id	sid	tid	token	lemma	pos
ejpam-5600	1	1	european	european	PROPN
ejpam-5600	1	2	journal	journal	PROPN
ejpam-5600	1	3	of	of	ADP
ejpam-5600	1	4	pure	pure	ADJ
ejpam-5600	1	5	and	and	CCONJ
ejpam-5600	1	6	applied	apply	VERB
ejpam-5600	1	7	mathematics	mathematic	NOUN
ejpam-5600	1	8	vol	vol	NOUN
ejpam-5600	1	9	.	.	PROPN
ejpam-5600	2	1	17	17	NUM
ejpam-5600	2	2	,	,	PUNCT
ejpam-5600	2	3	no	no	INTJ
ejpam-5600	2	4	.	.	NOUN
ejpam-5600	2	5	4	4	NUM
ejpam-5600	2	6	,	,	PUNCT
ejpam-5600	2	7	2024	2024	NUM
ejpam-5600	2	8	,	,	PUNCT
ejpam-5600	2	9	4225	4225	NUM
ejpam-5600	2	10	-	-	SYM
ejpam-5600	2	11	4237	4237	NUM
ejpam-5600	2	12	issn	issn	PROPN
ejpam-5600	2	13	1307	1307	NUM
ejpam-5600	2	14	-	-	SYM
ejpam-5600	2	15	5543	5543	NUM
ejpam-5600	2	16	–	–	PUNCT
ejpam-5600	2	17	ejpam.com	ejpam.com	X
ejpam-5600	2	18	published	publish	VERB
ejpam-5600	2	19	by	by	ADP
ejpam-5600	2	20	new	new	PROPN
ejpam-5600	2	21	york	york	PROPN
ejpam-5600	2	22	business	business	PROPN
ejpam-5600	2	23	global	global	ADJ
ejpam-5600	2	24	weights	weight	NOUN
ejpam-5600	2	25	of	of	ADP
ejpam-5600	2	26	codewords	codeword	NOUN
ejpam-5600	2	27	in	in	ADP
ejpam-5600	2	28	random	random	ADJ
ejpam-5600	2	29	binary	binary	ADJ
ejpam-5600	2	30	linear	linear	NOUN
ejpam-5600	2	31	codes	code	NOUN
ejpam-5600	2	32	and	and	CCONJ
ejpam-5600	2	33	their	their	PRON
ejpam-5600	2	34	correlation	correlation	NOUN
ejpam-5600	2	35	properties	property	NOUN
ejpam-5600	2	36	i̇brahim	i̇brahim	PUNCT
ejpam-5600	2	37	özen	özen	PROPN
ejpam-5600	2	38	department	department	NOUN
ejpam-5600	2	39	of	of	ADP
ejpam-5600	2	40	matheamatics	matheamatic	NOUN
ejpam-5600	2	41	,	,	PUNCT
ejpam-5600	2	42	faculty	faculty	NOUN
ejpam-5600	2	43	of	of	ADP
ejpam-5600	2	44	science	science	NOUN
ejpam-5600	2	45	,	,	PUNCT
ejpam-5600	2	46	marmara	marmara	PROPN
ejpam-5600	2	47	university	university	PROPN
ejpam-5600	2	48	,	,	PUNCT
ejpam-5600	2	49	istanbul	istanbul	PROPN
ejpam-5600	2	50	,	,	PUNCT
ejpam-5600	2	51	turkey	turkey	PROPN
ejpam-5600	2	52	.	.	PUNCT
ejpam-5600	3	1	abstract	abstract	ADJ
ejpam-5600	3	2	.	.	PUNCT
ejpam-5600	4	1	a	a	DET
ejpam-5600	4	2	classical	classical	ADJ
ejpam-5600	4	3	problem	problem	NOUN
ejpam-5600	4	4	in	in	ADP
ejpam-5600	4	5	coding	code	VERB
ejpam-5600	4	6	theory	theory	NOUN
ejpam-5600	4	7	addresses	address	VERB
ejpam-5600	4	8	moments	moment	NOUN
ejpam-5600	4	9	of	of	ADP
ejpam-5600	4	10	the	the	DET
ejpam-5600	4	11	weight	weight	NOUN
ejpam-5600	4	12	spectrum	spectrum	NOUN
ejpam-5600	4	13	distribution	distribution	NOUN
ejpam-5600	4	14	.	.	PUNCT
ejpam-5600	5	1	the	the	DET
ejpam-5600	5	2	results	result	NOUN
ejpam-5600	5	3	in	in	ADP
ejpam-5600	5	4	this	this	DET
ejpam-5600	5	5	work	work	NOUN
ejpam-5600	5	6	are	be	AUX
ejpam-5600	5	7	on	on	ADP
ejpam-5600	5	8	the	the	DET
ejpam-5600	5	9	weight	weight	NOUN
ejpam-5600	5	10	moments	moment	NOUN
ejpam-5600	5	11	of	of	ADP
ejpam-5600	5	12	individual	individual	ADJ
ejpam-5600	5	13	codewords	codeword	NOUN
ejpam-5600	5	14	rather	rather	ADV
ejpam-5600	5	15	than	than	ADP
ejpam-5600	5	16	the	the	DET
ejpam-5600	5	17	weight	weight	NOUN
ejpam-5600	5	18	spectrum	spectrum	NOUN
ejpam-5600	5	19	.	.	PUNCT
ejpam-5600	6	1	the	the	DET
ejpam-5600	6	2	expectations	expectation	NOUN
ejpam-5600	6	3	of	of	ADP
ejpam-5600	6	4	single	single	ADJ
ejpam-5600	6	5	and	and	CCONJ
ejpam-5600	6	6	pairwise	pairwise	NOUN
ejpam-5600	6	7	products	product	NOUN
ejpam-5600	6	8	of	of	ADP
ejpam-5600	6	9	weights	weight	NOUN
ejpam-5600	6	10	of	of	ADP
ejpam-5600	6	11	nonzero	nonzero	ADJ
ejpam-5600	6	12	words	word	NOUN
ejpam-5600	6	13	in	in	ADP
ejpam-5600	6	14	a	a	DET
ejpam-5600	6	15	random	random	ADJ
ejpam-5600	6	16	binary	binary	ADJ
ejpam-5600	6	17	linear	linear	PROPN
ejpam-5600	6	18	code	code	NOUN
ejpam-5600	6	19	are	be	AUX
ejpam-5600	6	20	given	give	VERB
ejpam-5600	6	21	.	.	PUNCT
ejpam-5600	7	1	we	we	PRON
ejpam-5600	7	2	show	show	VERB
ejpam-5600	7	3	that	that	SCONJ
ejpam-5600	7	4	the	the	DET
ejpam-5600	7	5	covariance	covariance	NOUN
ejpam-5600	7	6	between	between	ADP
ejpam-5600	7	7	the	the	DET
ejpam-5600	7	8	weights	weight	NOUN
ejpam-5600	7	9	of	of	ADP
ejpam-5600	7	10	any	any	DET
ejpam-5600	7	11	pair	pair	NOUN
ejpam-5600	7	12	of	of	ADP
ejpam-5600	7	13	distinct	distinct	ADJ
ejpam-5600	7	14	nonzero	nonzero	NOUN
ejpam-5600	7	15	words	word	NOUN
ejpam-5600	7	16	is	be	AUX
ejpam-5600	7	17	zero	zero	NUM
ejpam-5600	7	18	.	.	PUNCT
ejpam-5600	8	1	our	our	PRON
ejpam-5600	8	2	main	main	ADJ
ejpam-5600	8	3	theorem	theorem	NOUN
ejpam-5600	8	4	has	have	VERB
ejpam-5600	8	5	an	an	DET
ejpam-5600	8	6	application	application	NOUN
ejpam-5600	8	7	to	to	ADP
ejpam-5600	8	8	sequence	sequence	NOUN
ejpam-5600	8	9	correlations	correlation	NOUN
ejpam-5600	8	10	problem	problem	NOUN
ejpam-5600	8	11	.	.	PUNCT
ejpam-5600	9	1	we	we	PRON
ejpam-5600	9	2	prove	prove	VERB
ejpam-5600	9	3	that	that	SCONJ
ejpam-5600	9	4	the	the	DET
ejpam-5600	9	5	sums	sum	NOUN
ejpam-5600	9	6	of	of	ADP
ejpam-5600	9	7	out	out	ADP
ejpam-5600	9	8	of	of	ADP
ejpam-5600	9	9	phase	phase	NOUN
ejpam-5600	9	10	self	self	NOUN
ejpam-5600	9	11	correlations	correlation	NOUN
ejpam-5600	9	12	,	,	PUNCT
ejpam-5600	9	13	as	as	ADV
ejpam-5600	9	14	well	well	ADV
ejpam-5600	9	15	as	as	ADP
ejpam-5600	9	16	sums	sum	NOUN
ejpam-5600	9	17	of	of	ADP
ejpam-5600	9	18	cross	cross	NOUN
ejpam-5600	9	19	-	-	NOUN
ejpam-5600	9	20	correlations	correlation	NOUN
ejpam-5600	9	21	,	,	PUNCT
ejpam-5600	9	22	of	of	ADP
ejpam-5600	9	23	nonzero	nonzero	PROPN
ejpam-5600	9	24	words	word	NOUN
ejpam-5600	9	25	in	in	ADP
ejpam-5600	9	26	a	a	DET
ejpam-5600	9	27	random	random	ADJ
ejpam-5600	9	28	binary	binary	ADJ
ejpam-5600	9	29	linear	linear	PROPN
ejpam-5600	9	30	code	code	NOUN
ejpam-5600	9	31	are	be	AUX
ejpam-5600	9	32	equal	equal	ADJ
ejpam-5600	9	33	to	to	ADP
ejpam-5600	9	34	zero	zero	NUM
ejpam-5600	9	35	.	.	PUNCT
ejpam-5600	10	1	2020	2020	NUM
ejpam-5600	10	2	mathematics	mathematic	NOUN
ejpam-5600	10	3	subject	subject	NOUN
ejpam-5600	10	4	classifications	classification	NOUN
ejpam-5600	10	5	:	:	PUNCT
ejpam-5600	10	6	94b05	94b05	NUM
ejpam-5600	10	7	,	,	PUNCT
ejpam-5600	10	8	94a55	94a55	NUM
ejpam-5600	10	9	,	,	PUNCT
ejpam-5600	10	10	94b65	94b65	NUM
ejpam-5600	10	11	key	key	ADJ
ejpam-5600	10	12	words	word	NOUN
ejpam-5600	10	13	and	and	CCONJ
ejpam-5600	10	14	phrases	phrase	NOUN
ejpam-5600	10	15	:	:	PUNCT
ejpam-5600	10	16	random	random	ADJ
ejpam-5600	10	17	binary	binary	ADJ
ejpam-5600	10	18	linear	linear	PROPN
ejpam-5600	10	19	codes	code	NOUN
ejpam-5600	10	20	,	,	PUNCT
ejpam-5600	10	21	weight	weight	NOUN
ejpam-5600	10	22	moments	moment	NOUN
ejpam-5600	10	23	of	of	ADP
ejpam-5600	10	24	codewords	codeword	NOUN
ejpam-5600	10	25	,	,	PUNCT
ejpam-5600	10	26	binary	binary	ADJ
ejpam-5600	10	27	sequences	sequence	NOUN
ejpam-5600	10	28	,	,	PUNCT
ejpam-5600	10	29	auto	auto	NOUN
ejpam-5600	10	30	-	-	PUNCT
ejpam-5600	10	31	correlations	correlation	NOUN
ejpam-5600	10	32	,	,	PUNCT
ejpam-5600	10	33	cross	cros	NOUN
ejpam-5600	10	34	-	-	NOUN
ejpam-5600	10	35	correlations	correlation	NOUN
ejpam-5600	10	36	1	1	NUM
ejpam-5600	10	37	.	.	PUNCT
ejpam-5600	10	38	introduction	introduction	NOUN
ejpam-5600	10	39	a	a	DET
ejpam-5600	10	40	binary	binary	ADJ
ejpam-5600	10	41	linear	linear	PROPN
ejpam-5600	10	42	code	code	PROPN
ejpam-5600	10	43	c	c	PROPN
ejpam-5600	10	44	is	be	AUX
ejpam-5600	10	45	a	a	DET
ejpam-5600	10	46	subspace	subspace	NOUN
ejpam-5600	10	47	of	of	ADP
ejpam-5600	10	48	fn	fn	PROPN
ejpam-5600	10	49	2	2	NUM
ejpam-5600	10	50	.	.	PUNCT
ejpam-5600	11	1	we	we	PRON
ejpam-5600	11	2	call	call	VERB
ejpam-5600	11	3	n	n	ADV
ejpam-5600	11	4	the	the	DET
ejpam-5600	11	5	length	length	NOUN
ejpam-5600	11	6	of	of	ADP
ejpam-5600	11	7	the	the	DET
ejpam-5600	11	8	code	code	NOUN
ejpam-5600	11	9	.	.	PUNCT
ejpam-5600	12	1	dimension	dimension	NOUN
ejpam-5600	12	2	of	of	ADP
ejpam-5600	12	3	the	the	DET
ejpam-5600	12	4	code	code	NOUN
ejpam-5600	12	5	is	be	AUX
ejpam-5600	12	6	its	its	PRON
ejpam-5600	12	7	dimension	dimension	NOUN
ejpam-5600	12	8	as	as	ADP
ejpam-5600	12	9	a	a	DET
ejpam-5600	12	10	linear	linear	ADJ
ejpam-5600	12	11	space	space	NOUN
ejpam-5600	12	12	.	.	PUNCT
ejpam-5600	13	1	a	a	DET
ejpam-5600	13	2	vector	vector	NOUN
ejpam-5600	13	3	in	in	ADP
ejpam-5600	13	4	the	the	DET
ejpam-5600	13	5	code	code	NOUN
ejpam-5600	13	6	is	be	AUX
ejpam-5600	13	7	called	call	VERB
ejpam-5600	13	8	a	a	DET
ejpam-5600	13	9	codeword	codeword	NOUN
ejpam-5600	13	10	.	.	PUNCT
ejpam-5600	14	1	let	let	VERB
ejpam-5600	14	2	c	c	NOUN
ejpam-5600	14	3	=	=	SYM
ejpam-5600	14	4	(	(	PUNCT
ejpam-5600	14	5	c1	c1	PROPN
ejpam-5600	14	6	,	,	PUNCT
ejpam-5600	14	7	c2	c2	PROPN
ejpam-5600	14	8	,	,	PUNCT
ejpam-5600	14	9	.	.	PUNCT
ejpam-5600	14	10	.	.	PUNCT
ejpam-5600	15	1	.	.	PUNCT
ejpam-5600	16	1	,	,	PUNCT
ejpam-5600	16	2	cn	cn	PROPN
ejpam-5600	16	3	)	)	PUNCT
ejpam-5600	16	4	and	and	CCONJ
ejpam-5600	16	5	e	e	X
ejpam-5600	16	6	=	=	SYM
ejpam-5600	16	7	(	(	PUNCT
ejpam-5600	16	8	e1	e1	PROPN
ejpam-5600	16	9	,	,	PUNCT
ejpam-5600	16	10	e2	e2	PROPN
ejpam-5600	16	11	,	,	PUNCT
ejpam-5600	16	12	.	.	PUNCT
ejpam-5600	16	13	.	.	PUNCT
ejpam-5600	17	1	.	.	PUNCT
ejpam-5600	18	1	,	,	PUNCT
ejpam-5600	18	2	en	en	AUX
ejpam-5600	18	3	)	)	PUNCT
ejpam-5600	18	4	be	be	VERB
ejpam-5600	18	5	two	two	NUM
ejpam-5600	18	6	binary	binary	ADJ
ejpam-5600	18	7	vectors	vector	NOUN
ejpam-5600	18	8	.	.	PUNCT
ejpam-5600	19	1	the	the	DET
ejpam-5600	19	2	hamming	hamming	NOUN
ejpam-5600	19	3	distance	distance	NOUN
ejpam-5600	19	4	between	between	ADP
ejpam-5600	19	5	them	they	PRON
ejpam-5600	19	6	is	be	AUX
ejpam-5600	19	7	the	the	DET
ejpam-5600	19	8	number	number	NOUN
ejpam-5600	19	9	of	of	ADP
ejpam-5600	19	10	coordinates	coordinate	NOUN
ejpam-5600	19	11	that	that	PRON
ejpam-5600	19	12	they	they	PRON
ejpam-5600	19	13	differ	differ	VERB
ejpam-5600	19	14	and	and	CCONJ
ejpam-5600	19	15	is	be	AUX
ejpam-5600	19	16	defined	define	VERB
ejpam-5600	19	17	by	by	ADP
ejpam-5600	19	18	dh(c	dh(c	PROPN
ejpam-5600	19	19	,	,	PUNCT
ejpam-5600	19	20	e	e	NOUN
ejpam-5600	19	21	)	)	PUNCT
ejpam-5600	19	22	=	=	NOUN
ejpam-5600	19	23	|{i	|{i	X
ejpam-5600	19	24	:	:	PUNCT
ejpam-5600	19	25	ci	ci	PROPN
ejpam-5600	19	26	̸=	̸=	PROPN
ejpam-5600	19	27	ei}|	ei}|	NUM
ejpam-5600	19	28	.	.	PUNCT
ejpam-5600	20	1	for	for	ADP
ejpam-5600	20	2	every	every	DET
ejpam-5600	20	3	vector	vector	NOUN
ejpam-5600	20	4	c	c	NOUN
ejpam-5600	20	5	,	,	PUNCT
ejpam-5600	20	6	the	the	DET
ejpam-5600	20	7	number	number	NOUN
ejpam-5600	20	8	of	of	ADP
ejpam-5600	20	9	nonzero	nonzero	PROPN
ejpam-5600	20	10	positions	position	NOUN
ejpam-5600	20	11	in	in	ADP
ejpam-5600	20	12	c	c	PROPN
ejpam-5600	20	13	is	be	AUX
ejpam-5600	20	14	called	call	VERB
ejpam-5600	20	15	its	its	PRON
ejpam-5600	20	16	weight	weight	NOUN
ejpam-5600	20	17	and	and	CCONJ
ejpam-5600	20	18	we	we	PRON
ejpam-5600	20	19	denote	denote	VERB
ejpam-5600	20	20	it	it	PRON
ejpam-5600	20	21	by	by	ADP
ejpam-5600	20	22	∥c∥.	∥c∥.	PROPN
ejpam-5600	20	23	the	the	DET
ejpam-5600	20	24	smallest	small	ADJ
ejpam-5600	20	25	weight	weight	NOUN
ejpam-5600	20	26	of	of	ADP
ejpam-5600	20	27	the	the	DET
ejpam-5600	20	28	nonzero	nonzero	PROPN
ejpam-5600	20	29	codewords	codeword	NOUN
ejpam-5600	20	30	is	be	AUX
ejpam-5600	20	31	called	call	VERB
ejpam-5600	20	32	the	the	DET
ejpam-5600	20	33	minimum	minimum	ADJ
ejpam-5600	20	34	weight	weight	NOUN
ejpam-5600	20	35	of	of	ADP
ejpam-5600	20	36	the	the	DET
ejpam-5600	20	37	code	code	NOUN
ejpam-5600	20	38	.	.	PUNCT
ejpam-5600	21	1	since	since	SCONJ
ejpam-5600	21	2	c	c	PROPN
ejpam-5600	21	3	is	be	AUX
ejpam-5600	21	4	a	a	DET
ejpam-5600	21	5	linear	linear	ADJ
ejpam-5600	21	6	space	space	NOUN
ejpam-5600	21	7	,	,	PUNCT
ejpam-5600	21	8	the	the	DET
ejpam-5600	21	9	minimum	minimum	ADJ
ejpam-5600	21	10	weight	weight	NOUN
ejpam-5600	21	11	of	of	ADP
ejpam-5600	21	12	the	the	DET
ejpam-5600	21	13	code	code	NOUN
ejpam-5600	21	14	coincides	coincide	VERB
ejpam-5600	21	15	with	with	ADP
ejpam-5600	21	16	the	the	DET
ejpam-5600	21	17	minimum	minimum	NOUN
ejpam-5600	21	18	of	of	ADP
ejpam-5600	21	19	the	the	DET
ejpam-5600	21	20	distances	distance	NOUN
ejpam-5600	21	21	between	between	ADP
ejpam-5600	21	22	distinct	distinct	ADJ
ejpam-5600	21	23	codewords	codeword	NOUN
ejpam-5600	21	24	of	of	ADP
ejpam-5600	21	25	the	the	DET
ejpam-5600	21	26	code	code	NOUN
ejpam-5600	21	27	.	.	PUNCT
ejpam-5600	22	1	if	if	SCONJ
ejpam-5600	22	2	c	c	PROPN
ejpam-5600	22	3	⊂	⊂	PROPN
ejpam-5600	22	4	fn	fn	PART
ejpam-5600	22	5	2	2	NUM
ejpam-5600	22	6	is	be	AUX
ejpam-5600	22	7	a	a	DET
ejpam-5600	22	8	linear	linear	ADJ
ejpam-5600	22	9	code	code	NOUN
ejpam-5600	22	10	with	with	ADP
ejpam-5600	22	11	dimension	dimension	NOUN
ejpam-5600	22	12	k	k	PROPN
ejpam-5600	22	13	and	and	CCONJ
ejpam-5600	22	14	minimum	minimum	ADJ
ejpam-5600	22	15	weight	weight	NOUN
ejpam-5600	22	16	d	d	NOUN
ejpam-5600	22	17	,	,	PUNCT
ejpam-5600	22	18	we	we	PRON
ejpam-5600	22	19	say	say	VERB
ejpam-5600	22	20	that	that	SCONJ
ejpam-5600	22	21	c	c	PROPN
ejpam-5600	22	22	is	be	AUX
ejpam-5600	22	23	a	a	DET
ejpam-5600	22	24	binary	binary	ADJ
ejpam-5600	22	25	[	[	X
ejpam-5600	22	26	n	n	CCONJ
ejpam-5600	22	27	,	,	PUNCT
ejpam-5600	22	28	k	k	NOUN
ejpam-5600	22	29	,	,	PUNCT
ejpam-5600	22	30	d	d	X
ejpam-5600	22	31	]	]	X
ejpam-5600	22	32	code	code	NOUN
ejpam-5600	22	33	.	.	PUNCT
ejpam-5600	23	1	if	if	SCONJ
ejpam-5600	23	2	we	we	PRON
ejpam-5600	23	3	let	let	VERB
ejpam-5600	23	4	ai	ai	AUX
ejpam-5600	23	5	denote	denote	VERB
ejpam-5600	23	6	the	the	DET
ejpam-5600	23	7	number	number	NOUN
ejpam-5600	23	8	of	of	ADP
ejpam-5600	23	9	codewords	codeword	NOUN
ejpam-5600	23	10	with	with	ADP
ejpam-5600	23	11	weight	weight	NOUN
ejpam-5600	23	12	i	i	PRON
ejpam-5600	23	13	,	,	PUNCT
ejpam-5600	23	14	then	then	ADV
ejpam-5600	23	15	the	the	DET
ejpam-5600	23	16	sequence	sequence	NOUN
ejpam-5600	23	17	(	(	PUNCT
ejpam-5600	23	18	a0	a0	NOUN
ejpam-5600	23	19	,	,	PUNCT
ejpam-5600	23	20	ad	ad	NOUN
ejpam-5600	23	21	,	,	PUNCT
ejpam-5600	23	22	ad+1	ad+1	NUM
ejpam-5600	23	23	,	,	PUNCT
ejpam-5600	23	24	.	.	PUNCT
ejpam-5600	23	25	.	.	PUNCT
ejpam-5600	24	1	.	.	PUNCT
ejpam-5600	25	1	,	,	PUNCT
ejpam-5600	25	2	an	an	PRON
ejpam-5600	25	3	)	)	PUNCT
ejpam-5600	25	4	is	be	AUX
ejpam-5600	25	5	called	call	VERB
ejpam-5600	25	6	the	the	DET
ejpam-5600	25	7	weight	weight	NOUN
ejpam-5600	25	8	distribution	distribution	NOUN
ejpam-5600	25	9	or	or	CCONJ
ejpam-5600	25	10	the	the	DET
ejpam-5600	25	11	weight	weight	NOUN
ejpam-5600	25	12	spectrum	spectrum	NOUN
ejpam-5600	25	13	of	of	ADP
ejpam-5600	25	14	the	the	DET
ejpam-5600	25	15	code	code	NOUN
ejpam-5600	25	16	.	.	PUNCT
ejpam-5600	26	1	doi	doi	NOUN
ejpam-5600	26	2	:	:	PUNCT
ejpam-5600	26	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5600	https://doi.org/10.29020/nybg.ejpam.v17i4.5600	ADJ
ejpam-5600	26	4	email	email	NOUN
ejpam-5600	26	5	address	address	NOUN
ejpam-5600	26	6	:	:	PUNCT
ejpam-5600	26	7	iozen@marmara.edu.tr	iozen@marmara.edu.tr	PROPN
ejpam-5600	26	8	(	(	PUNCT
ejpam-5600	26	9	i̇.	i̇.	PROPN
ejpam-5600	26	10	özen	özen	PROPN
ejpam-5600	26	11	)	)	PUNCT
ejpam-5600	26	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5600	26	13	4225	4225	NUM
ejpam-5600	27	1	copyright	copyright	NOUN
ejpam-5600	27	2	:	:	PUNCT
ejpam-5600	27	3	©	©	PROPN
ejpam-5600	27	4	2024	2024	NUM
ejpam-5600	27	5	the	the	DET
ejpam-5600	27	6	author(s	author(s	NOUN
ejpam-5600	27	7	)	)	PUNCT
ejpam-5600	27	8	.	.	PUNCT
ejpam-5600	28	1	(	(	PUNCT
ejpam-5600	28	2	cc	cc	NOUN
ejpam-5600	28	3	by	by	ADP
ejpam-5600	28	4	-	-	PUNCT
ejpam-5600	28	5	nc	nc	PROPN
ejpam-5600	28	6	4.0	4.0	NUM
ejpam-5600	28	7	)	)	PUNCT
ejpam-5600	28	8	i̇brahim	i̇brahim	PUNCT
ejpam-5600	28	9	özen	özen	PROPN
ejpam-5600	28	10	/	/	SYM
ejpam-5600	28	11	eur	eur	PROPN
ejpam-5600	28	12	.	.	PUNCT
ejpam-5600	29	1	j.	j.	PROPN
ejpam-5600	29	2	pure	pure	PROPN
ejpam-5600	29	3	appl	appl	PROPN
ejpam-5600	29	4	.	.	PROPN
ejpam-5600	29	5	math	math	PROPN
ejpam-5600	29	6	,	,	PUNCT
ejpam-5600	29	7	17	17	NUM
ejpam-5600	29	8	(	(	PUNCT
ejpam-5600	29	9	4	4	NUM
ejpam-5600	29	10	)	)	PUNCT
ejpam-5600	29	11	(	(	PUNCT
ejpam-5600	29	12	2024	2024	NUM
ejpam-5600	29	13	)	)	PUNCT
ejpam-5600	29	14	,	,	PUNCT
ejpam-5600	29	15	4225	4225	NUM
ejpam-5600	29	16	-	-	SYM
ejpam-5600	29	17	4237	4237	NUM
ejpam-5600	29	18	4226	4226	NUM
ejpam-5600	29	19	every	every	DET
ejpam-5600	29	20	important	important	ADJ
ejpam-5600	29	21	feature	feature	NOUN
ejpam-5600	29	22	of	of	ADP
ejpam-5600	29	23	a	a	DET
ejpam-5600	29	24	code	code	NOUN
ejpam-5600	29	25	is	be	AUX
ejpam-5600	29	26	encoded	encode	VERB
ejpam-5600	29	27	in	in	ADP
ejpam-5600	29	28	its	its	PRON
ejpam-5600	29	29	weight	weight	NOUN
ejpam-5600	29	30	distribution	distribution	NOUN
ejpam-5600	29	31	.	.	PUNCT
ejpam-5600	30	1	for	for	ADP
ejpam-5600	30	2	example	example	NOUN
ejpam-5600	30	3	,	,	PUNCT
ejpam-5600	30	4	if	if	SCONJ
ejpam-5600	30	5	the	the	DET
ejpam-5600	30	6	weight	weight	NOUN
ejpam-5600	30	7	distribution	distribution	NOUN
ejpam-5600	30	8	of	of	ADP
ejpam-5600	30	9	a	a	DET
ejpam-5600	30	10	linear	linear	ADJ
ejpam-5600	30	11	code	code	NOUN
ejpam-5600	30	12	is	be	AUX
ejpam-5600	30	13	known	know	VERB
ejpam-5600	30	14	we	we	PRON
ejpam-5600	30	15	can	can	AUX
ejpam-5600	30	16	obtain	obtain	VERB
ejpam-5600	30	17	estimations	estimation	NOUN
ejpam-5600	30	18	of	of	ADP
ejpam-5600	30	19	its	its	PRON
ejpam-5600	30	20	decoding	decode	VERB
ejpam-5600	30	21	error	error	NOUN
ejpam-5600	30	22	probability	probability	NOUN
ejpam-5600	30	23	.	.	PUNCT
ejpam-5600	31	1	gallager	gallager	NOUN
ejpam-5600	31	2	estimated	estimate	VERB
ejpam-5600	31	3	the	the	DET
ejpam-5600	31	4	decoding	decode	VERB
ejpam-5600	31	5	error	error	NOUN
ejpam-5600	31	6	probability	probability	NOUN
ejpam-5600	31	7	of	of	ADP
ejpam-5600	31	8	a	a	DET
ejpam-5600	31	9	random	random	ADJ
ejpam-5600	31	10	linear	linear	NOUN
ejpam-5600	31	11	code	code	NOUN
ejpam-5600	31	12	in	in	ADP
ejpam-5600	31	13	[	[	X
ejpam-5600	31	14	4	4	NUM
ejpam-5600	31	15	]	]	PUNCT
ejpam-5600	31	16	.	.	PUNCT
ejpam-5600	32	1	so	so	ADV
ejpam-5600	32	2	we	we	PRON
ejpam-5600	32	3	have	have	VERB
ejpam-5600	32	4	a	a	DET
ejpam-5600	32	5	way	way	NOUN
ejpam-5600	32	6	to	to	PART
ejpam-5600	32	7	compare	compare	VERB
ejpam-5600	32	8	this	this	DET
ejpam-5600	32	9	property	property	NOUN
ejpam-5600	32	10	of	of	ADP
ejpam-5600	32	11	a	a	DET
ejpam-5600	32	12	specific	specific	ADJ
ejpam-5600	32	13	code	code	NOUN
ejpam-5600	32	14	as	as	ADV
ejpam-5600	32	15	well	well	ADV
ejpam-5600	32	16	as	as	ADP
ejpam-5600	32	17	information	information	NOUN
ejpam-5600	32	18	on	on	ADP
ejpam-5600	32	19	what	what	PRON
ejpam-5600	32	20	is	be	AUX
ejpam-5600	32	21	possible	possible	ADJ
ejpam-5600	32	22	for	for	ADP
ejpam-5600	32	23	the	the	DET
ejpam-5600	32	24	same	same	ADJ
ejpam-5600	32	25	quality	quality	NOUN
ejpam-5600	32	26	.	.	PUNCT
ejpam-5600	33	1	this	this	DET
ejpam-5600	33	2	estimation	estimation	NOUN
ejpam-5600	33	3	is	be	AUX
ejpam-5600	33	4	based	base	VERB
ejpam-5600	33	5	on	on	ADP
ejpam-5600	33	6	the	the	DET
ejpam-5600	33	7	expectations	expectation	NOUN
ejpam-5600	33	8	of	of	ADP
ejpam-5600	33	9	the	the	DET
ejpam-5600	33	10	weight	weight	NOUN
ejpam-5600	33	11	distribution	distribution	NOUN
ejpam-5600	33	12	of	of	ADP
ejpam-5600	33	13	random	random	ADJ
ejpam-5600	33	14	linear	linear	NOUN
ejpam-5600	33	15	codes	code	NOUN
ejpam-5600	33	16	.	.	PUNCT
ejpam-5600	34	1	the	the	DET
ejpam-5600	34	2	expectations	expectation	NOUN
ejpam-5600	34	3	of	of	ADP
ejpam-5600	34	4	weights	weight	NOUN
ejpam-5600	34	5	are	be	AUX
ejpam-5600	34	6	part	part	NOUN
ejpam-5600	34	7	of	of	ADP
ejpam-5600	34	8	the	the	DET
ejpam-5600	34	9	code	code	NOUN
ejpam-5600	34	10	weight	weight	NOUN
ejpam-5600	34	11	distribution	distribution	NOUN
ejpam-5600	34	12	problem	problem	NOUN
ejpam-5600	34	13	,	,	PUNCT
ejpam-5600	34	14	namely	namely	ADV
ejpam-5600	34	15	the	the	DET
ejpam-5600	34	16	evaluations	evaluation	NOUN
ejpam-5600	34	17	of	of	ADP
ejpam-5600	34	18	the	the	DET
ejpam-5600	34	19	expectations	expectation	NOUN
ejpam-5600	34	20	e	e	X
ejpam-5600	34	21	(	(	PUNCT
ejpam-5600	34	22	ai1ai2	ai1ai2	X
ejpam-5600	34	23	·	·	PUNCT
ejpam-5600	34	24	·	·	PUNCT
ejpam-5600	34	25	·	·	PUNCT
ejpam-5600	34	26	aik	aik	NOUN
ejpam-5600	34	27	)	)	PUNCT
ejpam-5600	34	28	for	for	ADP
ejpam-5600	34	29	random	random	ADJ
ejpam-5600	34	30	linear	linear	NOUN
ejpam-5600	34	31	codes	code	NOUN
ejpam-5600	34	32	.	.	PUNCT
ejpam-5600	35	1	second	second	ADJ
ejpam-5600	35	2	and	and	CCONJ
ejpam-5600	35	3	third	third	ADJ
ejpam-5600	35	4	joint	joint	ADJ
ejpam-5600	35	5	moments	moment	NOUN
ejpam-5600	35	6	of	of	ADP
ejpam-5600	35	7	the	the	DET
ejpam-5600	35	8	weight	weight	NOUN
ejpam-5600	35	9	distribution	distribution	NOUN
ejpam-5600	35	10	of	of	ADP
ejpam-5600	35	11	a	a	DET
ejpam-5600	35	12	random	random	ADJ
ejpam-5600	35	13	linear	linear	NOUN
ejpam-5600	35	14	code	code	NOUN
ejpam-5600	35	15	were	be	AUX
ejpam-5600	35	16	explored	explore	VERB
ejpam-5600	35	17	in	in	ADP
ejpam-5600	35	18	[	[	X
ejpam-5600	35	19	6	6	NUM
ejpam-5600	35	20	]	]	PUNCT
ejpam-5600	35	21	and	and	CCONJ
ejpam-5600	35	22	[	[	X
ejpam-5600	35	23	1	1	X
ejpam-5600	35	24	]	]	PUNCT
ejpam-5600	35	25	independently	independently	ADV
ejpam-5600	35	26	.	.	PUNCT
ejpam-5600	36	1	fourth	fourth	ADJ
ejpam-5600	36	2	moments	moment	NOUN
ejpam-5600	36	3	were	be	AUX
ejpam-5600	36	4	given	give	VERB
ejpam-5600	36	5	in	in	ADP
ejpam-5600	36	6	[	[	NOUN
ejpam-5600	36	7	8	8	NUM
ejpam-5600	36	8	]	]	PUNCT
ejpam-5600	36	9	.	.	PUNCT
ejpam-5600	37	1	in	in	ADP
ejpam-5600	37	2	[	[	X
ejpam-5600	37	3	9	9	NUM
ejpam-5600	37	4	]	]	PUNCT
ejpam-5600	37	5	and	and	CCONJ
ejpam-5600	37	6	[	[	X
ejpam-5600	37	7	7	7	NUM
ejpam-5600	37	8	]	]	PUNCT
ejpam-5600	37	9	,	,	PUNCT
ejpam-5600	37	10	big	big	ADJ
ejpam-5600	37	11	orders	order	NOUN
ejpam-5600	37	12	of	of	ADP
ejpam-5600	37	13	the	the	DET
ejpam-5600	37	14	moments	moment	NOUN
ejpam-5600	37	15	were	be	AUX
ejpam-5600	37	16	studied	study	VERB
ejpam-5600	37	17	.	.	PUNCT
ejpam-5600	38	1	in	in	ADP
ejpam-5600	38	2	this	this	DET
ejpam-5600	38	3	work	work	NOUN
ejpam-5600	38	4	we	we	PRON
ejpam-5600	38	5	focus	focus	VERB
ejpam-5600	38	6	on	on	ADP
ejpam-5600	38	7	the	the	DET
ejpam-5600	38	8	weight	weight	NOUN
ejpam-5600	38	9	moments	moment	NOUN
ejpam-5600	38	10	of	of	ADP
ejpam-5600	38	11	individual	individual	ADJ
ejpam-5600	38	12	codewords	codeword	NOUN
ejpam-5600	38	13	in	in	ADP
ejpam-5600	38	14	a	a	DET
ejpam-5600	38	15	random	random	ADJ
ejpam-5600	38	16	binary	binary	ADJ
ejpam-5600	38	17	linear	linear	PROPN
ejpam-5600	38	18	code	code	PROPN
ejpam-5600	38	19	.	.	PUNCT
ejpam-5600	39	1	our	our	PRON
ejpam-5600	39	2	results	result	NOUN
ejpam-5600	39	3	have	have	VERB
ejpam-5600	39	4	applications	application	NOUN
ejpam-5600	39	5	on	on	ADP
ejpam-5600	39	6	the	the	DET
ejpam-5600	39	7	expectations	expectation	NOUN
ejpam-5600	39	8	of	of	ADP
ejpam-5600	39	9	correlation	correlation	NOUN
ejpam-5600	39	10	sums	sum	NOUN
ejpam-5600	39	11	of	of	ADP
ejpam-5600	39	12	words	word	NOUN
ejpam-5600	39	13	.	.	PUNCT
ejpam-5600	40	1	let	let	VERB
ejpam-5600	40	2	us	we	PRON
ejpam-5600	40	3	denote	denote	VERB
ejpam-5600	40	4	the	the	DET
ejpam-5600	40	5	words	word	NOUN
ejpam-5600	40	6	of	of	ADP
ejpam-5600	40	7	an	an	DET
ejpam-5600	40	8	[	[	NOUN
ejpam-5600	40	9	n	n	CCONJ
ejpam-5600	40	10	,	,	PUNCT
ejpam-5600	40	11	k	k	X
ejpam-5600	40	12	]	]	X
ejpam-5600	40	13	random	random	ADJ
ejpam-5600	40	14	binary	binary	ADJ
ejpam-5600	40	15	linear	linear	PROPN
ejpam-5600	40	16	code	code	NOUN
ejpam-5600	40	17	by	by	ADP
ejpam-5600	40	18	c	c	PROPN
ejpam-5600	40	19	=	=	SYM
ejpam-5600	40	20	{	{	PUNCT
ejpam-5600	40	21	c0	c0	NOUN
ejpam-5600	40	22	=	=	SYM
ejpam-5600	40	23	0	0	PROPN
ejpam-5600	40	24	,	,	PUNCT
ejpam-5600	40	25	c1	c1	NOUN
ejpam-5600	40	26	,	,	PUNCT
ejpam-5600	40	27	.	.	PUNCT
ejpam-5600	40	28	.	.	PUNCT
ejpam-5600	41	1	.	.	PUNCT
ejpam-5600	42	1	,	,	PUNCT
ejpam-5600	42	2	c2k−1	c2k−1	PROPN
ejpam-5600	42	3	}	}	PUNCT
ejpam-5600	42	4	.	.	PUNCT
ejpam-5600	43	1	the	the	DET
ejpam-5600	43	2	weights	weight	NOUN
ejpam-5600	43	3	of	of	ADP
ejpam-5600	43	4	the	the	DET
ejpam-5600	43	5	words	word	NOUN
ejpam-5600	43	6	will	will	AUX
ejpam-5600	43	7	be	be	AUX
ejpam-5600	43	8	denoted	denote	VERB
ejpam-5600	43	9	by	by	ADP
ejpam-5600	43	10	{	{	PUNCT
ejpam-5600	43	11	w0	w0	PROPN
ejpam-5600	43	12	=	=	SYM
ejpam-5600	43	13	0	0	NUM
ejpam-5600	43	14	,	,	PUNCT
ejpam-5600	43	15	w1	w1	NOUN
ejpam-5600	43	16	,	,	PUNCT
ejpam-5600	43	17	.	.	PUNCT
ejpam-5600	43	18	.	.	PUNCT
ejpam-5600	44	1	.	.	PUNCT
ejpam-5600	45	1	,	,	PUNCT
ejpam-5600	45	2	w2k−1	w2k−1	PROPN
ejpam-5600	45	3	}	}	PUNCT
ejpam-5600	45	4	respectively	respectively	ADV
ejpam-5600	45	5	.	.	PUNCT
ejpam-5600	46	1	in	in	ADP
ejpam-5600	46	2	theorem	theorem	NOUN
ejpam-5600	46	3	1	1	NUM
ejpam-5600	46	4	we	we	PRON
ejpam-5600	46	5	obtain	obtain	VERB
ejpam-5600	46	6	the	the	DET
ejpam-5600	46	7	expectations	expectation	NOUN
ejpam-5600	46	8	of	of	ADP
ejpam-5600	46	9	the	the	DET
ejpam-5600	46	10	nonzero	nonzero	PROPN
ejpam-5600	46	11	words	word	NOUN
ejpam-5600	46	12	’	'	PUNCT
ejpam-5600	46	13	weights	weight	NOUN
ejpam-5600	46	14	in	in	ADP
ejpam-5600	46	15	a	a	DET
ejpam-5600	46	16	random	random	ADJ
ejpam-5600	46	17	[	[	X
ejpam-5600	46	18	n	n	CCONJ
ejpam-5600	46	19	,	,	PUNCT
ejpam-5600	46	20	k	k	X
ejpam-5600	46	21	]	]	X
ejpam-5600	46	22	binary	binary	PROPN
ejpam-5600	46	23	linear	linear	PROPN
ejpam-5600	46	24	code	code	PROPN
ejpam-5600	46	25	and	and	CCONJ
ejpam-5600	46	26	they	they	PRON
ejpam-5600	46	27	are	be	AUX
ejpam-5600	46	28	given	give	VERB
ejpam-5600	46	29	by	by	ADP
ejpam-5600	46	30	e(wi	e(wi	ADJ
ejpam-5600	46	31	)	)	PUNCT
ejpam-5600	46	32	=	=	SYM
ejpam-5600	46	33	n	n	DET
ejpam-5600	46	34	2	2	NUM
ejpam-5600	46	35	,	,	PUNCT
ejpam-5600	46	36	for	for	ADP
ejpam-5600	46	37	i	i	PRON
ejpam-5600	46	38	̸=	̸=	PROPN
ejpam-5600	46	39	0	0	NUM
ejpam-5600	46	40	.	.	PUNCT
ejpam-5600	47	1	expectations	expectation	NOUN
ejpam-5600	47	2	of	of	ADP
ejpam-5600	47	3	pairwise	pairwise	NOUN
ejpam-5600	47	4	products	product	NOUN
ejpam-5600	47	5	of	of	ADP
ejpam-5600	47	6	the	the	DET
ejpam-5600	47	7	weights	weight	NOUN
ejpam-5600	47	8	are	be	AUX
ejpam-5600	47	9	obtained	obtain	VERB
ejpam-5600	47	10	in	in	ADP
ejpam-5600	47	11	theorem	theorem	ADJ
ejpam-5600	47	12	2	2	NUM
ejpam-5600	47	13	and	and	CCONJ
ejpam-5600	47	14	they	they	PRON
ejpam-5600	47	15	can	can	AUX
ejpam-5600	47	16	be	be	AUX
ejpam-5600	47	17	stated	state	VERB
ejpam-5600	47	18	as	as	ADP
ejpam-5600	47	19	e(wiwj	e(wiwj	NOUN
ejpam-5600	47	20	)	)	PUNCT
ejpam-5600	48	1	=	=	PRON
ejpam-5600	48	2	{	{	PUNCT
ejpam-5600	48	3	n2+n	n2+n	PROPN
ejpam-5600	48	4	4	4	NUM
ejpam-5600	48	5	,	,	PUNCT
ejpam-5600	48	6	for	for	ADP
ejpam-5600	48	7	i	i	PROPN
ejpam-5600	48	8	=	=	SYM
ejpam-5600	48	9	j	j	PROPN
ejpam-5600	48	10	,	,	PUNCT
ejpam-5600	48	11	i	i	PRON
ejpam-5600	48	12	,	,	PUNCT
ejpam-5600	48	13	j	j	PROPN
ejpam-5600	48	14	≥	≥	PROPN
ejpam-5600	48	15	1	1	NUM
ejpam-5600	48	16	,	,	PUNCT
ejpam-5600	48	17	n2	n2	NOUN
ejpam-5600	48	18	4	4	NUM
ejpam-5600	48	19	,	,	PUNCT
ejpam-5600	48	20	for	for	ADP
ejpam-5600	48	21	i	i	PROPN
ejpam-5600	48	22	̸=	̸=	PROPN
ejpam-5600	48	23	j	j	PROPN
ejpam-5600	48	24	,	,	PUNCT
ejpam-5600	48	25	i	i	PRON
ejpam-5600	48	26	,	,	PUNCT
ejpam-5600	48	27	j	j	PROPN
ejpam-5600	48	28	≥	≥	PROPN
ejpam-5600	48	29	1	1	NUM
ejpam-5600	48	30	.	.	PUNCT
ejpam-5600	49	1	an	an	DET
ejpam-5600	49	2	immediate	immediate	ADJ
ejpam-5600	49	3	consequence	consequence	NOUN
ejpam-5600	49	4	is	be	AUX
ejpam-5600	49	5	that	that	SCONJ
ejpam-5600	49	6	the	the	DET
ejpam-5600	49	7	weights	weight	NOUN
ejpam-5600	49	8	of	of	ADP
ejpam-5600	49	9	distinct	distinct	ADJ
ejpam-5600	49	10	nonzero	nonzero	NOUN
ejpam-5600	49	11	words	word	NOUN
ejpam-5600	49	12	in	in	ADP
ejpam-5600	49	13	a	a	DET
ejpam-5600	49	14	random	random	ADJ
ejpam-5600	49	15	binary	binary	ADJ
ejpam-5600	49	16	linear	linear	PROPN
ejpam-5600	49	17	code	code	NOUN
ejpam-5600	49	18	are	be	AUX
ejpam-5600	49	19	statistically	statistically	ADV
ejpam-5600	49	20	uncorrelated	uncorrelate	VERB
ejpam-5600	49	21	.	.	PUNCT
ejpam-5600	50	1	covariance(wi	covariance(wi	PROPN
ejpam-5600	50	2	,	,	PUNCT
ejpam-5600	50	3	wj	wj	PROPN
ejpam-5600	50	4	)	)	PUNCT
ejpam-5600	50	5	=	=	PROPN
ejpam-5600	50	6	e(wiwj)−	e(wiwj)−	NOUN
ejpam-5600	50	7	e(wi)e(wj	e(wi)e(wj	PROPN
ejpam-5600	50	8	)	)	PUNCT
ejpam-5600	50	9	=	=	SYM
ejpam-5600	50	10	0	0	NUM
ejpam-5600	50	11	,	,	PUNCT
ejpam-5600	50	12	for	for	ADP
ejpam-5600	50	13	all	all	DET
ejpam-5600	50	14	i	i	PROPN
ejpam-5600	50	15	,	,	PUNCT
ejpam-5600	50	16	j	j	PROPN
ejpam-5600	50	17	≥	≥	NUM
ejpam-5600	50	18	1	1	NUM
ejpam-5600	50	19	and	and	CCONJ
ejpam-5600	50	20	i	i	PRON
ejpam-5600	50	21	̸=	̸=	PROPN
ejpam-5600	50	22	j	j	NOUN
ejpam-5600	50	23	we	we	PRON
ejpam-5600	50	24	apply	apply	VERB
ejpam-5600	50	25	these	these	DET
ejpam-5600	50	26	results	result	NOUN
ejpam-5600	50	27	to	to	PART
ejpam-5600	50	28	obtain	obtain	VERB
ejpam-5600	50	29	correlation	correlation	NOUN
ejpam-5600	50	30	properties	property	NOUN
ejpam-5600	50	31	of	of	ADP
ejpam-5600	50	32	words	word	NOUN
ejpam-5600	50	33	in	in	ADP
ejpam-5600	50	34	a	a	DET
ejpam-5600	50	35	random	random	ADJ
ejpam-5600	50	36	code	code	NOUN
ejpam-5600	50	37	.	.	PUNCT
ejpam-5600	51	1	let	let	VERB
ejpam-5600	51	2	c	c	NOUN
ejpam-5600	51	3	=	=	SYM
ejpam-5600	51	4	(	(	PUNCT
ejpam-5600	51	5	c1	c1	PROPN
ejpam-5600	51	6	,	,	PUNCT
ejpam-5600	51	7	c2	c2	PROPN
ejpam-5600	51	8	,	,	PUNCT
ejpam-5600	51	9	.	.	PUNCT
ejpam-5600	51	10	.	.	PUNCT
ejpam-5600	52	1	.	.	PUNCT
ejpam-5600	53	1	,	,	PUNCT
ejpam-5600	53	2	cn	cn	PROPN
ejpam-5600	53	3	)	)	PUNCT
ejpam-5600	53	4	and	and	CCONJ
ejpam-5600	53	5	e	e	X
ejpam-5600	53	6	=	=	SYM
ejpam-5600	53	7	(	(	PUNCT
ejpam-5600	53	8	e1	e1	PROPN
ejpam-5600	53	9	,	,	PUNCT
ejpam-5600	53	10	e2	e2	PROPN
ejpam-5600	53	11	,	,	PUNCT
ejpam-5600	53	12	.	.	PUNCT
ejpam-5600	53	13	.	.	PUNCT
ejpam-5600	54	1	.	.	PUNCT
ejpam-5600	55	1	,	,	PUNCT
ejpam-5600	55	2	en	en	AUX
ejpam-5600	55	3	)	)	PUNCT
ejpam-5600	55	4	be	be	VERB
ejpam-5600	55	5	two	two	NUM
ejpam-5600	55	6	vectors	vector	NOUN
ejpam-5600	55	7	in	in	ADP
ejpam-5600	55	8	fn	fn	PROPN
ejpam-5600	55	9	2	2	NUM
ejpam-5600	55	10	.	.	PUNCT
ejpam-5600	56	1	the	the	DET
ejpam-5600	56	2	periodic	periodic	ADJ
ejpam-5600	56	3	auto	auto	NOUN
ejpam-5600	56	4	-	-	PUNCT
ejpam-5600	56	5	correlation	correlation	NOUN
ejpam-5600	56	6	and	and	CCONJ
ejpam-5600	56	7	cross	cross	ADJ
ejpam-5600	56	8	-	-	ADJ
ejpam-5600	56	9	correlation	correlation	ADJ
ejpam-5600	56	10	functions	function	NOUN
ejpam-5600	56	11	on	on	ADP
ejpam-5600	56	12	vectors	vector	NOUN
ejpam-5600	56	13	of	of	ADP
ejpam-5600	56	14	fn	fn	PROPN
ejpam-5600	56	15	2	2	NUM
ejpam-5600	56	16	are	be	AUX
ejpam-5600	56	17	defined	define	VERB
ejpam-5600	56	18	respectively	respectively	ADV
ejpam-5600	56	19	by	by	ADP
ejpam-5600	56	20	rc	rc	PROPN
ejpam-5600	56	21	,	,	PUNCT
ejpam-5600	56	22	c(u	c(u	PROPN
ejpam-5600	56	23	)	)	PUNCT
ejpam-5600	56	24	=	=	SYM
ejpam-5600	57	1	rc(u	rc(u	X
ejpam-5600	57	2	)	)	PUNCT
ejpam-5600	58	1	=	=	SYM
ejpam-5600	58	2	n∑	n∑	NOUN
ejpam-5600	58	3	i=1	i=1	PROPN
ejpam-5600	59	1	(	(	PUNCT
ejpam-5600	59	2	−1)ci+ci+u	−1)ci+ci+u	PROPN
ejpam-5600	59	3	and	and	CCONJ
ejpam-5600	59	4	rc	rc	PROPN
ejpam-5600	59	5	,	,	PUNCT
ejpam-5600	59	6	e(u	e(u	PROPN
ejpam-5600	59	7	)	)	PUNCT
ejpam-5600	60	1	=	=	PUNCT
ejpam-5600	61	1	n∑	n∑	NOUN
ejpam-5600	61	2	i=1	i=1	PROPN
ejpam-5600	61	3	(	(	PUNCT
ejpam-5600	61	4	−1)ci+ei+u	−1)ci+ei+u	NOUN
ejpam-5600	61	5	,	,	PUNCT
ejpam-5600	61	6	i̇brahim	i̇brahim	PUNCT
ejpam-5600	61	7	özen	özen	PROPN
ejpam-5600	61	8	/	/	SYM
ejpam-5600	61	9	eur	eur	PROPN
ejpam-5600	61	10	.	.	PUNCT
ejpam-5600	62	1	j.	j.	PROPN
ejpam-5600	62	2	pure	pure	PROPN
ejpam-5600	62	3	appl	appl	PROPN
ejpam-5600	62	4	.	.	PROPN
ejpam-5600	62	5	math	math	PROPN
ejpam-5600	62	6	,	,	PUNCT
ejpam-5600	62	7	17	17	NUM
ejpam-5600	62	8	(	(	PUNCT
ejpam-5600	62	9	4	4	NUM
ejpam-5600	62	10	)	)	PUNCT
ejpam-5600	62	11	(	(	PUNCT
ejpam-5600	62	12	2024	2024	NUM
ejpam-5600	62	13	)	)	PUNCT
ejpam-5600	62	14	,	,	PUNCT
ejpam-5600	62	15	4225	4225	NUM
ejpam-5600	62	16	-	-	SYM
ejpam-5600	62	17	4237	4237	NUM
ejpam-5600	62	18	4227	4227	NUM
ejpam-5600	62	19	where	where	SCONJ
ejpam-5600	62	20	the	the	DET
ejpam-5600	62	21	indices	index	NOUN
ejpam-5600	62	22	are	be	AUX
ejpam-5600	62	23	evaluated	evaluate	VERB
ejpam-5600	62	24	modulo	modulo	PROPN
ejpam-5600	62	25	n.	n.	NOUN
ejpam-5600	62	26	let	let	VERB
ejpam-5600	62	27	c	c	NOUN
ejpam-5600	62	28	and	and	CCONJ
ejpam-5600	62	29	e	e	NOUN
ejpam-5600	62	30	be	be	AUX
ejpam-5600	62	31	two	two	NUM
ejpam-5600	62	32	distinct	distinct	ADJ
ejpam-5600	62	33	nonzero	nonzero	NOUN
ejpam-5600	62	34	codewords	codeword	NOUN
ejpam-5600	62	35	in	in	ADP
ejpam-5600	62	36	a	a	DET
ejpam-5600	62	37	random	random	ADJ
ejpam-5600	62	38	binary	binary	ADJ
ejpam-5600	62	39	linear	linear	PROPN
ejpam-5600	62	40	[	[	X
ejpam-5600	62	41	n	n	CCONJ
ejpam-5600	62	42	,	,	PUNCT
ejpam-5600	62	43	k	k	X
ejpam-5600	62	44	]	]	X
ejpam-5600	62	45	code	code	NOUN
ejpam-5600	62	46	.	.	PUNCT
ejpam-5600	63	1	we	we	PRON
ejpam-5600	63	2	obtain	obtain	VERB
ejpam-5600	63	3	in	in	ADP
ejpam-5600	63	4	theorem	theorem	ADJ
ejpam-5600	63	5	3	3	NUM
ejpam-5600	63	6	that	that	PRON
ejpam-5600	63	7	n−1∑	n−1∑	NUM
ejpam-5600	63	8	u=1	u=1	PRON
ejpam-5600	63	9	e(rc(u	e(rc(u	PROPN
ejpam-5600	63	10	)	)	PUNCT
ejpam-5600	63	11	)	)	PUNCT
ejpam-5600	64	1	=	=	SYM
ejpam-5600	64	2	0	0	NUM
ejpam-5600	64	3	and	and	CCONJ
ejpam-5600	64	4	n−1∑	n−1∑	NUM
ejpam-5600	64	5	u=0	u=0	SYM
ejpam-5600	64	6	e(rc	e(rc	PROPN
ejpam-5600	64	7	,	,	PUNCT
ejpam-5600	64	8	e(u	e(u	PROPN
ejpam-5600	64	9	)	)	PUNCT
ejpam-5600	64	10	)	)	PUNCT
ejpam-5600	65	1	=	=	PUNCT
ejpam-5600	65	2	0	0	X
ejpam-5600	65	3	.	.	NOUN
ejpam-5600	65	4	2	2	X
ejpam-5600	65	5	.	.	X
ejpam-5600	65	6	characteristic	characteristic	ADJ
ejpam-5600	65	7	vectors	vector	NOUN
ejpam-5600	65	8	of	of	ADP
ejpam-5600	65	9	codes	code	NOUN
ejpam-5600	65	10	and	and	CCONJ
ejpam-5600	65	11	weights	weight	NOUN
ejpam-5600	65	12	of	of	ADP
ejpam-5600	65	13	nonzero	nonzero	PROPN
ejpam-5600	65	14	codewords	codeword	VERB
ejpam-5600	65	15	our	our	PRON
ejpam-5600	65	16	main	main	ADJ
ejpam-5600	65	17	theorem	theorem	NOUN
ejpam-5600	65	18	is	be	AUX
ejpam-5600	65	19	based	base	VERB
ejpam-5600	65	20	on	on	ADP
ejpam-5600	65	21	the	the	DET
ejpam-5600	65	22	characterization	characterization	NOUN
ejpam-5600	65	23	of	of	ADP
ejpam-5600	65	24	weights	weight	NOUN
ejpam-5600	65	25	of	of	ADP
ejpam-5600	65	26	nonzero	nonzero	ADJ
ejpam-5600	65	27	words	word	NOUN
ejpam-5600	65	28	in	in	ADP
ejpam-5600	65	29	terms	term	NOUN
ejpam-5600	65	30	of	of	ADP
ejpam-5600	65	31	the	the	DET
ejpam-5600	65	32	characteristic	characteristic	ADJ
ejpam-5600	65	33	vector	vector	NOUN
ejpam-5600	65	34	of	of	ADP
ejpam-5600	65	35	a	a	DET
ejpam-5600	65	36	code	code	NOUN
ejpam-5600	65	37	,	,	PUNCT
ejpam-5600	65	38	given	give	VERB
ejpam-5600	65	39	in	in	ADP
ejpam-5600	65	40	[	[	X
ejpam-5600	65	41	2	2	NUM
ejpam-5600	65	42	]	]	PUNCT
ejpam-5600	65	43	.	.	PUNCT
ejpam-5600	66	1	we	we	PRON
ejpam-5600	66	2	will	will	AUX
ejpam-5600	66	3	review	review	VERB
ejpam-5600	66	4	this	this	DET
ejpam-5600	66	5	characterization	characterization	NOUN
ejpam-5600	66	6	in	in	ADP
ejpam-5600	66	7	the	the	DET
ejpam-5600	66	8	following	follow	VERB
ejpam-5600	66	9	paragraphs	paragraph	NOUN
ejpam-5600	66	10	.	.	PUNCT
ejpam-5600	67	1	let	let	VERB
ejpam-5600	67	2	k	k	PROPN
ejpam-5600	67	3	≥	≥	NUM
ejpam-5600	67	4	2	2	NUM
ejpam-5600	68	1	and	and	CCONJ
ejpam-5600	68	2	i	i	PRON
ejpam-5600	68	3	be	be	VERB
ejpam-5600	68	4	integers	integer	NOUN
ejpam-5600	68	5	with	with	ADP
ejpam-5600	68	6	1	1	NUM
ejpam-5600	68	7	≤	≤	NUM
ejpam-5600	68	8	i	i	PRON
ejpam-5600	68	9	≤	≤	ADJ
ejpam-5600	68	10	2k−1	2k−1	NUM
ejpam-5600	68	11	.	.	PUNCT
ejpam-5600	69	1	we	we	PRON
ejpam-5600	69	2	denote	denote	VERB
ejpam-5600	69	3	by	by	ADP
ejpam-5600	69	4	i	i	PRON
ejpam-5600	69	5	=	=	SYM
ejpam-5600	69	6	(	(	PUNCT
ejpam-5600	69	7	i0	i0	PROPN
ejpam-5600	69	8	,	,	PUNCT
ejpam-5600	69	9	i1	i1	PROPN
ejpam-5600	69	10	,	,	PUNCT
ejpam-5600	69	11	.	.	PUNCT
ejpam-5600	69	12	.	.	PUNCT
ejpam-5600	70	1	.	.	PUNCT
ejpam-5600	71	1	,	,	PUNCT
ejpam-5600	71	2	ik−1	ik−1	PROPN
ejpam-5600	71	3	)	)	PUNCT
ejpam-5600	71	4	∈	∈	PROPN
ejpam-5600	71	5	fk	fk	INTJ
ejpam-5600	71	6	2	2	NUM
ejpam-5600	71	7	,	,	PUNCT
ejpam-5600	71	8	the	the	DET
ejpam-5600	71	9	binary	binary	ADJ
ejpam-5600	71	10	expansion	expansion	NOUN
ejpam-5600	71	11	of	of	ADP
ejpam-5600	71	12	i	i	PROPN
ejpam-5600	71	13	=	=	PUNCT
ejpam-5600	71	14	∑k−1	∑k−1	X
ejpam-5600	71	15	j=0	j=0	PROPN
ejpam-5600	71	16	ij2	ij2	PROPN
ejpam-5600	71	17	j	j	PROPN
ejpam-5600	71	18	.	.	PUNCT
ejpam-5600	72	1	we	we	PRON
ejpam-5600	72	2	form	form	VERB
ejpam-5600	72	3	the	the	DET
ejpam-5600	72	4	k	k	PROPN
ejpam-5600	72	5	×	×	PROPN
ejpam-5600	72	6	(	(	PUNCT
ejpam-5600	72	7	2k	2k	NOUN
ejpam-5600	72	8	−	−	NOUN
ejpam-5600	72	9	1	1	NUM
ejpam-5600	72	10	)	)	PUNCT
ejpam-5600	72	11	matrix	matrix	NOUN
ejpam-5600	72	12	gk	gk	PROPN
ejpam-5600	72	13	,	,	PUNCT
ejpam-5600	72	14	whose	whose	DET
ejpam-5600	72	15	ith	ith	NOUN
ejpam-5600	72	16	column	column	NOUN
ejpam-5600	72	17	is	be	AUX
ejpam-5600	72	18	it	it	PRON
ejpam-5600	72	19	.	.	PUNCT
ejpam-5600	73	1	let	let	VERB
ejpam-5600	73	2	c	c	PRON
ejpam-5600	73	3	be	be	AUX
ejpam-5600	73	4	a	a	DET
ejpam-5600	73	5	binary	binary	ADJ
ejpam-5600	73	6	linear	linear	PROPN
ejpam-5600	73	7	[	[	X
ejpam-5600	73	8	n	n	CCONJ
ejpam-5600	73	9	,	,	PUNCT
ejpam-5600	73	10	k	k	X
ejpam-5600	73	11	]	]	X
ejpam-5600	73	12	code	code	NOUN
ejpam-5600	73	13	and	and	CCONJ
ejpam-5600	73	14	let	let	VERB
ejpam-5600	73	15	g	g	PRON
ejpam-5600	73	16	be	be	AUX
ejpam-5600	73	17	a	a	DET
ejpam-5600	73	18	generator	generator	NOUN
ejpam-5600	73	19	matrix	matrix	NOUN
ejpam-5600	73	20	of	of	ADP
ejpam-5600	73	21	c.	c.	NOUN
ejpam-5600	73	22	we	we	PRON
ejpam-5600	73	23	will	will	AUX
ejpam-5600	73	24	show	show	VERB
ejpam-5600	73	25	below	below	ADP
ejpam-5600	73	26	that	that	PRON
ejpam-5600	73	27	with	with	ADP
ejpam-5600	73	28	high	high	ADJ
ejpam-5600	73	29	probability	probability	NOUN
ejpam-5600	73	30	a	a	DET
ejpam-5600	73	31	random	random	ADJ
ejpam-5600	73	32	matrix	matrix	NOUN
ejpam-5600	73	33	g	g	NOUN
ejpam-5600	73	34	has	have	VERB
ejpam-5600	73	35	no	no	DET
ejpam-5600	73	36	columns	column	NOUN
ejpam-5600	73	37	of	of	ADP
ejpam-5600	73	38	zeros	zero	NOUN
ejpam-5600	73	39	.	.	PUNCT
ejpam-5600	74	1	we	we	PRON
ejpam-5600	74	2	will	will	AUX
ejpam-5600	74	3	assume	assume	VERB
ejpam-5600	74	4	from	from	ADP
ejpam-5600	74	5	now	now	ADV
ejpam-5600	74	6	on	on	ADV
ejpam-5600	74	7	that	that	PRON
ejpam-5600	74	8	c	c	PROPN
ejpam-5600	74	9	is	be	AUX
ejpam-5600	74	10	a	a	DET
ejpam-5600	74	11	code	code	NOUN
ejpam-5600	74	12	with	with	ADP
ejpam-5600	74	13	a	a	DET
ejpam-5600	74	14	generator	generator	NOUN
ejpam-5600	74	15	matrix	matrix	NOUN
ejpam-5600	74	16	without	without	ADP
ejpam-5600	74	17	zero	zero	NUM
ejpam-5600	74	18	columns	column	NOUN
ejpam-5600	74	19	.	.	PUNCT
ejpam-5600	75	1	for	for	ADP
ejpam-5600	75	2	such	such	ADJ
ejpam-5600	75	3	c	c	PROPN
ejpam-5600	75	4	and	and	CCONJ
ejpam-5600	75	5	g	g	NOUN
ejpam-5600	75	6	,	,	PUNCT
ejpam-5600	75	7	we	we	PRON
ejpam-5600	75	8	define	define	VERB
ejpam-5600	75	9	the	the	DET
ejpam-5600	75	10	characteristic	characteristic	ADJ
ejpam-5600	75	11	vector	vector	NOUN
ejpam-5600	75	12	χc	χc	NOUN
ejpam-5600	75	13	of	of	ADP
ejpam-5600	75	14	c	c	PROPN
ejpam-5600	75	15	with	with	ADP
ejpam-5600	75	16	respect	respect	NOUN
ejpam-5600	75	17	to	to	ADP
ejpam-5600	75	18	g	g	PROPN
ejpam-5600	75	19	as	as	ADP
ejpam-5600	75	20	the	the	DET
ejpam-5600	75	21	vector	vector	NOUN
ejpam-5600	75	22	χc	χc	PROPN
ejpam-5600	75	23	=	=	SYM
ejpam-5600	75	24	(	(	PUNCT
ejpam-5600	75	25	h1	h1	PROPN
ejpam-5600	75	26	,	,	PUNCT
ejpam-5600	75	27	h2	h2	PROPN
ejpam-5600	75	28	,	,	PUNCT
ejpam-5600	75	29	.	.	PUNCT
ejpam-5600	75	30	.	.	PUNCT
ejpam-5600	76	1	.	.	PUNCT
ejpam-5600	77	1	,	,	PUNCT
ejpam-5600	77	2	h2k−1	h2k−1	PROPN
ejpam-5600	77	3	)	)	PUNCT
ejpam-5600	77	4	t	t	PROPN
ejpam-5600	77	5	,	,	PUNCT
ejpam-5600	77	6	where	where	SCONJ
ejpam-5600	77	7	hi	hi	INTJ
ejpam-5600	77	8	is	be	AUX
ejpam-5600	77	9	the	the	DET
ejpam-5600	77	10	number	number	NOUN
ejpam-5600	77	11	of	of	ADP
ejpam-5600	77	12	columns	column	NOUN
ejpam-5600	77	13	in	in	ADP
ejpam-5600	77	14	g	g	PROPN
ejpam-5600	77	15	equal	equal	ADJ
ejpam-5600	77	16	to	to	ADP
ejpam-5600	77	17	the	the	DET
ejpam-5600	77	18	ith	ith	PROPN
ejpam-5600	77	19	column	column	NOUN
ejpam-5600	77	20	it	it	PRON
ejpam-5600	77	21	of	of	ADP
ejpam-5600	77	22	gk	gk	PROPN
ejpam-5600	77	23	.	.	PUNCT
ejpam-5600	78	1	clearly	clearly	ADV
ejpam-5600	78	2	we	we	PRON
ejpam-5600	78	3	have	have	VERB
ejpam-5600	78	4	∑	∑	PROPN
ejpam-5600	78	5	j	j	PROPN
ejpam-5600	78	6	hj	hj	PROPN
ejpam-5600	78	7	=	=	SYM
ejpam-5600	78	8	n	n	PROPN
ejpam-5600	78	9	(	(	PUNCT
ejpam-5600	78	10	recall	recall	VERB
ejpam-5600	78	11	that	that	SCONJ
ejpam-5600	78	12	g	g	PROPN
ejpam-5600	78	13	has	have	VERB
ejpam-5600	78	14	no	no	DET
ejpam-5600	78	15	zero	zero	NUM
ejpam-5600	78	16	columns	column	NOUN
ejpam-5600	78	17	)	)	PUNCT
ejpam-5600	78	18	.	.	PUNCT
ejpam-5600	79	1	now	now	ADV
ejpam-5600	79	2	since	since	SCONJ
ejpam-5600	79	3	any	any	DET
ejpam-5600	79	4	nonzero	nonzero	ADJ
ejpam-5600	79	5	codeword	codeword	NOUN
ejpam-5600	79	6	is	be	AUX
ejpam-5600	79	7	obtained	obtain	VERB
ejpam-5600	79	8	by	by	ADP
ejpam-5600	79	9	a	a	DET
ejpam-5600	79	10	nontrivial	nontrivial	ADJ
ejpam-5600	79	11	linear	linear	NOUN
ejpam-5600	79	12	combination	combination	NOUN
ejpam-5600	79	13	of	of	ADP
ejpam-5600	79	14	rows	row	NOUN
ejpam-5600	79	15	of	of	ADP
ejpam-5600	79	16	g	g	NOUN
ejpam-5600	79	17	,	,	PUNCT
ejpam-5600	79	18	all	all	DET
ejpam-5600	79	19	nonzero	nonzero	ADJ
ejpam-5600	79	20	codewords	codeword	NOUN
ejpam-5600	79	21	of	of	ADP
ejpam-5600	79	22	c	c	PROPN
ejpam-5600	79	23	are	be	AUX
ejpam-5600	79	24	obtained	obtain	VERB
ejpam-5600	79	25	as	as	ADP
ejpam-5600	79	26	the	the	DET
ejpam-5600	79	27	rows	row	NOUN
ejpam-5600	79	28	of	of	ADP
ejpam-5600	79	29	the	the	DET
ejpam-5600	79	30	matrix	matrix	NOUN
ejpam-5600	79	31	product	product	NOUN
ejpam-5600	79	32	gt	gt	INTJ
ejpam-5600	79	33	kg	kg	INTJ
ejpam-5600	79	34	.	.	PUNCT
ejpam-5600	80	1	so	so	ADV
ejpam-5600	80	2	we	we	PRON
ejpam-5600	80	3	identify	identify	VERB
ejpam-5600	80	4	the	the	DET
ejpam-5600	80	5	nonzero	nonzero	ADJ
ejpam-5600	80	6	words	word	NOUN
ejpam-5600	80	7	of	of	ADP
ejpam-5600	80	8	c	c	PROPN
ejpam-5600	80	9	with	with	ADP
ejpam-5600	80	10	the	the	DET
ejpam-5600	80	11	rows	row	NOUN
ejpam-5600	80	12	of	of	ADP
ejpam-5600	80	13	the	the	DET
ejpam-5600	80	14	product	product	NOUN
ejpam-5600	80	15	gt	gt	INTJ
ejpam-5600	80	16	kg	kg	NOUN
ejpam-5600	80	17	;	;	PUNCT
ejpam-5600	80	18	c	c	X
ejpam-5600	80	19	=	=	SYM
ejpam-5600	80	20	{	{	PUNCT
ejpam-5600	80	21	0}∪{ci}2	0}∪{ci}2	NUM
ejpam-5600	80	22	k−1	k−1	PROPN
ejpam-5600	80	23	i=1	i=1	PROPN
ejpam-5600	80	24	,	,	PUNCT
ejpam-5600	80	25	where	where	SCONJ
ejpam-5600	80	26	ci	ci	PROPN
ejpam-5600	80	27	is	be	AUX
ejpam-5600	80	28	the	the	DET
ejpam-5600	80	29	ith	ith	PROPN
ejpam-5600	80	30	row	row	NOUN
ejpam-5600	80	31	of	of	ADP
ejpam-5600	80	32	gt	gt	PROPN
ejpam-5600	80	33	kg	kg	INTJ
ejpam-5600	80	34	.	.	PUNCT
ejpam-5600	81	1	if	if	SCONJ
ejpam-5600	81	2	we	we	PRON
ejpam-5600	81	3	denote	denote	VERB
ejpam-5600	81	4	the	the	DET
ejpam-5600	81	5	matrix	matrix	NOUN
ejpam-5600	81	6	product	product	NOUN
ejpam-5600	81	7	gt	gt	PROPN
ejpam-5600	81	8	kgk	kgk	NOUN
ejpam-5600	81	9	by	by	ADP
ejpam-5600	81	10	mk	mk	PROPN
ejpam-5600	81	11	,	,	PUNCT
ejpam-5600	81	12	we	we	PRON
ejpam-5600	81	13	can	can	AUX
ejpam-5600	81	14	express	express	VERB
ejpam-5600	81	15	the	the	DET
ejpam-5600	81	16	relation	relation	NOUN
ejpam-5600	81	17	between	between	ADP
ejpam-5600	81	18	the	the	DET
ejpam-5600	81	19	weights	weight	NOUN
ejpam-5600	81	20	of	of	ADP
ejpam-5600	81	21	the	the	DET
ejpam-5600	81	22	nonzero	nonzero	PROPN
ejpam-5600	81	23	codewords	codeword	NOUN
ejpam-5600	81	24	of	of	ADP
ejpam-5600	81	25	c	c	PROPN
ejpam-5600	81	26	and	and	CCONJ
ejpam-5600	81	27	the	the	DET
ejpam-5600	81	28	characteristic	characteristic	ADJ
ejpam-5600	81	29	vector	vector	NOUN
ejpam-5600	81	30	χc	χc	PROPN
ejpam-5600	81	31	as	as	ADP
ejpam-5600	81	32	in	in	ADP
ejpam-5600	81	33	the	the	DET
ejpam-5600	81	34	following	follow	VERB
ejpam-5600	81	35	lemma	lemma	PROPN
ejpam-5600	81	36	.	.	PUNCT
ejpam-5600	82	1	lemma	lemma	PROPN
ejpam-5600	82	2	1	1	NUM
ejpam-5600	82	3	.	.	PUNCT
ejpam-5600	83	1	[	[	X
ejpam-5600	83	2	2	2	NUM
ejpam-5600	83	3	,	,	PUNCT
ejpam-5600	83	4	lemma	lemma	PROPN
ejpam-5600	83	5	1	1	NUM
ejpam-5600	83	6	]	]	PUNCT
ejpam-5600	83	7	let	let	VERB
ejpam-5600	83	8	c	c	PRON
ejpam-5600	83	9	be	be	AUX
ejpam-5600	83	10	a	a	DET
ejpam-5600	83	11	binary	binary	NOUN
ejpam-5600	83	12	[	[	X
ejpam-5600	83	13	n	n	CCONJ
ejpam-5600	83	14	,	,	PUNCT
ejpam-5600	83	15	k	k	X
ejpam-5600	83	16	]	]	X
ejpam-5600	83	17	linear	linear	PROPN
ejpam-5600	83	18	code	code	PROPN
ejpam-5600	83	19	,	,	PUNCT
ejpam-5600	83	20	let	let	VERB
ejpam-5600	83	21	g	g	PRON
ejpam-5600	83	22	be	be	AUX
ejpam-5600	83	23	a	a	DET
ejpam-5600	83	24	generator	generator	NOUN
ejpam-5600	83	25	matrix	matrix	NOUN
ejpam-5600	83	26	of	of	ADP
ejpam-5600	83	27	c	c	PROPN
ejpam-5600	83	28	and	and	CCONJ
ejpam-5600	83	29	let	let	VERB
ejpam-5600	83	30	χc	χc	PRON
ejpam-5600	83	31	be	be	AUX
ejpam-5600	83	32	the	the	DET
ejpam-5600	83	33	characteristic	characteristic	ADJ
ejpam-5600	83	34	vector	vector	NOUN
ejpam-5600	83	35	of	of	ADP
ejpam-5600	83	36	c	c	PROPN
ejpam-5600	83	37	with	with	ADP
ejpam-5600	83	38	respect	respect	NOUN
ejpam-5600	83	39	to	to	ADP
ejpam-5600	83	40	g.	g.	PROPN
ejpam-5600	83	41	then	then	ADV
ejpam-5600	83	42	the	the	DET
ejpam-5600	83	43	weight	weight	NOUN
ejpam-5600	83	44	of	of	ADP
ejpam-5600	83	45	ith	ith	PROPN
ejpam-5600	83	46	row	row	NOUN
ejpam-5600	83	47	ci	ci	PROPN
ejpam-5600	83	48	of	of	ADP
ejpam-5600	83	49	g	g	PROPN
ejpam-5600	83	50	t	t	PROPN
ejpam-5600	83	51	kg	kg	PROPN
ejpam-5600	83	52	equals	equal	VERB
ejpam-5600	83	53	to	to	ADP
ejpam-5600	83	54	the	the	DET
ejpam-5600	83	55	ith	ith	PROPN
ejpam-5600	83	56	entry	entry	NOUN
ejpam-5600	83	57	of	of	ADP
ejpam-5600	83	58	the	the	DET
ejpam-5600	83	59	column	column	NOUN
ejpam-5600	83	60	vector	vector	NOUN
ejpam-5600	83	61	mkχc	mkχc	NOUN
ejpam-5600	83	62	mkχc	mkχc	NOUN
ejpam-5600	83	63	=	=	SYM
ejpam-5600	83	64			PROPN
ejpam-5600	83	65	w1	w1	NOUN
ejpam-5600	83	66	w2	w2	NOUN
ejpam-5600	83	67	...	...	PUNCT
ejpam-5600	84	1	w2k−1	w2k−1	PROPN
ejpam-5600	84	2			ADJ
ejpam-5600	84	3	,	,	PUNCT
ejpam-5600	84	4	where	where	SCONJ
ejpam-5600	84	5	{	{	PUNCT
ejpam-5600	84	6	w1	w1	NOUN
ejpam-5600	84	7	,	,	PUNCT
ejpam-5600	84	8	w2	w2	NOUN
ejpam-5600	84	9	,	,	PUNCT
ejpam-5600	84	10	.	.	PUNCT
ejpam-5600	84	11	.	.	PUNCT
ejpam-5600	84	12	.	.	PUNCT
ejpam-5600	85	1	,	,	PUNCT
ejpam-5600	85	2	w2k−1	w2k−1	PROPN
ejpam-5600	85	3	}	}	PUNCT
ejpam-5600	85	4	is	be	AUX
ejpam-5600	85	5	the	the	DET
ejpam-5600	85	6	set	set	NOUN
ejpam-5600	85	7	of	of	ADP
ejpam-5600	85	8	weights	weight	NOUN
ejpam-5600	85	9	of	of	ADP
ejpam-5600	85	10	all	all	DET
ejpam-5600	85	11	nonzero	nonzero	ADJ
ejpam-5600	85	12	words	word	NOUN
ejpam-5600	85	13	in	in	ADP
ejpam-5600	85	14	c.	c.	PROPN
ejpam-5600	85	15	i̇brahim	i̇brahim	PUNCT
ejpam-5600	86	1	özen	özen	PROPN
ejpam-5600	86	2	/	/	SYM
ejpam-5600	86	3	eur	eur	PROPN
ejpam-5600	86	4	.	.	PUNCT
ejpam-5600	87	1	j.	j.	PROPN
ejpam-5600	87	2	pure	pure	PROPN
ejpam-5600	87	3	appl	appl	PROPN
ejpam-5600	87	4	.	.	PROPN
ejpam-5600	87	5	math	math	PROPN
ejpam-5600	87	6	,	,	PUNCT
ejpam-5600	87	7	17	17	NUM
ejpam-5600	87	8	(	(	PUNCT
ejpam-5600	87	9	4	4	NUM
ejpam-5600	87	10	)	)	PUNCT
ejpam-5600	87	11	(	(	PUNCT
ejpam-5600	87	12	2024	2024	NUM
ejpam-5600	87	13	)	)	PUNCT
ejpam-5600	87	14	,	,	PUNCT
ejpam-5600	87	15	4225	4225	NUM
ejpam-5600	87	16	-	-	SYM
ejpam-5600	87	17	4237	4237	NUM
ejpam-5600	87	18	4228	4228	NUM
ejpam-5600	87	19	let	let	VERB
ejpam-5600	87	20	f	f	PRON
ejpam-5600	87	21	be	be	AUX
ejpam-5600	87	22	a	a	DET
ejpam-5600	87	23	sequence	sequence	NOUN
ejpam-5600	87	24	of	of	ADP
ejpam-5600	87	25	real	real	ADJ
ejpam-5600	87	26	numbers	number	NOUN
ejpam-5600	87	27	of	of	ADP
ejpam-5600	87	28	length	length	NOUN
ejpam-5600	87	29	2k	2k	NUM
ejpam-5600	87	30	,	,	PUNCT
ejpam-5600	87	31	whose	whose	DET
ejpam-5600	87	32	terms	term	NOUN
ejpam-5600	87	33	are	be	AUX
ejpam-5600	87	34	indexed	index	VERB
ejpam-5600	87	35	from	from	ADP
ejpam-5600	87	36	0	0	NUM
ejpam-5600	87	37	to	to	ADP
ejpam-5600	87	38	2k−1	2k−1	NUM
ejpam-5600	87	39	and	and	CCONJ
ejpam-5600	87	40	let	let	VERB
ejpam-5600	87	41	us	we	PRON
ejpam-5600	87	42	denote	denote	VERB
ejpam-5600	87	43	by	by	ADP
ejpam-5600	87	44	f(i	f(i	PROPN
ejpam-5600	87	45	)	)	PUNCT
ejpam-5600	87	46	its	its	PRON
ejpam-5600	87	47	ith	ith	NOUN
ejpam-5600	87	48	coordinate	coordinate	NOUN
ejpam-5600	87	49	.	.	PUNCT
ejpam-5600	88	1	then	then	ADV
ejpam-5600	88	2	we	we	PRON
ejpam-5600	88	3	define	define	VERB
ejpam-5600	88	4	its	its	PRON
ejpam-5600	88	5	walsh	walsh	NOUN
ejpam-5600	88	6	transformation	transformation	NOUN
ejpam-5600	88	7	f̂	f̂	PROPN
ejpam-5600	88	8	as	as	ADP
ejpam-5600	88	9	a	a	DET
ejpam-5600	88	10	sequence	sequence	NOUN
ejpam-5600	88	11	of	of	ADP
ejpam-5600	88	12	real	real	ADJ
ejpam-5600	88	13	numbers	number	NOUN
ejpam-5600	88	14	with	with	ADP
ejpam-5600	88	15	the	the	DET
ejpam-5600	88	16	same	same	ADJ
ejpam-5600	88	17	length	length	NOUN
ejpam-5600	88	18	,	,	PUNCT
ejpam-5600	88	19	whose	whose	DET
ejpam-5600	88	20	ith	ith	NOUN
ejpam-5600	88	21	entry	entry	NOUN
ejpam-5600	88	22	is	be	AUX
ejpam-5600	88	23	given	give	VERB
ejpam-5600	88	24	by	by	ADP
ejpam-5600	88	25	f̂(i	f̂(i	NOUN
ejpam-5600	88	26	)	)	PUNCT
ejpam-5600	88	27	=	=	SYM
ejpam-5600	88	28	2k−1∑	2k−1∑	NUM
ejpam-5600	88	29	j=0	j=0	PROPN
ejpam-5600	88	30	f(j)(−1)⟨j	f(j)(−1)⟨j	PROPN
ejpam-5600	88	31	,	,	PUNCT
ejpam-5600	88	32	i⟩	i⟩	PRON
ejpam-5600	88	33	,	,	PUNCT
ejpam-5600	88	34	0	0	NUM
ejpam-5600	88	35	≤	≤	NUM
ejpam-5600	88	36	i	i	PRON
ejpam-5600	88	37	≤	≤	ADJ
ejpam-5600	88	38	2k	2k	NOUN
ejpam-5600	88	39	−	−	NOUN
ejpam-5600	88	40	1	1	NUM
ejpam-5600	88	41	,	,	PUNCT
ejpam-5600	88	42	where	where	SCONJ
ejpam-5600	88	43	⟨	⟨	NOUN
ejpam-5600	88	44	,	,	PUNCT
ejpam-5600	88	45	⟩	⟩	NOUN
ejpam-5600	88	46	is	be	AUX
ejpam-5600	88	47	the	the	DET
ejpam-5600	88	48	standard	standard	ADJ
ejpam-5600	88	49	inner	inner	ADJ
ejpam-5600	88	50	product	product	NOUN
ejpam-5600	88	51	on	on	ADP
ejpam-5600	88	52	fk	fk	INTJ
ejpam-5600	88	53	2	2	NUM
ejpam-5600	88	54	,	,	PUNCT
ejpam-5600	88	55	i	i	PRON
ejpam-5600	88	56	and	and	CCONJ
ejpam-5600	88	57	j	j	PROPN
ejpam-5600	88	58	are	be	AUX
ejpam-5600	88	59	the	the	DET
ejpam-5600	88	60	binary	binary	ADJ
ejpam-5600	88	61	expansions	expansion	NOUN
ejpam-5600	88	62	of	of	ADP
ejpam-5600	88	63	i	i	PRON
ejpam-5600	88	64	and	and	CCONJ
ejpam-5600	88	65	j	j	PROPN
ejpam-5600	88	66	respectively	respectively	ADV
ejpam-5600	88	67	.	.	PUNCT
ejpam-5600	89	1	from	from	ADP
ejpam-5600	89	2	χc	χc	PROPN
ejpam-5600	89	3	=	=	PUNCT
ejpam-5600	89	4	(	(	PUNCT
ejpam-5600	89	5	h1	h1	PROPN
ejpam-5600	89	6	,	,	PUNCT
ejpam-5600	89	7	h2	h2	PROPN
ejpam-5600	89	8	,	,	PUNCT
ejpam-5600	89	9	.	.	PUNCT
ejpam-5600	89	10	.	.	PUNCT
ejpam-5600	89	11	.	.	PUNCT
ejpam-5600	90	1	,	,	PUNCT
ejpam-5600	90	2	h2k−1	h2k−1	PROPN
ejpam-5600	90	3	)	)	PUNCT
ejpam-5600	90	4	t	t	NOUN
ejpam-5600	90	5	we	we	PRON
ejpam-5600	90	6	obtain	obtain	VERB
ejpam-5600	90	7	a	a	DET
ejpam-5600	90	8	sequence	sequence	NOUN
ejpam-5600	90	9	of	of	ADP
ejpam-5600	90	10	integers	integer	NOUN
ejpam-5600	90	11	of	of	ADP
ejpam-5600	90	12	length	length	NOUN
ejpam-5600	90	13	2k	2k	NUM
ejpam-5600	90	14	by	by	ADP
ejpam-5600	90	15	χc	χc	PROPN
ejpam-5600	90	16	=	=	SYM
ejpam-5600	90	17	(	(	PUNCT
ejpam-5600	90	18	h0	h0	NOUN
ejpam-5600	90	19	=	=	SYM
ejpam-5600	90	20	0	0	PROPN
ejpam-5600	90	21	,	,	PUNCT
ejpam-5600	90	22	h1	h1	NOUN
ejpam-5600	90	23	,	,	PUNCT
ejpam-5600	90	24	h2	h2	PROPN
ejpam-5600	90	25	,	,	PUNCT
ejpam-5600	90	26	.	.	PUNCT
ejpam-5600	90	27	.	.	PUNCT
ejpam-5600	91	1	.	.	PUNCT
ejpam-5600	92	1	,	,	PUNCT
ejpam-5600	92	2	h2k−1	h2k−1	PROPN
ejpam-5600	92	3	)	)	PUNCT
ejpam-5600	92	4	t	t	PROPN
ejpam-5600	92	5	.	.	PUNCT
ejpam-5600	93	1	then	then	ADV
ejpam-5600	93	2	the	the	DET
ejpam-5600	93	3	walsh	walsh	PROPN
ejpam-5600	93	4	transform	transform	NOUN
ejpam-5600	93	5	of	of	ADP
ejpam-5600	93	6	χc	χc	PRON
ejpam-5600	93	7	is	be	AUX
ejpam-5600	93	8	the	the	DET
ejpam-5600	93	9	vector	vector	NOUN
ejpam-5600	93	10	whose	whose	DET
ejpam-5600	93	11	ith	ith	NOUN
ejpam-5600	93	12	entry	entry	NOUN
ejpam-5600	93	13	is	be	AUX
ejpam-5600	93	14	given	give	VERB
ejpam-5600	93	15	by	by	ADP
ejpam-5600	93	16	χ̂c(i	χ̂c(i	NOUN
ejpam-5600	93	17	)	)	PUNCT
ejpam-5600	93	18	=	=	SYM
ejpam-5600	94	1	2k−1∑	2k−1∑	NUM
ejpam-5600	94	2	j=0	j=0	PROPN
ejpam-5600	94	3	χc(j)(−1)⟨j	χc(j)(−1)⟨j	NOUN
ejpam-5600	94	4	,	,	PUNCT
ejpam-5600	94	5	i⟩	i⟩	PUNCT
ejpam-5600	94	6	=	=	SYM
ejpam-5600	94	7	2k−1∑	2k−1∑	NOUN
ejpam-5600	94	8	j=0	j=0	PROPN
ejpam-5600	94	9	hj(−1)⟨j	hj(−1)⟨j	NOUN
ejpam-5600	94	10	,	,	PUNCT
ejpam-5600	94	11	i⟩.	i⟩.	INTJ
ejpam-5600	94	12	we	we	PRON
ejpam-5600	94	13	will	will	AUX
ejpam-5600	94	14	also	also	ADV
ejpam-5600	94	15	need	need	VERB
ejpam-5600	94	16	the	the	DET
ejpam-5600	94	17	matrix	matrix	NOUN
ejpam-5600	94	18	mk	mk	NOUN
ejpam-5600	95	1	=	=	PUNCT
ejpam-5600	96	1			NOUN
ejpam-5600	96	2	0	0	NUM
ejpam-5600	96	3	0	0	NUM
ejpam-5600	96	4	.	.	PUNCT
ejpam-5600	96	5	.	.	PUNCT
ejpam-5600	97	1	.	.	PUNCT
ejpam-5600	97	2	0	0	NUM
ejpam-5600	98	1	...	...	PUNCT
ejpam-5600	98	2	mk	mk	NOUN
ejpam-5600	98	3	0	0	NUM
ejpam-5600	99	1			NUM
ejpam-5600	99	2	.	.	PUNCT
ejpam-5600	100	1	the	the	DET
ejpam-5600	100	2	walsh	walsh	PROPN
ejpam-5600	100	3	transform	transform	NOUN
ejpam-5600	100	4	of	of	ADP
ejpam-5600	100	5	the	the	DET
ejpam-5600	100	6	characteristic	characteristic	ADJ
ejpam-5600	100	7	vector	vector	NOUN
ejpam-5600	100	8	is	be	AUX
ejpam-5600	100	9	expressed	express	VERB
ejpam-5600	100	10	in	in	ADP
ejpam-5600	100	11	terms	term	NOUN
ejpam-5600	100	12	of	of	ADP
ejpam-5600	100	13	the	the	DET
ejpam-5600	100	14	hadamard	hadamard	ADJ
ejpam-5600	100	15	matrix	matrix	NOUN
ejpam-5600	100	16	obtained	obtain	VERB
ejpam-5600	100	17	by	by	ADP
ejpam-5600	100	18	sylvester	sylvester	ADJ
ejpam-5600	100	19	construction	construction	NOUN
ejpam-5600	100	20	.	.	PUNCT
ejpam-5600	101	1	these	these	DET
ejpam-5600	101	2	matrices	matrix	NOUN
ejpam-5600	101	3	are	be	AUX
ejpam-5600	101	4	constructed	construct	VERB
ejpam-5600	101	5	recursively	recursively	ADV
ejpam-5600	101	6	with	with	ADP
ejpam-5600	101	7	the	the	DET
ejpam-5600	101	8	help	help	NOUN
ejpam-5600	101	9	of	of	ADP
ejpam-5600	101	10	the	the	DET
ejpam-5600	101	11	hadamard	hadamard	ADJ
ejpam-5600	101	12	product	product	NOUN
ejpam-5600	101	13	as	as	SCONJ
ejpam-5600	101	14	follows	follow	VERB
ejpam-5600	101	15	:	:	PUNCT
ejpam-5600	101	16	h1	h1	X
ejpam-5600	101	17	=	=	PUNCT
ejpam-5600	101	18	[	[	PUNCT
ejpam-5600	101	19	1	1	NUM
ejpam-5600	101	20	1	1	NUM
ejpam-5600	101	21	1	1	NUM
ejpam-5600	101	22	−1	−1	NOUN
ejpam-5600	101	23	]	]	PUNCT
ejpam-5600	101	24	,	,	PUNCT
ejpam-5600	101	25	hi	hi	INTJ
ejpam-5600	101	26	=	=	PUNCT
ejpam-5600	101	27	h1	h1	PROPN
ejpam-5600	101	28	⊗hi−1	⊗hi−1	PROPN
ejpam-5600	101	29	.	.	PUNCT
ejpam-5600	102	1	if	if	SCONJ
ejpam-5600	102	2	we	we	PRON
ejpam-5600	102	3	index	index	VERB
ejpam-5600	102	4	the	the	DET
ejpam-5600	102	5	rows	row	NOUN
ejpam-5600	102	6	and	and	CCONJ
ejpam-5600	102	7	columns	column	NOUN
ejpam-5600	102	8	of	of	ADP
ejpam-5600	102	9	hk	hk	PROPN
ejpam-5600	102	10	by	by	ADP
ejpam-5600	102	11	0	0	NUM
ejpam-5600	102	12	≤	≤	NOUN
ejpam-5600	102	13	i	i	PRON
ejpam-5600	102	14	≤	≤	ADJ
ejpam-5600	102	15	2k	2k	NOUN
ejpam-5600	102	16	−	−	NUM
ejpam-5600	102	17	1	1	NUM
ejpam-5600	102	18	and	and	CCONJ
ejpam-5600	102	19	0	0	NUM
ejpam-5600	102	20	≤	≤	NUM
ejpam-5600	102	21	j	j	PROPN
ejpam-5600	102	22	≤	≤	NOUN
ejpam-5600	102	23	2k	2k	NOUN
ejpam-5600	102	24	−	−	NOUN
ejpam-5600	102	25	1	1	NUM
ejpam-5600	102	26	respectively	respectively	ADV
ejpam-5600	102	27	,	,	PUNCT
ejpam-5600	102	28	then	then	ADV
ejpam-5600	102	29	the	the	DET
ejpam-5600	102	30	(	(	PUNCT
ejpam-5600	102	31	i	i	PROPN
ejpam-5600	102	32	,	,	PUNCT
ejpam-5600	102	33	j	j	PROPN
ejpam-5600	102	34	)	)	PUNCT
ejpam-5600	102	35	entry	entry	NOUN
ejpam-5600	102	36	of	of	ADP
ejpam-5600	102	37	hk	hk	PROPN
ejpam-5600	102	38	is	be	AUX
ejpam-5600	102	39	given	give	VERB
ejpam-5600	102	40	by	by	ADP
ejpam-5600	102	41	[	[	X
ejpam-5600	102	42	5	5	NUM
ejpam-5600	102	43	,	,	PUNCT
ejpam-5600	102	44	page	page	NOUN
ejpam-5600	102	45	11	11	NUM
ejpam-5600	102	46	]	]	SYM
ejpam-5600	102	47	hk[i	hk[i	PROPN
ejpam-5600	102	48	,	,	PUNCT
ejpam-5600	102	49	j	j	NOUN
ejpam-5600	102	50	]	]	X
ejpam-5600	102	51	=	=	X
ejpam-5600	102	52	(	(	PUNCT
ejpam-5600	102	53	−1)⟨i	−1)⟨i	NOUN
ejpam-5600	102	54	,	,	PUNCT
ejpam-5600	102	55	j⟩.	j⟩.	ADJ
ejpam-5600	102	56	(	(	PUNCT
ejpam-5600	102	57	1	1	X
ejpam-5600	102	58	)	)	PUNCT
ejpam-5600	102	59	the	the	DET
ejpam-5600	102	60	lemma	lemma	PROPN
ejpam-5600	102	61	below	below	ADV
ejpam-5600	102	62	is	be	AUX
ejpam-5600	102	63	taken	take	VERB
ejpam-5600	102	64	from	from	ADP
ejpam-5600	102	65	[	[	X
ejpam-5600	102	66	2	2	NUM
ejpam-5600	102	67	]	]	PUNCT
ejpam-5600	102	68	,	,	PUNCT
ejpam-5600	102	69	we	we	PRON
ejpam-5600	102	70	will	will	AUX
ejpam-5600	102	71	prove	prove	VERB
ejpam-5600	102	72	it	it	PRON
ejpam-5600	102	73	for	for	ADP
ejpam-5600	102	74	completeness	completeness	NOUN
ejpam-5600	102	75	.	.	PUNCT
ejpam-5600	103	1	lemma	lemma	PROPN
ejpam-5600	103	2	2	2	NUM
ejpam-5600	103	3	.	.	PUNCT
ejpam-5600	104	1	[	[	X
ejpam-5600	104	2	2	2	NUM
ejpam-5600	104	3	,	,	PUNCT
ejpam-5600	104	4	page	page	NOUN
ejpam-5600	104	5	267	267	NUM
ejpam-5600	104	6	]	]	PUNCT
ejpam-5600	104	7	let	let	VERB
ejpam-5600	104	8	c	c	PRON
ejpam-5600	104	9	be	be	AUX
ejpam-5600	104	10	a	a	DET
ejpam-5600	104	11	binary	binary	NOUN
ejpam-5600	104	12	[	[	X
ejpam-5600	104	13	n	n	CCONJ
ejpam-5600	104	14	,	,	PUNCT
ejpam-5600	104	15	k	k	X
ejpam-5600	104	16	]	]	X
ejpam-5600	104	17	linear	linear	PROPN
ejpam-5600	104	18	code	code	PROPN
ejpam-5600	104	19	,	,	PUNCT
ejpam-5600	104	20	let	let	VERB
ejpam-5600	104	21	g	g	PRON
ejpam-5600	104	22	be	be	AUX
ejpam-5600	104	23	a	a	DET
ejpam-5600	104	24	generator	generator	NOUN
ejpam-5600	104	25	matrix	matrix	NOUN
ejpam-5600	104	26	of	of	ADP
ejpam-5600	104	27	c	c	NOUN
ejpam-5600	104	28	,	,	PUNCT
ejpam-5600	104	29	and	and	CCONJ
ejpam-5600	104	30	let	let	VERB
ejpam-5600	104	31	χc	χc	PRON
ejpam-5600	104	32	be	be	AUX
ejpam-5600	104	33	the	the	DET
ejpam-5600	104	34	characteristic	characteristic	ADJ
ejpam-5600	104	35	vector	vector	NOUN
ejpam-5600	104	36	of	of	ADP
ejpam-5600	104	37	c	c	PROPN
ejpam-5600	104	38	with	with	ADP
ejpam-5600	104	39	respect	respect	NOUN
ejpam-5600	104	40	to	to	ADP
ejpam-5600	104	41	g.	g.	PROPN
ejpam-5600	104	42	then	then	ADV
ejpam-5600	104	43	we	we	PRON
ejpam-5600	104	44	have	have	VERB
ejpam-5600	104	45	hkχc	hkχc	NOUN
ejpam-5600	104	46	=	=	SYM
ejpam-5600	104	47	(	(	PUNCT
ejpam-5600	105	1	j	j	PROPN
ejpam-5600	105	2	−	−	NOUN
ejpam-5600	105	3	2mk)χc	2mk)χc	NUM
ejpam-5600	106	1	=	=	SYM
ejpam-5600	106	2			VERB
ejpam-5600	106	3	n	n	PROPN
ejpam-5600	106	4	n−	n−	PROPN
ejpam-5600	106	5	2w1	2w1	NUM
ejpam-5600	106	6	n−	n−	NOUN
ejpam-5600	106	7	2w2	2w2	NUM
ejpam-5600	106	8	...	...	PUNCT
ejpam-5600	107	1	n−	n−	NOUN
ejpam-5600	107	2	2w2k−1	2w2k−1	NUM
ejpam-5600	107	3			NOUN
ejpam-5600	107	4	=	=	PUNCT
ejpam-5600	107	5	χ̂c	χ̂c	ADP
ejpam-5600	107	6	,	,	PUNCT
ejpam-5600	107	7	where	where	SCONJ
ejpam-5600	107	8	j	j	PROPN
ejpam-5600	107	9	is	be	AUX
ejpam-5600	107	10	the	the	DET
ejpam-5600	107	11	all	all	DET
ejpam-5600	107	12	one	one	NUM
ejpam-5600	107	13	matrix	matrix	NOUN
ejpam-5600	107	14	,	,	PUNCT
ejpam-5600	107	15	{	{	PUNCT
ejpam-5600	107	16	w1	w1	NOUN
ejpam-5600	107	17	,	,	PUNCT
ejpam-5600	107	18	w2	w2	NOUN
ejpam-5600	107	19	,	,	PUNCT
ejpam-5600	107	20	.	.	PUNCT
ejpam-5600	107	21	.	.	PUNCT
ejpam-5600	107	22	.	.	PUNCT
ejpam-5600	108	1	,	,	PUNCT
ejpam-5600	108	2	w2k−1	w2k−1	PROPN
ejpam-5600	108	3	}	}	PUNCT
ejpam-5600	108	4	is	be	AUX
ejpam-5600	108	5	the	the	DET
ejpam-5600	108	6	set	set	NOUN
ejpam-5600	108	7	of	of	ADP
ejpam-5600	108	8	weights	weight	NOUN
ejpam-5600	108	9	of	of	ADP
ejpam-5600	108	10	all	all	DET
ejpam-5600	108	11	nonzero	nonzero	ADJ
ejpam-5600	108	12	words	word	NOUN
ejpam-5600	108	13	in	in	ADP
ejpam-5600	108	14	c.	c.	PROPN
ejpam-5600	108	15	i̇brahim	i̇brahim	PUNCT
ejpam-5600	109	1	özen	özen	PROPN
ejpam-5600	109	2	/	/	SYM
ejpam-5600	109	3	eur	eur	PROPN
ejpam-5600	109	4	.	.	PUNCT
ejpam-5600	110	1	j.	j.	PROPN
ejpam-5600	110	2	pure	pure	PROPN
ejpam-5600	110	3	appl	appl	PROPN
ejpam-5600	110	4	.	.	PROPN
ejpam-5600	110	5	math	math	PROPN
ejpam-5600	110	6	,	,	PUNCT
ejpam-5600	110	7	17	17	NUM
ejpam-5600	110	8	(	(	PUNCT
ejpam-5600	110	9	4	4	NUM
ejpam-5600	110	10	)	)	PUNCT
ejpam-5600	110	11	(	(	PUNCT
ejpam-5600	110	12	2024	2024	NUM
ejpam-5600	110	13	)	)	PUNCT
ejpam-5600	110	14	,	,	PUNCT
ejpam-5600	110	15	4225	4225	NUM
ejpam-5600	110	16	-	-	SYM
ejpam-5600	110	17	4237	4237	NUM
ejpam-5600	110	18	4229	4229	NUM
ejpam-5600	110	19	proof	proof	NOUN
ejpam-5600	110	20	.	.	PUNCT
ejpam-5600	111	1	we	we	PRON
ejpam-5600	111	2	will	will	AUX
ejpam-5600	111	3	index	index	VERB
ejpam-5600	111	4	all	all	DET
ejpam-5600	111	5	entries	entry	NOUN
ejpam-5600	111	6	of	of	ADP
ejpam-5600	111	7	the	the	DET
ejpam-5600	111	8	matrices	matrix	NOUN
ejpam-5600	111	9	and	and	CCONJ
ejpam-5600	111	10	vectors	vector	NOUN
ejpam-5600	111	11	starting	start	VERB
ejpam-5600	111	12	from	from	ADP
ejpam-5600	111	13	0	0	NUM
ejpam-5600	111	14	.	.	PUNCT
ejpam-5600	112	1	all	all	DET
ejpam-5600	112	2	assertions	assertion	NOUN
ejpam-5600	112	3	for	for	ADP
ejpam-5600	112	4	the	the	DET
ejpam-5600	112	5	terms	term	NOUN
ejpam-5600	112	6	indexed	index	VERB
ejpam-5600	112	7	by	by	ADP
ejpam-5600	112	8	zero	zero	NUM
ejpam-5600	112	9	are	be	AUX
ejpam-5600	112	10	trivial	trivial	ADJ
ejpam-5600	112	11	.	.	PUNCT
ejpam-5600	113	1	let	let	VERB
ejpam-5600	113	2	i	i	PRON
ejpam-5600	113	3	be	be	AUX
ejpam-5600	113	4	an	an	DET
ejpam-5600	113	5	integer	integer	NOUN
ejpam-5600	113	6	with	with	ADP
ejpam-5600	113	7	1	1	NUM
ejpam-5600	113	8	≤	≤	NUM
ejpam-5600	113	9	i	i	PRON
ejpam-5600	113	10	≤	≤	ADJ
ejpam-5600	113	11	2k−1	2k−1	NUM
ejpam-5600	113	12	.	.	PUNCT
ejpam-5600	114	1	then	then	ADV
ejpam-5600	114	2	by	by	ADP
ejpam-5600	114	3	(	(	PUNCT
ejpam-5600	114	4	1	1	X
ejpam-5600	114	5	)	)	PUNCT
ejpam-5600	114	6	the	the	DET
ejpam-5600	114	7	term	term	NOUN
ejpam-5600	114	8	indexed	index	VERB
ejpam-5600	114	9	by	by	ADP
ejpam-5600	114	10	i	i	PRON
ejpam-5600	114	11	in	in	ADP
ejpam-5600	114	12	the	the	DET
ejpam-5600	114	13	product	product	NOUN
ejpam-5600	114	14	hkχc	hkχc	NOUN
ejpam-5600	114	15	equals	equal	VERB
ejpam-5600	114	16	2k−1∑	2k−1∑	NUM
ejpam-5600	114	17	j=0	j=0	PROPN
ejpam-5600	114	18	(	(	PUNCT
ejpam-5600	114	19	−1)⟨i	−1)⟨i	NOUN
ejpam-5600	114	20	,	,	PUNCT
ejpam-5600	114	21	j⟩χc(j	j⟩χc(j	NOUN
ejpam-5600	114	22	)	)	PUNCT
ejpam-5600	114	23	=	=	SYM
ejpam-5600	114	24	2k−1∑	2k−1∑	NUM
ejpam-5600	114	25	j=0	j=0	PROPN
ejpam-5600	114	26	(	(	PUNCT
ejpam-5600	114	27	−1)⟨i	−1)⟨i	NOUN
ejpam-5600	114	28	,	,	PUNCT
ejpam-5600	114	29	j⟩hj	j⟩hj	NOUN
ejpam-5600	114	30	,	,	PUNCT
ejpam-5600	114	31	(	(	PUNCT
ejpam-5600	114	32	2	2	X
ejpam-5600	114	33	)	)	PUNCT
ejpam-5600	114	34	with	with	ADP
ejpam-5600	114	35	i	i	PRON
ejpam-5600	114	36	and	and	CCONJ
ejpam-5600	114	37	j	j	PROPN
ejpam-5600	114	38	being	be	AUX
ejpam-5600	114	39	the	the	DET
ejpam-5600	114	40	binary	binary	ADJ
ejpam-5600	114	41	representations	representation	NOUN
ejpam-5600	114	42	of	of	ADP
ejpam-5600	114	43	i	i	PRON
ejpam-5600	114	44	and	and	CCONJ
ejpam-5600	114	45	j	j	PROPN
ejpam-5600	114	46	respectively	respectively	ADV
ejpam-5600	114	47	.	.	PUNCT
ejpam-5600	115	1	the	the	DET
ejpam-5600	115	2	same	same	ADJ
ejpam-5600	115	3	term	term	NOUN
ejpam-5600	115	4	in	in	ADP
ejpam-5600	115	5	the	the	DET
ejpam-5600	115	6	product	product	NOUN
ejpam-5600	115	7	(	(	PUNCT
ejpam-5600	115	8	j	j	PROPN
ejpam-5600	115	9	−	−	NOUN
ejpam-5600	116	1	2mk)χc	2mk)χc	NUM
ejpam-5600	116	2	is	be	AUX
ejpam-5600	116	3	∑2k−1	∑2k−1	PROPN
ejpam-5600	116	4	j=0	j=0	PROPN
ejpam-5600	116	5	(	(	PUNCT
ejpam-5600	116	6	1−	1−	NUM
ejpam-5600	116	7	2⟨si	2⟨si	NUM
ejpam-5600	116	8	,	,	PUNCT
ejpam-5600	116	9	sj⟩)hj	sj⟩)hj	NOUN
ejpam-5600	116	10	,	,	PUNCT
ejpam-5600	116	11	where	where	SCONJ
ejpam-5600	116	12	sl	sl	PRON
ejpam-5600	116	13	’s	’s	X
ejpam-5600	116	14	are	be	AUX
ejpam-5600	116	15	the	the	DET
ejpam-5600	116	16	column	column	NOUN
ejpam-5600	116	17	vectors	vector	NOUN
ejpam-5600	116	18	of	of	ADP
ejpam-5600	116	19	gk	gk	PROPN
ejpam-5600	116	20	.	.	PROPN
ejpam-5600	117	1	one	one	PRON
ejpam-5600	117	2	can	can	AUX
ejpam-5600	117	3	easily	easily	ADV
ejpam-5600	117	4	confirm	confirm	VERB
ejpam-5600	117	5	that	that	SCONJ
ejpam-5600	117	6	we	we	PRON
ejpam-5600	117	7	have	have	VERB
ejpam-5600	117	8	1−	1−	NUM
ejpam-5600	117	9	2⟨si	2⟨si	NUM
ejpam-5600	117	10	,	,	PUNCT
ejpam-5600	117	11	sj⟩	sj⟩	PUNCT
ejpam-5600	117	12	=	=	SYM
ejpam-5600	117	13	1−	1−	NUM
ejpam-5600	117	14	2⟨i	2⟨i	NUM
ejpam-5600	117	15	,	,	PUNCT
ejpam-5600	117	16	j⟩	j⟩	NOUN
ejpam-5600	117	17	=	=	SYM
ejpam-5600	117	18	(	(	PUNCT
ejpam-5600	117	19	−1)⟨i	−1)⟨i	NOUN
ejpam-5600	117	20	,	,	PUNCT
ejpam-5600	117	21	j⟩.	j⟩.	ADJ
ejpam-5600	117	22	so	so	SCONJ
ejpam-5600	117	23	we	we	PRON
ejpam-5600	117	24	have	have	VERB
ejpam-5600	117	25	∑2k−1	∑2k−1	NUM
ejpam-5600	117	26	j=0	j=0	PROPN
ejpam-5600	117	27	(	(	PUNCT
ejpam-5600	117	28	1−	1−	NUM
ejpam-5600	117	29	2⟨si	2⟨si	NUM
ejpam-5600	117	30	,	,	PUNCT
ejpam-5600	117	31	sj⟩)hj	sj⟩)hj	X
ejpam-5600	117	32	=	=	SYM
ejpam-5600	117	33	∑2k−1	∑2k−1	PROPN
ejpam-5600	117	34	j=0	j=0	PROPN
ejpam-5600	117	35	(	(	PUNCT
ejpam-5600	117	36	−1)⟨i	−1)⟨i	NOUN
ejpam-5600	117	37	,	,	PUNCT
ejpam-5600	117	38	j⟩hj	j⟩hj	NOUN
ejpam-5600	117	39	and	and	CCONJ
ejpam-5600	117	40	by	by	ADP
ejpam-5600	117	41	(	(	PUNCT
ejpam-5600	117	42	2	2	NUM
ejpam-5600	117	43	)	)	PUNCT
ejpam-5600	117	44	,	,	PUNCT
ejpam-5600	117	45	the	the	DET
ejpam-5600	117	46	first	first	ADJ
ejpam-5600	117	47	equality	equality	NOUN
ejpam-5600	117	48	of	of	ADP
ejpam-5600	117	49	the	the	DET
ejpam-5600	117	50	lemma	lemma	PROPN
ejpam-5600	117	51	follows	follow	VERB
ejpam-5600	117	52	.	.	PUNCT
ejpam-5600	118	1	the	the	DET
ejpam-5600	118	2	second	second	ADJ
ejpam-5600	118	3	equality	equality	NOUN
ejpam-5600	118	4	follows	follow	VERB
ejpam-5600	118	5	from	from	ADP
ejpam-5600	118	6	lemma	lemma	PROPN
ejpam-5600	118	7	1	1	NUM
ejpam-5600	118	8	.	.	PUNCT
ejpam-5600	119	1	if	if	SCONJ
ejpam-5600	119	2	we	we	PRON
ejpam-5600	119	3	compare	compare	VERB
ejpam-5600	119	4	the	the	DET
ejpam-5600	119	5	ith	ith	PROPN
ejpam-5600	119	6	coordinates	coordinate	NOUN
ejpam-5600	119	7	of	of	ADP
ejpam-5600	119	8	hkχc	hkχc	PROPN
ejpam-5600	119	9	and	and	CCONJ
ejpam-5600	119	10	χ̂c	χ̂c	ADV
ejpam-5600	119	11	we	we	PRON
ejpam-5600	119	12	obtain	obtain	VERB
ejpam-5600	119	13	the	the	DET
ejpam-5600	119	14	last	last	ADJ
ejpam-5600	119	15	equality	equality	NOUN
ejpam-5600	119	16	of	of	ADP
ejpam-5600	119	17	the	the	DET
ejpam-5600	119	18	lemma	lemma	PROPN
ejpam-5600	119	19	(	(	PUNCT
ejpam-5600	119	20	hkχc)(i	hkχc)(i	PROPN
ejpam-5600	119	21	)	)	PUNCT
ejpam-5600	120	1	=	=	SYM
ejpam-5600	120	2	2k−1∑	2k−1∑	NUM
ejpam-5600	120	3	j=0	j=0	PROPN
ejpam-5600	120	4	hj(−1)⟨i	hj(−1)⟨i	NOUN
ejpam-5600	120	5	,	,	PUNCT
ejpam-5600	120	6	j⟩	j⟩	NOUN
ejpam-5600	120	7	=	=	PUNCT
ejpam-5600	120	8	χ̂c(i	χ̂c(i	NUM
ejpam-5600	120	9	)	)	PUNCT
ejpam-5600	120	10	.	.	PUNCT
ejpam-5600	121	1	in	in	ADP
ejpam-5600	121	2	the	the	DET
ejpam-5600	121	3	next	next	ADJ
ejpam-5600	121	4	section	section	NOUN
ejpam-5600	121	5	we	we	PRON
ejpam-5600	121	6	will	will	AUX
ejpam-5600	121	7	make	make	VERB
ejpam-5600	121	8	use	use	NOUN
ejpam-5600	121	9	of	of	ADP
ejpam-5600	121	10	the	the	DET
ejpam-5600	121	11	identity	identity	NOUN
ejpam-5600	121	12	in	in	ADP
ejpam-5600	121	13	the	the	DET
ejpam-5600	121	14	following	follow	VERB
ejpam-5600	121	15	lemma	lemma	PROPN
ejpam-5600	121	16	.	.	PUNCT
ejpam-5600	122	1	the	the	DET
ejpam-5600	122	2	assertion	assertion	NOUN
ejpam-5600	122	3	of	of	ADP
ejpam-5600	122	4	the	the	DET
ejpam-5600	122	5	first	first	ADJ
ejpam-5600	122	6	line	line	NOUN
ejpam-5600	122	7	is	be	AUX
ejpam-5600	122	8	trivial	trivial	ADJ
ejpam-5600	122	9	and	and	CCONJ
ejpam-5600	122	10	the	the	DET
ejpam-5600	122	11	second	second	ADJ
ejpam-5600	122	12	line	line	NOUN
ejpam-5600	122	13	is	be	AUX
ejpam-5600	122	14	an	an	DET
ejpam-5600	122	15	easy	easy	ADJ
ejpam-5600	122	16	consequence	consequence	NOUN
ejpam-5600	122	17	of	of	ADP
ejpam-5600	122	18	[	[	X
ejpam-5600	122	19	3	3	NUM
ejpam-5600	122	20	,	,	PUNCT
ejpam-5600	122	21	lemma	lemma	PROPN
ejpam-5600	122	22	3	3	NUM
ejpam-5600	122	23	,	,	PUNCT
ejpam-5600	122	24	page	page	NOUN
ejpam-5600	122	25	58	58	NUM
ejpam-5600	122	26	]	]	PUNCT
ejpam-5600	122	27	.	.	PUNCT
ejpam-5600	123	1	lemma	lemma	PROPN
ejpam-5600	123	2	3	3	X
ejpam-5600	123	3	.	.	X
ejpam-5600	124	1	for	for	ADP
ejpam-5600	124	2	any	any	DET
ejpam-5600	124	3	integer	integer	NOUN
ejpam-5600	124	4	0	0	NUM
ejpam-5600	124	5	≤	≤	NUM
ejpam-5600	124	6	i	i	PRON
ejpam-5600	124	7	≤	≤	ADJ
ejpam-5600	124	8	2k	2k	NOUN
ejpam-5600	124	9	−	−	NOUN
ejpam-5600	124	10	1	1	NUM
ejpam-5600	124	11	,	,	PUNCT
ejpam-5600	124	12	we	we	PRON
ejpam-5600	124	13	have	have	VERB
ejpam-5600	124	14	2k−1∑	2k−1∑	NUM
ejpam-5600	124	15	j=0	j=0	PROPN
ejpam-5600	124	16	(	(	PUNCT
ejpam-5600	124	17	−1)⟨j	−1)⟨j	PROPN
ejpam-5600	124	18	,	,	PUNCT
ejpam-5600	124	19	i⟩	i⟩	PUNCT
ejpam-5600	124	20	=	=	PUNCT
ejpam-5600	124	21	{	{	PUNCT
ejpam-5600	124	22	2k	2k	NUM
ejpam-5600	124	23	,	,	PUNCT
ejpam-5600	124	24	for	for	ADP
ejpam-5600	124	25	i	i	PROPN
ejpam-5600	124	26	=	=	SYM
ejpam-5600	124	27	0	0	NUM
ejpam-5600	124	28	,	,	PUNCT
ejpam-5600	124	29	0	0	NUM
ejpam-5600	124	30	,	,	PUNCT
ejpam-5600	124	31	for	for	ADP
ejpam-5600	124	32	i	i	PRON
ejpam-5600	124	33	̸=	̸=	PROPN
ejpam-5600	124	34	0	0	NUM
ejpam-5600	124	35	.	.	PUNCT
ejpam-5600	125	1	3	3	NUM
ejpam-5600	125	2	.	.	NUM
ejpam-5600	125	3	first	first	ADJ
ejpam-5600	125	4	and	and	CCONJ
ejpam-5600	125	5	second	second	ADJ
ejpam-5600	125	6	moments	moment	NOUN
ejpam-5600	125	7	of	of	ADP
ejpam-5600	125	8	the	the	DET
ejpam-5600	125	9	codeword	codeword	NOUN
ejpam-5600	125	10	weights	weight	VERB
ejpam-5600	125	11	a	a	DET
ejpam-5600	125	12	random	random	ADJ
ejpam-5600	125	13	binary	binary	ADJ
ejpam-5600	125	14	linear	linear	PROPN
ejpam-5600	125	15	code	code	NOUN
ejpam-5600	125	16	is	be	AUX
ejpam-5600	125	17	the	the	DET
ejpam-5600	125	18	row	row	NOUN
ejpam-5600	125	19	-	-	PUNCT
ejpam-5600	125	20	space	space	NOUN
ejpam-5600	125	21	of	of	ADP
ejpam-5600	125	22	a	a	DET
ejpam-5600	125	23	random	random	ADJ
ejpam-5600	125	24	k×n	k×n	PROPN
ejpam-5600	125	25	matrix	matrix	NOUN
ejpam-5600	125	26	,	,	PUNCT
ejpam-5600	125	27	whose	whose	DET
ejpam-5600	125	28	entries	entry	NOUN
ejpam-5600	125	29	are	be	AUX
ejpam-5600	125	30	identically	identically	ADV
ejpam-5600	125	31	and	and	CCONJ
ejpam-5600	125	32	independently	independently	ADV
ejpam-5600	125	33	distributed	distribute	VERB
ejpam-5600	125	34	in	in	ADP
ejpam-5600	125	35	f2	f2	PROPN
ejpam-5600	125	36	.	.	PUNCT
ejpam-5600	126	1	a	a	DET
ejpam-5600	126	2	well	well	ADV
ejpam-5600	126	3	known	know	VERB
ejpam-5600	126	4	property	property	NOUN
ejpam-5600	126	5	of	of	ADP
ejpam-5600	126	6	a	a	DET
ejpam-5600	126	7	random	random	ADJ
ejpam-5600	126	8	k×n	k×n	PROPN
ejpam-5600	126	9	matrix	matrix	NOUN
ejpam-5600	126	10	over	over	ADP
ejpam-5600	126	11	a	a	DET
ejpam-5600	126	12	finite	finite	ADJ
ejpam-5600	126	13	field	field	NOUN
ejpam-5600	126	14	is	be	AUX
ejpam-5600	126	15	that	that	SCONJ
ejpam-5600	126	16	when	when	SCONJ
ejpam-5600	126	17	k	k	X
ejpam-5600	126	18	/	/	SYM
ejpam-5600	126	19	n	n	CCONJ
ejpam-5600	126	20	<	<	X
ejpam-5600	126	21	1	1	NUM
ejpam-5600	126	22	,	,	PUNCT
ejpam-5600	126	23	the	the	DET
ejpam-5600	126	24	matrix	matrix	NOUN
ejpam-5600	126	25	has	have	VERB
ejpam-5600	126	26	rank	rank	NOUN
ejpam-5600	126	27	k	k	PROPN
ejpam-5600	126	28	with	with	ADP
ejpam-5600	126	29	probability	probability	NOUN
ejpam-5600	126	30	tending	tend	VERB
ejpam-5600	126	31	to	to	ADP
ejpam-5600	126	32	1	1	NUM
ejpam-5600	126	33	,	,	PUNCT
ejpam-5600	126	34	as	as	SCONJ
ejpam-5600	126	35	n	n	PRON
ejpam-5600	126	36	tends	tend	VERB
ejpam-5600	126	37	to	to	PART
ejpam-5600	126	38	infinity	infinity	VERB
ejpam-5600	126	39	.	.	PUNCT
ejpam-5600	127	1	so	so	ADV
ejpam-5600	127	2	we	we	PRON
ejpam-5600	127	3	will	will	AUX
ejpam-5600	127	4	assume	assume	VERB
ejpam-5600	127	5	that	that	SCONJ
ejpam-5600	127	6	a	a	DET
ejpam-5600	127	7	random	random	ADJ
ejpam-5600	127	8	binary	binary	NOUN
ejpam-5600	127	9	k	k	PROPN
ejpam-5600	127	10	×	×	PROPN
ejpam-5600	127	11	n	n	NOUN
ejpam-5600	127	12	matrix	matrix	NOUN
ejpam-5600	127	13	whose	whose	DET
ejpam-5600	127	14	terms	term	NOUN
ejpam-5600	127	15	are	be	AUX
ejpam-5600	127	16	distributed	distribute	VERB
ejpam-5600	127	17	identically	identically	ADV
ejpam-5600	127	18	and	and	CCONJ
ejpam-5600	127	19	independently	independently	ADV
ejpam-5600	127	20	in	in	ADP
ejpam-5600	127	21	f2	f2	PROPN
ejpam-5600	127	22	has	have	VERB
ejpam-5600	127	23	rank	rank	PROPN
ejpam-5600	127	24	k	k	PROPN
ejpam-5600	127	25	and	and	CCONJ
ejpam-5600	127	26	its	its	PRON
ejpam-5600	127	27	row	row	NOUN
ejpam-5600	127	28	space	space	NOUN
ejpam-5600	127	29	c	c	NOUN
ejpam-5600	127	30	is	be	AUX
ejpam-5600	127	31	an	an	DET
ejpam-5600	127	32	[	[	NOUN
ejpam-5600	127	33	n	n	CCONJ
ejpam-5600	127	34	,	,	PUNCT
ejpam-5600	127	35	k	k	X
ejpam-5600	127	36	]	]	X
ejpam-5600	127	37	linear	linear	PROPN
ejpam-5600	127	38	code	code	PROPN
ejpam-5600	127	39	.	.	PUNCT
ejpam-5600	128	1	the	the	DET
ejpam-5600	128	2	words	word	NOUN
ejpam-5600	128	3	of	of	ADP
ejpam-5600	128	4	such	such	DET
ejpam-5600	128	5	a	a	DET
ejpam-5600	128	6	code	code	NOUN
ejpam-5600	128	7	will	will	AUX
ejpam-5600	128	8	be	be	AUX
ejpam-5600	128	9	denoted	denote	VERB
ejpam-5600	128	10	by	by	ADP
ejpam-5600	128	11	c	c	NOUN
ejpam-5600	128	12	=	=	SYM
ejpam-5600	128	13	{	{	PUNCT
ejpam-5600	128	14	c0	c0	NOUN
ejpam-5600	128	15	=	=	SYM
ejpam-5600	128	16	0	0	PROPN
ejpam-5600	128	17	,	,	PUNCT
ejpam-5600	128	18	c1	c1	NOUN
ejpam-5600	128	19	,	,	PUNCT
ejpam-5600	128	20	c2	c2	PROPN
ejpam-5600	128	21	,	,	PUNCT
ejpam-5600	128	22	.	.	PUNCT
ejpam-5600	128	23	.	.	PUNCT
ejpam-5600	129	1	.	.	PUNCT
ejpam-5600	130	1	,	,	PUNCT
ejpam-5600	130	2	c2k−1	c2k−1	PROPN
ejpam-5600	130	3	}	}	PUNCT
ejpam-5600	130	4	,	,	PUNCT
ejpam-5600	130	5	with	with	ADP
ejpam-5600	130	6	the	the	DET
ejpam-5600	130	7	same	same	ADJ
ejpam-5600	130	8	relation	relation	NOUN
ejpam-5600	130	9	to	to	ADP
ejpam-5600	130	10	gt	gt	PROPN
ejpam-5600	130	11	kg	kg	PROPN
ejpam-5600	130	12	as	as	ADP
ejpam-5600	130	13	above	above	ADV
ejpam-5600	130	14	.	.	PUNCT
ejpam-5600	131	1	the	the	DET
ejpam-5600	131	2	weights	weight	NOUN
ejpam-5600	131	3	of	of	ADP
ejpam-5600	131	4	the	the	DET
ejpam-5600	131	5	nonzero	nonzero	NOUN
ejpam-5600	131	6	words	word	NOUN
ejpam-5600	131	7	will	will	AUX
ejpam-5600	131	8	be	be	AUX
ejpam-5600	131	9	denoted	denote	VERB
ejpam-5600	131	10	by	by	ADP
ejpam-5600	131	11	{	{	PUNCT
ejpam-5600	131	12	w1	w1	NOUN
ejpam-5600	131	13	,	,	PUNCT
ejpam-5600	131	14	w2	w2	NOUN
ejpam-5600	131	15	,	,	PUNCT
ejpam-5600	131	16	.	.	PUNCT
ejpam-5600	131	17	.	.	PUNCT
ejpam-5600	132	1	.	.	PUNCT
ejpam-5600	133	1	,	,	PUNCT
ejpam-5600	133	2	w2k−1	w2k−1	PROPN
ejpam-5600	133	3	}	}	PUNCT
ejpam-5600	133	4	respectively	respectively	ADV
ejpam-5600	133	5	.	.	PUNCT
ejpam-5600	134	1	another	another	DET
ejpam-5600	134	2	fact	fact	NOUN
ejpam-5600	134	3	about	about	ADP
ejpam-5600	134	4	this	this	DET
ejpam-5600	134	5	ensemble	ensemble	NOUN
ejpam-5600	134	6	of	of	ADP
ejpam-5600	134	7	matrices	matrix	NOUN
ejpam-5600	134	8	is	be	AUX
ejpam-5600	134	9	that	that	SCONJ
ejpam-5600	134	10	,	,	PUNCT
ejpam-5600	134	11	the	the	DET
ejpam-5600	134	12	probability	probability	NOUN
ejpam-5600	134	13	that	that	SCONJ
ejpam-5600	134	14	a	a	DET
ejpam-5600	134	15	random	random	ADJ
ejpam-5600	134	16	k	k	PROPN
ejpam-5600	134	17	×	×	NOUN
ejpam-5600	134	18	n	n	PRON
ejpam-5600	134	19	matrix	matrix	NOUN
ejpam-5600	134	20	has	have	AUX
ejpam-5600	134	21	zero	zero	NUM
ejpam-5600	134	22	columns	column	NOUN
ejpam-5600	134	23	tends	tend	VERB
ejpam-5600	134	24	to	to	ADP
ejpam-5600	134	25	0	0	NUM
ejpam-5600	134	26	as	as	SCONJ
ejpam-5600	134	27	n	n	PRON
ejpam-5600	134	28	tends	tend	VERB
ejpam-5600	134	29	to	to	PART
ejpam-5600	134	30	infinity	infinity	VERB
ejpam-5600	134	31	with	with	ADP
ejpam-5600	134	32	k	k	PROPN
ejpam-5600	134	33	/	/	SYM
ejpam-5600	134	34	n	n	PROPN
ejpam-5600	134	35	>	>	NOUN
ejpam-5600	134	36	0	0	X
ejpam-5600	134	37	.	.	PUNCT
ejpam-5600	135	1	this	this	PRON
ejpam-5600	135	2	can	can	AUX
ejpam-5600	135	3	easily	easily	ADV
ejpam-5600	135	4	be	be	AUX
ejpam-5600	135	5	observed	observe	VERB
ejpam-5600	135	6	by	by	ADP
ejpam-5600	135	7	lim	lim	PROPN
ejpam-5600	135	8	n→∞	n→∞	X
ejpam-5600	135	9	1−	1−	NUM
ejpam-5600	135	10	(	(	PUNCT
ejpam-5600	135	11	2k	2k	NOUN
ejpam-5600	135	12	−	−	PROPN
ejpam-5600	135	13	1)n	1)n	X
ejpam-5600	135	14	2kn	2kn	ADJ
ejpam-5600	135	15	=	=	SYM
ejpam-5600	135	16	0	0	NUM
ejpam-5600	135	17	,	,	PUNCT
ejpam-5600	135	18	i̇brahim	i̇brahim	PRON
ejpam-5600	135	19	özen	özen	PROPN
ejpam-5600	135	20	/	/	SYM
ejpam-5600	135	21	eur	eur	PROPN
ejpam-5600	135	22	.	.	PUNCT
ejpam-5600	136	1	j.	j.	PROPN
ejpam-5600	136	2	pure	pure	PROPN
ejpam-5600	136	3	appl	appl	PROPN
ejpam-5600	136	4	.	.	PROPN
ejpam-5600	136	5	math	math	PROPN
ejpam-5600	136	6	,	,	PUNCT
ejpam-5600	136	7	17	17	NUM
ejpam-5600	136	8	(	(	PUNCT
ejpam-5600	136	9	4	4	NUM
ejpam-5600	136	10	)	)	PUNCT
ejpam-5600	136	11	(	(	PUNCT
ejpam-5600	136	12	2024	2024	NUM
ejpam-5600	136	13	)	)	PUNCT
ejpam-5600	136	14	,	,	PUNCT
ejpam-5600	136	15	4225	4225	NUM
ejpam-5600	136	16	-	-	SYM
ejpam-5600	136	17	4237	4237	NUM
ejpam-5600	136	18	4230	4230	NUM
ejpam-5600	136	19	with	with	ADP
ejpam-5600	136	20	the	the	DET
ejpam-5600	136	21	condition	condition	NOUN
ejpam-5600	136	22	that	that	SCONJ
ejpam-5600	136	23	r	r	NOUN
ejpam-5600	136	24	=	=	SYM
ejpam-5600	136	25	k	k	NOUN
ejpam-5600	136	26	/	/	SYM
ejpam-5600	136	27	n	n	CCONJ
ejpam-5600	136	28	̸=	̸=	PROPN
ejpam-5600	136	29	0	0	NUM
ejpam-5600	136	30	.	.	PUNCT
ejpam-5600	137	1	by	by	ADP
ejpam-5600	137	2	lemma	lemma	PROPN
ejpam-5600	137	3	2	2	NUM
ejpam-5600	137	4	,	,	PUNCT
ejpam-5600	137	5	the	the	DET
ejpam-5600	137	6	expectations	expectation	NOUN
ejpam-5600	137	7	of	of	ADP
ejpam-5600	137	8	weights	weight	NOUN
ejpam-5600	137	9	of	of	ADP
ejpam-5600	137	10	the	the	DET
ejpam-5600	137	11	nonzero	nonzero	PROPN
ejpam-5600	137	12	codewords	codeword	NOUN
ejpam-5600	137	13	in	in	ADP
ejpam-5600	137	14	a	a	DET
ejpam-5600	137	15	random	random	ADJ
ejpam-5600	137	16	code	code	NOUN
ejpam-5600	137	17	can	can	AUX
ejpam-5600	137	18	be	be	AUX
ejpam-5600	137	19	calculated	calculate	VERB
ejpam-5600	137	20	by	by	ADP
ejpam-5600	137	21	e(n−	e(n−	PROPN
ejpam-5600	137	22	2wi	2wi	NOUN
ejpam-5600	137	23	)	)	PUNCT
ejpam-5600	138	1	=	=	SYM
ejpam-5600	138	2	e	e	X
ejpam-5600	138	3	(	(	PUNCT
ejpam-5600	138	4	χ̂c(i	χ̂c(i	NUM
ejpam-5600	138	5	)	)	PUNCT
ejpam-5600	138	6	)	)	PUNCT
ejpam-5600	139	1	=	=	SYM
ejpam-5600	139	2	2k−1∑	2k−1∑	NUM
ejpam-5600	139	3	j=0	j=0	PROPN
ejpam-5600	139	4	e(hj)(−1)⟨j	e(hj)(−1)⟨j	NOUN
ejpam-5600	139	5	,	,	PUNCT
ejpam-5600	139	6	i⟩.	i⟩.	VERB
ejpam-5600	139	7	for	for	ADP
ejpam-5600	139	8	a	a	DET
ejpam-5600	139	9	positive	positive	ADJ
ejpam-5600	139	10	integer	integer	NOUN
ejpam-5600	139	11	n	n	CCONJ
ejpam-5600	139	12	,	,	PUNCT
ejpam-5600	139	13	we	we	PRON
ejpam-5600	139	14	denote	denote	VERB
ejpam-5600	139	15	by	by	ADP
ejpam-5600	139	16	[	[	X
ejpam-5600	139	17	n	n	CCONJ
ejpam-5600	139	18	]	]	PUNCT
ejpam-5600	139	19	the	the	DET
ejpam-5600	139	20	set	set	NOUN
ejpam-5600	139	21	{	{	PUNCT
ejpam-5600	139	22	0	0	NUM
ejpam-5600	139	23	,	,	PUNCT
ejpam-5600	139	24	1	1	NUM
ejpam-5600	139	25	,	,	PUNCT
ejpam-5600	139	26	.	.	PUNCT
ejpam-5600	139	27	.	.	PUNCT
ejpam-5600	140	1	.	.	PUNCT
ejpam-5600	141	1	,	,	PUNCT
ejpam-5600	142	1	n	n	CCONJ
ejpam-5600	142	2	−	−	PROPN
ejpam-5600	142	3	1	1	NUM
ejpam-5600	142	4	}	}	PUNCT
ejpam-5600	142	5	.	.	PUNCT
ejpam-5600	143	1	we	we	PRON
ejpam-5600	143	2	can	can	AUX
ejpam-5600	143	3	calculate	calculate	VERB
ejpam-5600	143	4	the	the	DET
ejpam-5600	143	5	expectations	expectation	NOUN
ejpam-5600	143	6	of	of	ADP
ejpam-5600	143	7	the	the	DET
ejpam-5600	143	8	pairwise	pairwise	NOUN
ejpam-5600	143	9	products	product	NOUN
ejpam-5600	143	10	of	of	ADP
ejpam-5600	143	11	nonzero	nonzero	PROPN
ejpam-5600	143	12	words	word	NOUN
ejpam-5600	143	13	’	'	PUNCT
ejpam-5600	143	14	weights	weight	NOUN
ejpam-5600	143	15	as	as	SCONJ
ejpam-5600	143	16	follows	follow	VERB
ejpam-5600	143	17	.	.	PUNCT
ejpam-5600	144	1	e[(n−	e[(n−	VERB
ejpam-5600	144	2	2wi)(n−	2wi)(n−	NUM
ejpam-5600	144	3	2wj	2wj	NOUN
ejpam-5600	144	4	)	)	PUNCT
ejpam-5600	144	5	]	]	PUNCT
ejpam-5600	145	1	=	=	PUNCT
ejpam-5600	145	2	e	e	X
ejpam-5600	145	3	(	(	PUNCT
ejpam-5600	145	4	χ̂c(i)χ̂c(j	χ̂c(i)χ̂c(j	PROPN
ejpam-5600	145	5	)	)	PUNCT
ejpam-5600	145	6	)	)	PUNCT
ejpam-5600	146	1	=	=	PUNCT
ejpam-5600	146	2	∑	∑	PUNCT
ejpam-5600	146	3	s	s	PROPN
ejpam-5600	146	4	,	,	PUNCT
ejpam-5600	146	5	m∈[2k	m∈[2k	PROPN
ejpam-5600	146	6	]	]	PUNCT
ejpam-5600	146	7	e(hshm)(−1)⟨s	e(hshm)(−1)⟨s	PROPN
ejpam-5600	146	8	,	,	PUNCT
ejpam-5600	146	9	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	146	10	,	,	PUNCT
ejpam-5600	146	11	j⟩.	j⟩.	ADV
ejpam-5600	146	12	let	let	VERB
ejpam-5600	146	13	us	we	PRON
ejpam-5600	146	14	denote	denote	VERB
ejpam-5600	146	15	by	by	ADP
ejpam-5600	146	16	p	p	PROPN
ejpam-5600	146	17	(	(	PUNCT
ejpam-5600	146	18	hs	hs	PROPN
ejpam-5600	146	19	)	)	PUNCT
ejpam-5600	146	20	,	,	PUNCT
ejpam-5600	146	21	the	the	DET
ejpam-5600	146	22	probability	probability	NOUN
ejpam-5600	146	23	that	that	SCONJ
ejpam-5600	146	24	a	a	DET
ejpam-5600	146	25	random	random	ADJ
ejpam-5600	146	26	binary	binary	NOUN
ejpam-5600	146	27	k×n	k×n	PROPN
ejpam-5600	146	28	matrix	matrix	NOUN
ejpam-5600	146	29	has	have	AUX
ejpam-5600	146	30	exactly	exactly	ADV
ejpam-5600	146	31	hs	hs	ADP
ejpam-5600	146	32	columns	column	NOUN
ejpam-5600	146	33	that	that	PRON
ejpam-5600	146	34	are	be	AUX
ejpam-5600	146	35	equal	equal	ADJ
ejpam-5600	146	36	to	to	ADP
ejpam-5600	146	37	st	st	PROPN
ejpam-5600	146	38	,	,	PUNCT
ejpam-5600	146	39	for	for	ADP
ejpam-5600	146	40	0	0	NUM
ejpam-5600	146	41	≤	≤	NUM
ejpam-5600	146	42	s	s	PART
ejpam-5600	146	43	≤	≤	NOUN
ejpam-5600	146	44	2k	2k	NOUN
ejpam-5600	146	45	−	−	ADP
ejpam-5600	147	1	1	1	X
ejpam-5600	147	2	.	.	PUNCT
ejpam-5600	147	3	similarly	similarly	ADV
ejpam-5600	147	4	,	,	PUNCT
ejpam-5600	147	5	let	let	VERB
ejpam-5600	147	6	p	p	PROPN
ejpam-5600	147	7	(	(	PUNCT
ejpam-5600	147	8	hs	hs	PROPN
ejpam-5600	147	9	,	,	PUNCT
ejpam-5600	147	10	hm	hm	INTJ
ejpam-5600	147	11	)	)	PUNCT
ejpam-5600	147	12	denote	denote	VERB
ejpam-5600	147	13	the	the	DET
ejpam-5600	147	14	probability	probability	NOUN
ejpam-5600	147	15	that	that	SCONJ
ejpam-5600	147	16	a	a	DET
ejpam-5600	147	17	random	random	ADJ
ejpam-5600	147	18	matrix	matrix	NOUN
ejpam-5600	147	19	has	have	AUX
ejpam-5600	147	20	exactly	exactly	ADV
ejpam-5600	147	21	hs	hs	PROPN
ejpam-5600	147	22	columns	column	NOUN
ejpam-5600	147	23	equal	equal	ADJ
ejpam-5600	147	24	to	to	ADP
ejpam-5600	147	25	st	st	PROPN
ejpam-5600	147	26	and	and	CCONJ
ejpam-5600	147	27	hm	hm	INTJ
ejpam-5600	147	28	columns	column	NOUN
ejpam-5600	147	29	equal	equal	ADJ
ejpam-5600	147	30	to	to	ADP
ejpam-5600	147	31	mt	mt	PROPN
ejpam-5600	147	32	,	,	PUNCT
ejpam-5600	147	33	for	for	ADP
ejpam-5600	147	34	0	0	NUM
ejpam-5600	147	35	≤	≤	NUM
ejpam-5600	147	36	s	s	NOUN
ejpam-5600	147	37	,	,	PUNCT
ejpam-5600	147	38	m	m	VERB
ejpam-5600	147	39	≤	≤	NOUN
ejpam-5600	147	40	2k	2k	NOUN
ejpam-5600	147	41	−	−	NUM
ejpam-5600	147	42	1	1	NUM
ejpam-5600	147	43	and	and	CCONJ
ejpam-5600	147	44	s	s	PART
ejpam-5600	147	45	̸=	̸=	PROPN
ejpam-5600	147	46	m.	m.	NOUN
ejpam-5600	147	47	proposition	proposition	NOUN
ejpam-5600	147	48	1	1	NUM
ejpam-5600	147	49	.	.	PUNCT
ejpam-5600	148	1	for	for	ADP
ejpam-5600	148	2	a	a	DET
ejpam-5600	148	3	random	random	ADJ
ejpam-5600	148	4	binary	binary	NOUN
ejpam-5600	148	5	k	k	PROPN
ejpam-5600	148	6	×	×	PROPN
ejpam-5600	148	7	n	n	PRON
ejpam-5600	148	8	matrix	matrix	NOUN
ejpam-5600	148	9	,	,	PUNCT
ejpam-5600	148	10	we	we	PRON
ejpam-5600	148	11	have	have	VERB
ejpam-5600	148	12	p	p	PROPN
ejpam-5600	148	13	(	(	PUNCT
ejpam-5600	148	14	hs	hs	X
ejpam-5600	148	15	)	)	PUNCT
ejpam-5600	148	16	=	=	SYM
ejpam-5600	148	17	(	(	PUNCT
ejpam-5600	148	18	n	n	X
ejpam-5600	148	19	hs	hs	PROPN
ejpam-5600	148	20	)	)	PUNCT
ejpam-5600	148	21	(	(	PUNCT
ejpam-5600	148	22	2k	2k	NOUN
ejpam-5600	148	23	−	−	PROPN
ejpam-5600	148	24	1)(n−hs	1)(n−hs	NUM
ejpam-5600	148	25	)	)	PUNCT
ejpam-5600	148	26	2kn	2kn	ADJ
ejpam-5600	148	27	and	and	CCONJ
ejpam-5600	148	28	p	p	X
ejpam-5600	148	29	(	(	PUNCT
ejpam-5600	148	30	hs	hs	PROPN
ejpam-5600	148	31	,	,	PUNCT
ejpam-5600	148	32	hm	hm	INTJ
ejpam-5600	148	33	)	)	PUNCT
ejpam-5600	148	34	=	=	SYM
ejpam-5600	149	1	(	(	PUNCT
ejpam-5600	149	2	n	n	X
ejpam-5600	149	3	hs	hs	PROPN
ejpam-5600	150	1	+	+	NOUN
ejpam-5600	150	2	hm	hm	INTJ
ejpam-5600	150	3	)	)	PUNCT
ejpam-5600	150	4	(	(	PUNCT
ejpam-5600	150	5	hs	hs	PROPN
ejpam-5600	151	1	+	+	CCONJ
ejpam-5600	151	2	hm	hm	INTJ
ejpam-5600	151	3	hm	hm	INTJ
ejpam-5600	151	4	)	)	PUNCT
ejpam-5600	151	5	(	(	PUNCT
ejpam-5600	151	6	2k	2k	NOUN
ejpam-5600	151	7	−	−	NOUN
ejpam-5600	151	8	2)(n−(hs+hm	2)(n−(hs+hm	NUM
ejpam-5600	151	9	)	)	PUNCT
ejpam-5600	151	10	)	)	PUNCT
ejpam-5600	152	1	2kn	2kn	ADJ
ejpam-5600	152	2	·	·	PUNCT
ejpam-5600	152	3	proof	proof	NOUN
ejpam-5600	152	4	.	.	PUNCT
ejpam-5600	153	1	the	the	DET
ejpam-5600	153	2	number	number	NOUN
ejpam-5600	153	3	of	of	ADP
ejpam-5600	153	4	matrices	matrix	NOUN
ejpam-5600	153	5	with	with	ADP
ejpam-5600	153	6	exactly	exactly	ADV
ejpam-5600	153	7	hs	hs	PROPN
ejpam-5600	153	8	columns	column	NOUN
ejpam-5600	153	9	equal	equal	ADJ
ejpam-5600	153	10	to	to	ADP
ejpam-5600	153	11	st	st	PROPN
ejpam-5600	153	12	is	be	AUX
ejpam-5600	153	13	given	give	VERB
ejpam-5600	153	14	by	by	ADP
ejpam-5600	153	15	(	(	PUNCT
ejpam-5600	153	16	n	n	X
ejpam-5600	153	17	hs	hs	PROPN
ejpam-5600	153	18	)	)	PUNCT
ejpam-5600	153	19	(	(	PUNCT
ejpam-5600	153	20	2k	2k	NOUN
ejpam-5600	153	21	−	−	PROPN
ejpam-5600	153	22	1)(n−hs	1)(n−hs	NUM
ejpam-5600	153	23	)	)	PUNCT
ejpam-5600	153	24	.	.	PUNCT
ejpam-5600	154	1	the	the	DET
ejpam-5600	154	2	binomial	binomial	ADJ
ejpam-5600	154	3	coefficient	coefficient	NOUN
ejpam-5600	154	4	gives	give	VERB
ejpam-5600	154	5	the	the	DET
ejpam-5600	154	6	number	number	NOUN
ejpam-5600	154	7	of	of	ADP
ejpam-5600	154	8	different	different	ADJ
ejpam-5600	154	9	choices	choice	NOUN
ejpam-5600	154	10	for	for	ADP
ejpam-5600	154	11	placing	place	VERB
ejpam-5600	154	12	st	st	PROPN
ejpam-5600	154	13	and	and	CCONJ
ejpam-5600	154	14	the	the	DET
ejpam-5600	154	15	factor	factor	NOUN
ejpam-5600	154	16	(	(	PUNCT
ejpam-5600	154	17	2k	2k	NOUN
ejpam-5600	154	18	−	−	PROPN
ejpam-5600	154	19	1)(n−hs	1)(n−hs	NUM
ejpam-5600	154	20	)	)	PUNCT
ejpam-5600	154	21	counts	count	VERB
ejpam-5600	154	22	the	the	DET
ejpam-5600	154	23	number	number	NOUN
ejpam-5600	154	24	of	of	ADP
ejpam-5600	154	25	ways	way	NOUN
ejpam-5600	154	26	to	to	PART
ejpam-5600	154	27	fill	fill	VERB
ejpam-5600	154	28	the	the	DET
ejpam-5600	154	29	other	other	ADJ
ejpam-5600	154	30	columns	column	NOUN
ejpam-5600	154	31	with	with	ADP
ejpam-5600	154	32	the	the	DET
ejpam-5600	154	33	remaining	remain	VERB
ejpam-5600	154	34	(	(	PUNCT
ejpam-5600	154	35	2k	2k	NOUN
ejpam-5600	154	36	−	−	NOUN
ejpam-5600	154	37	1	1	NUM
ejpam-5600	154	38	)	)	PUNCT
ejpam-5600	154	39	vectors	vector	NOUN
ejpam-5600	154	40	arbitrarily	arbitrarily	ADV
ejpam-5600	154	41	.	.	PUNCT
ejpam-5600	155	1	the	the	DET
ejpam-5600	155	2	number	number	NOUN
ejpam-5600	155	3	of	of	ADP
ejpam-5600	155	4	k	k	PROPN
ejpam-5600	155	5	×	×	PROPN
ejpam-5600	155	6	n	n	CCONJ
ejpam-5600	155	7	binary	binary	ADJ
ejpam-5600	155	8	matrices	matrix	NOUN
ejpam-5600	155	9	is	be	AUX
ejpam-5600	155	10	2kn	2kn	ADJ
ejpam-5600	155	11	.	.	PUNCT
ejpam-5600	156	1	so	so	ADV
ejpam-5600	156	2	we	we	PRON
ejpam-5600	156	3	have	have	VERB
ejpam-5600	156	4	p	p	PROPN
ejpam-5600	156	5	(	(	PUNCT
ejpam-5600	156	6	hs	hs	X
ejpam-5600	156	7	)	)	PUNCT
ejpam-5600	156	8	=	=	SYM
ejpam-5600	156	9	(	(	PUNCT
ejpam-5600	156	10	n	n	X
ejpam-5600	156	11	hs	hs	PROPN
ejpam-5600	156	12	)	)	PUNCT
ejpam-5600	156	13	(	(	PUNCT
ejpam-5600	156	14	2k	2k	NOUN
ejpam-5600	156	15	−	−	PROPN
ejpam-5600	156	16	1)(n−hs	1)(n−hs	NUM
ejpam-5600	156	17	)	)	PUNCT
ejpam-5600	156	18	2kn	2kn	ADV
ejpam-5600	156	19	·	·	PUNCT
ejpam-5600	156	20	now	now	ADV
ejpam-5600	156	21	let	let	VERB
ejpam-5600	156	22	0	0	NUM
ejpam-5600	156	23	≤	≤	NUM
ejpam-5600	156	24	s	s	PART
ejpam-5600	156	25	,	,	PUNCT
ejpam-5600	156	26	m	m	VERB
ejpam-5600	156	27	≤	≤	NOUN
ejpam-5600	156	28	2k	2k	NOUN
ejpam-5600	156	29	−	−	NUM
ejpam-5600	156	30	1	1	NUM
ejpam-5600	156	31	and	and	CCONJ
ejpam-5600	156	32	s	s	PART
ejpam-5600	156	33	̸=	̸=	PROPN
ejpam-5600	156	34	m.	m.	NOUN
ejpam-5600	156	35	for	for	ADP
ejpam-5600	156	36	the	the	DET
ejpam-5600	156	37	number	number	NOUN
ejpam-5600	156	38	of	of	ADP
ejpam-5600	156	39	k	k	PROPN
ejpam-5600	156	40	×	×	PROPN
ejpam-5600	156	41	n	n	CCONJ
ejpam-5600	156	42	binary	binary	ADJ
ejpam-5600	156	43	matrices	matrix	NOUN
ejpam-5600	156	44	with	with	ADP
ejpam-5600	156	45	exactly	exactly	ADV
ejpam-5600	156	46	hs	hs	PROPN
ejpam-5600	156	47	columns	column	NOUN
ejpam-5600	156	48	equal	equal	ADJ
ejpam-5600	156	49	to	to	ADP
ejpam-5600	156	50	st	st	PROPN
ejpam-5600	156	51	and	and	CCONJ
ejpam-5600	156	52	hm	hm	INTJ
ejpam-5600	156	53	columns	column	NOUN
ejpam-5600	156	54	equal	equal	ADJ
ejpam-5600	156	55	to	to	ADP
ejpam-5600	156	56	mt	mt	PROPN
ejpam-5600	156	57	,	,	PUNCT
ejpam-5600	156	58	we	we	PRON
ejpam-5600	156	59	fix	fix	VERB
ejpam-5600	156	60	(	(	PUNCT
ejpam-5600	156	61	hs	hs	PROPN
ejpam-5600	156	62	+	+	PROPN
ejpam-5600	156	63	hm	hm	INTJ
ejpam-5600	156	64	)	)	PUNCT
ejpam-5600	156	65	positions	position	NOUN
ejpam-5600	156	66	for	for	ADP
ejpam-5600	156	67	st	st	PROPN
ejpam-5600	156	68	and	and	CCONJ
ejpam-5600	156	69	mt	mt	PROPN
ejpam-5600	156	70	.	.	PUNCT
ejpam-5600	157	1	hence	hence	ADV
ejpam-5600	157	2	we	we	PRON
ejpam-5600	157	3	have	have	VERB
ejpam-5600	157	4	the	the	DET
ejpam-5600	157	5	binomial	binomial	ADJ
ejpam-5600	157	6	coefficient	coefficient	NOUN
ejpam-5600	157	7	(	(	PUNCT
ejpam-5600	157	8	n	n	X
ejpam-5600	157	9	hs+hm	hs+hm	PROPN
ejpam-5600	157	10	)	)	PUNCT
ejpam-5600	157	11	.	.	PUNCT
ejpam-5600	158	1	then	then	ADV
ejpam-5600	158	2	we	we	PRON
ejpam-5600	158	3	determine	determine	VERB
ejpam-5600	158	4	the	the	DET
ejpam-5600	158	5	hm	hm	PROPN
ejpam-5600	158	6	positions	position	NOUN
ejpam-5600	158	7	among	among	ADP
ejpam-5600	158	8	the	the	DET
ejpam-5600	158	9	(	(	PUNCT
ejpam-5600	158	10	hs	hs	PROPN
ejpam-5600	158	11	+	+	PROPN
ejpam-5600	158	12	hm	hm	INTJ
ejpam-5600	158	13	)	)	PUNCT
ejpam-5600	158	14	columns	column	NOUN
ejpam-5600	158	15	for	for	ADP
ejpam-5600	158	16	the	the	DET
ejpam-5600	158	17	vector	vector	PROPN
ejpam-5600	158	18	mt	mt	PROPN
ejpam-5600	158	19	.	.	PUNCT
ejpam-5600	159	1	the	the	DET
ejpam-5600	159	2	number	number	NOUN
ejpam-5600	159	3	of	of	ADP
ejpam-5600	159	4	choices	choice	NOUN
ejpam-5600	159	5	i̇brahim	i̇brahim	PUNCT
ejpam-5600	159	6	özen	özen	PROPN
ejpam-5600	159	7	/	/	SYM
ejpam-5600	159	8	eur	eur	PROPN
ejpam-5600	159	9	.	.	PUNCT
ejpam-5600	160	1	j.	j.	PROPN
ejpam-5600	160	2	pure	pure	PROPN
ejpam-5600	160	3	appl	appl	PROPN
ejpam-5600	160	4	.	.	PROPN
ejpam-5600	160	5	math	math	PROPN
ejpam-5600	160	6	,	,	PUNCT
ejpam-5600	160	7	17	17	NUM
ejpam-5600	160	8	(	(	PUNCT
ejpam-5600	160	9	4	4	NUM
ejpam-5600	160	10	)	)	PUNCT
ejpam-5600	160	11	(	(	PUNCT
ejpam-5600	160	12	2024	2024	NUM
ejpam-5600	160	13	)	)	PUNCT
ejpam-5600	160	14	,	,	PUNCT
ejpam-5600	160	15	4225	4225	NUM
ejpam-5600	160	16	-	-	SYM
ejpam-5600	160	17	4237	4237	NUM
ejpam-5600	160	18	4231	4231	NUM
ejpam-5600	160	19	for	for	ADP
ejpam-5600	160	20	that	that	PRON
ejpam-5600	160	21	is	be	AUX
ejpam-5600	160	22	(	(	PUNCT
ejpam-5600	160	23	hs+hm	hs+hm	PROPN
ejpam-5600	160	24	hm	hm	INTJ
ejpam-5600	160	25	)	)	PUNCT
ejpam-5600	160	26	.	.	PUNCT
ejpam-5600	161	1	the	the	DET
ejpam-5600	161	2	choice	choice	NOUN
ejpam-5600	161	3	for	for	ADP
ejpam-5600	161	4	columns	column	NOUN
ejpam-5600	161	5	st	st	PROPN
ejpam-5600	161	6	is	be	AUX
ejpam-5600	161	7	determined	determine	VERB
ejpam-5600	161	8	by	by	ADP
ejpam-5600	161	9	that	that	PRON
ejpam-5600	161	10	of	of	ADP
ejpam-5600	161	11	mt	mt	PROPN
ejpam-5600	161	12	uniquely	uniquely	ADV
ejpam-5600	161	13	.	.	PUNCT
ejpam-5600	162	1	the	the	DET
ejpam-5600	162	2	columns	column	NOUN
ejpam-5600	162	3	other	other	ADJ
ejpam-5600	162	4	than	than	ADP
ejpam-5600	162	5	these	these	PRON
ejpam-5600	162	6	(	(	PUNCT
ejpam-5600	162	7	hs	hs	PROPN
ejpam-5600	162	8	+	+	PROPN
ejpam-5600	162	9	hm	hm	INTJ
ejpam-5600	162	10	)	)	PUNCT
ejpam-5600	162	11	positions	position	NOUN
ejpam-5600	162	12	can	can	AUX
ejpam-5600	162	13	be	be	AUX
ejpam-5600	162	14	filled	fill	VERB
ejpam-5600	162	15	by	by	ADP
ejpam-5600	162	16	the	the	DET
ejpam-5600	162	17	remaining	remain	VERB
ejpam-5600	162	18	(	(	PUNCT
ejpam-5600	162	19	2k	2k	NOUN
ejpam-5600	162	20	−	−	NOUN
ejpam-5600	162	21	2	2	NUM
ejpam-5600	162	22	)	)	PUNCT
ejpam-5600	162	23	vectors	vector	NOUN
ejpam-5600	162	24	arbitrarily	arbitrarily	ADV
ejpam-5600	162	25	.	.	PUNCT
ejpam-5600	163	1	so	so	ADV
ejpam-5600	163	2	we	we	PRON
ejpam-5600	163	3	have	have	VERB
ejpam-5600	163	4	p	p	PROPN
ejpam-5600	163	5	(	(	PUNCT
ejpam-5600	163	6	hs	hs	PROPN
ejpam-5600	163	7	,	,	PUNCT
ejpam-5600	163	8	hm	hm	INTJ
ejpam-5600	163	9	)	)	PUNCT
ejpam-5600	163	10	=	=	SYM
ejpam-5600	163	11	(	(	PUNCT
ejpam-5600	163	12	n	n	X
ejpam-5600	163	13	hs	hs	PROPN
ejpam-5600	164	1	+	+	NOUN
ejpam-5600	164	2	hm	hm	INTJ
ejpam-5600	164	3	)	)	PUNCT
ejpam-5600	164	4	(	(	PUNCT
ejpam-5600	164	5	hs	hs	PROPN
ejpam-5600	165	1	+	+	CCONJ
ejpam-5600	165	2	hm	hm	INTJ
ejpam-5600	165	3	hm	hm	INTJ
ejpam-5600	165	4	)	)	PUNCT
ejpam-5600	165	5	(	(	PUNCT
ejpam-5600	165	6	2k	2k	NOUN
ejpam-5600	165	7	−	−	NOUN
ejpam-5600	165	8	2)(n−(hs+hm	2)(n−(hs+hm	NUM
ejpam-5600	165	9	)	)	PUNCT
ejpam-5600	165	10	)	)	PUNCT
ejpam-5600	165	11	2kn	2kn	ADV
ejpam-5600	165	12	·	·	PUNCT
ejpam-5600	165	13	theorem	theorem	NOUN
ejpam-5600	165	14	1	1	X
ejpam-5600	165	15	.	.	PUNCT
ejpam-5600	166	1	let	let	VERB
ejpam-5600	166	2	c	c	PRON
ejpam-5600	166	3	be	be	AUX
ejpam-5600	166	4	a	a	DET
ejpam-5600	166	5	random	random	ADJ
ejpam-5600	166	6	binary	binary	ADJ
ejpam-5600	166	7	linear	linear	PROPN
ejpam-5600	167	1	[	[	X
ejpam-5600	167	2	n	n	CCONJ
ejpam-5600	167	3	,	,	PUNCT
ejpam-5600	167	4	k	k	X
ejpam-5600	167	5	]	]	X
ejpam-5600	167	6	code	code	NOUN
ejpam-5600	167	7	with	with	ADP
ejpam-5600	167	8	words	word	NOUN
ejpam-5600	167	9	and	and	CCONJ
ejpam-5600	167	10	weights	weight	NOUN
ejpam-5600	167	11	denoted	denote	VERB
ejpam-5600	167	12	as	as	ADP
ejpam-5600	167	13	above	above	ADV
ejpam-5600	167	14	.	.	PUNCT
ejpam-5600	168	1	then	then	ADV
ejpam-5600	168	2	the	the	DET
ejpam-5600	168	3	expectations	expectation	NOUN
ejpam-5600	168	4	of	of	ADP
ejpam-5600	168	5	the	the	DET
ejpam-5600	168	6	weights	weight	NOUN
ejpam-5600	168	7	of	of	ADP
ejpam-5600	168	8	nonzero	nonzero	PROPN
ejpam-5600	168	9	codewords	codeword	NOUN
ejpam-5600	168	10	are	be	AUX
ejpam-5600	168	11	given	give	VERB
ejpam-5600	168	12	by	by	ADP
ejpam-5600	168	13	e(wi	e(wi	ADJ
ejpam-5600	168	14	)	)	PUNCT
ejpam-5600	168	15	=	=	SYM
ejpam-5600	168	16	n	n	DET
ejpam-5600	168	17	2	2	NUM
ejpam-5600	168	18	for	for	ADP
ejpam-5600	168	19	i	i	PRON
ejpam-5600	168	20	≥	≥	NOUN
ejpam-5600	168	21	1	1	NUM
ejpam-5600	168	22	.	.	PUNCT
ejpam-5600	169	1	(	(	PUNCT
ejpam-5600	169	2	3	3	X
ejpam-5600	169	3	)	)	PUNCT
ejpam-5600	169	4	proof	proof	NOUN
ejpam-5600	169	5	.	.	PUNCT
ejpam-5600	170	1	by	by	ADP
ejpam-5600	170	2	lemma	lemma	PROPN
ejpam-5600	170	3	2	2	NUM
ejpam-5600	170	4	,	,	PUNCT
ejpam-5600	170	5	we	we	PRON
ejpam-5600	170	6	have	have	VERB
ejpam-5600	170	7	e(n−	e(n−	NOUN
ejpam-5600	170	8	2wi	2wi	NOUN
ejpam-5600	170	9	)	)	PUNCT
ejpam-5600	171	1	=	=	SYM
ejpam-5600	171	2	e	e	X
ejpam-5600	171	3	(	(	PUNCT
ejpam-5600	171	4	χ̂c(i	χ̂c(i	NUM
ejpam-5600	171	5	)	)	PUNCT
ejpam-5600	171	6	)	)	PUNCT
ejpam-5600	172	1	=	=	PUNCT
ejpam-5600	172	2	∑	∑	PUNCT
ejpam-5600	172	3	s∈[2k	s∈[2k	PROPN
ejpam-5600	172	4	]	]	PUNCT
ejpam-5600	172	5	e(hs)(−1)⟨s	e(hs)(−1)⟨s	X
ejpam-5600	172	6	,	,	PUNCT
ejpam-5600	172	7	i⟩.	i⟩.	X
ejpam-5600	172	8	by	by	ADP
ejpam-5600	172	9	proposition	proposition	NOUN
ejpam-5600	172	10	1	1	NUM
ejpam-5600	172	11	we	we	PRON
ejpam-5600	172	12	proceed	proceed	VERB
ejpam-5600	172	13	as	as	SCONJ
ejpam-5600	172	14	follows	follow	VERB
ejpam-5600	172	15	:	:	PUNCT
ejpam-5600	172	16	e(n−	e(n−	PROPN
ejpam-5600	172	17	2wi	2wi	NOUN
ejpam-5600	172	18	)	)	PUNCT
ejpam-5600	173	1	=	=	SYM
ejpam-5600	173	2	∑	∑	PUNCT
ejpam-5600	173	3	s∈[2k	s∈[2k	PROPN
ejpam-5600	173	4	]	]	PUNCT
ejpam-5600	173	5	e(hs)(−1)⟨s	e(hs)(−1)⟨s	NOUN
ejpam-5600	173	6	,	,	PUNCT
ejpam-5600	173	7	i⟩	i⟩	PUNCT
ejpam-5600	173	8	=	=	SYM
ejpam-5600	173	9	∑	∑	PUNCT
ejpam-5600	173	10	s∈[2k	s∈[2k	PROPN
ejpam-5600	173	11	]	]	PUNCT
ejpam-5600	173	12	∑	∑	PUNCT
ejpam-5600	173	13	hs∈[n+1	hs∈[n+1	VERB
ejpam-5600	173	14	]	]	PUNCT
ejpam-5600	173	15	p	p	X
ejpam-5600	173	16	(	(	PUNCT
ejpam-5600	173	17	hs)hs(−1)⟨s	hs)hs(−1)⟨s	PROPN
ejpam-5600	173	18	,	,	PUNCT
ejpam-5600	173	19	i⟩	i⟩	PUNCT
ejpam-5600	173	20	=	=	SYM
ejpam-5600	173	21	∑	∑	PUNCT
ejpam-5600	173	22	s∈[2k	s∈[2k	PROPN
ejpam-5600	173	23	]	]	PUNCT
ejpam-5600	173	24	∑	∑	PUNCT
ejpam-5600	173	25	hs∈[n+1	hs∈[n+1	VERB
ejpam-5600	173	26	]	]	PUNCT
ejpam-5600	173	27	(	(	PUNCT
ejpam-5600	173	28	n	n	X
ejpam-5600	173	29	hs	hs	PROPN
ejpam-5600	173	30	)	)	PUNCT
ejpam-5600	173	31	(	(	PUNCT
ejpam-5600	173	32	2k	2k	NOUN
ejpam-5600	173	33	−	−	PROPN
ejpam-5600	173	34	1)n−hs	1)n−hs	NUM
ejpam-5600	173	35	2kn	2kn	ADJ
ejpam-5600	173	36	hs(−1)⟨s	hs(−1)⟨s	NOUN
ejpam-5600	173	37	,	,	PUNCT
ejpam-5600	173	38	i⟩	i⟩	PUNCT
ejpam-5600	173	39	=	=	SYM
ejpam-5600	173	40	∑	∑	PUNCT
ejpam-5600	173	41	s∈[2k	s∈[2k	PROPN
ejpam-5600	173	42	]	]	PUNCT
ejpam-5600	173	43	∑	∑	PUNCT
ejpam-5600	173	44	hs∈[n+1	hs∈[n+1	VERB
ejpam-5600	173	45	]	]	PUNCT
ejpam-5600	173	46	(	(	PUNCT
ejpam-5600	173	47	n	n	X
ejpam-5600	173	48	hs	hs	PROPN
ejpam-5600	173	49	)	)	PUNCT
ejpam-5600	173	50	(	(	PUNCT
ejpam-5600	173	51	2k	2k	NOUN
ejpam-5600	173	52	−	−	PROPN
ejpam-5600	173	53	1)hs	1)hs	NUM
ejpam-5600	173	54	2kn	2kn	ADJ
ejpam-5600	174	1	(	(	PUNCT
ejpam-5600	174	2	n−	n−	NOUN
ejpam-5600	174	3	hs)(−1)⟨s	hs)(−1)⟨s	PROPN
ejpam-5600	174	4	,	,	PUNCT
ejpam-5600	174	5	i⟩	i⟩	VERB
ejpam-5600	174	6	in	in	ADP
ejpam-5600	174	7	the	the	DET
ejpam-5600	174	8	last	last	ADJ
ejpam-5600	174	9	equality	equality	NOUN
ejpam-5600	174	10	we	we	PRON
ejpam-5600	174	11	performed	perform	VERB
ejpam-5600	174	12	a	a	DET
ejpam-5600	174	13	change	change	NOUN
ejpam-5600	174	14	of	of	ADP
ejpam-5600	174	15	variables	variable	NOUN
ejpam-5600	174	16	and	and	CCONJ
ejpam-5600	174	17	put	put	VERB
ejpam-5600	174	18	(	(	PUNCT
ejpam-5600	174	19	n−hs	n−hs	PROPN
ejpam-5600	174	20	)	)	PUNCT
ejpam-5600	174	21	for	for	ADP
ejpam-5600	174	22	hs	hs	PROPN
ejpam-5600	174	23	,	,	PUNCT
ejpam-5600	174	24	by	by	ADP
ejpam-5600	174	25	the	the	DET
ejpam-5600	174	26	symmetry	symmetry	NOUN
ejpam-5600	174	27	of	of	ADP
ejpam-5600	174	28	the	the	DET
ejpam-5600	174	29	binomial	binomial	ADJ
ejpam-5600	174	30	coefficients	coefficient	NOUN
ejpam-5600	174	31	.	.	PUNCT
ejpam-5600	175	1	let	let	VERB
ejpam-5600	175	2	k1	k1	NOUN
ejpam-5600	175	3	=	=	NOUN
ejpam-5600	175	4	2k−1	2k−1	NUM
ejpam-5600	175	5	.	.	PUNCT
ejpam-5600	176	1	in	in	ADP
ejpam-5600	176	2	the	the	DET
ejpam-5600	176	3	following	follow	VERB
ejpam-5600	176	4	equation	equation	NOUN
ejpam-5600	176	5	we	we	PRON
ejpam-5600	176	6	have	have	VERB
ejpam-5600	176	7	derivative	derivative	NOUN
ejpam-5600	176	8	with	with	ADP
ejpam-5600	176	9	respect	respect	NOUN
ejpam-5600	176	10	to	to	ADP
ejpam-5600	176	11	k1	k1	NOUN
ejpam-5600	176	12	.	.	PUNCT
ejpam-5600	177	1	e(n−	e(n−	PROPN
ejpam-5600	177	2	2wi	2wi	NOUN
ejpam-5600	177	3	)	)	PUNCT
ejpam-5600	178	1	=	=	SYM
ejpam-5600	178	2	∑	∑	PUNCT
ejpam-5600	178	3	s∈[2k	s∈[2k	PROPN
ejpam-5600	178	4	]	]	PUNCT
ejpam-5600	178	5	(	(	PUNCT
ejpam-5600	178	6	n−	n−	NOUN
ejpam-5600	178	7	k1	k1	NOUN
ejpam-5600	178	8	2kn	2kn	ADV
ejpam-5600	179	1	[	[	X
ejpam-5600	179	2	(	(	PUNCT
ejpam-5600	179	3	k1	k1	NOUN
ejpam-5600	179	4	+	+	CCONJ
ejpam-5600	179	5	1)n]′	1)n]′	NUM
ejpam-5600	179	6	)	)	PUNCT
ejpam-5600	180	1	(	(	PUNCT
ejpam-5600	180	2	−1)⟨s	−1)⟨s	PROPN
ejpam-5600	180	3	,	,	PUNCT
ejpam-5600	180	4	i⟩	i⟩	PUNCT
ejpam-5600	180	5	=	=	PUNCT
ejpam-5600	180	6	(	(	PUNCT
ejpam-5600	180	7	n−	n−	NOUN
ejpam-5600	180	8	k1	k1	NOUN
ejpam-5600	180	9	2kn	2kn	ADV
ejpam-5600	180	10	[	[	PUNCT
ejpam-5600	180	11	n(2k)n−1	n(2k)n−1	ADV
ejpam-5600	180	12	]	]	PUNCT
ejpam-5600	180	13	)	)	PUNCT
ejpam-5600	180	14	∑	∑	PUNCT
ejpam-5600	180	15	s∈[2k	s∈[2k	PROPN
ejpam-5600	180	16	]	]	PUNCT
ejpam-5600	180	17	(	(	PUNCT
ejpam-5600	180	18	−1)⟨s	−1)⟨s	PROPN
ejpam-5600	180	19	,	,	PUNCT
ejpam-5600	180	20	i⟩	i⟩	PUNCT
ejpam-5600	180	21	=	=	PUNCT
ejpam-5600	180	22	(	(	PUNCT
ejpam-5600	180	23	n	n	CCONJ
ejpam-5600	180	24	2k	2k	NUM
ejpam-5600	180	25	)	)	PUNCT
ejpam-5600	180	26	∑	∑	PUNCT
ejpam-5600	180	27	s∈[2k	s∈[2k	PROPN
ejpam-5600	180	28	]	]	PUNCT
ejpam-5600	180	29	(	(	PUNCT
ejpam-5600	180	30	−1)⟨s	−1)⟨s	PROPN
ejpam-5600	180	31	,	,	PUNCT
ejpam-5600	180	32	i⟩	i⟩	PUNCT
ejpam-5600	180	33	=	=	SYM
ejpam-5600	180	34	0	0	NUM
ejpam-5600	180	35	for	for	SCONJ
ejpam-5600	180	36	i	i	PRON
ejpam-5600	180	37	≥	≥	NOUN
ejpam-5600	180	38	1	1	NUM
ejpam-5600	180	39	.	.	PUNCT
ejpam-5600	180	40	i̇brahim	i̇brahim	PROPN
ejpam-5600	181	1	özen	özen	PROPN
ejpam-5600	181	2	/	/	SYM
ejpam-5600	181	3	eur	eur	PROPN
ejpam-5600	181	4	.	.	PUNCT
ejpam-5600	182	1	j.	j.	PROPN
ejpam-5600	182	2	pure	pure	PROPN
ejpam-5600	182	3	appl	appl	PROPN
ejpam-5600	182	4	.	.	PROPN
ejpam-5600	182	5	math	math	PROPN
ejpam-5600	182	6	,	,	PUNCT
ejpam-5600	182	7	17	17	NUM
ejpam-5600	182	8	(	(	PUNCT
ejpam-5600	182	9	4	4	NUM
ejpam-5600	182	10	)	)	PUNCT
ejpam-5600	182	11	(	(	PUNCT
ejpam-5600	182	12	2024	2024	NUM
ejpam-5600	182	13	)	)	PUNCT
ejpam-5600	182	14	,	,	PUNCT
ejpam-5600	182	15	4225	4225	NUM
ejpam-5600	182	16	-	-	SYM
ejpam-5600	182	17	4237	4237	NUM
ejpam-5600	182	18	4232	4232	NUM
ejpam-5600	183	1	the	the	DET
ejpam-5600	183	2	last	last	ADJ
ejpam-5600	183	3	equality	equality	NOUN
ejpam-5600	183	4	is	be	AUX
ejpam-5600	183	5	obtained	obtain	VERB
ejpam-5600	183	6	by	by	ADP
ejpam-5600	183	7	lemma	lemma	PROPN
ejpam-5600	183	8	3	3	NUM
ejpam-5600	183	9	.	.	PUNCT
ejpam-5600	184	1	so	so	ADV
ejpam-5600	184	2	the	the	DET
ejpam-5600	184	3	expectations	expectation	NOUN
ejpam-5600	184	4	of	of	ADP
ejpam-5600	184	5	the	the	DET
ejpam-5600	184	6	nonzero	nonzero	NOUN
ejpam-5600	184	7	weights	weight	NOUN
ejpam-5600	184	8	follow	follow	VERB
ejpam-5600	184	9	e(wi	e(wi	ADJ
ejpam-5600	184	10	)	)	PUNCT
ejpam-5600	184	11	=	=	SYM
ejpam-5600	184	12	n	n	DET
ejpam-5600	184	13	2	2	NUM
ejpam-5600	184	14	for	for	SCONJ
ejpam-5600	184	15	i	i	PRON
ejpam-5600	184	16	≥	≥	NOUN
ejpam-5600	184	17	1	1	X
ejpam-5600	184	18	.	.	PUNCT
ejpam-5600	185	1	we	we	PRON
ejpam-5600	185	2	will	will	AUX
ejpam-5600	185	3	explore	explore	VERB
ejpam-5600	185	4	the	the	DET
ejpam-5600	185	5	expectations	expectation	NOUN
ejpam-5600	185	6	of	of	ADP
ejpam-5600	185	7	the	the	DET
ejpam-5600	185	8	products	product	NOUN
ejpam-5600	185	9	of	of	ADP
ejpam-5600	185	10	nonzero	nonzero	NOUN
ejpam-5600	185	11	weights	weight	NOUN
ejpam-5600	185	12	in	in	ADP
ejpam-5600	185	13	the	the	DET
ejpam-5600	185	14	next	next	ADJ
ejpam-5600	185	15	theorem	theorem	PROPN
ejpam-5600	185	16	.	.	PUNCT
ejpam-5600	185	17	theorem	theorem	PROPN
ejpam-5600	185	18	2	2	NUM
ejpam-5600	185	19	.	.	PUNCT
ejpam-5600	185	20	expectations	expectation	NOUN
ejpam-5600	185	21	of	of	ADP
ejpam-5600	185	22	the	the	DET
ejpam-5600	185	23	pairwise	pairwise	NOUN
ejpam-5600	185	24	products	product	NOUN
ejpam-5600	185	25	of	of	ADP
ejpam-5600	185	26	nonzero	nonzero	NOUN
ejpam-5600	185	27	weights	weight	NOUN
ejpam-5600	185	28	in	in	ADP
ejpam-5600	185	29	a	a	DET
ejpam-5600	185	30	random	random	ADJ
ejpam-5600	185	31	binary	binary	ADJ
ejpam-5600	185	32	linear	linear	PROPN
ejpam-5600	185	33	[	[	X
ejpam-5600	185	34	n	n	CCONJ
ejpam-5600	185	35	,	,	PUNCT
ejpam-5600	185	36	k	k	X
ejpam-5600	185	37	]	]	X
ejpam-5600	185	38	code	code	NOUN
ejpam-5600	185	39	are	be	AUX
ejpam-5600	185	40	given	give	VERB
ejpam-5600	185	41	by	by	ADP
ejpam-5600	185	42	e(wiwj	e(wiwj	NOUN
ejpam-5600	185	43	)	)	PUNCT
ejpam-5600	186	1	=	=	PRON
ejpam-5600	186	2	{	{	PUNCT
ejpam-5600	186	3	n2+n	n2+n	PROPN
ejpam-5600	186	4	4	4	NUM
ejpam-5600	186	5	,	,	PUNCT
ejpam-5600	186	6	for	for	ADP
ejpam-5600	186	7	i	i	PROPN
ejpam-5600	186	8	=	=	SYM
ejpam-5600	186	9	j	j	PROPN
ejpam-5600	186	10	,	,	PUNCT
ejpam-5600	186	11	i	i	PRON
ejpam-5600	186	12	,	,	PUNCT
ejpam-5600	186	13	j	j	PROPN
ejpam-5600	186	14	≥	≥	PROPN
ejpam-5600	186	15	1	1	NUM
ejpam-5600	186	16	,	,	PUNCT
ejpam-5600	186	17	n2	n2	NOUN
ejpam-5600	186	18	4	4	NUM
ejpam-5600	186	19	,	,	PUNCT
ejpam-5600	186	20	for	for	ADP
ejpam-5600	186	21	i	i	PROPN
ejpam-5600	186	22	̸=	̸=	PROPN
ejpam-5600	186	23	j	j	PROPN
ejpam-5600	186	24	,	,	PUNCT
ejpam-5600	186	25	i	i	PRON
ejpam-5600	186	26	,	,	PUNCT
ejpam-5600	186	27	j	j	PROPN
ejpam-5600	186	28	≥	≥	PROPN
ejpam-5600	186	29	1	1	NUM
ejpam-5600	186	30	.	.	PUNCT
ejpam-5600	187	1	(	(	PUNCT
ejpam-5600	187	2	4	4	X
ejpam-5600	187	3	)	)	PUNCT
ejpam-5600	187	4	proof	proof	NOUN
ejpam-5600	187	5	.	.	PUNCT
ejpam-5600	188	1	by	by	ADP
ejpam-5600	188	2	lemma	lemma	PROPN
ejpam-5600	188	3	2	2	NUM
ejpam-5600	188	4	,	,	PUNCT
ejpam-5600	188	5	the	the	DET
ejpam-5600	188	6	expectations	expectation	NOUN
ejpam-5600	188	7	of	of	ADP
ejpam-5600	188	8	the	the	DET
ejpam-5600	188	9	products	product	NOUN
ejpam-5600	188	10	of	of	ADP
ejpam-5600	188	11	nonzero	nonzero	PROPN
ejpam-5600	188	12	weights	weight	NOUN
ejpam-5600	188	13	are	be	AUX
ejpam-5600	188	14	given	give	VERB
ejpam-5600	188	15	by	by	ADP
ejpam-5600	188	16	e((n−	e((n−	PROPN
ejpam-5600	188	17	2wi)(n−	2wi)(n−	NUM
ejpam-5600	188	18	2wj	2wj	NOUN
ejpam-5600	188	19	)	)	PUNCT
ejpam-5600	188	20	)	)	PUNCT
ejpam-5600	189	1	=	=	SYM
ejpam-5600	189	2	e	e	X
ejpam-5600	189	3	(	(	PUNCT
ejpam-5600	189	4	χ̂c(i)χ̂c(j	χ̂c(i)χ̂c(j	PROPN
ejpam-5600	189	5	)	)	PUNCT
ejpam-5600	189	6	)	)	PUNCT
ejpam-5600	190	1	=	=	PUNCT
ejpam-5600	190	2	∑	∑	PUNCT
ejpam-5600	190	3	s	s	PROPN
ejpam-5600	190	4	,	,	PUNCT
ejpam-5600	190	5	m∈[2k	m∈[2k	PROPN
ejpam-5600	190	6	]	]	PUNCT
ejpam-5600	190	7	e(hshm)(−1)⟨s	e(hshm)(−1)⟨s	PROPN
ejpam-5600	190	8	,	,	PUNCT
ejpam-5600	190	9	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	190	10	,	,	PUNCT
ejpam-5600	190	11	j⟩	j⟩	NOUN
ejpam-5600	190	12	=	=	SYM
ejpam-5600	190	13	∑	∑	PUNCT
ejpam-5600	190	14	s∈[2k	s∈[2k	PROPN
ejpam-5600	190	15	]	]	PUNCT
ejpam-5600	190	16	e(h2s)(−1)⟨s,(i+j)⟩	e(h2s)(−1)⟨s,(i+j)⟩	X
ejpam-5600	190	17	+	+	CCONJ
ejpam-5600	190	18	∑	∑	PROPN
ejpam-5600	190	19	s	s	PROPN
ejpam-5600	190	20	,	,	PUNCT
ejpam-5600	190	21	m∈[2k	m∈[2k	PROPN
ejpam-5600	190	22	]	]	PUNCT
ejpam-5600	190	23	s	s	PROPN
ejpam-5600	190	24	̸=m	̸=m	PROPN
ejpam-5600	190	25	e(hshm)(−1)⟨s	e(hshm)(−1)⟨s	PROPN
ejpam-5600	190	26	,	,	PUNCT
ejpam-5600	190	27	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	190	28	,	,	PUNCT
ejpam-5600	190	29	j⟩.	j⟩.	ADJ
ejpam-5600	190	30	the	the	DET
ejpam-5600	190	31	first	first	ADJ
ejpam-5600	190	32	sum	sum	NOUN
ejpam-5600	190	33	in	in	ADP
ejpam-5600	190	34	the	the	DET
ejpam-5600	190	35	last	last	ADJ
ejpam-5600	190	36	equality	equality	NOUN
ejpam-5600	190	37	is	be	AUX
ejpam-5600	190	38	the	the	DET
ejpam-5600	190	39	contribution	contribution	NOUN
ejpam-5600	190	40	of	of	ADP
ejpam-5600	190	41	cases	case	NOUN
ejpam-5600	190	42	where	where	SCONJ
ejpam-5600	190	43	s	s	VERB
ejpam-5600	190	44	=	=	NOUN
ejpam-5600	190	45	m	m	PROPN
ejpam-5600	190	46	and	and	CCONJ
ejpam-5600	190	47	the	the	DET
ejpam-5600	190	48	second	second	ADJ
ejpam-5600	190	49	sum	sum	NOUN
ejpam-5600	190	50	is	be	AUX
ejpam-5600	190	51	the	the	DET
ejpam-5600	190	52	contribution	contribution	NOUN
ejpam-5600	190	53	of	of	ADP
ejpam-5600	190	54	the	the	DET
ejpam-5600	190	55	cases	case	NOUN
ejpam-5600	190	56	where	where	SCONJ
ejpam-5600	190	57	s	s	AUX
ejpam-5600	190	58	̸=	̸=	PROPN
ejpam-5600	190	59	m.	m.	NOUN
ejpam-5600	190	60	now	now	ADV
ejpam-5600	190	61	let	let	VERB
ejpam-5600	190	62	k1	k1	NOUN
ejpam-5600	190	63	and	and	CCONJ
ejpam-5600	190	64	k2	k2	PROPN
ejpam-5600	190	65	denote	denote	VERB
ejpam-5600	190	66	2k	2k	NOUN
ejpam-5600	190	67	−	−	NUM
ejpam-5600	190	68	1	1	NUM
ejpam-5600	190	69	and	and	CCONJ
ejpam-5600	190	70	2k	2k	NOUN
ejpam-5600	190	71	−	−	NUM
ejpam-5600	190	72	2	2	NUM
ejpam-5600	190	73	respectively	respectively	ADV
ejpam-5600	190	74	.	.	PUNCT
ejpam-5600	191	1	e((n−	e((n−	VERB
ejpam-5600	191	2	2wi)(n−	2wi)(n−	NUM
ejpam-5600	191	3	2wj))=	2wj))=	PROPN
ejpam-5600	191	4	1	1	NUM
ejpam-5600	191	5	2kn	2kn	ADJ
ejpam-5600	191	6	∑	∑	PART
ejpam-5600	191	7	s∈[2k	s∈[2k	PROPN
ejpam-5600	191	8	]	]	PUNCT
ejpam-5600	191	9	hs∈[n+1	hs∈[n+1	NOUN
ejpam-5600	191	10	]	]	PUNCT
ejpam-5600	191	11	(	(	PUNCT
ejpam-5600	191	12	n	n	X
ejpam-5600	191	13	hs	hs	INTJ
ejpam-5600	191	14	)	)	PUNCT
ejpam-5600	191	15	k	k	PROPN
ejpam-5600	191	16	(	(	PUNCT
ejpam-5600	191	17	n−hs	n−hs	PROPN
ejpam-5600	191	18	)	)	PUNCT
ejpam-5600	191	19	1	1	NUM
ejpam-5600	191	20	h2s(−1)⟨s,(i+j)⟩	h2s(−1)⟨s,(i+j)⟩	ADP
ejpam-5600	191	21	+	+	NUM
ejpam-5600	191	22	∑	∑	PROPN
ejpam-5600	191	23	s	s	PROPN
ejpam-5600	191	24	,	,	PUNCT
ejpam-5600	191	25	m∈[2k	m∈[2k	PROPN
ejpam-5600	191	26	]	]	PUNCT
ejpam-5600	191	27	s	s	PROPN
ejpam-5600	191	28	̸=m	̸=m	PROPN
ejpam-5600	191	29	hs	hs	PROPN
ejpam-5600	191	30	,	,	PUNCT
ejpam-5600	191	31	hm∈[n+1	hm∈[n+1	PROPN
ejpam-5600	191	32	]	]	X
ejpam-5600	191	33	(	(	PUNCT
ejpam-5600	191	34	n	n	ADV
ejpam-5600	191	35	hm	hm	INTJ
ejpam-5600	191	36	hs	hs	INTJ
ejpam-5600	191	37	)	)	PUNCT
ejpam-5600	192	1	k	k	PROPN
ejpam-5600	192	2	(	(	PUNCT
ejpam-5600	192	3	n−hs−hm	n−hs−hm	X
ejpam-5600	192	4	)	)	PUNCT
ejpam-5600	192	5	2	2	NUM
ejpam-5600	192	6	hshm(−1)⟨s	hshm(−1)⟨	NOUN
ejpam-5600	192	7	,	,	PUNCT
ejpam-5600	192	8	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	192	9	,	,	PUNCT
ejpam-5600	192	10	j⟩	j⟩	NOUN
ejpam-5600	192	11	2kn	2kn	ADV
ejpam-5600	192	12	,	,	PUNCT
ejpam-5600	192	13	where	where	SCONJ
ejpam-5600	192	14	(	(	PUNCT
ejpam-5600	192	15	n	n	ADV
ejpam-5600	192	16	hm	hm	INTJ
ejpam-5600	192	17	hs	hs	INTJ
ejpam-5600	192	18	)	)	PUNCT
ejpam-5600	192	19	=	=	SYM
ejpam-5600	192	20	n	n	X
ejpam-5600	192	21	!	!	PUNCT
ejpam-5600	193	1	(	(	PUNCT
ejpam-5600	193	2	hm)!(hs)!(n−	hm)!(hs)!(n−	PROPN
ejpam-5600	193	3	(	(	PUNCT
ejpam-5600	193	4	hm	hm	INTJ
ejpam-5600	193	5	+	+	CCONJ
ejpam-5600	193	6	hs	hs	PROPN
ejpam-5600	193	7	)	)	PUNCT
ejpam-5600	193	8	)	)	PUNCT
ejpam-5600	193	9	!	!	PUNCT
ejpam-5600	194	1	is	be	AUX
ejpam-5600	194	2	the	the	DET
ejpam-5600	194	3	multinomial	multinomial	ADJ
ejpam-5600	194	4	coefficient	coefficient	NOUN
ejpam-5600	194	5	.	.	PUNCT
ejpam-5600	195	1	we	we	PRON
ejpam-5600	195	2	continue	continue	VERB
ejpam-5600	195	3	with	with	ADP
ejpam-5600	195	4	a	a	DET
ejpam-5600	195	5	change	change	NOUN
ejpam-5600	195	6	of	of	ADP
ejpam-5600	195	7	variables	variable	NOUN
ejpam-5600	195	8	t	t	PROPN
ejpam-5600	195	9	=	=	SYM
ejpam-5600	195	10	hs	hs	PROPN
ejpam-5600	196	1	+	+	CCONJ
ejpam-5600	196	2	hm	hm	INTJ
ejpam-5600	196	3	in	in	ADP
ejpam-5600	196	4	the	the	DET
ejpam-5600	196	5	second	second	ADJ
ejpam-5600	196	6	sum	sum	NOUN
ejpam-5600	197	1	and	and	CCONJ
ejpam-5600	197	2	we	we	PRON
ejpam-5600	197	3	get	get	VERB
ejpam-5600	197	4	e((n−	e((n−	PROPN
ejpam-5600	197	5	2wi)(n−	2wi)(n−	NUM
ejpam-5600	197	6	2wj))=	2wj))=	PROPN
ejpam-5600	197	7	1	1	NUM
ejpam-5600	197	8	2kn	2kn	ADJ
ejpam-5600	197	9	∑	∑	PART
ejpam-5600	197	10	s∈[2k	s∈[2k	PROPN
ejpam-5600	197	11	]	]	PUNCT
ejpam-5600	197	12	hs∈[n+1	hs∈[n+1	NOUN
ejpam-5600	197	13	]	]	PUNCT
ejpam-5600	197	14	(	(	PUNCT
ejpam-5600	197	15	n	n	X
ejpam-5600	197	16	hs	hs	INTJ
ejpam-5600	197	17	)	)	PUNCT
ejpam-5600	197	18	k	k	PROPN
ejpam-5600	197	19	(	(	PUNCT
ejpam-5600	197	20	n−hs	n−hs	PROPN
ejpam-5600	197	21	)	)	PUNCT
ejpam-5600	197	22	1	1	NUM
ejpam-5600	197	23	h2s(−1)⟨s,(i+j)⟩	h2s(−1)⟨s,(i+j)⟩	ADP
ejpam-5600	197	24	i̇brahim	i̇brahim	PUNCT
ejpam-5600	197	25	özen	özen	PROPN
ejpam-5600	197	26	/	/	SYM
ejpam-5600	197	27	eur	eur	PROPN
ejpam-5600	197	28	.	.	PUNCT
ejpam-5600	198	1	j.	j.	PROPN
ejpam-5600	198	2	pure	pure	PROPN
ejpam-5600	198	3	appl	appl	PROPN
ejpam-5600	198	4	.	.	PROPN
ejpam-5600	198	5	math	math	PROPN
ejpam-5600	198	6	,	,	PUNCT
ejpam-5600	198	7	17	17	NUM
ejpam-5600	198	8	(	(	PUNCT
ejpam-5600	198	9	4	4	NUM
ejpam-5600	198	10	)	)	PUNCT
ejpam-5600	198	11	(	(	PUNCT
ejpam-5600	198	12	2024	2024	NUM
ejpam-5600	198	13	)	)	PUNCT
ejpam-5600	198	14	,	,	PUNCT
ejpam-5600	198	15	4225	4225	NUM
ejpam-5600	198	16	-	-	SYM
ejpam-5600	198	17	4237	4237	NUM
ejpam-5600	198	18	4233	4233	NUM
ejpam-5600	199	1	+	+	CCONJ
ejpam-5600	199	2	∑	∑	PROPN
ejpam-5600	199	3	s	s	PROPN
ejpam-5600	199	4	,	,	PUNCT
ejpam-5600	199	5	m∈[2k	m∈[2k	PROPN
ejpam-5600	199	6	]	]	PUNCT
ejpam-5600	199	7	s	s	PROPN
ejpam-5600	199	8	̸=m	̸=m	PROPN
ejpam-5600	199	9	t∈[n+1	t∈[n+1	PROPN
ejpam-5600	199	10	]	]	X
ejpam-5600	199	11	hm∈[t+1	hm∈[t+1	PROPN
ejpam-5600	199	12	]	]	X
ejpam-5600	199	13	(	(	PUNCT
ejpam-5600	199	14	n	n	X
ejpam-5600	199	15	t	t	NOUN
ejpam-5600	199	16	)	)	PUNCT
ejpam-5600	199	17	(	(	PUNCT
ejpam-5600	199	18	t	t	PROPN
ejpam-5600	199	19	hm	hm	INTJ
ejpam-5600	199	20	)	)	PUNCT
ejpam-5600	200	1	k	k	PROPN
ejpam-5600	200	2	(	(	PUNCT
ejpam-5600	200	3	n−t	n−t	PROPN
ejpam-5600	200	4	)	)	PUNCT
ejpam-5600	200	5	2	2	NUM
ejpam-5600	200	6	(	(	PUNCT
ejpam-5600	200	7	t	t	PROPN
ejpam-5600	200	8	−	−	PROPN
ejpam-5600	200	9	hm)hm(−1)⟨s	hm)hm(−1)⟨s	PROPN
ejpam-5600	200	10	,	,	PUNCT
ejpam-5600	200	11	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	200	12	,	,	PUNCT
ejpam-5600	200	13	j⟩	j⟩	NOUN
ejpam-5600	200	14	2kn	2kn	ADJ
ejpam-5600	200	15	=	=	PUNCT
ejpam-5600	200	16	1	1	NUM
ejpam-5600	200	17	2kn	2kn	ADJ
ejpam-5600	200	18	∑	∑	PART
ejpam-5600	200	19	s∈[2k	s∈[2k	PROPN
ejpam-5600	200	20	]	]	PUNCT
ejpam-5600	200	21	hs∈[n+1	hs∈[n+1	NOUN
ejpam-5600	200	22	]	]	PUNCT
ejpam-5600	200	23	(	(	PUNCT
ejpam-5600	200	24	n	n	X
ejpam-5600	200	25	hs	hs	INTJ
ejpam-5600	200	26	)	)	PUNCT
ejpam-5600	201	1	k	k	PROPN
ejpam-5600	201	2	(	(	PUNCT
ejpam-5600	201	3	n−hs	n−hs	PROPN
ejpam-5600	201	4	)	)	PUNCT
ejpam-5600	201	5	1	1	NUM
ejpam-5600	201	6	(	(	PUNCT
ejpam-5600	201	7	h2s	h2s	NOUN
ejpam-5600	201	8	−	−	PROPN
ejpam-5600	202	1	hs)(−1)⟨s,(i+j)⟩	hs)(−1)⟨s,(i+j)⟩	PROPN
ejpam-5600	202	2	+	+	CCONJ
ejpam-5600	202	3	1	1	NUM
ejpam-5600	202	4	2kn	2kn	ADJ
ejpam-5600	202	5	∑	∑	PART
ejpam-5600	202	6	s∈[2k	s∈[2k	PROPN
ejpam-5600	202	7	]	]	PUNCT
ejpam-5600	202	8	hs∈[n+1	hs∈[n+1	NOUN
ejpam-5600	202	9	]	]	PUNCT
ejpam-5600	202	10	(	(	PUNCT
ejpam-5600	202	11	n	n	X
ejpam-5600	202	12	hs	hs	INTJ
ejpam-5600	202	13	)	)	PUNCT
ejpam-5600	202	14	k	k	PROPN
ejpam-5600	202	15	(	(	PUNCT
ejpam-5600	202	16	n−hs	n−hs	PROPN
ejpam-5600	202	17	)	)	PUNCT
ejpam-5600	202	18	1	1	NUM
ejpam-5600	203	1	hs(−1)⟨s,(i+j)⟩	hs(−1)⟨s,(i+j)⟩	ADP
ejpam-5600	203	2	−	−	PROPN
ejpam-5600	203	3	∑	∑	PROPN
ejpam-5600	203	4	s	s	PROPN
ejpam-5600	203	5	,	,	PUNCT
ejpam-5600	203	6	m∈[2k	m∈[2k	PROPN
ejpam-5600	203	7	]	]	PUNCT
ejpam-5600	203	8	s	s	PROPN
ejpam-5600	203	9	̸=m	̸=m	PROPN
ejpam-5600	203	10	t∈[n+1	t∈[n+1	PROPN
ejpam-5600	203	11	]	]	X
ejpam-5600	203	12	hm∈[t+1	hm∈[t+1	PROPN
ejpam-5600	203	13	]	]	X
ejpam-5600	203	14	(	(	PUNCT
ejpam-5600	203	15	n	n	X
ejpam-5600	203	16	t	t	NOUN
ejpam-5600	203	17	)	)	PUNCT
ejpam-5600	203	18	(	(	PUNCT
ejpam-5600	203	19	t	t	PROPN
ejpam-5600	203	20	hm	hm	INTJ
ejpam-5600	203	21	)	)	PUNCT
ejpam-5600	204	1	k	k	PROPN
ejpam-5600	204	2	(	(	PUNCT
ejpam-5600	204	3	n−t	n−t	PROPN
ejpam-5600	204	4	)	)	PUNCT
ejpam-5600	204	5	2	2	NUM
ejpam-5600	204	6	(	(	PUNCT
ejpam-5600	204	7	h2	h2	NOUN
ejpam-5600	204	8	m	m	PROPN
ejpam-5600	204	9	−	−	PROPN
ejpam-5600	204	10	hm)(−1)⟨s	hm)(−1)⟨s	PROPN
ejpam-5600	204	11	,	,	PUNCT
ejpam-5600	204	12	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	204	13	,	,	PUNCT
ejpam-5600	204	14	j⟩	j⟩	NOUN
ejpam-5600	204	15	2kn	2kn	ADJ
ejpam-5600	205	1	+	+	CCONJ
ejpam-5600	205	2	∑	∑	PROPN
ejpam-5600	205	3	s	s	PROPN
ejpam-5600	205	4	,	,	PUNCT
ejpam-5600	205	5	m∈[2k	m∈[2k	PROPN
ejpam-5600	205	6	]	]	PUNCT
ejpam-5600	205	7	s	s	PROPN
ejpam-5600	205	8	̸=m	̸=m	PROPN
ejpam-5600	205	9	t∈[n+1	t∈[n+1	PROPN
ejpam-5600	205	10	]	]	X
ejpam-5600	205	11	hm∈[t+1	hm∈[t+1	PROPN
ejpam-5600	205	12	]	]	X
ejpam-5600	205	13	(	(	PUNCT
ejpam-5600	205	14	n	n	X
ejpam-5600	205	15	t	t	NOUN
ejpam-5600	205	16	)	)	PUNCT
ejpam-5600	205	17	(	(	PUNCT
ejpam-5600	205	18	t	t	PROPN
ejpam-5600	205	19	hm	hm	INTJ
ejpam-5600	205	20	)	)	PUNCT
ejpam-5600	206	1	k	k	PROPN
ejpam-5600	206	2	(	(	PUNCT
ejpam-5600	206	3	n−t	n−t	PROPN
ejpam-5600	206	4	)	)	PUNCT
ejpam-5600	206	5	2	2	NUM
ejpam-5600	206	6	(	(	PUNCT
ejpam-5600	206	7	t	t	PROPN
ejpam-5600	206	8	−	−	PROPN
ejpam-5600	206	9	1)hm(−1)⟨s	1)hm(−1)⟨s	NUM
ejpam-5600	206	10	,	,	PUNCT
ejpam-5600	206	11	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	206	12	,	,	PUNCT
ejpam-5600	206	13	j⟩	j⟩	NOUN
ejpam-5600	206	14	2kn	2kn	ADV
ejpam-5600	206	15	(	(	PUNCT
ejpam-5600	206	16	5	5	NUM
ejpam-5600	206	17	)	)	PUNCT
ejpam-5600	206	18	after	after	ADP
ejpam-5600	206	19	summation	summation	NOUN
ejpam-5600	206	20	over	over	ADP
ejpam-5600	206	21	hs	hs	PROPN
ejpam-5600	206	22	,	,	PUNCT
ejpam-5600	207	1	hm	hm	INTJ
ejpam-5600	208	1	and	and	CCONJ
ejpam-5600	208	2	t	t	NOUN
ejpam-5600	208	3	we	we	PRON
ejpam-5600	208	4	obtain	obtain	VERB
ejpam-5600	208	5	the	the	DET
ejpam-5600	208	6	following	following	NOUN
ejpam-5600	208	7	,	,	PUNCT
ejpam-5600	208	8	where	where	SCONJ
ejpam-5600	208	9	the	the	DET
ejpam-5600	208	10	derivatives	derivative	NOUN
ejpam-5600	208	11	are	be	AUX
ejpam-5600	208	12	taken	take	VERB
ejpam-5600	208	13	with	with	ADP
ejpam-5600	208	14	respect	respect	NOUN
ejpam-5600	208	15	to	to	ADP
ejpam-5600	208	16	the	the	DET
ejpam-5600	208	17	variables	variable	NOUN
ejpam-5600	208	18	u	u	NOUN
ejpam-5600	208	19	and	and	CCONJ
ejpam-5600	208	20	v.	v.	NOUN
ejpam-5600	208	21	after	after	ADP
ejpam-5600	208	22	derivatives	derivative	NOUN
ejpam-5600	208	23	we	we	PRON
ejpam-5600	208	24	substitute	substitute	VERB
ejpam-5600	208	25	u	u	NOUN
ejpam-5600	208	26	=	=	SYM
ejpam-5600	208	27	1	1	NUM
ejpam-5600	208	28	and	and	CCONJ
ejpam-5600	208	29	v	v	NOUN
ejpam-5600	208	30	=	=	SYM
ejpam-5600	208	31	2	2	X
ejpam-5600	208	32	.	.	PUNCT
ejpam-5600	209	1	e((n−	e((n−	VERB
ejpam-5600	209	2	2wi)(n−	2wi)(n−	NUM
ejpam-5600	209	3	2wj	2wj	NOUN
ejpam-5600	209	4	)	)	PUNCT
ejpam-5600	209	5	)	)	PUNCT
ejpam-5600	210	1	=	=	SYM
ejpam-5600	211	1	1	1	NUM
ejpam-5600	211	2	2kn	2kn	ADJ
ejpam-5600	211	3	∑	∑	PUNCT
ejpam-5600	211	4	s∈[2k	s∈[2k	NOUN
ejpam-5600	211	5	]	]	PUNCT
ejpam-5600	212	1	[	[	X
ejpam-5600	212	2	(	(	PUNCT
ejpam-5600	212	3	k1	k1	X
ejpam-5600	212	4	+	+	CCONJ
ejpam-5600	212	5	u)n]′′(−1)⟨s,(i+j)⟩	u)n]′′(−1)⟨s,(i+j)⟩	PROPN
ejpam-5600	212	6	+	+	CCONJ
ejpam-5600	212	7	1	1	NUM
ejpam-5600	212	8	2kn	2kn	ADJ
ejpam-5600	212	9	∑	∑	PUNCT
ejpam-5600	212	10	s∈[2k	s∈[2k	NOUN
ejpam-5600	212	11	]	]	PUNCT
ejpam-5600	213	1	[	[	X
ejpam-5600	213	2	(	(	PUNCT
ejpam-5600	213	3	k1	k1	X
ejpam-5600	213	4	+	+	CCONJ
ejpam-5600	213	5	u)n]′(−1)⟨s,(i+j)⟩	u)n]′(−1)⟨s,(i+j)⟩	PROPN
ejpam-5600	213	6	+	+	CCONJ
ejpam-5600	213	7	1	1	NUM
ejpam-5600	213	8	2kn	2kn	ADJ
ejpam-5600	213	9	∑	∑	PUNCT
ejpam-5600	213	10	s	s	PROPN
ejpam-5600	213	11	,	,	PUNCT
ejpam-5600	213	12	m∈[2k	m∈[2k	PROPN
ejpam-5600	213	13	]	]	PUNCT
ejpam-5600	213	14	s̸=m	s̸=m	PROPN
ejpam-5600	214	1	[	[	X
ejpam-5600	214	2	(	(	PUNCT
ejpam-5600	214	3	k2	k2	X
ejpam-5600	214	4	+	+	CCONJ
ejpam-5600	214	5	v)n]′′(−1)⟨s	v)n]′′(−1)⟨s	NUM
ejpam-5600	214	6	,	,	PUNCT
ejpam-5600	214	7	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	214	8	,	,	PUNCT
ejpam-5600	214	9	j)⟩	j)⟩	X
ejpam-5600	214	10	=	=	SYM
ejpam-5600	214	11	n(n−	n(n−	PROPN
ejpam-5600	214	12	1	1	NUM
ejpam-5600	214	13	)	)	PUNCT
ejpam-5600	214	14	22k	22k	NOUN
ejpam-5600	214	15	∑	∑	ADP
ejpam-5600	214	16	s∈[2k	s∈[2k	PROPN
ejpam-5600	214	17	]	]	PUNCT
ejpam-5600	214	18	(	(	PUNCT
ejpam-5600	214	19	−1)⟨s,(i+j)⟩	−1)⟨s,(i+j)⟩	NUM
ejpam-5600	214	20	i̇brahim	i̇brahim	PROPN
ejpam-5600	214	21	özen	özen	PROPN
ejpam-5600	214	22	/	/	SYM
ejpam-5600	214	23	eur	eur	PROPN
ejpam-5600	214	24	.	.	PUNCT
ejpam-5600	215	1	j.	j.	PROPN
ejpam-5600	215	2	pure	pure	PROPN
ejpam-5600	215	3	appl	appl	PROPN
ejpam-5600	215	4	.	.	PROPN
ejpam-5600	215	5	math	math	PROPN
ejpam-5600	215	6	,	,	PUNCT
ejpam-5600	215	7	17	17	NUM
ejpam-5600	215	8	(	(	PUNCT
ejpam-5600	215	9	4	4	NUM
ejpam-5600	215	10	)	)	PUNCT
ejpam-5600	215	11	(	(	PUNCT
ejpam-5600	215	12	2024	2024	NUM
ejpam-5600	215	13	)	)	PUNCT
ejpam-5600	215	14	,	,	PUNCT
ejpam-5600	215	15	4225	4225	NUM
ejpam-5600	215	16	-	-	SYM
ejpam-5600	215	17	4237	4237	NUM
ejpam-5600	215	18	4234	4234	NUM
ejpam-5600	215	19	+	+	CCONJ
ejpam-5600	215	20	n	n	CCONJ
ejpam-5600	215	21	2k	2k	NUM
ejpam-5600	215	22	∑	∑	ADV
ejpam-5600	215	23	s∈[2k	s∈[2k	PROPN
ejpam-5600	215	24	]	]	PUNCT
ejpam-5600	215	25	(	(	PUNCT
ejpam-5600	215	26	−1)⟨s,(i+j)⟩	−1)⟨s,(i+j)⟩	NUM
ejpam-5600	215	27	+	+	CCONJ
ejpam-5600	215	28	n(n−	n(n−	PROPN
ejpam-5600	215	29	1	1	NUM
ejpam-5600	215	30	)	)	PUNCT
ejpam-5600	215	31	22k	22k	NOUN
ejpam-5600	215	32	∑	∑	PROPN
ejpam-5600	215	33	s	s	NOUN
ejpam-5600	215	34	,	,	PUNCT
ejpam-5600	215	35	m∈[2k	m∈[2k	PROPN
ejpam-5600	215	36	]	]	PUNCT
ejpam-5600	215	37	s	s	PROPN
ejpam-5600	215	38	̸=m	̸=m	PROPN
ejpam-5600	215	39	(	(	PUNCT
ejpam-5600	215	40	−1)⟨s	−1)⟨s	PROPN
ejpam-5600	215	41	,	,	PUNCT
ejpam-5600	215	42	i⟩+⟨m	i⟩+⟨m	PROPN
ejpam-5600	215	43	,	,	PUNCT
ejpam-5600	215	44	j)⟩	j)⟩	X
ejpam-5600	215	45	by	by	ADP
ejpam-5600	215	46	lemma	lemma	PROPN
ejpam-5600	215	47	3	3	NUM
ejpam-5600	215	48	the	the	DET
ejpam-5600	215	49	result	result	NOUN
ejpam-5600	215	50	is	be	AUX
ejpam-5600	215	51	e((n−	e((n−	PROPN
ejpam-5600	215	52	2wi)(n−	2wi)(n−	NUM
ejpam-5600	215	53	2wj	2wj	NOUN
ejpam-5600	215	54	)	)	PUNCT
ejpam-5600	215	55	)	)	PUNCT
ejpam-5600	216	1	=	=	PRON
ejpam-5600	216	2	{	{	PUNCT
ejpam-5600	216	3	n	n	CCONJ
ejpam-5600	216	4	,	,	PUNCT
ejpam-5600	216	5	for	for	ADP
ejpam-5600	216	6	i	i	PROPN
ejpam-5600	216	7	=	=	SYM
ejpam-5600	216	8	j	j	PROPN
ejpam-5600	216	9	,	,	PUNCT
ejpam-5600	216	10	i	i	PRON
ejpam-5600	216	11	,	,	PUNCT
ejpam-5600	216	12	j	j	PROPN
ejpam-5600	216	13	≥	≥	NUM
ejpam-5600	216	14	1	1	NUM
ejpam-5600	216	15	,	,	PUNCT
ejpam-5600	216	16	0	0	NUM
ejpam-5600	216	17	,	,	PUNCT
ejpam-5600	216	18	for	for	ADP
ejpam-5600	216	19	i	i	PROPN
ejpam-5600	216	20	̸=	̸=	PROPN
ejpam-5600	216	21	j	j	PROPN
ejpam-5600	216	22	,	,	PUNCT
ejpam-5600	216	23	i	i	PRON
ejpam-5600	216	24	,	,	PUNCT
ejpam-5600	216	25	j	j	PROPN
ejpam-5600	216	26	≥	≥	NUM
ejpam-5600	216	27	1	1	NUM
ejpam-5600	216	28	.	.	PUNCT
ejpam-5600	217	1	finally	finally	ADV
ejpam-5600	217	2	we	we	PRON
ejpam-5600	217	3	get	get	VERB
ejpam-5600	217	4	the	the	DET
ejpam-5600	217	5	expectations	expectation	NOUN
ejpam-5600	217	6	of	of	ADP
ejpam-5600	217	7	products	product	NOUN
ejpam-5600	217	8	of	of	ADP
ejpam-5600	217	9	nonzero	nonzero	PROPN
ejpam-5600	217	10	codeword	codeword	NOUN
ejpam-5600	217	11	weights	weight	NOUN
ejpam-5600	217	12	as	as	ADP
ejpam-5600	217	13	e(wiwj	e(wiwj	NOUN
ejpam-5600	217	14	)	)	PUNCT
ejpam-5600	217	15	=	=	PRON
ejpam-5600	217	16	{	{	PUNCT
ejpam-5600	217	17	n2+n	n2+n	PROPN
ejpam-5600	217	18	4	4	NUM
ejpam-5600	217	19	,	,	PUNCT
ejpam-5600	217	20	for	for	ADP
ejpam-5600	217	21	i	i	PROPN
ejpam-5600	217	22	=	=	SYM
ejpam-5600	217	23	j	j	PROPN
ejpam-5600	217	24	,	,	PUNCT
ejpam-5600	217	25	i	i	PRON
ejpam-5600	217	26	,	,	PUNCT
ejpam-5600	217	27	j	j	PROPN
ejpam-5600	217	28	≥	≥	PROPN
ejpam-5600	217	29	1	1	NUM
ejpam-5600	217	30	,	,	PUNCT
ejpam-5600	217	31	n2	n2	NOUN
ejpam-5600	217	32	4	4	NUM
ejpam-5600	217	33	,	,	PUNCT
ejpam-5600	217	34	for	for	ADP
ejpam-5600	217	35	i	i	PROPN
ejpam-5600	217	36	̸=	̸=	PROPN
ejpam-5600	217	37	j	j	PROPN
ejpam-5600	217	38	,	,	PUNCT
ejpam-5600	217	39	i	i	PRON
ejpam-5600	217	40	,	,	PUNCT
ejpam-5600	217	41	j	j	PROPN
ejpam-5600	217	42	≥	≥	PROPN
ejpam-5600	217	43	1	1	NUM
ejpam-5600	217	44	.	.	PUNCT
ejpam-5600	218	1	two	two	NUM
ejpam-5600	218	2	random	random	ADJ
ejpam-5600	218	3	variables	variable	NOUN
ejpam-5600	218	4	x	x	PUNCT
ejpam-5600	218	5	and	and	CCONJ
ejpam-5600	218	6	y	y	PROPN
ejpam-5600	218	7	are	be	AUX
ejpam-5600	218	8	called	call	VERB
ejpam-5600	218	9	statistically	statistically	ADV
ejpam-5600	218	10	uncorrelated	uncorrelated	ADJ
ejpam-5600	218	11	if	if	SCONJ
ejpam-5600	218	12	the	the	DET
ejpam-5600	218	13	covariance	covariance	NOUN
ejpam-5600	218	14	between	between	ADP
ejpam-5600	218	15	them	they	PRON
ejpam-5600	218	16	is	be	AUX
ejpam-5600	218	17	0	0	NUM
ejpam-5600	218	18	,	,	PUNCT
ejpam-5600	218	19	cov(x	cov(x	PROPN
ejpam-5600	218	20	,	,	PUNCT
ejpam-5600	218	21	y	y	PROPN
ejpam-5600	218	22	)	)	PUNCT
ejpam-5600	219	1	=	=	SYM
ejpam-5600	219	2	e(xy	e(xy	PROPN
ejpam-5600	219	3	)	)	PUNCT
ejpam-5600	219	4	−	−	PROPN
ejpam-5600	219	5	e(x)e(y	e(x)e(y	ADV
ejpam-5600	219	6	)	)	PUNCT
ejpam-5600	219	7	=	=	SYM
ejpam-5600	220	1	0	0	X
ejpam-5600	220	2	.	.	PUNCT
ejpam-5600	221	1	we	we	PRON
ejpam-5600	221	2	observe	observe	VERB
ejpam-5600	221	3	that	that	SCONJ
ejpam-5600	221	4	this	this	PRON
ejpam-5600	221	5	is	be	AUX
ejpam-5600	221	6	the	the	DET
ejpam-5600	221	7	case	case	NOUN
ejpam-5600	221	8	for	for	ADP
ejpam-5600	221	9	the	the	DET
ejpam-5600	221	10	weights	weight	NOUN
ejpam-5600	221	11	of	of	ADP
ejpam-5600	221	12	distinct	distinct	ADJ
ejpam-5600	221	13	nonzero	nonzero	PROPN
ejpam-5600	221	14	codewords	codeword	NOUN
ejpam-5600	221	15	in	in	ADP
ejpam-5600	221	16	a	a	DET
ejpam-5600	221	17	random	random	ADJ
ejpam-5600	221	18	code	code	NOUN
ejpam-5600	221	19	.	.	PUNCT
ejpam-5600	222	1	corollary	corollary	ADJ
ejpam-5600	222	2	1	1	NUM
ejpam-5600	222	3	.	.	PUNCT
ejpam-5600	223	1	weights	weight	NOUN
ejpam-5600	223	2	of	of	ADP
ejpam-5600	223	3	distinct	distinct	ADJ
ejpam-5600	223	4	nonzero	nonzero	NOUN
ejpam-5600	223	5	words	word	NOUN
ejpam-5600	223	6	of	of	ADP
ejpam-5600	223	7	a	a	DET
ejpam-5600	223	8	random	random	ADJ
ejpam-5600	223	9	binary	binary	ADJ
ejpam-5600	223	10	linear	linear	PROPN
ejpam-5600	223	11	code	code	NOUN
ejpam-5600	223	12	are	be	AUX
ejpam-5600	223	13	uncorrelated	uncorrelated	ADJ
ejpam-5600	223	14	cov(wi	cov(wi	ADJ
ejpam-5600	223	15	,	,	PUNCT
ejpam-5600	223	16	wj	wj	PROPN
ejpam-5600	223	17	)	)	PUNCT
ejpam-5600	223	18	=	=	SYM
ejpam-5600	224	1	0	0	NUM
ejpam-5600	224	2	,	,	PUNCT
ejpam-5600	224	3	for	for	ADP
ejpam-5600	224	4	all	all	DET
ejpam-5600	224	5	i	i	PROPN
ejpam-5600	224	6	,	,	PUNCT
ejpam-5600	224	7	j	j	PROPN
ejpam-5600	224	8	≥	≥	NUM
ejpam-5600	224	9	1	1	NUM
ejpam-5600	224	10	and	and	CCONJ
ejpam-5600	224	11	i	i	PRON
ejpam-5600	224	12	̸=	̸=	PROPN
ejpam-5600	224	13	j.	j.	PROPN
ejpam-5600	224	14	4	4	PROPN
ejpam-5600	224	15	.	.	PUNCT
ejpam-5600	225	1	correlation	correlation	NOUN
ejpam-5600	225	2	properties	property	NOUN
ejpam-5600	225	3	of	of	ADP
ejpam-5600	225	4	nonzero	nonzero	ADJ
ejpam-5600	225	5	words	word	NOUN
ejpam-5600	225	6	in	in	ADP
ejpam-5600	225	7	a	a	DET
ejpam-5600	225	8	random	random	ADJ
ejpam-5600	225	9	binary	binary	NOUN
ejpam-5600	225	10	liner	liner	NOUN
ejpam-5600	225	11	code	code	NOUN
ejpam-5600	225	12	let	let	VERB
ejpam-5600	225	13	c	c	NOUN
ejpam-5600	225	14	=	=	SYM
ejpam-5600	225	15	(	(	PUNCT
ejpam-5600	225	16	c1	c1	PROPN
ejpam-5600	225	17	,	,	PUNCT
ejpam-5600	225	18	c2	c2	PROPN
ejpam-5600	225	19	,	,	PUNCT
ejpam-5600	225	20	.	.	PUNCT
ejpam-5600	225	21	.	.	PUNCT
ejpam-5600	225	22	.	.	PUNCT
ejpam-5600	226	1	,	,	PUNCT
ejpam-5600	226	2	cn	cn	PROPN
ejpam-5600	226	3	)	)	PUNCT
ejpam-5600	226	4	and	and	CCONJ
ejpam-5600	226	5	e	e	X
ejpam-5600	226	6	=	=	SYM
ejpam-5600	226	7	(	(	PUNCT
ejpam-5600	226	8	e1	e1	PROPN
ejpam-5600	226	9	,	,	PUNCT
ejpam-5600	226	10	e2	e2	PROPN
ejpam-5600	226	11	,	,	PUNCT
ejpam-5600	226	12	.	.	PUNCT
ejpam-5600	226	13	.	.	PUNCT
ejpam-5600	227	1	.	.	PUNCT
ejpam-5600	228	1	,	,	PUNCT
ejpam-5600	228	2	en	en	AUX
ejpam-5600	228	3	)	)	PUNCT
ejpam-5600	228	4	be	be	VERB
ejpam-5600	228	5	two	two	NUM
ejpam-5600	228	6	vectors	vector	NOUN
ejpam-5600	228	7	in	in	ADP
ejpam-5600	228	8	fn	fn	PROPN
ejpam-5600	228	9	2	2	NUM
ejpam-5600	228	10	.	.	PUNCT
ejpam-5600	229	1	we	we	PRON
ejpam-5600	229	2	define	define	VERB
ejpam-5600	229	3	the	the	DET
ejpam-5600	229	4	periodic	periodic	ADJ
ejpam-5600	229	5	auto	auto	NOUN
ejpam-5600	229	6	-	-	PUNCT
ejpam-5600	229	7	correlation	correlation	NOUN
ejpam-5600	229	8	and	and	CCONJ
ejpam-5600	229	9	cross	cross	ADJ
ejpam-5600	229	10	-	-	ADJ
ejpam-5600	229	11	correlation	correlation	ADJ
ejpam-5600	229	12	functions	function	NOUN
ejpam-5600	229	13	on	on	ADP
ejpam-5600	229	14	vectors	vector	NOUN
ejpam-5600	229	15	of	of	ADP
ejpam-5600	229	16	fn	fn	PROPN
ejpam-5600	229	17	2	2	NUM
ejpam-5600	229	18	as	as	SCONJ
ejpam-5600	229	19	follows	follow	VERB
ejpam-5600	229	20	rc	rc	PROPN
ejpam-5600	229	21	,	,	PUNCT
ejpam-5600	229	22	c(u	c(u	PROPN
ejpam-5600	229	23	)	)	PUNCT
ejpam-5600	229	24	=	=	SYM
ejpam-5600	229	25	rc(u	rc(u	X
ejpam-5600	229	26	)	)	PUNCT
ejpam-5600	230	1	=	=	SYM
ejpam-5600	230	2	n∑	n∑	NOUN
ejpam-5600	230	3	i=1	i=1	PROPN
ejpam-5600	231	1	(	(	PUNCT
ejpam-5600	231	2	−1)ci+ci+u	−1)ci+ci+u	PROPN
ejpam-5600	231	3	and	and	CCONJ
ejpam-5600	231	4	rc	rc	PROPN
ejpam-5600	231	5	,	,	PUNCT
ejpam-5600	231	6	e(u	e(u	PROPN
ejpam-5600	231	7	)	)	PUNCT
ejpam-5600	232	1	=	=	PUNCT
ejpam-5600	233	1	n∑	n∑	NOUN
ejpam-5600	233	2	i=1	i=1	PROPN
ejpam-5600	233	3	(	(	PUNCT
ejpam-5600	233	4	−1)ci+ei+u	−1)ci+ei+u	NOUN
ejpam-5600	233	5	respectively	respectively	ADV
ejpam-5600	233	6	.	.	PUNCT
ejpam-5600	234	1	the	the	DET
ejpam-5600	234	2	indices	index	NOUN
ejpam-5600	234	3	are	be	AUX
ejpam-5600	234	4	evaluated	evaluate	VERB
ejpam-5600	234	5	modulo	modulo	PROPN
ejpam-5600	234	6	n.	n.	NOUN
ejpam-5600	234	7	given	give	VERB
ejpam-5600	234	8	e	e	PROPN
ejpam-5600	234	9	∈	∈	PROPN
ejpam-5600	234	10	fn	fn	NOUN
ejpam-5600	234	11	2	2	NUM
ejpam-5600	234	12	let	let	VERB
ejpam-5600	234	13	us	we	PRON
ejpam-5600	234	14	denote	denote	VERB
ejpam-5600	234	15	by	by	ADP
ejpam-5600	234	16	eu	eu	PROPN
ejpam-5600	234	17	,	,	PUNCT
ejpam-5600	234	18	the	the	DET
ejpam-5600	234	19	vector	vector	NOUN
ejpam-5600	234	20	obtained	obtain	VERB
ejpam-5600	234	21	by	by	ADP
ejpam-5600	234	22	shifting	shift	VERB
ejpam-5600	234	23	each	each	DET
ejpam-5600	234	24	coordinate	coordinate	NOUN
ejpam-5600	234	25	of	of	ADP
ejpam-5600	234	26	e	e	NOUN
ejpam-5600	234	27	by	by	ADP
ejpam-5600	234	28	u	u	NOUN
ejpam-5600	234	29	to	to	ADP
ejpam-5600	234	30	the	the	DET
ejpam-5600	234	31	left	left	NOUN
ejpam-5600	234	32	eu	eu	PROPN
ejpam-5600	235	1	=	=	PRON
ejpam-5600	235	2	(	(	PUNCT
ejpam-5600	235	3	e1+u	e1+u	PROPN
ejpam-5600	235	4	,	,	PUNCT
ejpam-5600	235	5	e2+u	e2+u	NOUN
ejpam-5600	235	6	,	,	PUNCT
ejpam-5600	235	7	.	.	PUNCT
ejpam-5600	235	8	.	.	PUNCT
ejpam-5600	235	9	.	.	PUNCT
ejpam-5600	236	1	,	,	PUNCT
ejpam-5600	236	2	en	en	X
ejpam-5600	236	3	,	,	PUNCT
ejpam-5600	236	4	e1	e1	NOUN
ejpam-5600	236	5	,	,	PUNCT
ejpam-5600	236	6	.	.	PUNCT
ejpam-5600	236	7	.	.	PUNCT
ejpam-5600	237	1	.	.	PUNCT
ejpam-5600	238	1	,	,	PUNCT
ejpam-5600	238	2	eu	eu	PROPN
ejpam-5600	238	3	)	)	PUNCT
ejpam-5600	238	4	.	.	PUNCT
ejpam-5600	239	1	i̇brahim	i̇brahim	PUNCT
ejpam-5600	240	1	özen	özen	PROPN
ejpam-5600	240	2	/	/	SYM
ejpam-5600	240	3	eur	eur	PROPN
ejpam-5600	240	4	.	.	PUNCT
ejpam-5600	241	1	j.	j.	PROPN
ejpam-5600	241	2	pure	pure	PROPN
ejpam-5600	241	3	appl	appl	PROPN
ejpam-5600	241	4	.	.	PROPN
ejpam-5600	241	5	math	math	PROPN
ejpam-5600	241	6	,	,	PUNCT
ejpam-5600	241	7	17	17	NUM
ejpam-5600	241	8	(	(	PUNCT
ejpam-5600	241	9	4	4	NUM
ejpam-5600	241	10	)	)	PUNCT
ejpam-5600	241	11	(	(	PUNCT
ejpam-5600	241	12	2024	2024	NUM
ejpam-5600	241	13	)	)	PUNCT
ejpam-5600	241	14	,	,	PUNCT
ejpam-5600	241	15	4225	4225	NUM
ejpam-5600	241	16	-	-	SYM
ejpam-5600	241	17	4237	4237	NUM
ejpam-5600	241	18	4235	4235	NUM
ejpam-5600	241	19	the	the	DET
ejpam-5600	241	20	correlation	correlation	NOUN
ejpam-5600	241	21	functions	function	NOUN
ejpam-5600	241	22	rc	rc	PROPN
ejpam-5600	241	23	and	and	CCONJ
ejpam-5600	241	24	rc	rc	PROPN
ejpam-5600	241	25	,	,	PUNCT
ejpam-5600	241	26	e	e	PROPN
ejpam-5600	241	27	evaluates	evaluate	VERB
ejpam-5600	241	28	the	the	DET
ejpam-5600	241	29	following	following	NOUN
ejpam-5600	241	30	:	:	PUNCT
ejpam-5600	241	31	if	if	SCONJ
ejpam-5600	241	32	in	in	ADP
ejpam-5600	241	33	a	a	DET
ejpam-5600	241	34	coordinate	coordinate	NOUN
ejpam-5600	241	35	the	the	DET
ejpam-5600	241	36	vectors	vector	NOUN
ejpam-5600	241	37	agree	agree	VERB
ejpam-5600	241	38	,	,	PUNCT
ejpam-5600	241	39	then	then	ADV
ejpam-5600	241	40	this	this	DET
ejpam-5600	241	41	coordinates	coordinate	NOUN
ejpam-5600	241	42	contributes	contribute	VERB
ejpam-5600	241	43	a	a	DET
ejpam-5600	241	44	(	(	PUNCT
ejpam-5600	241	45	+1	+1	NOUN
ejpam-5600	241	46	)	)	PUNCT
ejpam-5600	241	47	and	and	CCONJ
ejpam-5600	241	48	if	if	SCONJ
ejpam-5600	241	49	the	the	DET
ejpam-5600	241	50	the	the	DET
ejpam-5600	241	51	entries	entry	NOUN
ejpam-5600	241	52	in	in	ADP
ejpam-5600	241	53	the	the	DET
ejpam-5600	241	54	same	same	ADJ
ejpam-5600	241	55	coordinate	coordinate	NOUN
ejpam-5600	241	56	are	be	AUX
ejpam-5600	241	57	different	different	ADJ
ejpam-5600	241	58	this	this	DET
ejpam-5600	241	59	coordinate	coordinate	NOUN
ejpam-5600	241	60	contributes	contribute	VERB
ejpam-5600	241	61	a	a	DET
ejpam-5600	241	62	(	(	PUNCT
ejpam-5600	241	63	−1	−1	NOUN
ejpam-5600	241	64	)	)	PUNCT
ejpam-5600	241	65	.	.	PUNCT
ejpam-5600	242	1	so	so	ADV
ejpam-5600	242	2	we	we	PRON
ejpam-5600	242	3	can	can	AUX
ejpam-5600	242	4	rewrite	rewrite	VERB
ejpam-5600	242	5	the	the	DET
ejpam-5600	242	6	correlation	correlation	NOUN
ejpam-5600	242	7	functions	function	NOUN
ejpam-5600	242	8	as	as	SCONJ
ejpam-5600	242	9	follows	follow	VERB
ejpam-5600	242	10	rc(u	rc(u	NOUN
ejpam-5600	242	11	)	)	PUNCT
ejpam-5600	243	1	=	=	SYM
ejpam-5600	243	2	n∑	n∑	NOUN
ejpam-5600	243	3	i=1	i=1	PROPN
ejpam-5600	244	1	(	(	PUNCT
ejpam-5600	244	2	−1)ci+ci+u	−1)ci+ci+u	NOUN
ejpam-5600	244	3	=	=	SYM
ejpam-5600	244	4	n−	n−	NOUN
ejpam-5600	244	5	2dh(c	2dh(c	NUM
ejpam-5600	244	6	,	,	PUNCT
ejpam-5600	244	7	cu	cu	PROPN
ejpam-5600	244	8	)	)	PUNCT
ejpam-5600	244	9	and	and	CCONJ
ejpam-5600	244	10	(	(	PUNCT
ejpam-5600	244	11	6	6	X
ejpam-5600	244	12	)	)	PUNCT
ejpam-5600	244	13	rc	rc	PROPN
ejpam-5600	244	14	,	,	PUNCT
ejpam-5600	244	15	e(u	e(u	PROPN
ejpam-5600	244	16	)	)	PUNCT
ejpam-5600	244	17	=	=	PUNCT
ejpam-5600	245	1	n∑	n∑	NOUN
ejpam-5600	245	2	i=1	i=1	PROPN
ejpam-5600	245	3	(	(	PUNCT
ejpam-5600	245	4	−1)ci+ei+u	−1)ci+ei+u	NOUN
ejpam-5600	245	5	=	=	SYM
ejpam-5600	245	6	n−	n−	NOUN
ejpam-5600	245	7	2dh(c	2dh(c	NUM
ejpam-5600	245	8	,	,	PUNCT
ejpam-5600	245	9	eu	eu	NOUN
ejpam-5600	245	10	)	)	PUNCT
ejpam-5600	245	11	,	,	PUNCT
ejpam-5600	245	12	(	(	PUNCT
ejpam-5600	245	13	7	7	X
ejpam-5600	245	14	)	)	PUNCT
ejpam-5600	245	15	where	where	SCONJ
ejpam-5600	245	16	dh	dh	NOUN
ejpam-5600	245	17	is	be	AUX
ejpam-5600	245	18	the	the	DET
ejpam-5600	245	19	hamming	hamming	NOUN
ejpam-5600	245	20	distance	distance	NOUN
ejpam-5600	245	21	.	.	PUNCT
ejpam-5600	246	1	the	the	DET
ejpam-5600	246	2	following	follow	VERB
ejpam-5600	246	3	formulation	formulation	NOUN
ejpam-5600	246	4	of	of	ADP
ejpam-5600	246	5	hamming	hamming	NOUN
ejpam-5600	246	6	distance	distance	NOUN
ejpam-5600	246	7	on	on	ADP
ejpam-5600	246	8	fn	fn	NOUN
ejpam-5600	246	9	2	2	NUM
ejpam-5600	246	10	will	will	AUX
ejpam-5600	246	11	be	be	AUX
ejpam-5600	246	12	useful	useful	ADJ
ejpam-5600	246	13	dh(c	dh(c	NOUN
ejpam-5600	246	14	,	,	PUNCT
ejpam-5600	246	15	e	e	NOUN
ejpam-5600	246	16	)	)	PUNCT
ejpam-5600	246	17	=	=	PUNCT
ejpam-5600	247	1	∥c∥+	∥c∥+	PUNCT
ejpam-5600	247	2	∥e∥	∥e∥	PROPN
ejpam-5600	247	3	−	−	PROPN
ejpam-5600	247	4	2⟨c	2⟨c	NUM
ejpam-5600	247	5	,	,	PUNCT
ejpam-5600	247	6	e⟩	e⟩	NOUN
ejpam-5600	247	7	,	,	PUNCT
ejpam-5600	247	8	(	(	PUNCT
ejpam-5600	247	9	8)	8)	NUM
ejpam-5600	247	10	where	where	SCONJ
ejpam-5600	247	11	∥	∥	PUNCT
ejpam-5600	247	12	·	·	PUNCT
ejpam-5600	247	13	∥	∥	PUNCT
ejpam-5600	247	14	denotes	denote	VERB
ejpam-5600	247	15	the	the	DET
ejpam-5600	247	16	weight	weight	NOUN
ejpam-5600	247	17	of	of	ADP
ejpam-5600	247	18	the	the	DET
ejpam-5600	247	19	vector	vector	NOUN
ejpam-5600	247	20	and	and	CCONJ
ejpam-5600	247	21	the	the	DET
ejpam-5600	247	22	inner	inner	ADJ
ejpam-5600	247	23	product	product	NOUN
ejpam-5600	247	24	is	be	AUX
ejpam-5600	247	25	evaluated	evaluate	VERB
ejpam-5600	247	26	over	over	ADP
ejpam-5600	247	27	r.	r.	PROPN
ejpam-5600	247	28	the	the	DET
ejpam-5600	247	29	following	follow	VERB
ejpam-5600	247	30	theorem	theorem	NOUN
ejpam-5600	247	31	gives	give	VERB
ejpam-5600	247	32	the	the	DET
ejpam-5600	247	33	expectations	expectation	NOUN
ejpam-5600	247	34	of	of	ADP
ejpam-5600	247	35	sums	sum	NOUN
ejpam-5600	247	36	of	of	ADP
ejpam-5600	247	37	auto	auto	NOUN
ejpam-5600	247	38	-	-	PUNCT
ejpam-5600	247	39	correlations	correlation	NOUN
ejpam-5600	247	40	and	and	CCONJ
ejpam-5600	247	41	sums	sum	NOUN
ejpam-5600	247	42	of	of	ADP
ejpam-5600	247	43	cross	cross	NOUN
ejpam-5600	247	44	-	-	NOUN
ejpam-5600	247	45	correlations	correlation	NOUN
ejpam-5600	247	46	between	between	ADP
ejpam-5600	247	47	the	the	DET
ejpam-5600	247	48	nonzero	nonzero	PROPN
ejpam-5600	247	49	words	word	NOUN
ejpam-5600	247	50	in	in	ADP
ejpam-5600	247	51	a	a	DET
ejpam-5600	247	52	random	random	ADJ
ejpam-5600	247	53	binary	binary	ADJ
ejpam-5600	247	54	linear	linear	PROPN
ejpam-5600	247	55	code	code	PROPN
ejpam-5600	247	56	.	.	PUNCT
ejpam-5600	248	1	theorem	theorem	NOUN
ejpam-5600	248	2	3	3	X
ejpam-5600	248	3	.	.	PUNCT
ejpam-5600	249	1	let	let	VERB
ejpam-5600	249	2	c	c	PRON
ejpam-5600	249	3	be	be	AUX
ejpam-5600	249	4	a	a	DET
ejpam-5600	249	5	random	random	ADJ
ejpam-5600	249	6	binary	binary	ADJ
ejpam-5600	249	7	linear	linear	PROPN
ejpam-5600	250	1	[	[	X
ejpam-5600	250	2	n	n	CCONJ
ejpam-5600	250	3	,	,	PUNCT
ejpam-5600	250	4	k	k	X
ejpam-5600	250	5	]	]	X
ejpam-5600	250	6	code	code	NOUN
ejpam-5600	250	7	and	and	CCONJ
ejpam-5600	250	8	let	let	VERB
ejpam-5600	250	9	c	c	NOUN
ejpam-5600	250	10	and	and	CCONJ
ejpam-5600	250	11	e	e	NOUN
ejpam-5600	250	12	be	be	AUX
ejpam-5600	250	13	two	two	NUM
ejpam-5600	250	14	distinct	distinct	ADJ
ejpam-5600	250	15	nonzero	nonzero	PROPN
ejpam-5600	250	16	codewords	codeword	NOUN
ejpam-5600	250	17	.	.	PUNCT
ejpam-5600	251	1	then	then	ADV
ejpam-5600	251	2	we	we	PRON
ejpam-5600	251	3	have	have	VERB
ejpam-5600	251	4	n−1∑	n−1∑	NUM
ejpam-5600	251	5	u=1	u=1	PROPN
ejpam-5600	251	6	e(rc(u	e(rc(u	PROPN
ejpam-5600	251	7	)	)	PUNCT
ejpam-5600	251	8	)	)	PUNCT
ejpam-5600	252	1	=	=	SYM
ejpam-5600	252	2	0	0	NUM
ejpam-5600	252	3	and	and	CCONJ
ejpam-5600	252	4	n−1∑	n−1∑	NUM
ejpam-5600	252	5	u=0	u=0	SYM
ejpam-5600	252	6	e(rc	e(rc	PROPN
ejpam-5600	252	7	,	,	PUNCT
ejpam-5600	252	8	e(u	e(u	PROPN
ejpam-5600	252	9	)	)	PUNCT
ejpam-5600	252	10	)	)	PUNCT
ejpam-5600	253	1	=	=	PUNCT
ejpam-5600	253	2	0	0	X
ejpam-5600	253	3	.	.	PUNCT
ejpam-5600	254	1	proof	proof	NOUN
ejpam-5600	254	2	.	.	PUNCT
ejpam-5600	255	1	by	by	ADP
ejpam-5600	255	2	(	(	PUNCT
ejpam-5600	255	3	6	6	NUM
ejpam-5600	255	4	)	)	PUNCT
ejpam-5600	255	5	and	and	CCONJ
ejpam-5600	255	6	(	(	PUNCT
ejpam-5600	255	7	8)	8)	NUM
ejpam-5600	255	8	we	we	PRON
ejpam-5600	255	9	have	have	VERB
ejpam-5600	255	10	rc(u	rc(u	NOUN
ejpam-5600	255	11	)	)	PUNCT
ejpam-5600	256	1	=	=	SYM
ejpam-5600	256	2	n−	n−	NOUN
ejpam-5600	256	3	2dh(c	2dh(c	NUM
ejpam-5600	256	4	,	,	PUNCT
ejpam-5600	256	5	cu	cu	NOUN
ejpam-5600	256	6	)	)	PUNCT
ejpam-5600	256	7	=	=	PUNCT
ejpam-5600	257	1	n−	n−	VERB
ejpam-5600	257	2	2(∥c∥+	2(∥c∥+	ADJ
ejpam-5600	257	3	∥cu∥	∥cu∥	PUNCT
ejpam-5600	257	4	−	−	PROPN
ejpam-5600	257	5	2⟨c	2⟨c	NUM
ejpam-5600	257	6	,	,	PUNCT
ejpam-5600	257	7	cu⟩	cu⟩	PROPN
ejpam-5600	257	8	)	)	PUNCT
ejpam-5600	257	9	.	.	PUNCT
ejpam-5600	258	1	summation	summation	NOUN
ejpam-5600	258	2	over	over	ADP
ejpam-5600	258	3	u	u	NOUN
ejpam-5600	258	4	and	and	CCONJ
ejpam-5600	258	5	taking	take	VERB
ejpam-5600	258	6	expectations	expectation	NOUN
ejpam-5600	258	7	of	of	ADP
ejpam-5600	258	8	both	both	DET
ejpam-5600	258	9	sides	side	NOUN
ejpam-5600	258	10	gives	give	VERB
ejpam-5600	258	11	n−1∑	n−1∑	NOUN
ejpam-5600	258	12	u=1	u=1	PROPN
ejpam-5600	258	13	e(rc(u	e(rc(u	PROPN
ejpam-5600	258	14	)	)	PUNCT
ejpam-5600	258	15	)	)	PUNCT
ejpam-5600	259	1	=	=	SYM
ejpam-5600	259	2	n−1∑	n−1∑	NOUN
ejpam-5600	259	3	u=1	u=1	PUNCT
ejpam-5600	260	1	[	[	X
ejpam-5600	260	2	n−	n−	NOUN
ejpam-5600	260	3	2(e(∥c∥	2(e(∥c∥	PROPN
ejpam-5600	260	4	)	)	PUNCT
ejpam-5600	261	1	+	+	CCONJ
ejpam-5600	261	2	e(∥cu∥)−	e(∥cu∥)−	PROPN
ejpam-5600	261	3	2e(⟨c	2e(⟨c	NUM
ejpam-5600	261	4	,	,	PUNCT
ejpam-5600	261	5	cu⟩	cu⟩	PROPN
ejpam-5600	261	6	)	)	PUNCT
ejpam-5600	261	7	)	)	PUNCT
ejpam-5600	261	8	]	]	PUNCT
ejpam-5600	262	1	=	=	PUNCT
ejpam-5600	262	2	−n(n−	−n(n−	VERB
ejpam-5600	262	3	1	1	X
ejpam-5600	262	4	)	)	PUNCT
ejpam-5600	262	5	+	+	NUM
ejpam-5600	262	6	4e	4e	NOUN
ejpam-5600	262	7	(	(	PUNCT
ejpam-5600	262	8	n−1∑	n−1∑	NUM
ejpam-5600	262	9	u=1	u=1	PROPN
ejpam-5600	262	10	⟨c	⟨c	PROPN
ejpam-5600	262	11	,	,	PUNCT
ejpam-5600	262	12	cu⟩	cu⟩	PROPN
ejpam-5600	262	13	)	)	PUNCT
ejpam-5600	262	14	.	.	PUNCT
ejpam-5600	263	1	in	in	ADP
ejpam-5600	263	2	the	the	DET
ejpam-5600	263	3	last	last	ADJ
ejpam-5600	263	4	equation	equation	NOUN
ejpam-5600	263	5	we	we	PRON
ejpam-5600	263	6	made	make	VERB
ejpam-5600	263	7	use	use	NOUN
ejpam-5600	263	8	of	of	ADP
ejpam-5600	263	9	(	(	PUNCT
ejpam-5600	263	10	3	3	NUM
ejpam-5600	263	11	)	)	PUNCT
ejpam-5600	263	12	.	.	PUNCT
ejpam-5600	264	1	now	now	ADV
ejpam-5600	264	2	we	we	PRON
ejpam-5600	264	3	will	will	AUX
ejpam-5600	264	4	utilize	utilize	VERB
ejpam-5600	264	5	the	the	DET
ejpam-5600	264	6	following	follow	VERB
ejpam-5600	264	7	simple	simple	ADJ
ejpam-5600	264	8	fact	fact	NOUN
ejpam-5600	264	9	:	:	PUNCT
ejpam-5600	264	10	for	for	ADP
ejpam-5600	264	11	any	any	DET
ejpam-5600	264	12	c	c	NOUN
ejpam-5600	264	13	=	=	SYM
ejpam-5600	264	14	(	(	PUNCT
ejpam-5600	264	15	c1	c1	PROPN
ejpam-5600	264	16	,	,	PUNCT
ejpam-5600	264	17	c2	c2	PROPN
ejpam-5600	264	18	,	,	PUNCT
ejpam-5600	264	19	.	.	PUNCT
ejpam-5600	264	20	.	.	PUNCT
ejpam-5600	264	21	.	.	PUNCT
ejpam-5600	265	1	,	,	PUNCT
ejpam-5600	265	2	cn	cn	PROPN
ejpam-5600	265	3	)	)	PUNCT
ejpam-5600	265	4	and	and	CCONJ
ejpam-5600	265	5	e	e	X
ejpam-5600	265	6	=	=	SYM
ejpam-5600	265	7	(	(	PUNCT
ejpam-5600	265	8	e1	e1	PROPN
ejpam-5600	265	9	,	,	PUNCT
ejpam-5600	265	10	e2	e2	PROPN
ejpam-5600	265	11	,	,	PUNCT
ejpam-5600	265	12	.	.	PUNCT
ejpam-5600	265	13	.	.	PUNCT
ejpam-5600	266	1	.	.	PUNCT
ejpam-5600	267	1	,	,	PUNCT
ejpam-5600	267	2	en	en	X
ejpam-5600	267	3	)	)	PUNCT
ejpam-5600	267	4	in	in	ADP
ejpam-5600	267	5	fn	fn	NOUN
ejpam-5600	267	6	2	2	NUM
ejpam-5600	267	7	we	we	PRON
ejpam-5600	267	8	have	have	VERB
ejpam-5600	267	9	∥c∥∥e∥	∥c∥∥e∥	NOUN
ejpam-5600	267	10	=	=	SYM
ejpam-5600	267	11	(	(	PUNCT
ejpam-5600	267	12	c1	c1	PROPN
ejpam-5600	267	13	+	+	CCONJ
ejpam-5600	267	14	c2	c2	PROPN
ejpam-5600	267	15	+	+	X
ejpam-5600	267	16	.	.	PUNCT
ejpam-5600	267	17	.	.	PUNCT
ejpam-5600	268	1	.+	.+	NOUN
ejpam-5600	268	2	cn)(e1	cn)(e1	NOUN
ejpam-5600	268	3	+	+	CCONJ
ejpam-5600	268	4	e2	e2	PROPN
ejpam-5600	268	5	+	+	CCONJ
ejpam-5600	268	6	.	.	PUNCT
ejpam-5600	268	7	.	.	PUNCT
ejpam-5600	269	1	.+	.+	PRON
ejpam-5600	269	2	en	en	ADP
ejpam-5600	269	3	)	)	PUNCT
ejpam-5600	269	4	references	reference	NOUN
ejpam-5600	269	5	4236	4236	NUM
ejpam-5600	269	6	=	=	SYM
ejpam-5600	269	7	n−1∑	n−1∑	NUM
ejpam-5600	269	8	u=0	u=0	SYM
ejpam-5600	269	9	⟨c	⟨c	PROPN
ejpam-5600	269	10	,	,	PUNCT
ejpam-5600	269	11	eu⟩.	eu⟩.	PROPN
ejpam-5600	269	12	(	(	PUNCT
ejpam-5600	269	13	9	9	NUM
ejpam-5600	269	14	)	)	PUNCT
ejpam-5600	269	15	with	with	ADP
ejpam-5600	269	16	this	this	DET
ejpam-5600	269	17	fact	fact	NOUN
ejpam-5600	269	18	,	,	PUNCT
ejpam-5600	269	19	(	(	PUNCT
ejpam-5600	269	20	3	3	X
ejpam-5600	269	21	)	)	PUNCT
ejpam-5600	269	22	and	and	CCONJ
ejpam-5600	269	23	(	(	PUNCT
ejpam-5600	269	24	4	4	NUM
ejpam-5600	269	25	)	)	PUNCT
ejpam-5600	269	26	,	,	PUNCT
ejpam-5600	269	27	we	we	PRON
ejpam-5600	269	28	have	have	VERB
ejpam-5600	269	29	n−1∑	n−1∑	NUM
ejpam-5600	269	30	u=1	u=1	PROPN
ejpam-5600	269	31	e(rc(u	e(rc(u	PROPN
ejpam-5600	269	32	)	)	PUNCT
ejpam-5600	269	33	)	)	PUNCT
ejpam-5600	270	1	=	=	PRON
ejpam-5600	270	2	−n(n−	−n(n−	VERB
ejpam-5600	270	3	1	1	X
ejpam-5600	270	4	)	)	PUNCT
ejpam-5600	270	5	+	+	CCONJ
ejpam-5600	270	6	4	4	NUM
ejpam-5600	270	7	(	(	PUNCT
ejpam-5600	270	8	e(∥c∥∥c∥)−	e(∥c∥∥c∥)−	PROPN
ejpam-5600	270	9	e(∥c∥	e(∥c∥	PROPN
ejpam-5600	270	10	)	)	PUNCT
ejpam-5600	270	11	)	)	PUNCT
ejpam-5600	271	1	=	=	PRON
ejpam-5600	271	2	−n(n−	−n(n−	VERB
ejpam-5600	271	3	1	1	X
ejpam-5600	271	4	)	)	PUNCT
ejpam-5600	271	5	+	+	CCONJ
ejpam-5600	271	6	4	4	NUM
ejpam-5600	271	7	(	(	PUNCT
ejpam-5600	271	8	n2	n2	NOUN
ejpam-5600	271	9	+	+	CCONJ
ejpam-5600	271	10	n	n	CCONJ
ejpam-5600	271	11	4	4	NUM
ejpam-5600	271	12	−	−	NOUN
ejpam-5600	271	13	n	n	PRON
ejpam-5600	271	14	2	2	NUM
ejpam-5600	271	15	)	)	PUNCT
ejpam-5600	271	16	=	=	SYM
ejpam-5600	271	17	0	0	X
ejpam-5600	271	18	.	.	PUNCT
ejpam-5600	272	1	(	(	PUNCT
ejpam-5600	272	2	10	10	NUM
ejpam-5600	272	3	)	)	PUNCT
ejpam-5600	272	4	now	now	ADV
ejpam-5600	272	5	let	let	VERB
ejpam-5600	272	6	c	c	NOUN
ejpam-5600	272	7	and	and	CCONJ
ejpam-5600	272	8	e	e	NOUN
ejpam-5600	272	9	be	be	AUX
ejpam-5600	272	10	two	two	NUM
ejpam-5600	272	11	distinct	distinct	ADJ
ejpam-5600	272	12	nonzero	nonzero	NOUN
ejpam-5600	272	13	codewords	codeword	NOUN
ejpam-5600	272	14	in	in	ADP
ejpam-5600	272	15	c.	c.	PROPN
ejpam-5600	272	16	for	for	ADP
ejpam-5600	272	17	the	the	DET
ejpam-5600	272	18	cross	cross	NOUN
ejpam-5600	272	19	-	-	NOUN
ejpam-5600	272	20	correlations	correlation	NOUN
ejpam-5600	272	21	,	,	PUNCT
ejpam-5600	272	22	following	follow	VERB
ejpam-5600	272	23	the	the	DET
ejpam-5600	272	24	same	same	ADJ
ejpam-5600	272	25	steps	step	NOUN
ejpam-5600	272	26	as	as	ADP
ejpam-5600	272	27	above	above	ADV
ejpam-5600	272	28	we	we	PRON
ejpam-5600	272	29	get	get	VERB
ejpam-5600	272	30	n−1∑	n−1∑	NUM
ejpam-5600	272	31	u=0	u=0	SYM
ejpam-5600	272	32	e(rc	e(rc	PROPN
ejpam-5600	272	33	,	,	PUNCT
ejpam-5600	272	34	e(u	e(u	PROPN
ejpam-5600	272	35	)	)	PUNCT
ejpam-5600	272	36	)	)	PUNCT
ejpam-5600	272	37	)	)	PUNCT
ejpam-5600	273	1	=	=	PRON
ejpam-5600	273	2	n−1∑	n−1∑	NOUN
ejpam-5600	273	3	u=0	u=0	PRON
ejpam-5600	273	4	e[n−	e[n−	VERB
ejpam-5600	273	5	2dh(c	2dh(c	NUM
ejpam-5600	273	6	,	,	PUNCT
ejpam-5600	273	7	eu	eu	NOUN
ejpam-5600	273	8	)	)	PUNCT
ejpam-5600	273	9	]	]	PUNCT
ejpam-5600	274	1	=	=	PUNCT
ejpam-5600	274	2	n−1∑	n−1∑	PROPN
ejpam-5600	274	3	u=0	u=0	PUNCT
ejpam-5600	275	1	[	[	X
ejpam-5600	275	2	n−	n−	NOUN
ejpam-5600	275	3	2(e(∥c∥	2(e(∥c∥	PROPN
ejpam-5600	275	4	)	)	PUNCT
ejpam-5600	276	1	+	+	CCONJ
ejpam-5600	276	2	e(∥eu∥)−	e(∥eu∥)−	PROPN
ejpam-5600	276	3	2e(⟨c	2e(⟨c	NUM
ejpam-5600	276	4	,	,	PUNCT
ejpam-5600	276	5	eu⟩	eu⟩	NOUN
ejpam-5600	276	6	)	)	PUNCT
ejpam-5600	276	7	)	)	PUNCT
ejpam-5600	276	8	]	]	PUNCT
ejpam-5600	277	1	=	=	PUNCT
ejpam-5600	278	1	−n2	−n2	PROPN
ejpam-5600	278	2	+	+	NUM
ejpam-5600	278	3	4e	4e	NOUN
ejpam-5600	278	4	(	(	PUNCT
ejpam-5600	278	5	n−1∑	n−1∑	PROPN
ejpam-5600	278	6	u=0	u=0	SYM
ejpam-5600	278	7	⟨c	⟨c	PROPN
ejpam-5600	278	8	,	,	PUNCT
ejpam-5600	278	9	eu⟩	eu⟩	NOUN
ejpam-5600	278	10	)	)	PUNCT
ejpam-5600	279	1	=	=	PUNCT
ejpam-5600	280	1	−n2	−n2	PROPN
ejpam-5600	280	2	+	+	CCONJ
ejpam-5600	280	3	4e(∥c∥∥e∥	4e(∥c∥∥e∥	NUM
ejpam-5600	280	4	)	)	PUNCT
ejpam-5600	280	5	.	.	PUNCT
ejpam-5600	281	1	finally	finally	ADV
ejpam-5600	281	2	by	by	ADP
ejpam-5600	281	3	(	(	PUNCT
ejpam-5600	281	4	4	4	X
ejpam-5600	281	5	)	)	PUNCT
ejpam-5600	281	6	we	we	PRON
ejpam-5600	281	7	get	get	VERB
ejpam-5600	281	8	the	the	DET
ejpam-5600	281	9	result	result	NOUN
ejpam-5600	281	10	n−1∑	n−1∑	PROPN
ejpam-5600	281	11	u=0	u=0	SYM
ejpam-5600	281	12	e(rc	e(rc	PROPN
ejpam-5600	281	13	,	,	PUNCT
ejpam-5600	281	14	e(u	e(u	PROPN
ejpam-5600	281	15	)	)	PUNCT
ejpam-5600	281	16	)	)	PUNCT
ejpam-5600	282	1	=	=	PUNCT
ejpam-5600	283	1	0	0	X
ejpam-5600	283	2	.	.	NOUN
ejpam-5600	283	3	5	5	NUM
ejpam-5600	283	4	.	.	X
ejpam-5600	283	5	conclusion	conclusion	NOUN
ejpam-5600	283	6	we	we	PRON
ejpam-5600	283	7	obtained	obtain	VERB
ejpam-5600	283	8	the	the	DET
ejpam-5600	283	9	expectations	expectation	NOUN
ejpam-5600	283	10	of	of	ADP
ejpam-5600	283	11	single	single	ADJ
ejpam-5600	283	12	and	and	CCONJ
ejpam-5600	283	13	pairwise	pairwise	NOUN
ejpam-5600	283	14	products	product	NOUN
ejpam-5600	283	15	of	of	ADP
ejpam-5600	283	16	weights	weight	NOUN
ejpam-5600	283	17	of	of	ADP
ejpam-5600	283	18	codewords	codeword	NOUN
ejpam-5600	283	19	in	in	ADP
ejpam-5600	283	20	random	random	ADJ
ejpam-5600	283	21	binary	binary	ADJ
ejpam-5600	283	22	linear	linear	PROPN
ejpam-5600	283	23	codes	code	NOUN
ejpam-5600	283	24	.	.	PUNCT
ejpam-5600	284	1	we	we	PRON
ejpam-5600	284	2	showed	show	VERB
ejpam-5600	284	3	that	that	SCONJ
ejpam-5600	284	4	the	the	DET
ejpam-5600	284	5	weights	weight	NOUN
ejpam-5600	284	6	of	of	ADP
ejpam-5600	284	7	two	two	NUM
ejpam-5600	284	8	nonzero	nonzero	NOUN
ejpam-5600	284	9	words	word	NOUN
ejpam-5600	284	10	are	be	AUX
ejpam-5600	284	11	statistically	statistically	ADV
ejpam-5600	284	12	uncorrelated	uncorrelate	VERB
ejpam-5600	284	13	.	.	PUNCT
ejpam-5600	285	1	we	we	PRON
ejpam-5600	285	2	used	use	VERB
ejpam-5600	285	3	the	the	DET
ejpam-5600	285	4	expectations	expectation	NOUN
ejpam-5600	285	5	of	of	ADP
ejpam-5600	285	6	the	the	DET
ejpam-5600	285	7	products	product	NOUN
ejpam-5600	285	8	of	of	ADP
ejpam-5600	285	9	nonzero	nonzero	PROPN
ejpam-5600	285	10	weights	weight	NOUN
ejpam-5600	285	11	to	to	PART
ejpam-5600	285	12	show	show	VERB
ejpam-5600	285	13	that	that	SCONJ
ejpam-5600	285	14	the	the	DET
ejpam-5600	285	15	expectations	expectation	NOUN
ejpam-5600	285	16	of	of	ADP
ejpam-5600	285	17	the	the	DET
ejpam-5600	285	18	sums	sum	NOUN
ejpam-5600	285	19	of	of	ADP
ejpam-5600	285	20	out	out	ADP
ejpam-5600	285	21	of	of	ADP
ejpam-5600	285	22	phase	phase	NOUN
ejpam-5600	285	23	auto	auto	NOUN
ejpam-5600	285	24	-	-	PUNCT
ejpam-5600	285	25	correlations	correlation	NOUN
ejpam-5600	285	26	and	and	CCONJ
ejpam-5600	285	27	the	the	DET
ejpam-5600	285	28	expectations	expectation	NOUN
ejpam-5600	285	29	of	of	ADP
ejpam-5600	285	30	the	the	DET
ejpam-5600	285	31	sums	sum	NOUN
ejpam-5600	285	32	of	of	ADP
ejpam-5600	285	33	cross	cross	NOUN
ejpam-5600	285	34	-	-	NOUN
ejpam-5600	285	35	correlations	correlation	NOUN
ejpam-5600	285	36	of	of	ADP
ejpam-5600	285	37	nonzero	nonzero	PROPN
ejpam-5600	285	38	words	word	NOUN
ejpam-5600	285	39	are	be	AUX
ejpam-5600	285	40	zero	zero	NUM
ejpam-5600	285	41	.	.	PUNCT
ejpam-5600	286	1	references	reference	NOUN
ejpam-5600	286	2	[	[	X
ejpam-5600	286	3	1	1	NUM
ejpam-5600	286	4	]	]	PUNCT
ejpam-5600	286	5	v	v	ADP
ejpam-5600	286	6	blinovsky	blinovsky	NOUN
ejpam-5600	286	7	,	,	PUNCT
ejpam-5600	286	8	u	u	NOUN
ejpam-5600	286	9	erez	erez	NOUN
ejpam-5600	286	10	,	,	PUNCT
ejpam-5600	286	11	and	and	CCONJ
ejpam-5600	286	12	s	s	AUX
ejpam-5600	286	13	litsyn	litsyn	NOUN
ejpam-5600	286	14	.	.	PUNCT
ejpam-5600	287	1	weight	weight	NOUN
ejpam-5600	287	2	distribution	distribution	NOUN
ejpam-5600	287	3	moments	moment	NOUN
ejpam-5600	287	4	of	of	ADP
ejpam-5600	287	5	random	random	ADJ
ejpam-5600	287	6	linear	linear	NOUN
ejpam-5600	287	7	/	/	SYM
ejpam-5600	287	8	coset	coset	NOUN
ejpam-5600	287	9	codes	code	NOUN
ejpam-5600	287	10	.	.	PUNCT
ejpam-5600	288	1	design	design	NOUN
ejpam-5600	288	2	.	.	PUNCT
ejpam-5600	289	1	code	code	PROPN
ejpam-5600	289	2	.	.	PUNCT
ejpam-5600	290	1	cryptogr	cryptogr	PROPN
ejpam-5600	290	2	.	.	PUNCT
ejpam-5600	290	3	,	,	PUNCT
ejpam-5600	291	1	57:127–138	57:127–138	NUM
ejpam-5600	291	2	,	,	PUNCT
ejpam-5600	291	3	2010	2010	NUM
ejpam-5600	291	4	.	.	PUNCT
ejpam-5600	292	1	references	reference	NOUN
ejpam-5600	292	2	4237	4237	NUM
ejpam-5600	293	1	[	[	X
ejpam-5600	293	2	2	2	X
ejpam-5600	293	3	]	]	X
ejpam-5600	293	4	i	i	PRON
ejpam-5600	293	5	bouyukliev	bouyukliev	ADV
ejpam-5600	293	6	,	,	PUNCT
ejpam-5600	293	7	s	s	VERB
ejpam-5600	293	8	bouyuklieva	bouyuklieva	ADJ
ejpam-5600	293	9	,	,	PUNCT
ejpam-5600	293	10	t	t	PROPN
ejpam-5600	293	11	maruta	maruta	PROPN
ejpam-5600	293	12	,	,	PUNCT
ejpam-5600	293	13	and	and	CCONJ
ejpam-5600	293	14	p	p	PROPN
ejpam-5600	293	15	piperkov	piperkov	NOUN
ejpam-5600	293	16	.	.	PUNCT
ejpam-5600	294	1	characteristic	characteristic	ADJ
ejpam-5600	294	2	vector	vector	NOUN
ejpam-5600	294	3	and	and	CCONJ
ejpam-5600	294	4	weight	weight	NOUN
ejpam-5600	294	5	distribution	distribution	NOUN
ejpam-5600	294	6	of	of	ADP
ejpam-5600	294	7	a	a	DET
ejpam-5600	294	8	linear	linear	PROPN
ejpam-5600	294	9	code	code	NOUN
ejpam-5600	294	10	.	.	PUNCT
ejpam-5600	295	1	cryptogr	cryptogr	NOUN
ejpam-5600	295	2	.	.	PUNCT
ejpam-5600	296	1	commun	commun	PROPN
ejpam-5600	296	2	.	.	PROPN
ejpam-5600	296	3	,	,	PUNCT
ejpam-5600	296	4	13:263–282	13:263–282	PROPN
ejpam-5600	296	5	,	,	PUNCT
ejpam-5600	296	6	2021	2021	NUM
ejpam-5600	296	7	.	.	PUNCT
ejpam-5600	297	1	[	[	X
ejpam-5600	297	2	3	3	NUM
ejpam-5600	297	3	]	]	X
ejpam-5600	297	4	c	c	NOUN
ejpam-5600	297	5	carlet	carlet	NOUN
ejpam-5600	297	6	.	.	PUNCT
ejpam-5600	298	1	boolean	boolean	ADJ
ejpam-5600	298	2	functions	function	NOUN
ejpam-5600	298	3	for	for	ADP
ejpam-5600	298	4	cryptography	cryptography	NOUN
ejpam-5600	298	5	and	and	CCONJ
ejpam-5600	298	6	coding	code	VERB
ejpam-5600	298	7	theory	theory	NOUN
ejpam-5600	298	8	.	.	PUNCT
ejpam-5600	299	1	cambridge	cambridge	PROPN
ejpam-5600	299	2	university	university	PROPN
ejpam-5600	299	3	press	press	PROPN
ejpam-5600	299	4	,	,	PUNCT
ejpam-5600	299	5	cambridge	cambridge	PROPN
ejpam-5600	299	6	,	,	PUNCT
ejpam-5600	299	7	2021	2021	NUM
ejpam-5600	299	8	.	.	PUNCT
ejpam-5600	300	1	[	[	X
ejpam-5600	300	2	4	4	NUM
ejpam-5600	300	3	]	]	SYM
ejpam-5600	300	4	r	r	NOUN
ejpam-5600	300	5	g	g	NOUN
ejpam-5600	300	6	gallager	gallager	NOUN
ejpam-5600	300	7	.	.	PUNCT
ejpam-5600	301	1	low	low	ADJ
ejpam-5600	301	2	density	density	NOUN
ejpam-5600	301	3	parity	parity	NOUN
ejpam-5600	301	4	check	check	NOUN
ejpam-5600	301	5	codes	code	NOUN
ejpam-5600	301	6	.	.	PUNCT
ejpam-5600	302	1	mit	mit	PROPN
ejpam-5600	302	2	press	press	PROPN
ejpam-5600	302	3	,	,	PUNCT
ejpam-5600	302	4	cambridge	cambridge	PROPN
ejpam-5600	302	5	,	,	PUNCT
ejpam-5600	302	6	1963	1963	NUM
ejpam-5600	302	7	.	.	PUNCT
ejpam-5600	303	1	[	[	X
ejpam-5600	303	2	5	5	NUM
ejpam-5600	303	3	]	]	PUNCT
ejpam-5600	303	4	k	k	PROPN
ejpam-5600	303	5	j	j	PROPN
ejpam-5600	303	6	horadam	horadam	PROPN
ejpam-5600	303	7	.	.	PUNCT
ejpam-5600	304	1	hadamard	hadamard	ADJ
ejpam-5600	304	2	matrices	matrix	NOUN
ejpam-5600	304	3	and	and	CCONJ
ejpam-5600	304	4	their	their	PRON
ejpam-5600	304	5	applications	application	NOUN
ejpam-5600	304	6	.	.	PUNCT
ejpam-5600	305	1	princeton	princeton	PROPN
ejpam-5600	305	2	university	university	PROPN
ejpam-5600	305	3	press	press	NOUN
ejpam-5600	305	4	,	,	PUNCT
ejpam-5600	305	5	2012	2012	NUM
ejpam-5600	305	6	.	.	PUNCT
ejpam-5600	306	1	[	[	X
ejpam-5600	306	2	6	6	NUM
ejpam-5600	306	3	]	]	PUNCT
ejpam-5600	306	4	a	a	DET
ejpam-5600	306	5	a	a	DET
ejpam-5600	306	6	klyachko	klyachko	ADJ
ejpam-5600	306	7	and	and	CCONJ
ejpam-5600	306	8	i.	i.	PROPN
ejpam-5600	306	9	özen	özen	PROPN
ejpam-5600	306	10	.	.	PUNCT
ejpam-5600	307	1	correlations	correlation	NOUN
ejpam-5600	307	2	between	between	ADP
ejpam-5600	307	3	the	the	DET
ejpam-5600	307	4	ranks	rank	NOUN
ejpam-5600	307	5	of	of	ADP
ejpam-5600	307	6	submatrices	submatrice	NOUN
ejpam-5600	307	7	and	and	CCONJ
ejpam-5600	307	8	weights	weight	NOUN
ejpam-5600	307	9	of	of	ADP
ejpam-5600	307	10	random	random	ADJ
ejpam-5600	307	11	codes	code	NOUN
ejpam-5600	307	12	.	.	PUNCT
ejpam-5600	308	1	finite	finite	PROPN
ejpam-5600	308	2	fields	fields	PROPN
ejpam-5600	308	3	t.	t.	PROPN
ejpam-5600	308	4	app	app	PROPN
ejpam-5600	308	5	.	.	PROPN
ejpam-5600	308	6	,	,	PUNCT
ejpam-5600	308	7	15(4):497–516	15(4):497–516	NUM
ejpam-5600	308	8	,	,	PUNCT
ejpam-5600	308	9	2009	2009	NUM
ejpam-5600	308	10	.	.	PUNCT
ejpam-5600	309	1	[	[	X
ejpam-5600	309	2	7	7	X
ejpam-5600	309	3	]	]	SYM
ejpam-5600	309	4	n	n	CCONJ
ejpam-5600	309	5	linial	linial	NOUN
ejpam-5600	309	6	and	and	CCONJ
ejpam-5600	309	7	j	j	PROPN
ejpam-5600	309	8	mosheiff	mosheiff	PROPN
ejpam-5600	309	9	.	.	PUNCT
ejpam-5600	310	1	on	on	ADP
ejpam-5600	310	2	the	the	DET
ejpam-5600	310	3	weight	weight	NOUN
ejpam-5600	310	4	distribution	distribution	NOUN
ejpam-5600	310	5	of	of	ADP
ejpam-5600	310	6	random	random	ADJ
ejpam-5600	310	7	binary	binary	ADJ
ejpam-5600	310	8	linear	linear	PROPN
ejpam-5600	310	9	codes	code	NOUN
ejpam-5600	310	10	.	.	PUNCT
ejpam-5600	311	1	random	random	ADJ
ejpam-5600	311	2	struct	struct	NOUN
ejpam-5600	311	3	.	.	PUNCT
ejpam-5600	312	1	alg	alg	PROPN
ejpam-5600	312	2	.	.	PROPN
ejpam-5600	312	3	,	,	PUNCT
ejpam-5600	312	4	56:5–36	56:5–36	NUM
ejpam-5600	312	5	,	,	PUNCT
ejpam-5600	312	6	2020	2020	NUM
ejpam-5600	312	7	.	.	PUNCT
ejpam-5600	313	1	[	[	X
ejpam-5600	313	2	8	8	NUM
ejpam-5600	313	3	]	]	X
ejpam-5600	313	4	i	i	PRON
ejpam-5600	313	5	özen	özen	PROPN
ejpam-5600	313	6	.	.	PUNCT
ejpam-5600	314	1	fourth	fourth	ADJ
ejpam-5600	314	2	moments	moment	NOUN
ejpam-5600	314	3	of	of	ADP
ejpam-5600	314	4	the	the	DET
ejpam-5600	314	5	code	code	NOUN
ejpam-5600	314	6	-	-	PUNCT
ejpam-5600	314	7	weights	weight	NOUN
ejpam-5600	314	8	.	.	PUNCT
ejpam-5600	315	1	commun	commun	PROPN
ejpam-5600	315	2	.	.	PUNCT
ejpam-5600	316	1	algebra	algebra	PROPN
ejpam-5600	316	2	,	,	PUNCT
ejpam-5600	316	3	51(4):1761–1771	51(4):1761–1771	NUM
ejpam-5600	316	4	,	,	PUNCT
ejpam-5600	316	5	2023	2023	NUM
ejpam-5600	316	6	.	.	PUNCT
ejpam-5600	317	1	[	[	X
ejpam-5600	317	2	9	9	NUM
ejpam-5600	317	3	]	]	PUNCT
ejpam-5600	317	4	a	a	DET
ejpam-5600	317	5	samorodnitsky	samorodnitsky	NOUN
ejpam-5600	317	6	.	.	PUNCT
ejpam-5600	318	1	weight	weight	NOUN
ejpam-5600	318	2	distribution	distribution	NOUN
ejpam-5600	318	3	of	of	ADP
ejpam-5600	318	4	random	random	ADJ
ejpam-5600	318	5	linear	linear	NOUN
ejpam-5600	318	6	codes	code	NOUN
ejpam-5600	318	7	and	and	CCONJ
ejpam-5600	318	8	krawtchouk	krawtchouk	NOUN
ejpam-5600	318	9	polynomials	polynomial	NOUN
ejpam-5600	318	10	.	.	PUNCT
ejpam-5600	319	1	random	random	ADJ
ejpam-5600	319	2	struct	struct	NOUN
ejpam-5600	319	3	.	.	PUNCT
ejpam-5600	320	1	alg	alg	PROPN
ejpam-5600	320	2	.	.	PROPN
ejpam-5600	320	3	,	,	PUNCT
ejpam-5600	321	1	65:261–274	65:261–274	NUM
ejpam-5600	321	2	,	,	PUNCT
ejpam-5600	321	3	2024	2024	NUM
ejpam-5600	321	4	.	.	PUNCT