id	sid	tid	token	lemma	pos
ejpam-4043	1	1	european	european	PROPN
ejpam-4043	1	2	journal	journal	PROPN
ejpam-4043	1	3	of	of	ADP
ejpam-4043	1	4	pure	pure	ADJ
ejpam-4043	1	5	and	and	CCONJ
ejpam-4043	1	6	applied	apply	VERB
ejpam-4043	1	7	mathematics	mathematic	NOUN
ejpam-4043	1	8	vol	vol	NOUN
ejpam-4043	1	9	.	.	PUNCT
ejpam-4043	2	1	14	14	NUM
ejpam-4043	2	2	,	,	PUNCT
ejpam-4043	2	3	no	no	INTJ
ejpam-4043	2	4	.	.	NOUN
ejpam-4043	2	5	3	3	NUM
ejpam-4043	2	6	,	,	PUNCT
ejpam-4043	2	7	2021	2021	NUM
ejpam-4043	2	8	,	,	PUNCT
ejpam-4043	2	9	1082	1082	NUM
ejpam-4043	2	10	-	-	SYM
ejpam-4043	2	11	1097	1097	NUM
ejpam-4043	2	12	issn	issn	PROPN
ejpam-4043	2	13	1307	1307	NUM
ejpam-4043	2	14	-	-	SYM
ejpam-4043	2	15	5543	5543	NUM
ejpam-4043	2	16	–	–	PUNCT
ejpam-4043	3	1	ejpam.com	ejpam.com	X
ejpam-4043	3	2	published	publish	VERB
ejpam-4043	3	3	by	by	ADP
ejpam-4043	3	4	new	new	PROPN
ejpam-4043	3	5	york	york	PROPN
ejpam-4043	3	6	business	business	PROPN
ejpam-4043	3	7	global	global	ADJ
ejpam-4043	3	8	quantum	quantum	NOUN
ejpam-4043	3	9	codes	code	NOUN
ejpam-4043	3	10	obtained	obtain	VERB
ejpam-4043	3	11	through	through	ADP
ejpam-4043	3	12	constacyclic	constacyclic	ADJ
ejpam-4043	3	13	codes	code	NOUN
ejpam-4043	3	14	over	over	ADP
ejpam-4043	3	15	z3	z3	PROPN
ejpam-4043	3	16	+	+	CCONJ
ejpam-4043	3	17	νz3	νz3	X
ejpam-4043	3	18	+	+	CCONJ
ejpam-4043	3	19	ωz3	ωz3	NOUN
ejpam-4043	3	20	+	+	CCONJ
ejpam-4043	3	21	νωz3	νωz3	PROPN
ejpam-4043	3	22	jagbir	jagbir	PROPN
ejpam-4043	3	23	singh1	singh1	PROPN
ejpam-4043	3	24	,	,	PUNCT
ejpam-4043	3	25	prateek	prateek	ADJ
ejpam-4043	3	26	mor2,∗	mor2,∗	PROPN
ejpam-4043	3	27	,	,	PUNCT
ejpam-4043	3	28	shikha3	shikha3	NOUN
ejpam-4043	3	29	,	,	PUNCT
ejpam-4043	3	30	meena4	meena4	NOUN
ejpam-4043	3	31	1	1	NUM
ejpam-4043	3	32	department	department	NOUN
ejpam-4043	3	33	of	of	ADP
ejpam-4043	3	34	mathematics	mathematics	PROPN
ejpam-4043	3	35	,	,	PUNCT
ejpam-4043	3	36	maharshi	maharshi	PROPN
ejpam-4043	3	37	dayanand	dayanand	PROPN
ejpam-4043	3	38	university	university	PROPN
ejpam-4043	3	39	,	,	PUNCT
ejpam-4043	3	40	rohtak-124001	rohtak-124001	PROPN
ejpam-4043	3	41	,	,	PUNCT
ejpam-4043	3	42	india	india	PROPN
ejpam-4043	3	43	2	2	NUM
ejpam-4043	3	44	department	department	NOUN
ejpam-4043	3	45	of	of	ADP
ejpam-4043	3	46	mathematics	mathematic	NOUN
ejpam-4043	3	47	,	,	PUNCT
ejpam-4043	3	48	government	government	NOUN
ejpam-4043	3	49	college	college	NOUN
ejpam-4043	3	50	israna	israna	PROPN
ejpam-4043	3	51	,	,	PUNCT
ejpam-4043	3	52	panipat-132103	panipat-132103	NOUN
ejpam-4043	3	53	,	,	PUNCT
ejpam-4043	3	54	india	india	PROPN
ejpam-4043	3	55	3	3	NUM
ejpam-4043	3	56	department	department	NOUN
ejpam-4043	3	57	of	of	ADP
ejpam-4043	3	58	mathematics	mathematic	NOUN
ejpam-4043	3	59	,	,	PUNCT
ejpam-4043	3	60	s.k	s.k	PROPN
ejpam-4043	3	61	government	government	NOUN
ejpam-4043	3	62	college	college	NOUN
ejpam-4043	3	63	kanwali	kanwali	PROPN
ejpam-4043	3	64	,	,	PUNCT
ejpam-4043	3	65	rewari-123411	rewari-123411	ADJ
ejpam-4043	3	66	,	,	PUNCT
ejpam-4043	3	67	india	india	PROPN
ejpam-4043	3	68	4	4	NUM
ejpam-4043	3	69	department	department	NOUN
ejpam-4043	3	70	of	of	ADP
ejpam-4043	3	71	mathematics	mathematic	NOUN
ejpam-4043	3	72	,	,	PUNCT
ejpam-4043	3	73	government	government	NOUN
ejpam-4043	3	74	college	college	PROPN
ejpam-4043	3	75	julana	julana	PROPN
ejpam-4043	3	76	,	,	PUNCT
ejpam-4043	3	77	jind-126101	jind-126101	PROPN
ejpam-4043	3	78	,	,	PUNCT
ejpam-4043	3	79	india	india	PROPN
ejpam-4043	3	80	abstract	abstract	NOUN
ejpam-4043	3	81	.	.	PUNCT
ejpam-4043	4	1	this	this	DET
ejpam-4043	4	2	paper	paper	NOUN
ejpam-4043	4	3	is	be	AUX
ejpam-4043	4	4	concerned	concern	VERB
ejpam-4043	4	5	with	with	ADP
ejpam-4043	4	6	,	,	PUNCT
ejpam-4043	4	7	structural	structural	ADJ
ejpam-4043	4	8	properties	property	NOUN
ejpam-4043	4	9	and	and	CCONJ
ejpam-4043	4	10	construction	construction	NOUN
ejpam-4043	4	11	of	of	ADP
ejpam-4043	4	12	quantum	quantum	ADJ
ejpam-4043	4	13	codes	code	NOUN
ejpam-4043	4	14	over	over	ADP
ejpam-4043	4	15	z3	z3	PROPN
ejpam-4043	4	16	by	by	ADP
ejpam-4043	4	17	using	use	VERB
ejpam-4043	4	18	constacyclic	constacyclic	ADJ
ejpam-4043	4	19	codes	code	NOUN
ejpam-4043	4	20	over	over	ADP
ejpam-4043	4	21	the	the	DET
ejpam-4043	4	22	finite	finite	PROPN
ejpam-4043	4	23	commutative	commutative	ADJ
ejpam-4043	4	24	non	non	ADJ
ejpam-4043	4	25	-	-	ADJ
ejpam-4043	4	26	chain	chain	ADJ
ejpam-4043	4	27	ring	ring	NOUN
ejpam-4043	5	1	<	<	X
ejpam-4043	5	2	=	=	X
ejpam-4043	5	3	z3	z3	PROPN
ejpam-4043	6	1	+	+	CCONJ
ejpam-4043	6	2	νz3	νz3	X
ejpam-4043	6	3	+	+	CCONJ
ejpam-4043	6	4	ωz3	ωz3	NOUN
ejpam-4043	6	5	+	+	CCONJ
ejpam-4043	6	6	νωz3	νωz3	NOUN
ejpam-4043	6	7	where	where	SCONJ
ejpam-4043	6	8	ν2	ν2	NOUN
ejpam-4043	6	9	=	=	SYM
ejpam-4043	6	10	1	1	NUM
ejpam-4043	6	11	,	,	PUNCT
ejpam-4043	6	12	ω2	ω2	NOUN
ejpam-4043	6	13	=	=	SYM
ejpam-4043	6	14	1	1	NUM
ejpam-4043	6	15	,	,	PUNCT
ejpam-4043	6	16	νω	νω	ADP
ejpam-4043	6	17	=	=	PUNCT
ejpam-4043	6	18	νω	νω	PROPN
ejpam-4043	6	19	and	and	CCONJ
ejpam-4043	6	20	z3	z3	PROPN
ejpam-4043	6	21	is	be	AUX
ejpam-4043	6	22	field	field	NOUN
ejpam-4043	6	23	having	have	VERB
ejpam-4043	6	24	3	3	NUM
ejpam-4043	6	25	elements	element	NOUN
ejpam-4043	6	26	with	with	ADP
ejpam-4043	6	27	characteristic	characteristic	ADJ
ejpam-4043	6	28	3	3	X
ejpam-4043	6	29	.	.	PUNCT
ejpam-4043	7	1	a	a	DET
ejpam-4043	7	2	gray	gray	ADJ
ejpam-4043	7	3	map	map	NOUN
ejpam-4043	7	4	is	be	AUX
ejpam-4043	7	5	defined	define	VERB
ejpam-4043	7	6	between	between	ADP
ejpam-4043	7	7	<	<	X
ejpam-4043	7	8	and	and	CCONJ
ejpam-4043	7	9	z4	z4	PROPN
ejpam-4043	7	10	3	3	NUM
ejpam-4043	7	11	.	.	PUNCT
ejpam-4043	8	1	the	the	DET
ejpam-4043	8	2	parameters	parameter	NOUN
ejpam-4043	8	3	of	of	ADP
ejpam-4043	8	4	quantum	quantum	NOUN
ejpam-4043	8	5	codes	code	NOUN
ejpam-4043	8	6	over	over	ADP
ejpam-4043	8	7	z3	z3	PROPN
ejpam-4043	8	8	are	be	AUX
ejpam-4043	8	9	obtained	obtain	VERB
ejpam-4043	8	10	by	by	ADP
ejpam-4043	8	11	decomposing	decompose	VERB
ejpam-4043	8	12	constacyclic	constacyclic	ADJ
ejpam-4043	8	13	codes	code	NOUN
ejpam-4043	8	14	into	into	ADP
ejpam-4043	8	15	cyclic	cyclic	ADJ
ejpam-4043	8	16	and	and	CCONJ
ejpam-4043	8	17	negacyclic	negacyclic	ADJ
ejpam-4043	8	18	codes	code	NOUN
ejpam-4043	8	19	over	over	ADP
ejpam-4043	8	20	z3	z3	PROPN
ejpam-4043	8	21	.	.	PUNCT
ejpam-4043	9	1	as	as	ADP
ejpam-4043	9	2	an	an	DET
ejpam-4043	9	3	application	application	NOUN
ejpam-4043	9	4	,	,	PUNCT
ejpam-4043	9	5	some	some	DET
ejpam-4043	9	6	examples	example	NOUN
ejpam-4043	9	7	of	of	ADP
ejpam-4043	9	8	quantum	quantum	ADJ
ejpam-4043	9	9	codes	code	NOUN
ejpam-4043	9	10	of	of	ADP
ejpam-4043	9	11	arbitrary	arbitrary	ADJ
ejpam-4043	9	12	length	length	NOUN
ejpam-4043	9	13	,	,	PUNCT
ejpam-4043	9	14	are	be	AUX
ejpam-4043	9	15	also	also	ADV
ejpam-4043	9	16	obtained	obtain	VERB
ejpam-4043	9	17	.	.	PUNCT
ejpam-4043	10	1	2020	2020	NUM
ejpam-4043	10	2	mathematics	mathematic	NOUN
ejpam-4043	10	3	subject	subject	NOUN
ejpam-4043	10	4	classifications	classification	NOUN
ejpam-4043	10	5	:	:	PUNCT
ejpam-4043	10	6	94b05	94b05	NUM
ejpam-4043	10	7	,	,	PUNCT
ejpam-4043	10	8	94b15	94b15	NUM
ejpam-4043	10	9	,	,	PUNCT
ejpam-4043	10	10	94b35	94b35	NUM
ejpam-4043	10	11	,	,	PUNCT
ejpam-4043	10	12	94b60	94b60	NUM
ejpam-4043	10	13	key	key	ADJ
ejpam-4043	10	14	words	word	NOUN
ejpam-4043	10	15	and	and	CCONJ
ejpam-4043	10	16	phrases	phrase	NOUN
ejpam-4043	10	17	:	:	PUNCT
ejpam-4043	10	18	finite	finite	PROPN
ejpam-4043	10	19	ring	ring	NOUN
ejpam-4043	10	20	,	,	PUNCT
ejpam-4043	10	21	linear	linear	PROPN
ejpam-4043	10	22	codes	code	NOUN
ejpam-4043	10	23	,	,	PUNCT
ejpam-4043	10	24	constacyclic	constacyclic	ADJ
ejpam-4043	10	25	codes	code	NOUN
ejpam-4043	10	26	,	,	PUNCT
ejpam-4043	10	27	negacyclic	negacyclic	ADJ
ejpam-4043	10	28	,	,	PUNCT
ejpam-4043	10	29	quantum	quantum	ADJ
ejpam-4043	10	30	codes	code	NOUN
ejpam-4043	10	31	1	1	NUM
ejpam-4043	10	32	.	.	PUNCT
ejpam-4043	10	33	introduction	introduction	NOUN
ejpam-4043	10	34	quantum	quantum	NOUN
ejpam-4043	10	35	error	error	NOUN
ejpam-4043	10	36	correction	correction	NOUN
ejpam-4043	10	37	shows	show	VERB
ejpam-4043	10	38	an	an	DET
ejpam-4043	10	39	significant	significant	ADJ
ejpam-4043	10	40	role	role	NOUN
ejpam-4043	10	41	in	in	ADP
ejpam-4043	10	42	quantum	quantum	NOUN
ejpam-4043	10	43	computing	computing	NOUN
ejpam-4043	10	44	as	as	SCONJ
ejpam-4043	10	45	it	it	PRON
ejpam-4043	10	46	is	be	AUX
ejpam-4043	10	47	used	use	VERB
ejpam-4043	10	48	to	to	PART
ejpam-4043	10	49	correct	correct	VERB
ejpam-4043	10	50	any	any	DET
ejpam-4043	10	51	errors	error	NOUN
ejpam-4043	10	52	in	in	ADP
ejpam-4043	10	53	quantum	quantum	ADJ
ejpam-4043	10	54	data	datum	NOUN
ejpam-4043	10	55	due	due	ADP
ejpam-4043	10	56	to	to	ADP
ejpam-4043	10	57	decoherence	decoherence	NOUN
ejpam-4043	10	58	and	and	CCONJ
ejpam-4043	10	59	other	other	ADJ
ejpam-4043	10	60	quantum	quantum	NOUN
ejpam-4043	10	61	noise	noise	NOUN
ejpam-4043	10	62	.	.	PUNCT
ejpam-4043	11	1	firstly	firstly	ADV
ejpam-4043	11	2	,	,	PUNCT
ejpam-4043	11	3	the	the	DET
ejpam-4043	11	4	existence	existence	NOUN
ejpam-4043	11	5	of	of	ADP
ejpam-4043	11	6	quantum	quantum	ADJ
ejpam-4043	11	7	error	error	NOUN
ejpam-4043	11	8	correction	correction	NOUN
ejpam-4043	11	9	code	code	NOUN
ejpam-4043	11	10	was	be	AUX
ejpam-4043	11	11	proven	prove	VERB
ejpam-4043	11	12	by	by	ADP
ejpam-4043	11	13	shor	shor	NOUN
ejpam-4043	11	14	[	[	X
ejpam-4043	11	15	14	14	NUM
ejpam-4043	11	16	]	]	PUNCT
ejpam-4043	11	17	and	and	CCONJ
ejpam-4043	11	18	individually	individually	ADV
ejpam-4043	11	19	by	by	ADP
ejpam-4043	11	20	steane	steane	ADJ
ejpam-4043	11	21	[	[	X
ejpam-4043	11	22	17	17	NUM
ejpam-4043	11	23	]	]	PUNCT
ejpam-4043	11	24	.	.	PUNCT
ejpam-4043	12	1	in	in	ADP
ejpam-4043	12	2	1998	1998	NUM
ejpam-4043	12	3	,	,	PUNCT
ejpam-4043	12	4	calderbank	calderbank	NOUN
ejpam-4043	12	5	et	et	PROPN
ejpam-4043	12	6	.	.	PUNCT
ejpam-4043	13	1	al	al	PROPN
ejpam-4043	14	1	[	[	X
ejpam-4043	14	2	3	3	NUM
ejpam-4043	14	3	]	]	PUNCT
ejpam-4043	14	4	published	publish	VERB
ejpam-4043	14	5	a	a	DET
ejpam-4043	14	6	paper	paper	NOUN
ejpam-4043	14	7	in	in	ADP
ejpam-4043	14	8	which	which	PRON
ejpam-4043	14	9	they	they	PRON
ejpam-4043	14	10	developed	develop	VERB
ejpam-4043	14	11	the	the	DET
ejpam-4043	14	12	theory	theory	NOUN
ejpam-4043	14	13	to	to	PART
ejpam-4043	14	14	construct	construct	VERB
ejpam-4043	14	15	quantum	quantum	ADJ
ejpam-4043	14	16	codes	code	NOUN
ejpam-4043	14	17	using	use	VERB
ejpam-4043	14	18	classical	classical	ADJ
ejpam-4043	14	19	error	error	NOUN
ejpam-4043	14	20	correction	correction	NOUN
ejpam-4043	14	21	codes	code	NOUN
ejpam-4043	14	22	.	.	PUNCT
ejpam-4043	15	1	in	in	ADP
ejpam-4043	15	2	current	current	ADJ
ejpam-4043	15	3	years	year	NOUN
ejpam-4043	15	4	,	,	PUNCT
ejpam-4043	15	5	an	an	DET
ejpam-4043	15	6	essential	essential	ADJ
ejpam-4043	15	7	literature	literature	NOUN
ejpam-4043	15	8	has	have	AUX
ejpam-4043	15	9	been	be	AUX
ejpam-4043	15	10	established	establish	VERB
ejpam-4043	15	11	about	about	ADP
ejpam-4043	15	12	the	the	DET
ejpam-4043	15	13	quantum	quantum	NOUN
ejpam-4043	15	14	error	error	NOUN
ejpam-4043	15	15	correcting	correct	VERB
ejpam-4043	15	16	codes	code	NOUN
ejpam-4043	15	17	.	.	PUNCT
ejpam-4043	16	1	some	some	DET
ejpam-4043	16	2	authors	author	NOUN
ejpam-4043	16	3	constructed	construct	VERB
ejpam-4043	16	4	quantum	quantum	NOUN
ejpam-4043	16	5	codes	code	NOUN
ejpam-4043	16	6	using	use	VERB
ejpam-4043	16	7	the	the	DET
ejpam-4043	16	8	gray	gray	ADJ
ejpam-4043	16	9	image	image	NOUN
ejpam-4043	16	10	of	of	ADP
ejpam-4043	16	11	cyclic	cyclic	ADJ
ejpam-4043	16	12	codes	code	NOUN
ejpam-4043	16	13	on	on	ADP
ejpam-4043	16	14	some	some	DET
ejpam-4043	16	15	finite	finite	ADJ
ejpam-4043	16	16	rings	ring	NOUN
ejpam-4043	16	17	.	.	PUNCT
ejpam-4043	17	1	for	for	ADP
ejpam-4043	17	2	example	example	NOUN
ejpam-4043	17	3	,	,	PUNCT
ejpam-4043	17	4	a	a	DET
ejpam-4043	17	5	new	new	ADJ
ejpam-4043	17	6	technique	technique	NOUN
ejpam-4043	17	7	of	of	ADP
ejpam-4043	17	8	constructing	construct	VERB
ejpam-4043	17	9	quantum	quantum	ADJ
ejpam-4043	17	10	codes	code	NOUN
ejpam-4043	17	11	from	from	ADP
ejpam-4043	17	12	cyclic	cyclic	ADJ
ejpam-4043	17	13	codes	code	NOUN
ejpam-4043	17	14	over	over	ADP
ejpam-4043	17	15	finite	finite	PROPN
ejpam-4043	17	16	ring	ring	NOUN
ejpam-4043	17	17	f2	f2	PROPN
ejpam-4043	17	18	+	+	CCONJ
ejpam-4043	17	19	vf2	vf2	NOUN
ejpam-4043	17	20	where	where	SCONJ
ejpam-4043	17	21	v2	v2	NOUN
ejpam-4043	17	22	=	=	SYM
ejpam-4043	17	23	v	v	NOUN
ejpam-4043	17	24	given	give	VERB
ejpam-4043	17	25	by	by	ADP
ejpam-4043	17	26	qian	qian	PROPN
ejpam-4043	18	1	[	[	X
ejpam-4043	18	2	13	13	NUM
ejpam-4043	18	3	]	]	PUNCT
ejpam-4043	18	4	.	.	PUNCT
ejpam-4043	19	1	kai	kai	PROPN
ejpam-4043	19	2	and	and	CCONJ
ejpam-4043	19	3	zhu	zhu	PROPN
ejpam-4043	20	1	[	[	X
ejpam-4043	20	2	8	8	NUM
ejpam-4043	20	3	]	]	PUNCT
ejpam-4043	20	4	created	create	VERB
ejpam-4043	20	5	quantum	quantum	NOUN
ejpam-4043	20	6	codes	code	NOUN
ejpam-4043	20	7	from	from	ADP
ejpam-4043	20	8	hermitian	hermitian	ADJ
ejpam-4043	20	9	self	self	NOUN
ejpam-4043	20	10	orthogonal	orthogonal	ADJ
ejpam-4043	20	11	codes	code	NOUN
ejpam-4043	20	12	over	over	ADP
ejpam-4043	20	13	f4	f4	NOUN
ejpam-4043	20	14	as	as	ADP
ejpam-4043	20	15	gray	gray	ADJ
ejpam-4043	20	16	images	image	NOUN
ejpam-4043	20	17	of	of	ADP
ejpam-4043	20	18	linear	linear	ADJ
ejpam-4043	20	19	and	and	CCONJ
ejpam-4043	20	20	cyclic	cyclic	ADJ
ejpam-4043	20	21	codes	code	NOUN
ejpam-4043	20	22	over	over	ADP
ejpam-4043	20	23	f4	f4	PROPN
ejpam-4043	20	24	+	+	CCONJ
ejpam-4043	20	25	uf4	uf4	PROPN
ejpam-4043	20	26	where	where	SCONJ
ejpam-4043	20	27	u2	u2	NOUN
ejpam-4043	20	28	=	=	NOUN
ejpam-4043	20	29	0	0	PROPN
ejpam-4043	20	30	.	.	PUNCT
ejpam-4043	20	31	yin	yin	PROPN
ejpam-4043	20	32	and	and	CCONJ
ejpam-4043	20	33	ma	ma	PROPN
ejpam-4043	21	1	[	[	X
ejpam-4043	21	2	18	18	NUM
ejpam-4043	21	3	]	]	PUNCT
ejpam-4043	21	4	gave	give	VERB
ejpam-4043	21	5	a	a	DET
ejpam-4043	21	6	condition	condition	NOUN
ejpam-4043	21	7	for	for	ADP
ejpam-4043	21	8	the	the	DET
ejpam-4043	21	9	existence	existence	NOUN
ejpam-4043	21	10	of	of	ADP
ejpam-4043	21	11	quantum	quantum	NOUN
ejpam-4043	21	12	codes	code	NOUN
ejpam-4043	21	13	from	from	ADP
ejpam-4043	21	14	cyclic	cyclic	ADJ
ejpam-4043	21	15	codes	code	NOUN
ejpam-4043	21	16	over	over	ADP
ejpam-4043	21	17	f2	f2	PROPN
ejpam-4043	21	18	+	+	CCONJ
ejpam-4043	21	19	uf2	uf2	NOUN
ejpam-4043	21	20	+	+	CCONJ
ejpam-4043	21	21	u2	u2	NOUN
ejpam-4043	21	22	+	+	CCONJ
ejpam-4043	21	23	f2	f2	PROPN
ejpam-4043	21	24	with	with	ADP
ejpam-4043	21	25	lee	lee	PROPN
ejpam-4043	21	26	∗corresponding	∗corresponde	VERB
ejpam-4043	21	27	author	author	NOUN
ejpam-4043	21	28	.	.	PUNCT
ejpam-4043	22	1	doi	doi	NOUN
ejpam-4043	22	2	:	:	PUNCT
ejpam-4043	22	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4043	https://doi.org/10.29020/nybg.ejpam.v14i3.4043	PROPN
ejpam-4043	22	4	email	email	NOUN
ejpam-4043	22	5	addresses	address	VERB
ejpam-4043	22	6	:	:	PUNCT
ejpam-4043	22	7	prateekmor1992@gmail.com	prateekmor1992@gmail.com	NOUN
ejpam-4043	22	8	(	(	PUNCT
ejpam-4043	22	9	prateek	prateek	PROPN
ejpam-4043	22	10	mor	mor	PROPN
ejpam-4043	22	11	)	)	PUNCT
ejpam-4043	22	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4043	22	13	1082	1082	NUM
ejpam-4043	23	1	c	c	AUX
ejpam-4043	23	2	©	©	PROPN
ejpam-4043	23	3	2021	2021	NUM
ejpam-4043	23	4	ejpam	ejpam	VERB
ejpam-4043	23	5	all	all	DET
ejpam-4043	23	6	rights	right	NOUN
ejpam-4043	23	7	reserved	reserve	VERB
ejpam-4043	23	8	.	.	PUNCT
ejpam-4043	24	1	prateek	prateek	PROPN
ejpam-4043	24	2	mor	mor	PROPN
ejpam-4043	24	3	et	et	PROPN
ejpam-4043	24	4	al	al	PROPN
ejpam-4043	24	5	.	.	PUNCT
ejpam-4043	24	6	/	/	SYM
ejpam-4043	24	7	eur	eur	PROPN
ejpam-4043	24	8	.	.	PUNCT
ejpam-4043	25	1	j.	j.	PROPN
ejpam-4043	25	2	pure	pure	PROPN
ejpam-4043	25	3	appl	appl	PROPN
ejpam-4043	25	4	.	.	PROPN
ejpam-4043	25	5	math	math	PROPN
ejpam-4043	25	6	,	,	PUNCT
ejpam-4043	25	7	14	14	NUM
ejpam-4043	25	8	(	(	PUNCT
ejpam-4043	25	9	3	3	NUM
ejpam-4043	25	10	)	)	PUNCT
ejpam-4043	25	11	(	(	PUNCT
ejpam-4043	25	12	2021	2021	NUM
ejpam-4043	25	13	)	)	PUNCT
ejpam-4043	25	14	,	,	PUNCT
ejpam-4043	25	15	1082	1082	NUM
ejpam-4043	25	16	-	-	SYM
ejpam-4043	25	17	1097	1097	NUM
ejpam-4043	25	18	1083	1083	NUM
ejpam-4043	25	19	metric	metric	NOUN
ejpam-4043	25	20	.	.	PUNCT
ejpam-4043	26	1	some	some	DET
ejpam-4043	26	2	non	non	ADJ
ejpam-4043	26	3	binary	binary	ADJ
ejpam-4043	26	4	quantum	quantum	ADJ
ejpam-4043	26	5	codes	code	NOUN
ejpam-4043	26	6	are	be	AUX
ejpam-4043	26	7	described	describe	VERB
ejpam-4043	26	8	using	use	VERB
ejpam-4043	26	9	classical	classical	ADJ
ejpam-4043	26	10	codes	code	NOUN
ejpam-4043	26	11	via	via	ADP
ejpam-4043	26	12	gaussian	gaussian	ADJ
ejpam-4043	26	13	integers	integer	NOUN
ejpam-4043	26	14	by	by	ADP
ejpam-4043	26	15	ozen	ozen	PROPN
ejpam-4043	26	16	et	et	PROPN
ejpam-4043	26	17	.	.	PUNCT
ejpam-4043	27	1	al	al	PROPN
ejpam-4043	28	1	[	[	X
ejpam-4043	28	2	11	11	NUM
ejpam-4043	28	3	]	]	PUNCT
ejpam-4043	28	4	.	.	PUNCT
ejpam-4043	29	1	guenda	guenda	PROPN
ejpam-4043	29	2	et	et	PROPN
ejpam-4043	29	3	.	.	PUNCT
ejpam-4043	30	1	al	al	PROPN
ejpam-4043	31	1	[	[	X
ejpam-4043	31	2	5	5	NUM
ejpam-4043	31	3	]	]	PUNCT
ejpam-4043	31	4	extended	extend	VERB
ejpam-4043	31	5	the	the	DET
ejpam-4043	31	6	css	css	PROPN
ejpam-4043	31	7	construction	construction	NOUN
ejpam-4043	31	8	to	to	PART
ejpam-4043	31	9	finite	finite	VERB
ejpam-4043	31	10	commutative	commutative	ADJ
ejpam-4043	31	11	frobenius	frobenius	NOUN
ejpam-4043	31	12	rings	ring	NOUN
ejpam-4043	31	13	.	.	PUNCT
ejpam-4043	32	1	dertli	dertli	PROPN
ejpam-4043	32	2	et	et	PROPN
ejpam-4043	32	3	.	.	PUNCT
ejpam-4043	33	1	al	al	PROPN
ejpam-4043	34	1	[	[	X
ejpam-4043	34	2	4	4	X
ejpam-4043	34	3	]	]	PUNCT
ejpam-4043	34	4	received	receive	VERB
ejpam-4043	34	5	quantum	quantum	NOUN
ejpam-4043	34	6	codes	code	NOUN
ejpam-4043	34	7	from	from	ADP
ejpam-4043	34	8	cyclic	cyclic	ADJ
ejpam-4043	34	9	codes	code	NOUN
ejpam-4043	34	10	over	over	ADP
ejpam-4043	34	11	f2	f2	PROPN
ejpam-4043	34	12	+	+	CCONJ
ejpam-4043	34	13	uf2	uf2	NOUN
ejpam-4043	34	14	+	+	CCONJ
ejpam-4043	34	15	vf2	vf2	NOUN
ejpam-4043	34	16	+	+	CCONJ
ejpam-4043	34	17	uvf2	uvf2	PROPN
ejpam-4043	34	18	.	.	PUNCT
ejpam-4043	35	1	ashraf	ashraf	PROPN
ejpam-4043	35	2	and	and	CCONJ
ejpam-4043	35	3	mohammad	mohammad	PROPN
ejpam-4043	36	1	[	[	X
ejpam-4043	36	2	1	1	NUM
ejpam-4043	36	3	]	]	PUNCT
ejpam-4043	36	4	gave	give	VERB
ejpam-4043	36	5	a	a	DET
ejpam-4043	36	6	construction	construction	NOUN
ejpam-4043	36	7	of	of	ADP
ejpam-4043	36	8	quantum	quantum	ADJ
ejpam-4043	36	9	codes	code	NOUN
ejpam-4043	36	10	from	from	ADP
ejpam-4043	36	11	cyclic	cyclic	ADJ
ejpam-4043	36	12	codes	code	NOUN
ejpam-4043	36	13	overf3	overf3	NOUN
ejpam-4043	37	1	+	+	CCONJ
ejpam-4043	37	2	vf3	vf3	INTJ
ejpam-4043	37	3	where	where	SCONJ
ejpam-4043	37	4	v2	v2	NOUN
ejpam-4043	37	5	=	=	SYM
ejpam-4043	37	6	1	1	X
ejpam-4043	37	7	.	.	PUNCT
ejpam-4043	37	8	in	in	ADP
ejpam-4043	37	9	2016	2016	NUM
ejpam-4043	37	10	,	,	PUNCT
ejpam-4043	37	11	ozen	ozen	NOUN
ejpam-4043	37	12	et	et	NOUN
ejpam-4043	37	13	al	al	PROPN
ejpam-4043	37	14	.	.	PUNCT
ejpam-4043	38	1	[	[	X
ejpam-4043	38	2	12	12	NUM
ejpam-4043	38	3	]	]	PUNCT
ejpam-4043	38	4	examined	examine	VERB
ejpam-4043	38	5	several	several	ADJ
ejpam-4043	38	6	ternary	ternary	ADJ
ejpam-4043	38	7	quantum	quantum	NOUN
ejpam-4043	38	8	codes	code	NOUN
ejpam-4043	38	9	from	from	ADP
ejpam-4043	38	10	the	the	DET
ejpam-4043	38	11	cyclic	cyclic	ADJ
ejpam-4043	38	12	codes	code	NOUN
ejpam-4043	38	13	over	over	ADP
ejpam-4043	38	14	f3	f3	PROPN
ejpam-4043	38	15	+	+	CCONJ
ejpam-4043	38	16	uf3	uf3	ADJ
ejpam-4043	38	17	+	+	CCONJ
ejpam-4043	38	18	vf3	vf3	X
ejpam-4043	38	19	+	+	CCONJ
ejpam-4043	38	20	uvf3	uvf3	PROPN
ejpam-4043	38	21	.	.	PUNCT
ejpam-4043	39	1	very	very	ADV
ejpam-4043	39	2	recently	recently	ADV
ejpam-4043	39	3	,	,	PUNCT
ejpam-4043	39	4	several	several	ADJ
ejpam-4043	39	5	researchers	researcher	NOUN
ejpam-4043	39	6	established	establish	VERB
ejpam-4043	39	7	a	a	DET
ejpam-4043	39	8	number	number	NOUN
ejpam-4043	39	9	of	of	ADP
ejpam-4043	39	10	new	new	ADJ
ejpam-4043	39	11	quantum	quantum	NOUN
ejpam-4043	39	12	codes	code	NOUN
ejpam-4043	39	13	via	via	ADP
ejpam-4043	39	14	fp	fp	INTJ
ejpam-4043	39	15	from	from	ADP
ejpam-4043	39	16	the	the	DET
ejpam-4043	39	17	classical	classical	ADJ
ejpam-4043	39	18	cyclic	cyclic	NOUN
ejpam-4043	39	19	and	and	CCONJ
ejpam-4043	39	20	constacyclic	constacyclic	ADJ
ejpam-4043	39	21	codes	code	NOUN
ejpam-4043	39	22	to	to	PART
ejpam-4043	39	23	which	which	PRON
ejpam-4043	39	24	we	we	PRON
ejpam-4043	39	25	refer	refer	VERB
ejpam-4043	39	26	[	[	X
ejpam-4043	39	27	2	2	NUM
ejpam-4043	39	28	,	,	PUNCT
ejpam-4043	39	29	6	6	NUM
ejpam-4043	39	30	,	,	PUNCT
ejpam-4043	39	31	9–11	9–11	NOUN
ejpam-4043	39	32	,	,	PUNCT
ejpam-4043	39	33	15	15	NUM
ejpam-4043	39	34	]	]	PUNCT
ejpam-4043	39	35	.	.	PUNCT
ejpam-4043	40	1	also	also	ADV
ejpam-4043	40	2	,	,	PUNCT
ejpam-4043	40	3	singh	singh	PROPN
ejpam-4043	40	4	and	and	CCONJ
ejpam-4043	40	5	mor	mor	PROPN
ejpam-4043	41	1	[	[	X
ejpam-4043	41	2	16	16	NUM
ejpam-4043	41	3	]	]	PUNCT
ejpam-4043	41	4	constructed	construct	VERB
ejpam-4043	41	5	quantum	quantum	NOUN
ejpam-4043	41	6	codes	code	NOUN
ejpam-4043	41	7	over	over	ADP
ejpam-4043	41	8	the	the	DET
ejpam-4043	41	9	finite	finite	ADJ
ejpam-4043	41	10	non	non	ADJ
ejpam-4043	41	11	-	-	ADJ
ejpam-4043	41	12	chain	chain	ADJ
ejpam-4043	41	13	ring	ring	NOUN
ejpam-4043	41	14	<	<	X
ejpam-4043	41	15	=	=	PUNCT
ejpam-4043	41	16	zp	zp	PROPN
ejpam-4043	41	17	+	+	CCONJ
ejpam-4043	41	18	νzp	νzp	NOUN
ejpam-4043	41	19	where	where	SCONJ
ejpam-4043	41	20	ν2	ν2	NOUN
ejpam-4043	41	21	=	=	SYM
ejpam-4043	41	22	ν	ν	NOUN
ejpam-4043	41	23	in	in	ADP
ejpam-4043	41	24	2021	2021	NUM
ejpam-4043	41	25	.	.	PUNCT
ejpam-4043	42	1	the	the	DET
ejpam-4043	42	2	remaining	remain	VERB
ejpam-4043	42	3	paper	paper	NOUN
ejpam-4043	42	4	is	be	AUX
ejpam-4043	42	5	arranged	arrange	VERB
ejpam-4043	42	6	as	as	SCONJ
ejpam-4043	42	7	follows	follow	VERB
ejpam-4043	42	8	,	,	PUNCT
ejpam-4043	42	9	section	section	NOUN
ejpam-4043	42	10	2	2	NUM
ejpam-4043	42	11	contains	contain	VERB
ejpam-4043	42	12	preliminaries	preliminary	NOUN
ejpam-4043	42	13	in	in	ADP
ejpam-4043	42	14	which	which	PRON
ejpam-4043	42	15	some	some	DET
ejpam-4043	42	16	fundamental	fundamental	ADJ
ejpam-4043	42	17	properties	property	NOUN
ejpam-4043	42	18	and	and	CCONJ
ejpam-4043	42	19	some	some	DET
ejpam-4043	42	20	essential	essential	ADJ
ejpam-4043	42	21	definitions	definition	NOUN
ejpam-4043	42	22	have	have	AUX
ejpam-4043	42	23	been	be	AUX
ejpam-4043	42	24	given	give	VERB
ejpam-4043	42	25	.	.	PUNCT
ejpam-4043	43	1	section	section	NOUN
ejpam-4043	43	2	3	3	NUM
ejpam-4043	43	3	defines	define	VERB
ejpam-4043	43	4	the	the	DET
ejpam-4043	43	5	gray	gray	ADJ
ejpam-4043	43	6	map	map	NOUN
ejpam-4043	43	7	from	from	ADP
ejpam-4043	43	8	<	<	X
ejpam-4043	43	9	to	to	ADP
ejpam-4043	43	10	z4	z4	PROPN
ejpam-4043	43	11	3	3	NUM
ejpam-4043	43	12	and	and	CCONJ
ejpam-4043	43	13	some	some	DET
ejpam-4043	43	14	related	related	ADJ
ejpam-4043	43	15	properties	property	NOUN
ejpam-4043	43	16	like	like	ADP
ejpam-4043	43	17	self	self	NOUN
ejpam-4043	43	18	orthogonal	orthogonal	NOUN
ejpam-4043	43	19	,	,	PUNCT
ejpam-4043	43	20	self	self	NOUN
ejpam-4043	43	21	dual	dual	ADJ
ejpam-4043	43	22	etc	etc	X
ejpam-4043	43	23	.	.	X
ejpam-4043	44	1	in	in	ADP
ejpam-4043	44	2	section	section	NOUN
ejpam-4043	44	3	4	4	NUM
ejpam-4043	44	4	,	,	PUNCT
ejpam-4043	44	5	we	we	PRON
ejpam-4043	44	6	presented	present	VERB
ejpam-4043	44	7	the	the	DET
ejpam-4043	44	8	development	development	NOUN
ejpam-4043	44	9	of	of	ADP
ejpam-4043	44	10	quantum	quantum	ADJ
ejpam-4043	44	11	codes	code	NOUN
ejpam-4043	44	12	through	through	ADP
ejpam-4043	44	13	constacyclic	constacyclic	ADJ
ejpam-4043	44	14	codes	code	NOUN
ejpam-4043	44	15	over	over	ADP
ejpam-4043	44	16	the	the	DET
ejpam-4043	44	17	ring	ring	NOUN
ejpam-4043	44	18	<	<	X
ejpam-4043	44	19	which	which	PRON
ejpam-4043	44	20	are	be	AUX
ejpam-4043	44	21	exemplified	exemplify	VERB
ejpam-4043	44	22	in	in	ADP
ejpam-4043	44	23	section	section	NOUN
ejpam-4043	44	24	5	5	NUM
ejpam-4043	44	25	.	.	PUNCT
ejpam-4043	45	1	finally	finally	ADV
ejpam-4043	45	2	,	,	PUNCT
ejpam-4043	45	3	the	the	DET
ejpam-4043	45	4	paper	paper	NOUN
ejpam-4043	45	5	is	be	AUX
ejpam-4043	45	6	concluded	conclude	VERB
ejpam-4043	45	7	in	in	ADP
ejpam-4043	45	8	the	the	DET
ejpam-4043	45	9	last	last	ADJ
ejpam-4043	45	10	section	section	NOUN
ejpam-4043	45	11	.	.	PUNCT
ejpam-4043	46	1	2	2	X
ejpam-4043	46	2	.	.	X
ejpam-4043	46	3	preliminaries	preliminary	NOUN
ejpam-4043	46	4	let	let	VERB
ejpam-4043	46	5	z3	z3	PROPN
ejpam-4043	46	6	is	be	AUX
ejpam-4043	46	7	a	a	DET
ejpam-4043	46	8	finite	finite	NOUN
ejpam-4043	46	9	filed	file	VERB
ejpam-4043	46	10	with	with	ADP
ejpam-4043	46	11	3	3	NUM
ejpam-4043	46	12	elements	element	NOUN
ejpam-4043	46	13	.	.	PUNCT
ejpam-4043	47	1	now	now	ADV
ejpam-4043	47	2	,	,	PUNCT
ejpam-4043	47	3	we	we	PRON
ejpam-4043	47	4	first	first	ADV
ejpam-4043	47	5	start	start	VERB
ejpam-4043	47	6	with	with	ADP
ejpam-4043	47	7	a	a	DET
ejpam-4043	47	8	general	general	ADJ
ejpam-4043	47	9	overview	overview	NOUN
ejpam-4043	47	10	of	of	ADP
ejpam-4043	47	11	the	the	DET
ejpam-4043	47	12	ring	ring	NOUN
ejpam-4043	47	13	<	<	X
ejpam-4043	47	14	=	=	X
ejpam-4043	47	15	z3+νz3+ωz3+νωz3	z3+νz3+ωz3+νωz3	NOUN
ejpam-4043	47	16	having	have	VERB
ejpam-4043	47	17	characteristic	characteristic	ADJ
ejpam-4043	47	18	3	3	NUM
ejpam-4043	47	19	with	with	ADP
ejpam-4043	47	20	restrictions	restriction	NOUN
ejpam-4043	47	21	ν2	ν2	NOUN
ejpam-4043	47	22	=	=	SYM
ejpam-4043	47	23	1	1	NUM
ejpam-4043	47	24	,	,	PUNCT
ejpam-4043	47	25	ω2	ω2	NOUN
ejpam-4043	47	26	=	=	SYM
ejpam-4043	47	27	1	1	NUM
ejpam-4043	47	28	and	and	CCONJ
ejpam-4043	47	29	νω	νω	ADV
ejpam-4043	47	30	=	=	ADJ
ejpam-4043	47	31	νω	νω	PROPN
ejpam-4043	47	32	.	.	PUNCT
ejpam-4043	47	33	<	<	X
ejpam-4043	47	34	is	be	AUX
ejpam-4043	47	35	a	a	DET
ejpam-4043	47	36	commutative	commutative	ADJ
ejpam-4043	47	37	,	,	PUNCT
ejpam-4043	47	38	principal	principal	ADJ
ejpam-4043	47	39	ideal	ideal	NOUN
ejpam-4043	47	40	but	but	CCONJ
ejpam-4043	47	41	non	non	ADJ
ejpam-4043	47	42	-	-	ADJ
ejpam-4043	47	43	chain	chain	ADJ
ejpam-4043	47	44	finite	finite	NOUN
ejpam-4043	47	45	ring	ring	NOUN
ejpam-4043	47	46	with	with	ADP
ejpam-4043	47	47	34	34	NUM
ejpam-4043	47	48	=	=	SYM
ejpam-4043	47	49	81	81	NUM
ejpam-4043	47	50	elements	element	NOUN
ejpam-4043	47	51	.	.	PUNCT
ejpam-4043	48	1	the	the	DET
ejpam-4043	48	2	maximal	maximal	ADJ
ejpam-4043	48	3	ideal	ideal	NOUN
ejpam-4043	48	4	of	of	ADP
ejpam-4043	48	5	<	<	X
ejpam-4043	48	6	are	be	AUX
ejpam-4043	48	7	<	<	X
ejpam-4043	48	8	2	2	NUM
ejpam-4043	48	9	+	+	CCONJ
ejpam-4043	48	10	ν	ν	NOUN
ejpam-4043	48	11	+	+	CCONJ
ejpam-4043	48	12	2ω	2ω	PROPN
ejpam-4043	48	13	>	>	X
ejpam-4043	48	14	,	,	PUNCT
ejpam-4043	48	15	<	<	X
ejpam-4043	48	16	2	2	NUM
ejpam-4043	48	17	+	+	CCONJ
ejpam-4043	48	18	ν	ν	NOUN
ejpam-4043	48	19	+	+	X
ejpam-4043	48	20	νω	νω	X
ejpam-4043	48	21	>	>	X
ejpam-4043	48	22	,	,	PUNCT
ejpam-4043	48	23	<	<	X
ejpam-4043	48	24	ν	ν	X
ejpam-4043	48	25	+	+	X
ejpam-4043	48	26	ω	ω	PROPN
ejpam-4043	48	27	+	+	X
ejpam-4043	48	28	2νω	2νω	NOUN
ejpam-4043	48	29	>	>	PUNCT
ejpam-4043	48	30	,	,	PUNCT
ejpam-4043	48	31	<	<	X
ejpam-4043	48	32	2ν	2ν	NOUN
ejpam-4043	48	33	+	+	CCONJ
ejpam-4043	48	34	2ω	2ω	NUM
ejpam-4043	48	35	+	+	X
ejpam-4043	48	36	2νω	2νω	ADJ
ejpam-4043	48	37	>	>	X
ejpam-4043	48	38	.	.	PUNCT
ejpam-4043	49	1	some	some	DET
ejpam-4043	49	2	units	unit	NOUN
ejpam-4043	49	3	of	of	ADP
ejpam-4043	49	4	<	<	X
ejpam-4043	49	5	is	be	AUX
ejpam-4043	49	6	1	1	NUM
ejpam-4043	49	7	+	+	CCONJ
ejpam-4043	49	8	ν	ν	X
ejpam-4043	49	9	+	+	X
ejpam-4043	49	10	ω	ω	NOUN
ejpam-4043	49	11	+	+	CCONJ
ejpam-4043	49	12	2νω	2νω	ADJ
ejpam-4043	49	13	,	,	PUNCT
ejpam-4043	49	14	1	1	NUM
ejpam-4043	49	15	+	+	NUM
ejpam-4043	49	16	2ν	2ν	NUM
ejpam-4043	49	17	+	+	CCONJ
ejpam-4043	49	18	2ω	2ω	NUM
ejpam-4043	49	19	+	+	CCONJ
ejpam-4043	49	20	2νω	2νω	ADJ
ejpam-4043	49	21	,	,	PUNCT
ejpam-4043	49	22	νω	νω	ADP
ejpam-4043	49	23	,	,	PUNCT
ejpam-4043	49	24	ν	ν	PROPN
ejpam-4043	49	25	,	,	PUNCT
ejpam-4043	49	26	ω	ω	NOUN
ejpam-4043	49	27	for	for	ADP
ejpam-4043	49	28	sake	sake	NOUN
ejpam-4043	49	29	of	of	ADP
ejpam-4043	49	30	simplicity	simplicity	NOUN
ejpam-4043	49	31	we	we	PRON
ejpam-4043	49	32	consider	consider	VERB
ejpam-4043	49	33	ϑ	ϑ	NOUN
ejpam-4043	49	34	is	be	AUX
ejpam-4043	49	35	a	a	DET
ejpam-4043	49	36	unit	unit	NOUN
ejpam-4043	49	37	of	of	ADP
ejpam-4043	49	38	<	<	X
ejpam-4043	49	39	and	and	CCONJ
ejpam-4043	49	40	also	also	ADV
ejpam-4043	49	41	we	we	PRON
ejpam-4043	49	42	note	note	VERB
ejpam-4043	49	43	that	that	SCONJ
ejpam-4043	49	44	ϑ−1	ϑ−1	PROPN
ejpam-4043	49	45	=	=	NOUN
ejpam-4043	49	46	ϑ	ϑ	PROPN
ejpam-4043	49	47	for	for	ADP
ejpam-4043	49	48	each	each	DET
ejpam-4043	49	49	case	case	NOUN
ejpam-4043	49	50	.	.	PUNCT
ejpam-4043	50	1	let	let	VERB
ejpam-4043	50	2	us	we	PRON
ejpam-4043	50	3	assume	assume	VERB
ejpam-4043	50	4	ξ1	ξ1	NOUN
ejpam-4043	50	5	=	=	PUNCT
ejpam-4043	50	6	1+ν+ω+νω	1+ν+ω+νω	NUM
ejpam-4043	50	7	,	,	PUNCT
ejpam-4043	50	8	ξ2	ξ2	NOUN
ejpam-4043	50	9	=	=	SYM
ejpam-4043	50	10	1−ν+ω−νω	1−ν+ω−νω	NUM
ejpam-4043	50	11	,	,	PUNCT
ejpam-4043	50	12	ξ3	ξ3	NOUN
ejpam-4043	50	13	=	=	SYM
ejpam-4043	50	14	1+ν−ω−νω	1+ν−ω−νω	PROPN
ejpam-4043	50	15	and	and	CCONJ
ejpam-4043	50	16	ξ4	ξ4	NOUN
ejpam-4043	50	17	=	=	PUNCT
ejpam-4043	50	18	1−ν−ω+νω	1−ν−ω+νω	NOUN
ejpam-4043	50	19	.	.	PUNCT
ejpam-4043	51	1	it	it	PRON
ejpam-4043	51	2	is	be	AUX
ejpam-4043	51	3	obvious	obvious	ADJ
ejpam-4043	51	4	to	to	PART
ejpam-4043	51	5	obtain	obtain	VERB
ejpam-4043	51	6	that	that	DET
ejpam-4043	51	7	ξ2i	ξ2i	NOUN
ejpam-4043	51	8	=	=	SYM
ejpam-4043	51	9	ξi	ξi	PROPN
ejpam-4043	51	10	,	,	PUNCT
ejpam-4043	51	11	ξiξj	ξiξj	PROPN
ejpam-4043	51	12	=	=	SYM
ejpam-4043	51	13	0	0	PROPN
ejpam-4043	52	1	and	and	CCONJ
ejpam-4043	52	2	∑4	∑4	PROPN
ejpam-4043	52	3	i=1	i=1	PROPN
ejpam-4043	53	1	ξi	ξi	NOUN
ejpam-4043	53	2	=	=	NOUN
ejpam-4043	53	3	1	1	NUM
ejpam-4043	53	4	for	for	ADP
ejpam-4043	53	5	all	all	DET
ejpam-4043	53	6	i	i	PROPN
ejpam-4043	53	7	,	,	PUNCT
ejpam-4043	53	8	j	j	PROPN
ejpam-4043	53	9	=	=	SYM
ejpam-4043	53	10	1	1	NUM
ejpam-4043	53	11	,	,	PUNCT
ejpam-4043	53	12	2	2	NUM
ejpam-4043	53	13	,	,	PUNCT
ejpam-4043	53	14	3	3	NUM
ejpam-4043	53	15	,	,	PUNCT
ejpam-4043	53	16	4	4	NUM
ejpam-4043	53	17	and	and	CCONJ
ejpam-4043	53	18	i	i	PRON
ejpam-4043	53	19	6=	6=	PUNCT
ejpam-4043	54	1	j.	j.	PROPN
ejpam-4043	54	2	now	now	ADV
ejpam-4043	54	3	by	by	ADP
ejpam-4043	54	4	chinese	chinese	ADJ
ejpam-4043	54	5	remainder	remainder	NOUN
ejpam-4043	54	6	theorem	theorem	PROPN
ejpam-4043	54	7	,	,	PUNCT
ejpam-4043	54	8	the	the	DET
ejpam-4043	54	9	considered	consider	VERB
ejpam-4043	54	10	ring	ring	NOUN
ejpam-4043	54	11	can	can	AUX
ejpam-4043	54	12	be	be	AUX
ejpam-4043	54	13	expressed	express	VERB
ejpam-4043	54	14	as	as	ADP
ejpam-4043	54	15	<	<	X
ejpam-4043	54	16	=	=	SYM
ejpam-4043	54	17	ξ1z3	ξ1z3	PROPN
ejpam-4043	54	18	⊕	⊕	PROPN
ejpam-4043	54	19	ξ2z3	ξ2z3	ADP
ejpam-4043	54	20	⊕	⊕	PROPN
ejpam-4043	54	21	ξ3z3	ξ3z3	PROPN
ejpam-4043	54	22	⊕	⊕	PROPN
ejpam-4043	54	23	ξ4z3	ξ4z3	PROPN
ejpam-4043	54	24	.	.	PUNCT
ejpam-4043	54	25	therefore	therefore	ADV
ejpam-4043	55	1	,	,	PUNCT
ejpam-4043	55	2	an	an	DET
ejpam-4043	55	3	arbitrary	arbitrary	ADJ
ejpam-4043	55	4	element	element	NOUN
ejpam-4043	55	5	e	e	NOUN
ejpam-4043	55	6	=	=	NOUN
ejpam-4043	55	7	e1	e1	PROPN
ejpam-4043	55	8	+	+	CCONJ
ejpam-4043	55	9	νe2	νe2	NOUN
ejpam-4043	55	10	+	+	CCONJ
ejpam-4043	55	11	ωe3	ωe3	NOUN
ejpam-4043	55	12	+	+	CCONJ
ejpam-4043	55	13	νωe4	νωe4	NOUN
ejpam-4043	55	14	of	of	ADP
ejpam-4043	55	15	<	<	X
ejpam-4043	55	16	where	where	SCONJ
ejpam-4043	55	17	ei	ei	PROPN
ejpam-4043	55	18	∈	∈	PROPN
ejpam-4043	55	19	z3	z3	PROPN
ejpam-4043	55	20	can	can	AUX
ejpam-4043	55	21	be	be	AUX
ejpam-4043	55	22	uniquely	uniquely	ADV
ejpam-4043	55	23	expressed	express	VERB
ejpam-4043	55	24	as	as	ADP
ejpam-4043	55	25	e	e	NOUN
ejpam-4043	55	26	=	=	NOUN
ejpam-4043	55	27	e1	e1	PROPN
ejpam-4043	55	28	+	+	CCONJ
ejpam-4043	55	29	νe2	νe2	NOUN
ejpam-4043	55	30	+	+	CCONJ
ejpam-4043	55	31	ωe3	ωe3	NOUN
ejpam-4043	55	32	+	+	CCONJ
ejpam-4043	55	33	νωe4	νωe4	NOUN
ejpam-4043	55	34	=	=	PUNCT
ejpam-4043	55	35	ξ1k1	ξ1k1	NOUN
ejpam-4043	55	36	+	+	NOUN
ejpam-4043	55	37	ξ2k2	ξ2k2	X
ejpam-4043	55	38	+	+	SYM
ejpam-4043	55	39	ξ3k3	ξ3k3	NOUN
ejpam-4043	56	1	+	+	CCONJ
ejpam-4043	56	2	ξ4k4	ξ4k4	X
ejpam-4043	56	3	where	where	SCONJ
ejpam-4043	56	4	ki	ki	PROPN
ejpam-4043	56	5	∈	∈	PROPN
ejpam-4043	56	6	z3	z3	PROPN
ejpam-4043	56	7	for	for	ADP
ejpam-4043	56	8	all	all	DET
ejpam-4043	56	9	i	i	PRON
ejpam-4043	56	10	=	=	NOUN
ejpam-4043	56	11	1	1	NUM
ejpam-4043	56	12	,	,	PUNCT
ejpam-4043	56	13	2	2	NUM
ejpam-4043	56	14	,	,	PUNCT
ejpam-4043	56	15	3	3	NUM
ejpam-4043	56	16	,	,	PUNCT
ejpam-4043	56	17	4	4	NUM
ejpam-4043	56	18	.	.	PUNCT
ejpam-4043	57	1	a	a	DET
ejpam-4043	57	2	nonempty	nonempty	NOUN
ejpam-4043	57	3	subset	subset	VERB
ejpam-4043	57	4	k	k	PROPN
ejpam-4043	57	5	of	of	ADP
ejpam-4043	57	6	<	<	X
ejpam-4043	57	7	n	n	X
ejpam-4043	57	8	is	be	AUX
ejpam-4043	57	9	a	a	DET
ejpam-4043	57	10	linear	linear	ADJ
ejpam-4043	57	11	code	code	NOUN
ejpam-4043	57	12	over	over	ADP
ejpam-4043	57	13	<	<	X
ejpam-4043	57	14	of	of	ADP
ejpam-4043	57	15	length	length	NOUN
ejpam-4043	57	16	n.	n.	PROPN
ejpam-4043	57	17	if	if	SCONJ
ejpam-4043	57	18	k	k	PROPN
ejpam-4043	57	19	is	be	AUX
ejpam-4043	57	20	an	an	DET
ejpam-4043	57	21	<	<	X
ejpam-4043	57	22	-submodule	-submodule	NOUN
ejpam-4043	57	23	prateek	prateek	NOUN
ejpam-4043	57	24	mor	mor	PROPN
ejpam-4043	57	25	et	et	PROPN
ejpam-4043	57	26	al	al	PROPN
ejpam-4043	57	27	.	.	PUNCT
ejpam-4043	57	28	/	/	SYM
ejpam-4043	57	29	eur	eur	PROPN
ejpam-4043	57	30	.	.	PUNCT
ejpam-4043	58	1	j.	j.	PROPN
ejpam-4043	58	2	pure	pure	PROPN
ejpam-4043	58	3	appl	appl	PROPN
ejpam-4043	58	4	.	.	PROPN
ejpam-4043	58	5	math	math	PROPN
ejpam-4043	58	6	,	,	PUNCT
ejpam-4043	58	7	14	14	NUM
ejpam-4043	58	8	(	(	PUNCT
ejpam-4043	58	9	3	3	NUM
ejpam-4043	58	10	)	)	PUNCT
ejpam-4043	58	11	(	(	PUNCT
ejpam-4043	58	12	2021	2021	NUM
ejpam-4043	58	13	)	)	PUNCT
ejpam-4043	58	14	,	,	PUNCT
ejpam-4043	58	15	1082	1082	NUM
ejpam-4043	58	16	-	-	SYM
ejpam-4043	58	17	1097	1097	NUM
ejpam-4043	58	18	1084	1084	NUM
ejpam-4043	58	19	of	of	ADP
ejpam-4043	58	20	<	<	X
ejpam-4043	58	21	n	n	NOUN
ejpam-4043	58	22	and	and	CCONJ
ejpam-4043	58	23	the	the	DET
ejpam-4043	58	24	elements	element	NOUN
ejpam-4043	58	25	of	of	ADP
ejpam-4043	58	26	k	k	PROPN
ejpam-4043	58	27	are	be	AUX
ejpam-4043	58	28	codewords	codeword	NOUN
ejpam-4043	58	29	.	.	PUNCT
ejpam-4043	59	1	let	let	VERB
ejpam-4043	59	2	k	k	PRON
ejpam-4043	59	3	be	be	AUX
ejpam-4043	59	4	a	a	DET
ejpam-4043	59	5	code	code	NOUN
ejpam-4043	59	6	over	over	ADP
ejpam-4043	59	7	<	<	X
ejpam-4043	59	8	of	of	ADP
ejpam-4043	59	9	length	length	NOUN
ejpam-4043	59	10	n	n	PROPN
ejpam-4043	59	11	and	and	CCONJ
ejpam-4043	59	12	its	its	PRON
ejpam-4043	59	13	polynomial	polynomial	ADJ
ejpam-4043	59	14	representation	representation	NOUN
ejpam-4043	59	15	be	be	AUX
ejpam-4043	59	16	t	t	NOUN
ejpam-4043	59	17	(	(	PUNCT
ejpam-4043	59	18	k	k	NOUN
ejpam-4043	59	19	)	)	PUNCT
ejpam-4043	59	20	,	,	PUNCT
ejpam-4043	59	21	that	that	ADV
ejpam-4043	59	22	is	is	ADV
ejpam-4043	59	23	,	,	PUNCT
ejpam-4043	59	24	t	t	PROPN
ejpam-4043	59	25	(	(	PUNCT
ejpam-4043	59	26	k	k	NOUN
ejpam-4043	59	27	)	)	PUNCT
ejpam-4043	60	1	=	=	SYM
ejpam-4043	60	2	{	{	PUNCT
ejpam-4043	60	3	n−1∑	n−1∑	PROPN
ejpam-4043	60	4	i=0	i=0	AUX
ejpam-4043	60	5	χit	χit	VERB
ejpam-4043	60	6	i	i	PRON
ejpam-4043	60	7	|	|	ADV
ejpam-4043	60	8	(	(	PUNCT
ejpam-4043	60	9	χ0	χ0	PROPN
ejpam-4043	60	10	,	,	PUNCT
ejpam-4043	60	11	χ1	χ1	PROPN
ejpam-4043	60	12	,	,	PUNCT
ejpam-4043	60	13	...	...	PUNCT
ejpam-4043	60	14	,	,	PUNCT
ejpam-4043	60	15	χn−1	χn−1	ADJ
ejpam-4043	60	16	)	)	PUNCT
ejpam-4043	60	17	∈	∈	PROPN
ejpam-4043	61	1	k	k	X
ejpam-4043	61	2	}	}	PUNCT
ejpam-4043	61	3	let	let	VERB
ejpam-4043	61	4	υ	υ	NOUN
ejpam-4043	61	5	,	,	PUNCT
ejpam-4043	61	6	λ	λ	PROPN
ejpam-4043	61	7	and	and	CCONJ
ejpam-4043	61	8	f	f	PROPN
ejpam-4043	61	9	be	be	VERB
ejpam-4043	61	10	the	the	DET
ejpam-4043	61	11	maps	map	NOUN
ejpam-4043	61	12	from	from	ADP
ejpam-4043	61	13	<	<	NOUN
ejpam-4043	61	14	n	n	X
ejpam-4043	61	15	to	to	ADP
ejpam-4043	61	16	<	<	X
ejpam-4043	61	17	n	n	CCONJ
ejpam-4043	61	18	defined	define	VERB
ejpam-4043	61	19	as	as	ADP
ejpam-4043	61	20	υ(χ0	υ(χ0	NOUN
ejpam-4043	61	21	,	,	PUNCT
ejpam-4043	61	22	χ1	χ1	NOUN
ejpam-4043	61	23	,	,	PUNCT
ejpam-4043	61	24	...	...	PUNCT
ejpam-4043	61	25	,	,	PUNCT
ejpam-4043	61	26	χn−1	χn−1	ADJ
ejpam-4043	61	27	)	)	PUNCT
ejpam-4043	62	1	=	=	SYM
ejpam-4043	62	2	(	(	PUNCT
ejpam-4043	62	3	χn−1	χn−1	PROPN
ejpam-4043	62	4	,	,	PUNCT
ejpam-4043	62	5	χ0	χ0	PROPN
ejpam-4043	62	6	,	,	PUNCT
ejpam-4043	62	7	...	...	PUNCT
ejpam-4043	62	8	,	,	PUNCT
ejpam-4043	62	9	χn−2	χn−2	PROPN
ejpam-4043	62	10	)	)	PUNCT
ejpam-4043	62	11	,	,	PUNCT
ejpam-4043	62	12	λ(χ0	λ(χ0	PROPN
ejpam-4043	62	13	,	,	PUNCT
ejpam-4043	62	14	χ1	χ1	NOUN
ejpam-4043	62	15	,	,	PUNCT
ejpam-4043	62	16	...	...	PUNCT
ejpam-4043	62	17	,	,	PUNCT
ejpam-4043	62	18	χn−1	χn−1	ADJ
ejpam-4043	62	19	)	)	PUNCT
ejpam-4043	62	20	=	=	SYM
ejpam-4043	62	21	(	(	PUNCT
ejpam-4043	62	22	−χn−1	−χn−1	PROPN
ejpam-4043	62	23	,	,	PUNCT
ejpam-4043	62	24	χ0	χ0	PROPN
ejpam-4043	62	25	,	,	PUNCT
ejpam-4043	62	26	...	...	PUNCT
ejpam-4043	62	27	,	,	PUNCT
ejpam-4043	62	28	χn−2	χn−2	PROPN
ejpam-4043	62	29	)	)	PUNCT
ejpam-4043	62	30	,	,	PUNCT
ejpam-4043	62	31	f(χ0	f(χ0	PROPN
ejpam-4043	62	32	,	,	PUNCT
ejpam-4043	62	33	χ1	χ1	NOUN
ejpam-4043	62	34	,	,	PUNCT
ejpam-4043	62	35	...	...	PUNCT
ejpam-4043	62	36	,	,	PUNCT
ejpam-4043	62	37	χn−1	χn−1	ADJ
ejpam-4043	62	38	)	)	PUNCT
ejpam-4043	62	39	=	=	SYM
ejpam-4043	62	40	(	(	PUNCT
ejpam-4043	62	41	ϑχn−1	ϑχn−1	PROPN
ejpam-4043	62	42	,	,	PUNCT
ejpam-4043	62	43	χ0	χ0	PROPN
ejpam-4043	62	44	,	,	PUNCT
ejpam-4043	62	45	...	...	PUNCT
ejpam-4043	62	46	,	,	PUNCT
ejpam-4043	62	47	χn−2	χn−2	PROPN
ejpam-4043	62	48	)	)	PUNCT
ejpam-4043	62	49	,	,	PUNCT
ejpam-4043	62	50	respectively	respectively	ADV
ejpam-4043	62	51	.	.	PUNCT
ejpam-4043	63	1	then	then	ADV
ejpam-4043	63	2	k	k	PROPN
ejpam-4043	63	3	is	be	AUX
ejpam-4043	63	4	a	a	DET
ejpam-4043	63	5	cyclic	cyclic	ADJ
ejpam-4043	63	6	,	,	PUNCT
ejpam-4043	63	7	negacyclic	negacyclic	ADJ
ejpam-4043	63	8	,	,	PUNCT
ejpam-4043	63	9	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	63	10	if	if	SCONJ
ejpam-4043	63	11	υ(k	υ(k	PROPN
ejpam-4043	63	12	)	)	PUNCT
ejpam-4043	63	13	=	=	SYM
ejpam-4043	64	1	k	k	X
ejpam-4043	64	2	,	,	PUNCT
ejpam-4043	64	3	λ(k	λ(k	PROPN
ejpam-4043	64	4	)	)	PUNCT
ejpam-4043	64	5	=	=	SYM
ejpam-4043	64	6	k	k	NOUN
ejpam-4043	64	7	,	,	PUNCT
ejpam-4043	64	8	f(k	f(k	ADJ
ejpam-4043	64	9	)	)	PUNCT
ejpam-4043	64	10	=	=	SYM
ejpam-4043	64	11	k	k	PROPN
ejpam-4043	64	12	respectively	respectively	ADV
ejpam-4043	64	13	.	.	PUNCT
ejpam-4043	65	1	a	a	DET
ejpam-4043	65	2	code	code	NOUN
ejpam-4043	65	3	k	k	NOUN
ejpam-4043	65	4	over	over	ADP
ejpam-4043	65	5	<	<	X
ejpam-4043	65	6	of	of	ADP
ejpam-4043	65	7	length	length	NOUN
ejpam-4043	65	8	n	n	NOUN
ejpam-4043	65	9	is	be	AUX
ejpam-4043	65	10	cyclic	cyclic	ADJ
ejpam-4043	65	11	,	,	PUNCT
ejpam-4043	65	12	negacyclic	negacyclic	ADJ
ejpam-4043	65	13	and	and	CCONJ
ejpam-4043	65	14	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	65	15	if	if	SCONJ
ejpam-4043	65	16	and	and	CCONJ
ejpam-4043	65	17	only	only	ADV
ejpam-4043	65	18	if	if	SCONJ
ejpam-4043	65	19	t	t	PROPN
ejpam-4043	65	20	(	(	PUNCT
ejpam-4043	65	21	k	k	NOUN
ejpam-4043	65	22	)	)	PUNCT
ejpam-4043	65	23	is	be	AUX
ejpam-4043	65	24	an	an	DET
ejpam-4043	65	25	ideal	ideal	NOUN
ejpam-4043	65	26	of	of	ADP
ejpam-4043	65	27	<	<	X
ejpam-4043	65	28	[	[	X
ejpam-4043	65	29	t]/	t]/	X
ejpam-4043	65	30	<	<	X
ejpam-4043	65	31	tn	tn	PROPN
ejpam-4043	65	32	−	−	NOUN
ejpam-4043	65	33	1	1	NUM
ejpam-4043	65	34	>	>	PUNCT
ejpam-4043	65	35	,	,	PUNCT
ejpam-4043	65	36	<	<	X
ejpam-4043	65	37	[	[	X
ejpam-4043	65	38	t]/	t]/	X
ejpam-4043	65	39	<	<	X
ejpam-4043	65	40	tn	tn	PROPN
ejpam-4043	66	1	+	+	CCONJ
ejpam-4043	66	2	1	1	NUM
ejpam-4043	66	3	>	>	X
ejpam-4043	66	4	and	and	CCONJ
ejpam-4043	66	5	<	<	X
ejpam-4043	66	6	[	[	X
ejpam-4043	66	7	t]/	t]/	X
ejpam-4043	66	8	<	<	X
ejpam-4043	66	9	tn	tn	PROPN
ejpam-4043	66	10	−	−	PROPN
ejpam-4043	66	11	ϑ	ϑ	X
ejpam-4043	66	12	>	>	X
ejpam-4043	66	13	respectively	respectively	ADV
ejpam-4043	66	14	.	.	PUNCT
ejpam-4043	67	1	for	for	ADP
ejpam-4043	67	2	the	the	DET
ejpam-4043	67	3	arbitrary	arbitrary	ADJ
ejpam-4043	67	4	elements	element	NOUN
ejpam-4043	67	5	χ	χ	X
ejpam-4043	67	6	=	=	SYM
ejpam-4043	67	7	(	(	PUNCT
ejpam-4043	67	8	χ0	χ0	PROPN
ejpam-4043	67	9	,	,	PUNCT
ejpam-4043	67	10	χ1	χ1	PROPN
ejpam-4043	67	11	,	,	PUNCT
ejpam-4043	67	12	...	...	PUNCT
ejpam-4043	67	13	,	,	PUNCT
ejpam-4043	67	14	χn−1	χn−1	ADJ
ejpam-4043	67	15	)	)	PUNCT
ejpam-4043	67	16	and	and	CCONJ
ejpam-4043	67	17	ψ	ψ	X
ejpam-4043	67	18	=	=	SYM
ejpam-4043	67	19	(	(	PUNCT
ejpam-4043	67	20	ψ0	ψ0	ADJ
ejpam-4043	67	21	,	,	PUNCT
ejpam-4043	67	22	ψ1	ψ1	ADJ
ejpam-4043	67	23	,	,	PUNCT
ejpam-4043	67	24	...	...	PUNCT
ejpam-4043	67	25	,	,	PUNCT
ejpam-4043	67	26	ψn−1	ψn−1	PROPN
ejpam-4043	67	27	)	)	PUNCT
ejpam-4043	67	28	of	of	ADP
ejpam-4043	67	29	<	<	X
ejpam-4043	67	30	,	,	PUNCT
ejpam-4043	67	31	the	the	DET
ejpam-4043	67	32	inner	inner	ADJ
ejpam-4043	67	33	product	product	NOUN
ejpam-4043	67	34	is	be	AUX
ejpam-4043	67	35	defined	define	VERB
ejpam-4043	67	36	as	as	ADP
ejpam-4043	67	37	χ.ψ	χ.ψ	PROPN
ejpam-4043	67	38	=	=	PROPN
ejpam-4043	67	39	n−1∑	n−1∑	PROPN
ejpam-4043	67	40	i=0	i=0	ADJ
ejpam-4043	67	41	χiψi	χiψi	NOUN
ejpam-4043	67	42	.	.	PUNCT
ejpam-4043	68	1	if	if	SCONJ
ejpam-4043	68	2	χ.ψ	χ.ψ	PROPN
ejpam-4043	68	3	=	=	NOUN
ejpam-4043	68	4	0	0	PROPN
ejpam-4043	68	5	,	,	PUNCT
ejpam-4043	68	6	then	then	ADV
ejpam-4043	68	7	χ	χ	NOUN
ejpam-4043	68	8	and	and	CCONJ
ejpam-4043	68	9	ψ	ψ	NOUN
ejpam-4043	68	10	are	be	AUX
ejpam-4043	68	11	orthogonal	orthogonal	ADJ
ejpam-4043	68	12	.	.	PUNCT
ejpam-4043	69	1	if	if	SCONJ
ejpam-4043	69	2	k	k	PROPN
ejpam-4043	69	3	is	be	AUX
ejpam-4043	69	4	a	a	DET
ejpam-4043	69	5	linear	linear	ADJ
ejpam-4043	69	6	code	code	NOUN
ejpam-4043	69	7	over	over	ADP
ejpam-4043	69	8	<	<	X
ejpam-4043	69	9	of	of	ADP
ejpam-4043	69	10	length	length	NOUN
ejpam-4043	69	11	n	n	CCONJ
ejpam-4043	69	12	,	,	PUNCT
ejpam-4043	69	13	then	then	ADV
ejpam-4043	69	14	the	the	DET
ejpam-4043	69	15	dual	dual	ADJ
ejpam-4043	69	16	code	code	NOUN
ejpam-4043	69	17	of	of	ADP
ejpam-4043	69	18	k	k	PROPN
ejpam-4043	69	19	is	be	AUX
ejpam-4043	69	20	defined	define	VERB
ejpam-4043	69	21	as	as	ADP
ejpam-4043	69	22	k⊥	k⊥	NOUN
ejpam-4043	69	23	=	=	PUNCT
ejpam-4043	69	24	{	{	PUNCT
ejpam-4043	69	25	χ	χ	PROPN
ejpam-4043	69	26	∈	∈	PROPN
ejpam-4043	69	27	<	<	X
ejpam-4043	69	28	n	n	X
ejpam-4043	69	29	:	:	PUNCT
ejpam-4043	69	30	χ.ψ	χ.ψ	PROPN
ejpam-4043	69	31	=	=	NOUN
ejpam-4043	69	32	0	0	PROPN
ejpam-4043	69	33	for	for	ADP
ejpam-4043	69	34	all	all	PRON
ejpam-4043	69	35	ψ	ψ	ADP
ejpam-4043	69	36	∈	∈	PROPN
ejpam-4043	69	37	k	k	NOUN
ejpam-4043	69	38	}	}	PUNCT
ejpam-4043	69	39	,	,	PUNCT
ejpam-4043	69	40	which	which	PRON
ejpam-4043	69	41	is	be	AUX
ejpam-4043	69	42	also	also	ADV
ejpam-4043	69	43	a	a	DET
ejpam-4043	69	44	linear	linear	ADJ
ejpam-4043	69	45	code	code	NOUN
ejpam-4043	69	46	over	over	ADP
ejpam-4043	69	47	the	the	DET
ejpam-4043	69	48	ring	ring	NOUN
ejpam-4043	69	49	<	<	X
ejpam-4043	69	50	of	of	ADP
ejpam-4043	69	51	length	length	NOUN
ejpam-4043	69	52	n.	n.	PROPN
ejpam-4043	69	53	a	a	DET
ejpam-4043	69	54	code	code	NOUN
ejpam-4043	70	1	k	k	PROPN
ejpam-4043	70	2	is	be	AUX
ejpam-4043	70	3	said	say	VERB
ejpam-4043	70	4	to	to	PART
ejpam-4043	70	5	be	be	AUX
ejpam-4043	70	6	self	self	NOUN
ejpam-4043	70	7	orthogonal	orthogonal	ADJ
ejpam-4043	70	8	if	if	SCONJ
ejpam-4043	70	9	k	k	PROPN
ejpam-4043	70	10	⊆	⊆	NUM
ejpam-4043	70	11	k⊥	k⊥	PROPN
ejpam-4043	70	12	and	and	CCONJ
ejpam-4043	70	13	said	say	VERB
ejpam-4043	70	14	to	to	PART
ejpam-4043	70	15	be	be	AUX
ejpam-4043	70	16	self	self	NOUN
ejpam-4043	70	17	dual	dual	ADJ
ejpam-4043	70	18	if	if	SCONJ
ejpam-4043	70	19	k	k	PROPN
ejpam-4043	70	20	=	=	PRON
ejpam-4043	70	21	k⊥.	k⊥.	PROPN
ejpam-4043	70	22	3	3	NUM
ejpam-4043	70	23	.	.	X
ejpam-4043	70	24	gray	gray	ADJ
ejpam-4043	70	25	map	map	NOUN
ejpam-4043	70	26	over	over	ADP
ejpam-4043	70	27	<	<	X
ejpam-4043	70	28	the	the	DET
ejpam-4043	70	29	hamming	hamming	NOUN
ejpam-4043	70	30	weight	weight	NOUN
ejpam-4043	70	31	wh(χ	wh(χ	PUNCT
ejpam-4043	70	32	)	)	PUNCT
ejpam-4043	70	33	for	for	ADP
ejpam-4043	70	34	any	any	DET
ejpam-4043	70	35	codeword	codeword	NOUN
ejpam-4043	70	36	χ	χ	NOUN
ejpam-4043	70	37	=	=	SYM
ejpam-4043	70	38	(	(	PUNCT
ejpam-4043	70	39	χ0	χ0	PROPN
ejpam-4043	70	40	,	,	PUNCT
ejpam-4043	70	41	χ1	χ1	PROPN
ejpam-4043	70	42	,	,	PUNCT
ejpam-4043	70	43	...	...	PUNCT
ejpam-4043	70	44	,	,	PUNCT
ejpam-4043	70	45	χn−1	χn−1	ADJ
ejpam-4043	70	46	)	)	PUNCT
ejpam-4043	70	47	∈	∈	PROPN
ejpam-4043	70	48	<	<	X
ejpam-4043	70	49	n	n	X
ejpam-4043	70	50	is	be	AUX
ejpam-4043	70	51	defined	define	VERB
ejpam-4043	70	52	as	as	ADP
ejpam-4043	70	53	the	the	DET
ejpam-4043	70	54	number	number	NOUN
ejpam-4043	70	55	of	of	ADP
ejpam-4043	70	56	all	all	DET
ejpam-4043	70	57	non	non	ADJ
ejpam-4043	70	58	-	-	ADJ
ejpam-4043	70	59	zero	zero	NUM
ejpam-4043	70	60	components	component	NOUN
ejpam-4043	70	61	in	in	ADP
ejpam-4043	70	62	χ	χ	NOUN
ejpam-4043	70	63	=	=	SYM
ejpam-4043	70	64	(	(	PUNCT
ejpam-4043	70	65	χ0	χ0	PROPN
ejpam-4043	70	66	,	,	PUNCT
ejpam-4043	70	67	χ1	χ1	PROPN
ejpam-4043	70	68	,	,	PUNCT
ejpam-4043	70	69	...	...	PUNCT
ejpam-4043	70	70	,	,	PUNCT
ejpam-4043	70	71	χn−1	χn−1	ADJ
ejpam-4043	70	72	)	)	PUNCT
ejpam-4043	70	73	.	.	PUNCT
ejpam-4043	71	1	the	the	DET
ejpam-4043	71	2	minimum	minimum	ADJ
ejpam-4043	71	3	weight	weight	NOUN
ejpam-4043	71	4	of	of	ADP
ejpam-4043	71	5	a	a	DET
ejpam-4043	71	6	code	code	NOUN
ejpam-4043	71	7	k	k	NOUN
ejpam-4043	71	8	,	,	PUNCT
ejpam-4043	71	9	that	that	ADV
ejpam-4043	71	10	is	be	AUX
ejpam-4043	71	11	,	,	PUNCT
ejpam-4043	71	12	wh(k	wh(k	X
ejpam-4043	71	13	)	)	PUNCT
ejpam-4043	71	14	is	be	AUX
ejpam-4043	71	15	the	the	DET
ejpam-4043	71	16	least	least	ADJ
ejpam-4043	71	17	weight	weight	NOUN
ejpam-4043	71	18	among	among	ADP
ejpam-4043	71	19	all	all	PRON
ejpam-4043	71	20	of	of	ADP
ejpam-4043	71	21	its	its	PRON
ejpam-4043	71	22	non	non	ADJ
ejpam-4043	71	23	zero	zero	NUM
ejpam-4043	71	24	codewords	codeword	NOUN
ejpam-4043	71	25	.	.	PUNCT
ejpam-4043	72	1	the	the	DET
ejpam-4043	72	2	hamming	hamming	NOUN
ejpam-4043	72	3	distance	distance	NOUN
ejpam-4043	72	4	between	between	ADP
ejpam-4043	72	5	two	two	NUM
ejpam-4043	72	6	codes	code	NOUN
ejpam-4043	72	7	χ	χ	X
ejpam-4043	72	8	=	=	SYM
ejpam-4043	72	9	(	(	PUNCT
ejpam-4043	72	10	χ0	χ0	PROPN
ejpam-4043	72	11	,	,	PUNCT
ejpam-4043	72	12	χ1	χ1	PROPN
ejpam-4043	72	13	,	,	PUNCT
ejpam-4043	72	14	...	...	PUNCT
ejpam-4043	72	15	,	,	PUNCT
ejpam-4043	72	16	χn−1	χn−1	ADJ
ejpam-4043	72	17	)	)	PUNCT
ejpam-4043	72	18	and	and	CCONJ
ejpam-4043	72	19	χ̂	χ̂	NUM
ejpam-4043	72	20	=	=	SYM
ejpam-4043	72	21	(	(	PUNCT
ejpam-4043	72	22	χ̂0	χ̂0	PROPN
ejpam-4043	72	23	,	,	PUNCT
ejpam-4043	72	24	χ̂1	χ̂1	PROPN
ejpam-4043	72	25	,	,	PUNCT
ejpam-4043	72	26	...	...	PUNCT
ejpam-4043	72	27	,	,	PUNCT
ejpam-4043	72	28	χ̂n−1	χ̂n−1	NUM
ejpam-4043	72	29	)	)	PUNCT
ejpam-4043	72	30	of	of	ADP
ejpam-4043	72	31	<	<	NOUN
ejpam-4043	72	32	n	n	CCONJ
ejpam-4043	72	33	,	,	PUNCT
ejpam-4043	72	34	denoted	denote	VERB
ejpam-4043	72	35	by	by	ADP
ejpam-4043	72	36	dh(χ	dh(χ	NOUN
ejpam-4043	72	37	,	,	PUNCT
ejpam-4043	72	38	χ̂	χ̂	PROPN
ejpam-4043	72	39	)	)	PUNCT
ejpam-4043	73	1	=	=	SYM
ejpam-4043	73	2	wh(χ−	wh(χ−	NOUN
ejpam-4043	73	3	χ̂	χ̂	NUM
ejpam-4043	73	4	)	)	PUNCT
ejpam-4043	74	1	and	and	CCONJ
ejpam-4043	74	2	is	be	AUX
ejpam-4043	74	3	defined	define	VERB
ejpam-4043	74	4	as	as	ADP
ejpam-4043	74	5	dh(χ	dh(χ	VERB
ejpam-4043	74	6	,	,	PUNCT
ejpam-4043	74	7	ψ	ψ	NOUN
ejpam-4043	74	8	)	)	PUNCT
ejpam-4043	75	1	=	=	SYM
ejpam-4043	75	2	|	|	ADV
ejpam-4043	75	3	{	{	PUNCT
ejpam-4043	75	4	i	i	PRON
ejpam-4043	75	5	|	|	ADV
ejpam-4043	75	6	χi	χi	VERB
ejpam-4043	75	7	6=	6=	ADP
ejpam-4043	75	8	ψi	ψi	ADP
ejpam-4043	75	9	}	}	PUNCT
ejpam-4043	75	10	|	|	ADV
ejpam-4043	75	11	.	.	PUNCT
ejpam-4043	76	1	minimum	minimum	ADJ
ejpam-4043	76	2	distance	distance	NOUN
ejpam-4043	76	3	of	of	ADP
ejpam-4043	76	4	k	k	NOUN
ejpam-4043	76	5	,	,	PUNCT
ejpam-4043	76	6	denoted	denote	VERB
ejpam-4043	76	7	by	by	ADP
ejpam-4043	76	8	dh	dh	NOUN
ejpam-4043	76	9	and	and	CCONJ
ejpam-4043	76	10	is	be	AUX
ejpam-4043	76	11	given	give	VERB
ejpam-4043	76	12	by	by	ADP
ejpam-4043	76	13	minimum	minimum	ADJ
ejpam-4043	76	14	distance	distance	NOUN
ejpam-4043	76	15	between	between	ADP
ejpam-4043	76	16	the	the	DET
ejpam-4043	76	17	different	different	ADJ
ejpam-4043	76	18	pairs	pair	NOUN
ejpam-4043	76	19	of	of	ADP
ejpam-4043	76	20	codewords	codeword	NOUN
ejpam-4043	76	21	of	of	ADP
ejpam-4043	76	22	the	the	DET
ejpam-4043	76	23	linear	linear	PROPN
ejpam-4043	76	24	code	code	PROPN
ejpam-4043	76	25	k.	k.	PROPN
ejpam-4043	76	26	for	for	ADP
ejpam-4043	76	27	any	any	DET
ejpam-4043	76	28	codeword	codeword	NOUN
ejpam-4043	76	29	χ	χ	NOUN
ejpam-4043	76	30	=	=	SYM
ejpam-4043	76	31	(	(	PUNCT
ejpam-4043	76	32	χ0	χ0	PROPN
ejpam-4043	76	33	,	,	PUNCT
ejpam-4043	76	34	χ1	χ1	PROPN
ejpam-4043	76	35	,	,	PUNCT
ejpam-4043	76	36	...	...	PUNCT
ejpam-4043	76	37	,	,	PUNCT
ejpam-4043	76	38	χn−1	χn−1	ADJ
ejpam-4043	76	39	)	)	PUNCT
ejpam-4043	76	40	∈	∈	PROPN
ejpam-4043	76	41	<	<	NOUN
ejpam-4043	76	42	n	n	CCONJ
ejpam-4043	76	43	,	,	PUNCT
ejpam-4043	76	44	the	the	DET
ejpam-4043	76	45	lee	lee	PROPN
ejpam-4043	76	46	weight	weight	NOUN
ejpam-4043	76	47	is	be	AUX
ejpam-4043	76	48	defined	define	VERB
ejpam-4043	76	49	as	as	ADP
ejpam-4043	76	50	wl(χ	wl(χ	X
ejpam-4043	76	51	)	)	PUNCT
ejpam-4043	76	52	=	=	SYM
ejpam-4043	76	53	∑n−1	∑n−1	ADP
ejpam-4043	76	54	i=0	i=0	PROPN
ejpam-4043	76	55	wl(χi	wl(χi	PROPN
ejpam-4043	76	56	)	)	PUNCT
ejpam-4043	76	57	and	and	CCONJ
ejpam-4043	76	58	lee	lee	PROPN
ejpam-4043	76	59	distance	distance	NOUN
ejpam-4043	76	60	of	of	ADP
ejpam-4043	76	61	(	(	PUNCT
ejpam-4043	76	62	χ	χ	NOUN
ejpam-4043	76	63	,	,	PUNCT
ejpam-4043	76	64	χ̂	χ̂	PRON
ejpam-4043	76	65	)	)	PUNCT
ejpam-4043	76	66	is	be	AUX
ejpam-4043	76	67	given	give	VERB
ejpam-4043	76	68	by	by	ADP
ejpam-4043	76	69	dl(χ	dl(χ	PROPN
ejpam-4043	76	70	,	,	PUNCT
ejpam-4043	76	71	χ̂	χ̂	PUNCT
ejpam-4043	76	72	)	)	PUNCT
ejpam-4043	77	1	=	=	SYM
ejpam-4043	77	2	wl(χ−	wl(χ−	ADP
ejpam-4043	77	3	χ̂	χ̂	PROPN
ejpam-4043	77	4	)	)	PUNCT
ejpam-4043	77	5	=	=	SYM
ejpam-4043	77	6	∑n−1	∑n−1	ADP
ejpam-4043	77	7	i=0	i=0	PROPN
ejpam-4043	77	8	wl(χi	wl(χi	VERB
ejpam-4043	77	9	−	−	PROPN
ejpam-4043	77	10	χ̂i	χ̂i	NOUN
ejpam-4043	77	11	)	)	PUNCT
ejpam-4043	77	12	.	.	PUNCT
ejpam-4043	78	1	minimum	minimum	PROPN
ejpam-4043	78	2	lee	lee	PROPN
ejpam-4043	78	3	distance	distance	NOUN
ejpam-4043	78	4	of	of	ADP
ejpam-4043	78	5	k	k	PROPN
ejpam-4043	78	6	is	be	AUX
ejpam-4043	78	7	denoted	denote	VERB
ejpam-4043	78	8	by	by	ADP
ejpam-4043	78	9	dl	dl	PROPN
ejpam-4043	78	10	and	and	CCONJ
ejpam-4043	78	11	is	be	AUX
ejpam-4043	78	12	given	give	VERB
ejpam-4043	78	13	by	by	ADP
ejpam-4043	78	14	minimum	minimum	ADJ
ejpam-4043	78	15	lee	lee	PROPN
ejpam-4043	78	16	distance	distance	NOUN
ejpam-4043	78	17	of	of	ADP
ejpam-4043	78	18	prateek	prateek	ADJ
ejpam-4043	78	19	mor	mor	PROPN
ejpam-4043	78	20	et	et	PROPN
ejpam-4043	78	21	al	al	PROPN
ejpam-4043	78	22	.	.	PUNCT
ejpam-4043	78	23	/	/	SYM
ejpam-4043	78	24	eur	eur	PROPN
ejpam-4043	78	25	.	.	PUNCT
ejpam-4043	79	1	j.	j.	PROPN
ejpam-4043	79	2	pure	pure	PROPN
ejpam-4043	79	3	appl	appl	PROPN
ejpam-4043	79	4	.	.	PROPN
ejpam-4043	79	5	math	math	PROPN
ejpam-4043	79	6	,	,	PUNCT
ejpam-4043	79	7	14	14	NUM
ejpam-4043	79	8	(	(	PUNCT
ejpam-4043	79	9	3	3	NUM
ejpam-4043	79	10	)	)	PUNCT
ejpam-4043	79	11	(	(	PUNCT
ejpam-4043	79	12	2021	2021	NUM
ejpam-4043	79	13	)	)	PUNCT
ejpam-4043	79	14	,	,	PUNCT
ejpam-4043	79	15	1082	1082	NUM
ejpam-4043	79	16	-	-	SYM
ejpam-4043	79	17	1097	1097	NUM
ejpam-4043	79	18	1085	1085	NUM
ejpam-4043	79	19	different	different	ADJ
ejpam-4043	79	20	pairs	pair	NOUN
ejpam-4043	79	21	of	of	ADP
ejpam-4043	79	22	codewords	codeword	NOUN
ejpam-4043	79	23	of	of	ADP
ejpam-4043	79	24	the	the	DET
ejpam-4043	79	25	linear	linear	PROPN
ejpam-4043	79	26	code	code	PROPN
ejpam-4043	79	27	k.	k.	PROPN
ejpam-4043	80	1	the	the	DET
ejpam-4043	80	2	gray	gray	ADJ
ejpam-4043	80	3	map	map	NOUN
ejpam-4043	80	4	ϕ	ϕ	NOUN
ejpam-4043	80	5	from	from	ADP
ejpam-4043	80	6	<	<	X
ejpam-4043	80	7	to	to	ADP
ejpam-4043	80	8	z4	z4	PROPN
ejpam-4043	80	9	3	3	NUM
ejpam-4043	80	10	,	,	PUNCT
ejpam-4043	80	11	that	that	ADV
ejpam-4043	80	12	is	is	ADV
ejpam-4043	80	13	,	,	PUNCT
ejpam-4043	80	14	ϕ	ϕ	NOUN
ejpam-4043	80	15	:	:	PUNCT
ejpam-4043	80	16	<	<	X
ejpam-4043	80	17	→	→	SYM
ejpam-4043	80	18	z4	z4	PROPN
ejpam-4043	80	19	3	3	NUM
ejpam-4043	80	20	is	be	AUX
ejpam-4043	80	21	defined	define	VERB
ejpam-4043	80	22	as	as	ADP
ejpam-4043	80	23	ϕ(k	ϕ(k	NOUN
ejpam-4043	80	24	=	=	SYM
ejpam-4043	80	25	ξ1k1	ξ1k1	NOUN
ejpam-4043	80	26	+	+	SYM
ejpam-4043	80	27	ξ2k2	ξ2k2	X
ejpam-4043	80	28	+	+	SYM
ejpam-4043	80	29	ξ3k3	ξ3k3	X
ejpam-4043	80	30	+	+	X
ejpam-4043	80	31	ξ4k4	ξ4k4	NOUN
ejpam-4043	80	32	)	)	PUNCT
ejpam-4043	81	1	=	=	SYM
ejpam-4043	81	2	(	(	PUNCT
ejpam-4043	81	3	k1	k1	X
ejpam-4043	81	4	+	+	CCONJ
ejpam-4043	81	5	k2	k2	NOUN
ejpam-4043	81	6	+	+	CCONJ
ejpam-4043	81	7	k3	k3	ADJ
ejpam-4043	81	8	+	+	CCONJ
ejpam-4043	81	9	k4	k4	ADJ
ejpam-4043	81	10	,	,	PUNCT
ejpam-4043	81	11	k1	k1	NOUN
ejpam-4043	81	12	−	−	PROPN
ejpam-4043	81	13	k2	k2	PROPN
ejpam-4043	81	14	+	+	CCONJ
ejpam-4043	81	15	k3	k3	PROPN
ejpam-4043	81	16	−	−	PROPN
ejpam-4043	81	17	k4	k4	NOUN
ejpam-4043	81	18	,	,	PUNCT
ejpam-4043	81	19	k1	k1	NOUN
ejpam-4043	81	20	+	+	CCONJ
ejpam-4043	81	21	k2	k2	ADJ
ejpam-4043	81	22	−	−	PROPN
ejpam-4043	81	23	k3	k3	VERB
ejpam-4043	81	24	−	−	PROPN
ejpam-4043	81	25	k4	k4	NOUN
ejpam-4043	81	26	,	,	PUNCT
ejpam-4043	81	27	k1	k1	NOUN
ejpam-4043	81	28	−	−	PROPN
ejpam-4043	81	29	k2	k2	PROPN
ejpam-4043	81	30	−	−	PROPN
ejpam-4043	81	31	k3	k3	X
ejpam-4043	81	32	+	+	CCONJ
ejpam-4043	81	33	k4	k4	ADJ
ejpam-4043	81	34	)	)	PUNCT
ejpam-4043	81	35	.	.	PUNCT
ejpam-4043	82	1	proposition	proposition	NOUN
ejpam-4043	82	2	1	1	NUM
ejpam-4043	82	3	.	.	PUNCT
ejpam-4043	83	1	the	the	DET
ejpam-4043	83	2	gray	gray	ADJ
ejpam-4043	83	3	map	map	NOUN
ejpam-4043	83	4	ϕ	ϕ	NOUN
ejpam-4043	83	5	is	be	AUX
ejpam-4043	83	6	linear	linear	ADJ
ejpam-4043	83	7	and	and	CCONJ
ejpam-4043	83	8	distance	distance	NOUN
ejpam-4043	83	9	preserving	preserve	VERB
ejpam-4043	83	10	isometry	isometry	NOUN
ejpam-4043	83	11	map	map	NOUN
ejpam-4043	83	12	from	from	ADP
ejpam-4043	83	13	(	(	PUNCT
ejpam-4043	83	14	<	<	NOUN
ejpam-4043	83	15	n	n	CCONJ
ejpam-4043	83	16	,	,	PUNCT
ejpam-4043	83	17	dl	dl	NOUN
ejpam-4043	83	18	)	)	PUNCT
ejpam-4043	83	19	to	to	ADP
ejpam-4043	83	20	(	(	PUNCT
ejpam-4043	83	21	z4n	z4n	PROPN
ejpam-4043	83	22	3	3	NUM
ejpam-4043	83	23	,	,	PUNCT
ejpam-4043	83	24	dh	dh	NOUN
ejpam-4043	83	25	)	)	PUNCT
ejpam-4043	83	26	,	,	PUNCT
ejpam-4043	83	27	where	where	SCONJ
ejpam-4043	83	28	dl	dl	PROPN
ejpam-4043	83	29	and	and	CCONJ
ejpam-4043	83	30	dh	dh	NOUN
ejpam-4043	83	31	are	be	AUX
ejpam-4043	83	32	the	the	DET
ejpam-4043	83	33	lee	lee	PROPN
ejpam-4043	83	34	distance	distance	NOUN
ejpam-4043	83	35	and	and	CCONJ
ejpam-4043	83	36	hamming	hamming	NOUN
ejpam-4043	83	37	distance	distance	NOUN
ejpam-4043	83	38	in	in	ADP
ejpam-4043	83	39	<	<	NOUN
ejpam-4043	83	40	n	n	NOUN
ejpam-4043	83	41	and	and	CCONJ
ejpam-4043	83	42	z4n	z4n	PROPN
ejpam-4043	83	43	3	3	NUM
ejpam-4043	83	44	respectively	respectively	ADV
ejpam-4043	83	45	.	.	PUNCT
ejpam-4043	84	1	proof	proof	NOUN
ejpam-4043	84	2	.	.	PUNCT
ejpam-4043	85	1	let	let	VERB
ejpam-4043	85	2	k1	k1	PROPN
ejpam-4043	85	3	,	,	PUNCT
ejpam-4043	85	4	k2	k2	PROPN
ejpam-4043	85	5	∈	∈	PROPN
ejpam-4043	85	6	<	<	X
ejpam-4043	85	7	and	and	CCONJ
ejpam-4043	85	8	α	α	NOUN
ejpam-4043	85	9	∈	∈	PROPN
ejpam-4043	85	10	z3	z3	PROPN
ejpam-4043	85	11	then	then	ADV
ejpam-4043	85	12	ϕ(αk1	ϕ(αk1	PROPN
ejpam-4043	85	13	+	+	CCONJ
ejpam-4043	85	14	k2	k2	ADJ
ejpam-4043	85	15	)	)	PUNCT
ejpam-4043	85	16	=	=	SYM
ejpam-4043	85	17	αϕ(k1	αϕ(k1	NOUN
ejpam-4043	85	18	)	)	PUNCT
ejpam-4043	85	19	+	+	NUM
ejpam-4043	85	20	ϕ(k1	ϕ(k1	NOUN
ejpam-4043	85	21	)	)	PUNCT
ejpam-4043	86	1	so	so	ADV
ejpam-4043	86	2	,	,	PUNCT
ejpam-4043	86	3	ϕ	ϕ	PROPN
ejpam-4043	86	4	is	be	AUX
ejpam-4043	86	5	linear	linear	PROPN
ejpam-4043	86	6	map	map	NOUN
ejpam-4043	86	7	.	.	PUNCT
ejpam-4043	87	1	now	now	ADV
ejpam-4043	87	2	we	we	PRON
ejpam-4043	87	3	show	show	VERB
ejpam-4043	87	4	that	that	SCONJ
ejpam-4043	87	5	ϕ	ϕ	NOUN
ejpam-4043	87	6	is	be	AUX
ejpam-4043	87	7	distance	distance	NOUN
ejpam-4043	87	8	preserving	preserve	VERB
ejpam-4043	87	9	map	map	NOUN
ejpam-4043	87	10	.	.	PUNCT
ejpam-4043	88	1	by	by	ADP
ejpam-4043	88	2	the	the	DET
ejpam-4043	88	3	above	above	ADJ
ejpam-4043	88	4	definitions	definition	NOUN
ejpam-4043	88	5	,	,	PUNCT
ejpam-4043	88	6	dl(χ	dl(χ	PROPN
ejpam-4043	88	7	,	,	PUNCT
ejpam-4043	88	8	χ̂	χ̂	PROPN
ejpam-4043	88	9	)	)	PUNCT
ejpam-4043	88	10	=	=	PRON
ejpam-4043	88	11	wl(χ	wl(χ	PUNCT
ejpam-4043	88	12	−	−	PROPN
ejpam-4043	88	13	χ̂	χ̂	PROPN
ejpam-4043	88	14	)	)	PUNCT
ejpam-4043	88	15	=	=	SYM
ejpam-4043	88	16	wh(ϕ(χ	wh(ϕ(χ	X
ejpam-4043	88	17	−	−	PROPN
ejpam-4043	88	18	χ̂	χ̂	NUM
ejpam-4043	88	19	)	)	PUNCT
ejpam-4043	88	20	)	)	PUNCT
ejpam-4043	88	21	=	=	SYM
ejpam-4043	88	22	wh(ϕ(χ	wh(ϕ(χ	X
ejpam-4043	88	23	)	)	PUNCT
ejpam-4043	88	24	−	−	PROPN
ejpam-4043	88	25	φ(χ̂	φ(χ̂	NOUN
ejpam-4043	88	26	)	)	PUNCT
ejpam-4043	88	27	)	)	PUNCT
ejpam-4043	89	1	=	=	PUNCT
ejpam-4043	89	2	dh(ϕ(χ	dh(ϕ(χ	NUM
ejpam-4043	89	3	)	)	PUNCT
ejpam-4043	89	4	,	,	PUNCT
ejpam-4043	89	5	ϕ(χ̂	ϕ(χ̂	PROPN
ejpam-4043	89	6	)	)	PUNCT
ejpam-4043	89	7	)	)	PUNCT
ejpam-4043	89	8	.	.	PUNCT
ejpam-4043	90	1	hence	hence	ADV
ejpam-4043	90	2	ϕ	ϕ	PROPN
ejpam-4043	90	3	is	be	AUX
ejpam-4043	90	4	distance	distance	NOUN
ejpam-4043	90	5	preserving	preserve	VERB
ejpam-4043	90	6	map	map	NOUN
ejpam-4043	90	7	from	from	ADP
ejpam-4043	90	8	(	(	PUNCT
ejpam-4043	90	9	<	<	NOUN
ejpam-4043	90	10	n	n	CCONJ
ejpam-4043	90	11	,	,	PUNCT
ejpam-4043	90	12	dl	dl	NOUN
ejpam-4043	90	13	)	)	PUNCT
ejpam-4043	90	14	to	to	ADP
ejpam-4043	90	15	(	(	PUNCT
ejpam-4043	90	16	z4n	z4n	PROPN
ejpam-4043	90	17	3	3	NUM
ejpam-4043	90	18	,	,	PUNCT
ejpam-4043	90	19	dh	dh	NOUN
ejpam-4043	90	20	)	)	PUNCT
ejpam-4043	90	21	.	.	PUNCT
ejpam-4043	91	1	proposition	proposition	NOUN
ejpam-4043	91	2	2	2	NUM
ejpam-4043	91	3	.	.	PUNCT
ejpam-4043	92	1	if	if	SCONJ
ejpam-4043	92	2	k	k	PROPN
ejpam-4043	92	3	is	be	AUX
ejpam-4043	92	4	a	a	DET
ejpam-4043	92	5	linear	linear	ADJ
ejpam-4043	92	6	code	code	NOUN
ejpam-4043	92	7	over	over	ADP
ejpam-4043	92	8	the	the	DET
ejpam-4043	92	9	ring	ring	NOUN
ejpam-4043	92	10	<	<	X
ejpam-4043	92	11	of	of	ADP
ejpam-4043	92	12	length	length	NOUN
ejpam-4043	92	13	n	n	PROPN
ejpam-4043	92	14	with	with	ADP
ejpam-4043	92	15	|k|	|k|	NOUN
ejpam-4043	92	16	=	=	SYM
ejpam-4043	92	17	3k	3k	NUM
ejpam-4043	92	18	,	,	PUNCT
ejpam-4043	92	19	dl(k	dl(k	NUM
ejpam-4043	92	20	)	)	PUNCT
ejpam-4043	93	1	=	=	SYM
ejpam-4043	93	2	d	d	NOUN
ejpam-4043	93	3	,	,	PUNCT
ejpam-4043	93	4	then	then	ADV
ejpam-4043	93	5	ϕ(k	ϕ(k	NOUN
ejpam-4043	93	6	)	)	PUNCT
ejpam-4043	93	7	is	be	AUX
ejpam-4043	93	8	a	a	DET
ejpam-4043	93	9	ternary	ternary	ADJ
ejpam-4043	93	10	linear	linear	NOUN
ejpam-4043	93	11	code	code	NOUN
ejpam-4043	93	12	having	have	VERB
ejpam-4043	93	13	parameters	parameter	NOUN
ejpam-4043	93	14	[	[	X
ejpam-4043	93	15	4n	4n	NOUN
ejpam-4043	93	16	,	,	PUNCT
ejpam-4043	93	17	k	k	X
ejpam-4043	93	18	,	,	PUNCT
ejpam-4043	93	19	d	d	X
ejpam-4043	93	20	]	]	PUNCT
ejpam-4043	93	21	.	.	PUNCT
ejpam-4043	94	1	proposition	proposition	NOUN
ejpam-4043	94	2	3	3	X
ejpam-4043	94	3	.	.	PUNCT
ejpam-4043	95	1	let	let	VERB
ejpam-4043	95	2	k	k	PRON
ejpam-4043	95	3	be	be	AUX
ejpam-4043	95	4	a	a	DET
ejpam-4043	95	5	linear	linear	ADJ
ejpam-4043	95	6	code	code	NOUN
ejpam-4043	95	7	over	over	ADP
ejpam-4043	95	8	the	the	DET
ejpam-4043	95	9	ring	ring	NOUN
ejpam-4043	95	10	<	<	X
ejpam-4043	95	11	of	of	ADP
ejpam-4043	95	12	length	length	NOUN
ejpam-4043	95	13	n.	n.	PROPN
ejpam-4043	95	14	if	if	SCONJ
ejpam-4043	95	15	k	k	PROPN
ejpam-4043	95	16	is	be	AUX
ejpam-4043	95	17	self	self	NOUN
ejpam-4043	95	18	orthogonal	orthogonal	NOUN
ejpam-4043	95	19	,	,	PUNCT
ejpam-4043	95	20	then	then	ADV
ejpam-4043	95	21	ϕ(k	ϕ(k	NOUN
ejpam-4043	95	22	)	)	PUNCT
ejpam-4043	95	23	is	be	AUX
ejpam-4043	95	24	also	also	ADV
ejpam-4043	95	25	self	self	NOUN
ejpam-4043	95	26	orthogonal	orthogonal	ADJ
ejpam-4043	95	27	.	.	PUNCT
ejpam-4043	96	1	proof	proof	NOUN
ejpam-4043	96	2	.	.	PUNCT
ejpam-4043	97	1	let	let	VERB
ejpam-4043	97	2	k	k	PRON
ejpam-4043	97	3	be	be	AUX
ejpam-4043	97	4	a	a	DET
ejpam-4043	97	5	self	self	NOUN
ejpam-4043	97	6	orthogonal	orthogonal	ADJ
ejpam-4043	97	7	code	code	NOUN
ejpam-4043	97	8	and	and	CCONJ
ejpam-4043	97	9	η1	η1	NOUN
ejpam-4043	97	10	,	,	PUNCT
ejpam-4043	97	11	η2	η2	PROPN
ejpam-4043	97	12	∈	∈	PROPN
ejpam-4043	98	1	k	k	PROPN
ejpam-4043	98	2	such	such	ADJ
ejpam-4043	98	3	that	that	DET
ejpam-4043	98	4	η1	η1	NOUN
ejpam-4043	98	5	=	=	SYM
ejpam-4043	98	6	ξ1a+ξ2b+ξ3c+ξ4d	ξ1a+ξ2b+ξ3c+ξ4d	NOUN
ejpam-4043	98	7	and	and	CCONJ
ejpam-4043	98	8	η2	η2	ADJ
ejpam-4043	98	9	=	=	PUNCT
ejpam-4043	98	10	ξ1a	ξ1a	NOUN
ejpam-4043	98	11	′	′	NOUN
ejpam-4043	99	1	+	+	CCONJ
ejpam-4043	100	1	ξ2b	ξ2b	PROPN
ejpam-4043	100	2	′	′	NUM
ejpam-4043	101	1	+	+	NUM
ejpam-4043	101	2	ξ3c	ξ3c	NOUN
ejpam-4043	101	3	′	′	NOUN
ejpam-4043	102	1	+	+	CCONJ
ejpam-4043	102	2	ξ4d	ξ4d	PROPN
ejpam-4043	102	3	′	′	NUM
ejpam-4043	102	4	where	where	SCONJ
ejpam-4043	102	5	a	a	DET
ejpam-4043	102	6	,	,	PUNCT
ejpam-4043	102	7	b	b	NOUN
ejpam-4043	102	8	,	,	PUNCT
ejpam-4043	102	9	c	c	NOUN
ejpam-4043	102	10	,	,	PUNCT
ejpam-4043	102	11	d	d	NOUN
ejpam-4043	102	12	,	,	PUNCT
ejpam-4043	102	13	a	a	DET
ejpam-4043	102	14	′	′	NOUN
ejpam-4043	102	15	,	,	PUNCT
ejpam-4043	102	16	b	b	NOUN
ejpam-4043	102	17	′	′	NUM
ejpam-4043	102	18	,	,	PUNCT
ejpam-4043	102	19	c	c	NOUN
ejpam-4043	102	20	′	′	NOUN
ejpam-4043	102	21	,	,	PUNCT
ejpam-4043	103	1	d	d	NOUN
ejpam-4043	103	2	′	′	NOUN
ejpam-4043	103	3	∈	∈	PROPN
ejpam-4043	103	4	z3	z3	PROPN
ejpam-4043	103	5	from	from	ADP
ejpam-4043	103	6	the	the	DET
ejpam-4043	103	7	definition	definition	NOUN
ejpam-4043	103	8	of	of	ADP
ejpam-4043	103	9	self	self	NOUN
ejpam-4043	103	10	orthogonality	orthogonality	NOUN
ejpam-4043	103	11	,	,	PUNCT
ejpam-4043	103	12	η1.η2	η1.η2	PROPN
ejpam-4043	103	13	=	=	SYM
ejpam-4043	103	14	0	0	NUM
ejpam-4043	103	15	,	,	PUNCT
ejpam-4043	103	16	that	that	ADV
ejpam-4043	103	17	is	is	ADV
ejpam-4043	103	18	,	,	PUNCT
ejpam-4043	103	19	ξ1aa	ξ1aa	ADP
ejpam-4043	103	20	′	′	NUM
ejpam-4043	104	1	+	+	CCONJ
ejpam-4043	104	2	ξ2bb	ξ2bb	PUNCT
ejpam-4043	104	3	′	′	NUM
ejpam-4043	105	1	+	+	CCONJ
ejpam-4043	105	2	ξ3cc	ξ3cc	NOUN
ejpam-4043	105	3	′	′	NUM
ejpam-4043	106	1	+	+	CCONJ
ejpam-4043	107	1	ξ4dd	ξ4dd	ADJ
ejpam-4043	107	2	′	′	NUM
ejpam-4043	107	3	=	=	SYM
ejpam-4043	107	4	0	0	NUM
ejpam-4043	107	5	,	,	PUNCT
ejpam-4043	107	6	it	it	PRON
ejpam-4043	107	7	follows	follow	VERB
ejpam-4043	107	8	that	that	SCONJ
ejpam-4043	107	9	aa	aa	INTJ
ejpam-4043	108	1	′	′	NUM
ejpam-4043	109	1	=	=	PUNCT
ejpam-4043	110	1	bb	bb	NOUN
ejpam-4043	111	1	′	′	NUM
ejpam-4043	112	1	=	=	PUNCT
ejpam-4043	112	2	cc	cc	NOUN
ejpam-4043	112	3	′	′	NOUN
ejpam-4043	113	1	=	=	PUNCT
ejpam-4043	113	2	dd	dd	NOUN
ejpam-4043	114	1	′	′	NUM
ejpam-4043	114	2	=	=	NOUN
ejpam-4043	114	3	0	0	X
ejpam-4043	114	4	.	.	PUNCT
ejpam-4043	115	1	now	now	ADV
ejpam-4043	115	2	,	,	PUNCT
ejpam-4043	115	3	applying	apply	VERB
ejpam-4043	115	4	ϕ	ϕ	NOUN
ejpam-4043	115	5	on	on	ADP
ejpam-4043	115	6	η1	η1	NOUN
ejpam-4043	115	7	,	,	PUNCT
ejpam-4043	115	8	η2	η2	NOUN
ejpam-4043	115	9	,	,	PUNCT
ejpam-4043	115	10	we	we	PRON
ejpam-4043	115	11	have	have	VERB
ejpam-4043	115	12	ϕ(η1	ϕ(η1	ADV
ejpam-4043	115	13	)	)	PUNCT
ejpam-4043	116	1	=	=	PRON
ejpam-4043	116	2	(	(	PUNCT
ejpam-4043	116	3	a+b+c+d	a+b+c+d	PROPN
ejpam-4043	116	4	,	,	PUNCT
ejpam-4043	116	5	a	a	DET
ejpam-4043	116	6	-	-	PUNCT
ejpam-4043	116	7	b+cd	b+cd	ADJ
ejpam-4043	116	8	,	,	PUNCT
ejpam-4043	116	9	a+b	a+b	NUM
ejpam-4043	116	10	-	-	SYM
ejpam-4043	116	11	c	c	NOUN
ejpam-4043	116	12	-	-	PUNCT
ejpam-4043	116	13	d	d	NOUN
ejpam-4043	116	14	,	,	PUNCT
ejpam-4043	116	15	a	a	PRON
ejpam-4043	116	16	-	-	PUNCT
ejpam-4043	116	17	b	b	NOUN
ejpam-4043	116	18	-	-	PUNCT
ejpam-4043	116	19	c+d	c+d	PROPN
ejpam-4043	116	20	)	)	PUNCT
ejpam-4043	116	21	and	and	CCONJ
ejpam-4043	116	22	ϕ(η2	ϕ(η2	NOUN
ejpam-4043	116	23	)	)	PUNCT
ejpam-4043	117	1	=	=	PRON
ejpam-4043	117	2	(	(	PUNCT
ejpam-4043	117	3	a	a	PRON
ejpam-4043	117	4	′	′	NUM
ejpam-4043	118	1	+	+	NOUN
ejpam-4043	118	2	b	b	NOUN
ejpam-4043	118	3	′	′	NUM
ejpam-4043	119	1	+	+	NOUN
ejpam-4043	119	2	c	c	NOUN
ejpam-4043	119	3	′	′	NOUN
ejpam-4043	120	1	+	+	ADP
ejpam-4043	120	2	d	d	NOUN
ejpam-4043	120	3	′	′	NOUN
ejpam-4043	120	4	,	,	PUNCT
ejpam-4043	120	5	a	a	DET
ejpam-4043	120	6	′−b′+c′−d′	′−b′+c′−d′	NOUN
ejpam-4043	120	7	,	,	PUNCT
ejpam-4043	120	8	a′+b′−c′−d′	a′+b′−c′−d′	PROPN
ejpam-4043	120	9	,	,	PUNCT
ejpam-4043	120	10	a′−b′−c′+d′	a′−b′−c′+d′	CCONJ
ejpam-4043	120	11	)	)	PUNCT
ejpam-4043	120	12	and	and	CCONJ
ejpam-4043	120	13	hence	hence	ADV
ejpam-4043	120	14	ϕ(η1).ϕ(η2	ϕ(η1).ϕ(η2	NUM
ejpam-4043	120	15	)	)	PUNCT
ejpam-4043	121	1	=	=	PUNCT
ejpam-4043	122	1	4a.a	4a.a	NUM
ejpam-4043	123	1	′	′	NOUN
ejpam-4043	123	2	+4bb′+4cc′+4dd′	+4bb′+4cc′+4dd′	PROPN
ejpam-4043	124	1	=	=	PUNCT
ejpam-4043	124	2	0	0	PROPN
ejpam-4043	124	3	that	that	PRON
ejpam-4043	124	4	implies	imply	VERB
ejpam-4043	124	5	ϕ(k	ϕ(k	NOUN
ejpam-4043	124	6	)	)	PUNCT
ejpam-4043	124	7	is	be	AUX
ejpam-4043	124	8	self	self	NOUN
ejpam-4043	124	9	orthogonal	orthogonal	ADJ
ejpam-4043	124	10	.	.	PUNCT
ejpam-4043	125	1	proposition	proposition	NOUN
ejpam-4043	125	2	4	4	NUM
ejpam-4043	125	3	.	.	PUNCT
ejpam-4043	126	1	[	[	X
ejpam-4043	126	2	7	7	X
ejpam-4043	126	3	]	]	X
ejpam-4043	126	4	let	let	VERB
ejpam-4043	126	5	k	k	PRON
ejpam-4043	126	6	be	be	AUX
ejpam-4043	126	7	a	a	DET
ejpam-4043	126	8	linear	linear	ADJ
ejpam-4043	126	9	code	code	NOUN
ejpam-4043	126	10	over	over	ADP
ejpam-4043	126	11	the	the	DET
ejpam-4043	126	12	ring	ring	NOUN
ejpam-4043	126	13	<	<	X
ejpam-4043	126	14	of	of	ADP
ejpam-4043	126	15	length	length	NOUN
ejpam-4043	126	16	n.	n.	PROPN
ejpam-4043	126	17	then	then	ADV
ejpam-4043	126	18	ϕ(k⊥	ϕ(k⊥	PROPN
ejpam-4043	126	19	)	)	PUNCT
ejpam-4043	127	1	=	=	SYM
ejpam-4043	127	2	(	(	PUNCT
ejpam-4043	127	3	ϕ(k))⊥.	ϕ(k))⊥.	NOUN
ejpam-4043	127	4	further	far	ADV
ejpam-4043	127	5	,	,	PUNCT
ejpam-4043	127	6	k	k	PROPN
ejpam-4043	127	7	is	be	AUX
ejpam-4043	127	8	self	self	NOUN
ejpam-4043	127	9	dual	dual	ADJ
ejpam-4043	127	10	if	if	SCONJ
ejpam-4043	127	11	and	and	CCONJ
ejpam-4043	127	12	only	only	ADV
ejpam-4043	127	13	if	if	SCONJ
ejpam-4043	127	14	ϕ(k	ϕ(k	NOUN
ejpam-4043	127	15	)	)	PUNCT
ejpam-4043	127	16	is	be	AUX
ejpam-4043	127	17	self	self	NOUN
ejpam-4043	127	18	dual	dual	ADJ
ejpam-4043	127	19	.	.	PUNCT
ejpam-4043	128	1	4	4	X
ejpam-4043	128	2	.	.	X
ejpam-4043	128	3	quantum	quantum	NOUN
ejpam-4043	128	4	codes	code	NOUN
ejpam-4043	128	5	obtained	obtain	VERB
ejpam-4043	128	6	through	through	ADP
ejpam-4043	128	7	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	128	8	codes	code	NOUN
ejpam-4043	128	9	let	let	VERB
ejpam-4043	128	10	s′is	s′is	PRON
ejpam-4043	128	11	be	be	AUX
ejpam-4043	128	12	the	the	DET
ejpam-4043	128	13	linear	linear	ADJ
ejpam-4043	128	14	codes	code	NOUN
ejpam-4043	128	15	for	for	ADP
ejpam-4043	128	16	i	i	PROPN
ejpam-4043	128	17	=	=	NOUN
ejpam-4043	128	18	1	1	NUM
ejpam-4043	128	19	,	,	PUNCT
ejpam-4043	128	20	2	2	NUM
ejpam-4043	128	21	,	,	PUNCT
ejpam-4043	128	22	3	3	NUM
ejpam-4043	128	23	,	,	PUNCT
ejpam-4043	128	24	4	4	NUM
ejpam-4043	128	25	.	.	X
ejpam-4043	129	1	we	we	PRON
ejpam-4043	129	2	denote	denote	VERB
ejpam-4043	129	3	s1	s1	PROPN
ejpam-4043	129	4	⊕	⊕	PROPN
ejpam-4043	129	5	s2	s2	PROPN
ejpam-4043	129	6	⊕	⊕	PROPN
ejpam-4043	129	7	s3	s3	PROPN
ejpam-4043	129	8	⊕	⊕	PROPN
ejpam-4043	129	9	s4	s4	PROPN
ejpam-4043	129	10	=	=	SYM
ejpam-4043	129	11	{	{	PUNCT
ejpam-4043	129	12	s1	s1	NOUN
ejpam-4043	129	13	+	+	CCONJ
ejpam-4043	129	14	s2	s2	NOUN
ejpam-4043	129	15	+	+	CCONJ
ejpam-4043	129	16	s3	s3	PROPN
ejpam-4043	129	17	+	+	CCONJ
ejpam-4043	129	18	s4	s4	PROPN
ejpam-4043	130	1	|	|	ADV
ejpam-4043	130	2	si	si	PROPN
ejpam-4043	130	3	∈	∈	PROPN
ejpam-4043	130	4	si	si	X
ejpam-4043	130	5	for	for	ADP
ejpam-4043	130	6	i	i	PROPN
ejpam-4043	130	7	=	=	NOUN
ejpam-4043	130	8	1	1	NUM
ejpam-4043	130	9	,	,	PUNCT
ejpam-4043	130	10	2	2	NUM
ejpam-4043	130	11	,	,	PUNCT
ejpam-4043	130	12	3	3	NUM
ejpam-4043	130	13	,	,	PUNCT
ejpam-4043	130	14	4	4	NUM
ejpam-4043	130	15	}	}	PUNCT
ejpam-4043	130	16	and	and	CCONJ
ejpam-4043	130	17	s1	s1	PROPN
ejpam-4043	130	18	⊗	⊗	PROPN
ejpam-4043	130	19	s2	s2	PROPN
ejpam-4043	130	20	⊗	⊗	PROPN
ejpam-4043	130	21	s3	s3	PROPN
ejpam-4043	130	22	⊗	⊗	PROPN
ejpam-4043	130	23	s4	s4	PROPN
ejpam-4043	130	24	=	=	SYM
ejpam-4043	130	25	{	{	PUNCT
ejpam-4043	130	26	(	(	PUNCT
ejpam-4043	130	27	s1	s1	NOUN
ejpam-4043	130	28	,	,	PUNCT
ejpam-4043	130	29	s2	s2	PROPN
ejpam-4043	130	30	,	,	PUNCT
ejpam-4043	130	31	s3	s3	PROPN
ejpam-4043	130	32	,	,	PUNCT
ejpam-4043	130	33	s4	s4	PROPN
ejpam-4043	130	34	)	)	PUNCT
ejpam-4043	131	1	|	|	ADV
ejpam-4043	131	2	si	si	PROPN
ejpam-4043	131	3	∈	∈	PROPN
ejpam-4043	131	4	si	si	X
ejpam-4043	131	5	for	for	ADP
ejpam-4043	131	6	i	i	PROPN
ejpam-4043	131	7	=	=	NOUN
ejpam-4043	131	8	1	1	NUM
ejpam-4043	131	9	,	,	PUNCT
ejpam-4043	131	10	2	2	NUM
ejpam-4043	131	11	,	,	PUNCT
ejpam-4043	131	12	3	3	NUM
ejpam-4043	131	13	,	,	PUNCT
ejpam-4043	131	14	4	4	NUM
ejpam-4043	131	15	}	}	PUNCT
ejpam-4043	131	16	prateek	prateek	ADJ
ejpam-4043	131	17	mor	mor	PROPN
ejpam-4043	131	18	et	et	PROPN
ejpam-4043	131	19	al	al	PROPN
ejpam-4043	131	20	.	.	PUNCT
ejpam-4043	131	21	/	/	SYM
ejpam-4043	131	22	eur	eur	PROPN
ejpam-4043	131	23	.	.	PUNCT
ejpam-4043	132	1	j.	j.	PROPN
ejpam-4043	132	2	pure	pure	PROPN
ejpam-4043	132	3	appl	appl	PROPN
ejpam-4043	132	4	.	.	PROPN
ejpam-4043	132	5	math	math	PROPN
ejpam-4043	132	6	,	,	PUNCT
ejpam-4043	132	7	14	14	NUM
ejpam-4043	132	8	(	(	PUNCT
ejpam-4043	132	9	3	3	NUM
ejpam-4043	132	10	)	)	PUNCT
ejpam-4043	132	11	(	(	PUNCT
ejpam-4043	132	12	2021	2021	NUM
ejpam-4043	132	13	)	)	PUNCT
ejpam-4043	132	14	,	,	PUNCT
ejpam-4043	132	15	1082	1082	NUM
ejpam-4043	132	16	-	-	SYM
ejpam-4043	132	17	1097	1097	NUM
ejpam-4043	132	18	1086	1086	NUM
ejpam-4043	132	19	for	for	ADP
ejpam-4043	132	20	a	a	DET
ejpam-4043	132	21	linear	linear	ADJ
ejpam-4043	132	22	code	code	NOUN
ejpam-4043	133	1	k	k	PROPN
ejpam-4043	133	2	of	of	ADP
ejpam-4043	133	3	length	length	NOUN
ejpam-4043	133	4	n	n	CCONJ
ejpam-4043	133	5	over	over	ADP
ejpam-4043	133	6	<	<	X
ejpam-4043	133	7	,	,	PUNCT
ejpam-4043	133	8	we	we	PRON
ejpam-4043	133	9	define	define	VERB
ejpam-4043	133	10	k∞	k∞	PROPN
ejpam-4043	133	11	=	=	PRON
ejpam-4043	133	12	{	{	PUNCT
ejpam-4043	133	13	s1	s1	PROPN
ejpam-4043	133	14	+	+	CCONJ
ejpam-4043	133	15	s2	s2	NOUN
ejpam-4043	133	16	+	+	CCONJ
ejpam-4043	133	17	s3	s3	PROPN
ejpam-4043	133	18	+	+	CCONJ
ejpam-4043	133	19	s4	s4	PROPN
ejpam-4043	133	20	∈	∈	PROPN
ejpam-4043	133	21	zn	zn	PROPN
ejpam-4043	133	22	3	3	NUM
ejpam-4043	133	23	such	such	ADJ
ejpam-4043	133	24	that	that	DET
ejpam-4043	133	25	s1	s1	NOUN
ejpam-4043	133	26	+	+	CCONJ
ejpam-4043	133	27	s2ν	s2ν	PROPN
ejpam-4043	133	28	+	+	CCONJ
ejpam-4043	133	29	s3ω	s3ω	PROPN
ejpam-4043	133	30	+	+	CCONJ
ejpam-4043	133	31	s4νω	s4νω	PUNCT
ejpam-4043	133	32	∈	∈	PROPN
ejpam-4043	133	33	k	k	NOUN
ejpam-4043	133	34	}	}	PUNCT
ejpam-4043	133	35	,	,	PUNCT
ejpam-4043	133	36	k∈	k∈	PROPN
ejpam-4043	133	37	=	=	PUNCT
ejpam-4043	133	38	{	{	PUNCT
ejpam-4043	133	39	s1	s1	PROPN
ejpam-4043	133	40	−	−	PROPN
ejpam-4043	133	41	s2	s2	NOUN
ejpam-4043	133	42	+	+	CCONJ
ejpam-4043	133	43	s3	s3	PROPN
ejpam-4043	133	44	−	−	PROPN
ejpam-4043	133	45	s4	s4	PROPN
ejpam-4043	133	46	∈	∈	PROPN
ejpam-4043	133	47	zn	zn	PROPN
ejpam-4043	133	48	3	3	NUM
ejpam-4043	133	49	such	such	ADJ
ejpam-4043	133	50	that	that	DET
ejpam-4043	133	51	s1	s1	NOUN
ejpam-4043	133	52	+	+	CCONJ
ejpam-4043	133	53	s2ν	s2ν	PROPN
ejpam-4043	133	54	+	+	CCONJ
ejpam-4043	133	55	s3ω	s3ω	PROPN
ejpam-4043	133	56	+	+	CCONJ
ejpam-4043	133	57	s4νω	s4νω	PUNCT
ejpam-4043	133	58	∈	∈	PROPN
ejpam-4043	133	59	k	k	NOUN
ejpam-4043	133	60	}	}	PUNCT
ejpam-4043	133	61	,	,	PUNCT
ejpam-4043	133	62	k3	k3	PROPN
ejpam-4043	133	63	=	=	SYM
ejpam-4043	133	64	{	{	PUNCT
ejpam-4043	133	65	s1	s1	NOUN
ejpam-4043	133	66	+	+	CCONJ
ejpam-4043	133	67	s2	s2	PROPN
ejpam-4043	133	68	−	−	PROPN
ejpam-4043	133	69	s3	s3	PROPN
ejpam-4043	133	70	−	−	PROPN
ejpam-4043	133	71	s4	s4	PROPN
ejpam-4043	133	72	∈	∈	PROPN
ejpam-4043	133	73	zn	zn	PROPN
ejpam-4043	133	74	3	3	NUM
ejpam-4043	133	75	such	such	ADJ
ejpam-4043	133	76	that	that	DET
ejpam-4043	133	77	s1	s1	NOUN
ejpam-4043	133	78	+	+	CCONJ
ejpam-4043	133	79	s2ν	s2ν	PROPN
ejpam-4043	133	80	+	+	CCONJ
ejpam-4043	133	81	s3ω	s3ω	PROPN
ejpam-4043	133	82	+	+	CCONJ
ejpam-4043	133	83	s4νω	s4νω	PUNCT
ejpam-4043	133	84	∈	∈	PROPN
ejpam-4043	133	85	k	k	NOUN
ejpam-4043	133	86	}	}	PUNCT
ejpam-4043	133	87	,	,	PUNCT
ejpam-4043	133	88	k4	k4	NOUN
ejpam-4043	133	89	=	=	SYM
ejpam-4043	133	90	{	{	PUNCT
ejpam-4043	133	91	s1	s1	PROPN
ejpam-4043	133	92	−	−	PROPN
ejpam-4043	133	93	s2	s2	PROPN
ejpam-4043	133	94	−	−	PROPN
ejpam-4043	133	95	s3	s3	PROPN
ejpam-4043	133	96	+	+	CCONJ
ejpam-4043	133	97	s4	s4	PROPN
ejpam-4043	133	98	∈	∈	PROPN
ejpam-4043	133	99	zn	zn	PROPN
ejpam-4043	133	100	3	3	NUM
ejpam-4043	133	101	such	such	ADJ
ejpam-4043	133	102	that	that	DET
ejpam-4043	133	103	s1	s1	NOUN
ejpam-4043	133	104	+	+	CCONJ
ejpam-4043	133	105	s2ν	s2ν	PROPN
ejpam-4043	133	106	+	+	CCONJ
ejpam-4043	133	107	s3ω	s3ω	PROPN
ejpam-4043	133	108	+	+	CCONJ
ejpam-4043	133	109	s4νω	s4νω	PUNCT
ejpam-4043	133	110	∈	∈	PROPN
ejpam-4043	133	111	k	k	NOUN
ejpam-4043	133	112	}	}	PUNCT
ejpam-4043	133	113	.	.	PUNCT
ejpam-4043	134	1	clearly	clearly	ADV
ejpam-4043	134	2	,	,	PUNCT
ejpam-4043	134	3	k∞	k∞	PROPN
ejpam-4043	134	4	,	,	PUNCT
ejpam-4043	134	5	k∈	k∈	PROPN
ejpam-4043	134	6	,	,	PUNCT
ejpam-4043	134	7	k3	k3	VERB
ejpam-4043	134	8	and	and	CCONJ
ejpam-4043	134	9	k4	k4	NOUN
ejpam-4043	134	10	are	be	AUX
ejpam-4043	134	11	the	the	DET
ejpam-4043	134	12	linear	linear	ADJ
ejpam-4043	134	13	codes	code	NOUN
ejpam-4043	134	14	over	over	ADP
ejpam-4043	134	15	z3	z3	PROPN
ejpam-4043	134	16	of	of	ADP
ejpam-4043	134	17	length	length	PROPN
ejpam-4043	134	18	n.	n.	PROPN
ejpam-4043	134	19	theorem	theorem	VERB
ejpam-4043	134	20	5	5	NUM
ejpam-4043	134	21	.	.	PUNCT
ejpam-4043	135	1	[	[	X
ejpam-4043	135	2	7	7	X
ejpam-4043	135	3	]	]	X
ejpam-4043	135	4	let	let	VERB
ejpam-4043	135	5	k	k	PRON
ejpam-4043	135	6	be	be	AUX
ejpam-4043	135	7	a	a	DET
ejpam-4043	135	8	linear	linear	ADJ
ejpam-4043	135	9	code	code	NOUN
ejpam-4043	135	10	over	over	ADP
ejpam-4043	135	11	the	the	DET
ejpam-4043	135	12	ring	ring	NOUN
ejpam-4043	135	13	<	<	X
ejpam-4043	135	14	of	of	ADP
ejpam-4043	135	15	length	length	NOUN
ejpam-4043	135	16	n.	n.	PROPN
ejpam-4043	135	17	then	then	ADV
ejpam-4043	135	18	ϕ(k	ϕ(k	NOUN
ejpam-4043	135	19	)	)	PUNCT
ejpam-4043	136	1	=	=	SYM
ejpam-4043	136	2	k∞	k∞	PROPN
ejpam-4043	137	1	⊗	⊗	PROPN
ejpam-4043	137	2	k∈	k∈	PROPN
ejpam-4043	137	3	⊗	⊗	PROPN
ejpam-4043	137	4	k3	k3	VERB
ejpam-4043	137	5	⊗	⊗	PROPN
ejpam-4043	137	6	k4	k4	NOUN
ejpam-4043	137	7	and	and	CCONJ
ejpam-4043	137	8	|k|=	|k|=	NOUN
ejpam-4043	137	9	|k∞||k∈||k3|k4|	|k∞||k∈||k3|k4|	PROPN
ejpam-4043	137	10	.	.	NOUN
ejpam-4043	137	11	corollary	corollary	ADJ
ejpam-4043	137	12	6	6	NUM
ejpam-4043	137	13	.	.	PUNCT
ejpam-4043	138	1	[	[	X
ejpam-4043	138	2	7	7	X
ejpam-4043	138	3	]	]	X
ejpam-4043	138	4	if	if	SCONJ
ejpam-4043	138	5	ϕ(k	ϕ(k	NOUN
ejpam-4043	138	6	)	)	PUNCT
ejpam-4043	139	1	=	=	SYM
ejpam-4043	139	2	k∞	k∞	PROPN
ejpam-4043	140	1	⊗	⊗	PROPN
ejpam-4043	140	2	k∈	k∈	PROPN
ejpam-4043	140	3	⊗	⊗	PROPN
ejpam-4043	140	4	k3	k3	VERB
ejpam-4043	140	5	⊗	⊗	PROPN
ejpam-4043	140	6	k4	k4	PROPN
ejpam-4043	140	7	then	then	ADV
ejpam-4043	140	8	k=	k=	PROPN
ejpam-4043	141	1	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	141	2	⊕	⊕	PROPN
ejpam-4043	141	3	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	142	1	⊕	⊕	PROPN
ejpam-4043	142	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	142	3	⊕	⊕	PROPN
ejpam-4043	142	4	ξ4k4	ξ4k4	PUNCT
ejpam-4043	143	1	by	by	ADP
ejpam-4043	143	2	the	the	DET
ejpam-4043	143	3	help	help	NOUN
ejpam-4043	143	4	of	of	ADP
ejpam-4043	143	5	theorem	theorem	ADJ
ejpam-4043	143	6	4.1	4.1	NUM
ejpam-4043	143	7	and	and	CCONJ
ejpam-4043	143	8	corollary	corollary	ADJ
ejpam-4043	143	9	4.2	4.2	NUM
ejpam-4043	143	10	,	,	PUNCT
ejpam-4043	143	11	we	we	PRON
ejpam-4043	143	12	say	say	VERB
ejpam-4043	143	13	that	that	SCONJ
ejpam-4043	143	14	the	the	DET
ejpam-4043	143	15	linear	linear	PROPN
ejpam-4043	143	16	code	code	NOUN
ejpam-4043	143	17	k	k	PROPN
ejpam-4043	143	18	can	can	AUX
ejpam-4043	143	19	be	be	AUX
ejpam-4043	143	20	uniquely	uniquely	ADV
ejpam-4043	143	21	expressed	express	VERB
ejpam-4043	143	22	as	as	ADP
ejpam-4043	143	23	k	k	PROPN
ejpam-4043	143	24	=	=	PROPN
ejpam-4043	143	25	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	143	26	⊕	⊕	PROPN
ejpam-4043	143	27	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	144	1	⊕	⊕	PROPN
ejpam-4043	144	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	144	3	⊕	⊕	PROPN
ejpam-4043	144	4	ξ4k4	ξ4k4	PROPN
ejpam-4043	144	5	and	and	CCONJ
ejpam-4043	144	6	also	also	ADV
ejpam-4043	144	7	|k|	|k|	PROPN
ejpam-4043	144	8	=	=	SYM
ejpam-4043	144	9	|k∞||k∈||k3|k4|	|k∞||k∈||k3|k4|	PROPN
ejpam-4043	144	10	.	.	PUNCT
ejpam-4043	145	1	if	if	SCONJ
ejpam-4043	145	2	g1	g1	NOUN
ejpam-4043	145	3	,	,	PUNCT
ejpam-4043	145	4	g2	g2	PROPN
ejpam-4043	145	5	,	,	PUNCT
ejpam-4043	145	6	g3	g3	NOUN
ejpam-4043	145	7	and	and	CCONJ
ejpam-4043	145	8	g4	g4	NOUN
ejpam-4043	145	9	,	,	PUNCT
ejpam-4043	145	10	are	be	AUX
ejpam-4043	145	11	the	the	DET
ejpam-4043	145	12	generator	generator	NOUN
ejpam-4043	145	13	matrices	matrix	NOUN
ejpam-4043	145	14	of	of	ADP
ejpam-4043	145	15	the	the	DET
ejpam-4043	145	16	linear	linear	PROPN
ejpam-4043	145	17	codes	code	NOUN
ejpam-4043	145	18	k∞	k∞	PROPN
ejpam-4043	145	19	,	,	PUNCT
ejpam-4043	145	20	k∈	k∈	PROPN
ejpam-4043	145	21	,	,	PUNCT
ejpam-4043	145	22	k3	k3	X
ejpam-4043	145	23	,	,	PUNCT
ejpam-4043	145	24	and	and	CCONJ
ejpam-4043	145	25	k4	k4	VERB
ejpam-4043	145	26	respectively	respectively	ADV
ejpam-4043	145	27	.	.	PUNCT
ejpam-4043	146	1	then	then	ADV
ejpam-4043	146	2	,	,	PUNCT
ejpam-4043	146	3	the	the	DET
ejpam-4043	146	4	generator	generator	NOUN
ejpam-4043	146	5	matrix	matrix	NOUN
ejpam-4043	146	6	of	of	ADP
ejpam-4043	146	7	k	k	PROPN
ejpam-4043	146	8	is	be	AUX
ejpam-4043	146	9	g	g	NOUN
ejpam-4043	146	10	=	=	PUNCT
ejpam-4043	146	11	[	[	PUNCT
ejpam-4043	146	12	ξ1g1	ξ1g1	PROPN
ejpam-4043	146	13	ξ2g2	ξ2g2	INTJ
ejpam-4043	146	14	ξ3g3	ξ3g3	PROPN
ejpam-4043	146	15	ξ4g4	ξ4g4	PROPN
ejpam-4043	146	16	]	]	X
ejpam-4043	146	17	t	t	NOUN
ejpam-4043	146	18	,	,	PUNCT
ejpam-4043	146	19	and	and	CCONJ
ejpam-4043	146	20	that	that	PRON
ejpam-4043	146	21	of	of	ADP
ejpam-4043	146	22	ϕ(k	ϕ(k	PROPN
ejpam-4043	146	23	)	)	PUNCT
ejpam-4043	146	24	is	be	AUX
ejpam-4043	146	25	ϕ(g	ϕ(g	PROPN
ejpam-4043	146	26	)	)	PUNCT
ejpam-4043	147	1	=	=	PRON
ejpam-4043	147	2	[	[	PUNCT
ejpam-4043	147	3	ϕ(ξ1g1	ϕ(ξ1g1	NOUN
ejpam-4043	147	4	)	)	PUNCT
ejpam-4043	147	5	ϕ(ξ2g2	ϕ(ξ2g2	PROPN
ejpam-4043	147	6	)	)	PUNCT
ejpam-4043	147	7	ϕ(ξ3g3	ϕ(ξ3g3	PROPN
ejpam-4043	147	8	)	)	PUNCT
ejpam-4043	147	9	ϕ(ξ4g4	ϕ(ξ4g4	NOUN
ejpam-4043	147	10	)	)	PUNCT
ejpam-4043	148	1	]	]	PUNCT
ejpam-4043	148	2	t	t	PROPN
ejpam-4043	148	3	note	note	NOUN
ejpam-4043	148	4	:	:	PUNCT
ejpam-4043	148	5	now	now	ADV
ejpam-4043	148	6	,	,	PUNCT
ejpam-4043	148	7	we	we	PRON
ejpam-4043	148	8	consider	consider	VERB
ejpam-4043	148	9	different	different	ADJ
ejpam-4043	148	10	case	case	NOUN
ejpam-4043	148	11	of	of	ADP
ejpam-4043	148	12	ϑ.	ϑ.	NOUN
ejpam-4043	148	13	case	case	NOUN
ejpam-4043	148	14	1	1	NUM
ejpam-4043	148	15	.	.	PUNCT
ejpam-4043	149	1	ϑ	ϑ	X
ejpam-4043	149	2	=	=	SYM
ejpam-4043	149	3	1	1	NUM
ejpam-4043	149	4	+	+	CCONJ
ejpam-4043	149	5	ν	ν	X
ejpam-4043	149	6	+	+	X
ejpam-4043	149	7	ω	ω	NUM
ejpam-4043	149	8	+	+	CCONJ
ejpam-4043	149	9	2νω	2νω	NOUN
ejpam-4043	149	10	theorem	theorem	ADJ
ejpam-4043	149	11	7	7	X
ejpam-4043	149	12	.	.	PUNCT
ejpam-4043	150	1	let	let	VERB
ejpam-4043	150	2	k	k	PROPN
ejpam-4043	150	3	=	=	SYM
ejpam-4043	150	4	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	150	5	⊕	⊕	PROPN
ejpam-4043	150	6	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	151	1	⊕	⊕	PROPN
ejpam-4043	151	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	151	3	⊕	⊕	PROPN
ejpam-4043	151	4	ξ4k4	ξ4k4	VERB
ejpam-4043	151	5	be	be	AUX
ejpam-4043	151	6	a	a	DET
ejpam-4043	151	7	linear	linear	ADJ
ejpam-4043	151	8	code	code	NOUN
ejpam-4043	151	9	over	over	ADP
ejpam-4043	151	10	the	the	DET
ejpam-4043	151	11	ring	ring	NOUN
ejpam-4043	151	12	<	<	X
ejpam-4043	151	13	of	of	ADP
ejpam-4043	151	14	length	length	NOUN
ejpam-4043	151	15	n	n	PROPN
ejpam-4043	151	16	where	where	SCONJ
ejpam-4043	151	17	k∞	k∞	PROPN
ejpam-4043	151	18	,	,	PUNCT
ejpam-4043	151	19	k∈	k∈	PROPN
ejpam-4043	151	20	,	,	PUNCT
ejpam-4043	151	21	k3	k3	PROPN
ejpam-4043	151	22	,	,	PUNCT
ejpam-4043	151	23	k4	k4	PROPN
ejpam-4043	151	24	are	be	AUX
ejpam-4043	151	25	the	the	DET
ejpam-4043	151	26	linear	linear	ADJ
ejpam-4043	151	27	codes	code	NOUN
ejpam-4043	151	28	over	over	ADP
ejpam-4043	151	29	z3	z3	PROPN
ejpam-4043	151	30	.	.	PUNCT
ejpam-4043	152	1	then	then	ADV
ejpam-4043	152	2	,	,	PUNCT
ejpam-4043	152	3	k	k	PROPN
ejpam-4043	152	4	is	be	AUX
ejpam-4043	152	5	a	a	DET
ejpam-4043	152	6	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	152	7	code	code	NOUN
ejpam-4043	152	8	over	over	ADP
ejpam-4043	152	9	the	the	DET
ejpam-4043	152	10	ring	ring	NOUN
ejpam-4043	152	11	<	<	X
ejpam-4043	152	12	of	of	ADP
ejpam-4043	152	13	length	length	NOUN
ejpam-4043	152	14	n	n	CCONJ
ejpam-4043	152	15	if	if	SCONJ
ejpam-4043	153	1	and	and	CCONJ
ejpam-4043	153	2	only	only	ADV
ejpam-4043	153	3	if	if	SCONJ
ejpam-4043	153	4	k∞	k∞	PROPN
ejpam-4043	153	5	,	,	PUNCT
ejpam-4043	153	6	k∈	k∈	PROPN
ejpam-4043	153	7	,	,	PUNCT
ejpam-4043	153	8	k3	k3	NOUN
ejpam-4043	153	9	are	be	AUX
ejpam-4043	153	10	negacyclic	negacyclic	ADJ
ejpam-4043	153	11	codes	code	NOUN
ejpam-4043	153	12	and	and	CCONJ
ejpam-4043	153	13	k4	k4	NOUN
ejpam-4043	153	14	is	be	AUX
ejpam-4043	153	15	cyclic	cyclic	ADJ
ejpam-4043	153	16	code	code	NOUN
ejpam-4043	153	17	over	over	ADP
ejpam-4043	153	18	z3	z3	PROPN
ejpam-4043	153	19	of	of	ADP
ejpam-4043	153	20	length	length	NOUN
ejpam-4043	153	21	n.	n.	PROPN
ejpam-4043	153	22	proof	proof	NOUN
ejpam-4043	153	23	.	.	PUNCT
ejpam-4043	154	1	let	let	VERB
ejpam-4043	154	2	,	,	PUNCT
ejpam-4043	154	3	ȧ	ȧ	PROPN
ejpam-4043	154	4	=	=	X
ejpam-4043	154	5	(	(	PUNCT
ejpam-4043	154	6	ȧ0	ȧ0	PROPN
ejpam-4043	154	7	,	,	PUNCT
ejpam-4043	154	8	ȧ1	ȧ1	PROPN
ejpam-4043	154	9	,	,	PUNCT
ejpam-4043	154	10	...	...	PUNCT
ejpam-4043	154	11	,	,	PUNCT
ejpam-4043	154	12	˙an−1	˙an−1	NUM
ejpam-4043	154	13	)	)	PUNCT
ejpam-4043	154	14	∈	∈	PROPN
ejpam-4043	154	15	k∞	k∞	PROPN
ejpam-4043	154	16	,	,	PUNCT
ejpam-4043	154	17	ḃ	ḃ	PROPN
ejpam-4043	155	1	=	=	PRON
ejpam-4043	155	2	(	(	PUNCT
ejpam-4043	155	3	ḃ0	ḃ0	PROPN
ejpam-4043	155	4	,	,	PUNCT
ejpam-4043	155	5	ḃ1	ḃ1	PROPN
ejpam-4043	155	6	,	,	PUNCT
ejpam-4043	155	7	...	...	PUNCT
ejpam-4043	155	8	,	,	PUNCT
ejpam-4043	155	9	˙bn−1	˙bn−1	X
ejpam-4043	155	10	)	)	PUNCT
ejpam-4043	155	11	∈	∈	PROPN
ejpam-4043	155	12	k∈	k∈	PROPN
ejpam-4043	155	13	,	,	PUNCT
ejpam-4043	155	14	ċ	ċ	NOUN
ejpam-4043	155	15	=	=	SYM
ejpam-4043	155	16	(	(	PUNCT
ejpam-4043	155	17	ċ0	ċ0	PROPN
ejpam-4043	155	18	,	,	PUNCT
ejpam-4043	155	19	ċ1	ċ1	PROPN
ejpam-4043	155	20	,	,	PUNCT
ejpam-4043	155	21	...	...	PUNCT
ejpam-4043	155	22	,	,	PUNCT
ejpam-4043	155	23	˙cn−1	˙cn−1	X
ejpam-4043	155	24	)	)	PUNCT
ejpam-4043	155	25	∈	∈	PROPN
ejpam-4043	155	26	k3	k3	PROPN
ejpam-4043	155	27	,	,	PUNCT
ejpam-4043	155	28	ḋ	ḋ	PROPN
ejpam-4043	155	29	=	=	SYM
ejpam-4043	155	30	(	(	PUNCT
ejpam-4043	155	31	ḋ0	ḋ0	PROPN
ejpam-4043	155	32	,	,	PUNCT
ejpam-4043	155	33	ḋ1	ḋ1	PROPN
ejpam-4043	155	34	,	,	PUNCT
ejpam-4043	155	35	...	...	PUNCT
ejpam-4043	155	36	,	,	PUNCT
ejpam-4043	155	37	˙dn−1	˙dn−1	X
ejpam-4043	155	38	)	)	PUNCT
ejpam-4043	155	39	∈	∈	PROPN
ejpam-4043	155	40	k4	k4	PROPN
ejpam-4043	155	41	.	.	PUNCT
ejpam-4043	156	1	prateek	prateek	PROPN
ejpam-4043	156	2	mor	mor	PROPN
ejpam-4043	156	3	et	et	PROPN
ejpam-4043	156	4	al	al	PROPN
ejpam-4043	156	5	.	.	PUNCT
ejpam-4043	156	6	/	/	SYM
ejpam-4043	156	7	eur	eur	PROPN
ejpam-4043	156	8	.	.	PUNCT
ejpam-4043	157	1	j.	j.	PROPN
ejpam-4043	157	2	pure	pure	PROPN
ejpam-4043	157	3	appl	appl	PROPN
ejpam-4043	157	4	.	.	PROPN
ejpam-4043	157	5	math	math	PROPN
ejpam-4043	157	6	,	,	PUNCT
ejpam-4043	157	7	14	14	NUM
ejpam-4043	157	8	(	(	PUNCT
ejpam-4043	157	9	3	3	NUM
ejpam-4043	157	10	)	)	PUNCT
ejpam-4043	157	11	(	(	PUNCT
ejpam-4043	157	12	2021	2021	NUM
ejpam-4043	157	13	)	)	PUNCT
ejpam-4043	157	14	,	,	PUNCT
ejpam-4043	157	15	1082	1082	NUM
ejpam-4043	157	16	-	-	SYM
ejpam-4043	157	17	1097	1097	NUM
ejpam-4043	157	18	1087	1087	NUM
ejpam-4043	157	19	for	for	ADP
ejpam-4043	157	20	an	an	DET
ejpam-4043	157	21	arbitrary	arbitrary	ADJ
ejpam-4043	157	22	element	element	NOUN
ejpam-4043	157	23	ζi	ζi	PROPN
ejpam-4043	157	24	∈	∈	PROPN
ejpam-4043	157	25	k	k	NOUN
ejpam-4043	157	26	,	,	PUNCT
ejpam-4043	157	27	uniquely	uniquely	ADV
ejpam-4043	157	28	expressed	express	VERB
ejpam-4043	157	29	as	as	ADP
ejpam-4043	157	30	ζi	ζi	PROPN
ejpam-4043	157	31	=	=	SYM
ejpam-4043	157	32	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	157	33	+	+	CCONJ
ejpam-4043	157	34	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	157	35	+	+	CCONJ
ejpam-4043	157	36	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	157	37	+	+	CCONJ
ejpam-4043	157	38	ξ4ḋi	ξ4ḋi	NUM
ejpam-4043	157	39	,	,	PUNCT
ejpam-4043	157	40	where	where	SCONJ
ejpam-4043	157	41	ȧi	ȧi	PROPN
ejpam-4043	157	42	,	,	PUNCT
ejpam-4043	157	43	ḃi	ḃi	PROPN
ejpam-4043	157	44	,	,	PUNCT
ejpam-4043	157	45	ċi	ċi	PROPN
ejpam-4043	157	46	,	,	PUNCT
ejpam-4043	157	47	ḋi	ḋi	PROPN
ejpam-4043	157	48	∈	∈	PROPN
ejpam-4043	157	49	z3	z3	PROPN
ejpam-4043	157	50	for	for	ADP
ejpam-4043	157	51	i	i	PROPN
ejpam-4043	157	52	=	=	SYM
ejpam-4043	157	53	0	0	NUM
ejpam-4043	157	54	,	,	PUNCT
ejpam-4043	157	55	1	1	NUM
ejpam-4043	157	56	,	,	PUNCT
ejpam-4043	157	57	...	...	PUNCT
ejpam-4043	157	58	,	,	PUNCT
ejpam-4043	157	59	n−	n−	NOUN
ejpam-4043	157	60	1	1	NUM
ejpam-4043	157	61	.	.	PUNCT
ejpam-4043	158	1	let	let	VERB
ejpam-4043	158	2	,	,	PUNCT
ejpam-4043	158	3	ζ	ζ	NOUN
ejpam-4043	158	4	=	=	SYM
ejpam-4043	158	5	(	(	PUNCT
ejpam-4043	158	6	ζ0	ζ0	PROPN
ejpam-4043	158	7	,	,	PUNCT
ejpam-4043	158	8	ζ1	ζ1	NOUN
ejpam-4043	158	9	,	,	PUNCT
ejpam-4043	158	10	...	...	PUNCT
ejpam-4043	158	11	,	,	PUNCT
ejpam-4043	158	12	ζn−1	ζn−1	PROPN
ejpam-4043	158	13	)	)	PUNCT
ejpam-4043	158	14	∈	∈	PROPN
ejpam-4043	158	15	<	<	X
ejpam-4043	158	16	n.	n.	PROPN
ejpam-4043	158	17	first	first	ADV
ejpam-4043	158	18	we	we	PRON
ejpam-4043	158	19	assume	assume	VERB
ejpam-4043	158	20	that	that	SCONJ
ejpam-4043	158	21	k	k	PROPN
ejpam-4043	158	22	is	be	AUX
ejpam-4043	158	23	ϑ-constacyclic	ϑ-constacyclic	PROPN
ejpam-4043	158	24	code	code	NOUN
ejpam-4043	158	25	over	over	ADP
ejpam-4043	158	26	the	the	DET
ejpam-4043	158	27	ring	ring	NOUN
ejpam-4043	158	28	<	<	X
ejpam-4043	158	29	of	of	ADP
ejpam-4043	158	30	length	length	NOUN
ejpam-4043	158	31	n	n	CCONJ
ejpam-4043	158	32	,	,	PUNCT
ejpam-4043	158	33	then	then	ADV
ejpam-4043	158	34	f(ζ	f(ζ	NOUN
ejpam-4043	158	35	)	)	PUNCT
ejpam-4043	159	1	=	=	PRON
ejpam-4043	159	2	(	(	PUNCT
ejpam-4043	159	3	(	(	PUNCT
ejpam-4043	159	4	1	1	NUM
ejpam-4043	159	5	+	+	NUM
ejpam-4043	159	6	ν	ν	X
ejpam-4043	159	7	+	+	X
ejpam-4043	159	8	ω	ω	NOUN
ejpam-4043	159	9	+	+	CCONJ
ejpam-4043	159	10	2νω)ζn−1	2νω)ζn−1	NUM
ejpam-4043	159	11	,	,	PUNCT
ejpam-4043	159	12	ζ0	ζ0	ADJ
ejpam-4043	159	13	,	,	PUNCT
ejpam-4043	159	14	...	...	PUNCT
ejpam-4043	159	15	,	,	PUNCT
ejpam-4043	159	16	ζn−2	ζn−2	PROPN
ejpam-4043	159	17	)	)	PUNCT
ejpam-4043	159	18	=	=	PUNCT
ejpam-4043	159	19	(	(	PUNCT
ejpam-4043	159	20	−(1	−(1	NOUN
ejpam-4043	159	21	+	+	CCONJ
ejpam-4043	159	22	ν	ν	X
ejpam-4043	159	23	+	+	X
ejpam-4043	159	24	ω	ω	PROPN
ejpam-4043	159	25	+	+	CCONJ
ejpam-4043	159	26	νω	νω	PROPN
ejpam-4043	159	27	)	)	PUNCT
ejpam-4043	159	28	˙an−1	˙an−1	PROPN
ejpam-4043	159	29	−	−	PROPN
ejpam-4043	160	1	(	(	PUNCT
ejpam-4043	160	2	1−	1−	NUM
ejpam-4043	160	3	ν	ν	X
ejpam-4043	160	4	+	+	X
ejpam-4043	160	5	ω	ω	NUM
ejpam-4043	160	6	−	−	PROPN
ejpam-4043	160	7	νω	νω	PROPN
ejpam-4043	160	8	)	)	PUNCT
ejpam-4043	160	9	˙bn−1	˙bn−1	NOUN
ejpam-4043	161	1	−	−	PROPN
ejpam-4043	161	2	(	(	PUNCT
ejpam-4043	161	3	1	1	NUM
ejpam-4043	161	4	+	+	ADP
ejpam-4043	161	5	ν	ν	X
ejpam-4043	161	6	−	−	PROPN
ejpam-4043	161	7	ω	ω	NUM
ejpam-4043	161	8	−	−	PROPN
ejpam-4043	161	9	νω	νω	PROPN
ejpam-4043	161	10	)	)	PUNCT
ejpam-4043	161	11	˙cn−1	˙cn−1	PROPN
ejpam-4043	162	1	+	+	CCONJ
ejpam-4043	162	2	(	(	PUNCT
ejpam-4043	162	3	1−	1−	NUM
ejpam-4043	162	4	ν	ν	NOUN
ejpam-4043	162	5	−	−	PROPN
ejpam-4043	162	6	ω	ω	PROPN
ejpam-4043	162	7	+	+	CCONJ
ejpam-4043	162	8	νω	νω	PROPN
ejpam-4043	162	9	)	)	PUNCT
ejpam-4043	162	10	˙dn−1	˙dn−1	NUM
ejpam-4043	162	11	,	,	PUNCT
ejpam-4043	162	12	(	(	PUNCT
ejpam-4043	162	13	1	1	NUM
ejpam-4043	162	14	+	+	ADP
ejpam-4043	162	15	ν	ν	X
ejpam-4043	162	16	+	+	X
ejpam-4043	162	17	ω	ω	NUM
ejpam-4043	162	18	+	+	PUNCT
ejpam-4043	162	19	νω)ȧ0	νω)ȧ0	VERB
ejpam-4043	162	20	+	+	CCONJ
ejpam-4043	162	21	(	(	PUNCT
ejpam-4043	162	22	1−	1−	NUM
ejpam-4043	162	23	ν	ν	X
ejpam-4043	162	24	+	+	PROPN
ejpam-4043	162	25	ω	ω	PROPN
ejpam-4043	162	26	−	−	X
ejpam-4043	162	27	νω)ḃ0	νω)ḃ0	PROPN
ejpam-4043	163	1	+	+	CCONJ
ejpam-4043	163	2	(	(	PUNCT
ejpam-4043	163	3	1	1	NUM
ejpam-4043	163	4	+	+	ADP
ejpam-4043	163	5	ν	ν	X
ejpam-4043	163	6	−	−	PROPN
ejpam-4043	163	7	ω	ω	NUM
ejpam-4043	163	8	−	−	PROPN
ejpam-4043	163	9	νω)ċ0	νω)ċ0	PROPN
ejpam-4043	164	1	+	+	CCONJ
ejpam-4043	164	2	(	(	PUNCT
ejpam-4043	164	3	1−	1−	NUM
ejpam-4043	164	4	ν	ν	NOUN
ejpam-4043	164	5	−	−	PROPN
ejpam-4043	164	6	ω	ω	PROPN
ejpam-4043	164	7	+	+	PROPN
ejpam-4043	164	8	νω)ḋ0	νω)ḋ0	PROPN
ejpam-4043	164	9	,	,	PUNCT
ejpam-4043	164	10	...	...	PUNCT
ejpam-4043	164	11	,	,	PUNCT
ejpam-4043	164	12	(	(	PUNCT
ejpam-4043	164	13	1	1	NUM
ejpam-4043	164	14	+	+	ADP
ejpam-4043	164	15	ν	ν	X
ejpam-4043	164	16	+	+	X
ejpam-4043	164	17	ω	ω	PROPN
ejpam-4043	164	18	+	+	CCONJ
ejpam-4043	164	19	νω	νω	PROPN
ejpam-4043	164	20	)	)	PUNCT
ejpam-4043	164	21	˙an−2	˙an−2	PUNCT
ejpam-4043	165	1	+	+	CCONJ
ejpam-4043	165	2	(	(	PUNCT
ejpam-4043	165	3	1−	1−	NUM
ejpam-4043	165	4	ν	ν	X
ejpam-4043	165	5	+	+	X
ejpam-4043	165	6	ω	ω	NUM
ejpam-4043	165	7	−	−	PROPN
ejpam-4043	165	8	νω	νω	PROPN
ejpam-4043	165	9	)	)	PUNCT
ejpam-4043	165	10	˙bn−2	˙bn−2	PUNCT
ejpam-4043	166	1	+	+	CCONJ
ejpam-4043	166	2	(	(	PUNCT
ejpam-4043	166	3	1	1	NUM
ejpam-4043	166	4	+	+	ADP
ejpam-4043	166	5	ν	ν	X
ejpam-4043	166	6	−	−	PROPN
ejpam-4043	166	7	ω	ω	NUM
ejpam-4043	166	8	−	−	PROPN
ejpam-4043	166	9	νω	νω	PROPN
ejpam-4043	166	10	)	)	PUNCT
ejpam-4043	166	11	˙cn−2	˙cn−2	NOUN
ejpam-4043	166	12	+	+	CCONJ
ejpam-4043	166	13	(	(	PUNCT
ejpam-4043	166	14	1−	1−	NUM
ejpam-4043	166	15	ν	ν	NOUN
ejpam-4043	166	16	−	−	PROPN
ejpam-4043	166	17	ω	ω	PROPN
ejpam-4043	166	18	+	+	CCONJ
ejpam-4043	166	19	νω	νω	PROPN
ejpam-4043	166	20	)	)	PUNCT
ejpam-4043	166	21	˙dn−2	˙dn−2	ADP
ejpam-4043	166	22	)	)	PUNCT
ejpam-4043	166	23	=	=	SYM
ejpam-4043	166	24	(	(	PUNCT
ejpam-4043	166	25	1	1	NUM
ejpam-4043	166	26	+	+	CCONJ
ejpam-4043	166	27	ν	ν	X
ejpam-4043	166	28	+	+	X
ejpam-4043	166	29	ω	ω	PROPN
ejpam-4043	166	30	+	+	CCONJ
ejpam-4043	166	31	νω)λ(ȧ	νω)λ(ȧ	NOUN
ejpam-4043	166	32	)	)	PUNCT
ejpam-4043	167	1	+	+	CCONJ
ejpam-4043	167	2	(	(	PUNCT
ejpam-4043	167	3	1−	1−	NUM
ejpam-4043	167	4	ν	ν	X
ejpam-4043	167	5	+	+	PROPN
ejpam-4043	167	6	ω	ω	NUM
ejpam-4043	167	7	−	−	PROPN
ejpam-4043	167	8	νω)λ(ḃ	νω)λ(ḃ	NOUN
ejpam-4043	167	9	)	)	PUNCT
ejpam-4043	168	1	+	+	CCONJ
ejpam-4043	168	2	(	(	PUNCT
ejpam-4043	168	3	1	1	NUM
ejpam-4043	168	4	+	+	ADP
ejpam-4043	168	5	ν	ν	X
ejpam-4043	168	6	−	−	PROPN
ejpam-4043	168	7	ω	ω	NUM
ejpam-4043	168	8	−	−	PROPN
ejpam-4043	168	9	νω)λ(ċ	νω)λ(ċ	PROPN
ejpam-4043	168	10	)	)	PUNCT
ejpam-4043	169	1	+	+	CCONJ
ejpam-4043	169	2	(	(	PUNCT
ejpam-4043	169	3	1−	1−	NUM
ejpam-4043	169	4	ν	ν	NOUN
ejpam-4043	169	5	−	−	PROPN
ejpam-4043	169	6	ω	ω	PROPN
ejpam-4043	169	7	+	+	CCONJ
ejpam-4043	169	8	νω)υ(ḋ	νω)υ(ḋ	NOUN
ejpam-4043	169	9	)	)	PUNCT
ejpam-4043	169	10	=	=	SYM
ejpam-4043	169	11	ξ1λ(ȧ	ξ1λ(ȧ	NUM
ejpam-4043	169	12	)	)	PUNCT
ejpam-4043	169	13	+	+	NUM
ejpam-4043	169	14	ξ2λ(ḃ	ξ2λ(ḃ	NOUN
ejpam-4043	169	15	)	)	PUNCT
ejpam-4043	169	16	+	+	NUM
ejpam-4043	169	17	ξ3λ(ċ	ξ3λ(ċ	NOUN
ejpam-4043	169	18	)	)	PUNCT
ejpam-4043	170	1	+	+	CCONJ
ejpam-4043	170	2	ξ4υ(ḋ	ξ4υ(ḋ	NOUN
ejpam-4043	170	3	)	)	PUNCT
ejpam-4043	170	4	,	,	PUNCT
ejpam-4043	170	5	which	which	PRON
ejpam-4043	170	6	is	be	AUX
ejpam-4043	170	7	an	an	DET
ejpam-4043	170	8	element	element	NOUN
ejpam-4043	170	9	of	of	ADP
ejpam-4043	170	10	the	the	DET
ejpam-4043	170	11	linear	linear	PROPN
ejpam-4043	170	12	code	code	PROPN
ejpam-4043	170	13	k.	k.	PROPN
ejpam-4043	171	1	therefore	therefore	ADV
ejpam-4043	171	2	,	,	PUNCT
ejpam-4043	171	3	k∞	k∞	PROPN
ejpam-4043	171	4	,	,	PUNCT
ejpam-4043	171	5	k∈	k∈	PROPN
ejpam-4043	171	6	,	,	PUNCT
ejpam-4043	171	7	k3	k3	PROPN
ejpam-4043	171	8	,	,	PUNCT
ejpam-4043	171	9	are	be	AUX
ejpam-4043	171	10	negacyclic	negacyclic	ADJ
ejpam-4043	171	11	codes	code	NOUN
ejpam-4043	171	12	and	and	CCONJ
ejpam-4043	171	13	k4	k4	NOUN
ejpam-4043	171	14	is	be	AUX
ejpam-4043	171	15	a	a	DET
ejpam-4043	171	16	cyclic	cyclic	ADJ
ejpam-4043	171	17	code	code	NOUN
ejpam-4043	171	18	over	over	ADP
ejpam-4043	171	19	the	the	DET
ejpam-4043	171	20	ring	ring	NOUN
ejpam-4043	171	21	z3	z3	PROPN
ejpam-4043	171	22	of	of	ADP
ejpam-4043	171	23	length	length	NOUN
ejpam-4043	171	24	n	n	PRON
ejpam-4043	171	25	respectively	respectively	ADV
ejpam-4043	171	26	.	.	PUNCT
ejpam-4043	172	1	conversely	conversely	ADV
ejpam-4043	172	2	,	,	PUNCT
ejpam-4043	172	3	for	for	ADP
ejpam-4043	172	4	any	any	DET
ejpam-4043	172	5	ζ	ζ	NOUN
ejpam-4043	172	6	=	=	SYM
ejpam-4043	172	7	(	(	PUNCT
ejpam-4043	172	8	ζ0	ζ0	PROPN
ejpam-4043	172	9	,	,	PUNCT
ejpam-4043	172	10	ζ1	ζ1	NOUN
ejpam-4043	172	11	,	,	PUNCT
ejpam-4043	172	12	...	...	PUNCT
ejpam-4043	172	13	,	,	PUNCT
ejpam-4043	172	14	ζn−1	ζn−1	PROPN
ejpam-4043	172	15	)	)	PUNCT
ejpam-4043	172	16	∈	∈	PROPN
ejpam-4043	173	1	k	k	NOUN
ejpam-4043	173	2	,	,	PUNCT
ejpam-4043	173	3	where	where	SCONJ
ejpam-4043	173	4	ζi	ζi	PROPN
ejpam-4043	173	5	=	=	SYM
ejpam-4043	173	6	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	173	7	+	+	CCONJ
ejpam-4043	173	8	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	174	1	+	+	CCONJ
ejpam-4043	175	1	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	175	2	+	+	CCONJ
ejpam-4043	175	3	ξ4ḋi	ξ4ḋi	PROPN
ejpam-4043	175	4	and	and	CCONJ
ejpam-4043	175	5	ȧi	ȧi	PROPN
ejpam-4043	175	6	,	,	PUNCT
ejpam-4043	175	7	ḃi	ḃi	PROPN
ejpam-4043	175	8	,	,	PUNCT
ejpam-4043	175	9	ċi	ċi	PROPN
ejpam-4043	175	10	,	,	PUNCT
ejpam-4043	175	11	ḋi	ḋi	PROPN
ejpam-4043	175	12	∈	∈	PROPN
ejpam-4043	175	13	z3	z3	PROPN
ejpam-4043	175	14	for	for	ADP
ejpam-4043	175	15	i	i	PROPN
ejpam-4043	175	16	=	=	SYM
ejpam-4043	175	17	0	0	NUM
ejpam-4043	175	18	,	,	PUNCT
ejpam-4043	175	19	1	1	NUM
ejpam-4043	175	20	,	,	PUNCT
ejpam-4043	175	21	...	...	PUNCT
ejpam-4043	175	22	,	,	PUNCT
ejpam-4043	175	23	n	n	CCONJ
ejpam-4043	175	24	−	−	PROPN
ejpam-4043	175	25	1	1	X
ejpam-4043	175	26	.	.	PUNCT
ejpam-4043	176	1	if	if	SCONJ
ejpam-4043	176	2	k∞	k∞	PROPN
ejpam-4043	176	3	,	,	PUNCT
ejpam-4043	176	4	k∈	k∈	PROPN
ejpam-4043	176	5	,	,	PUNCT
ejpam-4043	176	6	k3	k3	NOUN
ejpam-4043	176	7	are	be	AUX
ejpam-4043	176	8	negacyclic	negacyclic	ADJ
ejpam-4043	176	9	codes	code	NOUN
ejpam-4043	176	10	and	and	CCONJ
ejpam-4043	176	11	k4	k4	NOUN
ejpam-4043	176	12	is	be	AUX
ejpam-4043	176	13	a	a	DET
ejpam-4043	176	14	cyclic	cyclic	ADJ
ejpam-4043	176	15	code	code	NOUN
ejpam-4043	176	16	over	over	ADP
ejpam-4043	176	17	z3	z3	PROPN
ejpam-4043	176	18	of	of	ADP
ejpam-4043	176	19	length	length	NOUN
ejpam-4043	176	20	n	n	CCONJ
ejpam-4043	176	21	,	,	PUNCT
ejpam-4043	176	22	then	then	ADV
ejpam-4043	176	23	λ(ȧ	λ(ȧ	PROPN
ejpam-4043	176	24	)	)	PUNCT
ejpam-4043	176	25	∈	∈	PROPN
ejpam-4043	176	26	k∞	k∞	PROPN
ejpam-4043	176	27	,	,	PUNCT
ejpam-4043	176	28	λ(ḃ	λ(ḃ	PROPN
ejpam-4043	176	29	)	)	PUNCT
ejpam-4043	176	30	∈	∈	PROPN
ejpam-4043	176	31	k∈	k∈	PROPN
ejpam-4043	176	32	,	,	PUNCT
ejpam-4043	176	33	λ(ċ	λ(ċ	PROPN
ejpam-4043	176	34	)	)	PUNCT
ejpam-4043	176	35	∈	∈	PROPN
ejpam-4043	176	36	k3	k3	PROPN
ejpam-4043	176	37	,	,	PUNCT
ejpam-4043	176	38	υ(ḋ	υ(ḋ	NOUN
ejpam-4043	176	39	)	)	PUNCT
ejpam-4043	176	40	∈	∈	PROPN
ejpam-4043	176	41	k4	k4	NOUN
ejpam-4043	176	42	.	.	PUNCT
ejpam-4043	177	1	hence	hence	ADV
ejpam-4043	177	2	,	,	PUNCT
ejpam-4043	177	3	we	we	PRON
ejpam-4043	177	4	have	have	VERB
ejpam-4043	177	5	(	(	PUNCT
ejpam-4043	177	6	1+ν+ω+νω)λ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	1+ν+ω+νω)λ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	NUM
ejpam-4043	177	7	)	)	PUNCT
ejpam-4043	177	8	∈	∈	PROPN
ejpam-4043	178	1	k	k	X
ejpam-4043	178	2	where	where	SCONJ
ejpam-4043	178	3	it	it	PRON
ejpam-4043	178	4	given	give	VERB
ejpam-4043	178	5	that	that	DET
ejpam-4043	178	6	f(ζ	f(ζ	NOUN
ejpam-4043	178	7	)	)	PUNCT
ejpam-4043	179	1	=	=	PRON
ejpam-4043	179	2	(	(	PUNCT
ejpam-4043	179	3	1+ν+ω+νω)λ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	1+ν+ω+νω)λ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	NUM
ejpam-4043	179	4	)	)	PUNCT
ejpam-4043	179	5	,	,	PUNCT
ejpam-4043	179	6	which	which	PRON
ejpam-4043	179	7	implies	imply	VERB
ejpam-4043	179	8	that	that	SCONJ
ejpam-4043	179	9	f(ζ	f(ζ	NOUN
ejpam-4043	179	10	)	)	PUNCT
ejpam-4043	179	11	∈	∈	PROPN
ejpam-4043	179	12	k.	k.	PROPN
ejpam-4043	180	1	therefore	therefore	ADV
ejpam-4043	180	2	,	,	PUNCT
ejpam-4043	180	3	k	k	PROPN
ejpam-4043	180	4	is	be	AUX
ejpam-4043	180	5	a	a	DET
ejpam-4043	180	6	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	180	7	code	code	NOUN
ejpam-4043	180	8	over	over	ADP
ejpam-4043	180	9	the	the	DET
ejpam-4043	180	10	ring	ring	NOUN
ejpam-4043	180	11	<	<	X
ejpam-4043	180	12	of	of	ADP
ejpam-4043	180	13	length	length	NOUN
ejpam-4043	180	14	n	n	NOUN
ejpam-4043	180	15	.	.	PUNCT
ejpam-4043	181	1	case	case	NOUN
ejpam-4043	181	2	2	2	NUM
ejpam-4043	181	3	.	.	X
ejpam-4043	181	4	ϑ	ϑ	X
ejpam-4043	182	1	=	=	SYM
ejpam-4043	182	2	1	1	NUM
ejpam-4043	182	3	+	+	NUM
ejpam-4043	182	4	2ν	2ν	NUM
ejpam-4043	182	5	+	+	CCONJ
ejpam-4043	182	6	2ω	2ω	NUM
ejpam-4043	182	7	+	+	CCONJ
ejpam-4043	182	8	2νω	2νω	NOUN
ejpam-4043	182	9	theorem	theorem	NOUN
ejpam-4043	182	10	8	8	NUM
ejpam-4043	182	11	.	.	PUNCT
ejpam-4043	183	1	let	let	VERB
ejpam-4043	183	2	k	k	PROPN
ejpam-4043	183	3	=	=	SYM
ejpam-4043	183	4	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	183	5	⊕	⊕	PROPN
ejpam-4043	183	6	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	184	1	⊕	⊕	PROPN
ejpam-4043	184	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	184	3	⊕	⊕	PROPN
ejpam-4043	184	4	ξ4k4	ξ4k4	VERB
ejpam-4043	184	5	be	be	AUX
ejpam-4043	184	6	a	a	DET
ejpam-4043	184	7	linear	linear	ADJ
ejpam-4043	184	8	code	code	NOUN
ejpam-4043	184	9	over	over	ADP
ejpam-4043	184	10	the	the	DET
ejpam-4043	184	11	ring	ring	NOUN
ejpam-4043	184	12	<	<	X
ejpam-4043	184	13	of	of	ADP
ejpam-4043	184	14	length	length	NOUN
ejpam-4043	184	15	n	n	PROPN
ejpam-4043	184	16	where	where	SCONJ
ejpam-4043	184	17	k∞	k∞	PROPN
ejpam-4043	184	18	,	,	PUNCT
ejpam-4043	184	19	k∈	k∈	PROPN
ejpam-4043	184	20	,	,	PUNCT
ejpam-4043	184	21	k3	k3	PROPN
ejpam-4043	184	22	,	,	PUNCT
ejpam-4043	184	23	k4	k4	PROPN
ejpam-4043	184	24	are	be	AUX
ejpam-4043	184	25	the	the	DET
ejpam-4043	184	26	linear	linear	ADJ
ejpam-4043	184	27	codes	code	NOUN
ejpam-4043	184	28	over	over	ADP
ejpam-4043	184	29	z3	z3	PROPN
ejpam-4043	184	30	.	.	PUNCT
ejpam-4043	185	1	then	then	ADV
ejpam-4043	185	2	,	,	PUNCT
ejpam-4043	185	3	k	k	PROPN
ejpam-4043	185	4	is	be	AUX
ejpam-4043	185	5	a	a	DET
ejpam-4043	185	6	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	185	7	code	code	NOUN
ejpam-4043	185	8	over	over	ADP
ejpam-4043	185	9	the	the	DET
ejpam-4043	185	10	ring	ring	NOUN
ejpam-4043	185	11	<	<	X
ejpam-4043	185	12	of	of	ADP
ejpam-4043	185	13	length	length	NOUN
ejpam-4043	185	14	n	n	CCONJ
ejpam-4043	185	15	if	if	SCONJ
ejpam-4043	186	1	and	and	CCONJ
ejpam-4043	186	2	only	only	ADV
ejpam-4043	186	3	if	if	SCONJ
ejpam-4043	186	4	k∞	k∞	PROPN
ejpam-4043	186	5	is	be	AUX
ejpam-4043	186	6	cyclic	cyclic	ADJ
ejpam-4043	186	7	code	code	NOUN
ejpam-4043	186	8	and	and	CCONJ
ejpam-4043	186	9	k∈	k∈	PROPN
ejpam-4043	186	10	,	,	PUNCT
ejpam-4043	186	11	k3	k3	PROPN
ejpam-4043	186	12	,	,	PUNCT
ejpam-4043	186	13	k4	k4	PROPN
ejpam-4043	186	14	are	be	AUX
ejpam-4043	186	15	negacyclic	negacyclic	ADJ
ejpam-4043	186	16	codes	code	NOUN
ejpam-4043	186	17	over	over	ADP
ejpam-4043	186	18	z3	z3	PROPN
ejpam-4043	186	19	of	of	ADP
ejpam-4043	186	20	length	length	NOUN
ejpam-4043	186	21	n.	n.	PROPN
ejpam-4043	186	22	proof	proof	NOUN
ejpam-4043	186	23	.	.	PUNCT
ejpam-4043	187	1	let	let	VERB
ejpam-4043	187	2	,	,	PUNCT
ejpam-4043	187	3	ȧ	ȧ	PROPN
ejpam-4043	187	4	=	=	X
ejpam-4043	187	5	(	(	PUNCT
ejpam-4043	187	6	ȧ0	ȧ0	PROPN
ejpam-4043	187	7	,	,	PUNCT
ejpam-4043	187	8	ȧ1	ȧ1	PROPN
ejpam-4043	187	9	,	,	PUNCT
ejpam-4043	187	10	...	...	PUNCT
ejpam-4043	187	11	,	,	PUNCT
ejpam-4043	187	12	˙an−1	˙an−1	NUM
ejpam-4043	187	13	)	)	PUNCT
ejpam-4043	187	14	∈	∈	PROPN
ejpam-4043	187	15	k∞	k∞	PROPN
ejpam-4043	187	16	,	,	PUNCT
ejpam-4043	187	17	ḃ	ḃ	PROPN
ejpam-4043	188	1	=	=	PRON
ejpam-4043	188	2	(	(	PUNCT
ejpam-4043	188	3	ḃ0	ḃ0	PROPN
ejpam-4043	188	4	,	,	PUNCT
ejpam-4043	188	5	ḃ1	ḃ1	PROPN
ejpam-4043	188	6	,	,	PUNCT
ejpam-4043	188	7	...	...	PUNCT
ejpam-4043	188	8	,	,	PUNCT
ejpam-4043	188	9	˙bn−1	˙bn−1	X
ejpam-4043	188	10	)	)	PUNCT
ejpam-4043	188	11	∈	∈	PROPN
ejpam-4043	188	12	k∈	k∈	PROPN
ejpam-4043	188	13	,	,	PUNCT
ejpam-4043	188	14	prateek	prateek	VERB
ejpam-4043	188	15	mor	mor	PROPN
ejpam-4043	188	16	et	et	PROPN
ejpam-4043	188	17	al	al	PROPN
ejpam-4043	188	18	.	.	PUNCT
ejpam-4043	188	19	/	/	SYM
ejpam-4043	188	20	eur	eur	PROPN
ejpam-4043	188	21	.	.	PUNCT
ejpam-4043	189	1	j.	j.	PROPN
ejpam-4043	189	2	pure	pure	PROPN
ejpam-4043	189	3	appl	appl	PROPN
ejpam-4043	189	4	.	.	PROPN
ejpam-4043	189	5	math	math	PROPN
ejpam-4043	189	6	,	,	PUNCT
ejpam-4043	189	7	14	14	NUM
ejpam-4043	189	8	(	(	PUNCT
ejpam-4043	189	9	3	3	NUM
ejpam-4043	189	10	)	)	PUNCT
ejpam-4043	189	11	(	(	PUNCT
ejpam-4043	189	12	2021	2021	NUM
ejpam-4043	189	13	)	)	PUNCT
ejpam-4043	189	14	,	,	PUNCT
ejpam-4043	189	15	1082	1082	NUM
ejpam-4043	189	16	-	-	SYM
ejpam-4043	189	17	1097	1097	NUM
ejpam-4043	189	18	1088	1088	NUM
ejpam-4043	189	19	ċ	ċ	X
ejpam-4043	189	20	=	=	SYM
ejpam-4043	189	21	(	(	PUNCT
ejpam-4043	189	22	ċ0	ċ0	PROPN
ejpam-4043	189	23	,	,	PUNCT
ejpam-4043	189	24	ċ1	ċ1	PROPN
ejpam-4043	189	25	,	,	PUNCT
ejpam-4043	189	26	...	...	PUNCT
ejpam-4043	189	27	,	,	PUNCT
ejpam-4043	189	28	˙cn−1	˙cn−1	X
ejpam-4043	189	29	)	)	PUNCT
ejpam-4043	189	30	∈	∈	PROPN
ejpam-4043	189	31	k3	k3	PROPN
ejpam-4043	189	32	,	,	PUNCT
ejpam-4043	189	33	ḋ	ḋ	PROPN
ejpam-4043	189	34	=	=	SYM
ejpam-4043	189	35	(	(	PUNCT
ejpam-4043	189	36	ḋ0	ḋ0	PROPN
ejpam-4043	189	37	,	,	PUNCT
ejpam-4043	189	38	ḋ1	ḋ1	PROPN
ejpam-4043	189	39	,	,	PUNCT
ejpam-4043	189	40	...	...	PUNCT
ejpam-4043	189	41	,	,	PUNCT
ejpam-4043	189	42	˙dn−1	˙dn−1	X
ejpam-4043	189	43	)	)	PUNCT
ejpam-4043	189	44	∈	∈	PROPN
ejpam-4043	189	45	k4	k4	NOUN
ejpam-4043	189	46	.	.	PUNCT
ejpam-4043	190	1	for	for	ADP
ejpam-4043	190	2	an	an	DET
ejpam-4043	190	3	arbitrary	arbitrary	ADJ
ejpam-4043	190	4	element	element	NOUN
ejpam-4043	190	5	ζi	ζi	PROPN
ejpam-4043	190	6	∈	∈	PROPN
ejpam-4043	190	7	k	k	NOUN
ejpam-4043	190	8	,	,	PUNCT
ejpam-4043	190	9	uniquely	uniquely	ADV
ejpam-4043	190	10	expressed	express	VERB
ejpam-4043	190	11	as	as	ADP
ejpam-4043	190	12	ζi	ζi	PROPN
ejpam-4043	190	13	=	=	SYM
ejpam-4043	190	14	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	190	15	+	+	CCONJ
ejpam-4043	190	16	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	190	17	+	+	CCONJ
ejpam-4043	190	18	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	190	19	+	+	CCONJ
ejpam-4043	190	20	ξ4ḋi	ξ4ḋi	NUM
ejpam-4043	190	21	,	,	PUNCT
ejpam-4043	190	22	where	where	SCONJ
ejpam-4043	190	23	ȧi	ȧi	PROPN
ejpam-4043	190	24	,	,	PUNCT
ejpam-4043	190	25	ḃi	ḃi	PROPN
ejpam-4043	190	26	,	,	PUNCT
ejpam-4043	190	27	ċi	ċi	PROPN
ejpam-4043	190	28	,	,	PUNCT
ejpam-4043	190	29	ḋi	ḋi	PROPN
ejpam-4043	190	30	∈	∈	PROPN
ejpam-4043	190	31	z3	z3	PROPN
ejpam-4043	190	32	for	for	ADP
ejpam-4043	190	33	i	i	PROPN
ejpam-4043	190	34	=	=	SYM
ejpam-4043	190	35	0	0	NUM
ejpam-4043	190	36	,	,	PUNCT
ejpam-4043	190	37	1	1	NUM
ejpam-4043	190	38	,	,	PUNCT
ejpam-4043	190	39	...	...	PUNCT
ejpam-4043	190	40	,	,	PUNCT
ejpam-4043	190	41	n−	n−	NOUN
ejpam-4043	190	42	1	1	NUM
ejpam-4043	190	43	.	.	PUNCT
ejpam-4043	191	1	let	let	VERB
ejpam-4043	191	2	,	,	PUNCT
ejpam-4043	191	3	ζ	ζ	NOUN
ejpam-4043	191	4	=	=	SYM
ejpam-4043	191	5	(	(	PUNCT
ejpam-4043	191	6	ζ0	ζ0	PROPN
ejpam-4043	191	7	,	,	PUNCT
ejpam-4043	191	8	ζ1	ζ1	NOUN
ejpam-4043	191	9	,	,	PUNCT
ejpam-4043	191	10	...	...	PUNCT
ejpam-4043	191	11	,	,	PUNCT
ejpam-4043	191	12	ζn−1	ζn−1	PROPN
ejpam-4043	191	13	)	)	PUNCT
ejpam-4043	191	14	∈	∈	PROPN
ejpam-4043	191	15	<	<	X
ejpam-4043	191	16	n.	n.	PROPN
ejpam-4043	191	17	first	first	ADV
ejpam-4043	191	18	we	we	PRON
ejpam-4043	191	19	assume	assume	VERB
ejpam-4043	191	20	that	that	SCONJ
ejpam-4043	191	21	k	k	PROPN
ejpam-4043	191	22	is	be	AUX
ejpam-4043	191	23	ϑ-constacyclic	ϑ-constacyclic	PROPN
ejpam-4043	191	24	code	code	NOUN
ejpam-4043	191	25	over	over	ADP
ejpam-4043	191	26	the	the	DET
ejpam-4043	191	27	ring	ring	NOUN
ejpam-4043	191	28	<	<	X
ejpam-4043	191	29	of	of	ADP
ejpam-4043	191	30	length	length	NOUN
ejpam-4043	191	31	n	n	CCONJ
ejpam-4043	191	32	,	,	PUNCT
ejpam-4043	191	33	then	then	ADV
ejpam-4043	191	34	f(ζ	f(ζ	NOUN
ejpam-4043	191	35	)	)	PUNCT
ejpam-4043	192	1	=	=	PRON
ejpam-4043	192	2	(	(	PUNCT
ejpam-4043	192	3	(	(	PUNCT
ejpam-4043	192	4	1	1	NUM
ejpam-4043	192	5	+	+	NUM
ejpam-4043	192	6	2ν	2ν	NUM
ejpam-4043	192	7	+	+	CCONJ
ejpam-4043	192	8	2ω	2ω	NUM
ejpam-4043	192	9	+	+	CCONJ
ejpam-4043	192	10	2νω)ζn−1	2νω)ζn−1	NUM
ejpam-4043	192	11	,	,	PUNCT
ejpam-4043	192	12	ζ0	ζ0	ADJ
ejpam-4043	192	13	,	,	PUNCT
ejpam-4043	192	14	...	...	PUNCT
ejpam-4043	192	15	,	,	PUNCT
ejpam-4043	192	16	ζn−2	ζn−2	PROPN
ejpam-4043	192	17	)	)	PUNCT
ejpam-4043	192	18	=	=	SYM
ejpam-4043	193	1	(	(	PUNCT
ejpam-4043	193	2	(	(	PUNCT
ejpam-4043	193	3	1	1	NUM
ejpam-4043	193	4	+	+	NUM
ejpam-4043	193	5	ν	ν	X
ejpam-4043	193	6	+	+	X
ejpam-4043	193	7	ω	ω	PROPN
ejpam-4043	193	8	+	+	CCONJ
ejpam-4043	193	9	νω	νω	PROPN
ejpam-4043	193	10	)	)	PUNCT
ejpam-4043	193	11	˙an−1	˙an−1	PROPN
ejpam-4043	193	12	−	−	PROPN
ejpam-4043	194	1	(	(	PUNCT
ejpam-4043	194	2	1−	1−	NUM
ejpam-4043	194	3	ν	ν	X
ejpam-4043	194	4	+	+	X
ejpam-4043	194	5	ω	ω	NUM
ejpam-4043	194	6	−	−	PROPN
ejpam-4043	194	7	νω	νω	PROPN
ejpam-4043	194	8	)	)	PUNCT
ejpam-4043	194	9	˙bn−1	˙bn−1	NOUN
ejpam-4043	195	1	−	−	PROPN
ejpam-4043	195	2	(	(	PUNCT
ejpam-4043	195	3	1	1	NUM
ejpam-4043	195	4	+	+	ADP
ejpam-4043	195	5	ν	ν	X
ejpam-4043	195	6	−	−	PROPN
ejpam-4043	195	7	ω	ω	NUM
ejpam-4043	195	8	−	−	PROPN
ejpam-4043	195	9	νω	νω	PROPN
ejpam-4043	195	10	)	)	PUNCT
ejpam-4043	195	11	˙cn−1	˙cn−1	PROPN
ejpam-4043	195	12	−	−	PROPN
ejpam-4043	195	13	(	(	PUNCT
ejpam-4043	195	14	1−	1−	NUM
ejpam-4043	195	15	ν	ν	NOUN
ejpam-4043	195	16	−	−	PROPN
ejpam-4043	195	17	ω	ω	PROPN
ejpam-4043	195	18	+	+	CCONJ
ejpam-4043	195	19	νω	νω	PROPN
ejpam-4043	195	20	)	)	PUNCT
ejpam-4043	195	21	˙dn−1	˙dn−1	NUM
ejpam-4043	195	22	,	,	PUNCT
ejpam-4043	195	23	(	(	PUNCT
ejpam-4043	195	24	1	1	NUM
ejpam-4043	196	1	+	+	ADP
ejpam-4043	196	2	ν	ν	X
ejpam-4043	196	3	+	+	X
ejpam-4043	196	4	ω	ω	NUM
ejpam-4043	196	5	+	+	PUNCT
ejpam-4043	196	6	νω)ȧ0	νω)ȧ0	VERB
ejpam-4043	196	7	+	+	CCONJ
ejpam-4043	196	8	(	(	PUNCT
ejpam-4043	196	9	1−	1−	NUM
ejpam-4043	196	10	ν	ν	X
ejpam-4043	196	11	+	+	PROPN
ejpam-4043	196	12	ω	ω	PROPN
ejpam-4043	196	13	−	−	X
ejpam-4043	196	14	νω)ḃ0	νω)ḃ0	PROPN
ejpam-4043	197	1	+	+	CCONJ
ejpam-4043	197	2	(	(	PUNCT
ejpam-4043	197	3	1	1	NUM
ejpam-4043	197	4	+	+	ADP
ejpam-4043	197	5	ν	ν	X
ejpam-4043	197	6	−	−	PROPN
ejpam-4043	197	7	ω	ω	NUM
ejpam-4043	197	8	−	−	PROPN
ejpam-4043	197	9	νω)ċ0	νω)ċ0	PROPN
ejpam-4043	198	1	+	+	CCONJ
ejpam-4043	198	2	(	(	PUNCT
ejpam-4043	198	3	1−	1−	NUM
ejpam-4043	198	4	ν	ν	NOUN
ejpam-4043	198	5	−	−	PROPN
ejpam-4043	198	6	ω	ω	PROPN
ejpam-4043	198	7	+	+	PROPN
ejpam-4043	198	8	νω)ḋ0	νω)ḋ0	PROPN
ejpam-4043	198	9	,	,	PUNCT
ejpam-4043	198	10	...	...	PUNCT
ejpam-4043	198	11	,	,	PUNCT
ejpam-4043	198	12	(	(	PUNCT
ejpam-4043	198	13	1	1	NUM
ejpam-4043	198	14	+	+	ADP
ejpam-4043	198	15	ν	ν	X
ejpam-4043	198	16	+	+	X
ejpam-4043	198	17	ω	ω	PROPN
ejpam-4043	198	18	+	+	CCONJ
ejpam-4043	198	19	νω	νω	PROPN
ejpam-4043	198	20	)	)	PUNCT
ejpam-4043	198	21	˙an−2	˙an−2	PUNCT
ejpam-4043	199	1	+	+	CCONJ
ejpam-4043	199	2	(	(	PUNCT
ejpam-4043	199	3	1−	1−	NUM
ejpam-4043	199	4	ν	ν	X
ejpam-4043	199	5	+	+	X
ejpam-4043	199	6	ω	ω	NUM
ejpam-4043	199	7	−	−	PROPN
ejpam-4043	199	8	νω	νω	PROPN
ejpam-4043	199	9	)	)	PUNCT
ejpam-4043	199	10	˙bn−2	˙bn−2	PUNCT
ejpam-4043	200	1	+	+	CCONJ
ejpam-4043	200	2	(	(	PUNCT
ejpam-4043	200	3	1	1	NUM
ejpam-4043	200	4	+	+	ADP
ejpam-4043	200	5	ν	ν	X
ejpam-4043	200	6	−	−	PROPN
ejpam-4043	200	7	ω	ω	NUM
ejpam-4043	200	8	−	−	PROPN
ejpam-4043	200	9	νω	νω	PROPN
ejpam-4043	200	10	)	)	PUNCT
ejpam-4043	200	11	˙cn−2	˙cn−2	NOUN
ejpam-4043	200	12	+	+	CCONJ
ejpam-4043	200	13	(	(	PUNCT
ejpam-4043	200	14	1−	1−	NUM
ejpam-4043	200	15	ν	ν	NOUN
ejpam-4043	200	16	−	−	PROPN
ejpam-4043	200	17	ω	ω	PROPN
ejpam-4043	200	18	+	+	CCONJ
ejpam-4043	200	19	νω	νω	PROPN
ejpam-4043	200	20	)	)	PUNCT
ejpam-4043	200	21	˙dn−2	˙dn−2	ADP
ejpam-4043	200	22	)	)	PUNCT
ejpam-4043	200	23	=	=	SYM
ejpam-4043	200	24	(	(	PUNCT
ejpam-4043	200	25	1	1	NUM
ejpam-4043	200	26	+	+	CCONJ
ejpam-4043	200	27	ν	ν	X
ejpam-4043	200	28	+	+	X
ejpam-4043	200	29	ω	ω	PROPN
ejpam-4043	200	30	+	+	CCONJ
ejpam-4043	200	31	νω)υ(ȧ	νω)υ(ȧ	PROPN
ejpam-4043	200	32	)	)	PUNCT
ejpam-4043	201	1	+	+	CCONJ
ejpam-4043	201	2	(	(	PUNCT
ejpam-4043	201	3	1−	1−	NUM
ejpam-4043	201	4	ν	ν	X
ejpam-4043	201	5	+	+	PROPN
ejpam-4043	201	6	ω	ω	NUM
ejpam-4043	201	7	−	−	PROPN
ejpam-4043	201	8	νω)λ(ḃ	νω)λ(ḃ	NOUN
ejpam-4043	201	9	)	)	PUNCT
ejpam-4043	202	1	+	+	CCONJ
ejpam-4043	202	2	(	(	PUNCT
ejpam-4043	202	3	1	1	NUM
ejpam-4043	202	4	+	+	ADP
ejpam-4043	202	5	ν	ν	X
ejpam-4043	202	6	−	−	PROPN
ejpam-4043	202	7	ω	ω	NUM
ejpam-4043	202	8	−	−	PROPN
ejpam-4043	202	9	νω)λ(ċ	νω)λ(ċ	PROPN
ejpam-4043	202	10	)	)	PUNCT
ejpam-4043	203	1	+	+	CCONJ
ejpam-4043	203	2	(	(	PUNCT
ejpam-4043	203	3	1−	1−	NUM
ejpam-4043	203	4	ν	ν	NOUN
ejpam-4043	203	5	−	−	PROPN
ejpam-4043	203	6	ω	ω	PROPN
ejpam-4043	203	7	+	+	CCONJ
ejpam-4043	203	8	νω)λ(ḋ	νω)λ(ḋ	PROPN
ejpam-4043	203	9	)	)	PUNCT
ejpam-4043	203	10	=	=	SYM
ejpam-4043	203	11	ξ1υ(ȧ	ξ1υ(ȧ	NOUN
ejpam-4043	203	12	)	)	PUNCT
ejpam-4043	203	13	+	+	NUM
ejpam-4043	203	14	ξ2λ(ḃ	ξ2λ(ḃ	NOUN
ejpam-4043	203	15	)	)	PUNCT
ejpam-4043	203	16	+	+	NUM
ejpam-4043	203	17	ξ3λ(ċ	ξ3λ(ċ	NOUN
ejpam-4043	203	18	)	)	PUNCT
ejpam-4043	204	1	+	+	CCONJ
ejpam-4043	205	1	ξ4λ(ḋ	ξ4λ(ḋ	NOUN
ejpam-4043	205	2	)	)	PUNCT
ejpam-4043	205	3	,	,	PUNCT
ejpam-4043	205	4	which	which	PRON
ejpam-4043	205	5	is	be	AUX
ejpam-4043	205	6	an	an	DET
ejpam-4043	205	7	element	element	NOUN
ejpam-4043	205	8	of	of	ADP
ejpam-4043	205	9	the	the	DET
ejpam-4043	205	10	linear	linear	PROPN
ejpam-4043	205	11	code	code	PROPN
ejpam-4043	206	1	k.	k.	PROPN
ejpam-4043	207	1	therefore	therefore	ADV
ejpam-4043	207	2	,	,	PUNCT
ejpam-4043	207	3	k∞	k∞	PROPN
ejpam-4043	207	4	is	be	AUX
ejpam-4043	207	5	cyclic	cyclic	ADJ
ejpam-4043	207	6	code	code	NOUN
ejpam-4043	207	7	and	and	CCONJ
ejpam-4043	207	8	k∈	k∈	PROPN
ejpam-4043	207	9	,	,	PUNCT
ejpam-4043	207	10	k3	k3	PROPN
ejpam-4043	207	11	,	,	PUNCT
ejpam-4043	207	12	k4	k4	PROPN
ejpam-4043	207	13	are	be	AUX
ejpam-4043	207	14	negacyclic	negacyclic	ADJ
ejpam-4043	207	15	codes	code	NOUN
ejpam-4043	207	16	over	over	ADP
ejpam-4043	207	17	z3	z3	PROPN
ejpam-4043	207	18	of	of	ADP
ejpam-4043	207	19	length	length	NOUN
ejpam-4043	207	20	n	n	PRON
ejpam-4043	207	21	respectively	respectively	ADV
ejpam-4043	207	22	.	.	PUNCT
ejpam-4043	208	1	conversely	conversely	ADV
ejpam-4043	208	2	,	,	PUNCT
ejpam-4043	208	3	for	for	ADP
ejpam-4043	208	4	any	any	DET
ejpam-4043	208	5	ζ	ζ	NOUN
ejpam-4043	208	6	=	=	SYM
ejpam-4043	208	7	(	(	PUNCT
ejpam-4043	208	8	ζ0	ζ0	PROPN
ejpam-4043	208	9	,	,	PUNCT
ejpam-4043	208	10	ζ1	ζ1	NOUN
ejpam-4043	208	11	,	,	PUNCT
ejpam-4043	208	12	...	...	PUNCT
ejpam-4043	208	13	,	,	PUNCT
ejpam-4043	208	14	ζn−1	ζn−1	PROPN
ejpam-4043	208	15	)	)	PUNCT
ejpam-4043	208	16	∈	∈	PROPN
ejpam-4043	209	1	k	k	NOUN
ejpam-4043	209	2	,	,	PUNCT
ejpam-4043	209	3	where	where	SCONJ
ejpam-4043	209	4	ζi	ζi	PROPN
ejpam-4043	209	5	=	=	SYM
ejpam-4043	209	6	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	209	7	+	+	CCONJ
ejpam-4043	209	8	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	210	1	+	+	CCONJ
ejpam-4043	211	1	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	211	2	+	+	CCONJ
ejpam-4043	211	3	ξ4ḋi	ξ4ḋi	PROPN
ejpam-4043	211	4	and	and	CCONJ
ejpam-4043	211	5	ȧi	ȧi	PROPN
ejpam-4043	211	6	,	,	PUNCT
ejpam-4043	211	7	ḃi	ḃi	PROPN
ejpam-4043	211	8	,	,	PUNCT
ejpam-4043	211	9	ċi	ċi	PROPN
ejpam-4043	211	10	,	,	PUNCT
ejpam-4043	211	11	ḋi	ḋi	PROPN
ejpam-4043	211	12	∈	∈	PROPN
ejpam-4043	211	13	z3	z3	PROPN
ejpam-4043	211	14	for	for	ADP
ejpam-4043	211	15	i	i	PROPN
ejpam-4043	211	16	=	=	SYM
ejpam-4043	211	17	0	0	NUM
ejpam-4043	211	18	,	,	PUNCT
ejpam-4043	211	19	1	1	NUM
ejpam-4043	211	20	,	,	PUNCT
ejpam-4043	211	21	...	...	PUNCT
ejpam-4043	211	22	,	,	PUNCT
ejpam-4043	211	23	n−1	n−1	PROPN
ejpam-4043	211	24	.	.	PUNCT
ejpam-4043	212	1	if	if	SCONJ
ejpam-4043	212	2	k∞	k∞	PROPN
ejpam-4043	212	3	is	be	AUX
ejpam-4043	212	4	cyclic	cyclic	ADJ
ejpam-4043	212	5	code	code	NOUN
ejpam-4043	212	6	and	and	CCONJ
ejpam-4043	212	7	k∈	k∈	PROPN
ejpam-4043	212	8	,	,	PUNCT
ejpam-4043	212	9	k3	k3	PROPN
ejpam-4043	212	10	,	,	PUNCT
ejpam-4043	212	11	k4	k4	PROPN
ejpam-4043	212	12	are	be	AUX
ejpam-4043	212	13	negacyclic	negacyclic	ADJ
ejpam-4043	212	14	codes	code	NOUN
ejpam-4043	212	15	over	over	ADP
ejpam-4043	212	16	z3	z3	PROPN
ejpam-4043	212	17	of	of	ADP
ejpam-4043	212	18	length	length	NOUN
ejpam-4043	212	19	n.	n.	PROPN
ejpam-4043	212	20	,	,	PUNCT
ejpam-4043	212	21	then	then	ADV
ejpam-4043	212	22	υ(ȧ	υ(ȧ	X
ejpam-4043	212	23	)	)	PUNCT
ejpam-4043	212	24	∈	∈	PROPN
ejpam-4043	212	25	k∞	k∞	PROPN
ejpam-4043	212	26	,	,	PUNCT
ejpam-4043	212	27	λ(ḃ	λ(ḃ	PROPN
ejpam-4043	212	28	)	)	PUNCT
ejpam-4043	212	29	∈	∈	PROPN
ejpam-4043	212	30	k∈	k∈	PROPN
ejpam-4043	212	31	,	,	PUNCT
ejpam-4043	212	32	λ(ċ	λ(ċ	PROPN
ejpam-4043	212	33	)	)	PUNCT
ejpam-4043	212	34	∈	∈	PROPN
ejpam-4043	212	35	k3	k3	PROPN
ejpam-4043	212	36	,	,	PUNCT
ejpam-4043	212	37	λ(ḋ	λ(ḋ	NUM
ejpam-4043	212	38	)	)	PUNCT
ejpam-4043	212	39	∈	∈	PROPN
ejpam-4043	212	40	k4	k4	NOUN
ejpam-4043	212	41	.	.	PUNCT
ejpam-4043	213	1	hence	hence	ADV
ejpam-4043	213	2	,	,	PUNCT
ejpam-4043	213	3	we	we	PRON
ejpam-4043	213	4	have	have	VERB
ejpam-4043	213	5	(	(	PUNCT
ejpam-4043	213	6	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)λ(ḋ	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)λ(ḋ	NUM
ejpam-4043	213	7	)	)	PUNCT
ejpam-4043	213	8	∈	∈	PROPN
ejpam-4043	214	1	k	k	X
ejpam-4043	214	2	where	where	SCONJ
ejpam-4043	214	3	it	it	PRON
ejpam-4043	214	4	given	give	VERB
ejpam-4043	214	5	that	that	DET
ejpam-4043	214	6	f(ζ	f(ζ	NOUN
ejpam-4043	214	7	)	)	PUNCT
ejpam-4043	215	1	=	=	PRON
ejpam-4043	215	2	(	(	PUNCT
ejpam-4043	215	3	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)λ(ḋ	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)λ(ḋ	NUM
ejpam-4043	215	4	)	)	PUNCT
ejpam-4043	215	5	,	,	PUNCT
ejpam-4043	215	6	which	which	PRON
ejpam-4043	215	7	implies	imply	VERB
ejpam-4043	215	8	that	that	SCONJ
ejpam-4043	215	9	f(ζ	f(ζ	NOUN
ejpam-4043	215	10	)	)	PUNCT
ejpam-4043	215	11	∈	∈	PROPN
ejpam-4043	216	1	k.	k.	PROPN
ejpam-4043	216	2	therefore	therefore	ADV
ejpam-4043	216	3	,	,	PUNCT
ejpam-4043	216	4	k	k	PROPN
ejpam-4043	216	5	is	be	AUX
ejpam-4043	216	6	a	a	DET
ejpam-4043	216	7	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	216	8	code	code	NOUN
ejpam-4043	216	9	over	over	ADP
ejpam-4043	216	10	the	the	DET
ejpam-4043	216	11	ring	ring	NOUN
ejpam-4043	216	12	<	<	X
ejpam-4043	216	13	of	of	ADP
ejpam-4043	216	14	length	length	NOUN
ejpam-4043	216	15	n	n	NOUN
ejpam-4043	216	16	.	.	PUNCT
ejpam-4043	217	1	case	case	NOUN
ejpam-4043	217	2	3	3	NUM
ejpam-4043	217	3	.	.	PUNCT
ejpam-4043	217	4	ϑ	ϑ	X
ejpam-4043	217	5	=	=	X
ejpam-4043	217	6	νω	νω	SCONJ
ejpam-4043	217	7	theorem	theorem	ADJ
ejpam-4043	217	8	9	9	NUM
ejpam-4043	217	9	.	.	PUNCT
ejpam-4043	218	1	let	let	VERB
ejpam-4043	218	2	k	k	PROPN
ejpam-4043	218	3	=	=	SYM
ejpam-4043	218	4	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	218	5	⊕	⊕	PROPN
ejpam-4043	218	6	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	219	1	⊕	⊕	PROPN
ejpam-4043	219	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	219	3	⊕	⊕	PROPN
ejpam-4043	219	4	ξ4k4	ξ4k4	VERB
ejpam-4043	219	5	be	be	AUX
ejpam-4043	219	6	a	a	DET
ejpam-4043	219	7	linear	linear	ADJ
ejpam-4043	219	8	code	code	NOUN
ejpam-4043	219	9	over	over	ADP
ejpam-4043	219	10	the	the	DET
ejpam-4043	219	11	ring	ring	NOUN
ejpam-4043	219	12	<	<	X
ejpam-4043	219	13	of	of	ADP
ejpam-4043	219	14	length	length	NOUN
ejpam-4043	219	15	n	n	PROPN
ejpam-4043	219	16	where	where	SCONJ
ejpam-4043	219	17	k∞	k∞	PROPN
ejpam-4043	219	18	,	,	PUNCT
ejpam-4043	219	19	k∈	k∈	PROPN
ejpam-4043	219	20	,	,	PUNCT
ejpam-4043	219	21	k3	k3	PROPN
ejpam-4043	219	22	,	,	PUNCT
ejpam-4043	219	23	k4	k4	PROPN
ejpam-4043	219	24	are	be	AUX
ejpam-4043	219	25	the	the	DET
ejpam-4043	219	26	linear	linear	ADJ
ejpam-4043	219	27	codes	code	NOUN
ejpam-4043	219	28	over	over	ADP
ejpam-4043	219	29	z3	z3	PROPN
ejpam-4043	219	30	.	.	PUNCT
ejpam-4043	220	1	then	then	ADV
ejpam-4043	220	2	,	,	PUNCT
ejpam-4043	220	3	k	k	PROPN
ejpam-4043	220	4	is	be	AUX
ejpam-4043	220	5	a	a	DET
ejpam-4043	220	6	νωconstacyclic	νωconstacyclic	ADJ
ejpam-4043	220	7	code	code	NOUN
ejpam-4043	220	8	over	over	ADP
ejpam-4043	220	9	the	the	DET
ejpam-4043	220	10	ring	ring	NOUN
ejpam-4043	220	11	<	<	X
ejpam-4043	220	12	of	of	ADP
ejpam-4043	220	13	length	length	NOUN
ejpam-4043	220	14	n	n	CCONJ
ejpam-4043	220	15	if	if	SCONJ
ejpam-4043	221	1	and	and	CCONJ
ejpam-4043	221	2	only	only	ADV
ejpam-4043	221	3	if	if	SCONJ
ejpam-4043	221	4	k∞	k∞	PROPN
ejpam-4043	221	5	,	,	PUNCT
ejpam-4043	221	6	k4	k4	PROPN
ejpam-4043	221	7	are	be	AUX
ejpam-4043	221	8	cyclic	cyclic	ADJ
ejpam-4043	221	9	and	and	CCONJ
ejpam-4043	221	10	k∈	k∈	PROPN
ejpam-4043	221	11	,	,	PUNCT
ejpam-4043	221	12	k3	k3	NOUN
ejpam-4043	221	13	are	be	AUX
ejpam-4043	221	14	negacyclic	negacyclic	ADJ
ejpam-4043	221	15	codes	code	NOUN
ejpam-4043	221	16	over	over	ADP
ejpam-4043	221	17	z3	z3	PROPN
ejpam-4043	221	18	of	of	ADP
ejpam-4043	221	19	length	length	PROPN
ejpam-4043	221	20	n.	n.	PROPN
ejpam-4043	221	21	prateek	prateek	PROPN
ejpam-4043	222	1	mor	mor	PROPN
ejpam-4043	222	2	et	et	PROPN
ejpam-4043	222	3	al	al	PROPN
ejpam-4043	222	4	.	.	PUNCT
ejpam-4043	222	5	/	/	SYM
ejpam-4043	222	6	eur	eur	PROPN
ejpam-4043	222	7	.	.	PUNCT
ejpam-4043	223	1	j.	j.	PROPN
ejpam-4043	223	2	pure	pure	PROPN
ejpam-4043	223	3	appl	appl	PROPN
ejpam-4043	223	4	.	.	PROPN
ejpam-4043	223	5	math	math	PROPN
ejpam-4043	223	6	,	,	PUNCT
ejpam-4043	223	7	14	14	NUM
ejpam-4043	223	8	(	(	PUNCT
ejpam-4043	223	9	3	3	NUM
ejpam-4043	223	10	)	)	PUNCT
ejpam-4043	223	11	(	(	PUNCT
ejpam-4043	223	12	2021	2021	NUM
ejpam-4043	223	13	)	)	PUNCT
ejpam-4043	223	14	,	,	PUNCT
ejpam-4043	223	15	1082	1082	NUM
ejpam-4043	223	16	-	-	SYM
ejpam-4043	223	17	1097	1097	NUM
ejpam-4043	223	18	1089	1089	NUM
ejpam-4043	223	19	proof	proof	NOUN
ejpam-4043	223	20	.	.	PUNCT
ejpam-4043	224	1	let	let	VERB
ejpam-4043	224	2	,	,	PUNCT
ejpam-4043	224	3	ȧ	ȧ	PROPN
ejpam-4043	224	4	=	=	X
ejpam-4043	224	5	(	(	PUNCT
ejpam-4043	224	6	ȧ0	ȧ0	PROPN
ejpam-4043	224	7	,	,	PUNCT
ejpam-4043	224	8	ȧ1	ȧ1	PROPN
ejpam-4043	224	9	,	,	PUNCT
ejpam-4043	224	10	...	...	PUNCT
ejpam-4043	224	11	,	,	PUNCT
ejpam-4043	224	12	˙an−1	˙an−1	NUM
ejpam-4043	224	13	)	)	PUNCT
ejpam-4043	224	14	∈	∈	PROPN
ejpam-4043	224	15	k∞	k∞	PROPN
ejpam-4043	224	16	,	,	PUNCT
ejpam-4043	224	17	ḃ	ḃ	PROPN
ejpam-4043	225	1	=	=	PRON
ejpam-4043	225	2	(	(	PUNCT
ejpam-4043	225	3	ḃ0	ḃ0	PROPN
ejpam-4043	225	4	,	,	PUNCT
ejpam-4043	225	5	ḃ1	ḃ1	PROPN
ejpam-4043	225	6	,	,	PUNCT
ejpam-4043	225	7	...	...	PUNCT
ejpam-4043	225	8	,	,	PUNCT
ejpam-4043	225	9	˙bn−1	˙bn−1	X
ejpam-4043	225	10	)	)	PUNCT
ejpam-4043	225	11	∈	∈	PROPN
ejpam-4043	225	12	k∈	k∈	PROPN
ejpam-4043	225	13	,	,	PUNCT
ejpam-4043	225	14	ċ	ċ	NOUN
ejpam-4043	225	15	=	=	SYM
ejpam-4043	225	16	(	(	PUNCT
ejpam-4043	225	17	ċ0	ċ0	PROPN
ejpam-4043	225	18	,	,	PUNCT
ejpam-4043	225	19	ċ1	ċ1	PROPN
ejpam-4043	225	20	,	,	PUNCT
ejpam-4043	225	21	...	...	PUNCT
ejpam-4043	225	22	,	,	PUNCT
ejpam-4043	225	23	˙cn−1	˙cn−1	X
ejpam-4043	225	24	)	)	PUNCT
ejpam-4043	225	25	∈	∈	PROPN
ejpam-4043	225	26	k3	k3	PROPN
ejpam-4043	225	27	,	,	PUNCT
ejpam-4043	225	28	ḋ	ḋ	PROPN
ejpam-4043	225	29	=	=	SYM
ejpam-4043	225	30	(	(	PUNCT
ejpam-4043	225	31	ḋ0	ḋ0	PROPN
ejpam-4043	225	32	,	,	PUNCT
ejpam-4043	225	33	ḋ1	ḋ1	PROPN
ejpam-4043	225	34	,	,	PUNCT
ejpam-4043	225	35	...	...	PUNCT
ejpam-4043	225	36	,	,	PUNCT
ejpam-4043	225	37	˙dn−1	˙dn−1	X
ejpam-4043	225	38	)	)	PUNCT
ejpam-4043	225	39	∈	∈	PROPN
ejpam-4043	225	40	k4	k4	NOUN
ejpam-4043	225	41	.	.	PUNCT
ejpam-4043	226	1	for	for	ADP
ejpam-4043	226	2	an	an	DET
ejpam-4043	226	3	arbitrary	arbitrary	ADJ
ejpam-4043	226	4	element	element	NOUN
ejpam-4043	226	5	ζi	ζi	PROPN
ejpam-4043	226	6	∈	∈	PROPN
ejpam-4043	226	7	k	k	NOUN
ejpam-4043	226	8	,	,	PUNCT
ejpam-4043	226	9	uniquely	uniquely	ADV
ejpam-4043	226	10	expressed	express	VERB
ejpam-4043	226	11	as	as	ADP
ejpam-4043	226	12	ζi	ζi	PROPN
ejpam-4043	226	13	=	=	SYM
ejpam-4043	226	14	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	226	15	+	+	CCONJ
ejpam-4043	226	16	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	226	17	+	+	CCONJ
ejpam-4043	226	18	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	226	19	+	+	CCONJ
ejpam-4043	226	20	ξ4ḋi	ξ4ḋi	NUM
ejpam-4043	226	21	,	,	PUNCT
ejpam-4043	226	22	where	where	SCONJ
ejpam-4043	226	23	ȧi	ȧi	PROPN
ejpam-4043	226	24	,	,	PUNCT
ejpam-4043	226	25	ḃi	ḃi	PROPN
ejpam-4043	226	26	,	,	PUNCT
ejpam-4043	226	27	ċi	ċi	PROPN
ejpam-4043	226	28	,	,	PUNCT
ejpam-4043	226	29	ḋi	ḋi	PROPN
ejpam-4043	226	30	∈	∈	PROPN
ejpam-4043	226	31	z3	z3	PROPN
ejpam-4043	226	32	for	for	ADP
ejpam-4043	226	33	i	i	PROPN
ejpam-4043	226	34	=	=	SYM
ejpam-4043	226	35	0	0	NUM
ejpam-4043	226	36	,	,	PUNCT
ejpam-4043	226	37	1	1	NUM
ejpam-4043	226	38	,	,	PUNCT
ejpam-4043	226	39	...	...	PUNCT
ejpam-4043	226	40	,	,	PUNCT
ejpam-4043	226	41	n−	n−	NOUN
ejpam-4043	226	42	1	1	NUM
ejpam-4043	226	43	.	.	PUNCT
ejpam-4043	227	1	let	let	VERB
ejpam-4043	227	2	,	,	PUNCT
ejpam-4043	227	3	ζ	ζ	NOUN
ejpam-4043	227	4	=	=	SYM
ejpam-4043	227	5	(	(	PUNCT
ejpam-4043	227	6	ζ0	ζ0	PROPN
ejpam-4043	227	7	,	,	PUNCT
ejpam-4043	227	8	ζ1	ζ1	NOUN
ejpam-4043	227	9	,	,	PUNCT
ejpam-4043	227	10	...	...	PUNCT
ejpam-4043	227	11	,	,	PUNCT
ejpam-4043	227	12	ζn−1	ζn−1	PROPN
ejpam-4043	227	13	)	)	PUNCT
ejpam-4043	227	14	∈	∈	PROPN
ejpam-4043	227	15	<	<	X
ejpam-4043	227	16	n.	n.	PROPN
ejpam-4043	227	17	first	first	ADV
ejpam-4043	227	18	we	we	PRON
ejpam-4043	227	19	assume	assume	VERB
ejpam-4043	227	20	that	that	SCONJ
ejpam-4043	227	21	k	k	PROPN
ejpam-4043	227	22	is	be	AUX
ejpam-4043	227	23	νω	νω	PRON
ejpam-4043	227	24	-	-	ADJ
ejpam-4043	227	25	constacyclic	constacyclic	ADJ
ejpam-4043	227	26	code	code	NOUN
ejpam-4043	227	27	over	over	ADP
ejpam-4043	227	28	the	the	DET
ejpam-4043	227	29	ring	ring	NOUN
ejpam-4043	227	30	<	<	X
ejpam-4043	227	31	of	of	ADP
ejpam-4043	227	32	length	length	NOUN
ejpam-4043	227	33	n	n	CCONJ
ejpam-4043	227	34	,	,	PUNCT
ejpam-4043	227	35	then	then	ADV
ejpam-4043	227	36	f(ζ	f(ζ	NOUN
ejpam-4043	227	37	)	)	PUNCT
ejpam-4043	228	1	=	=	PRON
ejpam-4043	228	2	(	(	PUNCT
ejpam-4043	228	3	(	(	PUNCT
ejpam-4043	228	4	νω)ζn−1	νω)ζn−1	ADJ
ejpam-4043	228	5	,	,	PUNCT
ejpam-4043	228	6	ζ0	ζ0	ADJ
ejpam-4043	228	7	,	,	PUNCT
ejpam-4043	228	8	...	...	PUNCT
ejpam-4043	228	9	,	,	PUNCT
ejpam-4043	228	10	ζn−2	ζn−2	PROPN
ejpam-4043	228	11	)	)	PUNCT
ejpam-4043	228	12	=	=	PUNCT
ejpam-4043	228	13	(	(	PUNCT
ejpam-4043	228	14	α(1	α(1	PROPN
ejpam-4043	228	15	+	+	NUM
ejpam-4043	228	16	ν	ν	X
ejpam-4043	228	17	+	+	X
ejpam-4043	228	18	ω	ω	PROPN
ejpam-4043	228	19	+	+	CCONJ
ejpam-4043	228	20	νω	νω	PROPN
ejpam-4043	228	21	)	)	PUNCT
ejpam-4043	228	22	˙an−1	˙an−1	PROPN
ejpam-4043	228	23	−	−	PROPN
ejpam-4043	229	1	(	(	PUNCT
ejpam-4043	229	2	1−	1−	NUM
ejpam-4043	229	3	ν	ν	X
ejpam-4043	229	4	+	+	X
ejpam-4043	229	5	ω	ω	NUM
ejpam-4043	229	6	−	−	PROPN
ejpam-4043	229	7	νω	νω	PROPN
ejpam-4043	229	8	)	)	PUNCT
ejpam-4043	229	9	˙bn−1	˙bn−1	NOUN
ejpam-4043	230	1	−	−	PROPN
ejpam-4043	230	2	(	(	PUNCT
ejpam-4043	230	3	1	1	NUM
ejpam-4043	230	4	+	+	ADP
ejpam-4043	230	5	ν	ν	X
ejpam-4043	230	6	−	−	PROPN
ejpam-4043	230	7	ω	ω	NUM
ejpam-4043	230	8	−	−	PROPN
ejpam-4043	230	9	νω	νω	PROPN
ejpam-4043	230	10	)	)	PUNCT
ejpam-4043	230	11	˙cn−1	˙cn−1	PROPN
ejpam-4043	231	1	+	+	CCONJ
ejpam-4043	231	2	(	(	PUNCT
ejpam-4043	231	3	1−	1−	NUM
ejpam-4043	231	4	ν	ν	NOUN
ejpam-4043	231	5	−	−	PROPN
ejpam-4043	231	6	ω	ω	PROPN
ejpam-4043	231	7	+	+	CCONJ
ejpam-4043	231	8	νω	νω	PROPN
ejpam-4043	231	9	)	)	PUNCT
ejpam-4043	231	10	˙dn−1	˙dn−1	NUM
ejpam-4043	231	11	,	,	PUNCT
ejpam-4043	231	12	(	(	PUNCT
ejpam-4043	231	13	1	1	NUM
ejpam-4043	231	14	+	+	ADP
ejpam-4043	231	15	ν	ν	X
ejpam-4043	231	16	+	+	X
ejpam-4043	231	17	ω	ω	NUM
ejpam-4043	231	18	+	+	PUNCT
ejpam-4043	231	19	νω)ȧ0	νω)ȧ0	VERB
ejpam-4043	231	20	+	+	CCONJ
ejpam-4043	231	21	(	(	PUNCT
ejpam-4043	231	22	1−	1−	NUM
ejpam-4043	231	23	ν	ν	X
ejpam-4043	231	24	+	+	PROPN
ejpam-4043	231	25	ω	ω	PROPN
ejpam-4043	231	26	−	−	X
ejpam-4043	231	27	νω)ḃ0	νω)ḃ0	PROPN
ejpam-4043	232	1	+	+	CCONJ
ejpam-4043	232	2	(	(	PUNCT
ejpam-4043	232	3	1	1	NUM
ejpam-4043	232	4	+	+	ADP
ejpam-4043	232	5	ν	ν	X
ejpam-4043	232	6	−	−	PROPN
ejpam-4043	232	7	ω	ω	NUM
ejpam-4043	232	8	−	−	PROPN
ejpam-4043	232	9	νω)ċ0	νω)ċ0	PROPN
ejpam-4043	233	1	+	+	CCONJ
ejpam-4043	233	2	(	(	PUNCT
ejpam-4043	233	3	1−	1−	NUM
ejpam-4043	233	4	ν	ν	NOUN
ejpam-4043	233	5	−	−	PROPN
ejpam-4043	233	6	ω	ω	PROPN
ejpam-4043	233	7	+	+	PROPN
ejpam-4043	233	8	νω)ḋ0	νω)ḋ0	PROPN
ejpam-4043	233	9	,	,	PUNCT
ejpam-4043	233	10	...	...	PUNCT
ejpam-4043	233	11	,	,	PUNCT
ejpam-4043	233	12	(	(	PUNCT
ejpam-4043	233	13	1	1	NUM
ejpam-4043	233	14	+	+	ADP
ejpam-4043	233	15	ν	ν	X
ejpam-4043	233	16	+	+	X
ejpam-4043	233	17	ω	ω	PROPN
ejpam-4043	233	18	+	+	CCONJ
ejpam-4043	233	19	νω	νω	PROPN
ejpam-4043	233	20	)	)	PUNCT
ejpam-4043	233	21	˙an−2	˙an−2	PUNCT
ejpam-4043	234	1	+	+	CCONJ
ejpam-4043	234	2	(	(	PUNCT
ejpam-4043	234	3	1−	1−	NUM
ejpam-4043	234	4	ν	ν	X
ejpam-4043	234	5	+	+	X
ejpam-4043	234	6	ω	ω	NUM
ejpam-4043	234	7	−	−	PROPN
ejpam-4043	234	8	νω	νω	PROPN
ejpam-4043	234	9	)	)	PUNCT
ejpam-4043	234	10	˙bn−2	˙bn−2	PUNCT
ejpam-4043	235	1	+	+	CCONJ
ejpam-4043	235	2	(	(	PUNCT
ejpam-4043	235	3	1	1	NUM
ejpam-4043	235	4	+	+	ADP
ejpam-4043	235	5	ν	ν	X
ejpam-4043	235	6	−	−	PROPN
ejpam-4043	235	7	ω	ω	NUM
ejpam-4043	235	8	−	−	PROPN
ejpam-4043	235	9	νω	νω	PROPN
ejpam-4043	235	10	)	)	PUNCT
ejpam-4043	235	11	˙cn−2	˙cn−2	NOUN
ejpam-4043	235	12	+	+	CCONJ
ejpam-4043	235	13	(	(	PUNCT
ejpam-4043	235	14	1−	1−	NUM
ejpam-4043	235	15	ν	ν	NOUN
ejpam-4043	235	16	−	−	PROPN
ejpam-4043	235	17	ω	ω	PROPN
ejpam-4043	235	18	+	+	CCONJ
ejpam-4043	235	19	νω	νω	PROPN
ejpam-4043	235	20	)	)	PUNCT
ejpam-4043	235	21	˙dn−2	˙dn−2	ADP
ejpam-4043	235	22	)	)	PUNCT
ejpam-4043	235	23	=	=	SYM
ejpam-4043	235	24	(	(	PUNCT
ejpam-4043	235	25	1	1	NUM
ejpam-4043	235	26	+	+	CCONJ
ejpam-4043	235	27	ν	ν	X
ejpam-4043	235	28	+	+	X
ejpam-4043	235	29	ω	ω	PROPN
ejpam-4043	235	30	+	+	CCONJ
ejpam-4043	235	31	νω)υ(ȧ	νω)υ(ȧ	PROPN
ejpam-4043	235	32	)	)	PUNCT
ejpam-4043	236	1	+	+	CCONJ
ejpam-4043	236	2	(	(	PUNCT
ejpam-4043	236	3	1−	1−	NUM
ejpam-4043	236	4	ν	ν	X
ejpam-4043	236	5	+	+	PROPN
ejpam-4043	236	6	ω	ω	NUM
ejpam-4043	236	7	−	−	PROPN
ejpam-4043	236	8	νω)λ(ḃ	νω)λ(ḃ	NOUN
ejpam-4043	236	9	)	)	PUNCT
ejpam-4043	237	1	+	+	CCONJ
ejpam-4043	237	2	(	(	PUNCT
ejpam-4043	237	3	1	1	NUM
ejpam-4043	237	4	+	+	ADP
ejpam-4043	237	5	ν	ν	X
ejpam-4043	237	6	−	−	PROPN
ejpam-4043	237	7	ω	ω	NUM
ejpam-4043	237	8	−	−	PROPN
ejpam-4043	237	9	νω)λ(ċ	νω)λ(ċ	PROPN
ejpam-4043	237	10	)	)	PUNCT
ejpam-4043	238	1	+	+	CCONJ
ejpam-4043	238	2	(	(	PUNCT
ejpam-4043	238	3	1−	1−	NUM
ejpam-4043	238	4	ν	ν	NOUN
ejpam-4043	238	5	−	−	PROPN
ejpam-4043	238	6	ω	ω	PROPN
ejpam-4043	238	7	+	+	CCONJ
ejpam-4043	238	8	νω)υ(ḋ	νω)υ(ḋ	NOUN
ejpam-4043	238	9	)	)	PUNCT
ejpam-4043	238	10	=	=	SYM
ejpam-4043	238	11	ξ1υ(ȧ	ξ1υ(ȧ	NOUN
ejpam-4043	238	12	)	)	PUNCT
ejpam-4043	238	13	+	+	NUM
ejpam-4043	238	14	ξ2λ(ḃ	ξ2λ(ḃ	NOUN
ejpam-4043	238	15	)	)	PUNCT
ejpam-4043	238	16	+	+	NUM
ejpam-4043	238	17	ξ3λ(ċ	ξ3λ(ċ	NOUN
ejpam-4043	238	18	)	)	PUNCT
ejpam-4043	239	1	+	+	CCONJ
ejpam-4043	239	2	ξ4υ(ḋ	ξ4υ(ḋ	NOUN
ejpam-4043	239	3	)	)	PUNCT
ejpam-4043	239	4	,	,	PUNCT
ejpam-4043	239	5	which	which	PRON
ejpam-4043	239	6	is	be	AUX
ejpam-4043	239	7	an	an	DET
ejpam-4043	239	8	element	element	NOUN
ejpam-4043	239	9	of	of	ADP
ejpam-4043	239	10	the	the	DET
ejpam-4043	239	11	linear	linear	PROPN
ejpam-4043	239	12	code	code	PROPN
ejpam-4043	239	13	k.	k.	PROPN
ejpam-4043	240	1	therefore	therefore	ADV
ejpam-4043	240	2	,	,	PUNCT
ejpam-4043	240	3	k∞	k∞	PROPN
ejpam-4043	240	4	,	,	PUNCT
ejpam-4043	240	5	k4	k4	PROPN
ejpam-4043	240	6	are	be	AUX
ejpam-4043	240	7	cyclic	cyclic	ADJ
ejpam-4043	240	8	and	and	CCONJ
ejpam-4043	240	9	k∈	k∈	PROPN
ejpam-4043	240	10	,	,	PUNCT
ejpam-4043	240	11	k3	k3	VERB
ejpam-4043	240	12	,	,	PUNCT
ejpam-4043	240	13	are	be	AUX
ejpam-4043	240	14	negacyclic	negacyclic	ADJ
ejpam-4043	240	15	codes	code	NOUN
ejpam-4043	240	16	over	over	ADP
ejpam-4043	240	17	the	the	DET
ejpam-4043	240	18	ring	ring	NOUN
ejpam-4043	240	19	z3	z3	PROPN
ejpam-4043	240	20	of	of	ADP
ejpam-4043	240	21	length	length	NOUN
ejpam-4043	240	22	n	n	PRON
ejpam-4043	240	23	respectively	respectively	ADV
ejpam-4043	240	24	.	.	PUNCT
ejpam-4043	241	1	conversely	conversely	ADV
ejpam-4043	241	2	,	,	PUNCT
ejpam-4043	241	3	for	for	ADP
ejpam-4043	241	4	any	any	DET
ejpam-4043	241	5	ζ	ζ	NOUN
ejpam-4043	241	6	=	=	SYM
ejpam-4043	241	7	(	(	PUNCT
ejpam-4043	241	8	ζ0	ζ0	PROPN
ejpam-4043	241	9	,	,	PUNCT
ejpam-4043	241	10	ζ1	ζ1	NOUN
ejpam-4043	241	11	,	,	PUNCT
ejpam-4043	241	12	...	...	PUNCT
ejpam-4043	241	13	,	,	PUNCT
ejpam-4043	241	14	ζn−1	ζn−1	PROPN
ejpam-4043	241	15	)	)	PUNCT
ejpam-4043	241	16	∈	∈	PROPN
ejpam-4043	242	1	k	k	NOUN
ejpam-4043	242	2	,	,	PUNCT
ejpam-4043	242	3	where	where	SCONJ
ejpam-4043	242	4	ζi	ζi	PROPN
ejpam-4043	242	5	=	=	SYM
ejpam-4043	242	6	ξ1ȧi	ξ1ȧi	NOUN
ejpam-4043	242	7	+	+	CCONJ
ejpam-4043	242	8	ξ2ḃi	ξ2ḃi	PROPN
ejpam-4043	243	1	+	+	CCONJ
ejpam-4043	244	1	ξ3ċi	ξ3ċi	PROPN
ejpam-4043	244	2	+	+	CCONJ
ejpam-4043	244	3	ξ4ḋi	ξ4ḋi	PROPN
ejpam-4043	244	4	and	and	CCONJ
ejpam-4043	244	5	ȧi	ȧi	PROPN
ejpam-4043	244	6	,	,	PUNCT
ejpam-4043	244	7	ḃi	ḃi	PROPN
ejpam-4043	244	8	,	,	PUNCT
ejpam-4043	244	9	ċi	ċi	PROPN
ejpam-4043	244	10	,	,	PUNCT
ejpam-4043	244	11	ḋi	ḋi	PROPN
ejpam-4043	244	12	∈	∈	PROPN
ejpam-4043	244	13	z3	z3	PROPN
ejpam-4043	244	14	for	for	ADP
ejpam-4043	244	15	i	i	PROPN
ejpam-4043	244	16	=	=	SYM
ejpam-4043	244	17	0	0	NUM
ejpam-4043	244	18	,	,	PUNCT
ejpam-4043	244	19	1	1	NUM
ejpam-4043	244	20	,	,	PUNCT
ejpam-4043	244	21	...	...	PUNCT
ejpam-4043	244	22	,	,	PUNCT
ejpam-4043	244	23	n	n	CCONJ
ejpam-4043	244	24	−	−	PROPN
ejpam-4043	244	25	1	1	X
ejpam-4043	244	26	.	.	PUNCT
ejpam-4043	245	1	if	if	SCONJ
ejpam-4043	245	2	k∞	k∞	PROPN
ejpam-4043	245	3	,	,	PUNCT
ejpam-4043	245	4	k4	k4	PROPN
ejpam-4043	245	5	are	be	AUX
ejpam-4043	245	6	cyclic	cyclic	ADJ
ejpam-4043	245	7	and	and	CCONJ
ejpam-4043	245	8	k∈	k∈	PROPN
ejpam-4043	245	9	,	,	PUNCT
ejpam-4043	245	10	k3	k3	VERB
ejpam-4043	245	11	,	,	PUNCT
ejpam-4043	245	12	are	be	AUX
ejpam-4043	245	13	negacyclic	negacyclic	ADJ
ejpam-4043	245	14	codes	code	NOUN
ejpam-4043	245	15	over	over	ADP
ejpam-4043	245	16	the	the	DET
ejpam-4043	245	17	ringzp	ringzp	ADJ
ejpam-4043	245	18	of	of	ADP
ejpam-4043	245	19	length	length	NOUN
ejpam-4043	245	20	n	n	CCONJ
ejpam-4043	245	21	,	,	PUNCT
ejpam-4043	245	22	then	then	ADV
ejpam-4043	245	23	υ(ȧ	υ(ȧ	X
ejpam-4043	245	24	)	)	PUNCT
ejpam-4043	245	25	∈	∈	PROPN
ejpam-4043	245	26	k∞	k∞	PROPN
ejpam-4043	245	27	,	,	PUNCT
ejpam-4043	245	28	λ(ḃ	λ(ḃ	PROPN
ejpam-4043	245	29	)	)	PUNCT
ejpam-4043	245	30	∈	∈	PROPN
ejpam-4043	245	31	k∈	k∈	PROPN
ejpam-4043	245	32	,	,	PUNCT
ejpam-4043	245	33	λ(ċ	λ(ċ	PROPN
ejpam-4043	245	34	)	)	PUNCT
ejpam-4043	245	35	∈	∈	PROPN
ejpam-4043	245	36	k3	k3	PROPN
ejpam-4043	245	37	,	,	PUNCT
ejpam-4043	245	38	υ(ḋ	υ(ḋ	NOUN
ejpam-4043	245	39	)	)	PUNCT
ejpam-4043	245	40	∈	∈	PROPN
ejpam-4043	245	41	k4	k4	NOUN
ejpam-4043	245	42	.	.	PUNCT
ejpam-4043	246	1	hence	hence	ADV
ejpam-4043	246	2	,	,	PUNCT
ejpam-4043	246	3	we	we	PRON
ejpam-4043	246	4	have	have	VERB
ejpam-4043	246	5	(	(	PUNCT
ejpam-4043	246	6	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	NUM
ejpam-4043	246	7	)	)	PUNCT
ejpam-4043	246	8	∈	∈	PROPN
ejpam-4043	247	1	k	k	X
ejpam-4043	247	2	where	where	SCONJ
ejpam-4043	247	3	it	it	PRON
ejpam-4043	247	4	given	give	VERB
ejpam-4043	247	5	that	that	DET
ejpam-4043	247	6	f(ζ	f(ζ	NOUN
ejpam-4043	247	7	)	)	PUNCT
ejpam-4043	248	1	=	=	PRON
ejpam-4043	248	2	(	(	PUNCT
ejpam-4043	248	3	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	1+ν+ω+νω)υ(ȧ)+(1−ν+ω−νω)λ(ḃ)+(1+ν−ω−νω)λ(ċ)+(1−ν−ω+νω)υ(ḋ	NUM
ejpam-4043	248	4	)	)	PUNCT
ejpam-4043	248	5	,	,	PUNCT
ejpam-4043	248	6	which	which	PRON
ejpam-4043	248	7	implies	imply	VERB
ejpam-4043	248	8	that	that	SCONJ
ejpam-4043	248	9	f(ζ	f(ζ	NOUN
ejpam-4043	248	10	)	)	PUNCT
ejpam-4043	248	11	∈	∈	PROPN
ejpam-4043	248	12	k.	k.	PROPN
ejpam-4043	249	1	therefore	therefore	ADV
ejpam-4043	249	2	,	,	PUNCT
ejpam-4043	249	3	k	k	PROPN
ejpam-4043	249	4	is	be	AUX
ejpam-4043	249	5	a	a	DET
ejpam-4043	249	6	νω	νω	ADV
ejpam-4043	249	7	-	-	ADJ
ejpam-4043	249	8	constacyclic	constacyclic	ADJ
ejpam-4043	249	9	code	code	NOUN
ejpam-4043	249	10	over	over	ADP
ejpam-4043	249	11	the	the	DET
ejpam-4043	249	12	ring	ring	NOUN
ejpam-4043	249	13	<	<	X
ejpam-4043	249	14	of	of	ADP
ejpam-4043	249	15	length	length	NOUN
ejpam-4043	249	16	n	n	NOUN
ejpam-4043	249	17	.	.	PUNCT
ejpam-4043	250	1	case	case	NOUN
ejpam-4043	250	2	4	4	NUM
ejpam-4043	250	3	.	.	X
ejpam-4043	250	4	ϑ	ϑ	X
ejpam-4043	250	5	=	=	X
ejpam-4043	250	6	ν	ν	PROPN
ejpam-4043	250	7	prateek	prateek	ADJ
ejpam-4043	250	8	mor	mor	PROPN
ejpam-4043	250	9	et	et	PROPN
ejpam-4043	250	10	al	al	PROPN
ejpam-4043	250	11	.	.	PUNCT
ejpam-4043	250	12	/	/	SYM
ejpam-4043	250	13	eur	eur	PROPN
ejpam-4043	250	14	.	.	PUNCT
ejpam-4043	251	1	j.	j.	PROPN
ejpam-4043	251	2	pure	pure	PROPN
ejpam-4043	251	3	appl	appl	PROPN
ejpam-4043	251	4	.	.	PROPN
ejpam-4043	251	5	math	math	PROPN
ejpam-4043	251	6	,	,	PUNCT
ejpam-4043	251	7	14	14	NUM
ejpam-4043	251	8	(	(	PUNCT
ejpam-4043	251	9	3	3	NUM
ejpam-4043	251	10	)	)	PUNCT
ejpam-4043	251	11	(	(	PUNCT
ejpam-4043	251	12	2021	2021	NUM
ejpam-4043	251	13	)	)	PUNCT
ejpam-4043	251	14	,	,	PUNCT
ejpam-4043	251	15	1082	1082	NUM
ejpam-4043	251	16	-	-	SYM
ejpam-4043	251	17	1097	1097	NUM
ejpam-4043	251	18	1090	1090	NUM
ejpam-4043	251	19	theorem	theorem	NOUN
ejpam-4043	251	20	10	10	NUM
ejpam-4043	251	21	.	.	PUNCT
ejpam-4043	252	1	let	let	VERB
ejpam-4043	252	2	k	k	PROPN
ejpam-4043	252	3	=	=	SYM
ejpam-4043	252	4	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	252	5	⊕	⊕	PROPN
ejpam-4043	252	6	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	253	1	⊕	⊕	PROPN
ejpam-4043	253	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	253	3	⊕	⊕	PROPN
ejpam-4043	253	4	ξ4k4	ξ4k4	VERB
ejpam-4043	253	5	be	be	AUX
ejpam-4043	253	6	a	a	DET
ejpam-4043	253	7	linear	linear	ADJ
ejpam-4043	253	8	code	code	NOUN
ejpam-4043	253	9	over	over	ADP
ejpam-4043	253	10	the	the	DET
ejpam-4043	253	11	ring	ring	NOUN
ejpam-4043	253	12	<	<	X
ejpam-4043	253	13	of	of	ADP
ejpam-4043	253	14	length	length	NOUN
ejpam-4043	253	15	n	n	PROPN
ejpam-4043	253	16	where	where	SCONJ
ejpam-4043	253	17	k∞	k∞	PROPN
ejpam-4043	253	18	,	,	PUNCT
ejpam-4043	253	19	k∈	k∈	PROPN
ejpam-4043	253	20	,	,	PUNCT
ejpam-4043	253	21	k3	k3	PROPN
ejpam-4043	253	22	,	,	PUNCT
ejpam-4043	253	23	k4	k4	PROPN
ejpam-4043	253	24	are	be	AUX
ejpam-4043	253	25	the	the	DET
ejpam-4043	253	26	linear	linear	ADJ
ejpam-4043	253	27	codes	code	NOUN
ejpam-4043	253	28	over	over	ADP
ejpam-4043	253	29	z3	z3	PROPN
ejpam-4043	253	30	.	.	PUNCT
ejpam-4043	254	1	then	then	ADV
ejpam-4043	254	2	,	,	PUNCT
ejpam-4043	254	3	k	k	PROPN
ejpam-4043	254	4	is	be	AUX
ejpam-4043	254	5	a	a	DET
ejpam-4043	254	6	ν	ν	NOUN
ejpam-4043	254	7	-	-	ADJ
ejpam-4043	254	8	constacyclic	constacyclic	ADJ
ejpam-4043	254	9	code	code	NOUN
ejpam-4043	254	10	over	over	ADP
ejpam-4043	254	11	the	the	DET
ejpam-4043	254	12	ring	ring	NOUN
ejpam-4043	254	13	<	<	X
ejpam-4043	254	14	of	of	ADP
ejpam-4043	254	15	length	length	NOUN
ejpam-4043	254	16	n	n	CCONJ
ejpam-4043	254	17	if	if	SCONJ
ejpam-4043	255	1	and	and	CCONJ
ejpam-4043	255	2	only	only	ADV
ejpam-4043	255	3	if	if	SCONJ
ejpam-4043	255	4	k∞	k∞	PROPN
ejpam-4043	255	5	,	,	PUNCT
ejpam-4043	255	6	k3	k3	NOUN
ejpam-4043	255	7	are	be	AUX
ejpam-4043	255	8	cyclic	cyclic	ADJ
ejpam-4043	255	9	and	and	CCONJ
ejpam-4043	255	10	k∈	k∈	PROPN
ejpam-4043	255	11	,	,	PUNCT
ejpam-4043	255	12	k4	k4	PROPN
ejpam-4043	255	13	are	be	AUX
ejpam-4043	255	14	negacyclic	negacyclic	ADJ
ejpam-4043	255	15	codes	code	NOUN
ejpam-4043	255	16	over	over	ADP
ejpam-4043	255	17	z3	z3	PROPN
ejpam-4043	255	18	of	of	ADP
ejpam-4043	255	19	length	length	NOUN
ejpam-4043	255	20	n.	n.	PROPN
ejpam-4043	255	21	proof	proof	NOUN
ejpam-4043	255	22	.	.	PUNCT
ejpam-4043	256	1	the	the	DET
ejpam-4043	256	2	proof	proof	NOUN
ejpam-4043	256	3	of	of	ADP
ejpam-4043	256	4	this	this	DET
ejpam-4043	256	5	theorem	theorem	NOUN
ejpam-4043	256	6	is	be	AUX
ejpam-4043	256	7	similar	similar	ADJ
ejpam-4043	256	8	to	to	ADP
ejpam-4043	256	9	proof	proof	NOUN
ejpam-4043	256	10	of	of	ADP
ejpam-4043	256	11	theorem	theorem	ADJ
ejpam-4043	256	12	4.5	4.5	NUM
ejpam-4043	256	13	.	.	PUNCT
ejpam-4043	257	1	case	case	NOUN
ejpam-4043	257	2	5	5	NUM
ejpam-4043	257	3	.	.	PUNCT
ejpam-4043	257	4	ϑ	ϑ	X
ejpam-4043	257	5	=	=	SYM
ejpam-4043	257	6	ω	ω	PROPN
ejpam-4043	257	7	theorem	theorem	ADJ
ejpam-4043	257	8	11	11	NUM
ejpam-4043	257	9	.	.	PUNCT
ejpam-4043	258	1	let	let	VERB
ejpam-4043	258	2	k	k	PROPN
ejpam-4043	258	3	=	=	SYM
ejpam-4043	258	4	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	258	5	⊕	⊕	PROPN
ejpam-4043	258	6	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	259	1	⊕	⊕	PROPN
ejpam-4043	259	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	259	3	⊕	⊕	PROPN
ejpam-4043	259	4	ξ4k4	ξ4k4	VERB
ejpam-4043	259	5	be	be	AUX
ejpam-4043	259	6	a	a	DET
ejpam-4043	259	7	linear	linear	ADJ
ejpam-4043	259	8	code	code	NOUN
ejpam-4043	259	9	over	over	ADP
ejpam-4043	259	10	the	the	DET
ejpam-4043	259	11	ring	ring	NOUN
ejpam-4043	259	12	<	<	X
ejpam-4043	259	13	of	of	ADP
ejpam-4043	259	14	length	length	NOUN
ejpam-4043	259	15	n	n	PROPN
ejpam-4043	259	16	where	where	SCONJ
ejpam-4043	259	17	k∞	k∞	PROPN
ejpam-4043	259	18	,	,	PUNCT
ejpam-4043	259	19	k∈	k∈	PROPN
ejpam-4043	259	20	,	,	PUNCT
ejpam-4043	259	21	k3	k3	PROPN
ejpam-4043	259	22	,	,	PUNCT
ejpam-4043	259	23	k4	k4	PROPN
ejpam-4043	259	24	are	be	AUX
ejpam-4043	259	25	the	the	DET
ejpam-4043	259	26	linear	linear	ADJ
ejpam-4043	259	27	codes	code	NOUN
ejpam-4043	259	28	over	over	ADP
ejpam-4043	259	29	z3	z3	PROPN
ejpam-4043	259	30	.	.	PUNCT
ejpam-4043	260	1	then	then	ADV
ejpam-4043	260	2	,	,	PUNCT
ejpam-4043	260	3	k	k	PROPN
ejpam-4043	260	4	is	be	AUX
ejpam-4043	260	5	a	a	DET
ejpam-4043	260	6	ω	ω	ADJ
ejpam-4043	260	7	-	-	ADJ
ejpam-4043	260	8	constacyclic	constacyclic	ADJ
ejpam-4043	260	9	code	code	NOUN
ejpam-4043	260	10	over	over	ADP
ejpam-4043	260	11	the	the	DET
ejpam-4043	260	12	ring	ring	NOUN
ejpam-4043	260	13	<	<	X
ejpam-4043	260	14	of	of	ADP
ejpam-4043	260	15	length	length	NOUN
ejpam-4043	260	16	n	n	CCONJ
ejpam-4043	260	17	if	if	SCONJ
ejpam-4043	261	1	and	and	CCONJ
ejpam-4043	261	2	only	only	ADV
ejpam-4043	261	3	if	if	SCONJ
ejpam-4043	261	4	k∞	k∞	PROPN
ejpam-4043	261	5	,	,	PUNCT
ejpam-4043	261	6	k∈	k∈	PROPN
ejpam-4043	261	7	are	be	AUX
ejpam-4043	261	8	cyclic	cyclic	ADJ
ejpam-4043	261	9	and	and	CCONJ
ejpam-4043	261	10	k3	k3	PROPN
ejpam-4043	261	11	,	,	PUNCT
ejpam-4043	261	12	k4	k4	PROPN
ejpam-4043	261	13	are	be	AUX
ejpam-4043	261	14	negacyclic	negacyclic	ADJ
ejpam-4043	261	15	codes	code	NOUN
ejpam-4043	261	16	over	over	ADP
ejpam-4043	261	17	z3	z3	PROPN
ejpam-4043	261	18	of	of	ADP
ejpam-4043	261	19	length	length	NOUN
ejpam-4043	261	20	n.	n.	PROPN
ejpam-4043	261	21	proof	proof	NOUN
ejpam-4043	261	22	.	.	PUNCT
ejpam-4043	262	1	proof	proof	NOUN
ejpam-4043	262	2	of	of	ADP
ejpam-4043	262	3	the	the	DET
ejpam-4043	262	4	theorem	theorem	NOUN
ejpam-4043	262	5	is	be	AUX
ejpam-4043	262	6	similar	similar	ADJ
ejpam-4043	262	7	to	to	ADP
ejpam-4043	262	8	proof	proof	NOUN
ejpam-4043	262	9	of	of	ADP
ejpam-4043	262	10	theorem	theorem	ADJ
ejpam-4043	262	11	4.6	4.6	NUM
ejpam-4043	262	12	.	.	PUNCT
ejpam-4043	263	1	the	the	DET
ejpam-4043	263	2	following	follow	VERB
ejpam-4043	263	3	theorem	theorem	NOUN
ejpam-4043	263	4	is	be	AUX
ejpam-4043	263	5	similar	similar	ADJ
ejpam-4043	263	6	to	to	AUX
ejpam-4043	263	7	theorem	theorem	VERB
ejpam-4043	263	8	14	14	NUM
ejpam-4043	263	9	[	[	X
ejpam-4043	263	10	7	7	NUM
ejpam-4043	263	11	]	]	PUNCT
ejpam-4043	263	12	.	.	PUNCT
ejpam-4043	264	1	theorem	theorem	NOUN
ejpam-4043	264	2	12	12	NUM
ejpam-4043	264	3	.	.	PUNCT
ejpam-4043	265	1	let	let	VERB
ejpam-4043	265	2	k	k	PRON
ejpam-4043	265	3	be	be	AUX
ejpam-4043	265	4	a	a	DET
ejpam-4043	265	5	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	265	6	code	code	NOUN
ejpam-4043	265	7	over	over	ADP
ejpam-4043	265	8	the	the	DET
ejpam-4043	265	9	ring	ring	NOUN
ejpam-4043	265	10	<	<	X
ejpam-4043	265	11	of	of	ADP
ejpam-4043	265	12	length	length	NOUN
ejpam-4043	265	13	n.	n.	PROPN
ejpam-4043	266	1	then	then	ADV
ejpam-4043	266	2	k	k	PROPN
ejpam-4043	267	1	=	=	X
ejpam-4043	267	2	<	<	X
ejpam-4043	267	3	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	267	4	)	)	PUNCT
ejpam-4043	267	5	,	,	PUNCT
ejpam-4043	267	6	ξ2g2(t	ξ2g2(t	PROPN
ejpam-4043	267	7	)	)	PUNCT
ejpam-4043	267	8	,	,	PUNCT
ejpam-4043	267	9	ξ3g3(t	ξ3g3(t	VERB
ejpam-4043	267	10	)	)	PUNCT
ejpam-4043	267	11	,	,	PUNCT
ejpam-4043	267	12	ξ4g4(t	ξ4g4(t	NUM
ejpam-4043	267	13	)	)	PUNCT
ejpam-4043	267	14	>	>	X
ejpam-4043	268	1	=	=	PUNCT
ejpam-4043	268	2	<	<	X
ejpam-4043	268	3	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	268	4	)	)	PUNCT
ejpam-4043	268	5	+	+	X
ejpam-4043	268	6	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	268	7	)	)	PUNCT
ejpam-4043	268	8	+	+	CCONJ
ejpam-4043	268	9	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	268	10	)	)	PUNCT
ejpam-4043	268	11	+	+	X
ejpam-4043	268	12	ξ4g4(t	ξ4g4(t	X
ejpam-4043	268	13	)	)	PUNCT
ejpam-4043	268	14	>	>	X
ejpam-4043	268	15	where	where	SCONJ
ejpam-4043	268	16	gi(t	gi(t	NOUN
ejpam-4043	268	17	)	)	PUNCT
ejpam-4043	268	18	are	be	AUX
ejpam-4043	268	19	the	the	DET
ejpam-4043	268	20	generator	generator	NOUN
ejpam-4043	268	21	polynomials	polynomial	NOUN
ejpam-4043	268	22	of	of	ADP
ejpam-4043	268	23	k∞	k∞	PROPN
ejpam-4043	268	24	,	,	PUNCT
ejpam-4043	268	25	k∈	k∈	PROPN
ejpam-4043	268	26	,	,	PUNCT
ejpam-4043	268	27	k3	k3	VERB
ejpam-4043	268	28	and	and	CCONJ
ejpam-4043	268	29	k4	k4	VERB
ejpam-4043	268	30	for	for	ADP
ejpam-4043	268	31	i	i	PRON
ejpam-4043	268	32	=	=	NOUN
ejpam-4043	268	33	1	1	NUM
ejpam-4043	268	34	,	,	PUNCT
ejpam-4043	268	35	2	2	NUM
ejpam-4043	268	36	,	,	PUNCT
ejpam-4043	268	37	3	3	NUM
ejpam-4043	268	38	,	,	PUNCT
ejpam-4043	268	39	4	4	NUM
ejpam-4043	268	40	respectively	respectively	ADV
ejpam-4043	268	41	.	.	PUNCT
ejpam-4043	269	1	moreover	moreover	ADV
ejpam-4043	269	2	,	,	PUNCT
ejpam-4043	269	3	|k|	|k|	PROPN
ejpam-4043	269	4	=	=	SYM
ejpam-4043	269	5	34n−	34n−	NUM
ejpam-4043	269	6	∑4	∑4	PROPN
ejpam-4043	269	7	i=0	i=0	PROPN
ejpam-4043	269	8	deg(gi(t	deg(gi(t	PROPN
ejpam-4043	269	9	)	)	PUNCT
ejpam-4043	269	10	)	)	PUNCT
ejpam-4043	269	11	theorem	theorem	VERB
ejpam-4043	269	12	13	13	NUM
ejpam-4043	269	13	.	.	PUNCT
ejpam-4043	270	1	let	let	VERB
ejpam-4043	270	2	k	k	PRON
ejpam-4043	270	3	be	be	AUX
ejpam-4043	270	4	a	a	DET
ejpam-4043	270	5	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	270	6	code	code	NOUN
ejpam-4043	270	7	over	over	ADP
ejpam-4043	270	8	the	the	DET
ejpam-4043	270	9	ring	ring	NOUN
ejpam-4043	270	10	<	<	X
ejpam-4043	270	11	of	of	ADP
ejpam-4043	270	12	length	length	NOUN
ejpam-4043	270	13	n.	n.	PROPN
ejpam-4043	270	14	then	then	ADV
ejpam-4043	270	15	k⊥	k⊥	PROPN
ejpam-4043	270	16	is	be	AUX
ejpam-4043	270	17	also	also	ADV
ejpam-4043	270	18	a	a	DET
ejpam-4043	270	19	ϑ-constacyclic	ϑ-constacyclic	PROPN
ejpam-4043	270	20	code	code	NOUN
ejpam-4043	270	21	over	over	ADP
ejpam-4043	270	22	the	the	DET
ejpam-4043	270	23	ring	ring	NOUN
ejpam-4043	270	24	<	<	X
ejpam-4043	270	25	of	of	ADP
ejpam-4043	270	26	length	length	NOUN
ejpam-4043	270	27	n.	n.	PROPN
ejpam-4043	270	28	moreover	moreover	ADV
ejpam-4043	270	29	,	,	PUNCT
ejpam-4043	270	30	1	1	X
ejpam-4043	270	31	.	.	PUNCT
ejpam-4043	271	1	k⊥	k⊥	X
ejpam-4043	271	2	=	=	PUNCT
ejpam-4043	272	1	ξ1k⊥∞	ξ1k⊥∞	PROPN
ejpam-4043	272	2	⊕	⊕	PROPN
ejpam-4043	272	3	ξ2k⊥∈	ξ2k⊥∈	PROPN
ejpam-4043	272	4	⊕	⊕	PROPN
ejpam-4043	272	5	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	272	6	⊕	⊕	PROPN
ejpam-4043	273	1	ξ4k⊥4	ξ4k⊥4	PROPN
ejpam-4043	273	2	2	2	NUM
ejpam-4043	273	3	.	.	PUNCT
ejpam-4043	273	4	k⊥	k⊥	X
ejpam-4043	274	1	=	=	PUNCT
ejpam-4043	275	1	<	<	X
ejpam-4043	275	2	ξ1	ξ1	PROPN
ejpam-4043	275	3	g	g	NOUN
ejpam-4043	275	4	?	?	PUNCT
ejpam-4043	276	1	1(t	1(t	NUM
ejpam-4043	276	2	)	)	PUNCT
ejpam-4043	276	3	,	,	PUNCT
ejpam-4043	276	4	ξ2	ξ2	NOUN
ejpam-4043	276	5	g	g	NOUN
ejpam-4043	276	6	?	?	PUNCT
ejpam-4043	277	1	2(t	2(t	NUM
ejpam-4043	277	2	)	)	PUNCT
ejpam-4043	277	3	,	,	PUNCT
ejpam-4043	277	4	ξ3	ξ3	NOUN
ejpam-4043	277	5	g	g	NOUN
ejpam-4043	277	6	?	?	PUNCT
ejpam-4043	278	1	3(t	3(t	NUM
ejpam-4043	278	2	)	)	PUNCT
ejpam-4043	278	3	,	,	PUNCT
ejpam-4043	278	4	ξ4	ξ4	NOUN
ejpam-4043	278	5	g	g	NOUN
ejpam-4043	278	6	?	?	PUNCT
ejpam-4043	279	1	4(t	4(t	NUM
ejpam-4043	279	2	)	)	PUNCT
ejpam-4043	279	3	>	>	X
ejpam-4043	280	1	=	=	PUNCT
ejpam-4043	280	2	<	<	X
ejpam-4043	280	3	ξ1	ξ1	PROPN
ejpam-4043	280	4	g	g	NOUN
ejpam-4043	280	5	?	?	PUNCT
ejpam-4043	281	1	1(t	1(t	NUM
ejpam-4043	281	2	)	)	PUNCT
ejpam-4043	282	1	+	+	CCONJ
ejpam-4043	282	2	ξ2	ξ2	ADJ
ejpam-4043	282	3	g	g	NOUN
ejpam-4043	282	4	?	?	PUNCT
ejpam-4043	283	1	2(t	2(t	NUM
ejpam-4043	283	2	)	)	PUNCT
ejpam-4043	284	1	+	+	NOUN
ejpam-4043	284	2	ξ3	ξ3	NOUN
ejpam-4043	284	3	g	g	NOUN
ejpam-4043	284	4	?	?	PUNCT
ejpam-4043	285	1	3(t	3(t	NUM
ejpam-4043	285	2	)	)	PUNCT
ejpam-4043	285	3	+	+	CCONJ
ejpam-4043	285	4	ξ4	ξ4	NOUN
ejpam-4043	285	5	g	g	NOUN
ejpam-4043	285	6	?	?	PUNCT
ejpam-4043	286	1	4(t	4(t	NUM
ejpam-4043	286	2	)	)	PUNCT
ejpam-4043	286	3	>	>	X
ejpam-4043	287	1	3	3	X
ejpam-4043	287	2	.	.	PUNCT
ejpam-4043	288	1	|	|	ADV
ejpam-4043	288	2	k⊥	k⊥	PROPN
ejpam-4043	288	3	|	|	ADV
ejpam-4043	288	4	=	=	SYM
ejpam-4043	288	5	3	3	NUM
ejpam-4043	288	6	∑4	∑4	PROPN
ejpam-4043	288	7	i=1	i=1	PROPN
ejpam-4043	288	8	deg(gi(t	deg(gi(t	PROPN
ejpam-4043	288	9	)	)	PUNCT
ejpam-4043	288	10	)	)	PUNCT
ejpam-4043	288	11	where	where	SCONJ
ejpam-4043	288	12	g?i	g?i	X
ejpam-4043	288	13	(	(	PUNCT
ejpam-4043	288	14	t	t	NOUN
ejpam-4043	288	15	)	)	PUNCT
ejpam-4043	288	16	are	be	AUX
ejpam-4043	288	17	the	the	DET
ejpam-4043	288	18	reciprocal	reciprocal	ADJ
ejpam-4043	288	19	polynomial	polynomial	NOUN
ejpam-4043	288	20	of	of	ADP
ejpam-4043	288	21	xn+1	xn+1	PROPN
ejpam-4043	288	22	g1(t	g1(t	NOUN
ejpam-4043	288	23	)	)	PUNCT
ejpam-4043	288	24	,	,	PUNCT
ejpam-4043	288	25	x	x	PUNCT
ejpam-4043	288	26	n+1	n+1	SYM
ejpam-4043	288	27	g2(t	g2(t	PROPN
ejpam-4043	288	28	)	)	PUNCT
ejpam-4043	288	29	,	,	PUNCT
ejpam-4043	288	30	x	x	X
ejpam-4043	288	31	n+1	n+1	NUM
ejpam-4043	288	32	g3(t	g3(t	NUM
ejpam-4043	288	33	)	)	PUNCT
ejpam-4043	288	34	and	and	CCONJ
ejpam-4043	288	35	xn−1	xn−1	PROPN
ejpam-4043	288	36	g4(t	g4(t	PROPN
ejpam-4043	288	37	)	)	PUNCT
ejpam-4043	288	38	for	for	ADP
ejpam-4043	288	39	i	i	PROPN
ejpam-4043	288	40	=	=	NOUN
ejpam-4043	288	41	1	1	NUM
ejpam-4043	288	42	,	,	PUNCT
ejpam-4043	288	43	2	2	NUM
ejpam-4043	288	44	,	,	PUNCT
ejpam-4043	288	45	3	3	NUM
ejpam-4043	288	46	,	,	PUNCT
ejpam-4043	288	47	4	4	NUM
ejpam-4043	288	48	respectively	respectively	ADV
ejpam-4043	288	49	.	.	PUNCT
ejpam-4043	289	1	lemma	lemma	PROPN
ejpam-4043	289	2	1	1	NUM
ejpam-4043	289	3	.	.	PUNCT
ejpam-4043	290	1	[	[	X
ejpam-4043	290	2	4	4	X
ejpam-4043	290	3	]	]	X
ejpam-4043	290	4	if	if	SCONJ
ejpam-4043	290	5	k	k	PROPN
ejpam-4043	290	6	is	be	AUX
ejpam-4043	290	7	a	a	DET
ejpam-4043	290	8	cyclic	cyclic	ADJ
ejpam-4043	290	9	or	or	CCONJ
ejpam-4043	290	10	negacyclic	negacyclic	ADJ
ejpam-4043	290	11	code	code	NOUN
ejpam-4043	290	12	over	over	ADP
ejpam-4043	290	13	the	the	DET
ejpam-4043	290	14	ring	ring	NOUN
ejpam-4043	290	15	zp	zp	PROPN
ejpam-4043	290	16	with	with	ADP
ejpam-4043	290	17	a	a	DET
ejpam-4043	290	18	generator	generator	NOUN
ejpam-4043	290	19	polynomial	polynomial	PROPN
ejpam-4043	290	20	g(t	g(t	PROPN
ejpam-4043	290	21	)	)	PUNCT
ejpam-4043	290	22	.	.	PUNCT
ejpam-4043	291	1	then	then	ADV
ejpam-4043	291	2	,	,	PUNCT
ejpam-4043	291	3	k	k	PROPN
ejpam-4043	291	4	contains	contain	VERB
ejpam-4043	291	5	its	its	PRON
ejpam-4043	291	6	dual	dual	ADJ
ejpam-4043	291	7	code	code	NOUN
ejpam-4043	291	8	if	if	SCONJ
ejpam-4043	292	1	and	and	CCONJ
ejpam-4043	292	2	only	only	ADV
ejpam-4043	292	3	if	if	SCONJ
ejpam-4043	292	4	xn	xn	PROPN
ejpam-4043	292	5	−	−	NOUN
ejpam-4043	292	6	ι	ι	X
ejpam-4043	292	7	≡	≡	PROPN
ejpam-4043	292	8	0	0	NUM
ejpam-4043	292	9	mod(g(t)g?(t	mod(g(t)g?(t	NOUN
ejpam-4043	292	10	)	)	PUNCT
ejpam-4043	292	11	)	)	PUNCT
ejpam-4043	292	12	where	where	SCONJ
ejpam-4043	292	13	ι	ι	X
ejpam-4043	292	14	=	=	PUNCT
ejpam-4043	292	15	±1	±1	VERB
ejpam-4043	292	16	.	.	PUNCT
ejpam-4043	293	1	case	case	NOUN
ejpam-4043	293	2	1	1	NUM
ejpam-4043	293	3	.	.	PUNCT
ejpam-4043	294	1	ϑ	ϑ	X
ejpam-4043	294	2	=	=	SYM
ejpam-4043	294	3	1	1	NUM
ejpam-4043	294	4	+	+	CCONJ
ejpam-4043	294	5	ν	ν	X
ejpam-4043	294	6	+	+	X
ejpam-4043	294	7	ω	ω	NUM
ejpam-4043	294	8	+	+	CCONJ
ejpam-4043	294	9	2νω	2νω	NOUN
ejpam-4043	294	10	theorem	theorem	ADJ
ejpam-4043	294	11	14	14	NUM
ejpam-4043	294	12	.	.	PUNCT
ejpam-4043	295	1	if	if	SCONJ
ejpam-4043	295	2	k	k	PROPN
ejpam-4043	295	3	=	=	X
ejpam-4043	295	4	<	<	X
ejpam-4043	295	5	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	295	6	)	)	PUNCT
ejpam-4043	295	7	+	+	X
ejpam-4043	295	8	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	295	9	)	)	PUNCT
ejpam-4043	295	10	+	+	CCONJ
ejpam-4043	295	11	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	295	12	)	)	PUNCT
ejpam-4043	295	13	+	+	X
ejpam-4043	295	14	ξ4g4(t	ξ4g4(t	X
ejpam-4043	295	15	)	)	PUNCT
ejpam-4043	295	16	>	>	X
ejpam-4043	295	17	is	be	AUX
ejpam-4043	295	18	a	a	DET
ejpam-4043	295	19	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	295	20	code	code	NOUN
ejpam-4043	295	21	over	over	ADP
ejpam-4043	295	22	the	the	DET
ejpam-4043	295	23	ring	ring	NOUN
ejpam-4043	295	24	<	<	X
ejpam-4043	295	25	of	of	ADP
ejpam-4043	295	26	length	length	NOUN
ejpam-4043	295	27	n.	n.	PROPN
ejpam-4043	295	28	then	then	ADV
ejpam-4043	295	29	,	,	PUNCT
ejpam-4043	295	30	k⊥	k⊥	PROPN
ejpam-4043	295	31	⊆	⊆	NUM
ejpam-4043	295	32	k	k	NOUN
ejpam-4043	296	1	if	if	SCONJ
ejpam-4043	296	2	and	and	CCONJ
ejpam-4043	296	3	only	only	ADV
ejpam-4043	296	4	if	if	SCONJ
ejpam-4043	296	5	xn	xn	PROPN
ejpam-4043	296	6	+	+	SYM
ejpam-4043	296	7	1	1	NUM
ejpam-4043	296	8	≡	≡	PROPN
ejpam-4043	296	9	0	0	NUM
ejpam-4043	296	10	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	296	11	?	?	PUNCT
ejpam-4043	297	1	i	i	PRON
ejpam-4043	297	2	(	(	PUNCT
ejpam-4043	297	3	t	t	PROPN
ejpam-4043	297	4	)	)	PUNCT
ejpam-4043	297	5	)	)	PUNCT
ejpam-4043	298	1	and	and	CCONJ
ejpam-4043	298	2	xn	xn	NUM
ejpam-4043	298	3	−	−	PROPN
ejpam-4043	299	1	1	1	NUM
ejpam-4043	299	2	≡	≡	PROPN
ejpam-4043	299	3	0	0	PUNCT
ejpam-4043	299	4	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	299	5	?	?	PUNCT
ejpam-4043	300	1	j	j	PROPN
ejpam-4043	300	2	(	(	PUNCT
ejpam-4043	300	3	t	t	PROPN
ejpam-4043	300	4	)	)	PUNCT
ejpam-4043	300	5	)	)	PUNCT
ejpam-4043	300	6	.	.	PUNCT
ejpam-4043	301	1	for	for	ADP
ejpam-4043	301	2	i	i	PRON
ejpam-4043	301	3	=	=	NOUN
ejpam-4043	301	4	1	1	NUM
ejpam-4043	301	5	,	,	PUNCT
ejpam-4043	301	6	2	2	NUM
ejpam-4043	301	7	,	,	PUNCT
ejpam-4043	301	8	3	3	NUM
ejpam-4043	301	9	and	and	CCONJ
ejpam-4043	301	10	j	j	NOUN
ejpam-4043	301	11	=	=	NOUN
ejpam-4043	301	12	4	4	X
ejpam-4043	301	13	.	.	PUNCT
ejpam-4043	301	14	prateek	prateek	PROPN
ejpam-4043	301	15	mor	mor	PROPN
ejpam-4043	301	16	et	et	PROPN
ejpam-4043	301	17	al	al	PROPN
ejpam-4043	301	18	.	.	PUNCT
ejpam-4043	301	19	/	/	SYM
ejpam-4043	301	20	eur	eur	PROPN
ejpam-4043	301	21	.	.	PUNCT
ejpam-4043	302	1	j.	j.	PROPN
ejpam-4043	302	2	pure	pure	PROPN
ejpam-4043	302	3	appl	appl	PROPN
ejpam-4043	302	4	.	.	PROPN
ejpam-4043	302	5	math	math	PROPN
ejpam-4043	302	6	,	,	PUNCT
ejpam-4043	302	7	14	14	NUM
ejpam-4043	302	8	(	(	PUNCT
ejpam-4043	302	9	3	3	NUM
ejpam-4043	302	10	)	)	PUNCT
ejpam-4043	302	11	(	(	PUNCT
ejpam-4043	302	12	2021	2021	NUM
ejpam-4043	302	13	)	)	PUNCT
ejpam-4043	302	14	,	,	PUNCT
ejpam-4043	302	15	1082	1082	NUM
ejpam-4043	302	16	-	-	SYM
ejpam-4043	302	17	1097	1097	NUM
ejpam-4043	302	18	1091	1091	NUM
ejpam-4043	302	19	proof	proof	NOUN
ejpam-4043	302	20	.	.	PUNCT
ejpam-4043	303	1	let	let	VERB
ejpam-4043	303	2	k	k	NOUN
ejpam-4043	303	3	=	=	PUNCT
ejpam-4043	303	4	<	<	X
ejpam-4043	303	5	g(t	g(t	PROPN
ejpam-4043	303	6	)	)	PUNCT
ejpam-4043	303	7	>	>	X
ejpam-4043	304	1	=	=	PUNCT
ejpam-4043	304	2	<	<	X
ejpam-4043	304	3	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	304	4	)	)	PUNCT
ejpam-4043	304	5	+	+	X
ejpam-4043	304	6	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	304	7	)	)	PUNCT
ejpam-4043	304	8	+	+	CCONJ
ejpam-4043	304	9	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	304	10	)	)	PUNCT
ejpam-4043	304	11	+	+	X
ejpam-4043	304	12	ξ4g4(t	ξ4g4(t	X
ejpam-4043	304	13	)	)	PUNCT
ejpam-4043	304	14	>	>	X
ejpam-4043	304	15	be	be	AUX
ejpam-4043	304	16	a	a	DET
ejpam-4043	304	17	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	304	18	code	code	NOUN
ejpam-4043	304	19	over	over	ADP
ejpam-4043	304	20	<	<	X
ejpam-4043	304	21	of	of	ADP
ejpam-4043	304	22	length	length	NOUN
ejpam-4043	304	23	n.	n.	PROPN
ejpam-4043	304	24	then	then	ADV
ejpam-4043	304	25	,	,	PUNCT
ejpam-4043	304	26	k	k	PROPN
ejpam-4043	304	27	=	=	SYM
ejpam-4043	304	28	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	304	29	⊕	⊕	PROPN
ejpam-4043	304	30	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	305	1	⊕	⊕	PROPN
ejpam-4043	305	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	305	3	⊕	⊕	PROPN
ejpam-4043	305	4	ξ4k4	ξ4k4	PROPN
ejpam-4043	306	1	where	where	SCONJ
ejpam-4043	306	2	gi(t	gi(t	VERB
ejpam-4043	306	3	)	)	PUNCT
ejpam-4043	306	4	are	be	AUX
ejpam-4043	306	5	the	the	DET
ejpam-4043	306	6	generator	generator	NOUN
ejpam-4043	306	7	polynomial	polynomial	NOUN
ejpam-4043	306	8	of	of	ADP
ejpam-4043	306	9	k∞	k∞	PROPN
ejpam-4043	306	10	,	,	PUNCT
ejpam-4043	306	11	k∈	k∈	PROPN
ejpam-4043	306	12	,	,	PUNCT
ejpam-4043	306	13	k3	k3	VERB
ejpam-4043	306	14	and	and	CCONJ
ejpam-4043	306	15	k4	k4	VERB
ejpam-4043	306	16	for	for	ADP
ejpam-4043	306	17	i	i	PRON
ejpam-4043	306	18	=	=	NOUN
ejpam-4043	306	19	1	1	NUM
ejpam-4043	306	20	,	,	PUNCT
ejpam-4043	306	21	2	2	NUM
ejpam-4043	306	22	,	,	PUNCT
ejpam-4043	306	23	3	3	NUM
ejpam-4043	306	24	,	,	PUNCT
ejpam-4043	306	25	4	4	NUM
ejpam-4043	306	26	respectively	respectively	ADV
ejpam-4043	306	27	.	.	PUNCT
ejpam-4043	307	1	first	first	ADV
ejpam-4043	307	2	we	we	PRON
ejpam-4043	307	3	consider	consider	VERB
ejpam-4043	307	4	xn	xn	PROPN
ejpam-4043	308	1	+	+	CCONJ
ejpam-4043	308	2	1	1	NUM
ejpam-4043	308	3	≡	≡	PROPN
ejpam-4043	308	4	0	0	NUM
ejpam-4043	308	5	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	308	6	?	?	PUNCT
ejpam-4043	309	1	i	i	PRON
ejpam-4043	309	2	(	(	PUNCT
ejpam-4043	309	3	t	t	PROPN
ejpam-4043	309	4	)	)	PUNCT
ejpam-4043	309	5	)	)	PUNCT
ejpam-4043	310	1	and	and	CCONJ
ejpam-4043	310	2	xn	xn	NUM
ejpam-4043	310	3	−	−	PROPN
ejpam-4043	311	1	1	1	NUM
ejpam-4043	311	2	≡	≡	PROPN
ejpam-4043	311	3	0	0	PUNCT
ejpam-4043	311	4	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	311	5	?	?	PUNCT
ejpam-4043	312	1	j	j	PROPN
ejpam-4043	312	2	(	(	PUNCT
ejpam-4043	312	3	t	t	PROPN
ejpam-4043	312	4	)	)	PUNCT
ejpam-4043	312	5	)	)	PUNCT
ejpam-4043	312	6	.	.	PUNCT
ejpam-4043	313	1	for	for	ADP
ejpam-4043	313	2	i	i	PRON
ejpam-4043	313	3	=	=	NOUN
ejpam-4043	313	4	1	1	NUM
ejpam-4043	313	5	,	,	PUNCT
ejpam-4043	313	6	2	2	NUM
ejpam-4043	313	7	,	,	PUNCT
ejpam-4043	313	8	3	3	NUM
ejpam-4043	313	9	and	and	CCONJ
ejpam-4043	313	10	j	j	NOUN
ejpam-4043	313	11	=	=	NOUN
ejpam-4043	313	12	4	4	X
ejpam-4043	313	13	.	.	PUNCT
ejpam-4043	313	14	then	then	ADV
ejpam-4043	313	15	by	by	ADP
ejpam-4043	313	16	above	above	ADP
ejpam-4043	313	17	lemma	lemma	PROPN
ejpam-4043	313	18	,	,	PUNCT
ejpam-4043	313	19	we	we	PRON
ejpam-4043	313	20	have	have	VERB
ejpam-4043	313	21	k⊥∞	k⊥∞	PROPN
ejpam-4043	313	22	⊆	⊆	NUM
ejpam-4043	313	23	k∞	k∞	PROPN
ejpam-4043	313	24	,	,	PUNCT
ejpam-4043	313	25	k⊥∈	k⊥∈	PROPN
ejpam-4043	313	26	⊆	⊆	NUM
ejpam-4043	313	27	k∈,k⊥3	k∈,k⊥3	NOUN
ejpam-4043	313	28	⊆	⊆	NUM
ejpam-4043	313	29	k3	k3	ADJ
ejpam-4043	313	30	and	and	CCONJ
ejpam-4043	313	31	k⊥4	k⊥4	NOUN
ejpam-4043	313	32	⊆	⊆	NUM
ejpam-4043	313	33	k4	k4	NOUN
ejpam-4043	313	34	,	,	PUNCT
ejpam-4043	313	35	and	and	CCONJ
ejpam-4043	313	36	therefore	therefore	ADV
ejpam-4043	313	37	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	313	38	⊆	⊆	NUM
ejpam-4043	313	39	ξ1k∞	ξ1k∞	NOUN
ejpam-4043	313	40	,	,	PUNCT
ejpam-4043	313	41	ξ2k⊥∈	ξ2k⊥∈	NUM
ejpam-4043	313	42	⊆	⊆	NUM
ejpam-4043	313	43	ξ2k∈	ξ2k∈	NUM
ejpam-4043	313	44	,	,	PUNCT
ejpam-4043	313	45	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	313	46	⊆	⊆	NUM
ejpam-4043	313	47	ξ3k3	ξ3k3	NOUN
ejpam-4043	313	48	and	and	CCONJ
ejpam-4043	313	49	ξ4k⊥4	ξ4k⊥4	PROPN
ejpam-4043	313	50	⊆	⊆	NUM
ejpam-4043	313	51	ξ4k4	ξ4k4	NOUN
ejpam-4043	313	52	which	which	PRON
ejpam-4043	313	53	implies	imply	VERB
ejpam-4043	313	54	that	that	SCONJ
ejpam-4043	313	55	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	313	56	⊕	⊕	PROPN
ejpam-4043	313	57	ξ2k⊥∈	ξ2k⊥∈	PROPN
ejpam-4043	313	58	⊕	⊕	PROPN
ejpam-4043	313	59	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	313	60	⊕	⊕	PROPN
ejpam-4043	313	61	ξ4k⊥4	ξ4k⊥4	NOUN
ejpam-4043	313	62	⊆	⊆	NUM
ejpam-4043	313	63	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	313	64	⊕	⊕	PROPN
ejpam-4043	313	65	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	314	1	⊕	⊕	PROPN
ejpam-4043	314	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	314	3	⊕	⊕	PROPN
ejpam-4043	314	4	ξ4k4	ξ4k4	PUNCT
ejpam-4043	315	1	thus	thus	ADV
ejpam-4043	315	2	,	,	PUNCT
ejpam-4043	315	3	we	we	PRON
ejpam-4043	315	4	have	have	VERB
ejpam-4043	315	5	k⊥	k⊥	PROPN
ejpam-4043	315	6	⊆	⊆	NUM
ejpam-4043	315	7	k.	k.	NOUN
ejpam-4043	315	8	conversely	conversely	ADV
ejpam-4043	315	9	,	,	PUNCT
ejpam-4043	315	10	let	let	VERB
ejpam-4043	315	11	us	we	PRON
ejpam-4043	315	12	consider	consider	VERB
ejpam-4043	315	13	k⊥	k⊥	PROPN
ejpam-4043	315	14	⊆	⊆	NUM
ejpam-4043	315	15	k	k	NOUN
ejpam-4043	315	16	,	,	PUNCT
ejpam-4043	315	17	then	then	ADV
ejpam-4043	315	18	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	315	19	⊕	⊕	PROPN
ejpam-4043	315	20	ξ2k⊥∈	ξ2k⊥∈	PROPN
ejpam-4043	315	21	⊕	⊕	PROPN
ejpam-4043	315	22	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	315	23	⊕	⊕	PROPN
ejpam-4043	316	1	ξ4k⊥4	ξ4k⊥4	NOUN
ejpam-4043	316	2	⊆	⊆	NUM
ejpam-4043	316	3	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	316	4	⊕	⊕	PROPN
ejpam-4043	316	5	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	317	1	⊕	⊕	PROPN
ejpam-4043	317	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	317	3	⊕	⊕	PROPN
ejpam-4043	317	4	ξ4k4	ξ4k4	PROPN
ejpam-4043	317	5	,	,	PUNCT
ejpam-4043	317	6	which	which	PRON
ejpam-4043	317	7	implies	imply	VERB
ejpam-4043	317	8	that	that	SCONJ
ejpam-4043	317	9	ξ1k⊥∞	ξ1k⊥∞	ADP
ejpam-4043	317	10	⊆	⊆	NUM
ejpam-4043	317	11	ξ1k∞	ξ1k∞	NOUN
ejpam-4043	317	12	,	,	PUNCT
ejpam-4043	317	13	ξ2k⊥∈	ξ2k⊥∈	NUM
ejpam-4043	317	14	⊆	⊆	NUM
ejpam-4043	317	15	ξ2k∈	ξ2k∈	NUM
ejpam-4043	317	16	,	,	PUNCT
ejpam-4043	317	17	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	317	18	⊆	⊆	NUM
ejpam-4043	317	19	ξ3k3	ξ3k3	NOUN
ejpam-4043	317	20	and	and	CCONJ
ejpam-4043	317	21	ξ4k⊥4	ξ4k⊥4	PROPN
ejpam-4043	317	22	⊆	⊆	NUM
ejpam-4043	317	23	ξ4k4	ξ4k4	NOUN
ejpam-4043	317	24	,	,	PUNCT
ejpam-4043	317	25	that	that	PRON
ejpam-4043	317	26	implies	imply	VERB
ejpam-4043	317	27	k⊥∞	k⊥∞	PROPN
ejpam-4043	317	28	⊆	⊆	NUM
ejpam-4043	317	29	k∞	k∞	PROPN
ejpam-4043	317	30	,	,	PUNCT
ejpam-4043	317	31	k⊥∈	k⊥∈	PROPN
ejpam-4043	317	32	⊆	⊆	NUM
ejpam-4043	317	33	k∈	k∈	ADJ
ejpam-4043	317	34	,	,	PUNCT
ejpam-4043	317	35	k⊥3	k⊥3	X
ejpam-4043	317	36	⊆	⊆	NUM
ejpam-4043	317	37	k3	k3	ADJ
ejpam-4043	317	38	and	and	CCONJ
ejpam-4043	317	39	k⊥4	k⊥4	NOUN
ejpam-4043	317	40	⊆	⊆	NUM
ejpam-4043	317	41	k4	k4	NOUN
ejpam-4043	317	42	.	.	PUNCT
ejpam-4043	318	1	then	then	ADV
ejpam-4043	318	2	by	by	ADP
ejpam-4043	318	3	above	above	ADP
ejpam-4043	318	4	lemma	lemma	PROPN
ejpam-4043	318	5	,	,	PUNCT
ejpam-4043	318	6	xn	xn	PROPN
ejpam-4043	319	1	+	+	CCONJ
ejpam-4043	319	2	1	1	NUM
ejpam-4043	319	3	≡	≡	PROPN
ejpam-4043	319	4	0	0	NUM
ejpam-4043	319	5	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	319	6	?	?	PUNCT
ejpam-4043	320	1	i	i	PRON
ejpam-4043	320	2	(	(	PUNCT
ejpam-4043	320	3	t	t	PROPN
ejpam-4043	320	4	)	)	PUNCT
ejpam-4043	320	5	)	)	PUNCT
ejpam-4043	321	1	and	and	CCONJ
ejpam-4043	321	2	xn	xn	NUM
ejpam-4043	321	3	−	−	PROPN
ejpam-4043	322	1	1	1	NUM
ejpam-4043	322	2	≡	≡	PROPN
ejpam-4043	322	3	0	0	PUNCT
ejpam-4043	322	4	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	322	5	?	?	PUNCT
ejpam-4043	323	1	j	j	PROPN
ejpam-4043	323	2	(	(	PUNCT
ejpam-4043	323	3	t	t	PROPN
ejpam-4043	323	4	)	)	PUNCT
ejpam-4043	323	5	)	)	PUNCT
ejpam-4043	323	6	.	.	PUNCT
ejpam-4043	324	1	for	for	ADP
ejpam-4043	324	2	i	i	PRON
ejpam-4043	324	3	=	=	NOUN
ejpam-4043	324	4	1	1	NUM
ejpam-4043	324	5	,	,	PUNCT
ejpam-4043	324	6	2	2	NUM
ejpam-4043	324	7	,	,	PUNCT
ejpam-4043	324	8	3	3	NUM
ejpam-4043	324	9	and	and	CCONJ
ejpam-4043	324	10	j	j	NOUN
ejpam-4043	324	11	=	=	NOUN
ejpam-4043	324	12	4	4	X
ejpam-4043	324	13	.	.	PUNCT
ejpam-4043	324	14	case	case	NOUN
ejpam-4043	324	15	2	2	NUM
ejpam-4043	324	16	.	.	PUNCT
ejpam-4043	324	17	ϑ	ϑ	X
ejpam-4043	324	18	=	=	SYM
ejpam-4043	324	19	1	1	NUM
ejpam-4043	324	20	+	+	CCONJ
ejpam-4043	324	21	ν	ν	X
ejpam-4043	324	22	+	+	X
ejpam-4043	324	23	ω	ω	NUM
ejpam-4043	324	24	+	+	CCONJ
ejpam-4043	324	25	2νω	2νω	ADJ
ejpam-4043	324	26	prateek	prateek	NOUN
ejpam-4043	324	27	mor	mor	PROPN
ejpam-4043	324	28	et	et	PROPN
ejpam-4043	324	29	al	al	PROPN
ejpam-4043	324	30	.	.	PUNCT
ejpam-4043	324	31	/	/	SYM
ejpam-4043	324	32	eur	eur	PROPN
ejpam-4043	324	33	.	.	PUNCT
ejpam-4043	325	1	j.	j.	PROPN
ejpam-4043	325	2	pure	pure	PROPN
ejpam-4043	325	3	appl	appl	PROPN
ejpam-4043	325	4	.	.	PROPN
ejpam-4043	325	5	math	math	PROPN
ejpam-4043	325	6	,	,	PUNCT
ejpam-4043	325	7	14	14	NUM
ejpam-4043	325	8	(	(	PUNCT
ejpam-4043	325	9	3	3	NUM
ejpam-4043	325	10	)	)	PUNCT
ejpam-4043	325	11	(	(	PUNCT
ejpam-4043	325	12	2021	2021	NUM
ejpam-4043	325	13	)	)	PUNCT
ejpam-4043	325	14	,	,	PUNCT
ejpam-4043	325	15	1082	1082	NUM
ejpam-4043	325	16	-	-	SYM
ejpam-4043	325	17	1097	1097	NUM
ejpam-4043	325	18	1092	1092	NUM
ejpam-4043	325	19	theorem	theorem	VERB
ejpam-4043	325	20	15	15	NUM
ejpam-4043	325	21	.	.	PUNCT
ejpam-4043	326	1	if	if	SCONJ
ejpam-4043	326	2	k	k	PROPN
ejpam-4043	326	3	=	=	X
ejpam-4043	326	4	<	<	X
ejpam-4043	326	5	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	326	6	)	)	PUNCT
ejpam-4043	326	7	+	+	X
ejpam-4043	326	8	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	326	9	)	)	PUNCT
ejpam-4043	326	10	+	+	CCONJ
ejpam-4043	326	11	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	326	12	)	)	PUNCT
ejpam-4043	326	13	+	+	X
ejpam-4043	326	14	ξ4g4(t	ξ4g4(t	X
ejpam-4043	326	15	)	)	PUNCT
ejpam-4043	326	16	>	>	X
ejpam-4043	326	17	is	be	AUX
ejpam-4043	326	18	a	a	DET
ejpam-4043	326	19	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	326	20	code	code	NOUN
ejpam-4043	326	21	over	over	ADP
ejpam-4043	326	22	the	the	DET
ejpam-4043	326	23	ring	ring	NOUN
ejpam-4043	326	24	<	<	X
ejpam-4043	326	25	of	of	ADP
ejpam-4043	326	26	length	length	NOUN
ejpam-4043	326	27	n.	n.	PROPN
ejpam-4043	326	28	then	then	ADV
ejpam-4043	326	29	,	,	PUNCT
ejpam-4043	326	30	k⊥	k⊥	PROPN
ejpam-4043	326	31	⊆	⊆	NUM
ejpam-4043	326	32	k	k	NOUN
ejpam-4043	327	1	if	if	SCONJ
ejpam-4043	327	2	and	and	CCONJ
ejpam-4043	327	3	only	only	ADV
ejpam-4043	327	4	if	if	SCONJ
ejpam-4043	327	5	xn	xn	PROPN
ejpam-4043	327	6	−	−	PROPN
ejpam-4043	327	7	1	1	NUM
ejpam-4043	327	8	≡	≡	PROPN
ejpam-4043	327	9	0	0	NUM
ejpam-4043	328	1	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	328	2	?	?	PUNCT
ejpam-4043	329	1	i	i	PRON
ejpam-4043	329	2	(	(	PUNCT
ejpam-4043	329	3	t	t	PROPN
ejpam-4043	329	4	)	)	PUNCT
ejpam-4043	329	5	)	)	PUNCT
ejpam-4043	330	1	and	and	CCONJ
ejpam-4043	330	2	xn	xn	NUM
ejpam-4043	331	1	+	+	CCONJ
ejpam-4043	331	2	1	1	NUM
ejpam-4043	331	3	≡	≡	PROPN
ejpam-4043	331	4	0	0	PUNCT
ejpam-4043	331	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	331	6	?	?	PUNCT
ejpam-4043	332	1	j	j	PROPN
ejpam-4043	332	2	(	(	PUNCT
ejpam-4043	332	3	t	t	PROPN
ejpam-4043	332	4	)	)	PUNCT
ejpam-4043	332	5	)	)	PUNCT
ejpam-4043	332	6	.	.	PUNCT
ejpam-4043	333	1	for	for	ADP
ejpam-4043	333	2	i	i	PRON
ejpam-4043	333	3	=	=	SYM
ejpam-4043	333	4	1	1	NUM
ejpam-4043	333	5	and	and	CCONJ
ejpam-4043	333	6	j	j	NOUN
ejpam-4043	333	7	=	=	SYM
ejpam-4043	333	8	2	2	NUM
ejpam-4043	333	9	,	,	PUNCT
ejpam-4043	333	10	3	3	NUM
ejpam-4043	333	11	,	,	PUNCT
ejpam-4043	333	12	4	4	NUM
ejpam-4043	333	13	.	.	PUNCT
ejpam-4043	334	1	proof	proof	NOUN
ejpam-4043	334	2	.	.	PUNCT
ejpam-4043	335	1	let	let	VERB
ejpam-4043	335	2	k	k	NOUN
ejpam-4043	335	3	=	=	PUNCT
ejpam-4043	335	4	<	<	X
ejpam-4043	335	5	g(t	g(t	PROPN
ejpam-4043	335	6	)	)	PUNCT
ejpam-4043	335	7	>	>	X
ejpam-4043	336	1	=	=	PUNCT
ejpam-4043	336	2	<	<	X
ejpam-4043	336	3	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	336	4	)	)	PUNCT
ejpam-4043	336	5	+	+	X
ejpam-4043	336	6	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	336	7	)	)	PUNCT
ejpam-4043	336	8	+	+	CCONJ
ejpam-4043	336	9	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	336	10	)	)	PUNCT
ejpam-4043	336	11	+	+	X
ejpam-4043	336	12	ξ4g4(t	ξ4g4(t	X
ejpam-4043	336	13	)	)	PUNCT
ejpam-4043	336	14	>	>	X
ejpam-4043	336	15	be	be	AUX
ejpam-4043	336	16	a	a	DET
ejpam-4043	336	17	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	336	18	code	code	NOUN
ejpam-4043	336	19	over	over	ADP
ejpam-4043	336	20	<	<	X
ejpam-4043	336	21	of	of	ADP
ejpam-4043	336	22	length	length	NOUN
ejpam-4043	336	23	n.	n.	PROPN
ejpam-4043	336	24	then	then	ADV
ejpam-4043	336	25	,	,	PUNCT
ejpam-4043	336	26	k	k	PROPN
ejpam-4043	336	27	=	=	SYM
ejpam-4043	336	28	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	336	29	⊕	⊕	PROPN
ejpam-4043	336	30	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	337	1	⊕	⊕	PROPN
ejpam-4043	337	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	337	3	⊕	⊕	PROPN
ejpam-4043	337	4	ξ4k4	ξ4k4	PROPN
ejpam-4043	338	1	where	where	SCONJ
ejpam-4043	338	2	gi(t	gi(t	VERB
ejpam-4043	338	3	)	)	PUNCT
ejpam-4043	338	4	are	be	AUX
ejpam-4043	338	5	the	the	DET
ejpam-4043	338	6	generator	generator	NOUN
ejpam-4043	338	7	polynomial	polynomial	NOUN
ejpam-4043	338	8	of	of	ADP
ejpam-4043	338	9	k∞	k∞	PROPN
ejpam-4043	338	10	,	,	PUNCT
ejpam-4043	338	11	k∈	k∈	PROPN
ejpam-4043	338	12	,	,	PUNCT
ejpam-4043	338	13	k3	k3	VERB
ejpam-4043	338	14	and	and	CCONJ
ejpam-4043	338	15	k4	k4	VERB
ejpam-4043	338	16	for	for	ADP
ejpam-4043	338	17	i	i	PRON
ejpam-4043	338	18	=	=	NOUN
ejpam-4043	338	19	1	1	NUM
ejpam-4043	338	20	,	,	PUNCT
ejpam-4043	338	21	2	2	NUM
ejpam-4043	338	22	,	,	PUNCT
ejpam-4043	338	23	3	3	NUM
ejpam-4043	338	24	,	,	PUNCT
ejpam-4043	338	25	4	4	NUM
ejpam-4043	338	26	respectively	respectively	ADV
ejpam-4043	338	27	.	.	PUNCT
ejpam-4043	339	1	first	first	ADV
ejpam-4043	339	2	we	we	PRON
ejpam-4043	339	3	consider	consider	VERB
ejpam-4043	339	4	xn	xn	PROPN
ejpam-4043	339	5	−	−	PROPN
ejpam-4043	339	6	1	1	NUM
ejpam-4043	339	7	≡	≡	PROPN
ejpam-4043	339	8	0	0	NUM
ejpam-4043	339	9	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	339	10	?	?	PUNCT
ejpam-4043	340	1	i	i	PRON
ejpam-4043	340	2	(	(	PUNCT
ejpam-4043	340	3	t	t	PROPN
ejpam-4043	340	4	)	)	PUNCT
ejpam-4043	340	5	)	)	PUNCT
ejpam-4043	341	1	and	and	CCONJ
ejpam-4043	341	2	xn	xn	NUM
ejpam-4043	342	1	+	+	CCONJ
ejpam-4043	342	2	1	1	NUM
ejpam-4043	342	3	≡	≡	PROPN
ejpam-4043	342	4	0	0	PUNCT
ejpam-4043	342	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	342	6	?	?	PUNCT
ejpam-4043	343	1	j	j	PROPN
ejpam-4043	343	2	(	(	PUNCT
ejpam-4043	343	3	t	t	PROPN
ejpam-4043	343	4	)	)	PUNCT
ejpam-4043	343	5	)	)	PUNCT
ejpam-4043	343	6	.	.	PUNCT
ejpam-4043	344	1	for	for	ADP
ejpam-4043	344	2	i	i	PRON
ejpam-4043	344	3	=	=	SYM
ejpam-4043	344	4	1	1	NUM
ejpam-4043	344	5	and	and	CCONJ
ejpam-4043	344	6	j	j	NOUN
ejpam-4043	344	7	=	=	SYM
ejpam-4043	344	8	2	2	NUM
ejpam-4043	344	9	,	,	PUNCT
ejpam-4043	344	10	3	3	NUM
ejpam-4043	344	11	,	,	PUNCT
ejpam-4043	344	12	4	4	NUM
ejpam-4043	344	13	.	.	PUNCT
ejpam-4043	345	1	then	then	ADV
ejpam-4043	345	2	by	by	ADP
ejpam-4043	345	3	above	above	ADP
ejpam-4043	345	4	lemma	lemma	PROPN
ejpam-4043	345	5	,	,	PUNCT
ejpam-4043	345	6	we	we	PRON
ejpam-4043	345	7	have	have	VERB
ejpam-4043	345	8	k⊥∞	k⊥∞	PROPN
ejpam-4043	345	9	⊆	⊆	NUM
ejpam-4043	345	10	k∞	k∞	PROPN
ejpam-4043	345	11	,	,	PUNCT
ejpam-4043	345	12	k⊥∈	k⊥∈	PROPN
ejpam-4043	345	13	⊆	⊆	NUM
ejpam-4043	345	14	k∈,k⊥3	k∈,k⊥3	NOUN
ejpam-4043	345	15	⊆	⊆	NUM
ejpam-4043	345	16	k3	k3	ADJ
ejpam-4043	345	17	and	and	CCONJ
ejpam-4043	345	18	k⊥4	k⊥4	NOUN
ejpam-4043	345	19	⊆	⊆	NUM
ejpam-4043	345	20	k4	k4	NOUN
ejpam-4043	345	21	,	,	PUNCT
ejpam-4043	345	22	and	and	CCONJ
ejpam-4043	345	23	therefore	therefore	ADV
ejpam-4043	345	24	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	345	25	⊆	⊆	NUM
ejpam-4043	345	26	ξ1k∞	ξ1k∞	NOUN
ejpam-4043	345	27	,	,	PUNCT
ejpam-4043	345	28	ξ2k⊥∈	ξ2k⊥∈	NUM
ejpam-4043	345	29	⊆	⊆	NUM
ejpam-4043	345	30	ξ2k∈	ξ2k∈	NUM
ejpam-4043	345	31	,	,	PUNCT
ejpam-4043	345	32	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	345	33	⊆	⊆	NUM
ejpam-4043	345	34	ξ3k3	ξ3k3	NOUN
ejpam-4043	345	35	and	and	CCONJ
ejpam-4043	345	36	ξ4k⊥4	ξ4k⊥4	PROPN
ejpam-4043	345	37	⊆	⊆	NUM
ejpam-4043	345	38	ξ4k4	ξ4k4	NOUN
ejpam-4043	345	39	which	which	PRON
ejpam-4043	345	40	implies	imply	VERB
ejpam-4043	345	41	that	that	SCONJ
ejpam-4043	345	42	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	345	43	⊕	⊕	PROPN
ejpam-4043	345	44	ξ2k⊥∈	ξ2k⊥∈	PROPN
ejpam-4043	345	45	⊕	⊕	PROPN
ejpam-4043	345	46	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	345	47	⊕	⊕	PROPN
ejpam-4043	345	48	ξ4k⊥4	ξ4k⊥4	NOUN
ejpam-4043	345	49	⊆	⊆	NUM
ejpam-4043	345	50	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	345	51	⊕	⊕	PROPN
ejpam-4043	345	52	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	346	1	⊕	⊕	PROPN
ejpam-4043	346	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	346	3	⊕	⊕	PROPN
ejpam-4043	346	4	ξ4k4	ξ4k4	PUNCT
ejpam-4043	347	1	thus	thus	ADV
ejpam-4043	347	2	,	,	PUNCT
ejpam-4043	347	3	we	we	PRON
ejpam-4043	347	4	have	have	VERB
ejpam-4043	347	5	k⊥	k⊥	PROPN
ejpam-4043	347	6	⊆	⊆	NUM
ejpam-4043	347	7	k.	k.	NOUN
ejpam-4043	347	8	conversely	conversely	ADV
ejpam-4043	347	9	,	,	PUNCT
ejpam-4043	347	10	let	let	VERB
ejpam-4043	347	11	us	we	PRON
ejpam-4043	347	12	consider	consider	VERB
ejpam-4043	347	13	k⊥	k⊥	PROPN
ejpam-4043	347	14	⊆	⊆	NUM
ejpam-4043	347	15	k	k	NOUN
ejpam-4043	347	16	,	,	PUNCT
ejpam-4043	347	17	then	then	ADV
ejpam-4043	347	18	ξ1k⊥∞	ξ1k⊥∞	VERB
ejpam-4043	347	19	⊕	⊕	PROPN
ejpam-4043	347	20	ξ2k⊥∈	ξ2k⊥∈	PROPN
ejpam-4043	347	21	⊕	⊕	PROPN
ejpam-4043	347	22	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	347	23	⊕	⊕	PROPN
ejpam-4043	348	1	ξ4k⊥4	ξ4k⊥4	NOUN
ejpam-4043	348	2	⊆	⊆	NUM
ejpam-4043	348	3	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	348	4	⊕	⊕	PROPN
ejpam-4043	348	5	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	349	1	⊕	⊕	PROPN
ejpam-4043	349	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	349	3	⊕	⊕	PROPN
ejpam-4043	349	4	ξ4k4	ξ4k4	PROPN
ejpam-4043	349	5	,	,	PUNCT
ejpam-4043	349	6	which	which	PRON
ejpam-4043	349	7	implies	imply	VERB
ejpam-4043	349	8	that	that	SCONJ
ejpam-4043	349	9	ξ1k⊥∞	ξ1k⊥∞	ADP
ejpam-4043	349	10	⊆	⊆	NUM
ejpam-4043	349	11	ξ1k∞	ξ1k∞	NOUN
ejpam-4043	349	12	,	,	PUNCT
ejpam-4043	349	13	ξ2k⊥∈	ξ2k⊥∈	NUM
ejpam-4043	349	14	⊆	⊆	NUM
ejpam-4043	349	15	ξ2k∈	ξ2k∈	NUM
ejpam-4043	349	16	,	,	PUNCT
ejpam-4043	349	17	ξ3k⊥3	ξ3k⊥3	PROPN
ejpam-4043	349	18	⊆	⊆	NUM
ejpam-4043	349	19	ξ3k3	ξ3k3	NOUN
ejpam-4043	349	20	and	and	CCONJ
ejpam-4043	349	21	ξ4k⊥4	ξ4k⊥4	PROPN
ejpam-4043	349	22	⊆	⊆	NUM
ejpam-4043	349	23	ξ4k4	ξ4k4	NOUN
ejpam-4043	349	24	,	,	PUNCT
ejpam-4043	349	25	that	that	PRON
ejpam-4043	349	26	implies	imply	VERB
ejpam-4043	349	27	k⊥∞	k⊥∞	PROPN
ejpam-4043	349	28	⊆	⊆	NUM
ejpam-4043	349	29	k∞	k∞	PROPN
ejpam-4043	349	30	,	,	PUNCT
ejpam-4043	349	31	k⊥∈	k⊥∈	PROPN
ejpam-4043	349	32	⊆	⊆	NUM
ejpam-4043	349	33	k∈	k∈	ADJ
ejpam-4043	349	34	,	,	PUNCT
ejpam-4043	349	35	k⊥3	k⊥3	X
ejpam-4043	349	36	⊆	⊆	NUM
ejpam-4043	349	37	k3	k3	ADJ
ejpam-4043	349	38	and	and	CCONJ
ejpam-4043	349	39	k⊥4	k⊥4	NOUN
ejpam-4043	349	40	⊆	⊆	NUM
ejpam-4043	349	41	k4	k4	NOUN
ejpam-4043	349	42	.	.	PUNCT
ejpam-4043	350	1	prateek	prateek	PROPN
ejpam-4043	350	2	mor	mor	PROPN
ejpam-4043	350	3	et	et	PROPN
ejpam-4043	350	4	al	al	PROPN
ejpam-4043	350	5	.	.	PUNCT
ejpam-4043	350	6	/	/	SYM
ejpam-4043	350	7	eur	eur	PROPN
ejpam-4043	350	8	.	.	PUNCT
ejpam-4043	351	1	j.	j.	PROPN
ejpam-4043	351	2	pure	pure	PROPN
ejpam-4043	351	3	appl	appl	PROPN
ejpam-4043	351	4	.	.	PROPN
ejpam-4043	351	5	math	math	PROPN
ejpam-4043	351	6	,	,	PUNCT
ejpam-4043	351	7	14	14	NUM
ejpam-4043	351	8	(	(	PUNCT
ejpam-4043	351	9	3	3	NUM
ejpam-4043	351	10	)	)	PUNCT
ejpam-4043	351	11	(	(	PUNCT
ejpam-4043	351	12	2021	2021	NUM
ejpam-4043	351	13	)	)	PUNCT
ejpam-4043	351	14	,	,	PUNCT
ejpam-4043	351	15	1082	1082	NUM
ejpam-4043	351	16	-	-	SYM
ejpam-4043	351	17	1097	1097	NUM
ejpam-4043	351	18	1093	1093	NUM
ejpam-4043	351	19	then	then	ADV
ejpam-4043	351	20	by	by	ADP
ejpam-4043	351	21	above	above	ADP
ejpam-4043	351	22	lemma	lemma	PROPN
ejpam-4043	351	23	,	,	PUNCT
ejpam-4043	351	24	xn	xn	PROPN
ejpam-4043	352	1	−	−	PROPN
ejpam-4043	352	2	1	1	NUM
ejpam-4043	352	3	≡	≡	PROPN
ejpam-4043	352	4	0	0	NUM
ejpam-4043	352	5	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	352	6	?	?	PUNCT
ejpam-4043	353	1	i	i	PRON
ejpam-4043	353	2	(	(	PUNCT
ejpam-4043	353	3	t	t	PROPN
ejpam-4043	353	4	)	)	PUNCT
ejpam-4043	353	5	)	)	PUNCT
ejpam-4043	354	1	and	and	CCONJ
ejpam-4043	354	2	xn	xn	NUM
ejpam-4043	355	1	+	+	CCONJ
ejpam-4043	355	2	1	1	NUM
ejpam-4043	355	3	≡	≡	PROPN
ejpam-4043	355	4	0	0	PUNCT
ejpam-4043	355	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	355	6	?	?	PUNCT
ejpam-4043	356	1	j	j	PROPN
ejpam-4043	356	2	(	(	PUNCT
ejpam-4043	356	3	t	t	PROPN
ejpam-4043	356	4	)	)	PUNCT
ejpam-4043	356	5	)	)	PUNCT
ejpam-4043	356	6	.	.	PUNCT
ejpam-4043	357	1	for	for	ADP
ejpam-4043	357	2	i	i	PRON
ejpam-4043	357	3	=	=	SYM
ejpam-4043	357	4	1	1	NUM
ejpam-4043	357	5	and	and	CCONJ
ejpam-4043	357	6	j	j	NOUN
ejpam-4043	357	7	=	=	SYM
ejpam-4043	357	8	2	2	NUM
ejpam-4043	357	9	,	,	PUNCT
ejpam-4043	357	10	3	3	NUM
ejpam-4043	357	11	,	,	PUNCT
ejpam-4043	357	12	4	4	NUM
ejpam-4043	357	13	.	.	NOUN
ejpam-4043	357	14	case	case	NOUN
ejpam-4043	357	15	3	3	NUM
ejpam-4043	357	16	.	.	PUNCT
ejpam-4043	358	1	ϑ	ϑ	X
ejpam-4043	358	2	=	=	X
ejpam-4043	358	3	νω	νω	SCONJ
ejpam-4043	358	4	theorem	theorem	ADJ
ejpam-4043	358	5	16	16	NUM
ejpam-4043	358	6	.	.	PUNCT
ejpam-4043	359	1	if	if	SCONJ
ejpam-4043	359	2	k	k	PROPN
ejpam-4043	359	3	=	=	X
ejpam-4043	359	4	<	<	X
ejpam-4043	359	5	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	359	6	)	)	PUNCT
ejpam-4043	359	7	+	+	X
ejpam-4043	359	8	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	359	9	)	)	PUNCT
ejpam-4043	359	10	+	+	CCONJ
ejpam-4043	359	11	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	359	12	)	)	PUNCT
ejpam-4043	359	13	+	+	X
ejpam-4043	359	14	ξ4g4(t	ξ4g4(t	X
ejpam-4043	359	15	)	)	PUNCT
ejpam-4043	359	16	>	>	X
ejpam-4043	359	17	is	be	AUX
ejpam-4043	359	18	a	a	DET
ejpam-4043	359	19	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	359	20	code	code	NOUN
ejpam-4043	359	21	over	over	ADP
ejpam-4043	359	22	the	the	DET
ejpam-4043	359	23	ring	ring	NOUN
ejpam-4043	359	24	<	<	X
ejpam-4043	359	25	of	of	ADP
ejpam-4043	359	26	length	length	NOUN
ejpam-4043	359	27	n.	n.	PROPN
ejpam-4043	359	28	then	then	ADV
ejpam-4043	359	29	,	,	PUNCT
ejpam-4043	359	30	k⊥	k⊥	PROPN
ejpam-4043	359	31	⊆	⊆	NUM
ejpam-4043	359	32	k	k	NOUN
ejpam-4043	360	1	if	if	SCONJ
ejpam-4043	360	2	and	and	CCONJ
ejpam-4043	360	3	only	only	ADV
ejpam-4043	360	4	if	if	SCONJ
ejpam-4043	360	5	xn	xn	PROPN
ejpam-4043	360	6	−	−	PROPN
ejpam-4043	360	7	1	1	NUM
ejpam-4043	360	8	≡	≡	PROPN
ejpam-4043	360	9	0	0	NUM
ejpam-4043	361	1	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	361	2	?	?	PUNCT
ejpam-4043	362	1	i	i	PRON
ejpam-4043	362	2	(	(	PUNCT
ejpam-4043	362	3	t	t	PROPN
ejpam-4043	362	4	)	)	PUNCT
ejpam-4043	362	5	)	)	PUNCT
ejpam-4043	363	1	and	and	CCONJ
ejpam-4043	363	2	xn	xn	NUM
ejpam-4043	364	1	+	+	CCONJ
ejpam-4043	364	2	1	1	NUM
ejpam-4043	364	3	≡	≡	PROPN
ejpam-4043	364	4	0	0	PUNCT
ejpam-4043	364	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	364	6	?	?	PUNCT
ejpam-4043	365	1	j	j	PROPN
ejpam-4043	365	2	(	(	PUNCT
ejpam-4043	365	3	t	t	PROPN
ejpam-4043	365	4	)	)	PUNCT
ejpam-4043	365	5	)	)	PUNCT
ejpam-4043	365	6	.	.	PUNCT
ejpam-4043	366	1	for	for	ADP
ejpam-4043	366	2	i	i	PRON
ejpam-4043	366	3	=	=	SYM
ejpam-4043	366	4	1	1	NUM
ejpam-4043	366	5	,	,	PUNCT
ejpam-4043	366	6	4	4	NUM
ejpam-4043	366	7	and	and	CCONJ
ejpam-4043	366	8	j	j	PROPN
ejpam-4043	366	9	=	=	SYM
ejpam-4043	366	10	2	2	NUM
ejpam-4043	366	11	,	,	PUNCT
ejpam-4043	366	12	3	3	NUM
ejpam-4043	366	13	.	.	PUNCT
ejpam-4043	366	14	proof	proof	NOUN
ejpam-4043	366	15	.	.	PUNCT
ejpam-4043	367	1	proof	proof	NOUN
ejpam-4043	367	2	of	of	ADP
ejpam-4043	367	3	the	the	DET
ejpam-4043	367	4	theorem	theorem	NOUN
ejpam-4043	367	5	is	be	AUX
ejpam-4043	367	6	similar	similar	ADJ
ejpam-4043	367	7	to	to	ADP
ejpam-4043	367	8	proof	proof	NOUN
ejpam-4043	367	9	of	of	ADP
ejpam-4043	367	10	theorem	theorem	ADJ
ejpam-4043	367	11	4.12	4.12	NUM
ejpam-4043	367	12	.	.	PUNCT
ejpam-4043	367	13	case	case	NOUN
ejpam-4043	367	14	4	4	NUM
ejpam-4043	367	15	.	.	PUNCT
ejpam-4043	367	16	ϑ	ϑ	X
ejpam-4043	367	17	=	=	X
ejpam-4043	367	18	ν	ν	NOUN
ejpam-4043	367	19	theorem	theorem	VERB
ejpam-4043	367	20	17	17	NUM
ejpam-4043	367	21	.	.	PUNCT
ejpam-4043	368	1	if	if	SCONJ
ejpam-4043	368	2	k	k	PROPN
ejpam-4043	368	3	=	=	X
ejpam-4043	368	4	<	<	X
ejpam-4043	368	5	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	368	6	)	)	PUNCT
ejpam-4043	368	7	+	+	X
ejpam-4043	368	8	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	368	9	)	)	PUNCT
ejpam-4043	368	10	+	+	CCONJ
ejpam-4043	368	11	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	368	12	)	)	PUNCT
ejpam-4043	368	13	+	+	X
ejpam-4043	368	14	ξ4g4(t	ξ4g4(t	X
ejpam-4043	368	15	)	)	PUNCT
ejpam-4043	368	16	>	>	X
ejpam-4043	368	17	is	be	AUX
ejpam-4043	368	18	a	a	DET
ejpam-4043	368	19	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	368	20	code	code	NOUN
ejpam-4043	368	21	over	over	ADP
ejpam-4043	368	22	the	the	DET
ejpam-4043	368	23	ring	ring	NOUN
ejpam-4043	368	24	<	<	X
ejpam-4043	368	25	of	of	ADP
ejpam-4043	368	26	length	length	NOUN
ejpam-4043	368	27	n.	n.	PROPN
ejpam-4043	368	28	then	then	ADV
ejpam-4043	368	29	,	,	PUNCT
ejpam-4043	368	30	k⊥	k⊥	PROPN
ejpam-4043	368	31	⊆	⊆	NUM
ejpam-4043	368	32	k	k	NOUN
ejpam-4043	369	1	if	if	SCONJ
ejpam-4043	369	2	and	and	CCONJ
ejpam-4043	369	3	only	only	ADV
ejpam-4043	369	4	if	if	SCONJ
ejpam-4043	369	5	xn	xn	PROPN
ejpam-4043	369	6	−	−	PROPN
ejpam-4043	369	7	1	1	NUM
ejpam-4043	369	8	≡	≡	PROPN
ejpam-4043	369	9	0	0	NUM
ejpam-4043	370	1	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	370	2	?	?	PUNCT
ejpam-4043	371	1	i	i	PRON
ejpam-4043	371	2	(	(	PUNCT
ejpam-4043	371	3	t	t	PROPN
ejpam-4043	371	4	)	)	PUNCT
ejpam-4043	371	5	)	)	PUNCT
ejpam-4043	372	1	and	and	CCONJ
ejpam-4043	372	2	xn	xn	NUM
ejpam-4043	373	1	+	+	CCONJ
ejpam-4043	373	2	1	1	NUM
ejpam-4043	373	3	≡	≡	PROPN
ejpam-4043	373	4	0	0	PUNCT
ejpam-4043	373	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	373	6	?	?	PUNCT
ejpam-4043	374	1	j	j	PROPN
ejpam-4043	374	2	(	(	PUNCT
ejpam-4043	374	3	t	t	PROPN
ejpam-4043	374	4	)	)	PUNCT
ejpam-4043	374	5	)	)	PUNCT
ejpam-4043	374	6	.	.	PUNCT
ejpam-4043	375	1	for	for	ADP
ejpam-4043	375	2	i	i	PRON
ejpam-4043	375	3	=	=	SYM
ejpam-4043	375	4	1	1	NUM
ejpam-4043	375	5	,	,	PUNCT
ejpam-4043	375	6	3	3	NUM
ejpam-4043	375	7	and	and	CCONJ
ejpam-4043	375	8	j	j	PROPN
ejpam-4043	375	9	=	=	SYM
ejpam-4043	375	10	2	2	NUM
ejpam-4043	375	11	,	,	PUNCT
ejpam-4043	375	12	4	4	NUM
ejpam-4043	375	13	.	.	PUNCT
ejpam-4043	375	14	proof	proof	NOUN
ejpam-4043	375	15	.	.	PUNCT
ejpam-4043	376	1	proof	proof	NOUN
ejpam-4043	376	2	of	of	ADP
ejpam-4043	376	3	the	the	DET
ejpam-4043	376	4	theorem	theorem	NOUN
ejpam-4043	376	5	is	be	AUX
ejpam-4043	376	6	similar	similar	ADJ
ejpam-4043	376	7	to	to	ADP
ejpam-4043	376	8	proof	proof	NOUN
ejpam-4043	376	9	of	of	ADP
ejpam-4043	376	10	theorem	theorem	NOUN
ejpam-4043	376	11	4.13	4.13	NUM
ejpam-4043	376	12	.	.	PUNCT
ejpam-4043	377	1	case	case	NOUN
ejpam-4043	377	2	5	5	NUM
ejpam-4043	377	3	.	.	PUNCT
ejpam-4043	377	4	ϑ	ϑ	X
ejpam-4043	377	5	=	=	SYM
ejpam-4043	377	6	ω	ω	PROPN
ejpam-4043	377	7	theorem	theorem	ADJ
ejpam-4043	377	8	18	18	NUM
ejpam-4043	377	9	.	.	PUNCT
ejpam-4043	378	1	if	if	SCONJ
ejpam-4043	378	2	k	k	PROPN
ejpam-4043	378	3	=	=	X
ejpam-4043	378	4	<	<	X
ejpam-4043	378	5	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	378	6	)	)	PUNCT
ejpam-4043	378	7	+	+	X
ejpam-4043	378	8	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	378	9	)	)	PUNCT
ejpam-4043	378	10	+	+	CCONJ
ejpam-4043	378	11	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	378	12	)	)	PUNCT
ejpam-4043	378	13	+	+	X
ejpam-4043	378	14	ξ4g4(t	ξ4g4(t	X
ejpam-4043	378	15	)	)	PUNCT
ejpam-4043	378	16	>	>	X
ejpam-4043	378	17	is	be	AUX
ejpam-4043	378	18	a	a	DET
ejpam-4043	378	19	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	378	20	code	code	NOUN
ejpam-4043	378	21	over	over	ADP
ejpam-4043	378	22	the	the	DET
ejpam-4043	378	23	ring	ring	NOUN
ejpam-4043	378	24	<	<	X
ejpam-4043	378	25	of	of	ADP
ejpam-4043	378	26	length	length	NOUN
ejpam-4043	378	27	n.	n.	PROPN
ejpam-4043	378	28	then	then	ADV
ejpam-4043	378	29	,	,	PUNCT
ejpam-4043	378	30	k⊥	k⊥	PROPN
ejpam-4043	378	31	⊆	⊆	NUM
ejpam-4043	378	32	k	k	NOUN
ejpam-4043	379	1	if	if	SCONJ
ejpam-4043	379	2	and	and	CCONJ
ejpam-4043	379	3	only	only	ADV
ejpam-4043	379	4	if	if	SCONJ
ejpam-4043	379	5	xn	xn	PROPN
ejpam-4043	379	6	−	−	PROPN
ejpam-4043	379	7	1	1	NUM
ejpam-4043	379	8	≡	≡	PROPN
ejpam-4043	379	9	0	0	NUM
ejpam-4043	380	1	mod(gi(t)g	mod(gi(t)g	NOUN
ejpam-4043	380	2	?	?	PUNCT
ejpam-4043	381	1	i	i	PRON
ejpam-4043	381	2	(	(	PUNCT
ejpam-4043	381	3	t	t	PROPN
ejpam-4043	381	4	)	)	PUNCT
ejpam-4043	381	5	)	)	PUNCT
ejpam-4043	382	1	and	and	CCONJ
ejpam-4043	382	2	xn	xn	NUM
ejpam-4043	383	1	+	+	CCONJ
ejpam-4043	383	2	1	1	NUM
ejpam-4043	383	3	≡	≡	PROPN
ejpam-4043	383	4	0	0	PUNCT
ejpam-4043	383	5	mod(gj(t)g	mod(gj(t)g	NOUN
ejpam-4043	383	6	?	?	PUNCT
ejpam-4043	384	1	j	j	PROPN
ejpam-4043	384	2	(	(	PUNCT
ejpam-4043	384	3	t	t	PROPN
ejpam-4043	384	4	)	)	PUNCT
ejpam-4043	384	5	)	)	PUNCT
ejpam-4043	384	6	.	.	PUNCT
ejpam-4043	385	1	for	for	ADP
ejpam-4043	385	2	i	i	PRON
ejpam-4043	385	3	=	=	SYM
ejpam-4043	385	4	1	1	NUM
ejpam-4043	385	5	,	,	PUNCT
ejpam-4043	385	6	2	2	NUM
ejpam-4043	385	7	and	and	CCONJ
ejpam-4043	385	8	j	j	NOUN
ejpam-4043	385	9	=	=	SYM
ejpam-4043	385	10	3	3	NUM
ejpam-4043	385	11	,	,	PUNCT
ejpam-4043	385	12	4	4	NUM
ejpam-4043	385	13	.	.	PUNCT
ejpam-4043	385	14	proof	proof	NOUN
ejpam-4043	385	15	.	.	PUNCT
ejpam-4043	386	1	proof	proof	NOUN
ejpam-4043	386	2	of	of	ADP
ejpam-4043	386	3	the	the	DET
ejpam-4043	386	4	theorem	theorem	NOUN
ejpam-4043	386	5	is	be	AUX
ejpam-4043	386	6	similar	similar	ADJ
ejpam-4043	386	7	to	to	ADP
ejpam-4043	386	8	proof	proof	NOUN
ejpam-4043	386	9	of	of	ADP
ejpam-4043	386	10	theorem	theorem	ADJ
ejpam-4043	386	11	4.14	4.14	NUM
ejpam-4043	386	12	.	.	PUNCT
ejpam-4043	387	1	by	by	ADP
ejpam-4043	387	2	above	above	ADP
ejpam-4043	387	3	theorems	theorem	NOUN
ejpam-4043	387	4	,	,	PUNCT
ejpam-4043	387	5	we	we	PRON
ejpam-4043	387	6	have	have	VERB
ejpam-4043	387	7	the	the	DET
ejpam-4043	387	8	following	follow	VERB
ejpam-4043	387	9	corollary	corollary	NOUN
ejpam-4043	387	10	for	for	ADP
ejpam-4043	387	11	each	each	DET
ejpam-4043	387	12	case	case	NOUN
ejpam-4043	387	13	of	of	ADP
ejpam-4043	387	14	ϑ.	ϑ.	NOUN
ejpam-4043	387	15	prateek	prateek	VERB
ejpam-4043	387	16	mor	mor	PROPN
ejpam-4043	387	17	et	et	PROPN
ejpam-4043	387	18	al	al	PROPN
ejpam-4043	387	19	.	.	PUNCT
ejpam-4043	387	20	/	/	SYM
ejpam-4043	387	21	eur	eur	PROPN
ejpam-4043	387	22	.	.	PUNCT
ejpam-4043	388	1	j.	j.	PROPN
ejpam-4043	388	2	pure	pure	PROPN
ejpam-4043	388	3	appl	appl	PROPN
ejpam-4043	388	4	.	.	PROPN
ejpam-4043	388	5	math	math	PROPN
ejpam-4043	388	6	,	,	PUNCT
ejpam-4043	388	7	14	14	NUM
ejpam-4043	388	8	(	(	PUNCT
ejpam-4043	388	9	3	3	NUM
ejpam-4043	388	10	)	)	PUNCT
ejpam-4043	388	11	(	(	PUNCT
ejpam-4043	388	12	2021	2021	NUM
ejpam-4043	388	13	)	)	PUNCT
ejpam-4043	388	14	,	,	PUNCT
ejpam-4043	388	15	1082	1082	NUM
ejpam-4043	388	16	-	-	SYM
ejpam-4043	388	17	1097	1097	NUM
ejpam-4043	388	18	1094	1094	NUM
ejpam-4043	388	19	corollary	corollary	NOUN
ejpam-4043	388	20	19	19	NUM
ejpam-4043	388	21	.	.	PUNCT
ejpam-4043	389	1	let	let	VERB
ejpam-4043	389	2	k=	k=	X
ejpam-4043	389	3	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	389	4	⊕	⊕	PROPN
ejpam-4043	389	5	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	390	1	⊕	⊕	PROPN
ejpam-4043	390	2	ξ3k3	ξ3k3	PROPN
ejpam-4043	390	3	⊕	⊕	PROPN
ejpam-4043	390	4	ξ4k4	ξ4k4	VERB
ejpam-4043	390	5	be	be	AUX
ejpam-4043	390	6	a	a	DET
ejpam-4043	390	7	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	390	8	code	code	NOUN
ejpam-4043	390	9	over	over	ADP
ejpam-4043	390	10	<	<	X
ejpam-4043	390	11	of	of	ADP
ejpam-4043	390	12	length	length	NOUN
ejpam-4043	390	13	n	n	PROPN
ejpam-4043	390	14	where	where	SCONJ
ejpam-4043	390	15	k∞	k∞	PROPN
ejpam-4043	390	16	,	,	PUNCT
ejpam-4043	390	17	k∈	k∈	PROPN
ejpam-4043	390	18	,	,	PUNCT
ejpam-4043	390	19	k3	k3	PROPN
ejpam-4043	390	20	,	,	PUNCT
ejpam-4043	390	21	k4	k4	PROPN
ejpam-4043	390	22	are	be	AUX
ejpam-4043	390	23	linear	linear	ADJ
ejpam-4043	390	24	codes	code	NOUN
ejpam-4043	390	25	of	of	ADP
ejpam-4043	390	26	length	length	NOUN
ejpam-4043	390	27	n	n	NOUN
ejpam-4043	390	28	over	over	ADP
ejpam-4043	390	29	the	the	DET
ejpam-4043	390	30	ring	ring	NOUN
ejpam-4043	390	31	z3	z3	PROPN
ejpam-4043	390	32	.	.	PUNCT
ejpam-4043	391	1	then	then	ADV
ejpam-4043	391	2	,	,	PUNCT
ejpam-4043	391	3	k⊥	k⊥	PROPN
ejpam-4043	391	4	⊆	⊆	NUM
ejpam-4043	391	5	k	k	NOUN
ejpam-4043	391	6	if	if	SCONJ
ejpam-4043	391	7	and	and	CCONJ
ejpam-4043	391	8	only	only	ADV
ejpam-4043	391	9	if	if	SCONJ
ejpam-4043	391	10	k⊥∞	k⊥∞	PROPN
ejpam-4043	391	11	⊆	⊆	NUM
ejpam-4043	391	12	k∞	k∞	PROPN
ejpam-4043	391	13	,	,	PUNCT
ejpam-4043	391	14	k⊥∈	k⊥∈	PROPN
ejpam-4043	391	15	⊆	⊆	NUM
ejpam-4043	391	16	k∈	k∈	ADJ
ejpam-4043	391	17	,	,	PUNCT
ejpam-4043	391	18	k⊥3	k⊥3	X
ejpam-4043	391	19	⊆	⊆	NUM
ejpam-4043	391	20	k3	k3	ADJ
ejpam-4043	391	21	and	and	CCONJ
ejpam-4043	391	22	k⊥4	k⊥4	NOUN
ejpam-4043	391	23	⊆	⊆	NUM
ejpam-4043	391	24	k4	k4	NOUN
ejpam-4043	391	25	.	.	PUNCT
ejpam-4043	392	1	lemma	lemma	PROPN
ejpam-4043	392	2	2	2	NUM
ejpam-4043	392	3	.	.	PUNCT
ejpam-4043	393	1	[	[	X
ejpam-4043	393	2	4](css	4](css	NUM
ejpam-4043	393	3	construction	construction	NOUN
ejpam-4043	393	4	)	)	PUNCT
ejpam-4043	393	5	let	let	VERB
ejpam-4043	393	6	k	k	PRON
ejpam-4043	393	7	be	be	AUX
ejpam-4043	393	8	a	a	DET
ejpam-4043	393	9	linear	linear	ADJ
ejpam-4043	393	10	code	code	NOUN
ejpam-4043	393	11	over	over	ADP
ejpam-4043	393	12	the	the	DET
ejpam-4043	393	13	ring	ring	NOUN
ejpam-4043	393	14	z3	z3	PROPN
ejpam-4043	393	15	having	have	VERB
ejpam-4043	393	16	parameters	parameter	NOUN
ejpam-4043	393	17	[	[	X
ejpam-4043	393	18	n	n	CCONJ
ejpam-4043	393	19	,	,	PUNCT
ejpam-4043	393	20	k	k	NOUN
ejpam-4043	393	21	,	,	PUNCT
ejpam-4043	393	22	d	d	X
ejpam-4043	393	23	]	]	X
ejpam-4043	393	24	.	.	PUNCT
ejpam-4043	394	1	then	then	ADV
ejpam-4043	394	2	a	a	DET
ejpam-4043	394	3	quantum	quantum	NOUN
ejpam-4043	394	4	code	code	NOUN
ejpam-4043	394	5	having	have	VERB
ejpam-4043	394	6	parameters	parameter	NOUN
ejpam-4043	394	7	[	[	X
ejpam-4043	394	8	[	[	X
ejpam-4043	394	9	n	n	CCONJ
ejpam-4043	394	10	,	,	PUNCT
ejpam-4043	394	11	2k	2k	NOUN
ejpam-4043	394	12	−	−	PROPN
ejpam-4043	394	13	n	n	CCONJ
ejpam-4043	394	14	,	,	PUNCT
ejpam-4043	394	15	≥	≥	PROPN
ejpam-4043	394	16	d]]3	d]]3	PROPN
ejpam-4043	394	17	can	can	AUX
ejpam-4043	394	18	be	be	AUX
ejpam-4043	394	19	obtained	obtain	VERB
ejpam-4043	394	20	if	if	SCONJ
ejpam-4043	394	21	k⊥	k⊥	PROPN
ejpam-4043	394	22	⊆	⊆	NUM
ejpam-4043	394	23	k.	k.	NOUN
ejpam-4043	394	24	the	the	DET
ejpam-4043	394	25	following	follow	VERB
ejpam-4043	394	26	theorem	theorem	ADJ
ejpam-4043	394	27	defines	define	VERB
ejpam-4043	394	28	the	the	DET
ejpam-4043	394	29	construction	construction	NOUN
ejpam-4043	394	30	of	of	ADP
ejpam-4043	394	31	quantum	quantum	NOUN
ejpam-4043	394	32	codes	code	NOUN
ejpam-4043	394	33	by	by	ADP
ejpam-4043	394	34	the	the	DET
ejpam-4043	394	35	use	use	NOUN
ejpam-4043	394	36	of	of	ADP
ejpam-4043	394	37	corollary	corollary	ADJ
ejpam-4043	394	38	4.16	4.16	NUM
ejpam-4043	394	39	and	and	CCONJ
ejpam-4043	394	40	lemma	lemma	PROPN
ejpam-4043	394	41	4.17	4.17	NUM
ejpam-4043	394	42	.	.	PUNCT
ejpam-4043	395	1	theorem	theorem	VERB
ejpam-4043	395	2	20	20	NUM
ejpam-4043	395	3	.	.	PUNCT
ejpam-4043	396	1	if	if	SCONJ
ejpam-4043	396	2	k=	k=	PROPN
ejpam-4043	396	3	ξ1k∞	ξ1k∞	PROPN
ejpam-4043	396	4	⊕	⊕	PROPN
ejpam-4043	396	5	ξ2k∈	ξ2k∈	PROPN
ejpam-4043	396	6	⊕	⊕	PROPN
ejpam-4043	396	7	ξ3k3	ξ3k3	PROPN
ejpam-4043	396	8	⊕	⊕	PROPN
ejpam-4043	396	9	ξ4k4	ξ4k4	PUNCT
ejpam-4043	397	1	=	=	PUNCT
ejpam-4043	397	2	<	<	X
ejpam-4043	397	3	ξ1g1(t	ξ1g1(t	PROPN
ejpam-4043	397	4	)	)	PUNCT
ejpam-4043	397	5	+	+	X
ejpam-4043	397	6	ξ2g2(t	ξ2g2(t	NOUN
ejpam-4043	397	7	)	)	PUNCT
ejpam-4043	397	8	+	+	CCONJ
ejpam-4043	397	9	ξ3g3(t	ξ3g3(t	ADJ
ejpam-4043	397	10	)	)	PUNCT
ejpam-4043	397	11	+	+	X
ejpam-4043	397	12	ξ4g4(t	ξ4g4(t	X
ejpam-4043	397	13	)	)	PUNCT
ejpam-4043	397	14	>	>	X
ejpam-4043	397	15	is	be	AUX
ejpam-4043	397	16	a	a	DET
ejpam-4043	397	17	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	397	18	code	code	NOUN
ejpam-4043	397	19	over	over	ADP
ejpam-4043	397	20	the	the	DET
ejpam-4043	397	21	ring	ring	NOUN
ejpam-4043	397	22	<	<	X
ejpam-4043	397	23	of	of	ADP
ejpam-4043	397	24	length	length	NOUN
ejpam-4043	397	25	n	n	PROPN
ejpam-4043	397	26	where	where	SCONJ
ejpam-4043	397	27	gi(t	gi(t	NOUN
ejpam-4043	397	28	)	)	PUNCT
ejpam-4043	397	29	are	be	AUX
ejpam-4043	397	30	the	the	DET
ejpam-4043	397	31	generator	generator	NOUN
ejpam-4043	397	32	polynomials	polynomial	NOUN
ejpam-4043	397	33	of	of	ADP
ejpam-4043	397	34	k∞	k∞	PROPN
ejpam-4043	397	35	,	,	PUNCT
ejpam-4043	397	36	k∈	k∈	PROPN
ejpam-4043	397	37	,	,	PUNCT
ejpam-4043	397	38	k3	k3	VERB
ejpam-4043	397	39	and	and	CCONJ
ejpam-4043	397	40	k4	k4	VERB
ejpam-4043	397	41	for	for	ADP
ejpam-4043	397	42	i	i	PRON
ejpam-4043	397	43	=	=	NOUN
ejpam-4043	397	44	1	1	NUM
ejpam-4043	397	45	,	,	PUNCT
ejpam-4043	397	46	2	2	NUM
ejpam-4043	397	47	,	,	PUNCT
ejpam-4043	397	48	3	3	NUM
ejpam-4043	397	49	,	,	PUNCT
ejpam-4043	397	50	4	4	NUM
ejpam-4043	397	51	respectively	respectively	ADV
ejpam-4043	397	52	.	.	PUNCT
ejpam-4043	398	1	if	if	SCONJ
ejpam-4043	398	2	k⊥∞	k⊥∞	PROPN
ejpam-4043	398	3	⊆	⊆	NUM
ejpam-4043	398	4	k∞	k∞	PROPN
ejpam-4043	398	5	,	,	PUNCT
ejpam-4043	398	6	k⊥∈	k⊥∈	PROPN
ejpam-4043	398	7	⊆	⊆	NUM
ejpam-4043	398	8	k∈	k∈	ADJ
ejpam-4043	398	9	,	,	PUNCT
ejpam-4043	398	10	k⊥3	k⊥3	X
ejpam-4043	398	11	⊆	⊆	NUM
ejpam-4043	398	12	k3	k3	ADJ
ejpam-4043	398	13	and	and	CCONJ
ejpam-4043	398	14	k⊥4	k⊥4	NOUN
ejpam-4043	398	15	⊆	⊆	NUM
ejpam-4043	398	16	k4	k4	NOUN
ejpam-4043	398	17	,	,	PUNCT
ejpam-4043	398	18	then	then	ADV
ejpam-4043	398	19	k⊥	k⊥	PROPN
ejpam-4043	398	20	⊆	⊆	NUM
ejpam-4043	398	21	k	k	PROPN
ejpam-4043	398	22	and	and	CCONJ
ejpam-4043	398	23	there	there	PRON
ejpam-4043	398	24	exists	exist	VERB
ejpam-4043	398	25	a	a	DET
ejpam-4043	398	26	quantum	quantum	NOUN
ejpam-4043	398	27	code	code	NOUN
ejpam-4043	398	28	having	have	VERB
ejpam-4043	398	29	parameters	parameter	NOUN
ejpam-4043	398	30	[	[	X
ejpam-4043	398	31	4n	4n	NOUN
ejpam-4043	398	32	,	,	PUNCT
ejpam-4043	398	33	2k	2k	NOUN
ejpam-4043	398	34	−	−	PROPN
ejpam-4043	398	35	4n	4n	NOUN
ejpam-4043	398	36	,	,	PUNCT
ejpam-4043	398	37	≥	≥	PROPN
ejpam-4043	398	38	dl]3	dl]3	PROPN
ejpam-4043	398	39	where	where	SCONJ
ejpam-4043	398	40	k	k	PROPN
ejpam-4043	398	41	is	be	AUX
ejpam-4043	398	42	the	the	DET
ejpam-4043	398	43	dimension	dimension	NOUN
ejpam-4043	398	44	of	of	ADP
ejpam-4043	398	45	linear	linear	PROPN
ejpam-4043	398	46	code	code	PROPN
ejpam-4043	398	47	ϕ(k	ϕ(k	PROPN
ejpam-4043	398	48	)	)	PUNCT
ejpam-4043	398	49	and	and	CCONJ
ejpam-4043	398	50	dl	dl	PROPN
ejpam-4043	398	51	is	be	AUX
ejpam-4043	398	52	minimum	minimum	ADJ
ejpam-4043	398	53	lee	lee	PROPN
ejpam-4043	398	54	distance	distance	NOUN
ejpam-4043	398	55	of	of	ADP
ejpam-4043	398	56	a	a	DET
ejpam-4043	398	57	linear	linear	PROPN
ejpam-4043	398	58	code	code	NOUN
ejpam-4043	398	59	k.	k.	PROPN
ejpam-4043	398	60	5	5	X
ejpam-4043	398	61	.	.	PUNCT
ejpam-4043	398	62	examples	example	NOUN
ejpam-4043	398	63	in	in	ADP
ejpam-4043	398	64	this	this	DET
ejpam-4043	398	65	section	section	NOUN
ejpam-4043	398	66	some	some	DET
ejpam-4043	398	67	examples	example	NOUN
ejpam-4043	398	68	are	be	AUX
ejpam-4043	398	69	provided	provide	VERB
ejpam-4043	398	70	to	to	PART
ejpam-4043	398	71	illustrate	illustrate	VERB
ejpam-4043	398	72	the	the	DET
ejpam-4043	398	73	main	main	ADJ
ejpam-4043	398	74	result	result	NOUN
ejpam-4043	398	75	.	.	PUNCT
ejpam-4043	399	1	here	here	ADV
ejpam-4043	399	2	,	,	PUNCT
ejpam-4043	399	3	the	the	DET
ejpam-4043	399	4	quantum	quantum	NOUN
ejpam-4043	399	5	codes	code	NOUN
ejpam-4043	399	6	through	through	ADP
ejpam-4043	399	7	ϑ-constacyclic	ϑ-constacyclic	PROPN
ejpam-4043	399	8	code	code	NOUN
ejpam-4043	399	9	over	over	ADP
ejpam-4043	399	10	the	the	DET
ejpam-4043	399	11	ring	ring	NOUN
ejpam-4043	399	12	<	<	X
ejpam-4043	399	13	=	=	X
ejpam-4043	399	14	z3	z3	PROPN
ejpam-4043	399	15	+	+	CCONJ
ejpam-4043	399	16	νz3	νz3	X
ejpam-4043	399	17	+	+	CCONJ
ejpam-4043	399	18	ωz3	ωz3	NOUN
ejpam-4043	399	19	+	+	CCONJ
ejpam-4043	399	20	νωz3	νωz3	NOUN
ejpam-4043	399	21	where	where	SCONJ
ejpam-4043	399	22	ν2	ν2	NOUN
ejpam-4043	399	23	=	=	SYM
ejpam-4043	399	24	1	1	NUM
ejpam-4043	399	25	,	,	PUNCT
ejpam-4043	399	26	ω2	ω2	NOUN
ejpam-4043	399	27	=	=	SYM
ejpam-4043	399	28	1	1	NUM
ejpam-4043	399	29	and	and	CCONJ
ejpam-4043	399	30	νω	νω	ADV
ejpam-4043	399	31	=	=	NOUN
ejpam-4043	399	32	ων	ων	NOUN
ejpam-4043	399	33	are	be	AUX
ejpam-4043	399	34	obtains	obtain	NOUN
ejpam-4043	399	35	.	.	PUNCT
ejpam-4043	399	36	example	example	NOUN
ejpam-4043	400	1	1	1	NUM
ejpam-4043	400	2	.	.	PUNCT
ejpam-4043	401	1	in	in	ADP
ejpam-4043	401	2	z3[t	z3[t	PROPN
ejpam-4043	401	3	]	]	PUNCT
ejpam-4043	401	4	,	,	PUNCT
ejpam-4043	401	5	t	t	PROPN
ejpam-4043	401	6	3	3	NUM
ejpam-4043	401	7	−	−	PROPN
ejpam-4043	401	8	1	1	NUM
ejpam-4043	401	9	=	=	SYM
ejpam-4043	401	10	(	(	PUNCT
ejpam-4043	401	11	t	t	PROPN
ejpam-4043	401	12	+	+	NUM
ejpam-4043	401	13	2)3	2)3	NUM
ejpam-4043	401	14	and	and	CCONJ
ejpam-4043	401	15	t3	t3	PROPN
ejpam-4043	402	1	+	+	CCONJ
ejpam-4043	402	2	1	1	NUM
ejpam-4043	402	3	=	=	SYM
ejpam-4043	402	4	(	(	PUNCT
ejpam-4043	402	5	t	t	PROPN
ejpam-4043	402	6	+	+	CCONJ
ejpam-4043	402	7	1)(t2	1)(t2	NUM
ejpam-4043	402	8	−	−	NOUN
ejpam-4043	402	9	t	t	NOUN
ejpam-4043	402	10	+	+	CCONJ
ejpam-4043	402	11	1	1	NUM
ejpam-4043	402	12	)	)	PUNCT
ejpam-4043	402	13	.	.	PUNCT
ejpam-4043	403	1	now	now	ADV
ejpam-4043	403	2	,	,	PUNCT
ejpam-4043	403	3	let	let	VERB
ejpam-4043	403	4	k	k	PRON
ejpam-4043	403	5	be	be	AUX
ejpam-4043	403	6	a	a	DET
ejpam-4043	403	7	1	1	NUM
ejpam-4043	403	8	+	+	NUM
ejpam-4043	403	9	ν	ν	X
ejpam-4043	403	10	+	+	X
ejpam-4043	403	11	ω	ω	NUM
ejpam-4043	403	12	+	+	CCONJ
ejpam-4043	403	13	2νω	2νω	ADJ
ejpam-4043	403	14	-	-	PUNCT
ejpam-4043	403	15	constacyclic	constacyclic	ADJ
ejpam-4043	403	16	code	code	NOUN
ejpam-4043	403	17	over	over	ADP
ejpam-4043	403	18	the	the	DET
ejpam-4043	403	19	ring	ring	NOUN
ejpam-4043	403	20	<	<	X
ejpam-4043	403	21	=	=	X
ejpam-4043	403	22	z3	z3	PROPN
ejpam-4043	404	1	+	+	CCONJ
ejpam-4043	404	2	νz3	νz3	X
ejpam-4043	404	3	+	+	CCONJ
ejpam-4043	404	4	ωz3	ωz3	NOUN
ejpam-4043	404	5	+	+	CCONJ
ejpam-4043	404	6	νωz3	νωz3	NOUN
ejpam-4043	404	7	where	where	SCONJ
ejpam-4043	404	8	ν2	ν2	NOUN
ejpam-4043	404	9	=	=	SYM
ejpam-4043	404	10	1	1	NUM
ejpam-4043	404	11	,	,	PUNCT
ejpam-4043	404	12	ω2	ω2	NOUN
ejpam-4043	404	13	=	=	SYM
ejpam-4043	404	14	1	1	NUM
ejpam-4043	404	15	and	and	CCONJ
ejpam-4043	404	16	νω	νω	ADV
ejpam-4043	404	17	=	=	PUNCT
ejpam-4043	404	18	ων	ων	NUM
ejpam-4043	404	19	of	of	ADP
ejpam-4043	404	20	length	length	NOUN
ejpam-4043	404	21	3	3	NUM
ejpam-4043	404	22	.	.	PUNCT
ejpam-4043	405	1	let	let	VERB
ejpam-4043	405	2	g1(t	g1(t	X
ejpam-4043	405	3	)	)	PUNCT
ejpam-4043	405	4	=	=	SYM
ejpam-4043	405	5	g2(t	g2(t	NOUN
ejpam-4043	405	6	)	)	PUNCT
ejpam-4043	406	1	=	=	SYM
ejpam-4043	406	2	g3(t	g3(t	X
ejpam-4043	406	3	)	)	PUNCT
ejpam-4043	406	4	=	=	SYM
ejpam-4043	406	5	t	t	NOUN
ejpam-4043	406	6	+	+	CCONJ
ejpam-4043	406	7	1	1	NUM
ejpam-4043	406	8	and	and	CCONJ
ejpam-4043	406	9	g4(t	g4(t	ADJ
ejpam-4043	406	10	)	)	PUNCT
ejpam-4043	406	11	=	=	SYM
ejpam-4043	406	12	t2+t+1	t2+t+1	NUM
ejpam-4043	406	13	then	then	ADV
ejpam-4043	406	14	g(t	g(t	PROPN
ejpam-4043	406	15	)	)	PUNCT
ejpam-4043	407	1	=	=	SYM
ejpam-4043	407	2	ξ1(t+1)+ξ2(t+1)+ξ3(t+1)+ξ4(t	ξ1(t+1)+ξ2(t+1)+ξ3(t+1)+ξ4(t	PROPN
ejpam-4043	407	3	2+t+1	2+t+1	NUM
ejpam-4043	407	4	)	)	PUNCT
ejpam-4043	407	5	be	be	VERB
ejpam-4043	407	6	the	the	DET
ejpam-4043	407	7	generator	generator	NOUN
ejpam-4043	407	8	polynomial	polynomial	NOUN
ejpam-4043	407	9	of	of	ADP
ejpam-4043	407	10	k.	k.	PROPN
ejpam-4043	407	11	since	since	SCONJ
ejpam-4043	407	12	gi(t)g	gi(t)g	PROPN
ejpam-4043	407	13	∗	∗	NOUN
ejpam-4043	407	14	i	i	PRON
ejpam-4043	407	15	(	(	PUNCT
ejpam-4043	407	16	t)|t3	t)|t3	PROPN
ejpam-4043	408	1	+	+	ADP
ejpam-4043	408	2	1	1	NUM
ejpam-4043	408	3	for	for	ADP
ejpam-4043	408	4	i	i	PRON
ejpam-4043	408	5	=	=	NOUN
ejpam-4043	408	6	1	1	NUM
ejpam-4043	408	7	,	,	PUNCT
ejpam-4043	408	8	2	2	NUM
ejpam-4043	408	9	,	,	PUNCT
ejpam-4043	408	10	3	3	NUM
ejpam-4043	408	11	respectively	respectively	ADV
ejpam-4043	408	12	and	and	CCONJ
ejpam-4043	408	13	g4(t)g	g4(t)g	ADJ
ejpam-4043	408	14	∗	∗	NOUN
ejpam-4043	408	15	4(t)|t3	4(t)|t3	NUM
ejpam-4043	408	16	−	−	PROPN
ejpam-4043	408	17	1	1	NUM
ejpam-4043	408	18	,	,	PUNCT
ejpam-4043	408	19	then	then	ADV
ejpam-4043	408	20	by	by	ADP
ejpam-4043	408	21	the	the	DET
ejpam-4043	408	22	use	use	NOUN
ejpam-4043	408	23	of	of	ADP
ejpam-4043	408	24	theorem	theorem	NOUN
ejpam-4043	408	25	4.11	4.11	NUM
ejpam-4043	408	26	,	,	PUNCT
ejpam-4043	408	27	we	we	PRON
ejpam-4043	408	28	get	get	VERB
ejpam-4043	408	29	k⊥	k⊥	NOUN
ejpam-4043	408	30	⊆	⊆	NUM
ejpam-4043	408	31	k	k	PROPN
ejpam-4043	408	32	further	far	ADV
ejpam-4043	408	33	ϕ(k	ϕ(k	NOUN
ejpam-4043	408	34	)	)	PUNCT
ejpam-4043	408	35	is	be	AUX
ejpam-4043	408	36	a	a	DET
ejpam-4043	408	37	linear	linear	ADJ
ejpam-4043	408	38	code	code	NOUN
ejpam-4043	408	39	over	over	ADP
ejpam-4043	408	40	the	the	DET
ejpam-4043	408	41	ring	ring	NOUN
ejpam-4043	408	42	z3	z3	PROPN
ejpam-4043	408	43	having	have	VERB
ejpam-4043	408	44	parameters	parameter	NOUN
ejpam-4043	408	45	[	[	X
ejpam-4043	408	46	12	12	NUM
ejpam-4043	408	47	,	,	PUNCT
ejpam-4043	408	48	7	7	NUM
ejpam-4043	408	49	,	,	PUNCT
ejpam-4043	408	50	3	3	NUM
ejpam-4043	408	51	]	]	PUNCT
ejpam-4043	408	52	.	.	PUNCT
ejpam-4043	409	1	then	then	ADV
ejpam-4043	409	2	,	,	PUNCT
ejpam-4043	409	3	by	by	ADP
ejpam-4043	409	4	the	the	DET
ejpam-4043	409	5	application	application	NOUN
ejpam-4043	409	6	of	of	ADP
ejpam-4043	409	7	theorem	theorem	NOUN
ejpam-4043	409	8	4.18	4.18	NUM
ejpam-4043	409	9	,	,	PUNCT
ejpam-4043	409	10	we	we	PRON
ejpam-4043	409	11	obtain	obtain	VERB
ejpam-4043	409	12	the	the	DET
ejpam-4043	409	13	quantum	quantum	NOUN
ejpam-4043	409	14	code	code	NOUN
ejpam-4043	409	15	having	have	VERB
ejpam-4043	409	16	parameters	parameter	NOUN
ejpam-4043	409	17	[	[	X
ejpam-4043	409	18	12	12	NUM
ejpam-4043	409	19	,	,	PUNCT
ejpam-4043	409	20	2	2	NUM
ejpam-4043	409	21	,	,	PUNCT
ejpam-4043	409	22	≥	≥	NOUN
ejpam-4043	409	23	3]3	3]3	NOUN
ejpam-4043	409	24	.	.	PUNCT
ejpam-4043	409	25	example	example	NOUN
ejpam-4043	410	1	2	2	NUM
ejpam-4043	410	2	.	.	PUNCT
ejpam-4043	410	3	in	in	ADP
ejpam-4043	410	4	z3[t	z3[t	PROPN
ejpam-4043	410	5	]	]	PUNCT
ejpam-4043	410	6	,	,	PUNCT
ejpam-4043	410	7	t	t	PROPN
ejpam-4043	410	8	6	6	NUM
ejpam-4043	410	9	−	−	NOUN
ejpam-4043	410	10	1	1	NUM
ejpam-4043	410	11	=	=	SYM
ejpam-4043	410	12	(	(	PUNCT
ejpam-4043	410	13	t	t	PROPN
ejpam-4043	410	14	−	−	PROPN
ejpam-4043	410	15	1)3(t	1)3(t	NUM
ejpam-4043	410	16	+	+	CCONJ
ejpam-4043	410	17	1)3	1)3	PROPN
ejpam-4043	410	18	and	and	CCONJ
ejpam-4043	410	19	t6	t6	PROPN
ejpam-4043	410	20	+	+	CCONJ
ejpam-4043	410	21	1	1	NUM
ejpam-4043	410	22	=	=	SYM
ejpam-4043	410	23	(	(	PUNCT
ejpam-4043	410	24	t2	t2	PROPN
ejpam-4043	410	25	+	+	CCONJ
ejpam-4043	410	26	1)3	1)3	PROPN
ejpam-4043	410	27	.	.	PUNCT
ejpam-4043	411	1	now	now	ADV
ejpam-4043	411	2	,	,	PUNCT
ejpam-4043	411	3	let	let	VERB
ejpam-4043	411	4	k	k	PRON
ejpam-4043	411	5	be	be	AUX
ejpam-4043	411	6	a	a	DET
ejpam-4043	411	7	1	1	NUM
ejpam-4043	411	8	+	+	NOUN
ejpam-4043	411	9	2ν+2ω+2νω	2ν+2ω+2νω	ADJ
ejpam-4043	411	10	-	-	ADJ
ejpam-4043	411	11	constacyclic	constacyclic	ADJ
ejpam-4043	411	12	code	code	NOUN
ejpam-4043	411	13	over	over	ADP
ejpam-4043	411	14	the	the	DET
ejpam-4043	411	15	ring	ring	NOUN
ejpam-4043	411	16	<	<	X
ejpam-4043	411	17	=	=	PUNCT
ejpam-4043	411	18	z3+νz3+ωz3+νωz3	z3+νz3+ωz3+νωz3	NOUN
ejpam-4043	411	19	where	where	SCONJ
ejpam-4043	411	20	ν2	ν2	NOUN
ejpam-4043	411	21	=	=	SYM
ejpam-4043	411	22	1	1	NUM
ejpam-4043	411	23	,	,	PUNCT
ejpam-4043	411	24	ω2	ω2	NOUN
ejpam-4043	411	25	=	=	SYM
ejpam-4043	411	26	1	1	NUM
ejpam-4043	411	27	and	and	CCONJ
ejpam-4043	411	28	νω	νω	ADV
ejpam-4043	411	29	=	=	PUNCT
ejpam-4043	411	30	ων	ων	NUM
ejpam-4043	411	31	of	of	ADP
ejpam-4043	411	32	length	length	NOUN
ejpam-4043	411	33	6	6	NUM
ejpam-4043	411	34	.	.	PUNCT
ejpam-4043	412	1	let	let	VERB
ejpam-4043	412	2	g1(t	g1(t	X
ejpam-4043	412	3	)	)	PUNCT
ejpam-4043	412	4	=	=	PUNCT
ejpam-4043	412	5	t+	t+	PUNCT
ejpam-4043	412	6	1	1	NUM
ejpam-4043	412	7	and	and	CCONJ
ejpam-4043	412	8	g2(t	g2(t	NOUN
ejpam-4043	412	9	)	)	PUNCT
ejpam-4043	412	10	=	=	SYM
ejpam-4043	412	11	g3(t	g3(t	X
ejpam-4043	412	12	)	)	PUNCT
ejpam-4043	412	13	=	=	SYM
ejpam-4043	412	14	g4(t	g4(t	ADJ
ejpam-4043	412	15	)	)	PUNCT
ejpam-4043	412	16	=	=	SYM
ejpam-4043	412	17	t2	t2	NOUN
ejpam-4043	412	18	+	+	CCONJ
ejpam-4043	412	19	1	1	NUM
ejpam-4043	412	20	then	then	ADV
ejpam-4043	412	21	g(t	g(t	PROPN
ejpam-4043	412	22	)	)	PUNCT
ejpam-4043	413	1	=	=	PUNCT
ejpam-4043	413	2	ξ1(t+	ξ1(t+	PROPN
ejpam-4043	413	3	1	1	NUM
ejpam-4043	413	4	)	)	PUNCT
ejpam-4043	413	5	+	+	CCONJ
ejpam-4043	413	6	ξ2(t	ξ2(t	SYM
ejpam-4043	413	7	2	2	NUM
ejpam-4043	413	8	+	+	NUM
ejpam-4043	413	9	1	1	NUM
ejpam-4043	413	10	)	)	PUNCT
ejpam-4043	413	11	+	+	CCONJ
ejpam-4043	414	1	ξ3(t	ξ3(t	NUM
ejpam-4043	414	2	2	2	NUM
ejpam-4043	414	3	+	+	NUM
ejpam-4043	414	4	1	1	NUM
ejpam-4043	414	5	)	)	PUNCT
ejpam-4043	414	6	+	+	CCONJ
ejpam-4043	414	7	ξ4(t	ξ4(t	NUM
ejpam-4043	414	8	2	2	NUM
ejpam-4043	414	9	+	+	NUM
ejpam-4043	414	10	1	1	NUM
ejpam-4043	414	11	)	)	PUNCT
ejpam-4043	414	12	be	be	VERB
ejpam-4043	414	13	the	the	DET
ejpam-4043	414	14	generator	generator	NOUN
ejpam-4043	414	15	polynomial	polynomial	NOUN
ejpam-4043	414	16	of	of	ADP
ejpam-4043	414	17	k.	k.	PROPN
ejpam-4043	414	18	since	since	SCONJ
ejpam-4043	414	19	g1(t)g	g1(t)g	ADJ
ejpam-4043	414	20	∗	∗	NOUN
ejpam-4043	414	21	1(t)|t6−	1(t)|t6−	NUM
ejpam-4043	414	22	1	1	NUM
ejpam-4043	414	23	and	and	CCONJ
ejpam-4043	414	24	gi(t)g	gi(t)g	PROPN
ejpam-4043	414	25	∗	∗	NOUN
ejpam-4043	414	26	i	i	PRON
ejpam-4043	414	27	(	(	PUNCT
ejpam-4043	414	28	t)|t6	t)|t6	X
ejpam-4043	415	1	+	+	CCONJ
ejpam-4043	415	2	1	1	NUM
ejpam-4043	415	3	for	for	ADP
ejpam-4043	415	4	i	i	PRON
ejpam-4043	415	5	=	=	SYM
ejpam-4043	415	6	2	2	NUM
ejpam-4043	415	7	,	,	PUNCT
ejpam-4043	415	8	3	3	NUM
ejpam-4043	415	9	,	,	PUNCT
ejpam-4043	415	10	4	4	NUM
ejpam-4043	415	11	respectively	respectively	ADV
ejpam-4043	415	12	,	,	PUNCT
ejpam-4043	415	13	then	then	ADV
ejpam-4043	415	14	by	by	ADP
ejpam-4043	415	15	the	the	DET
ejpam-4043	415	16	use	use	NOUN
ejpam-4043	415	17	of	of	ADP
ejpam-4043	415	18	theorem	theorem	NOUN
ejpam-4043	415	19	4.12	4.12	NUM
ejpam-4043	415	20	,	,	PUNCT
ejpam-4043	415	21	we	we	PRON
ejpam-4043	415	22	get	get	VERB
ejpam-4043	415	23	k⊥	k⊥	NOUN
ejpam-4043	415	24	⊆	⊆	NUM
ejpam-4043	415	25	k	k	PROPN
ejpam-4043	415	26	further	far	ADV
ejpam-4043	415	27	ϕ(k	ϕ(k	NOUN
ejpam-4043	415	28	)	)	PUNCT
ejpam-4043	415	29	is	be	AUX
ejpam-4043	415	30	a	a	DET
ejpam-4043	415	31	linear	linear	ADJ
ejpam-4043	415	32	code	code	NOUN
ejpam-4043	415	33	over	over	ADP
ejpam-4043	415	34	the	the	DET
ejpam-4043	415	35	ring	ring	NOUN
ejpam-4043	415	36	z3	z3	PROPN
ejpam-4043	415	37	having	have	VERB
ejpam-4043	415	38	parameters	parameter	NOUN
ejpam-4043	415	39	[	[	X
ejpam-4043	415	40	24	24	NUM
ejpam-4043	415	41	,	,	PUNCT
ejpam-4043	415	42	17	17	NUM
ejpam-4043	415	43	,	,	PUNCT
ejpam-4043	415	44	3	3	NUM
ejpam-4043	415	45	]	]	PUNCT
ejpam-4043	415	46	.	.	PUNCT
ejpam-4043	416	1	then	then	ADV
ejpam-4043	416	2	,	,	PUNCT
ejpam-4043	416	3	by	by	ADP
ejpam-4043	416	4	the	the	DET
ejpam-4043	416	5	application	application	NOUN
ejpam-4043	416	6	of	of	ADP
ejpam-4043	416	7	theorem	theorem	NOUN
ejpam-4043	416	8	4.18	4.18	NUM
ejpam-4043	416	9	,	,	PUNCT
ejpam-4043	416	10	we	we	PRON
ejpam-4043	416	11	obtain	obtain	VERB
ejpam-4043	416	12	the	the	DET
ejpam-4043	416	13	quantum	quantum	NOUN
ejpam-4043	416	14	code	code	NOUN
ejpam-4043	416	15	having	have	VERB
ejpam-4043	416	16	parameters	parameter	NOUN
ejpam-4043	416	17	[	[	X
ejpam-4043	416	18	24	24	NUM
ejpam-4043	416	19	,	,	PUNCT
ejpam-4043	416	20	10	10	NUM
ejpam-4043	416	21	,	,	PUNCT
ejpam-4043	416	22	≥	≥	NOUN
ejpam-4043	416	23	3]3	3]3	NOUN
ejpam-4043	416	24	.	.	PUNCT
ejpam-4043	416	25	example	example	NOUN
ejpam-4043	417	1	3	3	NUM
ejpam-4043	417	2	.	.	PUNCT
ejpam-4043	418	1	in	in	ADP
ejpam-4043	418	2	z3[t	z3[t	PROPN
ejpam-4043	418	3	]	]	PUNCT
ejpam-4043	418	4	,	,	PUNCT
ejpam-4043	418	5	t	t	PROPN
ejpam-4043	418	6	9	9	NUM
ejpam-4043	418	7	−	−	PROPN
ejpam-4043	418	8	1	1	NUM
ejpam-4043	418	9	=	=	SYM
ejpam-4043	418	10	(	(	PUNCT
ejpam-4043	418	11	t	t	PROPN
ejpam-4043	418	12	−	−	PROPN
ejpam-4043	418	13	1)9	1)9	NUM
ejpam-4043	418	14	and	and	CCONJ
ejpam-4043	418	15	t9	t9	PROPN
ejpam-4043	419	1	+	+	CCONJ
ejpam-4043	419	2	1	1	X
ejpam-4043	419	3	=	=	SYM
ejpam-4043	419	4	(	(	PUNCT
ejpam-4043	419	5	t	t	PROPN
ejpam-4043	419	6	+	+	NOUN
ejpam-4043	419	7	1)9	1)9	NUM
ejpam-4043	419	8	.	.	PUNCT
ejpam-4043	420	1	now	now	ADV
ejpam-4043	420	2	,	,	PUNCT
ejpam-4043	420	3	let	let	VERB
ejpam-4043	420	4	k	k	PRON
ejpam-4043	420	5	be	be	AUX
ejpam-4043	420	6	a	a	DET
ejpam-4043	420	7	νωconstacyclic	νωconstacyclic	ADJ
ejpam-4043	420	8	code	code	NOUN
ejpam-4043	420	9	over	over	ADP
ejpam-4043	420	10	the	the	DET
ejpam-4043	420	11	ring	ring	NOUN
ejpam-4043	420	12	<	<	X
ejpam-4043	420	13	=	=	X
ejpam-4043	420	14	z3	z3	PROPN
ejpam-4043	420	15	+	+	CCONJ
ejpam-4043	420	16	νz3	νz3	X
ejpam-4043	421	1	+	+	CCONJ
ejpam-4043	421	2	ωz3	ωz3	NOUN
ejpam-4043	421	3	+	+	CCONJ
ejpam-4043	421	4	νωz3	νωz3	NOUN
ejpam-4043	421	5	where	where	SCONJ
ejpam-4043	421	6	ν2	ν2	NOUN
ejpam-4043	421	7	=	=	SYM
ejpam-4043	421	8	1	1	NUM
ejpam-4043	421	9	,	,	PUNCT
ejpam-4043	421	10	ω2	ω2	NOUN
ejpam-4043	421	11	=	=	SYM
ejpam-4043	421	12	1	1	NUM
ejpam-4043	421	13	and	and	CCONJ
ejpam-4043	421	14	prateek	prateek	ADJ
ejpam-4043	421	15	mor	mor	PROPN
ejpam-4043	421	16	et	et	PROPN
ejpam-4043	421	17	al	al	PROPN
ejpam-4043	421	18	.	.	PUNCT
ejpam-4043	421	19	/	/	SYM
ejpam-4043	421	20	eur	eur	PROPN
ejpam-4043	421	21	.	.	PUNCT
ejpam-4043	422	1	j.	j.	PROPN
ejpam-4043	422	2	pure	pure	PROPN
ejpam-4043	422	3	appl	appl	PROPN
ejpam-4043	422	4	.	.	PROPN
ejpam-4043	422	5	math	math	PROPN
ejpam-4043	422	6	,	,	PUNCT
ejpam-4043	422	7	14	14	NUM
ejpam-4043	422	8	(	(	PUNCT
ejpam-4043	422	9	3	3	NUM
ejpam-4043	422	10	)	)	PUNCT
ejpam-4043	422	11	(	(	PUNCT
ejpam-4043	422	12	2021	2021	NUM
ejpam-4043	422	13	)	)	PUNCT
ejpam-4043	422	14	,	,	PUNCT
ejpam-4043	422	15	1082	1082	NUM
ejpam-4043	422	16	-	-	SYM
ejpam-4043	422	17	1097	1097	NUM
ejpam-4043	422	18	1095	1095	NUM
ejpam-4043	422	19	νω	νω	PROPN
ejpam-4043	423	1	=	=	NOUN
ejpam-4043	423	2	ων	ων	NUM
ejpam-4043	423	3	of	of	ADP
ejpam-4043	423	4	length	length	NOUN
ejpam-4043	423	5	9	9	NUM
ejpam-4043	423	6	.	.	PUNCT
ejpam-4043	424	1	let	let	VERB
ejpam-4043	424	2	g1(t	g1(t	X
ejpam-4043	424	3	)	)	PUNCT
ejpam-4043	425	1	=	=	SYM
ejpam-4043	425	2	g4(t	g4(t	PROPN
ejpam-4043	425	3	)	)	PUNCT
ejpam-4043	425	4	=	=	SYM
ejpam-4043	425	5	t	t	NOUN
ejpam-4043	425	6	−	−	NOUN
ejpam-4043	425	7	1	1	NUM
ejpam-4043	425	8	and	and	CCONJ
ejpam-4043	425	9	g2(t	g2(t	NOUN
ejpam-4043	425	10	)	)	PUNCT
ejpam-4043	425	11	=	=	SYM
ejpam-4043	425	12	g3(t	g3(t	X
ejpam-4043	425	13	)	)	PUNCT
ejpam-4043	425	14	=	=	SYM
ejpam-4043	425	15	t	t	NOUN
ejpam-4043	425	16	+	+	CCONJ
ejpam-4043	425	17	1	1	NUM
ejpam-4043	425	18	then	then	ADV
ejpam-4043	425	19	g(t	g(t	PROPN
ejpam-4043	425	20	)	)	PUNCT
ejpam-4043	426	1	=	=	PUNCT
ejpam-4043	426	2	ξ1(t−	ξ1(t−	NOUN
ejpam-4043	426	3	1	1	X
ejpam-4043	426	4	)	)	PUNCT
ejpam-4043	426	5	+	+	CCONJ
ejpam-4043	427	1	ξ2(t+	ξ2(t+	PROPN
ejpam-4043	427	2	1	1	NUM
ejpam-4043	427	3	)	)	PUNCT
ejpam-4043	427	4	+	+	CCONJ
ejpam-4043	428	1	ξ3(t+	ξ3(t+	PROPN
ejpam-4043	428	2	1	1	NUM
ejpam-4043	428	3	)	)	PUNCT
ejpam-4043	428	4	+	+	NUM
ejpam-4043	428	5	ξ4(t−	ξ4(t−	NOUN
ejpam-4043	428	6	1	1	X
ejpam-4043	428	7	)	)	PUNCT
ejpam-4043	428	8	be	be	AUX
ejpam-4043	428	9	the	the	DET
ejpam-4043	428	10	generator	generator	NOUN
ejpam-4043	428	11	polynomial	polynomial	NOUN
ejpam-4043	428	12	of	of	ADP
ejpam-4043	428	13	k.	k.	PROPN
ejpam-4043	428	14	since	since	SCONJ
ejpam-4043	428	15	gi(t)g	gi(t)g	PROPN
ejpam-4043	428	16	∗	∗	NOUN
ejpam-4043	428	17	i	i	PRON
ejpam-4043	428	18	(	(	PUNCT
ejpam-4043	428	19	t)|t9	t)|t9	NOUN
ejpam-4043	428	20	−	−	PROPN
ejpam-4043	428	21	1	1	NUM
ejpam-4043	428	22	for	for	ADP
ejpam-4043	428	23	i	i	PRON
ejpam-4043	428	24	=	=	NOUN
ejpam-4043	428	25	1	1	NUM
ejpam-4043	428	26	,	,	PUNCT
ejpam-4043	428	27	4	4	NUM
ejpam-4043	428	28	respectively	respectively	ADV
ejpam-4043	428	29	and	and	CCONJ
ejpam-4043	428	30	gj(t)g	gj(t)g	PUNCT
ejpam-4043	428	31	∗	∗	X
ejpam-4043	428	32	j	j	PROPN
ejpam-4043	428	33	(	(	PUNCT
ejpam-4043	428	34	t)|t9	t)|t9	NOUN
ejpam-4043	428	35	+	+	CCONJ
ejpam-4043	428	36	1	1	NUM
ejpam-4043	428	37	for	for	ADP
ejpam-4043	428	38	j	j	PROPN
ejpam-4043	428	39	=	=	SYM
ejpam-4043	428	40	2	2	NUM
ejpam-4043	428	41	,	,	PUNCT
ejpam-4043	428	42	3	3	NUM
ejpam-4043	428	43	respectively	respectively	ADV
ejpam-4043	428	44	,	,	PUNCT
ejpam-4043	428	45	then	then	ADV
ejpam-4043	428	46	by	by	ADP
ejpam-4043	428	47	the	the	DET
ejpam-4043	428	48	use	use	NOUN
ejpam-4043	428	49	of	of	ADP
ejpam-4043	428	50	theorem	theorem	NOUN
ejpam-4043	428	51	4.13	4.13	NUM
ejpam-4043	428	52	,	,	PUNCT
ejpam-4043	428	53	we	we	PRON
ejpam-4043	428	54	get	get	VERB
ejpam-4043	428	55	k⊥	k⊥	NOUN
ejpam-4043	428	56	⊆	⊆	NUM
ejpam-4043	428	57	k	k	PROPN
ejpam-4043	428	58	further	far	ADV
ejpam-4043	428	59	ϕ(k	ϕ(k	NOUN
ejpam-4043	428	60	)	)	PUNCT
ejpam-4043	428	61	is	be	AUX
ejpam-4043	428	62	a	a	DET
ejpam-4043	428	63	linear	linear	ADJ
ejpam-4043	428	64	code	code	NOUN
ejpam-4043	428	65	over	over	ADP
ejpam-4043	428	66	the	the	DET
ejpam-4043	428	67	ring	ring	NOUN
ejpam-4043	428	68	z3	z3	PROPN
ejpam-4043	428	69	having	have	VERB
ejpam-4043	428	70	parameters	parameter	NOUN
ejpam-4043	428	71	[	[	X
ejpam-4043	428	72	36	36	NUM
ejpam-4043	428	73	,	,	PUNCT
ejpam-4043	428	74	32	32	NUM
ejpam-4043	428	75	,	,	PUNCT
ejpam-4043	428	76	2	2	NUM
ejpam-4043	428	77	]	]	PUNCT
ejpam-4043	428	78	.	.	PUNCT
ejpam-4043	429	1	then	then	ADV
ejpam-4043	429	2	,	,	PUNCT
ejpam-4043	429	3	by	by	ADP
ejpam-4043	429	4	the	the	DET
ejpam-4043	429	5	application	application	NOUN
ejpam-4043	429	6	of	of	ADP
ejpam-4043	429	7	theorem	theorem	NOUN
ejpam-4043	429	8	4.18	4.18	NUM
ejpam-4043	429	9	,	,	PUNCT
ejpam-4043	429	10	we	we	PRON
ejpam-4043	429	11	obtain	obtain	VERB
ejpam-4043	429	12	the	the	DET
ejpam-4043	429	13	quantum	quantum	NOUN
ejpam-4043	429	14	code	code	NOUN
ejpam-4043	429	15	having	have	VERB
ejpam-4043	429	16	parameters	parameter	NOUN
ejpam-4043	429	17	[	[	X
ejpam-4043	429	18	36	36	NUM
ejpam-4043	429	19	,	,	PUNCT
ejpam-4043	429	20	28	28	NUM
ejpam-4043	429	21	,	,	PUNCT
ejpam-4043	429	22	≥	≥	NOUN
ejpam-4043	429	23	2]3	2]3	NUM
ejpam-4043	429	24	.	.	PUNCT
ejpam-4043	429	25	example	example	NOUN
ejpam-4043	430	1	4	4	NUM
ejpam-4043	430	2	.	.	PUNCT
ejpam-4043	430	3	in	in	ADP
ejpam-4043	430	4	z3[t	z3[t	PROPN
ejpam-4043	430	5	]	]	PUNCT
ejpam-4043	430	6	,	,	PUNCT
ejpam-4043	430	7	t	t	PROPN
ejpam-4043	430	8	12−1	12−1	NUM
ejpam-4043	430	9	=	=	SYM
ejpam-4043	430	10	(	(	PUNCT
ejpam-4043	430	11	t+1)3(t+2)3(t2	t+1)3(t+2)3(t2	PROPN
ejpam-4043	430	12	+	+	NOUN
ejpam-4043	430	13	1)3	1)3	PROPN
ejpam-4043	430	14	and	and	CCONJ
ejpam-4043	430	15	t12	t12	PROPN
ejpam-4043	430	16	+	+	PROPN
ejpam-4043	430	17	1	1	NUM
ejpam-4043	430	18	=	=	SYM
ejpam-4043	430	19	(	(	PUNCT
ejpam-4043	430	20	t2	t2	PROPN
ejpam-4043	430	21	+	+	PROPN
ejpam-4043	430	22	2t+2)3(t2+t+2)3	2t+2)3(t2+t+2)3	NUM
ejpam-4043	430	23	.	.	PUNCT
ejpam-4043	431	1	now	now	ADV
ejpam-4043	431	2	,	,	PUNCT
ejpam-4043	431	3	let	let	VERB
ejpam-4043	431	4	k	k	PRON
ejpam-4043	431	5	be	be	AUX
ejpam-4043	431	6	a	a	DET
ejpam-4043	431	7	ν	ν	NOUN
ejpam-4043	431	8	-	-	ADJ
ejpam-4043	431	9	constacyclic	constacyclic	ADJ
ejpam-4043	431	10	code	code	NOUN
ejpam-4043	431	11	over	over	ADP
ejpam-4043	431	12	<	<	X
ejpam-4043	431	13	=	=	PUNCT
ejpam-4043	431	14	z3	z3	PROPN
ejpam-4043	431	15	+	+	CCONJ
ejpam-4043	431	16	νz3	νz3	X
ejpam-4043	431	17	+	+	CCONJ
ejpam-4043	431	18	ωz3	ωz3	NOUN
ejpam-4043	431	19	+	+	CCONJ
ejpam-4043	431	20	νωz3	νωz3	NOUN
ejpam-4043	431	21	where	where	SCONJ
ejpam-4043	431	22	ν2	ν2	NOUN
ejpam-4043	431	23	=	=	SYM
ejpam-4043	431	24	1	1	NUM
ejpam-4043	431	25	,	,	PUNCT
ejpam-4043	431	26	ω2	ω2	NOUN
ejpam-4043	431	27	=	=	SYM
ejpam-4043	431	28	1	1	NUM
ejpam-4043	431	29	and	and	CCONJ
ejpam-4043	431	30	νω	νω	ADV
ejpam-4043	431	31	=	=	PUNCT
ejpam-4043	431	32	ων	ων	NUM
ejpam-4043	431	33	and	and	CCONJ
ejpam-4043	431	34	ν2ω2	ν2ω2	PROPN
ejpam-4043	431	35	=	=	SYM
ejpam-4043	431	36	νω	νω	ADP
ejpam-4043	431	37	of	of	ADP
ejpam-4043	431	38	length	length	NOUN
ejpam-4043	431	39	12	12	NUM
ejpam-4043	431	40	.	.	PUNCT
ejpam-4043	432	1	let	let	VERB
ejpam-4043	432	2	g1(t	g1(t	X
ejpam-4043	432	3	)	)	PUNCT
ejpam-4043	432	4	=	=	SYM
ejpam-4043	432	5	g3(t	g3(t	X
ejpam-4043	432	6	)	)	PUNCT
ejpam-4043	433	1	=	=	SYM
ejpam-4043	433	2	t	t	NOUN
ejpam-4043	433	3	+	+	CCONJ
ejpam-4043	433	4	1	1	NUM
ejpam-4043	433	5	and	and	CCONJ
ejpam-4043	433	6	g2(t	g2(t	NOUN
ejpam-4043	433	7	)	)	PUNCT
ejpam-4043	434	1	=	=	PUNCT
ejpam-4043	434	2	g4(t	g4(t	ADJ
ejpam-4043	434	3	)	)	PUNCT
ejpam-4043	434	4	=	=	SYM
ejpam-4043	434	5	t2	t2	NOUN
ejpam-4043	434	6	+	+	CCONJ
ejpam-4043	434	7	t+	t+	NOUN
ejpam-4043	434	8	2	2	NUM
ejpam-4043	434	9	,	,	PUNCT
ejpam-4043	434	10	g(t	g(t	NOUN
ejpam-4043	434	11	)	)	PUNCT
ejpam-4043	435	1	=	=	PUNCT
ejpam-4043	435	2	ξ1(t+	ξ1(t+	PROPN
ejpam-4043	435	3	1	1	NUM
ejpam-4043	435	4	)	)	PUNCT
ejpam-4043	435	5	+	+	CCONJ
ejpam-4043	435	6	ξ2(t	ξ2(t	SYM
ejpam-4043	435	7	2	2	NUM
ejpam-4043	435	8	+	+	CCONJ
ejpam-4043	435	9	t+	t+	NOUN
ejpam-4043	435	10	2	2	NUM
ejpam-4043	435	11	)	)	PUNCT
ejpam-4043	435	12	+	+	CCONJ
ejpam-4043	436	1	ξ3(t+	ξ3(t+	PROPN
ejpam-4043	436	2	1	1	NUM
ejpam-4043	436	3	)	)	PUNCT
ejpam-4043	436	4	+	+	CCONJ
ejpam-4043	436	5	ξ4(t	ξ4(t	NUM
ejpam-4043	436	6	2	2	NUM
ejpam-4043	436	7	+	+	CCONJ
ejpam-4043	436	8	t+	t+	NOUN
ejpam-4043	436	9	2	2	NUM
ejpam-4043	436	10	)	)	PUNCT
ejpam-4043	436	11	be	be	AUX
ejpam-4043	436	12	the	the	DET
ejpam-4043	436	13	generator	generator	NOUN
ejpam-4043	436	14	polynomials	polynomial	NOUN
ejpam-4043	436	15	of	of	ADP
ejpam-4043	436	16	k.	k.	NOUN
ejpam-4043	436	17	since	since	SCONJ
ejpam-4043	436	18	gi(t)g	gi(t)g	PROPN
ejpam-4043	436	19	∗	∗	NOUN
ejpam-4043	436	20	i	i	PRON
ejpam-4043	436	21	(	(	PUNCT
ejpam-4043	436	22	t)|t12	t)|t12	NOUN
ejpam-4043	436	23	−	−	PROPN
ejpam-4043	436	24	1	1	NUM
ejpam-4043	436	25	for	for	ADP
ejpam-4043	436	26	i	i	PRON
ejpam-4043	436	27	=	=	NOUN
ejpam-4043	436	28	1	1	NUM
ejpam-4043	436	29	,	,	PUNCT
ejpam-4043	436	30	3	3	NUM
ejpam-4043	436	31	respectively	respectively	ADV
ejpam-4043	436	32	and	and	CCONJ
ejpam-4043	436	33	gj(t)g	gj(t)g	PUNCT
ejpam-4043	436	34	∗	∗	X
ejpam-4043	436	35	j	j	PROPN
ejpam-4043	436	36	(	(	PUNCT
ejpam-4043	436	37	t)|t12	t)|t12	NOUN
ejpam-4043	436	38	+	+	CCONJ
ejpam-4043	436	39	1	1	NUM
ejpam-4043	436	40	for	for	ADP
ejpam-4043	436	41	j	j	PROPN
ejpam-4043	436	42	=	=	SYM
ejpam-4043	436	43	2	2	NUM
ejpam-4043	436	44	,	,	PUNCT
ejpam-4043	436	45	4	4	NUM
ejpam-4043	436	46	respectively	respectively	ADV
ejpam-4043	436	47	,	,	PUNCT
ejpam-4043	436	48	then	then	ADV
ejpam-4043	436	49	by	by	ADP
ejpam-4043	436	50	the	the	DET
ejpam-4043	436	51	use	use	NOUN
ejpam-4043	436	52	of	of	ADP
ejpam-4043	436	53	theorem	theorem	NOUN
ejpam-4043	436	54	4.14	4.14	NUM
ejpam-4043	436	55	,	,	PUNCT
ejpam-4043	436	56	we	we	PRON
ejpam-4043	436	57	get	get	VERB
ejpam-4043	436	58	k⊥	k⊥	PROPN
ejpam-4043	436	59	⊆	⊆	NUM
ejpam-4043	436	60	k.	k.	NOUN
ejpam-4043	436	61	further	further	PROPN
ejpam-4043	436	62	ϕ(k	ϕ(k	NOUN
ejpam-4043	436	63	)	)	PUNCT
ejpam-4043	436	64	is	be	AUX
ejpam-4043	436	65	a	a	DET
ejpam-4043	436	66	linear	linear	ADJ
ejpam-4043	436	67	code	code	NOUN
ejpam-4043	436	68	over	over	ADP
ejpam-4043	436	69	z3	z3	PROPN
ejpam-4043	436	70	having	have	VERB
ejpam-4043	436	71	parameters	parameter	NOUN
ejpam-4043	436	72	[	[	X
ejpam-4043	436	73	48	48	NUM
ejpam-4043	436	74	,	,	PUNCT
ejpam-4043	436	75	43	43	NUM
ejpam-4043	436	76	,	,	PUNCT
ejpam-4043	436	77	3	3	NUM
ejpam-4043	436	78	]	]	PUNCT
ejpam-4043	436	79	.	.	PUNCT
ejpam-4043	437	1	then	then	ADV
ejpam-4043	437	2	,	,	PUNCT
ejpam-4043	437	3	by	by	ADP
ejpam-4043	437	4	the	the	DET
ejpam-4043	437	5	application	application	NOUN
ejpam-4043	437	6	of	of	ADP
ejpam-4043	437	7	theorem	theorem	NOUN
ejpam-4043	437	8	4.18	4.18	NUM
ejpam-4043	437	9	,	,	PUNCT
ejpam-4043	437	10	we	we	PRON
ejpam-4043	437	11	obtain	obtain	VERB
ejpam-4043	437	12	the	the	DET
ejpam-4043	437	13	quantum	quantum	NOUN
ejpam-4043	437	14	code	code	NOUN
ejpam-4043	437	15	having	have	VERB
ejpam-4043	437	16	parameters	parameter	NOUN
ejpam-4043	437	17	[	[	X
ejpam-4043	437	18	48	48	NUM
ejpam-4043	437	19	,	,	PUNCT
ejpam-4043	437	20	38	38	NUM
ejpam-4043	437	21	,	,	PUNCT
ejpam-4043	437	22	≥	≥	NOUN
ejpam-4043	437	23	3]3	3]3	NOUN
ejpam-4043	437	24	.	.	PUNCT
ejpam-4043	437	25	example	example	NOUN
ejpam-4043	438	1	5	5	NUM
ejpam-4043	438	2	.	.	PUNCT
ejpam-4043	439	1	in	in	ADP
ejpam-4043	439	2	z3[t	z3[t	PROPN
ejpam-4043	439	3	]	]	PUNCT
ejpam-4043	439	4	,	,	PUNCT
ejpam-4043	439	5	t	t	PROPN
ejpam-4043	439	6	15−1	15−1	NUM
ejpam-4043	439	7	=	=	SYM
ejpam-4043	439	8	(	(	PUNCT
ejpam-4043	439	9	t+2)3(t4+t3+t2+t+1)3	t+2)3(t4+t3+t2+t+1)3	NOUN
ejpam-4043	439	10	and	and	CCONJ
ejpam-4043	439	11	t15	t15	PROPN
ejpam-4043	439	12	+	+	PROPN
ejpam-4043	439	13	1	1	NUM
ejpam-4043	439	14	=	=	SYM
ejpam-4043	439	15	(	(	PUNCT
ejpam-4043	439	16	t+1)3(t4	t+1)3(t4	PROPN
ejpam-4043	439	17	+	+	NOUN
ejpam-4043	439	18	2t3	2t3	NUM
ejpam-4043	439	19	+	+	NOUN
ejpam-4043	439	20	t2	t2	NOUN
ejpam-4043	439	21	+	+	CCONJ
ejpam-4043	439	22	2t+	2t+	NUM
ejpam-4043	439	23	1)3	1)3	NUM
ejpam-4043	439	24	.	.	PUNCT
ejpam-4043	440	1	now	now	ADV
ejpam-4043	440	2	,	,	PUNCT
ejpam-4043	440	3	let	let	VERB
ejpam-4043	440	4	k	k	PRON
ejpam-4043	440	5	be	be	AUX
ejpam-4043	440	6	a	a	DET
ejpam-4043	440	7	ω	ω	ADJ
ejpam-4043	440	8	-	-	ADJ
ejpam-4043	440	9	constacyclic	constacyclic	ADJ
ejpam-4043	440	10	code	code	NOUN
ejpam-4043	440	11	over	over	ADP
ejpam-4043	440	12	<	<	X
ejpam-4043	440	13	=	=	PUNCT
ejpam-4043	440	14	z3	z3	PROPN
ejpam-4043	441	1	+	+	NOUN
ejpam-4043	441	2	νz3	νz3	ADJ
ejpam-4043	441	3	+	+	NOUN
ejpam-4043	441	4	ωz3	ωz3	NOUN
ejpam-4043	441	5	+	+	NOUN
ejpam-4043	441	6	νωz3	νωz3	NOUN
ejpam-4043	441	7	where	where	SCONJ
ejpam-4043	441	8	ν2	ν2	NOUN
ejpam-4043	441	9	=	=	SYM
ejpam-4043	441	10	1	1	NUM
ejpam-4043	441	11	,	,	PUNCT
ejpam-4043	441	12	ω2	ω2	NOUN
ejpam-4043	441	13	=	=	SYM
ejpam-4043	441	14	1	1	NUM
ejpam-4043	441	15	and	and	CCONJ
ejpam-4043	441	16	νω	νω	ADV
ejpam-4043	441	17	=	=	PUNCT
ejpam-4043	441	18	ων	ων	NUM
ejpam-4043	441	19	and	and	CCONJ
ejpam-4043	441	20	ν2ω2	ν2ω2	PROPN
ejpam-4043	441	21	=	=	SYM
ejpam-4043	441	22	νω	νω	ADP
ejpam-4043	441	23	of	of	ADP
ejpam-4043	441	24	length	length	NOUN
ejpam-4043	441	25	15	15	NUM
ejpam-4043	441	26	.	.	PUNCT
ejpam-4043	442	1	let	let	VERB
ejpam-4043	442	2	g1(t	g1(t	X
ejpam-4043	442	3	)	)	PUNCT
ejpam-4043	442	4	=	=	SYM
ejpam-4043	442	5	g2(t	g2(t	NOUN
ejpam-4043	442	6	)	)	PUNCT
ejpam-4043	442	7	=	=	NOUN
ejpam-4043	443	1	t+	t+	PUNCT
ejpam-4043	443	2	2	2	NUM
ejpam-4043	443	3	and	and	CCONJ
ejpam-4043	443	4	g3(t	g3(t	NUM
ejpam-4043	443	5	)	)	PUNCT
ejpam-4043	444	1	=	=	SYM
ejpam-4043	444	2	g4(t	g4(t	ADJ
ejpam-4043	444	3	)	)	PUNCT
ejpam-4043	444	4	=	=	NOUN
ejpam-4043	444	5	t+	t+	PUNCT
ejpam-4043	444	6	1	1	NUM
ejpam-4043	444	7	,	,	PUNCT
ejpam-4043	444	8	g(t	g(t	NOUN
ejpam-4043	444	9	)	)	PUNCT
ejpam-4043	444	10	=	=	PUNCT
ejpam-4043	445	1	ξ1(t+	ξ1(t+	PROPN
ejpam-4043	445	2	2	2	NUM
ejpam-4043	445	3	)	)	PUNCT
ejpam-4043	445	4	+	+	CCONJ
ejpam-4043	446	1	ξ2(t+	ξ2(t+	PROPN
ejpam-4043	446	2	2	2	NUM
ejpam-4043	446	3	)	)	PUNCT
ejpam-4043	446	4	+	+	CCONJ
ejpam-4043	446	5	ξ3(t+	ξ3(t+	PROPN
ejpam-4043	446	6	1	1	NUM
ejpam-4043	446	7	)	)	PUNCT
ejpam-4043	446	8	+	+	CCONJ
ejpam-4043	446	9	ξ4(t+	ξ4(t+	PROPN
ejpam-4043	446	10	1	1	NUM
ejpam-4043	446	11	)	)	PUNCT
ejpam-4043	446	12	be	be	AUX
ejpam-4043	446	13	the	the	DET
ejpam-4043	446	14	generator	generator	NOUN
ejpam-4043	446	15	polynomials	polynomial	NOUN
ejpam-4043	446	16	of	of	ADP
ejpam-4043	446	17	k.since	k.since	NOUN
ejpam-4043	446	18	gi(t)g∗i	gi(t)g∗i	NOUN
ejpam-4043	446	19	(	(	PUNCT
ejpam-4043	446	20	t)|t15−1	t)|t15−1	PROPN
ejpam-4043	446	21	for	for	ADP
ejpam-4043	446	22	i	i	PRON
ejpam-4043	446	23	=	=	NOUN
ejpam-4043	446	24	1	1	NUM
ejpam-4043	446	25	,	,	PUNCT
ejpam-4043	446	26	2	2	NUM
ejpam-4043	446	27	respectively	respectively	ADV
ejpam-4043	446	28	and	and	CCONJ
ejpam-4043	446	29	gj(t)g	gj(t)g	PUNCT
ejpam-4043	446	30	∗	∗	X
ejpam-4043	446	31	j	j	PROPN
ejpam-4043	446	32	(	(	PUNCT
ejpam-4043	446	33	t)|t15	t)|t15	PROPN
ejpam-4043	446	34	+1	+1	PROPN
ejpam-4043	446	35	for	for	ADP
ejpam-4043	446	36	j	j	PROPN
ejpam-4043	446	37	=	=	SYM
ejpam-4043	446	38	3	3	NUM
ejpam-4043	446	39	,	,	PUNCT
ejpam-4043	446	40	4	4	NUM
ejpam-4043	446	41	respectively	respectively	ADV
ejpam-4043	446	42	,	,	PUNCT
ejpam-4043	446	43	then	then	ADV
ejpam-4043	446	44	by	by	ADP
ejpam-4043	446	45	the	the	DET
ejpam-4043	446	46	use	use	NOUN
ejpam-4043	446	47	of	of	ADP
ejpam-4043	446	48	theorem	theorem	NOUN
ejpam-4043	446	49	4.15	4.15	NUM
ejpam-4043	446	50	,	,	PUNCT
ejpam-4043	446	51	we	we	PRON
ejpam-4043	446	52	get	get	VERB
ejpam-4043	446	53	k⊥	k⊥	PROPN
ejpam-4043	446	54	⊆	⊆	NUM
ejpam-4043	446	55	k.	k.	NOUN
ejpam-4043	446	56	further	further	PROPN
ejpam-4043	446	57	ϕ(k	ϕ(k	NOUN
ejpam-4043	446	58	)	)	PUNCT
ejpam-4043	446	59	is	be	AUX
ejpam-4043	446	60	a	a	DET
ejpam-4043	446	61	linear	linear	ADJ
ejpam-4043	446	62	code	code	NOUN
ejpam-4043	446	63	over	over	ADP
ejpam-4043	446	64	z3	z3	PROPN
ejpam-4043	446	65	having	have	VERB
ejpam-4043	446	66	parameters	parameter	NOUN
ejpam-4043	446	67	[	[	X
ejpam-4043	446	68	60	60	NUM
ejpam-4043	446	69	,	,	PUNCT
ejpam-4043	446	70	56	56	NUM
ejpam-4043	446	71	,	,	PUNCT
ejpam-4043	446	72	2	2	NUM
ejpam-4043	446	73	]	]	PUNCT
ejpam-4043	446	74	.	.	PUNCT
ejpam-4043	447	1	then	then	ADV
ejpam-4043	447	2	,	,	PUNCT
ejpam-4043	447	3	by	by	ADP
ejpam-4043	447	4	the	the	DET
ejpam-4043	447	5	application	application	NOUN
ejpam-4043	447	6	of	of	ADP
ejpam-4043	447	7	theorem	theorem	NOUN
ejpam-4043	447	8	4.18	4.18	NUM
ejpam-4043	447	9	,	,	PUNCT
ejpam-4043	447	10	we	we	PRON
ejpam-4043	447	11	obtain	obtain	VERB
ejpam-4043	447	12	the	the	DET
ejpam-4043	447	13	quantum	quantum	NOUN
ejpam-4043	447	14	code	code	NOUN
ejpam-4043	447	15	having	have	VERB
ejpam-4043	447	16	parameters	parameter	NOUN
ejpam-4043	447	17	[	[	X
ejpam-4043	447	18	60	60	NUM
ejpam-4043	447	19	,	,	PUNCT
ejpam-4043	447	20	52	52	NUM
ejpam-4043	447	21	,	,	PUNCT
ejpam-4043	447	22	≥	≥	NOUN
ejpam-4043	447	23	2]3	2]3	NUM
ejpam-4043	447	24	.	.	PUNCT
ejpam-4043	447	25	example	example	NOUN
ejpam-4043	448	1	6	6	NUM
ejpam-4043	448	2	.	.	PUNCT
ejpam-4043	449	1	in	in	ADP
ejpam-4043	449	2	z3[t	z3[t	PROPN
ejpam-4043	449	3	]	]	PUNCT
ejpam-4043	449	4	,	,	PUNCT
ejpam-4043	449	5	t	t	PROPN
ejpam-4043	449	6	20	20	NUM
ejpam-4043	449	7	−	−	NOUN
ejpam-4043	449	8	1	1	NUM
ejpam-4043	449	9	=	=	SYM
ejpam-4043	449	10	(	(	PUNCT
ejpam-4043	449	11	t+	t+	NOUN
ejpam-4043	449	12	1)(t+	1)(t+	NUM
ejpam-4043	449	13	2)(t2	2)(t2	NUM
ejpam-4043	449	14	+	+	CCONJ
ejpam-4043	449	15	1)(t4	1)(t4	NUM
ejpam-4043	449	16	+	+	CCONJ
ejpam-4043	449	17	t3	t3	PROPN
ejpam-4043	449	18	+	+	CCONJ
ejpam-4043	449	19	2t+	2t+	NUM
ejpam-4043	449	20	1)(t4	1)(t4	NUM
ejpam-4043	449	21	+	+	CCONJ
ejpam-4043	449	22	t3	t3	NOUN
ejpam-4043	449	23	+	+	CCONJ
ejpam-4043	449	24	t2	t2	NOUN
ejpam-4043	449	25	+	+	CCONJ
ejpam-4043	449	26	t+	t+	NOUN
ejpam-4043	449	27	1)(t4	1)(t4	NUM
ejpam-4043	449	28	+	+	SYM
ejpam-4043	449	29	2t3	2t3	NUM
ejpam-4043	449	30	+	+	SYM
ejpam-4043	449	31	t+	t+	NOUN
ejpam-4043	449	32	1)(t4	1)(t4	NUM
ejpam-4043	449	33	+	+	SYM
ejpam-4043	449	34	2t3	2t3	NUM
ejpam-4043	449	35	+	+	CCONJ
ejpam-4043	449	36	t2	t2	NOUN
ejpam-4043	449	37	+	+	CCONJ
ejpam-4043	449	38	2t+	2t+	NUM
ejpam-4043	449	39	1	1	NUM
ejpam-4043	449	40	)	)	PUNCT
ejpam-4043	449	41	and	and	CCONJ
ejpam-4043	449	42	t20	t20	VERB
ejpam-4043	449	43	+	+	NOUN
ejpam-4043	449	44	1	1	NUM
ejpam-4043	449	45	=	=	SYM
ejpam-4043	449	46	(	(	PUNCT
ejpam-4043	449	47	t2	t2	NOUN
ejpam-4043	449	48	+	+	CCONJ
ejpam-4043	449	49	t+	t+	NOUN
ejpam-4043	449	50	2)(t2	2)(t2	NUM
ejpam-4043	449	51	+	+	NUM
ejpam-4043	449	52	2t+	2t+	NUM
ejpam-4043	449	53	2)(t4	2)(t4	NUM
ejpam-4043	449	54	+	+	CCONJ
ejpam-4043	449	55	t2	t2	NOUN
ejpam-4043	449	56	+	+	CCONJ
ejpam-4043	449	57	t+	t+	NOUN
ejpam-4043	449	58	1)(t4	1)(t4	NOUN
ejpam-4043	449	59	+	+	CCONJ
ejpam-4043	449	60	t2	t2	NOUN
ejpam-4043	449	61	+	+	CCONJ
ejpam-4043	449	62	2t+	2t+	NUM
ejpam-4043	449	63	1)(t4	1)(t4	NUM
ejpam-4043	449	64	+	+	CCONJ
ejpam-4043	449	65	t3	t3	NOUN
ejpam-4043	449	66	+	+	CCONJ
ejpam-4043	449	67	t2	t2	PROPN
ejpam-4043	449	68	+	+	CCONJ
ejpam-4043	449	69	1)(t4	1)(t4	NUM
ejpam-4043	449	70	+	+	SYM
ejpam-4043	449	71	2t3	2t3	NUM
ejpam-4043	449	72	+	+	CCONJ
ejpam-4043	449	73	t2	t2	NOUN
ejpam-4043	449	74	+	+	CCONJ
ejpam-4043	449	75	1	1	NUM
ejpam-4043	449	76	)	)	PUNCT
ejpam-4043	449	77	.	.	PUNCT
ejpam-4043	450	1	now	now	ADV
ejpam-4043	450	2	,	,	PUNCT
ejpam-4043	450	3	let	let	VERB
ejpam-4043	450	4	k	k	PRON
ejpam-4043	450	5	be	be	AUX
ejpam-4043	450	6	a	a	DET
ejpam-4043	450	7	1	1	NUM
ejpam-4043	450	8	+	+	NOUN
ejpam-4043	450	9	ν	ν	X
ejpam-4043	450	10	+	+	NOUN
ejpam-4043	450	11	ω+	ω+	NUM
ejpam-4043	450	12	2νωconstacyclic	2νωconstacyclic	NUM
ejpam-4043	450	13	code	code	NOUN
ejpam-4043	450	14	over	over	ADP
ejpam-4043	450	15	<	<	X
ejpam-4043	450	16	=	=	PUNCT
ejpam-4043	450	17	z3	z3	PROPN
ejpam-4043	450	18	+	+	CCONJ
ejpam-4043	450	19	νz3	νz3	X
ejpam-4043	450	20	+	+	CCONJ
ejpam-4043	450	21	ωz3	ωz3	NOUN
ejpam-4043	450	22	+	+	CCONJ
ejpam-4043	450	23	νωz3	νωz3	NOUN
ejpam-4043	450	24	where	where	SCONJ
ejpam-4043	450	25	ν2	ν2	NOUN
ejpam-4043	450	26	=	=	SYM
ejpam-4043	450	27	1	1	NUM
ejpam-4043	450	28	,	,	PUNCT
ejpam-4043	450	29	ω2	ω2	NOUN
ejpam-4043	450	30	=	=	SYM
ejpam-4043	450	31	1	1	NUM
ejpam-4043	450	32	and	and	CCONJ
ejpam-4043	450	33	νω	νω	ADV
ejpam-4043	450	34	=	=	PUNCT
ejpam-4043	450	35	ων	ων	NUM
ejpam-4043	450	36	and	and	CCONJ
ejpam-4043	450	37	ν2ω2	ν2ω2	PROPN
ejpam-4043	450	38	=	=	SYM
ejpam-4043	450	39	νω	νω	ADP
ejpam-4043	450	40	of	of	ADP
ejpam-4043	450	41	length	length	NOUN
ejpam-4043	450	42	20	20	NUM
ejpam-4043	450	43	.	.	PUNCT
ejpam-4043	451	1	let	let	VERB
ejpam-4043	451	2	g1(t	g1(t	X
ejpam-4043	451	3	)	)	PUNCT
ejpam-4043	451	4	=	=	SYM
ejpam-4043	451	5	g2(t	g2(t	NOUN
ejpam-4043	451	6	)	)	PUNCT
ejpam-4043	451	7	=	=	SYM
ejpam-4043	451	8	g3(t	g3(t	X
ejpam-4043	451	9	)	)	PUNCT
ejpam-4043	451	10	=	=	SYM
ejpam-4043	451	11	t2	t2	NOUN
ejpam-4043	451	12	+	+	CCONJ
ejpam-4043	451	13	t+	t+	NOUN
ejpam-4043	451	14	2	2	NUM
ejpam-4043	451	15	and	and	CCONJ
ejpam-4043	451	16	g4(t	g4(t	PROPN
ejpam-4043	451	17	)	)	PUNCT
ejpam-4043	451	18	=	=	NOUN
ejpam-4043	451	19	t+	t+	PUNCT
ejpam-4043	451	20	2	2	NUM
ejpam-4043	451	21	,	,	PUNCT
ejpam-4043	451	22	g(t	g(t	PROPN
ejpam-4043	451	23	)	)	PUNCT
ejpam-4043	452	1	=	=	PUNCT
ejpam-4043	452	2	ξ1(t	ξ1(t	PROPN
ejpam-4043	452	3	2	2	NUM
ejpam-4043	452	4	+	+	NOUN
ejpam-4043	452	5	t+2)+ξ2(t	t+2)+ξ2(t	NOUN
ejpam-4043	452	6	2	2	NUM
ejpam-4043	452	7	+	+	CCONJ
ejpam-4043	452	8	t+2)+ξ3(t	t+2)+ξ3(t	PROPN
ejpam-4043	452	9	2	2	NUM
ejpam-4043	452	10	+	+	CCONJ
ejpam-4043	452	11	t+2)+ξ4(t+2	t+2)+ξ4(t+2	NOUN
ejpam-4043	452	12	)	)	PUNCT
ejpam-4043	452	13	be	be	AUX
ejpam-4043	452	14	the	the	DET
ejpam-4043	452	15	generator	generator	NOUN
ejpam-4043	452	16	polynomials	polynomial	NOUN
ejpam-4043	452	17	of	of	ADP
ejpam-4043	452	18	k.	k.	NOUN
ejpam-4043	452	19	since	since	SCONJ
ejpam-4043	452	20	gi(t)g	gi(t)g	PROPN
ejpam-4043	452	21	∗	∗	NOUN
ejpam-4043	452	22	i	i	PRON
ejpam-4043	452	23	(	(	PUNCT
ejpam-4043	452	24	t)|t20	t)|t20	VERB
ejpam-4043	452	25	+	+	NOUN
ejpam-4043	452	26	1	1	NUM
ejpam-4043	452	27	for	for	ADP
ejpam-4043	452	28	i	i	PRON
ejpam-4043	452	29	=	=	NOUN
ejpam-4043	452	30	1	1	NUM
ejpam-4043	452	31	,	,	PUNCT
ejpam-4043	452	32	2	2	NUM
ejpam-4043	452	33	,	,	PUNCT
ejpam-4043	452	34	3	3	NUM
ejpam-4043	452	35	respectively	respectively	ADV
ejpam-4043	452	36	and	and	CCONJ
ejpam-4043	452	37	g4(t)g	g4(t)g	ADJ
ejpam-4043	452	38	∗	∗	NOUN
ejpam-4043	452	39	4(t)|t20	4(t)|t20	NUM
ejpam-4043	452	40	−	−	NOUN
ejpam-4043	452	41	1	1	NUM
ejpam-4043	452	42	,	,	PUNCT
ejpam-4043	452	43	then	then	ADV
ejpam-4043	452	44	by	by	ADP
ejpam-4043	452	45	the	the	DET
ejpam-4043	452	46	use	use	NOUN
ejpam-4043	452	47	of	of	ADP
ejpam-4043	452	48	theorem	theorem	NOUN
ejpam-4043	452	49	4.11	4.11	NUM
ejpam-4043	452	50	,	,	PUNCT
ejpam-4043	452	51	we	we	PRON
ejpam-4043	452	52	get	get	VERB
ejpam-4043	452	53	k⊥	k⊥	PROPN
ejpam-4043	452	54	⊆	⊆	NUM
ejpam-4043	452	55	k.	k.	NOUN
ejpam-4043	452	56	further	further	PROPN
ejpam-4043	452	57	ϕ(k	ϕ(k	NOUN
ejpam-4043	452	58	)	)	PUNCT
ejpam-4043	452	59	is	be	AUX
ejpam-4043	452	60	a	a	DET
ejpam-4043	452	61	linear	linear	ADJ
ejpam-4043	452	62	code	code	NOUN
ejpam-4043	452	63	over	over	ADP
ejpam-4043	452	64	z3	z3	PROPN
ejpam-4043	452	65	having	have	VERB
ejpam-4043	452	66	parameters	parameter	NOUN
ejpam-4043	452	67	[	[	X
ejpam-4043	452	68	80	80	NUM
ejpam-4043	452	69	,	,	PUNCT
ejpam-4043	452	70	73	73	NUM
ejpam-4043	452	71	,	,	PUNCT
ejpam-4043	452	72	3	3	NUM
ejpam-4043	452	73	]	]	PUNCT
ejpam-4043	452	74	.	.	PUNCT
ejpam-4043	453	1	then	then	ADV
ejpam-4043	453	2	,	,	PUNCT
ejpam-4043	453	3	by	by	ADP
ejpam-4043	453	4	the	the	DET
ejpam-4043	453	5	application	application	NOUN
ejpam-4043	453	6	of	of	ADP
ejpam-4043	453	7	theorem	theorem	NOUN
ejpam-4043	453	8	4.18	4.18	NUM
ejpam-4043	453	9	,	,	PUNCT
ejpam-4043	453	10	we	we	PRON
ejpam-4043	453	11	obtain	obtain	VERB
ejpam-4043	453	12	the	the	DET
ejpam-4043	453	13	quantum	quantum	NOUN
ejpam-4043	453	14	code	code	NOUN
ejpam-4043	453	15	having	have	VERB
ejpam-4043	453	16	parameters	parameter	NOUN
ejpam-4043	453	17	[	[	X
ejpam-4043	453	18	80	80	NUM
ejpam-4043	453	19	,	,	PUNCT
ejpam-4043	453	20	66	66	NUM
ejpam-4043	453	21	,	,	PUNCT
ejpam-4043	453	22	≥	≥	NOUN
ejpam-4043	453	23	3]3	3]3	NOUN
ejpam-4043	453	24	.	.	PUNCT
ejpam-4043	454	1	6	6	NUM
ejpam-4043	454	2	.	.	X
ejpam-4043	454	3	conclusion	conclusion	NOUN
ejpam-4043	454	4	in	in	ADP
ejpam-4043	454	5	this	this	DET
ejpam-4043	454	6	work	work	NOUN
ejpam-4043	454	7	,	,	PUNCT
ejpam-4043	454	8	we	we	PRON
ejpam-4043	454	9	have	have	AUX
ejpam-4043	454	10	given	give	VERB
ejpam-4043	454	11	a	a	DET
ejpam-4043	454	12	construction	construction	NOUN
ejpam-4043	454	13	of	of	ADP
ejpam-4043	454	14	quantum	quantum	NOUN
ejpam-4043	454	15	code	code	NOUN
ejpam-4043	454	16	through	through	ADP
ejpam-4043	454	17	ϑ-constacyclic	ϑ-constacyclic	PROPN
ejpam-4043	454	18	code	code	NOUN
ejpam-4043	454	19	over	over	ADP
ejpam-4043	454	20	the	the	DET
ejpam-4043	454	21	finite	finite	ADJ
ejpam-4043	454	22	non	non	ADJ
ejpam-4043	454	23	-	-	ADJ
ejpam-4043	454	24	chain	chain	ADJ
ejpam-4043	454	25	ring	ring	NOUN
ejpam-4043	454	26	<	<	X
ejpam-4043	454	27	=	=	X
ejpam-4043	454	28	z3	z3	PROPN
ejpam-4043	454	29	+	+	CCONJ
ejpam-4043	454	30	νz3	νz3	X
ejpam-4043	454	31	+	+	CCONJ
ejpam-4043	454	32	ωz3	ωz3	NOUN
ejpam-4043	454	33	+	+	CCONJ
ejpam-4043	454	34	νωz3	νωz3	NOUN
ejpam-4043	454	35	where	where	SCONJ
ejpam-4043	454	36	ν2	ν2	NOUN
ejpam-4043	454	37	=	=	SYM
ejpam-4043	454	38	1	1	NUM
ejpam-4043	454	39	,	,	PUNCT
ejpam-4043	454	40	ω2	ω2	NOUN
ejpam-4043	454	41	=	=	SYM
ejpam-4043	454	42	1	1	NUM
ejpam-4043	454	43	and	and	CCONJ
ejpam-4043	454	44	νω	νω	ADV
ejpam-4043	454	45	=	=	PUNCT
ejpam-4043	454	46	ων	ων	NUM
ejpam-4043	454	47	and	and	CCONJ
ejpam-4043	454	48	ν2ω2	ν2ω2	PROPN
ejpam-4043	454	49	=	=	SYM
ejpam-4043	454	50	νω	νω	PROPN
ejpam-4043	454	51	.	.	PUNCT
ejpam-4043	455	1	we	we	PRON
ejpam-4043	455	2	have	have	AUX
ejpam-4043	455	3	derived	derive	VERB
ejpam-4043	455	4	self	self	NOUN
ejpam-4043	455	5	-	-	PUNCT
ejpam-4043	455	6	orthogonal	orthogonal	ADJ
ejpam-4043	455	7	code	code	NOUN
ejpam-4043	455	8	over	over	ADP
ejpam-4043	455	9	the	the	DET
ejpam-4043	455	10	ring	ring	NOUN
ejpam-4043	455	11	z3	z3	PROPN
ejpam-4043	455	12	as	as	ADP
ejpam-4043	455	13	gray	gray	ADJ
ejpam-4043	455	14	images	image	NOUN
ejpam-4043	455	15	of	of	ADP
ejpam-4043	455	16	linear	linear	PROPN
ejpam-4043	455	17	code	code	NOUN
ejpam-4043	455	18	over	over	ADP
ejpam-4043	455	19	the	the	DET
ejpam-4043	455	20	ring	ring	NOUN
ejpam-4043	455	21	z3	z3	PROPN
ejpam-4043	455	22	+	+	CCONJ
ejpam-4043	455	23	νz3	νz3	X
ejpam-4043	456	1	+	+	ADJ
ejpam-4043	456	2	ωz3	ωz3	NOUN
ejpam-4043	456	3	+	+	X
ejpam-4043	456	4	νωz3	νωz3	NOUN
ejpam-4043	456	5	.	.	PUNCT
ejpam-4043	457	1	in	in	ADP
ejpam-4043	457	2	particular	particular	ADJ
ejpam-4043	457	3	,	,	PUNCT
ejpam-4043	457	4	the	the	DET
ejpam-4043	457	5	parameters	parameter	NOUN
ejpam-4043	457	6	of	of	ADP
ejpam-4043	457	7	quantum	quantum	NOUN
ejpam-4043	457	8	code	code	NOUN
ejpam-4043	457	9	over	over	ADP
ejpam-4043	457	10	the	the	DET
ejpam-4043	457	11	ring	ring	NOUN
ejpam-4043	457	12	z3	z3	PROPN
ejpam-4043	457	13	are	be	AUX
ejpam-4043	457	14	obtained	obtain	VERB
ejpam-4043	457	15	by	by	ADP
ejpam-4043	457	16	decomposing	decompose	VERB
ejpam-4043	457	17	ϑ-constacyclic	ϑ-constacyclic	ADJ
ejpam-4043	457	18	code	code	NOUN
ejpam-4043	457	19	into	into	ADP
ejpam-4043	457	20	references	reference	NOUN
ejpam-4043	457	21	1096	1096	NUM
ejpam-4043	457	22	cyclic	cyclic	ADJ
ejpam-4043	457	23	and	and	CCONJ
ejpam-4043	457	24	negacyclic	negacyclic	ADJ
ejpam-4043	457	25	codes	code	NOUN
ejpam-4043	457	26	over	over	ADP
ejpam-4043	457	27	the	the	DET
ejpam-4043	457	28	ring	ring	NOUN
ejpam-4043	457	29	z3	z3	PROPN
ejpam-4043	457	30	.	.	PUNCT
ejpam-4043	458	1	for	for	ADP
ejpam-4043	458	2	the	the	DET
ejpam-4043	458	3	future	future	ADJ
ejpam-4043	458	4	scope	scope	NOUN
ejpam-4043	458	5	,	,	PUNCT
ejpam-4043	458	6	one	one	PRON
ejpam-4043	458	7	can	can	AUX
ejpam-4043	458	8	look	look	VERB
ejpam-4043	458	9	at	at	ADP
ejpam-4043	458	10	other	other	ADJ
ejpam-4043	458	11	classes	class	NOUN
ejpam-4043	458	12	of	of	ADP
ejpam-4043	458	13	constacyclic	constacyclic	ADJ
ejpam-4043	458	14	codes	code	NOUN
ejpam-4043	458	15	over	over	ADP
ejpam-4043	458	16	z3	z3	PROPN
ejpam-4043	458	17	+	+	CCONJ
ejpam-4043	458	18	νz3	νz3	X
ejpam-4043	458	19	+	+	CCONJ
ejpam-4043	458	20	ωz3	ωz3	NOUN
ejpam-4043	458	21	+	+	CCONJ
ejpam-4043	458	22	νωz3	νωz3	PROPN
ejpam-4043	458	23	and	and	CCONJ
ejpam-4043	458	24	zp	zp	NOUN
ejpam-4043	458	25	+	+	CCONJ
ejpam-4043	458	26	νzp	νzp	NOUN
ejpam-4043	458	27	+	+	CCONJ
ejpam-4043	458	28	ωzp	ωzp	NOUN
ejpam-4043	458	29	+	+	X
ejpam-4043	458	30	νωzp	νωzp	NOUN
ejpam-4043	458	31	.	.	PUNCT
ejpam-4043	459	1	acknowledgements	acknowledgement	NOUN
ejpam-4043	459	2	the	the	DET
ejpam-4043	459	3	authors	author	NOUN
ejpam-4043	459	4	are	be	AUX
ejpam-4043	459	5	grateful	grateful	ADJ
ejpam-4043	459	6	to	to	ADP
ejpam-4043	459	7	the	the	DET
ejpam-4043	459	8	anonymous	anonymous	ADJ
ejpam-4043	459	9	referees	referee	NOUN
ejpam-4043	459	10	for	for	ADP
ejpam-4043	459	11	useful	useful	ADJ
ejpam-4043	459	12	comments	comment	NOUN
ejpam-4043	459	13	and	and	CCONJ
ejpam-4043	459	14	suggestions	suggestion	NOUN
ejpam-4043	459	15	.	.	PUNCT
ejpam-4043	460	1	references	reference	NOUN
ejpam-4043	460	2	[	[	X
ejpam-4043	460	3	1	1	NUM
ejpam-4043	460	4	]	]	PUNCT
ejpam-4043	460	5	m	m	VERB
ejpam-4043	460	6	ashraf	ashraf	NOUN
ejpam-4043	460	7	and	and	CCONJ
ejpam-4043	460	8	g	g	PROPN
ejpam-4043	460	9	mohammad	mohammad	PROPN
ejpam-4043	460	10	.	.	PUNCT
ejpam-4043	461	1	quantum	quantum	ADJ
ejpam-4043	461	2	codes	code	NOUN
ejpam-4043	461	3	from	from	ADP
ejpam-4043	461	4	cyclic	cyclic	ADJ
ejpam-4043	461	5	codes	code	NOUN
ejpam-4043	461	6	f3	f3	PROPN
ejpam-4043	461	7	+	+	CCONJ
ejpam-4043	461	8	vf3	vf3	PROPN
ejpam-4043	461	9	.	.	PUNCT
ejpam-4043	461	10	int	int	NOUN
ejpam-4043	461	11	.	.	PUNCT
ejpam-4043	462	1	j.	j.	PROPN
ejpam-4043	462	2	quantum	quantum	PROPN
ejpam-4043	462	3	inform	inform	NOUN
ejpam-4043	462	4	,	,	PUNCT
ejpam-4043	462	5	12	12	NUM
ejpam-4043	462	6	,	,	PUNCT
ejpam-4043	462	7	2014	2014	NUM
ejpam-4043	462	8	.	.	PUNCT
ejpam-4043	463	1	[	[	X
ejpam-4043	463	2	2	2	NUM
ejpam-4043	463	3	]	]	PUNCT
ejpam-4043	463	4	m	m	VERB
ejpam-4043	463	5	ashraf	ashraf	NOUN
ejpam-4043	463	6	and	and	CCONJ
ejpam-4043	463	7	g	g	PROPN
ejpam-4043	463	8	mohammad	mohammad	PROPN
ejpam-4043	463	9	.	.	PUNCT
ejpam-4043	464	1	quantum	quantum	ADJ
ejpam-4043	464	2	codes	code	NOUN
ejpam-4043	464	3	over	over	ADP
ejpam-4043	464	4	fp	fp	NOUN
ejpam-4043	464	5	from	from	ADP
ejpam-4043	464	6	cyclic	cyclic	ADJ
ejpam-4043	464	7	codes	code	NOUN
ejpam-4043	464	8	over	over	ADP
ejpam-4043	464	9	fp[u	fp[u	PROPN
ejpam-4043	464	10	,	,	PUNCT
ejpam-4043	464	11	v]/(u2	v]/(u2	NOUN
ejpam-4043	464	12	−	−	PROPN
ejpam-4043	465	1	1	1	NUM
ejpam-4043	465	2	,	,	PUNCT
ejpam-4043	465	3	v3	v3	PROPN
ejpam-4043	465	4	−	−	PROPN
ejpam-4043	465	5	v	v	NOUN
ejpam-4043	465	6	,	,	PUNCT
ejpam-4043	465	7	uv	uv	NOUN
ejpam-4043	465	8	−	−	PROPN
ejpam-4043	465	9	vu	vu	PROPN
ejpam-4043	465	10	)	)	PUNCT
ejpam-4043	465	11	.	.	PUNCT
ejpam-4043	466	1	cryptogr	cryptogr	NOUN
ejpam-4043	466	2	.	.	PUNCT
ejpam-4043	467	1	commun	commun	PROPN
ejpam-4043	467	2	.	.	PROPN
ejpam-4043	467	3	,	,	PUNCT
ejpam-4043	467	4	2018	2018	NUM
ejpam-4043	467	5	.	.	PUNCT
ejpam-4043	468	1	[	[	X
ejpam-4043	468	2	3	3	X
ejpam-4043	468	3	]	]	PUNCT
ejpam-4043	468	4	a	a	DET
ejpam-4043	468	5	calderbank	calderbank	NOUN
ejpam-4043	468	6	,	,	PUNCT
ejpam-4043	468	7	e	e	NOUN
ejpam-4043	468	8	rains	rain	NOUN
ejpam-4043	468	9	,	,	PUNCT
ejpam-4043	468	10	p	p	NOUN
ejpam-4043	468	11	shor	shor	NOUN
ejpam-4043	468	12	,	,	PUNCT
ejpam-4043	468	13	and	and	CCONJ
ejpam-4043	468	14	n	n	PRON
ejpam-4043	468	15	j	j	PROPN
ejpam-4043	468	16	a	a	DET
ejpam-4043	468	17	sloane	sloane	NOUN
ejpam-4043	468	18	.	.	PUNCT
ejpam-4043	469	1	quantum	quantum	ADJ
ejpam-4043	469	2	error	error	NOUN
ejpam-4043	469	3	correction	correction	NOUN
ejpam-4043	469	4	via	via	ADP
ejpam-4043	469	5	codes	code	NOUN
ejpam-4043	469	6	over	over	ADP
ejpam-4043	469	7	gf(4	gf(4	NOUN
ejpam-4043	469	8	)	)	PUNCT
ejpam-4043	469	9	.	.	PUNCT
ejpam-4043	470	1	ieee	ieee	PROPN
ejpam-4043	470	2	trans	trans	PROPN
ejpam-4043	470	3	.	.	PROPN
ejpam-4043	470	4	inf	inf	PROPN
ejpam-4043	470	5	.	.	PUNCT
ejpam-4043	470	6	theory	theory	NOUN
ejpam-4043	470	7	,	,	PUNCT
ejpam-4043	470	8	44(4):1369–1387	44(4):1369–1387	NOUN
ejpam-4043	470	9	,	,	PUNCT
ejpam-4043	470	10	1998	1998	NUM
ejpam-4043	470	11	.	.	PUNCT
ejpam-4043	471	1	[	[	X
ejpam-4043	471	2	4	4	X
ejpam-4043	471	3	]	]	X
ejpam-4043	471	4	a	a	DET
ejpam-4043	471	5	dertli	dertli	NOUN
ejpam-4043	471	6	,	,	PUNCT
ejpam-4043	471	7	y	y	PROPN
ejpam-4043	471	8	cengellenmis	cengellenmis	NOUN
ejpam-4043	471	9	,	,	PUNCT
ejpam-4043	471	10	and	and	CCONJ
ejpam-4043	471	11	s	s	VERB
ejpam-4043	471	12	eren	eren	PROPN
ejpam-4043	471	13	.	.	PUNCT
ejpam-4043	472	1	on	on	ADP
ejpam-4043	472	2	quantum	quantum	NOUN
ejpam-4043	472	3	codes	code	NOUN
ejpam-4043	472	4	obtained	obtain	VERB
ejpam-4043	472	5	from	from	ADP
ejpam-4043	472	6	cyclic	cyclic	ADJ
ejpam-4043	472	7	codes	code	NOUN
ejpam-4043	472	8	over	over	ADP
ejpam-4043	472	9	a2	a2	PROPN
ejpam-4043	472	10	.	.	PUNCT
ejpam-4043	472	11	int	int	NOUN
ejpam-4043	472	12	.	.	PUNCT
ejpam-4043	473	1	j.	j.	PROPN
ejpam-4043	473	2	quantum	quantum	PROPN
ejpam-4043	473	3	inform	inform	NOUN
ejpam-4043	473	4	.	.	PUNCT
ejpam-4043	473	5	,	,	PUNCT
ejpam-4043	473	6	13(2	13(2	PROPN
ejpam-4043	473	7	)	)	PUNCT
ejpam-4043	473	8	,	,	PUNCT
ejpam-4043	473	9	2015	2015	NUM
ejpam-4043	473	10	.	.	PUNCT
ejpam-4043	474	1	[	[	X
ejpam-4043	474	2	5	5	NUM
ejpam-4043	474	3	]	]	X
ejpam-4043	474	4	k	k	PROPN
ejpam-4043	474	5	guenda	guenda	PROPN
ejpam-4043	474	6	and	and	CCONJ
ejpam-4043	474	7	t	t	X
ejpam-4043	474	8	a	a	DET
ejpam-4043	474	9	gulliver	gulliver	NOUN
ejpam-4043	474	10	.	.	PUNCT
ejpam-4043	475	1	quantum	quantum	ADJ
ejpam-4043	475	2	codes	code	NOUN
ejpam-4043	475	3	over	over	ADP
ejpam-4043	475	4	rings	ring	NOUN
ejpam-4043	475	5	.	.	PUNCT
ejpam-4043	476	1	int	int	NOUN
ejpam-4043	476	2	.	.	PUNCT
ejpam-4043	477	1	j.	j.	PROPN
ejpam-4043	477	2	quantum	quantum	PROPN
ejpam-4043	477	3	inform	inform	NOUN
ejpam-4043	477	4	,	,	PUNCT
ejpam-4043	477	5	12	12	NUM
ejpam-4043	477	6	,	,	PUNCT
ejpam-4043	477	7	2014	2014	NUM
ejpam-4043	477	8	.	.	PUNCT
ejpam-4043	478	1	[	[	X
ejpam-4043	478	2	6	6	NUM
ejpam-4043	478	3	]	]	X
ejpam-4043	478	4	h	h	NOUN
ejpam-4043	478	5	islam	islam	PROPN
ejpam-4043	478	6	and	and	CCONJ
ejpam-4043	478	7	o	o	PROPN
ejpam-4043	478	8	prakash	prakash	PROPN
ejpam-4043	478	9	.	.	PUNCT
ejpam-4043	479	1	quantum	quantum	PROPN
ejpam-4043	479	2	codes	code	NOUN
ejpam-4043	479	3	from	from	ADP
ejpam-4043	479	4	the	the	DET
ejpam-4043	479	5	cyclic	cyclic	ADJ
ejpam-4043	479	6	codes	code	NOUN
ejpam-4043	479	7	over	over	ADP
ejpam-4043	479	8	fp[u	fp[u	PROPN
ejpam-4043	479	9	,	,	PUNCT
ejpam-4043	479	10	v	v	NOUN
ejpam-4043	479	11	,	,	PUNCT
ejpam-4043	479	12	w]/(u2	w]/(u2	PROPN
ejpam-4043	480	1	−	−	PROPN
ejpam-4043	480	2	1	1	NUM
ejpam-4043	480	3	,	,	PUNCT
ejpam-4043	480	4	v2	v2	PROPN
ejpam-4043	480	5	−	−	PROPN
ejpam-4043	480	6	1	1	NUM
ejpam-4043	480	7	,	,	PUNCT
ejpam-4043	480	8	w2	w2	NOUN
ejpam-4043	480	9	−	−	PROPN
ejpam-4043	480	10	1	1	NUM
ejpam-4043	480	11	,	,	PUNCT
ejpam-4043	480	12	uv	uv	NOUN
ejpam-4043	480	13	−	−	PROPN
ejpam-4043	480	14	vu	vu	PROPN
ejpam-4043	480	15	,	,	PUNCT
ejpam-4043	480	16	vw	vw	PROPN
ejpam-4043	480	17	−	−	PROPN
ejpam-4043	480	18	wv	wv	PROPN
ejpam-4043	480	19	,	,	PUNCT
ejpam-4043	480	20	wu	wu	PROPN
ejpam-4043	480	21	−	−	PROPN
ejpam-4043	480	22	uw	uw	PROPN
ejpam-4043	480	23	)	)	PUNCT
ejpam-4043	480	24	.	.	PUNCT
ejpam-4043	481	1	j.	j.	PROPN
ejpam-4043	481	2	appl	appl	PROPN
ejpam-4043	481	3	.	.	PROPN
ejpam-4043	481	4	math	math	PROPN
ejpam-4043	481	5	.	.	PUNCT
ejpam-4043	482	1	comput	comput	NOUN
ejpam-4043	482	2	.	.	PUNCT
ejpam-4043	482	3	,	,	PUNCT
ejpam-4043	482	4	60:625–635	60:625–635	PROPN
ejpam-4043	482	5	,	,	PUNCT
ejpam-4043	482	6	2019	2019	NUM
ejpam-4043	482	7	.	.	PUNCT
ejpam-4043	483	1	[	[	X
ejpam-4043	483	2	7	7	X
ejpam-4043	483	3	]	]	X
ejpam-4043	483	4	h	h	NOUN
ejpam-4043	483	5	islam	islam	PROPN
ejpam-4043	483	6	,	,	PUNCT
ejpam-4043	483	7	r	r	PROPN
ejpam-4043	483	8	k	k	PROPN
ejpam-4043	483	9	verma	verma	PROPN
ejpam-4043	483	10	,	,	PUNCT
ejpam-4043	483	11	and	and	CCONJ
ejpam-4043	483	12	o	o	PROPN
ejpam-4043	483	13	prakash	prakash	PROPN
ejpam-4043	483	14	.	.	PUNCT
ejpam-4043	484	1	a	a	DET
ejpam-4043	484	2	family	family	NOUN
ejpam-4043	484	3	of	of	ADP
ejpam-4043	484	4	constacyclic	constacyclic	ADJ
ejpam-4043	484	5	codes	code	NOUN
ejpam-4043	484	6	over	over	ADP
ejpam-4043	484	7	fpm	fpm	NOUN
ejpam-4043	485	1	[	[	X
ejpam-4043	485	2	υ	υ	X
ejpam-4043	485	3	,	,	PUNCT
ejpam-4043	485	4	ω]/	ω]/	PROPN
ejpam-4043	485	5	<	<	X
ejpam-4043	485	6	ν2	ν2	NOUN
ejpam-4043	485	7	−	−	PROPN
ejpam-4043	485	8	1	1	NUM
ejpam-4043	485	9	,	,	PUNCT
ejpam-4043	485	10	ω2	ω2	ADV
ejpam-4043	485	11	−	−	PROPN
ejpam-4043	485	12	1	1	NUM
ejpam-4043	485	13	,	,	PUNCT
ejpam-4043	485	14	νω	νω	ADV
ejpam-4043	485	15	−	−	PROPN
ejpam-4043	485	16	ων	ων	VERB
ejpam-4043	485	17	>	>	PUNCT
ejpam-4043	485	18	.	.	PUNCT
ejpam-4043	486	1	int	int	NOUN
ejpam-4043	486	2	.	.	PUNCT
ejpam-4043	487	1	j.	j.	PROPN
ejpam-4043	487	2	information	information	PROPN
ejpam-4043	487	3	and	and	CCONJ
ejpam-4043	487	4	coding	code	VERB
ejpam-4043	487	5	theory	theory	NOUN
ejpam-4043	487	6	,	,	PUNCT
ejpam-4043	487	7	5:198–210	5:198–210	NUM
ejpam-4043	487	8	,	,	PUNCT
ejpam-4043	487	9	2020	2020	NUM
ejpam-4043	487	10	.	.	PUNCT
ejpam-4043	488	1	[	[	X
ejpam-4043	488	2	8	8	NUM
ejpam-4043	488	3	]	]	X
ejpam-4043	488	4	x	x	X
ejpam-4043	488	5	kai	kai	PROPN
ejpam-4043	488	6	and	and	CCONJ
ejpam-4043	488	7	s	s	PROPN
ejpam-4043	488	8	zhu	zhu	PROPN
ejpam-4043	488	9	.	.	PUNCT
ejpam-4043	489	1	quaternary	quaternary	ADJ
ejpam-4043	489	2	construction	construction	NOUN
ejpam-4043	489	3	of	of	ADP
ejpam-4043	489	4	quantum	quantum	ADJ
ejpam-4043	489	5	codes	code	NOUN
ejpam-4043	489	6	from	from	ADP
ejpam-4043	489	7	cyclic	cyclic	ADJ
ejpam-4043	489	8	codes	code	NOUN
ejpam-4043	489	9	over	over	ADP
ejpam-4043	489	10	f4	f4	PROPN
ejpam-4043	489	11	+	+	NOUN
ejpam-4043	490	1	uf4	uf4	PROPN
ejpam-4043	490	2	.	.	PUNCT
ejpam-4043	490	3	int	int	NOUN
ejpam-4043	490	4	.	.	PUNCT
ejpam-4043	491	1	j.	j.	PROPN
ejpam-4043	491	2	quantum	quantum	PROPN
ejpam-4043	491	3	inform	inform	NOUN
ejpam-4043	491	4	,	,	PUNCT
ejpam-4043	491	5	9:689–700	9:689–700	NUM
ejpam-4043	491	6	,	,	PUNCT
ejpam-4043	491	7	2011	2011	NUM
ejpam-4043	491	8	.	.	PUNCT
ejpam-4043	492	1	[	[	X
ejpam-4043	492	2	9	9	NUM
ejpam-4043	492	3	]	]	X
ejpam-4043	492	4	j	j	PROPN
ejpam-4043	492	5	li	li	PROPN
ejpam-4043	492	6	,	,	PUNCT
ejpam-4043	492	7	j	j	PROPN
ejpam-4043	492	8	gao	gao	PROPN
ejpam-4043	492	9	,	,	PUNCT
ejpam-4043	492	10	and	and	CCONJ
ejpam-4043	492	11	y	y	PROPN
ejpam-4043	492	12	wang	wang	PROPN
ejpam-4043	492	13	.	.	PUNCT
ejpam-4043	492	14	quantum	quantum	PROPN
ejpam-4043	492	15	codes	code	NOUN
ejpam-4043	492	16	from	from	ADP
ejpam-4043	492	17	1	1	NUM
ejpam-4043	492	18	−	−	NOUN
ejpam-4043	492	19	2v	2v	NUM
ejpam-4043	492	20	-	-	PUNCT
ejpam-4043	492	21	constacyclic	constacyclic	PROPN
ejpam-4043	492	22	codes	code	NOUN
ejpam-4043	492	23	over	over	ADP
ejpam-4043	492	24	the	the	DET
ejpam-4043	492	25	ring	ring	NOUN
ejpam-4043	492	26	fq	fq	PROPN
ejpam-4043	492	27	+	+	CCONJ
ejpam-4043	492	28	ufq	ufq	PROPN
ejpam-4043	492	29	+	+	NUM
ejpam-4043	492	30	vfq	vfq	NOUN
ejpam-4043	492	31	+	+	X
ejpam-4043	492	32	uvfq	uvfq	NOUN
ejpam-4043	492	33	.	.	PUNCT
ejpam-4043	492	34	discrete	discrete	ADJ
ejpam-4043	492	35	math	math	NOUN
ejpam-4043	492	36	.	.	PUNCT
ejpam-4043	493	1	algorithms	algorithms	PROPN
ejpam-4043	493	2	appl	appl	PROPN
ejpam-4043	493	3	.	.	PROPN
ejpam-4043	493	4	,	,	PUNCT
ejpam-4043	493	5	10(4	10(4	NUM
ejpam-4043	493	6	)	)	PUNCT
ejpam-4043	493	7	,	,	PUNCT
ejpam-4043	493	8	2018	2018	NUM
ejpam-4043	493	9	.	.	PUNCT
ejpam-4043	494	1	[	[	X
ejpam-4043	494	2	10	10	NUM
ejpam-4043	494	3	]	]	X
ejpam-4043	494	4	f	f	PROPN
ejpam-4043	494	5	ma	ma	PROPN
ejpam-4043	494	6	,	,	PUNCT
ejpam-4043	494	7	j	j	PROPN
ejpam-4043	494	8	gao	gao	PROPN
ejpam-4043	494	9	,	,	PUNCT
ejpam-4043	494	10	and	and	CCONJ
ejpam-4043	494	11	f	f	PROPN
ejpam-4043	494	12	w	w	PROPN
ejpam-4043	494	13	fu	fu	PROPN
ejpam-4043	494	14	.	.	PUNCT
ejpam-4043	495	1	constacyclic	constacyclic	ADJ
ejpam-4043	495	2	codes	code	NOUN
ejpam-4043	495	3	over	over	ADP
ejpam-4043	495	4	the	the	DET
ejpam-4043	495	5	ring	ring	NOUN
ejpam-4043	495	6	fp	fp	PROPN
ejpam-4043	495	7	+	+	PROPN
ejpam-4043	495	8	vfp	vfp	PROPN
ejpam-4043	495	9	+	+	NOUN
ejpam-4043	495	10	v2fp	v2fp	X
ejpam-4043	495	11	and	and	CCONJ
ejpam-4043	495	12	their	their	PRON
ejpam-4043	495	13	applications	application	NOUN
ejpam-4043	495	14	of	of	ADP
ejpam-4043	495	15	constructing	construct	VERB
ejpam-4043	495	16	new	new	ADJ
ejpam-4043	495	17	non	non	ADJ
ejpam-4043	495	18	-	-	ADJ
ejpam-4043	495	19	binary	binary	ADJ
ejpam-4043	495	20	quantum	quantum	ADJ
ejpam-4043	495	21	codes	code	NOUN
ejpam-4043	495	22	.	.	PUNCT
ejpam-4043	496	1	quantum	quantum	PROPN
ejpam-4043	496	2	inf	inf	PROPN
ejpam-4043	496	3	.	.	PUNCT
ejpam-4043	496	4	process	process	NOUN
ejpam-4043	496	5	.	.	PUNCT
ejpam-4043	496	6	,	,	PUNCT
ejpam-4043	496	7	17	17	NUM
ejpam-4043	496	8	,	,	PUNCT
ejpam-4043	496	9	2018	2018	NUM
ejpam-4043	496	10	.	.	PUNCT
ejpam-4043	497	1	[	[	X
ejpam-4043	497	2	11	11	NUM
ejpam-4043	497	3	]	]	X
ejpam-4043	497	4	m	m	VERB
ejpam-4043	497	5	ozen	ozen	ADJ
ejpam-4043	497	6	and	and	CCONJ
ejpam-4043	497	7	m	m	PROPN
ejpam-4043	497	8	guzeltepe	guzeltepe	NOUN
ejpam-4043	497	9	.	.	PUNCT
ejpam-4043	498	1	quantum	quantum	NOUN
ejpam-4043	498	2	codes	code	NOUN
ejpam-4043	498	3	from	from	ADP
ejpam-4043	498	4	codes	code	NOUN
ejpam-4043	498	5	over	over	ADP
ejpam-4043	498	6	gaussian	gaussian	ADJ
ejpam-4043	498	7	integers	integer	NOUN
ejpam-4043	498	8	with	with	ADP
ejpam-4043	498	9	respect	respect	NOUN
ejpam-4043	498	10	to	to	ADP
ejpam-4043	498	11	the	the	DET
ejpam-4043	498	12	mannheim	mannheim	PROPN
ejpam-4043	498	13	metric	metric	ADJ
ejpam-4043	498	14	.	.	PUNCT
ejpam-4043	499	1	quantum	quantum	ADJ
ejpam-4043	499	2	information	information	NOUN
ejpam-4043	499	3	and	and	CCONJ
ejpam-4043	499	4	computation	computation	NOUN
ejpam-4043	499	5	,	,	PUNCT
ejpam-4043	499	6	12:813	12:813	NUM
ejpam-4043	499	7	–	–	PUNCT
ejpam-4043	499	8	819	819	NUM
ejpam-4043	499	9	,	,	PUNCT
ejpam-4043	499	10	2012	2012	NUM
ejpam-4043	499	11	.	.	PUNCT
ejpam-4043	500	1	references	reference	NOUN
ejpam-4043	500	2	1097	1097	NUM
ejpam-4043	501	1	[	[	X
ejpam-4043	501	2	12	12	NUM
ejpam-4043	501	3	]	]	X
ejpam-4043	501	4	m	m	VERB
ejpam-4043	501	5	ozen	ozen	ADJ
ejpam-4043	501	6	,	,	PUNCT
ejpam-4043	501	7	n	n	NOUN
ejpam-4043	501	8	t	t	NOUN
ejpam-4043	501	9	ozzaim	ozzaim	NOUN
ejpam-4043	501	10	,	,	PUNCT
ejpam-4043	501	11	and	and	CCONJ
ejpam-4043	501	12	h	h	NOUN
ejpam-4043	501	13	ince	ince	NOUN
ejpam-4043	501	14	.	.	PUNCT
ejpam-4043	502	1	quantum	quantum	NOUN
ejpam-4043	502	2	codes	code	NOUN
ejpam-4043	502	3	from	from	ADP
ejpam-4043	502	4	cyclic	cyclic	ADJ
ejpam-4043	502	5	codes	code	NOUN
ejpam-4043	502	6	over	over	ADP
ejpam-4043	502	7	f3	f3	PROPN
ejpam-4043	502	8	+	+	NOUN
ejpam-4043	502	9	uf3	uf3	ADJ
ejpam-4043	502	10	+	+	CCONJ
ejpam-4043	502	11	vf3	vf3	X
ejpam-4043	502	12	+	+	CCONJ
ejpam-4043	502	13	uvf3	uvf3	PROPN
ejpam-4043	502	14	.	.	PUNCT
ejpam-4043	503	1	int	int	NOUN
ejpam-4043	503	2	.	.	PUNCT
ejpam-4043	503	3	conf	conf	NOUN
ejpam-4043	503	4	.	.	PUNCT
ejpam-4043	504	1	quantum	quantum	PROPN
ejpam-4043	504	2	sci	sci	PROPN
ejpam-4043	504	3	.	.	PUNCT
ejpam-4043	504	4	appl	appl	PROPN
ejpam-4043	504	5	.	.	PUNCT
ejpam-4043	505	1	j.	j.	PROPN
ejpam-4043	505	2	phys	phys	PROPN
ejpam-4043	505	3	.	.	PUNCT
ejpam-4043	505	4	conf	conf	PROPN
ejpam-4043	505	5	.	.	PUNCT
ejpam-4043	506	1	ser	ser	PROPN
ejpam-4043	506	2	.	.	PROPN
ejpam-4043	506	3	,	,	PUNCT
ejpam-4043	506	4	766	766	NUM
ejpam-4043	506	5	,	,	PUNCT
ejpam-4043	506	6	2016	2016	NUM
ejpam-4043	506	7	.	.	PUNCT
ejpam-4043	507	1	[	[	X
ejpam-4043	507	2	13	13	NUM
ejpam-4043	507	3	]	]	X
ejpam-4043	507	4	j	j	PROPN
ejpam-4043	507	5	qian	qian	PROPN
ejpam-4043	507	6	.	.	PUNCT
ejpam-4043	508	1	quantum	quantum	PROPN
ejpam-4043	508	2	codes	code	NOUN
ejpam-4043	508	3	from	from	ADP
ejpam-4043	508	4	cyclic	cyclic	ADJ
ejpam-4043	508	5	codes	code	NOUN
ejpam-4043	508	6	over	over	ADP
ejpam-4043	508	7	f2	f2	PROPN
ejpam-4043	508	8	+	+	CCONJ
ejpam-4043	508	9	vf2	vf2	ADJ
ejpam-4043	508	10	.	.	PUNCT
ejpam-4043	509	1	journal	journal	NOUN
ejpam-4043	509	2	of	of	ADP
ejpam-4043	509	3	inform	inform	NOUN
ejpam-4043	509	4	.	.	PUNCT
ejpam-4043	510	1	and	and	CCONJ
ejpam-4043	510	2	computational	computational	ADJ
ejpam-4043	510	3	science	science	NOUN
ejpam-4043	510	4	,	,	PUNCT
ejpam-4043	510	5	10:1715–1722	10:1715–1722	NUM
ejpam-4043	510	6	,	,	PUNCT
ejpam-4043	510	7	2013	2013	NUM
ejpam-4043	510	8	.	.	PUNCT
ejpam-4043	511	1	[	[	X
ejpam-4043	511	2	14	14	NUM
ejpam-4043	511	3	]	]	X
ejpam-4043	511	4	p	p	X
ejpam-4043	511	5	w	w	PROPN
ejpam-4043	511	6	shor	shor	PROPN
ejpam-4043	511	7	.	.	PUNCT
ejpam-4043	512	1	scheme	scheme	NOUN
ejpam-4043	512	2	for	for	ADP
ejpam-4043	512	3	reducing	reduce	VERB
ejpam-4043	512	4	decoherence	decoherence	NOUN
ejpam-4043	512	5	in	in	ADP
ejpam-4043	512	6	quantum	quantum	NOUN
ejpam-4043	512	7	memory	memory	NOUN
ejpam-4043	512	8	.	.	PUNCT
ejpam-4043	513	1	phys	phy	NOUN
ejpam-4043	513	2	.	.	PUNCT
ejpam-4043	514	1	rev	rev	PROPN
ejpam-4043	514	2	.	.	PROPN
ejpam-4043	514	3	,	,	PUNCT
ejpam-4043	514	4	52:2493–2496	52:2493–2496	NUM
ejpam-4043	514	5	,	,	PUNCT
ejpam-4043	514	6	1995	1995	NUM
ejpam-4043	514	7	.	.	PUNCT
ejpam-4043	515	1	[	[	X
ejpam-4043	515	2	15	15	NUM
ejpam-4043	515	3	]	]	X
ejpam-4043	515	4	a	a	DET
ejpam-4043	515	5	k	k	PROPN
ejpam-4043	515	6	singh	singh	PROPN
ejpam-4043	515	7	,	,	PUNCT
ejpam-4043	515	8	s	s	VERB
ejpam-4043	515	9	pattanayek	pattanayek	NOUN
ejpam-4043	515	10	,	,	PUNCT
ejpam-4043	515	11	and	and	CCONJ
ejpam-4043	515	12	p	p	PROPN
ejpam-4043	515	13	kumar	kumar	PROPN
ejpam-4043	515	14	.	.	PROPN
ejpam-4043	516	1	on	on	ADP
ejpam-4043	516	2	quantum	quantum	NOUN
ejpam-4043	516	3	codes	code	NOUN
ejpam-4043	516	4	from	from	ADP
ejpam-4043	516	5	cyclic	cyclic	ADJ
ejpam-4043	516	6	codes	code	NOUN
ejpam-4043	516	7	over	over	ADP
ejpam-4043	516	8	f2	f2	PROPN
ejpam-4043	516	9	+	+	CCONJ
ejpam-4043	516	10	uf2	uf2	NOUN
ejpam-4043	516	11	+	+	CCONJ
ejpam-4043	516	12	u2f2	u2f2	PROPN
ejpam-4043	516	13	.	.	PUNCT
ejpam-4043	517	1	asian	asian	ADJ
ejpam-4043	517	2	-	-	PUNCT
ejpam-4043	517	3	eur	eur	NOUN
ejpam-4043	517	4	.	.	PUNCT
ejpam-4043	518	1	j.	j.	PROPN
ejpam-4043	518	2	math	math	PROPN
ejpam-4043	518	3	.	.	PROPN
ejpam-4043	518	4	,	,	PUNCT
ejpam-4043	518	5	11(1	11(1	NUM
ejpam-4043	518	6	)	)	PUNCT
ejpam-4043	518	7	,	,	PUNCT
ejpam-4043	518	8	2018	2018	NUM
ejpam-4043	518	9	.	.	PUNCT
ejpam-4043	519	1	[	[	X
ejpam-4043	519	2	16	16	NUM
ejpam-4043	519	3	]	]	X
ejpam-4043	519	4	j	j	PROPN
ejpam-4043	519	5	singh	singh	PROPN
ejpam-4043	519	6	and	and	CCONJ
ejpam-4043	519	7	p	p	NOUN
ejpam-4043	519	8	mor	mor	PROPN
ejpam-4043	519	9	.	.	PUNCT
ejpam-4043	520	1	quantum	quantum	PROPN
ejpam-4043	520	2	codes	code	NOUN
ejpam-4043	520	3	obtained	obtain	VERB
ejpam-4043	520	4	through	through	ADP
ejpam-4043	520	5	(	(	PUNCT
ejpam-4043	520	6	1+(p−2)ν)-constacyclic	1+(p−2)ν)-constacyclic	NUM
ejpam-4043	520	7	codes	code	NOUN
ejpam-4043	520	8	over	over	ADP
ejpam-4043	520	9	zp	zp	PROPN
ejpam-4043	520	10	+	+	NOUN
ejpam-4043	520	11	νzp	νzp	PROPN
ejpam-4043	520	12	.	.	PUNCT
ejpam-4043	520	13	journal	journal	PROPN
ejpam-4043	520	14	of	of	ADP
ejpam-4043	520	15	mathematical	mathematical	ADJ
ejpam-4043	520	16	and	and	CCONJ
ejpam-4043	520	17	computational	computational	ADJ
ejpam-4043	520	18	science	science	NOUN
ejpam-4043	520	19	,	,	PUNCT
ejpam-4043	520	20	11(3):2583–2592	11(3):2583–2592	NUM
ejpam-4043	520	21	,	,	PUNCT
ejpam-4043	520	22	2021	2021	NUM
ejpam-4043	520	23	.	.	PUNCT
ejpam-4043	521	1	[	[	X
ejpam-4043	521	2	17	17	NUM
ejpam-4043	521	3	]	]	X
ejpam-4043	521	4	a	a	DET
ejpam-4043	521	5	m	m	NOUN
ejpam-4043	521	6	steane	steane	ADJ
ejpam-4043	521	7	.	.	PUNCT
ejpam-4043	522	1	simple	simple	ADJ
ejpam-4043	522	2	quantum	quantum	NOUN
ejpam-4043	522	3	error	error	NOUN
ejpam-4043	522	4	correcting	correct	VERB
ejpam-4043	522	5	codes	code	NOUN
ejpam-4043	522	6	.	.	PUNCT
ejpam-4043	523	1	phys	phy	NOUN
ejpam-4043	523	2	.	.	PUNCT
ejpam-4043	524	1	rev	rev	PROPN
ejpam-4043	524	2	.	.	PROPN
ejpam-4043	524	3	lett	lett	PROPN
ejpam-4043	524	4	.	.	PROPN
ejpam-4043	524	5	,	,	PUNCT
ejpam-4043	524	6	77:793	77:793	NUM
ejpam-4043	524	7	–	–	PUNCT
ejpam-4043	524	8	797	797	NUM
ejpam-4043	524	9	,	,	PUNCT
ejpam-4043	524	10	1996	1996	NUM
ejpam-4043	524	11	.	.	PUNCT
ejpam-4043	525	1	[	[	X
ejpam-4043	525	2	18	18	NUM
ejpam-4043	525	3	]	]	PUNCT
ejpam-4043	525	4	x	x	SYM
ejpam-4043	525	5	yin	yin	PROPN
ejpam-4043	525	6	and	and	CCONJ
ejpam-4043	525	7	w	w	PROPN
ejpam-4043	525	8	ma	ma	PROPN
ejpam-4043	525	9	.	.	PROPN
ejpam-4043	525	10	gray	gray	ADJ
ejpam-4043	525	11	map	map	NOUN
ejpam-4043	525	12	and	and	CCONJ
ejpam-4043	525	13	quantum	quantum	NOUN
ejpam-4043	525	14	codes	code	NOUN
ejpam-4043	525	15	over	over	ADP
ejpam-4043	525	16	the	the	DET
ejpam-4043	525	17	ring	ring	NOUN
ejpam-4043	525	18	f2	f2	PROPN
ejpam-4043	525	19	+	+	CCONJ
ejpam-4043	525	20	uf2	uf2	NOUN
ejpam-4043	525	21	+	+	CCONJ
ejpam-4043	525	22	u2f2	u2f2	PROPN
ejpam-4043	525	23	.	.	PUNCT
ejpam-4043	525	24	international	international	ADJ
ejpam-4043	525	25	joint	joint	ADJ
ejpam-4043	525	26	conferences	conference	NOUN
ejpam-4043	525	27	of	of	ADP
ejpam-4043	525	28	ieee	ieee	PROPN
ejpam-4043	525	29	trustcom	trustcom	PROPN
ejpam-4043	525	30	,	,	PUNCT
ejpam-4043	525	31	11	11	NUM
ejpam-4043	525	32	,	,	PUNCT
ejpam-4043	525	33	2011	2011	NUM
ejpam-4043	525	34	.	.	PUNCT