35	,	,	PUNCT
cana-3963	2	36	kamal	kamal	PROPN
cana-3963	2	37	upreti6	upreti6	PROPN
cana-3963	2	38	,	,	PUNCT
cana-3963	2	39	pratik	pratik	NOUN
cana-3963	2	40	gupta7	gupta7	PROPN
cana-3963	2	41	1,2,3,4department	1,2,3,4department	NUM
cana-3963	2	42	of	of	ADP
cana-3963	2	43	mathematics	mathematic	NOUN
cana-3963	2	44	and	and	CCONJ
cana-3963	2	45	statistics	statistic	NOUN
cana-3963	2	46	,	,	PUNCT
cana-3963	2	47	gurukula	gurukula	NOUN
cana-3963	2	48	kangri	kangri	NOUN
cana-3963	2	49	(	(	PUNCT
cana-3963	2	50	deemed	deem	VERB
cana-3963	2	51	to	to	PART
cana-3963	2	52	be	be	AUX
cana-3963	2	53	university	university	NOUN
cana-3963	2	54	)	)	PUNCT
cana-3963	2	55	,	,	PUNCT
cana-3963	2	56	haridwar	haridwar	PROPN
cana-3963	2	57	,	,	PUNCT
cana-3963	2	58	uttarakhand	uttarakhand	PROPN
cana-3963	2	59	,	,	PUNCT
cana-3963	2	60	india	india	PROPN
cana-3963	2	61	5department	5department	NUM
cana-3963	2	62	of	of	ADP
cana-3963	2	63	applied	apply	VERB
cana-3963	2	64	science	science	NOUN
cana-3963	2	65	and	and	CCONJ
cana-3963	2	66	humanities	humanity	NOUN
cana-3963	2	67	,	,	PUNCT
cana-3963	2	68	g.l	g.l	PROPN
cana-3963	2	69	.	.	PROPN
cana-3963	2	70	bajaj	bajaj	PROPN
cana-3963	2	71	institute	institute	PROPN
cana-3963	2	72	of	of	ADP
cana-3963	2	73	technology	technology	NOUN
cana-3963	2	74	and	and	CCONJ
cana-3963	2	75	management	management	NOUN
cana-3963	2	76	,	,	PUNCT
cana-3963	2	77	greater	great	ADJ
cana-3963	2	78	noida	noida	PROPN
cana-3963	2	79	,	,	PUNCT
cana-3963	2	80	uttar	uttar	PROPN
cana-3963	2	81	pradesh	pradesh	PROPN
cana-3963	2	82	,	,	PUNCT
cana-3963	2	83	india	india	PROPN
cana-3963	2	84	6school	6school	PROPN
cana-3963	2	85	of	of	ADP
cana-3963	2	86	sciences	science	NOUN
cana-3963	2	87	,	,	PUNCT
cana-3963	2	88	christ	christ	PROPN
cana-3963	2	89	university	university	PROPN
cana-3963	2	90	,	,	PUNCT
cana-3963	2	91	delhi	delhi	PROPN
cana-3963	2	92	ncr	ncr	PROPN
cana-3963	2	93	campus	campus	PROPN
cana-3963	2	94	,	,	PUNCT
cana-3963	2	95	ghaziabad	ghaziabad	PROPN
cana-3963	2	96	,	,	PUNCT
cana-3963	2	97	uttar	uttar	PROPN
cana-3963	2	98	pradesh	pradesh	PROPN
cana-3963	2	99	,	,	PUNCT
cana-3963	2	100	india	india	PROPN
cana-3963	2	101	7department	7department	NUM
cana-3963	2	102	of	of	ADP
cana-3963	2	103	mathematics	mathematic	NOUN
cana-3963	2	104	,	,	PUNCT
cana-3963	2	105	d.a.v	d.a.v	NOUN
cana-3963	2	106	degree	degree	NOUN
cana-3963	2	107	college	college	NOUN
cana-3963	2	108	,	,	PUNCT
cana-3963	2	109	lucknow	lucknow	PROPN
cana-3963	2	110	,	,	PUNCT
cana-3963	2	111	uttar	uttar	PROPN
cana-3963	2	112	pradesh	pradesh	PROPN
cana-3963	2	113	,	,	PUNCT
cana-3963	2	114	india	india	PROPN
cana-3963	2	115	email	email	NOUN
cana-3963	2	116	:	:	PUNCT
cana-3963	2	117	shivendrgoswami@gmail.com1	shivendrgoswami@gmail.com1	PROPN
cana-3963	2	118	,	,	PUNCT
cana-3963	2	119	sdmkg1@gmail.com2	sdmkg1@gmail.com2	NOUN
cana-3963	2	120	*	*	NOUN
cana-3963	2	121	,	,	PUNCT
cana-3963	2	122	akashrathor9760@gmail.com3	akashrathor9760@gmail.com3	ADJ
cana-3963	2	123	,	,	PUNCT
cana-3963	2	124	aakashdhama2016@gmail.com4	aakashdhama2016@gmail.com4	NUM
cana-3963	2	125	,	,	PUNCT
cana-3963	2	126	rkmsit@rediffmail.com5	rkmsit@rediffmail.com5	NOUN
cana-3963	2	127	,	,	PUNCT
cana-3963	2	128	kamalupreti1989@gmail.com6	kamalupreti1989@gmail.com6	PROPN
cana-3963	2	129	,	,	PUNCT
cana-3963	2	130	pratikgupta1810@gmail.com7	pratikgupta1810@gmail.com7	ADP
cana-3963	2	131	*	*	PUNCT
cana-3963	2	132	corresponding	correspond	VERB
cana-3963	2	133	author	author	NOUN
cana-3963	2	134	article	article	NOUN
cana-3963	2	135	history	history	NOUN
cana-3963	2	136	:	:	PUNCT
cana-3963	2	137	received	receive	VERB
cana-3963	2	138	:	:	PUNCT
cana-3963	2	139	10	10	NUM
cana-3963	2	140	-	-	SYM
cana-3963	2	141	11	11	NUM
cana-3963	2	142	-	-	PUNCT
cana-3963	2	143	2024	2024	NUM
cana-3963	2	144	revised	revise	VERB
cana-3963	2	145	:	:	PUNCT
cana-3963	2	146	13	13	NUM
cana-3963	2	147	-	-	SYM
cana-3963	2	148	12	12	NUM
cana-3963	2	149	-	-	PUNCT
cana-3963	2	150	2024	2024	NUM
cana-3963	2	151	accepted	accept	VERB
cana-3963	2	152	:	:	PUNCT
cana-3963	2	153	26	26	NUM
cana-3963	2	154	-	-	SYM
cana-3963	2	155	01	01	NUM
cana-3963	2	156	-	-	PUNCT
cana-3963	2	157	2025	2025	NUM
cana-3963	2	158	abstract	abstract	NOUN
cana-3963	2	159	:	:	PUNCT
cana-3963	2	160	quantum	quantum	ADJ
cana-3963	2	161	error	error	NOUN
cana-3963	2	162	correction	correction	NOUN
cana-3963	2	163	(	(	PUNCT
cana-3963	2	164	qec	qec	NOUN
cana-3963	2	165	)	)	PUNCT
cana-3963	2	166	is	be	AUX
cana-3963	2	167	beneficial	beneficial	ADJ
cana-3963	2	168	for	for	ADP
cana-3963	2	169	ensuring	ensure	VERB
cana-3963	2	170	reliable	reliable	ADJ
cana-3963	2	171	quantum	quantum	ADJ
cana-3963	2	172	computation	computation	NOUN
cana-3963	2	173	and	and	CCONJ
cana-3963	2	174	communication	communication	NOUN
cana-3963	2	175	by	by	ADP
cana-3963	2	176	addressing	address	VERB
cana-3963	2	177	the	the	DET
cana-3963	2	178	susceptibility	susceptibility	NOUN
cana-3963	2	179	of	of	ADP
cana-3963	2	180	quantum	quantum	ADJ
cana-3963	2	181	states	state	NOUN
cana-3963	2	182	to	to	ADP
cana-3963	2	183	errors	error	NOUN
cana-3963	2	184	from	from	ADP
cana-3963	2	185	decoherence	decoherence	NOUN
cana-3963	2	186	and	and	CCONJ
cana-3963	2	187	noise	noise	NOUN
cana-3963	2	188	.	.	PUNCT
cana-3963	3	1	this	this	DET
cana-3963	3	2	study	study	NOUN
cana-3963	3	3	explores	explore	VERB
cana-3963	3	4	the	the	DET
cana-3963	3	5	use	use	NOUN
cana-3963	3	6	of	of	ADP
cana-3963	3	7	quantum	quantum	ADJ
cana-3963	3	8	matrix	matrix	NOUN
cana-3963	3	9	product	product	NOUN
cana-3963	3	10	codes	code	NOUN
cana-3963	3	11	(	(	PUNCT
cana-3963	3	12	mpcs	mpcs	PROPN
cana-3963	3	13	)	)	PUNCT
cana-3963	3	14	with	with	ADP
cana-3963	3	15	an	an	DET
cana-3963	3	16	emphasis	emphasis	NOUN
cana-3963	3	17	on	on	ADP
cana-3963	3	18	monomial	monomial	ADJ
cana-3963	3	19	matrices	matrix	NOUN
cana-3963	3	20	and	and	CCONJ
cana-3963	3	21	hermitian	hermitian	ADJ
cana-3963	3	22	duals	dual	NOUN
cana-3963	3	23	to	to	PART
cana-3963	3	24	achieve	achieve	VERB
cana-3963	3	25	efficient	efficient	ADJ
cana-3963	3	26	and	and	CCONJ
cana-3963	3	27	robust	robust	ADJ
cana-3963	3	28	error	error	NOUN
cana-3963	3	29	correction	correction	NOUN
cana-3963	3	30	.	.	PUNCT
cana-3963	4	1	we	we	PRON
cana-3963	4	2	provide	provide	VERB
cana-3963	4	3	a	a	DET
cana-3963	4	4	detailed	detailed	ADJ
cana-3963	4	5	mathematical	mathematical	ADJ
cana-3963	4	6	formulation	formulation	NOUN
cana-3963	4	7	of	of	ADP
cana-3963	4	8	mpcs	mpcs	PROPN
cana-3963	4	9	utilizing	utilize	VERB
cana-3963	4	10	monomial	monomial	ADJ
cana-3963	4	11	matrices	matrix	NOUN
cana-3963	4	12	,	,	PUNCT
cana-3963	4	13	emphasizing	emphasize	VERB
cana-3963	4	14	the	the	DET
cana-3963	4	15	importance	importance	NOUN
cana-3963	4	16	of	of	ADP
cana-3963	4	17	hermitian	hermitian	ADJ
cana-3963	4	18	duals	dual	NOUN
cana-3963	4	19	in	in	ADP
cana-3963	4	20	maintaining	maintain	VERB
cana-3963	4	21	code	code	NOUN
cana-3963	4	22	integrity	integrity	NOUN
cana-3963	4	23	and	and	CCONJ
cana-3963	4	24	ensuring	ensure	VERB
cana-3963	4	25	effective	effective	ADJ
cana-3963	4	26	error	error	NOUN
cana-3963	4	27	correction	correction	NOUN
cana-3963	4	28	.	.	PUNCT
cana-3963	5	1	the	the	DET
cana-3963	5	2	paper	paper	NOUN
cana-3963	5	3	proposes	propose	VERB
cana-3963	5	4	a	a	DET
cana-3963	5	5	new	new	ADJ
cana-3963	5	6	criterion	criterion	NOUN
cana-3963	5	7	for	for	ADP
cana-3963	5	8	utilizing	utilize	VERB
cana-3963	5	9	the	the	DET
cana-3963	5	10	rank	rank	NOUN
cana-3963	5	11	of	of	ADP
cana-3963	5	12	the	the	DET
cana-3963	5	13	generator	generator	NOUN
cana-3963	5	14	matrix	matrix	NOUN
cana-3963	5	15	associated	associate	VERB
cana-3963	5	16	with	with	ADP
cana-3963	5	17	linear	linear	PROPN
cana-3963	5	18	codes	code	NOUN
cana-3963	5	19	established	establish	VERB
cana-3963	5	20	from	from	ADP
cana-3963	5	21	hermitian	hermitian	ADJ
cana-3963	5	22	dual	dual	ADV
cana-3963	5	23	-	-	PUNCT
cana-3963	5	24	containing	contain	VERB
cana-3963	5	25	(	(	PUNCT
cana-3963	5	26	hdc	hdc	NOUN
cana-3963	5	27	)	)	PUNCT
cana-3963	5	28	of	of	ADP
cana-3963	5	29	the	the	DET
cana-3963	5	30	mpcs	mpcs	PROPN
cana-3963	5	31	.	.	PUNCT
cana-3963	6	1	then	then	ADV
cana-3963	6	2	,	,	PUNCT
cana-3963	6	3	using	use	VERB
cana-3963	6	4	this	this	DET
cana-3963	6	5	criterion	criterion	NOUN
cana-3963	6	6	,	,	PUNCT
cana-3963	6	7	a	a	DET
cana-3963	6	8	new	new	ADJ
cana-3963	6	9	set	set	NOUN
cana-3963	6	10	of	of	ADP
cana-3963	6	11	quantum	quantum	ADJ
cana-3963	6	12	maximum	maximum	ADJ
cana-3963	6	13	-	-	PUNCT
cana-3963	6	14	distance	distance	NOUN
cana-3963	6	15	-	-	PUNCT
cana-3963	6	16	separable	separable	NOUN
cana-3963	6	17	(	(	PUNCT
cana-3963	6	18	mds	mds	PROPN
cana-3963	6	19	)	)	PUNCT
cana-3963	6	20	codes	code	NOUN
cana-3963	6	21	has	have	AUX
cana-3963	6	22	been	be	AUX
cana-3963	6	23	constructed	construct	VERB
cana-3963	6	24	with	with	ADP
cana-3963	6	25	better	well	ADJ
cana-3963	6	26	code	code	NOUN
cana-3963	6	27	parameters	parameter	NOUN
cana-3963	6	28	and	and	CCONJ
cana-3963	6	29	error	error	NOUN
cana-3963	6	30	-	-	PUNCT
cana-3963	6	31	correction	correction	NOUN
cana-3963	6	32	potential	potential	NOUN
cana-3963	6	33	.	.	PUNCT
cana-3963	7	1	for	for	ADP
cana-3963	7	2	comparison	comparison	NOUN
cana-3963	7	3	purpose	purpose	NOUN
cana-3963	7	4	,	,	PUNCT
cana-3963	7	5	different	different	ADJ
cana-3963	7	6	codes	code	NOUN
cana-3963	7	7	have	have	AUX
cana-3963	7	8	been	be	AUX
cana-3963	7	9	observed	observe	VERB
cana-3963	7	10	alongside	alongside	ADV
cana-3963	7	11	with	with	ADP
cana-3963	7	12	the	the	DET
cana-3963	7	13	obtained	obtain	VERB
cana-3963	7	14	codes	code	NOUN
cana-3963	7	15	to	to	PART
cana-3963	7	16	ascertain	ascertain	VERB
cana-3963	7	17	the	the	DET
cana-3963	7	18	uniqueness	uniqueness	NOUN
cana-3963	7	19	and	and	CCONJ
cana-3963	7	20	error	error	NOUN
cana-3963	7	21	correction	correction	NOUN
cana-3963	7	22	capabilities	capability	NOUN
cana-3963	7	23	.	.	PUNCT
cana-3963	8	1	keywords	keyword	NOUN
cana-3963	8	2	:	:	PUNCT
cana-3963	8	3	linear	linear	ADJ
cana-3963	8	4	codes	code	NOUN
cana-3963	8	5	,	,	PUNCT
cana-3963	8	6	hermitian	hermitian	ADJ
cana-3963	8	7	-	-	PUNCT
cana-3963	8	8	dual	dual	ADV
cana-3963	8	9	-	-	PUNCT
cana-3963	8	10	containing	contain	VERB
cana-3963	8	11	,	,	PUNCT
cana-3963	8	12	matrix	matrix	NOUN
cana-3963	8	13	-	-	PUNCT
cana-3963	8	14	product	product	NOUN
cana-3963	8	15	codes	code	NOUN
cana-3963	8	16	,	,	PUNCT
cana-3963	8	17	maximum	maximum	ADJ
cana-3963	8	18	distance	distance	NOUN
cana-3963	8	19	separable	separable	ADJ
cana-3963	8	20	codes	code	NOUN
cana-3963	8	21	,	,	PUNCT
cana-3963	8	22	monomial	monomial	ADJ
cana-3963	8	23	matrix	matrix	NOUN
cana-3963	8	24	.	.	PUNCT
cana-3963	9	1	1	1	X
cana-3963	9	2	.	.	X
cana-3963	9	3	introduction	introduction	NOUN
cana-3963	9	4	the	the	DET
cana-3963	9	5	concept	concept	NOUN
cana-3963	9	6	of	of	ADP
cana-3963	9	7	qec	qec	NOUN
cana-3963	9	8	is	be	AUX
cana-3963	9	9	pivotal	pivotal	ADJ
cana-3963	9	10	in	in	ADP
cana-3963	9	11	quantum	quantum	ADJ
cana-3963	9	12	computation	computation	NOUN
cana-3963	9	13	and	and	CCONJ
cana-3963	9	14	communication	communication	NOUN
cana-3963	9	15	,	,	PUNCT
cana-3963	9	16	addressing	address	VERB
cana-3963	9	17	issues	issue	NOUN
cana-3963	9	18	like	like	ADP
cana-3963	9	19	decoherence	decoherence	NOUN
cana-3963	9	20	and	and	CCONJ
cana-3963	9	21	quantum	quantum	NOUN
cana-3963	9	22	noise	noise	NOUN
cana-3963	9	23	.	.	PUNCT
cana-3963	10	1	since	since	SCONJ
cana-3963	10	2	seminal	seminal	ADJ
cana-3963	10	3	works	work	NOUN
cana-3963	10	4	[	[	X
cana-3963	10	5	1,2,3	1,2,3	NUM
cana-3963	10	6	]	]	PUNCT
cana-3963	10	7	,	,	PUNCT
cana-3963	10	8	research	research	NOUN
cana-3963	10	9	in	in	ADP
cana-3963	10	10	quantum	quantum	ADJ
cana-3963	10	11	codes	code	NOUN
cana-3963	10	12	has	have	AUX
cana-3963	10	13	flourished	flourish	VERB
cana-3963	10	14	,	,	PUNCT
cana-3963	10	15	particularly	particularly	ADV
cana-3963	10	16	in	in	ADP
cana-3963	10	17	constructing	construct	VERB
cana-3963	10	18	effective	effective	ADJ
cana-3963	10	19	quantum	quantum	ADJ
cana-3963	10	20	codes	code	NOUN
cana-3963	10	21	.	.	PUNCT
cana-3963	11	1	the	the	DET
cana-3963	11	2	notable	notable	ADJ
cana-3963	11	3	hermitian	hermitian	ADJ
cana-3963	11	4	construction	construction	NOUN
cana-3963	11	5	[	[	X
cana-3963	11	6	4	4	X
cana-3963	11	7	]	]	PUNCT
cana-3963	11	8	demonstrates	demonstrate	VERB
cana-3963	11	9	that	that	SCONJ
cana-3963	11	10	a	a	DET
cana-3963	11	11	linear	linear	ADJ
cana-3963	11	12	code	code	NOUN
cana-3963	11	13	having	have	VERB
cana-3963	11	14	parameters	parameter	NOUN
cana-3963	11	15	2,2	2,2	NUM
cana-3963	11	16	,	,	PUNCT
cana-3963	11	17	]	]	X
cana-3963	11	18	[	[	X
cana-3963	11	19	[	[	X
cana-3963	11	20	]	]	X
cana-3963	11	21	q	q	X
cana-3963	11	22	n	n	CCONJ
cana-3963	11	23	k	k	NOUN
cana-3963	11	24	n	n	CCONJ
cana-3963	11	25	d−	d−	PROPN
cana-3963	11	26			NUM
cana-3963	11	27	can	can	AUX
cana-3963	11	28	be	be	AUX
cana-3963	11	29	developed	develop	VERB
cana-3963	11	30	from	from	ADP
cana-3963	11	31	a	a	DET
cana-3963	11	32	hdc	hdc	NOUN
cana-3963	11	33	2	2	NUM
cana-3963	11	34	[	[	X
cana-3963	11	35	[	[	PUNCT
cana-3963	11	36	,	,	PUNCT
cana-3963	11	37	,	,	PUNCT
cana-3963	11	38	]	]	X
cana-3963	11	39	]	]	X
cana-3963	11	40	q	q	X
cana-3963	11	41	n	n	X
cana-3963	11	42	k	k	PROPN
cana-3963	11	43	d	d	PROPN
cana-3963	11	44	code	code	PROPN
cana-3963	11	45	.	.	PUNCT
cana-3963	12	1	thus	thus	ADV
cana-3963	12	2	,	,	PUNCT
cana-3963	12	3	developing	develop	VERB
cana-3963	12	4	2q	2q	NOUN
cana-3963	12	5	-ary	-ary	ADJ
cana-3963	12	6	hdc	hdc	NOUN
cana-3963	12	7	codes	code	NOUN
cana-3963	12	8	is	be	AUX
cana-3963	12	9	crucial	crucial	ADJ
cana-3963	12	10	for	for	ADP
cana-3963	12	11	obtaining	obtain	VERB
cana-3963	12	12	q	q	ADJ
cana-3963	12	13	-ary	-ary	ADJ
cana-3963	12	14	quantum	quantum	NOUN
cana-3963	12	15	codes	code	NOUN
cana-3963	12	16	[	[	X
cana-3963	12	17	5	5	NUM
cana-3963	12	18	]	]	PUNCT
cana-3963	12	19	.	.	PUNCT
cana-3963	13	1	communications	communication	NOUN
cana-3963	13	2	on	on	ADP
cana-3963	13	3	applied	apply	VERB
cana-3963	13	4	nonlinear	nonlinear	ADJ
cana-3963	13	5	analysis	analysis	NOUN
cana-3963	13	6	issn	issn	NOUN
cana-3963	13	7	:	:	PUNCT
cana-3963	13	8	1074	1074	NUM
cana-3963	13	9	-	-	PUNCT
cana-3963	13	10	133x	133x	NUM
cana-3963	13	11	vol	vol	NOUN
cana-3963	13	12	32	32	NUM
cana-3963	13	13	no	no	NOUN
cana-3963	13	14	.	.	PUNCT
cana-3963	14	1	9s	9s	NUM
cana-3963	14	2	(	(	PUNCT
cana-3963	14	3	2025	2025	NUM
cana-3963	14	4	)	)	PUNCT
cana-3963	14	5	543	543	NUM
cana-3963	14	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	14	7	a	a	DET
cana-3963	14	8	hdc	hdc	NOUN
cana-3963	14	9	code	code	NOUN
cana-3963	14	10			NOUN
cana-3963	14	11	is	be	AUX
cana-3963	14	12	a	a	DET
cana-3963	14	13	type	type	NOUN
cana-3963	14	14	of	of	ADP
cana-3963	14	15	linear	linear	PROPN
cana-3963	14	16	code	code	NOUN
cana-3963	14	17	where	where	SCONJ
cana-3963	14	18	its	its	PRON
cana-3963	14	19	hermitian	hermitian	ADJ
cana-3963	14	20	dual	dual	ADJ
cana-3963	14	21	code	code	NOUN
cana-3963	14	22	h	h	NOUN
cana-3963	14	23	⊥	⊥	X
cana-3963	14	24	meets	meet	VERB
cana-3963	14	25	condition	condition	NOUN
cana-3963	14	26	given	give	VERB
cana-3963	14	27	as	as	ADP
cana-3963	14	28	.h	.h	PROPN
cana-3963	14	29			PROPN
cana-3963	15	1	⊥	⊥	PROPN
cana-3963	15	2			PROPN
cana-3963	15	3	these	these	DET
cana-3963	15	4	quantum	quantum	ADJ
cana-3963	15	5	codes	code	NOUN
cana-3963	15	6	,	,	PUNCT
cana-3963	15	7	introduced	introduce	VERB
cana-3963	15	8	in	in	ADP
cana-3963	15	9	[	[	X
cana-3963	15	10	1	1	NUM
cana-3963	15	11	]	]	PUNCT
cana-3963	15	12	,	,	PUNCT
cana-3963	15	13	are	be	AUX
cana-3963	15	14	important	important	ADJ
cana-3963	15	15	for	for	ADP
cana-3963	15	16	creating	create	VERB
cana-3963	15	17	high	high	ADJ
cana-3963	15	18	-	-	PUNCT
cana-3963	15	19	quality	quality	NOUN
cana-3963	15	20	quantum	quantum	NOUN
cana-3963	15	21	codes	code	NOUN
cana-3963	15	22	.	.	PUNCT
cana-3963	16	1	much	much	ADJ
cana-3963	16	2	research	research	NOUN
cana-3963	16	3	has	have	AUX
cana-3963	16	4	focused	focus	VERB
cana-3963	16	5	on	on	ADP
cana-3963	16	6	defining	define	VERB
cana-3963	16	7	and	and	CCONJ
cana-3963	16	8	constructing	construct	VERB
cana-3963	16	9	hdc	hdc	NOUN
cana-3963	16	10	codes	code	NOUN
cana-3963	16	11	.	.	PUNCT
cana-3963	17	1	in	in	ADP
cana-3963	17	2	[	[	X
cana-3963	17	3	6	6	NUM
cana-3963	17	4	]	]	PUNCT
cana-3963	17	5	,	,	PUNCT
cana-3963	17	6	the	the	DET
cana-3963	17	7	conditions	condition	NOUN
cana-3963	17	8	for	for	ADP
cana-3963	17	9			ADJ
cana-3963	17	10	−	−	PROPN
cana-3963	17	11	constacyclic	constacyclic	ADJ
cana-3963	17	12	codes	code	NOUN
cana-3963	17	13	over	over	ADP
cana-3963	17	14	finite	finite	ADJ
cana-3963	17	15	fields	field	NOUN
cana-3963	17	16	to	to	PART
cana-3963	17	17	be	be	AUX
cana-3963	17	18	fig	fig	NOUN
cana-3963	17	19	.	.	PUNCT
cana-3963	18	1	1	1	X
cana-3963	18	2	.	.	X
cana-3963	18	3	process	process	NOUN
cana-3963	18	4	of	of	ADP
cana-3963	18	5	quantum	quantum	ADJ
cana-3963	18	6	error	error	NOUN
cana-3963	18	7	correction	correction	NOUN
cana-3963	18	8	using	use	VERB
cana-3963	18	9	ancila	ancila	NOUN
cana-3963	18	10	qubits	qubit	NOUN
cana-3963	18	11	.	.	PUNCT
cana-3963	19	1	hdc	hdc	PROPN
cana-3963	19	2	is	be	AUX
cana-3963	19	3	provided	provide	VERB
cana-3963	19	4	and	and	CCONJ
cana-3963	19	5	utilizing	utilize	VERB
cana-3963	19	6	these	these	DET
cana-3963	19	7	conditions	condition	NOUN
cana-3963	19	8	,	,	PUNCT
cana-3963	19	9	they	they	PRON
cana-3963	19	10	established	establish	VERB
cana-3963	19	11	several	several	ADJ
cana-3963	19	12	categories	category	NOUN
cana-3963	19	13	of	of	ADP
cana-3963	19	14	quantum	quantum	PROPN
cana-3963	19	15	mds	mds	NOUN
cana-3963	19	16	codes	code	NOUN
cana-3963	19	17	.	.	PUNCT
cana-3963	20	1	the	the	DET
cana-3963	20	2	existence	existence	NOUN
cana-3963	20	3	of	of	ADP
cana-3963	20	4	significant	significant	ADJ
cana-3963	20	5	hdc	hdc	NOUN
cana-3963	20	6	constacyclic	constacyclic	NOUN
cana-3963	20	7	codes	code	NOUN
cana-3963	20	8	over	over	ADP
cana-3963	20	9	finite	finite	ADJ
cana-3963	20	10	fields	field	NOUN
cana-3963	20	11	is	be	AUX
cana-3963	20	12	established	establish	VERB
cana-3963	20	13	in	in	ADP
cana-3963	20	14	[	[	X
cana-3963	20	15	7	7	NUM
cana-3963	20	16	]	]	PUNCT
cana-3963	20	17	.	.	PUNCT
cana-3963	21	1	recently	recently	ADV
cana-3963	21	2	,	,	PUNCT
cana-3963	21	3	the	the	DET
cana-3963	21	4	sufficient	sufficient	ADJ
cana-3963	21	5	conditions	condition	NOUN
cana-3963	21	6	are	be	AUX
cana-3963	21	7	provided	provide	VERB
cana-3963	21	8	for	for	ADP
cana-3963	21	9	pseudo	pseudo	NOUN
cana-3963	21	10	-	-	ADJ
cana-3963	21	11	cyclic	cyclic	ADJ
cana-3963	21	12	codes	code	NOUN
cana-3963	21	13	to	to	PART
cana-3963	21	14	be	be	AUX
cana-3963	21	15	hdc	hdc	NOUN
cana-3963	21	16	[	[	X
cana-3963	21	17	8	8	NUM
cana-3963	21	18	]	]	PUNCT
cana-3963	21	19	.	.	PUNCT
cana-3963	22	1	additionally	additionally	ADV
cana-3963	22	2	,	,	PUNCT
cana-3963	22	3	hdc	hdc	NOUN
cana-3963	22	4	codes	code	NOUN
cana-3963	22	5	have	have	AUX
cana-3963	22	6	been	be	AUX
cana-3963	22	7	utilized	utilize	VERB
cana-3963	22	8	on	on	ADP
cana-3963	22	9	finite	finite	ADJ
cana-3963	22	10	chain	chain	NOUN
cana-3963	22	11	rings	ring	NOUN
cana-3963	22	12	.	.	PUNCT
cana-3963	23	1	these	these	DET
cana-3963	23	2	criteria	criterion	NOUN
cana-3963	23	3	are	be	AUX
cana-3963	23	4	generally	generally	ADV
cana-3963	23	5	applicable	applicable	ADJ
cana-3963	23	6	to	to	ADP
cana-3963	23	7	constacyclic	constacyclic	ADJ
cana-3963	23	8	codes	code	NOUN
cana-3963	23	9	.	.	PUNCT
cana-3963	24	1	let	let	VERB
cana-3963	24	2	’s	’s	PRON
cana-3963	24	3	now	now	ADV
cana-3963	24	4	introduce	introduce	VERB
cana-3963	24	5	a	a	DET
cana-3963	24	6	criterion	criterion	NOUN
cana-3963	24	7	for	for	ADP
cana-3963	24	8	an	an	DET
cana-3963	24	9	mpc	mpc	NOUN
cana-3963	24	10	relying	rely	VERB
cana-3963	24	11	on	on	ADP
cana-3963	24	12	the	the	DET
cana-3963	24	13	rank	rank	NOUN
cana-3963	24	14	of	of	ADP
cana-3963	24	15	the	the	DET
cana-3963	24	16	generator	generator	NOUN
cana-3963	24	17	matrix	matrix	NOUN
cana-3963	24	18	and	and	CCONJ
cana-3963	24	19	exhibit	exhibit	VERB
cana-3963	24	20	its	its	PRON
cana-3963	24	21	employment	employment	NOUN
cana-3963	24	22	in	in	ADP
cana-3963	24	23	developing	develop	VERB
cana-3963	24	24	quantum	quantum	ADJ
cana-3963	24	25	codes	code	NOUN
cana-3963	24	26	.	.	PUNCT
cana-3963	25	1	previous	previous	ADJ
cana-3963	25	2	research	research	NOUN
cana-3963	25	3	has	have	AUX
cana-3963	25	4	developed	develop	VERB
cana-3963	25	5	quantum	quantum	ADJ
cana-3963	25	6	codes	code	NOUN
cana-3963	25	7	using	use	VERB
cana-3963	25	8	mpcs	mpcs	PROPN
cana-3963	25	9	over	over	ADP
cana-3963	25	10	finite	finite	ADJ
cana-3963	25	11	fields	field	NOUN
cana-3963	25	12	where	where	SCONJ
cana-3963	25	13	the	the	DET
cana-3963	25	14	corresponding	corresponding	ADJ
cana-3963	25	15	codes	code	NOUN
cana-3963	25	16	need	need	VERB
cana-3963	25	17	to	to	PART
cana-3963	25	18	be	be	AUX
cana-3963	25	19	satisfying	satisfy	VERB
cana-3963	25	20	the	the	DET
cana-3963	25	21	condition	condition	NOUN
cana-3963	25	22	of	of	ADP
cana-3963	25	23	dualcontaining	dualcontaine	VERB
cana-3963	25	24	.	.	PUNCT
cana-3963	26	1	however	however	ADV
cana-3963	26	2	,	,	PUNCT
cana-3963	26	3	when	when	SCONJ
cana-3963	26	4	the	the	DET
cana-3963	26	5	corresponding	corresponding	ADJ
cana-3963	26	6	codes	code	NOUN
cana-3963	26	7	of	of	ADP
cana-3963	26	8	mpc	mpc	NOUN
cana-3963	26	9	are	be	AUX
cana-3963	26	10	not	not	PART
cana-3963	26	11	limited	limited	ADJ
cana-3963	26	12	,	,	PUNCT
cana-3963	26	13	the	the	DET
cana-3963	26	14	method	method	NOUN
cana-3963	26	15	to	to	PART
cana-3963	26	16	produce	produce	VERB
cana-3963	26	17	quantum	quantum	NOUN
cana-3963	26	18	codes	code	NOUN
cana-3963	26	19	is	be	AUX
cana-3963	26	20	unclear	unclear	ADJ
cana-3963	26	21	.	.	PUNCT
cana-3963	27	1	recently	recently	ADV
cana-3963	27	2	,	,	PUNCT
cana-3963	27	3	exploring	explore	VERB
cana-3963	27	4	matrix	matrix	NOUN
cana-3963	27	5	-	-	PUNCT
cana-3963	27	6	product	product	NOUN
cana-3963	27	7	codes	code	NOUN
cana-3963	27	8	that	that	PRON
cana-3963	27	9	satisfy	satisfy	VERB
cana-3963	27	10	euclidean	euclidean	ADJ
cana-3963	27	11	or	or	CCONJ
cana-3963	27	12	hdc	hdc	NOUN
cana-3963	27	13	conditions	condition	NOUN
cana-3963	27	14	has	have	AUX
cana-3963	27	15	emerged	emerge	VERB
cana-3963	27	16	as	as	ADP
cana-3963	27	17	a	a	DET
cana-3963	27	18	new	new	ADJ
cana-3963	27	19	method	method	NOUN
cana-3963	27	20	for	for	ADP
cana-3963	27	21	constructing	construct	VERB
cana-3963	27	22	high	high	ADJ
cana-3963	27	23	-	-	PUNCT
cana-3963	27	24	quality	quality	NOUN
cana-3963	27	25	codes	code	NOUN
cana-3963	27	26	for	for	ADP
cana-3963	27	27	quantum	quantum	NOUN
cana-3963	27	28	systems	system	NOUN
cana-3963	27	29	.	.	PUNCT
cana-3963	28	1	for	for	ADP
cana-3963	28	2	example	example	NOUN
cana-3963	28	3	,	,	PUNCT
cana-3963	28	4	dual	dual	ADV
cana-3963	28	5	-	-	PUNCT
cana-3963	28	6	containing	contain	VERB
cana-3963	28	7	matrix	matrix	NOUN
cana-3963	28	8	-	-	PUNCT
cana-3963	28	9	product	product	NOUN
cana-3963	28	10	codes	code	NOUN
cana-3963	28	11	have	have	AUX
cana-3963	28	12	been	be	AUX
cana-3963	28	13	obtained	obtain	VERB
cana-3963	28	14	from	from	ADP
cana-3963	28	15	of	of	ADP
cana-3963	28	16	a	a	DET
cana-3963	28	17	novel	novel	ADJ
cana-3963	28	18	outlook	outlook	NOUN
cana-3963	28	19	to	to	PART
cana-3963	28	20	derive	derive	VERB
cana-3963	28	21	effective	effective	ADJ
cana-3963	28	22	quantum	quantum	NOUN
cana-3963	28	23	codes	code	NOUN
cana-3963	28	24	from	from	ADP
cana-3963	28	25	reed	reed	NOUN
cana-3963	28	26	-	-	PUNCT
cana-3963	28	27	muller	muller	NOUN
cana-3963	28	28	,	,	PUNCT
cana-3963	28	29	hyperbolic	hyperbolic	ADJ
cana-3963	28	30	,	,	PUNCT
cana-3963	28	31	and	and	CCONJ
cana-3963	28	32	affine	affine	PROPN
cana-3963	28	33	variety	variety	NOUN
cana-3963	28	34	codes	code	NOUN
cana-3963	28	35	[	[	X
cana-3963	28	36	10	10	NUM
cana-3963	28	37	]	]	PUNCT
cana-3963	28	38	.	.	PUNCT
cana-3963	29	1	in	in	ADP
cana-3963	29	2	the	the	DET
cana-3963	29	3	work	work	NOUN
cana-3963	29	4	[	[	X
cana-3963	29	5	11	11	NUM
cana-3963	29	6	]	]	PUNCT
cana-3963	29	7	,	,	PUNCT
cana-3963	29	8	zhang	zhang	PROPN
cana-3963	29	9	and	and	CCONJ
cana-3963	29	10	ge	ge	PROPN
cana-3963	29	11	introduced	introduce	VERB
cana-3963	29	12	three	three	NUM
cana-3963	29	13	novel	novel	ADJ
cana-3963	29	14	categories	category	NOUN
cana-3963	29	15	of	of	ADP
cana-3963	29	16	mds	mds	NOUN
cana-3963	29	17	codes	code	NOUN
cana-3963	29	18	which	which	PRON
cana-3963	29	19	are	be	AUX
cana-3963	29	20	obtained	obtain	VERB
cana-3963	29	21	using	use	VERB
cana-3963	29	22	mpcs	mpcs	PROPN
cana-3963	29	23	for	for	ADP
cana-3963	29	24	hermitian	hermitian	ADJ
cana-3963	29	25	selforthogonal	selforthogonal	PROPN
cana-3963	29	26	codes	code	NOUN
cana-3963	29	27	with	with	ADP
cana-3963	29	28	a	a	DET
cana-3963	29	29	length	length	NOUN
cana-3963	29	30	2n	2n	NUM
cana-3963	29	31	over	over	ADP
cana-3963	29	32	.qf	.qf	PUNCT
cana-3963	30	1	later	later	ADV
cana-3963	30	2	,	,	PUNCT
cana-3963	30	3	liu	liu	PROPN
cana-3963	30	4	et	et	PROPN
cana-3963	30	5	al	al	PROPN
cana-3963	30	6	.	.	PROPN
cana-3963	30	7	proposed	propose	VERB
cana-3963	30	8	two	two	NUM
cana-3963	30	9	techniques	technique	NOUN
cana-3963	30	10	for	for	ADP
cana-3963	30	11	constructing	construct	VERB
cana-3963	30	12	hdc	hdc	NOUN
cana-3963	30	13	matrix	matrix	NOUN
cana-3963	30	14	-	-	PUNCT
cana-3963	30	15	product	product	NOUN
cana-3963	30	16	codes	code	NOUN
cana-3963	30	17	,	,	PUNCT
cana-3963	30	18	leading	lead	VERB
cana-3963	30	19	to	to	ADP
cana-3963	30	20	the	the	DET
cana-3963	30	21	creation	creation	NOUN
cana-3963	30	22	of	of	ADP
cana-3963	30	23	new	new	ADJ
cana-3963	30	24	quantum	quantum	NOUN
cana-3963	30	25	codes	code	NOUN
cana-3963	30	26	that	that	PRON
cana-3963	30	27	surpass	surpass	VERB
cana-3963	30	28	previously	previously	ADV
cana-3963	30	29	known	know	VERB
cana-3963	30	30	ones	one	NOUN
cana-3963	30	31	in	in	ADP
cana-3963	30	32	performance	performance	NOUN
cana-3963	30	33	[	[	X
cana-3963	30	34	12	12	NUM
cana-3963	30	35	]	]	PUNCT
cana-3963	30	36	.	.	PUNCT
cana-3963	31	1	song	song	PROPN
cana-3963	31	2	et	et	PROPN
cana-3963	31	3	al	al	PROPN
cana-3963	31	4	.	.	PUNCT
cana-3963	32	1	[	[	X
cana-3963	32	2	13	13	NUM
cana-3963	32	3	]	]	SYM
cana-3963	32	4	utilized	utilize	VERB
cana-3963	32	5	special	special	ADJ
cana-3963	32	6	code	code	NOUN
cana-3963	32	7	chains	chain	NOUN
cana-3963	32	8	1	1	NUM
cana-3963	32	9	2	2	NUM
cana-3963	32	10	3	3	NUM
cana-3963	32	11			NOUN
cana-3963	33	1			PROPN
cana-3963	33	2			PROPN
cana-3963	33	3	to	to	PART
cana-3963	33	4	develop	develop	VERB
cana-3963	33	5	several	several	ADJ
cana-3963	33	6	3n	3n	NUM
cana-3963	33	7	length	length	NOUN
cana-3963	33	8	quantum	quantum	NOUN
cana-3963	33	9	codes	code	NOUN
cana-3963	33	10	using	use	VERB
cana-3963	33	11	hermitian	hermitian	PROPN
cana-3963	33	12	mpcs	mpcs	PROPN
cana-3963	33	13	of	of	ADP
cana-3963	33	14	1	1	NUM
cana-3963	33	15	2,	2,	NUM
cana-3963	33	16			NOUN
cana-3963	33	17	and	and	CCONJ
cana-3963	33	18	3	3	NUM
cana-3963	33	19	over	over	ADP
cana-3963	33	20	2	2	NUM
cana-3963	33	21	,	,	PUNCT
cana-3963	33	22	r	r	NOUN
cana-3963	33	23	f	f	NOUN
cana-3963	33	24	achieving	achieve	VERB
cana-3963	33	25	distances	distance	NOUN
cana-3963	33	26	greater	great	ADJ
cana-3963	33	27	than	than	ADP
cana-3963	33	28	1.r	1.r	NUM
cana-3963	33	29	+	+	CCONJ
cana-3963	33	30	in	in	ADP
cana-3963	33	31	this	this	DET
cana-3963	33	32	paper	paper	NOUN
cana-3963	33	33	,	,	PUNCT
cana-3963	33	34	we	we	PRON
cana-3963	33	35	first	first	ADV
cana-3963	33	36	demonstrate	demonstrate	VERB
cana-3963	33	37	that	that	SCONJ
cana-3963	33	38	any	any	DET
cana-3963	33	39	matrix	matrix	NOUN
cana-3963	33	40	-	-	PUNCT
cana-3963	33	41	product	product	NOUN
cana-3963	33	42	code	code	NOUN
cana-3963	33	43	can	can	AUX
cana-3963	33	44	be	be	AUX
cana-3963	33	45	hdc	hdc	ADJ
cana-3963	33	46	.	.	PUNCT
cana-3963	34	1	we	we	PRON
cana-3963	34	2	then	then	ADV
cana-3963	34	3	construct	construct	VERB
cana-3963	34	4	quantum	quantum	NOUN
cana-3963	34	5	codes	code	NOUN
cana-3963	34	6	using	use	VERB
cana-3963	34	7	monomial	monomial	ADJ
cana-3963	34	8	matrices	matrix	NOUN
cana-3963	34	9	and	and	CCONJ
cana-3963	34	10	mpcs	mpcs	PROPN
cana-3963	34	11	.	.	PUNCT
cana-3963	35	1	notably	notably	ADV
cana-3963	35	2	,	,	PUNCT
cana-3963	35	3	few	few	ADJ
cana-3963	35	4	quantum	quantum	NOUN
cana-3963	35	5	codes	code	NOUN
cana-3963	35	6	presented	present	VERB
cana-3963	35	7	by	by	ADP
cana-3963	35	8	proposed	propose	VERB
cana-3963	35	9	method	method	NOUN
cana-3963	35	10	are	be	AUX
cana-3963	35	11	novel	novel	ADJ
cana-3963	35	12	,	,	PUNCT
cana-3963	35	13	and	and	CCONJ
cana-3963	35	14	some	some	PRON
cana-3963	35	15	possess	possess	VERB
cana-3963	35	16	larger	large	ADJ
cana-3963	35	17	dimensions	dimension	NOUN
cana-3963	35	18	compared	compare	VERB
cana-3963	35	19	to	to	ADP
cana-3963	35	20	those	those	PRON
cana-3963	35	21	found	find	VERB
cana-3963	35	22	in	in	ADP
cana-3963	35	23	existing	exist	VERB
cana-3963	35	24	literature	literature	NOUN
cana-3963	35	25	.	.	PUNCT
cana-3963	36	1	this	this	DET
cana-3963	36	2	method	method	NOUN
cana-3963	36	3	stands	stand	VERB
cana-3963	36	4	out	out	ADP
cana-3963	36	5	due	due	ADP
cana-3963	36	6	to	to	ADP
cana-3963	36	7	its	its	PRON
cana-3963	36	8	use	use	NOUN
cana-3963	36	9	of	of	ADP
cana-3963	36	10	sophisticated	sophisticated	ADJ
cana-3963	36	11	algebraic	algebraic	ADJ
cana-3963	36	12	structures	structure	NOUN
cana-3963	36	13	and	and	CCONJ
cana-3963	36	14	properties	property	NOUN
cana-3963	36	15	,	,	PUNCT
cana-3963	36	16	especially	especially	ADV
cana-3963	36	17	the	the	DET
cana-3963	36	18	hdc	hdc	NOUN
cana-3963	36	19	property	property	NOUN
cana-3963	36	20	.	.	PUNCT
cana-3963	37	1	this	this	DET
cana-3963	37	2	characteristic	characteristic	ADJ
cana-3963	37	3	ensures	ensure	VERB
cana-3963	37	4	that	that	SCONJ
cana-3963	37	5	the	the	DET
cana-3963	37	6	constructed	construct	VERB
cana-3963	37	7	codes	code	NOUN
cana-3963	37	8	and	and	CCONJ
cana-3963	37	9	their	their	PRON
cana-3963	37	10	duals	dual	NOUN
cana-3963	37	11	intersect	intersect	ADJ
cana-3963	37	12	trivially	trivially	ADV
cana-3963	37	13	,	,	PUNCT
cana-3963	37	14	which	which	PRON
cana-3963	37	15	is	be	AUX
cana-3963	37	16	essential	essential	ADJ
cana-3963	37	17	for	for	ADP
cana-3963	37	18	effective	effective	ADJ
cana-3963	37	19	quantum	quantum	NOUN
cana-3963	37	20	error	error	NOUN
cana-3963	37	21	correction	correction	NOUN
cana-3963	37	22	.	.	PUNCT
cana-3963	38	1	additionally	additionally	ADV
cana-3963	38	2	,	,	PUNCT
cana-3963	38	3	communications	communication	NOUN
cana-3963	38	4	on	on	ADP
cana-3963	38	5	applied	apply	VERB
cana-3963	38	6	nonlinear	nonlinear	ADJ
cana-3963	38	7	analysis	analysis	NOUN
cana-3963	38	8	issn	issn	NOUN
cana-3963	38	9	:	:	PUNCT
cana-3963	38	10	1074	1074	NUM
cana-3963	38	11	-	-	PUNCT
cana-3963	38	12	133x	133x	NUM
cana-3963	38	13	vol	vol	NOUN
cana-3963	38	14	32	32	NUM
cana-3963	38	15	no	no	NOUN
cana-3963	38	16	.	.	PUNCT
cana-3963	39	1	9s	9s	NUM
cana-3963	39	2	(	(	PUNCT
cana-3963	39	3	2025	2025	NUM
cana-3963	39	4	)	)	PUNCT
cana-3963	39	5	544	544	NUM
cana-3963	39	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	39	7	the	the	DET
cana-3963	39	8	use	use	NOUN
cana-3963	39	9	of	of	ADP
cana-3963	39	10	minimal	minimal	ADJ
cana-3963	39	11	polynomials	polynomial	NOUN
cana-3963	39	12	allows	allow	VERB
cana-3963	39	13	for	for	ADP
cana-3963	39	14	precise	precise	ADJ
cana-3963	39	15	tuning	tuning	NOUN
cana-3963	39	16	of	of	ADP
cana-3963	39	17	code	code	NOUN
cana-3963	39	18	parameters	parameter	NOUN
cana-3963	39	19	,	,	PUNCT
cana-3963	39	20	resulting	result	VERB
cana-3963	39	21	in	in	ADP
cana-3963	39	22	highly	highly	ADV
cana-3963	39	23	efficient	efficient	ADJ
cana-3963	39	24	and	and	CCONJ
cana-3963	39	25	robust	robust	ADJ
cana-3963	39	26	quantum	quantum	ADJ
cana-3963	39	27	codes	code	NOUN
cana-3963	39	28	.	.	PUNCT
cana-3963	40	1	these	these	DET
cana-3963	40	2	features	feature	NOUN
cana-3963	40	3	make	make	VERB
cana-3963	40	4	the	the	DET
cana-3963	40	5	method	method	NOUN
cana-3963	40	6	particularly	particularly	ADV
cana-3963	40	7	well	well	ADV
cana-3963	40	8	-	-	PUNCT
cana-3963	40	9	suited	suit	VERB
cana-3963	40	10	for	for	ADP
cana-3963	40	11	practical	practical	ADJ
cana-3963	40	12	quantum	quantum	ADJ
cana-3963	40	13	computing	computing	NOUN
cana-3963	40	14	applications	application	NOUN
cana-3963	40	15	,	,	PUNCT
cana-3963	40	16	offering	offer	VERB
cana-3963	40	17	scalability	scalability	NOUN
cana-3963	40	18	and	and	CCONJ
cana-3963	40	19	adaptability	adaptability	NOUN
cana-3963	40	20	to	to	ADP
cana-3963	40	21	different	different	ADJ
cana-3963	40	22	quantum	quantum	ADJ
cana-3963	40	23	architectures	architecture	NOUN
cana-3963	40	24	[	[	X
cana-3963	40	25	14	14	NUM
cana-3963	40	26	,	,	PUNCT
cana-3963	40	27	15	15	NUM
cana-3963	40	28	]	]	PUNCT
cana-3963	40	29	.	.	PUNCT
cana-3963	41	1	the	the	DET
cana-3963	41	2	incorporation	incorporation	NOUN
cana-3963	41	3	of	of	ADP
cana-3963	41	4	these	these	DET
cana-3963	41	5	algebraic	algebraic	ADJ
cana-3963	41	6	techniques	technique	NOUN
cana-3963	41	7	enhances	enhance	VERB
cana-3963	41	8	the	the	DET
cana-3963	41	9	performance	performance	NOUN
cana-3963	41	10	of	of	ADP
cana-3963	41	11	quantum	quantum	NOUN
cana-3963	41	12	codes	code	NOUN
cana-3963	41	13	and	and	CCONJ
cana-3963	41	14	lays	lay	VERB
cana-3963	41	15	a	a	DET
cana-3963	41	16	strong	strong	ADJ
cana-3963	41	17	foundation	foundation	NOUN
cana-3963	41	18	for	for	ADP
cana-3963	41	19	future	future	ADJ
cana-3963	41	20	developments	development	NOUN
cana-3963	41	21	in	in	ADP
cana-3963	41	22	theory	theory	NOUN
cana-3963	41	23	of	of	ADP
cana-3963	41	24	quantum	quantum	NOUN
cana-3963	41	25	error	error	NOUN
cana-3963	41	26	codes	code	NOUN
cana-3963	41	27	[	[	X
cana-3963	41	28	16	16	NUM
cana-3963	41	29	]	]	PUNCT
cana-3963	41	30	.	.	PUNCT
cana-3963	42	1	the	the	DET
cana-3963	42	2	organisation	organisation	NOUN
cana-3963	42	3	of	of	ADP
cana-3963	42	4	the	the	DET
cana-3963	42	5	remaining	remain	VERB
cana-3963	42	6	paper	paper	NOUN
cana-3963	42	7	is	be	AUX
cana-3963	42	8	as	as	SCONJ
cana-3963	42	9	follows	follow	VERB
cana-3963	42	10	:	:	PUNCT
cana-3963	42	11	section	section	NOUN
cana-3963	42	12	2	2	NUM
cana-3963	42	13	covers	cover	VERB
cana-3963	42	14	the	the	DET
cana-3963	42	15	mathematical	mathematical	ADJ
cana-3963	42	16	concepts	concept	NOUN
cana-3963	42	17	necessary	necessary	ADJ
cana-3963	42	18	for	for	ADP
cana-3963	42	19	understanding	understand	VERB
cana-3963	42	20	the	the	DET
cana-3963	42	21	construction	construction	NOUN
cana-3963	42	22	of	of	ADP
cana-3963	42	23	quantum	quantum	ADJ
cana-3963	42	24	codes	code	NOUN
cana-3963	42	25	from	from	ADP
cana-3963	42	26	classical	classical	ADJ
cana-3963	42	27	hdc	hdc	NOUN
cana-3963	42	28	codes	code	NOUN
cana-3963	42	29	.	.	PUNCT
cana-3963	43	1	section	section	NOUN
cana-3963	43	2	3	3	NUM
cana-3963	43	3	outlines	outline	VERB
cana-3963	43	4	the	the	DET
cana-3963	43	5	proposed	propose	VERB
cana-3963	43	6	construction	construction	NOUN
cana-3963	43	7	method	method	NOUN
cana-3963	43	8	,	,	PUNCT
cana-3963	43	9	while	while	SCONJ
cana-3963	43	10	section	section	NOUN
cana-3963	43	11	4	4	NUM
cana-3963	43	12	provides	provide	VERB
cana-3963	43	13	the	the	DET
cana-3963	43	14	conditions	condition	NOUN
cana-3963	43	15	for	for	ADP
cana-3963	43	16	constructing	construct	VERB
cana-3963	43	17	quantum	quantum	ADJ
cana-3963	43	18	codes	code	NOUN
cana-3963	43	19	.	.	PUNCT
cana-3963	44	1	section	section	NOUN
cana-3963	44	2	5	5	NUM
cana-3963	44	3	discusses	discuss	VERB
cana-3963	44	4	the	the	DET
cana-3963	44	5	simulation	simulation	NOUN
cana-3963	44	6	results	result	NOUN
cana-3963	44	7	of	of	ADP
cana-3963	44	8	the	the	DET
cana-3963	44	9	obtained	obtain	VERB
cana-3963	44	10	codes	code	NOUN
cana-3963	44	11	,	,	PUNCT
cana-3963	44	12	and	and	CCONJ
cana-3963	44	13	finally	finally	ADV
cana-3963	44	14	section	section	NOUN
cana-3963	44	15	6	6	NUM
cana-3963	44	16	gives	give	VERB
cana-3963	44	17	the	the	DET
cana-3963	44	18	concluding	concluding	NOUN
cana-3963	44	19	remarks	remark	NOUN
cana-3963	44	20	.	.	PUNCT
cana-3963	45	1	2	2	X
cana-3963	45	2	.	.	X
cana-3963	45	3	mathematical	mathematical	ADJ
cana-3963	45	4	background	background	NOUN
cana-3963	45	5	throughout	throughout	ADP
cana-3963	45	6	this	this	DET
cana-3963	45	7	paper	paper	NOUN
cana-3963	45	8	,	,	PUNCT
cana-3963	45	9	take	take	VERB
cana-3963	45	10	q	q	NOUN
cana-3963	45	11	as	as	ADP
cana-3963	45	12	a	a	DET
cana-3963	45	13	prime	prime	ADJ
cana-3963	45	14	power	power	NOUN
cana-3963	45	15	.	.	PUNCT
cana-3963	46	1	let	let	VERB
cana-3963	46	2	2q	2q	NOUN
cana-3963	46	3	f	f	PRON
cana-3963	46	4	denote	denote	VERB
cana-3963	46	5	the	the	DET
cana-3963	46	6	finite	finite	ADJ
cana-3963	46	7	field	field	NOUN
cana-3963	46	8	with	with	ADP
cana-3963	46	9	2q	2q	NUM
cana-3963	46	10	number	number	NOUN
cana-3963	46	11	of	of	ADP
cana-3963	46	12	elements	element	NOUN
cana-3963	46	13	and	and	CCONJ
cana-3963	46	14	suppose	suppose	VERB
cana-3963	46	15	2	2	NUM
cana-3963	46	16	*	*	SYM
cana-3963	46	17	q	q	NOUN
cana-3963	46	18	f	f	PROPN
cana-3963	46	19	denotes	denote	VERB
cana-3963	46	20	the	the	DET
cana-3963	46	21	set	set	NOUN
cana-3963	46	22	having	have	VERB
cana-3963	46	23	nonzero	nonzero	ADJ
cana-3963	46	24	elements	element	NOUN
cana-3963	46	25	from	from	ADP
cana-3963	46	26	2	2	NUM
cana-3963	46	27	.	.	PUNCT
cana-3963	47	1	q	q	PUNCT
cana-3963	48	1	f	f	PRON
cana-3963	48	2	let	let	VERB
cana-3963	48	3	2q	2q	NOUN
cana-3963	48	4	a	a	DET
cana-3963	48	5	f	f	NOUN
cana-3963	48	6	be	be	AUX
cana-3963	48	7	any	any	DET
cana-3963	48	8	element	element	NOUN
cana-3963	48	9	then	then	ADV
cana-3963	48	10	qa	qa	PROPN
cana-3963	48	11	a=	a=	PROPN
cana-3963	48	12	denotes	denote	VERB
cana-3963	48	13	the	the	DET
cana-3963	48	14	conjugate	conjugate	NOUN
cana-3963	48	15	of	of	ADP
cana-3963	48	16	element	element	NOUN
cana-3963	48	17	.a	.a	PROPN
cana-3963	49	1	let	let	VERB
cana-3963	49	2	2	2	NUM
cana-3963	49	3	(	(	PUNCT
cana-3963	49	4	,	,	PUNCT
cana-3963	49	5	)	)	PUNCT
cana-3963	49	6	q	q	PUNCT
cana-3963	50	1	m	m	VERB
cana-3963	50	2	f	f	NOUN
cana-3963	50	3	s	s	VERB
cana-3963	50	4	l	l	NOUN
cana-3963	50	5	be	be	AUX
cana-3963	50	6	the	the	DET
cana-3963	50	7	collection	collection	NOUN
cana-3963	50	8	of	of	ADP
cana-3963	50	9	matrices	matrix	NOUN
cana-3963	50	10	over	over	ADP
cana-3963	50	11	2q	2q	NUM
cana-3963	50	12	f	f	NOUN
cana-3963	50	13	of	of	ADP
cana-3963	50	14	size	size	NOUN
cana-3963	50	15	.s	.s	NOUN
cana-3963	51	1	l	l	ADJ
cana-3963	51	2	if	if	SCONJ
cana-3963	51	3	2	2	NUM
cana-3963	51	4	(	(	PUNCT
cana-3963	51	5	)	)	PUNCT
cana-3963	51	6	(	(	PUNCT
cana-3963	51	7	,	,	PUNCT
cana-3963	51	8	)	)	PUNCT
cana-3963	51	9	ij	ij	INTJ
cana-3963	51	10	q	q	NOUN
cana-3963	51	11	a	a	DET
cana-3963	51	12	a	a	NOUN
cana-3963	51	13	m	m	NOUN
cana-3963	51	14	f	f	NOUN
cana-3963	51	15	s	s	PART
cana-3963	51	16	l=	l=	ADJ
cana-3963	51	17			PROPN
cana-3963	51	18			PROPN
cana-3963	51	19	then	then	ADV
cana-3963	51	20	conjugate	conjugate	VERB
cana-3963	51	21	transpose	transpose	NOUN
cana-3963	51	22	of	of	ADP
cana-3963	51	23	a	a	PRON
cana-3963	51	24	is	be	AUX
cana-3963	51	25	denoted	denote	VERB
cana-3963	51	26	by	by	ADP
cana-3963	51	27	†	†	PROPN
cana-3963	51	28	(	(	PUNCT
cana-3963	51	29	)	)	PUNCT
cana-3963	51	30	.jia	.jia	X
cana-3963	51	31	a=	a=	VERB
cana-3963	51	32	consider	consider	VERB
cana-3963	51	33	a	a	DET
cana-3963	51	34	code	code	NOUN
cana-3963	51	35	2	2	NUM
cana-3963	51	36	[	[	X
cana-3963	51	37	[	[	PUNCT
cana-3963	51	38	,	,	PUNCT
cana-3963	51	39	,	,	PUNCT
cana-3963	51	40	]	]	X
cana-3963	51	41	]	]	X
cana-3963	51	42	q	q	X
cana-3963	51	43	n	n	CCONJ
cana-3963	51	44	k	k	PROPN
cana-3963	51	45	d	d	PROPN
cana-3963	51	46	=	=	PRON
cana-3963	51	47	which	which	PRON
cana-3963	51	48	is	be	AUX
cana-3963	51	49	linear	linear	ADJ
cana-3963	51	50	,	,	PUNCT
cana-3963	51	51	is	be	AUX
cana-3963	51	52	a	a	DET
cana-3963	51	53	subspace	subspace	NOUN
cana-3963	51	54	of	of	ADP
cana-3963	51	55	2	2	NUM
cana-3963	51	56	n	n	NOUN
cana-3963	51	57	q	q	PROPN
cana-3963	51	58	f	f	PROPN
cana-3963	51	59	with	with	ADP
cana-3963	51	60	length	length	NOUN
cana-3963	51	61	.n	.n	PROPN
cana-3963	52	1	the	the	DET
cana-3963	52	2	singleton	singleton	NOUN
cana-3963	52	3	bound	bind	VERB
cana-3963	52	4	1	1	NUM
cana-3963	52	5	,	,	PUNCT
cana-3963	52	6	d	d	PROPN
cana-3963	52	7	n	n	X
cana-3963	52	8	k	k	NOUN
cana-3963	53	1	+	+	CCONJ
cana-3963	53	2	−	−	PROPN
cana-3963	53	3	must	must	AUX
cana-3963	53	4	be	be	AUX
cana-3963	53	5	satisfied	satisfied	ADJ
cana-3963	53	6	in	in	ADP
cana-3963	53	7	order	order	NOUN
cana-3963	53	8	for	for	SCONJ
cana-3963	53	9	linear	linear	PROPN
cana-3963	53	10	code	code	PROPN
cana-3963	53	11			NOUN
cana-3963	53	12	to	to	PART
cana-3963	53	13	be	be	AUX
cana-3963	53	14	maximum	maximum	ADJ
cana-3963	53	15	distance	distance	NOUN
cana-3963	53	16	separable	separable	NOUN
cana-3963	53	17	(	(	PUNCT
cana-3963	53	18	mds	mds	PROPN
cana-3963	53	19	)	)	PUNCT
cana-3963	53	20	.	.	PUNCT
cana-3963	54	1	let	let	VERB
cana-3963	54	2	’s	’s	NOUN
cana-3963	54	3	denote	denote	VERB
cana-3963	54	4	a	a	DET
cana-3963	54	5	q	q	ADJ
cana-3963	54	6	-	-	PUNCT
cana-3963	54	7	ary	ary	ADJ
cana-3963	54	8	quantum	quantum	PROPN
cana-3963	54	9	code	code	NOUN
cana-3963	54	10	q	q	PUNCT
cana-3963	54	11	with	with	ADP
cana-3963	54	12	length	length	NOUN
cana-3963	54	13	n	n	NOUN
cana-3963	54	14	by	by	ADP
cana-3963	54	15	[	[	X
cana-3963	54	16	[	[	PUNCT
cana-3963	54	17	,	,	PUNCT
cana-3963	54	18	,	,	PUNCT
cana-3963	54	19	]	]	X
cana-3963	54	20	]	]	X
cana-3963	54	21	qn	qn	X
cana-3963	54	22	k	k	PROPN
cana-3963	54	23	d	d	X
cana-3963	54	24	which	which	PRON
cana-3963	54	25	is	be	AUX
cana-3963	54	26	of	of	ADP
cana-3963	54	27	size	size	NOUN
cana-3963	54	28	kq	kq	PROPN
cana-3963	54	29	and	and	CCONJ
cana-3963	54	30	minimum	minimum	NOUN
cana-3963	54	31	distance	distance	NOUN
cana-3963	54	32	.d	.d	NOUN
cana-3963	54	33	then	then	ADV
cana-3963	54	34	,	,	PUNCT
cana-3963	54	35	the	the	DET
cana-3963	54	36	quantum	quantum	PROPN
cana-3963	54	37	code	code	NOUN
cana-3963	54	38	q	q	PROPN
cana-3963	54	39	happens	happen	VERB
cana-3963	54	40	to	to	PART
cana-3963	54	41	be	be	AUX
cana-3963	54	42	a	a	DET
cana-3963	54	43	subspace	subspace	NOUN
cana-3963	54	44	with	with	ADP
cana-3963	54	45	dimension	dimension	NOUN
cana-3963	54	46	kq	kq	PROPN
cana-3963	54	47	of	of	ADP
cana-3963	54	48	nq	nq	NUM
cana-3963	54	49	which	which	PRON
cana-3963	54	50	is	be	AUX
cana-3963	54	51	the	the	DET
cana-3963	54	52	nq	nq	PROPN
cana-3963	54	53	-dimensional	-dimensional	ADJ
cana-3963	54	54	hilbert	hilbert	NOUN
cana-3963	54	55	space	space	NOUN
cana-3963	54	56	written	write	VERB
cana-3963	54	57	as	as	ADP
cana-3963	54	58	·	·	PUNCT
cana-3963	54	59	·	·	PUNCT
cana-3963	54	60	·	·	PUNCT
cana-3963	54	61	.	.	PUNCT
cana-3963	55	1	nq	nq	PROPN
cana-3963	56	1	q	q	X
cana-3963	56	2	q	q	X
cana-3963	56	3	q	q	ADJ
cana-3963	56	4			NOUN
cana-3963	56	5			X
cana-3963	56	6			PUNCT
cana-3963	56	7			X
cana-3963	56	8			ADP
cana-3963	56	9			ADP
cana-3963	56	10	the	the	DET
cana-3963	56	11	quantum	quantum	PROPN
cana-3963	56	12	code	code	NOUN
cana-3963	56	13	q	q	NOUN
cana-3963	56	14	can	can	AUX
cana-3963	56	15	identify	identify	VERB
cana-3963	56	16	and	and	CCONJ
cana-3963	56	17	correct	correct	VERB
cana-3963	56	18	at	at	ADP
cana-3963	56	19	most	most	ADJ
cana-3963	56	20	1d	1d	NUM
cana-3963	56	21	−	−	NOUN
cana-3963	56	22	and	and	CCONJ
cana-3963	56	23	(	(	PUNCT
cana-3963	56	24	1	1	NUM
cana-3963	56	25	)	)	PUNCT
cana-3963	56	26	/	/	SYM
cana-3963	56	27	2d	2d	NOUN
cana-3963	56	28	−	−	NOUN
cana-3963	56	29	errors	error	NOUN
cana-3963	56	30	respectively	respectively	ADV
cana-3963	56	31	.	.	PUNCT
cana-3963	57	1	the	the	DET
cana-3963	57	2	quantum	quantum	PROPN
cana-3963	57	3	singleton	singleton	NOUN
cana-3963	57	4	bound	bind	VERB
cana-3963	57	5	2	2	NUM
cana-3963	57	6	2d	2d	NUM
cana-3963	57	7	n	n	PRON
cana-3963	57	8	k	k	NOUN
cana-3963	58	1	−	−	PROPN
cana-3963	59	1	+	+	CCONJ
cana-3963	59	2	must	must	AUX
cana-3963	59	3	be	be	AUX
cana-3963	59	4	satisfied	satisfied	ADJ
cana-3963	59	5	by	by	ADP
cana-3963	59	6	the	the	DET
cana-3963	59	7	parameters	parameter	NOUN
cana-3963	59	8	of	of	ADP
cana-3963	59	9	the	the	DET
cana-3963	59	10	quantum	quantum	PROPN
cana-3963	59	11	code	code	NOUN
cana-3963	59	12	.q	.q	PUNCT
cana-3963	60	1	the	the	DET
cana-3963	60	2	codes	code	NOUN
cana-3963	60	3	attaining	attain	VERB
cana-3963	60	4	the	the	DET
cana-3963	60	5	bound	bound	ADJ
cana-3963	60	6	2	2	NUM
cana-3963	60	7	=	=	SYM
cana-3963	60	8	2,d	2,d	NUM
cana-3963	60	9	n	n	DET
cana-3963	60	10	k−	k−	PROPN
cana-3963	60	11	+	+	CCONJ
cana-3963	60	12	are	be	AUX
cana-3963	60	13	known	know	VERB
cana-3963	60	14	as	as	ADP
cana-3963	60	15	maximum	maximum	ADJ
cana-3963	60	16	distance	distance	NOUN
cana-3963	60	17	separable	separable	ADJ
cana-3963	60	18	(	(	PUNCT
cana-3963	60	19	mds	mds	NOUN
cana-3963	60	20	)	)	PUNCT
cana-3963	60	21	codes	code	NOUN
cana-3963	60	22	.	.	PUNCT
cana-3963	61	1	we	we	PRON
cana-3963	61	2	can	can	AUX
cana-3963	61	3	define	define	VERB
cana-3963	61	4	hermitian	hermitian	ADJ
cana-3963	61	5	inner	inner	ADJ
cana-3963	61	6	product	product	NOUN
cana-3963	61	7	of	of	ADP
cana-3963	61	8	two	two	NUM
cana-3963	61	9	vectors	vector	NOUN
cana-3963	61	10	(	(	PUNCT
cana-3963	61	11	)	)	PUNCT
cana-3963	61	12	1	1	NUM
cana-3963	61	13	2	2	NUM
cana-3963	61	14	,	,	PUNCT
cana-3963	61	15	,	,	PUNCT
cana-3963	61	16	...	...	PUNCT
cana-3963	61	17	,	,	PUNCT
cana-3963	61	18	nx	nx	X
cana-3963	61	19	x	x	SYM
cana-3963	61	20	x	x	X
cana-3963	61	21	x=	x=	PROPN
cana-3963	61	22	and	and	CCONJ
cana-3963	61	23	(	(	PUNCT
cana-3963	61	24	)	)	PUNCT
cana-3963	61	25	21	21	NUM
cana-3963	61	26	2y	2y	NOUN
cana-3963	61	27	,	,	PUNCT
cana-3963	61	28	y	y	PROPN
cana-3963	61	29	,	,	PUNCT
cana-3963	61	30	...	...	PUNCT
cana-3963	61	31	,	,	PUNCT
cana-3963	61	32	yn	yn	PROPN
cana-3963	61	33	n	n	PROPN
cana-3963	61	34	q	q	PROPN
cana-3963	61	35	y	y	PROPN
cana-3963	61	36	f=	f=	PROPN
cana-3963	61	37	as	as	ADP
cana-3963	61	38	1	1	NUM
cana-3963	61	39	(	(	PUNCT
cana-3963	61	40	,	,	PUNCT
cana-3963	61	41	y	y	PROPN
cana-3963	61	42	)	)	PUNCT
cana-3963	61	43	.	.	PUNCT
cana-3963	62	1	n	n	PRON
cana-3963	62	2	h	h	NOUN
cana-3963	63	1	i	i	PRON
cana-3963	63	2	i	i	PRON
cana-3963	63	3	i	i	VERB
cana-3963	63	4	x	x	VERB
cana-3963	63	5	x	x	VERB
cana-3963	63	6	y	y	NOUN
cana-3963	63	7	=	=	PUNCT
cana-3963	64	1	=	=	NOUN
cana-3963	64	2			NOUN
cana-3963	64	3	consider	consider	VERB
cana-3963	64	4	a	a	DET
cana-3963	64	5	code	code	NOUN
cana-3963	64	6			NOUN
cana-3963	64	7	of	of	ADP
cana-3963	64	8	length	length	NOUN
cana-3963	64	9	n	n	CCONJ
cana-3963	64	10	which	which	PRON
cana-3963	64	11	is	be	AUX
cana-3963	64	12	linear	linear	ADJ
cana-3963	64	13	and	and	CCONJ
cana-3963	64	14	elements	element	NOUN
cana-3963	64	15	are	be	AUX
cana-3963	64	16	from	from	ADP
cana-3963	64	17	2	2	NUM
cana-3963	64	18	,	,	PUNCT
cana-3963	64	19	q	q	PROPN
cana-3963	64	20	f	f	PROPN
cana-3963	65	1	the	the	DET
cana-3963	65	2	hermitian	hermitian	PROPN
cana-3963	65	3	dual	dual	PROPN
cana-3963	65	4	corresponding	correspond	VERB
cana-3963	65	5	to	to	ADP
cana-3963	65	6	the	the	DET
cana-3963	65	7	code	code	NOUN
cana-3963	65	8			NOUN
cana-3963	65	9	is	be	AUX
cana-3963	65	10	written	write	VERB
cana-3963	65	11	as	as	ADP
cana-3963	65	12	2{a	2{a	NUM
cana-3963	65	13	(	(	PUNCT
cana-3963	65	14	a	a	DET
cana-3963	65	15	,	,	PUNCT
cana-3963	65	16	b	b	NOUN
cana-3963	65	17	)	)	PUNCT
cana-3963	65	18	0for	0for	ADP
cana-3963	65	19	all	all	PRON
cana-3963	65	20	}	}	PUNCT
cana-3963	65	21	.h	.h	NOUN
cana-3963	66	1	n	n	NUM
cana-3963	66	2	hq	hq	NOUN
cana-3963	66	3	f	f	PROPN
cana-3963	66	4	b	b	X
cana-3963	66	5	⊥	⊥	PUNCT
cana-3963	67	1	=	=	SYM
cana-3963	67	2			PROPN
cana-3963	67	3	=	=	PUNCT
cana-3963	67	4			NOUN
cana-3963	67	5	if	if	SCONJ
cana-3963	67	6	h	h	PRON
cana-3963	67	7			X
cana-3963	67	8	⊥	⊥	PROPN
cana-3963	67	9			PROPN
cana-3963	67	10	then	then	ADV
cana-3963	67	11	code	code	PROPN
cana-3963	67	12			PROPN
cana-3963	67	13	is	be	AUX
cana-3963	67	14	termed	term	VERB
cana-3963	67	15	as	as	ADP
cana-3963	67	16	hdc	hdc	NOUN
cana-3963	67	17	.	.	PUNCT
cana-3963	68	1	let	let	VERB
cana-3963	68	2	a	a	DET
cana-3963	68	3	vector	vector	NOUN
cana-3963	68	4	(	(	PUNCT
cana-3963	68	5	)	)	PUNCT
cana-3963	68	6	21	21	NUM
cana-3963	68	7	2	2	NUM
cana-3963	68	8	,	,	PUNCT
cana-3963	68	9	,	,	PUNCT
cana-3963	68	10	...	...	PUNCT
cana-3963	68	11	,	,	PUNCT
cana-3963	68	12	,	,	PUNCT
cana-3963	68	13	n	n	CCONJ
cana-3963	68	14	n	n	PROPN
cana-3963	68	15	q	q	PROPN
cana-3963	68	16	v	v	PROPN
cana-3963	68	17	v	v	NUM
cana-3963	68	18	v	v	NOUN
cana-3963	68	19	v	v	NOUN
cana-3963	68	20	f=	f=	ADJ
cana-3963	68	21			NOUN
cana-3963	68	22	then	then	ADV
cana-3963	68	23	we	we	PRON
cana-3963	68	24	find	find	VERB
cana-3963	68	25	(	(	PUNCT
cana-3963	68	26	)	)	PUNCT
cana-3963	68	27	1	1	NUM
cana-3963	68	28	2	2	NUM
cana-3963	68	29	,	,	PUNCT
cana-3963	68	30	,	,	PUNCT
cana-3963	68	31	.	.	PUNCT
cana-3963	69	1	,	,	PUNCT
cana-3963	69	2	...	...	PUNCT
cana-3963	69	3	q	q	X
cana-3963	69	4	q	q	X
cana-3963	69	5	q	q	X
cana-3963	69	6	q	q	X
cana-3963	69	7	nv	nv	PROPN
cana-3963	69	8	v	v	NUM
cana-3963	69	9	v	v	NOUN
cana-3963	69	10	v=	v=	NOUN
cana-3963	69	11	for	for	ADP
cana-3963	69	12	a	a	DET
cana-3963	69	13	given	give	VERB
cana-3963	69	14	subset	subset	NOUN
cana-3963	69	15	s	s	NOUN
cana-3963	69	16	of	of	ADP
cana-3963	69	17	2	2	NUM
cana-3963	69	18	,	,	PUNCT
cana-3963	69	19	n	n	CCONJ
cana-3963	69	20	q	q	NOUN
cana-3963	69	21	f	f	NOUN
cana-3963	69	22	qs	qs	PROPN
cana-3963	69	23	is	be	AUX
cana-3963	69	24	defined	define	VERB
cana-3963	69	25	as	as	ADP
cana-3963	69	26	the	the	DET
cana-3963	69	27	set	set	NOUN
cana-3963	69	28	{	{	PUNCT
cana-3963	69	29	}	}	PUNCT
cana-3963	69	30	.qv	.qv	PUNCT
cana-3963	70	1	v	v	X
cana-3963	70	2	s	s	PROPN
cana-3963	70	3	let	let	VERB
cana-3963	70	4	's	us	PRON
cana-3963	70	5	revisit	revisit	VERB
cana-3963	70	6	fundamental	fundamental	ADJ
cana-3963	70	7	concepts	concept	NOUN
cana-3963	70	8	related	relate	VERB
cana-3963	70	9	to	to	ADP
cana-3963	70	10	matrix	matrix	NOUN
cana-3963	70	11	-	-	PUNCT
cana-3963	70	12	product	product	NOUN
cana-3963	70	13	codes	code	NOUN
cana-3963	70	14	[	[	X
cana-3963	70	15	17],[18	17],[18	NUM
cana-3963	70	16	]	]	PUNCT
cana-3963	70	17	.	.	PUNCT
cana-3963	71	1	communications	communication	NOUN
cana-3963	71	2	on	on	ADP
cana-3963	71	3	applied	apply	VERB
cana-3963	71	4	nonlinear	nonlinear	ADJ
cana-3963	71	5	analysis	analysis	NOUN
cana-3963	71	6	issn	issn	NOUN
cana-3963	71	7	:	:	PUNCT
cana-3963	71	8	1074	1074	NUM
cana-3963	71	9	-	-	PUNCT
cana-3963	71	10	133x	133x	NUM
cana-3963	71	11	vol	vol	NOUN
cana-3963	71	12	32	32	NUM
cana-3963	71	13	no	no	NOUN
cana-3963	71	14	.	.	PUNCT
cana-3963	72	1	9s	9s	NUM
cana-3963	72	2	(	(	PUNCT
cana-3963	72	3	2025	2025	NUM
cana-3963	72	4	)	)	PUNCT
cana-3963	72	5	545	545	NUM
cana-3963	72	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	72	7	let	let	VERB
cana-3963	72	8	(	(	PUNCT
cana-3963	72	9	)	)	PUNCT
cana-3963	72	10	ija	ija	PROPN
cana-3963	72	11	a=	a=	AUX
cana-3963	72	12	denote	denote	VERB
cana-3963	72	13	a	a	DET
cana-3963	72	14	matrix	matrix	NOUN
cana-3963	72	15	of	of	ADP
cana-3963	72	16	size	size	NOUN
cana-3963	72	17	s	s	VERB
cana-3963	72	18	l	l	NOUN
cana-3963	72	19	with	with	ADP
cana-3963	72	20	s	s	PRON
cana-3963	72	21	l	l	ADJ
cana-3963	72	22	over	over	ADP
cana-3963	72	23	2q	2q	NUM
cana-3963	72	24	f	f	NOUN
cana-3963	72	25	and	and	CCONJ
cana-3963	72	26	let	let	VERB
cana-3963	72	27			PRON
cana-3963	72	28	1	1	VERB
cana-3963	72	29	2	2	NUM
cana-3963	72	30	,	,	PUNCT
cana-3963	72	31	,	,	PUNCT
cana-3963	72	32	...	...	PUNCT
cana-3963	72	33	,	,	PUNCT
cana-3963	72	34	ss	ss	INTJ
cana-3963	73	1			NOUN
cana-3963	74	1			X
cana-3963	75	1	=	=	PROPN
cana-3963	75	2	be	be	AUX
cana-3963	75	3	a	a	DET
cana-3963	75	4	family	family	NOUN
cana-3963	75	5	of	of	ADP
cana-3963	75	6	s	s	NOUN
cana-3963	75	7	linear	linear	NOUN
cana-3963	75	8	codes	code	NOUN
cana-3963	75	9	with	with	ADP
cana-3963	75	10	n	n	ADP
cana-3963	75	11	as	as	ADP
cana-3963	75	12	length	length	NOUN
cana-3963	75	13	of	of	ADP
cana-3963	75	14	each	each	DET
cana-3963	75	15	code	code	NOUN
cana-3963	75	16	i	i	PUNCT
cana-3963	75	17	having	have	VERB
cana-3963	75	18	elements	element	NOUN
cana-3963	75	19	in	in	ADP
cana-3963	75	20	2	2	NUM
cana-3963	75	21	.	.	PUNCT
cana-3963	76	1	q	q	PROPN
cana-3963	77	1	f	f	X
cana-3963	77	2	the	the	DET
cana-3963	77	3	matrix	matrix	NOUN
cana-3963	77	4	-	-	PUNCT
cana-3963	77	5	product	product	NOUN
cana-3963	77	6	code	code	NOUN
cana-3963	77	7	(	(	PUNCT
cana-3963	77	8	mpc	mpc	NOUN
cana-3963	77	9	)	)	PUNCT
cana-3963	77	10	generated	generate	VERB
cana-3963	77	11	by	by	ADP
cana-3963	77	12	1	1	NUM
cana-3963	77	13	2	2	NUM
cana-3963	77	14	[	[	PUNCT
cana-3963	77	15	,	,	PUNCT
cana-3963	77	16	,	,	PUNCT
cana-3963	77	17	...	...	PUNCT
cana-3963	77	18	,	,	PUNCT
cana-3963	78	1	]	]	PUNCT
cana-3963	78	2	.a	.a	NOUN
cana-3963	78	3	s	s	VERB
cana-3963	78	4	a	a	X
cana-3963	78	5			PROPN
cana-3963	78	6			X
cana-3963	78	7	=	=	PROPN
cana-3963	78	8	which	which	PRON
cana-3963	78	9	is	be	AUX
cana-3963	78	10	a	a	DET
cana-3963	78	11	code	code	NOUN
cana-3963	78	12	of	of	ADP
cana-3963	78	13	length	length	NOUN
cana-3963	78	14	nl	nl	PROPN
cana-3963	78	15	and	and	CCONJ
cana-3963	78	16	contains	contain	VERB
cana-3963	78	17	all	all	DET
cana-3963	78	18	mpcs	mpcs	PROPN
cana-3963	78	19	1	1	PROPN
cana-3963	78	20	2[c	2[c	NUM
cana-3963	78	21	,	,	PUNCT
cana-3963	78	22	c	c	NOUN
cana-3963	78	23	,	,	PUNCT
cana-3963	78	24	...	...	PUNCT
cana-3963	78	25	,	,	PUNCT
cana-3963	78	26	c	c	X
cana-3963	78	27	]	]	PUNCT
cana-3963	78	28	.s	.s	NOUN
cana-3963	78	29	a	a	PRON
cana-3963	78	30	for	for	ADP
cana-3963	78	31	some	some	DET
cana-3963	78	32	1	1	NUM
cana-3963	78	33	2(c	2(c	NUM
cana-3963	78	34	,	,	PUNCT
cana-3963	78	35	c	c	NOUN
cana-3963	78	36	,	,	PUNCT
cana-3963	78	37	,	,	PUNCT
cana-3963	78	38	c	c	NOUN
cana-3963	78	39	)	)	PUNCT
cana-3963	78	40	.t	.t	PROPN
cana-3963	79	1	i	i	PRON
cana-3963	79	2	i	i	PRON
cana-3963	80	1	i	i	PRON
cana-3963	80	2	ni	ni	PROPN
cana-3963	80	3	ic	ic	PROPN
cana-3963	80	4	=	=	PROPN
cana-3963	80	5			NOUN
cana-3963	80	6	here	here	ADV
cana-3963	80	7	ic	ic	PROPN
cana-3963	80	8	represents	represent	VERB
cana-3963	80	9	1n	1n	PROPN
cana-3963	80	10	column	column	NOUN
cana-3963	80	11	vector	vector	NOUN
cana-3963	80	12	for	for	ADP
cana-3963	80	13	each	each	DET
cana-3963	80	14	1,2	1,2	NUM
cana-3963	80	15	,	,	PUNCT
cana-3963	80	16	...	...	PUNCT
cana-3963	80	17	,	,	PUNCT
cana-3963	80	18	.i	.i	PROPN
cana-3963	80	19	s=	s=	PROPN
cana-3963	81	1	any	any	DET
cana-3963	81	2	above	above	ADV
cana-3963	81	3	defined	define	VERB
cana-3963	81	4	codeword	codeword	NOUN
cana-3963	81	5	of	of	ADP
cana-3963	81	6	the	the	DET
cana-3963	81	7	set	set	NOUN
cana-3963	81	8	(	(	PUNCT
cana-3963	81	9	)	)	PUNCT
cana-3963	81	10	a	a	PRON
cana-3963	81	11	is	be	AUX
cana-3963	81	12	an	an	DET
cana-3963	81	13	n	n	CCONJ
cana-3963	81	14	l	l	ADJ
cana-3963	81	15	matrix	matrix	NOUN
cana-3963	81	16	written	write	VERB
cana-3963	81	17	as	as	ADP
cana-3963	81	18	11	11	NUM
cana-3963	81	19	12	12	NUM
cana-3963	81	20	1	1	NUM
cana-3963	81	21	21	21	NUM
cana-3963	81	22	22	22	NUM
cana-3963	81	23	2	2	NUM
cana-3963	81	24	1	1	NUM
cana-3963	81	25	2	2	NUM
cana-3963	81	26	.	.	PUNCT
cana-3963	82	1	s	s	PART
cana-3963	82	2	s	s	X
cana-3963	82	3	n	n	CCONJ
cana-3963	82	4	n	n	ADV
cana-3963	82	5	ns	ns	NOUN
cana-3963	83	1	c	c	NOUN
cana-3963	83	2	c	c	NOUN
cana-3963	83	3	c	c	NOUN
cana-3963	83	4	c	c	NOUN
cana-3963	83	5	c	c	NOUN
cana-3963	83	6	c	c	NOUN
cana-3963	83	7	c	c	PROPN
cana-3963	83	8	a	a	DET
cana-3963	83	9	c	c	NOUN
cana-3963	83	10	c	c	NOUN
cana-3963	83	11	c	c	NOUN
cana-3963	83	12			PROPN
cana-3963	83	13			ADJ
cana-3963	83	14			NOUN
cana-3963	83	15			PROPN
cana-3963	83	16			NOUN
cana-3963	83	17	=	=	X
cana-3963	83	18			NOUN
cana-3963	83	19			NOUN
cana-3963	83	20			NOUN
cana-3963	83	21			NOUN
cana-3963	83	22			NOUN
cana-3963	83	23			PROPN
cana-3963	83	24	1	1	NUM
cana-3963	83	25	1	1	NUM
cana-3963	83	26	1	1	NUM
cana-3963	83	27	2	2	NUM
cana-3963	83	28	1	1	NUM
cana-3963	83	29	1	1	NUM
cana-3963	83	30	1	1	NUM
cana-3963	83	31	1	1	NUM
cana-3963	83	32	2	2	NUM
cana-3963	83	33	1	1	NUM
cana-3963	83	34	2	2	NUM
cana-3963	83	35	2	2	NUM
cana-3963	83	36	2	2	NUM
cana-3963	83	37	1	1	NUM
cana-3963	83	38	1	1	NUM
cana-3963	83	39	1	1	NUM
cana-3963	83	40	1	1	NUM
cana-3963	83	41	2	2	NUM
cana-3963	83	42	1	1	NUM
cana-3963	83	43	1	1	NUM
cana-3963	83	44	1	1	NUM
cana-3963	83	45	s	s	NOUN
cana-3963	83	46	s	s	NOUN
cana-3963	83	47	s	s	X
cana-3963	83	48	i	i	PRON
cana-3963	84	1	i	i	PRON
cana-3963	85	1	i	i	PRON
cana-3963	86	1	i	i	PRON
cana-3963	87	1	i	i	PRON
cana-3963	87	2	il	il	VERB
cana-3963	88	1	i	i	PRON
cana-3963	88	2	i	i	PRON
cana-3963	89	1	i	i	PRON
cana-3963	89	2	s	s	VERB
cana-3963	89	3	s	s	X
cana-3963	89	4	s	s	X
cana-3963	90	1	i	i	PRON
cana-3963	90	2	i	i	PRON
cana-3963	91	1	i	i	PRON
cana-3963	91	2	i	i	PRON
cana-3963	92	1	i	i	PRON
cana-3963	92	2	il	il	VERB
cana-3963	93	1	i	i	PRON
cana-3963	93	2	i	i	PRON
cana-3963	94	1	i	i	PRON
cana-3963	94	2	s	s	AUX
cana-3963	94	3	s	s	X
cana-3963	94	4	s	s	X
cana-3963	94	5	ni	ni	NOUN
cana-3963	95	1	i	i	PROPN
cana-3963	95	2	ni	ni	PROPN
cana-3963	96	1	i	i	PROPN
cana-3963	96	2	ni	ni	PROPN
cana-3963	96	3	il	il	PROPN
cana-3963	97	1	i	i	PRON
cana-3963	97	2	i	i	INTJ
cana-3963	98	1	i	i	PRON
cana-3963	98	2	c	c	VERB
cana-3963	98	3	a	a	DET
cana-3963	98	4	c	c	NOUN
cana-3963	98	5	a	a	DET
cana-3963	98	6	c	c	NOUN
cana-3963	98	7	a	a	DET
cana-3963	98	8	c	c	NOUN
cana-3963	98	9	a	a	DET
cana-3963	98	10	c	c	NOUN
cana-3963	98	11	a	a	DET
cana-3963	98	12	c	c	NOUN
cana-3963	98	13	a	a	DET
cana-3963	98	14	c	c	NOUN
cana-3963	98	15	a	a	DET
cana-3963	98	16	c	c	NOUN
cana-3963	98	17	a	a	DET
cana-3963	98	18	c	c	NOUN
cana-3963	99	1	a	a	NOUN
cana-3963	99	2	=	=	SYM
cana-3963	99	3	=	=	PUNCT
cana-3963	99	4	=	=	PUNCT
cana-3963	99	5	=	=	PUNCT
cana-3963	99	6	=	=	PUNCT
cana-3963	99	7	=	=	PUNCT
cana-3963	99	8	=	=	PUNCT
cana-3963	99	9	=	=	PUNCT
cana-3963	99	10	=	=	SYM
cana-3963	99	11			PROPN
cana-3963	99	12			ADJ
cana-3963	99	13			NOUN
cana-3963	99	14			PROPN
cana-3963	99	15			NOUN
cana-3963	99	16			NOUN
cana-3963	99	17			NOUN
cana-3963	99	18			NOUN
cana-3963	99	19			NOUN
cana-3963	99	20	=	=	X
cana-3963	99	21			NOUN
cana-3963	99	22			NOUN
cana-3963	99	23			NOUN
cana-3963	99	24			NOUN
cana-3963	99	25			NOUN
cana-3963	99	26			NOUN
cana-3963	99	27			NOUN
cana-3963	99	28			NOUN
cana-3963	99	29			NOUN
cana-3963	99	30			PROPN
cana-3963	99	31			PROPN
cana-3963	99	32			X
cana-3963	99	33			X
cana-3963	99	34			X
cana-3963	99	35			X
cana-3963	99	36			X
cana-3963	99	37			X
cana-3963	99	38			X
cana-3963	99	39			X
cana-3963	99	40			X
cana-3963	99	41	consider	consider	VERB
cana-3963	99	42	that	that	PRON
cana-3963	99	43	for	for	ADP
cana-3963	99	44	each	each	DET
cana-3963	99	45	1,2	1,2	NUM
cana-3963	99	46	,	,	PUNCT
cana-3963	99	47	...	...	PUNCT
cana-3963	99	48	,	,	PUNCT
cana-3963	99	49	,	,	PUNCT
cana-3963	99	50	i	i	PRON
cana-3963	99	51	s=	s=	VERB
cana-3963	99	52	ig	ig	PROPN
cana-3963	99	53	denotes	denote	VERB
cana-3963	99	54	the	the	DET
cana-3963	99	55	generator	generator	NOUN
cana-3963	99	56	matrix	matrix	NOUN
cana-3963	99	57	for	for	ADP
cana-3963	99	58	the	the	DET
cana-3963	99	59	linear	linear	PROPN
cana-3963	99	60	code	code	PROPN
cana-3963	99	61	i	i	PUNCT
cana-3963	99	62	then	then	ADV
cana-3963	99	63	a	a	VERB
cana-3963	99	64	is	be	VERB
cana-3963	99	65	a	a	DET
cana-3963	99	66	classical	classical	ADJ
cana-3963	99	67	code	code	NOUN
cana-3963	99	68	having	have	VERB
cana-3963	99	69	the	the	DET
cana-3963	99	70	generator	generator	NOUN
cana-3963	99	71	matrix	matrix	NOUN
cana-3963	99	72	given	give	VERB
cana-3963	99	73	below	below	ADP
cana-3963	99	74	11	11	NUM
cana-3963	99	75	1	1	NUM
cana-3963	99	76	12	12	NUM
cana-3963	99	77	1	1	NUM
cana-3963	99	78	1	1	NUM
cana-3963	99	79	1	1	NUM
cana-3963	99	80	21	21	NUM
cana-3963	99	81	2	2	NUM
cana-3963	99	82	22	22	NUM
cana-3963	99	83	2	2	NUM
cana-3963	99	84	2	2	NUM
cana-3963	99	85	2	2	NUM
cana-3963	99	86	1	1	NUM
cana-3963	99	87	2	2	NUM
cana-3963	99	88	.	.	PUNCT
cana-3963	100	1	l	l	NOUN
cana-3963	100	2	l	l	NOUN
cana-3963	101	1	a	a	PRON
cana-3963	101	2	s	s	X
cana-3963	101	3	s	s	X
cana-3963	101	4	s	s	X
cana-3963	101	5	s	s	NOUN
cana-3963	101	6	sl	sl	NOUN
cana-3963	101	7	s	s	VERB
cana-3963	101	8	a	a	DET
cana-3963	101	9	g	g	NOUN
cana-3963	101	10	a	a	DET
cana-3963	101	11	g	g	NOUN
cana-3963	101	12	a	a	DET
cana-3963	101	13	g	g	NOUN
cana-3963	101	14	a	a	DET
cana-3963	101	15	g	g	NOUN
cana-3963	101	16	a	a	DET
cana-3963	101	17	g	g	NOUN
cana-3963	101	18	a	a	DET
cana-3963	101	19	g	g	NOUN
cana-3963	101	20	g	g	PROPN
cana-3963	101	21	a	a	DET
cana-3963	101	22	g	g	NOUN
cana-3963	101	23	a	a	DET
cana-3963	101	24	g	g	NOUN
cana-3963	101	25	a	a	DET
cana-3963	101	26	g	g	NOUN
cana-3963	101	27			PROPN
cana-3963	101	28			NOUN
cana-3963	101	29			NOUN
cana-3963	101	30			PROPN
cana-3963	101	31			NOUN
cana-3963	101	32	=	=	X
cana-3963	101	33			NOUN
cana-3963	101	34			NOUN
cana-3963	101	35			NOUN
cana-3963	101	36			NOUN
cana-3963	101	37			VERB
cana-3963	101	38			PROPN
cana-3963	101	39	a	a	DET
cana-3963	101	40	matrix	matrix	NOUN
cana-3963	101	41	1	1	NUM
cana-3963	101	42	,	,	PUNCT
cana-3963	101	43	(	(	PUNCT
cana-3963	101	44	a	a	X
cana-3963	101	45	)	)	PUNCT
cana-3963	101	46	ij	ij	NOUN
cana-3963	102	1	i	i	PRON
cana-3963	102	2	j	j	PROPN
cana-3963	102	3	na	na	VERB
cana-3963	102	4			NUM
cana-3963	102	5	=	=	NOUN
cana-3963	102	6	of	of	ADP
cana-3963	102	7	size	size	NOUN
cana-3963	102	8	n	n	PRON
cana-3963	102	9	n	n	NOUN
cana-3963	102	10	is	be	AUX
cana-3963	102	11	called	call	VERB
cana-3963	102	12	a	a	DET
cana-3963	102	13	monomial	monomial	ADJ
cana-3963	102	14	matrix	matrix	NOUN
cana-3963	102	15	if	if	SCONJ
cana-3963	102	16	the	the	DET
cana-3963	102	17	matrix	matrix	NOUN
cana-3963	102	18	a	a	PRON
cana-3963	102	19	is	be	AUX
cana-3963	102	20	non	non	ADJ
cana-3963	102	21	-	-	ADJ
cana-3963	102	22	singular	singular	ADJ
cana-3963	102	23	and	and	CCONJ
cana-3963	102	24	each	each	DET
cana-3963	102	25	row	row	NOUN
cana-3963	102	26	and	and	CCONJ
cana-3963	102	27	column	column	NOUN
cana-3963	102	28	possess	possess	VERB
cana-3963	102	29	exactly	exactly	ADV
cana-3963	102	30	one	one	NUM
cana-3963	102	31	non	non	ADJ
cana-3963	102	32	-	-	ADJ
cana-3963	102	33	zero	zero	NUM
cana-3963	102	34	element	element	NOUN
cana-3963	102	35	.	.	PUNCT
cana-3963	103	1	3	3	X
cana-3963	103	2	.	.	NUM
cana-3963	103	3	proposed	propose	VERB
cana-3963	103	4	work	work	NOUN
cana-3963	103	5	denote	denote	VERB
cana-3963	103	6	by	by	ADP
cana-3963	103	7	(	(	PUNCT
cana-3963	103	8	)	)	PUNCT
cana-3963	103	9	,	,	PUNCT
cana-3963	103	10	ija	ija	PROPN
cana-3963	103	11	a=	a=	PROPN
cana-3963	103	12	an	an	DET
cana-3963	103	13	s	s	X
cana-3963	103	14	s	s	NOUN
cana-3963	103	15	matrix	matrix	NOUN
cana-3963	103	16	where	where	SCONJ
cana-3963	103	17	entries	entry	NOUN
cana-3963	103	18	belongs	belong	VERB
cana-3963	103	19	to	to	ADP
cana-3963	103	20	2	2	NUM
cana-3963	103	21	,	,	PUNCT
cana-3963	103	22	n	n	NOUN
cana-3963	104	1	q	q	NOUN
cana-3963	104	2	f	f	NOUN
cana-3963	104	3	then	then	ADV
cana-3963	104	4	we	we	PRON
cana-3963	104	5	designate	designate	VERB
cana-3963	104	6	(	(	PUNCT
cana-3963	104	7	)	)	PUNCT
cana-3963	104	8	,	,	PUNCT
cana-3963	104	9	q	q	PUNCT
cana-3963	104	10	q	q	PROPN
cana-3963	104	11	ija	ija	NOUN
cana-3963	104	12	a=	a=	NOUN
cana-3963	105	1	and	and	CCONJ
cana-3963	105	2	then	then	ADV
cana-3963	105	3	the	the	DET
cana-3963	105	4	condition	condition	NOUN
cana-3963	105	5	to	to	PART
cana-3963	105	6	be	be	AUX
cana-3963	105	7	hdc	hdc	NOUN
cana-3963	105	8	for	for	ADP
cana-3963	105	9	a	a	DET
cana-3963	105	10	linear	linear	ADJ
cana-3963	105	11	code	code	NOUN
cana-3963	105	12	is	be	AUX
cana-3963	105	13	outlined	outline	VERB
cana-3963	105	14	below	below	ADV
cana-3963	105	15	.	.	PUNCT
cana-3963	106	1	theorem	theorem	VERB
cana-3963	106	2	1	1	NUM
cana-3963	106	3	:	:	PUNCT
cana-3963	106	4	let	let	VERB
cana-3963	106	5			NOUN
cana-3963	106	6	gives	give	VERB
cana-3963	106	7	an	an	DET
cana-3963	106	8	2	2	NUM
cana-3963	106	9	[	[	PUNCT
cana-3963	106	10	,	,	PUNCT
cana-3963	106	11	,	,	PUNCT
cana-3963	106	12	]	]	PUNCT
cana-3963	106	13	q	q	PROPN
cana-3963	107	1	n	n	CCONJ
cana-3963	107	2	k	k	NOUN
cana-3963	107	3	d	d	X
cana-3963	107	4	linear	linear	PROPN
cana-3963	107	5	code	code	NOUN
cana-3963	107	6	with	with	ADP
cana-3963	107	7	elements	element	NOUN
cana-3963	107	8	from	from	ADP
cana-3963	107	9	2q	2q	NUM
cana-3963	107	10	f	f	X
cana-3963	107	11	and	and	CCONJ
cana-3963	107	12	g	g	PROPN
cana-3963	107	13	be	be	VERB
cana-3963	107	14	the	the	DET
cana-3963	107	15	generator	generator	NOUN
cana-3963	107	16	matrix	matrix	NOUN
cana-3963	107	17	of	of	ADP
cana-3963	107	18	code	code	NOUN
cana-3963	107	19			NOUN
cana-3963	107	20	.	.	PUNCT
cana-3963	108	1	then	then	ADV
cana-3963	108	2	the	the	DET
cana-3963	108	3	code	code	NOUN
cana-3963	108	4			NOUN
cana-3963	108	5	is	be	AUX
cana-3963	108	6	hdc	hdc	NOUN
cana-3963	108	7	if	if	SCONJ
cana-3963	109	1	and	and	CCONJ
cana-3963	109	2	only	only	ADV
cana-3963	109	3	if	if	SCONJ
cana-3963	109	4	(	(	PUNCT
cana-3963	109	5	(	(	PUNCT
cana-3963	109	6	)	)	PUNCT
cana-3963	109	7	)	)	PUNCT
cana-3963	109	8	2	2	NUM
cana-3963	109	9	,	,	PUNCT
cana-3963	109	10	q	q	NOUN
cana-3963	109	11	tg	tg	PROPN
cana-3963	109	12	g	g	PROPN
cana-3963	109	13	k	k	PROPN
cana-3963	109	14	n	n	VERB
cana-3963	109	15			NOUN
cana-3963	109	16	−	−	NOUN
cana-3963	109	17	where	where	SCONJ
cana-3963	109	18	(	(	PUNCT
cana-3963	109	19	)	)	PUNCT
cana-3963	109	20	a	a	NOUN
cana-3963	109	21	is	be	AUX
cana-3963	109	22	the	the	DET
cana-3963	109	23	number	number	NOUN
cana-3963	109	24	of	of	ADP
cana-3963	109	25	linearly	linearly	ADV
cana-3963	109	26	independent	independent	ADJ
cana-3963	109	27	rows	row	NOUN
cana-3963	109	28	of	of	ADP
cana-3963	109	29	the	the	DET
cana-3963	109	30	matrix	matrix	NOUN
cana-3963	109	31	.a	.a	PUNCT
cana-3963	110	1	communications	communication	NOUN
cana-3963	110	2	on	on	ADP
cana-3963	110	3	applied	apply	VERB
cana-3963	110	4	nonlinear	nonlinear	ADJ
cana-3963	110	5	analysis	analysis	NOUN
cana-3963	110	6	issn	issn	NOUN
cana-3963	110	7	:	:	PUNCT
cana-3963	110	8	1074	1074	NUM
cana-3963	110	9	-	-	PUNCT
cana-3963	110	10	133x	133x	NUM
cana-3963	110	11	vol	vol	NOUN
cana-3963	110	12	32	32	NUM
cana-3963	110	13	no	no	NOUN
cana-3963	110	14	.	.	PUNCT
cana-3963	111	1	9s	9s	NUM
cana-3963	111	2	(	(	PUNCT
cana-3963	111	3	2025	2025	NUM
cana-3963	111	4	)	)	PUNCT
cana-3963	112	1	546	546	NUM
cana-3963	112	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	112	3	proof	proof	NOUN
cana-3963	112	4	:	:	PUNCT
cana-3963	112	5	let	let	VERB
cana-3963	112	6	1	1	NUM
cana-3963	112	7	2	2	NUM
cana-3963	112	8	k	k	NOUN
cana-3963	112	9	a	a	DET
cana-3963	112	10	a	a	DET
cana-3963	112	11	g	g	NOUN
cana-3963	112	12	a	a	DET
cana-3963	112	13			PROPN
cana-3963	112	14			NOUN
cana-3963	112	15			NOUN
cana-3963	112	16			PROPN
cana-3963	112	17			NOUN
cana-3963	112	18	=	=	X
cana-3963	112	19			NOUN
cana-3963	112	20			NOUN
cana-3963	112	21			NOUN
cana-3963	112	22			NOUN
cana-3963	112	23			NOUN
cana-3963	112	24			PROPN
cana-3963	112	25	then	then	ADV
cana-3963	112	26	1	1	NUM
cana-3963	112	27	2	2	NUM
cana-3963	112	28	.	.	PUNCT
cana-3963	113	1	q	q	NOUN
cana-3963	113	2	q	q	X
cana-3963	114	1	q	q	X
cana-3963	114	2	q	q	X
cana-3963	115	1	k	k	X
cana-3963	115	2	a	a	DET
cana-3963	115	3	a	a	DET
cana-3963	115	4	g	g	NOUN
cana-3963	115	5	a	a	DET
cana-3963	115	6			PROPN
cana-3963	115	7			NOUN
cana-3963	115	8			NOUN
cana-3963	115	9			PROPN
cana-3963	115	10			NOUN
cana-3963	115	11	=	=	X
cana-3963	115	12			NOUN
cana-3963	115	13			NOUN
cana-3963	115	14			NOUN
cana-3963	115	15			NOUN
cana-3963	115	16			NOUN
cana-3963	115	17			PROPN
cana-3963	115	18			PROPN
cana-3963	115	19	let	let	VERB
cana-3963	115	20	1	1	NUM
cana-3963	115	21	2	2	NUM
cana-3963	115	22	n	n	NOUN
cana-3963	116	1	k	k	PROPN
cana-3963	116	2	b	b	PROPN
cana-3963	116	3	b	b	PROPN
cana-3963	116	4	h	h	NOUN
cana-3963	116	5	b	b	PROPN
cana-3963	116	6	−	−	PROPN
cana-3963	116	7			PROPN
cana-3963	116	8			ADJ
cana-3963	116	9			NOUN
cana-3963	116	10			PROPN
cana-3963	116	11			NOUN
cana-3963	116	12	=	=	X
cana-3963	116	13			NOUN
cana-3963	116	14			NOUN
cana-3963	116	15			NOUN
cana-3963	116	16			NOUN
cana-3963	116	17			NOUN
cana-3963	116	18			PROPN
cana-3963	116	19	be	be	VERB
cana-3963	116	20	the	the	DET
cana-3963	116	21	matrix	matrix	NOUN
cana-3963	116	22	of	of	ADP
cana-3963	116	23	parity	parity	NOUN
cana-3963	116	24	-	-	PUNCT
cana-3963	116	25	check	check	NOUN
cana-3963	116	26	for	for	ADP
cana-3963	116	27			NOUN
cana-3963	116	28	then	then	ADV
cana-3963	116	29			X
cana-3963	116	30	satisfies	satisfie	NOUN
cana-3963	116	31	(	(	PUNCT
cana-3963	116	32	)	)	PUNCT
cana-3963	116	33	q	q	X
cana-3963	116	34	⊥	⊥	VERB
cana-3963	116	35			PROPN
cana-3963	116	36	if	if	SCONJ
cana-3963	116	37	there	there	PRON
cana-3963	116	38	exists	exist	VERB
cana-3963	116	39	vectors	vector	NOUN
cana-3963	116	40	11	11	NUM
cana-3963	116	41	12	12	NUM
cana-3963	116	42	1	1	NUM
cana-3963	116	43	(	(	PUNCT
cana-3963	116	44	,	,	PUNCT
cana-3963	116	45	,	,	PUNCT
cana-3963	116	46	,	,	PUNCT
cana-3963	116	47	)	)	PUNCT
cana-3963	116	48	,	,	PUNCT
cana-3963	116	49	kl	kl	PROPN
cana-3963	116	50	l	l	NOUN
cana-3963	116	51	l	l	PROPN
cana-3963	116	52	21	21	NUM
cana-3963	116	53	22	22	NUM
cana-3963	116	54	2	2	NUM
cana-3963	116	55	(	(	PUNCT
cana-3963	116	56	,	,	PUNCT
cana-3963	116	57	,	,	PUNCT
cana-3963	116	58	,	,	PUNCT
cana-3963	116	59	)	)	PUNCT
cana-3963	116	60	,	,	PUNCT
cana-3963	116	61	kl	kl	PROPN
cana-3963	116	62	l	l	NOUN
cana-3963	116	63	l	l	PROPN
cana-3963	116	64	2,1	2,1	NUM
cana-3963	116	65	,	,	PUNCT
cana-3963	116	66	2	2	NUM
cana-3963	116	67	,	,	PUNCT
cana-3963	116	68	(	(	PUNCT
cana-3963	116	69	,	,	PUNCT
cana-3963	116	70	,	,	PUNCT
cana-3963	116	71	,	,	PUNCT
cana-3963	116	72	)	)	PUNCT
cana-3963	117	1	k	k	PROPN
cana-3963	117	2	n	n	CCONJ
cana-3963	117	3	k	k	PROPN
cana-3963	117	4	n	n	CCONJ
cana-3963	117	5	k	k	PROPN
cana-3963	118	1	n	n	CCONJ
cana-3963	118	2	k	k	PROPN
cana-3963	119	1	k	k	X
cana-3963	119	2	q	q	PUNCT
cana-3963	119	3	l	l	NOUN
cana-3963	119	4	l	l	NOUN
cana-3963	119	5	l	l	NOUN
cana-3963	120	1	f−	f−	NOUN
cana-3963	121	1	−	−	PROPN
cana-3963	121	2	−	−	ADJ
cana-3963	121	3			NOUN
cana-3963	121	4	such	such	ADJ
cana-3963	121	5	that	that	SCONJ
cana-3963	121	6	1	1	NUM
cana-3963	121	7	11	11	NUM
cana-3963	121	8	1	1	NUM
cana-3963	121	9	12	12	NUM
cana-3963	121	10	2	2	NUM
cana-3963	121	11	1	1	NUM
cana-3963	121	12	,	,	PUNCT
cana-3963	121	13	2	2	NUM
cana-3963	121	14	21	21	NUM
cana-3963	121	15	1	1	NUM
cana-3963	121	16	22	22	NUM
cana-3963	121	17	2	2	NUM
cana-3963	121	18	2	2	NUM
cana-3963	121	19	,	,	PUNCT
cana-3963	121	20	,	,	PUNCT
cana-3963	121	21	1	1	NUM
cana-3963	121	22	1	1	NUM
cana-3963	121	23	,	,	PUNCT
cana-3963	121	24	2	2	NUM
cana-3963	121	25	2	2	NUM
cana-3963	121	26	n	n	NOUN
cana-3963	121	27	k	k	NOUN
cana-3963	121	28	,	,	PUNCT
cana-3963	121	29	q	q	X
cana-3963	121	30	q	q	X
cana-3963	121	31	q	q	X
cana-3963	122	1	k	k	X
cana-3963	122	2	k	k	X
cana-3963	122	3	q	q	X
cana-3963	122	4	q	q	X
cana-3963	122	5	q	q	X
cana-3963	123	1	k	k	X
cana-3963	123	2	k	k	X
cana-3963	123	3	q	q	X
cana-3963	123	4	q	q	X
cana-3963	123	5	q	q	PROPN
cana-3963	123	6	n	n	CCONJ
cana-3963	123	7	k	k	PROPN
cana-3963	123	8	n	n	CCONJ
cana-3963	123	9	k	k	PROPN
cana-3963	123	10	n	n	CCONJ
cana-3963	123	11	k	k	PROPN
cana-3963	123	12	k	k	PROPN
cana-3963	124	1	k	k	PROPN
cana-3963	124	2	b	b	PROPN
cana-3963	124	3	l	l	NOUN
cana-3963	124	4	a	a	PROPN
cana-3963	124	5	l	l	NOUN
cana-3963	124	6	a	a	DET
cana-3963	124	7	l	l	NOUN
cana-3963	124	8	a	a	DET
cana-3963	124	9	b	b	NOUN
cana-3963	124	10	l	l	NOUN
cana-3963	124	11	a	a	X
cana-3963	124	12	l	l	NOUN
cana-3963	124	13	a	a	DET
cana-3963	124	14	l	l	NOUN
cana-3963	124	15	a	a	DET
cana-3963	124	16	b	b	NOUN
cana-3963	124	17	l	l	NOUN
cana-3963	124	18	a	a	DET
cana-3963	124	19	l	l	NOUN
cana-3963	124	20	a	a	DET
cana-3963	124	21	l	l	X
cana-3963	124	22	a−	a−	NOUN
cana-3963	124	23	−	−	PROPN
cana-3963	124	24	−	−	PROPN
cana-3963	124	25	−	−	PROPN
cana-3963	124	26	=	=	PUNCT
cana-3963	125	1	+	+	PUNCT
cana-3963	125	2	+	+	PUNCT
cana-3963	125	3	+	+	PUNCT
cana-3963	125	4	=	=	X
cana-3963	126	1	+	+	PUNCT
cana-3963	126	2	+	+	PUNCT
cana-3963	126	3	+	+	CCONJ
cana-3963	126	4	=	=	X
cana-3963	127	1	+	+	PUNCT
cana-3963	127	2	+	+	CCONJ
cana-3963	127	3	+	+	CCONJ
cana-3963	127	4	and	and	CCONJ
cana-3963	127	5	.n	.n	PROPN
cana-3963	128	1	k	k	PROPN
cana-3963	128	2	k−	k−	PROPN
cana-3963	128	3			NOUN
cana-3963	128	4	now	now	ADV
cana-3963	128	5	,	,	PUNCT
cana-3963	128	6	0tgh	0tgh	PRON
cana-3963	128	7	=	=	PUNCT
cana-3963	129	1	because	because	SCONJ
cana-3963	129	2	h	h	NOUN
cana-3963	129	3	is	be	AUX
cana-3963	129	4	the	the	DET
cana-3963	129	5	matrix	matrix	NOUN
cana-3963	129	6	for	for	ADP
cana-3963	129	7	parity	parity	NOUN
cana-3963	129	8	-	-	PUNCT
cana-3963	129	9	check	check	NOUN
cana-3963	129	10	of	of	ADP
cana-3963	129	11	.	.	NOUN
cana-3963	129	12	that	that	ADV
cana-3963	129	13	is	be	AUX
cana-3963	129	14	,	,	PUNCT
cana-3963	129	15	1	1	NUM
cana-3963	129	16	1	1	NUM
cana-3963	129	17	1	1	NUM
cana-3963	129	18	2	2	NUM
cana-3963	129	19	1	1	NUM
cana-3963	129	20	2	2	NUM
cana-3963	129	21	1	1	NUM
cana-3963	129	22	2	2	NUM
cana-3963	129	23	2	2	NUM
cana-3963	129	24	2	2	NUM
cana-3963	129	25	1	1	NUM
cana-3963	129	26	2	2	NUM
cana-3963	129	27	0	0	NUM
cana-3963	129	28	t	t	NOUN
cana-3963	129	29	t	t	PROPN
cana-3963	129	30	t	t	PROPN
cana-3963	130	1	n	n	PROPN
cana-3963	130	2	k	k	PROPN
cana-3963	130	3	t	t	PROPN
cana-3963	130	4	t	t	PROPN
cana-3963	130	5	t	t	PROPN
cana-3963	130	6	t	t	PROPN
cana-3963	131	1	n	n	PROPN
cana-3963	131	2	k	k	PROPN
cana-3963	131	3	t	t	PROPN
cana-3963	132	1	t	t	PROPN
cana-3963	132	2	t	t	PROPN
cana-3963	132	3	k	k	PROPN
cana-3963	132	4	k	k	PROPN
cana-3963	132	5	k	k	PROPN
cana-3963	133	1	n	n	PROPN
cana-3963	134	1	k	k	PROPN
cana-3963	134	2	a	a	DET
cana-3963	134	3	b	b	PROPN
cana-3963	134	4	a	a	DET
cana-3963	134	5	b	b	NOUN
cana-3963	134	6	a	a	DET
cana-3963	134	7	b	b	NOUN
cana-3963	134	8	a	a	DET
cana-3963	134	9	b	b	NOUN
cana-3963	134	10	a	a	DET
cana-3963	134	11	b	b	NOUN
cana-3963	134	12	a	a	DET
cana-3963	134	13	b	b	PROPN
cana-3963	134	14	gh	gh	PROPN
cana-3963	134	15	a	a	DET
cana-3963	134	16	b	b	PROPN
cana-3963	134	17	a	a	DET
cana-3963	134	18	b	b	NOUN
cana-3963	134	19	a	a	DET
cana-3963	134	20	b	b	NOUN
cana-3963	134	21	−	−	ADP
cana-3963	134	22	−	−	PROPN
cana-3963	134	23	−	−	PROPN
cana-3963	134	24			PROPN
cana-3963	134	25			ADJ
cana-3963	134	26			NOUN
cana-3963	134	27			PROPN
cana-3963	134	28			NOUN
cana-3963	134	29	=	=	NOUN
cana-3963	134	30	=	=	SYM
cana-3963	134	31			NOUN
cana-3963	134	32			NOUN
cana-3963	134	33			NOUN
cana-3963	134	34			NOUN
cana-3963	134	35			NOUN
cana-3963	134	36			PROPN
cana-3963	134	37			PROPN
cana-3963	134	38	the	the	DET
cana-3963	134	39	condition	condition	NOUN
cana-3963	134	40	(	(	PUNCT
cana-3963	134	41	)	)	PUNCT
cana-3963	134	42	q	q	X
cana-3963	134	43	⊥	⊥	VERB
cana-3963	135	1			PROPN
cana-3963	135	2	holds	hold	VERB
cana-3963	135	3	if	if	SCONJ
cana-3963	135	4	and	and	CCONJ
cana-3963	135	5	only	only	ADV
cana-3963	135	6	if	if	SCONJ
cana-3963	135	7	11	11	NUM
cana-3963	135	8	12	12	NUM
cana-3963	135	9	1	1	NUM
cana-3963	135	10	(	(	PUNCT
cana-3963	135	11	,	,	PUNCT
cana-3963	135	12	,	,	PUNCT
cana-3963	135	13	,	,	PUNCT
cana-3963	135	14	)	)	PUNCT
cana-3963	135	15	,	,	PUNCT
cana-3963	135	16	kl	kl	PROPN
cana-3963	135	17	l	l	NOUN
cana-3963	135	18	l	l	PROPN
cana-3963	135	19	21	21	NUM
cana-3963	135	20	22	22	NUM
cana-3963	135	21	2	2	NUM
cana-3963	135	22	(	(	PUNCT
cana-3963	135	23	,	,	PUNCT
cana-3963	135	24	,	,	PUNCT
cana-3963	135	25	,	,	PUNCT
cana-3963	135	26	)	)	PUNCT
cana-3963	135	27	,	,	PUNCT
cana-3963	135	28	kl	kl	X
cana-3963	135	29	l	l	NOUN
cana-3963	135	30	l	l	PROPN
cana-3963	135	31	,	,	PUNCT
cana-3963	135	32	1	1	NUM
cana-3963	135	33	,	,	PUNCT
cana-3963	135	34	2	2	NUM
cana-3963	135	35	,	,	PUNCT
cana-3963	135	36	(	(	PUNCT
cana-3963	135	37	,	,	PUNCT
cana-3963	135	38	,	,	PUNCT
cana-3963	135	39	,	,	PUNCT
cana-3963	135	40	)	)	PUNCT
cana-3963	135	41	n	n	CCONJ
cana-3963	135	42	k	k	PROPN
cana-3963	135	43	n	n	CCONJ
cana-3963	135	44	k	k	PROPN
cana-3963	135	45	n	n	CCONJ
cana-3963	135	46	k	k	PROPN
cana-3963	135	47	kl	kl	PROPN
cana-3963	135	48	l	l	PROPN
cana-3963	135	49	l−	l−	PROPN
cana-3963	135	50	−	−	PROPN
cana-3963	135	51	−	−	NOUN
cana-3963	135	52	are	be	AUX
cana-3963	135	53	solutions	solution	NOUN
cana-3963	135	54	of	of	ADP
cana-3963	135	55	the	the	DET
cana-3963	135	56	following	follow	VERB
cana-3963	135	57	system	system	NOUN
cana-3963	135	58	of	of	ADP
cana-3963	135	59	equations	equation	NOUN
cana-3963	135	60	with	with	ADP
cana-3963	135	61	full	full	ADJ
cana-3963	135	62	rank	rank	NOUN
cana-3963	135	63	,	,	PUNCT
cana-3963	135	64	1	1	NUM
cana-3963	135	65	1	1	NUM
cana-3963	135	66	1	1	NUM
cana-3963	135	67	1	1	NUM
cana-3963	135	68	2	2	NUM
cana-3963	135	69	2	2	NUM
cana-3963	135	70	1	1	NUM
cana-3963	135	71	2	2	NUM
cana-3963	135	72	1	1	NUM
cana-3963	135	73	1	1	NUM
cana-3963	135	74	2	2	NUM
cana-3963	135	75	2	2	NUM
cana-3963	135	76	2	2	NUM
cana-3963	135	77	2	2	NUM
cana-3963	135	78	1	1	NUM
cana-3963	135	79	1	1	NUM
cana-3963	135	80	2	2	NUM
cana-3963	135	81	2	2	NUM
cana-3963	135	82	(	(	PUNCT
cana-3963	135	83	)	)	PUNCT
cana-3963	135	84	(	(	PUNCT
cana-3963	135	85	)	)	PUNCT
cana-3963	135	86	(	(	PUNCT
cana-3963	135	87	)	)	PUNCT
cana-3963	135	88	,	,	PUNCT
cana-3963	135	89	(	(	PUNCT
cana-3963	135	90	)	)	PUNCT
cana-3963	135	91	(	(	PUNCT
cana-3963	135	92	)	)	PUNCT
cana-3963	135	93	(	(	PUNCT
cana-3963	135	94	)	)	PUNCT
cana-3963	135	95	,	,	PUNCT
cana-3963	135	96	(	(	PUNCT
cana-3963	135	97	)	)	PUNCT
cana-3963	135	98	(	(	PUNCT
cana-3963	135	99	)	)	PUNCT
cana-3963	135	100	(	(	PUNCT
cana-3963	135	101	)	)	PUNCT
cana-3963	135	102	,	,	PUNCT
cana-3963	135	103	q	q	PROPN
cana-3963	135	104	t	t	PROPN
cana-3963	135	105	q	q	PROPN
cana-3963	135	106	t	t	PROPN
cana-3963	135	107	q	q	PROPN
cana-3963	135	108	t	t	PROPN
cana-3963	136	1	k	k	PROPN
cana-3963	136	2	k	k	PROPN
cana-3963	136	3	q	q	PROPN
cana-3963	136	4	t	t	PROPN
cana-3963	136	5	q	q	PROPN
cana-3963	136	6	t	t	PROPN
cana-3963	137	1	q	q	PROPN
cana-3963	137	2	t	t	PROPN
cana-3963	138	1	k	k	PROPN
cana-3963	138	2	k	k	PROPN
cana-3963	138	3	q	q	PROPN
cana-3963	138	4	t	t	PROPN
cana-3963	138	5	q	q	PROPN
cana-3963	138	6	t	t	PROPN
cana-3963	139	1	q	q	PROPN
cana-3963	139	2	t	t	PROPN
cana-3963	140	1	k	k	PROPN
cana-3963	140	2	k	k	PROPN
cana-3963	141	1	k	k	PROPN
cana-3963	142	1	k	k	PROPN
cana-3963	143	1	k	k	PROPN
cana-3963	144	1	a	a	DET
cana-3963	144	2	a	a	X
cana-3963	144	3	x	x	X
cana-3963	144	4	a	a	DET
cana-3963	144	5	a	a	NOUN
cana-3963	144	6	x	x	NOUN
cana-3963	144	7	a	a	DET
cana-3963	144	8	a	a	NOUN
cana-3963	144	9	x	x	NOUN
cana-3963	144	10	a	a	DET
cana-3963	144	11	a	a	NOUN
cana-3963	144	12	x	x	NOUN
cana-3963	144	13	a	a	DET
cana-3963	144	14	a	a	NOUN
cana-3963	144	15	x	x	NOUN
cana-3963	144	16	a	a	DET
cana-3963	144	17	a	a	NOUN
cana-3963	144	18	x	x	NOUN
cana-3963	144	19	a	a	DET
cana-3963	144	20	a	a	NOUN
cana-3963	144	21	x	x	NOUN
cana-3963	144	22	a	a	DET
cana-3963	144	23	a	a	NOUN
cana-3963	144	24	x	x	NOUN
cana-3963	144	25	a	a	DET
cana-3963	144	26	a	a	DET
cana-3963	144	27	x	x	X
cana-3963	144	28			NOUN
cana-3963	144	29	+	+	PUNCT
cana-3963	145	1	+	+	PUNCT
cana-3963	145	2	+	+	NUM
cana-3963	145	3			NOUN
cana-3963	145	4	+	+	X
cana-3963	145	5	+	+	PUNCT
cana-3963	145	6	+	+	ADJ
cana-3963	145	7			NOUN
cana-3963	145	8			NUM
cana-3963	145	9			NUM
cana-3963	145	10			NUM
cana-3963	145	11	+	+	X
cana-3963	145	12	+	+	PUNCT
cana-3963	146	1	+	+	ADJ
cana-3963	146	2			PROPN
cana-3963	146	3	and	and	CCONJ
cana-3963	146	4	,	,	PUNCT
cana-3963	146	5	2	2	NUM
cana-3963	146	6	.k	.k	NOUN
cana-3963	146	7	n	n	VERB
cana-3963	146	8	so	so	ADV
cana-3963	146	9	,	,	PUNCT
cana-3963	146	10	the	the	DET
cana-3963	146	11	code	code	NOUN
cana-3963	146	12			NOUN
cana-3963	146	13	satisfies	satisfy	VERB
cana-3963	146	14	the	the	DET
cana-3963	146	15	condition	condition	NOUN
cana-3963	146	16	for	for	ADP
cana-3963	146	17	hermitian	hermitian	ADJ
cana-3963	146	18	dual	dual	ADV
cana-3963	146	19	-	-	PUNCT
cana-3963	146	20	containing	contain	VERB
cana-3963	146	21	.	.	PUNCT
cana-3963	147	1	hence	hence	ADV
cana-3963	147	2	,	,	PUNCT
cana-3963	147	3	if	if	SCONJ
cana-3963	147	4	(	(	PUNCT
cana-3963	147	5	(	(	PUNCT
cana-3963	147	6	)	)	PUNCT
cana-3963	147	7	)	)	PUNCT
cana-3963	147	8	2	2	NUM
cana-3963	147	9	,	,	PUNCT
cana-3963	147	10	q	q	NOUN
cana-3963	147	11	tg	tg	PROPN
cana-3963	147	12	g	g	PROPN
cana-3963	147	13	k	k	PROPN
cana-3963	147	14	n	n	VERB
cana-3963	147	15			NOUN
cana-3963	147	16	−	−	ADP
cana-3963	147	17	and	and	CCONJ
cana-3963	147	18	2	2	NUM
cana-3963	147	19	,	,	PUNCT
cana-3963	147	20	k	k	PROPN
cana-3963	147	21	n	n	PROPN
cana-3963	147	22	then	then	ADV
cana-3963	147	23	.h	.h	PUNCT
cana-3963	147	24	⊥	⊥	PROPN
cana-3963	148	1			PROPN
cana-3963	148	2	now	now	ADV
cana-3963	148	3	,	,	PUNCT
cana-3963	148	4	we	we	PRON
cana-3963	148	5	give	give	VERB
cana-3963	148	6	some	some	DET
cana-3963	148	7	theorems	theorem	NOUN
cana-3963	148	8	which	which	PRON
cana-3963	148	9	shows	show	VERB
cana-3963	148	10	that	that	SCONJ
cana-3963	148	11	the	the	DET
cana-3963	148	12	mpc	mpc	NOUN
cana-3963	148	13	is	be	AUX
cana-3963	148	14	also	also	ADV
cana-3963	148	15	hdc	hdc	NOUN
cana-3963	148	16	.	.	PUNCT
cana-3963	149	1	let	let	VERB
cana-3963	150	1	1	1	NUM
cana-3963	150	2	2	2	NUM
cana-3963	150	3	1	1	NUM
cana-3963	150	4	2	2	NUM
cana-3963	150	5	s	s	NOUN
cana-3963	150	6	s	s	NOUN
cana-3963	150	7	z	z	NOUN
cana-3963	150	8	z	z	PROPN
cana-3963	150	9	z	z	NOUN
cana-3963	150	10			PROPN
cana-3963	150	11			NOUN
cana-3963	150	12			NOUN
cana-3963	150	13	=	=	SYM
cana-3963	150	14			PROPN
cana-3963	150	15			PROPN
cana-3963	151	1			ADJ
cana-3963	151	2			NOUN
cana-3963	151	3	be	be	VERB
cana-3963	151	4	a	a	DET
cana-3963	151	5	permutation	permutation	NOUN
cana-3963	151	6	on	on	ADP
cana-3963	151	7	s	s	PART
cana-3963	151	8	symbols	symbol	NOUN
cana-3963	151	9	and	and	CCONJ
cana-3963	151	10	p	p	NOUN
cana-3963	151	11	be	be	AUX
cana-3963	151	12	the	the	DET
cana-3963	151	13	corresponding	correspond	VERB
cana-3963	151	14	permutation	permutation	NOUN
cana-3963	151	15	matrix	matrix	NOUN
cana-3963	151	16	where	where	SCONJ
cana-3963	151	17	th	th	X
cana-3963	151	18	iz	iz	NOUN
cana-3963	151	19	row	row	NOUN
cana-3963	151	20	of	of	ADP
cana-3963	151	21	the	the	DET
cana-3963	151	22	identity	identity	NOUN
cana-3963	151	23	matrix	matrix	NOUN
cana-3963	151	24	si	si	NOUN
cana-3963	151	25	is	be	AUX
cana-3963	151	26	placed	place	VERB
cana-3963	151	27	at	at	ADP
cana-3963	151	28	the	the	DET
cana-3963	151	29	thi	thi	PROPN
cana-3963	151	30	row	row	NOUN
cana-3963	151	31	of	of	ADP
cana-3963	151	32	p	p	NOUN
cana-3963	151	33	,	,	PUNCT
cana-3963	151	34	for	for	ADP
cana-3963	151	35	1,2	1,2	NUM
cana-3963	151	36	,	,	PUNCT
cana-3963	151	37	...	...	PUNCT
cana-3963	151	38	,	,	PUNCT
cana-3963	151	39	.i	.i	PROPN
cana-3963	151	40	s=	s=	PROPN
cana-3963	151	41	theorem	theorem	VERB
cana-3963	151	42	2	2	NUM
cana-3963	151	43	:	:	PUNCT
cana-3963	151	44	let	let	VERB
cana-3963	151	45	2	2	NUM
cana-3963	151	46	[	[	PUNCT
cana-3963	151	47	,	,	PUNCT
cana-3963	151	48	,	,	PUNCT
cana-3963	151	49	]	]	PUNCT
cana-3963	151	50	i	i	PRON
cana-3963	151	51	i	i	PRON
cana-3963	151	52	q	q	VERB
cana-3963	152	1	n	n	INTJ
cana-3963	152	2	k	k	NOUN
cana-3963	153	1	d	d	NOUN
cana-3963	153	2	be	be	AUX
cana-3963	153	3	linear	linear	ADJ
cana-3963	153	4	codes	code	NOUN
cana-3963	153	5	denoted	denote	VERB
cana-3963	153	6	by	by	ADP
cana-3963	153	7	i	i	NOUN
cana-3963	153	8	with	with	ADP
cana-3963	153	9	the	the	DET
cana-3963	153	10	condition	condition	NOUN
cana-3963	153	11	h	h	NOUN
cana-3963	153	12	i	i	PRON
cana-3963	153	13	i	i	VERB
cana-3963	153	14	⊥	⊥	X
cana-3963	153	15			PROPN
cana-3963	153	16	,	,	PUNCT
cana-3963	153	17	i.e.	i.e.	X
cana-3963	153	18	,	,	PUNCT
cana-3963	153	19	i	i	PRON
cana-3963	153	20	is	be	AUX
cana-3963	153	21	hdc	hdc	NOUN
cana-3963	153	22	for	for	ADP
cana-3963	153	23	every	every	DET
cana-3963	153	24	1,2	1,2	NUM
cana-3963	153	25	,	,	PUNCT
cana-3963	153	26	,	,	PUNCT
cana-3963	153	27	.i	.i	PROPN
cana-3963	153	28	s=	s=	PROPN
cana-3963	153	29	denote	denote	VERB
cana-3963	153	30	by	by	ADP
cana-3963	153	31	2	2	NUM
cana-3963	153	32	(	(	PUNCT
cana-3963	153	33	,	,	PUNCT
cana-3963	153	34	)	)	PUNCT
cana-3963	153	35	,	,	PUNCT
cana-3963	153	36	q	q	X
cana-3963	153	37	a	a	DET
cana-3963	153	38	m	m	NOUN
cana-3963	153	39	f	f	NOUN
cana-3963	153	40	s	s	PROPN
cana-3963	153	41	s	s	PROPN
cana-3963	153	42			PROPN
cana-3963	153	43	a	a	DET
cana-3963	153	44	non	non	ADJ
cana-3963	153	45	-	-	ADJ
cana-3963	153	46	singular	singular	ADJ
cana-3963	153	47	matrix	matrix	NOUN
cana-3963	153	48	with	with	ADP
cana-3963	153	49	the	the	DET
cana-3963	153	50	property	property	NOUN
cana-3963	153	51	that	that	PRON
cana-3963	153	52	communications	communication	NOUN
cana-3963	153	53	on	on	ADP
cana-3963	153	54	applied	apply	VERB
cana-3963	153	55	nonlinear	nonlinear	ADJ
cana-3963	153	56	analysis	analysis	NOUN
cana-3963	153	57	issn	issn	NOUN
cana-3963	153	58	:	:	PUNCT
cana-3963	153	59	1074	1074	NUM
cana-3963	153	60	-	-	PUNCT
cana-3963	153	61	133x	133x	NUM
cana-3963	153	62	vol	vol	NOUN
cana-3963	153	63	32	32	NUM
cana-3963	153	64	no	no	NOUN
cana-3963	153	65	.	.	PUNCT
cana-3963	154	1	9s	9s	NUM
cana-3963	154	2	(	(	PUNCT
cana-3963	154	3	2025	2025	NUM
cana-3963	154	4	)	)	PUNCT
cana-3963	154	5	547	547	NUM
cana-3963	154	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	155	1	*	*	PUNCT
cana-3963	155	2	aa	aa	PROPN
cana-3963	155	3	is	be	AUX
cana-3963	155	4	a	a	DET
cana-3963	155	5	monomial	monomial	ADJ
cana-3963	155	6	matrix	matrix	NOUN
cana-3963	155	7	for	for	ADP
cana-3963	155	8	some	some	DET
cana-3963	155	9	permutation	permutation	NOUN
cana-3963	155	10	,	,	PUNCT
cana-3963	155	11			PROPN
cana-3963	155	12	then	then	ADV
cana-3963	155	13	the	the	DET
cana-3963	155	14	set	set	NOUN
cana-3963	155	15	of	of	ADP
cana-3963	155	16	mpc	mpc	PROPN
cana-3963	155	17	1	1	NUM
cana-3963	155	18	2	2	NUM
cana-3963	155	19	[	[	PUNCT
cana-3963	155	20	,	,	PUNCT
cana-3963	155	21	,	,	PUNCT
cana-3963	155	22	,	,	PUNCT
cana-3963	155	23	]	]	PUNCT
cana-3963	155	24	.a	.a	NOUN
cana-3963	155	25	s	s	VERB
cana-3963	155	26	a	a	X
cana-3963	155	27			NOUN
cana-3963	155	28			X
cana-3963	156	1	=	=	PROPN
cana-3963	156	2			PROPN
cana-3963	156	3	is	be	AUX
cana-3963	156	4	a	a	DET
cana-3963	156	5	hermitian	hermitian	ADJ
cana-3963	156	6	dual	dual	ADV
cana-3963	156	7	-	-	PUNCT
cana-3963	156	8	containing	contain	VERB
cana-3963	156	9	code	code	NOUN
cana-3963	156	10	with	with	ADP
cana-3963	156	11	parameters	parameter	NOUN
cana-3963	156	12	2	2	NUM
cana-3963	156	13	1	1	NUM
cana-3963	156	14	[	[	PUNCT
cana-3963	156	15	,	,	PUNCT
cana-3963	156	16	,	,	PUNCT
cana-3963	156	17	]	]	X
cana-3963	156	18	s	s	VERB
cana-3963	156	19	i	i	INTJ
cana-3963	156	20	q	q	NOUN
cana-3963	157	1	i	i	INTJ
cana-3963	157	2	sn	sn	INTJ
cana-3963	158	1	k	k	PROPN
cana-3963	158	2	d	d	PROPN
cana-3963	158	3	=	=	SYM
cana-3963	158	4			PROPN
cana-3963	158	5	where	where	SCONJ
cana-3963	158	6	min	min	NOUN
cana-3963	158	7	{	{	PUNCT
cana-3963	158	8	(	(	PUNCT
cana-3963	158	9	)	)	PUNCT
cana-3963	158	10	}	}	PUNCT
cana-3963	158	11	.i	.i	NOUN
cana-3963	159	1	i	i	PRON
cana-3963	159	2	i	i	PROPN
cana-3963	160	1	d	d	PROPN
cana-3963	161	1	d	d	PROPN
cana-3963	161	2	a	a	DET
cana-3963	161	3	d=	d=	NOUN
cana-3963	161	4	proof	proof	NOUN
cana-3963	161	5	:	:	PUNCT
cana-3963	161	6	with	with	ADP
cana-3963	161	7	respect	respect	NOUN
cana-3963	161	8	to	to	ADP
cana-3963	161	9	the	the	DET
cana-3963	161	10	permutation	permutation	NOUN
cana-3963	161	11	,	,	PUNCT
cana-3963	161	12			PROPN
cana-3963	161	13	the	the	DET
cana-3963	161	14	matrix	matrix	NOUN
cana-3963	161	15	*	*	PUNCT
cana-3963	161	16	aa	aa	PROPN
cana-3963	161	17	is	be	AUX
cana-3963	161	18	given	give	VERB
cana-3963	161	19	to	to	PART
cana-3963	161	20	be	be	AUX
cana-3963	161	21	a	a	DET
cana-3963	161	22	monomial	monomial	ADJ
cana-3963	161	23	matrix	matrix	NOUN
cana-3963	161	24	therefore	therefore	ADV
cana-3963	161	25	,	,	PUNCT
cana-3963	161	26	there	there	PRON
cana-3963	161	27	exists	exist	VERB
cana-3963	161	28	an	an	DET
cana-3963	161	29	s	s	X
cana-3963	161	30	s	s	ADJ
cana-3963	161	31	diagonal	diagonal	ADJ
cana-3963	161	32	matrix	matrix	NOUN
cana-3963	161	33	11	11	NUM
cana-3963	161	34	22	22	NUM
cana-3963	161	35	(	(	PUNCT
cana-3963	161	36	,	,	PUNCT
cana-3963	161	37	,	,	PUNCT
cana-3963	161	38	,	,	PUNCT
cana-3963	161	39	)	)	PUNCT
cana-3963	161	40	ssd	ssd	NOUN
cana-3963	161	41	diag	diag	NOUN
cana-3963	162	1	d	d	PROPN
cana-3963	162	2	d	d	NOUN
cana-3963	162	3	d=	d=	NOUN
cana-3963	162	4	where	where	SCONJ
cana-3963	162	5	0,iid	0,iid	PROPN
cana-3963	162	6			VERB
cana-3963	162	7	such	such	ADJ
cana-3963	162	8	that	that	SCONJ
cana-3963	162	9	*	*	PUNCT
cana-3963	162	10	aa	aa	PROPN
cana-3963	162	11	dp=	dp=	PROPN
cana-3963	162	12	*	*	PUNCT
cana-3963	163	1	aa	aa	PROPN
cana-3963	163	2	dp	dp	PROPN
cana-3963	164	1	=	=	PUNCT
cana-3963	164	2	*	*	PUNCT
cana-3963	164	3	1	1	NUM
cana-3963	164	4	(	(	PUNCT
cana-3963	164	5	)	)	PUNCT
cana-3963	164	6	(	(	PUNCT
cana-3963	164	7	)	)	PUNCT
cana-3963	164	8	a	a	DET
cana-3963	164	9	dp	dp	NOUN
cana-3963	164	10	a	a	NOUN
cana-3963	164	11	−	−	NOUN
cana-3963	165	1	=	=	SYM
cana-3963	165	2	1	1	NUM
cana-3963	165	3	*	*	SYM
cana-3963	165	4	1	1	NUM
cana-3963	165	5	1	1	NUM
cana-3963	165	6	(	(	PUNCT
cana-3963	165	7	(	(	PUNCT
cana-3963	165	8	)	)	PUNCT
cana-3963	165	9	)	)	PUNCT
cana-3963	165	10	a	a	DET
cana-3963	165	11	dp	dp	NOUN
cana-3963	165	12	a	a	NOUN
cana-3963	165	13	−	−	PROPN
cana-3963	165	14	−	−	PROPN
cana-3963	165	15	−	−	NOUN
cana-3963	165	16	=	=	SYM
cana-3963	165	17	1	1	NUM
cana-3963	165	18	*	*	SYM
cana-3963	165	19	1	1	NUM
cana-3963	165	20	1a	1a	PROPN
cana-3963	165	21	a	a	DET
cana-3963	165	22	p	p	PROPN
cana-3963	165	23	d	d	NOUN
cana-3963	165	24	−	−	PROPN
cana-3963	165	25	−	−	PROPN
cana-3963	165	26	−	−	NOUN
cana-3963	165	27	=	=	SYM
cana-3963	165	28	1	1	NUM
cana-3963	165	29	*	*	PUNCT
cana-3963	165	30	1ta	1ta	NOUN
cana-3963	165	31	a	a	DET
cana-3963	165	32	p	p	NOUN
cana-3963	165	33	d	d	NOUN
cana-3963	165	34	−	−	PROPN
cana-3963	165	35	−	−	NOUN
cana-3963	165	36	=	=	NOUN
cana-3963	165	37	1	1	NUM
cana-3963	165	38	*	*	PUNCT
cana-3963	165	39	*	*	PUNCT
cana-3963	165	40	1	1	NUM
cana-3963	165	41	*	*	PUNCT
cana-3963	165	42	(	(	PUNCT
cana-3963	165	43	)	)	PUNCT
cana-3963	165	44	(	(	PUNCT
cana-3963	165	45	)	)	PUNCT
cana-3963	165	46	ta	ta	ADP
cana-3963	165	47	a	a	DET
cana-3963	165	48	p	p	PROPN
cana-3963	165	49	d	d	PROPN
cana-3963	165	50	−	−	PROPN
cana-3963	165	51	−	−	NOUN
cana-3963	165	52	=	=	SYM
cana-3963	166	1	1	1	NUM
cana-3963	166	2	*	*	SYM
cana-3963	166	3	1	1	NUM
cana-3963	166	4	*	*	PUNCT
cana-3963	166	5	*	*	PUNCT
cana-3963	167	1	*	*	PUNCT
cana-3963	167	2	*	*	PUNCT
cana-3963	167	3	(	(	PUNCT
cana-3963	167	4	)	)	PUNCT
cana-3963	167	5	(	(	PUNCT
cana-3963	167	6	)	)	PUNCT
cana-3963	167	7	(	(	PUNCT
cana-3963	167	8	)	)	PUNCT
cana-3963	167	9	(	(	PUNCT
cana-3963	167	10	)	)	PUNCT
cana-3963	167	11	ta	ta	X
cana-3963	168	1	d	d	NOUN
cana-3963	168	2	p	p	PROPN
cana-3963	168	3	a	a	PROPN
cana-3963	168	4	−	−	PROPN
cana-3963	168	5	−	−	NOUN
cana-3963	168	6	=	=	SYM
cana-3963	168	7	1	1	NUM
cana-3963	168	8	*	*	SYM
cana-3963	168	9	1	1	NUM
cana-3963	168	10	*	*	PUNCT
cana-3963	168	11	(	(	PUNCT
cana-3963	168	12	)	)	PUNCT
cana-3963	168	13	(	(	PUNCT
cana-3963	168	14	)	)	PUNCT
cana-3963	168	15	,	,	PUNCT
cana-3963	168	16	a	a	DET
cana-3963	168	17	d	d	X
cana-3963	168	18	p	p	PROPN
cana-3963	168	19	a	a	PROPN
cana-3963	168	20	−	−	PROPN
cana-3963	168	21	−	−	NOUN
cana-3963	168	22	=	=	PUNCT
cana-3963	168	23	using	use	VERB
cana-3963	168	24	the	the	DET
cana-3963	168	25	lemma	lemma	PROPN
cana-3963	169	1	[	[	X
cana-3963	169	2	11,19	11,19	NUM
cana-3963	169	3	]	]	PUNCT
cana-3963	169	4	,	,	PUNCT
cana-3963	169	5	it	it	PRON
cana-3963	169	6	gives	give	VERB
cana-3963	169	7	1	1	NUM
cana-3963	169	8	*	*	SYM
cana-3963	169	9	1	1	NUM
cana-3963	169	10	2	2	NUM
cana-3963	169	11	1	1	NUM
cana-3963	169	12	2	2	NUM
cana-3963	169	13	(	(	PUNCT
cana-3963	169	14	[	[	PUNCT
cana-3963	169	15	,	,	PUNCT
cana-3963	169	16	,	,	PUNCT
cana-3963	169	17	...	...	PUNCT
cana-3963	169	18	,	,	PUNCT
cana-3963	169	19	]	]	PUNCT
cana-3963	169	20	.	.	PUNCT
cana-3963	169	21	)	)	PUNCT
cana-3963	170	1	[	[	PUNCT
cana-3963	170	2	,	,	PUNCT
cana-3963	170	3	,	,	PUNCT
cana-3963	170	4	...	...	PUNCT
cana-3963	170	5	,	,	PUNCT
cana-3963	170	6	]	]	PUNCT
cana-3963	170	7	.	.	PUNCT
cana-3963	171	1	(	(	PUNCT
cana-3963	171	2	)	)	PUNCT
cana-3963	171	3	.h	.h	PUNCT
cana-3963	172	1	h	h	NOUN
cana-3963	172	2	h	h	NOUN
cana-3963	172	3	h	h	NOUN
cana-3963	172	4	s	s	PROPN
cana-3963	173	1	sa	sa	PROPN
cana-3963	173	2	d	d	PROPN
cana-3963	173	3	p	p	PROPN
cana-3963	173	4	a	a	NOUN
cana-3963	173	5			NOUN
cana-3963	173	6			INTJ
cana-3963	174	1			X
cana-3963	174	2			X
cana-3963	174	3	⊥	⊥	X
cana-3963	175	1	⊥	⊥	PROPN
cana-3963	175	2	⊥	⊥	PROPN
cana-3963	175	3	⊥	⊥	PROPN
cana-3963	175	4	−=	−=	NOUN
cana-3963	175	5	it	it	PRON
cana-3963	175	6	is	be	AUX
cana-3963	175	7	well	well	ADV
cana-3963	175	8	known	know	VERB
cana-3963	175	9	that	that	SCONJ
cana-3963	175	10	h	h	NOUN
cana-3963	175	11	i	i	PUNCT
cana-3963	175	12	⊥	⊥	PROPN
cana-3963	175	13	is	be	AUX
cana-3963	175	14	linear	linear	ADJ
cana-3963	175	15	,	,	PUNCT
cana-3963	175	16	so	so	ADV
cana-3963	175	17	q	q	PROPN
cana-3963	175	18	h	h	NOUN
cana-3963	176	1	h	h	NOUN
cana-3963	176	2	ii	ii	PROPN
cana-3963	177	1	i	i	PRON
cana-3963	177	2	i	i	PROPN
cana-3963	177	3	d	d	NOUN
cana-3963	177	4			AUX
cana-3963	177	5	−	−	VERB
cana-3963	177	6	⊥	⊥	PROPN
cana-3963	177	7	⊥=	⊥=	PROPN
cana-3963	177	8	for	for	ADP
cana-3963	177	9	every	every	DET
cana-3963	177	10	1,2	1,2	NUM
cana-3963	177	11	,	,	PUNCT
cana-3963	177	12	...	...	PUNCT
cana-3963	177	13	,	,	PUNCT
cana-3963	177	14	.i	.i	PROPN
cana-3963	177	15	s=	s=	PROPN
cana-3963	177	16	from	from	ADP
cana-3963	177	17	the	the	DET
cana-3963	177	18	theorem	theorem	ADJ
cana-3963	177	19	3	3	NUM
cana-3963	177	20	and	and	CCONJ
cana-3963	177	21	1	1	NUM
cana-3963	177	22	21	21	NUM
cana-3963	177	23	2	2	NUM
cana-3963	177	24	[	[	PUNCT
cana-3963	177	25	,	,	PUNCT
cana-3963	177	26	,	,	PUNCT
cana-3963	177	27	...	...	PUNCT
cana-3963	177	28	,	,	PUNCT
cana-3963	177	29	]	]	PUNCT
cana-3963	177	30	.	.	PUNCT
cana-3963	178	1	[	[	PUNCT
cana-3963	178	2	,	,	PUNCT
cana-3963	178	3	,	,	PUNCT
cana-3963	178	4	...	...	PUNCT
cana-3963	178	5	,	,	PUNCT
cana-3963	178	6	]	]	X
cana-3963	178	7	s	s	VERB
cana-3963	178	8	h	h	NOUN
cana-3963	178	9	h	h	NOUN
cana-3963	178	10	h	h	NOUN
cana-3963	179	1	h	h	NOUN
cana-3963	179	2	h	h	NOUN
cana-3963	179	3	h	h	NOUN
cana-3963	179	4	s	s	PROPN
cana-3963	179	5	z	z	NOUN
cana-3963	179	6	z	z	NOUN
cana-3963	179	7	zp	zp	NOUN
cana-3963	179	8			NOUN
cana-3963	180	1			NOUN
cana-3963	180	2			X
cana-3963	181	1			X
cana-3963	181	2	⊥	⊥	X
cana-3963	182	1	⊥	⊥	X
cana-3963	182	2	⊥	⊥	PROPN
cana-3963	182	3	⊥	⊥	PROPN
cana-3963	182	4	⊥	⊥	PROPN
cana-3963	182	5	⊥=	⊥=	PROPN
cana-3963	182	6	,	,	PUNCT
cana-3963	182	7	1	1	NUM
cana-3963	182	8	*	*	SYM
cana-3963	182	9	1	1	NUM
cana-3963	182	10	2	2	NUM
cana-3963	182	11	11	11	NUM
cana-3963	182	12	1	1	NUM
cana-3963	182	13	22	22	NUM
cana-3963	182	14	2	2	NUM
cana-3963	182	15	[	[	PUNCT
cana-3963	182	16	,	,	PUNCT
cana-3963	182	17	,	,	PUNCT
cana-3963	182	18	...	...	PUNCT
cana-3963	182	19	,	,	PUNCT
cana-3963	182	20	]	]	PUNCT
cana-3963	182	21	.	.	PUNCT
cana-3963	183	1	(	(	PUNCT
cana-3963	183	2	)	)	PUNCT
cana-3963	183	3	[	[	PUNCT
cana-3963	183	4	,	,	PUNCT
cana-3963	183	5	,	,	PUNCT
cana-3963	183	6	,	,	PUNCT
cana-3963	183	7	]	]	PUNCT
cana-3963	183	8	.h	.h	PUNCT
cana-3963	184	1	h	h	NOUN
cana-3963	184	2	h	h	NOUN
cana-3963	185	1	q	q	NOUN
cana-3963	185	2	h	h	NOUN
cana-3963	186	1	q	q	NOUN
cana-3963	186	2	h	h	NOUN
cana-3963	187	1	q	q	NOUN
cana-3963	187	2	h	h	NOUN
cana-3963	187	3	s	s	NOUN
cana-3963	187	4	ss	ss	NOUN
cana-3963	187	5	sd	sd	ADP
cana-3963	187	6	p	p	PROPN
cana-3963	188	1	a	a	PROPN
cana-3963	188	2	d	d	X
cana-3963	188	3	d	d	X
cana-3963	188	4	d	d	X
cana-3963	188	5	p	p	PROPN
cana-3963	188	6	a	a	PROPN
cana-3963	188	7			PROPN
cana-3963	188	8			NOUN
cana-3963	189	1			NOUN
cana-3963	189	2			X
cana-3963	190	1			X
cana-3963	190	2	⊥	⊥	X
cana-3963	191	1	⊥	⊥	PROPN
cana-3963	191	2	⊥	⊥	PROPN
cana-3963	192	1	−	−	PROPN
cana-3963	192	2	−	−	PROPN
cana-3963	193	1	⊥	⊥	NUM
cana-3963	193	2	−	−	PROPN
cana-3963	193	3	⊥	⊥	NOUN
cana-3963	193	4	−	−	PROPN
cana-3963	193	5	⊥=	⊥=	PROPN
cana-3963	193	6	1	1	NUM
cana-3963	193	7	2	2	NUM
cana-3963	193	8	[	[	PUNCT
cana-3963	193	9	,	,	PUNCT
cana-3963	193	10	,	,	PUNCT
cana-3963	193	11	...	...	PUNCT
cana-3963	193	12	,	,	PUNCT
cana-3963	193	13	]	]	PUNCT
cana-3963	193	14	.h	.h	PUNCT
cana-3963	194	1	h	h	NOUN
cana-3963	194	2	h	h	NOUN
cana-3963	194	3	s	s	PART
cana-3963	194	4	p	p	X
cana-3963	194	5	a	a	PROPN
cana-3963	194	6			PROPN
cana-3963	194	7	⊥	⊥	PUNCT
cana-3963	195	1	⊥	⊥	PROPN
cana-3963	195	2	⊥=	⊥=	PROPN
cana-3963	195	3	1	1	NUM
cana-3963	195	4	2	2	NUM
cana-3963	195	5	[	[	PUNCT
cana-3963	195	6	,	,	PUNCT
cana-3963	195	7	,	,	PUNCT
cana-3963	195	8	...	...	PUNCT
cana-3963	195	9	,	,	PUNCT
cana-3963	195	10	]	]	PUNCT
cana-3963	195	11	.	.	PUNCT
cana-3963	196	1	s	s	PROPN
cana-3963	196	2	h	h	NOUN
cana-3963	196	3	h	h	NOUN
cana-3963	197	1	h	h	NOUN
cana-3963	198	1	z	z	PROPN
cana-3963	198	2	z	z	PROPN
cana-3963	198	3	z	z	NOUN
cana-3963	198	4	a	a	X
cana-3963	198	5			NOUN
cana-3963	198	6	⊥	⊥	X
cana-3963	199	1	⊥	⊥	PROPN
cana-3963	199	2	⊥=	⊥=	PROPN
cana-3963	199	3	1	1	NUM
cana-3963	199	4	2	2	NUM
cana-3963	199	5	[	[	PUNCT
cana-3963	199	6	,	,	PUNCT
cana-3963	199	7	,	,	PUNCT
cana-3963	199	8	...	...	PUNCT
cana-3963	199	9	,	,	PUNCT
cana-3963	199	10	]	]	PUNCT
cana-3963	199	11	.	.	PUNCT
cana-3963	199	12	)	)	PUNCT
cana-3963	200	1	.s	.s	NOUN
cana-3963	200	2	a	a	X
cana-3963	200	3			NOUN
cana-3963	200	4			X
cana-3963	200	5	hence	hence	ADV
cana-3963	200	6	,	,	PUNCT
cana-3963	200	7	the	the	DET
cana-3963	200	8	linear	linear	PROPN
cana-3963	200	9	code	code	NOUN
cana-3963	200	10	together	together	ADV
cana-3963	200	11	with	with	ADP
cana-3963	200	12	the	the	DET
cana-3963	200	13	mpc	mpc	NOUN
cana-3963	200	14	satisfies	satisfy	VERB
cana-3963	200	15	the	the	DET
cana-3963	200	16	condition	condition	NOUN
cana-3963	200	17	for	for	ADP
cana-3963	200	18	hermitian	hermitian	ADJ
cana-3963	200	19	dual	dual	ADV
cana-3963	200	20	-	-	PUNCT
cana-3963	200	21	containing	contain	VERB
cana-3963	200	22	.	.	PUNCT
cana-3963	201	1	through	through	ADP
cana-3963	201	2	the	the	DET
cana-3963	201	3	use	use	NOUN
cana-3963	201	4	of	of	ADP
cana-3963	201	5	lemma	lemma	PROPN
cana-3963	202	1	[	[	X
cana-3963	202	2	17	17	NUM
cana-3963	202	3	]	]	PUNCT
cana-3963	202	4	,	,	PUNCT
cana-3963	202	5	the	the	DET
cana-3963	202	6	code	code	NOUN
cana-3963	202	7	’s	’s	PART
cana-3963	202	8	parameters	parameter	NOUN
cana-3963	202	9	are	be	AUX
cana-3963	202	10	2	2	NUM
cana-3963	202	11	1	1	NUM
cana-3963	202	12	[	[	PUNCT
cana-3963	202	13	,	,	PUNCT
cana-3963	202	14	,	,	PUNCT
cana-3963	202	15	]	]	PUNCT
cana-3963	202	16	,	,	PUNCT
cana-3963	202	17	s	s	VERB
cana-3963	202	18	i	i	NOUN
cana-3963	202	19	q	q	NOUN
cana-3963	203	1	i	i	INTJ
cana-3963	203	2	sn	sn	INTJ
cana-3963	204	1	k	k	PROPN
cana-3963	204	2	d	d	PROPN
cana-3963	204	3	=	=	SYM
cana-3963	204	4			PROPN
cana-3963	204	5	here	here	ADV
cana-3963	204	6	min	min	PROPN
cana-3963	204	7	{	{	PUNCT
cana-3963	204	8	(	(	PUNCT
cana-3963	204	9	)	)	PUNCT
cana-3963	204	10	}	}	PUNCT
cana-3963	204	11	.i	.i	NOUN
cana-3963	205	1	i	i	PRON
cana-3963	205	2	i	i	PROPN
cana-3963	206	1	d	d	PROPN
cana-3963	207	1	d	d	PROPN
cana-3963	207	2	a	a	DET
cana-3963	207	3	d=	d=	NOUN
cana-3963	207	4	communications	communication	NOUN
cana-3963	207	5	on	on	ADP
cana-3963	207	6	applied	apply	VERB
cana-3963	207	7	nonlinear	nonlinear	ADJ
cana-3963	207	8	analysis	analysis	NOUN
cana-3963	207	9	issn	issn	NOUN
cana-3963	207	10	:	:	PUNCT
cana-3963	207	11	1074	1074	NUM
cana-3963	207	12	-	-	PUNCT
cana-3963	207	13	133x	133x	NUM
cana-3963	207	14	vol	vol	NOUN
cana-3963	207	15	32	32	NUM
cana-3963	207	16	no	no	NOUN
cana-3963	207	17	.	.	PUNCT
cana-3963	208	1	9s	9s	NUM
cana-3963	208	2	(	(	PUNCT
cana-3963	208	3	2025	2025	NUM
cana-3963	208	4	)	)	PUNCT
cana-3963	208	5	548	548	NUM
cana-3963	208	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	208	7	4	4	NUM
cana-3963	208	8	.	.	PUNCT
cana-3963	209	1	codes	code	NOUN
cana-3963	209	2	obtained	obtain	VERB
cana-3963	209	3	from	from	ADP
cana-3963	209	4	mpc	mpc	PROPN
cana-3963	209	5	utilizing	utilize	VERB
cana-3963	209	6	hpc	hpc	NOUN
cana-3963	209	7	codes	code	NOUN
cana-3963	209	8	for	for	ADP
cana-3963	209	9	quantum	quantum	ADJ
cana-3963	209	10	system	system	NOUN
cana-3963	209	11	.	.	PUNCT
cana-3963	210	1	quantum	quantum	NOUN
cana-3963	210	2	codes	code	NOUN
cana-3963	210	3	are	be	AUX
cana-3963	210	4	crucial	crucial	ADJ
cana-3963	210	5	for	for	ADP
cana-3963	210	6	both	both	CCONJ
cana-3963	210	7	quantum	quantum	ADJ
cana-3963	210	8	communication	communication	NOUN
cana-3963	210	9	and	and	CCONJ
cana-3963	210	10	computation	computation	NOUN
cana-3963	210	11	.	.	PUNCT
cana-3963	211	1	from	from	ADP
cana-3963	211	2	the	the	DET
cana-3963	211	3	time	time	NOUN
cana-3963	211	4	of	of	ADP
cana-3963	211	5	noteworthy	noteworthy	ADJ
cana-3963	211	6	discoveries	discovery	NOUN
cana-3963	211	7	cited	cite	VERB
cana-3963	211	8	in	in	ADP
cana-3963	211	9	[	[	X
cana-3963	211	10	2	2	NUM
cana-3963	211	11	]	]	PUNCT
cana-3963	211	12	and	and	CCONJ
cana-3963	211	13	[	[	X
cana-3963	211	14	3	3	NUM
cana-3963	211	15	]	]	PUNCT
cana-3963	211	16	,	,	PUNCT
cana-3963	211	17	the	the	DET
cana-3963	211	18	field	field	NOUN
cana-3963	211	19	of	of	ADP
cana-3963	211	20	quantum	quantum	ADJ
cana-3963	211	21	information	information	NOUN
cana-3963	211	22	and	and	CCONJ
cana-3963	211	23	error	error	NOUN
cana-3963	211	24	correction	correction	NOUN
cana-3963	211	25	has	have	AUX
cana-3963	211	26	advanced	advance	VERB
cana-3963	211	27	rapidly	rapidly	ADV
cana-3963	211	28	.	.	PUNCT
cana-3963	212	1	recently	recently	ADV
cana-3963	212	2	,	,	PUNCT
cana-3963	212	3	the	the	DET
cana-3963	212	4	focus	focus	NOUN
cana-3963	212	5	has	have	AUX
cana-3963	212	6	been	be	AUX
cana-3963	212	7	on	on	ADP
cana-3963	212	8	constructing	construct	VERB
cana-3963	212	9	mds	mds	NOUN
cana-3963	212	10	codes	code	NOUN
cana-3963	212	11	,	,	PUNCT
cana-3963	212	12	which	which	PRON
cana-3963	212	13	are	be	AUX
cana-3963	212	14	central	central	ADJ
cana-3963	212	15	to	to	ADP
cana-3963	212	16	quantum	quantum	ADJ
cana-3963	212	17	coding	coding	NOUN
cana-3963	212	18	theory	theory	NOUN
cana-3963	212	19	.	.	PUNCT
cana-3963	213	1	these	these	DET
cana-3963	213	2	quantum	quantum	PROPN
cana-3963	213	3	mds	mds	NOUN
cana-3963	213	4	codes	code	NOUN
cana-3963	213	5	are	be	AUX
cana-3963	213	6	developed	develop	VERB
cana-3963	213	7	utilizing	utilize	VERB
cana-3963	213	8	the	the	DET
cana-3963	213	9	hermitian	hermitian	ADJ
cana-3963	213	10	codes	code	NOUN
cana-3963	213	11	together	together	ADV
cana-3963	213	12	with	with	ADP
cana-3963	213	13	quantum	quantum	PROPN
cana-3963	213	14	singleton	singleton	NOUN
cana-3963	213	15	bound	bind	VERB
cana-3963	213	16	.	.	PUNCT
cana-3963	214	1	to	to	PART
cana-3963	214	2	obtain	obtain	VERB
cana-3963	214	3	quantum	quantum	NOUN
cana-3963	214	4	mds	mds	NOUN
cana-3963	214	5	codes	code	NOUN
cana-3963	214	6	,	,	PUNCT
cana-3963	214	7	it	it	PRON
cana-3963	214	8	's	be	AUX
cana-3963	214	9	necessary	necessary	ADJ
cana-3963	214	10	to	to	PART
cana-3963	214	11	identify	identify	VERB
cana-3963	214	12	the	the	DET
cana-3963	214	13	mds	mds	NOUN
cana-3963	214	14	codes	code	NOUN
cana-3963	214	15	over	over	ADP
cana-3963	214	16	2q	2q	NUM
cana-3963	214	17	f	f	NOUN
cana-3963	214	18	that	that	PRON
cana-3963	214	19	satisfy	satisfy	VERB
cana-3963	214	20	h	h	NOUN
cana-3963	214	21	⊥	⊥	PROPN
cana-3963	214	22			PROPN
cana-3963	214	23	.	.	PUNCT
cana-3963	215	1	this	this	DET
cana-3963	215	2	approach	approach	NOUN
cana-3963	215	3	has	have	AUX
cana-3963	215	4	led	lead	VERB
cana-3963	215	5	to	to	ADP
cana-3963	215	6	the	the	DET
cana-3963	215	7	creation	creation	NOUN
cana-3963	215	8	of	of	ADP
cana-3963	215	9	several	several	ADJ
cana-3963	215	10	new	new	ADJ
cana-3963	215	11	category	category	NOUN
cana-3963	215	12	of	of	ADP
cana-3963	215	13	mds	mds	PROPN
cana-3963	215	14	codes	code	NOUN
cana-3963	215	15	for	for	ADP
cana-3963	215	16	quantum	quantum	ADJ
cana-3963	215	17	system	system	NOUN
cana-3963	215	18	.	.	PUNCT
cana-3963	216	1	for	for	ADP
cana-3963	216	2	instance	instance	NOUN
cana-3963	216	3	,	,	PUNCT
cana-3963	216	4	guardia	guardia	PROPN
cana-3963	216	5	[	[	X
cana-3963	216	6	20	20	NUM
cana-3963	216	7	]	]	PUNCT
cana-3963	216	8	constructed	construct	VERB
cana-3963	216	9	quantum	quantum	NOUN
cana-3963	216	10	codes	code	NOUN
cana-3963	216	11	utilizing	utilize	VERB
cana-3963	216	12	cyclic	cyclic	ADJ
cana-3963	216	13	codes	code	NOUN
cana-3963	216	14	,	,	PUNCT
cana-3963	216	15	while	while	SCONJ
cana-3963	216	16	kai	kai	PROPN
cana-3963	216	17	and	and	CCONJ
cana-3963	216	18	zhu	zhu	PROPN
cana-3963	216	19	gave	give	VERB
cana-3963	216	20	negacyclic	negacyclic	ADJ
cana-3963	216	21	codes	code	NOUN
cana-3963	216	22	which	which	PRON
cana-3963	216	23	aided	aid	VERB
cana-3963	216	24	in	in	ADP
cana-3963	216	25	developing	develop	VERB
cana-3963	216	26	new	new	ADJ
cana-3963	216	27	categories	category	NOUN
cana-3963	216	28	of	of	ADP
cana-3963	216	29	quantum	quantum	PROPN
cana-3963	216	30	mds	mds	NOUN
cana-3963	216	31	codes	code	NOUN
cana-3963	216	32	.	.	PUNCT
cana-3963	217	1	inspired	inspire	VERB
cana-3963	217	2	by	by	ADP
cana-3963	217	3	the	the	DET
cana-3963	217	4	work	work	NOUN
cana-3963	217	5	referenced	reference	VERB
cana-3963	217	6	in	in	ADP
cana-3963	217	7	[	[	X
cana-3963	217	8	6	6	NUM
cana-3963	217	9	]	]	PUNCT
cana-3963	217	10	,	,	PUNCT
cana-3963	217	11	kai	kai	PROPN
cana-3963	217	12	et	et	PROPN
cana-3963	217	13	al	al	PROPN
cana-3963	217	14	.	.	PROPN
cana-3963	217	15	introduced	introduce	VERB
cana-3963	217	16	many	many	ADJ
cana-3963	217	17	quantum	quantum	NOUN
cana-3963	217	18	mds	mds	NOUN
cana-3963	217	19	codes	code	NOUN
cana-3963	217	20	from	from	ADP
cana-3963	217	21	constacyclic	constacyclic	ADJ
cana-3963	217	22	codes	code	NOUN
cana-3963	217	23	with	with	ADP
cana-3963	217	24	advanced	advanced	ADJ
cana-3963	217	25	parameters	parameter	NOUN
cana-3963	217	26	.	.	PUNCT
cana-3963	218	1	let	let	VERB
cana-3963	218	2	’s	’s	PRON
cana-3963	218	3	review	review	VERB
cana-3963	218	4	some	some	DET
cana-3963	218	5	foundational	foundational	ADJ
cana-3963	218	6	idea	idea	NOUN
cana-3963	218	7	and	and	CCONJ
cana-3963	218	8	consequence	consequence	NOUN
cana-3963	218	9	of	of	ADP
cana-3963	218	10	quantum	quantum	ADJ
cana-3963	218	11	codes	code	NOUN
cana-3963	218	12	.	.	PUNCT
cana-3963	219	1	for	for	ADP
cana-3963	219	2	additional	additional	ADJ
cana-3963	219	3	details	detail	NOUN
cana-3963	219	4	,	,	PUNCT
cana-3963	219	5	refer	refer	VERB
cana-3963	219	6	to	to	ADP
cana-3963	219	7	[	[	X
cana-3963	219	8	21	21	NUM
cana-3963	219	9	]	]	PUNCT
cana-3963	219	10	.	.	PUNCT
cana-3963	220	1	let	let	VERB
cana-3963	220	2	...	...	PUNCT
cana-3963	221	1	nq	nq	PROPN
cana-3963	221	2	q	q	NOUN
cana-3963	221	3	q	q	X
cana-3963	221	4	q	q	PROPN
cana-3963	221	5	nv	nv	PROPN
cana-3963	221	6			NOUN
cana-3963	221	7			X
cana-3963	222	1			X
cana-3963	222	2	=	=	PROPN
cana-3963	222	3	=	=	PUNCT
cana-3963	222	4			NOUN
cana-3963	222	5			PRON
cana-3963	222	6			ADJ
cana-3963	222	7	(	(	PUNCT
cana-3963	222	8	n	n	CCONJ
cana-3963	222	9	-	-	PUNCT
cana-3963	222	10	times	time	NOUN
cana-3963	222	11	)	)	PUNCT
cana-3963	222	12	denote	denote	VERB
cana-3963	222	13	the	the	DET
cana-3963	222	14	hilbert	hilbert	NOUN
cana-3963	222	15	space	space	NOUN
cana-3963	222	16	.	.	PUNCT
cana-3963	223	1	suppose	suppose	VERB
cana-3963	223	2	that	that	SCONJ
cana-3963	223	3	x	x	SYM
cana-3963	223	4	ket	ket	NOUN
cana-3963	223	5	vector	vector	NOUN
cana-3963	223	6	belongs	belong	VERB
cana-3963	223	7	to	to	ADP
cana-3963	223	8	orthonormal	orthonormal	ADJ
cana-3963	223	9	basis	basis	NOUN
cana-3963	223	10	of	of	ADP
cana-3963	223	11	the	the	DET
cana-3963	223	12	code	code	NOUN
cana-3963	223	13	,	,	PUNCT
cana-3963	223	14	nq	nq	PUNCT
cana-3963	223	15	here	here	ADV
cana-3963	223	16	the	the	DET
cana-3963	223	17	elements	element	NOUN
cana-3963	223	18	x	x	PUNCT
cana-3963	223	19	belongs	belong	VERB
cana-3963	223	20	to	to	ADP
cana-3963	223	21	.qf	.qf	PUNCT
cana-3963	223	22	then	then	ADV
cana-3963	223	23	the	the	DET
cana-3963	223	24	orthonormal	orthonormal	ADJ
cana-3963	223	25	basis	basis	NOUN
cana-3963	223	26	of	of	ADP
cana-3963	223	27	nv	nv	PROPN
cana-3963	223	28	is	be	AUX
cana-3963	223	29	defined	define	VERB
cana-3963	223	30	as	as	ADP
cana-3963	223	31			PROPN
cana-3963	223	32	1	1	NOUN
cana-3963	223	33	2	2	NUM
cana-3963	223	34	...	...	PUNCT
cana-3963	223	35	nc	nc	PROPN
cana-3963	223	36	c	c	PROPN
cana-3963	223	37	c	c	PROPN
cana-3963	223	38	c=	c=	VERB
cana-3963	224	1			PROPN
cana-3963	224	2	1	1	NOUN
cana-3963	224	3	2	2	NUM
cana-3963	224	4	1	1	NUM
cana-3963	224	5	2	2	NUM
cana-3963	224	6	...	...	PUNCT
cana-3963	224	7	:	:	PUNCT
cana-3963	225	1	c	c	X
cana-3963	225	2	(	(	PUNCT
cana-3963	225	3	,	,	PUNCT
cana-3963	225	4	,	,	PUNCT
cana-3963	225	5	...	...	PUNCT
cana-3963	225	6	,	,	PUNCT
cana-3963	225	7	c	c	NOUN
cana-3963	225	8	)	)	PUNCT
cana-3963	225	9	}	}	PUNCT
cana-3963	225	10	q	q	PROPN
cana-3963	225	11	n	n	CCONJ
cana-3963	225	12	n	n	INTJ
cana-3963	225	13	nc	nc	PROPN
cana-3963	225	14	c	c	NOUN
cana-3963	225	15	c	c	PROPN
cana-3963	225	16	c	c	PROPN
cana-3963	225	17	c	c	NOUN
cana-3963	225	18	f=	f=	PROPN
cana-3963	225	19			ADP
cana-3963	225	20			PRON
cana-3963	225	21			NOUN
cana-3963	225	22	=	=	PRON
cana-3963	225	23			NOUN
cana-3963	225	24	let	let	VERB
cana-3963	225	25	,	,	PUNCT
cana-3963	225	26	qa	qa	PROPN
cana-3963	225	27	b	b	PROPN
cana-3963	225	28	f	f	PROPN
cana-3963	225	29	be	be	AUX
cana-3963	225	30	any	any	DET
cana-3963	225	31	two	two	NUM
cana-3963	225	32	elements	element	NOUN
cana-3963	225	33	and	and	CCONJ
cana-3963	225	34	exp(2	exp(2	NOUN
cana-3963	225	35	)	)	PUNCT
cana-3963	226	1	i	i	PRON
cana-3963	226	2	p	p	VERB
cana-3963	227	1	=	=	NOUN
cana-3963	227	2	denote	denote	VERB
cana-3963	227	3	the	the	DET
cana-3963	227	4	primitive	primitive	ADJ
cana-3963	227	5	thp	thp	PROPN
cana-3963	227	6	root	root	NOUN
cana-3963	227	7	of	of	ADP
cana-3963	227	8	unity	unity	NOUN
cana-3963	227	9	.	.	PUNCT
cana-3963	228	1	first	first	ADV
cana-3963	228	2	define	define	VERB
cana-3963	228	3	tr	tr	NOUN
cana-3963	228	4	as	as	ADP
cana-3963	228	5	the	the	DET
cana-3963	228	6	trace	trace	NOUN
cana-3963	228	7	map	map	NOUN
cana-3963	228	8	from	from	ADP
cana-3963	228	9	.q	.q	PROPN
cana-3963	228	10	pf	pf	PROPN
cana-3963	228	11	f→	f→	PROPN
cana-3963	228	12	then	then	ADV
cana-3963	228	13	unitary	unitary	ADJ
cana-3963	228	14	error	error	NOUN
cana-3963	228	15	operators	operator	NOUN
cana-3963	228	16	(	(	PUNCT
cana-3963	228	17	)	)	PUNCT
cana-3963	228	18	x	x	PROPN
cana-3963	228	19	a	a	PROPN
cana-3963	228	20	and	and	CCONJ
cana-3963	228	21	(	(	PUNCT
cana-3963	228	22	)	)	PUNCT
cana-3963	228	23	z	z	NOUN
cana-3963	228	24	b	b	NOUN
cana-3963	228	25	in	in	ADP
cana-3963	228	26	q	q	NOUN
cana-3963	228	27	are	be	AUX
cana-3963	228	28	defined	define	VERB
cana-3963	228	29	by	by	ADP
cana-3963	228	30	(	(	PUNCT
cana-3963	228	31	)	)	PUNCT
cana-3963	228	32	x	x	SYM
cana-3963	228	33	a	a	PRON
cana-3963	228	34	x	x	X
cana-3963	228	35	x	x	X
cana-3963	228	36	a=	a=	VERB
cana-3963	228	37	+	+	PUNCT
cana-3963	228	38	and	and	CCONJ
cana-3963	228	39	(	(	PUNCT
cana-3963	228	40	)	)	PUNCT
cana-3963	228	41	(	(	PUNCT
cana-3963	228	42	)	)	PUNCT
cana-3963	228	43	tr	tr	VERB
cana-3963	228	44	bxz	bxz	VERB
cana-3963	228	45	b	b	PROPN
cana-3963	228	46	x	x	X
cana-3963	228	47	x=	x=	NUM
cana-3963	228	48	respectively	respectively	ADV
cana-3963	228	49	.	.	PUNCT
cana-3963	229	1	for	for	ADP
cana-3963	229	2	1	1	NUM
cana-3963	229	3	2	2	NUM
cana-3963	229	4	(	(	PUNCT
cana-3963	229	5	,	,	PUNCT
cana-3963	229	6	,	,	PUNCT
cana-3963	229	7	...	...	PUNCT
cana-3963	229	8	,	,	PUNCT
cana-3963	229	9	)	)	PUNCT
cana-3963	229	10	q	q	PROPN
cana-3963	230	1	n	n	INTJ
cana-3963	230	2	na	na	ADP
cana-3963	230	3	a	a	DET
cana-3963	230	4	a	a	DET
cana-3963	230	5	a	a	DET
cana-3963	230	6	f=	f=	ADJ
cana-3963	230	7			NOUN
cana-3963	230	8	we	we	PRON
cana-3963	230	9	define	define	VERB
cana-3963	230	10	1	1	NUM
cana-3963	230	11	2	2	NUM
cana-3963	230	12	(	(	PUNCT
cana-3963	230	13	)	)	PUNCT
cana-3963	230	14	(	(	PUNCT
cana-3963	230	15	)	)	PUNCT
cana-3963	230	16	(	(	PUNCT
cana-3963	230	17	)	)	PUNCT
cana-3963	230	18	...	...	PUNCT
cana-3963	231	1	(	(	PUNCT
cana-3963	231	2	)	)	PUNCT
cana-3963	231	3	nx	nx	PROPN
cana-3963	231	4	a	a	DET
cana-3963	231	5	x	x	SYM
cana-3963	231	6	a	a	DET
cana-3963	231	7	x	x	SYM
cana-3963	231	8	a	a	DET
cana-3963	231	9	x	x	X
cana-3963	231	10	a=	a=	ADV
cana-3963	231	11			ADJ
cana-3963	231	12			ADP
cana-3963	231	13			ADP
cana-3963	231	14	and	and	CCONJ
cana-3963	231	15	1	1	NUM
cana-3963	231	16	2	2	NUM
cana-3963	231	17	(	(	PUNCT
cana-3963	231	18	)	)	PUNCT
cana-3963	231	19	(	(	PUNCT
cana-3963	231	20	)	)	PUNCT
cana-3963	231	21	(	(	PUNCT
cana-3963	231	22	)	)	PUNCT
cana-3963	231	23	...	...	PUNCT
cana-3963	232	1	(	(	PUNCT
cana-3963	232	2	)	)	PUNCT
cana-3963	232	3	nz	nz	PROPN
cana-3963	232	4	a	a	DET
cana-3963	232	5	z	z	NOUN
cana-3963	232	6	a	a	DET
cana-3963	232	7	z	z	NOUN
cana-3963	232	8	a	a	DET
cana-3963	232	9	z	z	NOUN
cana-3963	232	10	a=	a=	NOUN
cana-3963	232	11			NOUN
cana-3963	232	12			ADJ
cana-3963	232	13			ADP
cana-3963	232	14	to	to	PART
cana-3963	232	15	be	be	AUX
cana-3963	232	16	the	the	DET
cana-3963	232	17	error	error	NOUN
cana-3963	232	18	operators	operator	NOUN
cana-3963	232	19	.	.	PUNCT
cana-3963	233	1	the	the	DET
cana-3963	233	2	error	error	NOUN
cana-3963	233	3	basis	basis	NOUN
cana-3963	233	4	for	for	ADP
cana-3963	233	5	complex	complex	ADJ
cana-3963	233	6	vector	vector	NOUN
cana-3963	233	7	space	space	NOUN
cana-3963	233	8	nq	nq	VERB
cana-3963	233	9	is	be	AUX
cana-3963	233	10	{	{	PUNCT
cana-3963	233	11	(	(	PUNCT
cana-3963	233	12	)	)	PUNCT
cana-3963	233	13	(	(	PUNCT
cana-3963	233	14	)	)	PUNCT
cana-3963	233	15	}	}	PUNCT
cana-3963	233	16	,	,	PUNCT
cana-3963	233	17	q	q	NOUN
cana-3963	233	18	n	n	X
cana-3963	233	19	ne	ne	X
cana-3963	233	20	x	x	X
cana-3963	233	21	a	a	DET
cana-3963	233	22	z	z	PROPN
cana-3963	233	23	b	b	PROPN
cana-3963	233	24	a	a	DET
cana-3963	233	25	b	b	NOUN
cana-3963	233	26	f=	f=	ADJ
cana-3963	233	27	∣	∣	NOUN
cana-3963	233	28	and	and	CCONJ
cana-3963	233	29	{	{	PUNCT
cana-3963	233	30	(	(	PUNCT
cana-3963	233	31	)	)	PUNCT
cana-3963	233	32	(	(	PUNCT
cana-3963	233	33	)	)	PUNCT
cana-3963	233	34	,	,	PUNCT
cana-3963	233	35	}	}	PUNCT
cana-3963	233	36	,	,	PUNCT
cana-3963	233	37	c	c	PROPN
cana-3963	233	38	q	q	PROPN
cana-3963	233	39	n	n	PROPN
cana-3963	233	40	n	n	INTJ
cana-3963	233	41	pg	pg	VERB
cana-3963	233	42	x	x	PROPN
cana-3963	233	43	a	a	DET
cana-3963	233	44	z	z	PROPN
cana-3963	233	45	b	b	PROPN
cana-3963	233	46	a	a	PRON
cana-3963	233	47	b	b	NOUN
cana-3963	233	48	f	f	PROPN
cana-3963	233	49	c	c	PROPN
cana-3963	233	50	f=	f=	NOUN
cana-3963	233	51			PROPN
cana-3963	233	52	∣	∣	NOUN
cana-3963	233	53	is	be	AUX
cana-3963	233	54	the	the	DET
cana-3963	233	55	error	error	NOUN
cana-3963	233	56	group	group	NOUN
cana-3963	233	57	associated	associate	VERB
cana-3963	233	58	with	with	ADP
cana-3963	233	59	.ne	.ne	PUNCT
cana-3963	233	60	theorem	theorem	VERB
cana-3963	233	61	3	3	NUM
cana-3963	233	62	[	[	X
cana-3963	233	63	10	10	NUM
cana-3963	233	64	]	]	PUNCT
cana-3963	233	65	:	:	PUNCT
cana-3963	233	66	let	let	VERB
cana-3963	233	67	2	2	NUM
cana-3963	233	68	[	[	PUNCT
cana-3963	233	69	,	,	PUNCT
cana-3963	233	70	,	,	PUNCT
cana-3963	233	71	]	]	PUNCT
cana-3963	233	72	q	q	PROPN
cana-3963	234	1	n	n	CCONJ
cana-3963	234	2	k	k	PROPN
cana-3963	234	3	d	d	NOUN
cana-3963	234	4	is	be	AUX
cana-3963	234	5	a	a	DET
cana-3963	234	6	linear	linear	ADJ
cana-3963	234	7	code	code	NOUN
cana-3963	234	8	denoted	denote	VERB
cana-3963	234	9	by	by	ADP
cana-3963	234	10			NOUN
cana-3963	234	11	and	and	CCONJ
cana-3963	234	12	suppose	suppose	VERB
cana-3963	234	13	its	its	PRON
cana-3963	234	14	generator	generator	NOUN
cana-3963	234	15	matrix	matrix	NOUN
cana-3963	234	16	is	be	AUX
cana-3963	234	17	.g	.g	PROPN
cana-3963	234	18	then	then	ADV
cana-3963	234	19	a	a	DET
cana-3963	234	20	quantum	quantum	ADJ
cana-3963	234	21	code	code	NOUN
cana-3963	234	22	[	[	X
cana-3963	234	23	[	[	PUNCT
cana-3963	234	24	,	,	PUNCT
cana-3963	234	25	2	2	NUM
cana-3963	234	26	,	,	PUNCT
cana-3963	234	27	]	]	X
cana-3963	234	28	]	]	PUNCT
cana-3963	234	29	,	,	PUNCT
cana-3963	234	30	qn	qn	PROPN
cana-3963	234	31	k	k	PROPN
cana-3963	234	32	n	n	CCONJ
cana-3963	234	33	d−	d−	PROPN
cana-3963	234	34			NUM
cana-3963	234	35	exists	exist	VERB
cana-3963	234	36	if	if	SCONJ
cana-3963	234	37	(	(	PUNCT
cana-3963	234	38	(	(	PUNCT
cana-3963	234	39	)	)	PUNCT
cana-3963	234	40	)	)	PUNCT
cana-3963	234	41	2	2	NUM
cana-3963	234	42	,	,	PUNCT
cana-3963	234	43	q	q	NOUN
cana-3963	234	44	tg	tg	PROPN
cana-3963	234	45	g	g	PROPN
cana-3963	234	46	k	k	PROPN
cana-3963	234	47	n	n	VERB
cana-3963	234	48			NOUN
cana-3963	234	49	−	−	ADP
cana-3963	234	50	and	and	CCONJ
cana-3963	234	51	2	2	NUM
cana-3963	234	52	.k	.k	NOUN
cana-3963	234	53	n	n	PROPN
cana-3963	234	54	theorem	theorem	VERB
cana-3963	234	55	4	4	NUM
cana-3963	234	56	:	:	PUNCT
cana-3963	234	57	if	if	SCONJ
cana-3963	234	58	a	a	PRON
cana-3963	234	59	denote	denote	NOUN
cana-3963	234	60	a	a	DET
cana-3963	234	61	monomial	monomial	ADJ
cana-3963	234	62	matrix	matrix	NOUN
cana-3963	234	63	of	of	ADP
cana-3963	234	64	size	size	NOUN
cana-3963	234	65	n	n	CCONJ
cana-3963	234	66	with	with	ADP
cana-3963	234	67	non	non	ADJ
cana-3963	234	68	-	-	ADJ
cana-3963	234	69	zero	zero	NUM
cana-3963	234	70	elements	element	NOUN
cana-3963	234	71	0	0	NUM
cana-3963	234	72	1	1	NUM
cana-3963	234	73	1	1	NUM
cana-3963	234	74	,	,	PUNCT
cana-3963	234	75	,	,	PUNCT
cana-3963	234	76	,	,	PUNCT
cana-3963	234	77	,	,	PUNCT
cana-3963	234	78	n	n	PROPN
cana-3963	234	79	qa	qa	VERB
cana-3963	234	80	a	a	DET
cana-3963	234	81	a	a	DET
cana-3963	234	82	f−	f−	PROPN
cana-3963	234	83			NOUN
cana-3963	234	84	then	then	ADV
cana-3963	234	85	there	there	PRON
cana-3963	234	86	exist	exist	VERB
cana-3963	234	87	a	a	DET
cana-3963	234	88	permutation	permutation	NOUN
cana-3963	234	89	ns	ns	PROPN
cana-3963	234	90			NOUN
cana-3963	234	91	such	such	ADJ
cana-3963	234	92	that	that	SCONJ
cana-3963	234	93	0	0	NUM
cana-3963	234	94	1	1	NUM
cana-3963	234	95	1	1	NUM
cana-3963	234	96	(	(	PUNCT
cana-3963	234	97	,	,	PUNCT
cana-3963	234	98	,	,	PUNCT
cana-3963	234	99	,	,	PUNCT
cana-3963	234	100	)	)	PUNCT
cana-3963	234	101	na	na	PART
cana-3963	234	102	diag	diag	VERB
cana-3963	234	103	a	a	DET
cana-3963	234	104	a	a	DET
cana-3963	234	105	a	a	DET
cana-3963	234	106	p−=	p−=	PROPN
cana-3963	234	107			ADP
cana-3963	234	108	where	where	SCONJ
cana-3963	234	109	p	p	NOUN
cana-3963	234	110	is	be	AUX
cana-3963	234	111	the	the	DET
cana-3963	234	112	matrix	matrix	NOUN
cana-3963	234	113	with	with	ADP
cana-3963	234	114	respect	respect	NOUN
cana-3963	234	115	to	to	ADP
cana-3963	234	116	the	the	DET
cana-3963	234	117	permutation	permutation	NOUN
cana-3963	235	1	.	.	PROPN
cana-3963	235	2	proof	proof	NOUN
cana-3963	235	3	:	:	PUNCT
cana-3963	235	4	let	let	VERB
cana-3963	235	5	1	1	NUM
cana-3963	235	6	2	2	NUM
cana-3963	235	7	1	1	NUM
cana-3963	235	8	2	2	NUM
cana-3963	235	9	n	n	CCONJ
cana-3963	235	10	n	n	PROPN
cana-3963	235	11	z	z	NOUN
cana-3963	235	12	z	z	NOUN
cana-3963	235	13	z	z	NOUN
cana-3963	235	14			PROPN
cana-3963	235	15			NOUN
cana-3963	235	16			NOUN
cana-3963	235	17	=	=	SYM
cana-3963	235	18			PROPN
cana-3963	235	19			PROPN
cana-3963	236	1			ADJ
cana-3963	236	2			NOUN
cana-3963	236	3	be	be	VERB
cana-3963	236	4	any	any	DET
cana-3963	236	5	permutation	permutation	NOUN
cana-3963	236	6	on	on	ADP
cana-3963	236	7	,	,	PUNCT
cana-3963	236	8	ns	ns	INTJ
cana-3963	236	9	then	then	ADV
cana-3963	236	10	we	we	PRON
cana-3963	236	11	can	can	AUX
cana-3963	236	12	obtain	obtain	VERB
cana-3963	236	13	a	a	DET
cana-3963	236	14	permutation	permutation	NOUN
cana-3963	236	15	matrix	matrix	NOUN
cana-3963	236	16	p	p	NOUN
cana-3963	236	17	for	for	ADP
cana-3963	236	18			PROPN
cana-3963	236	19	as	as	SCONJ
cana-3963	236	20	communications	communication	NOUN
cana-3963	236	21	on	on	ADP
cana-3963	236	22	applied	apply	VERB
cana-3963	236	23	nonlinear	nonlinear	ADJ
cana-3963	236	24	analysis	analysis	NOUN
cana-3963	236	25	issn	issn	NOUN
cana-3963	236	26	:	:	PUNCT
cana-3963	236	27	1074	1074	NUM
cana-3963	236	28	-	-	PUNCT
cana-3963	236	29	133x	133x	NUM
cana-3963	236	30	vol	vol	NOUN
cana-3963	236	31	32	32	NUM
cana-3963	236	32	no	no	NOUN
cana-3963	236	33	.	.	PUNCT
cana-3963	237	1	9s	9s	NUM
cana-3963	237	2	(	(	PUNCT
cana-3963	237	3	2025	2025	NUM
cana-3963	237	4	)	)	PUNCT
cana-3963	237	5	549	549	NUM
cana-3963	237	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	237	7	1	1	NUM
cana-3963	237	8	2	2	NUM
cana-3963	237	9	n	n	PROPN
cana-3963	237	10	z	z	NOUN
cana-3963	237	11	z	z	NOUN
cana-3963	238	1	p	p	PROPN
cana-3963	238	2	z	z	PROPN
cana-3963	238	3			PROPN
cana-3963	238	4			NOUN
cana-3963	238	5			NOUN
cana-3963	238	6			PROPN
cana-3963	239	1			PROPN
cana-3963	239	2			PROPN
cana-3963	239	3	=	=	PROPN
cana-3963	239	4			PROPN
cana-3963	240	1			PROPN
cana-3963	241	1			PROPN
cana-3963	241	2			PROPN
cana-3963	242	1			ADJ
cana-3963	242	2			NOUN
cana-3963	242	3	where	where	SCONJ
cana-3963	242	4	thi	thi	AUX
cana-3963	242	5	row	row	NOUN
cana-3963	242	6	of	of	ADP
cana-3963	242	7	the	the	DET
cana-3963	242	8	identity	identity	NOUN
cana-3963	242	9	matrix	matrix	NOUN
cana-3963	242	10	goes	go	VERB
cana-3963	242	11	to	to	ADP
cana-3963	242	12	the	the	DET
cana-3963	242	13	th	th	X
cana-3963	242	14	iz	iz	NOUN
cana-3963	242	15	row	row	NOUN
cana-3963	242	16	of	of	ADP
cana-3963	242	17	the	the	DET
cana-3963	242	18	n	n	ADV
cana-3963	242	19	n	n	ADJ
cana-3963	242	20	identity	identity	NOUN
cana-3963	242	21	matrix	matrix	NOUN
cana-3963	242	22	.	.	PUNCT
cana-3963	243	1	now	now	ADV
cana-3963	243	2	,	,	PUNCT
cana-3963	243	3	let	let	VERB
cana-3963	243	4	11	11	NUM
cana-3963	243	5	22	22	NUM
cana-3963	243	6	0	0	NUM
cana-3963	243	7	0	0	NUM
cana-3963	243	8	0	0	NUM
cana-3963	243	9	0	0	NUM
cana-3963	243	10	0	0	NUM
cana-3963	243	11	0	0	NUM
cana-3963	243	12	0	0	NUM
cana-3963	243	13	0	0	NUM
cana-3963	243	14	0	0	NUM
cana-3963	243	15	nn	nn	PROPN
cana-3963	243	16	d	d	PROPN
cana-3963	243	17	d	d	PROPN
cana-3963	243	18	d	d	PROPN
cana-3963	243	19	d	d	X
cana-3963	243	20			NOUN
cana-3963	243	21			PROPN
cana-3963	243	22			PROPN
cana-3963	244	1			PROPN
cana-3963	244	2			PROPN
cana-3963	244	3	=	=	PROPN
cana-3963	244	4			PROPN
cana-3963	245	1			PROPN
cana-3963	246	1			PROPN
cana-3963	246	2			PROPN
cana-3963	247	1			PROPN
cana-3963	247	2			NOUN
cana-3963	247	3	be	be	VERB
cana-3963	247	4	a	a	DET
cana-3963	247	5	diagonal	diagonal	ADJ
cana-3963	247	6	matrix	matrix	NOUN
cana-3963	247	7	with	with	ADP
cana-3963	247	8	*	*	PUNCT
cana-3963	247	9	ii	ii	PROPN
cana-3963	247	10	qd	qd	ADP
cana-3963	247	11	f	f	PROPN
cana-3963	247	12	(	(	PUNCT
cana-3963	247	13	0iid	0iid	NOUN
cana-3963	247	14			VERB
cana-3963	247	15	for	for	ADP
cana-3963	247	16	each	each	DET
cana-3963	247	17	i	i	NOUN
cana-3963	247	18	)	)	PUNCT
cana-3963	247	19	.	.	PUNCT
cana-3963	248	1	to	to	PART
cana-3963	248	2	construct	construct	VERB
cana-3963	248	3	a	a	DET
cana-3963	248	4	monomial	monomial	ADJ
cana-3963	248	5	matrix	matrix	NOUN
cana-3963	248	6	from	from	ADP
cana-3963	248	7	the	the	DET
cana-3963	248	8	permutation	permutation	NOUN
cana-3963	248	9			X
cana-3963	248	10	and	and	CCONJ
cana-3963	248	11	diagonal	diagonal	ADJ
cana-3963	248	12	matrix	matrix	NOUN
cana-3963	248	13	,	,	PUNCT
cana-3963	248	14	d	d	NOUN
cana-3963	248	15	multiplying	multiplying	NOUN
cana-3963	248	16	d	d	PROPN
cana-3963	248	17	and	and	CCONJ
cana-3963	248	18	,	,	PUNCT
cana-3963	248	19	p	p	NOUN
cana-3963	248	20	we	we	PRON
cana-3963	248	21	get	get	VERB
cana-3963	248	22	a	a	DET
cana-3963	248	23	dp=	dp=	ADJ
cana-3963	248	24	11	11	NUM
cana-3963	248	25	1	1	NUM
cana-3963	248	26	22	22	NUM
cana-3963	248	27	2	2	NUM
cana-3963	248	28	0	0	NUM
cana-3963	248	29	0	0	NUM
cana-3963	248	30	0	0	NUM
cana-3963	248	31	0	0	NUM
cana-3963	248	32	0	0	NUM
cana-3963	248	33	0	0	NUM
cana-3963	248	34	0	0	NUM
cana-3963	248	35	0	0	NUM
cana-3963	248	36	0	0	NUM
cana-3963	248	37	nn	nn	PROPN
cana-3963	248	38	n	n	PROPN
cana-3963	249	1	d	d	PROPN
cana-3963	249	2	z	z	PROPN
cana-3963	249	3	d	d	X
cana-3963	249	4	z	z	NOUN
cana-3963	249	5	d	d	PROPN
cana-3963	249	6	z	z	PROPN
cana-3963	249	7			NOUN
cana-3963	249	8			PROPN
cana-3963	249	9			NOUN
cana-3963	249	10			PROPN
cana-3963	249	11			PROPN
cana-3963	250	1			PROPN
cana-3963	251	1			PROPN
cana-3963	252	1			INTJ
cana-3963	253	1			PROPN
cana-3963	254	1			PROPN
cana-3963	255	1			PROPN
cana-3963	256	1	=	=	PROPN
cana-3963	256	2			VERB
cana-3963	256	3			PROPN
cana-3963	257	1			PROPN
cana-3963	258	1			PROPN
cana-3963	259	1			INTJ
cana-3963	260	1			PROPN
cana-3963	261	1			INTJ
cana-3963	262	1			PROPN
cana-3963	262	2			PROPN
cana-3963	263	1			ADJ
cana-3963	263	2			PROPN
cana-3963	263	3			PROPN
cana-3963	263	4			NOUN
cana-3963	263	5	11	11	NUM
cana-3963	263	6	22	22	NUM
cana-3963	263	7	nn	nn	PROPN
cana-3963	264	1	d	d	PROPN
cana-3963	264	2	d	d	PROPN
cana-3963	264	3	d	d	X
cana-3963	264	4			NOUN
cana-3963	264	5			PROPN
cana-3963	264	6			PROPN
cana-3963	265	1			PROPN
cana-3963	265	2			PROPN
cana-3963	265	3	=	=	PROPN
cana-3963	265	4			PROPN
cana-3963	266	1			PROPN
cana-3963	267	1			PROPN
cana-3963	267	2			PROPN
cana-3963	268	1			ADJ
cana-3963	268	2			NOUN
cana-3963	268	3	where	where	SCONJ
cana-3963	268	4	each	each	DET
cana-3963	268	5	iid	iid	NOUN
cana-3963	268	6	occurs	occur	VERB
cana-3963	268	7	in	in	ADP
cana-3963	268	8	some	some	DET
cana-3963	268	9	order	order	NOUN
cana-3963	268	10	.	.	PUNCT
cana-3963	269	1	hence	hence	ADV
cana-3963	269	2	,	,	PUNCT
cana-3963	269	3	the	the	DET
cana-3963	269	4	matrix	matrix	NOUN
cana-3963	269	5	a	a	PRON
cana-3963	269	6	defined	define	VERB
cana-3963	269	7	above	above	ADV
cana-3963	269	8	is	be	AUX
cana-3963	269	9	a	a	DET
cana-3963	269	10	monomial	monomial	ADJ
cana-3963	269	11	matrix	matrix	NOUN
cana-3963	269	12	.	.	PUNCT
cana-3963	270	1	example	example	NOUN
cana-3963	270	2	1	1	NUM
cana-3963	270	3	:	:	PUNCT
cana-3963	270	4	let	let	VERB
cana-3963	270	5			NOUN
cana-3963	270	6	denote	denote	VERB
cana-3963	270	7	an	an	DET
cana-3963	270	8	2	2	NUM
cana-3963	270	9	[	[	PUNCT
cana-3963	270	10	,	,	PUNCT
cana-3963	270	11	,	,	PUNCT
cana-3963	270	12	]	]	PUNCT
cana-3963	270	13	q	q	PROPN
cana-3963	271	1	n	n	CCONJ
cana-3963	271	2	k	k	NOUN
cana-3963	271	3	d	d	X
cana-3963	271	4	linear	linear	PROPN
cana-3963	271	5	code	code	NOUN
cana-3963	271	6	with	with	ADP
cana-3963	271	7	length	length	NOUN
cana-3963	271	8	13	13	NUM
cana-3963	271	9	where	where	SCONJ
cana-3963	271	10	elements	element	NOUN
cana-3963	271	11	belongs	belong	VERB
cana-3963	271	12	to	to	ADP
cana-3963	271	13	the	the	DET
cana-3963	271	14	field	field	NOUN
cana-3963	272	1	25	25	NUM
cana-3963	272	2	f	f	NOUN
cana-3963	272	3	having	have	VERB
cana-3963	272	4	generator	generator	NOUN
cana-3963	272	5	matrix	matrix	NOUN
cana-3963	272	6	.g	.g	NOUN
cana-3963	273	1	the	the	DET
cana-3963	273	2	trace	trace	NOUN
cana-3963	273	3	function	function	NOUN
cana-3963	273	4	is	be	AUX
cana-3963	273	5	define	define	VERB
cana-3963	273	6	as	as	ADP
cana-3963	273	7	5	5	NUM
cana-3963	273	8	(	(	PUNCT
cana-3963	273	9	)	)	PUNCT
cana-3963	273	10	(	(	PUNCT
cana-3963	273	11	)	)	PUNCT
cana-3963	273	12	(	(	PUNCT
cana-3963	273	13	)	)	PUNCT
cana-3963	273	14	tr	tr	PROPN
cana-3963	273	15	bx	bx	PROPN
cana-3963	273	16	bx	bx	PROPN
cana-3963	273	17	bx=	bx=	PROPN
cana-3963	273	18	+	+	CCONJ
cana-3963	273	19	communications	communication	NOUN
cana-3963	273	20	on	on	ADP
cana-3963	273	21	applied	apply	VERB
cana-3963	273	22	nonlinear	nonlinear	ADJ
cana-3963	273	23	analysis	analysis	NOUN
cana-3963	273	24	issn	issn	NOUN
cana-3963	273	25	:	:	PUNCT
cana-3963	273	26	1074	1074	NUM
cana-3963	273	27	-	-	PUNCT
cana-3963	273	28	133x	133x	NUM
cana-3963	273	29	vol	vol	NOUN
cana-3963	273	30	32	32	NUM
cana-3963	273	31	no	no	NOUN
cana-3963	273	32	.	.	PUNCT
cana-3963	274	1	9s	9s	NUM
cana-3963	274	2	(	(	PUNCT
cana-3963	274	3	2025	2025	NUM
cana-3963	274	4	)	)	PUNCT
cana-3963	274	5	550	550	NUM
cana-3963	274	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	274	7	10	10	NUM
cana-3963	274	8	12	12	NUM
cana-3963	274	9	19	19	NUM
cana-3963	274	10	6	6	NUM
cana-3963	274	11	20	20	NUM
cana-3963	274	12	4	4	NUM
cana-3963	274	13	23	23	NUM
cana-3963	274	14	2	2	NUM
cana-3963	274	15	5	5	NUM
cana-3963	274	16	12	12	NUM
cana-3963	274	17	13	13	NUM
cana-3963	274	18	15	15	NUM
cana-3963	274	19	18	18	NUM
cana-3963	274	20	16	16	NUM
cana-3963	274	21	9	9	NUM
cana-3963	274	22	5	5	NUM
cana-3963	274	23	10	10	NUM
cana-3963	274	24	15	15	NUM
cana-3963	274	25	9	9	NUM
cana-3963	274	26	6	6	NUM
cana-3963	274	27	18	18	NUM
cana-3963	274	28	15	15	NUM
cana-3963	274	29	13	13	NUM
cana-3963	274	30	12	12	NUM
cana-3963	274	31	5	5	NUM
cana-3963	274	32	2	2	NUM
cana-3963	274	33	23	23	NUM
cana-3963	274	34	4	4	NUM
cana-3963	274	35	20	20	NUM
cana-3963	274	36	6	6	NUM
cana-3963	274	37	19	19	NUM
cana-3963	274	38	12	12	NUM
cana-3963	274	39	10	10	NUM
cana-3963	274	40	1	1	NUM
cana-3963	274	41	0	0	NUM
cana-3963	274	42	0	0	NUM
cana-3963	274	43	0	0	NUM
cana-3963	274	44	0	0	NUM
cana-3963	274	45	0	0	NUM
cana-3963	274	46	0	0	NUM
cana-3963	274	47	0	0	NUM
cana-3963	274	48	0	0	NUM
cana-3963	274	49	0	0	NUM
cana-3963	274	50	1	1	NUM
cana-3963	274	51	0	0	NUM
cana-3963	274	52	0	0	NUM
cana-3963	274	53	0	0	NUM
cana-3963	274	54	0	0	NUM
cana-3963	274	55	0	0	NUM
cana-3963	274	56	0	0	NUM
cana-3963	274	57	0	0	NUM
cana-3963	274	58	0	0	NUM
cana-3963	274	59	0	0	NUM
cana-3963	274	60	1	1	NUM
cana-3963	274	61	0	0	NUM
cana-3963	274	62	0	0	NUM
cana-3963	274	63	0	0	NUM
cana-3963	274	64	0	0	NUM
cana-3963	274	65	0	0	NUM
cana-3963	274	66	0	0	NUM
cana-3963	274	67	0	0	NUM
cana-3963	274	68	0	0	NUM
cana-3963	274	69	0	0	NUM
cana-3963	274	70	1	1	NUM
cana-3963	274	71	0	0	NUM
cana-3963	274	72	0	0	NUM
cana-3963	274	73	0	0	NUM
cana-3963	274	74	0	0	NUM
cana-3963	274	75	0	0	NUM
cana-3963	274	76	0	0	NUM
cana-3963	274	77	0	0	NUM
cana-3963	274	78	0	0	NUM
cana-3963	274	79	0	0	NUM
cana-3963	274	80	1	1	NUM
cana-3963	274	81	0	0	NUM
cana-3963	274	82	0	0	NUM
cana-3963	274	83	0	0	NUM
cana-3963	274	84	0	0	NUM
cana-3963	274	85	1	1	NUM
cana-3963	274	86	0	0	NUM
cana-3963	274	87	0	0	NUM
cana-3963	274	88	0	0	NUM
cana-3963	274	89	0	0	NUM
cana-3963	274	90	0	0	NUM
cana-3963	274	91	1	1	NUM
cana-3963	274	92	0	0	NUM
cana-3963	274	93	0	0	NUM
cana-3963	274	94	0	0	NUM
cana-3963	274	95	0	0	NUM
cana-3963	274	96	0	0	NUM
cana-3963	274	97	0	0	NUM
cana-3963	274	98	0	0	NUM
cana-3963	274	99	0	0	NUM
cana-3963	274	100	0	0	NUM
cana-3963	274	101	1	1	NUM
cana-3963	274	102	0	0	NUM
cana-3963	274	103	0	0	NUM
cana-3963	274	104	0	0	NUM
cana-3963	274	105	0	0	NUM
cana-3963	274	106	0	0	NUM
cana-3963	274	107	0	0	NUM
cana-3963	274	108	0	0	NUM
cana-3963	274	109	0	0	NUM
cana-3963	274	110	0	0	NUM
cana-3963	274	111	1	1	NUM
cana-3963	274	112	0	0	NUM
cana-3963	274	113	0	0	NUM
cana-3963	274	114	0	0	NUM
cana-3963	274	115	0	0	NUM
cana-3963	274	116	0	0	NUM
cana-3963	274	117	0	0	NUM
cana-3963	274	118	0	0	NUM
cana-3963	274	119	0	0	NUM
cana-3963	274	120	0	0	NUM
cana-3963	274	121	1	1	NUM
cana-3963	274	122	g	g	NOUN
cana-3963	274	123			X
cana-3963	274	124			X
cana-3963	274	125			X
cana-3963	274	126			X
cana-3963	274	127			X
cana-3963	274	128			X
cana-3963	274	129			X
cana-3963	274	130			X
cana-3963	274	131			X
cana-3963	274	132			X
cana-3963	274	133			X
cana-3963	274	134			X
cana-3963	274	135			X
cana-3963	274	136			X
cana-3963	274	137			X
cana-3963	274	138			X
cana-3963	274	139			X
cana-3963	274	140			X
cana-3963	274	141			X
cana-3963	274	142			X
cana-3963	274	143			X
cana-3963	274	144			X
cana-3963	274	145			X
cana-3963	274	146			X
cana-3963	274	147			X
cana-3963	274	148			X
cana-3963	274	149			X
cana-3963	274	150			X
cana-3963	274	151			X
cana-3963	274	152			X
cana-3963	274	153			X
cana-3963	274	154			X
cana-3963	274	155			X
cana-3963	274	156			X
cana-3963	274	157			X
cana-3963	274	158			PROPN
cana-3963	274	159			ADJ
cana-3963	274	160			NOUN
cana-3963	274	161			PROPN
cana-3963	274	162			NOUN
cana-3963	274	163			NOUN
cana-3963	274	164			NOUN
cana-3963	274	165			NOUN
cana-3963	274	166			NOUN
cana-3963	274	167			NOUN
cana-3963	274	168			NOUN
cana-3963	274	169			NOUN
cana-3963	274	170			NOUN
cana-3963	274	171	=	=	X
cana-3963	274	172			NOUN
cana-3963	274	173			NOUN
cana-3963	274	174			NOUN
cana-3963	274	175			NOUN
cana-3963	274	176			NOUN
cana-3963	274	177			NOUN
cana-3963	274	178			NOUN
cana-3963	274	179			NOUN
cana-3963	274	180			NOUN
cana-3963	274	181			NOUN
cana-3963	274	182			NOUN
cana-3963	274	183			NOUN
cana-3963	274	184			PROPN
cana-3963	274	185			PROPN
cana-3963	274	186	since	since	SCONJ
cana-3963	274	187	we	we	PRON
cana-3963	274	188	can	can	AUX
cana-3963	274	189	easily	easily	ADV
cana-3963	274	190	that	that	SCONJ
cana-3963	274	191	the	the	DET
cana-3963	274	192	rank	rank	NOUN
cana-3963	274	193	of	of	ADP
cana-3963	274	194	5	5	NUM
cana-3963	274	195	(	(	PUNCT
cana-3963	274	196	(	(	PUNCT
cana-3963	274	197	)	)	PUNCT
cana-3963	274	198	)	)	PUNCT
cana-3963	275	1	tg	tg	PROPN
cana-3963	275	2	g	g	PROPN
cana-3963	275	3	is	be	AUX
cana-3963	275	4	5	5	NUM
cana-3963	275	5	,	,	PUNCT
cana-3963	275	6	which	which	PRON
cana-3963	275	7	is	be	AUX
cana-3963	275	8	less	less	ADJ
cana-3963	275	9	than	than	ADP
cana-3963	275	10	or	or	CCONJ
cana-3963	275	11	equal	equal	ADJ
cana-3963	275	12	to	to	ADP
cana-3963	275	13	2	2	NUM
cana-3963	275	14	9	9	NUM
cana-3963	275	15	13.	13.	NUM
cana-3963	275	16	−	−	PROPN
cana-3963	275	17	by	by	ADP
cana-3963	275	18	theorem	theorem	NOUN
cana-3963	275	19	4	4	NUM
cana-3963	275	20	,	,	PUNCT
cana-3963	275	21	a	a	DET
cana-3963	275	22	code	code	NOUN
cana-3963	275	23	having	have	VERB
cana-3963	275	24	parameter	parameter	NOUN
cana-3963	275	25	5[[13,5,5	5[[13,5,5	PROPN
cana-3963	275	26	]	]	X
cana-3963	275	27	]	]	PUNCT
cana-3963	275	28	and	and	CCONJ
cana-3963	275	29	satisfying	satisfy	VERB
cana-3963	275	30	mds	mds	NOUN
cana-3963	275	31	condition	condition	NOUN
cana-3963	275	32	is	be	AUX
cana-3963	275	33	found	find	VERB
cana-3963	275	34	.	.	PUNCT
cana-3963	276	1	example	example	NOUN
cana-3963	276	2	2	2	NUM
cana-3963	276	3	:	:	PUNCT
cana-3963	276	4	let	let	VERB
cana-3963	276	5			NOUN
cana-3963	276	6	denote	denote	VERB
cana-3963	276	7	a	a	DET
cana-3963	276	8	linear	linear	ADJ
cana-3963	276	9	2	2	NUM
cana-3963	276	10	[	[	PUNCT
cana-3963	276	11	,	,	PUNCT
cana-3963	276	12	,	,	PUNCT
cana-3963	276	13	]	]	PUNCT
cana-3963	276	14	q	q	PROPN
cana-3963	277	1	n	n	X
cana-3963	277	2	k	k	PROPN
cana-3963	277	3	d	d	PROPN
cana-3963	277	4	code	code	NOUN
cana-3963	277	5	with	with	ADP
cana-3963	277	6	17n	17n	NOUN
cana-3963	277	7	=	=	PUNCT
cana-3963	277	8	over	over	ADP
cana-3963	277	9	the	the	DET
cana-3963	277	10	field	field	NOUN
cana-3963	278	1	27	27	NUM
cana-3963	278	2	f	f	NOUN
cana-3963	278	3	having	have	VERB
cana-3963	278	4	generator	generator	NOUN
cana-3963	278	5	matrix	matrix	NOUN
cana-3963	278	6	.g	.g	NOUN
cana-3963	279	1	the	the	DET
cana-3963	279	2	trace	trace	NOUN
cana-3963	279	3	function	function	NOUN
cana-3963	279	4	is	be	AUX
cana-3963	279	5	define	define	VERB
cana-3963	279	6	as	as	ADP
cana-3963	279	7	7	7	NUM
cana-3963	279	8	(	(	PUNCT
cana-3963	279	9	)	)	PUNCT
cana-3963	279	10	(	(	PUNCT
cana-3963	279	11	)	)	PUNCT
cana-3963	279	12	(	(	PUNCT
cana-3963	279	13	)	)	PUNCT
cana-3963	279	14	tr	tr	PROPN
cana-3963	279	15	bx	bx	PROPN
cana-3963	279	16	bx	bx	PROPN
cana-3963	279	17	bx=	bx=	PROPN
cana-3963	279	18	+	+	CCONJ
cana-3963	279	19	37	37	NUM
cana-3963	279	20	15	15	NUM
cana-3963	279	21	14	14	NUM
cana-3963	279	22	61	61	NUM
cana-3963	279	23	56	56	NUM
cana-3963	279	24	30	30	NUM
cana-3963	279	25	19	19	NUM
cana-3963	279	26	77	77	NUM
cana-3963	279	27	42	42	NUM
cana-3963	279	28	45	45	NUM
cana-3963	279	29	48	48	NUM
cana-3963	279	30	51	51	NUM
cana-3963	279	31	76	76	NUM
cana-3963	279	32	60	60	NUM
cana-3963	279	33	20	20	NUM
cana-3963	279	34	64	64	NUM
cana-3963	279	35	41	41	NUM
cana-3963	279	36	75	75	NUM
cana-3963	279	37	79	79	NUM
cana-3963	279	38	26	26	NUM
cana-3963	279	39	3	3	NUM
cana-3963	279	40	9	9	NUM
cana-3963	279	41	15	15	NUM
cana-3963	279	42	21	21	NUM
cana-3963	279	43	61	61	NUM
cana-3963	279	44	24	24	NUM
cana-3963	279	45	24	24	NUM
cana-3963	279	46	61	61	NUM
cana-3963	279	47	21	21	NUM
cana-3963	279	48	15	15	NUM
cana-3963	279	49	9	9	NUM
cana-3963	279	50	3	3	NUM
cana-3963	279	51	1	1	NUM
cana-3963	279	52	0	0	NUM
cana-3963	279	53	0	0	NUM
cana-3963	279	54	0	0	NUM
cana-3963	279	55	0	0	NUM
cana-3963	279	56	0	0	NUM
cana-3963	279	57	0	0	NUM
cana-3963	279	58	0	0	NUM
cana-3963	279	59	0	0	NUM
cana-3963	279	60	0	0	NUM
cana-3963	279	61	0	0	NUM
cana-3963	279	62	0	0	NUM
cana-3963	279	63	0	0	NUM
cana-3963	279	64	0	0	NUM
cana-3963	279	65	1	1	NUM
cana-3963	279	66	0	0	NUM
cana-3963	279	67	0	0	NUM
cana-3963	279	68	0	0	NUM
cana-3963	279	69	0	0	NUM
cana-3963	279	70	0	0	NUM
cana-3963	279	71	0	0	NUM
cana-3963	279	72	0	0	NUM
cana-3963	279	73	0	0	NUM
cana-3963	279	74	0	0	NUM
cana-3963	279	75	0	0	NUM
cana-3963	279	76	0	0	NUM
cana-3963	279	77	0	0	NUM
cana-3963	279	78	0	0	NUM
cana-3963	279	79	1	1	NUM
cana-3963	279	80	0	0	NUM
cana-3963	279	81	0	0	NUM
cana-3963	279	82	0	0	NUM
cana-3963	279	83	0	0	NUM
cana-3963	279	84	0	0	NUM
cana-3963	279	85	0	0	NUM
cana-3963	279	86	0	0	NUM
cana-3963	279	87	0	0	NUM
cana-3963	279	88	0	0	NUM
cana-3963	279	89	0	0	NUM
cana-3963	279	90	0	0	NUM
cana-3963	279	91	0	0	NUM
cana-3963	279	92	0	0	NUM
cana-3963	279	93	1	1	NUM
cana-3963	279	94	0	0	NUM
cana-3963	279	95	0	0	NUM
cana-3963	279	96	0	0	NUM
cana-3963	279	97	0	0	NUM
cana-3963	279	98	0	0	NUM
cana-3963	279	99	0	0	NUM
cana-3963	279	100	0	0	NUM
cana-3963	279	101	0	0	NUM
cana-3963	279	102	0	0	NUM
cana-3963	279	103	0	0	NUM
cana-3963	279	104	0	0	NUM
cana-3963	279	105	0	0	NUM
cana-3963	279	106	0	0	NUM
cana-3963	279	107	1	1	NUM
cana-3963	279	108	0	0	NUM
cana-3963	279	109	0	0	NUM
cana-3963	279	110	0	0	NUM
cana-3963	279	111	0	0	NUM
cana-3963	279	112	0	0	NUM
cana-3963	279	113	0	0	NUM
cana-3963	279	114	0	0	NUM
cana-3963	279	115	0	0	NUM
cana-3963	279	116	0	0	NUM
cana-3963	279	117	0	0	NUM
cana-3963	279	118	0	0	NUM
cana-3963	279	119	0	0	NUM
cana-3963	279	120	0	0	NUM
cana-3963	279	121	1	1	NUM
cana-3963	279	122	0	0	NUM
cana-3963	279	123	0	0	NUM
cana-3963	279	124	0	0	NUM
cana-3963	279	125	0	0	NUM
cana-3963	279	126	0	0	NUM
cana-3963	279	127	0	0	NUM
cana-3963	279	128	0	0	NUM
cana-3963	279	129	0	0	NUM
cana-3963	279	130	0	0	NUM
cana-3963	279	131	0	0	NUM
cana-3963	279	132	0	0	NUM
cana-3963	279	133	0	0	NUM
cana-3963	279	134	0	0	NUM
cana-3963	279	135	1	1	NUM
cana-3963	279	136	0	0	NUM
cana-3963	279	137	0	0	NUM
cana-3963	279	138	0	0	NUM
cana-3963	279	139	0	0	NUM
cana-3963	279	140	0	0	NUM
cana-3963	279	141	0	0	NUM
cana-3963	279	142	0	0	NUM
cana-3963	279	143	0	0	NUM
cana-3963	279	144	0	0	NUM
cana-3963	279	145	0	0	NUM
cana-3963	279	146	0	0	NUM
cana-3963	279	147	0	0	NUM
cana-3963	279	148	0	0	NUM
cana-3963	279	149	1	1	NUM
cana-3963	279	150	0	0	NUM
cana-3963	279	151	0	0	NUM
cana-3963	279	152	0	0	NUM
cana-3963	279	153	0	0	NUM
cana-3963	279	154	0	0	NUM
cana-3963	279	155	0	0	NUM
cana-3963	279	156	0	0	NUM
cana-3963	280	1	g	g	NOUN
cana-3963	280	2			PROPN
cana-3963	280	3			X
cana-3963	280	4			X
cana-3963	280	5			X
cana-3963	280	6			X
cana-3963	280	7			X
cana-3963	280	8			X
cana-3963	280	9			X
cana-3963	280	10			X
cana-3963	280	11			X
cana-3963	280	12			X
cana-3963	280	13			X
cana-3963	280	14			X
cana-3963	280	15			X
cana-3963	280	16			X
cana-3963	280	17			X
cana-3963	280	18			X
cana-3963	280	19			X
cana-3963	280	20			X
cana-3963	280	21			X
cana-3963	280	22			X
cana-3963	280	23			X
cana-3963	280	24			X
cana-3963	280	25			X
cana-3963	280	26			X
cana-3963	280	27			X
cana-3963	280	28			X
cana-3963	280	29			X
cana-3963	280	30			X
cana-3963	280	31			X
cana-3963	280	32			X
cana-3963	280	33			X
cana-3963	280	34	=	=	SYM
cana-3963	280	35	26	26	NUM
cana-3963	280	36	79	79	NUM
cana-3963	280	37	75	75	NUM
cana-3963	280	38	41	41	NUM
cana-3963	280	39	64	64	NUM
cana-3963	280	40	20	20	NUM
cana-3963	280	41	60	60	NUM
cana-3963	280	42	76	76	NUM
cana-3963	280	43	51	51	NUM
cana-3963	280	44	48	48	NUM
cana-3963	280	45	45	45	NUM
cana-3963	280	46	42	42	NUM
cana-3963	280	47	77	77	NUM
cana-3963	280	48	19	19	NUM
cana-3963	280	49	30	30	NUM
cana-3963	280	50	56	56	NUM
cana-3963	280	51	61	61	NUM
cana-3963	280	52	14	14	NUM
cana-3963	280	53	15	15	NUM
cana-3963	280	54	37	37	NUM
cana-3963	280	55	0	0	NUM
cana-3963	280	56	0	0	NUM
cana-3963	280	57	0	0	NUM
cana-3963	280	58	0	0	NUM
cana-3963	280	59	0	0	NUM
cana-3963	280	60	0	0	NUM
cana-3963	280	61	1	1	NUM
cana-3963	280	62	0	0	NUM
cana-3963	280	63	0	0	NUM
cana-3963	280	64	0	0	NUM
cana-3963	280	65	0	0	NUM
cana-3963	280	66	0	0	NUM
cana-3963	280	67	0	0	NUM
cana-3963	280	68	0	0	NUM
cana-3963	280	69	0	0	NUM
cana-3963	280	70	0	0	NUM
cana-3963	280	71	0	0	NUM
cana-3963	280	72	0	0	NUM
cana-3963	280	73	0	0	NUM
cana-3963	280	74	0	0	NUM
cana-3963	280	75	1	1	NUM
cana-3963	280	76	0	0	NUM
cana-3963	280	77	0	0	NUM
cana-3963	280	78	0	0	NUM
cana-3963	280	79	0	0	NUM
cana-3963	280	80	0	0	NUM
cana-3963	280	81	0	0	NUM
cana-3963	280	82	0	0	NUM
cana-3963	280	83	0	0	NUM
cana-3963	280	84	0	0	NUM
cana-3963	280	85	0	0	NUM
cana-3963	280	86	0	0	NUM
cana-3963	280	87	0	0	NUM
cana-3963	280	88	0	0	NUM
cana-3963	280	89	1	1	NUM
cana-3963	280	90	0	0	NUM
cana-3963	280	91	0	0	NUM
cana-3963	280	92	0	0	NUM
cana-3963	280	93	0	0	NUM
cana-3963	280	94	0	0	NUM
cana-3963	280	95	0	0	NUM
cana-3963	280	96	0	0	NUM
cana-3963	280	97	0	0	NUM
cana-3963	280	98	0	0	NUM
cana-3963	280	99	0	0	NUM
cana-3963	280	100	0	0	NUM
cana-3963	280	101	0	0	NUM
cana-3963	280	102	0	0	NUM
cana-3963	280	103	1	1	NUM
cana-3963	280	104	0	0	NUM
cana-3963	280	105	0	0	NUM
cana-3963	280	106	0	0	NUM
cana-3963	280	107	0	0	NUM
cana-3963	280	108	0	0	NUM
cana-3963	280	109	0	0	NUM
cana-3963	280	110	0	0	NUM
cana-3963	280	111	0	0	NUM
cana-3963	280	112	0	0	NUM
cana-3963	280	113	0	0	NUM
cana-3963	280	114	0	0	NUM
cana-3963	280	115	0	0	NUM
cana-3963	280	116	0	0	NUM
cana-3963	280	117	1	1	NUM
cana-3963	280	118			X
cana-3963	280	119			X
cana-3963	280	120			X
cana-3963	280	121			X
cana-3963	280	122			X
cana-3963	280	123			X
cana-3963	280	124			X
cana-3963	280	125			X
cana-3963	280	126			X
cana-3963	280	127			X
cana-3963	280	128			X
cana-3963	280	129			X
cana-3963	280	130			X
cana-3963	280	131			X
cana-3963	280	132			X
cana-3963	280	133			X
cana-3963	280	134			X
cana-3963	280	135			X
cana-3963	280	136			X
cana-3963	280	137			X
cana-3963	280	138			PROPN
cana-3963	280	139			ADJ
cana-3963	280	140			NOUN
cana-3963	280	141			PROPN
cana-3963	280	142			NOUN
cana-3963	280	143			NOUN
cana-3963	280	144			NOUN
cana-3963	280	145			NOUN
cana-3963	280	146			NOUN
cana-3963	280	147			NOUN
cana-3963	280	148			NOUN
cana-3963	280	149			NOUN
cana-3963	280	150			NOUN
cana-3963	280	151			NOUN
cana-3963	280	152			NOUN
cana-3963	280	153			NOUN
cana-3963	280	154			NOUN
cana-3963	280	155			NOUN
cana-3963	280	156			NOUN
cana-3963	280	157			NOUN
cana-3963	280	158			NOUN
cana-3963	280	159			NOUN
cana-3963	280	160			NOUN
cana-3963	280	161			NOUN
cana-3963	280	162			NOUN
cana-3963	280	163			NOUN
cana-3963	280	164			NOUN
cana-3963	280	165			NOUN
cana-3963	280	166			NOUN
cana-3963	280	167			NOUN
cana-3963	280	168			NOUN
cana-3963	280	169			NOUN
cana-3963	280	170			NOUN
cana-3963	280	171			NOUN
cana-3963	280	172			NOUN
cana-3963	280	173			NOUN
cana-3963	280	174			NOUN
cana-3963	280	175			NOUN
cana-3963	280	176			NOUN
cana-3963	280	177			PROPN
cana-3963	280	178			PROPN
cana-3963	280	179	since	since	SCONJ
cana-3963	280	180	7	7	NUM
cana-3963	280	181	(	(	PUNCT
cana-3963	280	182	(	(	PUNCT
cana-3963	280	183	)	)	PUNCT
cana-3963	280	184	)	)	PUNCT
cana-3963	280	185	9	9	NUM
cana-3963	280	186	2	2	NUM
cana-3963	280	187	13	13	NUM
cana-3963	280	188	17tg	17tg	NOUN
cana-3963	280	189	g	g	NOUN
cana-3963	280	190	=	=	PUNCT
cana-3963	280	191			NOUN
cana-3963	280	192			VERB
cana-3963	280	193	−	−	PROPN
cana-3963	280	194	,	,	PUNCT
cana-3963	280	195	using	use	VERB
cana-3963	280	196	the	the	DET
cana-3963	280	197	theorem	theorem	NOUN
cana-3963	280	198	5	5	NUM
cana-3963	280	199	,	,	PUNCT
cana-3963	280	200	a	a	DET
cana-3963	280	201	quantum	quantum	PROPN
cana-3963	280	202	mds	mds	NOUN
cana-3963	280	203	code	code	NOUN
cana-3963	280	204	with	with	ADP
cana-3963	280	205	parameters	parameter	NOUN
cana-3963	280	206	7[[17,9,5	7[[17,9,5	NUM
cana-3963	280	207	]	]	X
cana-3963	280	208	]	]	PUNCT
cana-3963	280	209	is	be	AUX
cana-3963	280	210	found	find	VERB
cana-3963	280	211	.	.	PUNCT
cana-3963	281	1	for	for	ADP
cana-3963	281	2	comparison	comparison	NOUN
cana-3963	281	3	,	,	PUNCT
cana-3963	281	4	the	the	DET
cana-3963	281	5	obtained	obtain	VERB
cana-3963	281	6	quantum	quantum	NOUN
cana-3963	281	7	code	code	NOUN
cana-3963	281	8	has	have	VERB
cana-3963	281	9	good	good	ADJ
cana-3963	281	10	and	and	CCONJ
cana-3963	281	11	new	new	ADJ
cana-3963	281	12	parameters	parameter	NOUN
cana-3963	281	13	than	than	ADP
cana-3963	281	14	in	in	ADP
cana-3963	281	15	[	[	X
cana-3963	281	16	12	12	NUM
cana-3963	281	17	]	]	PUNCT
cana-3963	281	18	.	.	PUNCT
cana-3963	282	1	other	other	ADJ
cana-3963	282	2	quantum	quantum	ADJ
cana-3963	282	3	codes	code	NOUN
cana-3963	282	4	such	such	ADJ
cana-3963	282	5	as	as	ADP
cana-3963	282	6	3[[11,5,4	3[[11,5,4	PROPN
cana-3963	282	7	]	]	X
cana-3963	282	8	]	]	X
cana-3963	282	9	,	,	PUNCT
cana-3963	282	10	7[[18,12	7[[18,12	NUM
cana-3963	282	11	,	,	PUNCT
cana-3963	282	12	4	4	NUM
cana-3963	282	13	]	]	PUNCT
cana-3963	282	14	]	]	PUNCT
cana-3963	282	15	and	and	CCONJ
cana-3963	282	16	9[[64,56,3	9[[64,56,3	NUM
cana-3963	282	17	]	]	X
cana-3963	282	18	]	]	X
cana-3963	282	19	are	be	AUX
cana-3963	282	20	also	also	ADV
cana-3963	282	21	obtained	obtain	VERB
cana-3963	282	22	.	.	PUNCT
cana-3963	283	1	5	5	X
cana-3963	283	2	.	.	NOUN
cana-3963	283	3	results	result	NOUN
cana-3963	283	4	and	and	CCONJ
cana-3963	283	5	comparison	comparison	NOUN
cana-3963	283	6	utilizing	utilize	VERB
cana-3963	283	7	hdc	hdc	NOUN
cana-3963	283	8	,	,	PUNCT
cana-3963	283	9	mpc	mpc	NOUN
cana-3963	283	10	and	and	CCONJ
cana-3963	283	11	minimal	minimal	ADJ
cana-3963	283	12	polynomials	polynomial	NOUN
cana-3963	283	13	with	with	ADP
cana-3963	283	14	the	the	DET
cana-3963	283	15	hdc	hdc	NOUN
cana-3963	283	16	property	property	NOUN
cana-3963	283	17	has	have	AUX
cana-3963	283	18	resulted	result	VERB
cana-3963	283	19	in	in	ADP
cana-3963	283	20	the	the	DET
cana-3963	283	21	development	development	NOUN
cana-3963	283	22	of	of	ADP
cana-3963	283	23	the	the	DET
cana-3963	283	24	5[[13,5,5	5[[13,5,5	PROPN
cana-3963	283	25	]	]	X
cana-3963	283	26	]	]	PUNCT
cana-3963	283	27	and	and	CCONJ
cana-3963	283	28	7[[17,9,5	7[[17,9,5	NOUN
cana-3963	283	29	]	]	X
cana-3963	283	30	]	]	X
cana-3963	283	31	quantum	quantum	NOUN
cana-3963	283	32	codes	code	NOUN
cana-3963	283	33	.	.	PUNCT
cana-3963	284	1	these	these	DET
cana-3963	284	2	newly	newly	ADV
cana-3963	284	3	constructed	construct	VERB
cana-3963	284	4	codes	code	NOUN
cana-3963	284	5	demonstrate	demonstrate	VERB
cana-3963	284	6	superior	superior	ADJ
cana-3963	284	7	communications	communication	NOUN
cana-3963	284	8	on	on	ADP
cana-3963	284	9	applied	apply	VERB
cana-3963	284	10	nonlinear	nonlinear	ADJ
cana-3963	284	11	analysis	analysis	NOUN
cana-3963	284	12	issn	issn	NOUN
cana-3963	284	13	:	:	PUNCT
cana-3963	284	14	1074	1074	NUM
cana-3963	284	15	-	-	PUNCT
cana-3963	284	16	133x	133x	NUM
cana-3963	284	17	vol	vol	NOUN
cana-3963	284	18	32	32	NUM
cana-3963	284	19	no	no	NOUN
cana-3963	284	20	.	.	PUNCT
cana-3963	285	1	9s	9s	NUM
cana-3963	285	2	(	(	PUNCT
cana-3963	285	3	2025	2025	NUM
cana-3963	285	4	)	)	PUNCT
cana-3963	286	1	551	551	NUM
cana-3963	286	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	286	3	error	error	NOUN
cana-3963	286	4	correction	correction	NOUN
cana-3963	286	5	capabilities	capability	NOUN
cana-3963	286	6	,	,	PUNCT
cana-3963	286	7	offering	offer	VERB
cana-3963	286	8	a	a	DET
cana-3963	286	9	practical	practical	ADJ
cana-3963	286	10	balance	balance	NOUN
cana-3963	286	11	of	of	ADP
cana-3963	286	12	rates	rate	NOUN
cana-3963	286	13	and	and	CCONJ
cana-3963	286	14	lengths	length	NOUN
cana-3963	286	15	suitable	suitable	ADJ
cana-3963	286	16	for	for	ADP
cana-3963	286	17	implementation	implementation	NOUN
cana-3963	286	18	in	in	ADP
cana-3963	286	19	quantum	quantum	NOUN
cana-3963	286	20	computing	computing	NOUN
cana-3963	286	21	systems	system	NOUN
cana-3963	286	22	.	.	PUNCT
cana-3963	287	1	the	the	DET
cana-3963	287	2	underlying	underlie	VERB
cana-3963	287	3	algebraic	algebraic	ADJ
cana-3963	287	4	structures	structure	NOUN
cana-3963	287	5	and	and	CCONJ
cana-3963	287	6	properties	property	NOUN
cana-3963	287	7	not	not	PART
cana-3963	287	8	only	only	ADV
cana-3963	287	9	enhance	enhance	VERB
cana-3963	287	10	the	the	DET
cana-3963	287	11	current	current	ADJ
cana-3963	287	12	performance	performance	NOUN
cana-3963	287	13	but	but	CCONJ
cana-3963	287	14	also	also	ADV
cana-3963	287	15	lay	lie	VERB
cana-3963	287	16	the	the	DET
cana-3963	287	17	foundation	foundation	NOUN
cana-3963	287	18	for	for	ADP
cana-3963	287	19	upcoming	upcoming	ADJ
cana-3963	287	20	improvements	improvement	NOUN
cana-3963	287	21	in	in	ADP
cana-3963	287	22	quantum	quantum	ADJ
cana-3963	287	23	error	error	NOUN
cana-3963	287	24	correction	correction	NOUN
cana-3963	287	25	technology	technology	NOUN
cana-3963	287	26	.	.	PUNCT
cana-3963	288	1	the	the	DET
cana-3963	288	2	newly	newly	ADV
cana-3963	288	3	developed	develop	VERB
cana-3963	288	4	quantum	quantum	ADJ
cana-3963	288	5	codes	code	NOUN
cana-3963	288	6	,	,	PUNCT
cana-3963	288	7	characterized	characterize	VERB
cana-3963	288	8	by	by	ADP
cana-3963	288	9	improved	improved	ADJ
cana-3963	288	10	parameters	parameter	NOUN
cana-3963	288	11	such	such	ADJ
cana-3963	288	12	as	as	ADP
cana-3963	288	13	distance	distance	NOUN
cana-3963	288	14	,	,	PUNCT
cana-3963	288	15	rate	rate	NOUN
cana-3963	288	16	,	,	PUNCT
cana-3963	288	17	and	and	CCONJ
cana-3963	288	18	length	length	NOUN
cana-3963	288	19	,	,	PUNCT
cana-3963	288	20	are	be	AUX
cana-3963	288	21	explicitly	explicitly	ADV
cana-3963	288	22	adapted	adapt	VERB
cana-3963	288	23	for	for	ADP
cana-3963	288	24	practical	practical	ADJ
cana-3963	288	25	quantum	quantum	NOUN
cana-3963	288	26	computing	computing	NOUN
cana-3963	288	27	implementation	implementation	NOUN
cana-3963	288	28	.	.	PUNCT
cana-3963	289	1	the	the	DET
cana-3963	289	2	use	use	NOUN
cana-3963	289	3	of	of	ADP
cana-3963	289	4	advanced	advanced	ADJ
cana-3963	289	5	algebraic	algebraic	ADJ
cana-3963	289	6	structures	structure	NOUN
cana-3963	289	7	and	and	CCONJ
cana-3963	289	8	properties	property	NOUN
cana-3963	289	9	in	in	ADP
cana-3963	289	10	their	their	PRON
cana-3963	289	11	construction	construction	NOUN
cana-3963	289	12	not	not	PART
cana-3963	289	13	only	only	ADV
cana-3963	289	14	boosts	boost	VERB
cana-3963	289	15	their	their	PRON
cana-3963	289	16	performance	performance	NOUN
cana-3963	289	17	but	but	CCONJ
cana-3963	289	18	also	also	ADV
cana-3963	289	19	lays	lay	VERB
cana-3963	289	20	a	a	DET
cana-3963	289	21	robust	robust	ADJ
cana-3963	289	22	groundwork	groundwork	NOUN
cana-3963	289	23	for	for	ADP
cana-3963	289	24	future	future	ADJ
cana-3963	289	25	advancements	advancement	NOUN
cana-3963	289	26	in	in	ADP
cana-3963	289	27	quantum	quantum	NOUN
cana-3963	289	28	coding	code	VERB
cana-3963	289	29	theory	theory	NOUN
cana-3963	289	30	[	[	X
cana-3963	289	31	22,23	22,23	NOUN
cana-3963	289	32	]	]	X
cana-3963	289	33	.	.	PUNCT
cana-3963	290	1	in	in	ADP
cana-3963	290	2	quantum	quantum	ADJ
cana-3963	290	3	codes	code	NOUN
cana-3963	290	4	obtained	obtain	VERB
cana-3963	290	5	using	use	VERB
cana-3963	290	6	the	the	DET
cana-3963	290	7	proposed	propose	VERB
cana-3963	290	8	construction	construction	NOUN
cana-3963	290	9	method	method	NOUN
cana-3963	290	10	,	,	PUNCT
cana-3963	290	11	the	the	DET
cana-3963	290	12	parameters	parameter	NOUN
cana-3963	290	13	are	be	AUX
cana-3963	290	14	better	well	ADJ
cana-3963	290	15	because	because	SCONJ
cana-3963	290	16	we	we	PRON
cana-3963	290	17	have	have	AUX
cana-3963	290	18	encoded	encode	VERB
cana-3963	290	19	a	a	DET
cana-3963	290	20	greater	great	ADJ
cana-3963	290	21	number	number	NOUN
cana-3963	290	22	of	of	ADP
cana-3963	290	23	physical	physical	ADJ
cana-3963	290	24	qubits	qubit	NOUN
cana-3963	290	25	increasing	increase	VERB
cana-3963	290	26	the	the	DET
cana-3963	290	27	rate	rate	NOUN
cana-3963	290	28	of	of	ADP
cana-3963	290	29	the	the	DET
cana-3963	290	30	codes	code	NOUN
cana-3963	290	31	have	have	VERB
cana-3963	290	32	a	a	DET
cana-3963	290	33	larger	large	ADJ
cana-3963	290	34	minimum	minimum	ADJ
cana-3963	290	35	distance	distance	NOUN
cana-3963	290	36	of	of	ADP
cana-3963	290	37	these	these	DET
cana-3963	290	38	codes	code	NOUN
cana-3963	290	39	.	.	PUNCT
cana-3963	291	1	a	a	DET
cana-3963	291	2	larger	large	ADJ
cana-3963	291	3	minimum	minimum	NOUN
cana-3963	291	4	distance	distance	NOUN
cana-3963	291	5	enables	enable	VERB
cana-3963	291	6	the	the	DET
cana-3963	291	7	code	code	NOUN
cana-3963	291	8	to	to	PART
cana-3963	291	9	identify	identify	VERB
cana-3963	291	10	and	and	CCONJ
cana-3963	291	11	fix	fix	VERB
cana-3963	291	12	a	a	DET
cana-3963	291	13	greater	great	ADJ
cana-3963	291	14	number	number	NOUN
cana-3963	291	15	of	of	ADP
cana-3963	291	16	errors	error	NOUN
cana-3963	291	17	.	.	PUNCT
cana-3963	292	1	this	this	PRON
cana-3963	292	2	is	be	AUX
cana-3963	292	3	essential	essential	ADJ
cana-3963	292	4	because	because	SCONJ
cana-3963	292	5	quantum	quantum	ADJ
cana-3963	292	6	systems	system	NOUN
cana-3963	292	7	are	be	AUX
cana-3963	292	8	extremely	extremely	ADV
cana-3963	292	9	vulnerable	vulnerable	ADJ
cana-3963	292	10	to	to	ADP
cana-3963	292	11	various	various	ADJ
cana-3963	292	12	types	type	NOUN
cana-3963	292	13	of	of	ADP
cana-3963	292	14	noise	noise	NOUN
cana-3963	292	15	and	and	CCONJ
cana-3963	292	16	errors	error	NOUN
cana-3963	292	17	,	,	PUNCT
cana-3963	292	18	including	include	VERB
cana-3963	292	19	bit	bit	NOUN
cana-3963	292	20	-	-	PUNCT
cana-3963	292	21	flips	flips	ADJ
cana-3963	292	22	,	,	PUNCT
cana-3963	292	23	phase	phase	NOUN
cana-3963	292	24	-	-	PUNCT
cana-3963	292	25	flips	flips	NOUN
cana-3963	292	26	,	,	PUNCT
cana-3963	292	27	and	and	CCONJ
cana-3963	292	28	their	their	PRON
cana-3963	292	29	combinations	combination	NOUN
cana-3963	292	30	.	.	PUNCT
cana-3963	293	1	faulttolerant	faulttolerant	ADJ
cana-3963	293	2	quantum	quantum	ADJ
cana-3963	293	3	computation	computation	NOUN
cana-3963	293	4	necessitates	necessitate	VERB
cana-3963	293	5	maintaining	maintain	VERB
cana-3963	293	6	error	error	NOUN
cana-3963	293	7	rates	rate	NOUN
cana-3963	293	8	below	below	ADP
cana-3963	293	9	a	a	DET
cana-3963	293	10	specific	specific	ADJ
cana-3963	293	11	threshold	threshold	NOUN
cana-3963	293	12	.	.	PUNCT
cana-3963	294	1	codes	code	NOUN
cana-3963	294	2	with	with	ADP
cana-3963	294	3	larger	large	ADJ
cana-3963	294	4	minimum	minimum	ADJ
cana-3963	294	5	distances	distance	NOUN
cana-3963	294	6	generally	generally	ADV
cana-3963	294	7	possess	possess	VERB
cana-3963	294	8	higher	high	ADJ
cana-3963	294	9	error	error	NOUN
cana-3963	294	10	thresholds	threshold	NOUN
cana-3963	294	11	,	,	PUNCT
cana-3963	294	12	enhancing	enhance	VERB
cana-3963	294	13	their	their	PRON
cana-3963	294	14	suitability	suitability	NOUN
cana-3963	294	15	for	for	ADP
cana-3963	294	16	practical	practical	ADJ
cana-3963	294	17	quantum	quantum	ADJ
cana-3963	294	18	computing	computing	NOUN
cana-3963	294	19	applications	application	NOUN
cana-3963	294	20	.	.	PUNCT
cana-3963	295	1	although	although	SCONJ
cana-3963	295	2	codes	code	NOUN
cana-3963	295	3	with	with	ADP
cana-3963	295	4	larger	large	ADJ
cana-3963	295	5	minimum	minimum	ADJ
cana-3963	295	6	distances	distance	NOUN
cana-3963	295	7	often	often	ADV
cana-3963	295	8	need	need	VERB
cana-3963	295	9	more	more	ADJ
cana-3963	295	10	physical	physical	ADJ
cana-3963	295	11	qubits	qubit	NOUN
cana-3963	295	12	for	for	ADP
cana-3963	295	13	encoding	encoding	NOUN
cana-3963	295	14	,	,	PUNCT
cana-3963	295	15	they	they	PRON
cana-3963	295	16	decrease	decrease	VERB
cana-3963	295	17	the	the	DET
cana-3963	295	18	overhead	overhead	NOUN
cana-3963	295	19	required	require	VERB
cana-3963	295	20	for	for	ADP
cana-3963	295	21	repeated	repeat	VERB
cana-3963	295	22	error	error	NOUN
cana-3963	295	23	correction	correction	NOUN
cana-3963	295	24	cycles	cycle	NOUN
cana-3963	295	25	,	,	PUNCT
cana-3963	295	26	resulting	result	VERB
cana-3963	295	27	in	in	ADP
cana-3963	295	28	more	more	ADV
cana-3963	295	29	efficient	efficient	ADJ
cana-3963	295	30	resource	resource	NOUN
cana-3963	295	31	utilization	utilization	NOUN
cana-3963	295	32	in	in	ADP
cana-3963	295	33	large	large	ADJ
cana-3963	295	34	-	-	PUNCT
cana-3963	295	35	scale	scale	NOUN
cana-3963	295	36	quantum	quantum	NOUN
cana-3963	295	37	systems	system	NOUN
cana-3963	295	38	.	.	PUNCT
cana-3963	296	1	table	table	NOUN
cana-3963	296	2	1	1	NUM
cana-3963	296	3	.	.	PUNCT
cana-3963	296	4	comparison	comparison	NOUN
cana-3963	296	5	of	of	ADP
cana-3963	296	6	various	various	ADJ
cana-3963	296	7	codes	code	NOUN
cana-3963	296	8	obtained	obtain	VERB
cana-3963	296	9	from	from	ADP
cana-3963	296	10	the	the	DET
cana-3963	296	11	proposed	propose	VERB
cana-3963	296	12	method	method	NOUN
cana-3963	296	13	and	and	CCONJ
cana-3963	296	14	[	[	X
cana-3963	296	15	24	24	NUM
cana-3963	296	16	]	]	PUNCT
cana-3963	296	17	.	.	PUNCT
cana-3963	297	1	proposed	propose	VERB
cana-3963	297	2	quantum	quantum	NOUN
cana-3963	297	3	codes	code	NOUN
cana-3963	297	4	existing	exist	VERB
cana-3963	297	5	codes	code	NOUN
cana-3963	297	6	from	from	ADP
cana-3963	297	7	[	[	X
cana-3963	297	8	24	24	NUM
cana-3963	297	9	]	]	SYM
cana-3963	297	10	3[[11,5	3[[11,5	NUM
cana-3963	297	11	,	,	PUNCT
cana-3963	297	12	4	4	NUM
cana-3963	297	13	]	]	PUNCT
cana-3963	297	14	]	]	X
cana-3963	297	15	3[[11,1	3[[11,1	NUM
cana-3963	297	16	,	,	PUNCT
cana-3963	297	17	4	4	NUM
cana-3963	297	18	]	]	PUNCT
cana-3963	297	19	]	]	X
cana-3963	298	1	5[[13,5,5	5[[13,5,5	NUM
cana-3963	298	2	]	]	X
cana-3963	298	3	]	]	X
cana-3963	299	1	5[[13,9,3	5[[13,9,3	X
cana-3963	299	2	]	]	PUNCT
cana-3963	299	3	]	]	X
cana-3963	299	4	7[[17,9,5	7[[17,9,5	NUM
cana-3963	299	5	]	]	X
cana-3963	299	6	]	]	X
cana-3963	300	1	7[[17,13,3	7[[17,13,3	NOUN
cana-3963	300	2	]	]	X
cana-3963	300	3	]	]	X
cana-3963	301	1	7[[18,12	7[[18,12	NUM
cana-3963	301	2	,	,	PUNCT
cana-3963	301	3	4	4	NUM
cana-3963	301	4	]	]	PUNCT
cana-3963	301	5	]	]	X
cana-3963	301	6	7[[18,10	7[[18,10	NUM
cana-3963	301	7	,	,	PUNCT
cana-3963	301	8	4	4	NUM
cana-3963	301	9	]	]	PUNCT
cana-3963	301	10	]	]	X
cana-3963	301	11	fig	fig	NOUN
cana-3963	301	12	.	.	PUNCT
cana-3963	302	1	2	2	NUM
cana-3963	302	2	comparison	comparison	NOUN
cana-3963	302	3	of	of	ADP
cana-3963	302	4	various	various	ADJ
cana-3963	302	5	codes	code	NOUN
cana-3963	302	6	obtained	obtain	VERB
cana-3963	302	7	with	with	ADP
cana-3963	302	8	different	different	ADJ
cana-3963	302	9	parameters	parameter	NOUN
cana-3963	302	10	from	from	ADP
cana-3963	302	11	the	the	DET
cana-3963	302	12	fig	fig	NOUN
cana-3963	302	13	.	.	PUNCT
cana-3963	303	1	2	2	NUM
cana-3963	303	2	,	,	PUNCT
cana-3963	303	3	it	it	PRON
cana-3963	303	4	is	be	AUX
cana-3963	303	5	evident	evident	ADJ
cana-3963	303	6	that	that	SCONJ
cana-3963	303	7	the	the	DET
cana-3963	303	8	codes	code	NOUN
cana-3963	303	9	constructed	construct	VERB
cana-3963	303	10	exhibits	exhibit	VERB
cana-3963	303	11	better	well	ADJ
cana-3963	303	12	error	error	NOUN
cana-3963	303	13	correction	correction	NOUN
cana-3963	303	14	proficiency	proficiency	NOUN
cana-3963	303	15	.	.	PUNCT
cana-3963	304	1	these	these	DET
cana-3963	304	2	codes	code	NOUN
cana-3963	304	3	have	have	VERB
cana-3963	304	4	a	a	DET
cana-3963	304	5	lower	low	ADJ
cana-3963	304	6	qubit	qubit	NOUN
cana-3963	304	7	error	error	NOUN
cana-3963	304	8	rate	rate	NOUN
cana-3963	304	9	with	with	ADP
cana-3963	304	10	respect	respect	NOUN
cana-3963	304	11	to	to	ADP
cana-3963	304	12	the	the	DET
cana-3963	304	13	total	total	ADJ
cana-3963	304	14	channel	channel	NOUN
cana-3963	304	15	flip	flip	NOUN
cana-3963	304	16	probability	probability	NOUN
cana-3963	304	17	with	with	ADP
cana-3963	304	18	varying	vary	VERB
cana-3963	304	19	depolarizing	depolarizing	NOUN
cana-3963	304	20	probability	probability	NOUN
cana-3963	304	21	under	under	ADP
cana-3963	304	22	consideration	consideration	NOUN
cana-3963	304	23	.	.	PUNCT
cana-3963	305	1	also	also	ADV
cana-3963	305	2	,	,	PUNCT
cana-3963	305	3	the	the	DET
cana-3963	305	4	codes	code	NOUN
cana-3963	305	5	constructed	construct	VERB
cana-3963	305	6	from	from	ADP
cana-3963	305	7	the	the	DET
cana-3963	305	8	proposed	propose	VERB
cana-3963	305	9	method	method	NOUN
cana-3963	305	10	have	have	VERB
cana-3963	305	11	better	well	ADJ
cana-3963	305	12	parameters	parameter	NOUN
cana-3963	305	13	than	than	ADP
cana-3963	305	14	[	[	X
cana-3963	305	15	24	24	NUM
cana-3963	305	16	]	]	PUNCT
cana-3963	305	17	.	.	PUNCT
cana-3963	306	1	the	the	DET
cana-3963	306	2	analysis	analysis	NOUN
cana-3963	306	3	explored	explore	VERB
cana-3963	306	4	a	a	DET
cana-3963	306	5	range	range	NOUN
cana-3963	306	6	of	of	ADP
cana-3963	306	7	qubit	qubit	NOUN
cana-3963	306	8	error	error	NOUN
cana-3963	306	9	rates	rate	NOUN
cana-3963	306	10	from	from	ADP
cana-3963	306	11	0	0	NUM
cana-3963	306	12	to	to	ADP
cana-3963	306	13	0.3	0.3	NUM
cana-3963	306	14	,	,	PUNCT
cana-3963	306	15	reflecting	reflect	VERB
cana-3963	306	16	practical	practical	ADJ
cana-3963	306	17	error	error	NOUN
cana-3963	306	18	rates	rate	NOUN
cana-3963	306	19	in	in	ADP
cana-3963	306	20	current	current	ADJ
cana-3963	306	21	quantum	quantum	ADJ
cana-3963	306	22	hardware	hardware	NOUN
cana-3963	306	23	.	.	PUNCT
cana-3963	307	1	this	this	DET
cana-3963	307	2	selection	selection	NOUN
cana-3963	307	3	aimed	aim	VERB
cana-3963	307	4	to	to	PART
cana-3963	307	5	cover	cover	VERB
cana-3963	307	6	both	both	PRON
cana-3963	307	7	standard	standard	ADJ
cana-3963	307	8	and	and	CCONJ
cana-3963	307	9	challenging	challenging	ADJ
cana-3963	307	10	operational	operational	ADJ
cana-3963	307	11	conditions	condition	NOUN
cana-3963	307	12	for	for	ADP
cana-3963	307	13	quantum	quantum	NOUN
cana-3963	307	14	systems	system	NOUN
cana-3963	307	15	.	.	PUNCT
cana-3963	308	1	at	at	ADP
cana-3963	308	2	lower	low	ADJ
cana-3963	308	3	error	error	NOUN
cana-3963	308	4	rates	rate	NOUN
cana-3963	308	5	,	,	PUNCT
cana-3963	308	6	the	the	DET
cana-3963	308	7	communications	communication	NOUN
cana-3963	308	8	on	on	ADP
cana-3963	308	9	applied	apply	VERB
cana-3963	308	10	nonlinear	nonlinear	ADJ
cana-3963	308	11	analysis	analysis	NOUN
cana-3963	308	12	issn	issn	NOUN
cana-3963	308	13	:	:	PUNCT
cana-3963	308	14	1074	1074	NUM
cana-3963	308	15	-	-	PUNCT
cana-3963	308	16	133x	133x	NUM
cana-3963	308	17	vol	vol	NOUN
cana-3963	308	18	32	32	NUM
cana-3963	308	19	no	no	NOUN
cana-3963	308	20	.	.	PUNCT
cana-3963	309	1	9s	9s	NUM
cana-3963	309	2	(	(	PUNCT
cana-3963	309	3	2025	2025	NUM
cana-3963	309	4	)	)	PUNCT
cana-3963	309	5	552	552	NUM
cana-3963	310	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	310	2	7[[17,9,5	7[[17,9,5	NUM
cana-3963	310	3	]	]	X
cana-3963	310	4	]	]	X
cana-3963	310	5	code	code	NOUN
cana-3963	310	6	showed	show	VERB
cana-3963	310	7	a	a	DET
cana-3963	310	8	notable	notable	ADJ
cana-3963	310	9	ability	ability	NOUN
cana-3963	310	10	to	to	PART
cana-3963	310	11	mitigate	mitigate	VERB
cana-3963	310	12	errors	error	NOUN
cana-3963	310	13	,	,	PUNCT
cana-3963	310	14	maintaining	maintain	VERB
cana-3963	310	15	a	a	DET
cana-3963	310	16	low	low	ADJ
cana-3963	310	17	total	total	ADJ
cana-3963	310	18	channel	channel	NOUN
cana-3963	310	19	flip	flip	NOUN
cana-3963	310	20	probability	probability	NOUN
cana-3963	310	21	(	(	PUNCT
cana-3963	310	22	tcfp	tcfp	NOUN
cana-3963	310	23	)	)	PUNCT
cana-3963	310	24	.	.	PUNCT
cana-3963	311	1	this	this	DET
cana-3963	311	2	performance	performance	NOUN
cana-3963	311	3	suggests	suggest	VERB
cana-3963	311	4	that	that	SCONJ
cana-3963	311	5	the	the	DET
cana-3963	311	6	code	code	NOUN
cana-3963	311	7	effectively	effectively	ADV
cana-3963	311	8	corrected	correct	VERB
cana-3963	311	9	errors	error	NOUN
cana-3963	311	10	introduced	introduce	VERB
cana-3963	311	11	by	by	ADP
cana-3963	311	12	depolarizing	depolarizing	NOUN
cana-3963	311	13	noise	noise	NOUN
cana-3963	311	14	,	,	PUNCT
cana-3963	311	15	thereby	thereby	ADV
cana-3963	311	16	preserving	preserve	VERB
cana-3963	311	17	the	the	DET
cana-3963	311	18	state	state	NOUN
cana-3963	311	19	of	of	ADP
cana-3963	311	20	logical	logical	ADJ
cana-3963	311	21	qubits	qubit	NOUN
cana-3963	311	22	.	.	PUNCT
cana-3963	312	1	as	as	SCONJ
cana-3963	312	2	the	the	DET
cana-3963	312	3	qubit	qubit	NOUN
cana-3963	312	4	error	error	NOUN
cana-3963	312	5	rate	rate	NOUN
cana-3963	312	6	increased	increase	VERB
cana-3963	312	7	,	,	PUNCT
cana-3963	312	8	the	the	DET
cana-3963	312	9	tcfp	tcfp	NOUN
cana-3963	312	10	exhibited	exhibit	VERB
cana-3963	312	11	a	a	DET
cana-3963	312	12	linear	linear	ADJ
cana-3963	312	13	rise	rise	NOUN
cana-3963	312	14	,	,	PUNCT
cana-3963	312	15	indicating	indicate	VERB
cana-3963	312	16	the	the	DET
cana-3963	312	17	growing	grow	VERB
cana-3963	312	18	difficulty	difficulty	NOUN
cana-3963	312	19	in	in	ADP
cana-3963	312	20	keeping	keep	VERB
cana-3963	312	21	qubits	qubit	NOUN
cana-3963	312	22	error	error	NOUN
cana-3963	312	23	-	-	PUNCT
cana-3963	312	24	free	free	ADJ
cana-3963	312	25	.	.	PUNCT
cana-3963	313	1	despite	despite	SCONJ
cana-3963	313	2	this	this	DET
cana-3963	313	3	rise	rise	NOUN
cana-3963	313	4	,	,	PUNCT
cana-3963	313	5	the	the	DET
cana-3963	313	6	code	code	NOUN
cana-3963	313	7	's	's	PART
cana-3963	313	8	error	error	NOUN
cana-3963	313	9	correction	correction	NOUN
cana-3963	313	10	remained	remain	VERB
cana-3963	313	11	effective	effective	ADJ
cana-3963	313	12	at	at	ADP
cana-3963	313	13	moderate	moderate	ADJ
cana-3963	313	14	error	error	NOUN
cana-3963	313	15	rates	rate	NOUN
cana-3963	313	16	,	,	PUNCT
cana-3963	313	17	highlighting	highlight	VERB
cana-3963	313	18	its	its	PRON
cana-3963	313	19	reliability	reliability	NOUN
cana-3963	313	20	under	under	ADP
cana-3963	313	21	typical	typical	ADJ
cana-3963	313	22	conditions	condition	NOUN
cana-3963	313	23	found	find	VERB
cana-3963	313	24	in	in	ADP
cana-3963	313	25	quantum	quantum	ADJ
cana-3963	313	26	hardware	hardware	NOUN
cana-3963	313	27	.	.	PUNCT
cana-3963	314	1	however	however	ADV
cana-3963	314	2	,	,	PUNCT
cana-3963	314	3	when	when	SCONJ
cana-3963	314	4	the	the	DET
cana-3963	314	5	error	error	NOUN
cana-3963	314	6	rate	rate	NOUN
cana-3963	314	7	approached	approach	VERB
cana-3963	314	8	0.3	0.3	NUM
cana-3963	314	9	,	,	PUNCT
cana-3963	314	10	the	the	DET
cana-3963	314	11	tcfp	tcfp	NOUN
cana-3963	314	12	escalated	escalate	VERB
cana-3963	314	13	sharply	sharply	ADV
cana-3963	314	14	.	.	PUNCT
cana-3963	315	1	this	this	DET
cana-3963	315	2	increase	increase	NOUN
cana-3963	315	3	marked	mark	VERB
cana-3963	315	4	the	the	DET
cana-3963	315	5	point	point	NOUN
cana-3963	315	6	where	where	SCONJ
cana-3963	315	7	the	the	DET
cana-3963	315	8	error	error	NOUN
cana-3963	315	9	-	-	PUNCT
cana-3963	315	10	correcting	correct	VERB
cana-3963	315	11	capabilities	capability	NOUN
cana-3963	315	12	of	of	ADP
cana-3963	315	13	the	the	DET
cana-3963	315	14	codes	code	NOUN
cana-3963	315	15	began	begin	VERB
cana-3963	315	16	to	to	PART
cana-3963	315	17	diminish	diminish	VERB
cana-3963	315	18	,	,	PUNCT
cana-3963	315	19	struggling	struggle	VERB
cana-3963	315	20	to	to	PART
cana-3963	315	21	handle	handle	VERB
cana-3963	315	22	the	the	DET
cana-3963	315	23	higher	high	ADJ
cana-3963	315	24	frequency	frequency	NOUN
cana-3963	315	25	of	of	ADP
cana-3963	315	26	errors	error	NOUN
cana-3963	315	27	.	.	PUNCT
cana-3963	316	1	this	this	DET
cana-3963	316	2	observation	observation	NOUN
cana-3963	316	3	underscores	underscore	VERB
cana-3963	316	4	the	the	DET
cana-3963	316	5	limitations	limitation	NOUN
cana-3963	316	6	of	of	ADP
cana-3963	316	7	the	the	DET
cana-3963	316	8	code	code	NOUN
cana-3963	316	9	at	at	ADP
cana-3963	316	10	elevated	elevated	ADJ
cana-3963	316	11	noise	noise	NOUN
cana-3963	316	12	levels	level	NOUN
cana-3963	316	13	,	,	PUNCT
cana-3963	316	14	pointing	point	VERB
cana-3963	316	15	to	to	ADP
cana-3963	316	16	the	the	DET
cana-3963	316	17	need	need	NOUN
cana-3963	316	18	for	for	ADP
cana-3963	316	19	further	further	ADJ
cana-3963	316	20	optimization	optimization	NOUN
cana-3963	316	21	or	or	CCONJ
cana-3963	316	22	alternative	alternative	ADJ
cana-3963	316	23	strategies	strategy	NOUN
cana-3963	316	24	to	to	PART
cana-3963	316	25	manage	manage	VERB
cana-3963	316	26	such	such	ADJ
cana-3963	316	27	extreme	extreme	ADJ
cana-3963	316	28	conditions	condition	NOUN
cana-3963	316	29	more	more	ADV
cana-3963	316	30	effectively	effectively	ADV
cana-3963	316	31	.	.	PUNCT
cana-3963	317	1	https://github.com/shivendergoswami/quantum-mpcs	https://github.com/shivendergoswami/quantum-mpcs	PROPN
cana-3963	317	2	6	6	NUM
cana-3963	317	3	.	.	PUNCT
cana-3963	317	4	conclusion	conclusion	VERB
cana-3963	317	5	the	the	DET
cana-3963	317	6	method	method	NOUN
cana-3963	317	7	of	of	ADP
cana-3963	317	8	establishing	establish	VERB
cana-3963	317	9	quantum	quantum	ADJ
cana-3963	317	10	codes	code	NOUN
cana-3963	317	11	using	use	VERB
cana-3963	317	12	hdc	hdc	NOUN
cana-3963	317	13	together	together	ADV
cana-3963	317	14	with	with	ADP
cana-3963	317	15	mpc	mpc	NOUN
cana-3963	317	16	and	and	CCONJ
cana-3963	317	17	minimal	minimal	ADJ
cana-3963	317	18	polynomials	polynomial	NOUN
cana-3963	317	19	with	with	ADP
cana-3963	317	20	the	the	DET
cana-3963	317	21	hdc	hdc	NOUN
cana-3963	317	22	property	property	NOUN
cana-3963	317	23	has	have	AUX
cana-3963	317	24	led	lead	VERB
cana-3963	317	25	to	to	ADP
cana-3963	317	26	significant	significant	ADJ
cana-3963	317	27	advancements	advancement	NOUN
cana-3963	317	28	.	.	PUNCT
cana-3963	318	1	the	the	DET
cana-3963	318	2	resulting	result	VERB
cana-3963	318	3	codes	code	NOUN
cana-3963	318	4	,	,	PUNCT
cana-3963	318	5	such	such	ADJ
cana-3963	318	6	as	as	ADP
cana-3963	318	7	the	the	DET
cana-3963	318	8	5[[13,5,5	5[[13,5,5	PROPN
cana-3963	318	9	]	]	X
cana-3963	318	10	]	]	PUNCT
cana-3963	318	11	and	and	CCONJ
cana-3963	318	12	7[[17,9,5	7[[17,9,5	NOUN
cana-3963	318	13	]	]	X
cana-3963	318	14	]	]	X
cana-3963	318	15	codes	code	NOUN
cana-3963	318	16	,	,	PUNCT
cana-3963	318	17	feature	feature	VERB
cana-3963	318	18	excellent	excellent	ADJ
cana-3963	318	19	parameters	parameter	NOUN
cana-3963	318	20	in	in	ADP
cana-3963	318	21	terms	term	NOUN
cana-3963	318	22	of	of	ADP
cana-3963	318	23	distance	distance	NOUN
cana-3963	318	24	,	,	PUNCT
cana-3963	318	25	rate	rate	NOUN
cana-3963	318	26	,	,	PUNCT
cana-3963	318	27	and	and	CCONJ
cana-3963	318	28	length	length	NOUN
cana-3963	318	29	,	,	PUNCT
cana-3963	318	30	making	make	VERB
cana-3963	318	31	them	they	PRON
cana-3963	318	32	highly	highly	ADV
cana-3963	318	33	suitable	suitable	ADJ
cana-3963	318	34	for	for	ADP
cana-3963	318	35	practical	practical	ADJ
cana-3963	318	36	quantum	quantum	ADJ
cana-3963	318	37	computing	computing	NOUN
cana-3963	318	38	applications	application	NOUN
cana-3963	318	39	.	.	PUNCT
cana-3963	319	1	these	these	DET
cana-3963	319	2	codes	code	NOUN
cana-3963	319	3	exhibit	exhibit	VERB
cana-3963	319	4	robust	robust	ADJ
cana-3963	319	5	error	error	NOUN
cana-3963	319	6	correction	correction	NOUN
cana-3963	319	7	capabilities	capability	NOUN
cana-3963	319	8	,	,	PUNCT
cana-3963	319	9	making	make	VERB
cana-3963	319	10	them	they	PRON
cana-3963	319	11	resilient	resilient	ADJ
cana-3963	319	12	to	to	ADP
cana-3963	319	13	various	various	ADJ
cana-3963	319	14	forms	form	NOUN
cana-3963	319	15	of	of	ADP
cana-3963	319	16	quantum	quantum	NOUN
cana-3963	319	17	noise	noise	NOUN
cana-3963	319	18	and	and	CCONJ
cana-3963	319	19	errors	error	NOUN
cana-3963	319	20	.	.	PUNCT
cana-3963	320	1	additionally	additionally	ADV
cana-3963	320	2	,	,	PUNCT
cana-3963	320	3	the	the	DET
cana-3963	320	4	integration	integration	NOUN
cana-3963	320	5	of	of	ADP
cana-3963	320	6	specific	specific	ADJ
cana-3963	320	7	algebraic	algebraic	ADJ
cana-3963	320	8	structures	structure	NOUN
cana-3963	320	9	and	and	CCONJ
cana-3963	320	10	properties	property	NOUN
cana-3963	320	11	enhances	enhance	VERB
cana-3963	320	12	their	their	PRON
cana-3963	320	13	performance	performance	NOUN
cana-3963	320	14	and	and	CCONJ
cana-3963	320	15	establishes	establish	VERB
cana-3963	320	16	a	a	DET
cana-3963	320	17	strong	strong	ADJ
cana-3963	320	18	foundation	foundation	NOUN
cana-3963	320	19	for	for	ADP
cana-3963	320	20	ongoing	ongoing	ADJ
cana-3963	320	21	research	research	NOUN
cana-3963	320	22	and	and	CCONJ
cana-3963	320	23	development	development	NOUN
cana-3963	320	24	in	in	ADP
cana-3963	320	25	quantum	quantum	NOUN
cana-3963	320	26	coding	coding	NOUN
cana-3963	320	27	theory	theory	NOUN
cana-3963	320	28	.	.	PUNCT
cana-3963	321	1	this	this	DET
cana-3963	321	2	innovative	innovative	ADJ
cana-3963	321	3	approach	approach	NOUN
cana-3963	321	4	opens	open	VERB
cana-3963	321	5	new	new	ADJ
cana-3963	321	6	pathways	pathway	NOUN
cana-3963	321	7	for	for	ADP
cana-3963	321	8	the	the	DET
cana-3963	321	9	creation	creation	NOUN
cana-3963	321	10	of	of	ADP
cana-3963	321	11	more	more	ADV
cana-3963	321	12	efficient	efficient	ADJ
cana-3963	321	13	and	and	CCONJ
cana-3963	321	14	reliable	reliable	ADJ
cana-3963	321	15	quantum	quantum	ADJ
cana-3963	321	16	codes	code	NOUN
cana-3963	321	17	,	,	PUNCT
cana-3963	321	18	advancing	advance	VERB
cana-3963	321	19	the	the	DET
cana-3963	321	20	field	field	NOUN
cana-3963	321	21	of	of	ADP
cana-3963	321	22	quantum	quantum	ADJ
cana-3963	321	23	information	information	NOUN
cana-3963	321	24	science	science	NOUN
cana-3963	321	25	.	.	PUNCT
cana-3963	322	1	references	reference	NOUN
cana-3963	322	2	[	[	X
cana-3963	322	3	1	1	NUM
cana-3963	322	4	]	]	X
cana-3963	322	5	calderbank	calderbank	NOUN
cana-3963	322	6	,	,	PUNCT
cana-3963	322	7	a.r	a.r	PROPN
cana-3963	322	8	.	.	PROPN
cana-3963	322	9	,	,	PUNCT
cana-3963	322	10	rains	rain	NOUN
cana-3963	322	11	,	,	PUNCT
cana-3963	322	12	e.m	e.m	PROPN
cana-3963	322	13	.	.	PROPN
cana-3963	322	14	,	,	PUNCT
cana-3963	322	15	shor	shor	PROPN
cana-3963	322	16	,	,	PUNCT
cana-3963	322	17	p.w	p.w	PROPN
cana-3963	322	18	.	.	PROPN
cana-3963	322	19	,	,	PUNCT
cana-3963	322	20	sloane	sloane	NOUN
cana-3963	322	21	,	,	PUNCT
cana-3963	322	22	n.j.a	n.j.a	NOUN
cana-3963	322	23	.	.	PUNCT
cana-3963	322	24	:	:	PUNCT
cana-3963	322	25	quantum	quantum	ADJ
cana-3963	322	26	error	error	NOUN
cana-3963	322	27	correction	correction	NOUN
cana-3963	322	28	via	via	ADP
cana-3963	322	29	codes	code	NOUN
cana-3963	322	30	over	over	ADP
cana-3963	322	31	gf	gf	PROPN
cana-3963	322	32	(	(	PUNCT
cana-3963	322	33	4	4	NUM
cana-3963	322	34	)	)	PUNCT
cana-3963	322	35	.	.	PUNCT
cana-3963	323	1	ieee	ieee	PROPN
cana-3963	323	2	trans	trans	PROPN
cana-3963	323	3	.	.	PROPN
cana-3963	323	4	inf	inf	PROPN
cana-3963	323	5	.	.	PUNCT
cana-3963	323	6	theory	theory	NOUN
cana-3963	323	7	44(4	44(4	NOUN
cana-3963	323	8	)	)	PUNCT
cana-3963	323	9	,	,	PUNCT
cana-3963	323	10	1369–1387	1369–1387	NUM
cana-3963	323	11	(	(	PUNCT
cana-3963	323	12	1998	1998	NUM
cana-3963	323	13	)	)	PUNCT
cana-3963	324	1	[	[	X
cana-3963	324	2	2	2	NUM
cana-3963	324	3	]	]	PUNCT
cana-3963	324	4	shor	shor	NOUN
cana-3963	324	5	,	,	PUNCT
cana-3963	324	6	p.w	p.w	PROPN
cana-3963	324	7	.	.	PUNCT
cana-3963	324	8	:	:	PUNCT
cana-3963	324	9	scheme	scheme	NOUN
cana-3963	324	10	for	for	ADP
cana-3963	324	11	reducing	reduce	VERB
cana-3963	324	12	decoherence	decoherence	NOUN
cana-3963	324	13	in	in	ADP
cana-3963	324	14	quantum	quantum	ADJ
cana-3963	324	15	computer	computer	NOUN
cana-3963	324	16	memory	memory	NOUN
cana-3963	324	17	.	.	PUNCT
cana-3963	325	1	phys	phy	NOUN
cana-3963	325	2	.	.	PUNCT
cana-3963	326	1	rev	rev	PROPN
cana-3963	326	2	.	.	PUNCT
cana-3963	327	1	a	a	DET
cana-3963	327	2	52	52	NUM
cana-3963	327	3	,	,	PUNCT
cana-3963	327	4	2493	2493	NUM
cana-3963	327	5	–	–	PUNCT
cana-3963	327	6	2496	2496	NUM
cana-3963	327	7	(	(	PUNCT
cana-3963	327	8	1995	1995	NUM
cana-3963	327	9	)	)	PUNCT
cana-3963	328	1	[	[	X
cana-3963	328	2	3	3	NUM
cana-3963	328	3	]	]	X
cana-3963	328	4	steane	steane	ADJ
cana-3963	328	5	,	,	PUNCT
cana-3963	328	6	a.m.	a.m.	ADV
cana-3963	328	7	:	:	PUNCT
cana-3963	328	8	multiple	multiple	ADJ
cana-3963	328	9	-	-	PUNCT
cana-3963	328	10	particle	particle	NOUN
cana-3963	328	11	interference	interference	NOUN
cana-3963	328	12	and	and	CCONJ
cana-3963	328	13	quantum	quantum	NOUN
cana-3963	328	14	error	error	NOUN
cana-3963	328	15	correction	correction	NOUN
cana-3963	328	16	.	.	PUNCT
cana-3963	329	1	proc	proc	PROPN
cana-3963	329	2	.	.	PUNCT
cana-3963	330	1	r.	r.	PROPN
cana-3963	330	2	soc	soc	PROPN
cana-3963	330	3	.	.	PUNCT
cana-3963	331	1	lond	lond	PROPN
cana-3963	331	2	.	.	PUNCT
cana-3963	332	1	ser	ser	PROPN
cana-3963	332	2	.	.	PUNCT
cana-3963	333	1	a	a	DET
cana-3963	333	2	452	452	NUM
cana-3963	333	3	,	,	PUNCT
cana-3963	333	4	2551	2551	NUM
cana-3963	333	5	–	–	PUNCT
cana-3963	333	6	2577	2577	NUM
cana-3963	333	7	(	(	PUNCT
cana-3963	333	8	1996	1996	NUM
cana-3963	333	9	)	)	PUNCT
cana-3963	334	1	[	[	X
cana-3963	334	2	4	4	NUM
cana-3963	334	3	]	]	X
cana-3963	334	4	ashikhmin	ashikhmin	PROPN
cana-3963	334	5	,	,	PUNCT
cana-3963	334	6	a.	a.	NOUN
cana-3963	334	7	,	,	PUNCT
cana-3963	334	8	knill	knill	NOUN
cana-3963	334	9	,	,	PUNCT
cana-3963	334	10	e.	e.	PROPN
cana-3963	334	11	:	:	PUNCT
cana-3963	334	12	nonbinary	nonbinary	ADJ
cana-3963	334	13	quantum	quantum	ADJ
cana-3963	334	14	stabilizer	stabilizer	NOUN
cana-3963	334	15	codes	code	NOUN
cana-3963	334	16	.	.	PUNCT
cana-3963	335	1	ieee	ieee	PROPN
cana-3963	335	2	trans	trans	PROPN
cana-3963	335	3	.	.	PROPN
cana-3963	335	4	inf	inf	PROPN
cana-3963	335	5	.	.	PUNCT
cana-3963	335	6	theory	theory	PROPN
cana-3963	335	7	47(7	47(7	PROPN
cana-3963	335	8	)	)	PUNCT
cana-3963	335	9	,	,	PUNCT
cana-3963	335	10	3065	3065	NUM
cana-3963	335	11	–	–	PUNCT
cana-3963	335	12	3072	3072	NUM
cana-3963	335	13	(	(	PUNCT
cana-3963	335	14	2001	2001	NUM
cana-3963	335	15	)	)	PUNCT
cana-3963	336	1	[	[	X
cana-3963	336	2	5	5	X
cana-3963	336	3	]	]	PUNCT
cana-3963	336	4	grassl	grassl	NOUN
cana-3963	336	5	,	,	PUNCT
cana-3963	336	6	m.	m.	NOUN
cana-3963	336	7	,	,	PUNCT
cana-3963	336	8	beth	beth	PROPN
cana-3963	336	9	,	,	PUNCT
cana-3963	336	10	t.	t.	PROPN
cana-3963	336	11	,	,	PUNCT
cana-3963	336	12	rötteler	rötteler	NOUN
cana-3963	336	13	,	,	PUNCT
cana-3963	336	14	m.	m.	NOUN
cana-3963	336	15	:	:	PUNCT
cana-3963	336	16	on	on	ADP
cana-3963	336	17	optimal	optimal	ADJ
cana-3963	336	18	quantum	quantum	ADJ
cana-3963	336	19	codes	code	NOUN
cana-3963	336	20	.	.	PUNCT
cana-3963	337	1	int	int	NOUN
cana-3963	337	2	.	.	PUNCT
cana-3963	338	1	j.	j.	PROPN
cana-3963	338	2	quantum	quantum	PROPN
cana-3963	338	3	inf	inf	PROPN
cana-3963	338	4	.	.	PUNCT
cana-3963	339	1	2(1	2(1	NUM
cana-3963	339	2	)	)	PUNCT
cana-3963	339	3	,	,	PUNCT
cana-3963	340	1	55–64	55–64	NUM
cana-3963	340	2	(	(	PUNCT
cana-3963	340	3	2004	2004	NUM
cana-3963	340	4	)	)	PUNCT
cana-3963	341	1	[	[	X
cana-3963	341	2	6	6	NUM
cana-3963	341	3	]	]	SYM
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cana-3963	341	5	,	,	PUNCT
cana-3963	341	6	x.	x.	PROPN
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cana-3963	341	8	zhu	zhu	PROPN
cana-3963	341	9	,	,	PUNCT
cana-3963	341	10	s.	s.	PROPN
cana-3963	341	11	,	,	PUNCT
cana-3963	341	12	li	li	PROPN
cana-3963	341	13	,	,	PUNCT
cana-3963	341	14	p.	p.	NOUN
cana-3963	341	15	:	:	PUNCT
cana-3963	341	16	ieee	ieee	PROPN
cana-3963	341	17	trans	trans	PROPN
cana-3963	341	18	.	.	PROPN
cana-3963	341	19	inf	inf	PROPN
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cana-3963	341	22	60(4	60(4	NUM
cana-3963	341	23	)	)	PUNCT
cana-3963	341	24	,	,	PUNCT
cana-3963	341	25	2080	2080	NUM
cana-3963	341	26	(	(	PUNCT
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cana-3963	341	28	)	)	PUNCT
cana-3963	342	1	[	[	X
cana-3963	342	2	7	7	NUM
cana-3963	342	3	]	]	X
cana-3963	342	4	chen	chen	PROPN
cana-3963	342	5	,	,	PUNCT
cana-3963	342	6	b.	b.	PROPN
cana-3963	342	7	,	,	PUNCT
cana-3963	342	8	ling	ling	PROPN
cana-3963	342	9	,	,	PUNCT
cana-3963	342	10	s.	s.	PROPN
cana-3963	342	11	,	,	PUNCT
cana-3963	342	12	zhang	zhang	PROPN
cana-3963	342	13	,	,	PUNCT
cana-3963	342	14	g.	g.	PROPN
cana-3963	342	15	:	:	PUNCT
cana-3963	342	16	ieee	ieee	PROPN
cana-3963	342	17	trans	trans	PROPN
cana-3963	342	18	.	.	PUNCT
cana-3963	343	1	inform	inform	VERB
cana-3963	343	2	.	.	PUNCT
cana-3963	344	1	theory	theory	NOUN
cana-3963	344	2	61(3	61(3	NUM
cana-3963	344	3	)	)	PUNCT
cana-3963	344	4	,	,	PUNCT
cana-3963	344	5	1474	1474	NUM
cana-3963	344	6	(	(	PUNCT
cana-3963	344	7	2015	2015	NUM
cana-3963	344	8	)	)	PUNCT
cana-3963	345	1	[	[	X
cana-3963	345	2	8	8	NUM
cana-3963	345	3	]	]	SYM
cana-3963	345	4	li	li	PROPN
cana-3963	345	5	,	,	PUNCT
cana-3963	345	6	s.	s.	PROPN
cana-3963	345	7	,	,	PUNCT
cana-3963	345	8	xiong	xiong	PROPN
cana-3963	345	9	,	,	PUNCT
cana-3963	345	10	m.	m.	NOUN
cana-3963	345	11	,	,	PUNCT
cana-3963	345	12	ge	ge	PROPN
cana-3963	345	13	,	,	PUNCT
cana-3963	345	14	g.	g.	PROPN
cana-3963	345	15	:	:	PUNCT
cana-3963	345	16	ieee	ieee	PROPN
cana-3963	345	17	trans	trans	PROPN
cana-3963	345	18	.	.	PUNCT
cana-3963	345	19	inform	inform	VERB
cana-3963	345	20	.	.	PUNCT
cana-3963	345	21	theory	theory	NOUN
cana-3963	345	22	64(4	64(4	NOUN
cana-3963	345	23	)	)	PUNCT
cana-3963	345	24	,	,	PUNCT
cana-3963	345	25	1703	1703	NUM
cana-3963	345	26	(	(	PUNCT
cana-3963	345	27	2016	2016	NUM
cana-3963	345	28	)	)	PUNCT
cana-3963	346	1	[	[	X
cana-3963	346	2	9	9	NUM
cana-3963	346	3	]	]	X
cana-3963	346	4	liu	liu	PROPN
cana-3963	346	5	,	,	PUNCT
cana-3963	346	6	x.	x.	PROPN
cana-3963	346	7	s.	s.	PROPN
cana-3963	346	8	,	,	PUNCT
cana-3963	346	9	liu	liu	PROPN
cana-3963	346	10	,	,	PUNCT
cana-3963	346	11	h.	h.	PROPN
cana-3963	346	12	:	:	PUNCT
cana-3963	346	13	quantum	quantum	PROPN
cana-3963	346	14	inf	inf	PROPN
cana-3963	346	15	.	.	PROPN
cana-3963	346	16	process	process	PROPN
cana-3963	346	17	16	16	NUM
cana-3963	346	18	,	,	PUNCT
cana-3963	346	19	240	240	NUM
cana-3963	346	20	(	(	PUNCT
cana-3963	346	21	2017	2017	NUM
cana-3963	346	22	)	)	PUNCT
cana-3963	346	23	.	.	PUNCT
cana-3963	347	1	doi	doi	NOUN
cana-3963	347	2	:	:	PUNCT
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cana-3963	347	4	/	/	SYM
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cana-3963	347	6	-	-	PUNCT
cana-3963	347	7	0171695	0171695	NUM
cana-3963	347	8	-	-	SYM
cana-3963	347	9	7	7	NUM
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cana-3963	348	2	10	10	NUM
cana-3963	348	3	]	]	X
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cana-3963	348	5	,	,	PUNCT
cana-3963	348	6	c.	c.	PROPN
cana-3963	348	7	,	,	PUNCT
cana-3963	348	8	hernando	hernando	PROPN
cana-3963	348	9	,	,	PUNCT
cana-3963	348	10	f.	f.	PROPN
cana-3963	348	11	,	,	PUNCT
cana-3963	348	12	ruano	ruano	PROPN
cana-3963	348	13	,	,	PUNCT
cana-3963	348	14	d.	d.	PROPN
cana-3963	348	15	:	:	PUNCT
cana-3963	348	16	new	new	ADJ
cana-3963	348	17	quantum	quantum	NOUN
cana-3963	348	18	codes	code	NOUN
cana-3963	348	19	from	from	ADP
cana-3963	348	20	evaluation	evaluation	NOUN
cana-3963	348	21	and	and	CCONJ
cana-3963	348	22	matrix	matrix	NOUN
cana-3963	348	23	-	-	PUNCT
cana-3963	348	24	product	product	NOUN
cana-3963	348	25	codes	code	NOUN
cana-3963	348	26	.	.	PUNCT
cana-3963	349	1	finite	finite	PROPN
cana-3963	349	2	fields	field	NOUN
cana-3963	349	3	appl	appl	PROPN
cana-3963	349	4	.	.	PUNCT
cana-3963	350	1	36	36	NUM
cana-3963	350	2	,	,	PUNCT
cana-3963	350	3	98–120	98–120	NUM
cana-3963	350	4	(	(	PUNCT
cana-3963	350	5	2015	2015	NUM
cana-3963	350	6	)	)	PUNCT
cana-3963	351	1	[	[	X
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cana-3963	351	3	]	]	X
cana-3963	351	4	zhang	zhang	PROPN
cana-3963	351	5	,	,	PUNCT
cana-3963	351	6	t.	t.	PROPN
cana-3963	351	7	,	,	PUNCT
cana-3963	351	8	ge	ge	PROPN
cana-3963	351	9	,	,	PUNCT
cana-3963	351	10	g.	g.	NOUN
cana-3963	351	11	:	:	PUNCT
cana-3963	351	12	quantum	quantum	NOUN
cana-3963	351	13	codes	code	NOUN
cana-3963	351	14	from	from	ADP
cana-3963	351	15	generalized	generalized	ADJ
cana-3963	351	16	reed	reed	PROPN
cana-3963	351	17	-	-	PUNCT
cana-3963	351	18	solomon	solomon	PROPN
cana-3963	351	19	codes	code	NOUN
cana-3963	351	20	and	and	CCONJ
cana-3963	351	21	matrix	matrix	NOUN
cana-3963	351	22	-	-	PUNCT
cana-3963	351	23	product	product	NOUN
cana-3963	351	24	codes	code	NOUN
cana-3963	351	25	,	,	PUNCT
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cana-3963	351	27	(	(	PUNCT
cana-3963	351	28	2015	2015	NUM
cana-3963	351	29	)	)	PUNCT
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cana-3963	352	2	12	12	NUM
cana-3963	352	3	]	]	X
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cana-3963	352	6	x.	x.	PROPN
cana-3963	352	7	,	,	PUNCT
cana-3963	352	8	hu	hu	PROPN
cana-3963	352	9	,	,	PUNCT
cana-3963	352	10	p.	p.	NOUN
cana-3963	352	11	:	:	PUNCT
cana-3963	352	12	new	new	ADJ
cana-3963	352	13	quantum	quantum	NOUN
cana-3963	352	14	codes	code	NOUN
cana-3963	352	15	from	from	ADP
cana-3963	352	16	two	two	NUM
cana-3963	352	17	linear	linear	ADJ
cana-3963	352	18	codes	code	NOUN
cana-3963	352	19	.	.	PUNCT
cana-3963	353	1	quantum	quantum	PROPN
cana-3963	353	2	inf	inf	PROPN
cana-3963	353	3	process	process	NOUN
cana-3963	353	4	19	19	NUM
cana-3963	353	5	,	,	PUNCT
cana-3963	353	6	78	78	NUM
cana-3963	353	7	(	(	PUNCT
cana-3963	353	8	2020	2020	NUM
cana-3963	353	9	)	)	PUNCT
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cana-3963	354	2	13	13	NUM
cana-3963	354	3	]	]	SYM
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cana-3963	354	8	li	li	PROPN
cana-3963	354	9	,	,	PUNCT
cana-3963	354	10	r.	r.	PROPN
cana-3963	354	11	,	,	PUNCT
cana-3963	354	12	wang	wang	PROPN
cana-3963	354	13	,	,	PUNCT
cana-3963	354	14	j.	j.	PROPN
cana-3963	354	15	,	,	PUNCT
cana-3963	354	16	lv	lv	PROPN
cana-3963	354	17	,	,	PUNCT
cana-3963	354	18	j.	j.	PROPN
cana-3963	354	19	:	:	PUNCT
cana-3963	354	20	construction	construction	NOUN
cana-3963	354	21	of	of	ADP
cana-3963	354	22	new	new	ADJ
cana-3963	354	23	matrix	matrix	NOUN
cana-3963	354	24	-	-	PUNCT
cana-3963	354	25	product	product	NOUN
cana-3963	354	26	codes	code	NOUN
cana-3963	354	27	and	and	CCONJ
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cana-3963	354	29	applications	application	NOUN
cana-3963	354	30	.	.	PUNCT
cana-3963	355	1	ieee	ieee	NOUN
cana-3963	355	2	access	access	NOUN
cana-3963	355	3	(	(	PUNCT
cana-3963	355	4	2019	2019	NUM
cana-3963	355	5	)	)	PUNCT
cana-3963	355	6	.	.	PUNCT
cana-3963	356	1	[	[	X
cana-3963	356	2	14	14	NUM
cana-3963	356	3	]	]	X
cana-3963	356	4	rathor	rathor	NOUN
cana-3963	356	5	,	,	PUNCT
cana-3963	356	6	a.	a.	PROPN
cana-3963	356	7	,	,	PUNCT
cana-3963	356	8	kumar	kumar	PROPN
cana-3963	356	9	,	,	PUNCT
cana-3963	356	10	m.	m.	NOUN
cana-3963	356	11	,	,	PUNCT
cana-3963	356	12	mishra	mishra	PROPN
cana-3963	356	13	,	,	PUNCT
cana-3963	356	14	r.k	r.k	PROPN
cana-3963	356	15	.	.	PROPN
cana-3963	356	16	,	,	PUNCT
cana-3963	356	17	goswami	goswami	PROPN
cana-3963	356	18	,	,	PUNCT
cana-3963	356	19	s.	s.	PROPN
cana-3963	356	20	,	,	PUNCT
cana-3963	356	21	chaudhary	chaudhary	PROPN
cana-3963	356	22	,	,	PUNCT
cana-3963	356	23	a.	a.	NOUN
cana-3963	356	24	:	:	PUNCT
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cana-3963	356	29	over	over	ADP
cana-3963	356	30	huff	huff	PROPN
cana-3963	356	31	curve	curve	NOUN
cana-3963	356	32	for	for	ADP
cana-3963	356	33	post	post	ADJ
cana-3963	356	34	quantum	quantum	ADJ
cana-3963	356	35	cryptography	cryptography	NOUN
cana-3963	356	36	.	.	PUNCT
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cana-3963	357	3	of	of	ADP
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cana-3963	357	6	and	and	CCONJ
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cana-3963	357	8	,	,	PUNCT
cana-3963	357	9	16(6	16(6	NUM
cana-3963	357	10	)	)	PUNCT
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cana-3963	357	13	-	-	SYM
cana-3963	357	14	457	457	NUM
cana-3963	357	15	(	(	PUNCT
cana-3963	357	16	2023	2023	NUM
cana-3963	357	17	)	)	PUNCT
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cana-3963	357	19	on	on	ADP
cana-3963	357	20	applied	apply	VERB
cana-3963	357	21	nonlinear	nonlinear	ADJ
cana-3963	357	22	analysis	analysis	NOUN
cana-3963	357	23	issn	issn	NOUN
cana-3963	357	24	:	:	PUNCT
cana-3963	357	25	1074	1074	NUM
cana-3963	357	26	-	-	PUNCT
cana-3963	357	27	133x	133x	NUM
cana-3963	357	28	vol	vol	NOUN
cana-3963	357	29	32	32	NUM
cana-3963	357	30	no	no	NOUN
cana-3963	357	31	.	.	PUNCT
cana-3963	358	1	9s	9s	NUM
cana-3963	358	2	(	(	PUNCT
cana-3963	358	3	2025	2025	NUM
cana-3963	358	4	)	)	PUNCT
cana-3963	358	5	553	553	NUM
cana-3963	358	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3963	359	1	[	[	X
cana-3963	359	2	15	15	NUM
cana-3963	359	3	]	]	X
cana-3963	359	4	kumar	kumar	PROPN
cana-3963	359	5	,	,	PUNCT
cana-3963	359	6	m.	m.	NOUN
cana-3963	359	7	gupta	gupta	PROPN
cana-3963	359	8	,	,	PUNCT
cana-3963	359	9	m.	m.	PROPN
cana-3963	359	10	k.	k.	PROPN
cana-3963	359	11	,	,	PUNCT
cana-3963	359	12	mishra	mishra	PROPN
cana-3963	359	13	,	,	PUNCT
cana-3963	359	14	r.k	r.k	PROPN
cana-3963	359	15	.	.	PROPN
cana-3963	359	16	,	,	PUNCT
cana-3963	359	17	dubey	dubey	PROPN
cana-3963	359	18	,	,	PUNCT
cana-3963	359	19	s.s	s.s	PROPN
cana-3963	359	20	.	.	PROPN
cana-3963	359	21	,	,	PUNCT
cana-3963	359	22	kumar	kumar	PROPN
cana-3963	359	23	,	,	PUNCT
cana-3963	359	24	a.	a.	PROPN
cana-3963	359	25	,	,	PUNCT
cana-3963	359	26	hardeep	hardeep	NOUN
cana-3963	359	27	:	:	PUNCT
cana-3963	359	28	security	security	NOUN
cana-3963	359	29	analysis	analysis	NOUN
cana-3963	359	30	of	of	ADP
cana-3963	359	31	a	a	DET
cana-3963	359	32	threshold	threshold	NOUN
cana-3963	359	33	quantum	quantum	NOUN
cana-3963	359	34	state	state	NOUN
cana-3963	359	35	sharing	sharing	NOUN
cana-3963	359	36	scheme	scheme	NOUN
cana-3963	359	37	of	of	ADP
cana-3963	359	38	an	an	DET
cana-3963	359	39	arbitrary	arbitrary	ADJ
cana-3963	359	40	single	single	ADJ
cana-3963	359	41	-	-	PUNCT
cana-3963	359	42	qutrit	qutrit	NOUN
cana-3963	359	43	based	base	VERB
cana-3963	359	44	on	on	ADP
cana-3963	359	45	lagrange	lagrange	NOUN
cana-3963	359	46	interpolation	interpolation	NOUN
cana-3963	359	47	method	method	NOUN
cana-3963	359	48	.	.	PUNCT
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cana-3963	360	2	evolving	evolve	VERB
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cana-3963	360	4	for	for	ADP
cana-3963	360	5	computing	computing	NOUN
cana-3963	360	6	,	,	PUNCT
cana-3963	360	7	communication	communication	NOUN
cana-3963	360	8	and	and	CCONJ
cana-3963	360	9	smart	smart	ADJ
cana-3963	360	10	world	world	NOUN
cana-3963	360	11	,	,	PUNCT
cana-3963	360	12	lecture	lecture	NOUN
cana-3963	360	13	notes	note	NOUN
cana-3963	360	14	in	in	ADP
cana-3963	360	15	electrical	electrical	ADJ
cana-3963	360	16	engineering	engineering	NOUN
cana-3963	360	17	,	,	PUNCT
cana-3963	360	18	694	694	NUM
cana-3963	360	19	,	,	PUNCT
cana-3963	360	20	373389	373389	NUM
cana-3963	360	21	(	(	PUNCT
cana-3963	360	22	2020	2020	NUM
cana-3963	360	23	)	)	PUNCT
cana-3963	361	1	[	[	X
cana-3963	361	2	16	16	NUM
cana-3963	361	3	]	]	PUNCT
cana-3963	361	4	hardeep	hardeep	PROPN
cana-3963	361	5	,	,	PUNCT
cana-3963	361	6	kumar	kumar	PROPN
cana-3963	361	7	,	,	PUNCT
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cana-3963	361	9	,	,	PUNCT
cana-3963	361	10	mishra	mishra	PROPN
cana-3963	361	11	,	,	PUNCT
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cana-3963	361	13	k.	k.	PROPN
cana-3963	361	14	:	:	PUNCT
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cana-3963	362	2	of	of	ADP
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cana-3963	362	4	using	use	VERB
cana-3963	362	5	bi	bi	ADJ
cana-3963	362	6	-	-	ADJ
cana-3963	362	7	qutrit	qutrit	ADJ
cana-3963	362	8	quantum	quantum	NOUN
cana-3963	362	9	states	state	NOUN
cana-3963	362	10	based	base	VERB
cana-3963	362	11	on	on	ADP
cana-3963	362	12	bivariate	bivariate	ADJ
cana-3963	362	13	quantum	quantum	ADJ
cana-3963	362	14	gates	gate	NOUN
cana-3963	362	15	.	.	PUNCT
cana-3963	363	1	journal	journal	PROPN
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cana-3963	363	3	xi'an	xi'an	PROPN
cana-3963	363	4	shiyou	shiyou	PROPN
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cana-3963	363	6	,	,	PUNCT
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cana-3963	363	8	sciences	science	NOUN
cana-3963	363	9	edition	edition	NOUN
cana-3963	363	10	,	,	PUNCT
cana-3963	363	11	64(12	64(12	NUM
cana-3963	363	12	)	)	PUNCT
cana-3963	363	13	,	,	PUNCT
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cana-3963	363	15	-	-	SYM
cana-3963	363	16	101	101	NUM
cana-3963	363	17	(	(	PUNCT
cana-3963	363	18	2021	2021	NUM
cana-3963	363	19	)	)	PUNCT
cana-3963	364	1	[	[	X
cana-3963	364	2	17	17	NUM
cana-3963	364	3	]	]	X
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cana-3963	364	5	,	,	PUNCT
cana-3963	364	6	t.	t.	PROPN
cana-3963	364	7	,	,	PUNCT
cana-3963	364	8	norton	norton	PROPN
cana-3963	364	9	,	,	PUNCT
cana-3963	364	10	g.h	g.h	PROPN
cana-3963	364	11	.	.	PUNCT
cana-3963	364	12	:	:	PUNCT
cana-3963	364	13	matrix	matrix	NOUN
cana-3963	364	14	-	-	PUNCT
cana-3963	364	15	product	product	NOUN
cana-3963	364	16	codes	code	NOUN
cana-3963	364	17	over	over	ADP
cana-3963	364	18	fq	fq	PROPN
cana-3963	364	19	.	.	PROPN
cana-3963	364	20	appl	appl	PROPN
cana-3963	364	21	.	.	PUNCT
cana-3963	365	1	algebra	algebra	PROPN
cana-3963	365	2	eng	eng	PROPN
cana-3963	365	3	.	.	PUNCT
cana-3963	365	4	commun	commun	PROPN
cana-3963	365	5	.	.	PUNCT
cana-3963	366	1	comput	comput	NOUN
cana-3963	366	2	.	.	PUNCT
cana-3963	367	1	12	12	NUM
cana-3963	367	2	,	,	PUNCT
cana-3963	367	3	477–500	477–500	NUM
cana-3963	367	4	(	(	PUNCT
cana-3963	367	5	2001	2001	NUM
cana-3963	367	6	)	)	PUNCT
cana-3963	368	1	[	[	X
cana-3963	368	2	18	18	NUM
cana-3963	368	3	]	]	X
cana-3963	368	4	hernando	hernando	PROPN
cana-3963	368	5	,	,	PUNCT
cana-3963	368	6	f.	f.	PROPN
cana-3963	368	7	,	,	PUNCT
cana-3963	368	8	lally	lally	PROPN
cana-3963	368	9	,	,	PUNCT
cana-3963	368	10	k.	k.	PROPN
cana-3963	368	11	,	,	PUNCT
cana-3963	368	12	ruano	ruano	PROPN
cana-3963	368	13	,	,	PUNCT
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cana-3963	368	15	:	:	PUNCT
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cana-3963	368	23	codes	code	NOUN
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cana-3963	368	25	nested	nested	ADJ
cana-3963	368	26	codes	code	NOUN
cana-3963	368	27	.	.	PUNCT
cana-3963	369	1	appl	appl	PROPN
cana-3963	369	2	.	.	PUNCT
cana-3963	370	1	algebra	algebra	PROPN
cana-3963	370	2	eng	eng	PROPN
cana-3963	370	3	.	.	PUNCT
cana-3963	370	4	commun	commun	PROPN
cana-3963	370	5	.	.	PUNCT
cana-3963	371	1	comput	comput	NOUN
cana-3963	371	2	.	.	PUNCT
cana-3963	372	1	20(5–6	20(5–6	NUM
cana-3963	372	2	)	)	PUNCT
cana-3963	372	3	,	,	PUNCT
cana-3963	372	4	497–507	497–507	NUM
cana-3963	372	5	(	(	PUNCT
cana-3963	372	6	2009	2009	NUM
cana-3963	372	7	)	)	PUNCT
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cana-3963	373	2	19	19	NUM
cana-3963	373	3	]	]	X
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cana-3963	373	5	,	,	PUNCT
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cana-3963	373	12	,	,	PUNCT
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cana-3963	373	14	,	,	PUNCT
cana-3963	373	15	h.	h.	PROPN
cana-3963	373	16	,	,	PUNCT
cana-3963	373	17	yu	yu	PROPN
cana-3963	373	18	,	,	PUNCT
cana-3963	373	19	l.	l.	PROPN
cana-3963	373	20	:	:	PUNCT
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cana-3963	373	23	quantum	quantum	NOUN
cana-3963	373	24	codes	code	NOUN
cana-3963	373	25	from	from	ADP
cana-3963	373	26	matrix	matrix	NOUN
cana-3963	373	27	product	product	NOUN
cana-3963	373	28	codes	code	NOUN
cana-3963	373	29	.	.	PUNCT
cana-3963	373	30	cryptogr	cryptogr	NOUN
cana-3963	373	31	.	.	PUNCT
cana-3963	374	1	commun	commun	PROPN
cana-3963	374	2	.	.	PUNCT
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cana-3963	375	2	,	,	PUNCT
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cana-3963	375	4	(	(	PUNCT
cana-3963	375	5	2018	2018	NUM
cana-3963	375	6	)	)	PUNCT
cana-3963	376	1	[	[	X
cana-3963	376	2	20	20	NUM
cana-3963	376	3	]	]	X
cana-3963	376	4	la	la	X
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cana-3963	376	6	,	,	PUNCT
cana-3963	376	7	g.g	g.g	PROPN
cana-3963	376	8	.	.	PROPN
cana-3963	376	9	:	:	PUNCT
cana-3963	376	10	ieee	ieee	PROPN
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cana-3963	376	12	.	.	PROPN
cana-3963	376	13	inf	inf	PROPN
cana-3963	376	14	.	.	PROPN
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cana-3963	376	17	)	)	PUNCT
cana-3963	376	18	,	,	PUNCT
cana-3963	376	19	5551	5551	NUM
cana-3963	376	20	(	(	PUNCT
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cana-3963	376	22	)	)	PUNCT
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cana-3963	377	12	,	,	PUNCT
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cana-3963	377	14	,	,	PUNCT
cana-3963	377	15	p.	p.	PROPN
cana-3963	377	16	k.	k.	PROPN
cana-3963	377	17	:	:	PUNCT
cana-3963	378	1	ieee	ieee	PROPN
cana-3963	378	2	trans	trans	PROPN
cana-3963	378	3	.	.	PROPN
cana-3963	378	4	inf	inf	PROPN
cana-3963	378	5	.	.	PROPN
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cana-3963	378	8	,	,	PUNCT
cana-3963	378	9	1183	1183	NUM
cana-3963	378	10	(	(	PUNCT
cana-3963	378	11	2007	2007	NUM
cana-3963	378	12	)	)	PUNCT
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cana-3963	379	3	]	]	X
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cana-3963	379	7	,	,	PUNCT
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cana-3963	379	9	,	,	PUNCT
cana-3963	379	10	m.	m.	NOUN
cana-3963	379	11	,	,	PUNCT
cana-3963	379	12	mishra	mishra	PROPN
cana-3963	379	13	,	,	PUNCT
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cana-3963	379	20	:	:	PUNCT
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cana-3963	379	25	stabilizer	stabilizer	NOUN
cana-3963	379	26	codes	code	NOUN
cana-3963	379	27	over	over	ADP
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cana-3963	379	29	hadamard	hadamard	ADJ
cana-3963	379	30	difference	difference	NOUN
cana-3963	379	31	sets	set	NOUN
cana-3963	379	32	for	for	ADP
cana-3963	379	33	quantum	quantum	ADJ
cana-3963	379	34	system	system	NOUN
cana-3963	379	35	.	.	PUNCT
cana-3963	380	1	iaeng	iaeng	PROPN
cana-3963	380	2	international	international	PROPN
cana-3963	380	3	journal	journal	PROPN
cana-3963	380	4	of	of	ADP
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cana-3963	380	6	mathematics	mathematic	NOUN
cana-3963	380	7	,	,	PUNCT
cana-3963	380	8	54(7	54(7	NOUN
cana-3963	380	9	)	)	PUNCT
cana-3963	380	10	,	,	PUNCT
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cana-3963	380	12	(	(	PUNCT
cana-3963	380	13	2024	2024	NUM
cana-3963	380	14	)	)	PUNCT
cana-3963	381	1	[	[	X
cana-3963	381	2	23	23	NUM
cana-3963	381	3	]	]	X
cana-3963	381	4	rathor	rathor	NOUN
cana-3963	381	5	,	,	PUNCT
cana-3963	381	6	a.	a.	PROPN
cana-3963	381	7	,	,	PUNCT
cana-3963	381	8	kumar	kumar	PROPN
cana-3963	381	9	,	,	PUNCT
cana-3963	381	10	m.	m.	NOUN
cana-3963	381	11	,	,	PUNCT
cana-3963	381	12	mishra	mishra	PROPN
cana-3963	381	13	,	,	PUNCT
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cana-3963	381	20	:	:	PUNCT
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cana-3963	381	25	on	on	ADP
cana-3963	381	26	hessian	hessian	ADJ
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cana-3963	381	28	.	.	PUNCT
cana-3963	382	1	iaeng	iaeng	PROPN
cana-3963	382	2	international	international	PROPN
cana-3963	382	3	journal	journal	PROPN
cana-3963	382	4	of	of	ADP
cana-3963	382	5	computer	computer	NOUN
cana-3963	382	6	science	science	NOUN
cana-3963	382	7	,	,	PUNCT
cana-3963	382	8	51(7	51(7	PROPN
cana-3963	382	9	)	)	PUNCT
cana-3963	382	10	,	,	PUNCT
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cana-3963	382	12	-	-	SYM
cana-3963	382	13	917	917	NUM
cana-3963	382	14	(	(	PUNCT
cana-3963	382	15	2024	2024	NUM
cana-3963	382	16	)	)	PUNCT
cana-3963	383	1	[	[	X
cana-3963	383	2	24	24	NUM
cana-3963	383	3	]	]	X
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cana-3963	383	5	,	,	PUNCT
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cana-3963	383	7	:	:	PUNCT
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cana-3963	383	13	,	,	PUNCT
cana-3963	383	14	online	online	ADV
cana-3963	383	15	available	available	ADJ
cana-3963	383	16	at	at	ADP
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cana-3963	383	18	.	.	PUNCT