id	sid	tid	token	lemma	pos
cana-5711	1	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	1	2	communications	communication	NOUN
cana-5711	1	3	on	on	ADP
cana-5711	1	4	applied	apply	VERB
cana-5711	1	5	nonlinear	nonlinear	ADJ
cana-5711	1	6	analysis	analysis	NOUN
cana-5711	1	7	issn	issn	NOUN
cana-5711	1	8	:	:	PUNCT
cana-5711	1	9	1074	1074	NUM
cana-5711	1	10	-	-	PUNCT
cana-5711	1	11	133x	133x	NUM
cana-5711	1	12	vol	vol	VERB
cana-5711	1	13	32	32	NUM
cana-5711	1	14	no	no	NOUN
cana-5711	1	15	.	.	PUNCT
cana-5711	2	1	10s	10	NOUN
cana-5711	2	2	(	(	PUNCT
cana-5711	2	3	2025	2025	NUM
cana-5711	2	4	)	)	PUNCT
cana-5711	2	5	2695	2695	NUM
cana-5711	2	6	on	on	ADP
cana-5711	2	7	additive	additive	ADJ
cana-5711	2	8	complementary	complementary	ADJ
cana-5711	2	9	dual	dual	ADJ
cana-5711	2	10	codes	code	NOUN
cana-5711	2	11	over	over	ADP
cana-5711	2	12	ℤ2rs	ℤ2r	NOUN
cana-5711	2	13	and	and	CCONJ
cana-5711	2	14	their	their	PRON
cana-5711	2	15	macwilliams	macwilliam	NOUN
cana-5711	2	16	identities	identity	NOUN
cana-5711	2	17	r.	r.	PROPN
cana-5711	2	18	gokul1	gokul1	PROPN
cana-5711	2	19	*	*	PROPN
cana-5711	2	20	,	,	PUNCT
cana-5711	2	21	g.	g.	PROPN
cana-5711	2	22	karthick2	karthick2	PROPN
cana-5711	2	23	,	,	PUNCT
cana-5711	2	24	m.	m.	NOUN
cana-5711	2	25	cruz3	cruz3	PROPN
cana-5711	2	26	,	,	PUNCT
cana-5711	2	27	c.	c.	PROPN
cana-5711	2	28	durairajan4	durairajan4	PROPN
cana-5711	3	1	1,4department	1,4department	NUM
cana-5711	3	2	of	of	ADP
cana-5711	3	3	mathematics	mathematic	NOUN
cana-5711	3	4	,	,	PUNCT
cana-5711	3	5	bharathidasan	bharathidasan	ADJ
cana-5711	3	6	university	university	NOUN
cana-5711	3	7	,	,	PUNCT
cana-5711	3	8	tiruchirappalli	tiruchirappalli	PROPN
cana-5711	3	9	–	–	PUNCT
cana-5711	3	10	620	620	NUM
cana-5711	3	11	024	024	NUM
cana-5711	3	12	,	,	PUNCT
cana-5711	3	13	tamil	tamil	PROPN
cana-5711	3	14	nadu	nadu	PROPN
cana-5711	3	15	,	,	PUNCT
cana-5711	3	16	india	india	PROPN
cana-5711	3	17	.	.	PUNCT
cana-5711	4	1	1gokulradha0598@gmail.com,4cdurai66@bdu.ac.in	1gokulradha0598@gmail.com,4cdurai66@bdu.ac.in	NUM
cana-5711	5	1	2department	2department	NUM
cana-5711	5	2	of	of	ADP
cana-5711	5	3	mathematics	mathematic	NOUN
cana-5711	5	4	,	,	PUNCT
cana-5711	5	5	sastra	sastra	PROPN
cana-5711	5	6	deemed	deem	VERB
cana-5711	5	7	university	university	NOUN
cana-5711	5	8	,	,	PUNCT
cana-5711	5	9	thanjavur-613401	thanjavur-613401	NOUN
cana-5711	5	10	,	,	PUNCT
cana-5711	5	11	tamil	tamil	PROPN
cana-5711	5	12	nadu	nadu	PROPN
cana-5711	5	13	,	,	PUNCT
cana-5711	5	14	india	india	PROPN
cana-5711	5	15	.	.	PUNCT
cana-5711	6	1	karthygowtham@gmail.com	karthygowtham@gmail.com	X
cana-5711	7	1	3department	3department	NUM
cana-5711	7	2	of	of	ADP
cana-5711	7	3	mathematics	mathematic	NOUN
cana-5711	7	4	,	,	PUNCT
cana-5711	7	5	bishop	bishop	PROPN
cana-5711	7	6	heber	heber	PROPN
cana-5711	7	7	college	college	PROPN
cana-5711	7	8	,	,	PUNCT
cana-5711	7	9	tiruchirapalli	tiruchirapalli	NOUN
cana-5711	7	10	620	620	NUM
cana-5711	7	11	017	017	NUM
cana-5711	7	12	,	,	PUNCT
cana-5711	7	13	tamil	tamil	PROPN
cana-5711	7	14	nadu	nadu	PROPN
cana-5711	7	15	,	,	PUNCT
cana-5711	7	16	india	india	PROPN
cana-5711	7	17	.	.	PUNCT
cana-5711	8	1	cruzmohan@gmail.com	cruzmohan@gmail.com	X
cana-5711	8	2	article	article	NOUN
cana-5711	8	3	history	history	NOUN
cana-5711	8	4	:	:	PUNCT
cana-5711	8	5	received	receive	VERB
cana-5711	8	6	:	:	PUNCT
cana-5711	8	7	12	12	NUM
cana-5711	8	8	-	-	SYM
cana-5711	8	9	01	01	NUM
cana-5711	8	10	-	-	PUNCT
cana-5711	8	11	2025	2025	NUM
cana-5711	8	12	revised	revise	VERB
cana-5711	8	13	:	:	PUNCT
cana-5711	8	14	15	15	NUM
cana-5711	8	15	-	-	NUM
cana-5711	8	16	02	02	NUM
cana-5711	8	17	-	-	PUNCT
cana-5711	8	18	2025	2025	NUM
cana-5711	8	19	accepted	accept	VERB
cana-5711	8	20	:	:	PUNCT
cana-5711	8	21	01	01	NUM
cana-5711	8	22	-	-	SYM
cana-5711	8	23	03	03	NUM
cana-5711	8	24	-	-	PUNCT
cana-5711	8	25	2025	2025	NUM
cana-5711	8	26	abstract	abstract	NOUN
cana-5711	8	27	:	:	PUNCT
cana-5711	8	28	in	in	ADP
cana-5711	8	29	this	this	DET
cana-5711	8	30	paper	paper	NOUN
cana-5711	8	31	,	,	PUNCT
cana-5711	8	32	we	we	PRON
cana-5711	8	33	study	study	VERB
cana-5711	8	34	additive	additive	ADJ
cana-5711	8	35	complementary	complementary	ADJ
cana-5711	8	36	dual	dual	ADJ
cana-5711	8	37	(	(	PUNCT
cana-5711	8	38	acd	acd	NOUN
cana-5711	8	39	)	)	PUNCT
cana-5711	8	40	codes	code	NOUN
cana-5711	8	41	over	over	ADP
cana-5711	8	42	a	a	DET
cana-5711	8	43	mixed	mixed	ADJ
cana-5711	8	44	alphabet	alphabet	NOUN
cana-5711	8	45	ℤ2rs	ℤ2r	NOUN
cana-5711	8	46	,	,	PUNCT
cana-5711	8	47	where	where	SCONJ
cana-5711	8	48	r	r	NOUN
cana-5711	8	49	=	=	SYM
cana-5711	8	50	ℤ2	ℤ2	PROPN
cana-5711	8	51	+	+	CCONJ
cana-5711	8	52	uℤ2	uℤ2	PROPN
cana-5711	8	53	and	and	CCONJ
cana-5711	8	54	s	s	NOUN
cana-5711	8	55	=	=	NOUN
cana-5711	8	56	ℤ2	ℤ2	PROPN
cana-5711	8	57	+	+	CCONJ
cana-5711	8	58	uℤ2	uℤ2	PROPN
cana-5711	8	59	+	+	CCONJ
cana-5711	8	60	vℤ2	vℤ2	PROPN
cana-5711	8	61	+	+	SYM
cana-5711	8	62	uvℤ2	uvℤ2	PROPN
cana-5711	8	63	,	,	PUNCT
cana-5711	8	64	under	under	ADP
cana-5711	8	65	the	the	DET
cana-5711	8	66	conditions	condition	NOUN
cana-5711	8	67	u2	u2	NOUN
cana-5711	8	68	=	=	SYM
cana-5711	8	69	0	0	NUM
cana-5711	8	70	,	,	PUNCT
cana-5711	8	71	v2	v2	NOUN
cana-5711	8	72	=	=	SYM
cana-5711	8	73	0	0	NUM
cana-5711	8	74	,	,	PUNCT
cana-5711	8	75	and	and	CCONJ
cana-5711	8	76	uv	uv	NOUN
cana-5711	8	77	=	=	SYM
cana-5711	8	78	vu	vu	PROPN
cana-5711	8	79	.	.	PUNCT
cana-5711	9	1	an	an	DET
cana-5711	9	2	additive	additive	ADJ
cana-5711	9	3	code	code	NOUN
cana-5711	9	4	will	will	AUX
cana-5711	9	5	prove	prove	VERB
cana-5711	9	6	to	to	PART
cana-5711	9	7	be	be	AUX
cana-5711	9	8	an	an	DET
cana-5711	9	9	acd	acd	NOUN
cana-5711	9	10	code	code	NOUN
cana-5711	9	11	under	under	ADP
cana-5711	9	12	certain	certain	ADJ
cana-5711	9	13	conditions	condition	NOUN
cana-5711	9	14	.	.	PUNCT
cana-5711	10	1	in	in	ADP
cana-5711	10	2	addition	addition	NOUN
cana-5711	10	3	,	,	PUNCT
cana-5711	10	4	it	it	PRON
cana-5711	10	5	is	be	AUX
cana-5711	10	6	a	a	DET
cana-5711	10	7	necessary	necessary	ADJ
cana-5711	10	8	and	and	CCONJ
cana-5711	10	9	sufficient	sufficient	ADJ
cana-5711	10	10	condition	condition	NOUN
cana-5711	10	11	for	for	ADP
cana-5711	10	12	a	a	DET
cana-5711	10	13	separable	separable	ADJ
cana-5711	10	14	additive	additive	ADJ
cana-5711	10	15	code	code	NOUN
cana-5711	10	16	to	to	PART
cana-5711	10	17	be	be	AUX
cana-5711	10	18	an	an	DET
cana-5711	10	19	acd	acd	NOUN
cana-5711	10	20	code	code	NOUN
cana-5711	10	21	.	.	PUNCT
cana-5711	11	1	certain	certain	ADJ
cana-5711	11	2	additive	additive	ADJ
cana-5711	11	3	codes	code	NOUN
cana-5711	11	4	improve	improve	VERB
cana-5711	11	5	into	into	ADP
cana-5711	11	6	binary	binary	ADJ
cana-5711	11	7	linear	linear	PROPN
cana-5711	11	8	complementary	complementary	ADJ
cana-5711	11	9	dual	dual	ADJ
cana-5711	11	10	codes	code	NOUN
cana-5711	11	11	under	under	ADP
cana-5711	11	12	a	a	DET
cana-5711	11	13	gray	gray	ADJ
cana-5711	11	14	map	map	NOUN
cana-5711	11	15	that	that	PRON
cana-5711	11	16	we	we	PRON
cana-5711	11	17	investigate	investigate	VERB
cana-5711	11	18	.	.	PUNCT
cana-5711	12	1	furthermore	furthermore	ADV
cana-5711	12	2	,	,	PUNCT
cana-5711	12	3	a	a	DET
cana-5711	12	4	few	few	ADJ
cana-5711	12	5	types	type	NOUN
cana-5711	12	6	of	of	ADP
cana-5711	12	7	weight	weight	NOUN
cana-5711	12	8	enumerators	enumerator	NOUN
cana-5711	12	9	are	be	AUX
cana-5711	12	10	also	also	ADV
cana-5711	12	11	calculated	calculate	VERB
cana-5711	12	12	,	,	PUNCT
cana-5711	12	13	and	and	CCONJ
cana-5711	12	14	the	the	DET
cana-5711	12	15	associated	associated	ADJ
cana-5711	12	16	macwilliams	macwilliam	NOUN
cana-5711	12	17	identities	identity	NOUN
cana-5711	12	18	are	be	AUX
cana-5711	12	19	discussed	discuss	VERB
cana-5711	12	20	with	with	ADP
cana-5711	12	21	supportive	supportive	ADJ
cana-5711	12	22	examples	example	NOUN
cana-5711	12	23	.	.	PUNCT
cana-5711	13	1	keywords	keyword	NOUN
cana-5711	13	2	:	:	PUNCT
cana-5711	13	3	linear	linear	PROPN
cana-5711	13	4	code	code	PROPN
cana-5711	13	5	,	,	PUNCT
cana-5711	13	6	additive	additive	ADJ
cana-5711	13	7	code	code	NOUN
cana-5711	13	8	,	,	PUNCT
cana-5711	13	9	gray	gray	ADJ
cana-5711	13	10	map	map	NOUN
cana-5711	13	11	,	,	PUNCT
cana-5711	13	12	weight	weight	NOUN
cana-5711	13	13	enumerator	enumerator	NOUN
cana-5711	13	14	,	,	PUNCT
cana-5711	13	15	mac	mac	PROPN
cana-5711	13	16	williams	williams	PROPN
cana-5711	13	17	identities	identities	PROPN
cana-5711	13	18	.	.	PUNCT
cana-5711	14	1	1	1	X
cana-5711	14	2	.	.	X
cana-5711	14	3	introduction	introduction	NOUN
cana-5711	14	4	a	a	DET
cana-5711	14	5	linear	linear	ADJ
cana-5711	14	6	code	code	NOUN
cana-5711	14	7	with	with	ADP
cana-5711	14	8	a	a	DET
cana-5711	14	9	complementary	complementary	ADJ
cana-5711	14	10	dual	dual	ADJ
cana-5711	14	11	property	property	NOUN
cana-5711	14	12	was	be	AUX
cana-5711	14	13	defined	define	VERB
cana-5711	14	14	in	in	ADP
cana-5711	14	15	[	[	X
cana-5711	14	16	11	11	NUM
cana-5711	14	17	]	]	PUNCT
cana-5711	14	18	.	.	PUNCT
cana-5711	15	1	if	if	SCONJ
cana-5711	15	2	a	a	DET
cana-5711	15	3	linear	linear	ADJ
cana-5711	15	4	code	code	NOUN
cana-5711	15	5	c	c	NOUN
cana-5711	15	6	satisfies	satisfie	NOUN
cana-5711	15	7	c∩c⊥	c∩c⊥	ADJ
cana-5711	15	8	=	=	PUNCT
cana-5711	15	9	{	{	PUNCT
cana-5711	15	10	0	0	NUM
cana-5711	15	11	}	}	PUNCT
cana-5711	15	12	,	,	PUNCT
cana-5711	15	13	it	it	PRON
cana-5711	15	14	is	be	AUX
cana-5711	15	15	called	call	VERB
cana-5711	15	16	an	an	DET
cana-5711	15	17	lcd	lcd	NOUN
cana-5711	15	18	code	code	NOUN
cana-5711	15	19	.	.	PUNCT
cana-5711	16	1	in	in	ADP
cana-5711	16	2	the	the	DET
cana-5711	16	3	same	same	ADJ
cana-5711	16	4	paper	paper	NOUN
cana-5711	16	5	,	,	PUNCT
cana-5711	16	6	massey	massey	PROPN
cana-5711	16	7	showed	show	VERB
cana-5711	16	8	that	that	SCONJ
cana-5711	16	9	asymptotically	asymptotically	ADV
cana-5711	16	10	good	good	ADJ
cana-5711	16	11	lcd	lcd	NOUN
cana-5711	16	12	codes	code	NOUN
cana-5711	16	13	exist	exist	VERB
cana-5711	16	14	and	and	CCONJ
cana-5711	16	15	highlighted	highlight	VERB
cana-5711	16	16	applications	application	NOUN
cana-5711	16	17	such	such	ADJ
cana-5711	16	18	as	as	ADP
cana-5711	16	19	providing	provide	VERB
cana-5711	16	20	an	an	DET
cana-5711	16	21	optimal	optimal	ADJ
cana-5711	16	22	linear	linear	ADJ
cana-5711	16	23	coding	code	VERB
cana-5711	16	24	solution	solution	NOUN
cana-5711	16	25	for	for	ADP
cana-5711	16	26	the	the	DET
cana-5711	16	27	two	two	NUM
cana-5711	16	28	-	-	PUNCT
cana-5711	16	29	user	user	NOUN
cana-5711	16	30	binary	binary	PROPN
cana-5711	16	31	adder	adder	PROPN
cana-5711	16	32	channel	channel	PROPN
cana-5711	16	33	.	.	PUNCT
cana-5711	17	1	in	in	ADP
cana-5711	17	2	[	[	X
cana-5711	17	3	4	4	NUM
cana-5711	17	4	]	]	PUNCT
cana-5711	17	5	,	,	PUNCT
cana-5711	17	6	lcd	lcd	NOUN
cana-5711	17	7	codes	code	NOUN
cana-5711	17	8	were	be	AUX
cana-5711	17	9	utilized	utilize	VERB
cana-5711	17	10	in	in	ADP
cana-5711	17	11	the	the	DET
cana-5711	17	12	context	context	NOUN
cana-5711	17	13	of	of	ADP
cana-5711	17	14	digital	digital	ADJ
cana-5711	17	15	communication	communication	NOUN
cana-5711	17	16	security	security	NOUN
cana-5711	17	17	.	.	PUNCT
cana-5711	18	1	recently	recently	ADV
cana-5711	18	2	,	,	PUNCT
cana-5711	18	3	many	many	ADJ
cana-5711	18	4	authors	author	NOUN
cana-5711	18	5	have	have	AUX
cana-5711	18	6	studied	study	VERB
cana-5711	18	7	codes	code	NOUN
cana-5711	18	8	over	over	ADP
cana-5711	18	9	rings	ring	NOUN
cana-5711	18	10	due	due	ADP
cana-5711	18	11	to	to	ADP
cana-5711	18	12	their	their	PRON
cana-5711	18	13	emerging	emerge	VERB
cana-5711	18	14	role	role	NOUN
cana-5711	18	15	in	in	ADP
cana-5711	18	16	algebraic	algebraic	ADJ
cana-5711	18	17	coding	code	VERB
cana-5711	18	18	theory	theory	NOUN
cana-5711	18	19	and	and	CCONJ
cana-5711	18	20	successful	successful	ADJ
cana-5711	18	21	application	application	NOUN
cana-5711	18	22	in	in	ADP
cana-5711	18	23	combined	combined	ADJ
cana-5711	18	24	coding	coding	NOUN
cana-5711	18	25	and	and	CCONJ
cana-5711	18	26	modulation	modulation	NOUN
cana-5711	18	27	.	.	PUNCT
cana-5711	19	1	li	li	PROPN
cana-5711	19	2	et	et	PROPN
cana-5711	19	3	al	al	PROPN
cana-5711	19	4	.	.	PROPN
cana-5711	19	5	established	establish	VERB
cana-5711	19	6	families	family	NOUN
cana-5711	19	7	of	of	ADP
cana-5711	19	8	reversible	reversible	ADJ
cana-5711	19	9	codes	code	NOUN
cana-5711	19	10	and	and	CCONJ
cana-5711	19	11	demonstrated	demonstrate	VERB
cana-5711	19	12	that	that	SCONJ
cana-5711	19	13	some	some	PRON
cana-5711	19	14	are	be	AUX
cana-5711	19	15	optimal	optimal	ADJ
cana-5711	19	16	[	[	X
cana-5711	19	17	7	7	NUM
cana-5711	19	18	]	]	PUNCT
cana-5711	19	19	.	.	PUNCT
cana-5711	20	1	in	in	ADP
cana-5711	20	2	[	[	X
cana-5711	20	3	8	8	NUM
cana-5711	20	4	]	]	PUNCT
cana-5711	20	5	,	,	PUNCT
cana-5711	20	6	lcd	lcd	NOUN
cana-5711	20	7	codes	code	NOUN
cana-5711	20	8	were	be	AUX
cana-5711	20	9	explored	explore	VERB
cana-5711	20	10	over	over	ADP
cana-5711	20	11	finite	finite	ADJ
cana-5711	20	12	chain	chain	NOUN
cana-5711	20	13	rings	ring	NOUN
cana-5711	20	14	.	.	PUNCT
cana-5711	21	1	the	the	DET
cana-5711	21	2	concept	concept	NOUN
cana-5711	21	3	of	of	ADP
cana-5711	21	4	lcd	lcd	NOUN
cana-5711	21	5	codes	code	NOUN
cana-5711	21	6	was	be	AUX
cana-5711	21	7	generalized	generalize	VERB
cana-5711	21	8	to	to	ADP
cana-5711	21	9	additive	additive	VERB
cana-5711	21	10	complementary	complementary	ADJ
cana-5711	21	11	dual	dual	ADJ
cana-5711	21	12	(	(	PUNCT
cana-5711	21	13	acd	acd	NOUN
cana-5711	21	14	)	)	PUNCT
cana-5711	21	15	codes	code	NOUN
cana-5711	21	16	,	,	PUNCT
cana-5711	21	17	and	and	CCONJ
cana-5711	21	18	these	these	PRON
cana-5711	21	19	were	be	AUX
cana-5711	21	20	studied	study	VERB
cana-5711	21	21	over	over	ADP
cana-5711	21	22	ℤ2	ℤ2	PROPN
cana-5711	21	23	×	×	PROPN
cana-5711	21	24	ℤ4	ℤ4	NOUN
cana-5711	21	25	in	in	ADP
cana-5711	21	26	[	[	X
cana-5711	21	27	2	2	NUM
cana-5711	21	28	]	]	PUNCT
cana-5711	21	29	.	.	PUNCT
cana-5711	22	1	macwilliams	macwilliam	NOUN
cana-5711	22	2	established	establish	VERB
cana-5711	22	3	a	a	DET
cana-5711	22	4	relationship	relationship	NOUN
cana-5711	22	5	between	between	ADP
cana-5711	22	6	a	a	DET
cana-5711	22	7	code	code	NOUN
cana-5711	22	8	’s	’s	PART
cana-5711	22	9	weight	weight	NOUN
cana-5711	22	10	distribution	distribution	NOUN
cana-5711	22	11	and	and	CCONJ
cana-5711	22	12	that	that	PRON
cana-5711	22	13	of	of	ADP
cana-5711	22	14	its	its	PRON
cana-5711	22	15	dual	dual	ADJ
cana-5711	22	16	in	in	ADP
cana-5711	22	17	[	[	X
cana-5711	22	18	10	10	NUM
cana-5711	22	19	]	]	PUNCT
cana-5711	22	20	,	,	PUNCT
cana-5711	22	21	leading	lead	VERB
cana-5711	22	22	to	to	ADP
cana-5711	22	23	the	the	DET
cana-5711	22	24	development	development	NOUN
cana-5711	22	25	of	of	ADP
cana-5711	22	26	macwilliams	macwilliam	NOUN
cana-5711	22	27	identities	identity	NOUN
cana-5711	22	28	and	and	CCONJ
cana-5711	22	29	consideration	consideration	NOUN
cana-5711	22	30	of	of	ADP
cana-5711	22	31	weight	weight	NOUN
cana-5711	22	32	enumerators	enumerator	NOUN
cana-5711	22	33	for	for	ADP
cana-5711	22	34	codes	code	NOUN
cana-5711	22	35	over	over	ADP
cana-5711	22	36	finite	finite	ADJ
cana-5711	22	37	frobenius	frobenius	NOUN
cana-5711	22	38	rings	ring	NOUN
cana-5711	22	39	.	.	PUNCT
cana-5711	23	1	various	various	ADJ
cana-5711	23	2	macwilliams	macwilliam	NOUN
cana-5711	23	3	identities	identity	NOUN
cana-5711	23	4	over	over	ADP
cana-5711	23	5	ℤ4	ℤ4	PROPN
cana-5711	23	6	were	be	AUX
cana-5711	23	7	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	23	8	communications	communication	NOUN
cana-5711	23	9	on	on	ADP
cana-5711	23	10	applied	apply	VERB
cana-5711	23	11	nonlinear	nonlinear	ADJ
cana-5711	23	12	analysis	analysis	NOUN
cana-5711	23	13	issn	issn	NOUN
cana-5711	23	14	:	:	PUNCT
cana-5711	23	15	1074	1074	NUM
cana-5711	23	16	-	-	PUNCT
cana-5711	23	17	133x	133x	NUM
cana-5711	23	18	vol	vol	VERB
cana-5711	23	19	32	32	NUM
cana-5711	23	20	no	no	NOUN
cana-5711	23	21	.	.	PUNCT
cana-5711	24	1	10s	10	NOUN
cana-5711	24	2	(	(	PUNCT
cana-5711	24	3	2025	2025	NUM
cana-5711	24	4	)	)	PUNCT
cana-5711	24	5	2696	2696	NUM
cana-5711	24	6	studied	study	VERB
cana-5711	24	7	in	in	ADP
cana-5711	24	8	[	[	X
cana-5711	24	9	6	6	NUM
cana-5711	24	10	]	]	PUNCT
cana-5711	24	11	.	.	PUNCT
cana-5711	25	1	weight	weight	NOUN
cana-5711	25	2	enumerators	enumerator	NOUN
cana-5711	25	3	over	over	ADP
cana-5711	25	4	ℤl	ℤl	NOUN
cana-5711	25	5	and	and	CCONJ
cana-5711	25	6	conditions	condition	NOUN
cana-5711	25	7	ensuring	ensure	VERB
cana-5711	25	8	the	the	DET
cana-5711	25	9	presence	presence	NOUN
cana-5711	25	10	of	of	ADP
cana-5711	25	11	such	such	ADJ
cana-5711	25	12	identities	identity	NOUN
cana-5711	25	13	were	be	AUX
cana-5711	25	14	discussed	discuss	VERB
cana-5711	25	15	in	in	ADP
cana-5711	25	16	[	[	X
cana-5711	25	17	12	12	NUM
cana-5711	25	18	]	]	PUNCT
cana-5711	25	19	and	and	CCONJ
cana-5711	25	20	[	[	X
cana-5711	25	21	14	14	NUM
cana-5711	25	22	]	]	PUNCT
cana-5711	25	23	.	.	PUNCT
cana-5711	26	1	in	in	ADP
cana-5711	26	2	2014	2014	NUM
cana-5711	26	3	,	,	PUNCT
cana-5711	26	4	the	the	DET
cana-5711	26	5	investigation	investigation	NOUN
cana-5711	26	6	of	of	ADP
cana-5711	26	7	linear	linear	PROPN
cana-5711	26	8	codes	code	NOUN
cana-5711	26	9	over	over	ADP
cana-5711	26	10	ℤ4	ℤ4	PROPN
cana-5711	26	11	+	+	NOUN
cana-5711	26	12	uℤ4	uℤ4	PROPN
cana-5711	26	13	and	and	CCONJ
cana-5711	26	14	their	their	PRON
cana-5711	26	15	weight	weight	NOUN
cana-5711	26	16	enumerators	enumerator	NOUN
cana-5711	26	17	was	be	AUX
cana-5711	26	18	presented	present	VERB
cana-5711	26	19	in	in	ADP
cana-5711	26	20	[	[	X
cana-5711	26	21	16	16	NUM
cana-5711	26	22	]	]	PUNCT
cana-5711	26	23	.	.	PUNCT
cana-5711	27	1	ℤ2	ℤ2	PROPN
cana-5711	27	2	ℤ2	ℤ2	PROPN
cana-5711	28	1	[	[	X
cana-5711	28	2	u]-additive	u]-additive	ADJ
cana-5711	28	3	codes	code	NOUN
cana-5711	28	4	and	and	CCONJ
cana-5711	28	5	their	their	PRON
cana-5711	28	6	standard	standard	ADJ
cana-5711	28	7	generator	generator	NOUN
cana-5711	28	8	matrices	matrix	NOUN
cana-5711	28	9	,	,	PUNCT
cana-5711	28	10	along	along	ADP
cana-5711	28	11	with	with	ADP
cana-5711	28	12	the	the	DET
cana-5711	28	13	link	link	NOUN
cana-5711	28	14	between	between	ADP
cana-5711	28	15	their	their	PRON
cana-5711	28	16	weight	weight	NOUN
cana-5711	28	17	enumerators	enumerator	NOUN
cana-5711	28	18	and	and	CCONJ
cana-5711	28	19	their	their	PRON
cana-5711	28	20	duals	dual	NOUN
cana-5711	28	21	,	,	PUNCT
cana-5711	28	22	were	be	AUX
cana-5711	28	23	introduced	introduce	VERB
cana-5711	28	24	in	in	ADP
cana-5711	28	25	[	[	X
cana-5711	28	26	1	1	NUM
cana-5711	28	27	]	]	PUNCT
cana-5711	28	28	.	.	PUNCT
cana-5711	29	1	further	further	ADJ
cana-5711	29	2	research	research	NOUN
cana-5711	29	3	into	into	ADP
cana-5711	29	4	macwilliams	macwilliam	NOUN
cana-5711	29	5	identities	identity	NOUN
cana-5711	29	6	for	for	ADP
cana-5711	29	7	various	various	ADJ
cana-5711	29	8	weight	weight	NOUN
cana-5711	29	9	enumerators	enumerator	NOUN
cana-5711	29	10	was	be	AUX
cana-5711	29	11	conducted	conduct	VERB
cana-5711	29	12	in	in	ADP
cana-5711	29	13	[	[	X
cana-5711	29	14	13	13	NUM
cana-5711	29	15	]	]	PUNCT
cana-5711	29	16	,	,	PUNCT
cana-5711	29	17	examining	examine	VERB
cana-5711	29	18	linear	linear	NOUN
cana-5711	29	19	codes	code	NOUN
cana-5711	29	20	over	over	ADP
cana-5711	29	21	the	the	DET
cana-5711	29	22	new	new	ADJ
cana-5711	29	23	ring	ring	NOUN
cana-5711	29	24	s	s	PART
cana-5711	29	25	=	=	X
cana-5711	29	26	𝔽2	𝔽2	PROPN
cana-5711	29	27	+	+	NOUN
cana-5711	29	28	u𝔽2	u𝔽2	PROPN
cana-5711	29	29	+	+	PROPN
cana-5711	29	30	v𝔽2	v𝔽2	PROPN
cana-5711	29	31	+	+	NOUN
cana-5711	29	32	uv𝔽2	uv𝔽2	NOUN
cana-5711	29	33	,	,	PUNCT
cana-5711	29	34	with	with	ADP
cana-5711	29	35	identities	identity	NOUN
cana-5711	29	36	for	for	ADP
cana-5711	29	37	the	the	DET
cana-5711	29	38	lee	lee	PROPN
cana-5711	29	39	weight	weight	NOUN
cana-5711	29	40	enumerator	enumerator	NOUN
cana-5711	29	41	derived	derive	VERB
cana-5711	29	42	using	use	VERB
cana-5711	29	43	a	a	DET
cana-5711	29	44	gray	gray	ADJ
cana-5711	29	45	map	map	NOUN
cana-5711	29	46	from	from	ADP
cana-5711	29	47	sn	sn	PROPN
cana-5711	29	48	to	to	PART
cana-5711	29	49	(	(	PUNCT
cana-5711	29	50	𝔽2	𝔽2	PROPN
cana-5711	29	51	+	+	CCONJ
cana-5711	29	52	u𝔽2	u𝔽2	PROPN
cana-5711	29	53	)	)	PUNCT
cana-5711	29	54	n	n	CCONJ
cana-5711	29	55	.	.	PUNCT
cana-5711	30	1	additionally	additionally	ADV
cana-5711	30	2	,	,	PUNCT
cana-5711	30	3	self	self	NOUN
cana-5711	30	4	-	-	PUNCT
cana-5711	30	5	dual	dual	ADJ
cana-5711	30	6	and	and	CCONJ
cana-5711	30	7	cyclic	cyclic	ADJ
cana-5711	30	8	codes	code	NOUN
cana-5711	30	9	over	over	ADP
cana-5711	30	10	s	s	PRON
cana-5711	30	11	were	be	AUX
cana-5711	30	12	studied	study	VERB
cana-5711	30	13	.	.	PUNCT
cana-5711	31	1	motivated	motivate	VERB
cana-5711	31	2	by	by	ADP
cana-5711	31	3	the	the	DET
cana-5711	31	4	aforementioned	aforementioned	ADJ
cana-5711	31	5	research	research	NOUN
cana-5711	31	6	,	,	PUNCT
cana-5711	31	7	we	we	PRON
cana-5711	31	8	explore	explore	VERB
cana-5711	31	9	acd	acd	NOUN
cana-5711	31	10	codes	code	NOUN
cana-5711	31	11	over	over	ADP
cana-5711	31	12	the	the	DET
cana-5711	31	13	finite	finite	PROPN
cana-5711	31	14	commutative	commutative	ADJ
cana-5711	31	15	frobenius	frobenius	ADJ
cana-5711	31	16	non	non	ADJ
cana-5711	31	17	-	-	ADJ
cana-5711	31	18	chain	chain	ADJ
cana-5711	31	19	ring	ring	NOUN
cana-5711	31	20	ℤ2	ℤ2	PROPN
cana-5711	31	21	rs	r	NOUN
cana-5711	31	22	,	,	PUNCT
cana-5711	31	23	where	where	SCONJ
cana-5711	31	24	r	r	NOUN
cana-5711	31	25	=	=	SYM
cana-5711	31	26	ℤ2	ℤ2	PROPN
cana-5711	31	27	+	+	CCONJ
cana-5711	31	28	uℤ2	uℤ2	PROPN
cana-5711	31	29	and	and	CCONJ
cana-5711	31	30	s	s	NOUN
cana-5711	31	31	=	=	NOUN
cana-5711	31	32	ℤ2	ℤ2	PROPN
cana-5711	31	33	+	+	CCONJ
cana-5711	31	34	uℤ2	uℤ2	PROPN
cana-5711	31	35	+	+	CCONJ
cana-5711	31	36	vℤ2	vℤ2	NOUN
cana-5711	31	37	+	+	CCONJ
cana-5711	31	38	uvℤ2	uvℤ2	PROPN
cana-5711	31	39	.	.	PUNCT
cana-5711	32	1	throughout	throughout	ADP
cana-5711	32	2	this	this	DET
cana-5711	32	3	discussion	discussion	NOUN
cana-5711	32	4	,	,	PUNCT
cana-5711	32	5	we	we	PRON
cana-5711	32	6	let	let	VERB
cana-5711	32	7	q	q	NOUN
cana-5711	32	8	=	=	PUNCT
cana-5711	32	9	rs	rs	NOUN
cana-5711	32	10	.	.	PUNCT
cana-5711	33	1	we	we	PRON
cana-5711	33	2	discuss	discuss	VERB
cana-5711	33	3	a	a	DET
cana-5711	33	4	necessary	necessary	ADJ
cana-5711	33	5	condition	condition	NOUN
cana-5711	33	6	for	for	ADP
cana-5711	33	7	a	a	DET
cana-5711	33	8	ℤ2q	ℤ2q	PROPN
cana-5711	33	9	-	-	PUNCT
cana-5711	33	10	additive	additive	NOUN
cana-5711	33	11	code	code	NOUN
cana-5711	33	12	to	to	PART
cana-5711	33	13	be	be	AUX
cana-5711	33	14	a	a	DET
cana-5711	33	15	ℤ2q	ℤ2q	PROPN
cana-5711	33	16	-	-	PUNCT
cana-5711	33	17	acd	acd	NOUN
cana-5711	33	18	code	code	NOUN
cana-5711	33	19	.	.	PUNCT
cana-5711	34	1	we	we	PRON
cana-5711	34	2	examine	examine	VERB
cana-5711	34	3	a	a	DET
cana-5711	34	4	gray	gray	ADJ
cana-5711	34	5	map	map	NOUN
cana-5711	34	6	wherein	wherein	SCONJ
cana-5711	34	7	specific	specific	ADJ
cana-5711	34	8	additive	additive	ADJ
cana-5711	34	9	codes	code	NOUN
cana-5711	34	10	over	over	ADP
cana-5711	34	11	ℤ2q	ℤ2q	PROPN
cana-5711	34	12	correspond	correspond	VERB
cana-5711	34	13	to	to	ADP
cana-5711	34	14	binary	binary	PROPN
cana-5711	34	15	lcd	lcd	PROPN
cana-5711	34	16	codes	code	NOUN
cana-5711	34	17	.	.	PUNCT
cana-5711	35	1	we	we	PRON
cana-5711	35	2	explore	explore	VERB
cana-5711	35	3	different	different	ADJ
cana-5711	35	4	weight	weight	NOUN
cana-5711	35	5	enumerators	enumerator	NOUN
cana-5711	35	6	of	of	ADP
cana-5711	35	7	additive	additive	ADJ
cana-5711	35	8	codes	code	NOUN
cana-5711	35	9	over	over	ADP
cana-5711	35	10	ℤ2q	ℤ2q	PROPN
cana-5711	35	11	and	and	CCONJ
cana-5711	35	12	the	the	DET
cana-5711	35	13	corresponding	correspond	VERB
cana-5711	35	14	macwilliams	macwilliam	NOUN
cana-5711	35	15	identities	identity	NOUN
cana-5711	35	16	,	,	PUNCT
cana-5711	35	17	providing	provide	VERB
cana-5711	35	18	examples	example	NOUN
cana-5711	35	19	to	to	PART
cana-5711	35	20	demonstrate	demonstrate	VERB
cana-5711	35	21	our	our	PRON
cana-5711	35	22	findings	finding	NOUN
cana-5711	35	23	.	.	PUNCT
cana-5711	36	1	all	all	DET
cana-5711	36	2	computations	computation	NOUN
cana-5711	36	3	in	in	ADP
cana-5711	36	4	this	this	DET
cana-5711	36	5	paper	paper	NOUN
cana-5711	36	6	are	be	AUX
cana-5711	36	7	performed	perform	VERB
cana-5711	36	8	using	use	VERB
cana-5711	36	9	the	the	DET
cana-5711	36	10	magma	magma	NOUN
cana-5711	36	11	computational	computational	ADJ
cana-5711	36	12	algebra	algebra	NOUN
cana-5711	36	13	system	system	NOUN
cana-5711	36	14	[	[	X
cana-5711	36	15	3	3	NUM
cana-5711	36	16	]	]	PUNCT
cana-5711	36	17	.	.	PUNCT
cana-5711	37	1	this	this	DET
cana-5711	37	2	paper	paper	NOUN
cana-5711	37	3	is	be	AUX
cana-5711	37	4	structured	structure	VERB
cana-5711	37	5	as	as	SCONJ
cana-5711	37	6	follows	follow	VERB
cana-5711	37	7	:	:	PUNCT
cana-5711	37	8	in	in	ADP
cana-5711	37	9	section	section	NOUN
cana-5711	37	10	3	3	NUM
cana-5711	37	11	,	,	PUNCT
cana-5711	37	12	we	we	PRON
cana-5711	37	13	examine	examine	VERB
cana-5711	37	14	ℤ2q	ℤ2q	PROPN
cana-5711	37	15	-	-	PUNCT
cana-5711	37	16	acd	acd	NOUN
cana-5711	37	17	codes	code	NOUN
cana-5711	37	18	and	and	CCONJ
cana-5711	37	19	determine	determine	VERB
cana-5711	37	20	a	a	DET
cana-5711	37	21	condition	condition	NOUN
cana-5711	37	22	for	for	SCONJ
cana-5711	37	23	an	an	DET
cana-5711	37	24	additive	additive	ADJ
cana-5711	37	25	code	code	NOUN
cana-5711	37	26	to	to	PART
cana-5711	37	27	be	be	AUX
cana-5711	37	28	an	an	DET
cana-5711	37	29	acd	acd	NOUN
cana-5711	37	30	code	code	NOUN
cana-5711	37	31	.	.	PUNCT
cana-5711	38	1	in	in	ADP
cana-5711	38	2	section	section	NOUN
cana-5711	38	3	4	4	NUM
cana-5711	38	4	,	,	PUNCT
cana-5711	38	5	we	we	PRON
cana-5711	38	6	explore	explore	VERB
cana-5711	38	7	a	a	DET
cana-5711	38	8	gray	gray	ADJ
cana-5711	38	9	map	map	NOUN
cana-5711	38	10	and	and	CCONJ
cana-5711	38	11	demonstrate	demonstrate	VERB
cana-5711	38	12	how	how	SCONJ
cana-5711	38	13	some	some	DET
cana-5711	38	14	additive	additive	ADJ
cana-5711	38	15	codes	code	NOUN
cana-5711	38	16	are	be	AUX
cana-5711	38	17	mapped	map	VERB
cana-5711	38	18	to	to	ADP
cana-5711	38	19	binary	binary	PROPN
cana-5711	38	20	lcd	lcd	PROPN
cana-5711	38	21	codes	code	NOUN
cana-5711	38	22	.	.	PUNCT
cana-5711	39	1	weight	weight	NOUN
cana-5711	39	2	enumerators	enumerator	NOUN
cana-5711	39	3	of	of	ADP
cana-5711	39	4	ℤ2qadditive	ℤ2qadditive	ADJ
cana-5711	39	5	codes	code	NOUN
cana-5711	39	6	are	be	AUX
cana-5711	39	7	studied	study	VERB
cana-5711	39	8	in	in	ADP
cana-5711	39	9	section	section	NOUN
cana-5711	39	10	5	5	NUM
cana-5711	39	11	,	,	PUNCT
cana-5711	39	12	and	and	CCONJ
cana-5711	39	13	the	the	DET
cana-5711	39	14	corresponding	correspond	VERB
cana-5711	39	15	macwilliams	macwilliam	NOUN
cana-5711	39	16	identities	identity	NOUN
cana-5711	39	17	are	be	AUX
cana-5711	39	18	discussed	discuss	VERB
cana-5711	39	19	.	.	PUNCT
cana-5711	40	1	2	2	X
cana-5711	40	2	.	.	X
cana-5711	40	3	preliminary	preliminary	NOUN
cana-5711	40	4	let	let	VERB
cana-5711	40	5	ℤ2	ℤ2	PROPN
cana-5711	40	6	be	be	AUX
cana-5711	40	7	the	the	DET
cana-5711	40	8	binary	binary	ADJ
cana-5711	40	9	finite	finite	PROPN
cana-5711	40	10	field	field	NOUN
cana-5711	40	11	.	.	PUNCT
cana-5711	41	1	then	then	ADV
cana-5711	41	2	q	q	X
cana-5711	41	3	=	=	SYM
cana-5711	41	4	(	(	PUNCT
cana-5711	41	5	ℤ2	ℤ2	PROPN
cana-5711	41	6	+	+	CCONJ
cana-5711	41	7	uℤ2	uℤ2	PROPN
cana-5711	41	8	)	)	PUNCT
cana-5711	41	9	×	×	NOUN
cana-5711	41	10	(	(	PUNCT
cana-5711	41	11	ℤ2	ℤ2	PROPN
cana-5711	41	12	+	+	CCONJ
cana-5711	41	13	uℤ2	uℤ2	PROPN
cana-5711	41	14	+	+	CCONJ
cana-5711	41	15	vℤ2	vℤ2	NOUN
cana-5711	41	16	+	+	ADJ
cana-5711	41	17	uvℤ2	uvℤ2	PROPN
cana-5711	41	18	)	)	PUNCT
cana-5711	41	19	,	,	PUNCT
cana-5711	41	20	where	where	SCONJ
cana-5711	41	21	u2	u2	NOUN
cana-5711	41	22	=	=	SYM
cana-5711	41	23	0	0	PROPN
cana-5711	41	24	,	,	PUNCT
cana-5711	41	25	v2	v2	NOUN
cana-5711	41	26	=	=	SYM
cana-5711	41	27	0	0	NUM
cana-5711	41	28	and	and	CCONJ
cana-5711	41	29	uv	uv	NOUN
cana-5711	41	30	=	=	SYM
cana-5711	41	31	vu	vu	PROPN
cana-5711	41	32	,	,	PUNCT
cana-5711	41	33	is	be	AUX
cana-5711	41	34	a	a	DET
cana-5711	41	35	commutative	commutative	ADJ
cana-5711	41	36	ring	ring	NOUN
cana-5711	41	37	with	with	ADP
cana-5711	41	38	characteristic	characteristic	ADJ
cana-5711	41	39	2	2	NUM
cana-5711	41	40	.	.	PUNCT
cana-5711	41	41	observe	observe	VERB
cana-5711	41	42	that	that	PRON
cana-5711	41	43	q	q	NOUN
cana-5711	41	44	is	be	AUX
cana-5711	41	45	a	a	DET
cana-5711	41	46	local	local	ADJ
cana-5711	41	47	ring	ring	NOUN
cana-5711	41	48	with	with	ADP
cana-5711	41	49	its	its	PRON
cana-5711	41	50	group	group	NOUN
cana-5711	41	51	of	of	ADP
cana-5711	41	52	units	unit	NOUN
cana-5711	41	53	u	u	NOUN
cana-5711	41	54	(	(	PUNCT
cana-5711	41	55	q	q	NOUN
cana-5711	41	56	)	)	PUNCT
cana-5711	41	57	=	=	PRON
cana-5711	41	58	{	{	PUNCT
cana-5711	41	59	(	(	PUNCT
cana-5711	41	60	1	1	NUM
cana-5711	41	61	+	+	CCONJ
cana-5711	41	62	ub	ub	ADJ
cana-5711	41	63	,	,	PUNCT
cana-5711	41	64	1	1	NUM
cana-5711	41	65	+	+	CCONJ
cana-5711	41	66	ub	ub	ADJ
cana-5711	42	1	+	+	CCONJ
cana-5711	42	2	vc	vc	PROPN
cana-5711	42	3	+	+	CCONJ
cana-5711	42	4	uvd	uvd	NOUN
cana-5711	42	5	)	)	PUNCT
cana-5711	42	6	|	|	ADV
cana-5711	42	7	b	b	NOUN
cana-5711	42	8	,	,	PUNCT
cana-5711	42	9	c	c	X
cana-5711	42	10	,	,	PUNCT
cana-5711	43	1	d	d	PROPN
cana-5711	43	2	∈	∈	PROPN
cana-5711	43	3	ℤ2	ℤ2	PROPN
cana-5711	43	4	}	}	PUNCT
cana-5711	43	5	and	and	CCONJ
cana-5711	43	6	maximal	maximal	ADJ
cana-5711	43	7	ideal	ideal	NOUN
cana-5711	43	8	m	m	NOUN
cana-5711	43	9	=	=	SYM
cana-5711	43	10	{	{	PUNCT
cana-5711	43	11	(	(	PUNCT
cana-5711	43	12	ub	ub	PROPN
cana-5711	43	13	,	,	PUNCT
cana-5711	43	14	ub	ub	ADP
cana-5711	44	1	+	+	CCONJ
cana-5711	44	2	vc	vc	PROPN
cana-5711	44	3	+	+	CCONJ
cana-5711	44	4	uvd	uvd	NOUN
cana-5711	44	5	)	)	PUNCT
cana-5711	44	6	|	|	ADV
cana-5711	44	7	b	b	NOUN
cana-5711	44	8	,	,	PUNCT
cana-5711	44	9	c	c	X
cana-5711	44	10	,	,	PUNCT
cana-5711	44	11	d	d	PROPN
cana-5711	44	12	∈	∈	PROPN
cana-5711	44	13	ℤ2	ℤ2	PROPN
cana-5711	44	14	}	}	PUNCT
cana-5711	44	15	such	such	ADJ
cana-5711	44	16	that	that	SCONJ
cana-5711	44	17	m	m	VERB
cana-5711	44	18	=	=	PUNCT
cana-5711	44	19	q	q	X
cana-5711	44	20	\	\	PROPN
cana-5711	44	21	u	u	NOUN
cana-5711	44	22	(	(	PUNCT
cana-5711	44	23	q	q	NOUN
cana-5711	44	24	)	)	PUNCT
cana-5711	44	25	.	.	PUNCT
cana-5711	45	1	multiplication	multiplication	NOUN
cana-5711	45	2	in	in	ADP
cana-5711	45	3	ℤ2q	ℤ2q	PROPN
cana-5711	45	4	is	be	AUX
cana-5711	45	5	defined	define	VERB
cana-5711	45	6	as	as	SCONJ
cana-5711	45	7	follows	follow	VERB
cana-5711	45	8	:	:	PUNCT
cana-5711	45	9	𝑥	𝑥	X
cana-5711	45	10	⋆	⋆	X
cana-5711	45	11	(	(	PUNCT
cana-5711	45	12	𝑧	𝑧	PROPN
cana-5711	45	13	,	,	PUNCT
cana-5711	45	14	𝑟	𝑟	NOUN
cana-5711	45	15	,	,	PUNCT
cana-5711	45	16	𝑠	𝑠	NOUN
cana-5711	45	17	)	)	PUNCT
cana-5711	45	18	=	=	SYM
cana-5711	45	19	(	(	PUNCT
cana-5711	45	20	𝜂(𝑥)𝑧	𝜂(𝑥)𝑧	PROPN
cana-5711	45	21	,	,	PUNCT
cana-5711	45	22	𝛿(𝑥)𝑟	𝛿(𝑥)𝑟	PROPN
cana-5711	45	23	,	,	PUNCT
cana-5711	45	24	𝑥𝑠	𝑥𝑠	PROPN
cana-5711	45	25	)	)	PUNCT
cana-5711	45	26	,	,	PUNCT
cana-5711	45	27	(	(	PUNCT
cana-5711	45	28	2.1	2.1	NUM
cana-5711	45	29	)	)	PUNCT
cana-5711	45	30	where	where	SCONJ
cana-5711	45	31	η	η	PROPN
cana-5711	45	32	:	:	PUNCT
cana-5711	45	33	s→	s→	X
cana-5711	45	34	ℤ2	ℤ2	PROPN
cana-5711	45	35	is	be	AUX
cana-5711	45	36	defined	define	VERB
cana-5711	45	37	by	by	ADP
cana-5711	45	38	η	η	PROPN
cana-5711	45	39	(	(	PUNCT
cana-5711	45	40	a	a	PRON
cana-5711	45	41	+	+	X
cana-5711	45	42	ub	ub	ADJ
cana-5711	45	43	+	+	CCONJ
cana-5711	45	44	vc	vc	PROPN
cana-5711	45	45	+	+	CCONJ
cana-5711	45	46	uvd	uvd	NOUN
cana-5711	45	47	)	)	PUNCT
cana-5711	45	48	=	=	SYM
cana-5711	45	49	a	a	PROPN
cana-5711	45	50	and	and	CCONJ
cana-5711	45	51	δ	δ	NOUN
cana-5711	45	52	:	:	PUNCT
cana-5711	46	1	s→	s→	X
cana-5711	46	2	r	r	NOUN
cana-5711	46	3	is	be	AUX
cana-5711	46	4	defined	define	VERB
cana-5711	46	5	by	by	ADP
cana-5711	46	6	δ	δ	PROPN
cana-5711	46	7	(	(	PUNCT
cana-5711	46	8	a	a	PRON
cana-5711	46	9	+	+	X
cana-5711	46	10	ub	ub	ADJ
cana-5711	46	11	+	+	CCONJ
cana-5711	46	12	vc	vc	PROPN
cana-5711	46	13	+	+	CCONJ
cana-5711	46	14	uvd	uvd	NOUN
cana-5711	46	15	)	)	PUNCT
cana-5711	46	16	=	=	PUNCT
cana-5711	47	1	a	a	DET
cana-5711	47	2	+	+	X
cana-5711	47	3	ub	ub	ADJ
cana-5711	47	4	.	.	PUNCT
cana-5711	48	1	throughout	throughout	ADP
cana-5711	48	2	the	the	DET
cana-5711	48	3	manuscript	manuscript	NOUN
cana-5711	48	4	,	,	PUNCT
cana-5711	48	5	we	we	PRON
cana-5711	48	6	will	will	AUX
cana-5711	48	7	use	use	VERB
cana-5711	48	8	(	(	PUNCT
cana-5711	48	9	x	x	NOUN
cana-5711	48	10	,	,	PUNCT
cana-5711	48	11	y	y	NOUN
cana-5711	48	12	)	)	PUNCT
cana-5711	48	13	to	to	PART
cana-5711	48	14	represent	represent	VERB
cana-5711	48	15	(	(	PUNCT
cana-5711	48	16	z	z	NOUN
cana-5711	48	17	,	,	PUNCT
cana-5711	48	18	r	r	NOUN
cana-5711	48	19	,	,	PUNCT
cana-5711	48	20	s	s	PART
cana-5711	48	21	)	)	PUNCT
cana-5711	48	22	,	,	PUNCT
cana-5711	48	23	where	where	SCONJ
cana-5711	48	24	x	x	ADP
cana-5711	48	25	=	=	PUNCT
cana-5711	48	26	z	z	PROPN
cana-5711	48	27	and	and	CCONJ
cana-5711	48	28	y	y	PROPN
cana-5711	48	29	=	=	SYM
cana-5711	48	30	(	(	PUNCT
cana-5711	48	31	r	r	NOUN
cana-5711	48	32	,	,	PUNCT
cana-5711	48	33	s	s	PART
cana-5711	48	34	)	)	PUNCT
cana-5711	48	35	.	.	PUNCT
cana-5711	49	1	multiplication	multiplication	NOUN
cana-5711	49	2	will	will	AUX
cana-5711	49	3	be	be	AUX
cana-5711	49	4	represented	represent	VERB
cana-5711	49	5	by	by	ADP
cana-5711	49	6	𝑏	𝑏	PROPN
cana-5711	49	7	⋆	⋆	X
cana-5711	49	8	(	(	PUNCT
cana-5711	49	9	𝑥	𝑥	PROPN
cana-5711	49	10	,	,	PUNCT
cana-5711	49	11	𝑦	𝑦	NOUN
cana-5711	49	12	)	)	PUNCT
cana-5711	49	13	=	=	SYM
cana-5711	49	14	(	(	PUNCT
cana-5711	49	15	𝜂(𝑏)𝑥	𝜂(𝑏)𝑥	PROPN
cana-5711	49	16	,	,	PUNCT
cana-5711	49	17	𝑏𝑦	𝑏𝑦	NOUN
cana-5711	49	18	)	)	PUNCT
cana-5711	49	19	.	.	PUNCT
cana-5711	50	1	(	(	PUNCT
cana-5711	50	2	2.2	2.2	NUM
cana-5711	50	3	)	)	PUNCT
cana-5711	50	4	let	let	VERB
cana-5711	50	5	us	we	PRON
cana-5711	50	6	take	take	VERB
cana-5711	50	7	ℤ2q	ℤ2q	PROPN
cana-5711	50	8	as	as	ADP
cana-5711	50	9	a	a	DET
cana-5711	50	10	cross	cross	NOUN
cana-5711	50	11	product	product	NOUN
cana-5711	50	12	of	of	ADP
cana-5711	50	13	the	the	DET
cana-5711	50	14	rings	ring	NOUN
cana-5711	50	15	ℤ2	ℤ2	PROPN
cana-5711	50	16	and	and	CCONJ
cana-5711	50	17	q.	q.	PROPN
cana-5711	50	18	observe	observe	VERB
cana-5711	50	19	that	that	SCONJ
cana-5711	50	20	the	the	DET
cana-5711	50	21	ring	ring	NOUN
cana-5711	50	22	ℤ2q	ℤ2q	PROPN
cana-5711	50	23	is	be	AUX
cana-5711	50	24	an	an	DET
cana-5711	50	25	s	s	NOUN
cana-5711	50	26	-	-	NOUN
cana-5711	50	27	module	module	NOUN
cana-5711	50	28	with	with	ADP
cana-5711	50	29	respect	respect	NOUN
cana-5711	50	30	to	to	ADP
cana-5711	50	31	usual	usual	ADJ
cana-5711	50	32	addition	addition	NOUN
cana-5711	50	33	and	and	CCONJ
cana-5711	50	34	⋆-multiplication	⋆-multiplication	NOUN
cana-5711	50	35	.	.	PUNCT
cana-5711	51	1	definition	definition	NOUN
cana-5711	51	2	2.1	2.1	NUM
cana-5711	51	3	.	.	PUNCT
cana-5711	52	1	a	a	DET
cana-5711	52	2	subset	subset	NOUN
cana-5711	52	3	c	c	NOUN
cana-5711	52	4	of	of	ADP
cana-5711	52	5	ℤ2	ℤ2	PROPN
cana-5711	52	6	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	52	7	is	be	AUX
cana-5711	52	8	said	say	VERB
cana-5711	52	9	to	to	PART
cana-5711	52	10	be	be	AUX
cana-5711	52	11	an	an	DET
cana-5711	52	12	additive	additive	ADJ
cana-5711	52	13	code	code	NOUN
cana-5711	52	14	with	with	ADP
cana-5711	52	15	block	block	NOUN
cana-5711	52	16	length	length	NOUN
cana-5711	52	17	(	(	PUNCT
cana-5711	52	18	p	p	X
cana-5711	52	19	,	,	PUNCT
cana-5711	52	20	q	q	NOUN
cana-5711	52	21	)	)	PUNCT
cana-5711	52	22	if	if	SCONJ
cana-5711	52	23	it	it	PRON
cana-5711	52	24	is	be	AUX
cana-5711	52	25	a	a	DET
cana-5711	52	26	ssubmodule	ssubmodule	NOUN
cana-5711	52	27	of	of	ADP
cana-5711	52	28	ℤ2	ℤ2	PROPN
cana-5711	52	29	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	52	30	.	.	PUNCT
cana-5711	53	1	note	note	VERB
cana-5711	53	2	that	that	SCONJ
cana-5711	53	3	if	if	SCONJ
cana-5711	53	4	p	p	X
cana-5711	53	5	=	=	NOUN
cana-5711	53	6	q	q	ADJ
cana-5711	53	7	,	,	PUNCT
cana-5711	53	8	then	then	ADV
cana-5711	53	9	ℤ2	ℤ2	PROPN
cana-5711	53	10	𝑝𝑄𝑝=	𝑝𝑄𝑝=	PROPN
cana-5711	53	11	(	(	PUNCT
cana-5711	53	12	ℤ2q)p	ℤ2q)p	PROPN
cana-5711	53	13	.	.	PUNCT
cana-5711	54	1	it	it	PRON
cana-5711	54	2	can	can	AUX
cana-5711	54	3	be	be	AUX
cana-5711	54	4	treated	treat	VERB
cana-5711	54	5	as	as	ADP
cana-5711	54	6	a	a	DET
cana-5711	54	7	ℤ2q	ℤ2q	PROPN
cana-5711	54	8	-	-	PUNCT
cana-5711	54	9	additive	additive	NOUN
cana-5711	54	10	code	code	NOUN
cana-5711	54	11	with	with	ADP
cana-5711	54	12	block	block	NOUN
cana-5711	54	13	length	length	NOUN
cana-5711	54	14	(	(	PUNCT
cana-5711	54	15	p	p	X
cana-5711	54	16	,	,	PUNCT
cana-5711	54	17	p	p	NOUN
cana-5711	54	18	)	)	PUNCT
cana-5711	54	19	,	,	PUNCT
cana-5711	54	20	equivalent	equivalent	ADJ
cana-5711	54	21	to	to	ADP
cana-5711	54	22	a	a	DET
cana-5711	54	23	ℤ2q	ℤ2q	PROPN
cana-5711	54	24	-	-	PUNCT
cana-5711	54	25	additive	additive	NOUN
cana-5711	54	26	code	code	NOUN
cana-5711	54	27	of	of	ADP
cana-5711	54	28	length	length	NOUN
cana-5711	54	29	p.	p.	NOUN
cana-5711	54	30	definition	definition	NOUN
cana-5711	54	31	2.2	2.2	NUM
cana-5711	54	32	.	.	PUNCT
cana-5711	55	1	the	the	DET
cana-5711	55	2	inner	inner	ADJ
cana-5711	55	3	product	product	NOUN
cana-5711	55	4	in	in	ADP
cana-5711	55	5	ℤ2	ℤ2	PROPN
cana-5711	55	6	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	55	7	is	be	AUX
cana-5711	55	8	defined	define	VERB
cana-5711	55	9	as	as	SCONJ
cana-5711	55	10	follows	follow	VERB
cana-5711	55	11	:	:	PUNCT
cana-5711	55	12	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	55	13	communications	communication	NOUN
cana-5711	55	14	on	on	ADP
cana-5711	55	15	applied	apply	VERB
cana-5711	55	16	nonlinear	nonlinear	ADJ
cana-5711	55	17	analysis	analysis	NOUN
cana-5711	55	18	issn	issn	NOUN
cana-5711	55	19	:	:	PUNCT
cana-5711	55	20	1074	1074	NUM
cana-5711	55	21	-	-	PUNCT
cana-5711	55	22	133x	133x	NUM
cana-5711	55	23	vol	vol	VERB
cana-5711	55	24	32	32	NUM
cana-5711	55	25	no	no	NOUN
cana-5711	55	26	.	.	PUNCT
cana-5711	56	1	10s	10	NOUN
cana-5711	56	2	(	(	PUNCT
cana-5711	56	3	2025	2025	NUM
cana-5711	56	4	)	)	PUNCT
cana-5711	56	5	2697	2697	NUM
cana-5711	56	6	•	•	NOUN
cana-5711	56	7	let	let	VERB
cana-5711	56	8	w	w	NOUN
cana-5711	56	9	=	=	SYM
cana-5711	56	10	(	(	PUNCT
cana-5711	56	11	α	α	X
cana-5711	56	12	,	,	PUNCT
cana-5711	56	13	β	β	NOUN
cana-5711	56	14	)	)	PUNCT
cana-5711	56	15	and	and	CCONJ
cana-5711	56	16	w	w	AUX
cana-5711	56	17	'	'	PUNCT
cana-5711	56	18	=	=	SYM
cana-5711	56	19	(	(	PUNCT
cana-5711	56	20	α	α	NOUN
cana-5711	56	21	'	'	X
cana-5711	56	22	,	,	PUNCT
cana-5711	56	23	β	β	X
cana-5711	56	24	'	'	PUNCT
cana-5711	56	25	)	)	PUNCT
cana-5711	56	26	be	be	AUX
cana-5711	56	27	elements	element	NOUN
cana-5711	56	28	of	of	ADP
cana-5711	56	29	qp	qp	NOUN
cana-5711	56	30	=	=	SYM
cana-5711	56	31	(	(	PUNCT
cana-5711	56	32	rp	rp	NOUN
cana-5711	56	33	×	×	NOUN
cana-5711	56	34	sp	sp	ADP
cana-5711	56	35	)	)	PUNCT
cana-5711	56	36	.	.	PUNCT
cana-5711	57	1	then	then	ADV
cana-5711	57	2	⟨·|·⟩	⟨·|·⟩	PUNCT
cana-5711	57	3	:	:	PUNCT
cana-5711	57	4	qp	qp	ADP
cana-5711	57	5	×	×	PROPN
cana-5711	57	6	qp→	qp→	NOUN
cana-5711	57	7	s	s	VERB
cana-5711	57	8	is	be	AUX
cana-5711	57	9	defined	define	VERB
cana-5711	57	10	as	as	SCONJ
cana-5711	57	11	follows	follow	VERB
cana-5711	57	12	:	:	PUNCT
cana-5711	57	13	⟨𝑤,𝑤′⟩	⟨𝑤,𝑤′⟩	PROPN
cana-5711	57	14	=	=	SYM
cana-5711	57	15	⟨(𝛼	⟨(𝛼	NOUN
cana-5711	57	16	,	,	PUNCT
cana-5711	57	17	𝛽	𝛽	NOUN
cana-5711	57	18	)	)	PUNCT
cana-5711	57	19	,	,	PUNCT
cana-5711	57	20	(	(	PUNCT
cana-5711	57	21	𝛼′	𝛼′	NUM
cana-5711	57	22	,	,	PUNCT
cana-5711	57	23	𝛽′)⟩	𝛽′)⟩	PROPN
cana-5711	57	24	=	=	SYM
cana-5711	57	25	𝛼𝛼′	𝛼𝛼′	PROPN
cana-5711	57	26	+	+	NUM
cana-5711	57	27	𝛽𝛽′.	𝛽𝛽′.	PROPN
cana-5711	57	28	(	(	PUNCT
cana-5711	57	29	2.3	2.3	NUM
cana-5711	57	30	)	)	PUNCT
cana-5711	57	31	•	•	NOUN
cana-5711	57	32	by	by	ADP
cana-5711	57	33	using	use	VERB
cana-5711	57	34	equation	equation	NOUN
cana-5711	57	35	2.3	2.3	NUM
cana-5711	57	36	,	,	PUNCT
cana-5711	57	37	we	we	PRON
cana-5711	57	38	define	define	VERB
cana-5711	57	39	an	an	DET
cana-5711	57	40	inner	inner	ADJ
cana-5711	57	41	product	product	NOUN
cana-5711	57	42	over	over	ADP
cana-5711	57	43	ℤ2	ℤ2	PROPN
cana-5711	57	44	𝑝	𝑝	PROPN
cana-5711	58	1	𝑄𝑝	𝑄𝑝	PROPN
cana-5711	58	2	as	as	ADP
cana-5711	58	3	⟨·|·⟩	⟨·|·⟩	NUM
cana-5711	58	4	:	:	PUNCT
cana-5711	58	5	ℤ2	ℤ2	PROPN
cana-5711	58	6	𝑝	𝑝	PROPN
cana-5711	58	7	𝑄𝑝×	𝑄𝑝×	PROPN
cana-5711	58	8	ℤ2	ℤ2	PROPN
cana-5711	58	9	𝑝	𝑝	PROPN
cana-5711	58	10	𝑄𝑝→	𝑄𝑝→	PROPN
cana-5711	58	11	s.	s.	PROPN
cana-5711	58	12	let	let	VERB
cana-5711	58	13	x	x	PUNCT
cana-5711	58	14	=	=	SYM
cana-5711	58	15	(	(	PUNCT
cana-5711	58	16	v	v	NOUN
cana-5711	58	17	,	,	PUNCT
cana-5711	58	18	w	w	NOUN
cana-5711	58	19	)	)	PUNCT
cana-5711	58	20	and	and	CCONJ
cana-5711	58	21	x	x	X
cana-5711	58	22	'	'	PUNCT
cana-5711	58	23	=	=	SYM
cana-5711	58	24	(	(	PUNCT
cana-5711	58	25	v	v	NOUN
cana-5711	58	26	'	'	PUNCT
cana-5711	58	27	,	,	PUNCT
cana-5711	58	28	w	w	PROPN
cana-5711	58	29	'	'	PUNCT
cana-5711	58	30	)	)	PUNCT
cana-5711	58	31	be	be	AUX
cana-5711	58	32	elements	element	NOUN
cana-5711	58	33	of	of	ADP
cana-5711	58	34	ℤ2	ℤ2	NOUN
cana-5711	58	35	𝑝𝑄𝑝.	𝑝𝑄𝑝.	PROPN
cana-5711	58	36	then	then	ADV
cana-5711	58	37	⟨𝑥	⟨𝑥	VERB
cana-5711	58	38	,	,	PUNCT
cana-5711	58	39	𝑥′⟩	𝑥′⟩	PUNCT
cana-5711	58	40	=	=	SYM
cana-5711	58	41	⟨(𝑣,𝑤	⟨(𝑣,𝑤	PROPN
cana-5711	58	42	)	)	PUNCT
cana-5711	58	43	,	,	PUNCT
cana-5711	58	44	(	(	PUNCT
cana-5711	58	45	𝑣′	𝑣′	PROPN
cana-5711	58	46	,	,	PUNCT
cana-5711	58	47	𝑤′)⟩	𝑤′)⟩	NOUN
cana-5711	58	48	=	=	PUNCT
cana-5711	58	49	𝑢𝑣⟨𝑣	𝑢𝑣⟨𝑣	NOUN
cana-5711	58	50	,	,	PUNCT
cana-5711	58	51	𝑣′⟩	𝑣′⟩	PROPN
cana-5711	58	52	+	+	CCONJ
cana-5711	58	53	⟨𝑤,𝑤′⟩.	⟨𝑤,𝑤′⟩.	NOUN
cana-5711	58	54	(	(	PUNCT
cana-5711	58	55	2.4	2.4	NUM
cana-5711	58	56	)	)	PUNCT
cana-5711	58	57	definition	definition	NOUN
cana-5711	58	58	2.3	2.3	NUM
cana-5711	58	59	.	.	PUNCT
cana-5711	59	1	let	let	VERB
cana-5711	59	2	c	c	NOUN
cana-5711	59	3	⊆	⊆	NUM
cana-5711	59	4	ℤ2	ℤ2	PROPN
cana-5711	59	5	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	59	6	be	be	AUX
cana-5711	59	7	an	an	DET
cana-5711	59	8	additive	additive	ADJ
cana-5711	59	9	code	code	NOUN
cana-5711	59	10	.	.	PUNCT
cana-5711	60	1	the	the	DET
cana-5711	60	2	dual	dual	PROPN
cana-5711	60	3	code	code	NOUN
cana-5711	60	4	c⊥	c⊥	NOUN
cana-5711	60	5	is	be	AUX
cana-5711	60	6	defined	define	VERB
cana-5711	60	7	as	as	ADP
cana-5711	60	8	:	:	PUNCT
cana-5711	60	9	c⊥	c⊥	PROPN
cana-5711	60	10	=	=	PUNCT
cana-5711	60	11	{	{	PUNCT
cana-5711	60	12	x	x	PUNCT
cana-5711	60	13	∈	∈	PROPN
cana-5711	60	14	ℤ2	ℤ2	PROPN
cana-5711	60	15	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	60	16	|	|	ADV
cana-5711	60	17	⟨x	⟨x	VERB
cana-5711	60	18	,	,	PUNCT
cana-5711	60	19	y⟩	y⟩	NOUN
cana-5711	60	20	=	=	NOUN
cana-5711	60	21	0	0	NUM
cana-5711	60	22	for	for	ADP
cana-5711	60	23	all	all	DET
cana-5711	60	24	y	y	PROPN
cana-5711	60	25	∈	∈	PROPN
cana-5711	60	26	c	c	AUX
cana-5711	60	27	}	}	PUNCT
cana-5711	60	28	where	where	SCONJ
cana-5711	60	29	⟨	⟨	NOUN
cana-5711	60	30	·	·	SYM
cana-5711	60	31	,	,	PUNCT
cana-5711	60	32	·	·	PUNCT
cana-5711	60	33	⟩	⟩	NOUN
cana-5711	60	34	denotes	denote	VERB
cana-5711	60	35	an	an	DET
cana-5711	60	36	appropriate	appropriate	ADJ
cana-5711	60	37	inner	inner	ADJ
cana-5711	60	38	product	product	NOUN
cana-5711	60	39	over	over	ADP
cana-5711	60	40	the	the	DET
cana-5711	60	41	module	module	NOUN
cana-5711	60	42	ℤ2	ℤ2	PROPN
cana-5711	60	43	𝑝𝑄𝑞.	𝑝𝑄𝑞.	PROPN
cana-5711	60	44	definition	definition	NOUN
cana-5711	60	45	2.4	2.4	NUM
cana-5711	60	46	.	.	PUNCT
cana-5711	61	1	the	the	DET
cana-5711	61	2	subset	subset	NOUN
cana-5711	61	3	a	a	X
cana-5711	61	4	=	=	X
cana-5711	61	5	{	{	PUNCT
cana-5711	61	6	v1	v1	NOUN
cana-5711	61	7	,	,	PUNCT
cana-5711	61	8	v2	v2	PROPN
cana-5711	61	9	,	,	PUNCT
cana-5711	61	10	.	.	PUNCT
cana-5711	61	11	.	.	PUNCT
cana-5711	62	1	.	.	PUNCT
cana-5711	63	1	,	,	PUNCT
cana-5711	63	2	vt	vt	PROPN
cana-5711	63	3	}	}	PUNCT
cana-5711	63	4	of	of	ADP
cana-5711	63	5	qq	qq	PROPN
cana-5711	63	6	is	be	AUX
cana-5711	63	7	called	call	VERB
cana-5711	63	8	a	a	DET
cana-5711	63	9	q	q	ADJ
cana-5711	63	10	-	-	PUNCT
cana-5711	63	11	linearly	linearly	ADV
cana-5711	63	12	independent	independent	ADJ
cana-5711	63	13	set	set	NOUN
cana-5711	63	14	if	if	SCONJ
cana-5711	63	15	the	the	DET
cana-5711	63	16	equation	equation	NOUN
cana-5711	63	17	λ1v1	λ1v1	X
cana-5711	64	1	+	+	CCONJ
cana-5711	64	2	λ2v2	λ2v2	X
cana-5711	64	3	+	+	X
cana-5711	64	4	·	·	PUNCT
cana-5711	64	5	·	·	PUNCT
cana-5711	64	6	·	·	PUNCT
cana-5711	65	1	+	+	NUM
cana-5711	65	2	λtvt	λtvt	NOUN
cana-5711	65	3	=	=	SYM
cana-5711	65	4	0	0	PROPN
cana-5711	65	5	,	,	PUNCT
cana-5711	65	6	where	where	SCONJ
cana-5711	65	7	λ1	λ1	ADJ
cana-5711	65	8	,	,	PUNCT
cana-5711	65	9	.	.	PUNCT
cana-5711	65	10	.	.	PUNCT
cana-5711	65	11	.	.	PUNCT
cana-5711	66	1	,	,	PUNCT
cana-5711	66	2	λt	λt	ADP
cana-5711	66	3	∈	∈	PROPN
cana-5711	66	4	q	q	NOUN
cana-5711	66	5	,	,	PUNCT
cana-5711	66	6	has	have	VERB
cana-5711	66	7	only	only	ADV
cana-5711	66	8	the	the	DET
cana-5711	66	9	trivial	trivial	ADJ
cana-5711	66	10	solution	solution	NOUN
cana-5711	66	11	λi	λi	ADP
cana-5711	66	12	=	=	NOUN
cana-5711	66	13	0	0	NUM
cana-5711	66	14	for	for	ADP
cana-5711	66	15	all	all	PRON
cana-5711	66	16	i	i	PRON
cana-5711	66	17	∈	∈	PROPN
cana-5711	66	18	{	{	PUNCT
cana-5711	66	19	1	1	NUM
cana-5711	66	20	,	,	PUNCT
cana-5711	66	21	2	2	NUM
cana-5711	66	22	,	,	PUNCT
cana-5711	66	23	.	.	PUNCT
cana-5711	66	24	.	.	PUNCT
cana-5711	67	1	.	.	PUNCT
cana-5711	68	1	,	,	PUNCT
cana-5711	68	2	t	t	PROPN
cana-5711	68	3	}	}	PUNCT
cana-5711	68	4	.	.	PUNCT
cana-5711	69	1	definition	definition	NOUN
cana-5711	69	2	2.5	2.5	NUM
cana-5711	69	3	.	.	PUNCT
cana-5711	70	1	an	an	DET
cana-5711	70	2	additive	additive	ADJ
cana-5711	70	3	code	code	NOUN
cana-5711	70	4	c	c	NOUN
cana-5711	70	5	over	over	ADP
cana-5711	70	6	ℤ2q	ℤ2q	PROPN
cana-5711	70	7	is	be	AUX
cana-5711	70	8	said	say	VERB
cana-5711	70	9	to	to	PART
cana-5711	70	10	be	be	AUX
cana-5711	70	11	an	an	DET
cana-5711	70	12	additive	additive	ADJ
cana-5711	70	13	complementary	complementary	ADJ
cana-5711	70	14	dual	dual	ADJ
cana-5711	70	15	(	(	PUNCT
cana-5711	70	16	acd	acd	NOUN
cana-5711	70	17	)	)	PUNCT
cana-5711	70	18	code	code	NOUN
cana-5711	70	19	if	if	SCONJ
cana-5711	70	20	𝐶	𝐶	PROPN
cana-5711	70	21	∩	∩	NOUN
cana-5711	70	22	𝐶⊥=	𝐶⊥=	NOUN
cana-5711	70	23	{	{	PUNCT
cana-5711	70	24	0	0	NUM
cana-5711	70	25	}	}	PUNCT
cana-5711	70	26	.	.	PUNCT
cana-5711	71	1	if	if	SCONJ
cana-5711	71	2	p	p	NOUN
cana-5711	71	3	=	=	NOUN
cana-5711	71	4	0	0	NUM
cana-5711	71	5	,	,	PUNCT
cana-5711	71	6	then	then	ADV
cana-5711	71	7	c	c	PROPN
cana-5711	71	8	is	be	AUX
cana-5711	71	9	an	an	DET
cana-5711	71	10	acd	acd	NOUN
cana-5711	71	11	code	code	NOUN
cana-5711	71	12	of	of	ADP
cana-5711	71	13	length	length	NOUN
cana-5711	71	14	q	q	PROPN
cana-5711	71	15	,	,	PUNCT
cana-5711	71	16	and	and	CCONJ
cana-5711	71	17	if	if	SCONJ
cana-5711	71	18	q	q	X
cana-5711	71	19	=	=	SYM
cana-5711	71	20	0	0	NUM
cana-5711	71	21	,	,	PUNCT
cana-5711	71	22	then	then	ADV
cana-5711	71	23	c	c	PROPN
cana-5711	71	24	is	be	AUX
cana-5711	71	25	a	a	DET
cana-5711	71	26	binary	binary	ADJ
cana-5711	71	27	lcd	lcd	PROPN
cana-5711	71	28	code	code	NOUN
cana-5711	71	29	of	of	ADP
cana-5711	71	30	length	length	NOUN
cana-5711	71	31	p.	p.	NOUN
cana-5711	72	1	an	an	DET
cana-5711	72	2	additive	additive	ADJ
cana-5711	72	3	code	code	NOUN
cana-5711	72	4	c	c	NOUN
cana-5711	72	5	over	over	ADP
cana-5711	72	6	a	a	DET
cana-5711	72	7	finite	finite	NOUN
cana-5711	72	8	ring	ring	NOUN
cana-5711	72	9	ℤ2q	ℤ2q	PROPN
cana-5711	72	10	is	be	AUX
cana-5711	72	11	called	call	VERB
cana-5711	72	12	self	self	NOUN
cana-5711	72	13	-	-	PUNCT
cana-5711	72	14	orthogonal	orthogonal	ADJ
cana-5711	72	15	(	(	PUNCT
cana-5711	72	16	self	self	NOUN
cana-5711	72	17	-	-	PUNCT
cana-5711	72	18	dual	dual	ADJ
cana-5711	72	19	)	)	PUNCT
cana-5711	72	20	if	if	SCONJ
cana-5711	72	21	c	c	PROPN
cana-5711	72	22	⊆	⊆	NUM
cana-5711	72	23	c⊥	c⊥	X
cana-5711	72	24	(	(	PUNCT
cana-5711	72	25	c	c	NOUN
cana-5711	72	26	=	=	NOUN
cana-5711	72	27	c⊥	c⊥	NOUN
cana-5711	72	28	)	)	PUNCT
cana-5711	72	29	.	.	PUNCT
cana-5711	73	1	if	if	SCONJ
cana-5711	73	2	c	c	PROPN
cana-5711	73	3	has	have	VERB
cana-5711	73	4	a	a	DET
cana-5711	73	5	basis	basis	NOUN
cana-5711	73	6	over	over	ADP
cana-5711	73	7	ℤ2q	ℤ2q	PROPN
cana-5711	73	8	,	,	PUNCT
cana-5711	73	9	then	then	ADV
cana-5711	73	10	it	it	PRON
cana-5711	73	11	is	be	AUX
cana-5711	73	12	called	call	VERB
cana-5711	73	13	a	a	DET
cana-5711	73	14	free	free	ADJ
cana-5711	73	15	additive	additive	ADJ
cana-5711	73	16	code	code	NOUN
cana-5711	73	17	and	and	CCONJ
cana-5711	73	18	the	the	DET
cana-5711	73	19	cardinality	cardinality	NOUN
cana-5711	73	20	of	of	ADP
cana-5711	73	21	the	the	DET
cana-5711	73	22	basis	basis	NOUN
cana-5711	73	23	is	be	AUX
cana-5711	73	24	called	call	VERB
cana-5711	73	25	the	the	DET
cana-5711	73	26	rank	rank	NOUN
cana-5711	73	27	of	of	ADP
cana-5711	73	28	c.	c.	PROPN
cana-5711	73	29	3	3	NUM
cana-5711	73	30	.	.	PUNCT
cana-5711	73	31	additive	additive	ADJ
cana-5711	73	32	complementary	complementary	ADJ
cana-5711	73	33	dual	dual	ADJ
cana-5711	73	34	code	code	NOUN
cana-5711	73	35	over	over	ADP
cana-5711	73	36	ℤ2q	ℤ2q	PROPN
cana-5711	73	37	let	let	VERB
cana-5711	73	38	cp	cp	PRON
cana-5711	73	39	be	be	AUX
cana-5711	73	40	a	a	DET
cana-5711	73	41	code	code	NOUN
cana-5711	73	42	over	over	ADP
cana-5711	73	43	ℤ2	ℤ2	PROPN
cana-5711	73	44	generated	generate	VERB
cana-5711	73	45	by	by	ADP
cana-5711	73	46	an	an	DET
cana-5711	73	47	m	m	PROPN
cana-5711	73	48	×	×	NOUN
cana-5711	73	49	p	p	NOUN
cana-5711	73	50	matrix	matrix	NOUN
cana-5711	73	51	gp	gp	NOUN
cana-5711	73	52	,	,	PUNCT
cana-5711	73	53	and	and	CCONJ
cana-5711	73	54	let	let	VERB
cana-5711	73	55	cq	cq	PRON
cana-5711	73	56	be	be	AUX
cana-5711	73	57	a	a	DET
cana-5711	73	58	code	code	NOUN
cana-5711	73	59	over	over	ADP
cana-5711	73	60	q	q	AUX
cana-5711	73	61	generated	generate	VERB
cana-5711	73	62	by	by	ADP
cana-5711	73	63	an	an	DET
cana-5711	73	64	m	m	PROPN
cana-5711	73	65	×	×	NOUN
cana-5711	73	66	q	q	NOUN
cana-5711	73	67	matrix	matrix	NOUN
cana-5711	73	68	gq	gq	NOUN
cana-5711	73	69	.	.	PUNCT
cana-5711	74	1	then	then	ADV
cana-5711	74	2	the	the	DET
cana-5711	74	3	m	m	ADJ
cana-5711	74	4	×	×	NOUN
cana-5711	74	5	(	(	PUNCT
cana-5711	74	6	p	p	X
cana-5711	74	7	+	+	NOUN
cana-5711	74	8	q	q	ADJ
cana-5711	74	9	)	)	PUNCT
cana-5711	74	10	matrix	matrix	NOUN
cana-5711	74	11	g	g	NOUN
cana-5711	75	1	=	=	PUNCT
cana-5711	76	1	[	[	X
cana-5711	76	2	gp	gp	X
cana-5711	76	3	|	|	ADV
cana-5711	76	4	gq	gq	VERB
cana-5711	76	5	]	]	PUNCT
cana-5711	76	6	over	over	ADP
cana-5711	76	7	ℤ2q	ℤ2q	PROPN
cana-5711	76	8	generates	generate	VERB
cana-5711	76	9	an	an	DET
cana-5711	76	10	additive	additive	ADJ
cana-5711	76	11	code	code	NOUN
cana-5711	76	12	c.	c.	NOUN
cana-5711	76	13	now	now	ADV
cana-5711	76	14	,	,	PUNCT
cana-5711	76	15	we	we	PRON
cana-5711	76	16	have	have	AUX
cana-5711	76	17	using	use	VERB
cana-5711	76	18	the	the	DET
cana-5711	76	19	inner	inner	ADJ
cana-5711	76	20	product	product	NOUN
cana-5711	76	21	equation	equation	NOUN
cana-5711	76	22	2.4	2.4	NUM
cana-5711	76	23	.	.	PUNCT
cana-5711	77	1	we	we	PRON
cana-5711	77	2	define	define	VERB
cana-5711	77	3	the	the	DET
cana-5711	77	4	matrix	matrix	NOUN
cana-5711	77	5	product	product	NOUN
cana-5711	77	6	as	as	SCONJ
cana-5711	77	7	follows	follow	VERB
cana-5711	77	8	:	:	PUNCT
cana-5711	77	9	𝐺	𝐺	NOUN
cana-5711	77	10	◦	◦	NOUN
cana-5711	77	11	𝐺𝑡	𝐺𝑡	NOUN
cana-5711	77	12	=	=	PUNCT
cana-5711	77	13	𝑢𝑣𝐺𝑝𝐺𝑝	𝑢𝑣𝐺𝑝𝐺𝑝	X
cana-5711	77	14	𝑡	𝑡	PROPN
cana-5711	77	15	+	+	PROPN
cana-5711	77	16	𝐺𝑞𝐺𝑞	𝐺𝑞𝐺𝑞	PROPN
cana-5711	77	17	𝑡	𝑡	PROPN
cana-5711	77	18	,	,	PUNCT
cana-5711	77	19	(	(	PUNCT
cana-5711	77	20	3.1	3.1	NUM
cana-5711	77	21	)	)	PUNCT
cana-5711	77	22	where	where	SCONJ
cana-5711	77	23	gt	gt	PROPN
cana-5711	77	24	is	be	AUX
cana-5711	77	25	the	the	DET
cana-5711	77	26	transpose	transpose	ADJ
cana-5711	77	27	matrix	matrix	NOUN
cana-5711	77	28	of	of	ADP
cana-5711	77	29	g.	g.	PROPN
cana-5711	77	30	theorem	theorem	VERB
cana-5711	77	31	3.1	3.1	NUM
cana-5711	77	32	.	.	PUNCT
cana-5711	78	1	let	let	VERB
cana-5711	78	2	c	c	PRON
cana-5711	78	3	be	be	AUX
cana-5711	78	4	a	a	DET
cana-5711	78	5	ℤ2qadditive	ℤ2qadditive	ADJ
cana-5711	78	6	code	code	NOUN
cana-5711	78	7	with	with	ADP
cana-5711	78	8	the	the	DET
cana-5711	78	9	generator	generator	NOUN
cana-5711	78	10	matrix	matrix	NOUN
cana-5711	78	11	g	g	NOUN
cana-5711	78	12	of	of	ADP
cana-5711	78	13	size	size	NOUN
cana-5711	78	14	m	m	PROPN
cana-5711	78	15	×	×	NOUN
cana-5711	78	16	(	(	PUNCT
cana-5711	78	17	p	p	X
cana-5711	78	18	+	+	NOUN
cana-5711	78	19	q	q	NOUN
cana-5711	78	20	)	)	PUNCT
cana-5711	78	21	.	.	PUNCT
cana-5711	79	1	let	let	VERB
cana-5711	79	2	nonzero	nonzero	PROPN
cana-5711	79	3	vector	vector	PROPN
cana-5711	79	4	vi	vi	PROPN
cana-5711	79	5	be	be	AUX
cana-5711	79	6	the	the	DET
cana-5711	79	7	ith	ith	NOUN
cana-5711	79	8	row	row	NOUN
cana-5711	79	9	of	of	ADP
cana-5711	79	10	g	g	NOUN
cana-5711	80	1	such	such	ADJ
cana-5711	80	2	that	that	SCONJ
cana-5711	80	3	⟨vi	⟨vi	NOUN
cana-5711	80	4	,	,	PUNCT
cana-5711	80	5	vj	vj	INTJ
cana-5711	80	6	⟩	⟩	PROPN
cana-5711	80	7	∈	∈	PROPN
cana-5711	80	8	{	{	PUNCT
cana-5711	80	9	0	0	NUM
cana-5711	80	10	,	,	PUNCT
cana-5711	80	11	uv	uv	NOUN
cana-5711	80	12	}	}	PUNCT
cana-5711	80	13	and	and	CCONJ
cana-5711	80	14	⟨vi	⟨vi	NOUN
cana-5711	80	15	,	,	PUNCT
cana-5711	80	16	vi	vi	NOUN
cana-5711	80	17	⟩	⟩	NOUN
cana-5711	80	18	∈	∈	PROPN
cana-5711	80	19	u	u	NOUN
cana-5711	80	20	(	(	PUNCT
cana-5711	80	21	q	q	NOUN
cana-5711	80	22	)	)	PUNCT
cana-5711	80	23	for	for	ADP
cana-5711	80	24	all	all	DET
cana-5711	80	25	i	i	PROPN
cana-5711	80	26	,	,	PUNCT
cana-5711	80	27	j	j	PROPN
cana-5711	80	28	∈	∈	PROPN
cana-5711	80	29	{	{	PUNCT
cana-5711	80	30	1	1	NUM
cana-5711	80	31	,	,	PUNCT
cana-5711	80	32	2	2	NUM
cana-5711	80	33	,	,	PUNCT
cana-5711	80	34	.	.	PUNCT
cana-5711	80	35	.	.	PUNCT
cana-5711	80	36	.	.	PUNCT
cana-5711	81	1	,	,	PUNCT
cana-5711	81	2	m	m	VERB
cana-5711	81	3	}	}	PUNCT
cana-5711	81	4	such	such	ADJ
cana-5711	81	5	that	that	SCONJ
cana-5711	81	6	i	i	PRON
cana-5711	81	7	≠	≠	PROPN
cana-5711	81	8	j	j	PROPN
cana-5711	81	9	,	,	PUNCT
cana-5711	81	10	then	then	ADV
cana-5711	81	11	c	c	PROPN
cana-5711	81	12	is	be	AUX
cana-5711	81	13	a	a	DET
cana-5711	81	14	ℤ2q	ℤ2q	PROPN
cana-5711	81	15	–	–	PUNCT
cana-5711	81	16	acd	acd	NOUN
cana-5711	81	17	code	code	NOUN
cana-5711	81	18	.	.	PUNCT
cana-5711	82	1	proof	proof	NOUN
cana-5711	82	2	.	.	PUNCT
cana-5711	83	1	let	let	VERB
cana-5711	83	2	u	u	PRON
cana-5711	83	3	be	be	AUX
cana-5711	83	4	any	any	DET
cana-5711	83	5	nonzero	nonzero	ADJ
cana-5711	83	6	codeword	codeword	NOUN
cana-5711	83	7	of	of	ADP
cana-5711	83	8	c.	c.	PROPN
cana-5711	83	9	if	if	SCONJ
cana-5711	83	10	u	u	PROPN
cana-5711	83	11	≠	≠	PROPN
cana-5711	83	12	c⊥	c⊥	VERB
cana-5711	83	13	,	,	PUNCT
cana-5711	83	14	then	then	ADV
cana-5711	83	15	c	c	PROPN
cana-5711	83	16	is	be	AUX
cana-5711	83	17	a	a	DET
cana-5711	83	18	ℤ2q	ℤ2q	PROPN
cana-5711	83	19	-	-	PUNCT
cana-5711	83	20	acd	acd	NOUN
cana-5711	83	21	codes	code	NOUN
cana-5711	83	22	.	.	PUNCT
cana-5711	84	1	since	since	SCONJ
cana-5711	84	2	u	u	PROPN
cana-5711	84	3	∈	∈	PROPN
cana-5711	84	4	c	c	NOUN
cana-5711	84	5	,	,	PUNCT
cana-5711	84	6	then	then	ADV
cana-5711	84	7	u	u	NOUN
cana-5711	84	8	=	=	NOUN
cana-5711	84	9	σi∈j	σi∈j	ADP
cana-5711	84	10	λi	λi	X
cana-5711	84	11	vi	vi	NOUN
cana-5711	84	12	,	,	PUNCT
cana-5711	84	13	where	where	SCONJ
cana-5711	84	14	j	j	PROPN
cana-5711	84	15	=	=	PRON
cana-5711	84	16	{	{	PUNCT
cana-5711	84	17	1	1	NUM
cana-5711	84	18	,	,	PUNCT
cana-5711	84	19	2	2	NUM
cana-5711	84	20	,	,	PUNCT
cana-5711	84	21	.	.	PUNCT
cana-5711	84	22	.	.	PUNCT
cana-5711	84	23	.	.	PUNCT
cana-5711	85	1	,	,	PUNCT
cana-5711	85	2	m	m	VERB
cana-5711	85	3	}	}	PUNCT
cana-5711	85	4	and	and	CCONJ
cana-5711	85	5	λi	λi	ADP
cana-5711	85	6	∈	∈	PROPN
cana-5711	85	7	q.	q.	NOUN
cana-5711	85	8	firstly	firstly	ADV
cana-5711	85	9	,	,	PUNCT
cana-5711	85	10	we	we	PRON
cana-5711	85	11	assume	assume	VERB
cana-5711	85	12	that	that	SCONJ
cana-5711	85	13	there	there	PRON
cana-5711	85	14	exist	exist	VERB
cana-5711	85	15	j	j	PROPN
cana-5711	85	16	∈	∈	PROPN
cana-5711	85	17	j	j	PROPN
cana-5711	85	18	such	such	ADJ
cana-5711	85	19	that	that	SCONJ
cana-5711	85	20	λj	λj	PROPN
cana-5711	85	21	∈	∈	PROPN
cana-5711	85	22	u	u	PROPN
cana-5711	85	23	(	(	PUNCT
cana-5711	85	24	q	q	NOUN
cana-5711	85	25	)	)	PUNCT
cana-5711	85	26	.	.	PUNCT
cana-5711	86	1	then	then	ADV
cana-5711	86	2	,	,	PUNCT
cana-5711	86	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	86	4	communications	communication	NOUN
cana-5711	86	5	on	on	ADP
cana-5711	86	6	applied	apply	VERB
cana-5711	86	7	nonlinear	nonlinear	ADJ
cana-5711	86	8	analysis	analysis	NOUN
cana-5711	86	9	issn	issn	NOUN
cana-5711	86	10	:	:	PUNCT
cana-5711	86	11	1074	1074	NUM
cana-5711	86	12	-	-	PUNCT
cana-5711	86	13	133x	133x	NUM
cana-5711	86	14	vol	vol	VERB
cana-5711	86	15	32	32	NUM
cana-5711	86	16	no	no	NOUN
cana-5711	86	17	.	.	PUNCT
cana-5711	87	1	10s	10	NOUN
cana-5711	87	2	(	(	PUNCT
cana-5711	87	3	2025	2025	NUM
cana-5711	87	4	)	)	PUNCT
cana-5711	87	5	2698	2698	NUM
cana-5711	87	6	⟨𝑢	⟨𝑢	NOUN
cana-5711	87	7	,	,	PUNCT
cana-5711	87	8	𝑣𝑗⟩	𝑣𝑗⟩	PUNCT
cana-5711	87	9	=	=	NOUN
cana-5711	87	10	∑	∑	PUNCT
cana-5711	87	11	𝜆𝑖𝑖∈𝐽	𝜆𝑖𝑖∈𝐽	ADP
cana-5711	87	12	⟨𝑣𝑖	⟨𝑣𝑖	NUM
cana-5711	87	13	,	,	PUNCT
cana-5711	87	14	𝑣𝑗⟩	𝑣𝑗⟩	PUNCT
cana-5711	87	15	=	=	NOUN
cana-5711	87	16	∑	∑	PART
cana-5711	87	17	𝜆𝑖𝑖∈𝐽{𝑗	𝜆𝑖𝑖∈𝐽{𝑗	NOUN
cana-5711	87	18	⟨𝑣𝑖	⟨𝑣𝑖	NUM
cana-5711	87	19	,	,	PUNCT
cana-5711	87	20	𝑣𝑗⟩	𝑣𝑗⟩	PUNCT
cana-5711	88	1	+	+	CCONJ
cana-5711	88	2	𝜆𝑗⟨𝑣𝑗	𝜆𝑗⟨𝑣𝑗	NUM
cana-5711	88	3	,	,	PUNCT
cana-5711	88	4	𝑣𝑗⟩.	𝑣𝑗⟩.	PROPN
cana-5711	88	5	for	for	ADP
cana-5711	88	6	i	i	PRON
cana-5711	88	7	≠	≠	PROPN
cana-5711	88	8	j	j	PROPN
cana-5711	88	9	,	,	PUNCT
cana-5711	88	10	since	since	SCONJ
cana-5711	88	11	⟨vi	⟨vi	NOUN
cana-5711	88	12	,	,	PUNCT
cana-5711	88	13	vj	vj	INTJ
cana-5711	88	14	⟩	⟩	PROPN
cana-5711	88	15	∈	∈	PROPN
cana-5711	88	16	{	{	PUNCT
cana-5711	88	17	0	0	NUM
cana-5711	88	18	,	,	PUNCT
cana-5711	88	19	uv	uv	NOUN
cana-5711	88	20	}	}	PUNCT
cana-5711	88	21	,	,	PUNCT
cana-5711	88	22	then	then	ADV
cana-5711	88	23	λi	λi	ADP
cana-5711	88	24	⟨vi	⟨vi	NOUN
cana-5711	88	25	,	,	PUNCT
cana-5711	88	26	vj	vj	INTJ
cana-5711	88	27	⟩	⟩	PROPN
cana-5711	88	28	∈	∈	PROPN
cana-5711	88	29	{	{	PUNCT
cana-5711	88	30	0	0	NUM
cana-5711	88	31	,	,	PUNCT
cana-5711	88	32	uv	uv	NOUN
cana-5711	88	33	}	}	PUNCT
cana-5711	88	34	.	.	PUNCT
cana-5711	89	1	since	since	SCONJ
cana-5711	89	2	⟨vj	⟨vj	PROPN
cana-5711	89	3	,	,	PUNCT
cana-5711	89	4	vj	vj	PROPN
cana-5711	89	5	⟩	⟩	PROPN
cana-5711	89	6	∈	∈	PROPN
cana-5711	89	7	u	u	NOUN
cana-5711	89	8	(	(	PUNCT
cana-5711	89	9	q	q	NOUN
cana-5711	89	10	)	)	PUNCT
cana-5711	89	11	,	,	PUNCT
cana-5711	89	12	then	then	ADV
cana-5711	89	13	λj	λj	INTJ
cana-5711	89	14	⟨vj	⟨vj	PROPN
cana-5711	89	15	,	,	PUNCT
cana-5711	89	16	vj	vj	PROPN
cana-5711	89	17	⟩	⟩	PROPN
cana-5711	89	18	∈	∈	PROPN
cana-5711	89	19	u	u	NOUN
cana-5711	89	20	(	(	PUNCT
cana-5711	89	21	q	q	NOUN
cana-5711	89	22	)	)	PUNCT
cana-5711	89	23	.	.	PUNCT
cana-5711	90	1	thus	thus	ADV
cana-5711	90	2	⟨u	⟨u	NUM
cana-5711	90	3	,	,	PUNCT
cana-5711	90	4	vj	vj	ADP
cana-5711	90	5	⟩	⟩	PROPN
cana-5711	90	6	≠	≠	PROPN
cana-5711	90	7	0	0	PUNCT
cana-5711	90	8	and	and	CCONJ
cana-5711	90	9	u	u	PROPN
cana-5711	90	10	≠	≠	PROPN
cana-5711	90	11	c⊥.	c⊥.	NOUN
cana-5711	90	12	further	far	ADV
cana-5711	90	13	,	,	PUNCT
cana-5711	90	14	if	if	SCONJ
cana-5711	90	15	λi	λi	ADP
cana-5711	90	16	∈	∈	PROPN
cana-5711	90	17	m	m	PRON
cana-5711	90	18	,	,	PUNCT
cana-5711	90	19	the	the	DET
cana-5711	90	20	maximal	maximal	ADJ
cana-5711	90	21	ideal	ideal	NOUN
cana-5711	90	22	.	.	PUNCT
cana-5711	91	1	let	let	VERB
cana-5711	91	2	j	j	PROPN
cana-5711	91	3	∈	∈	PROPN
cana-5711	91	4	j	j	PROPN
cana-5711	91	5	such	such	ADJ
cana-5711	91	6	that	that	SCONJ
cana-5711	91	7	λj	λj	PROPN
cana-5711	91	8	∈	∈	PROPN
cana-5711	91	9	m	m	VERB
cana-5711	91	10	\	\	X
cana-5711	91	11	{	{	PUNCT
cana-5711	91	12	0	0	NUM
cana-5711	91	13	}	}	PUNCT
cana-5711	91	14	.	.	PUNCT
cana-5711	92	1	since	since	SCONJ
cana-5711	92	2	⟨vi	⟨vi	NOUN
cana-5711	92	3	,	,	PUNCT
cana-5711	92	4	vj	vj	INTJ
cana-5711	92	5	⟩	⟩	PROPN
cana-5711	92	6	∈	∈	PROPN
cana-5711	92	7	{	{	PUNCT
cana-5711	92	8	0	0	NUM
cana-5711	92	9	,	,	PUNCT
cana-5711	92	10	uv	uv	NOUN
cana-5711	92	11	}	}	PUNCT
cana-5711	92	12	,	,	PUNCT
cana-5711	92	13	then	then	ADV
cana-5711	92	14	λi	λi	ADP
cana-5711	92	15	⟨vi	⟨vi	NOUN
cana-5711	92	16	,	,	PUNCT
cana-5711	92	17	vj	vj	INTJ
cana-5711	92	18	⟩	⟩	NOUN
cana-5711	92	19	=	=	NOUN
cana-5711	92	20	0	0	NUM
cana-5711	92	21	.	.	PUNCT
cana-5711	93	1	thus	thus	ADV
cana-5711	93	2	,	,	PUNCT
cana-5711	93	3	⟨𝑢	⟨𝑢	NOUN
cana-5711	93	4	,	,	PUNCT
cana-5711	93	5	𝑣𝑗⟩	𝑣𝑗⟩	PUNCT
cana-5711	93	6	=	=	SYM
cana-5711	93	7	∑	∑	PUNCT
cana-5711	93	8	𝜆𝑖𝑖∈𝐽{𝑗	𝜆𝑖𝑖∈𝐽{𝑗	NOUN
cana-5711	93	9	⟨𝑣𝑖	⟨𝑣𝑖	NUM
cana-5711	93	10	,	,	PUNCT
cana-5711	93	11	𝑣𝑗⟩	𝑣𝑗⟩	PUNCT
cana-5711	93	12	+	+	CCONJ
cana-5711	93	13	𝜆𝑗⟨𝑣𝑗	𝜆𝑗⟨𝑣𝑗	NUM
cana-5711	93	14	,	,	PUNCT
cana-5711	93	15	𝑣𝑗⟩.	𝑣𝑗⟩.	PROPN
cana-5711	93	16	=	=	SYM
cana-5711	93	17	𝜆𝑗⟨𝑣𝑗	𝜆𝑗⟨𝑣𝑗	PROPN
cana-5711	93	18	,	,	PUNCT
cana-5711	93	19	𝑣𝑗⟩.	𝑣𝑗⟩.	PROPN
cana-5711	93	20	since	since	SCONJ
cana-5711	93	21	⟨vj	⟨vj	PROPN
cana-5711	93	22	,	,	PUNCT
cana-5711	93	23	vj	vj	PROPN
cana-5711	93	24	⟩	⟩	PROPN
cana-5711	93	25	∈	∈	PROPN
cana-5711	93	26	u	u	NOUN
cana-5711	93	27	(	(	PUNCT
cana-5711	93	28	q	q	NOUN
cana-5711	93	29	)	)	PUNCT
cana-5711	93	30	,	,	PUNCT
cana-5711	93	31	then	then	ADV
cana-5711	93	32	λj	λj	INTJ
cana-5711	93	33	⟨vj	⟨vj	PROPN
cana-5711	93	34	,	,	PUNCT
cana-5711	93	35	vj	vj	INTJ
cana-5711	93	36	⟩	⟩	PROPN
cana-5711	93	37	≠	≠	PROPN
cana-5711	93	38	0	0	NUM
cana-5711	93	39	.	.	PUNCT
cana-5711	94	1	thus	thus	ADV
cana-5711	94	2	⟨u	⟨u	NUM
cana-5711	94	3	,	,	PUNCT
cana-5711	94	4	vj	vj	ADP
cana-5711	94	5	⟩	⟩	PROPN
cana-5711	94	6	≠	≠	PROPN
cana-5711	94	7	0	0	PUNCT
cana-5711	94	8	and	and	CCONJ
cana-5711	94	9	u	u	PROPN
cana-5711	94	10	≠	≠	PROPN
cana-5711	94	11	c⊥	c⊥	NOUN
cana-5711	94	12	.	.	PUNCT
cana-5711	95	1	thus	thus	ADV
cana-5711	95	2	c	c	PROPN
cana-5711	95	3	is	be	AUX
cana-5711	95	4	a	a	DET
cana-5711	95	5	ℤ2qacd	ℤ2qacd	NOUN
cana-5711	95	6	codes	code	NOUN
cana-5711	95	7	.	.	PUNCT
cana-5711	96	1	hence	hence	ADV
cana-5711	96	2	the	the	DET
cana-5711	96	3	proved	prove	VERB
cana-5711	96	4	.	.	PUNCT
cana-5711	97	1	theorem	theorem	VERB
cana-5711	97	2	3.1	3.1	NUM
cana-5711	97	3	directly	directly	ADV
cana-5711	97	4	leads	lead	VERB
cana-5711	97	5	to	to	ADP
cana-5711	97	6	the	the	DET
cana-5711	97	7	deduction	deduction	NOUN
cana-5711	97	8	of	of	ADP
cana-5711	97	9	the	the	DET
cana-5711	97	10	following	follow	VERB
cana-5711	97	11	corollaries	corollary	NOUN
cana-5711	97	12	.	.	PUNCT
cana-5711	98	1	corollary	corollary	ADJ
cana-5711	98	2	3.2	3.2	NUM
cana-5711	98	3	.	.	PUNCT
cana-5711	99	1	let	let	VERB
cana-5711	99	2	c	c	PRON
cana-5711	99	3	be	be	AUX
cana-5711	99	4	a	a	DET
cana-5711	99	5	ℤ2qadditive	ℤ2qadditive	ADJ
cana-5711	99	6	code	code	NOUN
cana-5711	99	7	with	with	ADP
cana-5711	99	8	the	the	DET
cana-5711	99	9	generator	generator	NOUN
cana-5711	99	10	matrix	matrix	NOUN
cana-5711	99	11	g	g	NOUN
cana-5711	99	12	of	of	ADP
cana-5711	99	13	size	size	NOUN
cana-5711	99	14	m	m	PROPN
cana-5711	99	15	×	×	NOUN
cana-5711	99	16	(	(	PUNCT
cana-5711	99	17	p	p	X
cana-5711	99	18	+	+	NOUN
cana-5711	99	19	q	q	NOUN
cana-5711	99	20	)	)	PUNCT
cana-5711	99	21	and	and	CCONJ
cana-5711	99	22	g	g	PROPN
cana-5711	99	23	◦	◦	NOUN
cana-5711	99	24	gt	gt	PROPN
cana-5711	100	1	=	=	SYM
cana-5711	101	1	[	[	X
cana-5711	101	2	vij	vij	X
cana-5711	101	3	]	]	X
cana-5711	101	4	m×m	m×m	PROPN
cana-5711	101	5	.	.	PUNCT
cana-5711	102	1	if	if	SCONJ
cana-5711	102	2	vii	vii	PROPN
cana-5711	102	3	∈	∈	PROPN
cana-5711	102	4	u	u	NOUN
cana-5711	102	5	(	(	PUNCT
cana-5711	102	6	q	q	NOUN
cana-5711	102	7	)	)	PUNCT
cana-5711	102	8	and	and	CCONJ
cana-5711	102	9	vij	vij	PROPN
cana-5711	102	10	∈	∈	PROPN
cana-5711	102	11	{	{	PUNCT
cana-5711	102	12	0	0	NUM
cana-5711	102	13	,	,	PUNCT
cana-5711	102	14	uv	uv	NOUN
cana-5711	102	15	}	}	PUNCT
cana-5711	102	16	for	for	ADP
cana-5711	102	17	i	i	PRON
cana-5711	102	18	≠	≠	PROPN
cana-5711	102	19	j	j	PROPN
cana-5711	102	20	,	,	PUNCT
cana-5711	102	21	1	1	NUM
cana-5711	102	22	≤	≤	NUM
cana-5711	102	23	i	i	PRON
cana-5711	102	24	,	,	PUNCT
cana-5711	102	25	j	j	PROPN
cana-5711	102	26	≤	≤	PROPN
cana-5711	102	27	m	m	PROPN
cana-5711	102	28	,	,	PUNCT
cana-5711	102	29	then	then	ADV
cana-5711	102	30	c	c	PROPN
cana-5711	102	31	is	be	AUX
cana-5711	102	32	a	a	DET
cana-5711	102	33	ℤ2q	ℤ2q	PROPN
cana-5711	102	34	-	-	PUNCT
cana-5711	102	35	acd	acd	NOUN
cana-5711	102	36	code	code	NOUN
cana-5711	102	37	.	.	PUNCT
cana-5711	103	1	it	it	PRON
cana-5711	103	2	is	be	AUX
cana-5711	103	3	important	important	ADJ
cana-5711	103	4	to	to	PART
cana-5711	103	5	note	note	VERB
cana-5711	103	6	that	that	SCONJ
cana-5711	103	7	the	the	DET
cana-5711	103	8	conditions	condition	NOUN
cana-5711	103	9	presented	present	VERB
cana-5711	103	10	in	in	ADP
cana-5711	103	11	theorem	theorem	ADJ
cana-5711	103	12	3.1	3.1	NUM
cana-5711	103	13	and	and	CCONJ
cana-5711	103	14	corollaries	corollary	NOUN
cana-5711	103	15	3.2	3.2	NUM
cana-5711	103	16	are	be	AUX
cana-5711	103	17	solely	solely	ADV
cana-5711	103	18	sufficient	sufficient	ADJ
cana-5711	103	19	to	to	PART
cana-5711	103	20	establish	establish	VERB
cana-5711	103	21	that	that	SCONJ
cana-5711	103	22	c	c	PROPN
cana-5711	103	23	is	be	AUX
cana-5711	103	24	a	a	DET
cana-5711	103	25	ℤ2q	ℤ2q	PROPN
cana-5711	103	26	-	-	PUNCT
cana-5711	103	27	acd	acd	NOUN
cana-5711	103	28	code	code	NOUN
cana-5711	103	29	.	.	PUNCT
cana-5711	104	1	in	in	ADP
cana-5711	104	2	general	general	ADJ
cana-5711	104	3	,	,	PUNCT
cana-5711	104	4	the	the	DET
cana-5711	104	5	converse	converse	NOUN
cana-5711	104	6	statements	statement	NOUN
cana-5711	104	7	do	do	AUX
cana-5711	104	8	not	not	PART
cana-5711	104	9	hold	hold	VERB
cana-5711	104	10	true	true	ADJ
cana-5711	104	11	.	.	PUNCT
cana-5711	105	1	following	follow	VERB
cana-5711	105	2	example	example	NOUN
cana-5711	105	3	justifies	justify	VERB
cana-5711	105	4	this	this	PRON
cana-5711	105	5	.	.	PUNCT
cana-5711	106	1	example	example	NOUN
cana-5711	106	2	3.3	3.3	NUM
cana-5711	106	3	.	.	PUNCT
cana-5711	107	1	consider	consider	VERB
cana-5711	107	2	an	an	DET
cana-5711	107	3	additive	additive	ADJ
cana-5711	107	4	code	code	NOUN
cana-5711	107	5	c	c	PROPN
cana-5711	107	6	of	of	ADP
cana-5711	107	7	block	block	NOUN
cana-5711	107	8	length	length	NOUN
cana-5711	107	9	(	(	PUNCT
cana-5711	107	10	2	2	NUM
cana-5711	107	11	,	,	PUNCT
cana-5711	107	12	4	4	NUM
cana-5711	107	13	)	)	PUNCT
cana-5711	107	14	over	over	ADP
cana-5711	107	15	ℤ2q	ℤ2q	PROPN
cana-5711	107	16	generated	generate	VERB
cana-5711	107	17	by	by	ADP
cana-5711	107	18	𝐺	𝐺	PROPN
cana-5711	107	19	=	=	PUNCT
cana-5711	107	20	(	(	PUNCT
cana-5711	107	21	1	1	NUM
cana-5711	107	22	0	0	NUM
cana-5711	107	23	0	0	NUM
cana-5711	107	24	0	0	NUM
cana-5711	107	25	0	0	NUM
cana-5711	107	26	0	0	NUM
cana-5711	107	27	0	0	NUM
cana-5711	107	28	1	1	NUM
cana-5711	107	29	0	0	NUM
cana-5711	107	30	0	0	NUM
cana-5711	107	31	0	0	NUM
cana-5711	107	32	0	0	NUM
cana-5711	107	33	0	0	NUM
cana-5711	107	34	0	0	NUM
cana-5711	107	35	1	1	NUM
cana-5711	107	36	+	+	CCONJ
cana-5711	107	37	𝑢	𝑢	X
cana-5711	107	38	0	0	NUM
cana-5711	107	39	0	0	NUM
cana-5711	107	40	0	0	NUM
cana-5711	107	41	0	0	NUM
cana-5711	107	42	0	0	NUM
cana-5711	107	43	0	0	NUM
cana-5711	107	44	1	1	NUM
cana-5711	107	45	+	+	CCONJ
cana-5711	107	46	𝑢	𝑢	X
cana-5711	107	47	0	0	NUM
cana-5711	107	48	0	0	NUM
cana-5711	107	49	0	0	NUM
cana-5711	107	50	0	0	NUM
cana-5711	107	51	0	0	NUM
cana-5711	107	52	0	0	NUM
cana-5711	107	53	1	1	NUM
cana-5711	108	1	+	+	CCONJ
cana-5711	108	2	𝑣	𝑣	DET
cana-5711	108	3	0	0	NUM
cana-5711	108	4	0	0	NUM
cana-5711	108	5	0	0	NUM
cana-5711	108	6	0	0	NUM
cana-5711	108	7	0	0	NUM
cana-5711	108	8	0	0	NUM
cana-5711	108	9	1	1	NUM
cana-5711	108	10	+	+	NUM
cana-5711	108	11	𝑢	𝑢	X
cana-5711	108	12	+	+	X
cana-5711	108	13	𝑣	𝑣	X
cana-5711	108	14	)	)	PUNCT
cana-5711	108	15	=	=	PUNCT
cana-5711	109	1	[	[	X
cana-5711	109	2	gp	gp	X
cana-5711	110	1	|	|	INTJ
cana-5711	110	2	(	(	PUNCT
cana-5711	110	3	gq	gq	NOUN
cana-5711	110	4	=	=	PUNCT
cana-5711	110	5	r	r	NOUN
cana-5711	110	6	|	|	NOUN
cana-5711	110	7	s	s	NOUN
cana-5711	110	8	)	)	PUNCT
cana-5711	110	9	]	]	PUNCT
cana-5711	110	10	.	.	PUNCT
cana-5711	111	1	from	from	ADP
cana-5711	111	2	this	this	DET
cana-5711	111	3	c	c	NOUN
cana-5711	111	4	is	be	AUX
cana-5711	111	5	an	an	DET
cana-5711	111	6	acd	acd	NOUN
cana-5711	111	7	code	code	NOUN
cana-5711	111	8	and	and	CCONJ
cana-5711	111	9	it	it	PRON
cana-5711	111	10	is	be	AUX
cana-5711	111	11	c∩c⊥	c∩c⊥	ADJ
cana-5711	111	12	=	=	PUNCT
cana-5711	111	13	{	{	PUNCT
cana-5711	111	14	0	0	NUM
cana-5711	111	15	}	}	PUNCT
cana-5711	111	16	.	.	PUNCT
cana-5711	112	1	but	but	CCONJ
cana-5711	112	2	if	if	SCONJ
cana-5711	112	3	u1	u1	NOUN
cana-5711	112	4	is	be	AUX
cana-5711	112	5	a	a	DET
cana-5711	112	6	first	first	ADJ
cana-5711	112	7	row	row	NOUN
cana-5711	112	8	of	of	ADP
cana-5711	112	9	g	g	NOUN
cana-5711	112	10	,	,	PUNCT
cana-5711	112	11	then	then	ADV
cana-5711	112	12	the	the	DET
cana-5711	112	13	(	(	PUNCT
cana-5711	112	14	1	1	NUM
cana-5711	112	15	,	,	PUNCT
cana-5711	112	16	1	1	NUM
cana-5711	112	17	)	)	PUNCT
cana-5711	112	18	entry	entry	NOUN
cana-5711	112	19	of	of	ADP
cana-5711	112	20	g	g	PROPN
cana-5711	112	21	◦	◦	PROPN
cana-5711	112	22	gt	gt	PROPN
cana-5711	112	23	is	be	AUX
cana-5711	112	24	v11	v11	NOUN
cana-5711	112	25	=	=	SYM
cana-5711	112	26	⟨v1	⟨v1	PROPN
cana-5711	112	27	,	,	PUNCT
cana-5711	112	28	v1	v1	VERB
cana-5711	112	29	⟩	⟩	NOUN
cana-5711	112	30	=	=	PUNCT
cana-5711	112	31	uv	uv	NOUN
cana-5711	112	32	∉	∉	PROPN
cana-5711	112	33	u	u	PROPN
cana-5711	112	34	(	(	PUNCT
cana-5711	112	35	q	q	NOUN
cana-5711	112	36	)	)	PUNCT
cana-5711	112	37	.	.	PUNCT
cana-5711	113	1	through	through	ADP
cana-5711	113	2	the	the	DET
cana-5711	113	3	use	use	NOUN
cana-5711	113	4	of	of	ADP
cana-5711	113	5	corollary	corollary	ADJ
cana-5711	113	6	3.2	3.2	NUM
cana-5711	113	7	,	,	PUNCT
cana-5711	113	8	the	the	DET
cana-5711	113	9	following	following	ADJ
cana-5711	113	10	result	result	NOUN
cana-5711	113	11	is	be	AUX
cana-5711	113	12	obtained	obtain	VERB
cana-5711	113	13	.	.	PUNCT
cana-5711	114	1	proposition	proposition	NOUN
cana-5711	114	2	3.4	3.4	NUM
cana-5711	114	3	.	.	PUNCT
cana-5711	115	1	let	let	VERB
cana-5711	115	2	g	g	NOUN
cana-5711	115	3	=	=	PUNCT
cana-5711	115	4	(	(	PUNCT
cana-5711	115	5	gp	gp	NOUN
cana-5711	115	6	|	|	ADV
cana-5711	115	7	λim	λim	X
cana-5711	115	8	)	)	PUNCT
cana-5711	115	9	where	where	SCONJ
cana-5711	115	10	𝜆	𝜆	PRON
cana-5711	115	11	∈	∈	PROPN
cana-5711	115	12	𝑈(𝑄	𝑈(𝑄	NUM
cana-5711	115	13	)	)	PUNCT
cana-5711	115	14	,	,	PUNCT
cana-5711	115	15	gp	gp	NOUN
cana-5711	115	16	is	be	AUX
cana-5711	115	17	an	an	DET
cana-5711	115	18	m	m	NOUN
cana-5711	115	19	×	×	NOUN
cana-5711	115	20	p	p	NOUN
cana-5711	115	21	matrix	matrix	NOUN
cana-5711	115	22	over	over	ADP
cana-5711	115	23	ℤ2	ℤ2	PROPN
cana-5711	115	24	and	and	CCONJ
cana-5711	115	25	i	i	PRON
cana-5711	115	26	m	m	VERB
cana-5711	115	27	is	be	AUX
cana-5711	115	28	the	the	DET
cana-5711	115	29	identity	identity	NOUN
cana-5711	115	30	matrix	matrix	NOUN
cana-5711	115	31	of	of	ADP
cana-5711	115	32	size	size	NOUN
cana-5711	115	33	m	m	PROPN
cana-5711	115	34	×	×	NOUN
cana-5711	115	35	m.	m.	NOUN
cana-5711	115	36	then	then	ADV
cana-5711	115	37	g	g	PROPN
cana-5711	115	38	generates	generate	VERB
cana-5711	115	39	an	an	DET
cana-5711	115	40	acd	acd	NOUN
cana-5711	115	41	code	code	NOUN
cana-5711	115	42	over	over	ADP
cana-5711	115	43	ℤ2q	ℤ2q	PROPN
cana-5711	115	44	.	.	PUNCT
cana-5711	116	1	proof	proof	NOUN
cana-5711	116	2	.	.	PUNCT
cana-5711	117	1	consider	consider	VERB
cana-5711	117	2	g	g	NOUN
cana-5711	117	3	◦	◦	NOUN
cana-5711	117	4	gt	gt	NOUN
cana-5711	118	1	=	=	PUNCT
cana-5711	118	2	uvgp	uvgp	PROPN
cana-5711	118	3	g	g	PROPN
cana-5711	118	4	t	t	PROPN
cana-5711	118	5	p	p	PROPN
cana-5711	119	1	+	+	CCONJ
cana-5711	119	2	λim	λim	X
cana-5711	119	3	it	it	PRON
cana-5711	119	4	m	m	VERB
cana-5711	119	5	=	=	VERB
cana-5711	119	6	uvgp	uvgp	PROPN
cana-5711	119	7	g	g	NOUN
cana-5711	119	8	t	t	PROPN
cana-5711	119	9	p	p	X
cana-5711	120	1	+	+	X
cana-5711	120	2	λim	λim	ADP
cana-5711	120	3	g	g	PROPN
cana-5711	120	4	◦	◦	NOUN
cana-5711	120	5	gt	gt	PROPN
cana-5711	121	1	=	=	SYM
cana-5711	122	1	[	[	X
cana-5711	122	2	vij	vij	X
cana-5711	122	3	]	]	X
cana-5711	122	4	m×m	m×m	PROPN
cana-5711	122	5	.	.	PUNCT
cana-5711	123	1	so	so	ADV
cana-5711	123	2	,	,	PUNCT
cana-5711	123	3	vij	vij	PROPN
cana-5711	123	4	∈	∈	PROPN
cana-5711	123	5	{	{	PUNCT
cana-5711	123	6	0	0	NUM
cana-5711	123	7	,	,	PUNCT
cana-5711	123	8	uv	uv	NOUN
cana-5711	123	9	}	}	PUNCT
cana-5711	123	10	for	for	ADP
cana-5711	123	11	i	i	PRON
cana-5711	123	12	≠	≠	PROPN
cana-5711	123	13	j	j	PROPN
cana-5711	123	14	and	and	CCONJ
cana-5711	123	15	vii	vii	PROPN
cana-5711	123	16	∈	∈	PROPN
cana-5711	123	17	{	{	PUNCT
cana-5711	123	18	λ	λ	PROPN
cana-5711	123	19	,	,	PUNCT
cana-5711	123	20	λ	λ	X
cana-5711	123	21	+	+	NOUN
cana-5711	123	22	uv	uv	NOUN
cana-5711	123	23	}	}	PUNCT
cana-5711	123	24	⊂	⊂	PROPN
cana-5711	123	25	u	u	NOUN
cana-5711	123	26	(	(	PUNCT
cana-5711	123	27	q	q	NOUN
cana-5711	123	28	)	)	PUNCT
cana-5711	123	29	for	for	ADP
cana-5711	123	30	1	1	NUM
cana-5711	123	31	≤	≤	NUM
cana-5711	123	32	i	i	PRON
cana-5711	123	33	≤	≤	NUM
cana-5711	123	34	m.	m.	NOUN
cana-5711	123	35	therefore	therefore	ADV
cana-5711	123	36	,	,	PUNCT
cana-5711	123	37	using	use	VERB
cana-5711	123	38	corollary	corollary	ADJ
cana-5711	123	39	3.2	3.2	NUM
cana-5711	123	40	g	g	NOUN
cana-5711	123	41	generates	generate	VERB
cana-5711	123	42	an	an	DET
cana-5711	123	43	acd	acd	NOUN
cana-5711	123	44	code	code	NOUN
cana-5711	123	45	over	over	ADP
cana-5711	123	46	ℤ2q	ℤ2q	PROPN
cana-5711	123	47	.	.	PUNCT
cana-5711	124	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	124	2	communications	communication	NOUN
cana-5711	124	3	on	on	ADP
cana-5711	124	4	applied	apply	VERB
cana-5711	124	5	nonlinear	nonlinear	ADJ
cana-5711	124	6	analysis	analysis	NOUN
cana-5711	124	7	issn	issn	NOUN
cana-5711	124	8	:	:	PUNCT
cana-5711	124	9	1074	1074	NUM
cana-5711	124	10	-	-	PUNCT
cana-5711	124	11	133x	133x	NUM
cana-5711	124	12	vol	vol	VERB
cana-5711	124	13	32	32	NUM
cana-5711	124	14	no	no	NOUN
cana-5711	124	15	.	.	PUNCT
cana-5711	125	1	10s	10	NOUN
cana-5711	125	2	(	(	PUNCT
cana-5711	125	3	2025	2025	NUM
cana-5711	125	4	)	)	PUNCT
cana-5711	125	5	2699	2699	NUM
cana-5711	125	6	example	example	NOUN
cana-5711	125	7	3.5	3.5	NUM
cana-5711	125	8	.	.	PUNCT
cana-5711	126	1	let	let	VERB
cana-5711	126	2	us	we	PRON
cana-5711	126	3	take	take	VERB
cana-5711	126	4	𝐺2	𝐺2	NOUN
cana-5711	126	5	=	=	PUNCT
cana-5711	126	6	(	(	PUNCT
cana-5711	126	7	0	0	NUM
cana-5711	126	8	1	1	NUM
cana-5711	126	9	1	1	NUM
cana-5711	126	10	0	0	NUM
cana-5711	126	11	0	0	NUM
cana-5711	126	12	0	0	NUM
cana-5711	126	13	0	0	NUM
cana-5711	126	14	0	0	NUM
cana-5711	126	15	)	)	PUNCT
cana-5711	126	16	over	over	ADP
cana-5711	126	17	ℤ2	ℤ2	PROPN
cana-5711	126	18	and	and	CCONJ
cana-5711	126	19	λ	λ	X
cana-5711	126	20	=	=	NOUN
cana-5711	126	21	1	1	NUM
cana-5711	126	22	+	+	CCONJ
cana-5711	126	23	u.	u.	VERB
cana-5711	126	24	then	then	ADV
cana-5711	126	25	the	the	DET
cana-5711	126	26	ℤ2q	ℤ2q	PROPN
cana-5711	126	27	-	-	PUNCT
cana-5711	126	28	additive	additive	NOUN
cana-5711	126	29	code	code	NOUN
cana-5711	126	30	generated	generate	VERB
cana-5711	126	31	by	by	ADP
cana-5711	126	32	g	g	PROPN
cana-5711	126	33	𝐺	𝐺	PROPN
cana-5711	126	34	=	=	SYM
cana-5711	126	35	(	(	PUNCT
cana-5711	126	36	𝐺2|𝜆𝐼4	𝐺2|𝜆𝐼4	PROPN
cana-5711	126	37	)	)	PUNCT
cana-5711	126	38	=	=	PUNCT
cana-5711	127	1	(	(	PUNCT
cana-5711	127	2	0	0	NUM
cana-5711	127	3	1	1	NUM
cana-5711	127	4	1	1	NUM
cana-5711	127	5	+	+	NUM
cana-5711	127	6	𝑢	𝑢	X
cana-5711	127	7	0	0	NUM
cana-5711	127	8	0	0	NUM
cana-5711	127	9	0	0	NUM
cana-5711	127	10	1	1	NUM
cana-5711	127	11	0	0	NUM
cana-5711	127	12	0	0	NUM
cana-5711	127	13	1	1	NUM
cana-5711	127	14	+	+	CCONJ
cana-5711	127	15	𝑢	𝑢	X
cana-5711	127	16	0	0	NUM
cana-5711	127	17	0	0	NUM
cana-5711	127	18	0	0	NUM
cana-5711	127	19	0	0	NUM
cana-5711	127	20	0	0	NUM
cana-5711	127	21	0	0	NUM
cana-5711	127	22	1	1	NUM
cana-5711	127	23	+	+	CCONJ
cana-5711	127	24	𝑢	𝑢	X
cana-5711	127	25	0	0	NUM
cana-5711	127	26	0	0	NUM
cana-5711	127	27	0	0	NUM
cana-5711	127	28	0	0	NUM
cana-5711	127	29	0	0	NUM
cana-5711	127	30	0	0	NUM
cana-5711	127	31	1	1	NUM
cana-5711	127	32	+	+	NUM
cana-5711	127	33	𝑢	𝑢	NOUN
cana-5711	127	34	)	)	PUNCT
cana-5711	127	35	is	be	AUX
cana-5711	127	36	an	an	DET
cana-5711	127	37	acd	acd	NOUN
cana-5711	127	38	code	code	NOUN
cana-5711	127	39	.	.	PUNCT
cana-5711	128	1	in	in	ADP
cana-5711	128	2	[	[	X
cana-5711	128	3	2	2	NUM
cana-5711	128	4	]	]	PUNCT
cana-5711	128	5	,	,	PUNCT
cana-5711	128	6	the	the	DET
cana-5711	128	7	authors	author	NOUN
cana-5711	128	8	defined	define	VERB
cana-5711	128	9	separable	separable	ADJ
cana-5711	128	10	codes	code	NOUN
cana-5711	128	11	over	over	ADP
cana-5711	128	12	a	a	DET
cana-5711	128	13	ring	ring	NOUN
cana-5711	128	14	.	.	PUNCT
cana-5711	129	1	now	now	ADV
cana-5711	129	2	,	,	PUNCT
cana-5711	129	3	we	we	PRON
cana-5711	129	4	generalize	generalize	VERB
cana-5711	129	5	it	it	PRON
cana-5711	129	6	.	.	PUNCT
cana-5711	130	1	an	an	DET
cana-5711	130	2	additive	additive	ADJ
cana-5711	130	3	code	code	NOUN
cana-5711	130	4	c	c	NOUN
cana-5711	130	5	over	over	ADP
cana-5711	130	6	ℤ2q	ℤ2q	PROPN
cana-5711	130	7	of	of	ADP
cana-5711	130	8	block	block	NOUN
cana-5711	130	9	length	length	NOUN
cana-5711	130	10	(	(	PUNCT
cana-5711	130	11	p	p	X
cana-5711	130	12	,	,	PUNCT
cana-5711	130	13	q	q	NOUN
cana-5711	130	14	)	)	PUNCT
cana-5711	130	15	is	be	AUX
cana-5711	130	16	said	say	VERB
cana-5711	130	17	to	to	PART
cana-5711	130	18	be	be	AUX
cana-5711	130	19	a	a	DET
cana-5711	130	20	separable	separable	ADJ
cana-5711	130	21	code	code	NOUN
cana-5711	130	22	if	if	SCONJ
cana-5711	130	23	c	c	PROPN
cana-5711	130	24	is	be	AUX
cana-5711	130	25	the	the	DET
cana-5711	130	26	direct	direct	ADJ
cana-5711	130	27	product	product	NOUN
cana-5711	130	28	of	of	ADP
cana-5711	130	29	cp	cp	PROPN
cana-5711	130	30	and	and	CCONJ
cana-5711	130	31	cq	cq	PROPN
cana-5711	130	32	.	.	PUNCT
cana-5711	131	1	in	in	ADP
cana-5711	131	2	this	this	DET
cana-5711	131	3	case	case	NOUN
cana-5711	131	4	,	,	PUNCT
cana-5711	131	5	c⊥	c⊥	PROPN
cana-5711	131	6	is	be	AUX
cana-5711	131	7	the	the	DET
cana-5711	131	8	direct	direct	ADJ
cana-5711	131	9	product	product	NOUN
cana-5711	131	10	of	of	ADP
cana-5711	131	11	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	131	12	⊥and	⊥and	PROPN
cana-5711	131	13	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	131	14	⊥.	⊥.	PROPN
cana-5711	131	15	thus	thus	ADV
cana-5711	131	16	,	,	PUNCT
cana-5711	131	17	c⊥	c⊥	PROPN
cana-5711	131	18	is	be	AUX
cana-5711	131	19	separable	separable	ADJ
cana-5711	131	20	.	.	PUNCT
cana-5711	132	1	the	the	DET
cana-5711	132	2	following	follow	VERB
cana-5711	132	3	theorem	theorem	NOUN
cana-5711	132	4	gives	give	VERB
cana-5711	132	5	a	a	DET
cana-5711	132	6	necessary	necessary	ADJ
cana-5711	132	7	and	and	CCONJ
cana-5711	132	8	sufficient	sufficient	ADJ
cana-5711	132	9	condition	condition	NOUN
cana-5711	132	10	for	for	ADP
cana-5711	132	11	an	an	DET
cana-5711	132	12	additive	additive	ADJ
cana-5711	132	13	separable	separable	NOUN
cana-5711	132	14	code	code	NOUN
cana-5711	132	15	to	to	PART
cana-5711	132	16	be	be	AUX
cana-5711	132	17	an	an	DET
cana-5711	132	18	acd	acd	NOUN
cana-5711	132	19	code	code	NOUN
cana-5711	132	20	.	.	PUNCT
cana-5711	133	1	theorem	theorem	VERB
cana-5711	133	2	3.6	3.6	NUM
cana-5711	133	3	.	.	PUNCT
cana-5711	134	1	let	let	VERB
cana-5711	134	2	c	c	PRON
cana-5711	134	3	be	be	AUX
cana-5711	134	4	an	an	DET
cana-5711	134	5	additive	additive	ADJ
cana-5711	134	6	separable	separable	NOUN
cana-5711	134	7	code	code	NOUN
cana-5711	134	8	over	over	ADP
cana-5711	134	9	ℤ2q	ℤ2q	PROPN
cana-5711	134	10	of	of	ADP
cana-5711	134	11	block	block	NOUN
cana-5711	134	12	length	length	NOUN
cana-5711	134	13	(	(	PUNCT
cana-5711	134	14	p	p	X
cana-5711	134	15	,	,	PUNCT
cana-5711	134	16	q	q	NOUN
cana-5711	134	17	)	)	PUNCT
cana-5711	134	18	.	.	PUNCT
cana-5711	135	1	then	then	ADV
cana-5711	135	2	cp	cp	PROPN
cana-5711	135	3	and	and	CCONJ
cana-5711	135	4	cq	cq	PROPN
cana-5711	135	5	are	be	AUX
cana-5711	135	6	lcd	lcd	NOUN
cana-5711	135	7	codes	code	NOUN
cana-5711	135	8	over	over	ADP
cana-5711	135	9	ℤ2	ℤ2	PROPN
cana-5711	135	10	and	and	CCONJ
cana-5711	135	11	q	q	NOUN
cana-5711	135	12	,	,	PUNCT
cana-5711	135	13	respectively	respectively	ADV
cana-5711	135	14	,	,	PUNCT
cana-5711	135	15	if	if	SCONJ
cana-5711	136	1	and	and	CCONJ
cana-5711	136	2	only	only	ADV
cana-5711	136	3	if	if	SCONJ
cana-5711	136	4	c	c	PROPN
cana-5711	136	5	is	be	AUX
cana-5711	136	6	an	an	DET
cana-5711	136	7	acd	acd	NOUN
cana-5711	136	8	code	code	NOUN
cana-5711	136	9	.	.	PUNCT
cana-5711	137	1	proof	proof	NOUN
cana-5711	137	2	.	.	PUNCT
cana-5711	138	1	given	give	VERB
cana-5711	138	2	that	that	PRON
cana-5711	138	3	c	c	NOUN
cana-5711	138	4	=	=	SYM
cana-5711	138	5	cp	cp	INTJ
cana-5711	138	6	×	×	PROPN
cana-5711	138	7	cq	cq	PROPN
cana-5711	138	8	is	be	AUX
cana-5711	138	9	an	an	DET
cana-5711	138	10	additive	additive	ADJ
cana-5711	138	11	separable	separable	NOUN
cana-5711	138	12	code	code	NOUN
cana-5711	138	13	over	over	ADP
cana-5711	138	14	ℤ2q	ℤ2q	PROPN
cana-5711	138	15	of	of	ADP
cana-5711	138	16	block	block	NOUN
cana-5711	138	17	length	length	NOUN
cana-5711	138	18	(	(	PUNCT
cana-5711	138	19	p	p	X
cana-5711	138	20	,	,	PUNCT
cana-5711	138	21	q	q	NOUN
cana-5711	138	22	)	)	PUNCT
cana-5711	138	23	.	.	PUNCT
cana-5711	139	1	then	then	ADV
cana-5711	139	2	cp	cp	PROPN
cana-5711	139	3	⊆	⊆	NUM
cana-5711	139	4	ℤ2	ℤ2	PROPN
cana-5711	139	5	𝑝	𝑝	PROPN
cana-5711	139	6	and	and	CCONJ
cana-5711	139	7	cq	cq	PROPN
cana-5711	139	8	⊆	⊆	NUM
cana-5711	139	9	qq	qq	NOUN
cana-5711	139	10	,	,	PUNCT
cana-5711	139	11	and	and	CCONJ
cana-5711	139	12	hence	hence	ADV
cana-5711	139	13	𝐶⊥	𝐶⊥	ADJ
cana-5711	139	14	=	=	SYM
cana-5711	139	15	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	139	16	⊥	⊥	NOUN
cana-5711	139	17	∩	∩	NOUN
cana-5711	139	18	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	139	19	⊥.	⊥.	PROPN
cana-5711	139	20	suppose	suppose	VERB
cana-5711	139	21	cp	cp	PROPN
cana-5711	139	22	and	and	CCONJ
cana-5711	139	23	cq	cq	PROPN
cana-5711	139	24	are	be	AUX
cana-5711	139	25	lcd	lcd	NOUN
cana-5711	139	26	codes	code	NOUN
cana-5711	139	27	over	over	ADP
cana-5711	139	28	ℤ2	ℤ2	PROPN
cana-5711	139	29	and	and	CCONJ
cana-5711	139	30	q	q	NOUN
cana-5711	139	31	,	,	PUNCT
cana-5711	139	32	respectively	respectively	ADV
cana-5711	139	33	.	.	PUNCT
cana-5711	140	1	let	let	VERB
cana-5711	140	2	(	(	PUNCT
cana-5711	140	3	u	u	NOUN
cana-5711	140	4	,	,	PUNCT
cana-5711	140	5	u′)∈	u′)∈	NOUN
cana-5711	140	6	𝐶	𝐶	PROPN
cana-5711	140	7	∩	∩	NOUN
cana-5711	140	8	𝐶⊥,then	𝐶⊥,then	ADP
cana-5711	140	9	we	we	PRON
cana-5711	140	10	have	have	VERB
cana-5711	140	11	u∈	u∈	VERB
cana-5711	140	12	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	140	13	∩	∩	NOUN
cana-5711	140	14	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	140	15	⊥	⊥	NOUN
cana-5711	140	16	=	=	SYM
cana-5711	140	17	{	{	PUNCT
cana-5711	140	18	0}and	0}and	NUM
cana-5711	140	19	u′∈	u′∈	PROPN
cana-5711	140	20	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	140	21	∩	∩	NOUN
cana-5711	140	22	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	140	23	⊥	⊥	NOUN
cana-5711	140	24	=	=	PUNCT
cana-5711	140	25	{	{	PUNCT
cana-5711	140	26	0	0	NUM
cana-5711	140	27	}	}	PUNCT
cana-5711	140	28	,	,	PUNCT
cana-5711	140	29	since	since	SCONJ
cana-5711	140	30	c	c	PROPN
cana-5711	140	31	is	be	AUX
cana-5711	140	32	separable	separable	ADJ
cana-5711	140	33	.	.	PUNCT
cana-5711	141	1	therefore	therefore	ADV
cana-5711	141	2	,	,	PUNCT
cana-5711	141	3	the	the	DET
cana-5711	141	4	intersection	intersection	NOUN
cana-5711	141	5	of	of	ADP
cana-5711	141	6	c	c	PROPN
cana-5711	141	7	and	and	CCONJ
cana-5711	141	8	c⊥	c⊥	PROPN
cana-5711	141	9	is	be	AUX
cana-5711	141	10	trivial	trivial	ADJ
cana-5711	141	11	,	,	PUNCT
cana-5711	141	12	and	and	CCONJ
cana-5711	141	13	hence	hence	ADV
cana-5711	141	14	c	c	PROPN
cana-5711	141	15	is	be	AUX
cana-5711	141	16	an	an	DET
cana-5711	141	17	acd	acd	NOUN
cana-5711	141	18	code	code	NOUN
cana-5711	141	19	.	.	PUNCT
cana-5711	142	1	conversely	conversely	ADV
cana-5711	142	2	,	,	PUNCT
cana-5711	142	3	assume	assume	VERB
cana-5711	142	4	that	that	SCONJ
cana-5711	142	5	c	c	PROPN
cana-5711	142	6	is	be	AUX
cana-5711	142	7	an	an	DET
cana-5711	142	8	acd	acd	NOUN
cana-5711	142	9	code	code	NOUN
cana-5711	142	10	.	.	PUNCT
cana-5711	143	1	let	let	VERB
cana-5711	143	2	u	u	PRON
cana-5711	143	3	∈	∈	PROPN
cana-5711	143	4	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	143	5	∩	∩	NOUN
cana-5711	143	6	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	143	7	⊥	⊥	NOUN
cana-5711	143	8	and	and	CCONJ
cana-5711	143	9	u′	u′	PROPN
cana-5711	143	10	∈	∈	PROPN
cana-5711	143	11	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	143	12	∩	∩	NOUN
cana-5711	143	13	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	143	14	⊥	⊥	NOUN
cana-5711	143	15	,	,	PUNCT
cana-5711	143	16	then	then	ADV
cana-5711	143	17	(	(	PUNCT
cana-5711	143	18	u	u	NOUN
cana-5711	143	19	,	,	PUNCT
cana-5711	143	20	u′	u′	PROPN
cana-5711	143	21	)	)	PUNCT
cana-5711	143	22	∈	∈	PROPN
cana-5711	143	23	𝐶	𝐶	PROPN
cana-5711	143	24	∩	∩	NOUN
cana-5711	143	25	𝐶⊥	𝐶⊥	NOUN
cana-5711	143	26	=	=	SYM
cana-5711	143	27	{	{	PUNCT
cana-5711	143	28	0	0	NUM
cana-5711	143	29	}	}	PUNCT
cana-5711	143	30	,	,	PUNCT
cana-5711	143	31	and	and	CCONJ
cana-5711	143	32	hence	hence	ADV
cana-5711	143	33	u	u	X
cana-5711	143	34	=	=	NOUN
cana-5711	143	35	0	0	NUM
cana-5711	143	36	and	and	CCONJ
cana-5711	143	37	u′	u′	PROPN
cana-5711	143	38	=	=	SYM
cana-5711	143	39	0	0	PROPN
cana-5711	143	40	.	.	PUNCT
cana-5711	144	1	this	this	PRON
cana-5711	144	2	implies	imply	VERB
cana-5711	144	3	that	that	SCONJ
cana-5711	144	4	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	144	5	∩	∩	NOUN
cana-5711	144	6	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	144	7	⊥	⊥	NOUN
cana-5711	144	8	=	=	PUNCT
cana-5711	144	9	{	{	PUNCT
cana-5711	144	10	0}and	0}and	NUM
cana-5711	144	11	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	144	12	∩	∩	NOUN
cana-5711	144	13	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	144	14	⊥	⊥	NOUN
cana-5711	144	15	=	=	PUNCT
cana-5711	144	16	{	{	PUNCT
cana-5711	144	17	0	0	NUM
cana-5711	144	18	}	}	PUNCT
cana-5711	144	19	.	.	PUNCT
cana-5711	145	1	hence	hence	ADV
cana-5711	145	2	,	,	PUNCT
cana-5711	145	3	cp	cp	INTJ
cana-5711	145	4	and	and	CCONJ
cana-5711	145	5	cq	cq	PROPN
cana-5711	145	6	are	be	AUX
cana-5711	145	7	lcd	lcd	NOUN
cana-5711	145	8	codes	code	NOUN
cana-5711	145	9	over	over	ADP
cana-5711	145	10	ℤ2	ℤ2	PROPN
cana-5711	145	11	and	and	CCONJ
cana-5711	145	12	q.	q.	PROPN
cana-5711	145	13	example	example	NOUN
cana-5711	145	14	3.7	3.7	NUM
cana-5711	145	15	.	.	PUNCT
cana-5711	146	1	consider	consider	VERB
cana-5711	146	2	the	the	DET
cana-5711	146	3	additive	additive	ADJ
cana-5711	146	4	code	code	NOUN
cana-5711	146	5	c	c	NOUN
cana-5711	146	6	over	over	ADP
cana-5711	146	7	ℤ2q	ℤ2q	PROPN
cana-5711	146	8	generated	generate	VERB
cana-5711	146	9	by	by	ADP
cana-5711	146	10	(	(	PUNCT
cana-5711	146	11	1	1	NUM
cana-5711	146	12	0	0	NUM
cana-5711	146	13	0	0	NUM
cana-5711	146	14	1	1	NUM
cana-5711	146	15	0	0	NUM
cana-5711	146	16	0	0	NUM
cana-5711	146	17	0	0	NUM
cana-5711	146	18	0	0	NUM
cana-5711	146	19	0	0	NUM
cana-5711	146	20	1	1	NUM
cana-5711	147	1	+	+	CCONJ
cana-5711	147	2	𝑢	𝑢	X
cana-5711	147	3	0	0	NUM
cana-5711	147	4	0	0	NUM
cana-5711	147	5	1	1	NUM
cana-5711	147	6	+	+	CCONJ
cana-5711	147	7	𝑢𝑣	𝑢𝑣	X
cana-5711	147	8	0	0	NUM
cana-5711	147	9	0	0	NUM
cana-5711	147	10	0	0	NUM
cana-5711	147	11	0	0	NUM
cana-5711	147	12	0	0	NUM
cana-5711	147	13	0	0	NUM
cana-5711	147	14	1	1	NUM
cana-5711	147	15	0	0	NUM
cana-5711	147	16	1	1	NUM
cana-5711	147	17	0	0	NUM
cana-5711	147	18	0	0	NUM
cana-5711	147	19	0	0	NUM
cana-5711	147	20	0	0	NUM
cana-5711	147	21	1	1	NUM
cana-5711	147	22	+	+	CCONJ
cana-5711	147	23	𝑢	𝑢	X
cana-5711	147	24	0	0	NUM
cana-5711	147	25	0	0	NUM
cana-5711	147	26	0	0	NUM
cana-5711	147	27	1	1	NUM
cana-5711	148	1	+	+	CCONJ
cana-5711	148	2	𝑢𝑣	𝑢𝑣	X
cana-5711	148	3	0	0	NUM
cana-5711	148	4	0	0	NUM
cana-5711	148	5	0	0	NUM
cana-5711	148	6	0	0	NUM
cana-5711	148	7	0	0	NUM
cana-5711	148	8	0	0	NUM
cana-5711	148	9	1	1	NUM
cana-5711	148	10	0	0	NUM
cana-5711	148	11	1	1	NUM
cana-5711	148	12	0	0	NUM
cana-5711	148	13	1	1	NUM
cana-5711	148	14	+	+	CCONJ
cana-5711	148	15	𝑢	𝑢	NUM
cana-5711	148	16	1	1	NUM
cana-5711	148	17	+	+	NUM
cana-5711	148	18	𝑢	𝑢	X
cana-5711	148	19	0	0	NUM
cana-5711	148	20	1	1	NUM
cana-5711	148	21	+	+	CCONJ
cana-5711	148	22	𝑢𝑣	𝑢𝑣	NOUN
cana-5711	148	23	0	0	NUM
cana-5711	148	24	1	1	NUM
cana-5711	148	25	+	+	CCONJ
cana-5711	148	26	𝑢𝑣	𝑢𝑣	NOUN
cana-5711	148	27	0	0	NUM
cana-5711	148	28	1	1	NUM
cana-5711	148	29	0	0	NUM
cana-5711	148	30	0	0	NUM
cana-5711	148	31	1	1	NUM
cana-5711	148	32	0	0	NUM
cana-5711	148	33	1	1	NUM
cana-5711	148	34	0	0	NUM
cana-5711	148	35	1	1	NUM
cana-5711	148	36	0	0	NUM
cana-5711	148	37	0	0	NUM
cana-5711	148	38	0	0	NUM
cana-5711	148	39	0	0	NUM
cana-5711	148	40	0	0	NUM
cana-5711	148	41	0	0	NUM
cana-5711	148	42	0	0	NUM
cana-5711	148	43	0	0	NUM
cana-5711	148	44	)	)	PUNCT
cana-5711	148	45	clearly	clearly	ADV
cana-5711	148	46	,	,	PUNCT
cana-5711	148	47	c	c	PROPN
cana-5711	148	48	is	be	AUX
cana-5711	148	49	a	a	DET
cana-5711	148	50	separable	separable	ADJ
cana-5711	148	51	code	code	NOUN
cana-5711	148	52	.	.	PUNCT
cana-5711	149	1	then	then	ADV
cana-5711	149	2	𝐶	𝐶	PROPN
cana-5711	149	3	∩	∩	NOUN
cana-5711	149	4	𝐶⊥	𝐶⊥	NOUN
cana-5711	149	5	=	=	SYM
cana-5711	149	6	{	{	PUNCT
cana-5711	149	7	0	0	NUM
cana-5711	149	8	}	}	PUNCT
cana-5711	149	9	.	.	PUNCT
cana-5711	150	1	thus	thus	ADV
cana-5711	150	2	c	c	PROPN
cana-5711	150	3	is	be	AUX
cana-5711	150	4	acd	acd	NOUN
cana-5711	150	5	code	code	NOUN
cana-5711	150	6	over	over	ADP
cana-5711	150	7	ℤ2q	ℤ2q	PROPN
cana-5711	150	8	.	.	PUNCT
cana-5711	151	1	moreover	moreover	ADV
cana-5711	151	2	,	,	PUNCT
cana-5711	151	3	we	we	PRON
cana-5711	151	4	have	have	VERB
cana-5711	151	5	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	151	6	∩	∩	ADJ
cana-5711	151	7	𝐶𝑝	𝐶𝑝	PROPN
cana-5711	151	8	⊥	⊥	NOUN
cana-5711	151	9	=	=	PUNCT
cana-5711	151	10	{	{	PUNCT
cana-5711	151	11	0}and	0}and	NUM
cana-5711	151	12	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	151	13	∩	∩	NOUN
cana-5711	151	14	𝐶𝑞	𝐶𝑞	PROPN
cana-5711	151	15	⊥	⊥	NOUN
cana-5711	151	16	=	=	PUNCT
cana-5711	151	17	{	{	PUNCT
cana-5711	151	18	0	0	NUM
cana-5711	151	19	}	}	PUNCT
cana-5711	151	20	.	.	PUNCT
cana-5711	152	1	thus	thus	ADV
cana-5711	152	2	cp	cp	PROPN
cana-5711	152	3	and	and	CCONJ
cana-5711	152	4	cq	cq	PROPN
cana-5711	152	5	is	be	AUX
cana-5711	152	6	an	an	DET
cana-5711	152	7	lcd	lcd	NOUN
cana-5711	152	8	code	code	NOUN
cana-5711	152	9	over	over	ADP
cana-5711	152	10	ℤ2	ℤ2	PROPN
cana-5711	152	11	and	and	CCONJ
cana-5711	152	12	q.	q.	PROPN
cana-5711	152	13	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	152	14	communications	communication	NOUN
cana-5711	152	15	on	on	ADP
cana-5711	152	16	applied	apply	VERB
cana-5711	152	17	nonlinear	nonlinear	ADJ
cana-5711	152	18	analysis	analysis	NOUN
cana-5711	152	19	issn	issn	NOUN
cana-5711	152	20	:	:	PUNCT
cana-5711	152	21	1074	1074	NUM
cana-5711	152	22	-	-	PUNCT
cana-5711	152	23	133x	133x	NUM
cana-5711	152	24	vol	vol	VERB
cana-5711	152	25	32	32	NUM
cana-5711	152	26	no	no	NOUN
cana-5711	152	27	.	.	PUNCT
cana-5711	153	1	10s	10	NOUN
cana-5711	153	2	(	(	PUNCT
cana-5711	153	3	2025	2025	NUM
cana-5711	153	4	)	)	PUNCT
cana-5711	153	5	2700	2700	NUM
cana-5711	153	6	4	4	NUM
cana-5711	153	7	.	.	PUNCT
cana-5711	153	8	gray	gray	ADJ
cana-5711	153	9	map	map	NOUN
cana-5711	153	10	in	in	ADP
cana-5711	153	11	this	this	DET
cana-5711	153	12	section	section	NOUN
cana-5711	153	13	,	,	PUNCT
cana-5711	153	14	we	we	PRON
cana-5711	153	15	have	have	AUX
cana-5711	153	16	introduced	introduce	VERB
cana-5711	153	17	a	a	DET
cana-5711	153	18	new	new	ADJ
cana-5711	153	19	gray	gray	ADJ
cana-5711	153	20	map	map	NOUN
cana-5711	153	21	from	from	ADP
cana-5711	153	22	ℤ2q	ℤ2q	PROPN
cana-5711	153	23	to	to	ADP
cana-5711	153	24	ℤ2	ℤ2	PROPN
cana-5711	153	25	7	7	NUM
cana-5711	153	26	and	and	CCONJ
cana-5711	153	27	have	have	AUX
cana-5711	153	28	discussed	discuss	VERB
cana-5711	153	29	the	the	DET
cana-5711	153	30	properties	property	NOUN
cana-5711	153	31	in	in	ADP
cana-5711	153	32	it	it	PRON
cana-5711	153	33	.	.	PUNCT
cana-5711	154	1	define	define	VERB
cana-5711	154	2	the	the	DET
cana-5711	154	3	gray	gray	ADJ
cana-5711	154	4	map	map	NOUN
cana-5711	154	5	𝜙	𝜙	NOUN
cana-5711	154	6	:	:	PUNCT
cana-5711	154	7	q	q	NOUN
cana-5711	154	8	→ℤ2	→ℤ2	SYM
cana-5711	154	9	6	6	NUM
cana-5711	154	10	by	by	ADP
cana-5711	154	11	𝜙(b	𝜙(b	NOUN
cana-5711	154	12	+	+	CCONJ
cana-5711	154	13	ud	ud	PROPN
cana-5711	154	14	,	,	PUNCT
cana-5711	154	15	e	e	PROPN
cana-5711	155	1	+	+	NUM
cana-5711	156	1	uf	uf	NOUN
cana-5711	157	1	+	+	CCONJ
cana-5711	157	2	vg	vg	NOUN
cana-5711	157	3	+	+	CCONJ
cana-5711	157	4	uvh	uvh	NOUN
cana-5711	157	5	)	)	PUNCT
cana-5711	157	6	=	=	PUNCT
cana-5711	158	1	(	(	PUNCT
cana-5711	158	2	d	d	X
cana-5711	158	3	+	+	NUM
cana-5711	158	4	b	b	PROPN
cana-5711	158	5	,	,	PUNCT
cana-5711	158	6	d	d	NOUN
cana-5711	158	7	,	,	PUNCT
cana-5711	158	8	h	h	NOUN
cana-5711	159	1	+	+	CCONJ
cana-5711	159	2	g	g	PROPN
cana-5711	160	1	+	+	NOUN
cana-5711	160	2	f	f	PROPN
cana-5711	161	1	+	+	CCONJ
cana-5711	161	2	e	e	NOUN
cana-5711	161	3	,	,	PUNCT
cana-5711	161	4	h	h	NOUN
cana-5711	162	1	+	+	CCONJ
cana-5711	162	2	g	g	NOUN
cana-5711	162	3	,	,	PUNCT
cana-5711	162	4	h	h	NOUN
cana-5711	163	1	+	+	CCONJ
cana-5711	163	2	f	f	X
cana-5711	163	3	,	,	PUNCT
cana-5711	163	4	h	h	NOUN
cana-5711	163	5	)	)	PUNCT
cana-5711	163	6	for	for	ADP
cana-5711	163	7	all	all	DET
cana-5711	163	8	element	element	NOUN
cana-5711	163	9	in	in	ADP
cana-5711	163	10	q.	q.	PROPN
cana-5711	163	11	let	let	PROPN
cana-5711	163	12	(	(	PUNCT
cana-5711	163	13	u	u	NOUN
cana-5711	163	14	,	,	PUNCT
cana-5711	163	15	u′	u′	PROPN
cana-5711	163	16	)	)	PUNCT
cana-5711	163	17	,	,	PUNCT
cana-5711	163	18	(	(	PUNCT
cana-5711	163	19	u1	u1	NOUN
cana-5711	163	20	,	,	PUNCT
cana-5711	163	21	u′1)∈ℤ2	u′1)∈ℤ2	ADP
cana-5711	163	22	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	163	23	,	,	PUNCT
cana-5711	163	24	then	then	ADV
cana-5711	163	25	the	the	DET
cana-5711	163	26	hamming	hamming	ADJ
cana-5711	163	27	weight	weight	NOUN
cana-5711	163	28	of	of	ADP
cana-5711	163	29	(	(	PUNCT
cana-5711	163	30	u	u	NOUN
cana-5711	163	31	,	,	PUNCT
cana-5711	163	32	u′	u′	PROPN
cana-5711	163	33	)	)	PUNCT
cana-5711	163	34	is	be	AUX
cana-5711	163	35	the	the	DET
cana-5711	163	36	number	number	NOUN
cana-5711	163	37	of	of	ADP
cana-5711	163	38	non	non	ADJ
cana-5711	163	39	-	-	ADJ
cana-5711	163	40	zero	zero	NUM
cana-5711	163	41	coordinates	coordinate	NOUN
cana-5711	163	42	of	of	ADP
cana-5711	163	43	(	(	PUNCT
cana-5711	163	44	u	u	NOUN
cana-5711	163	45	,	,	PUNCT
cana-5711	163	46	u′	u′	PROPN
cana-5711	163	47	)	)	PUNCT
cana-5711	163	48	and	and	CCONJ
cana-5711	163	49	is	be	AUX
cana-5711	163	50	denoted	denote	VERB
cana-5711	163	51	by	by	ADP
cana-5711	163	52	wh	wh	PROPN
cana-5711	163	53	(	(	PUNCT
cana-5711	163	54	u	u	NOUN
cana-5711	163	55	,	,	PUNCT
cana-5711	163	56	u′	u′	PROPN
cana-5711	163	57	)	)	PUNCT
cana-5711	163	58	.	.	PUNCT
cana-5711	164	1	we	we	PRON
cana-5711	164	2	define	define	VERB
cana-5711	164	3	the	the	DET
cana-5711	164	4	lee	lee	PROPN
cana-5711	164	5	weight	weight	NOUN
cana-5711	164	6	of	of	ADP
cana-5711	164	7	(	(	PUNCT
cana-5711	164	8	u	u	NOUN
cana-5711	164	9	,	,	PUNCT
cana-5711	164	10	u′	u′	PROPN
cana-5711	164	11	)	)	PUNCT
cana-5711	164	12	∈ℤ2	∈ℤ2	PUNCT
cana-5711	164	13	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	164	14	by	by	ADP
cana-5711	164	15	wl	wl	PROPN
cana-5711	164	16	(	(	PUNCT
cana-5711	164	17	u	u	NOUN
cana-5711	164	18	,	,	PUNCT
cana-5711	164	19	u′	u′	X
cana-5711	164	20	)	)	PUNCT
cana-5711	164	21	=	=	SYM
cana-5711	164	22	wh	wh	X
cana-5711	164	23	(	(	PUNCT
cana-5711	164	24	𝜙(u	𝜙(u	PROPN
cana-5711	164	25	,	,	PUNCT
cana-5711	164	26	u′	u′	PROPN
cana-5711	164	27	)	)	PUNCT
cana-5711	164	28	)	)	PUNCT
cana-5711	165	1	=	=	SYM
cana-5711	165	2	wh	wh	X
cana-5711	165	3	(	(	PUNCT
cana-5711	165	4	u	u	NOUN
cana-5711	165	5	)	)	PUNCT
cana-5711	165	6	+	+	CCONJ
cana-5711	165	7	wh	wh	X
cana-5711	165	8	(	(	PUNCT
cana-5711	165	9	𝜙(u′	𝜙(u′	NOUN
cana-5711	165	10	)	)	PUNCT
cana-5711	165	11	)	)	PUNCT
cana-5711	165	12	and	and	CCONJ
cana-5711	165	13	the	the	DET
cana-5711	165	14	lee	lee	PROPN
cana-5711	165	15	distance	distance	NOUN
cana-5711	165	16	between	between	ADP
cana-5711	165	17	(	(	PUNCT
cana-5711	165	18	u	u	NOUN
cana-5711	165	19	,	,	PUNCT
cana-5711	165	20	u′	u′	PROPN
cana-5711	165	21	)	)	PUNCT
cana-5711	165	22	and	and	CCONJ
cana-5711	165	23	(	(	PUNCT
cana-5711	165	24	u1	u1	NOUN
cana-5711	165	25	,	,	PUNCT
cana-5711	165	26	u′1	u′1	NOUN
cana-5711	165	27	)	)	PUNCT
cana-5711	165	28	by	by	ADP
cana-5711	165	29	dl	dl	PROPN
cana-5711	165	30	(	(	PUNCT
cana-5711	165	31	(	(	PUNCT
cana-5711	165	32	u	u	NOUN
cana-5711	165	33	,	,	PUNCT
cana-5711	165	34	u′	u′	PROPN
cana-5711	165	35	)	)	PUNCT
cana-5711	165	36	,	,	PUNCT
cana-5711	165	37	(	(	PUNCT
cana-5711	165	38	u1	u1	NOUN
cana-5711	165	39	,	,	PUNCT
cana-5711	165	40	u′1	u′1	NOUN
cana-5711	165	41	)	)	PUNCT
cana-5711	165	42	)	)	PUNCT
cana-5711	166	1	=	=	PUNCT
cana-5711	166	2	wl	wl	X
cana-5711	166	3	(	(	PUNCT
cana-5711	166	4	u	u	NOUN
cana-5711	166	5	−	−	PROPN
cana-5711	166	6	u1	u1	NOUN
cana-5711	166	7	,	,	PUNCT
cana-5711	166	8	u′	u′	PROPN
cana-5711	166	9	−	−	NOUN
cana-5711	166	10	u′1	u′1	NOUN
cana-5711	166	11	)	)	PUNCT
cana-5711	167	1	=	=	SYM
cana-5711	167	2	wh	wh	X
cana-5711	167	3	(	(	PUNCT
cana-5711	167	4	u	u	NOUN
cana-5711	167	5	−	−	PROPN
cana-5711	167	6	u1	u1	NOUN
cana-5711	167	7	)	)	PUNCT
cana-5711	168	1	+	+	CCONJ
cana-5711	168	2	wh	wh	X
cana-5711	168	3	(	(	PUNCT
cana-5711	168	4	𝜙(u′	𝜙(u′	NOUN
cana-5711	168	5	−	−	PROPN
cana-5711	168	6	u′1	u′1	NOUN
cana-5711	168	7	)	)	PUNCT
cana-5711	168	8	)	)	PUNCT
cana-5711	168	9	.	.	PUNCT
cana-5711	169	1	the	the	DET
cana-5711	169	2	hamming	hamming	NOUN
cana-5711	169	3	distance	distance	NOUN
cana-5711	169	4	between	between	ADP
cana-5711	169	5	(	(	PUNCT
cana-5711	169	6	u	u	NOUN
cana-5711	169	7	,	,	PUNCT
cana-5711	169	8	u′	u′	PROPN
cana-5711	169	9	)	)	PUNCT
cana-5711	169	10	and	and	CCONJ
cana-5711	169	11	(	(	PUNCT
cana-5711	169	12	u1	u1	NOUN
cana-5711	169	13	,	,	PUNCT
cana-5711	169	14	u′1	u′1	NOUN
cana-5711	169	15	)	)	PUNCT
cana-5711	169	16	is	be	AUX
cana-5711	169	17	defined	define	VERB
cana-5711	169	18	by	by	ADP
cana-5711	169	19	dh	dh	PROPN
cana-5711	169	20	(	(	PUNCT
cana-5711	169	21	(	(	PUNCT
cana-5711	169	22	u	u	NOUN
cana-5711	169	23	,	,	PUNCT
cana-5711	169	24	u′	u′	PROPN
cana-5711	169	25	)	)	PUNCT
cana-5711	169	26	,	,	PUNCT
cana-5711	169	27	(	(	PUNCT
cana-5711	169	28	u1	u1	NOUN
cana-5711	169	29	,	,	PUNCT
cana-5711	169	30	u′1	u′1	ADJ
cana-5711	169	31	)	)	PUNCT
cana-5711	169	32	)	)	PUNCT
cana-5711	170	1	=	=	SYM
cana-5711	170	2	wh	wh	X
cana-5711	170	3	(	(	PUNCT
cana-5711	170	4	u	u	NOUN
cana-5711	170	5	−	−	PROPN
cana-5711	170	6	u1	u1	NOUN
cana-5711	170	7	,	,	PUNCT
cana-5711	170	8	u′	u′	PROPN
cana-5711	170	9	−	−	NOUN
cana-5711	170	10	u′1	u′1	NOUN
cana-5711	170	11	)	)	PUNCT
cana-5711	170	12	.	.	PUNCT
cana-5711	171	1	then	then	ADV
cana-5711	171	2	the	the	DET
cana-5711	171	3	lee	lee	PROPN
cana-5711	171	4	weight	weight	NOUN
cana-5711	171	5	of	of	ADP
cana-5711	171	6	elements	element	NOUN
cana-5711	171	7	of	of	ADP
cana-5711	171	8	q	q	NOUN
cana-5711	171	9	:	:	PUNCT
cana-5711	171	10	element	element	NOUN
cana-5711	171	11	in	in	ADP
cana-5711	171	12	the	the	DET
cana-5711	171	13	ring	ring	NOUN
cana-5711	171	14	q	q	NOUN
cana-5711	171	15	its	its	PRON
cana-5711	171	16	lee	lee	PROPN
cana-5711	171	17	weight	weight	NOUN
cana-5711	171	18	(	(	PUNCT
cana-5711	171	19	0,0	0,0	NOUN
cana-5711	171	20	)	)	PUNCT
cana-5711	171	21	0	0	NUM
cana-5711	171	22	(	(	PUNCT
cana-5711	171	23	0,1	0,1	NUM
cana-5711	171	24	)	)	PUNCT
cana-5711	171	25	,	,	PUNCT
cana-5711	171	26	(	(	PUNCT
cana-5711	171	27	0,1+u	0,1+u	NUM
cana-5711	171	28	)	)	PUNCT
cana-5711	171	29	,	,	PUNCT
cana-5711	171	30	(	(	PUNCT
cana-5711	171	31	0,1+v	0,1+v	NUM
cana-5711	171	32	)	)	PUNCT
cana-5711	171	33	,	,	PUNCT
cana-5711	171	34	(	(	PUNCT
cana-5711	171	35	0,1+u+v+uv	0,1+u+v+uv	NUM
cana-5711	171	36	)	)	PUNCT
cana-5711	171	37	,	,	PUNCT
cana-5711	171	38	(	(	PUNCT
cana-5711	171	39	1,0	1,0	NUM
cana-5711	171	40	)	)	PUNCT
cana-5711	171	41	,	,	PUNCT
cana-5711	171	42	(	(	PUNCT
cana-5711	171	43	1+u,0	1+u,0	NUM
cana-5711	171	44	)	)	PUNCT
cana-5711	171	45	1	1	NUM
cana-5711	171	46	(	(	PUNCT
cana-5711	171	47	0,u	0,u	NUM
cana-5711	171	48	)	)	PUNCT
cana-5711	171	49	,	,	PUNCT
cana-5711	171	50	(	(	PUNCT
cana-5711	171	51	0,v	0,v	X
cana-5711	171	52	)	)	PUNCT
cana-5711	171	53	,	,	PUNCT
cana-5711	171	54	(	(	PUNCT
cana-5711	171	55	0,u+v	0,u+v	NOUN
cana-5711	171	56	)	)	PUNCT
cana-5711	171	57	,	,	PUNCT
cana-5711	171	58	(	(	PUNCT
cana-5711	171	59	0,u+uv	0,u+uv	X
cana-5711	171	60	)	)	PUNCT
cana-5711	171	61	,	,	PUNCT
cana-5711	171	62	(	(	PUNCT
cana-5711	171	63	0,v+uv	0,v+uv	INTJ
cana-5711	171	64	)	)	PUNCT
cana-5711	171	65	,	,	PUNCT
cana-5711	171	66	(	(	PUNCT
cana-5711	171	67	0,u+v+uv	0,u+v+uv	NOUN
cana-5711	171	68	)	)	PUNCT
cana-5711	171	69	,	,	PUNCT
cana-5711	171	70	(	(	PUNCT
cana-5711	171	71	1,1	1,1	NUM
cana-5711	171	72	)	)	PUNCT
cana-5711	171	73	,	,	PUNCT
cana-5711	171	74	(	(	PUNCT
cana-5711	171	75	1,1+u),(1,1+v	1,1+u),(1,1+v	NUM
cana-5711	171	76	)	)	PUNCT
cana-5711	171	77	,	,	PUNCT
cana-5711	171	78	(	(	PUNCT
cana-5711	171	79	1,1+u+v+uv	1,1+u+v+uv	NUM
cana-5711	171	80	)	)	PUNCT
cana-5711	171	81	,	,	PUNCT
cana-5711	171	82	(	(	PUNCT
cana-5711	171	83	u,0	u,0	PROPN
cana-5711	171	84	)	)	PUNCT
cana-5711	171	85	,	,	PUNCT
cana-5711	171	86	(	(	PUNCT
cana-5711	171	87	1+u,1	1+u,1	NUM
cana-5711	171	88	)	)	PUNCT
cana-5711	171	89	,	,	PUNCT
cana-5711	171	90	(	(	PUNCT
cana-5711	171	91	1+u,1+u	1+u,1+u	NOUN
cana-5711	171	92	)	)	PUNCT
cana-5711	171	93	,	,	PUNCT
cana-5711	171	94	(	(	PUNCT
cana-5711	171	95	1+u,1+v),(1+u,1+u+v+uv	1+u,1+v),(1+u,1+u+v+uv	X
cana-5711	171	96	)	)	PUNCT
cana-5711	171	97	2	2	NUM
cana-5711	171	98	(	(	PUNCT
cana-5711	171	99	0,1+uv	0,1+uv	NUM
cana-5711	171	100	)	)	PUNCT
cana-5711	171	101	,	,	PUNCT
cana-5711	171	102	(	(	PUNCT
cana-5711	171	103	0,1+u+v	0,1+u+v	NOUN
cana-5711	171	104	)	)	PUNCT
cana-5711	171	105	,	,	PUNCT
cana-5711	171	106	(	(	PUNCT
cana-5711	171	107	0,1+u+uv	0,1+u+uv	NUM
cana-5711	171	108	)	)	PUNCT
cana-5711	171	109	,	,	PUNCT
cana-5711	171	110	(	(	PUNCT
cana-5711	171	111	0,1+v+uv	0,1+v+uv	NUM
cana-5711	171	112	)	)	PUNCT
cana-5711	171	113	,	,	PUNCT
cana-5711	171	114	(	(	PUNCT
cana-5711	171	115	1,u	1,u	NUM
cana-5711	171	116	)	)	PUNCT
cana-5711	171	117	,	,	PUNCT
cana-5711	171	118	(	(	PUNCT
cana-5711	171	119	1,v	1,v	NOUN
cana-5711	171	120	)	)	PUNCT
cana-5711	171	121	,	,	PUNCT
cana-5711	171	122	(	(	PUNCT
cana-5711	171	123	1,u+v),(1,u+uv	1,u+v),(1,u+uv	NUM
cana-5711	171	124	)	)	PUNCT
cana-5711	171	125	,	,	PUNCT
cana-5711	171	126	(	(	PUNCT
cana-5711	171	127	1,v+uv	1,v+uv	X
cana-5711	171	128	)	)	PUNCT
cana-5711	171	129	,	,	PUNCT
cana-5711	171	130	(	(	PUNCT
cana-5711	171	131	1,u+v+uv	1,u+v+uv	NUM
cana-5711	171	132	)	)	PUNCT
cana-5711	171	133	,	,	PUNCT
cana-5711	171	134	(	(	PUNCT
cana-5711	171	135	u,1	u,1	ADJ
cana-5711	171	136	)	)	PUNCT
cana-5711	171	137	,	,	PUNCT
cana-5711	171	138	(	(	PUNCT
cana-5711	171	139	u,1+u	u,1+u	NOUN
cana-5711	171	140	)	)	PUNCT
cana-5711	171	141	,	,	PUNCT
cana-5711	171	142	(	(	PUNCT
cana-5711	171	143	u,1+v	u,1+v	NOUN
cana-5711	171	144	)	)	PUNCT
cana-5711	171	145	,	,	PUNCT
cana-5711	171	146	(	(	PUNCT
cana-5711	171	147	u,1+u+v+uv),(1+u	u,1+u+v+uv),(1+u	PROPN
cana-5711	171	148	,	,	PUNCT
cana-5711	171	149	u	u	NOUN
cana-5711	171	150	)	)	PUNCT
cana-5711	171	151	,	,	PUNCT
cana-5711	171	152	(	(	PUNCT
cana-5711	171	153	1+u	1+u	NUM
cana-5711	171	154	,	,	PUNCT
cana-5711	171	155	v	v	NOUN
cana-5711	171	156	)	)	PUNCT
cana-5711	171	157	,	,	PUNCT
cana-5711	171	158	(	(	PUNCT
cana-5711	171	159	1+u	1+u	NUM
cana-5711	171	160	,	,	PUNCT
cana-5711	171	161	u+v	u+v	NUM
cana-5711	171	162	)	)	PUNCT
cana-5711	171	163	,	,	PUNCT
cana-5711	171	164	(	(	PUNCT
cana-5711	171	165	1+u	1+u	NUM
cana-5711	171	166	,	,	PUNCT
cana-5711	171	167	u+uv	u+uv	X
cana-5711	171	168	)	)	PUNCT
cana-5711	171	169	,	,	PUNCT
cana-5711	171	170	(	(	PUNCT
cana-5711	171	171	1+u	1+u	NUM
cana-5711	171	172	,	,	PUNCT
cana-5711	171	173	v+uv	v+uv	ADJ
cana-5711	171	174	)	)	PUNCT
cana-5711	171	175	,	,	PUNCT
cana-5711	171	176	(	(	PUNCT
cana-5711	171	177	1+u	1+u	NUM
cana-5711	171	178	,	,	PUNCT
cana-5711	171	179	u+v+uv	u+v+uv	ADJ
cana-5711	171	180	)	)	PUNCT
cana-5711	171	181	3	3	NUM
cana-5711	171	182	(	(	PUNCT
cana-5711	171	183	0,uv	0,uv	NUM
cana-5711	171	184	)	)	PUNCT
cana-5711	171	185	,	,	PUNCT
cana-5711	171	186	(	(	PUNCT
cana-5711	171	187	1,1+uv	1,1+uv	NUM
cana-5711	171	188	)	)	PUNCT
cana-5711	171	189	,	,	PUNCT
cana-5711	171	190	(	(	PUNCT
cana-5711	171	191	1,1+u+v	1,1+u+v	NOUN
cana-5711	171	192	)	)	PUNCT
cana-5711	171	193	,	,	PUNCT
cana-5711	171	194	(	(	PUNCT
cana-5711	171	195	1,1+u+uv	1,1+u+uv	NUM
cana-5711	171	196	)	)	PUNCT
cana-5711	171	197	,	,	PUNCT
cana-5711	171	198	(	(	PUNCT
cana-5711	171	199	1,1+v+uv	1,1+v+uv	NUM
cana-5711	171	200	)	)	PUNCT
cana-5711	171	201	,	,	PUNCT
cana-5711	171	202	(	(	PUNCT
cana-5711	171	203	u	u	NOUN
cana-5711	171	204	,	,	PUNCT
cana-5711	171	205	u	u	NOUN
cana-5711	171	206	)	)	PUNCT
cana-5711	171	207	,	,	PUNCT
cana-5711	171	208	(	(	PUNCT
cana-5711	171	209	u	u	NOUN
cana-5711	171	210	,	,	PUNCT
cana-5711	171	211	v	v	NOUN
cana-5711	171	212	)	)	PUNCT
cana-5711	171	213	,	,	PUNCT
cana-5711	171	214	(	(	PUNCT
cana-5711	171	215	u	u	NOUN
cana-5711	171	216	,	,	PUNCT
cana-5711	171	217	u+v),(u	u+v),(u	ADV
cana-5711	171	218	,	,	PUNCT
cana-5711	171	219	u+uv	u+uv	PROPN
cana-5711	171	220	)	)	PUNCT
cana-5711	171	221	,	,	PUNCT
cana-5711	171	222	(	(	PUNCT
cana-5711	171	223	u	u	NOUN
cana-5711	171	224	,	,	PUNCT
cana-5711	171	225	v+uv	v+uv	ADJ
cana-5711	171	226	)	)	PUNCT
cana-5711	171	227	,	,	PUNCT
cana-5711	171	228	(	(	PUNCT
cana-5711	171	229	u	u	NOUN
cana-5711	171	230	,	,	PUNCT
cana-5711	171	231	u+v+uv	u+v+uv	PROPN
cana-5711	171	232	)	)	PUNCT
cana-5711	171	233	,	,	PUNCT
cana-5711	171	234	(	(	PUNCT
cana-5711	171	235	1+u,1+uv	1+u,1+uv	X
cana-5711	171	236	)	)	PUNCT
cana-5711	171	237	,	,	PUNCT
cana-5711	171	238	(	(	PUNCT
cana-5711	171	239	1+u,1+u+v	1+u,1+u+v	NOUN
cana-5711	171	240	)	)	PUNCT
cana-5711	171	241	,	,	PUNCT
cana-5711	171	242	(	(	PUNCT
cana-5711	171	243	1+u,1+u+uv),(1+u,1+v+uv	1+u,1+u+uv),(1+u,1+v+uv	NOUN
cana-5711	171	244	)	)	PUNCT
cana-5711	171	245	4	4	NUM
cana-5711	171	246	(	(	PUNCT
cana-5711	171	247	1,uv	1,uv	NUM
cana-5711	171	248	)	)	PUNCT
cana-5711	171	249	,	,	PUNCT
cana-5711	171	250	(	(	PUNCT
cana-5711	171	251	u,1+uv	u,1+uv	NOUN
cana-5711	171	252	)	)	PUNCT
cana-5711	171	253	,	,	PUNCT
cana-5711	171	254	(	(	PUNCT
cana-5711	171	255	u,1+u+v	u,1+u+v	NOUN
cana-5711	171	256	)	)	PUNCT
cana-5711	171	257	,	,	PUNCT
cana-5711	171	258	(	(	PUNCT
cana-5711	171	259	u,1+u+uv	u,1+u+uv	X
cana-5711	171	260	)	)	PUNCT
cana-5711	171	261	,	,	PUNCT
cana-5711	171	262	(	(	PUNCT
cana-5711	171	263	u,1+v+uv	u,1+v+uv	PROPN
cana-5711	171	264	)	)	PUNCT
cana-5711	171	265	,	,	PUNCT
cana-5711	171	266	(	(	PUNCT
cana-5711	171	267	1+u	1+u	NUM
cana-5711	171	268	,	,	PUNCT
cana-5711	171	269	uv	uv	NOUN
cana-5711	171	270	)	)	PUNCT
cana-5711	171	271	5	5	NUM
cana-5711	171	272	(	(	PUNCT
cana-5711	171	273	u	u	NOUN
cana-5711	171	274	,	,	PUNCT
cana-5711	171	275	uv	uv	NOUN
cana-5711	171	276	)	)	PUNCT
cana-5711	171	277	6	6	NUM
cana-5711	171	278	lemma	lemma	PROPN
cana-5711	171	279	4.1	4.1	NUM
cana-5711	171	280	.	.	PUNCT
cana-5711	172	1	the	the	DET
cana-5711	172	2	gray	gray	ADJ
cana-5711	172	3	map	map	NOUN
cana-5711	172	4	𝜙	𝜙	NOUN
cana-5711	172	5	is	be	AUX
cana-5711	172	6	ℤ2	ℤ2	PROPN
cana-5711	172	7	-linear	-linear	NOUN
cana-5711	172	8	.	.	PUNCT
cana-5711	173	1	proof	proof	NOUN
cana-5711	173	2	.	.	PUNCT
cana-5711	174	1	the	the	DET
cana-5711	174	2	lee	lee	PROPN
cana-5711	174	3	weight	weight	NOUN
cana-5711	174	4	of	of	ADP
cana-5711	174	5	x	x	PUNCT
cana-5711	174	6	∈	∈	PROPN
cana-5711	174	7	q	q	NOUN
cana-5711	174	8	is	be	AUX
cana-5711	174	9	the	the	DET
cana-5711	174	10	hamming	hamming	ADJ
cana-5711	174	11	weight	weight	NOUN
cana-5711	174	12	of	of	ADP
cana-5711	174	13	𝜙(x	𝜙(x	PROPN
cana-5711	174	14	)	)	PUNCT
cana-5711	174	15	.	.	PUNCT
cana-5711	175	1	then	then	ADV
cana-5711	175	2	the	the	DET
cana-5711	175	3	lee	lee	PROPN
cana-5711	175	4	distance	distance	NOUN
cana-5711	175	5	between	between	ADP
cana-5711	175	6	two	two	NUM
cana-5711	175	7	elements	element	NOUN
cana-5711	175	8	is	be	AUX
cana-5711	175	9	given	give	VERB
cana-5711	175	10	as	as	SCONJ
cana-5711	175	11	dl	dl	PROPN
cana-5711	175	12	(	(	PUNCT
cana-5711	175	13	x	x	PROPN
cana-5711	175	14	,	,	PUNCT
cana-5711	175	15	y	y	NOUN
cana-5711	175	16	)	)	PUNCT
cana-5711	175	17	is	be	AUX
cana-5711	175	18	a	a	DET
cana-5711	175	19	lee	lee	PROPN
cana-5711	175	20	weight	weight	NOUN
cana-5711	175	21	of	of	ADP
cana-5711	175	22	x	x	SYM
cana-5711	175	23	−	−	PROPN
cana-5711	175	24	y	y	PROPN
cana-5711	175	25	for	for	ADP
cana-5711	175	26	all	all	DET
cana-5711	175	27	x	x	NOUN
cana-5711	175	28	,	,	PUNCT
cana-5711	175	29	y	y	PROPN
cana-5711	175	30	∈	∈	PROPN
cana-5711	175	31	q.	q.	PROPN
cana-5711	175	32	see	see	VERB
cana-5711	175	33	that	that	DET
cana-5711	175	34	table	table	NOUN
cana-5711	175	35	1	1	NUM
cana-5711	175	36	is	be	AUX
cana-5711	175	37	the	the	DET
cana-5711	175	38	lee	lee	PROPN
cana-5711	175	39	weight	weight	NOUN
cana-5711	175	40	of	of	ADP
cana-5711	175	41	element	element	NOUN
cana-5711	175	42	in	in	ADP
cana-5711	175	43	q.	q.	PROPN
cana-5711	175	44	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	175	45	communications	communication	NOUN
cana-5711	175	46	on	on	ADP
cana-5711	175	47	applied	apply	VERB
cana-5711	175	48	nonlinear	nonlinear	ADJ
cana-5711	175	49	analysis	analysis	NOUN
cana-5711	175	50	issn	issn	NOUN
cana-5711	175	51	:	:	PUNCT
cana-5711	175	52	1074	1074	NUM
cana-5711	175	53	-	-	PUNCT
cana-5711	175	54	133x	133x	NUM
cana-5711	175	55	vol	vol	VERB
cana-5711	175	56	32	32	NUM
cana-5711	175	57	no	no	NOUN
cana-5711	175	58	.	.	PUNCT
cana-5711	176	1	10s	10	NOUN
cana-5711	176	2	(	(	PUNCT
cana-5711	176	3	2025	2025	NUM
cana-5711	176	4	)	)	PUNCT
cana-5711	176	5	2701	2701	NUM
cana-5711	176	6	for	for	ADP
cana-5711	176	7	p	p	NOUN
cana-5711	176	8	,	,	PUNCT
cana-5711	176	9	q	q	PROPN
cana-5711	176	10	∈	∈	PROPN
cana-5711	176	11	ℤ	ℤ	PROPN
cana-5711	176	12	,	,	PUNCT
cana-5711	176	13	p	p	X
cana-5711	176	14	,	,	PUNCT
cana-5711	176	15	q	q	X
cana-5711	176	16	≥	≥	NOUN
cana-5711	176	17	0,the	0,the	DET
cana-5711	176	18	gray	gray	ADJ
cana-5711	176	19	mapping	mapping	NOUN
cana-5711	176	20	𝜙	𝜙	PROPN
cana-5711	176	21	extended	extend	VERB
cana-5711	176	22	to	to	ADP
cana-5711	176	23	𝜙	𝜙	PROPN
cana-5711	176	24	:	:	PUNCT
cana-5711	176	25	ℤ2	ℤ2	PROPN
cana-5711	176	26	𝑝	𝑝	PROPN
cana-5711	176	27	×	×	PROPN
cana-5711	176	28	qq	qq	NOUN
cana-5711	176	29	→ℤ2	→ℤ2	PUNCT
cana-5711	176	30	𝑝+6𝑞	𝑝+6𝑞	NOUN
cana-5711	176	31	where	where	SCONJ
cana-5711	176	32	𝜙(𝑢0	𝜙(𝑢0	ADJ
cana-5711	176	33	,	,	PUNCT
cana-5711	176	34	𝑢1	𝑢1	NOUN
cana-5711	176	35	,	,	PUNCT
cana-5711	176	36	.	.	PUNCT
cana-5711	176	37	.	.	PUNCT
cana-5711	176	38	.	.	PUNCT
cana-5711	177	1	,	,	PUNCT
cana-5711	177	2	𝑢𝑝−1	𝑢𝑝−1	PROPN
cana-5711	177	3	,	,	PUNCT
cana-5711	177	4	𝑢′0	𝑢′0	NOUN
cana-5711	177	5	,	,	PUNCT
cana-5711	177	6	𝑢′1	𝑢′1	VERB
cana-5711	177	7	,	,	PUNCT
cana-5711	177	8	.	.	PUNCT
cana-5711	177	9	.	.	PUNCT
cana-5711	178	1	.	.	PUNCT
cana-5711	179	1	,	,	PUNCT
cana-5711	179	2	𝑢′𝑞−1	𝑢′𝑞−1	NOUN
cana-5711	179	3	)	)	PUNCT
cana-5711	179	4	=	=	SYM
cana-5711	180	1	(	(	PUNCT
cana-5711	180	2	(	(	PUNCT
cana-5711	180	3	𝑢0	𝑢0	PROPN
cana-5711	180	4	,	,	PUNCT
cana-5711	180	5	𝑢1	𝑢1	NOUN
cana-5711	180	6	,	,	PUNCT
cana-5711	180	7	.	.	PUNCT
cana-5711	180	8	.	.	PUNCT
cana-5711	181	1	.	.	PUNCT
cana-5711	182	1	,	,	PUNCT
cana-5711	182	2	𝑢𝑝−1	𝑢𝑝−1	PROPN
cana-5711	182	3	)	)	PUNCT
cana-5711	182	4	,	,	PUNCT
cana-5711	182	5	𝜙(𝑢′0	𝜙(𝑢′0	NOUN
cana-5711	182	6	)	)	PUNCT
cana-5711	182	7	,	,	PUNCT
cana-5711	182	8	𝜙(𝑢′1	𝜙(𝑢′1	NOUN
cana-5711	182	9	)	)	PUNCT
cana-5711	182	10	.	.	PUNCT
cana-5711	182	11	.	.	PUNCT
cana-5711	183	1	.	.	PUNCT
cana-5711	184	1	,	,	PUNCT
cana-5711	184	2	𝜙(𝑢′𝑞−1	𝜙(𝑢′𝑞−1	NOUN
cana-5711	184	3	)	)	PUNCT
cana-5711	184	4	)	)	PUNCT
cana-5711	184	5	.	.	PUNCT
cana-5711	185	1	the	the	DET
cana-5711	185	2	lee	lee	PROPN
cana-5711	185	3	weight	weight	PROPN
cana-5711	185	4	of	of	ADP
cana-5711	185	5	(	(	PUNCT
cana-5711	185	6	𝑢0	𝑢0	PROPN
cana-5711	185	7	,	,	PUNCT
cana-5711	185	8	𝑢1	𝑢1	NOUN
cana-5711	185	9	,	,	PUNCT
cana-5711	185	10	.	.	PUNCT
cana-5711	185	11	.	.	PUNCT
cana-5711	185	12	.	.	PUNCT
cana-5711	186	1	,	,	PUNCT
cana-5711	186	2	𝑢𝑝−1	𝑢𝑝−1	NOUN
cana-5711	186	3	,	,	PUNCT
cana-5711	186	4	𝜙(𝑢′0	𝜙(𝑢′0	NOUN
cana-5711	186	5	)	)	PUNCT
cana-5711	186	6	,	,	PUNCT
cana-5711	186	7	𝜙(𝑢′1	𝜙(𝑢′1	NOUN
cana-5711	186	8	)	)	PUNCT
cana-5711	186	9	,	,	PUNCT
cana-5711	186	10	.	.	PUNCT
cana-5711	186	11	.	.	PUNCT
cana-5711	187	1	,	,	PUNCT
cana-5711	187	2	𝜙(𝑢′𝑞−1	𝜙(𝑢′𝑞−1	NOUN
cana-5711	187	3	)	)	PUNCT
cana-5711	187	4	)	)	PUNCT
cana-5711	188	1	∈	∈	PROPN
cana-5711	188	2	ℤ2	ℤ2	PROPN
cana-5711	188	3	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	188	4	is	be	AUX
cana-5711	188	5	𝛴𝑖=0	𝛴𝑖=0	ADJ
cana-5711	188	6	𝑝−1𝑤𝑡𝐻(𝑢𝑖	𝑝−1𝑤𝑡𝐻(𝑢𝑖	NOUN
cana-5711	188	7	)	)	PUNCT
cana-5711	189	1	+	+	CCONJ
cana-5711	189	2	𝛴𝑗=0	𝛴𝑗=0	X
cana-5711	189	3	𝑞−1𝑤𝑡𝐿(𝑢′𝑗	𝑞−1𝑤𝑡𝐿(𝑢′𝑗	NOUN
cana-5711	189	4	)	)	PUNCT
cana-5711	189	5	and	and	CCONJ
cana-5711	189	6	the	the	DET
cana-5711	189	7	lee	lee	PROPN
cana-5711	189	8	distance	distance	NOUN
cana-5711	189	9	between	between	ADP
cana-5711	189	10	x	x	PROPN
cana-5711	189	11	,	,	PUNCT
cana-5711	189	12	y	y	PROPN
cana-5711	189	13	∈ℤ2	∈ℤ2	ADJ
cana-5711	189	14	𝑝𝑄𝑞	𝑝𝑄𝑞	NOUN
cana-5711	189	15	is	be	AUX
cana-5711	189	16	d	d	X
cana-5711	189	17	l	l	NOUN
cana-5711	189	18	(	(	PUNCT
cana-5711	189	19	x	x	NOUN
cana-5711	189	20	,	,	PUNCT
cana-5711	189	21	y	y	NOUN
cana-5711	189	22	)	)	PUNCT
cana-5711	189	23	=	=	SYM
cana-5711	189	24	wtl	wtl	PROPN
cana-5711	189	25	(	(	PUNCT
cana-5711	189	26	x	x	PROPN
cana-5711	189	27	−	−	PROPN
cana-5711	189	28	y	y	PROPN
cana-5711	189	29	)	)	PUNCT
cana-5711	189	30	.	.	PUNCT
cana-5711	190	1	in	in	ADP
cana-5711	190	2	this	this	DET
cana-5711	190	3	section	section	NOUN
cana-5711	190	4	,	,	PUNCT
cana-5711	190	5	we	we	PRON
cana-5711	190	6	study	study	VERB
cana-5711	190	7	certain	certain	ADJ
cana-5711	190	8	conditions	condition	NOUN
cana-5711	190	9	that	that	PRON
cana-5711	190	10	make	make	VERB
cana-5711	190	11	the	the	DET
cana-5711	190	12	gray	gray	ADJ
cana-5711	190	13	image	image	NOUN
cana-5711	190	14	of	of	ADP
cana-5711	190	15	an	an	DET
cana-5711	190	16	additive	additive	ADJ
cana-5711	190	17	code	code	NOUN
cana-5711	190	18	over	over	ADP
cana-5711	190	19	ℤ2q	ℤ2q	PROPN
cana-5711	190	20	the	the	DET
cana-5711	190	21	binary	binary	PROPN
cana-5711	190	22	lcd	lcd	PROPN
cana-5711	190	23	code	code	PROPN
cana-5711	190	24	.	.	PUNCT
cana-5711	191	1	theorem	theorem	VERB
cana-5711	191	2	4.2	4.2	NUM
cana-5711	191	3	.	.	PUNCT
cana-5711	192	1	let	let	VERB
cana-5711	192	2	c	c	PRON
cana-5711	192	3	be	be	AUX
cana-5711	192	4	an	an	DET
cana-5711	192	5	additive	additive	ADJ
cana-5711	192	6	code	code	NOUN
cana-5711	192	7	over	over	ADP
cana-5711	192	8	ℤ2q	ℤ2q	PROPN
cana-5711	192	9	generated	generate	VERB
cana-5711	192	10	by	by	ADP
cana-5711	192	11	the	the	DET
cana-5711	192	12	matrix	matrix	NOUN
cana-5711	192	13	g	g	NOUN
cana-5711	192	14	=	=	PUNCT
cana-5711	192	15	(	(	PUNCT
cana-5711	192	16	gp	gp	NOUN
cana-5711	192	17	|gq)m×(p+q	|gq)m×(p+q	PROPN
cana-5711	192	18	)	)	PUNCT
cana-5711	192	19	where	where	SCONJ
cana-5711	192	20	gp	gp	NOUN
cana-5711	192	21	generates	generate	VERB
cana-5711	192	22	a	a	DET
cana-5711	192	23	self	self	NOUN
cana-5711	192	24	-	-	PUNCT
cana-5711	192	25	orthogonal	orthogonal	ADJ
cana-5711	192	26	code	code	NOUN
cana-5711	192	27	cp	cp	NUM
cana-5711	192	28	over	over	ADP
cana-5711	192	29	ℤ2	ℤ2	PROPN
cana-5711	192	30	and	and	CCONJ
cana-5711	192	31	gq	gq	PROPN
cana-5711	192	32	generates	generate	VERB
cana-5711	192	33	a	a	DET
cana-5711	192	34	additive	additive	ADJ
cana-5711	192	35	code	code	NOUN
cana-5711	192	36	cq	cq	NOUN
cana-5711	192	37	over	over	ADP
cana-5711	192	38	q.	q.	PROPN
cana-5711	192	39	if	if	SCONJ
cana-5711	192	40	the	the	DET
cana-5711	192	41	rows	row	NOUN
cana-5711	192	42	of	of	ADP
cana-5711	192	43	the	the	DET
cana-5711	192	44	matrics	matric	NOUN
cana-5711	192	45	gq	gq	PROPN
cana-5711	192	46	is	be	AUX
cana-5711	192	47	q	q	ADJ
cana-5711	192	48	-	-	PUNCT
cana-5711	192	49	linealy	linealy	ADJ
cana-5711	192	50	independent	independent	ADJ
cana-5711	192	51	and	and	CCONJ
cana-5711	192	52	𝜙	𝜙	PROPN
cana-5711	192	53	(	(	PUNCT
cana-5711	192	54	cq	cq	NOUN
cana-5711	192	55	)	)	PUNCT
cana-5711	192	56	is	be	AUX
cana-5711	192	57	an	an	DET
cana-5711	192	58	binary	binary	ADJ
cana-5711	192	59	lcd	lcd	NOUN
cana-5711	192	60	codes	code	NOUN
cana-5711	192	61	,	,	PUNCT
cana-5711	192	62	then	then	ADV
cana-5711	192	63	the	the	DET
cana-5711	192	64	binary	binary	ADJ
cana-5711	192	65	gray	gray	ADJ
cana-5711	192	66	image	image	NOUN
cana-5711	192	67	𝜙	𝜙	X
cana-5711	192	68	(	(	PUNCT
cana-5711	192	69	c	c	NOUN
cana-5711	192	70	)	)	PUNCT
cana-5711	192	71	is	be	AUX
cana-5711	192	72	an	an	DET
cana-5711	192	73	lcd	lcd	NOUN
cana-5711	192	74	code	code	NOUN
cana-5711	192	75	.	.	PUNCT
cana-5711	193	1	proof	proof	NOUN
cana-5711	193	2	.	.	PUNCT
cana-5711	194	1	let	let	VERB
cana-5711	194	2	𝜙(𝑥	𝜙(𝑥	PRON
cana-5711	194	3	)	)	PUNCT
cana-5711	195	1	=	=	PUNCT
cana-5711	195	2	(	(	PUNCT
cana-5711	195	3	𝑢	𝑢	X
cana-5711	195	4	,	,	PUNCT
cana-5711	195	5	𝜙(𝑢′	𝜙(𝑢′	ADJ
cana-5711	195	6	)	)	PUNCT
cana-5711	195	7	)	)	PUNCT
cana-5711	195	8	∈	∈	PROPN
cana-5711	195	9	𝜙(𝐶	𝜙(𝐶	PROPN
cana-5711	195	10	)	)	PUNCT
cana-5711	195	11	∩	∩	NOUN
cana-5711	195	12	𝜙(𝐶)⊥	𝜙(𝐶)⊥	PROPN
cana-5711	195	13	where	where	SCONJ
cana-5711	195	14	x	x	X
cana-5711	195	15	=	=	SYM
cana-5711	195	16	(	(	PUNCT
cana-5711	195	17	u	u	NOUN
cana-5711	195	18	,	,	PUNCT
cana-5711	195	19	u′	u′	PROPN
cana-5711	195	20	)	)	PUNCT
cana-5711	195	21	∈	∈	PROPN
cana-5711	195	22	c.	c.	NOUN
cana-5711	195	23	since	since	SCONJ
cana-5711	195	24	for	for	ADP
cana-5711	195	25	all	all	DET
cana-5711	195	26	y	y	NOUN
cana-5711	195	27	=	=	SYM
cana-5711	195	28	(	(	PUNCT
cana-5711	195	29	v	v	NOUN
cana-5711	195	30	,	,	PUNCT
cana-5711	195	31	v′	v′	NOUN
cana-5711	195	32	)	)	PUNCT
cana-5711	195	33	∈	∈	PROPN
cana-5711	195	34	c	c	NOUN
cana-5711	195	35	,	,	PUNCT
cana-5711	195	36	𝜙(𝑦	𝜙(𝑦	NOUN
cana-5711	195	37	)	)	PUNCT
cana-5711	195	38	=	=	PUNCT
cana-5711	195	39	(	(	PUNCT
cana-5711	195	40	𝑣	𝑣	NOUN
cana-5711	195	41	,	,	PUNCT
cana-5711	195	42	𝜙(𝑣′	𝜙(𝑣′	NOUN
cana-5711	195	43	)	)	PUNCT
cana-5711	195	44	)	)	PUNCT
cana-5711	196	1	∈	∈	PROPN
cana-5711	196	2	𝜙(𝐶)and	𝜙(𝐶)and	NUM
cana-5711	196	3	𝜙(𝑥	𝜙(𝑥	NOUN
cana-5711	196	4	)	)	PUNCT
cana-5711	196	5	∈	∈	PROPN
cana-5711	196	6	𝜙(𝐶)⊥	𝜙(𝐶)⊥	PROPN
cana-5711	196	7	,	,	PUNCT
cana-5711	196	8	(	(	PUNCT
cana-5711	196	9	𝑢	𝑢	X
cana-5711	196	10	,	,	PUNCT
cana-5711	196	11	𝜙(𝑢′	𝜙(𝑢′	NOUN
cana-5711	196	12	)	)	PUNCT
cana-5711	196	13	)	)	PUNCT
cana-5711	196	14	.	.	PUNCT
cana-5711	197	1	(	(	PUNCT
cana-5711	197	2	𝑣	𝑣	X
cana-5711	197	3	,	,	PUNCT
cana-5711	197	4	𝜙(𝑣′	𝜙(𝑣′	PROPN
cana-5711	197	5	)	)	PUNCT
cana-5711	197	6	)	)	PUNCT
cana-5711	198	1	=	=	SYM
cana-5711	198	2	0	0	NUM
cana-5711	199	1	for	for	ADP
cana-5711	199	2	all	all	DET
cana-5711	199	3	y	y	NOUN
cana-5711	199	4	=	=	SYM
cana-5711	199	5	(	(	PUNCT
cana-5711	199	6	v	v	NOUN
cana-5711	199	7	,	,	PUNCT
cana-5711	199	8	v′	v′	NOUN
cana-5711	199	9	)	)	PUNCT
cana-5711	199	10	∈	∈	PROPN
cana-5711	199	11	c	c	PROPN
cana-5711	199	12	(	(	PUNCT
cana-5711	199	13	𝑢.	𝑢.	NOUN
cana-5711	199	14	𝑣	𝑣	X
cana-5711	199	15	)	)	PUNCT
cana-5711	199	16	+	+	CCONJ
cana-5711	199	17	(	(	PUNCT
cana-5711	199	18	𝜙(𝑢′	𝜙(𝑢′	PROPN
cana-5711	199	19	)	)	PUNCT
cana-5711	199	20	.	.	PUNCT
cana-5711	199	21	𝜙(𝑣′	𝜙(𝑣′	PROPN
cana-5711	199	22	)	)	PUNCT
cana-5711	199	23	)	)	PUNCT
cana-5711	200	1	=	=	PUNCT
cana-5711	200	2	0	0	PUNCT
cana-5711	201	1	since	since	SCONJ
cana-5711	201	2	u	u	NOUN
cana-5711	201	3	,	,	PUNCT
cana-5711	201	4	v	v	PROPN
cana-5711	201	5	∈	∈	ADJ
cana-5711	202	1	cp	cp	INTJ
cana-5711	202	2	and	and	CCONJ
cana-5711	202	3	cp	cp	PROPN
cana-5711	202	4	is	be	AUX
cana-5711	202	5	a	a	DET
cana-5711	202	6	self	self	NOUN
cana-5711	202	7	-	-	PUNCT
cana-5711	202	8	orthogonal	orthogonal	ADJ
cana-5711	202	9	code	code	NOUN
cana-5711	202	10	,	,	PUNCT
cana-5711	202	11	(	(	PUNCT
cana-5711	202	12	u	u	NOUN
cana-5711	202	13	,	,	PUNCT
cana-5711	202	14	v)=0	v)=0	PROPN
cana-5711	202	15	.	.	PUNCT
cana-5711	202	16	therefore,(𝜙(𝑢′	therefore,(𝜙(𝑢′	ADJ
cana-5711	202	17	)	)	PUNCT
cana-5711	202	18	,	,	PUNCT
cana-5711	202	19	𝜙(𝑣′	𝜙(𝑣′	PROPN
cana-5711	202	20	)	)	PUNCT
cana-5711	202	21	)	)	PUNCT
cana-5711	203	1	=	=	PUNCT
cana-5711	203	2	0	0	X
cana-5711	203	3	.	.	PUNCT
cana-5711	203	4	since	since	SCONJ
cana-5711	203	5	𝜙(𝑢′	𝜙(𝑢′	PROPN
cana-5711	203	6	)	)	PUNCT
cana-5711	203	7	,	,	PUNCT
cana-5711	203	8	𝜙(𝑣′	𝜙(𝑣′	PROPN
cana-5711	203	9	)	)	PUNCT
cana-5711	203	10	∈	∈	PROPN
cana-5711	203	11	𝜙(𝐶𝑞)and	𝜙(𝐶𝑞)and	PROPN
cana-5711	203	12	cq	cq	PROPN
cana-5711	203	13	is	be	AUX
cana-5711	203	14	a	a	DET
cana-5711	203	15	binary	binary	PROPN
cana-5711	203	16	lcd	lcd	PROPN
cana-5711	203	17	code	code	PROPN
cana-5711	203	18	,	,	PUNCT
cana-5711	203	19	implies	imply	VERB
cana-5711	203	20	(	(	PUNCT
cana-5711	203	21	𝜙(𝑢′	𝜙(𝑢′	ADJ
cana-5711	203	22	)	)	PUNCT
cana-5711	203	23	,	,	PUNCT
cana-5711	203	24	𝜙(𝑣′	𝜙(𝑣′	PROPN
cana-5711	203	25	)	)	PUNCT
cana-5711	203	26	)	)	PUNCT
cana-5711	204	1	=	=	SYM
cana-5711	204	2	0	0	PUNCT
cana-5711	204	3	and	and	CCONJ
cana-5711	204	4	hence	hence	ADV
cana-5711	204	5	𝜙(𝑢′	𝜙(𝑢′	VERB
cana-5711	204	6	)	)	PUNCT
cana-5711	204	7	=	=	SYM
cana-5711	204	8	0	0	NUM
cana-5711	204	9	,	,	PUNCT
cana-5711	204	10	thus	thus	ADV
cana-5711	204	11	u′	u′	X
cana-5711	204	12	=	=	SYM
cana-5711	204	13	0	0	PUNCT
cana-5711	204	14	because	because	SCONJ
cana-5711	204	15	𝜙	𝜙	PROPN
cana-5711	204	16	is	be	AUX
cana-5711	204	17	linear	linear	ADJ
cana-5711	204	18	.	.	PUNCT
cana-5711	205	1	we	we	PRON
cana-5711	205	2	will	will	AUX
cana-5711	205	3	prove	prove	VERB
cana-5711	205	4	that	that	SCONJ
cana-5711	205	5	for	for	ADP
cana-5711	205	6	any	any	DET
cana-5711	205	7	c	c	NOUN
cana-5711	205	8	=	=	SYM
cana-5711	205	9	(	(	PUNCT
cana-5711	205	10	u	u	NOUN
cana-5711	205	11	,	,	PUNCT
cana-5711	205	12	u′	u′	PROPN
cana-5711	205	13	)	)	PUNCT
cana-5711	205	14	∈	∈	PROPN
cana-5711	206	1	c	c	X
cana-5711	206	2	,	,	PUNCT
cana-5711	206	3	if	if	SCONJ
cana-5711	206	4	u′	u′	PROPN
cana-5711	206	5	=	=	SYM
cana-5711	206	6	0	0	NUM
cana-5711	206	7	,	,	PUNCT
cana-5711	206	8	then	then	ADV
cana-5711	206	9	the	the	DET
cana-5711	206	10	c	c	NOUN
cana-5711	206	11	=	=	SYM
cana-5711	206	12	0	0	PROPN
cana-5711	206	13	.	.	PUNCT
cana-5711	207	1	for	for	ADP
cana-5711	207	2	i	i	PROPN
cana-5711	207	3	∈	∈	PROPN
cana-5711	207	4	{	{	PUNCT
cana-5711	207	5	0	0	NUM
cana-5711	207	6	,	,	PUNCT
cana-5711	207	7	1	1	NUM
cana-5711	207	8	,	,	PUNCT
cana-5711	207	9	·	·	PUNCT
cana-5711	207	10	·	·	PUNCT
cana-5711	207	11	·	·	PUNCT
cana-5711	207	12	,	,	PUNCT
cana-5711	207	13	m	m	VERB
cana-5711	207	14	−	−	NOUN
cana-5711	207	15	1	1	NUM
cana-5711	207	16	}	}	PUNCT
cana-5711	207	17	,	,	PUNCT
cana-5711	207	18	let	let	VERB
cana-5711	207	19	gi	gi	VERB
cana-5711	207	20	=	=	SYM
cana-5711	207	21	(	(	PUNCT
cana-5711	207	22	vi	vi	PROPN
cana-5711	207	23	,	,	PUNCT
cana-5711	207	24	vi′	vi′	NOUN
cana-5711	207	25	)	)	PUNCT
cana-5711	207	26	be	be	VERB
cana-5711	207	27	the	the	DET
cana-5711	207	28	ith	ith	NOUN
cana-5711	207	29	row	row	NOUN
cana-5711	207	30	of	of	ADP
cana-5711	207	31	g	g	PROPN
cana-5711	207	32	where	where	SCONJ
cana-5711	207	33	vi	vi	NOUN
cana-5711	207	34	and	and	CCONJ
cana-5711	207	35	vi′	vi′	NOUN
cana-5711	207	36	denotes	denote	NOUN
cana-5711	207	37	the	the	DET
cana-5711	207	38	ith	ith	PROPN
cana-5711	207	39	row	row	NOUN
cana-5711	207	40	of	of	ADP
cana-5711	207	41	gp	gp	NOUN
cana-5711	207	42	and	and	CCONJ
cana-5711	207	43	gq	gq	NOUN
cana-5711	207	44	,	,	PUNCT
cana-5711	207	45	respectively	respectively	ADV
cana-5711	207	46	.	.	PUNCT
cana-5711	208	1	since	since	SCONJ
cana-5711	208	2	c	c	PROPN
cana-5711	208	3	∈	∈	PROPN
cana-5711	208	4	c	c	X
cana-5711	208	5	,	,	PUNCT
cana-5711	208	6	there	there	PRON
cana-5711	208	7	exist	exist	VERB
cana-5711	208	8	scalars	scalar	NOUN
cana-5711	208	9	λ0	λ0	NOUN
cana-5711	208	10	,	,	PUNCT
cana-5711	208	11	λ1	λ1	PROPN
cana-5711	208	12	,	,	PUNCT
cana-5711	208	13	·	·	PUNCT
cana-5711	208	14	·	·	PUNCT
cana-5711	208	15	·	·	PUNCT
cana-5711	209	1	,	,	PUNCT
cana-5711	209	2	λ	λ	X
cana-5711	209	3	m−1	m−1	PROPN
cana-5711	209	4	∈	∈	PROPN
cana-5711	209	5	q	q	NOUN
cana-5711	209	6	such	such	ADJ
cana-5711	209	7	that	that	PRON
cana-5711	209	8	𝑐	𝑐	NOUN
cana-5711	209	9	=	=	SYM
cana-5711	209	10	(	(	PUNCT
cana-5711	209	11	𝑢	𝑢	X
cana-5711	209	12	,	,	PUNCT
cana-5711	209	13	𝑢′	𝑢′	NUM
cana-5711	209	14	)	)	PUNCT
cana-5711	209	15	=	=	SYM
cana-5711	209	16	∑𝑖=0	∑𝑖=0	ADJ
cana-5711	209	17	𝑚−1𝜆𝑖𝑔𝑖	𝑚−1𝜆𝑖𝑔𝑖	NOUN
cana-5711	209	18	=	=	PUNCT
cana-5711	209	19	(	(	PUNCT
cana-5711	209	20	∑𝑖=0	∑𝑖=0	PROPN
cana-5711	209	21	𝑚−1𝜂(𝜆𝑖)𝑣𝑖	𝑚−1𝜂(𝜆𝑖)𝑣𝑖	NOUN
cana-5711	209	22	,	,	PUNCT
cana-5711	209	23	∑𝑖=0	∑𝑖=0	PROPN
cana-5711	209	24	𝑚−1𝜆𝑖𝑣𝑖′	𝑚−1𝜆𝑖𝑣𝑖′	PROPN
cana-5711	209	25	)	)	PUNCT
cana-5711	209	26	thus	thus	ADV
cana-5711	209	27	𝑢	𝑢	X
cana-5711	209	28	=	=	SYM
cana-5711	209	29	∑𝑖=0	∑𝑖=0	PROPN
cana-5711	209	30	𝑚−1𝜂(𝜆𝑖)𝑣𝑖	𝑚−1𝜂(𝜆𝑖)𝑣𝑖	NOUN
cana-5711	209	31	and	and	CCONJ
cana-5711	209	32	𝑢′	𝑢′	ADJ
cana-5711	209	33	=	=	PUNCT
cana-5711	209	34	∑𝑖=0	∑𝑖=0	PROPN
cana-5711	209	35	𝑚−1𝜆𝑖𝑣𝑖	𝑚−1𝜆𝑖𝑣𝑖	NOUN
cana-5711	210	1	=	=	NOUN
cana-5711	210	2	0	0	X
cana-5711	210	3	.	.	PUNCT
cana-5711	211	1	since	since	SCONJ
cana-5711	211	2	the	the	DET
cana-5711	211	3	set	set	NOUN
cana-5711	211	4	of	of	ADP
cana-5711	211	5	all	all	DET
cana-5711	211	6	rows	row	NOUN
cana-5711	211	7	of	of	ADP
cana-5711	211	8	gq	gq	PROPN
cana-5711	211	9	is	be	AUX
cana-5711	211	10	q	q	ADJ
cana-5711	211	11	-	-	PUNCT
cana-5711	211	12	linealy	linealy	ADJ
cana-5711	211	13	independent	independent	ADJ
cana-5711	211	14	,	,	PUNCT
cana-5711	211	15	λi	λi	NOUN
cana-5711	211	16	=	=	NOUN
cana-5711	211	17	0	0	NUM
cana-5711	211	18	for	for	ADP
cana-5711	211	19	all	all	PRON
cana-5711	211	20	i	i	PRON
cana-5711	211	21	∈	∈	PROPN
cana-5711	211	22	{	{	PUNCT
cana-5711	211	23	0	0	NUM
cana-5711	211	24	,	,	PUNCT
cana-5711	211	25	1	1	NUM
cana-5711	211	26	,	,	PUNCT
cana-5711	211	27	·	·	PUNCT
cana-5711	211	28	·	·	PUNCT
cana-5711	211	29	·	·	PUNCT
cana-5711	211	30	,	,	PUNCT
cana-5711	211	31	m	m	VERB
cana-5711	211	32	−	−	NOUN
cana-5711	211	33	1	1	NUM
cana-5711	211	34	}	}	PUNCT
cana-5711	211	35	.	.	PUNCT
cana-5711	212	1	therefore	therefore	ADV
cana-5711	212	2	(	(	PUNCT
cana-5711	212	3	u	u	NOUN
cana-5711	212	4	,	,	PUNCT
cana-5711	212	5	u′	u′	X
cana-5711	212	6	)	)	PUNCT
cana-5711	212	7	=	=	SYM
cana-5711	212	8	0	0	NUM
cana-5711	212	9	and	and	CCONJ
cana-5711	212	10	hence	hence	ADV
cana-5711	212	11	𝜙(𝑢	𝜙(𝑢	PROPN
cana-5711	212	12	,	,	PUNCT
cana-5711	212	13	𝑢′	𝑢′	NUM
cana-5711	212	14	)	)	PUNCT
cana-5711	212	15	=	=	SYM
cana-5711	212	16	0	0	X
cana-5711	212	17	.	.	PUNCT
cana-5711	213	1	here	here	ADV
cana-5711	213	2	is	be	AUX
cana-5711	213	3	an	an	DET
cana-5711	213	4	example	example	NOUN
cana-5711	213	5	to	to	PART
cana-5711	213	6	illustrate	illustrate	VERB
cana-5711	213	7	theorem	theorem	VERB
cana-5711	213	8	4.2	4.2	NUM
cana-5711	213	9	example	example	NOUN
cana-5711	213	10	4.3	4.3	NUM
cana-5711	213	11	.	.	PUNCT
cana-5711	214	1	let	let	VERB
cana-5711	214	2	c	c	PRON
cana-5711	214	3	be	be	AUX
cana-5711	214	4	an	an	DET
cana-5711	214	5	additive	additive	ADJ
cana-5711	214	6	code	code	NOUN
cana-5711	214	7	over	over	ADP
cana-5711	214	8	ℤ2q	ℤ2q	PROPN
cana-5711	214	9	generated	generate	VERB
cana-5711	214	10	by	by	ADP
cana-5711	214	11	the	the	DET
cana-5711	214	12	matrix	matrix	NOUN
cana-5711	214	13	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	214	14	communications	communication	NOUN
cana-5711	214	15	on	on	ADP
cana-5711	214	16	applied	apply	VERB
cana-5711	214	17	nonlinear	nonlinear	ADJ
cana-5711	214	18	analysis	analysis	NOUN
cana-5711	214	19	issn	issn	NOUN
cana-5711	214	20	:	:	PUNCT
cana-5711	214	21	1074	1074	NUM
cana-5711	214	22	-	-	PUNCT
cana-5711	214	23	133x	133x	NUM
cana-5711	214	24	vol	vol	VERB
cana-5711	214	25	32	32	NUM
cana-5711	214	26	no	no	NOUN
cana-5711	214	27	.	.	PUNCT
cana-5711	215	1	10s	10	NOUN
cana-5711	215	2	(	(	PUNCT
cana-5711	215	3	2025	2025	NUM
cana-5711	215	4	)	)	PUNCT
cana-5711	215	5	2702	2702	NUM
cana-5711	216	1	𝐺	𝐺	NOUN
cana-5711	216	2	=	=	PUNCT
cana-5711	216	3	(	(	PUNCT
cana-5711	216	4	1	1	NUM
cana-5711	216	5	1	1	NUM
cana-5711	216	6	0	0	NUM
cana-5711	216	7	0	0	NUM
cana-5711	216	8	𝑢	𝑢	NOUN
cana-5711	216	9	+	+	NOUN
cana-5711	216	10	1	1	NUM
cana-5711	216	11	𝑢	𝑢	NOUN
cana-5711	216	12	𝑢𝑣	𝑢𝑣	NOUN
cana-5711	216	13	+	+	X
cana-5711	216	14	𝑣	𝑣	ADP
cana-5711	216	15	+	+	NUM
cana-5711	216	16	𝑢	𝑢	X
cana-5711	216	17	+	+	NOUN
cana-5711	216	18	1	1	NUM
cana-5711	216	19	𝑣	𝑣	X
cana-5711	216	20	+	+	NOUN
cana-5711	216	21	1	1	NUM
cana-5711	216	22	0	0	NUM
cana-5711	216	23	0	0	NUM
cana-5711	216	24	1	1	NUM
cana-5711	216	25	1	1	NUM
cana-5711	216	26	0	0	NUM
cana-5711	216	27	𝑢	𝑢	NOUN
cana-5711	216	28	+	+	NOUN
cana-5711	216	29	1	1	NUM
cana-5711	216	30	𝑢𝑣	𝑢𝑣	NOUN
cana-5711	216	31	+	+	NOUN
cana-5711	216	32	𝑣	𝑣	ADP
cana-5711	216	33	𝑣	𝑣	X
cana-5711	216	34	+	+	NOUN
cana-5711	216	35	𝑢	𝑢	X
cana-5711	216	36	0	0	NUM
cana-5711	216	37	0	0	NUM
cana-5711	216	38	0	0	NUM
cana-5711	216	39	0	0	NUM
cana-5711	216	40	0	0	NUM
cana-5711	216	41	0	0	NUM
cana-5711	217	1	𝑣	𝑣	DET
cana-5711	217	2	+	+	NOUN
cana-5711	217	3	1	1	NUM
cana-5711	217	4	𝑣	𝑣	NOUN
cana-5711	217	5	)	)	PUNCT
cana-5711	217	6	=	=	PUNCT
cana-5711	218	1	[	[	X
cana-5711	218	2	gp	gp	X
cana-5711	218	3	|	|	INTJ
cana-5711	218	4	(	(	PUNCT
cana-5711	218	5	gq	gq	NOUN
cana-5711	218	6	=	=	PUNCT
cana-5711	218	7	r	r	NOUN
cana-5711	218	8	|	|	NOUN
cana-5711	218	9	s	s	NOUN
cana-5711	218	10	)	)	PUNCT
cana-5711	218	11	]	]	PUNCT
cana-5711	218	12	.	.	PUNCT
cana-5711	219	1	then	then	ADV
cana-5711	219	2	clearly	clearly	ADV
cana-5711	219	3	,	,	PUNCT
cana-5711	219	4	gp	gp	NOUN
cana-5711	219	5	generates	generate	VERB
cana-5711	219	6	a	a	DET
cana-5711	219	7	self	self	NOUN
cana-5711	219	8	-	-	PUNCT
cana-5711	219	9	orthogonal	orthogonal	ADJ
cana-5711	219	10	code	code	NOUN
cana-5711	219	11	cp	cp	INTJ
cana-5711	219	12	and	and	CCONJ
cana-5711	219	13	the	the	DET
cana-5711	219	14	set	set	NOUN
cana-5711	219	15	of	of	ADP
cana-5711	219	16	all	all	DET
cana-5711	219	17	row	row	NOUN
cana-5711	219	18	vectors	vector	NOUN
cana-5711	219	19	of	of	ADP
cana-5711	219	20	gq	gq	PROPN
cana-5711	219	21	are	be	AUX
cana-5711	219	22	q	q	ADJ
cana-5711	219	23	-	-	PUNCT
cana-5711	219	24	linearly	linearly	ADV
cana-5711	219	25	independent	independent	ADJ
cana-5711	219	26	.	.	PUNCT
cana-5711	220	1	the	the	DET
cana-5711	220	2	gray	gray	ADJ
cana-5711	220	3	image𝜙(𝐶𝑞)of	image𝜙(𝐶𝑞)of	PROPN
cana-5711	220	4	cq	cq	PROPN
cana-5711	220	5	is	be	AUX
cana-5711	220	6	a	a	DET
cana-5711	220	7	binary	binary	NOUN
cana-5711	220	8	[	[	X
cana-5711	220	9	64	64	NUM
cana-5711	220	10	,	,	PUNCT
cana-5711	220	11	12	12	NUM
cana-5711	220	12	,	,	PUNCT
cana-5711	220	13	25	25	NUM
cana-5711	220	14	]	]	PUNCT
cana-5711	220	15	linear	linear	PROPN
cana-5711	220	16	lcd	lcd	PROPN
cana-5711	220	17	code	code	PROPN
cana-5711	220	18	.	.	PUNCT
cana-5711	221	1	5	5	X
cana-5711	221	2	.	.	X
cana-5711	221	3	weight	weight	NOUN
cana-5711	221	4	enumerators	enumerator	NOUN
cana-5711	221	5	and	and	CCONJ
cana-5711	221	6	macwilliams	macwilliam	NOUN
cana-5711	221	7	identities	identity	NOUN
cana-5711	221	8	in	in	ADP
cana-5711	221	9	this	this	DET
cana-5711	221	10	section	section	NOUN
cana-5711	221	11	,	,	PUNCT
cana-5711	221	12	we	we	PRON
cana-5711	221	13	present	present	VERB
cana-5711	221	14	the	the	DET
cana-5711	221	15	weight	weight	NOUN
cana-5711	221	16	enumerators	enumerator	NOUN
cana-5711	221	17	of	of	ADP
cana-5711	221	18	some	some	DET
cana-5711	221	19	ℤ2q	ℤ2q	PROPN
cana-5711	221	20	-	-	PUNCT
cana-5711	221	21	additive	additive	ADJ
cana-5711	221	22	codes	code	NOUN
cana-5711	221	23	and	and	CCONJ
cana-5711	221	24	discuss	discuss	VERB
cana-5711	221	25	related	related	ADJ
cana-5711	221	26	results	result	NOUN
cana-5711	221	27	.	.	PUNCT
cana-5711	222	1	5	5	NUM
cana-5711	222	2	.	.	SYM
cana-5711	222	3	1	1	NUM
cana-5711	222	4	.	.	X
cana-5711	222	5	complete	complete	ADJ
cana-5711	222	6	weight	weight	NOUN
cana-5711	222	7	enumerators	enumerator	NOUN
cana-5711	222	8	and	and	CCONJ
cana-5711	222	9	macwilliams	macwilliam	NOUN
cana-5711	222	10	identity	identity	NOUN
cana-5711	222	11	we	we	PRON
cana-5711	222	12	arrange	arrange	VERB
cana-5711	222	13	the	the	DET
cana-5711	222	14	elements	element	NOUN
cana-5711	222	15	of	of	ADP
cana-5711	222	16	ℤ2q	ℤ2q	PROPN
cana-5711	222	17	in	in	ADP
cana-5711	222	18	a	a	DET
cana-5711	222	19	fixed	fix	VERB
cana-5711	222	20	order	order	NOUN
cana-5711	222	21	as	as	SCONJ
cana-5711	222	22	follows	follow	VERB
cana-5711	222	23	and	and	CCONJ
cana-5711	222	24	denote	denote	VERB
cana-5711	222	25	them	they	PRON
cana-5711	222	26	as	as	ADP
cana-5711	222	27	{	{	PUNCT
cana-5711	222	28	f1	f1	NOUN
cana-5711	222	29	,	,	PUNCT
cana-5711	222	30	f2	f2	PROPN
cana-5711	222	31	,	,	PUNCT
cana-5711	222	32	f3	f3	NOUN
cana-5711	222	33	,	,	PUNCT
cana-5711	222	34	.	.	PUNCT
cana-5711	222	35	.	.	PUNCT
cana-5711	223	1	.	.	PUNCT
cana-5711	224	1	,	,	PUNCT
cana-5711	224	2	f128	f128	PROPN
cana-5711	224	3	}	}	PUNCT
cana-5711	224	4	:	:	PUNCT
cana-5711	225	1	ℤ2q	ℤ2q	PROPN
cana-5711	225	2	=	=	PRON
cana-5711	225	3	{	{	PUNCT
cana-5711	225	4	(	(	PUNCT
cana-5711	225	5	0	0	NUM
cana-5711	225	6	,	,	PUNCT
cana-5711	225	7	0	0	NUM
cana-5711	225	8	,	,	PUNCT
cana-5711	225	9	0	0	NUM
cana-5711	225	10	)	)	PUNCT
cana-5711	225	11	,	,	PUNCT
cana-5711	225	12	(	(	PUNCT
cana-5711	225	13	0	0	NUM
cana-5711	225	14	,	,	PUNCT
cana-5711	225	15	0	0	NUM
cana-5711	225	16	,	,	PUNCT
cana-5711	225	17	1	1	NUM
cana-5711	225	18	)	)	PUNCT
cana-5711	225	19	,	,	PUNCT
cana-5711	225	20	(	(	PUNCT
cana-5711	225	21	0	0	NUM
cana-5711	225	22	,	,	PUNCT
cana-5711	225	23	0	0	NUM
cana-5711	225	24	,	,	PUNCT
cana-5711	225	25	u	u	NOUN
cana-5711	225	26	)	)	PUNCT
cana-5711	225	27	,	,	PUNCT
cana-5711	225	28	(	(	PUNCT
cana-5711	225	29	0	0	NUM
cana-5711	225	30	,	,	PUNCT
cana-5711	225	31	0	0	NUM
cana-5711	225	32	,	,	PUNCT
cana-5711	225	33	v	v	NOUN
cana-5711	225	34	)	)	PUNCT
cana-5711	225	35	,	,	PUNCT
cana-5711	225	36	(	(	PUNCT
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cana-5711	225	973	1	1	NUM
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cana-5711	225	975	1	1	NUM
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cana-5711	225	979	uv	uv	NOUN
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cana-5711	225	983	1	1	NUM
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cana-5711	225	985	1	1	NUM
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cana-5711	225	995	1	1	NUM
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cana-5711	225	997	1	1	NUM
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cana-5711	225	1000	+	+	NUM
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cana-5711	225	1037	v	v	NOUN
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cana-5711	225	1049	1	1	NUM
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cana-5711	225	1079	1	1	NUM
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cana-5711	225	1089	1	1	NUM
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cana-5711	225	1091	u	u	NOUN
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cana-5711	225	1093	u	u	NOUN
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cana-5711	225	1097	,	,	PUNCT
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cana-5711	225	1099	1	1	NUM
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cana-5711	225	1102	,	,	PUNCT
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cana-5711	225	1104	+	+	CCONJ
cana-5711	225	1105	uv	uv	NOUN
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cana-5711	225	1107	,	,	PUNCT
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cana-5711	225	1109	1	1	NUM
cana-5711	225	1110	,	,	PUNCT
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cana-5711	225	1112	,	,	PUNCT
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cana-5711	225	1117	uv	uv	NOUN
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cana-5711	225	1119	,	,	PUNCT
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cana-5711	225	1122	,	,	PUNCT
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cana-5711	225	1124	,	,	PUNCT
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cana-5711	225	1131	,	,	PUNCT
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cana-5711	225	1140	+	+	NOUN
cana-5711	225	1141	uv	uv	NOUN
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cana-5711	225	1143	,	,	PUNCT
cana-5711	225	1144	(	(	PUNCT
cana-5711	225	1145	1	1	NUM
cana-5711	225	1146	,	,	PUNCT
cana-5711	225	1147	u	u	NOUN
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cana-5711	225	1149	1	1	NUM
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cana-5711	225	1152	+	+	CCONJ
cana-5711	225	1153	uv	uv	NOUN
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cana-5711	225	1155	,	,	PUNCT
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cana-5711	225	1159	u	u	NOUN
cana-5711	225	1160	,	,	PUNCT
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cana-5711	225	1165	v	v	NOUN
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cana-5711	225	1167	uv	uv	NOUN
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cana-5711	225	1169	,	,	PUNCT
cana-5711	225	1170	(	(	PUNCT
cana-5711	225	1171	1	1	NUM
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cana-5711	225	1173	1	1	NUM
cana-5711	225	1174	+	+	NUM
cana-5711	225	1175	u	u	NOUN
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cana-5711	225	1179	,	,	PUNCT
cana-5711	225	1180	(	(	PUNCT
cana-5711	225	1181	1	1	NUM
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cana-5711	225	1183	1	1	NUM
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cana-5711	225	1187	1	1	NUM
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cana-5711	225	1189	,	,	PUNCT
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cana-5711	225	1191	1	1	NUM
cana-5711	225	1192	,	,	PUNCT
cana-5711	225	1193	1	1	NUM
cana-5711	225	1194	+	+	NUM
cana-5711	225	1195	u	u	NOUN
cana-5711	225	1196	,	,	PUNCT
cana-5711	225	1197	u	u	NOUN
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cana-5711	225	1199	,	,	PUNCT
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cana-5711	225	1201	1	1	NUM
cana-5711	225	1202	,	,	PUNCT
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cana-5711	225	1204	+	+	NUM
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cana-5711	225	1206	,	,	PUNCT
cana-5711	225	1207	v	v	NOUN
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cana-5711	225	1209	,	,	PUNCT
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cana-5711	225	1231	,	,	PUNCT
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cana-5711	225	1255	,	,	PUNCT
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cana-5711	225	1267	,	,	PUNCT
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cana-5711	225	1275	u	u	NOUN
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cana-5711	225	1279	,	,	PUNCT
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cana-5711	225	1281	1	1	NUM
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cana-5711	225	1283	1	1	NUM
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cana-5711	225	1288	+	+	CCONJ
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cana-5711	225	1291	,	,	PUNCT
cana-5711	225	1292	(	(	PUNCT
cana-5711	225	1293	1	1	NUM
cana-5711	225	1294	,	,	PUNCT
cana-5711	225	1295	1	1	NUM
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cana-5711	225	1299	u	u	NOUN
cana-5711	225	1300	+	+	X
cana-5711	225	1301	v	v	X
cana-5711	225	1302	+	+	CCONJ
cana-5711	225	1303	uv	uv	NOUN
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cana-5711	225	1305	,	,	PUNCT
cana-5711	225	1306	(	(	PUNCT
cana-5711	225	1307	1	1	NUM
cana-5711	225	1308	,	,	PUNCT
cana-5711	225	1309	1	1	NUM
cana-5711	225	1310	+	+	NUM
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cana-5711	225	1319	,	,	PUNCT
cana-5711	225	1320	(	(	PUNCT
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cana-5711	225	1322	,	,	PUNCT
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cana-5711	225	1333	,	,	PUNCT
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cana-5711	225	1335	1	1	NUM
cana-5711	225	1336	,	,	PUNCT
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cana-5711	225	1344	+	+	CCONJ
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cana-5711	225	1347	,	,	PUNCT
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cana-5711	225	1352	+	+	NUM
cana-5711	225	1353	u	u	NOUN
cana-5711	225	1354	,	,	PUNCT
cana-5711	225	1355	1	1	NUM
cana-5711	225	1356	+	+	NUM
cana-5711	225	1357	u	u	NOUN
cana-5711	225	1358	+	+	X
cana-5711	225	1359	v	v	NOUN
cana-5711	225	1360	+	+	CCONJ
cana-5711	225	1361	uv	uv	NOUN
cana-5711	225	1362	)	)	PUNCT
cana-5711	225	1363	}	}	PUNCT
cana-5711	225	1364	.	.	PUNCT
cana-5711	226	1	the	the	DET
cana-5711	226	2	complete	complete	ADJ
cana-5711	226	3	weight	weight	NOUN
cana-5711	226	4	enumerator	enumerator	NOUN
cana-5711	226	5	of	of	ADP
cana-5711	226	6	an	an	DET
cana-5711	226	7	additive	additive	ADJ
cana-5711	226	8	code	code	NOUN
cana-5711	226	9	c	c	NOUN
cana-5711	226	10	over	over	ADP
cana-5711	226	11	ℤ2q	ℤ2q	PROPN
cana-5711	226	12	is	be	AUX
cana-5711	226	13	defined	define	VERB
cana-5711	226	14	by	by	ADP
cana-5711	226	15	cwec	cwec	NOUN
cana-5711	226	16	(	(	PUNCT
cana-5711	226	17	x1	x1	INTJ
cana-5711	226	18	,	,	PUNCT
cana-5711	226	19	x2	x2	INTJ
cana-5711	226	20	,	,	PUNCT
cana-5711	226	21	.	.	PUNCT
cana-5711	226	22	.	.	PUNCT
cana-5711	227	1	.	.	PUNCT
cana-5711	228	1	,	,	PUNCT
cana-5711	228	2	x128	x128	PROPN
cana-5711	228	3	)	)	PUNCT
cana-5711	229	1	=	=	PROPN
cana-5711	229	2	∑	∑	PUNCT
cana-5711	229	3	𝑥1	𝑥1	NOUN
cana-5711	229	4	𝑤𝑓1	𝑤𝑓1	NOUN
cana-5711	229	5	(	(	PUNCT
cana-5711	229	6	𝑐	𝑐	NOUN
cana-5711	229	7	)	)	PUNCT
cana-5711	229	8	𝑐∈𝐶	𝑐∈𝐶	NOUN
cana-5711	229	9	𝑥2	𝑥2	NOUN
cana-5711	229	10	𝑤𝑓2	𝑤𝑓2	NOUN
cana-5711	229	11	(	(	PUNCT
cana-5711	229	12	𝑐	𝑐	NOUN
cana-5711	229	13	)	)	PUNCT
cana-5711	229	14	𝑥3	𝑥3	NOUN
cana-5711	229	15	𝑤𝑓3(𝑐	𝑤𝑓3(𝑐	PROPN
cana-5711	229	16	)	)	PUNCT
cana-5711	229	17	.	.	PUNCT
cana-5711	229	18	.	.	PUNCT
cana-5711	229	19	.	.	PUNCT
cana-5711	230	1	𝑥128	𝑥128	NUM
cana-5711	230	2	𝑤𝑓128	𝑤𝑓128	NOUN
cana-5711	230	3	(	(	PUNCT
cana-5711	230	4	𝑐	𝑐	NOUN
cana-5711	230	5	)	)	PUNCT
cana-5711	230	6	(	(	PUNCT
cana-5711	230	7	5.1	5.1	NUM
cana-5711	230	8	)	)	PUNCT
cana-5711	230	9	where	where	SCONJ
cana-5711	230	10	𝑤𝑓𝑖	𝑤𝑓𝑖	PROPN
cana-5711	230	11	(	(	PUNCT
cana-5711	230	12	𝑐)=|{j	𝑐)=|{j	ADV
cana-5711	230	13	|	|	ADV
cana-5711	230	14	cj	cj	VERB
cana-5711	231	1	=	=	SYM
cana-5711	231	2	f	f	X
cana-5711	232	1	i	i	PRON
cana-5711	232	2	,	,	PUNCT
cana-5711	232	3	1	1	NUM
cana-5711	232	4	≤	≤	NUM
cana-5711	232	5	j	j	PROPN
cana-5711	232	6	≤	≤	PROPN
cana-5711	232	7	n}|	n}|	NOUN
cana-5711	232	8	for	for	ADP
cana-5711	232	9	1	1	NUM
cana-5711	232	10	≤	≤	NUM
cana-5711	232	11	i	i	PRON
cana-5711	232	12	≤	≤	NOUN
cana-5711	232	13	128	128	NUM
cana-5711	232	14	and	and	CCONJ
cana-5711	232	15	c	c	NOUN
cana-5711	232	16	=	=	SYM
cana-5711	232	17	(	(	PUNCT
cana-5711	232	18	c1	c1	PROPN
cana-5711	232	19	,	,	PUNCT
cana-5711	232	20	c2	c2	PROPN
cana-5711	232	21	,	,	PUNCT
cana-5711	232	22	c3	c3	PROPN
cana-5711	232	23	,	,	PUNCT
cana-5711	232	24	.	.	PUNCT
cana-5711	232	25	.	.	PUNCT
cana-5711	232	26	.	.	PUNCT
cana-5711	233	1	,	,	PUNCT
cana-5711	233	2	cn	cn	PROPN
cana-5711	233	3	)	)	PUNCT
cana-5711	233	4	∈c	∈c	PROPN
cana-5711	233	5	.	.	PUNCT
cana-5711	234	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	234	2	communications	communication	NOUN
cana-5711	234	3	on	on	ADP
cana-5711	234	4	applied	apply	VERB
cana-5711	234	5	nonlinear	nonlinear	ADJ
cana-5711	234	6	analysis	analysis	NOUN
cana-5711	234	7	issn	issn	NOUN
cana-5711	234	8	:	:	PUNCT
cana-5711	234	9	1074	1074	NUM
cana-5711	234	10	-	-	PUNCT
cana-5711	234	11	133x	133x	NUM
cana-5711	234	12	vol	vol	VERB
cana-5711	234	13	32	32	NUM
cana-5711	234	14	no	no	NOUN
cana-5711	234	15	.	.	PUNCT
cana-5711	235	1	10s	10	NOUN
cana-5711	235	2	(	(	PUNCT
cana-5711	235	3	2025	2025	NUM
cana-5711	235	4	)	)	PUNCT
cana-5711	235	5	2703	2703	NUM
cana-5711	235	6	remark	remark	VERB
cana-5711	235	7	5.1	5.1	NUM
cana-5711	235	8	.	.	PUNCT
cana-5711	236	1	note	note	VERB
cana-5711	236	2	that	that	DET
cana-5711	236	3	cwec	cwec	NOUN
cana-5711	236	4	(	(	PUNCT
cana-5711	236	5	x1	x1	INTJ
cana-5711	236	6	,	,	PUNCT
cana-5711	236	7	x2	x2	INTJ
cana-5711	236	8	,	,	PUNCT
cana-5711	236	9	.	.	PUNCT
cana-5711	236	10	.	.	PUNCT
cana-5711	237	1	.	.	PUNCT
cana-5711	238	1	,	,	PUNCT
cana-5711	238	2	x128	x128	PROPN
cana-5711	238	3	)	)	PUNCT
cana-5711	238	4	is	be	AUX
cana-5711	238	5	a	a	DET
cana-5711	238	6	homogeneous	homogeneous	ADJ
cana-5711	238	7	polynomial	polynomial	NOUN
cana-5711	238	8	.	.	PUNCT
cana-5711	239	1	the	the	DET
cana-5711	239	2	total	total	ADJ
cana-5711	239	3	degree	degree	NOUN
cana-5711	239	4	of	of	ADP
cana-5711	239	5	each	each	DET
cana-5711	239	6	monomial	monomial	NOUN
cana-5711	239	7	in	in	ADP
cana-5711	239	8	cwec	cwec	PROPN
cana-5711	239	9	(	(	PUNCT
cana-5711	239	10	x1	x1	INTJ
cana-5711	239	11	,	,	PUNCT
cana-5711	239	12	x2	x2	INTJ
cana-5711	239	13	,	,	PUNCT
cana-5711	239	14	.	.	PUNCT
cana-5711	239	15	.	.	PUNCT
cana-5711	239	16	.	.	PUNCT
cana-5711	240	1	,	,	PUNCT
cana-5711	240	2	x128	x128	PROPN
cana-5711	240	3	)	)	PUNCT
cana-5711	240	4	is	be	AUX
cana-5711	240	5	n.	n.	ADJ
cana-5711	240	6	the	the	DET
cana-5711	240	7	term	term	NOUN
cana-5711	240	8	xn	xn	PROPN
cana-5711	240	9	1	1	NUM
cana-5711	240	10	always	always	ADV
cana-5711	240	11	appears	appear	VERB
cana-5711	240	12	in	in	ADP
cana-5711	240	13	cwec	cwec	NOUN
cana-5711	240	14	(	(	PUNCT
cana-5711	240	15	x1	x1	INTJ
cana-5711	240	16	,	,	PUNCT
cana-5711	240	17	x2	x2	INTJ
cana-5711	240	18	,	,	PUNCT
cana-5711	240	19	.	.	PUNCT
cana-5711	240	20	.	.	PUNCT
cana-5711	241	1	.	.	PUNCT
cana-5711	242	1	,	,	PUNCT
cana-5711	242	2	x128	x128	PROPN
cana-5711	242	3	)	)	PUNCT
cana-5711	242	4	as	as	ADP
cana-5711	242	5	(	(	PUNCT
cana-5711	242	6	0	0	NUM
cana-5711	242	7	,	,	PUNCT
cana-5711	242	8	0	0	NUM
cana-5711	242	9	,	,	PUNCT
cana-5711	242	10	0	0	NUM
cana-5711	242	11	,	,	PUNCT
cana-5711	242	12	.	.	PUNCT
cana-5711	242	13	.	.	PUNCT
cana-5711	242	14	.	.	PUNCT
cana-5711	243	1	,	,	PUNCT
cana-5711	243	2	0	0	X
cana-5711	243	3	)	)	PUNCT
cana-5711	243	4	is	be	AUX
cana-5711	243	5	a	a	DET
cana-5711	243	6	codeword	codeword	NOUN
cana-5711	243	7	in	in	ADP
cana-5711	243	8	c.	c.	PROPN
cana-5711	243	9	furthermore	furthermore	ADV
cana-5711	243	10	,	,	PUNCT
cana-5711	243	11	note	note	VERB
cana-5711	243	12	that	that	SCONJ
cana-5711	243	13	cwec	cwec	NOUN
cana-5711	243	14	(	(	PUNCT
cana-5711	243	15	1	1	NUM
cana-5711	243	16	,	,	PUNCT
cana-5711	243	17	1	1	NUM
cana-5711	243	18	,	,	PUNCT
cana-5711	243	19	1	1	NUM
cana-5711	243	20	,	,	PUNCT
cana-5711	243	21	.	.	PUNCT
cana-5711	243	22	.	.	PUNCT
cana-5711	244	1	.	.	PUNCT
cana-5711	245	1	,	,	PUNCT
cana-5711	245	2	1	1	X
cana-5711	245	3	)	)	PUNCT
cana-5711	245	4	=	=	PUNCT
cana-5711	245	5	|c|	|c|	PROPN
cana-5711	245	6	and	and	CCONJ
cana-5711	245	7	cwec	cwec	PROPN
cana-5711	245	8	(	(	PUNCT
cana-5711	245	9	a	a	PRON
cana-5711	245	10	,	,	PUNCT
cana-5711	245	11	0	0	NUM
cana-5711	245	12	,	,	PUNCT
cana-5711	245	13	0	0	NUM
cana-5711	245	14	,	,	PUNCT
cana-5711	245	15	.	.	PUNCT
cana-5711	245	16	.	.	PUNCT
cana-5711	246	1	.	.	PUNCT
cana-5711	247	1	,	,	PUNCT
cana-5711	247	2	0	0	X
cana-5711	247	3	)	)	PUNCT
cana-5711	247	4	=	=	SYM
cana-5711	248	1	an	an	X
cana-5711	248	2	.	.	PUNCT
cana-5711	249	1	let	let	VERB
cana-5711	249	2	r	r	PRON
cana-5711	249	3	be	be	AUX
cana-5711	249	4	a	a	DET
cana-5711	249	5	finite	finite	ADJ
cana-5711	249	6	commutative	commutative	ADJ
cana-5711	249	7	ring	ring	NOUN
cana-5711	249	8	with	with	ADP
cana-5711	249	9	unity	unity	NOUN
cana-5711	249	10	.	.	PUNCT
cana-5711	250	1	a	a	DET
cana-5711	250	2	character	character	NOUN
cana-5711	250	3	𝜒	𝜒	NOUN
cana-5711	250	4	of	of	ADP
cana-5711	250	5	r	r	NOUN
cana-5711	250	6	is	be	AUX
cana-5711	250	7	a	a	DET
cana-5711	250	8	group	group	NOUN
cana-5711	250	9	homomorphism	homomorphism	NOUN
cana-5711	250	10	from	from	ADP
cana-5711	250	11	r	r	NOUN
cana-5711	250	12	to	to	ADP
cana-5711	250	13	c	c	NOUN
cana-5711	250	14	*	*	PUNCT
cana-5711	250	15	.	.	PUNCT
cana-5711	251	1	in	in	ADP
cana-5711	251	2	[	[	X
cana-5711	251	3	5	5	NUM
cana-5711	251	4	]	]	PUNCT
cana-5711	251	5	,	,	PUNCT
cana-5711	251	6	the	the	DET
cana-5711	251	7	authors	author	NOUN
cana-5711	251	8	defined	define	VERB
cana-5711	251	9	that	that	SCONJ
cana-5711	251	10	if	if	SCONJ
cana-5711	251	11	r	r	NOUN
cana-5711	251	12	is	be	AUX
cana-5711	251	13	a	a	DET
cana-5711	251	14	frobenius	frobenius	ADJ
cana-5711	251	15	ring	ring	NOUN
cana-5711	251	16	and	and	CCONJ
cana-5711	251	17	𝑅	𝑅	PROPN
cana-5711	251	18	is	be	AUX
cana-5711	251	19	the	the	DET
cana-5711	251	20	character	character	NOUN
cana-5711	251	21	module	module	NOUN
cana-5711	251	22	of	of	ADP
cana-5711	251	23	r	r	NOUN
cana-5711	251	24	such	such	ADJ
cana-5711	251	25	that	that	PRON
cana-5711	251	26	𝑅	𝑅	PROPN
cana-5711	251	27	is	be	AUX
cana-5711	251	28	r	r	NOUN
cana-5711	251	29	-	-	PUNCT
cana-5711	251	30	module	module	NOUN
cana-5711	251	31	isomorphic	isomorphic	ADJ
cana-5711	251	32	to	to	ADP
cana-5711	251	33	r	r	NOUN
cana-5711	251	34	,	,	PUNCT
cana-5711	251	35	and	and	CCONJ
cana-5711	251	36	if	if	SCONJ
cana-5711	251	37	γ	γ	X
cana-5711	251	38	:	:	PUNCT
cana-5711	251	39	r→	r→	PROPN
cana-5711	251	40	𝑅	𝑅	PROPN
cana-5711	251	41	is	be	AUX
cana-5711	251	42	an	an	DET
cana-5711	251	43	r	r	NOUN
cana-5711	251	44	-	-	PUNCT
cana-5711	251	45	module	module	NOUN
cana-5711	251	46	isomorphism	isomorphism	NOUN
cana-5711	251	47	,	,	PUNCT
cana-5711	251	48	then	then	ADV
cana-5711	251	49	𝜒:=	𝜒:=	PROPN
cana-5711	251	50	γ(1	γ(1	PROPN
cana-5711	251	51	)	)	PUNCT
cana-5711	251	52	is	be	AUX
cana-5711	251	53	said	say	VERB
cana-5711	251	54	to	to	PART
cana-5711	251	55	be	be	AUX
cana-5711	251	56	a	a	DET
cana-5711	251	57	generating	generate	VERB
cana-5711	251	58	character	character	NOUN
cana-5711	251	59	of	of	ADP
cana-5711	251	60	r.	r.	PROPN
cana-5711	251	61	lemma	lemma	PROPN
cana-5711	251	62	5.2	5.2	NUM
cana-5711	251	63	.	.	PUNCT
cana-5711	252	1	[	[	X
cana-5711	252	2	5	5	NUM
cana-5711	252	3	]	]	PUNCT
cana-5711	252	4	let	let	VERB
cana-5711	252	5	𝜒	𝜒	PRON
cana-5711	252	6	be	be	AUX
cana-5711	252	7	a	a	DET
cana-5711	252	8	character	character	NOUN
cana-5711	252	9	of	of	ADP
cana-5711	252	10	a	a	DET
cana-5711	252	11	finite	finite	ADJ
cana-5711	252	12	commutative	commutative	PROPN
cana-5711	252	13	ring	ring	PROPN
cana-5711	252	14	r.	r.	PROPN
cana-5711	252	15	then	then	ADV
cana-5711	252	16	𝜒	𝜒	NOUN
cana-5711	252	17	is	be	AUX
cana-5711	252	18	a	a	DET
cana-5711	252	19	generating	generate	VERB
cana-5711	252	20	character	character	NOUN
cana-5711	252	21	if	if	SCONJ
cana-5711	252	22	and	and	CCONJ
cana-5711	252	23	only	only	ADV
cana-5711	252	24	if	if	SCONJ
cana-5711	252	25	ker	ker	X
cana-5711	252	26	(	(	PUNCT
cana-5711	252	27	𝜒	𝜒	NOUN
cana-5711	252	28	)	)	PUNCT
cana-5711	252	29	contains	contain	VERB
cana-5711	252	30	no	no	DET
cana-5711	252	31	nonzero	nonzero	NOUN
cana-5711	252	32	ideals	ideal	NOUN
cana-5711	252	33	of	of	ADP
cana-5711	252	34	r.	r.	PROPN
cana-5711	252	35	definition	definition	NOUN
cana-5711	252	36	5.3	5.3	NUM
cana-5711	252	37	.	.	PUNCT
cana-5711	253	1	the	the	DET
cana-5711	253	2	generating	generate	VERB
cana-5711	253	3	character	character	NOUN
cana-5711	253	4	:	:	PUNCT
cana-5711	253	5	ℤ2q	ℤ2q	PROPN
cana-5711	253	6	→	→	PUNCT
cana-5711	253	7	c	c	AUX
cana-5711	253	8	*	*	PUNCT
cana-5711	253	9	is	be	AUX
cana-5711	253	10	defined	define	VERB
cana-5711	253	11	as	as	ADP
cana-5711	253	12	𝜒(𝑎	𝜒(𝑎	ADJ
cana-5711	253	13	,	,	PUNCT
cana-5711	253	14	𝑏	𝑏	PROPN
cana-5711	253	15	+	+	SYM
cana-5711	253	16	𝑑	𝑑	NOUN
cana-5711	253	17	,	,	PUNCT
cana-5711	253	18	𝑒	𝑒	ADV
cana-5711	253	19	+	+	PRON
cana-5711	253	20	𝑓	𝑓	PRON
cana-5711	253	21	+	+	X
cana-5711	253	22	𝑔	𝑔	PROPN
cana-5711	253	23	+	+	CCONJ
cana-5711	253	24	ℎ	ℎ	NOUN
cana-5711	253	25	)	)	PUNCT
cana-5711	253	26	=	=	SYM
cana-5711	254	1	(	(	PUNCT
cana-5711	254	2	−1)𝑎+𝑏+𝑑+𝑒+𝑓+𝑔+ℎ.	−1)𝑎+𝑏+𝑑+𝑒+𝑓+𝑔+ℎ.	X
cana-5711	254	3	(	(	PUNCT
cana-5711	254	4	5.2	5.2	NUM
cana-5711	254	5	)	)	PUNCT
cana-5711	254	6	observe	observe	VERB
cana-5711	254	7	that	that	SCONJ
cana-5711	254	8	the	the	DET
cana-5711	254	9	restriction	restriction	NOUN
cana-5711	254	10	of	of	ADP
cana-5711	254	11	𝜒	𝜒	NUM
cana-5711	254	12	to	to	ADP
cana-5711	254	13	every	every	DET
cana-5711	254	14	nonzero	nonzero	NOUN
cana-5711	254	15	ideal	ideal	NOUN
cana-5711	254	16	of	of	ADP
cana-5711	254	17	ℤ2q	ℤ2q	PROPN
cana-5711	254	18	is	be	AUX
cana-5711	254	19	nontrivial	nontrivial	ADJ
cana-5711	254	20	.	.	PUNCT
cana-5711	255	1	therefore	therefore	ADV
cana-5711	255	2	,	,	PUNCT
cana-5711	255	3	by	by	ADP
cana-5711	255	4	lemma	lemma	PROPN
cana-5711	255	5	5.2	5.2	NUM
cana-5711	255	6	,	,	PUNCT
cana-5711	255	7	it	it	PRON
cana-5711	255	8	is	be	AUX
cana-5711	255	9	a	a	DET
cana-5711	255	10	generating	generate	VERB
cana-5711	255	11	character	character	NOUN
cana-5711	255	12	of	of	ADP
cana-5711	255	13	the	the	DET
cana-5711	255	14	ring	ring	NOUN
cana-5711	255	15	ℤ2q	ℤ2q	PROPN
cana-5711	255	16	.	.	PUNCT
cana-5711	256	1	lemma	lemma	PROPN
cana-5711	256	2	5.4	5.4	NUM
cana-5711	256	3	.	.	PUNCT
cana-5711	257	1	for	for	ADP
cana-5711	257	2	a	a	DET
cana-5711	257	3	nonzero	nonzero	NOUN
cana-5711	257	4	ideal	ideal	NOUN
cana-5711	257	5	i	i	PRON
cana-5711	257	6	of	of	ADP
cana-5711	257	7	ℤ2q	ℤ2q	PROPN
cana-5711	257	8	,	,	PUNCT
cana-5711	257	9	we	we	PRON
cana-5711	257	10	have∑	have∑	VERB
cana-5711	257	11	𝜒𝑥∈𝐼	𝜒𝑥∈𝐼	PROPN
cana-5711	257	12	(	(	PUNCT
cana-5711	257	13	𝑥	𝑥	NOUN
cana-5711	257	14	)	)	PUNCT
cana-5711	257	15	=	=	SYM
cana-5711	258	1	0	0	NUM
cana-5711	258	2	where	where	SCONJ
cana-5711	258	3	𝜒	𝜒	NOUN
cana-5711	258	4	is	be	AUX
cana-5711	258	5	defined	define	VERB
cana-5711	258	6	in	in	ADP
cana-5711	258	7	equation	equation	NOUN
cana-5711	258	8	5.2	5.2	NUM
cana-5711	258	9	.	.	PUNCT
cana-5711	259	1	proof	proof	NOUN
cana-5711	259	2	.	.	PUNCT
cana-5711	260	1	suppose	suppose	VERB
cana-5711	260	2	that	that	SCONJ
cana-5711	260	3	i	i	PRON
cana-5711	260	4	is	be	AUX
cana-5711	260	5	an	an	DET
cana-5711	260	6	ideal	ideal	NOUN
cana-5711	260	7	generated	generate	VERB
cana-5711	260	8	by	by	ADP
cana-5711	260	9	(	(	PUNCT
cana-5711	260	10	0	0	NUM
cana-5711	260	11	,	,	PUNCT
cana-5711	260	12	u	u	NOUN
cana-5711	260	13	,	,	PUNCT
cana-5711	260	14	uv	uv	NOUN
cana-5711	260	15	)	)	PUNCT
cana-5711	260	16	.	.	PUNCT
cana-5711	261	1	then	then	ADV
cana-5711	261	2	i	i	PRON
cana-5711	261	3	=	=	PUNCT
cana-5711	261	4	{	{	PUNCT
cana-5711	261	5	(	(	PUNCT
cana-5711	261	6	0	0	NUM
cana-5711	261	7	,	,	PUNCT
cana-5711	261	8	0	0	NUM
cana-5711	261	9	,	,	PUNCT
cana-5711	261	10	0	0	NUM
cana-5711	261	11	)	)	PUNCT
cana-5711	261	12	,	,	PUNCT
cana-5711	261	13	(	(	PUNCT
cana-5711	261	14	0	0	NUM
cana-5711	261	15	,	,	PUNCT
cana-5711	261	16	0	0	NUM
cana-5711	261	17	,	,	PUNCT
cana-5711	261	18	u	u	NOUN
cana-5711	261	19	)	)	PUNCT
cana-5711	261	20	,	,	PUNCT
cana-5711	261	21	(	(	PUNCT
cana-5711	261	22	0	0	NUM
cana-5711	261	23	,	,	PUNCT
cana-5711	261	24	0	0	NUM
cana-5711	261	25	,	,	PUNCT
cana-5711	261	26	v	v	NOUN
cana-5711	261	27	)	)	PUNCT
cana-5711	261	28	,	,	PUNCT
cana-5711	261	29	(	(	PUNCT
cana-5711	261	30	0	0	NUM
cana-5711	261	31	,	,	PUNCT
cana-5711	261	32	0	0	NUM
cana-5711	261	33	,	,	PUNCT
cana-5711	261	34	uv	uv	NOUN
cana-5711	261	35	)	)	PUNCT
cana-5711	261	36	,	,	PUNCT
cana-5711	261	37	(	(	PUNCT
cana-5711	261	38	0	0	NUM
cana-5711	261	39	,	,	PUNCT
cana-5711	261	40	0	0	NUM
cana-5711	261	41	,	,	PUNCT
cana-5711	261	42	u	u	NOUN
cana-5711	261	43	+	+	PROPN
cana-5711	261	44	v	v	NOUN
cana-5711	261	45	)	)	PUNCT
cana-5711	261	46	,	,	PUNCT
cana-5711	261	47	(	(	PUNCT
cana-5711	261	48	0	0	NUM
cana-5711	261	49	,	,	PUNCT
cana-5711	261	50	0	0	NUM
cana-5711	261	51	,	,	PUNCT
cana-5711	261	52	u	u	NOUN
cana-5711	261	53	+	+	NOUN
cana-5711	261	54	uv	uv	NOUN
cana-5711	261	55	)	)	PUNCT
cana-5711	261	56	,	,	PUNCT
cana-5711	261	57	(	(	PUNCT
cana-5711	261	58	0	0	NUM
cana-5711	261	59	,	,	PUNCT
cana-5711	261	60	0	0	NUM
cana-5711	261	61	,	,	PUNCT
cana-5711	261	62	v	v	NOUN
cana-5711	261	63	+	+	CCONJ
cana-5711	261	64	uv	uv	NOUN
cana-5711	261	65	)	)	PUNCT
cana-5711	261	66	,	,	PUNCT
cana-5711	261	67	(	(	PUNCT
cana-5711	261	68	0	0	NUM
cana-5711	261	69	,	,	PUNCT
cana-5711	261	70	0	0	NUM
cana-5711	261	71	,	,	PUNCT
cana-5711	261	72	u	u	NOUN
cana-5711	261	73	+	+	X
cana-5711	261	74	v	v	X
cana-5711	261	75	+	+	CCONJ
cana-5711	261	76	uv	uv	NOUN
cana-5711	261	77	)	)	PUNCT
cana-5711	261	78	,	,	PUNCT
cana-5711	261	79	(	(	PUNCT
cana-5711	261	80	0	0	NUM
cana-5711	261	81	,	,	PUNCT
cana-5711	261	82	u	u	NOUN
cana-5711	261	83	,	,	PUNCT
cana-5711	261	84	0	0	NUM
cana-5711	261	85	)	)	PUNCT
cana-5711	261	86	,	,	PUNCT
cana-5711	261	87	(	(	PUNCT
cana-5711	261	88	0	0	NUM
cana-5711	261	89	,	,	PUNCT
cana-5711	261	90	u	u	NOUN
cana-5711	261	91	,	,	PUNCT
cana-5711	261	92	u	u	NOUN
cana-5711	261	93	)	)	PUNCT
cana-5711	261	94	,	,	PUNCT
cana-5711	261	95	(	(	PUNCT
cana-5711	261	96	0	0	NUM
cana-5711	261	97	,	,	PUNCT
cana-5711	261	98	u	u	NOUN
cana-5711	261	99	,	,	PUNCT
cana-5711	261	100	v	v	NOUN
cana-5711	261	101	)	)	PUNCT
cana-5711	261	102	,	,	PUNCT
cana-5711	261	103	(	(	PUNCT
cana-5711	261	104	0	0	NUM
cana-5711	261	105	,	,	PUNCT
cana-5711	261	106	u	u	NOUN
cana-5711	261	107	,	,	PUNCT
cana-5711	261	108	uv	uv	NOUN
cana-5711	261	109	)	)	PUNCT
cana-5711	261	110	,	,	PUNCT
cana-5711	261	111	(	(	PUNCT
cana-5711	261	112	0	0	NUM
cana-5711	261	113	,	,	PUNCT
cana-5711	261	114	u	u	NOUN
cana-5711	261	115	,	,	PUNCT
cana-5711	261	116	u	u	NOUN
cana-5711	261	117	+	+	PROPN
cana-5711	261	118	v	v	NOUN
cana-5711	261	119	)	)	PUNCT
cana-5711	261	120	,	,	PUNCT
cana-5711	261	121	(	(	PUNCT
cana-5711	261	122	0	0	NUM
cana-5711	261	123	,	,	PUNCT
cana-5711	261	124	u	u	NOUN
cana-5711	261	125	,	,	PUNCT
cana-5711	261	126	u	u	NOUN
cana-5711	261	127	+	+	NOUN
cana-5711	261	128	uv	uv	NOUN
cana-5711	261	129	)	)	PUNCT
cana-5711	261	130	,	,	PUNCT
cana-5711	261	131	(	(	PUNCT
cana-5711	261	132	0	0	NUM
cana-5711	261	133	,	,	PUNCT
cana-5711	261	134	u	u	NOUN
cana-5711	261	135	,	,	PUNCT
cana-5711	261	136	v	v	X
cana-5711	261	137	+	+	CCONJ
cana-5711	261	138	uv	uv	NOUN
cana-5711	261	139	)	)	PUNCT
cana-5711	261	140	,	,	PUNCT
cana-5711	261	141	(	(	PUNCT
cana-5711	261	142	0	0	NUM
cana-5711	261	143	,	,	PUNCT
cana-5711	261	144	u	u	NOUN
cana-5711	261	145	,	,	PUNCT
cana-5711	261	146	u	u	NOUN
cana-5711	261	147	+	+	X
cana-5711	261	148	v	v	X
cana-5711	261	149	+	+	CCONJ
cana-5711	261	150	uv	uv	NOUN
cana-5711	261	151	)	)	PUNCT
cana-5711	261	152	}	}	PUNCT
cana-5711	261	153	is	be	AUX
cana-5711	261	154	a	a	DET
cana-5711	261	155	maximal	maximal	ADJ
cana-5711	261	156	ideal	ideal	NOUN
cana-5711	261	157	of	of	ADP
cana-5711	261	158	ℤ2q	ℤ2q	PROPN
cana-5711	261	159	.	.	PUNCT
cana-5711	262	1	observe	observe	VERB
cana-5711	262	2	that	that	SCONJ
cana-5711	262	3	,	,	PUNCT
cana-5711	262	4	∑𝜒	∑𝜒	PROPN
cana-5711	262	5	𝑥∈𝐼	𝑥∈𝐼	ADJ
cana-5711	262	6	(	(	PUNCT
cana-5711	262	7	𝑥	𝑥	NOUN
cana-5711	262	8	)	)	PUNCT
cana-5711	262	9	=	=	SYM
cana-5711	262	10	1	1	NUM
cana-5711	262	11	+	+	CCONJ
cana-5711	262	12	(	(	PUNCT
cana-5711	262	13	−1	−1	NOUN
cana-5711	262	14	)	)	PUNCT
cana-5711	262	15	+	+	CCONJ
cana-5711	262	16	(	(	PUNCT
cana-5711	262	17	−1	−1	NOUN
cana-5711	262	18	)	)	PUNCT
cana-5711	262	19	+	+	CCONJ
cana-5711	262	20	(	(	PUNCT
cana-5711	262	21	−1	−1	NOUN
cana-5711	262	22	)	)	PUNCT
cana-5711	263	1	+	+	CCONJ
cana-5711	263	2	1	1	NUM
cana-5711	263	3	+	+	NUM
cana-5711	263	4	1	1	NUM
cana-5711	263	5	+	+	NUM
cana-5711	263	6	1	1	NUM
cana-5711	263	7	+	+	CCONJ
cana-5711	263	8	(	(	PUNCT
cana-5711	263	9	−1	−1	NOUN
cana-5711	263	10	)	)	PUNCT
cana-5711	264	1	+	+	CCONJ
cana-5711	264	2	(	(	PUNCT
cana-5711	264	3	−1	−1	NOUN
cana-5711	264	4	)	)	PUNCT
cana-5711	265	1	+	+	CCONJ
cana-5711	265	2	1	1	NUM
cana-5711	265	3	+	+	NUM
cana-5711	265	4	1	1	NUM
cana-5711	265	5	+	+	NUM
cana-5711	265	6	1	1	NUM
cana-5711	265	7	+	+	CCONJ
cana-5711	265	8	(	(	PUNCT
cana-5711	265	9	−1	−1	NOUN
cana-5711	265	10	)	)	PUNCT
cana-5711	266	1	+	+	CCONJ
cana-5711	266	2	(	(	PUNCT
cana-5711	266	3	−1	−1	NOUN
cana-5711	266	4	)	)	PUNCT
cana-5711	267	1	+	+	CCONJ
cana-5711	267	2	(	(	PUNCT
cana-5711	267	3	−1	−1	NOUN
cana-5711	267	4	)	)	PUNCT
cana-5711	268	1	+	+	CCONJ
cana-5711	268	2	1	1	NUM
cana-5711	268	3	=	=	SYM
cana-5711	268	4	0	0	NUM
cana-5711	268	5	.	.	PUNCT
cana-5711	269	1	similarly	similarly	ADV
cana-5711	269	2	,	,	PUNCT
cana-5711	269	3	we	we	PRON
cana-5711	269	4	can	can	AUX
cana-5711	269	5	verify	verify	VERB
cana-5711	269	6	the	the	DET
cana-5711	269	7	equation	equation	NOUN
cana-5711	269	8	if	if	SCONJ
cana-5711	269	9	i	i	PRON
cana-5711	269	10	is	be	AUX
cana-5711	269	11	replaced	replace	VERB
cana-5711	269	12	by	by	ADP
cana-5711	269	13	any	any	DET
cana-5711	269	14	other	other	ADJ
cana-5711	269	15	nonzero	nonzero	NOUN
cana-5711	269	16	ideal	ideal	NOUN
cana-5711	269	17	of	of	ADP
cana-5711	269	18	ℤ2q	ℤ2q	PROPN
cana-5711	269	19	.	.	PUNCT
cana-5711	270	1	suppose	suppose	VERB
cana-5711	270	2	that	that	SCONJ
cana-5711	270	3	𝑇	𝑇	PROPN
cana-5711	270	4	=	=	PUNCT
cana-5711	271	1	[	[	X
cana-5711	271	2	𝑡𝑖,𝑗]128×128	𝑡𝑖,𝑗]128×128	NOUN
cana-5711	271	3	is	be	AUX
cana-5711	271	4	a	a	DET
cana-5711	271	5	matrix	matrix	NOUN
cana-5711	271	6	such	such	ADJ
cana-5711	271	7	that	that	SCONJ
cana-5711	271	8	𝑡𝑖,𝑗	𝑡𝑖,𝑗	PRON
cana-5711	271	9	=	=	SYM
cana-5711	271	10	𝜒(𝑓𝑖,𝑗	𝜒(𝑓𝑖,𝑗	NOUN
cana-5711	271	11	)	)	PUNCT
cana-5711	271	12	,	,	PUNCT
cana-5711	271	13	where	where	SCONJ
cana-5711	271	14	fi	fi	NOUN
cana-5711	271	15	,	,	PUNCT
cana-5711	271	16	fj	fj	PROPN
cana-5711	271	17	∈	∈	PROPN
cana-5711	271	18	ℤ2q	ℤ2q	PROPN
cana-5711	271	19	for	for	ADP
cana-5711	271	20	1	1	NUM
cana-5711	271	21	≤	≤	NOUN
cana-5711	271	22	i	i	PRON
cana-5711	271	23	,	,	PUNCT
cana-5711	271	24	j	j	PROPN
cana-5711	271	25	≤	≤	PROPN
cana-5711	271	26	128	128	NUM
cana-5711	271	27	,	,	PUNCT
cana-5711	271	28	and	and	CCONJ
cana-5711	271	29	𝜒	𝜒	X
cana-5711	271	30	is	be	AUX
cana-5711	271	31	the	the	DET
cana-5711	271	32	generating	generate	VERB
cana-5711	271	33	character	character	NOUN
cana-5711	271	34	defined	define	VERB
cana-5711	271	35	in	in	ADP
cana-5711	271	36	equation	equation	NOUN
cana-5711	271	37	5.2	5.2	NUM
cana-5711	271	38	.	.	PUNCT
cana-5711	272	1	then	then	ADV
cana-5711	272	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	272	3	communications	communication	NOUN
cana-5711	272	4	on	on	ADP
cana-5711	272	5	applied	apply	VERB
cana-5711	272	6	nonlinear	nonlinear	ADJ
cana-5711	272	7	analysis	analysis	NOUN
cana-5711	272	8	issn	issn	NOUN
cana-5711	272	9	:	:	PUNCT
cana-5711	272	10	1074	1074	NUM
cana-5711	272	11	-	-	PUNCT
cana-5711	272	12	133x	133x	NUM
cana-5711	272	13	vol	vol	VERB
cana-5711	272	14	32	32	NUM
cana-5711	272	15	no	no	NOUN
cana-5711	272	16	.	.	PUNCT
cana-5711	273	1	10s	10	NOUN
cana-5711	273	2	(	(	PUNCT
cana-5711	273	3	2025	2025	NUM
cana-5711	273	4	)	)	PUNCT
cana-5711	273	5	2704	2704	NUM
cana-5711	273	6	𝑇	𝑇	PROPN
cana-5711	273	7	=	=	SYM
cana-5711	273	8	[	[	PUNCT
cana-5711	273	9	𝐴	𝐴	NOUN
cana-5711	273	10	𝐴	𝐴	PROPN
cana-5711	273	11	𝐴	𝐴	NOUN
cana-5711	273	12	𝐴	𝐴	NOUN
cana-5711	273	13	𝐴	𝐴	NOUN
cana-5711	273	14	𝐴	𝐴	NOUN
cana-5711	273	15	𝐴	𝐴	NOUN
cana-5711	273	16	𝐴	𝐴	NOUN
cana-5711	273	17	𝐴	𝐴	NOUN
cana-5711	273	18	𝐴	𝐴	NOUN
cana-5711	273	19	𝐴	𝐴	NOUN
cana-5711	273	20	𝐴	𝐴	NOUN
cana-5711	273	21	𝐴	𝐴	NOUN
cana-5711	273	22	𝐴	𝐴	NOUN
cana-5711	273	23	𝐴	𝐴	NOUN
cana-5711	273	24	𝐴	𝐴	NOUN
cana-5711	273	25	𝐴	𝐴	NOUN
cana-5711	273	26	𝐴	𝐴	NOUN
cana-5711	273	27	𝐴	𝐴	NOUN
cana-5711	273	28	𝐴	𝐴	NOUN
cana-5711	273	29	𝐴	𝐴	NOUN
cana-5711	273	30	𝐴	𝐴	NOUN
cana-5711	273	31	𝐴	𝐴	NOUN
cana-5711	273	32	𝐴	𝐴	NOUN
cana-5711	273	33	𝐴	𝐴	NOUN
cana-5711	273	34	𝐴	𝐴	NOUN
cana-5711	273	35	𝐴	𝐴	NOUN
cana-5711	273	36	𝐴	𝐴	NOUN
cana-5711	273	37	𝐴	𝐴	NOUN
cana-5711	273	38	𝐴	𝐴	NOUN
cana-5711	273	39	𝐴	𝐴	NOUN
cana-5711	273	40	𝐴	𝐴	NOUN
cana-5711	273	41	𝐴	𝐴	NOUN
cana-5711	273	42	𝐴	𝐴	NOUN
cana-5711	273	43	𝐴	𝐴	NOUN
cana-5711	273	44	𝐴	𝐴	NOUN
cana-5711	273	45	𝐴	𝐴	NOUN
cana-5711	273	46	𝐴	𝐴	NOUN
cana-5711	273	47	𝐴	𝐴	NOUN
cana-5711	273	48	𝐴	𝐴	NOUN
cana-5711	273	49	𝐴	𝐴	NOUN
cana-5711	273	50	𝐴	𝐴	NOUN
cana-5711	273	51	𝐴	𝐴	NOUN
cana-5711	273	52	𝐴	𝐴	NOUN
cana-5711	273	53	𝐴	𝐴	NOUN
cana-5711	273	54	𝐴	𝐴	NOUN
cana-5711	273	55	𝐴	𝐴	NOUN
cana-5711	273	56	𝐴	𝐴	NOUN
cana-5711	273	57	𝐴	𝐴	NOUN
cana-5711	273	58	𝐴	𝐴	NOUN
cana-5711	273	59	𝐴	𝐴	NOUN
cana-5711	273	60	𝐴	𝐴	NOUN
cana-5711	273	61	𝐴	𝐴	NOUN
cana-5711	273	62	𝐴	𝐴	NOUN
cana-5711	273	63	𝐴	𝐴	NOUN
cana-5711	273	64	𝐴	𝐴	NOUN
cana-5711	273	65	𝐴	𝐴	NOUN
cana-5711	273	66	𝐴	𝐴	NOUN
cana-5711	273	67	𝐴	𝐴	NOUN
cana-5711	273	68	𝐴	𝐴	NOUN
cana-5711	273	69	𝐴	𝐴	NOUN
cana-5711	273	70	𝐴	𝐴	PROPN
cana-5711	273	71	𝐴	𝐴	PROPN
cana-5711	273	72	𝐴	𝐴	PROPN
cana-5711	273	73	]	]	X
cana-5711	273	74	(	(	PUNCT
cana-5711	273	75	5.3	5.3	NUM
cana-5711	273	76	)	)	PUNCT
cana-5711	273	77	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
cana-5711	273	78	,	,	PUNCT
cana-5711	273	79	𝐴	𝐴	PROPN
cana-5711	273	80	=	=	PUNCT
cana-5711	273	81	(	(	PUNCT
cana-5711	273	82	1	1	NUM
cana-5711	273	83	1	1	NUM
cana-5711	273	84	1	1	NUM
cana-5711	273	85	1	1	NUM
cana-5711	273	86	1	1	NUM
cana-5711	273	87	1	1	NUM
cana-5711	273	88	1	1	NUM
cana-5711	273	89	1	1	NUM
cana-5711	273	90	1	1	NUM
cana-5711	273	91	1	1	NUM
cana-5711	273	92	1	1	NUM
cana-5711	273	93	1	1	NUM
cana-5711	273	94	1	1	NUM
cana-5711	273	95	1	1	NUM
cana-5711	273	96	1	1	NUM
cana-5711	273	97	1	1	NUM
cana-5711	273	98	1	1	NUM
cana-5711	273	99	−1	−1	NOUN
cana-5711	273	100	−1	−1	NOUN
cana-5711	273	101	−1	−1	NOUN
cana-5711	273	102	−1	−1	NOUN
cana-5711	273	103	1	1	NUM
cana-5711	273	104	1	1	NUM
cana-5711	273	105	1	1	NUM
cana-5711	273	106	1	1	NUM
cana-5711	273	107	1	1	NUM
cana-5711	273	108	1	1	NUM
cana-5711	273	109	−1	−1	NOUN
cana-5711	273	110	−1	−1	NOUN
cana-5711	273	111	−1	−1	NOUN
cana-5711	273	112	−1	−1	NOUN
cana-5711	273	113	1	1	NUM
cana-5711	273	114	1	1	NUM
cana-5711	273	115	−1	−1	NOUN
cana-5711	273	116	1	1	NUM
cana-5711	273	117	−1	−1	NOUN
cana-5711	273	118	1	1	NUM
cana-5711	273	119	−1	−1	NOUN
cana-5711	273	120	1	1	NUM
cana-5711	273	121	−1	−1	NOUN
cana-5711	273	122	1	1	NUM
cana-5711	273	123	1	1	NUM
cana-5711	273	124	−1	−1	NOUN
cana-5711	273	125	−1	−1	NOUN
cana-5711	273	126	1	1	NUM
cana-5711	273	127	−1	−1	NOUN
cana-5711	273	128	1	1	NUM
cana-5711	273	129	1	1	NUM
cana-5711	273	130	1	1	NUM
cana-5711	273	131	−1	−1	NOUN
cana-5711	273	132	−1	−1	NOUN
cana-5711	273	133	1	1	NUM
cana-5711	273	134	1	1	NUM
cana-5711	273	135	1	1	NUM
cana-5711	273	136	−1	−1	NOUN
cana-5711	273	137	−1	−1	NOUN
cana-5711	273	138	−1	−1	NOUN
cana-5711	273	139	−1	−1	NOUN
cana-5711	273	140	1	1	NUM
cana-5711	273	141	−1	−1	NOUN
cana-5711	273	142	1	1	NUM
cana-5711	273	143	1	1	NUM
cana-5711	273	144	−1	−1	NOUN
cana-5711	273	145	1	1	NUM
cana-5711	273	146	1	1	NUM
cana-5711	273	147	−1	−1	NOUN
cana-5711	273	148	1	1	NUM
cana-5711	273	149	1	1	NUM
cana-5711	273	150	1	1	NUM
cana-5711	273	151	−1	−1	NOUN
cana-5711	273	152	−1	−1	NOUN
cana-5711	273	153	−1	−1	NOUN
cana-5711	273	154	1	1	NUM
cana-5711	273	155	1	1	NUM
cana-5711	273	156	1	1	NUM
cana-5711	273	157	1	1	NUM
cana-5711	273	158	−1	−1	NOUN
cana-5711	273	159	−1	−1	NOUN
cana-5711	273	160	−1	−1	NOUN
cana-5711	273	161	−1	−1	NOUN
cana-5711	273	162	1	1	NUM
cana-5711	273	163	1	1	NUM
cana-5711	273	164	−1	−1	NOUN
cana-5711	273	165	1	1	NUM
cana-5711	273	166	−1	−1	NOUN
cana-5711	273	167	1	1	NUM
cana-5711	273	168	1	1	NUM
cana-5711	273	169	−1	−1	NOUN
cana-5711	273	170	−1	−1	NOUN
cana-5711	273	171	1	1	NUM
cana-5711	273	172	1	1	NUM
cana-5711	273	173	−1	−1	NOUN
cana-5711	273	174	1	1	NUM
cana-5711	273	175	−1	−1	NOUN
cana-5711	273	176	1	1	NUM
cana-5711	273	177	1	1	NUM
cana-5711	273	178	1	1	NUM
cana-5711	273	179	1	1	NUM
cana-5711	273	180	1	1	NUM
cana-5711	273	181	−1	−1	NOUN
cana-5711	273	182	−1	−1	NOUN
cana-5711	273	183	1	1	NUM
cana-5711	273	184	1	1	NUM
cana-5711	273	185	−1	−1	NOUN
cana-5711	273	186	−1	−1	NOUN
cana-5711	273	187	1	1	NUM
cana-5711	273	188	1	1	NUM
cana-5711	273	189	−1	−1	NOUN
cana-5711	273	190	−1	−1	NOUN
cana-5711	273	191	1	1	NUM
cana-5711	273	192	−1	−1	NOUN
cana-5711	273	193	1	1	NUM
cana-5711	273	194	1	1	NUM
cana-5711	273	195	1	1	NUM
cana-5711	273	196	−1	−1	NOUN
cana-5711	273	197	−1	−1	NOUN
cana-5711	273	198	−1	−1	NOUN
cana-5711	273	199	−1	−1	NOUN
cana-5711	273	200	1	1	NUM
cana-5711	273	201	1	1	NUM
cana-5711	273	202	1	1	NUM
cana-5711	273	203	1	1	NUM
cana-5711	273	204	−1	−1	NOUN
cana-5711	273	205	1	1	NUM
cana-5711	273	206	1	1	NUM
cana-5711	273	207	1	1	NUM
cana-5711	273	208	−1	−1	NOUN
cana-5711	273	209	1	1	NUM
cana-5711	273	210	1	1	NUM
cana-5711	273	211	1	1	NUM
cana-5711	273	212	−1	−1	NOUN
cana-5711	273	213	−1	−1	NOUN
cana-5711	273	214	1	1	NUM
cana-5711	273	215	−1	−1	NOUN
cana-5711	273	216	−1	−1	NOUN
cana-5711	273	217	−1	−1	NOUN
cana-5711	273	218	−1	−1	NOUN
cana-5711	273	219	−1	−1	NOUN
cana-5711	273	220	−1	−1	NOUN
cana-5711	273	221	−1	−1	NOUN
cana-5711	273	222	−1	−1	NOUN
cana-5711	273	223	−1	−1	NOUN
cana-5711	273	224	−1	−1	NOUN
cana-5711	273	225	−1	−1	NOUN
cana-5711	273	226	1	1	NUM
cana-5711	273	227	1	1	NUM
cana-5711	273	228	1	1	NUM
cana-5711	273	229	−1	−1	NOUN
cana-5711	273	230	1	1	NUM
cana-5711	273	231	1	1	NUM
cana-5711	273	232	1	1	NUM
cana-5711	273	233	1	1	NUM
cana-5711	273	234	−1	−1	NOUN
cana-5711	273	235	1	1	NUM
cana-5711	273	236	−1	−1	NOUN
cana-5711	273	237	−1	−1	NOUN
cana-5711	273	238	1	1	NUM
cana-5711	273	239	1	1	NUM
cana-5711	273	240	1	1	NUM
cana-5711	273	241	−1	−1	NOUN
cana-5711	273	242	1	1	NUM
cana-5711	273	243	1	1	NUM
cana-5711	273	244	−1	−1	NOUN
cana-5711	273	245	1	1	NUM
cana-5711	273	246	1	1	NUM
cana-5711	273	247	−1	−1	NOUN
cana-5711	273	248	1	1	NUM
cana-5711	273	249	1	1	NUM
cana-5711	273	250	−1	−1	NOUN
cana-5711	273	251	−1	−1	NOUN
cana-5711	273	252	1	1	NUM
cana-5711	273	253	−1	−1	NOUN
cana-5711	273	254	1	1	NUM
cana-5711	273	255	1	1	NUM
cana-5711	273	256	1	1	NUM
cana-5711	273	257	1	1	NUM
cana-5711	273	258	1	1	NUM
cana-5711	273	259	−1	−1	NOUN
cana-5711	273	260	−1	−1	NOUN
cana-5711	273	261	−1	−1	NOUN
cana-5711	273	262	1	1	NUM
cana-5711	273	263	−1	−1	NOUN
cana-5711	273	264	−1	−1	NOUN
cana-5711	273	265	−1	−1	NOUN
cana-5711	273	266	−1	−1	NOUN
cana-5711	273	267	−1	−1	NOUN
cana-5711	273	268	−1	−1	NOUN
cana-5711	273	269	−1	−1	NOUN
cana-5711	273	270	−1	−1	NOUN
cana-5711	273	271	−1	−1	NOUN
cana-5711	273	272	−1	−1	NOUN
cana-5711	273	273	−1	−1	NOUN
cana-5711	273	274	1	1	NUM
cana-5711	273	275	−1	−1	NOUN
cana-5711	273	276	1	1	NUM
cana-5711	273	277	1	1	NUM
cana-5711	273	278	−1	−1	NOUN
cana-5711	273	279	1	1	NUM
cana-5711	273	280	1	1	NUM
cana-5711	273	281	1	1	NUM
cana-5711	273	282	−1	−1	NOUN
cana-5711	273	283	1	1	NUM
cana-5711	273	284	1	1	NUM
cana-5711	273	285	−1	−1	NOUN
cana-5711	273	286	1	1	NUM
cana-5711	273	287	1	1	NUM
cana-5711	273	288	1	1	NUM
cana-5711	273	289	1	1	NUM
cana-5711	273	290	1	1	NUM
cana-5711	273	291	−1	−1	NOUN
cana-5711	273	292	−1	−1	NOUN
cana-5711	273	293	−1	−1	NOUN
cana-5711	273	294	−1	−1	NOUN
cana-5711	273	295	−1	−1	NOUN
cana-5711	273	296	1	1	NUM
cana-5711	273	297	−1	−1	NOUN
cana-5711	273	298	−1	−1	NOUN
cana-5711	273	299	1	1	NUM
cana-5711	273	300	1	1	NUM
cana-5711	273	301	−1	−1	NOUN
cana-5711	273	302	1	1	NUM
cana-5711	273	303	−1	−1	NOUN
cana-5711	273	304	1	1	NUM
cana-5711	273	305	1	1	NUM
cana-5711	273	306	1	1	NUM
cana-5711	273	307	−1	−1	NOUN
cana-5711	273	308	1	1	NUM
cana-5711	273	309	−1	−1	NOUN
cana-5711	273	310	−1	−1	NOUN
cana-5711	273	311	1	1	NUM
cana-5711	273	312	−1	−1	NOUN
cana-5711	273	313	−1	−1	NOUN
cana-5711	273	314	−1	−1	NOUN
cana-5711	273	315	1	1	NUM
cana-5711	273	316	1	1	NUM
cana-5711	273	317	−1	−1	NOUN
cana-5711	273	318	1	1	NUM
cana-5711	273	319	1	1	NUM
cana-5711	273	320	−1	−1	NOUN
cana-5711	273	321	1	1	NUM
cana-5711	273	322	1	1	NUM
cana-5711	273	323	1	1	NUM
cana-5711	273	324	1	1	NUM
cana-5711	273	325	1	1	NUM
cana-5711	273	326	−1	−1	NOUN
cana-5711	273	327	1	1	NUM
cana-5711	273	328	1	1	NUM
cana-5711	273	329	1	1	NUM
cana-5711	273	330	−1	−1	NOUN
cana-5711	273	331	1	1	NUM
cana-5711	273	332	1	1	NUM
cana-5711	273	333	−1	−1	NOUN
cana-5711	273	334	1	1	NUM
cana-5711	273	335	1	1	NUM
cana-5711	273	336	1	1	NUM
cana-5711	273	337	1	1	NUM
cana-5711	273	338	)	)	PUNCT
cana-5711	273	339	for	for	ADP
cana-5711	273	340	further	further	ADJ
cana-5711	273	341	discussion	discussion	NOUN
cana-5711	273	342	,	,	PUNCT
cana-5711	273	343	we	we	PRON
cana-5711	273	344	need	need	VERB
cana-5711	273	345	the	the	DET
cana-5711	273	346	following	follow	VERB
cana-5711	273	347	result	result	NOUN
cana-5711	273	348	from	from	ADP
cana-5711	273	349	[	[	X
cana-5711	273	350	15	15	NUM
cana-5711	273	351	]	]	PUNCT
cana-5711	273	352	.	.	PUNCT
cana-5711	274	1	theorem	theorem	VERB
cana-5711	274	2	5.5	5.5	NUM
cana-5711	274	3	.	.	PUNCT
cana-5711	275	1	if	if	SCONJ
cana-5711	275	2	c	c	PROPN
cana-5711	275	3	is	be	AUX
cana-5711	275	4	an	an	DET
cana-5711	275	5	additive	additive	ADJ
cana-5711	275	6	code	code	NOUN
cana-5711	275	7	of	of	ADP
cana-5711	275	8	length	length	NOUN
cana-5711	275	9	n	n	CCONJ
cana-5711	275	10	over	over	ADP
cana-5711	275	11	ℤ2q	ℤ2q	PROPN
cana-5711	275	12	,	,	PUNCT
cana-5711	275	13	then	then	ADV
cana-5711	275	14	cwec⊥	cwec⊥	VERB
cana-5711	275	15	(	(	PUNCT
cana-5711	275	16	x1	x1	INTJ
cana-5711	275	17	,	,	PUNCT
cana-5711	275	18	x2	x2	PROPN
cana-5711	275	19	,	,	PUNCT
cana-5711	275	20	x3	x3	ADJ
cana-5711	275	21	,	,	PUNCT
cana-5711	275	22	.	.	PUNCT
cana-5711	275	23	.	.	PUNCT
cana-5711	275	24	.	.	PUNCT
cana-5711	276	1	,	,	PUNCT
cana-5711	276	2	x128	x128	PROPN
cana-5711	276	3	)	)	PUNCT
cana-5711	277	1	=	=	SYM
cana-5711	277	2	1	1	NUM
cana-5711	277	3	|𝑐|	|𝑐|	NUM
cana-5711	277	4	cwec	cwec	NOUN
cana-5711	277	5	(	(	PUNCT
cana-5711	277	6	t	t	NOUN
cana-5711	277	7	·	·	PUNCT
cana-5711	277	8	(	(	PUNCT
cana-5711	277	9	x1	x1	INTJ
cana-5711	277	10	,	,	PUNCT
cana-5711	277	11	x2	x2	PROPN
cana-5711	277	12	,	,	PUNCT
cana-5711	277	13	x3	x3	ADJ
cana-5711	277	14	,	,	PUNCT
cana-5711	277	15	.	.	PUNCT
cana-5711	277	16	.	.	PUNCT
cana-5711	278	1	.	.	PUNCT
cana-5711	279	1	,	,	PUNCT
cana-5711	279	2	x128	x128	PROPN
cana-5711	279	3	)	)	PUNCT
cana-5711	279	4	t	t	PROPN
cana-5711	279	5	)	)	PUNCT
cana-5711	279	6	,	,	PUNCT
cana-5711	279	7	where	where	SCONJ
cana-5711	279	8	t	t	PROPN
cana-5711	279	9	is	be	AUX
cana-5711	279	10	denoted	denote	VERB
cana-5711	279	11	by	by	ADP
cana-5711	279	12	the	the	DET
cana-5711	279	13	transpose	transpose	NOUN
cana-5711	279	14	and	and	CCONJ
cana-5711	279	15	t	t	PROPN
cana-5711	279	16	is	be	AUX
cana-5711	279	17	an	an	PRON
cana-5711	279	18	in	in	ADP
cana-5711	279	19	equation	equation	NOUN
cana-5711	279	20	5.3	5.3	NUM
cana-5711	279	21	.	.	PUNCT
cana-5711	279	22	example	example	NOUN
cana-5711	280	1	5.6	5.6	NUM
cana-5711	280	2	.	.	PUNCT
cana-5711	281	1	let	let	VERB
cana-5711	281	2	c	c	PRON
cana-5711	281	3	be	be	AUX
cana-5711	281	4	the	the	DET
cana-5711	281	5	r	r	NOUN
cana-5711	281	6	-	-	PUNCT
cana-5711	281	7	submodule	submodule	NOUN
cana-5711	281	8	of	of	ADP
cana-5711	281	9	(	(	PUNCT
cana-5711	281	10	ℤ2q)2	ℤ2q)2	ADV
cana-5711	281	11	spanned	span	VERB
cana-5711	281	12	by	by	ADP
cana-5711	281	13	{	{	PUNCT
cana-5711	281	14	(	(	PUNCT
cana-5711	281	15	1	1	NUM
cana-5711	281	16	,	,	PUNCT
cana-5711	281	17	0	0	NUM
cana-5711	281	18	;	;	PUNCT
cana-5711	281	19	0	0	NUM
cana-5711	281	20	,	,	PUNCT
cana-5711	281	21	0	0	NUM
cana-5711	281	22	;	;	PUNCT
cana-5711	281	23	0	0	NUM
cana-5711	281	24	,	,	PUNCT
cana-5711	281	25	0	0	NUM
cana-5711	281	26	)	)	PUNCT
cana-5711	281	27	,	,	PUNCT
cana-5711	281	28	(	(	PUNCT
cana-5711	281	29	0	0	NUM
cana-5711	281	30	,	,	PUNCT
cana-5711	281	31	0	0	NUM
cana-5711	281	32	;	;	PUNCT
cana-5711	281	33	0	0	NUM
cana-5711	281	34	,	,	PUNCT
cana-5711	281	35	u	u	NOUN
cana-5711	281	36	;	;	PUNCT
cana-5711	281	37	0	0	NUM
cana-5711	281	38	,	,	PUNCT
cana-5711	281	39	0	0	NUM
cana-5711	281	40	)	)	PUNCT
cana-5711	281	41	,	,	PUNCT
cana-5711	281	42	(	(	PUNCT
cana-5711	281	43	0	0	NUM
cana-5711	281	44	,	,	PUNCT
cana-5711	281	45	0	0	NUM
cana-5711	281	46	;	;	PUNCT
cana-5711	281	47	0	0	NUM
cana-5711	281	48	,	,	PUNCT
cana-5711	281	49	0	0	NUM
cana-5711	281	50	;	;	PUNCT
cana-5711	281	51	0	0	NUM
cana-5711	281	52	,	,	PUNCT
cana-5711	281	53	uv	uv	NOUN
cana-5711	281	54	)	)	PUNCT
cana-5711	281	55	,	,	PUNCT
cana-5711	281	56	(	(	PUNCT
cana-5711	281	57	0	0	NUM
cana-5711	281	58	,	,	PUNCT
cana-5711	281	59	0	0	NUM
cana-5711	281	60	;	;	PUNCT
cana-5711	281	61	0	0	NUM
cana-5711	281	62	,	,	PUNCT
cana-5711	281	63	u	u	NOUN
cana-5711	281	64	;	;	PUNCT
cana-5711	281	65	0	0	NUM
cana-5711	281	66	,	,	PUNCT
cana-5711	281	67	uv	uv	NOUN
cana-5711	281	68	)	)	PUNCT
cana-5711	281	69	}	}	PUNCT
cana-5711	281	70	.	.	PUNCT
cana-5711	282	1	clearly	clearly	ADV
cana-5711	282	2	,	,	PUNCT
cana-5711	282	3	c	c	PROPN
cana-5711	282	4	is	be	AUX
cana-5711	282	5	a	a	DET
cana-5711	282	6	vector	vector	NOUN
cana-5711	282	7	space	space	NOUN
cana-5711	282	8	over	over	ADP
cana-5711	282	9	ℤ2	ℤ2	NOUN
cana-5711	282	10	of	of	ADP
cana-5711	282	11	dimension	dimension	NOUN
cana-5711	282	12	7	7	NUM
cana-5711	282	13	.	.	PUNCT
cana-5711	283	1	then	then	ADV
cana-5711	283	2	the	the	DET
cana-5711	283	3	dual	dual	ADJ
cana-5711	283	4	c⊥	c⊥	NOUN
cana-5711	283	5	of	of	ADP
cana-5711	283	6	the	the	DET
cana-5711	283	7	additive	additive	ADJ
cana-5711	283	8	code	code	NOUN
cana-5711	283	9	c	c	PROPN
cana-5711	283	10	is	be	AUX
cana-5711	283	11	the	the	DET
cana-5711	283	12	r	r	NOUN
cana-5711	283	13	-	-	PUNCT
cana-5711	283	14	submodule	submodule	NOUN
cana-5711	283	15	of	of	ADP
cana-5711	283	16	(	(	PUNCT
cana-5711	283	17	ℤ2q)2	ℤ2q)2	ADV
cana-5711	283	18	spanned	span	VERB
cana-5711	283	19	by	by	ADP
cana-5711	283	20	{	{	PUNCT
cana-5711	283	21	(	(	PUNCT
cana-5711	283	22	0	0	NUM
cana-5711	283	23	,	,	PUNCT
cana-5711	283	24	1	1	NUM
cana-5711	283	25	;	;	PUNCT
cana-5711	283	26	0	0	NUM
cana-5711	283	27	,	,	PUNCT
cana-5711	283	28	0	0	NUM
cana-5711	283	29	;	;	PUNCT
cana-5711	283	30	0	0	NUM
cana-5711	283	31	,	,	PUNCT
cana-5711	283	32	0	0	NUM
cana-5711	283	33	)	)	PUNCT
cana-5711	283	34	,	,	PUNCT
cana-5711	283	35	(	(	PUNCT
cana-5711	283	36	0	0	NUM
cana-5711	283	37	,	,	PUNCT
cana-5711	283	38	0	0	NUM
cana-5711	283	39	;	;	PUNCT
cana-5711	283	40	0	0	NUM
cana-5711	283	41	,	,	PUNCT
cana-5711	283	42	u	u	NOUN
cana-5711	283	43	;	;	PUNCT
cana-5711	283	44	0	0	NUM
cana-5711	283	45	,	,	PUNCT
cana-5711	283	46	0	0	NUM
cana-5711	283	47	)	)	PUNCT
cana-5711	283	48	,	,	PUNCT
cana-5711	283	49	(	(	PUNCT
cana-5711	283	50	0	0	NUM
cana-5711	283	51	,	,	PUNCT
cana-5711	283	52	0	0	NUM
cana-5711	283	53	;	;	PUNCT
cana-5711	283	54	0	0	NUM
cana-5711	283	55	,	,	PUNCT
cana-5711	283	56	0	0	NUM
cana-5711	283	57	;	;	PUNCT
cana-5711	283	58	0	0	NUM
cana-5711	283	59	,	,	PUNCT
cana-5711	283	60	uv	uv	NOUN
cana-5711	283	61	)	)	PUNCT
cana-5711	283	62	,	,	PUNCT
cana-5711	283	63	(	(	PUNCT
cana-5711	283	64	0	0	NUM
cana-5711	283	65	,	,	PUNCT
cana-5711	283	66	0	0	NUM
cana-5711	283	67	;	;	PUNCT
cana-5711	283	68	0	0	NUM
cana-5711	283	69	,	,	PUNCT
cana-5711	283	70	u	u	NOUN
cana-5711	283	71	;	;	PUNCT
cana-5711	283	72	0	0	NUM
cana-5711	283	73	,	,	PUNCT
cana-5711	283	74	uv	uv	NOUN
cana-5711	283	75	)	)	PUNCT
cana-5711	283	76	}	}	PUNCT
cana-5711	283	77	,	,	PUNCT
cana-5711	283	78	which	which	PRON
cana-5711	283	79	is	be	AUX
cana-5711	283	80	also	also	ADV
cana-5711	283	81	a	a	DET
cana-5711	283	82	7	7	NUM
cana-5711	283	83	-	-	PUNCT
cana-5711	283	84	dimensional	dimensional	ADJ
cana-5711	283	85	vector	vector	NOUN
cana-5711	283	86	space	space	NOUN
cana-5711	283	87	over	over	ADP
cana-5711	283	88	ℤ2	ℤ2	PROPN
cana-5711	283	89	.	.	PUNCT
cana-5711	284	1	the	the	DET
cana-5711	284	2	complete	complete	ADJ
cana-5711	284	3	weight	weight	NOUN
cana-5711	284	4	enumerator	enumerator	NOUN
cana-5711	284	5	of	of	ADP
cana-5711	284	6	c	c	PROPN
cana-5711	284	7	and	and	CCONJ
cana-5711	284	8	c⊥	c⊥	PROPN
cana-5711	284	9	are	be	AUX
cana-5711	284	10	:	:	PUNCT
cana-5711	284	11	cwec	cwec	PROPN
cana-5711	284	12	(	(	PUNCT
cana-5711	284	13	x1	x1	INTJ
cana-5711	284	14	,	,	PUNCT
cana-5711	284	15	x2	x2	PROPN
cana-5711	284	16	,	,	PUNCT
cana-5711	284	17	x3	x3	ADJ
cana-5711	284	18	,	,	PUNCT
cana-5711	284	19	.	.	PUNCT
cana-5711	284	20	.	.	PUNCT
cana-5711	285	1	.	.	PUNCT
cana-5711	286	1	,	,	PUNCT
cana-5711	286	2	x128	x128	PROPN
cana-5711	286	3	)	)	PUNCT
cana-5711	287	1	=	=	SYM
cana-5711	287	2	x2	x2	NOUN
cana-5711	287	3	1	1	NUM
cana-5711	288	1	+	+	NUM
cana-5711	288	2	x2	x2	PROPN
cana-5711	288	3	5	5	NUM
cana-5711	289	1	+	+	CCONJ
cana-5711	289	2	x2	x2	PROPN
cana-5711	290	1	33	33	NUM
cana-5711	291	1	+	+	NUM
cana-5711	291	2	x2	x2	PROPN
cana-5711	292	1	37	37	NUM
cana-5711	292	2	+	+	NOUN
cana-5711	292	3	2x1	2x1	NUM
cana-5711	292	4	x5	x5	NOUN
cana-5711	292	5	+	+	CCONJ
cana-5711	292	6	2x1	2x1	NUM
cana-5711	292	7	x33	x33	NOUN
cana-5711	292	8	+	+	CCONJ
cana-5711	292	9	2x1	2x1	NUM
cana-5711	292	10	x37	x37	NOUN
cana-5711	293	1	+	+	CCONJ
cana-5711	293	2	x1	x1	NUM
cana-5711	293	3	x3	x3	PROPN
cana-5711	293	4	+	+	CCONJ
cana-5711	293	5	x1	x1	PROPN
cana-5711	293	6	x4	x4	PROPN
cana-5711	293	7	+	+	PROPN
cana-5711	293	8	x1	x1	NUM
cana-5711	293	9	x9	x9	NOUN
cana-5711	294	1	+	+	CCONJ
cana-5711	295	1	x1	x1	NUM
cana-5711	295	2	x10	x10	NOUN
cana-5711	296	1	+	+	CCONJ
cana-5711	296	2	x1	x1	NUM
cana-5711	296	3	x11	x11	NOUN
cana-5711	297	1	+	+	CCONJ
cana-5711	297	2	x1	x1	NUM
cana-5711	297	3	x12	x12	NUM
cana-5711	298	1	+	+	CCONJ
cana-5711	299	1	x1	x1	NUM
cana-5711	299	2	x35	x35	NOUN
cana-5711	300	1	+	+	CCONJ
cana-5711	300	2	x1	x1	PROPN
cana-5711	300	3	x36	x36	NUM
cana-5711	301	1	+	+	CCONJ
cana-5711	301	2	x1	x1	NUM
cana-5711	301	3	x41	x41	NOUN
cana-5711	301	4	+	+	CCONJ
cana-5711	301	5	x1	x1	ADJ
cana-5711	301	6	x42	x42	NOUN
cana-5711	302	1	+	+	CCONJ
cana-5711	302	2	x1	x1	NUM
cana-5711	302	3	x43	x43	NOUN
cana-5711	303	1	+	+	CCONJ
cana-5711	303	2	x1	x1	NUM
cana-5711	303	3	x44	x44	NOUN
cana-5711	304	1	+	+	CCONJ
cana-5711	304	2	x1	x1	NUM
cana-5711	304	3	x65	x65	NOUN
cana-5711	305	1	+	+	CCONJ
cana-5711	305	2	x1	x1	NUM
cana-5711	305	3	x67	x67	NOUN
cana-5711	306	1	+	+	CCONJ
cana-5711	307	1	x1	x1	NUM
cana-5711	307	2	x68	x68	NOUN
cana-5711	308	1	+	+	CCONJ
cana-5711	308	2	x1	x1	NUM
cana-5711	308	3	x69	x69	NOUN
cana-5711	309	1	+	+	CCONJ
cana-5711	310	1	x1	x1	PROPN
cana-5711	310	2	x73	x73	NOUN
cana-5711	311	1	+	+	CCONJ
cana-5711	311	2	x1	x1	NUM
cana-5711	311	3	x74	x74	NOUN
cana-5711	312	1	+	+	CCONJ
cana-5711	313	1	x1	x1	NUM
cana-5711	313	2	x75	x75	NUM
cana-5711	314	1	+	+	CCONJ
cana-5711	315	1	x1	x1	NUM
cana-5711	315	2	x76	x76	NUM
cana-5711	316	1	+	+	CCONJ
cana-5711	316	2	x1	x1	NUM
cana-5711	316	3	x97	x97	NOUN
cana-5711	317	1	+	+	CCONJ
cana-5711	317	2	x1	x1	NUM
cana-5711	317	3	x99	x99	NOUN
cana-5711	318	1	+	+	CCONJ
cana-5711	318	2	x1	x1	PROPN
cana-5711	318	3	x100	x100	PUNCT
cana-5711	319	1	+	+	CCONJ
cana-5711	320	1	x1	x1	NOUN
cana-5711	320	2	x101	x101	PROPN
cana-5711	321	1	+	+	CCONJ
cana-5711	322	1	x1	x1	PROPN
cana-5711	322	2	x105	x105	PROPN
cana-5711	323	1	+	+	CCONJ
cana-5711	324	1	x1	x1	PROPN
cana-5711	324	2	x106	x106	PUNCT
cana-5711	325	1	+	+	CCONJ
cana-5711	325	2	x1	x1	NUM
cana-5711	325	3	x107	x107	PUNCT
cana-5711	326	1	+	+	CCONJ
cana-5711	327	1	x1	x1	PROPN
cana-5711	327	2	x108	x108	PUNCT
cana-5711	328	1	+	+	CCONJ
cana-5711	328	2	2x5	2x5	NUM
cana-5711	328	3	x33	x33	NOUN
cana-5711	328	4	+	+	CCONJ
cana-5711	328	5	2x5	2x5	NUM
cana-5711	328	6	x37	x37	NUM
cana-5711	328	7	+	+	NUM
cana-5711	328	8	x5	x5	NOUN
cana-5711	328	9	x3	x3	ADJ
cana-5711	328	10	+	+	CCONJ
cana-5711	328	11	x5	x5	PROPN
cana-5711	328	12	x4	x4	PROPN
cana-5711	328	13	+	+	CCONJ
cana-5711	328	14	x5	x5	PROPN
cana-5711	328	15	x9	x9	NOUN
cana-5711	328	16	+	+	CCONJ
cana-5711	328	17	x5	x5	NOUN
cana-5711	328	18	x10	x10	NOUN
cana-5711	328	19	+	+	CCONJ
cana-5711	328	20	x5	x5	NOUN
cana-5711	328	21	x11	x11	PROPN
cana-5711	328	22	+	+	CCONJ
cana-5711	328	23	x5	x5	NOUN
cana-5711	328	24	x12	x12	NUM
cana-5711	328	25	+	+	NUM
cana-5711	328	26	x5	x5	NOUN
cana-5711	328	27	x35	x35	NOUN
cana-5711	328	28	+	+	NUM
cana-5711	328	29	x5	x5	NOUN
cana-5711	328	30	x36	x36	X
cana-5711	328	31	+	+	NUM
cana-5711	328	32	x5	x5	NOUN
cana-5711	328	33	x41	x41	ADJ
cana-5711	328	34	+	+	CCONJ
cana-5711	328	35	x5	x5	NOUN
cana-5711	328	36	x42	x42	NOUN
cana-5711	328	37	+	+	CCONJ
cana-5711	328	38	x5	x5	NOUN
cana-5711	328	39	x43	x43	PROPN
cana-5711	328	40	+	+	CCONJ
cana-5711	328	41	x5	x5	NOUN
cana-5711	328	42	x44	x44	NOUN
cana-5711	328	43	+	+	CCONJ
cana-5711	328	44	x5	x5	NOUN
cana-5711	328	45	x65	x65	NOUN
cana-5711	328	46	+	+	NUM
cana-5711	328	47	x5	x5	PROPN
cana-5711	328	48	x67	x67	PROPN
cana-5711	328	49	+	+	CCONJ
cana-5711	328	50	x5	x5	PROPN
cana-5711	328	51	x68	x68	PROPN
cana-5711	329	1	+	+	CCONJ
cana-5711	329	2	x5	x5	PROPN
cana-5711	329	3	x69	x69	PROPN
cana-5711	329	4	+	+	NUM
cana-5711	329	5	x5	x5	PROPN
cana-5711	329	6	x73	x73	NOUN
cana-5711	329	7	+	+	CCONJ
cana-5711	329	8	x5	x5	NOUN
cana-5711	329	9	x74	x74	NOUN
cana-5711	329	10	+	+	NUM
cana-5711	329	11	x5	x5	NOUN
cana-5711	329	12	x75	x75	PROPN
cana-5711	329	13	+	+	NUM
cana-5711	329	14	x5	x5	NOUN
cana-5711	329	15	x76	x76	PROPN
cana-5711	330	1	+	+	NUM
cana-5711	330	2	x5	x5	NOUN
cana-5711	330	3	x97	x97	PROPN
cana-5711	330	4	+	+	CCONJ
cana-5711	330	5	x5	x5	PROPN
cana-5711	330	6	x99	x99	PROPN
cana-5711	330	7	+	+	CCONJ
cana-5711	330	8	x5	x5	PROPN
cana-5711	330	9	x100	x100	PUNCT
cana-5711	331	1	+	+	NUM
cana-5711	331	2	x5	x5	NOUN
cana-5711	331	3	x101	x101	PROPN
cana-5711	331	4	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	331	5	communications	communication	NOUN
cana-5711	331	6	on	on	ADP
cana-5711	331	7	applied	apply	VERB
cana-5711	331	8	nonlinear	nonlinear	ADJ
cana-5711	331	9	analysis	analysis	NOUN
cana-5711	331	10	issn	issn	NOUN
cana-5711	331	11	:	:	PUNCT
cana-5711	331	12	1074	1074	NUM
cana-5711	331	13	-	-	PUNCT
cana-5711	331	14	133x	133x	NUM
cana-5711	331	15	vol	vol	VERB
cana-5711	331	16	32	32	NUM
cana-5711	331	17	no	no	NOUN
cana-5711	331	18	.	.	PUNCT
cana-5711	332	1	10s	10	NOUN
cana-5711	332	2	(	(	PUNCT
cana-5711	332	3	2025	2025	NUM
cana-5711	332	4	)	)	PUNCT
cana-5711	332	5	2705	2705	NUM
cana-5711	333	1	+	+	CCONJ
cana-5711	333	2	x5	x5	PROPN
cana-5711	333	3	x105	x105	PROPN
cana-5711	333	4	+	+	NUM
cana-5711	333	5	x5	x5	PROPN
cana-5711	333	6	x106	x106	PROPN
cana-5711	334	1	+	+	NUM
cana-5711	334	2	x5	x5	NOUN
cana-5711	334	3	x107	x107	PUNCT
cana-5711	334	4	+	+	NUM
cana-5711	334	5	x5	x5	PROPN
cana-5711	334	6	x108	x108	PUNCT
cana-5711	334	7	+	+	NUM
cana-5711	334	8	2x33	2x33	NUM
cana-5711	334	9	x37	x37	NOUN
cana-5711	335	1	+	+	CCONJ
cana-5711	335	2	x33	x33	NUM
cana-5711	335	3	x3	x3	PROPN
cana-5711	335	4	+	+	CCONJ
cana-5711	335	5	x33	x33	PROPN
cana-5711	335	6	x4	x4	PROPN
cana-5711	335	7	+	+	CCONJ
cana-5711	335	8	x33	x33	NUM
cana-5711	335	9	x9	x9	NOUN
cana-5711	335	10	+	+	CCONJ
cana-5711	335	11	x33	x33	NUM
cana-5711	335	12	x10	x10	NOUN
cana-5711	336	1	+	+	CCONJ
cana-5711	336	2	x33	x33	NUM
cana-5711	336	3	x11	x11	NOUN
cana-5711	336	4	+	+	CCONJ
cana-5711	336	5	x33	x33	NUM
cana-5711	336	6	x12	x12	NUM
cana-5711	337	1	+	+	CCONJ
cana-5711	337	2	x33	x33	NUM
cana-5711	337	3	x35	x35	NOUN
cana-5711	338	1	+	+	CCONJ
cana-5711	338	2	x33	x33	NUM
cana-5711	338	3	x36	x36	NUM
cana-5711	339	1	+	+	CCONJ
cana-5711	339	2	x33	x33	NUM
cana-5711	339	3	x41	x41	NOUN
cana-5711	339	4	+	+	CCONJ
cana-5711	339	5	x33	x33	NUM
cana-5711	339	6	x42	x42	NOUN
cana-5711	339	7	+	+	CCONJ
cana-5711	339	8	x33	x33	NUM
cana-5711	339	9	x43	x43	X
cana-5711	340	1	+	+	CCONJ
cana-5711	340	2	x33	x33	NUM
cana-5711	340	3	x44	x44	NOUN
cana-5711	340	4	+	+	CCONJ
cana-5711	340	5	x33	x33	NUM
cana-5711	340	6	x65	x65	NOUN
cana-5711	340	7	+	+	CCONJ
cana-5711	340	8	x33	x33	NUM
cana-5711	340	9	x67	x67	NOUN
cana-5711	341	1	+	+	CCONJ
cana-5711	341	2	x33	x33	NUM
cana-5711	341	3	x68	x68	NOUN
cana-5711	342	1	+	+	CCONJ
cana-5711	342	2	x33	x33	NUM
cana-5711	342	3	x69	x69	PROPN
cana-5711	342	4	+	+	CCONJ
cana-5711	342	5	x33	x33	NUM
cana-5711	342	6	x73	x73	PROPN
cana-5711	343	1	+	+	CCONJ
cana-5711	343	2	x33	x33	NUM
cana-5711	343	3	x74	x74	NOUN
cana-5711	344	1	+	+	CCONJ
cana-5711	344	2	x33	x33	NUM
cana-5711	344	3	x75	x75	PROPN
cana-5711	345	1	+	+	CCONJ
cana-5711	345	2	x33	x33	NUM
cana-5711	345	3	x76	x76	PROPN
cana-5711	346	1	+	+	CCONJ
cana-5711	346	2	x33	x33	NUM
cana-5711	346	3	x97	x97	PROPN
cana-5711	346	4	+	+	CCONJ
cana-5711	346	5	x33	x33	NUM
cana-5711	346	6	x99	x99	NOUN
cana-5711	347	1	+	+	CCONJ
cana-5711	347	2	x33	x33	PROPN
cana-5711	347	3	x100	x100	PUNCT
cana-5711	348	1	+	+	CCONJ
cana-5711	348	2	x33	x33	NOUN
cana-5711	348	3	x101	x101	PROPN
cana-5711	348	4	+	+	CCONJ
cana-5711	348	5	x33	x33	NUM
cana-5711	348	6	x105	x105	PROPN
cana-5711	348	7	+	+	CCONJ
cana-5711	348	8	x33	x33	PROPN
cana-5711	348	9	x106	x106	PUNCT
cana-5711	349	1	+	+	CCONJ
cana-5711	349	2	x33	x33	NOUN
cana-5711	349	3	x107	x107	PUNCT
cana-5711	350	1	+	+	CCONJ
cana-5711	350	2	x33	x33	PROPN
cana-5711	350	3	x108	x108	PROPN
cana-5711	351	1	+	+	CCONJ
cana-5711	351	2	x37	x37	NUM
cana-5711	351	3	x3	x3	VERB
cana-5711	351	4	+	+	CCONJ
cana-5711	351	5	x37	x37	PROPN
cana-5711	351	6	x4	x4	PROPN
cana-5711	352	1	+	+	CCONJ
cana-5711	352	2	x37	x37	NUM
cana-5711	352	3	x9	x9	NOUN
cana-5711	352	4	+	+	CCONJ
cana-5711	352	5	x37	x37	NUM
cana-5711	352	6	x10	x10	NOUN
cana-5711	353	1	+	+	CCONJ
cana-5711	353	2	x37	x37	NUM
cana-5711	353	3	x11	x11	NOUN
cana-5711	354	1	+	+	CCONJ
cana-5711	355	1	x37	x37	NUM
cana-5711	355	2	x12	x12	NUM
cana-5711	356	1	+	+	CCONJ
cana-5711	357	1	x37	x37	NUM
cana-5711	357	2	x35	x35	NOUN
cana-5711	358	1	+	+	CCONJ
cana-5711	358	2	x37	x37	NUM
cana-5711	359	1	x36	x36	NUM
cana-5711	360	1	+	+	CCONJ
cana-5711	360	2	x37	x37	NUM
cana-5711	360	3	x41	x41	VERB
cana-5711	360	4	+	+	CCONJ
cana-5711	360	5	x37	x37	NUM
cana-5711	360	6	x42	x42	NOUN
cana-5711	361	1	+	+	CCONJ
cana-5711	361	2	x37	x37	NUM
cana-5711	361	3	x43	x43	NOUN
cana-5711	362	1	+	+	CCONJ
cana-5711	362	2	x37	x37	ADJ
cana-5711	362	3	x44	x44	NOUN
cana-5711	363	1	+	+	CCONJ
cana-5711	363	2	x37	x37	NUM
cana-5711	363	3	x65	x65	NOUN
cana-5711	363	4	+	+	CCONJ
cana-5711	363	5	x37	x37	NUM
cana-5711	363	6	x67	x67	NOUN
cana-5711	364	1	+	+	CCONJ
cana-5711	365	1	x37	x37	NUM
cana-5711	365	2	x68	x68	NOUN
cana-5711	366	1	+	+	CCONJ
cana-5711	366	2	x37	x37	NUM
cana-5711	366	3	x69	x69	NOUN
cana-5711	367	1	+	+	CCONJ
cana-5711	368	1	x37	x37	NUM
cana-5711	368	2	x73	x73	NOUN
cana-5711	369	1	+	+	CCONJ
cana-5711	370	1	x37	x37	NUM
cana-5711	370	2	x74	x74	NOUN
cana-5711	371	1	+	+	CCONJ
cana-5711	372	1	x37	x37	NUM
cana-5711	372	2	x75	x75	NOUN
cana-5711	373	1	+	+	CCONJ
cana-5711	374	1	x37	x37	NUM
cana-5711	374	2	x76	x76	INTJ
cana-5711	375	1	+	+	CCONJ
cana-5711	375	2	x37	x37	NUM
cana-5711	375	3	x97	x97	NOUN
cana-5711	375	4	+	+	CCONJ
cana-5711	375	5	x37	x37	NUM
cana-5711	375	6	x99	x99	NOUN
cana-5711	376	1	+	+	CCONJ
cana-5711	376	2	x37	x37	PROPN
cana-5711	376	3	x100	x100	PUNCT
cana-5711	377	1	+	+	CCONJ
cana-5711	377	2	x37	x37	NOUN
cana-5711	377	3	x101	x101	PROPN
cana-5711	378	1	+	+	CCONJ
cana-5711	379	1	x37	x37	PROPN
cana-5711	379	2	x105	x105	PROPN
cana-5711	380	1	+	+	CCONJ
cana-5711	381	1	x37	x37	PROPN
cana-5711	381	2	x106	x106	PUNCT
cana-5711	382	1	+	+	NUM
cana-5711	382	2	x37	x37	NUM
cana-5711	382	3	x107	x107	PUNCT
cana-5711	383	1	+	+	CCONJ
cana-5711	383	2	x37	x37	PROPN
cana-5711	383	3	x108	x108	PROPN
cana-5711	383	4	,	,	PUNCT
cana-5711	383	5	cwec	cwec	PROPN
cana-5711	383	6	⊥	⊥	X
cana-5711	383	7	(	(	PUNCT
cana-5711	383	8	x1	x1	INTJ
cana-5711	383	9	,	,	PUNCT
cana-5711	383	10	x2	x2	PROPN
cana-5711	383	11	,	,	PUNCT
cana-5711	383	12	x3	x3	ADJ
cana-5711	383	13	,	,	PUNCT
cana-5711	383	14	.	.	PUNCT
cana-5711	383	15	.	.	PUNCT
cana-5711	384	1	.	.	PUNCT
cana-5711	385	1	,	,	PUNCT
cana-5711	385	2	x128	x128	PROPN
cana-5711	385	3	)	)	PUNCT
cana-5711	386	1	=	=	SYM
cana-5711	386	2	x2	x2	NOUN
cana-5711	387	1	1	1	NUM
cana-5711	388	1	+	+	NUM
cana-5711	388	2	x2	x2	PROPN
cana-5711	388	3	5	5	NUM
cana-5711	389	1	+	+	CCONJ
cana-5711	389	2	x2	x2	PROPN
cana-5711	390	1	33	33	NUM
cana-5711	391	1	+	+	NUM
cana-5711	391	2	x2	x2	PROPN
cana-5711	392	1	37	37	NUM
cana-5711	392	2	+	+	NOUN
cana-5711	392	3	2x1	2x1	NUM
cana-5711	392	4	x5	x5	NOUN
cana-5711	392	5	+	+	CCONJ
cana-5711	392	6	2x1	2x1	NUM
cana-5711	392	7	x33	x33	NOUN
cana-5711	392	8	+	+	CCONJ
cana-5711	392	9	2x1	2x1	NUM
cana-5711	392	10	x37	x37	NOUN
cana-5711	393	1	+	+	CCONJ
cana-5711	393	2	x1	x1	NUM
cana-5711	393	3	x3	x3	PROPN
cana-5711	393	4	+	+	CCONJ
cana-5711	393	5	x1	x1	PROPN
cana-5711	393	6	x4	x4	PROPN
cana-5711	393	7	+	+	PROPN
cana-5711	393	8	x1	x1	NUM
cana-5711	393	9	x9	x9	NOUN
cana-5711	394	1	+	+	CCONJ
cana-5711	395	1	x1	x1	NUM
cana-5711	395	2	x10	x10	NOUN
cana-5711	396	1	+	+	CCONJ
cana-5711	396	2	x1	x1	NUM
cana-5711	396	3	x11	x11	NOUN
cana-5711	397	1	+	+	CCONJ
cana-5711	397	2	x1	x1	NUM
cana-5711	397	3	x12	x12	NUM
cana-5711	398	1	+	+	CCONJ
cana-5711	399	1	x1	x1	NUM
cana-5711	399	2	x35	x35	NOUN
cana-5711	400	1	+	+	CCONJ
cana-5711	400	2	x1	x1	PROPN
cana-5711	400	3	x36	x36	NUM
cana-5711	401	1	+	+	CCONJ
cana-5711	401	2	x1	x1	NUM
cana-5711	401	3	x41	x41	NOUN
cana-5711	401	4	+	+	CCONJ
cana-5711	401	5	x1	x1	ADJ
cana-5711	401	6	x42	x42	NOUN
cana-5711	402	1	+	+	CCONJ
cana-5711	402	2	x1	x1	NUM
cana-5711	402	3	x43	x43	NOUN
cana-5711	403	1	+	+	CCONJ
cana-5711	403	2	x1	x1	NUM
cana-5711	403	3	x44	x44	NOUN
cana-5711	404	1	+	+	CCONJ
cana-5711	404	2	x1	x1	NUM
cana-5711	404	3	x65	x65	NOUN
cana-5711	405	1	+	+	CCONJ
cana-5711	405	2	x1	x1	NUM
cana-5711	405	3	x67	x67	NOUN
cana-5711	406	1	+	+	CCONJ
cana-5711	407	1	x1	x1	NUM
cana-5711	407	2	x68	x68	NOUN
cana-5711	408	1	+	+	CCONJ
cana-5711	408	2	x1	x1	NUM
cana-5711	408	3	x69	x69	NOUN
cana-5711	409	1	+	+	CCONJ
cana-5711	410	1	x1	x1	PROPN
cana-5711	410	2	x73	x73	NOUN
cana-5711	411	1	+	+	CCONJ
cana-5711	411	2	x1	x1	NUM
cana-5711	411	3	x74	x74	NOUN
cana-5711	412	1	+	+	CCONJ
cana-5711	413	1	x1	x1	NUM
cana-5711	413	2	x75	x75	NUM
cana-5711	414	1	+	+	CCONJ
cana-5711	415	1	x1	x1	NUM
cana-5711	415	2	x76	x76	NUM
cana-5711	416	1	+	+	CCONJ
cana-5711	416	2	x1	x1	NUM
cana-5711	416	3	x97	x97	NOUN
cana-5711	417	1	+	+	CCONJ
cana-5711	417	2	x1	x1	NUM
cana-5711	417	3	x99	x99	NOUN
cana-5711	418	1	+	+	CCONJ
cana-5711	418	2	x1	x1	PROPN
cana-5711	418	3	x100	x100	PUNCT
cana-5711	419	1	+	+	CCONJ
cana-5711	420	1	x1	x1	NOUN
cana-5711	420	2	x101	x101	PROPN
cana-5711	421	1	+	+	CCONJ
cana-5711	422	1	x1	x1	PROPN
cana-5711	422	2	x105	x105	PROPN
cana-5711	423	1	+	+	CCONJ
cana-5711	424	1	x1	x1	PROPN
cana-5711	424	2	x106	x106	PUNCT
cana-5711	425	1	+	+	CCONJ
cana-5711	425	2	x1	x1	NUM
cana-5711	425	3	x107	x107	PUNCT
cana-5711	426	1	+	+	CCONJ
cana-5711	427	1	x1	x1	PROPN
cana-5711	427	2	x108	x108	PUNCT
cana-5711	428	1	+	+	CCONJ
cana-5711	428	2	2x5	2x5	NUM
cana-5711	428	3	x33	x33	NOUN
cana-5711	428	4	+	+	CCONJ
cana-5711	428	5	2x5	2x5	NUM
cana-5711	428	6	x37	x37	NUM
cana-5711	428	7	+	+	NUM
cana-5711	428	8	x5	x5	NOUN
cana-5711	428	9	x3	x3	ADJ
cana-5711	428	10	+	+	CCONJ
cana-5711	428	11	x5	x5	PROPN
cana-5711	428	12	x4	x4	PROPN
cana-5711	428	13	+	+	CCONJ
cana-5711	428	14	x5	x5	PROPN
cana-5711	428	15	x9	x9	NOUN
cana-5711	428	16	+	+	CCONJ
cana-5711	428	17	x5	x5	NOUN
cana-5711	428	18	x10	x10	NOUN
cana-5711	428	19	+	+	CCONJ
cana-5711	428	20	x5	x5	NOUN
cana-5711	428	21	x11	x11	PROPN
cana-5711	428	22	+	+	CCONJ
cana-5711	428	23	x5	x5	NOUN
cana-5711	428	24	x12	x12	NUM
cana-5711	428	25	+	+	NUM
cana-5711	428	26	x5	x5	NOUN
cana-5711	428	27	x35	x35	NOUN
cana-5711	428	28	+	+	NUM
cana-5711	428	29	x5	x5	NOUN
cana-5711	428	30	x36	x36	X
cana-5711	428	31	+	+	NUM
cana-5711	428	32	x5	x5	NOUN
cana-5711	428	33	x41	x41	ADJ
cana-5711	428	34	+	+	CCONJ
cana-5711	428	35	x5	x5	NOUN
cana-5711	428	36	x42	x42	NOUN
cana-5711	428	37	+	+	CCONJ
cana-5711	428	38	x5	x5	NOUN
cana-5711	428	39	x43	x43	PROPN
cana-5711	428	40	+	+	CCONJ
cana-5711	428	41	x5	x5	NOUN
cana-5711	428	42	x44	x44	NOUN
cana-5711	428	43	+	+	CCONJ
cana-5711	428	44	x5	x5	NOUN
cana-5711	428	45	x65	x65	NOUN
cana-5711	428	46	+	+	NUM
cana-5711	428	47	x5	x5	PROPN
cana-5711	428	48	x67	x67	PROPN
cana-5711	428	49	+	+	CCONJ
cana-5711	428	50	x5	x5	PROPN
cana-5711	428	51	x68	x68	PROPN
cana-5711	429	1	+	+	CCONJ
cana-5711	429	2	x5	x5	PROPN
cana-5711	429	3	x69	x69	PROPN
cana-5711	429	4	+	+	NUM
cana-5711	429	5	x5	x5	PROPN
cana-5711	429	6	x73	x73	NOUN
cana-5711	429	7	+	+	CCONJ
cana-5711	429	8	x5	x5	NOUN
cana-5711	429	9	x74	x74	NOUN
cana-5711	429	10	+	+	NUM
cana-5711	429	11	x5	x5	NOUN
cana-5711	429	12	x75	x75	PROPN
cana-5711	429	13	+	+	NUM
cana-5711	429	14	x5	x5	NOUN
cana-5711	429	15	x76	x76	PROPN
cana-5711	430	1	+	+	NUM
cana-5711	430	2	x5	x5	NOUN
cana-5711	430	3	x97	x97	PROPN
cana-5711	430	4	+	+	CCONJ
cana-5711	430	5	x5	x5	PROPN
cana-5711	430	6	x99	x99	PROPN
cana-5711	430	7	+	+	CCONJ
cana-5711	430	8	x5	x5	PROPN
cana-5711	430	9	x100	x100	PUNCT
cana-5711	431	1	+	+	NUM
cana-5711	431	2	x5	x5	NOUN
cana-5711	431	3	x101	x101	PROPN
cana-5711	431	4	+	+	NUM
cana-5711	431	5	x5	x5	PROPN
cana-5711	431	6	x105	x105	PROPN
cana-5711	431	7	+	+	NUM
cana-5711	431	8	x5	x5	PROPN
cana-5711	431	9	x106	x106	PROPN
cana-5711	432	1	+	+	NUM
cana-5711	432	2	x5	x5	NOUN
cana-5711	432	3	x107	x107	PUNCT
cana-5711	432	4	+	+	NUM
cana-5711	432	5	x5	x5	PROPN
cana-5711	432	6	x108	x108	PUNCT
cana-5711	432	7	+	+	NUM
cana-5711	432	8	2x33	2x33	NUM
cana-5711	432	9	x37	x37	NOUN
cana-5711	433	1	+	+	CCONJ
cana-5711	433	2	x33	x33	NUM
cana-5711	433	3	x3	x3	PROPN
cana-5711	433	4	+	+	CCONJ
cana-5711	433	5	x33	x33	PROPN
cana-5711	433	6	x4	x4	PROPN
cana-5711	433	7	+	+	CCONJ
cana-5711	433	8	x33	x33	NUM
cana-5711	433	9	x9	x9	NOUN
cana-5711	433	10	+	+	CCONJ
cana-5711	433	11	x33	x33	NUM
cana-5711	433	12	x10	x10	NOUN
cana-5711	434	1	+	+	CCONJ
cana-5711	434	2	x33	x33	NUM
cana-5711	434	3	x11	x11	NOUN
cana-5711	434	4	+	+	CCONJ
cana-5711	434	5	x33	x33	NUM
cana-5711	434	6	x12	x12	NUM
cana-5711	435	1	+	+	CCONJ
cana-5711	435	2	x33	x33	NUM
cana-5711	435	3	x35	x35	NOUN
cana-5711	436	1	+	+	CCONJ
cana-5711	436	2	x33	x33	NUM
cana-5711	436	3	x36	x36	NUM
cana-5711	437	1	+	+	CCONJ
cana-5711	437	2	x33	x33	NUM
cana-5711	437	3	x41	x41	NOUN
cana-5711	437	4	+	+	CCONJ
cana-5711	437	5	x33	x33	NUM
cana-5711	437	6	x42	x42	NOUN
cana-5711	437	7	+	+	CCONJ
cana-5711	437	8	x33	x33	NUM
cana-5711	437	9	x43	x43	X
cana-5711	438	1	+	+	CCONJ
cana-5711	438	2	x33	x33	NUM
cana-5711	438	3	x44	x44	NOUN
cana-5711	438	4	+	+	CCONJ
cana-5711	438	5	x33	x33	NUM
cana-5711	438	6	x65	x65	NOUN
cana-5711	438	7	+	+	CCONJ
cana-5711	438	8	x33	x33	NUM
cana-5711	438	9	x67	x67	NOUN
cana-5711	439	1	+	+	CCONJ
cana-5711	439	2	x33	x33	NUM
cana-5711	439	3	x68	x68	NOUN
cana-5711	440	1	+	+	CCONJ
cana-5711	440	2	x33	x33	NUM
cana-5711	440	3	x69	x69	PROPN
cana-5711	440	4	+	+	CCONJ
cana-5711	440	5	x33	x33	NUM
cana-5711	440	6	x73	x73	PROPN
cana-5711	441	1	+	+	CCONJ
cana-5711	441	2	x33	x33	NUM
cana-5711	441	3	x74	x74	NOUN
cana-5711	442	1	+	+	CCONJ
cana-5711	442	2	x33	x33	NUM
cana-5711	442	3	x75	x75	PROPN
cana-5711	443	1	+	+	CCONJ
cana-5711	443	2	x33	x33	NUM
cana-5711	443	3	x76	x76	PROPN
cana-5711	444	1	+	+	CCONJ
cana-5711	444	2	x33	x33	NUM
cana-5711	444	3	x97	x97	PROPN
cana-5711	444	4	+	+	CCONJ
cana-5711	444	5	x33	x33	NUM
cana-5711	444	6	x99	x99	NOUN
cana-5711	445	1	+	+	CCONJ
cana-5711	445	2	x33	x33	PROPN
cana-5711	445	3	x100	x100	PUNCT
cana-5711	446	1	+	+	CCONJ
cana-5711	446	2	x33	x33	NOUN
cana-5711	446	3	x101	x101	PROPN
cana-5711	446	4	+	+	CCONJ
cana-5711	446	5	x33	x33	NUM
cana-5711	446	6	x105	x105	PROPN
cana-5711	446	7	+	+	CCONJ
cana-5711	446	8	x33	x33	PROPN
cana-5711	446	9	x106	x106	PUNCT
cana-5711	447	1	+	+	CCONJ
cana-5711	447	2	x33	x33	NOUN
cana-5711	447	3	x107	x107	PUNCT
cana-5711	448	1	+	+	CCONJ
cana-5711	448	2	x33	x33	PROPN
cana-5711	448	3	x108	x108	PROPN
cana-5711	449	1	+	+	CCONJ
cana-5711	449	2	x37	x37	NUM
cana-5711	449	3	x3	x3	VERB
cana-5711	449	4	+	+	CCONJ
cana-5711	449	5	x37	x37	PROPN
cana-5711	449	6	x4	x4	PROPN
cana-5711	450	1	+	+	CCONJ
cana-5711	450	2	x37	x37	NUM
cana-5711	450	3	x9	x9	NOUN
cana-5711	450	4	+	+	CCONJ
cana-5711	450	5	x37	x37	NUM
cana-5711	450	6	x10	x10	NOUN
cana-5711	451	1	+	+	CCONJ
cana-5711	451	2	x37	x37	NUM
cana-5711	451	3	x11	x11	NOUN
cana-5711	452	1	+	+	CCONJ
cana-5711	453	1	x37	x37	NUM
cana-5711	453	2	x12	x12	NUM
cana-5711	454	1	+	+	CCONJ
cana-5711	455	1	x37	x37	NUM
cana-5711	455	2	x35	x35	NOUN
cana-5711	456	1	+	+	CCONJ
cana-5711	456	2	x37	x37	NUM
cana-5711	457	1	x36	x36	NUM
cana-5711	458	1	+	+	CCONJ
cana-5711	458	2	x37	x37	NUM
cana-5711	458	3	x41	x41	VERB
cana-5711	458	4	+	+	CCONJ
cana-5711	458	5	x37	x37	NUM
cana-5711	458	6	x42	x42	NOUN
cana-5711	459	1	+	+	CCONJ
cana-5711	459	2	x37	x37	NUM
cana-5711	459	3	x43	x43	NOUN
cana-5711	460	1	+	+	CCONJ
cana-5711	460	2	x37	x37	ADJ
cana-5711	460	3	x44	x44	NOUN
cana-5711	461	1	+	+	CCONJ
cana-5711	461	2	x37	x37	NUM
cana-5711	461	3	x65	x65	NOUN
cana-5711	461	4	+	+	CCONJ
cana-5711	461	5	x37	x37	NUM
cana-5711	461	6	x67	x67	NOUN
cana-5711	462	1	+	+	CCONJ
cana-5711	463	1	x37	x37	NUM
cana-5711	463	2	x68	x68	NOUN
cana-5711	464	1	+	+	CCONJ
cana-5711	464	2	x37	x37	NUM
cana-5711	464	3	x69	x69	NOUN
cana-5711	465	1	+	+	CCONJ
cana-5711	466	1	x37	x37	NUM
cana-5711	466	2	x73	x73	NOUN
cana-5711	467	1	+	+	CCONJ
cana-5711	468	1	x37	x37	NUM
cana-5711	468	2	x74	x74	NOUN
cana-5711	469	1	+	+	CCONJ
cana-5711	470	1	x37	x37	NUM
cana-5711	470	2	x75	x75	NOUN
cana-5711	471	1	+	+	CCONJ
cana-5711	472	1	x37	x37	NUM
cana-5711	472	2	x76	x76	INTJ
cana-5711	473	1	+	+	CCONJ
cana-5711	473	2	x37	x37	NUM
cana-5711	473	3	x97	x97	NOUN
cana-5711	473	4	+	+	CCONJ
cana-5711	473	5	x37	x37	NUM
cana-5711	473	6	x99	x99	NOUN
cana-5711	474	1	+	+	CCONJ
cana-5711	474	2	x37	x37	PROPN
cana-5711	474	3	x100	x100	PUNCT
cana-5711	475	1	+	+	CCONJ
cana-5711	475	2	x37	x37	NOUN
cana-5711	475	3	x101	x101	PROPN
cana-5711	476	1	+	+	CCONJ
cana-5711	477	1	x37	x37	PROPN
cana-5711	477	2	x105	x105	PROPN
cana-5711	478	1	+	+	CCONJ
cana-5711	479	1	x37	x37	PROPN
cana-5711	479	2	x106	x106	PUNCT
cana-5711	480	1	+	+	NUM
cana-5711	480	2	x37	x37	NUM
cana-5711	480	3	x107	x107	PUNCT
cana-5711	481	1	+	+	CCONJ
cana-5711	481	2	x37	x37	PROPN
cana-5711	481	3	x108	x108	PROPN
cana-5711	481	4	.	.	PUNCT
cana-5711	482	1	definition	definition	NOUN
cana-5711	482	2	5.7	5.7	NUM
cana-5711	482	3	.	.	PUNCT
cana-5711	483	1	let	let	VERB
cana-5711	483	2	c	c	PRON
cana-5711	483	3	be	be	AUX
cana-5711	483	4	an	an	DET
cana-5711	483	5	additive	additive	ADJ
cana-5711	483	6	code	code	NOUN
cana-5711	483	7	of	of	ADP
cana-5711	483	8	length	length	NOUN
cana-5711	483	9	n	n	CCONJ
cana-5711	483	10	over	over	ADP
cana-5711	483	11	ℤ2q	ℤ2q	PROPN
cana-5711	483	12	.	.	PUNCT
cana-5711	484	1	then	then	ADV
cana-5711	484	2	the	the	DET
cana-5711	484	3	hamming	hamming	ADJ
cana-5711	484	4	weight	weight	NOUN
cana-5711	484	5	enumerator	enumerator	NOUN
cana-5711	484	6	of	of	ADP
cana-5711	484	7	c	c	PROPN
cana-5711	484	8	over	over	ADP
cana-5711	484	9	ℤ2q	ℤ2q	PROPN
cana-5711	484	10	is	be	AUX
cana-5711	484	11	defined	define	VERB
cana-5711	484	12	as	as	ADP
cana-5711	484	13	𝑊𝐶(𝑥	𝑊𝐶(𝑥	PROPN
cana-5711	484	14	,	,	PUNCT
cana-5711	484	15	𝑦	𝑦	NOUN
cana-5711	484	16	)	)	PUNCT
cana-5711	484	17	=	=	SYM
cana-5711	484	18	∑	∑	PUNCT
cana-5711	484	19	𝑥𝑛−𝑤𝑡𝐻(𝑐	𝑥𝑛−𝑤𝑡𝐻(𝑐	NUM
cana-5711	484	20	)	)	PUNCT
cana-5711	484	21	𝑐∈𝐶	𝑐∈𝐶	NOUN
cana-5711	484	22	𝑦𝑤𝑡𝐻(𝑐	𝑦𝑤𝑡𝐻(𝑐	NOUN
cana-5711	484	23	)	)	PUNCT
cana-5711	484	24	=	=	SYM
cana-5711	484	25	𝐶𝑊𝐸𝐶(𝑥	𝐶𝑊𝐸𝐶(𝑥	ADJ
cana-5711	484	26	,	,	PUNCT
cana-5711	484	27	𝑦	𝑦	NOUN
cana-5711	484	28	,	,	PUNCT
cana-5711	484	29	𝑦	𝑦	NOUN
cana-5711	484	30	,	,	PUNCT
cana-5711	484	31	.	.	PUNCT
cana-5711	484	32	.	.	PUNCT
cana-5711	485	1	.	.	PUNCT
cana-5711	486	1	,	,	PUNCT
cana-5711	486	2	𝑦	𝑦	X
cana-5711	486	3	)	)	PUNCT
cana-5711	486	4	.	.	PUNCT
cana-5711	487	1	(	(	PUNCT
cana-5711	487	2	5.4	5.4	NUM
cana-5711	487	3	)	)	PUNCT
cana-5711	487	4	note	note	NOUN
cana-5711	487	5	that	that	SCONJ
cana-5711	487	6	the	the	DET
cana-5711	487	7	polynomial	polynomial	ADJ
cana-5711	487	8	wc	wc	NOUN
cana-5711	487	9	(	(	PUNCT
cana-5711	487	10	x	x	PROPN
cana-5711	487	11	,	,	PUNCT
cana-5711	487	12	y	y	NOUN
cana-5711	487	13	)	)	PUNCT
cana-5711	487	14	is	be	AUX
cana-5711	487	15	homogeneous	homogeneous	ADJ
cana-5711	487	16	of	of	ADP
cana-5711	487	17	degree	degree	NOUN
cana-5711	487	18	n.	n.	NOUN
cana-5711	487	19	theorem	theorem	VERB
cana-5711	487	20	5.8	5.8	NUM
cana-5711	487	21	.	.	PUNCT
cana-5711	488	1	let	let	VERB
cana-5711	488	2	c	c	PRON
cana-5711	488	3	be	be	AUX
cana-5711	488	4	an	an	DET
cana-5711	488	5	additive	additive	ADJ
cana-5711	488	6	code	code	NOUN
cana-5711	488	7	of	of	ADP
cana-5711	488	8	length	length	NOUN
cana-5711	488	9	n	n	CCONJ
cana-5711	488	10	over	over	ADP
cana-5711	488	11	ℤ2q	ℤ2q	PROPN
cana-5711	488	12	.	.	PUNCT
cana-5711	489	1	then	then	ADV
cana-5711	489	2	wc	wc	PROPN
cana-5711	489	3	⊥	⊥	PROPN
cana-5711	489	4	(	(	PUNCT
cana-5711	489	5	x	x	PROPN
cana-5711	489	6	,	,	PUNCT
cana-5711	489	7	y	y	NOUN
cana-5711	489	8	)	)	PUNCT
cana-5711	489	9	=	=	SYM
cana-5711	489	10	1	1	NUM
cana-5711	489	11	|𝑐|	|𝑐|	NUM
cana-5711	489	12	wc	wc	PROPN
cana-5711	489	13	(	(	PUNCT
cana-5711	489	14	x	x	PROPN
cana-5711	489	15	+	+	NUM
cana-5711	489	16	127y	127y	NOUN
cana-5711	489	17	,	,	PUNCT
cana-5711	489	18	x	x	PUNCT
cana-5711	489	19	−	−	PROPN
cana-5711	489	20	y	y	NOUN
cana-5711	489	21	)	)	PUNCT
cana-5711	489	22	proof	proof	NOUN
cana-5711	489	23	.	.	PUNCT
cana-5711	490	1	consider	consider	VERB
cana-5711	490	2	wc	wc	PROPN
cana-5711	490	3	⊥	⊥	PROPN
cana-5711	490	4	(	(	PUNCT
cana-5711	490	5	x	x	X
cana-5711	490	6	,	,	PUNCT
cana-5711	490	7	y	y	NOUN
cana-5711	490	8	)	)	PUNCT
cana-5711	490	9	=	=	VERB
cana-5711	491	1	cwec	cwec	NOUN
cana-5711	491	2	⊥	⊥	NOUN
cana-5711	491	3	(	(	PUNCT
cana-5711	491	4	x	x	X
cana-5711	491	5	,	,	PUNCT
cana-5711	491	6	y	y	PROPN
cana-5711	491	7	,	,	PUNCT
cana-5711	491	8	y	y	PROPN
cana-5711	491	9	,	,	PUNCT
cana-5711	491	10	y	y	PROPN
cana-5711	491	11	,	,	PUNCT
cana-5711	491	12	.	.	PUNCT
cana-5711	491	13	.	.	PUNCT
cana-5711	491	14	.	.	PUNCT
cana-5711	492	1	,	,	PUNCT
cana-5711	492	2	y	y	X
cana-5711	492	3	)	)	PUNCT
cana-5711	492	4	=	=	SYM
cana-5711	492	5	1	1	NUM
cana-5711	492	6	|𝑐|	|𝑐|	NUM
cana-5711	492	7	cwec	cwec	NOUN
cana-5711	492	8	(	(	PUNCT
cana-5711	492	9	t	t	NOUN
cana-5711	492	10	·	·	PUNCT
cana-5711	492	11	(	(	PUNCT
cana-5711	492	12	x	x	X
cana-5711	492	13	,	,	PUNCT
cana-5711	492	14	y	y	PROPN
cana-5711	492	15	,	,	PUNCT
cana-5711	492	16	y	y	PROPN
cana-5711	492	17	,	,	PUNCT
cana-5711	492	18	y	y	PROPN
cana-5711	492	19	,	,	PUNCT
cana-5711	492	20	.	.	PUNCT
cana-5711	492	21	.	.	PUNCT
cana-5711	492	22	.	.	PUNCT
cana-5711	493	1	,	,	PUNCT
cana-5711	493	2	y)t	y)t	PUNCT
cana-5711	493	3	)	)	PUNCT
cana-5711	493	4	=	=	SYM
cana-5711	493	5	1	1	NUM
cana-5711	493	6	|𝑐|	|𝑐|	NUM
cana-5711	493	7	cwec	cwec	NOUN
cana-5711	493	8	(	(	PUNCT
cana-5711	493	9	x	x	SYM
cana-5711	493	10	+	+	NUM
cana-5711	493	11	127y	127y	NOUN
cana-5711	493	12	,	,	PUNCT
cana-5711	493	13	x	x	PUNCT
cana-5711	493	14	−	−	PROPN
cana-5711	493	15	y	y	PROPN
cana-5711	493	16	,	,	PUNCT
cana-5711	493	17	x	x	PUNCT
cana-5711	493	18	−	−	PROPN
cana-5711	493	19	y	y	PROPN
cana-5711	493	20	,	,	PUNCT
cana-5711	493	21	.	.	PUNCT
cana-5711	493	22	.	.	PUNCT
cana-5711	493	23	.	.	PUNCT
cana-5711	494	1	,	,	PUNCT
cana-5711	494	2	x	x	X
cana-5711	494	3	−	−	PROPN
cana-5711	494	4	y	y	PROPN
cana-5711	494	5	)	)	PUNCT
cana-5711	494	6	wc	wc	PROPN
cana-5711	494	7	⊥	⊥	PROPN
cana-5711	494	8	(	(	PUNCT
cana-5711	494	9	x	x	PROPN
cana-5711	494	10	,	,	PUNCT
cana-5711	494	11	y	y	NOUN
cana-5711	494	12	)	)	PUNCT
cana-5711	494	13	=	=	SYM
cana-5711	495	1	1	1	NUM
cana-5711	495	2	|𝑐|	|𝑐|	NUM
cana-5711	495	3	wc	wc	PROPN
cana-5711	495	4	(	(	PUNCT
cana-5711	495	5	x	x	PROPN
cana-5711	495	6	+	+	NUM
cana-5711	495	7	127y	127y	NOUN
cana-5711	495	8	,	,	PUNCT
cana-5711	495	9	x	x	PUNCT
cana-5711	495	10	−	−	PROPN
cana-5711	495	11	y	y	PROPN
cana-5711	495	12	)	)	PUNCT
cana-5711	495	13	.	.	PUNCT
cana-5711	496	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	496	2	communications	communication	NOUN
cana-5711	496	3	on	on	ADP
cana-5711	496	4	applied	apply	VERB
cana-5711	496	5	nonlinear	nonlinear	ADJ
cana-5711	496	6	analysis	analysis	NOUN
cana-5711	496	7	issn	issn	NOUN
cana-5711	496	8	:	:	PUNCT
cana-5711	496	9	1074	1074	NUM
cana-5711	496	10	-	-	PUNCT
cana-5711	496	11	133x	133x	NUM
cana-5711	496	12	vol	vol	VERB
cana-5711	496	13	32	32	NUM
cana-5711	496	14	no	no	NOUN
cana-5711	496	15	.	.	PUNCT
cana-5711	497	1	10s	10	NOUN
cana-5711	497	2	(	(	PUNCT
cana-5711	497	3	2025	2025	NUM
cana-5711	497	4	)	)	PUNCT
cana-5711	497	5	2706	2706	NUM
cana-5711	497	6	example	example	NOUN
cana-5711	497	7	5.9	5.9	NUM
cana-5711	497	8	.	.	PUNCT
cana-5711	498	1	let	let	VERB
cana-5711	498	2	c	c	PRON
cana-5711	498	3	be	be	AUX
cana-5711	498	4	the	the	DET
cana-5711	498	5	code	code	NOUN
cana-5711	498	6	in	in	ADP
cana-5711	498	7	example	example	NOUN
cana-5711	498	8	5.6	5.6	NUM
cana-5711	498	9	.	.	PUNCT
cana-5711	499	1	then	then	ADV
cana-5711	499	2	wc	wc	PROPN
cana-5711	499	3	(	(	PUNCT
cana-5711	499	4	x	x	PROPN
cana-5711	499	5	,	,	PUNCT
cana-5711	499	6	y	y	NOUN
cana-5711	499	7	)	)	PUNCT
cana-5711	499	8	=	=	SYM
cana-5711	500	1	x2	x2	PROPN
cana-5711	501	1	+	+	CCONJ
cana-5711	501	2	34xy	34xy	ADJ
cana-5711	501	3	+	+	CCONJ
cana-5711	501	4	93y	93y	NOUN
cana-5711	501	5	2	2	NUM
cana-5711	501	6	and	and	CCONJ
cana-5711	501	7	wc	wc	PROPN
cana-5711	501	8	⊥	⊥	PROPN
cana-5711	501	9	(	(	PUNCT
cana-5711	501	10	x	x	PROPN
cana-5711	501	11	,	,	PUNCT
cana-5711	501	12	y	y	NOUN
cana-5711	501	13	)	)	PUNCT
cana-5711	501	14	=	=	SYM
cana-5711	501	15	1	1	NUM
cana-5711	501	16	128	128	NUM
cana-5711	501	17	{	{	PUNCT
cana-5711	501	18	(	(	PUNCT
cana-5711	501	19	x	x	SYM
cana-5711	501	20	+	+	NUM
cana-5711	501	21	127y)2	127y)2	NUM
cana-5711	501	22	+	+	SYM
cana-5711	501	23	93(x	93(x	NUM
cana-5711	501	24	−	−	NOUN
cana-5711	501	25	y)2	y)2	NOUN
cana-5711	501	26	+	+	CCONJ
cana-5711	501	27	34(x	34(x	NUM
cana-5711	501	28	+	+	CCONJ
cana-5711	501	29	127y)(x	127y)(x	NUM
cana-5711	501	30	−	−	PROPN
cana-5711	501	31	y	y	NOUN
cana-5711	501	32	)	)	PUNCT
cana-5711	501	33	}	}	PUNCT
cana-5711	501	34	=	=	SYM
cana-5711	502	1	1	1	NUM
cana-5711	502	2	128	128	NUM
cana-5711	502	3	{	{	PUNCT
cana-5711	502	4	128x2	128x2	NUM
cana-5711	502	5	+	+	NUM
cana-5711	502	6	4	4	NUM
cana-5711	502	7	,	,	PUNCT
cana-5711	502	8	352xy	352xy	NOUN
cana-5711	502	9	+	+	CCONJ
cana-5711	502	10	11	11	NUM
cana-5711	502	11	,	,	PUNCT
cana-5711	502	12	904y	904y	PROPN
cana-5711	502	13	2	2	NUM
cana-5711	502	14	}	}	PUNCT
cana-5711	502	15	wc	wc	PROPN
cana-5711	502	16	⊥	⊥	PROPN
cana-5711	502	17	(	(	PUNCT
cana-5711	502	18	x	x	PROPN
cana-5711	502	19	,	,	PUNCT
cana-5711	502	20	y	y	NOUN
cana-5711	502	21	)	)	PUNCT
cana-5711	503	1	=	=	SYM
cana-5711	503	2	x2	x2	PROPN
cana-5711	504	1	+	+	NUM
cana-5711	504	2	34xy	34xy	ADJ
cana-5711	504	3	+	+	CCONJ
cana-5711	504	4	93y2	93y2	NUM
cana-5711	504	5	.	.	PUNCT
cana-5711	505	1	5	5	NUM
cana-5711	505	2	.	.	SYM
cana-5711	505	3	2	2	NUM
cana-5711	505	4	.	.	NUM
cana-5711	505	5	symmetrized	symmetrize	VERB
cana-5711	505	6	weight	weight	NOUN
cana-5711	505	7	enumerator	enumerator	NOUN
cana-5711	505	8	and	and	CCONJ
cana-5711	505	9	lee	lee	PROPN
cana-5711	505	10	weight	weight	NOUN
cana-5711	505	11	enumerator	enumerator	NOUN
cana-5711	505	12	the	the	DET
cana-5711	505	13	lee	lee	PROPN
cana-5711	505	14	weight	weight	NOUN
cana-5711	505	15	of	of	ADP
cana-5711	505	16	each	each	DET
cana-5711	505	17	element	element	NOUN
cana-5711	505	18	of	of	ADP
cana-5711	505	19	ℤ2q	ℤ2q	PROPN
cana-5711	505	20	is	be	AUX
cana-5711	505	21	listed	list	VERB
cana-5711	505	22	below	below	ADV
cana-5711	505	23	:	:	PUNCT
cana-5711	505	24	element	element	NOUN
cana-5711	505	25	in	in	ADP
cana-5711	505	26	ℤ2q	ℤ2q	PROPN
cana-5711	505	27	lee	lee	PROPN
cana-5711	505	28	weight	weight	NOUN
cana-5711	505	29	(	(	PUNCT
cana-5711	505	30	0,0,0	0,0,0	NOUN
cana-5711	505	31	)	)	PUNCT
cana-5711	505	32	0	0	NUM
cana-5711	506	1	(	(	PUNCT
cana-5711	506	2	0,0,1	0,0,1	NOUN
cana-5711	506	3	)	)	PUNCT
cana-5711	506	4	,	,	PUNCT
cana-5711	506	5	(	(	PUNCT
cana-5711	506	6	0,0,1+u	0,0,1+u	NUM
cana-5711	506	7	)	)	PUNCT
cana-5711	506	8	,	,	PUNCT
cana-5711	506	9	(	(	PUNCT
cana-5711	506	10	0,0,1+v	0,0,1+v	NOUN
cana-5711	506	11	)	)	PUNCT
cana-5711	506	12	,	,	PUNCT
cana-5711	506	13	(	(	PUNCT
cana-5711	506	14	0,0,1+u+v+uv	0,0,1+u+v+uv	PROPN
cana-5711	506	15	)	)	PUNCT
cana-5711	506	16	,	,	PUNCT
cana-5711	506	17	(	(	PUNCT
cana-5711	506	18	0,1,0	0,1,0	NUM
cana-5711	506	19	)	)	PUNCT
cana-5711	506	20	,	,	PUNCT
cana-5711	506	21	(	(	PUNCT
cana-5711	506	22	0,1+u,0	0,1+u,0	NUM
cana-5711	506	23	)	)	PUNCT
cana-5711	506	24	,	,	PUNCT
cana-5711	506	25	(	(	PUNCT
cana-5711	506	26	1,0,0	1,0,0	NUM
cana-5711	506	27	)	)	PUNCT
cana-5711	506	28	1	1	NUM
cana-5711	506	29	(	(	PUNCT
cana-5711	506	30	0,0,u	0,0,u	NOUN
cana-5711	506	31	)	)	PUNCT
cana-5711	506	32	,	,	PUNCT
cana-5711	506	33	(	(	PUNCT
cana-5711	506	34	0,0,v	0,0,v	NUM
cana-5711	506	35	)	)	PUNCT
cana-5711	506	36	,	,	PUNCT
cana-5711	506	37	(	(	PUNCT
cana-5711	506	38	0,0,u+v	0,0,u+v	NOUN
cana-5711	506	39	)	)	PUNCT
cana-5711	506	40	,	,	PUNCT
cana-5711	506	41	(	(	PUNCT
cana-5711	506	42	0,0,u+uv	0,0,u+uv	NOUN
cana-5711	506	43	)	)	PUNCT
cana-5711	506	44	,	,	PUNCT
cana-5711	506	45	(	(	PUNCT
cana-5711	506	46	0,0,v+uv	0,0,v+uv	NUM
cana-5711	506	47	)	)	PUNCT
cana-5711	506	48	,	,	PUNCT
cana-5711	506	49	(	(	PUNCT
cana-5711	506	50	0,0,u+v+uv	0,0,u+v+uv	NUM
cana-5711	506	51	)	)	PUNCT
cana-5711	506	52	,	,	PUNCT
cana-5711	506	53	(	(	PUNCT
cana-5711	506	54	0,1,1	0,1,1	NOUN
cana-5711	506	55	)	)	PUNCT
cana-5711	506	56	,	,	PUNCT
cana-5711	506	57	(	(	PUNCT
cana-5711	506	58	0,1,1+u	0,1,1+u	NOUN
cana-5711	506	59	)	)	PUNCT
cana-5711	506	60	,	,	PUNCT
cana-5711	506	61	(	(	PUNCT
cana-5711	506	62	0,1,1+v	0,1,1+v	NOUN
cana-5711	506	63	)	)	PUNCT
cana-5711	506	64	,	,	PUNCT
cana-5711	506	65	(	(	PUNCT
cana-5711	506	66	0,1,1+u+v+uv	0,1,1+u+v+uv	PROPN
cana-5711	506	67	)	)	PUNCT
cana-5711	506	68	,	,	PUNCT
cana-5711	506	69	(	(	PUNCT
cana-5711	506	70	0,u,0	0,u,0	NOUN
cana-5711	506	71	)	)	PUNCT
cana-5711	506	72	,	,	PUNCT
cana-5711	506	73	(	(	PUNCT
cana-5711	506	74	0,1+u,1	0,1+u,1	NUM
cana-5711	506	75	)	)	PUNCT
cana-5711	506	76	,	,	PUNCT
cana-5711	506	77	(	(	PUNCT
cana-5711	506	78	0,1+u,1+u	0,1+u,1+u	NUM
cana-5711	506	79	)	)	PUNCT
cana-5711	506	80	,	,	PUNCT
cana-5711	506	81	(	(	PUNCT
cana-5711	506	82	0,1+u,1+v	0,1+u,1+v	NOUN
cana-5711	506	83	)	)	PUNCT
cana-5711	506	84	,	,	PUNCT
cana-5711	506	85	(	(	PUNCT
cana-5711	506	86	0,1+u,1+u+v+uv	0,1+u,1+u+v+uv	PROPN
cana-5711	506	87	)	)	PUNCT
cana-5711	506	88	,	,	PUNCT
cana-5711	506	89	(	(	PUNCT
cana-5711	506	90	1,0,1	1,0,1	NUM
cana-5711	506	91	)	)	PUNCT
cana-5711	506	92	,	,	PUNCT
cana-5711	506	93	(	(	PUNCT
cana-5711	506	94	1,0,1+u	1,0,1+u	NUM
cana-5711	506	95	)	)	PUNCT
cana-5711	506	96	,	,	PUNCT
cana-5711	506	97	(	(	PUNCT
cana-5711	506	98	1,0,1+v	1,0,1+v	NUM
cana-5711	506	99	)	)	PUNCT
cana-5711	506	100	,	,	PUNCT
cana-5711	506	101	(	(	PUNCT
cana-5711	507	1	1,0,1+u+v+uv	1,0,1+u+v+uv	PROPN
cana-5711	507	2	)	)	PUNCT
cana-5711	507	3	,	,	PUNCT
cana-5711	507	4	(	(	PUNCT
cana-5711	507	5	1,1,0	1,1,0	NUM
cana-5711	507	6	)	)	PUNCT
cana-5711	507	7	,	,	PUNCT
cana-5711	507	8	(	(	PUNCT
cana-5711	507	9	1,1+u,0	1,1+u,0	NUM
cana-5711	507	10	)	)	PUNCT
cana-5711	507	11	2	2	NUM
cana-5711	507	12	(	(	PUNCT
cana-5711	507	13	0,0,1+uv	0,0,1+uv	NUM
cana-5711	507	14	)	)	PUNCT
cana-5711	507	15	,	,	PUNCT
cana-5711	507	16	(	(	PUNCT
cana-5711	507	17	0,0,1+u+v	0,0,1+u+v	NOUN
cana-5711	507	18	)	)	PUNCT
cana-5711	507	19	,	,	PUNCT
cana-5711	507	20	(	(	PUNCT
cana-5711	507	21	0,0,1+u+uv	0,0,1+u+uv	NUM
cana-5711	507	22	)	)	PUNCT
cana-5711	507	23	,	,	PUNCT
cana-5711	507	24	(	(	PUNCT
cana-5711	507	25	0,0,1+v+uv	0,0,1+v+uv	NUM
cana-5711	507	26	)	)	PUNCT
cana-5711	507	27	,	,	PUNCT
cana-5711	507	28	(	(	PUNCT
cana-5711	507	29	0,1u	0,1u	NOUN
cana-5711	507	30	)	)	PUNCT
cana-5711	507	31	,	,	PUNCT
cana-5711	507	32	(	(	PUNCT
cana-5711	507	33	0,1,v	0,1,v	NOUN
cana-5711	507	34	)	)	PUNCT
cana-5711	507	35	,	,	PUNCT
cana-5711	507	36	(	(	PUNCT
cana-5711	507	37	0,1,u+v	0,1,u+v	NOUN
cana-5711	507	38	)	)	PUNCT
cana-5711	507	39	,	,	PUNCT
cana-5711	507	40	(	(	PUNCT
cana-5711	507	41	0,1,u+uv	0,1,u+uv	NUM
cana-5711	507	42	)	)	PUNCT
cana-5711	507	43	,	,	PUNCT
cana-5711	507	44	(	(	PUNCT
cana-5711	507	45	0,1,v+uv	0,1,v+uv	NUM
cana-5711	507	46	)	)	PUNCT
cana-5711	507	47	,	,	PUNCT
cana-5711	507	48	(	(	PUNCT
cana-5711	507	49	0,1,u+v+uv	0,1,u+v+uv	PROPN
cana-5711	507	50	)	)	PUNCT
cana-5711	507	51	,	,	PUNCT
cana-5711	507	52	(	(	PUNCT
cana-5711	507	53	0,u,1	0,u,1	ADJ
cana-5711	507	54	)	)	PUNCT
cana-5711	507	55	,	,	PUNCT
cana-5711	507	56	(	(	PUNCT
cana-5711	507	57	0,u,1+u	0,u,1+u	NUM
cana-5711	507	58	)	)	PUNCT
cana-5711	507	59	,	,	PUNCT
cana-5711	507	60	(	(	PUNCT
cana-5711	507	61	0,u,1+v	0,u,1+v	NOUN
cana-5711	507	62	)	)	PUNCT
cana-5711	507	63	,	,	PUNCT
cana-5711	507	64	(	(	PUNCT
cana-5711	507	65	0,u,1+u+v+uv	0,u,1+u+v+uv	PROPN
cana-5711	507	66	)	)	PUNCT
cana-5711	507	67	,	,	PUNCT
cana-5711	507	68	(	(	PUNCT
cana-5711	507	69	0,1+u	0,1+u	NUM
cana-5711	507	70	,	,	PUNCT
cana-5711	507	71	u	u	NOUN
cana-5711	507	72	)	)	PUNCT
cana-5711	507	73	,	,	PUNCT
cana-5711	507	74	(	(	PUNCT
cana-5711	507	75	0,1+u	0,1+u	NUM
cana-5711	507	76	,	,	PUNCT
cana-5711	507	77	v	v	NOUN
cana-5711	507	78	)	)	PUNCT
cana-5711	507	79	,	,	PUNCT
cana-5711	507	80	(	(	PUNCT
cana-5711	507	81	0,1+u	0,1+u	NUM
cana-5711	507	82	,	,	PUNCT
cana-5711	507	83	u+v	u+v	NUM
cana-5711	507	84	)	)	PUNCT
cana-5711	507	85	,	,	PUNCT
cana-5711	507	86	(	(	PUNCT
cana-5711	507	87	0,1+u	0,1+u	NUM
cana-5711	507	88	,	,	PUNCT
cana-5711	507	89	u+uv	u+uv	PROPN
cana-5711	507	90	)	)	PUNCT
cana-5711	507	91	,	,	PUNCT
cana-5711	507	92	(	(	PUNCT
cana-5711	507	93	0,1+u	0,1+u	NUM
cana-5711	507	94	,	,	PUNCT
cana-5711	507	95	v+uv	v+uv	ADJ
cana-5711	507	96	)	)	PUNCT
cana-5711	507	97	,	,	PUNCT
cana-5711	507	98	(	(	PUNCT
cana-5711	507	99	0,1+u	0,1+u	NUM
cana-5711	507	100	,	,	PUNCT
cana-5711	507	101	u+v+uv	u+v+uv	PROPN
cana-5711	507	102	)	)	PUNCT
cana-5711	507	103	,	,	PUNCT
cana-5711	507	104	(	(	PUNCT
cana-5711	507	105	1,0,u	1,0,u	NUM
cana-5711	507	106	)	)	PUNCT
cana-5711	507	107	,	,	PUNCT
cana-5711	507	108	(	(	PUNCT
cana-5711	507	109	1,0,v	1,0,v	NUM
cana-5711	507	110	)	)	PUNCT
cana-5711	507	111	,	,	PUNCT
cana-5711	507	112	(	(	PUNCT
cana-5711	507	113	1,0,u+v	1,0,u+v	NUM
cana-5711	507	114	)	)	PUNCT
cana-5711	507	115	,	,	PUNCT
cana-5711	507	116	(	(	PUNCT
cana-5711	507	117	1,0,u+uv	1,0,u+uv	NUM
cana-5711	507	118	)	)	PUNCT
cana-5711	507	119	,	,	PUNCT
cana-5711	507	120	(	(	PUNCT
cana-5711	507	121	1,0,v+uv	1,0,v+uv	NUM
cana-5711	507	122	)	)	PUNCT
cana-5711	507	123	,	,	PUNCT
cana-5711	507	124	(	(	PUNCT
cana-5711	507	125	1,0,u+v+uv	1,0,u+v+uv	NUM
cana-5711	507	126	)	)	PUNCT
cana-5711	507	127	,	,	PUNCT
cana-5711	507	128	(	(	PUNCT
cana-5711	507	129	1,1,1	1,1,1	NUM
cana-5711	507	130	)	)	PUNCT
cana-5711	507	131	,	,	PUNCT
cana-5711	507	132	(	(	PUNCT
cana-5711	507	133	1,1,1+u	1,1,1+u	NUM
cana-5711	507	134	)	)	PUNCT
cana-5711	507	135	,	,	PUNCT
cana-5711	507	136	(	(	PUNCT
cana-5711	507	137	1,1,1+v	1,1,1+v	NUM
cana-5711	507	138	)	)	PUNCT
cana-5711	507	139	,	,	PUNCT
cana-5711	507	140	(	(	PUNCT
cana-5711	507	141	1,1,1+u+v+uv	1,1,1+u+v+uv	NUM
cana-5711	507	142	)	)	PUNCT
cana-5711	507	143	,	,	PUNCT
cana-5711	507	144	(	(	PUNCT
cana-5711	507	145	1,u,0	1,u,0	NUM
cana-5711	507	146	)	)	PUNCT
cana-5711	507	147	,	,	PUNCT
cana-5711	507	148	(	(	PUNCT
cana-5711	507	149	1,1+u,1	1,1+u,1	NUM
cana-5711	507	150	)	)	PUNCT
cana-5711	507	151	,	,	PUNCT
cana-5711	507	152	(	(	PUNCT
cana-5711	507	153	1,1+u,1+u	1,1+u,1+u	NUM
cana-5711	507	154	)	)	PUNCT
cana-5711	507	155	,	,	PUNCT
cana-5711	507	156	(	(	PUNCT
cana-5711	507	157	1,1+u,1+v	1,1+u,1+v	NUM
cana-5711	507	158	)	)	PUNCT
cana-5711	507	159	,	,	PUNCT
cana-5711	507	160	(	(	PUNCT
cana-5711	507	161	1,1+u,1+u+v+uv	1,1+u,1+u+v+uv	NUM
cana-5711	507	162	)	)	PUNCT
cana-5711	507	163	3	3	NUM
cana-5711	507	164	(	(	PUNCT
cana-5711	507	165	0,0,uv	0,0,uv	NUM
cana-5711	507	166	)	)	PUNCT
cana-5711	507	167	,	,	PUNCT
cana-5711	507	168	(	(	PUNCT
cana-5711	507	169	0,1,1+uv	0,1,1+uv	ADJ
cana-5711	507	170	)	)	PUNCT
cana-5711	507	171	,	,	PUNCT
cana-5711	507	172	(	(	PUNCT
cana-5711	507	173	0,1,1+u+v	0,1,1+u+v	NOUN
cana-5711	507	174	)	)	PUNCT
cana-5711	507	175	,	,	PUNCT
cana-5711	507	176	(	(	PUNCT
cana-5711	507	177	0,1,1+u+uv	0,1,1+u+uv	NUM
cana-5711	507	178	)	)	PUNCT
cana-5711	507	179	,	,	PUNCT
cana-5711	507	180	(	(	PUNCT
cana-5711	507	181	0,1,1+v+uv	0,1,1+v+uv	NUM
cana-5711	507	182	)	)	PUNCT
cana-5711	507	183	,	,	PUNCT
cana-5711	507	184	(	(	PUNCT
cana-5711	507	185	0,u	0,u	NOUN
cana-5711	507	186	,	,	PUNCT
cana-5711	507	187	u	u	NOUN
cana-5711	507	188	)	)	PUNCT
cana-5711	507	189	,	,	PUNCT
cana-5711	507	190	(	(	PUNCT
cana-5711	507	191	0,u	0,u	NOUN
cana-5711	507	192	,	,	PUNCT
cana-5711	507	193	v	v	NOUN
cana-5711	507	194	)	)	PUNCT
cana-5711	507	195	,	,	PUNCT
cana-5711	507	196	(	(	PUNCT
cana-5711	507	197	0,u	0,u	NOUN
cana-5711	507	198	,	,	PUNCT
cana-5711	507	199	u+v	u+v	NUM
cana-5711	507	200	)	)	PUNCT
cana-5711	507	201	,	,	PUNCT
cana-5711	507	202	(	(	PUNCT
cana-5711	507	203	0,u	0,u	NOUN
cana-5711	507	204	,	,	PUNCT
cana-5711	507	205	u+uv	u+uv	PROPN
cana-5711	507	206	)	)	PUNCT
cana-5711	507	207	,	,	PUNCT
cana-5711	507	208	(	(	PUNCT
cana-5711	507	209	0,u	0,u	NOUN
cana-5711	507	210	,	,	PUNCT
cana-5711	507	211	v+uv	v+uv	ADJ
cana-5711	507	212	)	)	PUNCT
cana-5711	507	213	,	,	PUNCT
cana-5711	507	214	(	(	PUNCT
cana-5711	507	215	0,u	0,u	NOUN
cana-5711	507	216	,	,	PUNCT
cana-5711	507	217	u+v+uv	u+v+uv	PROPN
cana-5711	507	218	)	)	PUNCT
cana-5711	507	219	,	,	PUNCT
cana-5711	507	220	(	(	PUNCT
cana-5711	507	221	0,1+u,1+uv	0,1+u,1+uv	NUM
cana-5711	507	222	)	)	PUNCT
cana-5711	507	223	,	,	PUNCT
cana-5711	507	224	(	(	PUNCT
cana-5711	507	225	0,1+u,1+u+v	0,1+u,1+u+v	NOUN
cana-5711	507	226	)	)	PUNCT
cana-5711	507	227	,	,	PUNCT
cana-5711	507	228	(	(	PUNCT
cana-5711	507	229	0,1+u,1+u+uv	0,1+u,1+u+uv	NUM
cana-5711	507	230	)	)	PUNCT
cana-5711	507	231	,	,	PUNCT
cana-5711	507	232	(	(	PUNCT
cana-5711	507	233	0,1+u,1+v+uv	0,1+u,1+v+uv	NUM
cana-5711	507	234	)	)	PUNCT
cana-5711	507	235	,	,	PUNCT
cana-5711	507	236	(	(	PUNCT
cana-5711	507	237	1,0,1+uv	1,0,1+uv	NOUN
cana-5711	507	238	)	)	PUNCT
cana-5711	507	239	,	,	PUNCT
cana-5711	507	240	(	(	PUNCT
cana-5711	507	241	1,0,1+u+v	1,0,1+u+v	NUM
cana-5711	507	242	)	)	PUNCT
cana-5711	507	243	,	,	PUNCT
cana-5711	507	244	(	(	PUNCT
cana-5711	507	245	1,0,1+u+uv	1,0,1+u+uv	NUM
cana-5711	507	246	)	)	PUNCT
cana-5711	507	247	,	,	PUNCT
cana-5711	507	248	(	(	PUNCT
cana-5711	507	249	1,0,1+v+uv	1,0,1+v+uv	NUM
cana-5711	507	250	)	)	PUNCT
cana-5711	507	251	,	,	PUNCT
cana-5711	507	252	(	(	PUNCT
cana-5711	507	253	1,1,u	1,1,u	NUM
cana-5711	507	254	)	)	PUNCT
cana-5711	507	255	,	,	PUNCT
cana-5711	507	256	(	(	PUNCT
cana-5711	507	257	1,1,v	1,1,v	NUM
cana-5711	507	258	)	)	PUNCT
cana-5711	507	259	,	,	PUNCT
cana-5711	507	260	(	(	PUNCT
cana-5711	507	261	1,1,u+v	1,1,u+v	NUM
cana-5711	507	262	)	)	PUNCT
cana-5711	507	263	,	,	PUNCT
cana-5711	507	264	(	(	PUNCT
cana-5711	507	265	1,1,u+uv	1,1,u+uv	NUM
cana-5711	507	266	)	)	PUNCT
cana-5711	507	267	,	,	PUNCT
cana-5711	507	268	(	(	PUNCT
cana-5711	507	269	1,1,v+uv	1,1,v+uv	NUM
cana-5711	507	270	)	)	PUNCT
cana-5711	507	271	,	,	PUNCT
cana-5711	507	272	(	(	PUNCT
cana-5711	507	273	1,1,u+v+uv	1,1,u+v+uv	NUM
cana-5711	507	274	)	)	PUNCT
cana-5711	507	275	,	,	PUNCT
cana-5711	507	276	(	(	PUNCT
cana-5711	507	277	1,u,1	1,u,1	NUM
cana-5711	507	278	)	)	PUNCT
cana-5711	507	279	,	,	PUNCT
cana-5711	507	280	(	(	PUNCT
cana-5711	507	281	1,u,1+u	1,u,1+u	NUM
cana-5711	507	282	)	)	PUNCT
cana-5711	507	283	,	,	PUNCT
cana-5711	507	284	(	(	PUNCT
cana-5711	507	285	1,u,1+v	1,u,1+v	NUM
cana-5711	507	286	)	)	PUNCT
cana-5711	507	287	,	,	PUNCT
cana-5711	507	288	(	(	PUNCT
cana-5711	507	289	1,u,1+u+v+uv	1,u,1+u+v+uv	NUM
cana-5711	507	290	)	)	PUNCT
cana-5711	507	291	,	,	PUNCT
cana-5711	507	292	(	(	PUNCT
cana-5711	507	293	1,1+u	1,1+u	NUM
cana-5711	507	294	,	,	PUNCT
cana-5711	507	295	u	u	NOUN
cana-5711	507	296	)	)	PUNCT
cana-5711	507	297	,	,	PUNCT
cana-5711	507	298	(	(	PUNCT
cana-5711	507	299	1,1+u	1,1+u	NUM
cana-5711	507	300	,	,	PUNCT
cana-5711	507	301	v	v	NOUN
cana-5711	507	302	)	)	PUNCT
cana-5711	507	303	,	,	PUNCT
cana-5711	507	304	(	(	PUNCT
cana-5711	507	305	1,1+u	1,1+u	NUM
cana-5711	507	306	,	,	PUNCT
cana-5711	507	307	u+v	u+v	NUM
cana-5711	507	308	)	)	PUNCT
cana-5711	507	309	,	,	PUNCT
cana-5711	507	310	(	(	PUNCT
cana-5711	507	311	1,1+u	1,1+u	NUM
cana-5711	507	312	,	,	PUNCT
cana-5711	507	313	u+uv	u+uv	PROPN
cana-5711	507	314	)	)	PUNCT
cana-5711	507	315	,	,	PUNCT
cana-5711	507	316	(	(	PUNCT
cana-5711	507	317	1,1+u	1,1+u	NUM
cana-5711	507	318	,	,	PUNCT
cana-5711	507	319	v+uv	v+uv	ADJ
cana-5711	507	320	)	)	PUNCT
cana-5711	507	321	,	,	PUNCT
cana-5711	507	322	(	(	PUNCT
cana-5711	507	323	1,1+u	1,1+u	NUM
cana-5711	507	324	,	,	PUNCT
cana-5711	507	325	u+v+uv	u+v+uv	PROPN
cana-5711	507	326	)	)	PUNCT
cana-5711	507	327	4	4	NUM
cana-5711	507	328	(	(	PUNCT
cana-5711	507	329	0,1,uv	0,1,uv	NUM
cana-5711	507	330	)	)	PUNCT
cana-5711	507	331	,	,	PUNCT
cana-5711	507	332	(	(	PUNCT
cana-5711	507	333	0,u,1+uv	0,u,1+uv	NUM
cana-5711	507	334	)	)	PUNCT
cana-5711	507	335	,	,	PUNCT
cana-5711	507	336	(	(	PUNCT
cana-5711	507	337	0,u,1+u+v	0,u,1+u+v	NOUN
cana-5711	507	338	)	)	PUNCT
cana-5711	507	339	,	,	PUNCT
cana-5711	507	340	(	(	PUNCT
cana-5711	507	341	0,u,1+u+uv	0,u,1+u+uv	NOUN
cana-5711	507	342	)	)	PUNCT
cana-5711	507	343	,	,	PUNCT
cana-5711	507	344	(	(	PUNCT
cana-5711	507	345	0,u,1+v+uv	0,u,1+v+uv	NOUN
cana-5711	507	346	)	)	PUNCT
cana-5711	507	347	,	,	PUNCT
cana-5711	507	348	(	(	PUNCT
cana-5711	507	349	0,1+u	0,1+u	NUM
cana-5711	507	350	,	,	PUNCT
cana-5711	507	351	uv	uv	NOUN
cana-5711	507	352	)	)	PUNCT
cana-5711	507	353	,	,	PUNCT
cana-5711	507	354	(	(	PUNCT
cana-5711	507	355	1,0,uv	1,0,uv	NUM
cana-5711	507	356	)	)	PUNCT
cana-5711	507	357	,	,	PUNCT
cana-5711	507	358	(	(	PUNCT
cana-5711	507	359	1,1,1+uv	1,1,1+uv	NUM
cana-5711	507	360	)	)	PUNCT
cana-5711	507	361	,	,	PUNCT
cana-5711	507	362	(	(	PUNCT
cana-5711	507	363	1,1,1+u+v	1,1,1+u+v	NUM
cana-5711	507	364	)	)	PUNCT
cana-5711	507	365	,	,	PUNCT
cana-5711	507	366	(	(	PUNCT
cana-5711	507	367	1,1,1+u+uv	1,1,1+u+uv	NUM
cana-5711	507	368	)	)	PUNCT
cana-5711	507	369	,	,	PUNCT
cana-5711	507	370	(	(	PUNCT
cana-5711	507	371	1,1,1+v+uv	1,1,1+v+uv	NUM
cana-5711	507	372	)	)	PUNCT
cana-5711	507	373	,	,	PUNCT
cana-5711	507	374	(	(	PUNCT
cana-5711	507	375	1,u	1,u	NUM
cana-5711	507	376	,	,	PUNCT
cana-5711	507	377	u	u	NOUN
cana-5711	507	378	)	)	PUNCT
cana-5711	507	379	,	,	PUNCT
cana-5711	507	380	(	(	PUNCT
cana-5711	507	381	1,u	1,u	NUM
cana-5711	507	382	,	,	PUNCT
cana-5711	507	383	v	v	NOUN
cana-5711	507	384	)	)	PUNCT
cana-5711	507	385	,	,	PUNCT
cana-5711	507	386	(	(	PUNCT
cana-5711	507	387	1,u	1,u	NUM
cana-5711	507	388	,	,	PUNCT
cana-5711	507	389	u+v	u+v	NUM
cana-5711	507	390	)	)	PUNCT
cana-5711	507	391	,	,	PUNCT
cana-5711	507	392	(	(	PUNCT
cana-5711	507	393	1,u	1,u	NUM
cana-5711	507	394	,	,	PUNCT
cana-5711	507	395	u+uv	u+uv	PROPN
cana-5711	507	396	)	)	PUNCT
cana-5711	507	397	,	,	PUNCT
cana-5711	507	398	(	(	PUNCT
cana-5711	507	399	1,u	1,u	NUM
cana-5711	507	400	,	,	PUNCT
cana-5711	507	401	v+uv	v+uv	ADJ
cana-5711	507	402	)	)	PUNCT
cana-5711	507	403	,	,	PUNCT
cana-5711	507	404	(	(	PUNCT
cana-5711	507	405	1,u	1,u	NUM
cana-5711	507	406	,	,	PUNCT
cana-5711	507	407	u+v+uv	u+v+uv	PROPN
cana-5711	507	408	)	)	PUNCT
cana-5711	507	409	,	,	PUNCT
cana-5711	507	410	(	(	PUNCT
cana-5711	507	411	1,1+u,1+uv	1,1+u,1+uv	NUM
cana-5711	507	412	)	)	PUNCT
cana-5711	507	413	,	,	PUNCT
cana-5711	507	414	(	(	PUNCT
cana-5711	507	415	1,1+u,1+u+v	1,1+u,1+u+v	NOUN
cana-5711	507	416	)	)	PUNCT
cana-5711	507	417	,	,	PUNCT
cana-5711	507	418	(	(	PUNCT
cana-5711	507	419	1,1+u,1+u+uv	1,1+u,1+u+uv	NUM
cana-5711	507	420	)	)	PUNCT
cana-5711	507	421	,	,	PUNCT
cana-5711	507	422	(	(	PUNCT
cana-5711	507	423	1,1+u,1+v+uv	1,1+u,1+v+uv	NUM
cana-5711	507	424	)	)	PUNCT
cana-5711	507	425	5	5	NUM
cana-5711	507	426	(	(	PUNCT
cana-5711	507	427	0,u	0,u	NOUN
cana-5711	507	428	,	,	PUNCT
cana-5711	507	429	uv	uv	NOUN
cana-5711	507	430	)	)	PUNCT
cana-5711	507	431	,	,	PUNCT
cana-5711	507	432	(	(	PUNCT
cana-5711	507	433	1,1,uv	1,1,uv	NUM
cana-5711	507	434	)	)	PUNCT
cana-5711	507	435	,	,	PUNCT
cana-5711	507	436	(	(	PUNCT
cana-5711	507	437	1,u,1+uv	1,u,1+uv	NUM
cana-5711	507	438	)	)	PUNCT
cana-5711	507	439	,	,	PUNCT
cana-5711	507	440	(	(	PUNCT
cana-5711	507	441	1,u,1+u+v	1,u,1+u+v	NUM
cana-5711	507	442	)	)	PUNCT
cana-5711	507	443	,	,	PUNCT
cana-5711	507	444	(	(	PUNCT
cana-5711	507	445	1,u,1+u+uv	1,u,1+u+uv	NUM
cana-5711	507	446	)	)	PUNCT
cana-5711	507	447	,	,	PUNCT
cana-5711	507	448	(	(	PUNCT
cana-5711	507	449	1,u,1+v+uv	1,u,1+v+uv	NUM
cana-5711	507	450	)	)	PUNCT
cana-5711	507	451	,	,	PUNCT
cana-5711	507	452	(	(	PUNCT
cana-5711	507	453	1,1+u	1,1+u	NUM
cana-5711	507	454	,	,	PUNCT
cana-5711	507	455	uv	uv	NOUN
cana-5711	507	456	)	)	PUNCT
cana-5711	507	457	6	6	NUM
cana-5711	507	458	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	507	459	communications	communication	NOUN
cana-5711	507	460	on	on	ADP
cana-5711	507	461	applied	apply	VERB
cana-5711	507	462	nonlinear	nonlinear	ADJ
cana-5711	507	463	analysis	analysis	NOUN
cana-5711	507	464	issn	issn	NOUN
cana-5711	507	465	:	:	PUNCT
cana-5711	507	466	1074	1074	NUM
cana-5711	507	467	-	-	PUNCT
cana-5711	507	468	133x	133x	NUM
cana-5711	507	469	vol	vol	VERB
cana-5711	507	470	32	32	NUM
cana-5711	507	471	no	no	NOUN
cana-5711	507	472	.	.	PUNCT
cana-5711	508	1	10s	10	NOUN
cana-5711	508	2	(	(	PUNCT
cana-5711	508	3	2025	2025	NUM
cana-5711	508	4	)	)	PUNCT
cana-5711	508	5	2707	2707	NUM
cana-5711	508	6	(	(	PUNCT
cana-5711	508	7	1,u	1,u	NUM
cana-5711	508	8	,	,	PUNCT
cana-5711	508	9	uv	uv	NOUN
cana-5711	508	10	)	)	PUNCT
cana-5711	508	11	7	7	NUM
cana-5711	508	12	definition	definition	NOUN
cana-5711	508	13	5.10	5.10	NUM
cana-5711	508	14	.	.	PUNCT
cana-5711	509	1	let	let	VERB
cana-5711	509	2	c	c	PRON
cana-5711	509	3	be	be	AUX
cana-5711	509	4	an	an	DET
cana-5711	509	5	additive	additive	ADJ
cana-5711	509	6	code	code	NOUN
cana-5711	509	7	of	of	ADP
cana-5711	509	8	length	length	NOUN
cana-5711	509	9	n	n	CCONJ
cana-5711	509	10	over	over	ADP
cana-5711	509	11	ℤ2q	ℤ2q	PROPN
cana-5711	509	12	.	.	PUNCT
cana-5711	510	1	its	its	PRON
cana-5711	510	2	symmetrized	symmetrize	VERB
cana-5711	510	3	weight	weight	NOUN
cana-5711	510	4	enumerator	enumerator	NOUN
cana-5711	510	5	is	be	AUX
cana-5711	510	6	defined	define	VERB
cana-5711	510	7	by	by	ADP
cana-5711	510	8	swec	swec	NOUN
cana-5711	510	9	(	(	PUNCT
cana-5711	510	10	x	x	X
cana-5711	510	11	,	,	PUNCT
cana-5711	510	12	y	y	PROPN
cana-5711	510	13	,	,	PUNCT
cana-5711	510	14	z	z	PROPN
cana-5711	510	15	,	,	PUNCT
cana-5711	510	16	w	w	PROPN
cana-5711	510	17	,	,	PUNCT
cana-5711	510	18	t	t	PROPN
cana-5711	510	19	,	,	PUNCT
cana-5711	510	20	p	p	X
cana-5711	510	21	,	,	PUNCT
cana-5711	510	22	q	q	NOUN
cana-5711	510	23	,	,	PUNCT
cana-5711	510	24	n	n	NOUN
cana-5711	510	25	)	)	PUNCT
cana-5711	511	1	=	=	X
cana-5711	511	2	cwec	cwec	NOUN
cana-5711	511	3	(	(	PUNCT
cana-5711	511	4	x	x	NOUN
cana-5711	511	5	,	,	PUNCT
cana-5711	511	6	y	y	PROPN
cana-5711	511	7	,	,	PUNCT
cana-5711	511	8	z	z	PROPN
cana-5711	511	9	,	,	PUNCT
cana-5711	511	10	z	z	PROPN
cana-5711	511	11	,	,	PUNCT
cana-5711	511	12	t	t	PROPN
cana-5711	511	13	,	,	PUNCT
cana-5711	511	14	y	y	PROPN
cana-5711	511	15	,	,	PUNCT
cana-5711	511	16	y	y	PROPN
cana-5711	511	17	,	,	PUNCT
cana-5711	511	18	w	w	PROPN
cana-5711	511	19	,	,	PUNCT
cana-5711	511	20	z	z	PROPN
cana-5711	511	21	,	,	PUNCT
cana-5711	511	22	z	z	PROPN
cana-5711	511	23	,	,	PUNCT
cana-5711	511	24	z	z	PROPN
cana-5711	511	25	,	,	PUNCT
cana-5711	511	26	z	z	PROPN
cana-5711	511	27	,	,	PUNCT
cana-5711	511	28	w	w	PROPN
cana-5711	511	29	,	,	PUNCT
cana-5711	511	30	w	w	PROPN
cana-5711	511	31	,	,	PUNCT
cana-5711	511	32	w	w	PROPN
cana-5711	511	33	,	,	PUNCT
cana-5711	511	34	y	y	PROPN
cana-5711	511	35	,	,	PUNCT
cana-5711	511	36	y	y	PROPN
cana-5711	511	37	,	,	PUNCT
cana-5711	511	38	z	z	PROPN
cana-5711	511	39	,	,	PUNCT
cana-5711	511	40	w	w	PROPN
cana-5711	511	41	,	,	PUNCT
cana-5711	511	42	w	w	PROPN
cana-5711	511	43	,	,	PUNCT
cana-5711	511	44	p	p	X
cana-5711	511	45	,	,	PUNCT
cana-5711	511	46	z	z	PROPN
cana-5711	511	47	,	,	PUNCT
cana-5711	511	48	z	z	PROPN
cana-5711	511	49	,	,	PUNCT
cana-5711	511	50	t	t	PROPN
cana-5711	511	51	,	,	PUNCT
cana-5711	511	52	w	w	PROPN
cana-5711	511	53	,	,	PUNCT
cana-5711	511	54	w	w	PROPN
cana-5711	511	55	,	,	PUNCT
cana-5711	511	56	w	w	PROPN
cana-5711	511	57	,	,	PUNCT
cana-5711	511	58	w	w	PROPN
cana-5711	511	59	,	,	PUNCT
cana-5711	511	60	t	t	PROPN
cana-5711	511	61	,	,	PUNCT
cana-5711	511	62	t	t	PROPN
cana-5711	511	63	,	,	PUNCT
cana-5711	511	64	t	t	PROPN
cana-5711	511	65	,	,	PUNCT
cana-5711	511	66	z	z	PROPN
cana-5711	511	67	,	,	PUNCT
cana-5711	511	68	z	z	PROPN
cana-5711	511	69	,	,	PUNCT
cana-5711	511	70	w	w	PROPN
cana-5711	511	71	,	,	PUNCT
cana-5711	511	72	t	t	PROPN
cana-5711	511	73	,	,	PUNCT
cana-5711	511	74	t	t	PROPN
cana-5711	511	75	,	,	PUNCT
cana-5711	511	76	q	q	NOUN
cana-5711	511	77	,	,	PUNCT
cana-5711	511	78	w	w	PROPN
cana-5711	511	79	,	,	PUNCT
cana-5711	511	80	w	w	PROPN
cana-5711	511	81	,	,	PUNCT
cana-5711	511	82	p	p	X
cana-5711	511	83	,	,	PUNCT
cana-5711	511	84	t	t	PROPN
cana-5711	511	85	,	,	PUNCT
cana-5711	511	86	t	t	PROPN
cana-5711	511	87	,	,	PUNCT
cana-5711	511	88	t	t	PROPN
cana-5711	511	89	,	,	PUNCT
cana-5711	511	90	t	t	PROPN
cana-5711	511	91	,	,	PUNCT
cana-5711	511	92	p	p	X
cana-5711	511	93	,	,	PUNCT
cana-5711	511	94	p	p	X
cana-5711	511	95	,	,	PUNCT
cana-5711	511	96	p	p	X
cana-5711	511	97	,	,	PUNCT
cana-5711	511	98	w	w	PROPN
cana-5711	511	99	,	,	PUNCT
cana-5711	511	100	y	y	PROPN
cana-5711	511	101	,	,	PUNCT
cana-5711	511	102	z	z	PROPN
cana-5711	511	103	,	,	PUNCT
cana-5711	511	104	w	w	PROPN
cana-5711	511	105	,	,	PUNCT
cana-5711	511	106	w	w	PROPN
cana-5711	511	107	,	,	PUNCT
cana-5711	511	108	p	p	X
cana-5711	511	109	,	,	PUNCT
cana-5711	511	110	z	z	PROPN
cana-5711	511	111	,	,	PUNCT
cana-5711	511	112	z	z	PROPN
cana-5711	511	113	,	,	PUNCT
cana-5711	511	114	t	t	PROPN
cana-5711	511	115	,	,	PUNCT
cana-5711	511	116	w	w	PROPN
cana-5711	511	117	,	,	PUNCT
cana-5711	511	118	w	w	PROPN
cana-5711	511	119	,	,	PUNCT
cana-5711	511	120	w	w	PROPN
cana-5711	511	121	,	,	PUNCT
cana-5711	511	122	w	w	PROPN
cana-5711	511	123	,	,	PUNCT
cana-5711	511	124	t	t	PROPN
cana-5711	511	125	,	,	PUNCT
cana-5711	511	126	t	t	PROPN
cana-5711	511	127	,	,	PUNCT
cana-5711	511	128	t	t	PROPN
cana-5711	511	129	,	,	PUNCT
cana-5711	511	130	z	z	PROPN
cana-5711	511	131	,	,	PUNCT
cana-5711	511	132	y	y	PROPN
cana-5711	511	133	,	,	PUNCT
cana-5711	511	134	z	z	PROPN
cana-5711	511	135	,	,	PUNCT
cana-5711	511	136	w	w	PROPN
cana-5711	511	137	,	,	PUNCT
cana-5711	511	138	w	w	PROPN
cana-5711	511	139	,	,	PUNCT
cana-5711	511	140	p	p	X
cana-5711	511	141	,	,	PUNCT
cana-5711	511	142	z	z	PROPN
cana-5711	511	143	,	,	PUNCT
cana-5711	511	144	z	z	PROPN
cana-5711	511	145	,	,	PUNCT
cana-5711	511	146	t	t	PROPN
cana-5711	511	147	,	,	PUNCT
cana-5711	511	148	w	w	PROPN
cana-5711	511	149	,	,	PUNCT
cana-5711	511	150	w	w	PROPN
cana-5711	511	151	,	,	PUNCT
cana-5711	511	152	w	w	PROPN
cana-5711	511	153	,	,	PUNCT
cana-5711	511	154	w	w	PROPN
cana-5711	511	155	,	,	PUNCT
cana-5711	511	156	t	t	PROPN
cana-5711	511	157	,	,	PUNCT
cana-5711	511	158	t	t	PROPN
cana-5711	511	159	,	,	PUNCT
cana-5711	511	160	t	t	PROPN
cana-5711	511	161	,	,	PUNCT
cana-5711	511	162	z	z	PROPN
cana-5711	511	163	,	,	PUNCT
cana-5711	511	164	z	z	PROPN
cana-5711	511	165	,	,	PUNCT
cana-5711	511	166	w	w	PROPN
cana-5711	511	167	,	,	PUNCT
cana-5711	511	168	t	t	PROPN
cana-5711	511	169	,	,	PUNCT
cana-5711	511	170	t	t	PROPN
cana-5711	511	171	,	,	PUNCT
cana-5711	511	172	q	q	NOUN
cana-5711	511	173	,	,	PUNCT
cana-5711	511	174	w	w	PROPN
cana-5711	511	175	,	,	PUNCT
cana-5711	511	176	w	w	PROPN
cana-5711	511	177	,	,	PUNCT
cana-5711	511	178	p	p	X
cana-5711	511	179	,	,	PUNCT
cana-5711	511	180	t	t	PROPN
cana-5711	511	181	,	,	PUNCT
cana-5711	511	182	t	t	PROPN
cana-5711	511	183	,	,	PUNCT
cana-5711	511	184	t	t	PROPN
cana-5711	511	185	,	,	PUNCT
cana-5711	511	186	t	t	PROPN
cana-5711	511	187	,	,	PUNCT
cana-5711	511	188	p	p	X
cana-5711	511	189	,	,	PUNCT
cana-5711	511	190	p	p	X
cana-5711	511	191	,	,	PUNCT
cana-5711	511	192	p	p	X
cana-5711	511	193	,	,	PUNCT
cana-5711	511	194	w	w	PROPN
cana-5711	511	195	,	,	PUNCT
cana-5711	511	196	w	w	PROPN
cana-5711	511	197	,	,	PUNCT
cana-5711	511	198	t	t	PROPN
cana-5711	511	199	,	,	PUNCT
cana-5711	511	200	p	p	X
cana-5711	511	201	,	,	PUNCT
cana-5711	511	202	p	p	X
cana-5711	511	203	,	,	PUNCT
cana-5711	511	204	n	n	CCONJ
cana-5711	511	205	,	,	PUNCT
cana-5711	511	206	t	t	PROPN
cana-5711	511	207	,	,	PUNCT
cana-5711	511	208	t	t	PROPN
cana-5711	511	209	,	,	PUNCT
cana-5711	511	210	q	q	X
cana-5711	511	211	,	,	PUNCT
cana-5711	511	212	p	p	X
cana-5711	511	213	,	,	PUNCT
cana-5711	511	214	p	p	X
cana-5711	511	215	,	,	PUNCT
cana-5711	511	216	p	p	X
cana-5711	511	217	,	,	PUNCT
cana-5711	511	218	p	p	X
cana-5711	511	219	,	,	PUNCT
cana-5711	511	220	q	q	ADJ
cana-5711	511	221	,	,	PUNCT
cana-5711	511	222	q	q	ADJ
cana-5711	511	223	,	,	PUNCT
cana-5711	511	224	q	q	ADJ
cana-5711	511	225	,	,	PUNCT
cana-5711	511	226	t	t	PROPN
cana-5711	511	227	,	,	PUNCT
cana-5711	511	228	z	z	PROPN
cana-5711	511	229	,	,	PUNCT
cana-5711	511	230	w	w	PROPN
cana-5711	511	231	,	,	PUNCT
cana-5711	511	232	t	t	PROPN
cana-5711	511	233	,	,	PUNCT
cana-5711	511	234	t	t	PROPN
cana-5711	511	235	,	,	PUNCT
cana-5711	511	236	q	q	NOUN
cana-5711	511	237	,	,	PUNCT
cana-5711	511	238	w	w	PROPN
cana-5711	511	239	,	,	PUNCT
cana-5711	511	240	w	w	PROPN
cana-5711	511	241	,	,	PUNCT
cana-5711	511	242	p	p	X
cana-5711	511	243	,	,	PUNCT
cana-5711	511	244	t	t	PROPN
cana-5711	511	245	,	,	PUNCT
cana-5711	511	246	t	t	PROPN
cana-5711	511	247	,	,	PUNCT
cana-5711	511	248	t	t	PROPN
cana-5711	511	249	,	,	PUNCT
cana-5711	511	250	t	t	PROPN
cana-5711	511	251	,	,	PUNCT
cana-5711	511	252	p	p	X
cana-5711	511	253	,	,	PUNCT
cana-5711	511	254	p	p	X
cana-5711	511	255	,	,	PUNCT
cana-5711	511	256	p	p	X
cana-5711	511	257	,	,	PUNCT
cana-5711	511	258	w	w	PROPN
cana-5711	511	259	)	)	PUNCT
cana-5711	511	260	.	.	PUNCT
cana-5711	512	1	where	where	SCONJ
cana-5711	512	2	the	the	DET
cana-5711	512	3	lee	lee	PROPN
cana-5711	512	4	weight	weight	NOUN
cana-5711	512	5	of	of	ADP
cana-5711	512	6	the	the	DET
cana-5711	512	7	elements	element	NOUN
cana-5711	512	8	0	0	NUM
cana-5711	512	9	,	,	PUNCT
cana-5711	512	10	1	1	NUM
cana-5711	512	11	,	,	PUNCT
cana-5711	512	12	2	2	NUM
cana-5711	512	13	,	,	PUNCT
cana-5711	512	14	3	3	NUM
cana-5711	512	15	,	,	PUNCT
cana-5711	512	16	4	4	NUM
cana-5711	512	17	,	,	PUNCT
cana-5711	512	18	5	5	NUM
cana-5711	512	19	,	,	PUNCT
cana-5711	512	20	6	6	NUM
cana-5711	512	21	,	,	PUNCT
cana-5711	512	22	and	and	CCONJ
cana-5711	512	23	7	7	NUM
cana-5711	512	24	is	be	AUX
cana-5711	512	25	represented	represent	VERB
cana-5711	512	26	by	by	ADP
cana-5711	512	27	the	the	DET
cana-5711	512	28	variables	variable	NOUN
cana-5711	512	29	x	x	NOUN
cana-5711	512	30	,	,	PUNCT
cana-5711	512	31	y	y	PROPN
cana-5711	512	32	,	,	PUNCT
cana-5711	512	33	z	z	PROPN
cana-5711	512	34	,	,	PUNCT
cana-5711	512	35	w	w	PROPN
cana-5711	512	36	,	,	PUNCT
cana-5711	512	37	t	t	PROPN
cana-5711	512	38	,	,	PUNCT
cana-5711	512	39	p	p	X
cana-5711	512	40	,	,	PUNCT
cana-5711	512	41	q	q	X
cana-5711	512	42	,	,	PUNCT
cana-5711	512	43	and	and	CCONJ
cana-5711	512	44	n	n	CCONJ
cana-5711	512	45	,	,	PUNCT
cana-5711	512	46	respectively	respectively	ADV
cana-5711	512	47	.	.	PUNCT
cana-5711	513	1	by	by	ADP
cana-5711	513	2	definition	definition	NOUN
cana-5711	513	3	,	,	PUNCT
cana-5711	513	4	we	we	PRON
cana-5711	513	5	have	have	VERB
cana-5711	513	6	𝑆𝑊𝐸𝐶(𝑋	𝑆𝑊𝐸𝐶(𝑋	PROPN
cana-5711	513	7	,	,	PUNCT
cana-5711	513	8	𝑌	𝑌	PROPN
cana-5711	513	9	,	,	PUNCT
cana-5711	513	10	𝑍	𝑍	PROPN
cana-5711	513	11	,	,	PUNCT
cana-5711	513	12	𝑊	𝑊	PROPN
cana-5711	513	13	,	,	PUNCT
cana-5711	513	14	𝑇	𝑇	PROPN
cana-5711	513	15	,	,	PUNCT
cana-5711	513	16	𝑃	𝑃	PROPN
cana-5711	513	17	,	,	PUNCT
cana-5711	513	18	𝑄,𝑁	𝑄,𝑁	ADJ
cana-5711	513	19	)	)	PUNCT
cana-5711	513	20	=	=	SYM
cana-5711	513	21	∑	∑	PUNCT
cana-5711	513	22	𝑋𝑛0(𝑐	𝑋𝑛0(𝑐	PROPN
cana-5711	513	23	)	)	PUNCT
cana-5711	513	24	𝑐∈𝐶	𝑐∈𝐶	X
cana-5711	513	25	𝑌𝑛1(𝑐)𝑍𝑛2(𝑐)𝑊𝑛3(𝑐)𝑇𝑛4(𝑐)𝑃𝑛5(𝑐)𝑄𝑛6(𝑐)𝑁𝑛7(𝑐	𝑌𝑛1(𝑐)𝑍𝑛2(𝑐)𝑊𝑛3(𝑐)𝑇𝑛4(𝑐)𝑃𝑛5(𝑐)𝑄𝑛6(𝑐)𝑁𝑛7(𝑐	NUM
cana-5711	513	26	)	)	PUNCT
cana-5711	513	27	(	(	PUNCT
cana-5711	513	28	5.5	5.5	NUM
cana-5711	513	29	)	)	PUNCT
cana-5711	514	1	where	where	SCONJ
cana-5711	514	2	𝑛0(𝑐	𝑛0(𝑐	NOUN
cana-5711	514	3	)	)	PUNCT
cana-5711	514	4	=	=	NOUN
cana-5711	514	5	𝑤𝑓1	𝑤𝑓1	NOUN
cana-5711	514	6	(	(	PUNCT
cana-5711	514	7	𝑐	𝑐	NOUN
cana-5711	514	8	)	)	PUNCT
cana-5711	514	9	,	,	PUNCT
cana-5711	514	10	𝑛1(𝑐	𝑛1(𝑐	NOUN
cana-5711	514	11	)	)	PUNCT
cana-5711	514	12	=	=	SYM
cana-5711	514	13	𝑤𝑓2	𝑤𝑓2	NOUN
cana-5711	514	14	(	(	PUNCT
cana-5711	514	15	𝑐	𝑐	NOUN
cana-5711	514	16	)	)	PUNCT
cana-5711	515	1	+	+	CCONJ
cana-5711	515	2	𝑤𝑓6	𝑤𝑓6	NOUN
cana-5711	515	3	(	(	PUNCT
cana-5711	515	4	𝑐	𝑐	NOUN
cana-5711	515	5	)	)	PUNCT
cana-5711	515	6	+	+	CCONJ
cana-5711	515	7	𝑤𝑓7	𝑤𝑓7	PROPN
cana-5711	515	8	(	(	PUNCT
cana-5711	515	9	𝑐	𝑐	NOUN
cana-5711	515	10	)	)	PUNCT
cana-5711	515	11	+	+	CCONJ
cana-5711	516	1	𝑤𝑓16	𝑤𝑓16	PROPN
cana-5711	516	2	(	(	PUNCT
cana-5711	516	3	𝑐	𝑐	NOUN
cana-5711	516	4	)	)	PUNCT
cana-5711	516	5	+	+	CCONJ
cana-5711	516	6	𝑤𝑓17	𝑤𝑓17	NOUN
cana-5711	516	7	(	(	PUNCT
cana-5711	516	8	𝑐	𝑐	NOUN
cana-5711	516	9	)	)	PUNCT
cana-5711	516	10	+	+	CCONJ
cana-5711	517	1	𝑤𝑓49	𝑤𝑓49	PROPN
cana-5711	517	2	(	(	PUNCT
cana-5711	517	3	𝑐	𝑐	NOUN
cana-5711	517	4	)	)	PUNCT
cana-5711	517	5	+	+	CCONJ
cana-5711	517	6	𝑤𝑓65	𝑤𝑓65	PROPN
cana-5711	517	7	(	(	PUNCT
cana-5711	517	8	𝑐	𝑐	NOUN
cana-5711	517	9	)	)	PUNCT
cana-5711	517	10	,	,	PUNCT
cana-5711	517	11	𝑛2(𝑐	𝑛2(𝑐	X
cana-5711	517	12	)	)	PUNCT
cana-5711	517	13	=	=	SYM
cana-5711	517	14	𝑤𝑓3	𝑤𝑓3	NOUN
cana-5711	517	15	(	(	PUNCT
cana-5711	517	16	𝑐	𝑐	NOUN
cana-5711	517	17	)	)	PUNCT
cana-5711	517	18	+	+	CCONJ
cana-5711	517	19	𝑤𝑓4	𝑤𝑓4	NOUN
cana-5711	517	20	(	(	PUNCT
cana-5711	517	21	𝑐	𝑐	NOUN
cana-5711	517	22	)	)	PUNCT
cana-5711	517	23	+	+	CCONJ
cana-5711	517	24	𝑤𝑓9	𝑤𝑓9	ADJ
cana-5711	517	25	(	(	PUNCT
cana-5711	517	26	𝑐	𝑐	NOUN
cana-5711	517	27	)	)	PUNCT
cana-5711	517	28	+	+	CCONJ
cana-5711	518	1	𝑤𝑓10	𝑤𝑓10	PROPN
cana-5711	518	2	(	(	PUNCT
cana-5711	518	3	𝑐	𝑐	NOUN
cana-5711	518	4	)	)	PUNCT
cana-5711	518	5	+	+	CCONJ
cana-5711	518	6	𝑤𝑓11	𝑤𝑓11	PROPN
cana-5711	518	7	(	(	PUNCT
cana-5711	518	8	𝑐	𝑐	NOUN
cana-5711	518	9	)	)	PUNCT
cana-5711	518	10	+	+	CCONJ
cana-5711	518	11	𝑤𝑓12	𝑤𝑓12	PROPN
cana-5711	518	12	(	(	PUNCT
cana-5711	518	13	𝑐	𝑐	NOUN
cana-5711	518	14	)	)	PUNCT
cana-5711	518	15	+	+	CCONJ
cana-5711	519	1	𝑤𝑓18	𝑤𝑓18	PROPN
cana-5711	519	2	(	(	PUNCT
cana-5711	519	3	𝑐	𝑐	NOUN
cana-5711	519	4	)	)	PUNCT
cana-5711	519	5	+	+	CCONJ
cana-5711	519	6	𝑤𝑓22	𝑤𝑓22	PROPN
cana-5711	519	7	(	(	PUNCT
cana-5711	519	8	𝑐	𝑐	NOUN
cana-5711	519	9	)	)	PUNCT
cana-5711	519	10	+	+	CCONJ
cana-5711	519	11	𝑤𝑓23	𝑤𝑓23	PROPN
cana-5711	519	12	(	(	PUNCT
cana-5711	519	13	𝑐	𝑐	NOUN
cana-5711	519	14	)	)	PUNCT
cana-5711	519	15	+	+	CCONJ
cana-5711	520	1	𝑤𝑓32	𝑤𝑓32	PROPN
cana-5711	520	2	(	(	PUNCT
cana-5711	520	3	𝑐	𝑐	NOUN
cana-5711	520	4	)	)	PUNCT
cana-5711	520	5	+	+	CCONJ
cana-5711	521	1	𝑤𝑓33	𝑤𝑓33	PROPN
cana-5711	521	2	(	(	PUNCT
cana-5711	521	3	𝑐	𝑐	NOUN
cana-5711	521	4	)	)	PUNCT
cana-5711	521	5	+	+	PROPN
cana-5711	521	6	𝑤𝑓50	𝑤𝑓50	PROPN
cana-5711	521	7	(	(	PUNCT
cana-5711	521	8	𝑐	𝑐	NOUN
cana-5711	521	9	)	)	PUNCT
cana-5711	521	10	+	+	CCONJ
cana-5711	521	11	𝑤𝑓54	𝑤𝑓54	PROPN
cana-5711	521	12	(	(	PUNCT
cana-5711	521	13	𝑐	𝑐	NOUN
cana-5711	521	14	)	)	PUNCT
cana-5711	521	15	+	+	CCONJ
cana-5711	521	16	𝑤𝑓55	𝑤𝑓55	PROPN
cana-5711	521	17	(	(	PUNCT
cana-5711	521	18	𝑐	𝑐	NOUN
cana-5711	521	19	)	)	PUNCT
cana-5711	521	20	+	+	CCONJ
cana-5711	521	21	𝑤𝑓64	𝑤𝑓64	PROPN
cana-5711	521	22	(	(	PUNCT
cana-5711	521	23	𝑐	𝑐	NOUN
cana-5711	521	24	)	)	PUNCT
cana-5711	521	25	+	+	CCONJ
cana-5711	521	26	𝑤𝑓66	𝑤𝑓66	PROPN
cana-5711	521	27	(	(	PUNCT
cana-5711	521	28	𝑐	𝑐	NOUN
cana-5711	521	29	)	)	PUNCT
cana-5711	521	30	+	+	CCONJ
cana-5711	522	1	𝑤𝑓70	𝑤𝑓70	PROPN
cana-5711	522	2	(	(	PUNCT
cana-5711	522	3	𝑐	𝑐	NOUN
cana-5711	522	4	)	)	PUNCT
cana-5711	522	5	+	+	CCONJ
cana-5711	522	6	𝑤𝑓71	𝑤𝑓71	PROPN
cana-5711	522	7	(	(	PUNCT
cana-5711	522	8	𝑐	𝑐	NOUN
cana-5711	522	9	)	)	PUNCT
cana-5711	522	10	+	+	CCONJ
cana-5711	522	11	𝑤𝑓80	𝑤𝑓80	PROPN
cana-5711	522	12	(	(	PUNCT
cana-5711	522	13	𝑐	𝑐	NOUN
cana-5711	522	14	)	)	PUNCT
cana-5711	522	15	+	+	CCONJ
cana-5711	522	16	𝑤𝑓81	𝑤𝑓81	PROPN
cana-5711	522	17	(	(	PUNCT
cana-5711	522	18	𝑐	𝑐	NOUN
cana-5711	522	19	)	)	PUNCT
cana-5711	522	20	+	+	CCONJ
cana-5711	522	21	𝑤𝑓113	𝑤𝑓113	ADJ
cana-5711	522	22	(	(	PUNCT
cana-5711	522	23	𝑐	𝑐	NOUN
cana-5711	522	24	)	)	PUNCT
cana-5711	522	25	,	,	PUNCT
cana-5711	522	26	𝑛3(𝑐	𝑛3(𝑐	PROPN
cana-5711	522	27	)	)	PUNCT
cana-5711	522	28	=	=	SYM
cana-5711	522	29	𝑤𝑓8	𝑤𝑓8	NOUN
cana-5711	522	30	(	(	PUNCT
cana-5711	522	31	𝑐	𝑐	NOUN
cana-5711	522	32	)	)	PUNCT
cana-5711	522	33	+	+	CCONJ
cana-5711	522	34	𝑤𝑓13	𝑤𝑓13	PROPN
cana-5711	522	35	(	(	PUNCT
cana-5711	522	36	𝑐	𝑐	NOUN
cana-5711	522	37	)	)	PUNCT
cana-5711	522	38	+	+	CCONJ
cana-5711	522	39	𝑤𝑓14	𝑤𝑓14	PROPN
cana-5711	522	40	(	(	PUNCT
cana-5711	522	41	𝑐	𝑐	NOUN
cana-5711	522	42	)	)	PUNCT
cana-5711	522	43	+	+	CCONJ
cana-5711	522	44	𝑤𝑓15	𝑤𝑓15	PROPN
cana-5711	522	45	(	(	PUNCT
cana-5711	522	46	𝑐	𝑐	NOUN
cana-5711	522	47	)	)	PUNCT
cana-5711	522	48	+	+	CCONJ
cana-5711	522	49	𝑤𝑓19	𝑤𝑓19	PROPN
cana-5711	522	50	(	(	PUNCT
cana-5711	522	51	𝑐	𝑐	NOUN
cana-5711	522	52	)	)	PUNCT
cana-5711	522	53	+	+	CCONJ
cana-5711	522	54	𝑤𝑓20	𝑤𝑓20	PROPN
cana-5711	522	55	(	(	PUNCT
cana-5711	522	56	𝑐	𝑐	NOUN
cana-5711	522	57	)	)	PUNCT
cana-5711	522	58	+	+	CCONJ
cana-5711	522	59	𝑤𝑓25	𝑤𝑓25	PROPN
cana-5711	522	60	(	(	PUNCT
cana-5711	522	61	𝑐	𝑐	NOUN
cana-5711	522	62	)	)	PUNCT
cana-5711	522	63	+	+	CCONJ
cana-5711	522	64	𝑤𝑓26	𝑤𝑓26	PROPN
cana-5711	522	65	(	(	PUNCT
cana-5711	522	66	𝑐	𝑐	NOUN
cana-5711	522	67	)	)	PUNCT
cana-5711	522	68	+	+	CCONJ
cana-5711	522	69	𝑤𝑓27	𝑤𝑓27	PROPN
cana-5711	522	70	(	(	PUNCT
cana-5711	522	71	𝑐	𝑐	NOUN
cana-5711	522	72	)	)	PUNCT
cana-5711	522	73	+	+	CCONJ
cana-5711	522	74	𝑤𝑓28	𝑤𝑓28	PROPN
cana-5711	522	75	(	(	PUNCT
cana-5711	522	76	𝑐	𝑐	NOUN
cana-5711	522	77	)	)	PUNCT
cana-5711	522	78	+	+	CCONJ
cana-5711	523	1	𝑤𝑓34	𝑤𝑓34	PROPN
cana-5711	523	2	(	(	PUNCT
cana-5711	523	3	𝑐	𝑐	NOUN
cana-5711	523	4	)	)	PUNCT
cana-5711	523	5	+	+	NOUN
cana-5711	523	6	𝑤𝑓38	𝑤𝑓38	PROPN
cana-5711	523	7	(	(	PUNCT
cana-5711	523	8	𝑐	𝑐	NOUN
cana-5711	523	9	)	)	PUNCT
cana-5711	523	10	+	+	CCONJ
cana-5711	524	1	𝑤𝑓39	𝑤𝑓39	PROPN
cana-5711	524	2	(	(	PUNCT
cana-5711	524	3	𝑐	𝑐	NOUN
cana-5711	524	4	)	)	PUNCT
cana-5711	524	5	+	+	CCONJ
cana-5711	524	6	𝑤𝑓48	𝑤𝑓48	PROPN
cana-5711	524	7	(	(	PUNCT
cana-5711	524	8	𝑐	𝑐	NOUN
cana-5711	524	9	)	)	PUNCT
cana-5711	524	10	+	+	CCONJ
cana-5711	524	11	𝑤𝑓51	𝑤𝑓51	PROPN
cana-5711	524	12	(	(	PUNCT
cana-5711	524	13	𝑐	𝑐	NOUN
cana-5711	524	14	)	)	PUNCT
cana-5711	524	15	+	+	CCONJ
cana-5711	525	1	𝑤𝑓52	𝑤𝑓52	PROPN
cana-5711	525	2	(	(	PUNCT
cana-5711	525	3	𝑐	𝑐	NOUN
cana-5711	525	4	)	)	PUNCT
cana-5711	525	5	+	+	CCONJ
cana-5711	525	6	𝑤𝑓57	𝑤𝑓57	PROPN
cana-5711	525	7	(	(	PUNCT
cana-5711	525	8	𝑐	𝑐	NOUN
cana-5711	525	9	)	)	PUNCT
cana-5711	525	10	+	+	CCONJ
cana-5711	525	11	𝑤𝑓58	𝑤𝑓58	PROPN
cana-5711	525	12	(	(	PUNCT
cana-5711	525	13	𝑐	𝑐	NOUN
cana-5711	525	14	)	)	PUNCT
cana-5711	525	15	+	+	CCONJ
cana-5711	525	16	𝑤𝑓59	𝑤𝑓59	PROPN
cana-5711	525	17	(	(	PUNCT
cana-5711	525	18	𝑐	𝑐	NOUN
cana-5711	525	19	)	)	PUNCT
cana-5711	526	1	+	+	CCONJ
cana-5711	527	1	𝑤𝑓60	𝑤𝑓60	PROPN
cana-5711	527	2	(	(	PUNCT
cana-5711	527	3	𝑐	𝑐	NOUN
cana-5711	527	4	)	)	PUNCT
cana-5711	527	5	+	+	CCONJ
cana-5711	527	6	𝑤𝑓67	𝑤𝑓67	PROPN
cana-5711	527	7	(	(	PUNCT
cana-5711	527	8	𝑐	𝑐	NOUN
cana-5711	527	9	)	)	PUNCT
cana-5711	527	10	+	+	CCONJ
cana-5711	527	11	𝑤𝑓68	𝑤𝑓68	PROPN
cana-5711	527	12	(	(	PUNCT
cana-5711	527	13	𝑐	𝑐	NOUN
cana-5711	527	14	)	)	PUNCT
cana-5711	527	15	+	+	CCONJ
cana-5711	527	16	𝑤𝑓73	𝑤𝑓73	PROPN
cana-5711	527	17	(	(	PUNCT
cana-5711	527	18	𝑐	𝑐	NOUN
cana-5711	527	19	)	)	PUNCT
cana-5711	527	20	+	+	NOUN
cana-5711	527	21	𝑤𝑓74	𝑤𝑓74	PROPN
cana-5711	527	22	(	(	PUNCT
cana-5711	527	23	𝑐	𝑐	NOUN
cana-5711	527	24	)	)	PUNCT
cana-5711	527	25	+	+	CCONJ
cana-5711	527	26	𝑤𝑓75	𝑤𝑓75	PROPN
cana-5711	527	27	(	(	PUNCT
cana-5711	527	28	𝑐	𝑐	NOUN
cana-5711	527	29	)	)	PUNCT
cana-5711	527	30	+	+	CCONJ
cana-5711	527	31	𝑤𝑓76	𝑤𝑓76	PROPN
cana-5711	527	32	(	(	PUNCT
cana-5711	527	33	𝑐	𝑐	NOUN
cana-5711	527	34	)	)	PUNCT
cana-5711	527	35	+	+	CCONJ
cana-5711	527	36	𝑤𝑓82	𝑤𝑓82	PROPN
cana-5711	527	37	(	(	PUNCT
cana-5711	527	38	𝑐	𝑐	NOUN
cana-5711	527	39	)	)	PUNCT
cana-5711	527	40	+	+	CCONJ
cana-5711	527	41	𝑤𝑓86	𝑤𝑓86	PROPN
cana-5711	527	42	(	(	PUNCT
cana-5711	527	43	𝑐	𝑐	NOUN
cana-5711	527	44	)	)	PUNCT
cana-5711	527	45	+	+	CCONJ
cana-5711	527	46	𝑤𝑓87	𝑤𝑓87	PROPN
cana-5711	527	47	(	(	PUNCT
cana-5711	527	48	𝑐	𝑐	NOUN
cana-5711	527	49	)	)	PUNCT
cana-5711	527	50	+	+	CCONJ
cana-5711	527	51	𝑤𝑓90	𝑤𝑓90	PROPN
cana-5711	527	52	(	(	PUNCT
cana-5711	527	53	𝑐	𝑐	NOUN
cana-5711	527	54	)	)	PUNCT
cana-5711	527	55	+	+	CCONJ
cana-5711	527	56	𝑤𝑓97	𝑤𝑓97	PROPN
cana-5711	527	57	(	(	PUNCT
cana-5711	527	58	𝑐	𝑐	NOUN
cana-5711	527	59	)	)	PUNCT
cana-5711	527	60	+	+	CCONJ
cana-5711	527	61	𝑤𝑓114	𝑤𝑓114	X
cana-5711	527	62	(	(	PUNCT
cana-5711	527	63	𝑐	𝑐	NOUN
cana-5711	527	64	)	)	PUNCT
cana-5711	527	65	+	+	CCONJ
cana-5711	527	66	𝑤𝑓118	𝑤𝑓118	PROPN
cana-5711	527	67	(	(	PUNCT
cana-5711	527	68	𝑐	𝑐	NOUN
cana-5711	527	69	)	)	PUNCT
cana-5711	527	70	+	+	NUM
cana-5711	527	71	𝑤𝑓119	𝑤𝑓119	PUNCT
cana-5711	527	72	(	(	PUNCT
cana-5711	527	73	𝑐	𝑐	NOUN
cana-5711	527	74	)	)	PUNCT
cana-5711	527	75	+	+	CCONJ
cana-5711	527	76	𝑤𝑓128	𝑤𝑓128	NOUN
cana-5711	527	77	(	(	PUNCT
cana-5711	527	78	𝑐	𝑐	NOUN
cana-5711	527	79	)	)	PUNCT
cana-5711	527	80	,	,	PUNCT
cana-5711	527	81	𝑛4(𝑐	𝑛4(𝑐	X
cana-5711	527	82	)	)	PUNCT
cana-5711	527	83	=	=	SYM
cana-5711	527	84	𝑤𝑓5	𝑤𝑓5	ADP
cana-5711	527	85	(	(	PUNCT
cana-5711	527	86	𝑐	𝑐	NOUN
cana-5711	527	87	)	)	PUNCT
cana-5711	527	88	+	+	CCONJ
cana-5711	527	89	𝑤𝑓24	𝑤𝑓24	PROPN
cana-5711	527	90	(	(	PUNCT
cana-5711	527	91	𝑐	𝑐	NOUN
cana-5711	527	92	)	)	PUNCT
cana-5711	527	93	+	+	CCONJ
cana-5711	528	1	𝑤𝑓29	𝑤𝑓29	PROPN
cana-5711	528	2	(	(	PUNCT
cana-5711	528	3	𝑐	𝑐	NOUN
cana-5711	528	4	)	)	PUNCT
cana-5711	528	5	+	+	CCONJ
cana-5711	528	6	𝑤𝑓30	𝑤𝑓30	PROPN
cana-5711	528	7	(	(	PUNCT
cana-5711	528	8	𝑐	𝑐	NOUN
cana-5711	528	9	)	)	PUNCT
cana-5711	528	10	+	+	CCONJ
cana-5711	528	11	𝑤𝑓31	𝑤𝑓31	PROPN
cana-5711	528	12	(	(	PUNCT
cana-5711	528	13	𝑐	𝑐	NOUN
cana-5711	528	14	)	)	PUNCT
cana-5711	528	15	+	+	CCONJ
cana-5711	528	16	𝑤𝑓35	𝑤𝑓35	PROPN
cana-5711	528	17	(	(	PUNCT
cana-5711	528	18	𝑐	𝑐	NOUN
cana-5711	528	19	)	)	PUNCT
cana-5711	528	20	+	+	CCONJ
cana-5711	528	21	𝑤𝑓36	𝑤𝑓36	PROPN
cana-5711	528	22	(	(	PUNCT
cana-5711	528	23	𝑐	𝑐	NOUN
cana-5711	528	24	)	)	PUNCT
cana-5711	528	25	+	+	CCONJ
cana-5711	529	1	𝑤𝑓41	𝑤𝑓41	PROPN
cana-5711	529	2	(	(	PUNCT
cana-5711	529	3	𝑐	𝑐	NOUN
cana-5711	529	4	)	)	PUNCT
cana-5711	529	5	+	+	CCONJ
cana-5711	529	6	𝑤𝑓42	𝑤𝑓42	PROPN
cana-5711	529	7	(	(	PUNCT
cana-5711	529	8	𝑐	𝑐	NOUN
cana-5711	529	9	)	)	PUNCT
cana-5711	529	10	+	+	CCONJ
cana-5711	530	1	𝑤𝑓43	𝑤𝑓43	PROPN
cana-5711	530	2	(	(	PUNCT
cana-5711	530	3	𝑐	𝑐	NOUN
cana-5711	530	4	)	)	PUNCT
cana-5711	530	5	+	+	CCONJ
cana-5711	531	1	𝑤𝑓44	𝑤𝑓44	PROPN
cana-5711	531	2	(	(	PUNCT
cana-5711	531	3	𝑐	𝑐	NOUN
cana-5711	531	4	)	)	PUNCT
cana-5711	532	1	+	+	PROPN
cana-5711	532	2	𝑤𝑓56	𝑤𝑓56	PROPN
cana-5711	532	3	(	(	PUNCT
cana-5711	532	4	𝑐	𝑐	NOUN
cana-5711	532	5	)	)	PUNCT
cana-5711	532	6	+	+	CCONJ
cana-5711	533	1	𝑤𝑓61	𝑤𝑓61	PROPN
cana-5711	533	2	(	(	PUNCT
cana-5711	533	3	𝑐	𝑐	NOUN
cana-5711	533	4	)	)	PUNCT
cana-5711	533	5	+	+	CCONJ
cana-5711	534	1	𝑤𝑓62	𝑤𝑓62	PROPN
cana-5711	534	2	(	(	PUNCT
cana-5711	534	3	𝑐	𝑐	NOUN
cana-5711	534	4	)	)	PUNCT
cana-5711	534	5	+	+	CCONJ
cana-5711	534	6	𝑤𝑓63	𝑤𝑓63	PROPN
cana-5711	534	7	(	(	PUNCT
cana-5711	534	8	𝑐	𝑐	NOUN
cana-5711	534	9	)	)	PUNCT
cana-5711	534	10	+	+	CCONJ
cana-5711	534	11	𝑤𝑓72	𝑤𝑓72	PROPN
cana-5711	534	12	(	(	PUNCT
cana-5711	534	13	𝑐	𝑐	NOUN
cana-5711	534	14	)	)	PUNCT
cana-5711	534	15	+	+	CCONJ
cana-5711	535	1	𝑤𝑓77	𝑤𝑓77	PROPN
cana-5711	535	2	(	(	PUNCT
cana-5711	535	3	𝑐	𝑐	NOUN
cana-5711	535	4	)	)	PUNCT
cana-5711	535	5	+	+	CCONJ
cana-5711	535	6	𝑤𝑓78	𝑤𝑓78	PROPN
cana-5711	535	7	(	(	PUNCT
cana-5711	535	8	𝑐	𝑐	NOUN
cana-5711	535	9	)	)	PUNCT
cana-5711	535	10	+	+	CCONJ
cana-5711	535	11	𝑤𝑓79	𝑤𝑓79	PROPN
cana-5711	535	12	(	(	PUNCT
cana-5711	535	13	𝑐	𝑐	NOUN
cana-5711	535	14	)	)	PUNCT
cana-5711	535	15	+	+	CCONJ
cana-5711	535	16	𝑤𝑓83	𝑤𝑓83	PROPN
cana-5711	535	17	(	(	PUNCT
cana-5711	535	18	𝑐	𝑐	NOUN
cana-5711	535	19	)	)	PUNCT
cana-5711	535	20	+	+	CCONJ
cana-5711	536	1	𝑤𝑓84	𝑤𝑓84	NOUN
cana-5711	536	2	(	(	PUNCT
cana-5711	536	3	𝑐	𝑐	NOUN
cana-5711	536	4	)	)	PUNCT
cana-5711	536	5	+	+	CCONJ
cana-5711	536	6	𝑤𝑓89	𝑤𝑓89	PROPN
cana-5711	536	7	(	(	PUNCT
cana-5711	536	8	𝑐	𝑐	NOUN
cana-5711	536	9	)	)	PUNCT
cana-5711	537	1	+	+	PROPN
cana-5711	537	2	𝑤𝑓90	𝑤𝑓90	PROPN
cana-5711	537	3	(	(	PUNCT
cana-5711	537	4	𝑐	𝑐	NOUN
cana-5711	537	5	)	)	PUNCT
cana-5711	537	6	+	+	CCONJ
cana-5711	538	1	𝑤𝑓91	𝑤𝑓91	PROPN
cana-5711	538	2	(	(	PUNCT
cana-5711	538	3	𝑐	𝑐	NOUN
cana-5711	538	4	)	)	PUNCT
cana-5711	538	5	+	+	CCONJ
cana-5711	538	6	𝑤𝑓92	𝑤𝑓92	PROPN
cana-5711	538	7	(	(	PUNCT
cana-5711	538	8	𝑐	𝑐	NOUN
cana-5711	538	9	)	)	PUNCT
cana-5711	538	10	+	+	CCONJ
cana-5711	539	1	𝑤𝑓98	𝑤𝑓98	PROPN
cana-5711	539	2	(	(	PUNCT
cana-5711	539	3	𝑐	𝑐	NOUN
cana-5711	539	4	)	)	PUNCT
cana-5711	539	5	+	+	NUM
cana-5711	539	6	𝑤𝑓102	𝑤𝑓102	PROPN
cana-5711	539	7	(	(	PUNCT
cana-5711	539	8	𝑐	𝑐	NOUN
cana-5711	539	9	)	)	PUNCT
cana-5711	539	10	+	+	CCONJ
cana-5711	539	11	𝑤𝑓103	𝑤𝑓103	NOUN
cana-5711	539	12	(	(	PUNCT
cana-5711	539	13	𝑐	𝑐	NOUN
cana-5711	539	14	)	)	PUNCT
cana-5711	539	15	+	+	CCONJ
cana-5711	539	16	𝑤𝑓112	𝑤𝑓112	PROPN
cana-5711	539	17	(	(	PUNCT
cana-5711	539	18	𝑐	𝑐	NOUN
cana-5711	539	19	)	)	PUNCT
cana-5711	539	20	+	+	CCONJ
cana-5711	539	21	𝑤𝑓115	𝑤𝑓115	PROPN
cana-5711	539	22	(	(	PUNCT
cana-5711	539	23	𝑐	𝑐	NOUN
cana-5711	539	24	)	)	PUNCT
cana-5711	539	25	+	+	NUM
cana-5711	539	26	𝑤𝑓116	𝑤𝑓116	PROPN
cana-5711	539	27	(	(	PUNCT
cana-5711	539	28	𝑐	𝑐	NOUN
cana-5711	539	29	)	)	PUNCT
cana-5711	539	30	+	+	CCONJ
cana-5711	539	31	𝑤𝑓121	𝑤𝑓121	NUM
cana-5711	539	32	(	(	PUNCT
cana-5711	539	33	𝑐	𝑐	NOUN
cana-5711	539	34	)	)	PUNCT
cana-5711	539	35	+	+	NUM
cana-5711	539	36	𝑤𝑓122	𝑤𝑓122	PROPN
cana-5711	539	37	(	(	PUNCT
cana-5711	539	38	𝑐	𝑐	NOUN
cana-5711	539	39	)	)	PUNCT
cana-5711	539	40	+	+	NOUN
cana-5711	539	41	𝑤𝑓123	𝑤𝑓123	NOUN
cana-5711	539	42	(	(	PUNCT
cana-5711	539	43	𝑐	𝑐	NOUN
cana-5711	539	44	)	)	PUNCT
cana-5711	539	45	+	+	CCONJ
cana-5711	539	46	𝑤𝑓124	𝑤𝑓124	PROPN
cana-5711	539	47	(	(	PUNCT
cana-5711	539	48	𝑐	𝑐	NOUN
cana-5711	539	49	)	)	PUNCT
cana-5711	539	50	,	,	PUNCT
cana-5711	539	51	𝑛5(𝑐	𝑛5(𝑐	NOUN
cana-5711	539	52	)	)	PUNCT
cana-5711	539	53	=	=	SYM
cana-5711	539	54	𝑤𝑓21	𝑤𝑓21	PROPN
cana-5711	539	55	(	(	PUNCT
cana-5711	539	56	𝑐	𝑐	NOUN
cana-5711	539	57	)	)	PUNCT
cana-5711	539	58	+	+	CCONJ
cana-5711	540	1	𝑤𝑓40	𝑤𝑓40	PROPN
cana-5711	540	2	(	(	PUNCT
cana-5711	540	3	𝑐	𝑐	NOUN
cana-5711	540	4	)	)	PUNCT
cana-5711	540	5	+	+	CCONJ
cana-5711	540	6	𝑤𝑓45	𝑤𝑓45	PROPN
cana-5711	540	7	(	(	PUNCT
cana-5711	540	8	𝑐	𝑐	NOUN
cana-5711	540	9	)	)	PUNCT
cana-5711	540	10	+	+	CCONJ
cana-5711	541	1	𝑤𝑓46	𝑤𝑓46	PROPN
cana-5711	541	2	(	(	PUNCT
cana-5711	541	3	𝑐	𝑐	NOUN
cana-5711	541	4	)	)	PUNCT
cana-5711	541	5	+	+	CCONJ
cana-5711	542	1	𝑤𝑓47	𝑤𝑓47	PROPN
cana-5711	542	2	(	(	PUNCT
cana-5711	542	3	𝑐	𝑐	NOUN
cana-5711	542	4	)	)	PUNCT
cana-5711	542	5	+	+	CCONJ
cana-5711	542	6	𝑤𝑓53	𝑤𝑓53	PROPN
cana-5711	542	7	(	(	PUNCT
cana-5711	542	8	𝑐	𝑐	NOUN
cana-5711	542	9	)	)	PUNCT
cana-5711	542	10	+	+	CCONJ
cana-5711	542	11	𝑤𝑓69	𝑤𝑓69	PROPN
cana-5711	542	12	(	(	PUNCT
cana-5711	542	13	𝑐	𝑐	NOUN
cana-5711	542	14	)	)	PUNCT
cana-5711	542	15	+	+	CCONJ
cana-5711	542	16	𝑤𝑓88	𝑤𝑓88	PROPN
cana-5711	542	17	(	(	PUNCT
cana-5711	542	18	𝑐	𝑐	NOUN
cana-5711	542	19	)	)	PUNCT
cana-5711	542	20	+	+	CCONJ
cana-5711	543	1	𝑤𝑓93	𝑤𝑓93	PROPN
cana-5711	543	2	(	(	PUNCT
cana-5711	543	3	𝑐	𝑐	NOUN
cana-5711	543	4	)	)	PUNCT
cana-5711	543	5	+	+	CCONJ
cana-5711	543	6	𝑤𝑓94	𝑤𝑓94	PROPN
cana-5711	543	7	(	(	PUNCT
cana-5711	543	8	𝑐	𝑐	NOUN
cana-5711	543	9	)	)	PUNCT
cana-5711	543	10	+	+	CCONJ
cana-5711	544	1	𝑤𝑓95	𝑤𝑓95	PROPN
cana-5711	544	2	(	(	PUNCT
cana-5711	544	3	𝑐	𝑐	NOUN
cana-5711	544	4	)	)	PUNCT
cana-5711	544	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	544	6	communications	communication	NOUN
cana-5711	544	7	on	on	ADP
cana-5711	544	8	applied	apply	VERB
cana-5711	544	9	nonlinear	nonlinear	ADJ
cana-5711	544	10	analysis	analysis	NOUN
cana-5711	544	11	issn	issn	NOUN
cana-5711	544	12	:	:	PUNCT
cana-5711	544	13	1074	1074	NUM
cana-5711	544	14	-	-	PUNCT
cana-5711	544	15	133x	133x	NUM
cana-5711	544	16	vol	vol	VERB
cana-5711	544	17	32	32	NUM
cana-5711	544	18	no	no	NOUN
cana-5711	544	19	.	.	PUNCT
cana-5711	545	1	10s	10	NOUN
cana-5711	545	2	(	(	PUNCT
cana-5711	545	3	2025	2025	NUM
cana-5711	545	4	)	)	PUNCT
cana-5711	545	5	2708	2708	NUM
cana-5711	546	1	+	+	ADJ
cana-5711	546	2	𝑤𝑓99	𝑤𝑓99	PROPN
cana-5711	546	3	(	(	PUNCT
cana-5711	546	4	𝑐	𝑐	NOUN
cana-5711	546	5	)	)	PUNCT
cana-5711	546	6	+	+	NUM
cana-5711	546	7	𝑤𝑓100	𝑤𝑓100	PROPN
cana-5711	546	8	(	(	PUNCT
cana-5711	546	9	𝑐	𝑐	NOUN
cana-5711	546	10	)	)	PUNCT
cana-5711	546	11	+	+	CCONJ
cana-5711	546	12	𝑤𝑓105	𝑤𝑓105	NUM
cana-5711	546	13	(	(	PUNCT
cana-5711	546	14	𝑐	𝑐	NOUN
cana-5711	546	15	)	)	PUNCT
cana-5711	546	16	+	+	CCONJ
cana-5711	546	17	𝑤𝑓106	𝑤𝑓106	PROPN
cana-5711	546	18	(	(	PUNCT
cana-5711	546	19	𝑐	𝑐	NOUN
cana-5711	546	20	)	)	PUNCT
cana-5711	546	21	+	+	NUM
cana-5711	546	22	𝑤𝑓107	𝑤𝑓107	PROPN
cana-5711	546	23	(	(	PUNCT
cana-5711	546	24	𝑐	𝑐	NOUN
cana-5711	546	25	)	)	PUNCT
cana-5711	546	26	+	+	NUM
cana-5711	546	27	𝑤𝑓108	𝑤𝑓108	SYM
cana-5711	546	28	(	(	PUNCT
cana-5711	546	29	𝑐	𝑐	NOUN
cana-5711	546	30	)	)	PUNCT
cana-5711	546	31	+	+	NUM
cana-5711	546	32	𝑤𝑓120	𝑤𝑓120	ADJ
cana-5711	546	33	(	(	PUNCT
cana-5711	546	34	𝑐	𝑐	NOUN
cana-5711	546	35	)	)	PUNCT
cana-5711	546	36	+	+	CCONJ
cana-5711	546	37	𝑤𝑓125	𝑤𝑓125	NOUN
cana-5711	546	38	(	(	PUNCT
cana-5711	546	39	𝑐	𝑐	NOUN
cana-5711	546	40	)	)	PUNCT
cana-5711	546	41	+	+	CCONJ
cana-5711	546	42	𝑤𝑓126	𝑤𝑓126	NOUN
cana-5711	546	43	(	(	PUNCT
cana-5711	546	44	𝑐	𝑐	NOUN
cana-5711	546	45	)	)	PUNCT
cana-5711	546	46	+	+	NUM
cana-5711	546	47	𝑤𝑓127	𝑤𝑓127	NOUN
cana-5711	546	48	(	(	PUNCT
cana-5711	546	49	𝑐	𝑐	NOUN
cana-5711	546	50	)	)	PUNCT
cana-5711	546	51	,	,	PUNCT
cana-5711	546	52	𝑛6(𝑐	𝑛6(𝑐	NOUN
cana-5711	546	53	)	)	PUNCT
cana-5711	546	54	=	=	SYM
cana-5711	547	1	𝑤𝑓37	𝑤𝑓37	PROPN
cana-5711	547	2	(	(	PUNCT
cana-5711	547	3	𝑐	𝑐	NOUN
cana-5711	547	4	)	)	PUNCT
cana-5711	547	5	+	+	CCONJ
cana-5711	548	1	𝑤𝑓85	𝑤𝑓85	PROPN
cana-5711	548	2	(	(	PUNCT
cana-5711	548	3	𝑐	𝑐	NOUN
cana-5711	548	4	)	)	PUNCT
cana-5711	548	5	+	+	NUM
cana-5711	548	6	𝑤𝑓104	𝑤𝑓104	X
cana-5711	548	7	(	(	PUNCT
cana-5711	548	8	𝑐	𝑐	NOUN
cana-5711	548	9	)	)	PUNCT
cana-5711	548	10	+	+	CCONJ
cana-5711	548	11	𝑤𝑓109	𝑤𝑓109	VERB
cana-5711	548	12	(	(	PUNCT
cana-5711	548	13	𝑐	𝑐	NOUN
cana-5711	548	14	)	)	PUNCT
cana-5711	548	15	+	+	CCONJ
cana-5711	548	16	𝑤𝑓110	𝑤𝑓110	PROPN
cana-5711	548	17	(	(	PUNCT
cana-5711	548	18	𝑐	𝑐	NOUN
cana-5711	548	19	)	)	PUNCT
cana-5711	548	20	+	+	CCONJ
cana-5711	548	21	𝑤𝑓111	𝑤𝑓111	NOUN
cana-5711	548	22	(	(	PUNCT
cana-5711	548	23	𝑐	𝑐	NOUN
cana-5711	548	24	)	)	PUNCT
cana-5711	548	25	+	+	CCONJ
cana-5711	548	26	𝑤𝑓117	𝑤𝑓117	NUM
cana-5711	548	27	(	(	PUNCT
cana-5711	548	28	𝑐	𝑐	NOUN
cana-5711	548	29	)	)	PUNCT
cana-5711	548	30	,	,	PUNCT
cana-5711	548	31	𝑛7(𝑐	𝑛7(𝑐	X
cana-5711	548	32	)	)	PUNCT
cana-5711	548	33	=	=	SYM
cana-5711	548	34	𝑤𝑓101	𝑤𝑓101	PROPN
cana-5711	548	35	(	(	PUNCT
cana-5711	548	36	𝑐	𝑐	NOUN
cana-5711	548	37	)	)	PUNCT
cana-5711	548	38	.	.	PUNCT
cana-5711	549	1	combining	combine	VERB
cana-5711	549	2	theorem	theorem	ADJ
cana-5711	549	3	5.5	5.5	NUM
cana-5711	549	4	and	and	CCONJ
cana-5711	549	5	definition	definition	NOUN
cana-5711	549	6	5.10	5.10	NUM
cana-5711	549	7	,	,	PUNCT
cana-5711	549	8	we	we	PRON
cana-5711	549	9	have	have	VERB
cana-5711	549	10	the	the	DET
cana-5711	549	11	following	following	NOUN
cana-5711	549	12	:	:	PUNCT
cana-5711	549	13	theorem	theorem	VERB
cana-5711	549	14	5.11	5.11	NUM
cana-5711	549	15	.	.	PUNCT
cana-5711	550	1	suppose	suppose	VERB
cana-5711	550	2	c	c	NOUN
cana-5711	550	3	is	be	AUX
cana-5711	550	4	an	an	DET
cana-5711	550	5	additive	additive	ADJ
cana-5711	550	6	code	code	NOUN
cana-5711	550	7	over	over	ADP
cana-5711	550	8	ℤ2q	ℤ2q	PROPN
cana-5711	550	9	of	of	ADP
cana-5711	550	10	length	length	NOUN
cana-5711	550	11	n.	n.	PROPN
cana-5711	550	12	then	then	ADV
cana-5711	550	13	swec	swec	VERB
cana-5711	550	14	⊥	⊥	PROPN
cana-5711	550	15	(	(	PUNCT
cana-5711	550	16	x	x	X
cana-5711	550	17	,	,	PUNCT
cana-5711	550	18	y	y	PROPN
cana-5711	550	19	,	,	PUNCT
cana-5711	550	20	z	z	PROPN
cana-5711	550	21	,	,	PUNCT
cana-5711	550	22	w	w	PROPN
cana-5711	550	23	,	,	PUNCT
cana-5711	550	24	t	t	PROPN
cana-5711	550	25	,	,	PUNCT
cana-5711	550	26	p	p	X
cana-5711	550	27	,	,	PUNCT
cana-5711	550	28	q	q	NOUN
cana-5711	550	29	,	,	PUNCT
cana-5711	550	30	n	n	NOUN
cana-5711	550	31	)	)	PUNCT
cana-5711	550	32	=	=	SYM
cana-5711	550	33	1	1	NUM
cana-5711	550	34	|𝑐|	|𝑐|	PROPN
cana-5711	550	35	swec	swec	NOUN
cana-5711	550	36	(	(	PUNCT
cana-5711	550	37	s	s	X
cana-5711	550	38	·	·	PUNCT
cana-5711	550	39	(	(	PUNCT
cana-5711	550	40	x	x	X
cana-5711	550	41	,	,	PUNCT
cana-5711	550	42	y	y	PROPN
cana-5711	550	43	,	,	PUNCT
cana-5711	550	44	z	z	PROPN
cana-5711	550	45	,	,	PUNCT
cana-5711	550	46	w	w	PROPN
cana-5711	550	47	,	,	PUNCT
cana-5711	550	48	t	t	PROPN
cana-5711	550	49	,	,	PUNCT
cana-5711	550	50	p	p	X
cana-5711	550	51	,	,	PUNCT
cana-5711	550	52	q	q	ADJ
cana-5711	550	53	,	,	PUNCT
cana-5711	550	54	n	n	NOUN
cana-5711	550	55	)	)	PUNCT
cana-5711	550	56	t	t	NOUN
cana-5711	550	57	)	)	PUNCT
cana-5711	550	58	,	,	PUNCT
cana-5711	550	59	where	where	SCONJ
cana-5711	550	60	𝑆	𝑆	PROPN
cana-5711	550	61	=	=	SYM
cana-5711	550	62	(	(	PUNCT
cana-5711	550	63	1	1	NUM
cana-5711	550	64	7	7	NUM
cana-5711	550	65	21	21	NUM
cana-5711	550	66	35	35	NUM
cana-5711	550	67	35	35	NUM
cana-5711	550	68	21	21	NUM
cana-5711	550	69	7	7	NUM
cana-5711	550	70	1	1	NUM
cana-5711	550	71	1	1	NUM
cana-5711	550	72	5	5	NUM
cana-5711	550	73	9	9	NUM
cana-5711	550	74	5	5	NUM
cana-5711	550	75	−5	−5	NOUN
cana-5711	550	76	−9	−9	NOUN
cana-5711	550	77	−5	−5	NOUN
cana-5711	550	78	−1	−1	NOUN
cana-5711	550	79	1	1	NUM
cana-5711	550	80	3	3	NUM
cana-5711	550	81	1	1	NUM
cana-5711	550	82	−5	−5	NOUN
cana-5711	550	83	−5	−5	ADP
cana-5711	550	84	1	1	NUM
cana-5711	550	85	3	3	NUM
cana-5711	550	86	1	1	NUM
cana-5711	550	87	1	1	NUM
cana-5711	550	88	1	1	NUM
cana-5711	550	89	−3	−3	ADV
cana-5711	550	90	−3	−3	NOUN
cana-5711	550	91	3	3	NUM
cana-5711	550	92	3	3	NUM
cana-5711	550	93	−1	−1	NOUN
cana-5711	550	94	−1	−1	NOUN
cana-5711	550	95	1	1	NUM
cana-5711	550	96	−1	−1	NOUN
cana-5711	550	97	−3	−3	NOUN
cana-5711	550	98	3	3	NUM
cana-5711	550	99	3	3	NUM
cana-5711	550	100	−3	−3	NOUN
cana-5711	550	101	−1	−1	NOUN
cana-5711	550	102	1	1	NUM
cana-5711	550	103	1	1	NUM
cana-5711	550	104	−3	−3	NOUN
cana-5711	550	105	1	1	NUM
cana-5711	550	106	5	5	NUM
cana-5711	550	107	−5	−5	NOUN
cana-5711	550	108	−1	−1	NOUN
cana-5711	550	109	3	3	NUM
cana-5711	550	110	−1	−1	NOUN
cana-5711	550	111	1	1	NUM
cana-5711	550	112	−5	−5	NOUN
cana-5711	550	113	9	9	NUM
cana-5711	550	114	−5	−5	NOUN
cana-5711	550	115	−5	−5	ADP
cana-5711	550	116	9	9	NUM
cana-5711	550	117	−5	−5	NOUN
cana-5711	550	118	1	1	NUM
cana-5711	550	119	1	1	NUM
cana-5711	550	120	−7	−7	NOUN
cana-5711	550	121	21	21	NUM
cana-5711	550	122	−35	−35	NUM
cana-5711	550	123	35	35	NUM
cana-5711	550	124	−21	−21	PROPN
cana-5711	550	125	7	7	NUM
cana-5711	550	126	−1	−1	NOUN
cana-5711	550	127	)	)	PUNCT
cana-5711	550	128	proof	proof	NOUN
cana-5711	550	129	.	.	PUNCT
cana-5711	551	1	since	since	SCONJ
cana-5711	551	2	c	c	PROPN
cana-5711	551	3	is	be	AUX
cana-5711	551	4	an	an	DET
cana-5711	551	5	additive	additive	ADJ
cana-5711	551	6	code	code	NOUN
cana-5711	551	7	over	over	ADP
cana-5711	551	8	ℤ2q	ℤ2q	PROPN
cana-5711	551	9	,	,	PUNCT
cana-5711	551	10	by	by	ADP
cana-5711	551	11	definition	definition	NOUN
cana-5711	551	12	5.10	5.10	NUM
cana-5711	551	13	and	and	CCONJ
cana-5711	551	14	theorem	theorem	VERB
cana-5711	551	15	5.5	5.5	NUM
cana-5711	551	16	,	,	PUNCT
cana-5711	551	17	we	we	PRON
cana-5711	551	18	obtain	obtain	VERB
cana-5711	551	19	swec	swec	NOUN
cana-5711	551	20	⊥	⊥	NOUN
cana-5711	551	21	(	(	PUNCT
cana-5711	551	22	x	x	X
cana-5711	551	23	,	,	PUNCT
cana-5711	551	24	y	y	PROPN
cana-5711	551	25	,	,	PUNCT
cana-5711	551	26	z	z	PROPN
cana-5711	551	27	,	,	PUNCT
cana-5711	551	28	w	w	PROPN
cana-5711	551	29	,	,	PUNCT
cana-5711	551	30	t	t	PROPN
cana-5711	551	31	,	,	PUNCT
cana-5711	551	32	p	p	X
cana-5711	551	33	,	,	PUNCT
cana-5711	551	34	q	q	NOUN
cana-5711	551	35	,	,	PUNCT
cana-5711	551	36	n	n	NOUN
cana-5711	551	37	)	)	PUNCT
cana-5711	551	38	=	=	VERB
cana-5711	552	1	cwec	cwec	NOUN
cana-5711	552	2	⊥	⊥	NOUN
cana-5711	552	3	(	(	PUNCT
cana-5711	552	4	x	x	X
cana-5711	552	5	,	,	PUNCT
cana-5711	552	6	y	y	PROPN
cana-5711	552	7	,	,	PUNCT
cana-5711	552	8	z	z	PROPN
cana-5711	552	9	,	,	PUNCT
cana-5711	552	10	z	z	PROPN
cana-5711	552	11	,	,	PUNCT
cana-5711	552	12	t	t	PROPN
cana-5711	552	13	,	,	PUNCT
cana-5711	552	14	y	y	PROPN
cana-5711	552	15	,	,	PUNCT
cana-5711	552	16	y	y	PROPN
cana-5711	552	17	,	,	PUNCT
cana-5711	552	18	w	w	PROPN
cana-5711	552	19	,	,	PUNCT
cana-5711	552	20	z	z	PROPN
cana-5711	552	21	,	,	PUNCT
cana-5711	552	22	z	z	PROPN
cana-5711	552	23	,	,	PUNCT
cana-5711	552	24	z	z	PROPN
cana-5711	552	25	,	,	PUNCT
cana-5711	552	26	z	z	PROPN
cana-5711	552	27	,	,	PUNCT
cana-5711	552	28	w	w	PROPN
cana-5711	552	29	,	,	PUNCT
cana-5711	552	30	w	w	PROPN
cana-5711	552	31	,	,	PUNCT
cana-5711	552	32	w	w	PROPN
cana-5711	552	33	,	,	PUNCT
cana-5711	552	34	y	y	PROPN
cana-5711	552	35	,	,	PUNCT
cana-5711	552	36	y	y	PROPN
cana-5711	552	37	,	,	PUNCT
cana-5711	552	38	z	z	PROPN
cana-5711	552	39	,	,	PUNCT
cana-5711	552	40	w	w	PROPN
cana-5711	552	41	,	,	PUNCT
cana-5711	552	42	w	w	PROPN
cana-5711	552	43	,	,	PUNCT
cana-5711	552	44	p	p	X
cana-5711	552	45	,	,	PUNCT
cana-5711	552	46	z	z	PROPN
cana-5711	552	47	,	,	PUNCT
cana-5711	552	48	z	z	PROPN
cana-5711	552	49	,	,	PUNCT
cana-5711	552	50	t	t	PROPN
cana-5711	552	51	,	,	PUNCT
cana-5711	552	52	w	w	PROPN
cana-5711	552	53	,	,	PUNCT
cana-5711	552	54	w	w	PROPN
cana-5711	552	55	,	,	PUNCT
cana-5711	552	56	w	w	PROPN
cana-5711	552	57	,	,	PUNCT
cana-5711	552	58	w	w	PROPN
cana-5711	552	59	,	,	PUNCT
cana-5711	552	60	t	t	PROPN
cana-5711	552	61	,	,	PUNCT
cana-5711	552	62	t	t	PROPN
cana-5711	552	63	,	,	PUNCT
cana-5711	552	64	t	t	PROPN
cana-5711	552	65	,	,	PUNCT
cana-5711	552	66	z	z	PROPN
cana-5711	552	67	,	,	PUNCT
cana-5711	552	68	z	z	PROPN
cana-5711	552	69	,	,	PUNCT
cana-5711	552	70	w	w	PROPN
cana-5711	552	71	,	,	PUNCT
cana-5711	552	72	t	t	PROPN
cana-5711	552	73	,	,	PUNCT
cana-5711	552	74	t	t	PROPN
cana-5711	552	75	,	,	PUNCT
cana-5711	552	76	q	q	NOUN
cana-5711	552	77	,	,	PUNCT
cana-5711	552	78	w	w	PROPN
cana-5711	552	79	,	,	PUNCT
cana-5711	552	80	w	w	PROPN
cana-5711	552	81	,	,	PUNCT
cana-5711	552	82	p	p	X
cana-5711	552	83	,	,	PUNCT
cana-5711	552	84	t	t	PROPN
cana-5711	552	85	,	,	PUNCT
cana-5711	552	86	t	t	PROPN
cana-5711	552	87	,	,	PUNCT
cana-5711	552	88	t	t	PROPN
cana-5711	552	89	,	,	PUNCT
cana-5711	552	90	t	t	PROPN
cana-5711	552	91	,	,	PUNCT
cana-5711	552	92	p	p	X
cana-5711	552	93	,	,	PUNCT
cana-5711	552	94	p	p	X
cana-5711	552	95	,	,	PUNCT
cana-5711	552	96	p	p	X
cana-5711	552	97	,	,	PUNCT
cana-5711	552	98	w	w	PROPN
cana-5711	552	99	,	,	PUNCT
cana-5711	552	100	y	y	PROPN
cana-5711	552	101	,	,	PUNCT
cana-5711	552	102	z	z	PROPN
cana-5711	552	103	,	,	PUNCT
cana-5711	552	104	w	w	PROPN
cana-5711	552	105	,	,	PUNCT
cana-5711	552	106	w	w	PROPN
cana-5711	552	107	,	,	PUNCT
cana-5711	552	108	p	p	X
cana-5711	552	109	,	,	PUNCT
cana-5711	552	110	z	z	PROPN
cana-5711	552	111	,	,	PUNCT
cana-5711	552	112	z	z	PROPN
cana-5711	552	113	,	,	PUNCT
cana-5711	552	114	t	t	PROPN
cana-5711	552	115	,	,	PUNCT
cana-5711	552	116	w	w	PROPN
cana-5711	552	117	,	,	PUNCT
cana-5711	552	118	w	w	PROPN
cana-5711	552	119	,	,	PUNCT
cana-5711	552	120	w	w	PROPN
cana-5711	552	121	,	,	PUNCT
cana-5711	552	122	w	w	PROPN
cana-5711	552	123	,	,	PUNCT
cana-5711	552	124	t	t	PROPN
cana-5711	552	125	,	,	PUNCT
cana-5711	552	126	t	t	PROPN
cana-5711	552	127	,	,	PUNCT
cana-5711	552	128	t	t	PROPN
cana-5711	552	129	,	,	PUNCT
cana-5711	552	130	z	z	PROPN
cana-5711	552	131	,	,	PUNCT
cana-5711	552	132	y	y	PROPN
cana-5711	552	133	,	,	PUNCT
cana-5711	552	134	z	z	PROPN
cana-5711	552	135	,	,	PUNCT
cana-5711	552	136	w	w	PROPN
cana-5711	552	137	,	,	PUNCT
cana-5711	552	138	w	w	PROPN
cana-5711	552	139	,	,	PUNCT
cana-5711	552	140	p	p	X
cana-5711	552	141	,	,	PUNCT
cana-5711	552	142	z	z	PROPN
cana-5711	552	143	,	,	PUNCT
cana-5711	552	144	z	z	PROPN
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cana-5711	552	583	−	−	PROPN
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cana-5711	552	585	−	−	PROPN
cana-5711	552	586	w	w	PROPN
cana-5711	552	587	+	+	NUM
cana-5711	552	588	t	t	NOUN
cana-5711	552	589	+	+	CCONJ
cana-5711	552	590	p	p	X
cana-5711	552	591	+	+	NOUN
cana-5711	552	592	q	q	NOUN
cana-5711	552	593	−	−	PROPN
cana-5711	552	594	n	n	CCONJ
cana-5711	552	595	,	,	PUNCT
cana-5711	552	596	x	x	PROPN
cana-5711	552	597	−	−	NOUN
cana-5711	552	598	y	y	NOUN
cana-5711	552	599	−	−	PROPN
cana-5711	552	600	z	z	PROPN
cana-5711	553	1	+	+	CCONJ
cana-5711	553	2	w	w	PROPN
cana-5711	553	3	−	−	PROPN
cana-5711	553	4	t	t	NOUN
cana-5711	554	1	+	+	CCONJ
cana-5711	554	2	p	p	NOUN
cana-5711	554	3	−	−	PROPN
cana-5711	554	4	q	q	NOUN
cana-5711	554	5	+	+	CCONJ
cana-5711	554	6	n	n	CCONJ
cana-5711	554	7	,	,	PUNCT
cana-5711	554	8	x	x	PUNCT
cana-5711	554	9	−	−	NOUN
cana-5711	554	10	2y	2y	NUM
cana-5711	554	11	−	−	NOUN
cana-5711	554	12	z	z	NOUN
cana-5711	554	13	−	−	PROPN
cana-5711	554	14	2w+	2w+	NUM
cana-5711	554	15	2	2	NUM
cana-5711	554	16	t	t	NOUN
cana-5711	554	17	+	+	CCONJ
cana-5711	554	18	p	p	NOUN
cana-5711	555	1	+	+	X
cana-5711	555	2	2q	2q	NUM
cana-5711	555	3	−	−	NUM
cana-5711	555	4	n	n	CCONJ
cana-5711	555	5	,	,	PUNCT
cana-5711	555	6	x	x	PROPN
cana-5711	555	7	−	−	PROPN
cana-5711	555	8	4y	4y	PRON
cana-5711	555	9	+	+	CCONJ
cana-5711	555	10	3z	3z	NUM
cana-5711	555	11	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	555	12	communications	communication	NOUN
cana-5711	555	13	on	on	ADP
cana-5711	555	14	applied	apply	VERB
cana-5711	555	15	nonlinear	nonlinear	ADJ
cana-5711	555	16	analysis	analysis	NOUN
cana-5711	555	17	issn	issn	NOUN
cana-5711	555	18	:	:	PUNCT
cana-5711	555	19	1074	1074	NUM
cana-5711	555	20	-	-	PUNCT
cana-5711	555	21	133x	133x	NUM
cana-5711	555	22	vol	vol	VERB
cana-5711	555	23	32	32	NUM
cana-5711	555	24	no	no	NOUN
cana-5711	555	25	.	.	PUNCT
cana-5711	556	1	10s	10	NOUN
cana-5711	556	2	(	(	PUNCT
cana-5711	556	3	2025	2025	NUM
cana-5711	556	4	)	)	PUNCT
cana-5711	556	5	2709	2709	NUM
cana-5711	557	1	+	+	CCONJ
cana-5711	557	2	2w	2w	NUM
cana-5711	557	3	−	−	PROPN
cana-5711	557	4	2	2	NUM
cana-5711	557	5	t	t	NOUN
cana-5711	557	6	+	+	NOUN
cana-5711	557	7	3p	3p	NUM
cana-5711	557	8	−	−	NOUN
cana-5711	557	9	4q	4q	NOUN
cana-5711	557	10	+	+	CCONJ
cana-5711	557	11	n	n	CCONJ
cana-5711	557	12	,	,	PUNCT
cana-5711	557	13	x	x	PUNCT
cana-5711	557	14	−	−	NOUN
cana-5711	558	1	7y	7y	NOUN
cana-5711	558	2	+	+	NUM
cana-5711	558	3	21z	21z	PROPN
cana-5711	558	4	−	−	PROPN
cana-5711	558	5	35w	35w	NOUN
cana-5711	558	6	+	+	CCONJ
cana-5711	558	7	35	35	NUM
cana-5711	558	8	t	t	NOUN
cana-5711	558	9	−	−	NOUN
cana-5711	558	10	21p	21p	NOUN
cana-5711	558	11	+	+	CCONJ
cana-5711	558	12	7q	7q	NUM
cana-5711	558	13	−	−	NOUN
cana-5711	558	14	n	n	CCONJ
cana-5711	558	15	}	}	PUNCT
cana-5711	558	16	.	.	PUNCT
cana-5711	559	1	hence	hence	ADV
cana-5711	559	2	,	,	PUNCT
cana-5711	559	3	swec	swec	PROPN
cana-5711	559	4	⊥	⊥	PROPN
cana-5711	559	5	(	(	PUNCT
cana-5711	559	6	x	x	X
cana-5711	559	7	,	,	PUNCT
cana-5711	559	8	y	y	PROPN
cana-5711	559	9	,	,	PUNCT
cana-5711	559	10	z	z	PROPN
cana-5711	559	11	,	,	PUNCT
cana-5711	559	12	w	w	PROPN
cana-5711	559	13	,	,	PUNCT
cana-5711	559	14	t	t	PROPN
cana-5711	559	15	,	,	PUNCT
cana-5711	559	16	p	p	X
cana-5711	559	17	,	,	PUNCT
cana-5711	559	18	q	q	NOUN
cana-5711	559	19	,	,	PUNCT
cana-5711	559	20	n	n	NOUN
cana-5711	559	21	)	)	PUNCT
cana-5711	559	22	=	=	SYM
cana-5711	559	23	1	1	NUM
cana-5711	559	24	|𝑐|	|𝑐|	PROPN
cana-5711	559	25	swec	swec	NOUN
cana-5711	559	26	(	(	PUNCT
cana-5711	559	27	s	s	X
cana-5711	559	28	·	·	PUNCT
cana-5711	559	29	(	(	PUNCT
cana-5711	559	30	x	x	X
cana-5711	559	31	,	,	PUNCT
cana-5711	559	32	y	y	PROPN
cana-5711	559	33	,	,	PUNCT
cana-5711	559	34	z	z	PROPN
cana-5711	559	35	,	,	PUNCT
cana-5711	559	36	w	w	PROPN
cana-5711	559	37	,	,	PUNCT
cana-5711	559	38	t	t	PROPN
cana-5711	559	39	,	,	PUNCT
cana-5711	559	40	p	p	X
cana-5711	559	41	,	,	PUNCT
cana-5711	559	42	q	q	ADJ
cana-5711	559	43	,	,	PUNCT
cana-5711	559	44	n	n	NOUN
cana-5711	559	45	)	)	PUNCT
cana-5711	559	46	t	t	NOUN
cana-5711	559	47	)	)	PUNCT
cana-5711	559	48	.	.	PUNCT
cana-5711	559	49	example	example	NOUN
cana-5711	560	1	5.12	5.12	NUM
cana-5711	560	2	.	.	PUNCT
cana-5711	561	1	let	let	VERB
cana-5711	561	2	c	c	NOUN
cana-5711	561	3	be	be	AUX
cana-5711	561	4	the	the	DET
cana-5711	561	5	code	code	NOUN
cana-5711	561	6	in	in	ADP
cana-5711	561	7	example	example	NOUN
cana-5711	561	8	5.6	5.6	NUM
cana-5711	561	9	.	.	PUNCT
cana-5711	562	1	then	then	ADV
cana-5711	562	2	swec	swec	NOUN
cana-5711	562	3	(	(	PUNCT
cana-5711	562	4	x	x	X
cana-5711	562	5	,	,	PUNCT
cana-5711	562	6	y	y	PROPN
cana-5711	562	7	,	,	PUNCT
cana-5711	562	8	z	z	PROPN
cana-5711	562	9	,	,	PUNCT
cana-5711	562	10	w	w	PROPN
cana-5711	562	11	,	,	PUNCT
cana-5711	562	12	t	t	PROPN
cana-5711	562	13	,	,	PUNCT
cana-5711	562	14	p	p	X
cana-5711	562	15	,	,	PUNCT
cana-5711	562	16	q	q	NOUN
cana-5711	562	17	,	,	PUNCT
cana-5711	562	18	n	n	NOUN
cana-5711	562	19	)	)	PUNCT
cana-5711	562	20	=	=	SYM
cana-5711	563	1	x2	x2	PROPN
cana-5711	564	1	+	+	NUM
cana-5711	564	2	7z2	7z2	NUM
cana-5711	565	1	+	+	CCONJ
cana-5711	565	2	7t2	7t2	NUM
cana-5711	565	3	+	+	NUM
cana-5711	565	4	q2	q2	NOUN
cana-5711	565	5	+	+	CCONJ
cana-5711	565	6	8xz	8xz	ADJ
cana-5711	565	7	+	+	CCONJ
cana-5711	565	8	8xt	8xt	ADJ
cana-5711	565	9	+	+	CCONJ
cana-5711	565	10	2xq	2xq	ADJ
cana-5711	566	1	+	+	CCONJ
cana-5711	566	2	xn	xn	PROPN
cana-5711	567	1	+	+	NUM
cana-5711	567	2	xy+	xy+	PROPN
cana-5711	567	3	7xp	7xp	NOUN
cana-5711	567	4	+	+	CCONJ
cana-5711	567	5	7xw	7xw	ADJ
cana-5711	567	6	+	+	CCONJ
cana-5711	567	7	14zt	14zt	ADJ
cana-5711	567	8	+	+	CCONJ
cana-5711	567	9	8zq	8zq	NOUN
cana-5711	567	10	+	+	CCONJ
cana-5711	567	11	zy	zy	X
cana-5711	567	12	+	+	CCONJ
cana-5711	567	13	7zp	7zp	ADJ
cana-5711	567	14	+	+	CCONJ
cana-5711	567	15	7zw	7zw	ADJ
cana-5711	567	16	+	+	CCONJ
cana-5711	567	17	zn+	zn+	PROPN
cana-5711	567	18	8tq	8tq	NOUN
cana-5711	567	19	+	+	CCONJ
cana-5711	567	20	t	t	PROPN
cana-5711	567	21	y	y	PROPN
cana-5711	567	22	+	+	CCONJ
cana-5711	567	23	7	7	NUM
cana-5711	567	24	t	t	NOUN
cana-5711	567	25	w	w	NOUN
cana-5711	567	26	+	+	PROPN
cana-5711	567	27	7	7	NUM
cana-5711	567	28	t	t	NOUN
cana-5711	567	29	p	p	NOUN
cana-5711	567	30	+	+	PROPN
cana-5711	567	31	t	t	PROPN
cana-5711	567	32	n	n	PROPN
cana-5711	567	33	+	+	NUM
cana-5711	567	34	qy	qy	NOUN
cana-5711	567	35	+	+	X
cana-5711	567	36	7qw	7qw	ADJ
cana-5711	567	37	+	+	CCONJ
cana-5711	567	38	7qp	7qp	ADJ
cana-5711	567	39	+	+	SYM
cana-5711	567	40	qw	qw	NOUN
cana-5711	567	41	.	.	PROPN
cana-5711	567	42	and	and	CCONJ
cana-5711	567	43	swec	swec	PROPN
cana-5711	567	44	⊥	⊥	PROPN
cana-5711	567	45	(	(	PUNCT
cana-5711	567	46	x	x	X
cana-5711	567	47	,	,	PUNCT
cana-5711	567	48	y	y	PROPN
cana-5711	567	49	,	,	PUNCT
cana-5711	567	50	z	z	PROPN
cana-5711	567	51	,	,	PUNCT
cana-5711	567	52	w	w	PROPN
cana-5711	567	53	,	,	PUNCT
cana-5711	567	54	t	t	PROPN
cana-5711	567	55	,	,	PUNCT
cana-5711	567	56	p	p	X
cana-5711	567	57	,	,	PUNCT
cana-5711	567	58	q	q	NOUN
cana-5711	567	59	,	,	PUNCT
cana-5711	567	60	n	n	NOUN
cana-5711	567	61	)	)	PUNCT
cana-5711	568	1	=	=	SYM
cana-5711	568	2	x2	x2	PROPN
cana-5711	569	1	+	+	NUM
cana-5711	569	2	7z2	7z2	NUM
cana-5711	570	1	+	+	CCONJ
cana-5711	570	2	7t2	7t2	NUM
cana-5711	570	3	+	+	NUM
cana-5711	570	4	q2	q2	NOUN
cana-5711	570	5	+	+	CCONJ
cana-5711	570	6	8xt	8xt	NOUN
cana-5711	571	1	+	+	CCONJ
cana-5711	571	2	7zp	7zp	ADJ
cana-5711	571	3	+	+	CCONJ
cana-5711	571	4	xn	xn	PROPN
cana-5711	572	1	+	+	NUM
cana-5711	572	2	8xz	8xz	ADJ
cana-5711	572	3	+	+	CCONJ
cana-5711	572	4	14zt+	14zt+	NUM
cana-5711	572	5	7xw	7xw	ADJ
cana-5711	572	6	+	+	CCONJ
cana-5711	572	7	7xp	7xp	ADJ
cana-5711	572	8	+	+	CCONJ
cana-5711	572	9	8zq	8zq	NOUN
cana-5711	573	1	+	+	CCONJ
cana-5711	574	1	zy	zy	X
cana-5711	574	2	+	+	CCONJ
cana-5711	574	3	2xq	2xq	ADJ
cana-5711	575	1	+	+	CCONJ
cana-5711	576	1	7zw	7zw	ADJ
cana-5711	577	1	+	+	CCONJ
cana-5711	577	2	zn	zn	X
cana-5711	577	3	+	+	CCONJ
cana-5711	577	4	8	8	NUM
cana-5711	577	5	t	t	NOUN
cana-5711	577	6	q+	q+	ADP
cana-5711	577	7	7	7	NUM
cana-5711	577	8	t	t	NOUN
cana-5711	577	9	w	w	PROPN
cana-5711	578	1	+	+	PROPN
cana-5711	578	2	t	t	PROPN
cana-5711	578	3	y	y	PROPN
cana-5711	578	4	+	+	CCONJ
cana-5711	578	5	7	7	NUM
cana-5711	578	6	t	t	NOUN
cana-5711	578	7	p	p	NOUN
cana-5711	578	8	+	+	PROPN
cana-5711	578	9	t	t	PROPN
cana-5711	578	10	n	n	PROPN
cana-5711	578	11	+	+	NUM
cana-5711	578	12	qy	qy	NOUN
cana-5711	578	13	+	+	X
cana-5711	578	14	7qw	7qw	ADJ
cana-5711	578	15	+	+	CCONJ
cana-5711	578	16	7qp	7qp	ADJ
cana-5711	578	17	+	+	CCONJ
cana-5711	578	18	qw	qw	X
cana-5711	578	19	+	+	NOUN
cana-5711	578	20	xy	xy	PROPN
cana-5711	578	21	.	.	PUNCT
cana-5711	579	1	let	let	VERB
cana-5711	579	2	c	c	NOUN
cana-5711	579	3	∈	∈	PROPN
cana-5711	579	4	(	(	PUNCT
cana-5711	579	5	z2q)n	z2q)n	NOUN
cana-5711	579	6	.	.	PUNCT
cana-5711	580	1	the	the	DET
cana-5711	580	2	lee	lee	PROPN
cana-5711	580	3	weight	weight	NOUN
cana-5711	580	4	of	of	ADP
cana-5711	580	5	c	c	PROPN
cana-5711	580	6	is	be	AUX
cana-5711	580	7	wtl	wtl	PROPN
cana-5711	580	8	(	(	PUNCT
cana-5711	580	9	c	c	NOUN
cana-5711	580	10	)	)	PUNCT
cana-5711	580	11	=	=	SYM
cana-5711	580	12	n1(c	n1(c	NOUN
cana-5711	580	13	)	)	PUNCT
cana-5711	580	14	+	+	NOUN
cana-5711	580	15	2n2(c	2n2(c	NUM
cana-5711	580	16	)	)	PUNCT
cana-5711	580	17	+	+	CCONJ
cana-5711	580	18	3n3(c	3n3(c	NUM
cana-5711	580	19	)	)	PUNCT
cana-5711	580	20	+	+	CCONJ
cana-5711	580	21	4n4(c	4n4(c	NOUN
cana-5711	580	22	)	)	PUNCT
cana-5711	580	23	+	+	CCONJ
cana-5711	580	24	5n5(c	5n5(c	NUM
cana-5711	580	25	)	)	PUNCT
cana-5711	580	26	+	+	NOUN
cana-5711	580	27	6n6(c	6n6(c	NUM
cana-5711	580	28	)	)	PUNCT
cana-5711	580	29	+	+	CCONJ
cana-5711	580	30	7n7(c	7n7(c	NOUN
cana-5711	580	31	)	)	PUNCT
cana-5711	580	32	,	,	PUNCT
cana-5711	580	33	where	where	SCONJ
cana-5711	580	34	ni	ni	PROPN
cana-5711	580	35	(	(	PUNCT
cana-5711	580	36	c	c	NOUN
cana-5711	580	37	)	)	PUNCT
cana-5711	580	38	is	be	AUX
cana-5711	580	39	defined	define	VERB
cana-5711	580	40	in	in	ADP
cana-5711	580	41	equation	equation	NOUN
cana-5711	580	42	5.5	5.5	NUM
cana-5711	580	43	for	for	ADP
cana-5711	580	44	1	1	NUM
cana-5711	580	45	≤	≤	NUM
cana-5711	580	46	i	i	PRON
cana-5711	580	47	≤	≤	ADV
cana-5711	580	48	7	7	NUM
cana-5711	580	49	.	.	PUNCT
cana-5711	580	50	definition	definition	NOUN
cana-5711	580	51	5.13	5.13	NUM
cana-5711	580	52	.	.	PUNCT
cana-5711	581	1	the	the	DET
cana-5711	581	2	lee	lee	PROPN
cana-5711	581	3	weight	weight	NOUN
cana-5711	581	4	enumerator	enumerator	NOUN
cana-5711	581	5	of	of	ADP
cana-5711	581	6	an	an	DET
cana-5711	581	7	additive	additive	ADJ
cana-5711	581	8	code	code	NOUN
cana-5711	581	9	c	c	NOUN
cana-5711	581	10	over	over	ADP
cana-5711	581	11	ℤ2q	ℤ2q	PROPN
cana-5711	581	12	is	be	AUX
cana-5711	581	13	given	give	VERB
cana-5711	581	14	by	by	ADP
cana-5711	581	15	𝐿𝐶(𝑥	𝐿𝐶(𝑥	PROPN
cana-5711	581	16	,	,	PUNCT
cana-5711	581	17	𝑦	𝑦	X
cana-5711	581	18	)	)	PUNCT
cana-5711	581	19	=	=	SYM
cana-5711	581	20	∑	∑	PUNCT
cana-5711	581	21	𝑥7𝑛−𝑤𝑡𝐿(𝑐	𝑥7𝑛−𝑤𝑡𝐿(𝑐	NUM
cana-5711	581	22	)	)	PUNCT
cana-5711	581	23	𝑐∈𝐶	𝑐∈𝐶	NOUN
cana-5711	581	24	𝑦𝑤𝑡𝐿(𝑐	𝑦𝑤𝑡𝐿(𝑐	NOUN
cana-5711	581	25	)	)	PUNCT
cana-5711	581	26	.	.	PUNCT
cana-5711	582	1	theorem	theorem	VERB
cana-5711	582	2	5.14	5.14	NUM
cana-5711	582	3	.	.	PUNCT
cana-5711	583	1	let	let	VERB
cana-5711	583	2	c	c	PRON
cana-5711	583	3	be	be	AUX
cana-5711	583	4	a	a	DET
cana-5711	583	5	additive	additive	ADJ
cana-5711	583	6	code	code	NOUN
cana-5711	583	7	of	of	ADP
cana-5711	583	8	length	length	NOUN
cana-5711	583	9	n	n	CCONJ
cana-5711	583	10	over	over	ADP
cana-5711	583	11	ℤ2q	ℤ2q	PROPN
cana-5711	583	12	.	.	PUNCT
cana-5711	584	1	then	then	ADV
cana-5711	584	2	lc	lc	PROPN
cana-5711	584	3	(	(	PUNCT
cana-5711	584	4	x	x	PROPN
cana-5711	584	5	,	,	PUNCT
cana-5711	584	6	y	y	NOUN
cana-5711	584	7	)	)	PUNCT
cana-5711	584	8	=	=	SYM
cana-5711	584	9	swec	swec	NOUN
cana-5711	584	10	(	(	PUNCT
cana-5711	584	11	x7	x7	NOUN
cana-5711	584	12	,	,	PUNCT
cana-5711	584	13	x6	x6	PROPN
cana-5711	584	14	y	y	PROPN
cana-5711	584	15	,	,	PUNCT
cana-5711	584	16	x5	x5	PROPN
cana-5711	584	17	y2	y2	PROPN
cana-5711	584	18	,	,	PUNCT
cana-5711	584	19	x4	x4	PROPN
cana-5711	584	20	y3	y3	NOUN
cana-5711	584	21	,	,	PUNCT
cana-5711	584	22	x3	x3	PROPN
cana-5711	584	23	y4	y4	PROPN
cana-5711	584	24	,	,	PUNCT
cana-5711	584	25	x2	x2	PROPN
cana-5711	584	26	y5	y5	PROPN
cana-5711	584	27	,	,	PUNCT
cana-5711	584	28	xy6	xy6	PROPN
cana-5711	584	29	,	,	PUNCT
cana-5711	584	30	y7	y7	PROPN
cana-5711	584	31	)	)	PUNCT
cana-5711	584	32	.	.	PUNCT
cana-5711	585	1	proof	proof	NOUN
cana-5711	585	2	.	.	PUNCT
cana-5711	586	1	let	let	VERB
cana-5711	586	2	c	c	PROPN
cana-5711	586	3	∈	∈	PROPN
cana-5711	586	4	c.	c.	NOUN
cana-5711	586	5	then	then	ADV
cana-5711	586	6	wt	wt	PROPN
cana-5711	586	7	l	l	NOUN
cana-5711	586	8	(	(	PUNCT
cana-5711	586	9	c	c	NOUN
cana-5711	586	10	)	)	PUNCT
cana-5711	587	1	=	=	NOUN
cana-5711	587	2	∑	∑	PART
cana-5711	587	3	𝑖7	𝑖7	PROPN
cana-5711	587	4	𝑖=0	𝑖=0	PROPN
cana-5711	587	5	𝑛𝑖(𝑐	𝑛𝑖(𝑐	PRON
cana-5711	587	6	)	)	PUNCT
cana-5711	587	7	and	and	CCONJ
cana-5711	587	8	n	n	CCONJ
cana-5711	587	9	=	=	SYM
cana-5711	587	10	∑	∑	NOUN
cana-5711	587	11	𝑛𝑖(𝑐	𝑛𝑖(𝑐	NOUN
cana-5711	587	12	)	)	PUNCT
cana-5711	587	13	7	7	NUM
cana-5711	587	14	𝑖=0	𝑖=0	PROPN
cana-5711	587	15	.	.	PUNCT
cana-5711	588	1	by	by	ADP
cana-5711	588	2	definition	definition	NOUN
cana-5711	588	3	5.13	5.13	NUM
cana-5711	588	4	,	,	PUNCT
cana-5711	588	5	we	we	PRON
cana-5711	588	6	have	have	VERB
cana-5711	588	7	lc	lc	NOUN
cana-5711	588	8	(	(	PUNCT
cana-5711	588	9	x	x	X
cana-5711	588	10	,	,	PUNCT
cana-5711	588	11	y	y	NOUN
cana-5711	588	12	)	)	PUNCT
cana-5711	589	1	=	=	NOUN
cana-5711	589	2	∑	∑	PUNCT
cana-5711	589	3	𝑥𝑐∈𝐶	𝑥𝑐∈𝐶	PROPN
cana-5711	589	4	7n−wtl	7n−wtl	PROPN
cana-5711	589	5	(	(	PUNCT
cana-5711	589	6	c	c	X
cana-5711	589	7	)	)	PUNCT
cana-5711	589	8	y	y	PROPN
cana-5711	589	9	wtl	wtl	PROPN
cana-5711	589	10	(	(	PUNCT
cana-5711	589	11	c	c	X
cana-5711	589	12	)	)	PUNCT
cana-5711	589	13	=	=	SYM
cana-5711	589	14	∑	∑	PUNCT
cana-5711	589	15	𝑥7𝑛0(𝑐)+6𝑛1(𝑐)+5𝑛2(𝑐)+4𝑛3(𝑐)+3𝑛4(𝑐)+2𝑛5(𝑐)+6𝑛6(𝑐	𝑥7𝑛0(𝑐)+6𝑛1(𝑐)+5𝑛2(𝑐)+4𝑛3(𝑐)+3𝑛4(𝑐)+2𝑛5(𝑐)+6𝑛6(𝑐	PROPN
cana-5711	589	16	)	)	PUNCT
cana-5711	589	17	𝑐∈𝐶	𝑐∈𝐶	NUM
cana-5711	589	18	𝑦𝑛1(𝑐)+2𝑛2(𝑐)+3𝑛3(𝑐)+4𝑛4(𝑐)+5𝑛5(𝑐)+6𝑛6(𝑐)+7𝑛7(𝑐	𝑦𝑛1(𝑐)+2𝑛2(𝑐)+3𝑛3(𝑐)+4𝑛4(𝑐)+5𝑛5(𝑐)+6𝑛6(𝑐)+7𝑛7(𝑐	NOUN
cana-5711	589	19	)	)	PUNCT
cana-5711	589	20	=	=	NOUN
cana-5711	589	21	∑	∑	PROPN
cana-5711	589	22	(	(	PUNCT
cana-5711	589	23	𝑥7)𝑛0(𝑐	𝑥7)𝑛0(𝑐	NOUN
cana-5711	589	24	)	)	PUNCT
cana-5711	589	25	𝑐∈𝐶	𝑐∈𝐶	NOUN
cana-5711	589	26	(	(	PUNCT
cana-5711	589	27	𝑥6𝑦)𝑛1(𝑐)(𝑥5𝑦2)𝑛2(𝑐)(𝑥4𝑦3)𝑛3(𝑐)(𝑥3𝑦4)𝑛4(𝑐)(𝑥2𝑦5)𝑛5(𝑐)(𝑥𝑦6)𝑛6(𝑐	𝑥6𝑦)𝑛1(𝑐)(𝑥5𝑦2)𝑛2(𝑐)(𝑥4𝑦3)𝑛3(𝑐)(𝑥3𝑦4)𝑛4(𝑐)(𝑥2𝑦5)𝑛5(𝑐)(𝑥𝑦6)𝑛6(𝑐	NOUN
cana-5711	589	28	)	)	PUNCT
cana-5711	589	29	.	.	PUNCT
cana-5711	590	1	by	by	ADP
cana-5711	590	2	equation	equation	NOUN
cana-5711	590	3	5.5	5.5	NUM
cana-5711	590	4	,	,	PUNCT
cana-5711	590	5	lc	lc	PROPN
cana-5711	590	6	(	(	PUNCT
cana-5711	590	7	x	x	X
cana-5711	590	8	,	,	PUNCT
cana-5711	590	9	y	y	NOUN
cana-5711	590	10	)	)	PUNCT
cana-5711	590	11	=	=	SYM
cana-5711	590	12	swec	swec	NOUN
cana-5711	590	13	(	(	PUNCT
cana-5711	590	14	x7	x7	NOUN
cana-5711	590	15	,	,	PUNCT
cana-5711	590	16	x6	x6	PROPN
cana-5711	590	17	y	y	PROPN
cana-5711	590	18	,	,	PUNCT
cana-5711	590	19	x5	x5	PROPN
cana-5711	590	20	y2	y2	PROPN
cana-5711	590	21	,	,	PUNCT
cana-5711	590	22	x4	x4	PROPN
cana-5711	590	23	y3	y3	NOUN
cana-5711	590	24	,	,	PUNCT
cana-5711	590	25	x3	x3	PROPN
cana-5711	590	26	y4	y4	PROPN
cana-5711	590	27	,	,	PUNCT
cana-5711	590	28	x2	x2	PROPN
cana-5711	590	29	y5	y5	PROPN
cana-5711	590	30	,	,	PUNCT
cana-5711	590	31	xy6	xy6	PROPN
cana-5711	590	32	,	,	PUNCT
cana-5711	590	33	y7	y7	PROPN
cana-5711	590	34	)	)	PUNCT
cana-5711	590	35	.	.	PUNCT
cana-5711	591	1	theorem	theorem	VERB
cana-5711	591	2	5.15	5.15	NUM
cana-5711	591	3	.	.	PUNCT
cana-5711	592	1	let	let	VERB
cana-5711	592	2	c	c	PRON
cana-5711	592	3	be	be	AUX
cana-5711	592	4	an	an	DET
cana-5711	592	5	additive	additive	ADJ
cana-5711	592	6	code	code	NOUN
cana-5711	592	7	of	of	ADP
cana-5711	592	8	length	length	NOUN
cana-5711	592	9	n	n	CCONJ
cana-5711	592	10	over	over	ADP
cana-5711	592	11	ℤ2q	ℤ2q	PROPN
cana-5711	592	12	.	.	PUNCT
cana-5711	593	1	then	then	ADV
cana-5711	593	2	lc	lc	PROPN
cana-5711	593	3	⊥	⊥	PROPN
cana-5711	593	4	(	(	PUNCT
cana-5711	593	5	x	x	NOUN
cana-5711	593	6	,	,	PUNCT
cana-5711	593	7	y	y	NOUN
cana-5711	593	8	)	)	PUNCT
cana-5711	593	9	=	=	SYM
cana-5711	593	10	1	1	NUM
cana-5711	593	11	|𝑐|	|𝑐|	NUM
cana-5711	593	12	lc	lc	NOUN
cana-5711	593	13	(	(	PUNCT
cana-5711	593	14	x	x	PROPN
cana-5711	593	15	+	+	NUM
cana-5711	593	16	y	y	NOUN
cana-5711	593	17	,	,	PUNCT
cana-5711	593	18	x	x	PUNCT
cana-5711	593	19	−	−	PROPN
cana-5711	593	20	y	y	PROPN
cana-5711	593	21	)	)	PUNCT
cana-5711	593	22	.	.	PUNCT
cana-5711	594	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5711	594	2	communications	communication	NOUN
cana-5711	594	3	on	on	ADP
cana-5711	594	4	applied	apply	VERB
cana-5711	594	5	nonlinear	nonlinear	ADJ
cana-5711	594	6	analysis	analysis	NOUN
cana-5711	594	7	issn	issn	NOUN
cana-5711	594	8	:	:	PUNCT
cana-5711	594	9	1074	1074	NUM
cana-5711	594	10	-	-	PUNCT
cana-5711	594	11	133x	133x	NUM
cana-5711	594	12	vol	vol	VERB
cana-5711	594	13	32	32	NUM
cana-5711	594	14	no	no	NOUN
cana-5711	594	15	.	.	PUNCT
cana-5711	595	1	10s	10	NOUN
cana-5711	595	2	(	(	PUNCT
cana-5711	595	3	2025	2025	NUM
cana-5711	595	4	)	)	PUNCT
cana-5711	595	5	2710	2710	NUM
cana-5711	595	6	proof	proof	NOUN
cana-5711	595	7	.	.	PUNCT
cana-5711	596	1	by	by	ADP
cana-5711	596	2	definition	definition	NOUN
cana-5711	596	3	5.13	5.13	NUM
cana-5711	596	4	,	,	PUNCT
cana-5711	596	5	lc	lc	PROPN
cana-5711	596	6	⊥	⊥	PROPN
cana-5711	596	7	(	(	PUNCT
cana-5711	596	8	x	x	NOUN
cana-5711	596	9	,	,	PUNCT
cana-5711	596	10	y	y	NOUN
cana-5711	596	11	)	)	PUNCT
cana-5711	596	12	=	=	NOUN
cana-5711	596	13	swec	swec	NOUN
cana-5711	596	14	⊥	⊥	NOUN
cana-5711	596	15	(	(	PUNCT
cana-5711	596	16	x7	x7	NOUN
cana-5711	596	17	,	,	PUNCT
cana-5711	596	18	x6	x6	PROPN
cana-5711	596	19	y	y	PROPN
cana-5711	596	20	,	,	PUNCT
cana-5711	596	21	x5	x5	PROPN
cana-5711	596	22	y2	y2	PROPN
cana-5711	596	23	,	,	PUNCT
cana-5711	596	24	x4	x4	PROPN
cana-5711	596	25	y3	y3	NOUN
cana-5711	596	26	,	,	PUNCT
cana-5711	596	27	x3	x3	PROPN
cana-5711	596	28	y4	y4	PROPN
cana-5711	596	29	,	,	PUNCT
cana-5711	596	30	x2	x2	PROPN
cana-5711	596	31	y5	y5	PROPN
cana-5711	596	32	,	,	PUNCT
cana-5711	596	33	xy6	xy6	PROPN
cana-5711	596	34	,	,	PUNCT
cana-5711	596	35	y7	y7	PROPN
cana-5711	596	36	)	)	PUNCT
cana-5711	596	37	=	=	SYM
cana-5711	596	38	1	1	NUM
cana-5711	596	39	|𝑐|	|𝑐|	PROPN
cana-5711	596	40	swec	swec	NOUN
cana-5711	596	41	(	(	PUNCT
cana-5711	596	42	s	s	X
cana-5711	596	43	·	·	PUNCT
cana-5711	596	44	(	(	PUNCT
cana-5711	596	45	x7	x7	NOUN
cana-5711	596	46	,	,	PUNCT
cana-5711	596	47	x6	x6	PROPN
cana-5711	596	48	y	y	PROPN
cana-5711	596	49	,	,	PUNCT
cana-5711	596	50	x5	x5	PROPN
cana-5711	596	51	y2	y2	PROPN
cana-5711	596	52	,	,	PUNCT
cana-5711	596	53	x4	x4	PROPN
cana-5711	596	54	y3	y3	NOUN
cana-5711	596	55	,	,	PUNCT
cana-5711	596	56	x3	x3	PROPN
cana-5711	596	57	y4	y4	PROPN
cana-5711	596	58	,	,	PUNCT
cana-5711	596	59	x2	x2	PROPN
cana-5711	596	60	y5	y5	PROPN
cana-5711	596	61	,	,	PUNCT
cana-5711	596	62	xy6	xy6	PROPN
cana-5711	596	63	,	,	PUNCT
cana-5711	596	64	y7	y7	PROPN
cana-5711	596	65	)	)	PUNCT
cana-5711	596	66	t	t	NOUN
cana-5711	596	67	)	)	PUNCT
cana-5711	596	68	(	(	PUNCT
cana-5711	596	69	by	by	ADP
cana-5711	596	70	theorem	theorem	NOUN
cana-5711	596	71	5.11	5.11	NUM
cana-5711	596	72	)	)	PUNCT
cana-5711	596	73	=	=	SYM
cana-5711	596	74	1	1	NUM
cana-5711	596	75	|𝑐|	|𝑐|	PROPN
cana-5711	596	76	swec	swec	NOUN
cana-5711	596	77	(	(	PUNCT
cana-5711	596	78	(	(	PUNCT
cana-5711	596	79	x	x	SYM
cana-5711	596	80	+	+	CCONJ
cana-5711	596	81	y)7	y)7	NOUN
cana-5711	596	82	,	,	PUNCT
cana-5711	596	83	(	(	PUNCT
cana-5711	596	84	x	x	X
cana-5711	596	85	+	+	NUM
cana-5711	596	86	y)6	y)6	PROPN
cana-5711	596	87	(	(	PUNCT
cana-5711	596	88	x	x	PROPN
cana-5711	596	89	−	−	PROPN
cana-5711	596	90	y	y	PROPN
cana-5711	596	91	)	)	PUNCT
cana-5711	596	92	,	,	PUNCT
cana-5711	596	93	(	(	PUNCT
cana-5711	596	94	x	x	X
cana-5711	596	95	+	+	NUM
cana-5711	596	96	y)5	y)5	NOUN
cana-5711	596	97	(	(	PUNCT
cana-5711	596	98	x	x	X
cana-5711	596	99	−	−	NOUN
cana-5711	596	100	y)2	y)2	NOUN
cana-5711	596	101	,	,	PUNCT
cana-5711	596	102	(	(	PUNCT
cana-5711	596	103	x	x	X
cana-5711	596	104	+	+	PUNCT
cana-5711	596	105	y)4(x	y)4(x	NUM
cana-5711	596	106	−	−	PROPN
cana-5711	596	107	y)3	y)3	PROPN
cana-5711	596	108	,	,	PUNCT
cana-5711	596	109	(	(	PUNCT
cana-5711	596	110	x	x	X
cana-5711	596	111	+	+	NOUN
cana-5711	596	112	y)3	y)3	PROPN
cana-5711	596	113	(	(	PUNCT
cana-5711	596	114	x	x	X
cana-5711	596	115	−	−	VERB
cana-5711	596	116	y)4	y)4	NOUN
cana-5711	596	117	,	,	PUNCT
cana-5711	596	118	(	(	PUNCT
cana-5711	596	119	x	x	SYM
cana-5711	596	120	+	+	PUNCT
cana-5711	596	121	y)2	y)2	NOUN
cana-5711	596	122	(	(	PUNCT
cana-5711	596	123	x	x	NOUN
cana-5711	596	124	−	−	NOUN
cana-5711	596	125	y)5	y)5	NOUN
cana-5711	596	126	,	,	PUNCT
cana-5711	596	127	(	(	PUNCT
cana-5711	596	128	x	x	SYM
cana-5711	596	129	+	+	NUM
cana-5711	596	130	y)(x	y)(x	PROPN
cana-5711	596	131	−	−	PROPN
cana-5711	596	132	y)6	y)6	PROPN
cana-5711	596	133	,	,	PUNCT
cana-5711	596	134	(	(	PUNCT
cana-5711	596	135	x	x	X
cana-5711	596	136	−	−	PROPN
cana-5711	596	137	y)7	y)7	NOUN
cana-5711	596	138	)	)	PUNCT
cana-5711	596	139	=	=	SYM
cana-5711	596	140	1	1	NUM
cana-5711	596	141	|𝑐|	|𝑐|	NUM
cana-5711	596	142	lc	lc	NOUN
cana-5711	596	143	(	(	PUNCT
cana-5711	596	144	x	x	PROPN
cana-5711	596	145	+	+	NUM
cana-5711	596	146	y	y	NOUN
cana-5711	596	147	,	,	PUNCT
cana-5711	596	148	x	x	PUNCT
cana-5711	596	149	−	−	PROPN
cana-5711	596	150	y	y	PROPN
cana-5711	596	151	)	)	PUNCT
cana-5711	596	152	(	(	PUNCT
cana-5711	596	153	by	by	ADP
cana-5711	596	154	theorem	theorem	NOUN
cana-5711	596	155	5.14	5.14	NUM
cana-5711	596	156	)	)	PUNCT
cana-5711	596	157	.	.	PUNCT
cana-5711	597	1	example	example	NOUN
cana-5711	598	1	5.16	5.16	NUM
cana-5711	598	2	.	.	PUNCT
cana-5711	598	3	suppose	suppose	VERB
cana-5711	598	4	c	c	NOUN
cana-5711	598	5	is	be	AUX
cana-5711	598	6	as	as	ADP
cana-5711	598	7	in	in	ADP
cana-5711	598	8	example	example	NOUN
cana-5711	598	9	5.6	5.6	NUM
cana-5711	598	10	.	.	PUNCT
cana-5711	599	1	then	then	ADV
cana-5711	599	2	by	by	ADP
cana-5711	599	3	using	use	VERB
cana-5711	599	4	theorem	theorem	NOUN
cana-5711	599	5	5.14	5.14	NUM
cana-5711	599	6	,	,	PUNCT
cana-5711	599	7	lc	lc	PROPN
cana-5711	599	8	⊥	⊥	PROPN
cana-5711	599	9	(	(	PUNCT
cana-5711	599	10	x	x	NOUN
cana-5711	599	11	,	,	PUNCT
cana-5711	599	12	y	y	NOUN
cana-5711	599	13	)	)	PUNCT
cana-5711	599	14	=	=	X
cana-5711	599	15	swec	swec	NOUN
cana-5711	599	16	⊥	⊥	NOUN
cana-5711	599	17	(	(	PUNCT
cana-5711	599	18	x	x	SYM
cana-5711	599	19	7	7	NUM
cana-5711	599	20	,	,	PUNCT
cana-5711	599	21	x6	x6	PROPN
cana-5711	599	22	y	y	PROPN
cana-5711	599	23	,	,	PUNCT
cana-5711	599	24	x5	x5	PROPN
cana-5711	599	25	y2	y2	PROPN
cana-5711	599	26	,	,	PUNCT
cana-5711	599	27	x4	x4	PROPN
cana-5711	599	28	y3	y3	NOUN
cana-5711	599	29	,	,	PUNCT
cana-5711	599	30	x3	x3	PROPN
cana-5711	599	31	y4	y4	PROPN
cana-5711	599	32	,	,	PUNCT
cana-5711	599	33	x2	x2	PROPN
cana-5711	599	34	y5	y5	PROPN
cana-5711	599	35	,	,	PUNCT
cana-5711	599	36	xy6	xy6	PROPN
cana-5711	599	37	,	,	PUNCT
cana-5711	599	38	y7	y7	PROPN
cana-5711	599	39	)	)	PUNCT
cana-5711	600	1	=	=	SYM
cana-5711	600	2	x14	x14	PROPN
cana-5711	601	1	+	+	CCONJ
cana-5711	601	2	x13	x13	PROPN
cana-5711	601	3	y	y	PROPN
cana-5711	601	4	+	+	NUM
cana-5711	601	5	8x12	8x12	NUM
cana-5711	602	1	y2	y2	NOUN
cana-5711	602	2	+	+	CCONJ
cana-5711	602	3	8x11	8x11	NUM
cana-5711	602	4	y3	y3	NOUN
cana-5711	602	5	+	+	PROPN
cana-5711	602	6	15x10y4	15x10y4	PROPN
cana-5711	602	7	+	+	CCONJ
cana-5711	602	8	15x9	15x9	NUM
cana-5711	602	9	y5	y5	NOUN
cana-5711	602	10	+	+	CCONJ
cana-5711	602	11	16x8	16x8	NUM
cana-5711	602	12	y6	y6	ADJ
cana-5711	602	13	+	+	CCONJ
cana-5711	602	14	16x7	16x7	NUM
cana-5711	602	15	y7	y7	NOUN
cana-5711	603	1	+	+	CCONJ
cana-5711	604	1	15x6	15x6	NUM
cana-5711	604	2	y8	y8	ADJ
cana-5711	604	3	+	+	CCONJ
cana-5711	604	4	15x5	15x5	NUM
cana-5711	604	5	y9	y9	NOUN
cana-5711	604	6	+	+	CCONJ
cana-5711	604	7	8x4	8x4	NUM
cana-5711	604	8	y10	y10	NOUN
cana-5711	604	9	+	+	CCONJ
cana-5711	604	10	8x3	8x3	NUM
cana-5711	604	11	y11	y11	NOUN
cana-5711	604	12	+	+	CCONJ
cana-5711	604	13	x2y12	x2y12	PROPN
cana-5711	605	1	+	+	CCONJ
cana-5711	605	2	xy13	xy13	PROPN
cana-5711	605	3	and	and	CCONJ
cana-5711	605	4	lc	lc	PROPN
cana-5711	605	5	(	(	PUNCT
cana-5711	605	6	x	x	PROPN
cana-5711	605	7	+	+	NUM
cana-5711	605	8	y	y	NOUN
cana-5711	605	9	,	,	PUNCT
cana-5711	605	10	x	x	PUNCT
cana-5711	605	11	−	−	PROPN
cana-5711	605	12	y	y	NOUN
cana-5711	605	13	)	)	PUNCT
cana-5711	605	14	=	=	SYM
cana-5711	605	15	swec	swec	NOUN
cana-5711	605	16	(	(	PUNCT
cana-5711	605	17	(	(	PUNCT
cana-5711	605	18	x	x	SYM
cana-5711	605	19	+	+	CCONJ
cana-5711	605	20	y)7	y)7	NOUN
cana-5711	605	21	,	,	PUNCT
cana-5711	605	22	(	(	PUNCT
cana-5711	605	23	x	x	X
cana-5711	605	24	+	+	NUM
cana-5711	605	25	y)6(x	y)6(x	PROPN
cana-5711	605	26	−	−	PROPN
cana-5711	605	27	y),(x	y),(x	NOUN
cana-5711	606	1	+	+	CCONJ
cana-5711	606	2	y)5(x	y)5(x	PROPN
cana-5711	606	3	−	−	NOUN
cana-5711	606	4	y)2	y)2	NOUN
cana-5711	606	5	,	,	PUNCT
cana-5711	606	6	(	(	PUNCT
cana-5711	606	7	x	x	X
cana-5711	606	8	+	+	NUM
cana-5711	606	9	y)4	y)4	NOUN
cana-5711	606	10	(	(	PUNCT
cana-5711	606	11	x	x	SYM
cana-5711	606	12	−	−	PROPN
cana-5711	606	13	y)3	y)3	PROPN
cana-5711	606	14	,	,	PUNCT
cana-5711	606	15	(	(	PUNCT
cana-5711	606	16	x	x	X
cana-5711	607	1	+	+	NOUN
cana-5711	607	2	y)3	y)3	PROPN
cana-5711	607	3	(	(	PUNCT
cana-5711	607	4	x	x	X
cana-5711	607	5	−	−	VERB
cana-5711	607	6	y)4	y)4	NOUN
cana-5711	607	7	,	,	PUNCT
cana-5711	607	8	(	(	PUNCT
cana-5711	607	9	x	x	SYM
cana-5711	607	10	+	+	PUNCT
cana-5711	607	11	y)2	y)2	NOUN
cana-5711	607	12	(	(	PUNCT
cana-5711	607	13	x	x	NOUN
cana-5711	607	14	−	−	NOUN
cana-5711	607	15	y)5	y)5	NOUN
cana-5711	607	16	,	,	PUNCT
cana-5711	607	17	(	(	PUNCT
cana-5711	607	18	x	x	SYM
cana-5711	607	19	+	+	NUM
cana-5711	607	20	y)(x	y)(x	PROPN
cana-5711	607	21	−	−	PROPN
cana-5711	607	22	y)6	y)6	PROPN
cana-5711	607	23	,	,	PUNCT
cana-5711	607	24	(	(	PUNCT
cana-5711	607	25	x	x	X
cana-5711	607	26	−	−	PROPN
cana-5711	607	27	y)7	y)7	NOUN
cana-5711	607	28	)	)	PUNCT
cana-5711	608	1	=	=	SYM
cana-5711	608	2	128[x14	128[x14	NOUN
cana-5711	608	3	+	+	NUM
cana-5711	608	4	x13	x13	PROPN
cana-5711	608	5	y	y	PROPN
cana-5711	608	6	+	+	PROPN
cana-5711	608	7	8x12	8x12	NOUN
cana-5711	608	8	y	y	PROPN
cana-5711	608	9	2	2	NUM
cana-5711	608	10	+	+	NUM
cana-5711	608	11	8x11	8x11	NUM
cana-5711	608	12	y	y	NOUN
cana-5711	608	13	3	3	NUM
cana-5711	608	14	+	+	CCONJ
cana-5711	608	15	15x10	15x10	NUM
cana-5711	608	16	y	y	NOUN
cana-5711	608	17	4	4	NUM
cana-5711	608	18	+	+	CCONJ
cana-5711	608	19	15x9	15x9	NUM
cana-5711	608	20	y	y	PROPN
cana-5711	608	21	5	5	NUM
cana-5711	608	22	+	+	CCONJ
cana-5711	608	23	16x8	16x8	NUM
cana-5711	608	24	y	y	NOUN
cana-5711	608	25	6	6	NUM
cana-5711	608	26	+16x7y	+16x7y	VERB
cana-5711	608	27	7	7	NUM
cana-5711	609	1	+	+	CCONJ
cana-5711	609	2	15x6	15x6	NUM
cana-5711	609	3	y	y	NUM
cana-5711	609	4	8	8	NUM
cana-5711	609	5	+	+	CCONJ
cana-5711	609	6	15x5	15x5	NUM
cana-5711	609	7	y	y	NOUN
cana-5711	609	8	9	9	NUM
cana-5711	609	9	+	+	NUM
cana-5711	609	10	8x4	8x4	NUM
cana-5711	609	11	y	y	NOUN
cana-5711	609	12	10	10	NUM
cana-5711	609	13	+	+	NUM
cana-5711	609	14	8x3	8x3	NUM
cana-5711	609	15	y	y	PROPN
cana-5711	609	16	11	11	NUM
cana-5711	610	1	+	+	CCONJ
cana-5711	610	2	x2	x2	PROPN
cana-5711	610	3	y	y	NOUN
cana-5711	610	4	12	12	NUM
cana-5711	611	1	+	+	CCONJ
cana-5711	611	2	xy	xy	PROPN
cana-5711	611	3	13	13	NUM
cana-5711	611	4	]	]	PUNCT
cana-5711	611	5	.	.	PUNCT
cana-5711	612	1	6	6	X
cana-5711	612	2	.	.	X
cana-5711	612	3	conclusion	conclusion	NOUN
cana-5711	612	4	in	in	ADP
cana-5711	612	5	this	this	DET
cana-5711	612	6	paper	paper	NOUN
cana-5711	612	7	,	,	PUNCT
cana-5711	612	8	we	we	PRON
cana-5711	612	9	studied	study	VERB
cana-5711	612	10	the	the	DET
cana-5711	612	11	acd	acd	NOUN
cana-5711	612	12	codes	code	NOUN
cana-5711	612	13	over	over	ADP
cana-5711	612	14	the	the	DET
cana-5711	612	15	finite	finite	PROPN
cana-5711	612	16	commutative	commutative	ADJ
cana-5711	612	17	frobenius	frobenius	NOUN
cana-5711	612	18	ring	ring	NOUN
cana-5711	612	19	ℤ2rs	ℤ2r	NOUN
cana-5711	612	20	,	,	PUNCT
cana-5711	612	21	where	where	SCONJ
cana-5711	612	22	r=	r=	ADJ
cana-5711	612	23	ℤ2	ℤ2	VERB
cana-5711	612	24	+	+	CCONJ
cana-5711	612	25	uℤ2	uℤ2	PROPN
cana-5711	612	26	and	and	CCONJ
cana-5711	612	27	s	s	NOUN
cana-5711	612	28	=	=	NOUN
cana-5711	612	29	ℤ2	ℤ2	PROPN
cana-5711	612	30	+	+	CCONJ
cana-5711	612	31	uℤ2	uℤ2	PROPN
cana-5711	612	32	+	+	CCONJ
cana-5711	612	33	vℤ2	vℤ2	NOUN
cana-5711	612	34	+	+	CCONJ
cana-5711	612	35	uvℤ2	uvℤ2	PROPN
cana-5711	612	36	.	.	PUNCT
cana-5711	613	1	we	we	PRON
cana-5711	613	2	established	establish	VERB
cana-5711	613	3	a	a	DET
cana-5711	613	4	condition	condition	NOUN
cana-5711	613	5	to	to	PART
cana-5711	613	6	ensure	ensure	VERB
cana-5711	613	7	that	that	SCONJ
cana-5711	613	8	an	an	DET
cana-5711	613	9	additive	additive	ADJ
cana-5711	613	10	code	code	NOUN
cana-5711	613	11	is	be	AUX
cana-5711	613	12	an	an	DET
cana-5711	613	13	acd	acd	NOUN
cana-5711	613	14	code	code	NOUN
cana-5711	613	15	.	.	PUNCT
cana-5711	614	1	furthermore	furthermore	ADV
cana-5711	614	2	,	,	PUNCT
cana-5711	614	3	we	we	PRON
cana-5711	614	4	derived	derive	VERB
cana-5711	614	5	a	a	DET
cana-5711	614	6	necessary	necessary	ADJ
cana-5711	614	7	and	and	CCONJ
cana-5711	614	8	sufficient	sufficient	ADJ
cana-5711	614	9	condition	condition	NOUN
cana-5711	614	10	for	for	ADP
cana-5711	614	11	a	a	DET
cana-5711	614	12	separable	separable	ADJ
cana-5711	614	13	additive	additive	ADJ
cana-5711	614	14	code	code	NOUN
cana-5711	614	15	to	to	PART
cana-5711	614	16	be	be	AUX
cana-5711	614	17	an	an	DET
cana-5711	614	18	acd	acd	NOUN
cana-5711	614	19	code	code	NOUN
cana-5711	614	20	.	.	PUNCT
cana-5711	615	1	we	we	PRON
cana-5711	615	2	also	also	ADV
cana-5711	615	3	examined	examine	VERB
cana-5711	615	4	a	a	DET
cana-5711	615	5	gray	gray	ADJ
cana-5711	615	6	map	map	NOUN
cana-5711	615	7	that	that	PRON
cana-5711	615	8	transforms	transform	VERB
cana-5711	615	9	certain	certain	ADJ
cana-5711	615	10	additive	additive	ADJ
cana-5711	615	11	codes	code	NOUN
cana-5711	615	12	into	into	ADP
cana-5711	615	13	binary	binary	ADJ
cana-5711	615	14	linear	linear	PROPN
cana-5711	615	15	complementary	complementary	ADJ
cana-5711	615	16	dual	dual	ADJ
cana-5711	615	17	(	(	PUNCT
cana-5711	615	18	lcd	lcd	NOUN
cana-5711	615	19	)	)	PUNCT
cana-5711	615	20	codes	code	NOUN
cana-5711	615	21	.	.	PUNCT
cana-5711	616	1	additionally	additionally	ADV
cana-5711	616	2	,	,	PUNCT
cana-5711	616	3	the	the	DET
cana-5711	616	4	macwilliams	macwilliam	NOUN
cana-5711	616	5	identities	identity	NOUN
cana-5711	616	6	corresponding	correspond	VERB
cana-5711	616	7	to	to	ADP
cana-5711	616	8	different	different	ADJ
cana-5711	616	9	weight	weight	NOUN
cana-5711	616	10	enumerators	enumerator	NOUN
cana-5711	616	11	were	be	AUX
cana-5711	616	12	discussed	discuss	VERB
cana-5711	616	13	.	.	PUNCT
cana-5711	617	1	conflict	conflict	NOUN
cana-5711	617	2	of	of	ADP
cana-5711	617	3	interest	interest	NOUN
cana-5711	617	4	the	the	DET
cana-5711	617	5	authors	author	NOUN
cana-5711	617	6	confirm	confirm	VERB
cana-5711	617	7	that	that	SCONJ
cana-5711	617	8	there	there	PRON
cana-5711	617	9	is	be	VERB
cana-5711	617	10	no	no	DET
cana-5711	617	11	conflict	conflict	NOUN
cana-5711	617	12	of	of	ADP
cana-5711	617	13	interest	interest	NOUN
cana-5711	617	14	to	to	PART
cana-5711	617	15	declare	declare	VERB
cana-5711	617	16	for	for	ADP
cana-5711	617	17	this	this	DET
cana-5711	617	18	publication	publication	NOUN
cana-5711	617	19	.	.	PUNCT
cana-5711	618	1	acknowledgment	acknowledgment	NOUN
cana-5711	618	2	the	the	DET
cana-5711	618	3	authors	author	NOUN
cana-5711	618	4	declare	declare	VERB
cana-5711	618	5	that	that	SCONJ
cana-5711	618	6	,	,	PUNCT
cana-5711	618	7	there	there	PRON
cana-5711	618	8	is	be	VERB
cana-5711	618	9	no	no	DET
cana-5711	618	10	financial	financial	ADJ
cana-5711	618	11	support	support	NOUN
cana-5711	618	12	from	from	ADP
cana-5711	618	13	any	any	PRON
cana-5711	618	14	of	of	ADP
cana-5711	618	15	the	the	DET
cana-5711	618	16	institutions	institution	NOUN
cana-5711	618	17	or	or	CCONJ
cana-5711	618	18	personal	personal	ADJ
cana-5711	618	19	relationship	relationship	NOUN
cana-5711	618	20	to	to	PART
cana-5711	618	21	affect	affect	VERB
cana-5711	618	22	the	the	DET
cana-5711	618	23	quality	quality	NOUN
cana-5711	618	24	of	of	ADP
cana-5711	618	25	the	the	DET
cana-5711	618	26	paper	paper	NOUN
cana-5711	618	27	.	.	PUNCT
cana-5711	619	1	references	reference	NOUN
cana-5711	619	2	:	:	PUNCT
cana-5711	620	1	[	[	X
cana-5711	620	2	1	1	NUM
cana-5711	620	3	]	]	PUNCT
cana-5711	620	4	i.	i.	NOUN
cana-5711	620	5	aydogdu	aydogdu	PROPN
cana-5711	620	6	,	,	PUNCT
cana-5711	620	7	t.	t.	PROPN
cana-5711	620	8	abualrub	abualrub	PROPN
cana-5711	620	9	,	,	PUNCT
cana-5711	620	10	i.	i.	PROPN
cana-5711	620	11	siap	siap	PROPN
cana-5711	620	12	,	,	PUNCT
cana-5711	620	13	on	on	ADP
cana-5711	620	14	ℤ2ℤ2	ℤ2ℤ2	NOUN
cana-5711	620	15	[	[	X
cana-5711	620	16	u]-additive	u]-additive	ADJ
cana-5711	620	17	codes	code	NOUN
cana-5711	620	18	,	,	PUNCT
cana-5711	620	19	comput	comput	NOUN
cana-5711	620	20	.	.	PUNCT
cana-5711	621	1	math	math	NOUN
cana-5711	621	2	.	.	PUNCT
cana-5711	622	1	92(9	92(9	NUM
cana-5711	622	2	)	)	PUNCT
cana-5711	622	3	,	,	PUNCT
cana-5711	622	4	1806–1814	1806–1814	NUM
cana-5711	622	5	,	,	PUNCT
cana-5711	622	6	2015.int	2015.int	NOUN
cana-5711	622	7	.	.	PUNCT
cana-5711	623	1	j.	j.	PROPN
cana-5711	623	2	https://internationalpubls.com	https://internationalpubls.com	PROPN
cana-5711	623	3	communications	communication	NOUN
cana-5711	623	4	on	on	ADP
cana-5711	623	5	applied	apply	VERB
cana-5711	623	6	nonlinear	nonlinear	ADJ
cana-5711	623	7	analysis	analysis	NOUN
cana-5711	623	8	issn	issn	NOUN
cana-5711	623	9	:	:	PUNCT
cana-5711	623	10	1074	1074	NUM
cana-5711	623	11	-	-	PUNCT
cana-5711	623	12	133x	133x	NUM
cana-5711	623	13	vol	vol	VERB
cana-5711	623	14	32	32	NUM
cana-5711	623	15	no	no	NOUN
cana-5711	623	16	.	.	PUNCT
cana-5711	624	1	10s	10	NOUN
cana-5711	624	2	(	(	PUNCT
cana-5711	624	3	2025	2025	NUM
cana-5711	624	4	)	)	PUNCT
cana-5711	624	5	2711	2711	NUM
cana-5711	625	1	[	[	X
cana-5711	625	2	2	2	NUM
cana-5711	625	3	]	]	X
cana-5711	625	4	n.	n.	PROPN
cana-5711	625	5	benbelkacem	benbelkacem	PROPN
cana-5711	625	6	,	,	PUNCT
cana-5711	625	7	j.	j.	PROPN
cana-5711	625	8	borges	borges	PROPN
cana-5711	625	9	,	,	PUNCT
cana-5711	625	10	s.	s.	PROPN
cana-5711	625	11	t.	t.	PROPN
cana-5711	625	12	dougherty	dougherty	PROPN
cana-5711	625	13	,	,	PUNCT
cana-5711	625	14	c.	c.	PROPN
cana-5711	625	15	fernández	fernández	PROPN
cana-5711	625	16	-	-	PUNCT
cana-5711	625	17	córdoba	córdoba	PROPN
cana-5711	625	18	,	,	PUNCT
cana-5711	625	19	on	on	ADP
cana-5711	625	20	ℤ2ℤ4	ℤ2ℤ4	ADJ
cana-5711	625	21	-additive	-additive	ADJ
cana-5711	625	22	complementary	complementary	ADJ
cana-5711	625	23	dual	dual	ADJ
cana-5711	625	24	codes	code	NOUN
cana-5711	625	25	and	and	CCONJ
cana-5711	625	26	related	relate	VERB
cana-5711	625	27	lcd	lcd	NOUN
cana-5711	625	28	codes	code	NOUN
cana-5711	625	29	,	,	PUNCT
cana-5711	625	30	finite	finite	PROPN
cana-5711	625	31	fields	field	VERB
cana-5711	625	32	their	their	PRON
cana-5711	625	33	appl	appl	NOUN
cana-5711	625	34	.	.	PROPN
cana-5711	626	1	62	62	NUM
cana-5711	626	2	,	,	PUNCT
cana-5711	626	3	101622	101622	NUM
cana-5711	626	4	,	,	PUNCT
cana-5711	626	5	2020	2020	NUM
cana-5711	626	6	.	.	PUNCT
cana-5711	627	1	[	[	X
cana-5711	627	2	3	3	X
cana-5711	627	3	]	]	X
cana-5711	627	4	w.	w.	PROPN
cana-5711	627	5	bosma	bosma	PROPN
cana-5711	627	6	,	,	PUNCT
cana-5711	627	7	j.	j.	PROPN
cana-5711	627	8	cannon	cannon	PROPN
cana-5711	627	9	,	,	PUNCT
cana-5711	627	10	c.	c.	PROPN
cana-5711	627	11	playoust	playoust	PROPN
cana-5711	627	12	,	,	PUNCT
cana-5711	627	13	magma	magma	NOUN
cana-5711	627	14	algebra	algebra	NOUN
cana-5711	627	15	system	system	NOUN
cana-5711	628	1	i	i	PRON
cana-5711	628	2	:	:	PUNCT
cana-5711	628	3	the	the	DET
cana-5711	628	4	user	user	NOUN
cana-5711	628	5	language	language	NOUN
cana-5711	628	6	.	.	PUNCT
cana-5711	629	1	j.	j.	PROPN
cana-5711	629	2	symb	symb	PROPN
cana-5711	629	3	.	.	PUNCT
cana-5711	630	1	comput	comput	NOUN
cana-5711	630	2	.	.	PUNCT
cana-5711	631	1	24(3–4	24(3–4	ADJ
cana-5711	631	2	)	)	PUNCT
cana-5711	631	3	,	,	PUNCT
cana-5711	631	4	235–265	235–265	NUM
cana-5711	631	5	,	,	PUNCT
cana-5711	631	6	1997	1997	NUM
cana-5711	631	7	.	.	PUNCT
cana-5711	632	1	[	[	X
cana-5711	632	2	4	4	NUM
cana-5711	632	3	]	]	X
cana-5711	632	4	c.	c.	PROPN
cana-5711	632	5	carlet	carlet	PROPN
cana-5711	632	6	,	,	PUNCT
cana-5711	632	7	s.	s.	PROPN
cana-5711	632	8	guilley	guilley	PROPN
cana-5711	632	9	,	,	PUNCT
cana-5711	632	10	complementary	complementary	ADJ
cana-5711	632	11	dual	dual	ADJ
cana-5711	632	12	codes	code	NOUN
cana-5711	632	13	for	for	ADP
cana-5711	632	14	counter	counter	NOUN
cana-5711	632	15	-	-	NOUN
cana-5711	632	16	measures	measure	NOUN
cana-5711	632	17	to	to	ADP
cana-5711	632	18	side	side	NOUN
cana-5711	632	19	-	-	PUNCT
cana-5711	632	20	channel	channel	NOUN
cana-5711	632	21	attacks	attack	NOUN
cana-5711	632	22	.	.	PUNCT
cana-5711	633	1	adv	adv	PROPN
cana-5711	633	2	.	.	PUNCT
cana-5711	633	3	math	math	PROPN
cana-5711	633	4	.	.	PUNCT
cana-5711	634	1	commun	commun	PROPN
cana-5711	634	2	.	.	PUNCT
cana-5711	635	1	10(1	10(1	NUM
cana-5711	635	2	)	)	PUNCT
cana-5711	635	3	,	,	PUNCT
cana-5711	635	4	131–150	131–150	NUM
cana-5711	635	5	,	,	PUNCT
cana-5711	635	6	2016	2016	NUM
cana-5711	635	7	.	.	PUNCT
cana-5711	636	1	[	[	X
cana-5711	636	2	5	5	X
cana-5711	636	3	]	]	PUNCT
cana-5711	636	4	s.	s.	PROPN
cana-5711	636	5	t.	t.	PROPN
cana-5711	636	6	dougherty	dougherty	PROPN
cana-5711	636	7	,	,	PUNCT
cana-5711	636	8	algebraic	algebraic	PROPN
cana-5711	636	9	coding	code	VERB
cana-5711	636	10	theory	theory	NOUN
cana-5711	636	11	over	over	ADP
cana-5711	636	12	finite	finite	PROPN
cana-5711	636	13	commutative	commutative	ADJ
cana-5711	636	14	rings	ring	NOUN
cana-5711	636	15	,	,	PUNCT
cana-5711	636	16	springer	springer	NOUN
cana-5711	636	17	briefs	brief	NOUN
cana-5711	636	18	in	in	ADP
cana-5711	636	19	mathematics	mathematic	NOUN
cana-5711	636	20	,	,	PUNCT
cana-5711	636	21	springer	springer	NOUN
cana-5711	636	22	,	,	PUNCT
cana-5711	636	23	2017	2017	NUM
cana-5711	636	24	.	.	PUNCT
cana-5711	637	1	[	[	X
cana-5711	637	2	6	6	NUM
cana-5711	637	3	]	]	PUNCT
cana-5711	637	4	a.	a.	PROPN
cana-5711	637	5	r.	r.	PROPN
cana-5711	637	6	hammons	hammons	PROPN
cana-5711	637	7	,	,	PUNCT
cana-5711	637	8	p.	p.	NOUN
cana-5711	637	9	v.	v.	PROPN
cana-5711	637	10	kumar	kumar	PROPN
cana-5711	637	11	,	,	PUNCT
cana-5711	637	12	a.	a.	PROPN
cana-5711	637	13	r.	r.	PROPN
cana-5711	637	14	calderbank	calderbank	PROPN
cana-5711	637	15	,	,	PUNCT
cana-5711	637	16	n.	n.	PROPN
cana-5711	637	17	j.	j.	PROPN
cana-5711	637	18	a.	a.	PROPN
cana-5711	637	19	slone	slone	PROPN
cana-5711	637	20	,	,	PUNCT
cana-5711	637	21	p.	p.	PROPN
cana-5711	637	22	solé	solé	NOUN
cana-5711	637	23	,	,	PUNCT
cana-5711	637	24	the	the	DET
cana-5711	637	25	z4	z4	PROPN
cana-5711	637	26	linearity	linearity	PROPN
cana-5711	637	27	of	of	ADP
cana-5711	637	28	kerdock	kerdock	NOUN
cana-5711	637	29	,	,	PUNCT
cana-5711	637	30	preparata	preparata	NOUN
cana-5711	637	31	,	,	PUNCT
cana-5711	637	32	goethals	goethal	NOUN
cana-5711	637	33	and	and	CCONJ
cana-5711	637	34	related	related	ADJ
cana-5711	637	35	codes	code	NOUN
cana-5711	637	36	.	.	PUNCT
cana-5711	638	1	ieee	ieee	PROPN
cana-5711	638	2	trans	trans	PROPN
cana-5711	638	3	.	.	PROPN
cana-5711	638	4	inf	inf	PROPN
cana-5711	638	5	.	.	PROPN
cana-5711	638	6	theory	theory	PROPN
cana-5711	638	7	40(2	40(2	NUM
cana-5711	638	8	)	)	PUNCT
cana-5711	638	9	,	,	PUNCT
cana-5711	638	10	301–319	301–319	NUM
cana-5711	638	11	,	,	PUNCT
cana-5711	638	12	1994	1994	NUM
cana-5711	638	13	.	.	PUNCT
cana-5711	639	1	[	[	X
cana-5711	639	2	7	7	X
cana-5711	639	3	]	]	X
cana-5711	639	4	c.	c.	PROPN
cana-5711	639	5	li	li	PROPN
cana-5711	639	6	,	,	PUNCT
cana-5711	639	7	c.	c.	PROPN
cana-5711	639	8	ding	ding	PROPN
cana-5711	639	9	,	,	PUNCT
cana-5711	639	10	s.	s.	PROPN
cana-5711	639	11	li	li	PROPN
cana-5711	639	12	,	,	PUNCT
cana-5711	639	13	lcd	lcd	PROPN
cana-5711	639	14	cyclic	cyclic	NOUN
cana-5711	639	15	codes	code	NOUN
cana-5711	639	16	over	over	ADP
cana-5711	639	17	finite	finite	ADJ
cana-5711	639	18	fields	field	NOUN
cana-5711	639	19	.	.	PUNCT
cana-5711	640	1	ieee	ieee	PROPN
cana-5711	640	2	trans	trans	PROPN
cana-5711	640	3	.	.	PROPN
cana-5711	640	4	inf	inf	PROPN
cana-5711	640	5	.	.	PROPN
cana-5711	640	6	theory	theory	PROPN
cana-5711	640	7	63(7	63(7	NUM
cana-5711	640	8	)	)	PUNCT
cana-5711	640	9	,	,	PUNCT
cana-5711	640	10	4344	4344	NUM
cana-5711	640	11	–	–	PUNCT
cana-5711	640	12	4356	4356	NUM
cana-5711	640	13	,	,	PUNCT
cana-5711	640	14	2017	2017	NUM
cana-5711	640	15	.	.	PUNCT
cana-5711	641	1	[	[	X
cana-5711	641	2	8	8	NUM
cana-5711	641	3	]	]	PUNCT
cana-5711	641	4	x.	x.	NOUN
cana-5711	641	5	liu	liu	PROPN
cana-5711	641	6	,	,	PUNCT
cana-5711	641	7	h.	h.	PROPN
cana-5711	641	8	liu	liu	PROPN
cana-5711	641	9	,	,	PUNCT
cana-5711	641	10	lcd	lcd	NOUN
cana-5711	641	11	codes	code	NOUN
cana-5711	641	12	over	over	ADP
cana-5711	641	13	finite	finite	ADJ
cana-5711	641	14	chain	chain	NOUN
cana-5711	641	15	rings	ring	NOUN
cana-5711	641	16	.	.	PUNCT
cana-5711	642	1	finite	finite	PROPN
cana-5711	642	2	fields	field	VERB
cana-5711	642	3	their	their	PRON
cana-5711	642	4	appl	appl	NOUN
cana-5711	642	5	.	.	PUNCT
cana-5711	643	1	34	34	NUM
cana-5711	643	2	,	,	PUNCT
cana-5711	643	3	1–19	1–19	PROPN
cana-5711	643	4	,	,	PUNCT
cana-5711	643	5	2015	2015	NUM
cana-5711	643	6	.	.	PUNCT
cana-5711	644	1	versity	versity	NOUN
cana-5711	644	2	,	,	PUNCT
cana-5711	644	3	1961	1961	NUM
cana-5711	644	4	.	.	PUNCT
cana-5711	645	1	[	[	X
cana-5711	645	2	9	9	NUM
cana-5711	645	3	]	]	PUNCT
cana-5711	645	4	m.	m.	NOUN
cana-5711	645	5	shi	shi	PROPN
cana-5711	645	6	,	,	PUNCT
cana-5711	645	7	d.	d.	PROPN
cana-5711	645	8	wang	wang	PROPN
cana-5711	645	9	,	,	PUNCT
cana-5711	645	10	p.	p.	PROPN
cana-5711	645	11	solé	solé	NOUN
cana-5711	645	12	,	,	PUNCT
cana-5711	645	13	linear	linear	ADJ
cana-5711	645	14	codes	code	NOUN
cana-5711	645	15	over	over	ADP
cana-5711	645	16	f3	f3	PROPN
cana-5711	645	17	+	+	CCONJ
cana-5711	645	18	uf3	uf3	ADJ
cana-5711	645	19	+	+	CCONJ
cana-5711	645	20	u2	u2	PROPN
cana-5711	645	21	f3	f3	PROPN
cana-5711	645	22	:	:	PUNCT
cana-5711	645	23	macwilliams	macwilliam	NOUN
cana-5711	645	24	identities	identity	NOUN
cana-5711	645	25	,	,	PUNCT
cana-5711	645	26	optimal	optimal	ADJ
cana-5711	645	27	ternary	ternary	ADJ
cana-5711	645	28	codes	code	NOUN
cana-5711	645	29	from	from	ADP
cana-5711	645	30	one	one	NUM
cana-5711	645	31	-	-	PUNCT
cana-5711	645	32	lee	lee	NOUN
cana-5711	645	33	weight	weight	NOUN
cana-5711	645	34	codes	code	NOUN
cana-5711	645	35	and	and	CCONJ
cana-5711	645	36	two	two	NUM
cana-5711	645	37	-	-	PUNCT
cana-5711	645	38	lee	lee	PROPN
cana-5711	645	39	weight	weight	NOUN
cana-5711	645	40	codes	code	NOUN
cana-5711	645	41	.	.	PUNCT
cana-5711	646	1	j.	j.	PROPN
cana-5711	646	2	appl	appl	PROPN
cana-5711	646	3	.	.	PROPN
cana-5711	646	4	math	math	PROPN
cana-5711	646	5	.	.	PUNCT
cana-5711	647	1	comput	comput	NOUN
cana-5711	647	2	.	.	PUNCT
cana-5711	648	1	51(1	51(1	NUM
cana-5711	648	2	)	)	PUNCT
cana-5711	648	3	,	,	PUNCT
cana-5711	648	4	527–544	527–544	NUM
cana-5711	648	5	(	(	PUNCT
cana-5711	648	6	2016	2016	NUM
cana-5711	648	7	)	)	PUNCT
cana-5711	648	8	.	.	PUNCT
cana-5711	649	1	[	[	X
cana-5711	649	2	10	10	NUM
cana-5711	649	3	]	]	X
cana-5711	649	4	f.	f.	PROPN
cana-5711	649	5	j.	j.	PROPN
cana-5711	649	6	macwilliams	macwilliams	PROPN
cana-5711	649	7	,	,	PUNCT
cana-5711	649	8	a	a	DET
cana-5711	649	9	theorem	theorem	NOUN
cana-5711	649	10	on	on	ADP
cana-5711	649	11	the	the	DET
cana-5711	649	12	distribution	distribution	NOUN
cana-5711	649	13	of	of	ADP
cana-5711	649	14	weights	weight	NOUN
cana-5711	649	15	in	in	ADP
cana-5711	649	16	a	a	DET
cana-5711	649	17	systematic	systematic	ADJ
cana-5711	649	18	code	code	NOUN
cana-5711	649	19	.	.	PUNCT
cana-5711	650	1	bell	bell	PROPN
cana-5711	650	2	syst	syst	PROPN
cana-5711	650	3	.	.	PUNCT
cana-5711	651	1	tech	tech	PROPN
cana-5711	651	2	.	.	PUNCT
cana-5711	652	1	j.	j.	PROPN
cana-5711	652	2	42(1	42(1	PROPN
cana-5711	652	3	)	)	PUNCT
cana-5711	652	4	,	,	PUNCT
cana-5711	652	5	79–94	79–94	NUM
cana-5711	652	6	,	,	PUNCT
cana-5711	652	7	1963	1963	NUM
cana-5711	652	8	.	.	PUNCT
cana-5711	653	1	[	[	X
cana-5711	653	2	11	11	NUM
cana-5711	653	3	]	]	PUNCT
cana-5711	653	4	j.	j.	PROPN
cana-5711	653	5	l.	l.	PROPN
cana-5711	653	6	massey	massey	PROPN
cana-5711	653	7	,	,	PUNCT
cana-5711	653	8	linear	linear	PROPN
cana-5711	653	9	codes	code	NOUN
cana-5711	653	10	with	with	ADP
cana-5711	653	11	complementary	complementary	ADJ
cana-5711	653	12	duals	dual	NOUN
cana-5711	653	13	,	,	PUNCT
cana-5711	653	14	discrete	discrete	ADJ
cana-5711	653	15	math	math	NOUN
cana-5711	653	16	.	.	PUNCT
cana-5711	654	1	106	106	NUM
cana-5711	654	2	–	–	PUNCT
cana-5711	654	3	107	107	NUM
cana-5711	654	4	,	,	PUNCT
cana-5711	654	5	337	337	NUM
cana-5711	654	6	–	–	PUNCT
cana-5711	654	7	342	342	NUM
cana-5711	654	8	,	,	PUNCT
cana-5711	654	9	1992	1992	NUM
cana-5711	654	10	.	.	PUNCT
cana-5711	655	1	[	[	X
cana-5711	655	2	12	12	NUM
cana-5711	655	3	]	]	PUNCT
cana-5711	655	4	k.	k.	PROPN
cana-5711	655	5	shiromoto	shiromoto	PROPN
cana-5711	655	6	,	,	PUNCT
cana-5711	655	7	:	:	PUNCT
cana-5711	655	8	a	a	DET
cana-5711	655	9	basic	basic	ADJ
cana-5711	655	10	exact	exact	ADJ
cana-5711	655	11	sequence	sequence	NOUN
cana-5711	655	12	for	for	ADP
cana-5711	655	13	the	the	DET
cana-5711	655	14	lee	lee	PROPN
cana-5711	655	15	and	and	CCONJ
cana-5711	655	16	euclidean	euclidean	VERB
cana-5711	655	17	weights	weight	NOUN
cana-5711	655	18	of	of	ADP
cana-5711	655	19	linear	linear	ADJ
cana-5711	655	20	codes	code	NOUN
cana-5711	655	21	over	over	ADP
cana-5711	655	22	zl	zl	PROPN
cana-5711	655	23	.	.	PUNCT
cana-5711	656	1	linear	linear	PROPN
cana-5711	656	2	algebra	algebra	PROPN
cana-5711	656	3	appl	appl	NOUN
cana-5711	656	4	.	.	PUNCT
cana-5711	657	1	295(1–3	295(1–3	NUM
cana-5711	657	2	)	)	PUNCT
cana-5711	657	3	,	,	PUNCT
cana-5711	657	4	191–200	191–200	NUM
cana-5711	657	5	,	,	PUNCT
cana-5711	657	6	1999	1999	NUM
cana-5711	657	7	.	.	PUNCT
cana-5711	658	1	[	[	X
cana-5711	658	2	13	13	NUM
cana-5711	658	3	]	]	X
cana-5711	658	4	b.	b.	PROPN
cana-5711	658	5	srinivasulu	srinivasulu	PROPN
cana-5711	658	6	,	,	PUNCT
cana-5711	658	7	m.	m.	NOUN
cana-5711	658	8	bhaintwal	bhaintwal	NOUN
cana-5711	658	9	,	,	PUNCT
cana-5711	658	10	on	on	ADP
cana-5711	658	11	linear	linear	ADJ
cana-5711	658	12	codes	code	NOUN
cana-5711	658	13	over	over	ADP
cana-5711	658	14	a	a	DET
cana-5711	658	15	non	non	ADJ
cana-5711	658	16	-	-	ADJ
cana-5711	658	17	chain	chain	ADJ
cana-5711	658	18	extension	extension	NOUN
cana-5711	658	19	of	of	ADP
cana-5711	658	20	f2	f2	PROPN
cana-5711	658	21	+	+	CCONJ
cana-5711	658	22	uf2	uf2	NOUN
cana-5711	658	23	.	.	PUNCT
cana-5711	659	1	in	in	ADP
cana-5711	659	2	:	:	PUNCT
cana-5711	659	3	computer	computer	NOUN
cana-5711	659	4	,	,	PUNCT
cana-5711	659	5	communication	communication	NOUN
cana-5711	659	6	,	,	PUNCT
cana-5711	659	7	control	control	NOUN
cana-5711	659	8	and	and	CCONJ
cana-5711	659	9	information	information	NOUN
cana-5711	659	10	technology	technology	NOUN
cana-5711	659	11	(	(	PUNCT
cana-5711	659	12	c3it	c3it	NUM
cana-5711	659	13	)	)	PUNCT
cana-5711	659	14	,	,	PUNCT
cana-5711	659	15	2015	2015	NUM
cana-5711	659	16	third	third	ADJ
cana-5711	659	17	international	international	ADJ
cana-5711	659	18	conference	conference	NOUN
cana-5711	659	19	on	on	ADP
cana-5711	659	20	.	.	PUNCT
cana-5711	660	1	ieee	ieee	PROPN
cana-5711	660	2	,	,	PUNCT
cana-5711	660	3	pp	pp	ADP
cana-5711	660	4	.	.	PUNCT
cana-5711	661	1	1–5	1–5	NUM
cana-5711	661	2	,	,	PUNCT
cana-5711	661	3	2015	2015	NUM
cana-5711	661	4	.	.	PUNCT
cana-5711	662	1	[	[	X
cana-5711	662	2	14	14	NUM
cana-5711	662	3	]	]	X
cana-5711	662	4	y.	y.	PROPN
cana-5711	662	5	tang	tang	PROPN
cana-5711	662	6	,	,	PUNCT
cana-5711	662	7	s.	s.	PROPN
cana-5711	662	8	zhu	zhu	PROPN
cana-5711	662	9	,	,	PUNCT
cana-5711	662	10	x.	x.	PROPN
cana-5711	662	11	kai	kai	PROPN
cana-5711	662	12	,	,	PUNCT
cana-5711	662	13	macwilliams	macwilliam	NOUN
cana-5711	662	14	type	type	VERB
cana-5711	662	15	identities	identity	NOUN
cana-5711	662	16	on	on	ADP
cana-5711	662	17	the	the	DET
cana-5711	662	18	lee	lee	PROPN
cana-5711	662	19	and	and	CCONJ
cana-5711	662	20	euclidean	euclidean	VERB
cana-5711	662	21	weights	weight	NOUN
cana-5711	662	22	for	for	ADP
cana-5711	662	23	linear	linear	ADJ
cana-5711	662	24	codes	code	NOUN
cana-5711	662	25	over	over	ADP
cana-5711	662	26	zl	zl	PROPN
cana-5711	662	27	.	.	PUNCT
cana-5711	663	1	linear	linear	PROPN
cana-5711	663	2	algebra	algebra	PROPN
cana-5711	663	3	appl	appl	NOUN
cana-5711	663	4	.	.	PUNCT
cana-5711	664	1	516	516	NUM
cana-5711	664	2	,	,	PUNCT
cana-5711	664	3	82–92	82–92	NUM
cana-5711	664	4	,	,	PUNCT
cana-5711	664	5	2017	2017	NUM
cana-5711	664	6	.	.	PUNCT
cana-5711	665	1	[	[	X
cana-5711	665	2	15	15	NUM
cana-5711	665	3	]	]	X
cana-5711	665	4	j.	j.	PROPN
cana-5711	665	5	a.	a.	PROPN
cana-5711	665	6	wood	wood	PROPN
cana-5711	665	7	,	,	PUNCT
cana-5711	665	8	duality	duality	NOUN
cana-5711	665	9	for	for	ADP
cana-5711	665	10	modules	module	NOUN
cana-5711	665	11	over	over	ADP
cana-5711	665	12	finite	finite	ADJ
cana-5711	665	13	rings	ring	NOUN
cana-5711	665	14	and	and	CCONJ
cana-5711	665	15	applications	application	NOUN
cana-5711	665	16	to	to	ADP
cana-5711	665	17	coding	code	VERB
cana-5711	665	18	theory	theory	NOUN
cana-5711	665	19	.	.	PUNCT
cana-5711	666	1	am	be	AUX
cana-5711	666	2	.	.	PUNCT
cana-5711	667	1	j.	j.	PROPN
cana-5711	667	2	math	math	PROPN
cana-5711	667	3	.	.	PUNCT
cana-5711	668	1	121(3	121(3	NUM
cana-5711	668	2	)	)	PUNCT
cana-5711	668	3	,	,	PUNCT
cana-5711	669	1	555–575	555–575	NUM
cana-5711	669	2	,	,	PUNCT
cana-5711	669	3	1999	1999	NUM
cana-5711	669	4	.	.	PUNCT
cana-5711	670	1	[	[	X
cana-5711	670	2	16	16	NUM
cana-5711	670	3	]	]	X
cana-5711	670	4	b.	b.	PROPN
cana-5711	670	5	yildiz	yildiz	PROPN
cana-5711	670	6	,	,	PUNCT
cana-5711	670	7	s.	s.	PROPN
cana-5711	670	8	karadeniz	karadeniz	PROPN
cana-5711	670	9	,	,	PUNCT
cana-5711	670	10	linear	linear	PROPN
cana-5711	670	11	codes	code	NOUN
cana-5711	670	12	over	over	ADP
cana-5711	670	13	z4	z4	PROPN
cana-5711	670	14	+	+	CCONJ
cana-5711	670	15	uz4	uz4	X
cana-5711	670	16	:	:	PUNCT
cana-5711	670	17	macwilliams	macwilliam	NOUN
cana-5711	670	18	identities	identity	NOUN
cana-5711	670	19	,	,	PUNCT
cana-5711	670	20	projections	projection	NOUN
cana-5711	670	21	,	,	PUNCT
cana-5711	670	22	and	and	CCONJ
cana-5711	670	23	formally	formally	ADV
cana-5711	670	24	self	self	NOUN
cana-5711	670	25	-	-	PUNCT
cana-5711	670	26	dual	dual	ADJ
cana-5711	670	27	codes	code	NOUN
cana-5711	670	28	.	.	PUNCT
cana-5711	671	1	finite	finite	PROPN
cana-5711	671	2	fields	field	VERB
cana-5711	671	3	their	their	PRON
cana-5711	671	4	appl	appl	NOUN
cana-5711	671	5	.	.	PROPN
cana-5711	672	1	27	27	NUM
cana-5711	672	2	,	,	PUNCT
cana-5711	672	3	24–40	24–40	NUM
cana-5711	672	4	,	,	PUNCT
cana-5711	672	5	2014	2014	NUM
cana-5711	672	6	.	.	PUNCT