id	sid	tid	token	lemma	pos
ejpam-890	1	1	4_xxx_siap.dvi	4_xxx_siap.dvi	NUM
ejpam-890	1	2	european	european	ADJ
ejpam-890	1	3	journal	journal	NOUN
ejpam-890	1	4	of	of	ADP
ejpam-890	1	5	pure	pure	ADJ
ejpam-890	1	6	and	and	CCONJ
ejpam-890	1	7	applied	apply	VERB
ejpam-890	1	8	mathematics	mathematic	NOUN
ejpam-890	1	9	vol	vol	NOUN
ejpam-890	1	10	.	.	PUNCT
ejpam-890	2	1	3	3	NUM
ejpam-890	2	2	,	,	PUNCT
ejpam-890	2	3	no	no	INTJ
ejpam-890	2	4	.	.	NOUN
ejpam-890	2	5	4	4	NUM
ejpam-890	2	6	,	,	PUNCT
ejpam-890	2	7	2010	2010	NUM
ejpam-890	2	8	,	,	PUNCT
ejpam-890	2	9	653	653	NUM
ejpam-890	2	10	-	-	SYM
ejpam-890	2	11	669	669	NUM
ejpam-890	2	12	issn	issn	PROPN
ejpam-890	2	13	1307	1307	NUM
ejpam-890	2	14	-	-	SYM
ejpam-890	2	15	5543	5543	NUM
ejpam-890	2	16	–	–	PUNCT
ejpam-890	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-890	2	18	burst	burst	VERB
ejpam-890	2	19	error	error	NOUN
ejpam-890	2	20	enumeration	enumeration	NOUN
ejpam-890	2	21	of	of	ADP
ejpam-890	2	22	m	m	PROPN
ejpam-890	2	23	-	-	PUNCT
ejpam-890	2	24	array	array	NOUN
ejpam-890	2	25	codes	code	NOUN
ejpam-890	2	26	over	over	ADP
ejpam-890	2	27	rings	ring	NOUN
ejpam-890	2	28	and	and	CCONJ
ejpam-890	2	29	its	its	PRON
ejpam-890	2	30	applications	application	NOUN
ejpam-890	2	31	i̇rfan	i̇rfan	PROPN
ejpam-890	2	32	şiap	şiap	PROPN
ejpam-890	2	33	department	department	PROPN
ejpam-890	2	34	of	of	ADP
ejpam-890	2	35	mathematics	mathematics	PROPN
ejpam-890	2	36	,	,	PUNCT
ejpam-890	2	37	yildiz	yildiz	PROPN
ejpam-890	2	38	technical	technical	PROPN
ejpam-890	2	39	university	university	PROPN
ejpam-890	2	40	,	,	PUNCT
ejpam-890	2	41	istanbul	istanbul	PROPN
ejpam-890	2	42	,	,	PUNCT
ejpam-890	2	43	turkey	turkey	PROPN
ejpam-890	2	44	abstract	abstract	NOUN
ejpam-890	2	45	.	.	PUNCT
ejpam-890	3	1	enumerating	enumerate	VERB
ejpam-890	3	2	burst	burst	ADJ
ejpam-890	3	3	errors	error	NOUN
ejpam-890	3	4	enables	enable	VERB
ejpam-890	3	5	to	to	PART
ejpam-890	3	6	obtain	obtain	VERB
ejpam-890	3	7	bounds	bound	NOUN
ejpam-890	3	8	on	on	ADP
ejpam-890	3	9	parameters	parameter	NOUN
ejpam-890	3	10	of	of	ADP
ejpam-890	3	11	codes	code	NOUN
ejpam-890	3	12	.	.	PUNCT
ejpam-890	4	1	recently	recently	ADV
ejpam-890	4	2	,	,	PUNCT
ejpam-890	4	3	jain	jain	NOUN
ejpam-890	4	4	in	in	ADP
ejpam-890	4	5	[	[	X
ejpam-890	4	6	5	5	NUM
ejpam-890	4	7	]	]	PUNCT
ejpam-890	4	8	established	establish	VERB
ejpam-890	4	9	a	a	DET
ejpam-890	4	10	reiger	reiger	NOUN
ejpam-890	4	11	’s	’s	PART
ejpam-890	4	12	type	type	NOUN
ejpam-890	4	13	bound	bind	VERB
ejpam-890	4	14	for	for	ADP
ejpam-890	4	15	burst	burst	ADJ
ejpam-890	4	16	error	error	NOUN
ejpam-890	4	17	correcting	correct	VERB
ejpam-890	4	18	matrix	matrix	NOUN
ejpam-890	4	19	codes	code	NOUN
ejpam-890	4	20	over	over	ADP
ejpam-890	4	21	finite	finite	ADJ
ejpam-890	4	22	fields	field	NOUN
ejpam-890	4	23	with	with	ADP
ejpam-890	4	24	respect	respect	NOUN
ejpam-890	4	25	to	to	ADP
ejpam-890	4	26	a	a	DET
ejpam-890	4	27	non	non	ADJ
ejpam-890	4	28	hamming	hamming	NOUN
ejpam-890	4	29	metric	metric	ADJ
ejpam-890	4	30	.	.	PUNCT
ejpam-890	5	1	here	here	ADV
ejpam-890	5	2	,	,	PUNCT
ejpam-890	5	3	we	we	PRON
ejpam-890	5	4	extend	extend	VERB
ejpam-890	5	5	these	these	DET
ejpam-890	5	6	results	result	NOUN
ejpam-890	5	7	to	to	PART
ejpam-890	5	8	array	array	VERB
ejpam-890	5	9	codes	code	NOUN
ejpam-890	5	10	over	over	ADP
ejpam-890	5	11	finite	finite	ADJ
ejpam-890	5	12	rings	ring	NOUN
ejpam-890	5	13	.	.	PUNCT
ejpam-890	6	1	further	far	ADV
ejpam-890	6	2	,	,	PUNCT
ejpam-890	6	3	we	we	PRON
ejpam-890	6	4	also	also	ADV
ejpam-890	6	5	introduce	introduce	VERB
ejpam-890	6	6	a	a	DET
ejpam-890	6	7	new	new	ADJ
ejpam-890	6	8	constructive	constructive	ADJ
ejpam-890	6	9	method	method	NOUN
ejpam-890	6	10	for	for	ADP
ejpam-890	6	11	counting	count	VERB
ejpam-890	6	12	burst	burst	ADJ
ejpam-890	6	13	errors	error	NOUN
ejpam-890	6	14	that	that	PRON
ejpam-890	6	15	avoids	avoid	VERB
ejpam-890	6	16	solving	solve	VERB
ejpam-890	6	17	diophantine	diophantine	NOUN
ejpam-890	6	18	inequalities	inequality	NOUN
ejpam-890	6	19	in	in	ADP
ejpam-890	6	20	order	order	NOUN
ejpam-890	6	21	to	to	PART
ejpam-890	6	22	compute	compute	VERB
ejpam-890	6	23	burst	burst	ADJ
ejpam-890	6	24	errors	error	NOUN
ejpam-890	6	25	for	for	ADP
ejpam-890	6	26	each	each	DET
ejpam-890	6	27	given	give	VERB
ejpam-890	6	28	weight	weight	NOUN
ejpam-890	6	29	.	.	PUNCT
ejpam-890	7	1	finally	finally	ADV
ejpam-890	7	2	,	,	PUNCT
ejpam-890	7	3	we	we	PRON
ejpam-890	7	4	apply	apply	VERB
ejpam-890	7	5	our	our	PRON
ejpam-890	7	6	results	result	NOUN
ejpam-890	7	7	on	on	ADP
ejpam-890	7	8	establishing	establish	VERB
ejpam-890	7	9	some	some	DET
ejpam-890	7	10	bounds	bound	NOUN
ejpam-890	7	11	for	for	ADP
ejpam-890	7	12	array	array	NOUN
ejpam-890	7	13	codes	code	NOUN
ejpam-890	7	14	over	over	ADP
ejpam-890	7	15	finite	finite	ADJ
ejpam-890	7	16	rings	ring	NOUN
ejpam-890	7	17	.	.	PUNCT
ejpam-890	8	1	2000	2000	NUM
ejpam-890	8	2	mathematics	mathematic	NOUN
ejpam-890	8	3	subject	subject	NOUN
ejpam-890	8	4	classifications	classification	NOUN
ejpam-890	8	5	:	:	PUNCT
ejpam-890	8	6	94b05	94b05	NUM
ejpam-890	8	7	,	,	PUNCT
ejpam-890	8	8	94b20,94b25	94b20,94b25	NUM
ejpam-890	8	9	.	.	PUNCT
ejpam-890	9	1	key	key	ADJ
ejpam-890	9	2	words	word	NOUN
ejpam-890	9	3	and	and	CCONJ
ejpam-890	9	4	phrases	phrase	NOUN
ejpam-890	9	5	:	:	PUNCT
ejpam-890	9	6	matrix	matrix	NOUN
ejpam-890	9	7	array	array	NOUN
ejpam-890	9	8	codes	code	NOUN
ejpam-890	9	9	,	,	PUNCT
ejpam-890	9	10	non	non	ADJ
ejpam-890	9	11	hamming	ham	VERB
ejpam-890	9	12	metric	metric	ADJ
ejpam-890	9	13	,	,	PUNCT
ejpam-890	9	14	burst	burst	ADJ
ejpam-890	9	15	errors	error	NOUN
ejpam-890	9	16	,	,	PUNCT
ejpam-890	9	17	burst	burst	ADJ
ejpam-890	9	18	weight	weight	NOUN
ejpam-890	9	19	enumerator	enumerator	NOUN
ejpam-890	9	20	.	.	PUNCT
ejpam-890	10	1	1	1	X
ejpam-890	10	2	.	.	X
ejpam-890	10	3	introduction	introduction	NOUN
ejpam-890	10	4	the	the	DET
ejpam-890	10	5	rt	rt	PROPN
ejpam-890	10	6	(	(	PUNCT
ejpam-890	10	7	non	non	X
ejpam-890	10	8	hamming	hamming	NOUN
ejpam-890	10	9	)	)	PUNCT
ejpam-890	10	10	metric	metric	NOUN
ejpam-890	10	11	for	for	ADP
ejpam-890	10	12	m	m	NOUN
ejpam-890	10	13	-	-	PUNCT
ejpam-890	10	14	array	array	NOUN
ejpam-890	10	15	codes	code	NOUN
ejpam-890	10	16	has	have	AUX
ejpam-890	10	17	gained	gain	VERB
ejpam-890	10	18	quite	quite	ADV
ejpam-890	10	19	interest	interest	NOUN
ejpam-890	10	20	recently	recently	ADV
ejpam-890	10	21	.	.	PUNCT
ejpam-890	11	1	on	on	ADP
ejpam-890	11	2	the	the	DET
ejpam-890	11	3	other	other	ADJ
ejpam-890	11	4	hand	hand	NOUN
ejpam-890	11	5	,	,	PUNCT
ejpam-890	11	6	burst	burst	ADJ
ejpam-890	11	7	error	error	NOUN
ejpam-890	11	8	correction	correction	NOUN
ejpam-890	11	9	of	of	ADP
ejpam-890	11	10	array	array	NOUN
ejpam-890	11	11	codes	code	NOUN
ejpam-890	11	12	is	be	AUX
ejpam-890	11	13	also	also	ADV
ejpam-890	11	14	another	another	DET
ejpam-890	11	15	important	important	ADJ
ejpam-890	11	16	topic	topic	NOUN
ejpam-890	11	17	investigated	investigate	VERB
ejpam-890	11	18	by	by	ADP
ejpam-890	11	19	several	several	ADJ
ejpam-890	11	20	researchers	researcher	NOUN
ejpam-890	11	21	lately	lately	ADV
ejpam-890	11	22	[	[	X
ejpam-890	11	23	1	1	NUM
ejpam-890	11	24	,	,	PUNCT
ejpam-890	11	25	11	11	NUM
ejpam-890	11	26	,	,	PUNCT
ejpam-890	11	27	2	2	NUM
ejpam-890	11	28	]	]	PUNCT
ejpam-890	11	29	.	.	PUNCT
ejpam-890	12	1	in	in	ADP
ejpam-890	12	2	[	[	X
ejpam-890	12	3	5	5	NUM
ejpam-890	12	4	]	]	PUNCT
ejpam-890	12	5	,	,	PUNCT
ejpam-890	12	6	the	the	DET
ejpam-890	12	7	author	author	NOUN
ejpam-890	12	8	emphasizes	emphasize	VERB
ejpam-890	12	9	the	the	DET
ejpam-890	12	10	importance	importance	NOUN
ejpam-890	12	11	of	of	ADP
ejpam-890	12	12	considering	consider	VERB
ejpam-890	12	13	burst	burst	ADJ
ejpam-890	12	14	errors	error	NOUN
ejpam-890	12	15	by	by	ADP
ejpam-890	12	16	giving	give	VERB
ejpam-890	12	17	an	an	DET
ejpam-890	12	18	application	application	NOUN
ejpam-890	12	19	of	of	ADP
ejpam-890	12	20	array	array	NOUN
ejpam-890	12	21	codes	code	NOUN
ejpam-890	12	22	with	with	ADP
ejpam-890	12	23	respect	respect	NOUN
ejpam-890	12	24	to	to	ADP
ejpam-890	12	25	the	the	DET
ejpam-890	12	26	rt	rt	PROPN
ejpam-890	12	27	metric	metric	NOUN
ejpam-890	12	28	.	.	PUNCT
ejpam-890	13	1	by	by	ADP
ejpam-890	13	2	enumerating	enumerate	VERB
ejpam-890	13	3	burst	burst	ADJ
ejpam-890	13	4	errors	error	NOUN
ejpam-890	13	5	of	of	ADP
ejpam-890	13	6	particular	particular	ADJ
ejpam-890	13	7	weights	weight	NOUN
ejpam-890	13	8	,	,	PUNCT
ejpam-890	13	9	a	a	DET
ejpam-890	13	10	rigger	rigger	NOUN
ejpam-890	13	11	’s	’s	PART
ejpam-890	13	12	type	type	NOUN
ejpam-890	13	13	bound	bind	VERB
ejpam-890	13	14	is	be	AUX
ejpam-890	13	15	established	establish	VERB
ejpam-890	13	16	.	.	PUNCT
ejpam-890	14	1	recently	recently	ADV
ejpam-890	14	2	,	,	PUNCT
ejpam-890	14	3	an	an	DET
ejpam-890	14	4	alternative	alternative	ADJ
ejpam-890	14	5	approach	approach	NOUN
ejpam-890	14	6	that	that	PRON
ejpam-890	14	7	relies	rely	VERB
ejpam-890	14	8	on	on	ADP
ejpam-890	14	9	generating	generate	VERB
ejpam-890	14	10	type	type	NOUN
ejpam-890	14	11	of	of	ADP
ejpam-890	14	12	multivariable	multivariable	ADJ
ejpam-890	14	13	polynomials	polynomial	NOUN
ejpam-890	14	14	in	in	ADP
ejpam-890	14	15	order	order	NOUN
ejpam-890	14	16	of	of	ADP
ejpam-890	14	17	computing	compute	VERB
ejpam-890	14	18	the	the	DET
ejpam-890	14	19	number	number	NOUN
ejpam-890	14	20	of	of	ADP
ejpam-890	14	21	a	a	DET
ejpam-890	14	22	class	class	NOUN
ejpam-890	14	23	of	of	ADP
ejpam-890	14	24	burst	burst	ADJ
ejpam-890	14	25	errors	error	NOUN
ejpam-890	14	26	is	be	AUX
ejpam-890	14	27	presented	present	VERB
ejpam-890	14	28	in	in	ADP
ejpam-890	14	29	[	[	X
ejpam-890	14	30	10	10	NUM
ejpam-890	14	31	]	]	PUNCT
ejpam-890	14	32	.	.	PUNCT
ejpam-890	15	1	here	here	ADV
ejpam-890	15	2	,	,	PUNCT
ejpam-890	15	3	we	we	PRON
ejpam-890	15	4	generalize	generalize	VERB
ejpam-890	15	5	these	these	DET
ejpam-890	15	6	results	result	NOUN
ejpam-890	15	7	to	to	PART
ejpam-890	15	8	array	array	VERB
ejpam-890	15	9	codes	code	NOUN
ejpam-890	15	10	over	over	ADP
ejpam-890	15	11	finite	finite	ADJ
ejpam-890	15	12	rings	ring	NOUN
ejpam-890	15	13	.	.	PUNCT
ejpam-890	16	1	in	in	ADP
ejpam-890	16	2	[	[	X
ejpam-890	16	3	5	5	NUM
ejpam-890	16	4	]	]	PUNCT
ejpam-890	16	5	,	,	PUNCT
ejpam-890	16	6	counting	counting	NOUN
ejpam-890	16	7	of	of	ADP
ejpam-890	16	8	burst	burst	ADJ
ejpam-890	16	9	errors	error	NOUN
ejpam-890	16	10	over	over	ADP
ejpam-890	16	11	fields	field	NOUN
ejpam-890	16	12	relies	rely	VERB
ejpam-890	16	13	on	on	ADP
ejpam-890	16	14	solving	solve	VERB
ejpam-890	16	15	diophantine	diophantine	NOUN
ejpam-890	16	16	inequalities	inequality	NOUN
ejpam-890	16	17	2	2	NUM
ejpam-890	16	18	.	.	PUNCT
ejpam-890	16	19	further	far	ADV
ejpam-890	16	20	,	,	PUNCT
ejpam-890	16	21	this	this	DET
ejpam-890	16	22	computation	computation	NOUN
ejpam-890	16	23	needs	need	VERB
ejpam-890	16	24	to	to	PART
ejpam-890	16	25	be	be	AUX
ejpam-890	16	26	carried	carry	VERB
ejpam-890	16	27	out	out	ADP
ejpam-890	16	28	for	for	ADP
ejpam-890	16	29	each	each	DET
ejpam-890	16	30	particular	particular	ADJ
ejpam-890	16	31	weight	weight	NOUN
ejpam-890	16	32	when	when	SCONJ
ejpam-890	16	33	the	the	DET
ejpam-890	16	34	question	question	NOUN
ejpam-890	16	35	is	be	AUX
ejpam-890	16	36	to	to	PART
ejpam-890	16	37	compute	compute	VERB
ejpam-890	16	38	the	the	DET
ejpam-890	16	39	number	number	NOUN
ejpam-890	16	40	of	of	ADP
ejpam-890	16	41	burst	burst	ADJ
ejpam-890	16	42	errors	error	NOUN
ejpam-890	16	43	of	of	ADP
ejpam-890	16	44	a	a	DET
ejpam-890	16	45	particular	particular	ADJ
ejpam-890	16	46	weight	weight	NOUN
ejpam-890	16	47	or	or	CCONJ
ejpam-890	16	48	less	less	ADJ
ejpam-890	16	49	which	which	PRON
ejpam-890	16	50	is	be	AUX
ejpam-890	16	51	the	the	DET
ejpam-890	16	52	case	case	NOUN
ejpam-890	16	53	.	.	PUNCT
ejpam-890	17	1	here	here	ADV
ejpam-890	17	2	,	,	PUNCT
ejpam-890	17	3	we	we	PRON
ejpam-890	17	4	also	also	ADV
ejpam-890	17	5	introduce	introduce	VERB
ejpam-890	17	6	a	a	DET
ejpam-890	17	7	new	new	ADJ
ejpam-890	17	8	constructive	constructive	ADJ
ejpam-890	17	9	method	method	NOUN
ejpam-890	17	10	for	for	ADP
ejpam-890	17	11	counting	count	VERB
ejpam-890	17	12	burst	burst	ADJ
ejpam-890	17	13	errors	error	NOUN
ejpam-890	17	14	that	that	PRON
ejpam-890	17	15	avoids	avoid	VERB
ejpam-890	17	16	solving	solve	VERB
ejpam-890	17	17	diophantine	diophantine	NOUN
ejpam-890	17	18	inequalities	inequality	NOUN
ejpam-890	17	19	in	in	ADP
ejpam-890	17	20	order	order	NOUN
ejpam-890	17	21	to	to	PART
ejpam-890	17	22	compute	compute	VERB
ejpam-890	17	23	burst	burst	ADJ
ejpam-890	17	24	errors	error	NOUN
ejpam-890	17	25	for	for	ADP
ejpam-890	17	26	each	each	DET
ejpam-890	17	27	given	give	VERB
ejpam-890	17	28	weight	weight	NOUN
ejpam-890	17	29	.	.	PUNCT
ejpam-890	18	1	moreover	moreover	ADV
ejpam-890	18	2	,	,	PUNCT
ejpam-890	18	3	we	we	PRON
ejpam-890	18	4	introduce	introduce	VERB
ejpam-890	18	5	a	a	DET
ejpam-890	18	6	multivariable	multivariable	ADJ
ejpam-890	18	7	polynomial	polynomial	NOUN
ejpam-890	18	8	whose	whose	DET
ejpam-890	18	9	coefficients	coefficient	NOUN
ejpam-890	18	10	enumerate	enumerate	VERB
ejpam-890	18	11	the	the	DET
ejpam-890	18	12	number	number	NOUN
ejpam-890	18	13	of	of	ADP
ejpam-890	18	14	burst	burst	ADJ
ejpam-890	18	15	errors	error	NOUN
ejpam-890	18	16	of	of	ADP
ejpam-890	18	17	particular	particular	ADJ
ejpam-890	18	18	weight	weight	NOUN
ejpam-890	18	19	and	and	CCONJ
ejpam-890	18	20	hence	hence	ADV
ejpam-890	18	21	this	this	DET
ejpam-890	18	22	email	email	NOUN
ejpam-890	18	23	address	address	NOUN
ejpam-890	18	24	:	:	PUNCT
ejpam-890	18	25	isiap�yildiz.edu.tr	isiap�yildiz.edu.tr	PROPN
ejpam-890	18	26	(	(	PUNCT
ejpam-890	18	27	̇i	̇i	ADJ
ejpam-890	18	28	.	.	PUNCT
ejpam-890	19	1	siap	siap	PROPN
ejpam-890	19	2	)	)	PUNCT
ejpam-890	20	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-890	21	1	653	653	NUM
ejpam-890	21	2	c	c	X
ejpam-890	21	3	©	©	PROPN
ejpam-890	21	4	2010	2010	NUM
ejpam-890	21	5	ejpam	ejpam	NOUN
ejpam-890	21	6	all	all	DET
ejpam-890	21	7	rights	right	NOUN
ejpam-890	21	8	reserved	reserve	VERB
ejpam-890	21	9	.	.	PUNCT
ejpam-890	22	1	i̇.	i̇.	PROPN
ejpam-890	22	2	siap	siap	PROPN
ejpam-890	22	3	/	/	SYM
ejpam-890	22	4	eur	eur	PROPN
ejpam-890	22	5	.	.	PUNCT
ejpam-890	23	1	j.	j.	PROPN
ejpam-890	23	2	pure	pure	PROPN
ejpam-890	23	3	appl	appl	PROPN
ejpam-890	23	4	.	.	PROPN
ejpam-890	23	5	math	math	PROPN
ejpam-890	23	6	,	,	PUNCT
ejpam-890	23	7	3	3	NUM
ejpam-890	23	8	(	(	PUNCT
ejpam-890	23	9	2010	2010	NUM
ejpam-890	23	10	)	)	PUNCT
ejpam-890	23	11	,	,	PUNCT
ejpam-890	23	12	653	653	NUM
ejpam-890	23	13	-	-	SYM
ejpam-890	23	14	669	669	NUM
ejpam-890	23	15	654	654	NUM
ejpam-890	23	16	method	method	NOUN
ejpam-890	23	17	avoids	avoid	VERB
ejpam-890	23	18	recalculations	recalculation	NOUN
ejpam-890	23	19	.	.	PUNCT
ejpam-890	24	1	finally	finally	ADV
ejpam-890	24	2	,	,	PUNCT
ejpam-890	24	3	we	we	PRON
ejpam-890	24	4	apply	apply	VERB
ejpam-890	24	5	our	our	PRON
ejpam-890	24	6	results	result	NOUN
ejpam-890	24	7	on	on	ADP
ejpam-890	24	8	establishing	establish	VERB
ejpam-890	24	9	some	some	DET
ejpam-890	24	10	bounds	bound	NOUN
ejpam-890	24	11	for	for	ADP
ejpam-890	24	12	array	array	NOUN
ejpam-890	24	13	codes	code	NOUN
ejpam-890	24	14	over	over	ADP
ejpam-890	24	15	finite	finite	ADJ
ejpam-890	24	16	rings	ring	NOUN
ejpam-890	24	17	.	.	PUNCT
ejpam-890	25	1	the	the	DET
ejpam-890	25	2	rt	rt	PROPN
ejpam-890	25	3	(	(	PUNCT
ejpam-890	25	4	non	non	X
ejpam-890	25	5	hamming	hamming	NOUN
ejpam-890	25	6	)	)	PUNCT
ejpam-890	25	7	metric	metric	NOUN
ejpam-890	25	8	for	for	ADP
ejpam-890	25	9	array	array	NOUN
ejpam-890	25	10	(	(	PUNCT
ejpam-890	25	11	matrix	matrix	NOUN
ejpam-890	25	12	)	)	PUNCT
ejpam-890	25	13	codes	code	NOUN
ejpam-890	25	14	over	over	ADP
ejpam-890	25	15	fields	field	NOUN
ejpam-890	25	16	is	be	AUX
ejpam-890	25	17	defined	define	VERB
ejpam-890	25	18	in	in	ADP
ejpam-890	25	19	[	[	X
ejpam-890	25	20	7	7	NUM
ejpam-890	25	21	]	]	PUNCT
ejpam-890	25	22	and	and	CCONJ
ejpam-890	25	23	some	some	DET
ejpam-890	25	24	bounds	bound	NOUN
ejpam-890	25	25	for	for	ADP
ejpam-890	25	26	the	the	DET
ejpam-890	25	27	minimum	minimum	ADJ
ejpam-890	25	28	distance	distance	NOUN
ejpam-890	25	29	are	be	AUX
ejpam-890	25	30	established	establish	VERB
ejpam-890	25	31	.	.	PUNCT
ejpam-890	26	1	some	some	DET
ejpam-890	26	2	applications	application	NOUN
ejpam-890	26	3	of	of	ADP
ejpam-890	26	4	this	this	DET
ejpam-890	26	5	metric	metric	NOUN
ejpam-890	26	6	to	to	ADP
ejpam-890	26	7	uniform	uniform	ADJ
ejpam-890	26	8	distributions	distribution	NOUN
ejpam-890	26	9	are	be	AUX
ejpam-890	26	10	given	give	VERB
ejpam-890	26	11	in	in	ADP
ejpam-890	26	12	[	[	NOUN
ejpam-890	26	13	8	8	NUM
ejpam-890	26	14	]	]	PUNCT
ejpam-890	26	15	.	.	PUNCT
ejpam-890	27	1	a	a	DET
ejpam-890	27	2	macwilliams	macwilliam	NOUN
ejpam-890	27	3	type	type	NOUN
ejpam-890	27	4	identity	identity	NOUN
ejpam-890	27	5	for	for	ADP
ejpam-890	27	6	codes	code	NOUN
ejpam-890	27	7	over	over	ADP
ejpam-890	27	8	matrices	matrix	NOUN
ejpam-890	27	9	with	with	ADP
ejpam-890	27	10	respect	respect	NOUN
ejpam-890	27	11	to	to	ADP
ejpam-890	27	12	the	the	DET
ejpam-890	27	13	rt	rt	PROPN
ejpam-890	27	14	metric	metric	NOUN
ejpam-890	27	15	is	be	AUX
ejpam-890	27	16	proven	prove	VERB
ejpam-890	27	17	in	in	ADP
ejpam-890	27	18	[	[	X
ejpam-890	27	19	3	3	NUM
ejpam-890	27	20	]	]	PUNCT
ejpam-890	27	21	.	.	PUNCT
ejpam-890	28	1	further	far	ADV
ejpam-890	28	2	,	,	PUNCT
ejpam-890	28	3	a	a	DET
ejpam-890	28	4	macwilliams	macwilliam	NOUN
ejpam-890	28	5	type	type	VERB
ejpam-890	28	6	identity	identity	NOUN
ejpam-890	28	7	for	for	ADP
ejpam-890	28	8	complete	complete	ADJ
ejpam-890	28	9	weight	weight	NOUN
ejpam-890	28	10	enumerators	enumerator	NOUN
ejpam-890	28	11	of	of	ADP
ejpam-890	28	12	codes	code	NOUN
ejpam-890	28	13	over	over	ADP
ejpam-890	28	14	matrices	matrix	NOUN
ejpam-890	28	15	with	with	ADP
ejpam-890	28	16	respect	respect	NOUN
ejpam-890	28	17	to	to	ADP
ejpam-890	28	18	the	the	DET
ejpam-890	28	19	rt	rt	PROPN
ejpam-890	28	20	metric	metric	NOUN
ejpam-890	28	21	is	be	AUX
ejpam-890	28	22	proven	prove	VERB
ejpam-890	28	23	in	in	ADP
ejpam-890	28	24	[	[	X
ejpam-890	28	25	9	9	NUM
ejpam-890	28	26	]	]	PUNCT
ejpam-890	28	27	.	.	PUNCT
ejpam-890	29	1	r	r	NOUN
ejpam-890	29	2	be	be	VERB
ejpam-890	29	3	a	a	DET
ejpam-890	29	4	commutative	commutative	ADJ
ejpam-890	29	5	finite	finite	NOUN
ejpam-890	29	6	ring	ring	NOUN
ejpam-890	29	7	with	with	ADP
ejpam-890	29	8	unity	unity	NOUN
ejpam-890	29	9	.	.	PUNCT
ejpam-890	30	1	throughout	throughout	ADP
ejpam-890	30	2	the	the	DET
ejpam-890	30	3	paper	paper	NOUN
ejpam-890	30	4	we	we	PRON
ejpam-890	30	5	assume	assume	VERB
ejpam-890	30	6	that	that	SCONJ
ejpam-890	30	7	the	the	DET
ejpam-890	30	8	cardinality	cardinality	NOUN
ejpam-890	30	9	of	of	ADP
ejpam-890	30	10	r	r	NOUN
ejpam-890	30	11	equals	equal	VERB
ejpam-890	30	12	to	to	ADP
ejpam-890	30	13	q.	q.	NOUN
ejpam-890	30	14	definition	definition	NOUN
ejpam-890	30	15	1	1	NUM
ejpam-890	30	16	.	.	PUNCT
ejpam-890	31	1	let	let	VERB
ejpam-890	31	2	m	m	VERB
ejpam-890	31	3	=	=	ADJ
ejpam-890	31	4	mm×s(r	mm×s(r	PROPN
ejpam-890	31	5	)	)	PUNCT
ejpam-890	31	6	be	be	VERB
ejpam-890	31	7	the	the	DET
ejpam-890	31	8	set	set	NOUN
ejpam-890	31	9	of	of	ADP
ejpam-890	31	10	m×	m×	PROPN
ejpam-890	31	11	s	s	PART
ejpam-890	31	12	matrices	matrix	NOUN
ejpam-890	31	13	with	with	ADP
ejpam-890	31	14	components	component	NOUN
ejpam-890	31	15	from	from	ADP
ejpam-890	31	16	r	r	NOUN
ejpam-890	31	17	.	.	PUNCT
ejpam-890	32	1	a	a	DET
ejpam-890	32	2	subset	subset	NOUN
ejpam-890	32	3	c	c	NOUN
ejpam-890	32	4	of	of	ADP
ejpam-890	32	5	m	m	PROPN
ejpam-890	32	6	is	be	AUX
ejpam-890	32	7	called	call	VERB
ejpam-890	32	8	an	an	DET
ejpam-890	32	9	m	m	NOUN
ejpam-890	32	10	-	-	PUNCT
ejpam-890	32	11	array	array	NOUN
ejpam-890	32	12	code	code	NOUN
ejpam-890	32	13	.	.	PUNCT
ejpam-890	33	1	if	if	SCONJ
ejpam-890	33	2	c	c	PROPN
ejpam-890	33	3	is	be	AUX
ejpam-890	33	4	a	a	DET
ejpam-890	33	5	linear	linear	ADJ
ejpam-890	33	6	r	r	NOUN
ejpam-890	33	7	-	-	PUNCT
ejpam-890	33	8	submodule	submodule	NOUN
ejpam-890	33	9	,	,	PUNCT
ejpam-890	33	10	then	then	ADV
ejpam-890	33	11	c	c	PROPN
ejpam-890	33	12	is	be	AUX
ejpam-890	33	13	called	call	VERB
ejpam-890	33	14	a	a	DET
ejpam-890	33	15	linear	linear	PROPN
ejpam-890	33	16	m	m	PROPN
ejpam-890	33	17	-	-	PUNCT
ejpam-890	33	18	array	array	NOUN
ejpam-890	33	19	code	code	NOUN
ejpam-890	33	20	.	.	PUNCT
ejpam-890	34	1	in	in	ADP
ejpam-890	34	2	this	this	DET
ejpam-890	34	3	paper	paper	NOUN
ejpam-890	34	4	we	we	PRON
ejpam-890	34	5	will	will	AUX
ejpam-890	34	6	always	always	ADV
ejpam-890	34	7	refer	refer	VERB
ejpam-890	34	8	to	to	ADP
ejpam-890	34	9	linear	linear	ADJ
ejpam-890	34	10	array	array	NOUN
ejpam-890	34	11	codes	code	NOUN
ejpam-890	34	12	.	.	PUNCT
ejpam-890	35	1	definition	definition	NOUN
ejpam-890	35	2	2	2	NUM
ejpam-890	35	3	(	(	PUNCT
ejpam-890	35	4	non	non	ADJ
ejpam-890	35	5	hamming	hamming	NOUN
ejpam-890	35	6	-	-	PUNCT
ejpam-890	35	7	rt	rt	NOUN
ejpam-890	35	8	weight	weight	NOUN
ejpam-890	35	9	)	)	PUNCT
ejpam-890	35	10	.	.	PUNCT
ejpam-890	36	1	let	let	VERB
ejpam-890	36	2	x	x	PUNCT
ejpam-890	36	3	=	=	SYM
ejpam-890	36	4	(	(	PUNCT
ejpam-890	36	5	x1	x1	PROPN
ejpam-890	36	6	,	,	PUNCT
ejpam-890	36	7	x2	x2	PROPN
ejpam-890	36	8	,	,	PUNCT
ejpam-890	36	9	.	.	PUNCT
ejpam-890	36	10	.	.	PUNCT
ejpam-890	37	1	.	.	PUNCT
ejpam-890	37	2	,	,	PUNCT
ejpam-890	37	3	xs	xs	PROPN
ejpam-890	37	4	)	)	PUNCT
ejpam-890	37	5	∈	∈	PROPN
ejpam-890	37	6	rs	rs	NOUN
ejpam-890	37	7	.	.	PUNCT
ejpam-890	38	1	the	the	DET
ejpam-890	38	2	rt	rt	PROPN
ejpam-890	38	3	weight	weight	NOUN
ejpam-890	38	4	(	(	PUNCT
ejpam-890	38	5	or	or	CCONJ
ejpam-890	38	6	ρ	ρ	NOUN
ejpam-890	38	7	-	-	PUNCT
ejpam-890	38	8	weight	weight	NOUN
ejpam-890	38	9	)	)	PUNCT
ejpam-890	38	10	of	of	ADP
ejpam-890	38	11	x	x	SYM
ejpam-890	38	12	is	be	AUX
ejpam-890	38	13	defined	define	VERB
ejpam-890	38	14	by	by	ADP
ejpam-890	38	15	wn(x	wn(x	NOUN
ejpam-890	38	16	)	)	PUNCT
ejpam-890	38	17	=	=	SYM
ejpam-890	38	18	�	�	PROPN
ejpam-890	38	19	max{i|x	max{i|x	PROPN
ejpam-890	38	20	i	i	PROPN
ejpam-890	38	21	6=	6=	PROPN
ejpam-890	38	22	0	0	NUM
ejpam-890	38	23	}	}	PUNCT
ejpam-890	38	24	,	,	PUNCT
ejpam-890	38	25	x	x	SYM
ejpam-890	38	26	6=	6=	ADP
ejpam-890	38	27	0	0	NUM
ejpam-890	38	28	0	0	NUM
ejpam-890	38	29	,	,	PUNCT
ejpam-890	38	30	x	x	SYM
ejpam-890	39	1	=	=	NOUN
ejpam-890	39	2	0	0	X
ejpam-890	39	3	.	.	PUNCT
ejpam-890	40	1	let	let	VERB
ejpam-890	40	2	a	a	DET
ejpam-890	40	3	∈	∈	PROPN
ejpam-890	40	4	mm×s(r	mm×s(r	NOUN
ejpam-890	40	5	)	)	PUNCT
ejpam-890	40	6	and	and	CCONJ
ejpam-890	40	7	ai	ai	VERB
ejpam-890	40	8	be	be	AUX
ejpam-890	40	9	the	the	DET
ejpam-890	40	10	ith	ith	PROPN
ejpam-890	40	11	row	row	NOUN
ejpam-890	40	12	of	of	ADP
ejpam-890	40	13	the	the	DET
ejpam-890	40	14	matrix	matrix	NOUN
ejpam-890	40	15	a.	a.	NOUN
ejpam-890	40	16	then	then	ADV
ejpam-890	40	17	the	the	DET
ejpam-890	40	18	rt	rt	PROPN
ejpam-890	40	19	weight	weight	NOUN
ejpam-890	40	20	of	of	ADP
ejpam-890	40	21	the	the	DET
ejpam-890	40	22	matrix	matrix	NOUN
ejpam-890	40	23	a	a	PRON
ejpam-890	40	24	is	be	AUX
ejpam-890	40	25	the	the	DET
ejpam-890	40	26	sum	sum	NOUN
ejpam-890	40	27	of	of	ADP
ejpam-890	40	28	the	the	DET
ejpam-890	40	29	rt	rt	PROPN
ejpam-890	40	30	weights	weight	NOUN
ejpam-890	40	31	of	of	ADP
ejpam-890	40	32	its	its	PRON
ejpam-890	40	33	rows	row	NOUN
ejpam-890	40	34	,	,	PUNCT
ejpam-890	40	35	in	in	ADP
ejpam-890	40	36	other	other	ADJ
ejpam-890	40	37	words	word	NOUN
ejpam-890	40	38	wn	wn	X
ejpam-890	40	39	(	(	PUNCT
ejpam-890	40	40	a	a	NOUN
ejpam-890	40	41	)	)	PUNCT
ejpam-890	41	1	=	=	SYM
ejpam-890	41	2	∑m	∑m	PROPN
ejpam-890	41	3	i=1	i=1	PROPN
ejpam-890	41	4	wn	wn	PROPN
ejpam-890	41	5	(	(	PUNCT
ejpam-890	41	6	ai	ai	PROPN
ejpam-890	41	7	)	)	PUNCT
ejpam-890	41	8	.	.	PUNCT
ejpam-890	42	1	the	the	DET
ejpam-890	42	2	rt	rt	PROPN
ejpam-890	42	3	metric	metric	NOUN
ejpam-890	42	4	(	(	PUNCT
ejpam-890	42	5	ρ	ρ	PROPN
ejpam-890	42	6	distance	distance	NOUN
ejpam-890	42	7	)	)	PUNCT
ejpam-890	42	8	is	be	AUX
ejpam-890	42	9	defined	define	VERB
ejpam-890	42	10	by	by	ADP
ejpam-890	42	11	ρ(x	ρ(x	PROPN
ejpam-890	42	12	,	,	PUNCT
ejpam-890	42	13	y	y	PROPN
ejpam-890	42	14	)	)	PUNCT
ejpam-890	42	15	=	=	SYM
ejpam-890	42	16	wn	wn	INTJ
ejpam-890	42	17	(	(	PUNCT
ejpam-890	42	18	x	x	PROPN
ejpam-890	42	19	−	−	PROPN
ejpam-890	42	20	y	y	PROPN
ejpam-890	42	21	)	)	PUNCT
ejpam-890	42	22	where	where	SCONJ
ejpam-890	42	23	x	x	X
ejpam-890	42	24	,	,	PUNCT
ejpam-890	42	25	y	y	PROPN
ejpam-890	42	26	∈	∈	PROPN
ejpam-890	42	27	m	m	VERB
ejpam-890	42	28	.	.	PUNCT
ejpam-890	43	1	note	note	VERB
ejpam-890	43	2	the	the	DET
ejpam-890	43	3	difference	difference	NOUN
ejpam-890	43	4	between	between	ADP
ejpam-890	43	5	the	the	DET
ejpam-890	43	6	weight	weight	NOUN
ejpam-890	43	7	and	and	CCONJ
ejpam-890	43	8	distance	distance	NOUN
ejpam-890	43	9	notations	notation	NOUN
ejpam-890	43	10	of	of	ADP
ejpam-890	43	11	hamming	hamming	NOUN
ejpam-890	43	12	and	and	CCONJ
ejpam-890	43	13	rt	rt	PROPN
ejpam-890	43	14	(	(	PUNCT
ejpam-890	43	15	non	non	X
ejpam-890	43	16	hamming	hamming	NOUN
ejpam-890	43	17	)	)	PUNCT
ejpam-890	43	18	metrics	metric	NOUN
ejpam-890	43	19	.	.	PUNCT
ejpam-890	44	1	the	the	DET
ejpam-890	44	2	letter	letter	NOUN
ejpam-890	44	3	"	"	PUNCT
ejpam-890	44	4	n	n	CCONJ
ejpam-890	44	5	"	"	PUNCT
ejpam-890	44	6	for	for	ADP
ejpam-890	44	7	rt	rt	PROPN
ejpam-890	44	8	metric	metric	NOUN
ejpam-890	44	9	is	be	AUX
ejpam-890	44	10	used	use	VERB
ejpam-890	44	11	to	to	PART
ejpam-890	44	12	emphasize	emphasize	VERB
ejpam-890	44	13	the	the	DET
ejpam-890	44	14	non	non	ADJ
ejpam-890	44	15	hamming	hamming	NOUN
ejpam-890	44	16	case	case	NOUN
ejpam-890	44	17	.	.	PUNCT
ejpam-890	45	1	definition	definition	NOUN
ejpam-890	45	2	3	3	X
ejpam-890	45	3	.	.	PUNCT
ejpam-890	46	1	let	let	VERB
ejpam-890	46	2	c	c	PRON
ejpam-890	46	3	be	be	AUX
ejpam-890	46	4	an	an	DET
ejpam-890	46	5	r	r	NOUN
ejpam-890	46	6	-	-	PUNCT
ejpam-890	46	7	linear	linear	NOUN
ejpam-890	46	8	code	code	NOUN
ejpam-890	46	9	.	.	PUNCT
ejpam-890	47	1	the	the	DET
ejpam-890	47	2	minimum	minimum	ADJ
ejpam-890	47	3	nonzero	nonzero	PROPN
ejpam-890	47	4	ρ	ρ	PROPN
ejpam-890	47	5	distance	distance	NOUN
ejpam-890	47	6	between	between	ADP
ejpam-890	47	7	the	the	DET
ejpam-890	47	8	codewords	codeword	NOUN
ejpam-890	47	9	of	of	ADP
ejpam-890	47	10	c	c	PROPN
ejpam-890	47	11	is	be	AUX
ejpam-890	47	12	denoted	denote	VERB
ejpam-890	47	13	by	by	ADP
ejpam-890	47	14	dn	dn	PROPN
ejpam-890	47	15	(	(	PUNCT
ejpam-890	47	16	c	c	NOUN
ejpam-890	47	17	)	)	PUNCT
ejpam-890	47	18	.	.	PUNCT
ejpam-890	48	1	the	the	DET
ejpam-890	48	2	minimum	minimum	ADJ
ejpam-890	48	3	nonzero	nonzero	PROPN
ejpam-890	48	4	ρ	ρ	NUM
ejpam-890	48	5	weight	weight	NOUN
ejpam-890	48	6	among	among	ADP
ejpam-890	48	7	all	all	DET
ejpam-890	48	8	codewords	codeword	NOUN
ejpam-890	48	9	of	of	ADP
ejpam-890	48	10	c	c	PROPN
ejpam-890	48	11	is	be	AUX
ejpam-890	48	12	denoted	denote	VERB
ejpam-890	48	13	by	by	ADP
ejpam-890	48	14	wn	wn	PROPN
ejpam-890	48	15	(	(	PUNCT
ejpam-890	48	16	c	c	NOUN
ejpam-890	48	17	)	)	PUNCT
ejpam-890	48	18	.	.	PUNCT
ejpam-890	49	1	in	in	ADP
ejpam-890	49	2	linear	linear	PROPN
ejpam-890	49	3	case	case	NOUN
ejpam-890	49	4	,	,	PUNCT
ejpam-890	49	5	dn	dn	PROPN
ejpam-890	49	6	(	(	PUNCT
ejpam-890	49	7	c	c	X
ejpam-890	49	8	)	)	PUNCT
ejpam-890	49	9	=	=	SYM
ejpam-890	49	10	wn	wn	X
ejpam-890	49	11	(	(	PUNCT
ejpam-890	49	12	c	c	NOUN
ejpam-890	49	13	)	)	PUNCT
ejpam-890	49	14	,	,	PUNCT
ejpam-890	49	15	and	and	CCONJ
ejpam-890	49	16	dn	dn	PROPN
ejpam-890	49	17	(	(	PUNCT
ejpam-890	49	18	c	c	X
ejpam-890	49	19	)	)	PUNCT
ejpam-890	49	20	is	be	AUX
ejpam-890	49	21	called	call	VERB
ejpam-890	49	22	the	the	DET
ejpam-890	49	23	minimum	minimum	ADJ
ejpam-890	49	24	distance	distance	NOUN
ejpam-890	49	25	of	of	ADP
ejpam-890	49	26	c	c	NOUN
ejpam-890	49	27	with	with	ADP
ejpam-890	49	28	respect	respect	NOUN
ejpam-890	49	29	to	to	ADP
ejpam-890	49	30	the	the	DET
ejpam-890	49	31	rt	rt	PROPN
ejpam-890	49	32	metric	metric	NOUN
ejpam-890	49	33	.	.	PUNCT
ejpam-890	50	1	the	the	DET
ejpam-890	50	2	concept	concept	NOUN
ejpam-890	50	3	of	of	ADP
ejpam-890	50	4	burst	burst	ADJ
ejpam-890	50	5	errors	error	NOUN
ejpam-890	50	6	for	for	ADP
ejpam-890	50	7	codes	code	NOUN
ejpam-890	50	8	in	in	ADP
ejpam-890	50	9	a	a	DET
ejpam-890	50	10	classical	classical	ADJ
ejpam-890	50	11	setup	setup	NOUN
ejpam-890	50	12	is	be	AUX
ejpam-890	50	13	introduced	introduce	VERB
ejpam-890	50	14	in	in	ADP
ejpam-890	50	15	[	[	X
ejpam-890	50	16	4	4	NUM
ejpam-890	50	17	]	]	PUNCT
ejpam-890	50	18	.	.	PUNCT
ejpam-890	51	1	recently	recently	ADV
ejpam-890	51	2	,	,	PUNCT
ejpam-890	51	3	in	in	ADP
ejpam-890	51	4	[	[	PUNCT
ejpam-890	51	5	5	5	NUM
ejpam-890	51	6	]	]	PUNCT
ejpam-890	51	7	,	,	PUNCT
ejpam-890	51	8	the	the	DET
ejpam-890	51	9	notion	notion	NOUN
ejpam-890	51	10	of	of	ADP
ejpam-890	51	11	burst	burst	ADJ
ejpam-890	51	12	errors	error	NOUN
ejpam-890	51	13	for	for	ADP
ejpam-890	51	14	matrix	matrix	NOUN
ejpam-890	51	15	codes	code	NOUN
ejpam-890	51	16	with	with	ADP
ejpam-890	51	17	respect	respect	NOUN
ejpam-890	51	18	to	to	ADP
ejpam-890	51	19	rt	rt	PROPN
ejpam-890	51	20	metric	metric	NOUN
ejpam-890	51	21	has	have	AUX
ejpam-890	51	22	been	be	AUX
ejpam-890	51	23	introduced	introduce	VERB
ejpam-890	51	24	and	and	CCONJ
ejpam-890	51	25	some	some	DET
ejpam-890	51	26	formulas	formula	NOUN
ejpam-890	51	27	on	on	ADP
ejpam-890	51	28	enumeration	enumeration	NOUN
ejpam-890	51	29	of	of	ADP
ejpam-890	51	30	burst	burst	ADJ
ejpam-890	51	31	errors	error	NOUN
ejpam-890	51	32	has	have	AUX
ejpam-890	51	33	been	be	AUX
ejpam-890	51	34	obtained	obtain	VERB
ejpam-890	51	35	and	and	CCONJ
ejpam-890	51	36	by	by	ADP
ejpam-890	51	37	use	use	NOUN
ejpam-890	51	38	of	of	ADP
ejpam-890	51	39	this	this	DET
ejpam-890	51	40	enumeration	enumeration	NOUN
ejpam-890	51	41	reiger	reiger	NOUN
ejpam-890	51	42	’s	’s	PART
ejpam-890	51	43	type	type	NOUN
ejpam-890	51	44	bounds	bound	NOUN
ejpam-890	51	45	are	be	AUX
ejpam-890	51	46	stated	state	VERB
ejpam-890	51	47	and	and	CCONJ
ejpam-890	51	48	proved	prove	VERB
ejpam-890	51	49	.	.	PUNCT
ejpam-890	52	1	we	we	PRON
ejpam-890	52	2	extend	extend	VERB
ejpam-890	52	3	the	the	DET
ejpam-890	52	4	definitions	definition	NOUN
ejpam-890	52	5	introduced	introduce	VERB
ejpam-890	52	6	by	by	ADP
ejpam-890	52	7	jain	jain	NOUN
ejpam-890	52	8	in	in	ADP
ejpam-890	52	9	[	[	X
ejpam-890	52	10	5	5	NUM
ejpam-890	52	11	]	]	PUNCT
ejpam-890	52	12	from	from	ADP
ejpam-890	52	13	finite	finite	ADJ
ejpam-890	52	14	field	field	NOUN
ejpam-890	52	15	case	case	NOUN
ejpam-890	52	16	to	to	PART
ejpam-890	52	17	finite	finite	VERB
ejpam-890	52	18	commutative	commutative	ADJ
ejpam-890	52	19	ring	ring	NOUN
ejpam-890	52	20	case	case	NOUN
ejpam-890	52	21	.	.	PUNCT
ejpam-890	53	1	work	work	NOUN
ejpam-890	53	2	on	on	ADP
ejpam-890	53	3	linear	linear	PROPN
ejpam-890	53	4	codes	code	NOUN
ejpam-890	53	5	over	over	ADP
ejpam-890	53	6	rings	ring	NOUN
ejpam-890	53	7	is	be	AUX
ejpam-890	53	8	an	an	DET
ejpam-890	53	9	interesting	interesting	ADJ
ejpam-890	53	10	and	and	CCONJ
ejpam-890	53	11	ongoing	ongoing	ADJ
ejpam-890	53	12	topic	topic	NOUN
ejpam-890	53	13	in	in	ADP
ejpam-890	53	14	coding	code	VERB
ejpam-890	53	15	theory	theory	NOUN
ejpam-890	53	16	.	.	PUNCT
ejpam-890	54	1	mostly	mostly	ADV
ejpam-890	54	2	,	,	PUNCT
ejpam-890	54	3	the	the	DET
ejpam-890	54	4	work	work	NOUN
ejpam-890	54	5	is	be	AUX
ejpam-890	54	6	done	do	VERB
ejpam-890	54	7	over	over	ADP
ejpam-890	54	8	finite	finite	ADJ
ejpam-890	54	9	rings	ring	NOUN
ejpam-890	54	10	such	such	ADJ
ejpam-890	54	11	as	as	ADP
ejpam-890	54	12	zm	zm	PROPN
ejpam-890	54	13	,	,	PUNCT
ejpam-890	54	14	galois	galois	PROPN
ejpam-890	54	15	rings	ring	NOUN
ejpam-890	54	16	,	,	PUNCT
ejpam-890	54	17	chain	chain	NOUN
ejpam-890	54	18	rings	ring	NOUN
ejpam-890	54	19	and	and	CCONJ
ejpam-890	54	20	etc	etc	X
ejpam-890	54	21	.	.	X
ejpam-890	54	22	in	in	ADP
ejpam-890	54	23	this	this	DET
ejpam-890	54	24	paper	paper	NOUN
ejpam-890	54	25	,	,	PUNCT
ejpam-890	54	26	all	all	DET
ejpam-890	54	27	this	this	DET
ejpam-890	54	28	well	well	ADV
ejpam-890	54	29	known	know	VERB
ejpam-890	54	30	rings	ring	NOUN
ejpam-890	54	31	are	be	AUX
ejpam-890	54	32	covered	cover	VERB
ejpam-890	54	33	.	.	PUNCT
ejpam-890	55	1	in	in	ADP
ejpam-890	55	2	the	the	DET
ejpam-890	55	3	introduction	introduction	NOUN
ejpam-890	55	4	,	,	PUNCT
ejpam-890	55	5	the	the	DET
ejpam-890	55	6	basics	basic	NOUN
ejpam-890	55	7	and	and	CCONJ
ejpam-890	55	8	definitions	definition	NOUN
ejpam-890	55	9	are	be	AUX
ejpam-890	55	10	covered	cover	VERB
ejpam-890	55	11	.	.	PUNCT
ejpam-890	56	1	in	in	ADP
ejpam-890	56	2	section	section	NOUN
ejpam-890	56	3	2	2	NUM
ejpam-890	56	4	,	,	PUNCT
ejpam-890	56	5	generic	generic	ADJ
ejpam-890	56	6	burst	burst	ADJ
ejpam-890	56	7	errors	error	NOUN
ejpam-890	56	8	are	be	AUX
ejpam-890	56	9	defined	define	VERB
ejpam-890	56	10	.	.	PUNCT
ejpam-890	57	1	an	an	DET
ejpam-890	57	2	equivalence	equivalence	NOUN
ejpam-890	57	3	relation	relation	NOUN
ejpam-890	57	4	on	on	ADP
ejpam-890	57	5	the	the	DET
ejpam-890	57	6	set	set	NOUN
ejpam-890	57	7	of	of	ADP
ejpam-890	57	8	burst	burst	ADJ
ejpam-890	57	9	errors	error	NOUN
ejpam-890	57	10	is	be	AUX
ejpam-890	57	11	introduced	introduce	VERB
ejpam-890	57	12	.	.	PUNCT
ejpam-890	58	1	the	the	DET
ejpam-890	58	2	equivalence	equivalence	NOUN
ejpam-890	58	3	classes	class	NOUN
ejpam-890	58	4	are	be	AUX
ejpam-890	58	5	shown	show	VERB
ejpam-890	58	6	to	to	PART
ejpam-890	58	7	be	be	AUX
ejpam-890	58	8	the	the	DET
ejpam-890	58	9	generic	generic	ADJ
ejpam-890	58	10	burst	burst	ADJ
ejpam-890	58	11	errors	error	NOUN
ejpam-890	58	12	.	.	PUNCT
ejpam-890	59	1	later	later	ADV
ejpam-890	59	2	,	,	PUNCT
ejpam-890	59	3	a	a	DET
ejpam-890	59	4	generic	generic	ADJ
ejpam-890	59	5	multi	multi	ADJ
ejpam-890	59	6	variable	variable	ADJ
ejpam-890	59	7	polynomial	polynomial	NOUN
ejpam-890	59	8	that	that	PRON
ejpam-890	59	9	represents	represent	VERB
ejpam-890	59	10	all	all	DET
ejpam-890	59	11	generic	generic	ADJ
ejpam-890	59	12	burst	burst	ADJ
ejpam-890	59	13	errors	error	NOUN
ejpam-890	59	14	is	be	AUX
ejpam-890	59	15	introduced	introduce	VERB
ejpam-890	59	16	.	.	PUNCT
ejpam-890	60	1	by	by	ADP
ejpam-890	60	2	substituting	substitute	VERB
ejpam-890	60	3	suitable	suitable	ADJ
ejpam-890	60	4	i̇.	i̇.	NOUN
ejpam-890	60	5	siap	siap	PROPN
ejpam-890	60	6	/	/	SYM
ejpam-890	60	7	eur	eur	PROPN
ejpam-890	60	8	.	.	PUNCT
ejpam-890	61	1	j.	j.	PROPN
ejpam-890	61	2	pure	pure	PROPN
ejpam-890	61	3	appl	appl	PROPN
ejpam-890	61	4	.	.	PROPN
ejpam-890	61	5	math	math	PROPN
ejpam-890	61	6	,	,	PUNCT
ejpam-890	61	7	3	3	NUM
ejpam-890	61	8	(	(	PUNCT
ejpam-890	61	9	2010	2010	NUM
ejpam-890	61	10	)	)	PUNCT
ejpam-890	61	11	,	,	PUNCT
ejpam-890	61	12	653	653	NUM
ejpam-890	61	13	-	-	SYM
ejpam-890	61	14	669	669	NUM
ejpam-890	61	15	655	655	NUM
ejpam-890	61	16	variables	variable	NOUN
ejpam-890	61	17	in	in	ADP
ejpam-890	61	18	a	a	DET
ejpam-890	61	19	generic	generic	ADJ
ejpam-890	61	20	multivariable	multivariable	ADJ
ejpam-890	61	21	polynomial	polynomial	NOUN
ejpam-890	61	22	,	,	PUNCT
ejpam-890	61	23	we	we	PRON
ejpam-890	61	24	show	show	VERB
ejpam-890	61	25	how	how	SCONJ
ejpam-890	61	26	to	to	PART
ejpam-890	61	27	obtain	obtain	VERB
ejpam-890	61	28	a	a	DET
ejpam-890	61	29	new	new	ADJ
ejpam-890	61	30	polynomial	polynomial	NOUN
ejpam-890	61	31	that	that	PRON
ejpam-890	61	32	gives	give	VERB
ejpam-890	61	33	the	the	DET
ejpam-890	61	34	number	number	NOUN
ejpam-890	61	35	of	of	ADP
ejpam-890	61	36	burst	burst	ADJ
ejpam-890	61	37	errors	error	NOUN
ejpam-890	61	38	and	and	CCONJ
ejpam-890	61	39	their	their	PRON
ejpam-890	61	40	weights	weight	NOUN
ejpam-890	61	41	.	.	PUNCT
ejpam-890	62	1	finally	finally	ADV
ejpam-890	62	2	,	,	PUNCT
ejpam-890	62	3	applying	apply	VERB
ejpam-890	62	4	a	a	DET
ejpam-890	62	5	final	final	ADJ
ejpam-890	62	6	substitution	substitution	NOUN
ejpam-890	62	7	,	,	PUNCT
ejpam-890	62	8	we	we	PRON
ejpam-890	62	9	obtain	obtain	VERB
ejpam-890	62	10	a	a	DET
ejpam-890	62	11	new	new	ADJ
ejpam-890	62	12	polynomial	polynomial	NOUN
ejpam-890	62	13	called	call	VERB
ejpam-890	62	14	the	the	DET
ejpam-890	62	15	burst	burst	ADJ
ejpam-890	62	16	weight	weight	NOUN
ejpam-890	62	17	enumerator	enumerator	NOUN
ejpam-890	62	18	polynomial	polynomial	ADJ
ejpam-890	62	19	with	with	ADP
ejpam-890	62	20	coefficients	coefficient	NOUN
ejpam-890	62	21	being	be	AUX
ejpam-890	62	22	the	the	DET
ejpam-890	62	23	number	number	NOUN
ejpam-890	62	24	of	of	ADP
ejpam-890	62	25	burst	burst	ADJ
ejpam-890	62	26	errors	error	NOUN
ejpam-890	62	27	that	that	PRON
ejpam-890	62	28	correspond	correspond	VERB
ejpam-890	62	29	to	to	ADP
ejpam-890	62	30	the	the	DET
ejpam-890	62	31	powers	power	NOUN
ejpam-890	62	32	which	which	PRON
ejpam-890	62	33	gives	give	VERB
ejpam-890	62	34	the	the	DET
ejpam-890	62	35	rt	rt	PROPN
ejpam-890	62	36	weights	weight	NOUN
ejpam-890	62	37	.	.	PUNCT
ejpam-890	63	1	thus	thus	ADV
ejpam-890	63	2	,	,	PUNCT
ejpam-890	63	3	the	the	DET
ejpam-890	63	4	new	new	ADJ
ejpam-890	63	5	computation	computation	NOUN
ejpam-890	63	6	method	method	NOUN
ejpam-890	63	7	of	of	ADP
ejpam-890	63	8	burst	burst	ADJ
ejpam-890	63	9	errors	error	NOUN
ejpam-890	63	10	of	of	ADP
ejpam-890	63	11	order	order	NOUN
ejpam-890	63	12	p×	p×	NOUN
ejpam-890	63	13	r	r	NOUN
ejpam-890	63	14	in	in	ADP
ejpam-890	63	15	the	the	DET
ejpam-890	63	16	space	space	NOUN
ejpam-890	63	17	mp×r(r	mp×r(r	NOUN
ejpam-890	63	18	)	)	PUNCT
ejpam-890	63	19	(	(	PUNCT
ejpam-890	63	20	the	the	DET
ejpam-890	63	21	set	set	NOUN
ejpam-890	63	22	of	of	ADP
ejpam-890	63	23	matrices	matrix	NOUN
ejpam-890	63	24	of	of	ADP
ejpam-890	63	25	order	order	NOUN
ejpam-890	63	26	p×	p×	NOUN
ejpam-890	63	27	r	r	NOUN
ejpam-890	63	28	with	with	ADP
ejpam-890	63	29	entries	entry	NOUN
ejpam-890	63	30	from	from	ADP
ejpam-890	63	31	a	a	DET
ejpam-890	63	32	finite	finite	ADJ
ejpam-890	63	33	commutative	commutative	ADJ
ejpam-890	63	34	ring	ring	NOUN
ejpam-890	63	35	with	with	ADP
ejpam-890	63	36	q	q	NOUN
ejpam-890	63	37	elements	element	NOUN
ejpam-890	63	38	r	r	NOUN
ejpam-890	63	39	)	)	PUNCT
ejpam-890	63	40	is	be	AUX
ejpam-890	63	41	given	give	VERB
ejpam-890	63	42	.	.	PUNCT
ejpam-890	64	1	in	in	ADP
ejpam-890	64	2	section	section	NOUN
ejpam-890	64	3	3	3	NUM
ejpam-890	64	4	,	,	PUNCT
ejpam-890	64	5	the	the	DET
ejpam-890	64	6	computation	computation	NOUN
ejpam-890	64	7	method	method	NOUN
ejpam-890	64	8	of	of	ADP
ejpam-890	64	9	burst	burst	ADJ
ejpam-890	64	10	errors	error	NOUN
ejpam-890	64	11	of	of	ADP
ejpam-890	64	12	order	order	NOUN
ejpam-890	64	13	p	p	X
ejpam-890	64	14	×	×	NOUN
ejpam-890	64	15	r	r	NOUN
ejpam-890	64	16	in	in	ADP
ejpam-890	64	17	the	the	DET
ejpam-890	64	18	space	space	NOUN
ejpam-890	64	19	mm×s(r	mm×s(r	NOUN
ejpam-890	64	20	)	)	PUNCT
ejpam-890	64	21	where	where	SCONJ
ejpam-890	64	22	1	1	NUM
ejpam-890	64	23	≤	≤	NOUN
ejpam-890	64	24	p	p	X
ejpam-890	64	25	≤	≤	NUM
ejpam-890	64	26	m	m	NOUN
ejpam-890	64	27	,	,	PUNCT
ejpam-890	64	28	1	1	NUM
ejpam-890	64	29	≤	≤	NOUN
ejpam-890	64	30	r	r	NOUN
ejpam-890	64	31	≤	≤	NUM
ejpam-890	64	32	s	s	VERB
ejpam-890	64	33	is	be	AUX
ejpam-890	64	34	presented	present	VERB
ejpam-890	64	35	by	by	ADP
ejpam-890	64	36	making	make	VERB
ejpam-890	64	37	use	use	NOUN
ejpam-890	64	38	of	of	ADP
ejpam-890	64	39	the	the	DET
ejpam-890	64	40	results	result	NOUN
ejpam-890	64	41	obtained	obtain	VERB
ejpam-890	64	42	in	in	ADP
ejpam-890	64	43	section	section	NOUN
ejpam-890	64	44	2	2	NUM
ejpam-890	64	45	.	.	PUNCT
ejpam-890	65	1	in	in	ADP
ejpam-890	65	2	section	section	NOUN
ejpam-890	65	3	4	4	NUM
ejpam-890	65	4	,	,	PUNCT
ejpam-890	65	5	some	some	DET
ejpam-890	65	6	applications	application	NOUN
ejpam-890	65	7	for	for	ADP
ejpam-890	65	8	obtaining	obtain	VERB
ejpam-890	65	9	bounds	bound	NOUN
ejpam-890	65	10	are	be	AUX
ejpam-890	65	11	presented	present	VERB
ejpam-890	65	12	.	.	PUNCT
ejpam-890	66	1	finally	finally	ADV
ejpam-890	66	2	,	,	PUNCT
ejpam-890	66	3	the	the	DET
ejpam-890	66	4	paper	paper	NOUN
ejpam-890	66	5	is	be	AUX
ejpam-890	66	6	concluded	conclude	VERB
ejpam-890	66	7	by	by	ADP
ejpam-890	66	8	some	some	DET
ejpam-890	66	9	remarks	remark	NOUN
ejpam-890	66	10	.	.	PUNCT
ejpam-890	67	1	definition	definition	NOUN
ejpam-890	67	2	4	4	NUM
ejpam-890	67	3	.	.	PUNCT
ejpam-890	68	1	a	a	DET
ejpam-890	68	2	burst	burst	NOUN
ejpam-890	68	3	of	of	ADP
ejpam-890	68	4	order	order	NOUN
ejpam-890	68	5	pr	pr	X
ejpam-890	68	6	or	or	CCONJ
ejpam-890	68	7	(	(	PUNCT
ejpam-890	68	8	p×	p×	NOUN
ejpam-890	68	9	r	r	NOUN
ejpam-890	68	10	)	)	PUNCT
ejpam-890	68	11	(	(	PUNCT
ejpam-890	68	12	1≤	1≤	X
ejpam-890	68	13	p	p	X
ejpam-890	68	14	≤	≤	NUM
ejpam-890	68	15	m	m	NOUN
ejpam-890	68	16	,	,	PUNCT
ejpam-890	68	17	1	1	NUM
ejpam-890	68	18	≤	≤	NOUN
ejpam-890	68	19	r	r	NOUN
ejpam-890	68	20	≤	≤	NUM
ejpam-890	68	21	s	s	NOUN
ejpam-890	68	22	)	)	PUNCT
ejpam-890	68	23	in	in	ADP
ejpam-890	68	24	the	the	DET
ejpam-890	68	25	space	space	NOUN
ejpam-890	68	26	mm×s(r	mm×s(r	NOUN
ejpam-890	68	27	)	)	PUNCT
ejpam-890	68	28	is	be	AUX
ejpam-890	68	29	an	an	DET
ejpam-890	68	30	m×s	m×s	PROPN
ejpam-890	68	31	matrix	matrix	NOUN
ejpam-890	68	32	in	in	ADP
ejpam-890	68	33	which	which	PRON
ejpam-890	68	34	all	all	DET
ejpam-890	68	35	the	the	DET
ejpam-890	68	36	nonzero	nonzero	PROPN
ejpam-890	68	37	entries	entry	NOUN
ejpam-890	68	38	are	be	AUX
ejpam-890	68	39	confined	confine	VERB
ejpam-890	68	40	to	to	ADP
ejpam-890	68	41	some	some	DET
ejpam-890	68	42	p×	p×	NOUN
ejpam-890	68	43	r	r	NOUN
ejpam-890	68	44	submatrix	submatrix	NOUN
ejpam-890	68	45	which	which	PRON
ejpam-890	68	46	has	have	VERB
ejpam-890	68	47	non	non	ADJ
ejpam-890	68	48	zero	zero	NUM
ejpam-890	68	49	first	first	ADV
ejpam-890	68	50	and	and	CCONJ
ejpam-890	68	51	last	last	ADJ
ejpam-890	68	52	rows	row	NOUN
ejpam-890	68	53	as	as	ADV
ejpam-890	68	54	well	well	ADV
ejpam-890	68	55	as	as	ADP
ejpam-890	68	56	nonzero	nonzero	NOUN
ejpam-890	68	57	first	first	ADJ
ejpam-890	68	58	and	and	CCONJ
ejpam-890	68	59	last	last	ADJ
ejpam-890	68	60	columns	column	NOUN
ejpam-890	68	61	.	.	PUNCT
ejpam-890	69	1	b	b	X
ejpam-890	69	2	p×r	p×r	PROPN
ejpam-890	69	3	m×s(r	m×s(r	NUM
ejpam-890	69	4	)	)	PUNCT
ejpam-890	69	5	denotes	denote	VERB
ejpam-890	69	6	the	the	DET
ejpam-890	69	7	number	number	NOUN
ejpam-890	69	8	of	of	ADP
ejpam-890	69	9	burst	burst	ADJ
ejpam-890	69	10	errors	error	NOUN
ejpam-890	69	11	of	of	ADP
ejpam-890	69	12	order	order	NOUN
ejpam-890	69	13	p×	p×	PROPN
ejpam-890	69	14	r.	r.	NOUN
ejpam-890	69	15	the	the	DET
ejpam-890	69	16	number	number	NOUN
ejpam-890	69	17	b	b	PROPN
ejpam-890	69	18	p×r	p×r	PROPN
ejpam-890	69	19	m×s(fq	m×s(fq	PROPN
ejpam-890	69	20	)	)	PUNCT
ejpam-890	69	21	that	that	PRON
ejpam-890	69	22	is	be	AUX
ejpam-890	69	23	used	use	VERB
ejpam-890	69	24	in	in	ADP
ejpam-890	69	25	establishing	establish	VERB
ejpam-890	69	26	some	some	DET
ejpam-890	69	27	bounds	bound	NOUN
ejpam-890	69	28	for	for	ADP
ejpam-890	69	29	array	array	NOUN
ejpam-890	69	30	codes	code	NOUN
ejpam-890	69	31	over	over	ADP
ejpam-890	69	32	a	a	DET
ejpam-890	69	33	finite	finite	ADJ
ejpam-890	69	34	field	field	NOUN
ejpam-890	69	35	fq	fq	PROPN
ejpam-890	69	36	is	be	AUX
ejpam-890	69	37	presented	present	VERB
ejpam-890	69	38	by	by	ADP
ejpam-890	69	39	jain	jain	NOUN
ejpam-890	69	40	in	in	ADP
ejpam-890	69	41	[	[	X
ejpam-890	69	42	5	5	NUM
ejpam-890	69	43	]	]	PUNCT
ejpam-890	69	44	with	with	ADP
ejpam-890	69	45	the	the	DET
ejpam-890	69	46	following	follow	VERB
ejpam-890	69	47	theorem	theorem	NOUN
ejpam-890	69	48	:	:	PUNCT
ejpam-890	69	49	theorem	theorem	ADJ
ejpam-890	69	50	1	1	NUM
ejpam-890	69	51	(	(	PUNCT
ejpam-890	69	52	[	[	X
ejpam-890	69	53	5	5	NUM
ejpam-890	69	54	]	]	PUNCT
ejpam-890	69	55	)	)	PUNCT
ejpam-890	69	56	.	.	PUNCT
ejpam-890	70	1	let	let	VERB
ejpam-890	70	2	b	b	PRON
ejpam-890	70	3	p×r	p×r	PROPN
ejpam-890	70	4	m×s(fq	m×s(fq	PROPN
ejpam-890	70	5	)	)	PUNCT
ejpam-890	70	6	denote	denote	VERB
ejpam-890	70	7	the	the	DET
ejpam-890	70	8	number	number	NOUN
ejpam-890	70	9	of	of	ADP
ejpam-890	70	10	bursts	burst	NOUN
ejpam-890	70	11	of	of	ADP
ejpam-890	70	12	order	order	NOUN
ejpam-890	70	13	pr	pr	NOUN
ejpam-890	70	14	in	in	ADP
ejpam-890	70	15	mm×s(fq	mm×s(fq	PROPN
ejpam-890	70	16	)	)	PUNCT
ejpam-890	70	17	.	.	PUNCT
ejpam-890	71	1	then	then	ADV
ejpam-890	71	2	,	,	PUNCT
ejpam-890	71	3	b	b	PROPN
ejpam-890	71	4	p×r	p×r	PROPN
ejpam-890	71	5	m×s(fq	m×s(fq	PROPN
ejpam-890	71	6	)	)	PUNCT
ejpam-890	71	7	=	=	PUNCT
ejpam-890	72	1			PROPN
ejpam-890	72	2			VERB
ejpam-890	72	3			PROPN
ejpam-890	72	4			NOUN
ejpam-890	72	5			ADJ
ejpam-890	72	6			ADJ
ejpam-890	72	7			NOUN
ejpam-890	72	8	ms(q−	ms(q−	NOUN
ejpam-890	72	9	1	1	NUM
ejpam-890	72	10	)	)	PUNCT
ejpam-890	72	11	,	,	PUNCT
ejpam-890	72	12	p	p	NOUN
ejpam-890	72	13	=	=	NOUN
ejpam-890	72	14	1	1	NUM
ejpam-890	72	15	,	,	PUNCT
ejpam-890	72	16	r	r	NOUN
ejpam-890	72	17	=	=	SYM
ejpam-890	72	18	1	1	NUM
ejpam-890	72	19	,	,	PUNCT
ejpam-890	72	20	m(s−	m(s−	PROPN
ejpam-890	72	21	r	r	NOUN
ejpam-890	72	22	+	+	PROPN
ejpam-890	72	23	1)(q−	1)(q−	NUM
ejpam-890	72	24	1)2qr−2	1)2qr−2	NUM
ejpam-890	72	25	,	,	PUNCT
ejpam-890	72	26	p	p	NOUN
ejpam-890	72	27	=	=	NOUN
ejpam-890	72	28	1	1	NUM
ejpam-890	72	29	,	,	PUNCT
ejpam-890	72	30	r	r	NOUN
ejpam-890	72	31	≥	≥	NUM
ejpam-890	72	32	2	2	NUM
ejpam-890	72	33	(	(	PUNCT
ejpam-890	72	34	m−	m−	PROPN
ejpam-890	72	35	p+	p+	VERB
ejpam-890	72	36	1)s(q−	1)s(q−	PROPN
ejpam-890	72	37	1)2qp−2	1)2qp−2	NUM
ejpam-890	72	38	,	,	PUNCT
ejpam-890	72	39	p	p	PRON
ejpam-890	72	40	≥	≥	NUM
ejpam-890	72	41	2	2	NUM
ejpam-890	72	42	,	,	PUNCT
ejpam-890	72	43	r	r	NOUN
ejpam-890	72	44	=	=	SYM
ejpam-890	72	45	1	1	NUM
ejpam-890	72	46	,	,	PUNCT
ejpam-890	72	47	(	(	PUNCT
ejpam-890	72	48	m−	m−	PROPN
ejpam-890	72	49	p+	p+	VERB
ejpam-890	72	50	1)(s−	1)(s−	PROPN
ejpam-890	72	51	r	r	NOUN
ejpam-890	72	52	+	+	NOUN
ejpam-890	72	53	1)qr(p−2)[(qr	1)qr(p−2)[(qr	PROPN
ejpam-890	72	54	−	−	PROPN
ejpam-890	72	55	1)2	1)2	NUM
ejpam-890	72	56	−2(qr−1−	−2(qr−1−	NOUN
ejpam-890	72	57	1)2q2−p	1)2q2−p	NUM
ejpam-890	73	1	+	+	CCONJ
ejpam-890	73	2	(	(	PUNCT
ejpam-890	73	3	qr−2	qr−2	NOUN
ejpam-890	73	4	−	−	PROPN
ejpam-890	73	5	1)2q4−2p	1)2q4−2p	PROPN
ejpam-890	73	6	]	]	X
ejpam-890	73	7	,	,	PUNCT
ejpam-890	73	8	p	p	NOUN
ejpam-890	73	9	≥	≥	NUM
ejpam-890	73	10	2	2	NUM
ejpam-890	73	11	,	,	PUNCT
ejpam-890	73	12	r	r	NOUN
ejpam-890	73	13	≥	≥	NOUN
ejpam-890	73	14	2	2	NUM
ejpam-890	73	15	.	.	PUNCT
ejpam-890	73	16	further	far	ADV
ejpam-890	73	17	,	,	PUNCT
ejpam-890	73	18	in	in	ADP
ejpam-890	73	19	[	[	X
ejpam-890	73	20	5	5	NUM
ejpam-890	73	21	]	]	PUNCT
ejpam-890	73	22	a	a	DET
ejpam-890	73	23	formula	formula	NOUN
ejpam-890	73	24	for	for	ADP
ejpam-890	73	25	the	the	DET
ejpam-890	73	26	number	number	NOUN
ejpam-890	73	27	of	of	ADP
ejpam-890	73	28	bursts	burst	NOUN
ejpam-890	73	29	of	of	ADP
ejpam-890	73	30	a	a	DET
ejpam-890	73	31	particular	particular	ADJ
ejpam-890	73	32	order	order	NOUN
ejpam-890	73	33	and	and	CCONJ
ejpam-890	73	34	not	not	PART
ejpam-890	73	35	exceeding	exceed	VERB
ejpam-890	73	36	a	a	DET
ejpam-890	73	37	given	give	VERB
ejpam-890	73	38	ρ	ρ	NOUN
ejpam-890	73	39	-	-	PUNCT
ejpam-890	73	40	weight	weight	NOUN
ejpam-890	73	41	is	be	AUX
ejpam-890	73	42	stated	state	VERB
ejpam-890	73	43	and	and	CCONJ
ejpam-890	73	44	proved	prove	VERB
ejpam-890	73	45	in	in	ADP
ejpam-890	73	46	the	the	DET
ejpam-890	73	47	following	following	NOUN
ejpam-890	73	48	theorem	theorem	NOUN
ejpam-890	73	49	:	:	PUNCT
ejpam-890	73	50	theorem	theorem	ADJ
ejpam-890	73	51	2	2	NUM
ejpam-890	73	52	(	(	PUNCT
ejpam-890	73	53	[	[	X
ejpam-890	73	54	5	5	NUM
ejpam-890	73	55	]	]	NUM
ejpam-890	73	56	)	)	PUNCT
ejpam-890	73	57	.	.	PUNCT
ejpam-890	74	1	the	the	DET
ejpam-890	74	2	number	number	NOUN
ejpam-890	74	3	of	of	ADP
ejpam-890	74	4	bursts	burst	NOUN
ejpam-890	74	5	of	of	ADP
ejpam-890	74	6	order	order	NOUN
ejpam-890	74	7	pr	pr	X
ejpam-890	74	8	(	(	PUNCT
ejpam-890	74	9	1≤	1≤	NUM
ejpam-890	74	10	p	p	X
ejpam-890	74	11	≤	≤	NUM
ejpam-890	74	12	m	m	NOUN
ejpam-890	74	13	,	,	PUNCT
ejpam-890	74	14	1	1	NUM
ejpam-890	74	15	≤	≤	NOUN
ejpam-890	74	16	r	r	NOUN
ejpam-890	74	17	≤	≤	NUM
ejpam-890	74	18	s	s	NOUN
ejpam-890	74	19	)	)	PUNCT
ejpam-890	74	20	in	in	ADP
ejpam-890	74	21	mm×s(fq	mm×s(fq	PROPN
ejpam-890	74	22	)	)	PUNCT
ejpam-890	74	23	having	have	VERB
ejpam-890	74	24	ρ	ρ	NOUN
ejpam-890	74	25	-	-	PUNCT
ejpam-890	74	26	weight	weight	NOUN
ejpam-890	74	27	w	w	NOUN
ejpam-890	74	28	or	or	CCONJ
ejpam-890	74	29	less	less	ADJ
ejpam-890	74	30	(	(	PUNCT
ejpam-890	74	31	1≤	1≤	NUM
ejpam-890	74	32	w	w	PROPN
ejpam-890	74	33	≤	≤	NUM
ejpam-890	74	34	ms	ms	NOUN
ejpam-890	74	35	)	)	PUNCT
ejpam-890	74	36	is	be	AUX
ejpam-890	74	37	given	give	VERB
ejpam-890	74	38	by	by	ADP
ejpam-890	74	39	b	b	PROPN
ejpam-890	74	40	p×r	p×r	PROPN
ejpam-890	74	41	m×s(fq	m×s(fq	PROPN
ejpam-890	74	42	,	,	PUNCT
ejpam-890	74	43	w	w	NOUN
ejpam-890	74	44	)	)	PUNCT
ejpam-890	74	45	=	=	PUNCT
ejpam-890	75	1			PROPN
ejpam-890	75	2			ADP
ejpam-890	75	3			NOUN
ejpam-890	75	4	m(q−	m(q−	PROPN
ejpam-890	75	5	1)min(w	1)min(w	NUM
ejpam-890	75	6	,	,	PUNCT
ejpam-890	75	7	s	s	PART
ejpam-890	75	8	)	)	PUNCT
ejpam-890	75	9	,	,	PUNCT
ejpam-890	75	10	p	p	NOUN
ejpam-890	75	11	=	=	NOUN
ejpam-890	75	12	1	1	NUM
ejpam-890	75	13	,	,	PUNCT
ejpam-890	75	14	r	r	NOUN
ejpam-890	75	15	=	=	SYM
ejpam-890	75	16	1	1	NUM
ejpam-890	75	17	,	,	PUNCT
ejpam-890	75	18	mmin(w	mmin(w	NOUN
ejpam-890	75	19	−	−	NOUN
ejpam-890	75	20	r	r	NOUN
ejpam-890	75	21	+	+	NUM
ejpam-890	75	22	1	1	NUM
ejpam-890	75	23	,	,	PUNCT
ejpam-890	75	24	s−	s−	PROPN
ejpam-890	75	25	r	r	NOUN
ejpam-890	75	26	+	+	PROPN
ejpam-890	75	27	1)(q−	1)(q−	NUM
ejpam-890	75	28	1)2qr−2	1)2qr−2	NUM
ejpam-890	75	29	,	,	PUNCT
ejpam-890	75	30	p	p	NOUN
ejpam-890	75	31	=	=	NOUN
ejpam-890	75	32	1	1	NUM
ejpam-890	75	33	,	,	PUNCT
ejpam-890	75	34	r	r	NOUN
ejpam-890	75	35	≥	≥	NOUN
ejpam-890	75	36	2	2	NUM
ejpam-890	75	37	,	,	PUNCT
ejpam-890	75	38	(	(	PUNCT
ejpam-890	75	39	m−	m−	PROPN
ejpam-890	75	40	p+	p+	PROPN
ejpam-890	75	41	1)b3	1)b3	NUM
ejpam-890	75	42	,	,	PUNCT
ejpam-890	75	43	p	p	PRON
ejpam-890	75	44	≥	≥	NOUN
ejpam-890	75	45	2	2	NUM
ejpam-890	75	46	,	,	PUNCT
ejpam-890	75	47	r	r	NOUN
ejpam-890	75	48	=	=	SYM
ejpam-890	75	49	1	1	NUM
ejpam-890	75	50	,	,	PUNCT
ejpam-890	75	51	(	(	PUNCT
ejpam-890	75	52	m−	m−	PROPN
ejpam-890	75	53	p+	p+	PROPN
ejpam-890	75	54	1)b4	1)b4	NUM
ejpam-890	75	55	,	,	PUNCT
ejpam-890	75	56	p	p	PRON
ejpam-890	75	57	≥	≥	NUM
ejpam-890	75	58	2	2	NUM
ejpam-890	75	59	,	,	PUNCT
ejpam-890	75	60	r	r	NOUN
ejpam-890	75	61	≥	≥	NOUN
ejpam-890	75	62	2	2	NUM
ejpam-890	75	63	.	.	PUNCT
ejpam-890	75	64	where	where	SCONJ
ejpam-890	75	65	b3	b3	PROPN
ejpam-890	75	66	=	=	SYM
ejpam-890	75	67	min([w/2],s	min([w/2],s	NOUN
ejpam-890	75	68	)	)	PUNCT
ejpam-890	75	69	∑	∑	PUNCT
ejpam-890	75	70	j=1	j=1	PROPN
ejpam-890	75	71	p−1	p−1	PROPN
ejpam-890	75	72	∑	∑	PUNCT
ejpam-890	75	73	η=0	η=0	PROPN
ejpam-890	75	74	:	:	PUNCT
ejpam-890	75	75	η	η	PROPN
ejpam-890	75	76	j≤w−2	j≤w−2	PROPN
ejpam-890	75	77	j	j	PROPN
ejpam-890	75	78	(	(	PUNCT
ejpam-890	75	79	q−	q−	PROPN
ejpam-890	75	80	1)2	1)2	NUM
ejpam-890	75	81	�	�	PROPN
ejpam-890	75	82	p−	p−	NOUN
ejpam-890	75	83	2	2	NUM
ejpam-890	75	84	η	η	X
ejpam-890	75	85	�	�	PROPN
ejpam-890	75	86	(	(	PUNCT
ejpam-890	75	87	q−	q−	PROPN
ejpam-890	75	88	1)η	1)η	NUM
ejpam-890	75	89	,	,	PUNCT
ejpam-890	75	90	b4	b4	NOUN
ejpam-890	75	91	=	=	SYM
ejpam-890	75	92	(	(	PUNCT
ejpam-890	75	93	m−	m−	PROPN
ejpam-890	75	94	p+	p+	ADJ
ejpam-890	75	95	1	1	NUM
ejpam-890	75	96	)	)	PUNCT
ejpam-890	75	97	min(w−r+1,s−r+1	min(w−r+1,s−r+1	PROPN
ejpam-890	75	98	)	)	PUNCT
ejpam-890	75	99	∑	∑	PUNCT
ejpam-890	75	100	j=1	j=1	NOUN
ejpam-890	75	101	(	(	PUNCT
ejpam-890	75	102	l	l	NOUN
ejpam-890	75	103	p	p	X
ejpam-890	75	104	j	j	PROPN
ejpam-890	76	1	−	−	PROPN
ejpam-890	76	2	2l	2l	PROPN
ejpam-890	77	1	p−1	p−1	PROPN
ejpam-890	77	2	j	j	PROPN
ejpam-890	77	3	+	+	CCONJ
ejpam-890	77	4	l	l	PROPN
ejpam-890	77	5	p−2	p−2	PROPN
ejpam-890	77	6	j	j	PROPN
ejpam-890	77	7	)	)	PUNCT
ejpam-890	77	8	,	,	PUNCT
ejpam-890	77	9	i̇.	i̇.	PROPN
ejpam-890	77	10	siap	siap	PROPN
ejpam-890	77	11	/	/	SYM
ejpam-890	77	12	eur	eur	PROPN
ejpam-890	77	13	.	.	PUNCT
ejpam-890	78	1	j.	j.	PROPN
ejpam-890	78	2	pure	pure	PROPN
ejpam-890	78	3	appl	appl	PROPN
ejpam-890	78	4	.	.	PROPN
ejpam-890	78	5	math	math	PROPN
ejpam-890	78	6	,	,	PUNCT
ejpam-890	78	7	3	3	NUM
ejpam-890	78	8	(	(	PUNCT
ejpam-890	78	9	2010	2010	NUM
ejpam-890	78	10	)	)	PUNCT
ejpam-890	78	11	,	,	PUNCT
ejpam-890	78	12	653	653	NUM
ejpam-890	78	13	-	-	SYM
ejpam-890	78	14	669	669	NUM
ejpam-890	78	15	656	656	NUM
ejpam-890	78	16	and	and	CCONJ
ejpam-890	78	17	l	l	NOUN
ejpam-890	79	1	p	p	X
ejpam-890	79	2	j	j	PROPN
ejpam-890	79	3	=	=	PUNCT
ejpam-890	79	4	∑	∑	PUNCT
ejpam-890	79	5	k	k	PROPN
ejpam-890	79	6	j	j	PROPN
ejpam-890	79	7	,	,	PUNCT
ejpam-890	79	8	...	...	PUNCT
ejpam-890	79	9	,	,	PUNCT
ejpam-890	79	10	k	k	PROPN
ejpam-890	80	1	j+r−1	j+r−1	PROPN
ejpam-890	81	1	p	p	X
ejpam-890	81	2	!	!	PUNCT
ejpam-890	82	1	∏r−1	∏r−1	INTJ
ejpam-890	82	2	l=0	l=0	PROPN
ejpam-890	82	3	k	k	PROPN
ejpam-890	83	1	j+1	j+1	X
ejpam-890	83	2	!	!	PUNCT
ejpam-890	83	3	�	�	PROPN
ejpam-890	83	4	p−	p−	VERB
ejpam-890	83	5	∑r−1	∑r−1	ADJ
ejpam-890	84	1	l=0	l=0	PROPN
ejpam-890	84	2	k	k	PROPN
ejpam-890	84	3	j+l	j+l	PROPN
ejpam-890	84	4	�	�	PROPN
ejpam-890	84	5	!	!	PUNCT
ejpam-890	85	1	�	�	PROPN
ejpam-890	85	2	q−	q−	PROPN
ejpam-890	85	3	1	1	NUM
ejpam-890	85	4	q	q	PROPN
ejpam-890	85	5	�	�	PROPN
ejpam-890	85	6	∑r−1	∑r−1	PROPN
ejpam-890	86	1	l=0	l=0	PROPN
ejpam-890	86	2	k	k	X
ejpam-890	86	3	j+l	j+l	PROPN
ejpam-890	86	4	q	q	X
ejpam-890	87	1	∑r−1	∑r−1	PROPN
ejpam-890	87	2	l=0	l=0	PROPN
ejpam-890	87	3	(	(	PUNCT
ejpam-890	87	4	l+1)k	l+1)k	PROPN
ejpam-890	87	5	j+l	j+l	PROPN
ejpam-890	87	6	(	(	PUNCT
ejpam-890	87	7	1	1	NUM
ejpam-890	87	8	)	)	PUNCT
ejpam-890	88	1	where	where	SCONJ
ejpam-890	88	2	k	k	PROPN
ejpam-890	88	3	j	j	PROPN
ejpam-890	88	4	,	,	PUNCT
ejpam-890	88	5	k	k	PROPN
ejpam-890	88	6	j+1	j+1	PROPN
ejpam-890	88	7	,	,	PUNCT
ejpam-890	88	8	.	.	PUNCT
ejpam-890	88	9	.	.	PUNCT
ejpam-890	89	1	.	.	PUNCT
ejpam-890	90	1	,	,	PUNCT
ejpam-890	91	1	k	k	PROPN
ejpam-890	91	2	j+r−1	j+r−1	PROPN
ejpam-890	91	3	being	be	AUX
ejpam-890	91	4	nonnegative	nonnegative	ADJ
ejpam-890	91	5	integers	integer	NOUN
ejpam-890	91	6	such	such	ADJ
ejpam-890	91	7	that	that	SCONJ
ejpam-890	91	8	k	k	PROPN
ejpam-890	91	9	j	j	PROPN
ejpam-890	91	10	>	>	X
ejpam-890	91	11	0	0	PROPN
ejpam-890	91	12	,	,	PUNCT
ejpam-890	91	13	k	k	PROPN
ejpam-890	91	14	j+1	j+1	PROPN
ejpam-890	91	15	,	,	PUNCT
ejpam-890	91	16	k	k	PROPN
ejpam-890	91	17	j+2	j+2	PROPN
ejpam-890	91	18	,	,	PUNCT
ejpam-890	91	19	.	.	PUNCT
ejpam-890	91	20	.	.	PUNCT
ejpam-890	92	1	.	.	PUNCT
ejpam-890	93	1	,	,	PUNCT
ejpam-890	93	2	k	k	PROPN
ejpam-890	93	3	j+r−2	j+r−2	PROPN
ejpam-890	93	4	≥	≥	NUM
ejpam-890	93	5	0	0	NUM
ejpam-890	93	6	,	,	PUNCT
ejpam-890	93	7	k	k	PROPN
ejpam-890	93	8	j+r−1	j+r−1	PROPN
ejpam-890	93	9	>	>	X
ejpam-890	93	10	0	0	PROPN
ejpam-890	93	11	,	,	PUNCT
ejpam-890	93	12	r−1	r−1	PROPN
ejpam-890	93	13	∑	∑	ADP
ejpam-890	93	14	l=0	l=0	PROPN
ejpam-890	93	15	k	k	X
ejpam-890	93	16	j+l	j+l	PROPN
ejpam-890	93	17	≤	≤	PROPN
ejpam-890	94	1	p	p	PROPN
ejpam-890	94	2	r−1	r−1	PROPN
ejpam-890	94	3	∑	∑	PUNCT
ejpam-890	94	4	l=0	l=0	PROPN
ejpam-890	94	5	(	(	PUNCT
ejpam-890	94	6	j+	j+	PROPN
ejpam-890	94	7	l)k	l)k	X
ejpam-890	94	8	j+l	j+l	PROPN
ejpam-890	94	9	≤	≤	PROPN
ejpam-890	94	10	w.	w.	NOUN
ejpam-890	94	11	(	(	PUNCT
ejpam-890	94	12	2	2	NUM
ejpam-890	94	13	)	)	PUNCT
ejpam-890	94	14	in	in	ADP
ejpam-890	94	15	theorem	theorem	NOUN
ejpam-890	94	16	2	2	NUM
ejpam-890	94	17	,	,	PUNCT
ejpam-890	94	18	computing	compute	VERB
ejpam-890	94	19	the	the	DET
ejpam-890	94	20	number	number	NOUN
ejpam-890	94	21	of	of	ADP
ejpam-890	94	22	burst	burst	ADJ
ejpam-890	94	23	errors	error	NOUN
ejpam-890	94	24	of	of	ADP
ejpam-890	94	25	a	a	DET
ejpam-890	94	26	particular	particular	ADJ
ejpam-890	94	27	order	order	NOUN
ejpam-890	94	28	is	be	AUX
ejpam-890	94	29	still	still	ADV
ejpam-890	94	30	a	a	DET
ejpam-890	94	31	challenging	challenging	ADJ
ejpam-890	94	32	task	task	NOUN
ejpam-890	94	33	.	.	PUNCT
ejpam-890	95	1	in	in	ADP
ejpam-890	95	2	equation	equation	NOUN
ejpam-890	95	3	2	2	NUM
ejpam-890	95	4	,	,	PUNCT
ejpam-890	95	5	the	the	DET
ejpam-890	95	6	two	two	NUM
ejpam-890	95	7	diophantine	diophantine	NOUN
ejpam-890	95	8	inequalities	inequality	NOUN
ejpam-890	95	9	are	be	AUX
ejpam-890	95	10	first	first	ADJ
ejpam-890	95	11	to	to	PART
ejpam-890	95	12	be	be	AUX
ejpam-890	95	13	solved	solve	VERB
ejpam-890	95	14	in	in	ADP
ejpam-890	95	15	the	the	DET
ejpam-890	95	16	set	set	NOUN
ejpam-890	95	17	of	of	ADP
ejpam-890	95	18	natural	natural	ADJ
ejpam-890	95	19	numbers	number	NOUN
ejpam-890	95	20	.	.	PUNCT
ejpam-890	96	1	then	then	ADV
ejpam-890	96	2	,	,	PUNCT
ejpam-890	96	3	the	the	DET
ejpam-890	96	4	l	l	NOUN
ejpam-890	96	5	p	p	NOUN
ejpam-890	96	6	j	j	PROPN
ejpam-890	96	7	numbers	number	NOUN
ejpam-890	96	8	are	be	AUX
ejpam-890	96	9	computed	compute	VERB
ejpam-890	96	10	by	by	ADP
ejpam-890	96	11	using	use	VERB
ejpam-890	96	12	the	the	DET
ejpam-890	96	13	ki	ki	PROPN
ejpam-890	96	14	solutions	solution	NOUN
ejpam-890	96	15	.	.	PUNCT
ejpam-890	97	1	in	in	ADP
ejpam-890	97	2	[	[	X
ejpam-890	97	3	5	5	NUM
ejpam-890	97	4	]	]	PUNCT
ejpam-890	97	5	,	,	PUNCT
ejpam-890	97	6	some	some	DET
ejpam-890	97	7	examples	example	NOUN
ejpam-890	97	8	using	use	VERB
ejpam-890	97	9	this	this	DET
ejpam-890	97	10	approach	approach	NOUN
ejpam-890	97	11	are	be	AUX
ejpam-890	97	12	worked	work	VERB
ejpam-890	97	13	out	out	ADP
ejpam-890	97	14	explicitly	explicitly	ADV
ejpam-890	97	15	.	.	PUNCT
ejpam-890	98	1	in	in	ADP
ejpam-890	98	2	the	the	DET
ejpam-890	98	3	next	next	ADJ
ejpam-890	98	4	sections	section	NOUN
ejpam-890	98	5	,	,	PUNCT
ejpam-890	98	6	we	we	PRON
ejpam-890	98	7	first	first	ADV
ejpam-890	98	8	extend	extend	VERB
ejpam-890	98	9	the	the	DET
ejpam-890	98	10	results	result	NOUN
ejpam-890	98	11	obtained	obtain	VERB
ejpam-890	98	12	by	by	ADP
ejpam-890	98	13	jain	jain	NOUN
ejpam-890	98	14	in	in	ADP
ejpam-890	98	15	[	[	X
ejpam-890	98	16	5	5	NUM
ejpam-890	98	17	]	]	PUNCT
ejpam-890	98	18	to	to	PART
ejpam-890	98	19	array	array	VERB
ejpam-890	98	20	codes	code	NOUN
ejpam-890	98	21	over	over	ADP
ejpam-890	98	22	r	r	NOUN
ejpam-890	98	23	by	by	ADP
ejpam-890	98	24	introducing	introduce	VERB
ejpam-890	98	25	a	a	DET
ejpam-890	98	26	new	new	ADJ
ejpam-890	98	27	constructive	constructive	ADJ
ejpam-890	98	28	method	method	NOUN
ejpam-890	98	29	that	that	PRON
ejpam-890	98	30	gives	give	VERB
ejpam-890	98	31	the	the	DET
ejpam-890	98	32	number	number	NOUN
ejpam-890	98	33	of	of	ADP
ejpam-890	98	34	burst	burst	ADJ
ejpam-890	98	35	errors	error	NOUN
ejpam-890	98	36	.	.	PUNCT
ejpam-890	99	1	this	this	DET
ejpam-890	99	2	new	new	ADJ
ejpam-890	99	3	method	method	NOUN
ejpam-890	99	4	,	,	PUNCT
ejpam-890	99	5	it	it	PRON
ejpam-890	99	6	does	do	AUX
ejpam-890	99	7	not	not	PART
ejpam-890	99	8	only	only	ADV
ejpam-890	99	9	give	give	VERB
ejpam-890	99	10	the	the	DET
ejpam-890	99	11	number	number	NOUN
ejpam-890	99	12	of	of	ADP
ejpam-890	99	13	a	a	DET
ejpam-890	99	14	particular	particular	ADJ
ejpam-890	99	15	burst	burst	NOUN
ejpam-890	99	16	error	error	NOUN
ejpam-890	99	17	weight	weight	NOUN
ejpam-890	99	18	but	but	CCONJ
ejpam-890	99	19	it	it	PRON
ejpam-890	99	20	also	also	ADV
ejpam-890	99	21	gives	give	VERB
ejpam-890	99	22	all	all	DET
ejpam-890	99	23	spectra	spectra	NOUN
ejpam-890	99	24	of	of	ADP
ejpam-890	99	25	the	the	DET
ejpam-890	99	26	weights	weight	NOUN
ejpam-890	99	27	in	in	ADP
ejpam-890	99	28	a	a	DET
ejpam-890	99	29	single	single	ADJ
ejpam-890	99	30	computation	computation	NOUN
ejpam-890	99	31	.	.	PUNCT
ejpam-890	100	1	the	the	DET
ejpam-890	100	2	spectra	spectra	NOUN
ejpam-890	100	3	of	of	ADP
ejpam-890	100	4	the	the	DET
ejpam-890	100	5	number	number	NOUN
ejpam-890	100	6	of	of	ADP
ejpam-890	100	7	burst	burst	ADJ
ejpam-890	100	8	errors	error	NOUN
ejpam-890	100	9	shall	shall	AUX
ejpam-890	100	10	be	be	AUX
ejpam-890	100	11	called	call	VERB
ejpam-890	100	12	the	the	DET
ejpam-890	100	13	burst	burst	VERB
ejpam-890	100	14	error	error	NOUN
ejpam-890	100	15	weight	weight	NOUN
ejpam-890	100	16	enumerator	enumerator	NOUN
ejpam-890	100	17	.	.	PUNCT
ejpam-890	101	1	finally	finally	ADV
ejpam-890	101	2	,	,	PUNCT
ejpam-890	101	3	we	we	PRON
ejpam-890	101	4	apply	apply	VERB
ejpam-890	101	5	our	our	PRON
ejpam-890	101	6	results	result	NOUN
ejpam-890	101	7	to	to	PART
ejpam-890	101	8	obtain	obtain	VERB
ejpam-890	101	9	new	new	ADJ
ejpam-890	101	10	bounds	bound	NOUN
ejpam-890	101	11	for	for	ADP
ejpam-890	101	12	array	array	NOUN
ejpam-890	101	13	codes	code	NOUN
ejpam-890	101	14	over	over	ADP
ejpam-890	101	15	rings	ring	NOUN
ejpam-890	101	16	.	.	PUNCT
ejpam-890	102	1	2	2	X
ejpam-890	102	2	.	.	X
ejpam-890	102	3	enumerating	enumerate	VERB
ejpam-890	102	4	burst	burst	ADJ
ejpam-890	102	5	errors	error	NOUN
ejpam-890	102	6	in	in	ADP
ejpam-890	102	7	this	this	DET
ejpam-890	102	8	section	section	NOUN
ejpam-890	102	9	,	,	PUNCT
ejpam-890	102	10	we	we	PRON
ejpam-890	102	11	shall	shall	AUX
ejpam-890	102	12	work	work	VERB
ejpam-890	102	13	on	on	ADP
ejpam-890	102	14	the	the	DET
ejpam-890	102	15	space	space	NOUN
ejpam-890	102	16	mp×r(r	mp×r(r	NOUN
ejpam-890	102	17	)	)	PUNCT
ejpam-890	102	18	and	and	CCONJ
ejpam-890	102	19	consider	consider	VERB
ejpam-890	102	20	only	only	ADV
ejpam-890	102	21	burst	burst	ADJ
ejpam-890	102	22	errors	error	NOUN
ejpam-890	102	23	of	of	ADP
ejpam-890	102	24	order	order	NOUN
ejpam-890	102	25	p×	p×	PROPN
ejpam-890	102	26	r.	r.	PROPN
ejpam-890	102	27	in	in	ADP
ejpam-890	102	28	the	the	DET
ejpam-890	102	29	next	next	ADJ
ejpam-890	102	30	section	section	NOUN
ejpam-890	102	31	,	,	PUNCT
ejpam-890	102	32	we	we	PRON
ejpam-890	102	33	shall	shall	AUX
ejpam-890	102	34	consider	consider	VERB
ejpam-890	102	35	burst	burst	ADJ
ejpam-890	102	36	errors	error	NOUN
ejpam-890	102	37	of	of	ADP
ejpam-890	102	38	order	order	NOUN
ejpam-890	102	39	p×	p×	NOUN
ejpam-890	102	40	r	r	NOUN
ejpam-890	102	41	in	in	ADP
ejpam-890	102	42	the	the	DET
ejpam-890	102	43	space	space	NOUN
ejpam-890	102	44	mm×s(r	mm×s(r	NOUN
ejpam-890	102	45	)	)	PUNCT
ejpam-890	102	46	where	where	SCONJ
ejpam-890	102	47	1≤	1≤	NUM
ejpam-890	102	48	p	p	X
ejpam-890	102	49	≤	≤	NUM
ejpam-890	102	50	m	m	PROPN
ejpam-890	102	51	,	,	PUNCT
ejpam-890	102	52	1≤	1≤	PRON
ejpam-890	102	53	r	r	NOUN
ejpam-890	102	54	≤	≤	PUNCT
ejpam-890	102	55	s.	s.	PROPN
ejpam-890	102	56	in	in	ADP
ejpam-890	102	57	order	order	NOUN
ejpam-890	102	58	to	to	PART
ejpam-890	102	59	introduce	introduce	VERB
ejpam-890	102	60	the	the	DET
ejpam-890	102	61	new	new	ADJ
ejpam-890	102	62	approach	approach	NOUN
ejpam-890	102	63	for	for	ADP
ejpam-890	102	64	computing	compute	VERB
ejpam-890	102	65	burst	burst	NOUN
ejpam-890	102	66	error	error	NOUN
ejpam-890	102	67	matrices	matrix	NOUN
ejpam-890	102	68	we	we	PRON
ejpam-890	102	69	need	need	VERB
ejpam-890	102	70	to	to	PART
ejpam-890	102	71	state	state	VERB
ejpam-890	102	72	some	some	DET
ejpam-890	102	73	definitions	definition	NOUN
ejpam-890	102	74	and	and	CCONJ
ejpam-890	102	75	introduce	introduce	VERB
ejpam-890	102	76	some	some	DET
ejpam-890	102	77	new	new	ADJ
ejpam-890	102	78	concepts	concept	NOUN
ejpam-890	102	79	.	.	PUNCT
ejpam-890	103	1	definition	definition	NOUN
ejpam-890	103	2	5	5	NUM
ejpam-890	103	3	.	.	PUNCT
ejpam-890	104	1	if	if	SCONJ
ejpam-890	104	2	a	a	DET
ejpam-890	104	3	∈	∈	PROPN
ejpam-890	104	4	mm×s(fq	mm×s(fq	NOUN
ejpam-890	104	5	)	)	PUNCT
ejpam-890	104	6	and	and	CCONJ
ejpam-890	104	7	wn	wn	PROPN
ejpam-890	104	8	(	(	PUNCT
ejpam-890	104	9	ai	ai	PROPN
ejpam-890	104	10	)	)	PUNCT
ejpam-890	104	11	=	=	SYM
ejpam-890	104	12	αi	αi	NOUN
ejpam-890	104	13	,	,	PUNCT
ejpam-890	104	14	then	then	ADV
ejpam-890	104	15	the	the	DET
ejpam-890	104	16	matrix	matrix	NOUN
ejpam-890	104	17	a	a	PRON
ejpam-890	104	18	is	be	AUX
ejpam-890	104	19	said	say	VERB
ejpam-890	104	20	to	to	PART
ejpam-890	104	21	have	have	VERB
ejpam-890	104	22	a	a	DET
ejpam-890	104	23	weight	weight	NOUN
ejpam-890	104	24	distribution	distribution	NOUN
ejpam-890	104	25	of	of	ADP
ejpam-890	104	26	type	type	NOUN
ejpam-890	104	27	(	(	PUNCT
ejpam-890	104	28	α1,α2	α1,α2	PROPN
ejpam-890	104	29	,	,	PUNCT
ejpam-890	104	30	.	.	PUNCT
ejpam-890	104	31	.	.	PUNCT
ejpam-890	104	32	.	.	PUNCT
ejpam-890	105	1	,	,	PUNCT
ejpam-890	105	2	αm	αm	NOUN
ejpam-890	105	3	)	)	PUNCT
ejpam-890	105	4	.	.	PUNCT
ejpam-890	106	1	if	if	SCONJ
ejpam-890	106	2	a	a	DET
ejpam-890	106	3	j	j	PROPN
ejpam-890	106	4	is	be	AUX
ejpam-890	106	5	the	the	DET
ejpam-890	106	6	jth	jth	PROPN
ejpam-890	106	7	row	row	NOUN
ejpam-890	106	8	of	of	ADP
ejpam-890	106	9	an	an	DET
ejpam-890	106	10	a	a	DET
ejpam-890	106	11	∈	∈	ADJ
ejpam-890	106	12	mp×r	mp×r	PROPN
ejpam-890	106	13	matrix	matrix	NOUN
ejpam-890	106	14	,	,	PUNCT
ejpam-890	106	15	then	then	ADV
ejpam-890	106	16	the	the	DET
ejpam-890	106	17	index	index	NOUN
ejpam-890	106	18	of	of	ADP
ejpam-890	106	19	a	a	DET
ejpam-890	106	20	j	j	NOUN
ejpam-890	106	21	denoted	denote	VERB
ejpam-890	106	22	by	by	ADP
ejpam-890	106	23	(	(	PUNCT
ejpam-890	106	24	k	k	PROPN
ejpam-890	106	25	j	j	PROPN
ejpam-890	106	26	,	,	PUNCT
ejpam-890	106	27	l	l	PROPN
ejpam-890	106	28	j	j	PROPN
ejpam-890	106	29	)	)	PUNCT
ejpam-890	106	30	where	where	SCONJ
ejpam-890	106	31	1	1	NUM
ejpam-890	106	32	≤	≤	NUM
ejpam-890	106	33	k	k	X
ejpam-890	106	34	j	j	PROPN
ejpam-890	106	35	≤	≤	PROPN
ejpam-890	106	36	l	l	NOUN
ejpam-890	106	37	j	j	PROPN
ejpam-890	106	38	≤	≤	NOUN
ejpam-890	106	39	r	r	NOUN
ejpam-890	106	40	is	be	AUX
ejpam-890	106	41	defined	define	VERB
ejpam-890	106	42	by	by	ADP
ejpam-890	106	43	a	a	DET
ejpam-890	106	44	ji	ji	PROPN
ejpam-890	106	45	=	=	NOUN
ejpam-890	106	46	0	0	NUM
ejpam-890	106	47	for	for	ADP
ejpam-890	106	48	all	all	DET
ejpam-890	106	49	1	1	NUM
ejpam-890	106	50	≤	≤	NUM
ejpam-890	106	51	i	i	NOUN
ejpam-890	106	52	≤	≤	NUM
ejpam-890	107	1	k	k	PROPN
ejpam-890	107	2	j	j	PROPN
ejpam-890	108	1	−	−	PROPN
ejpam-890	108	2	1	1	NUM
ejpam-890	108	3	and	and	CCONJ
ejpam-890	108	4	a	a	DET
ejpam-890	108	5	jk	jk	PROPN
ejpam-890	108	6	j	j	PROPN
ejpam-890	108	7	6=	6=	ADP
ejpam-890	108	8	0	0	NUM
ejpam-890	108	9	and	and	CCONJ
ejpam-890	108	10	l	l	PROPN
ejpam-890	108	11	j	j	PROPN
ejpam-890	108	12	=	=	SYM
ejpam-890	108	13	wn	wn	PROPN
ejpam-890	108	14	(	(	PUNCT
ejpam-890	108	15	a	a	DET
ejpam-890	108	16	j	j	NOUN
ejpam-890	108	17	)	)	PUNCT
ejpam-890	108	18	.	.	PUNCT
ejpam-890	109	1	the	the	DET
ejpam-890	109	2	index	index	NOUN
ejpam-890	109	3	of	of	ADP
ejpam-890	109	4	a	a	DET
ejpam-890	109	5	matrix	matrix	NOUN
ejpam-890	109	6	with	with	ADP
ejpam-890	109	7	rows	row	NOUN
ejpam-890	109	8	a1,a2	a1,a2	PROPN
ejpam-890	109	9	,	,	PUNCT
ejpam-890	109	10	.	.	PUNCT
ejpam-890	109	11	.	.	PUNCT
ejpam-890	109	12	.	.	PUNCT
ejpam-890	110	1	ap	ap	PROPN
ejpam-890	110	2	is	be	AUX
ejpam-890	110	3	defined	define	VERB
ejpam-890	110	4	by	by	ADP
ejpam-890	110	5	(	(	PUNCT
ejpam-890	110	6	(	(	PUNCT
ejpam-890	110	7	k1	k1	PROPN
ejpam-890	110	8	,	,	PUNCT
ejpam-890	110	9	l1	l1	PROPN
ejpam-890	110	10	)	)	PUNCT
ejpam-890	110	11	,	,	PUNCT
ejpam-890	110	12	(	(	PUNCT
ejpam-890	110	13	k2	k2	ADJ
ejpam-890	110	14	,	,	PUNCT
ejpam-890	110	15	l2	l2	NOUN
ejpam-890	110	16	)	)	PUNCT
ejpam-890	110	17	,	,	PUNCT
ejpam-890	110	18	.	.	PUNCT
ejpam-890	110	19	.	.	PUNCT
ejpam-890	110	20	.	.	PUNCT
ejpam-890	111	1	,	,	PUNCT
ejpam-890	111	2	(	(	PUNCT
ejpam-890	111	3	kp	kp	INTJ
ejpam-890	111	4	,	,	PUNCT
ejpam-890	111	5	lp	lp	NOUN
ejpam-890	111	6	)	)	PUNCT
ejpam-890	111	7	)	)	PUNCT
ejpam-890	111	8	.	.	PUNCT
ejpam-890	112	1	let	let	VERB
ejpam-890	112	2	a=	a=	ADV
ejpam-890	112	3			VERB
ejpam-890	112	4			NOUN
ejpam-890	112	5			NOUN
ejpam-890	112	6			NOUN
ejpam-890	112	7			NOUN
ejpam-890	112	8			PROPN
ejpam-890	112	9	a11	a11	X
ejpam-890	112	10	·	·	PUNCT
ejpam-890	112	11	·	·	PUNCT
ejpam-890	112	12	·	·	PUNCT
ejpam-890	112	13	a1r	a1r	PROPN
ejpam-890	112	14	a21	a21	NOUN
ejpam-890	112	15	·	·	PUNCT
ejpam-890	112	16	·	·	PUNCT
ejpam-890	112	17	·	·	PUNCT
ejpam-890	113	1	a2r	a2r	PROPN
ejpam-890	113	2	...	...	PUNCT
ejpam-890	113	3	...	...	PUNCT
ejpam-890	113	4	...	...	PUNCT
ejpam-890	114	1	ap1	ap1	PROPN
ejpam-890	114	2	·	·	PUNCT
ejpam-890	114	3	·	·	PUNCT
ejpam-890	114	4	·	·	PUNCT
ejpam-890	114	5	apr	apr	NOUN
ejpam-890	114	6			PROPN
ejpam-890	114	7			NOUN
ejpam-890	114	8			VERB
ejpam-890	114	9			NOUN
ejpam-890	114	10			NOUN
ejpam-890	114	11			PUNCT
ejpam-890	114	12	.	.	PUNCT
ejpam-890	115	1	the	the	DET
ejpam-890	115	2	first	first	ADJ
ejpam-890	115	3	row	row	NOUN
ejpam-890	115	4	and	and	CCONJ
ejpam-890	115	5	column	column	NOUN
ejpam-890	115	6	,	,	PUNCT
ejpam-890	115	7	and	and	CCONJ
ejpam-890	115	8	the	the	DET
ejpam-890	115	9	last	last	ADJ
ejpam-890	115	10	row	row	NOUN
ejpam-890	115	11	and	and	CCONJ
ejpam-890	115	12	column	column	NOUN
ejpam-890	115	13	of	of	ADP
ejpam-890	115	14	the	the	DET
ejpam-890	115	15	matrix	matrix	NOUN
ejpam-890	115	16	a	a	PRON
ejpam-890	115	17	are	be	AUX
ejpam-890	115	18	shown	show	VERB
ejpam-890	115	19	in	in	ADP
ejpam-890	115	20	the	the	DET
ejpam-890	115	21	following	follow	VERB
ejpam-890	115	22	rectangle	rectangle	NOUN
ejpam-890	115	23	which	which	PRON
ejpam-890	115	24	is	be	AUX
ejpam-890	115	25	called	call	VERB
ejpam-890	115	26	the	the	DET
ejpam-890	115	27	frame	frame	NOUN
ejpam-890	115	28	of	of	ADP
ejpam-890	115	29	matrix	matrix	NOUN
ejpam-890	115	30	a.	a.	NOUN
ejpam-890	115	31	i̇.	i̇.	PROPN
ejpam-890	115	32	siap	siap	PROPN
ejpam-890	115	33	/	/	SYM
ejpam-890	115	34	eur	eur	PROPN
ejpam-890	115	35	.	.	PUNCT
ejpam-890	116	1	j.	j.	PROPN
ejpam-890	116	2	pure	pure	PROPN
ejpam-890	116	3	appl	appl	PROPN
ejpam-890	116	4	.	.	PROPN
ejpam-890	116	5	math	math	PROPN
ejpam-890	116	6	,	,	PUNCT
ejpam-890	116	7	3	3	NUM
ejpam-890	116	8	(	(	PUNCT
ejpam-890	116	9	2010	2010	NUM
ejpam-890	116	10	)	)	PUNCT
ejpam-890	116	11	,	,	PUNCT
ejpam-890	116	12	653	653	NUM
ejpam-890	116	13	-	-	SYM
ejpam-890	116	14	669	669	NUM
ejpam-890	116	15	657	657	NUM
ejpam-890	116	16	a11	a11	PROPN
ejpam-890	116	17	a12	a12	NOUN
ejpam-890	116	18	·	·	PUNCT
ejpam-890	116	19	·	·	PUNCT
ejpam-890	116	20	·	·	PUNCT
ejpam-890	117	1	a1r−1	a1r−1	PROPN
ejpam-890	117	2	a1r	a1r	PROPN
ejpam-890	117	3	a21	a21	X
ejpam-890	117	4	·	·	PUNCT
ejpam-890	117	5	·	·	PUNCT
ejpam-890	117	6	·	·	PUNCT
ejpam-890	117	7	·	·	PUNCT
ejpam-890	117	8	·	·	PUNCT
ejpam-890	117	9	·	·	PUNCT
ejpam-890	117	10	·	·	PUNCT
ejpam-890	117	11	·	·	PUNCT
ejpam-890	117	12	·	·	PUNCT
ejpam-890	117	13	a2r	a2r	PROPN
ejpam-890	117	14	...	...	PUNCT
ejpam-890	117	15	...	...	PUNCT
ejpam-890	117	16	...	...	PUNCT
ejpam-890	117	17	...	...	PUNCT
ejpam-890	117	18	...	...	PUNCT
ejpam-890	118	1	ap1	ap1	PROPN
ejpam-890	118	2	ap2	ap2	PROPN
ejpam-890	118	3	·	·	PUNCT
ejpam-890	118	4	·	·	PUNCT
ejpam-890	118	5	·	·	PUNCT
ejpam-890	119	1	apr−1	apr−1	PRON
ejpam-890	119	2	apr	apr	VERB
ejpam-890	119	3	the	the	DET
ejpam-890	119	4	restrictions	restriction	NOUN
ejpam-890	119	5	on	on	ADP
ejpam-890	119	6	the	the	DET
ejpam-890	119	7	first	first	ADJ
ejpam-890	119	8	and	and	CCONJ
ejpam-890	119	9	last	last	ADJ
ejpam-890	119	10	rows	row	NOUN
ejpam-890	119	11	together	together	ADV
ejpam-890	119	12	with	with	ADP
ejpam-890	119	13	the	the	DET
ejpam-890	119	14	first	first	ADJ
ejpam-890	119	15	and	and	CCONJ
ejpam-890	119	16	last	last	ADJ
ejpam-890	119	17	columns	column	NOUN
ejpam-890	119	18	determine	determine	VERB
ejpam-890	119	19	whether	whether	SCONJ
ejpam-890	119	20	a	a	DET
ejpam-890	119	21	matrix	matrix	NOUN
ejpam-890	119	22	is	be	AUX
ejpam-890	119	23	a	a	DET
ejpam-890	119	24	burst	burst	ADJ
ejpam-890	119	25	error	error	NOUN
ejpam-890	119	26	or	or	CCONJ
ejpam-890	119	27	not	not	PART
ejpam-890	119	28	.	.	PUNCT
ejpam-890	120	1	hence	hence	ADV
ejpam-890	120	2	,	,	PUNCT
ejpam-890	120	3	we	we	PRON
ejpam-890	120	4	focus	focus	VERB
ejpam-890	120	5	on	on	ADP
ejpam-890	120	6	the	the	DET
ejpam-890	120	7	frame	frame	NOUN
ejpam-890	120	8	of	of	ADP
ejpam-890	120	9	the	the	DET
ejpam-890	120	10	matrix	matrix	NOUN
ejpam-890	120	11	and	and	CCONJ
ejpam-890	120	12	introduce	introduce	VERB
ejpam-890	120	13	some	some	DET
ejpam-890	120	14	new	new	ADJ
ejpam-890	120	15	definitions	definition	NOUN
ejpam-890	120	16	in	in	ADP
ejpam-890	120	17	order	order	NOUN
ejpam-890	120	18	to	to	PART
ejpam-890	120	19	control	control	VERB
ejpam-890	120	20	these	these	DET
ejpam-890	120	21	entries	entry	NOUN
ejpam-890	120	22	and	and	CCONJ
ejpam-890	120	23	transform	transform	VERB
ejpam-890	120	24	the	the	DET
ejpam-890	120	25	problem	problem	NOUN
ejpam-890	120	26	of	of	ADP
ejpam-890	120	27	computing	compute	VERB
ejpam-890	120	28	the	the	DET
ejpam-890	120	29	number	number	NOUN
ejpam-890	120	30	of	of	ADP
ejpam-890	120	31	these	these	DET
ejpam-890	120	32	errors	error	NOUN
ejpam-890	120	33	into	into	ADP
ejpam-890	120	34	an	an	DET
ejpam-890	120	35	algebraic	algebraic	ADJ
ejpam-890	120	36	problem	problem	NOUN
ejpam-890	120	37	.	.	PUNCT
ejpam-890	121	1	further	far	ADV
ejpam-890	121	2	,	,	PUNCT
ejpam-890	121	3	the	the	DET
ejpam-890	121	4	four	four	NUM
ejpam-890	121	5	entries	entry	NOUN
ejpam-890	121	6	a11	a11	PROPN
ejpam-890	121	7	,	,	PUNCT
ejpam-890	121	8	a1r	a1r	PROPN
ejpam-890	121	9	,	,	PUNCT
ejpam-890	121	10	ap1	ap1	PROPN
ejpam-890	121	11	and	and	CCONJ
ejpam-890	121	12	apr	apr	NOUN
ejpam-890	121	13	of	of	ADP
ejpam-890	121	14	a	a	PRON
ejpam-890	121	15	shall	shall	AUX
ejpam-890	121	16	be	be	AUX
ejpam-890	121	17	referred	refer	VERB
ejpam-890	121	18	as	as	ADP
ejpam-890	121	19	the	the	DET
ejpam-890	121	20	corners	corner	NOUN
ejpam-890	121	21	of	of	ADP
ejpam-890	121	22	the	the	DET
ejpam-890	121	23	matrix	matrix	NOUN
ejpam-890	121	24	.	.	PUNCT
ejpam-890	122	1	definition	definition	NOUN
ejpam-890	122	2	6	6	NUM
ejpam-890	122	3	.	.	PUNCT
ejpam-890	123	1	a	a	DET
ejpam-890	123	2	generic	generic	ADJ
ejpam-890	123	3	burst	burst	NOUN
ejpam-890	123	4	error	error	NOUN
ejpam-890	123	5	a	a	DET
ejpam-890	123	6	∈	∈	PROPN
ejpam-890	123	7	mp×r	mp×r	PROPN
ejpam-890	123	8	of	of	ADP
ejpam-890	123	9	order	order	NOUN
ejpam-890	123	10	p×	p×	NOUN
ejpam-890	123	11	r	r	NOUN
ejpam-890	123	12	is	be	AUX
ejpam-890	123	13	a	a	DET
ejpam-890	123	14	burst	burst	ADJ
ejpam-890	123	15	error	error	NOUN
ejpam-890	123	16	of	of	ADP
ejpam-890	123	17	order	order	NOUN
ejpam-890	123	18	p×	p×	NOUN
ejpam-890	123	19	r	r	NOUN
ejpam-890	123	20	such	such	ADJ
ejpam-890	123	21	that	that	SCONJ
ejpam-890	123	22	the	the	DET
ejpam-890	123	23	first	first	ADJ
ejpam-890	123	24	and	and	CCONJ
ejpam-890	123	25	the	the	DET
ejpam-890	123	26	last	last	ADJ
ejpam-890	123	27	rows	row	NOUN
ejpam-890	123	28	have	have	VERB
ejpam-890	123	29	exactly	exactly	ADV
ejpam-890	123	30	two	two	NUM
ejpam-890	123	31	or	or	CCONJ
ejpam-890	123	32	one	one	NUM
ejpam-890	123	33	nonzero	nonzero	NOUN
ejpam-890	123	34	entries	entry	NOUN
ejpam-890	123	35	,	,	PUNCT
ejpam-890	123	36	and	and	CCONJ
ejpam-890	123	37	the	the	DET
ejpam-890	123	38	submatrix	submatrix	NOUN
ejpam-890	123	39	of	of	ADP
ejpam-890	123	40	size	size	NOUN
ejpam-890	123	41	p−	p−	NOUN
ejpam-890	123	42	2×	2×	NOUN
ejpam-890	123	43	r	r	NOUN
ejpam-890	123	44	−	−	PROPN
ejpam-890	123	45	2	2	NUM
ejpam-890	123	46	that	that	PRON
ejpam-890	123	47	is	be	AUX
ejpam-890	123	48	obtained	obtain	VERB
ejpam-890	123	49	by	by	ADP
ejpam-890	123	50	removing	remove	VERB
ejpam-890	123	51	first	first	ADV
ejpam-890	123	52	and	and	CCONJ
ejpam-890	123	53	last	last	ADJ
ejpam-890	123	54	rows	row	NOUN
ejpam-890	123	55	and	and	CCONJ
ejpam-890	123	56	first	first	ADJ
ejpam-890	123	57	and	and	CCONJ
ejpam-890	123	58	last	last	ADJ
ejpam-890	123	59	columns	column	NOUN
ejpam-890	123	60	(	(	PUNCT
ejpam-890	123	61	i.e.	i.e.	X
ejpam-890	123	62	the	the	DET
ejpam-890	123	63	borders	border	NOUN
ejpam-890	123	64	)	)	PUNCT
ejpam-890	123	65	has	have	VERB
ejpam-890	123	66	all	all	DET
ejpam-890	123	67	entries	entry	NOUN
ejpam-890	123	68	equal	equal	ADJ
ejpam-890	123	69	to	to	ADP
ejpam-890	123	70	zeroes	zero	NOUN
ejpam-890	123	71	,	,	PUNCT
ejpam-890	123	72	i.e	i.e	PRON
ejpam-890	123	73	,	,	PUNCT
ejpam-890	123	74	the	the	DET
ejpam-890	123	75	entries	entry	NOUN
ejpam-890	123	76	that	that	PRON
ejpam-890	123	77	fall	fall	VERB
ejpam-890	123	78	out	out	ADP
ejpam-890	123	79	off	off	ADP
ejpam-890	123	80	the	the	DET
ejpam-890	123	81	frame	frame	NOUN
ejpam-890	123	82	are	be	AUX
ejpam-890	123	83	all	all	ADV
ejpam-890	123	84	equal	equal	ADJ
ejpam-890	123	85	to	to	ADP
ejpam-890	123	86	zeroes	zero	NOUN
ejpam-890	123	87	.	.	PUNCT
ejpam-890	124	1	example	example	NOUN
ejpam-890	125	1	1	1	NUM
ejpam-890	125	2	.	.	X
ejpam-890	125	3	b1	b1	NOUN
ejpam-890	125	4	=	=	PUNCT
ejpam-890	125	5			PROPN
ejpam-890	125	6			ADJ
ejpam-890	125	7			ADJ
ejpam-890	125	8			ADJ
ejpam-890	125	9			NOUN
ejpam-890	125	10	0	0	NUM
ejpam-890	125	11	0	0	NUM
ejpam-890	125	12	1	1	NUM
ejpam-890	125	13	0	0	NUM
ejpam-890	125	14	0	0	NUM
ejpam-890	125	15	0	0	NUM
ejpam-890	125	16	0	0	NUM
ejpam-890	125	17	0	0	NUM
ejpam-890	125	18	1	1	NUM
ejpam-890	125	19	0	0	NUM
ejpam-890	125	20	0	0	NUM
ejpam-890	125	21	1	1	NUM
ejpam-890	125	22	0	0	NUM
ejpam-890	125	23	0	0	NUM
ejpam-890	125	24	1	1	NUM
ejpam-890	125	25	0	0	NUM
ejpam-890	125	26			PROPN
ejpam-890	125	27			PROPN
ejpam-890	125	28			PROPN
ejpam-890	125	29			PROPN
ejpam-890	125	30			PROPN
ejpam-890	125	31	4×4	4×4	NUM
ejpam-890	125	32	b2	b2	NOUN
ejpam-890	125	33	=	=	PUNCT
ejpam-890	125	34			NOUN
ejpam-890	125	35			ADJ
ejpam-890	125	36			ADJ
ejpam-890	125	37			ADJ
ejpam-890	125	38			NUM
ejpam-890	125	39	1	1	NUM
ejpam-890	125	40	0	0	NUM
ejpam-890	125	41	1	1	NUM
ejpam-890	125	42	0	0	NUM
ejpam-890	125	43	0	0	NUM
ejpam-890	125	44	0	0	NUM
ejpam-890	125	45	0	0	NUM
ejpam-890	125	46	0	0	NUM
ejpam-890	125	47	0	0	NUM
ejpam-890	125	48	0	0	NUM
ejpam-890	125	49	0	0	NUM
ejpam-890	125	50	1	1	NUM
ejpam-890	125	51			PROPN
ejpam-890	125	52			PROPN
ejpam-890	125	53			PROPN
ejpam-890	125	54			PROPN
ejpam-890	125	55			PROPN
ejpam-890	125	56	4×3	4×3	NOUN
ejpam-890	125	57	b3	b3	NOUN
ejpam-890	125	58	=	=	SYM
ejpam-890	125	59	�	�	PROPN
ejpam-890	125	60	1	1	NUM
ejpam-890	125	61	0	0	NUM
ejpam-890	125	62	1	1	NUM
ejpam-890	125	63	0	0	NUM
ejpam-890	125	64	1	1	NUM
ejpam-890	125	65	0	0	NUM
ejpam-890	125	66	�	�	PROPN
ejpam-890	125	67	2×3	2×3	NUM
ejpam-890	125	68	.	.	PUNCT
ejpam-890	126	1	the	the	DET
ejpam-890	126	2	matrices	matrix	NOUN
ejpam-890	126	3	b1	b1	NOUN
ejpam-890	126	4	,	,	PUNCT
ejpam-890	126	5	b2	b2	NOUN
ejpam-890	126	6	and	and	CCONJ
ejpam-890	126	7	b3	b3	PROPN
ejpam-890	126	8	are	be	AUX
ejpam-890	126	9	generic	generic	ADJ
ejpam-890	126	10	burst	burst	ADJ
ejpam-890	126	11	errors	error	NOUN
ejpam-890	126	12	.	.	PUNCT
ejpam-890	127	1	note	note	VERB
ejpam-890	127	2	that	that	SCONJ
ejpam-890	127	3	the	the	DET
ejpam-890	127	4	matrices	matrix	NOUN
ejpam-890	127	5	e	e	X
ejpam-890	127	6	=	=	PUNCT
ejpam-890	127	7	�	�	PROPN
ejpam-890	127	8	1	1	NUM
ejpam-890	127	9	0	0	NUM
ejpam-890	127	10	1	1	NUM
ejpam-890	127	11	1	1	NUM
ejpam-890	127	12	1	1	NUM
ejpam-890	127	13	1	1	NUM
ejpam-890	127	14	�	�	NOUN
ejpam-890	127	15	2×3	2×3	NUM
ejpam-890	127	16	and	and	CCONJ
ejpam-890	127	17	d	d	NOUN
ejpam-890	127	18	=	=	PUNCT
ejpam-890	127	19			PROPN
ejpam-890	127	20			NOUN
ejpam-890	127	21			NUM
ejpam-890	127	22	1	1	NUM
ejpam-890	127	23	0	0	NUM
ejpam-890	127	24	1	1	NUM
ejpam-890	127	25	0	0	NUM
ejpam-890	127	26	1	1	NUM
ejpam-890	127	27	0	0	NUM
ejpam-890	127	28	1	1	NUM
ejpam-890	127	29	0	0	NUM
ejpam-890	127	30	1	1	NUM
ejpam-890	127	31			PROPN
ejpam-890	127	32			PROPN
ejpam-890	127	33			PROPN
ejpam-890	127	34	3×3	3×3	NOUN
ejpam-890	127	35	are	be	AUX
ejpam-890	127	36	burst	burst	ADJ
ejpam-890	127	37	errors	error	NOUN
ejpam-890	127	38	but	but	CCONJ
ejpam-890	127	39	they	they	PRON
ejpam-890	127	40	are	be	AUX
ejpam-890	127	41	not	not	PART
ejpam-890	127	42	generic	generic	ADJ
ejpam-890	127	43	burst	burst	ADJ
ejpam-890	127	44	errors	error	NOUN
ejpam-890	127	45	.	.	PUNCT
ejpam-890	128	1	however	however	ADV
ejpam-890	128	2	,	,	PUNCT
ejpam-890	128	3	the	the	DET
ejpam-890	128	4	matrix	matrix	NOUN
ejpam-890	128	5			VERB
ejpam-890	128	6			NOUN
ejpam-890	128	7			NUM
ejpam-890	128	8	1	1	NUM
ejpam-890	128	9	0	0	NUM
ejpam-890	128	10	1	1	NUM
ejpam-890	128	11	0	0	NUM
ejpam-890	128	12	0	0	NUM
ejpam-890	128	13	0	0	NUM
ejpam-890	128	14	1	1	NUM
ejpam-890	128	15	0	0	NUM
ejpam-890	128	16	1	1	NUM
ejpam-890	128	17			PROPN
ejpam-890	128	18			PROPN
ejpam-890	128	19			PROPN
ejpam-890	128	20	3×3	3×3	NUM
ejpam-890	128	21	is	be	AUX
ejpam-890	128	22	a	a	DET
ejpam-890	128	23	generic	generic	ADJ
ejpam-890	128	24	burst	burst	NOUN
ejpam-890	128	25	error	error	NOUN
ejpam-890	128	26	.	.	PUNCT
ejpam-890	129	1	in	in	ADP
ejpam-890	129	2	order	order	NOUN
ejpam-890	129	3	to	to	PART
ejpam-890	129	4	determine	determine	VERB
ejpam-890	129	5	the	the	DET
ejpam-890	129	6	generic	generic	ADJ
ejpam-890	129	7	burst	burst	ADJ
ejpam-890	129	8	errors	error	NOUN
ejpam-890	129	9	,	,	PUNCT
ejpam-890	129	10	we	we	PRON
ejpam-890	129	11	need	need	VERB
ejpam-890	129	12	to	to	PART
ejpam-890	129	13	classify	classify	VERB
ejpam-890	129	14	matrices	matrix	NOUN
ejpam-890	129	15	according	accord	VERB
ejpam-890	129	16	to	to	ADP
ejpam-890	129	17	their	their	PRON
ejpam-890	129	18	corners	corner	NOUN
ejpam-890	129	19	.	.	PUNCT
ejpam-890	130	1	let	let	VERB
ejpam-890	130	2	a	a	DET
ejpam-890	130	3	=	=	PUNCT
ejpam-890	130	4	(	(	PUNCT
ejpam-890	130	5	ai	ai	PROPN
ejpam-890	130	6	j	j	PROPN
ejpam-890	130	7	)	)	PUNCT
ejpam-890	130	8	∈	∈	PROPN
ejpam-890	130	9	mp×r(r	mp×r(r	NOUN
ejpam-890	130	10	)	)	PUNCT
ejpam-890	130	11	be	be	VERB
ejpam-890	130	12	a	a	DET
ejpam-890	130	13	generic	generic	ADJ
ejpam-890	130	14	burst	burst	NOUN
ejpam-890	130	15	error	error	NOUN
ejpam-890	130	16	and	and	CCONJ
ejpam-890	130	17	the	the	DET
ejpam-890	130	18	jth	jth	PROPN
ejpam-890	130	19	row	row	NOUN
ejpam-890	130	20	a	a	DET
ejpam-890	130	21	j	j	NOUN
ejpam-890	131	1	=	=	PUNCT
ejpam-890	131	2	(	(	PUNCT
ejpam-890	131	3	a	a	DET
ejpam-890	131	4	j1	j1	PROPN
ejpam-890	131	5	,	,	PUNCT
ejpam-890	131	6	a	a	DET
ejpam-890	131	7	j2	j2	NOUN
ejpam-890	131	8	,	,	PUNCT
ejpam-890	131	9	.	.	PUNCT
ejpam-890	131	10	.	.	PUNCT
ejpam-890	131	11	.	.	PUNCT
ejpam-890	132	1	,	,	PUNCT
ejpam-890	132	2	a	a	DET
ejpam-890	132	3	jr	jr	NOUN
ejpam-890	132	4	)	)	PUNCT
ejpam-890	132	5	.	.	PUNCT
ejpam-890	133	1	by	by	ADP
ejpam-890	133	2	definition	definition	NOUN
ejpam-890	133	3	,	,	PUNCT
ejpam-890	133	4	the	the	DET
ejpam-890	133	5	jth	jth	PROPN
ejpam-890	133	6	row	row	NOUN
ejpam-890	133	7	has	have	VERB
ejpam-890	133	8	at	at	ADP
ejpam-890	133	9	most	most	ADV
ejpam-890	133	10	two	two	NUM
ejpam-890	133	11	nonzero	nonzero	ADJ
ejpam-890	133	12	entries	entry	NOUN
ejpam-890	133	13	.	.	PUNCT
ejpam-890	134	1	let	let	VERB
ejpam-890	134	2	(	(	PUNCT
ejpam-890	134	3	k	k	PROPN
ejpam-890	134	4	j	j	PROPN
ejpam-890	134	5	,	,	PUNCT
ejpam-890	134	6	l	l	PROPN
ejpam-890	134	7	j	j	PROPN
ejpam-890	134	8	)	)	PUNCT
ejpam-890	134	9	be	be	VERB
ejpam-890	134	10	the	the	DET
ejpam-890	134	11	index	index	NOUN
ejpam-890	134	12	of	of	ADP
ejpam-890	134	13	a	a	DET
ejpam-890	134	14	j.	j.	PROPN
ejpam-890	134	15	we	we	PRON
ejpam-890	134	16	i̇.	i̇.	VERB
ejpam-890	134	17	siap	siap	PROPN
ejpam-890	134	18	/	/	SYM
ejpam-890	134	19	eur	eur	PROPN
ejpam-890	134	20	.	.	PUNCT
ejpam-890	135	1	j.	j.	PROPN
ejpam-890	135	2	pure	pure	PROPN
ejpam-890	135	3	appl	appl	PROPN
ejpam-890	135	4	.	.	PROPN
ejpam-890	135	5	math	math	PROPN
ejpam-890	135	6	,	,	PUNCT
ejpam-890	135	7	3	3	NUM
ejpam-890	135	8	(	(	PUNCT
ejpam-890	135	9	2010	2010	NUM
ejpam-890	135	10	)	)	PUNCT
ejpam-890	135	11	,	,	PUNCT
ejpam-890	135	12	653	653	NUM
ejpam-890	135	13	-	-	SYM
ejpam-890	135	14	669	669	NUM
ejpam-890	135	15	658	658	NUM
ejpam-890	135	16	associate	associate	NOUN
ejpam-890	135	17	a	a	DET
ejpam-890	135	18	multi	multi	ADJ
ejpam-890	135	19	variable	variable	ADJ
ejpam-890	135	20	term	term	NOUN
ejpam-890	135	21	to	to	ADP
ejpam-890	135	22	the	the	DET
ejpam-890	135	23	jth	jth	PROPN
ejpam-890	135	24	row	row	NOUN
ejpam-890	135	25	of	of	ADP
ejpam-890	135	26	a	a	PRON
ejpam-890	135	27	in	in	ADP
ejpam-890	135	28	the	the	DET
ejpam-890	135	29	following	following	ADJ
ejpam-890	135	30	way	way	NOUN
ejpam-890	135	31	:	:	PUNCT
ejpam-890	135	32	µ(a	µ(a	PROPN
ejpam-890	135	33	j	j	PROPN
ejpam-890	135	34	)	)	PUNCT
ejpam-890	135	35	=	=	PUNCT
ejpam-890	135	36			PROPN
ejpam-890	135	37			X
ejpam-890	135	38			PROPN
ejpam-890	135	39			PROPN
ejpam-890	135	40			PROPN
ejpam-890	135	41			PROPN
ejpam-890	135	42			PROPN
ejpam-890	135	43			PROPN
ejpam-890	135	44			PROPN
ejpam-890	135	45			NOUN
ejpam-890	135	46			PROPN
ejpam-890	135	47			PROPN
ejpam-890	135	48			PROPN
ejpam-890	135	49			PROPN
ejpam-890	135	50			PROPN
ejpam-890	135	51			PROPN
ejpam-890	135	52			PROPN
ejpam-890	135	53			PROPN
ejpam-890	135	54			PROPN
ejpam-890	135	55	z	z	PROPN
ejpam-890	135	56	j	j	PROPN
ejpam-890	135	57	,	,	PUNCT
ejpam-890	135	58	1=	1=	X
ejpam-890	135	59	k	k	PROPN
ejpam-890	136	1	j	j	PROPN
ejpam-890	136	2	=	=	SYM
ejpam-890	137	1	l	l	PROPN
ejpam-890	137	2	j	j	PROPN
ejpam-890	137	3	x	x	X
ejpam-890	137	4	k	k	PROPN
ejpam-890	137	5	j	j	PROPN
ejpam-890	137	6	j	j	PROPN
ejpam-890	137	7	,	,	PUNCT
ejpam-890	137	8	1	1	NUM
ejpam-890	137	9	<	<	X
ejpam-890	137	10	k	k	PROPN
ejpam-890	137	11	j	j	PROPN
ejpam-890	137	12	=	=	SYM
ejpam-890	137	13	l	l	PROPN
ejpam-890	137	14	j	j	NOUN
ejpam-890	137	15	<	<	X
ejpam-890	137	16	r	r	X
ejpam-890	137	17	y	y	PROPN
ejpam-890	137	18	j	j	PROPN
ejpam-890	137	19	,	,	PUNCT
ejpam-890	137	20	1	1	NUM
ejpam-890	137	21	<	<	X
ejpam-890	137	22	k	k	PROPN
ejpam-890	137	23	j	j	PROPN
ejpam-890	137	24	=	=	SYM
ejpam-890	137	25	l	l	PROPN
ejpam-890	137	26	j	j	NOUN
ejpam-890	138	1	=	=	SYM
ejpam-890	138	2	r	r	NOUN
ejpam-890	138	3	x	x	PUNCT
ejpam-890	139	1	k	k	PROPN
ejpam-890	139	2	j	j	PROPN
ejpam-890	139	3	j	j	PROPN
ejpam-890	139	4	x	x	X
ejpam-890	140	1	l	l	PUNCT
ejpam-890	140	2	j	j	PROPN
ejpam-890	140	3	j	j	PROPN
ejpam-890	140	4	,	,	PUNCT
ejpam-890	140	5	k	k	PROPN
ejpam-890	140	6	j	j	PROPN
ejpam-890	140	7	<	<	X
ejpam-890	140	8	l	l	X
ejpam-890	140	9	j	j	X
ejpam-890	140	10	<	<	X
ejpam-890	140	11	r	r	X
ejpam-890	140	12	x	x	PUNCT
ejpam-890	140	13	k	k	PROPN
ejpam-890	140	14	j	j	PROPN
ejpam-890	140	15	j	j	PROPN
ejpam-890	140	16	y	y	PROPN
ejpam-890	140	17	j	j	PROPN
ejpam-890	140	18	,	,	PUNCT
ejpam-890	140	19	1	1	NUM
ejpam-890	140	20	<	<	X
ejpam-890	140	21	k	k	X
ejpam-890	140	22	j	j	PROPN
ejpam-890	140	23	<	<	X
ejpam-890	140	24	l	l	X
ejpam-890	140	25	j	j	PROPN
ejpam-890	141	1	=	=	SYM
ejpam-890	141	2	r	r	NOUN
ejpam-890	141	3	z	z	NOUN
ejpam-890	141	4	jx	jx	PROPN
ejpam-890	142	1	l	l	PROPN
ejpam-890	142	2	j	j	PROPN
ejpam-890	142	3	j	j	PROPN
ejpam-890	142	4	,	,	PUNCT
ejpam-890	142	5	1=	1=	X
ejpam-890	143	1	k	k	X
ejpam-890	143	2	j	j	PROPN
ejpam-890	143	3	<	<	X
ejpam-890	143	4	l	l	X
ejpam-890	143	5	j	j	X
ejpam-890	143	6	<	<	X
ejpam-890	143	7	r	r	X
ejpam-890	143	8	z	z	PROPN
ejpam-890	143	9	j	j	PROPN
ejpam-890	143	10	y	y	PROPN
ejpam-890	143	11	j	j	PROPN
ejpam-890	143	12	,	,	PUNCT
ejpam-890	143	13	1=	1=	X
ejpam-890	143	14	k	k	X
ejpam-890	143	15	j	j	X
ejpam-890	143	16	<	<	X
ejpam-890	143	17	l	l	X
ejpam-890	143	18	j	j	PROPN
ejpam-890	143	19	=	=	SYM
ejpam-890	143	20	r.	r.	PROPN
ejpam-890	143	21	we	we	PRON
ejpam-890	143	22	associate	associate	VERB
ejpam-890	143	23	z	z	PROPN
ejpam-890	143	24	j	j	PROPN
ejpam-890	143	25	and	and	CCONJ
ejpam-890	143	26	y	y	PROPN
ejpam-890	143	27	j	j	PROPN
ejpam-890	143	28	variables	variable	VERB
ejpam-890	143	29	for	for	ADP
ejpam-890	143	30	the	the	DET
ejpam-890	143	31	first	first	ADJ
ejpam-890	143	32	and	and	CCONJ
ejpam-890	143	33	last	last	ADJ
ejpam-890	143	34	column	column	NOUN
ejpam-890	143	35	entries	entry	NOUN
ejpam-890	143	36	respectively	respectively	ADV
ejpam-890	143	37	.	.	PUNCT
ejpam-890	144	1	if	if	SCONJ
ejpam-890	144	2	there	there	PRON
ejpam-890	144	3	exist	exist	VERB
ejpam-890	144	4	two	two	NUM
ejpam-890	144	5	nonzero	nonzero	ADJ
ejpam-890	144	6	entries	entry	NOUN
ejpam-890	144	7	in	in	ADP
ejpam-890	144	8	the	the	DET
ejpam-890	144	9	first	first	ADJ
ejpam-890	144	10	or	or	CCONJ
ejpam-890	144	11	last	last	ADJ
ejpam-890	144	12	row	row	NOUN
ejpam-890	144	13	which	which	PRON
ejpam-890	144	14	are	be	AUX
ejpam-890	144	15	different	different	ADJ
ejpam-890	144	16	from	from	ADP
ejpam-890	144	17	the	the	DET
ejpam-890	144	18	corner	corner	NOUN
ejpam-890	144	19	entries	entry	NOUN
ejpam-890	144	20	,	,	PUNCT
ejpam-890	144	21	then	then	ADV
ejpam-890	144	22	we	we	PRON
ejpam-890	144	23	associate	associate	VERB
ejpam-890	144	24	x	x	PROPN
ejpam-890	144	25	k	k	PROPN
ejpam-890	144	26	j	j	PROPN
ejpam-890	144	27	x	x	X
ejpam-890	144	28	l	l	PUNCT
ejpam-890	144	29	j	j	NOUN
ejpam-890	144	30	where	where	SCONJ
ejpam-890	144	31	the	the	DET
ejpam-890	144	32	small	small	ADJ
ejpam-890	144	33	letter	letter	NOUN
ejpam-890	144	34	indicates	indicate	VERB
ejpam-890	144	35	the	the	DET
ejpam-890	144	36	beginning	beginning	NOUN
ejpam-890	144	37	and	and	CCONJ
ejpam-890	144	38	capital	capital	NOUN
ejpam-890	144	39	x	x	PROPN
ejpam-890	144	40	j	j	PROPN
ejpam-890	144	41	indicates	indicate	VERB
ejpam-890	144	42	the	the	DET
ejpam-890	144	43	end	end	NOUN
ejpam-890	144	44	of	of	ADP
ejpam-890	144	45	the	the	DET
ejpam-890	144	46	nonzero	nonzero	ADJ
ejpam-890	144	47	entries	entry	NOUN
ejpam-890	144	48	.	.	PUNCT
ejpam-890	145	1	we	we	PRON
ejpam-890	145	2	use	use	VERB
ejpam-890	145	3	x	x	PUNCT
ejpam-890	145	4	i	i	PRON
ejpam-890	145	5	j	j	PROPN
ejpam-890	145	6	,	,	PUNCT
ejpam-890	145	7	when	when	SCONJ
ejpam-890	145	8	the	the	DET
ejpam-890	145	9	jth	jth	PROPN
ejpam-890	145	10	row	row	NOUN
ejpam-890	145	11	has	have	VERB
ejpam-890	145	12	only	only	ADV
ejpam-890	145	13	one	one	NUM
ejpam-890	145	14	nonzero	nonzero	NOUN
ejpam-890	145	15	entry	entry	NOUN
ejpam-890	145	16	on	on	ADP
ejpam-890	145	17	the	the	DET
ejpam-890	145	18	i	i	PROPN
ejpam-890	145	19	-	-	PUNCT
ejpam-890	145	20	th	th	NOUN
ejpam-890	145	21	entry	entry	NOUN
ejpam-890	145	22	,	,	PUNCT
ejpam-890	145	23	1	1	NUM
ejpam-890	145	24	<	<	X
ejpam-890	145	25	i	i	X
ejpam-890	145	26	<	<	X
ejpam-890	145	27	r.	r.	PROPN
ejpam-890	145	28	in	in	ADP
ejpam-890	145	29	a	a	DET
ejpam-890	145	30	natural	natural	ADJ
ejpam-890	145	31	way	way	NOUN
ejpam-890	145	32	,	,	PUNCT
ejpam-890	145	33	we	we	PRON
ejpam-890	145	34	extend	extend	VERB
ejpam-890	145	35	this	this	DET
ejpam-890	145	36	representation	representation	NOUN
ejpam-890	145	37	to	to	ADP
ejpam-890	145	38	the	the	DET
ejpam-890	145	39	matrix	matrix	NOUN
ejpam-890	145	40	a	a	NOUN
ejpam-890	145	41	by	by	ADP
ejpam-890	145	42	taking	take	VERB
ejpam-890	145	43	the	the	DET
ejpam-890	145	44	product	product	NOUN
ejpam-890	145	45	of	of	ADP
ejpam-890	145	46	all	all	DET
ejpam-890	145	47	terms	term	NOUN
ejpam-890	145	48	µ(a	µ(a	PROPN
ejpam-890	145	49	j	j	PROPN
ejpam-890	145	50	)	)	PUNCT
ejpam-890	145	51	corresponding	correspond	VERB
ejpam-890	145	52	to	to	ADP
ejpam-890	145	53	the	the	DET
ejpam-890	145	54	rows	row	NOUN
ejpam-890	145	55	of	of	ADP
ejpam-890	145	56	a.	a.	NOUN
ejpam-890	145	57	the	the	DET
ejpam-890	145	58	terms	term	NOUN
ejpam-890	145	59	that	that	PRON
ejpam-890	145	60	correspond	correspond	VERB
ejpam-890	145	61	to	to	ADP
ejpam-890	145	62	the	the	DET
ejpam-890	145	63	rows	row	NOUN
ejpam-890	145	64	different	different	ADJ
ejpam-890	145	65	from	from	ADP
ejpam-890	145	66	the	the	DET
ejpam-890	145	67	first	first	ADJ
ejpam-890	145	68	and	and	CCONJ
ejpam-890	145	69	last	last	ADJ
ejpam-890	145	70	contain	contain	VERB
ejpam-890	145	71	only	only	ADV
ejpam-890	145	72	the	the	DET
ejpam-890	145	73	terms	term	NOUN
ejpam-890	145	74	composed	compose	VERB
ejpam-890	145	75	by	by	ADP
ejpam-890	145	76	z	z	PROPN
ejpam-890	145	77	and	and	CCONJ
ejpam-890	145	78	y	y	PROPN
ejpam-890	145	79	variables	variable	NOUN
ejpam-890	145	80	.	.	PUNCT
ejpam-890	146	1	for	for	ADP
ejpam-890	146	2	example	example	NOUN
ejpam-890	146	3	,	,	PUNCT
ejpam-890	146	4	the	the	DET
ejpam-890	146	5	representations	representation	NOUN
ejpam-890	146	6	of	of	ADP
ejpam-890	146	7	the	the	DET
ejpam-890	146	8	following	follow	VERB
ejpam-890	146	9	matrices	matrix	NOUN
ejpam-890	146	10	are	be	AUX
ejpam-890	146	11	given	give	VERB
ejpam-890	146	12	below	below	ADP
ejpam-890	146	13	:	:	PUNCT
ejpam-890	146	14	example	example	NOUN
ejpam-890	146	15	2	2	NUM
ejpam-890	146	16	.	.	X
ejpam-890	146	17	generic	generic	ADJ
ejpam-890	146	18	errors	error	NOUN
ejpam-890	146	19	a=	a=	VERB
ejpam-890	146	20			VERB
ejpam-890	146	21			ADJ
ejpam-890	146	22			NOUN
ejpam-890	146	23	0	0	NUM
ejpam-890	147	1	1	1	NUM
ejpam-890	147	2	0	0	NUM
ejpam-890	147	3	1	1	NUM
ejpam-890	147	4	0	0	NUM
ejpam-890	147	5	0	0	NUM
ejpam-890	147	6	0	0	NUM
ejpam-890	147	7	0	0	NUM
ejpam-890	147	8	1	1	NUM
ejpam-890	147	9			PROPN
ejpam-890	147	10			PROPN
ejpam-890	147	11			PROPN
ejpam-890	147	12	b	b	NOUN
ejpam-890	147	13	=	=	NOUN
ejpam-890	147	14			X
ejpam-890	147	15			NOUN
ejpam-890	147	16			NUM
ejpam-890	147	17	1	1	NUM
ejpam-890	147	18	0	0	NUM
ejpam-890	147	19	1	1	NUM
ejpam-890	147	20	0	0	NUM
ejpam-890	147	21	0	0	NUM
ejpam-890	147	22	0	0	NUM
ejpam-890	147	23	0	0	NUM
ejpam-890	147	24	1	1	NUM
ejpam-890	147	25	0	0	NUM
ejpam-890	147	26			PROPN
ejpam-890	147	27			PROPN
ejpam-890	147	28			PROPN
ejpam-890	147	29	c	c	NOUN
ejpam-890	147	30	=	=	SYM
ejpam-890	147	31	�	�	PROPN
ejpam-890	147	32	0	0	NUM
ejpam-890	147	33	1	1	NUM
ejpam-890	147	34	0	0	NUM
ejpam-890	147	35	1	1	NUM
ejpam-890	147	36	0	0	NUM
ejpam-890	147	37	1	1	NUM
ejpam-890	147	38	0	0	NUM
ejpam-890	147	39	0	0	NUM
ejpam-890	147	40	0	0	NUM
ejpam-890	147	41	1	1	NUM
ejpam-890	147	42	�	�	PROPN
ejpam-890	147	43	.	.	PUNCT
ejpam-890	148	1	the	the	DET
ejpam-890	148	2	terms	term	NOUN
ejpam-890	148	3	x2	x2	X
ejpam-890	148	4	1z2	1z2	NUM
ejpam-890	148	5	y3	y3	NOUN
ejpam-890	148	6	z1	z1	ADJ
ejpam-890	148	7	y1	y1	NOUN
ejpam-890	148	8	x2	x2	PROPN
ejpam-890	148	9	3	3	NUM
ejpam-890	148	10	x2	x2	NOUN
ejpam-890	148	11	1x	1x	NUM
ejpam-890	148	12	4	4	NUM
ejpam-890	148	13	1z2	1z2	NUM
ejpam-890	148	14	y2	y2	NOUN
ejpam-890	148	15	given	give	VERB
ejpam-890	148	16	a	a	DET
ejpam-890	148	17	p	p	X
ejpam-890	148	18	multi	multi	ADJ
ejpam-890	148	19	variable	variable	ADJ
ejpam-890	148	20	representation	representation	NOUN
ejpam-890	148	21	of	of	ADP
ejpam-890	148	22	a	a	DET
ejpam-890	148	23	generic	generic	ADJ
ejpam-890	148	24	burst	burst	NOUN
ejpam-890	148	25	error	error	NOUN
ejpam-890	148	26	,	,	PUNCT
ejpam-890	148	27	it	it	PRON
ejpam-890	148	28	is	be	AUX
ejpam-890	148	29	possible	possible	ADJ
ejpam-890	148	30	to	to	PART
ejpam-890	148	31	list	list	VERB
ejpam-890	148	32	all	all	DET
ejpam-890	148	33	burst	burst	ADJ
ejpam-890	148	34	errors	error	NOUN
ejpam-890	148	35	by	by	ADP
ejpam-890	148	36	using	use	VERB
ejpam-890	148	37	it	it	PRON
ejpam-890	148	38	.	.	PUNCT
ejpam-890	149	1	in	in	ADP
ejpam-890	149	2	general	general	ADJ
ejpam-890	149	3	,	,	PUNCT
ejpam-890	149	4	we	we	PRON
ejpam-890	149	5	have	have	VERB
ejpam-890	149	6	g	g	PROPN
ejpam-890	149	7	=	=	SYM
ejpam-890	149	8	a11	a11	PROPN
ejpam-890	149	9	·	·	PUNCT
ejpam-890	149	10	·	·	PUNCT
ejpam-890	149	11	·	·	PUNCT
ejpam-890	149	12	a1r	a1r	NOUN
ejpam-890	149	13	...	...	PUNCT
ejpam-890	149	14	...	...	PUNCT
ejpam-890	149	15	...	...	PUNCT
ejpam-890	150	1	ap1	ap1	PROPN
ejpam-890	150	2	·	·	PUNCT
ejpam-890	150	3	·	·	PUNCT
ejpam-890	150	4	·	·	PUNCT
ejpam-890	151	1	apr	apr	VERB
ejpam-890	151	2	↔	↔	PROPN
ejpam-890	151	3	z1	z1	PROPN
ejpam-890	151	4	·	·	PUNCT
ejpam-890	151	5	·	·	PUNCT
ejpam-890	151	6	·	·	PUNCT
ejpam-890	152	1	x	x	SYM
ejpam-890	152	2	j	j	PROPN
ejpam-890	152	3	1	1	NUM
ejpam-890	152	4	,	,	PUNCT
ejpam-890	152	5	xk1	xk1	PROPN
ejpam-890	152	6	x	x	X
ejpam-890	152	7	l1	l1	PROPN
ejpam-890	152	8	,	,	PUNCT
ejpam-890	152	9	x	x	PROPN
ejpam-890	152	10	l1	l1	PROPN
ejpam-890	152	11	·	·	PUNCT
ejpam-890	152	12	·	·	PUNCT
ejpam-890	152	13	·	·	PUNCT
ejpam-890	153	1	y1	y1	INTJ
ejpam-890	153	2	...	...	PUNCT
ejpam-890	153	3	zi	zi	NOUN
ejpam-890	153	4	...	...	PUNCT
ejpam-890	153	5	...	...	PUNCT
ejpam-890	153	6	...	...	PUNCT
ejpam-890	154	1	yi	yi	INTJ
ejpam-890	154	2	...	...	PUNCT
ejpam-890	155	1	zp	zp	X
ejpam-890	155	2	·	·	PUNCT
ejpam-890	155	3	·	·	PUNCT
ejpam-890	155	4	·	·	PUNCT
ejpam-890	156	1	x	x	PUNCT
ejpam-890	156	2	j	j	PROPN
ejpam-890	156	3	p	p	X
ejpam-890	156	4	,	,	PUNCT
ejpam-890	156	5	xkp	xkp	PROPN
ejpam-890	156	6	x	x	SYM
ejpam-890	156	7	lp	lp	INTJ
ejpam-890	156	8	,	,	PUNCT
ejpam-890	156	9	x	x	VERB
ejpam-890	156	10	lp	lp	X
ejpam-890	156	11	·	·	PUNCT
ejpam-890	156	12	·	·	PUNCT
ejpam-890	156	13	·	·	PUNCT
ejpam-890	156	14	yp	yp	PROPN
ejpam-890	156	15	and	and	CCONJ
ejpam-890	156	16	the	the	DET
ejpam-890	156	17	term	term	NOUN
ejpam-890	157	1	∏p	∏p	PART
ejpam-890	157	2	j=1	j=1	NOUN
ejpam-890	157	3	µ(a	µ(a	PROPN
ejpam-890	157	4	j	j	PROPN
ejpam-890	157	5	)	)	PUNCT
ejpam-890	157	6	corresponds	correspond	VERB
ejpam-890	157	7	to	to	ADP
ejpam-890	157	8	the	the	DET
ejpam-890	157	9	term	term	NOUN
ejpam-890	157	10	of	of	ADP
ejpam-890	157	11	the	the	DET
ejpam-890	157	12	matrix	matrix	NOUN
ejpam-890	157	13	a.	a.	NOUN
ejpam-890	157	14	we	we	PRON
ejpam-890	157	15	classify	classify	VERB
ejpam-890	157	16	generic	generic	ADJ
ejpam-890	157	17	burst	burst	ADJ
ejpam-890	157	18	errors	error	NOUN
ejpam-890	157	19	by	by	ADP
ejpam-890	157	20	considering	consider	VERB
ejpam-890	157	21	their	their	PRON
ejpam-890	157	22	corners	corner	NOUN
ejpam-890	157	23	.	.	PUNCT
ejpam-890	158	1	there	there	PRON
ejpam-890	158	2	are	be	VERB
ejpam-890	158	3	24	24	NUM
ejpam-890	158	4	=	=	SYM
ejpam-890	158	5	16	16	NUM
ejpam-890	158	6	possible	possible	ADJ
ejpam-890	158	7	cases	case	NOUN
ejpam-890	158	8	for	for	ADP
ejpam-890	158	9	these	these	DET
ejpam-890	158	10	corners	corner	NOUN
ejpam-890	158	11	and	and	CCONJ
ejpam-890	158	12	corresponding	correspond	VERB
ejpam-890	158	13	multi	multi	ADJ
ejpam-890	158	14	variable	variable	ADJ
ejpam-890	158	15	terms	term	NOUN
ejpam-890	158	16	.	.	PUNCT
ejpam-890	159	1	we	we	PRON
ejpam-890	159	2	list	list	VERB
ejpam-890	159	3	them	they	PRON
ejpam-890	159	4	in	in	ADP
ejpam-890	159	5	table	table	NOUN
ejpam-890	159	6	1	1	NUM
ejpam-890	159	7	.	.	PUNCT
ejpam-890	160	1	in	in	ADP
ejpam-890	160	2	order	order	NOUN
ejpam-890	160	3	to	to	PART
ejpam-890	160	4	solve	solve	VERB
ejpam-890	160	5	the	the	DET
ejpam-890	160	6	problem	problem	NOUN
ejpam-890	160	7	of	of	ADP
ejpam-890	160	8	representing	represent	VERB
ejpam-890	160	9	burst	burst	ADJ
ejpam-890	160	10	array	array	NOUN
ejpam-890	160	11	errors	error	NOUN
ejpam-890	160	12	in	in	ADP
ejpam-890	160	13	terms	term	NOUN
ejpam-890	160	14	,	,	PUNCT
ejpam-890	160	15	we	we	PRON
ejpam-890	160	16	need	need	VERB
ejpam-890	160	17	to	to	PART
ejpam-890	160	18	split	split	VERB
ejpam-890	160	19	it	it	PRON
ejpam-890	160	20	into	into	ADP
ejpam-890	160	21	cases	case	NOUN
ejpam-890	160	22	.	.	PUNCT
ejpam-890	161	1	first	first	ADV
ejpam-890	161	2	,	,	PUNCT
ejpam-890	161	3	we	we	PRON
ejpam-890	161	4	need	need	VERB
ejpam-890	161	5	to	to	PART
ejpam-890	161	6	split	split	VERB
ejpam-890	161	7	it	it	PRON
ejpam-890	161	8	to	to	ADP
ejpam-890	161	9	two	two	NUM
ejpam-890	161	10	main	main	ADJ
ejpam-890	161	11	cases	case	NOUN
ejpam-890	161	12	as	as	ADP
ejpam-890	161	13	p	p	X
ejpam-890	161	14	≥	≥	NOUN
ejpam-890	161	15	3	3	NUM
ejpam-890	161	16	and	and	CCONJ
ejpam-890	161	17	r	r	NOUN
ejpam-890	161	18	≥	≥	NOUN
ejpam-890	161	19	3	3	NUM
ejpam-890	161	20	and	and	CCONJ
ejpam-890	161	21	otherwise	otherwise	ADV
ejpam-890	161	22	.	.	PUNCT
ejpam-890	162	1	we	we	PRON
ejpam-890	162	2	work	work	VERB
ejpam-890	162	3	out	out	ADP
ejpam-890	162	4	these	these	DET
ejpam-890	162	5	cases	case	NOUN
ejpam-890	162	6	by	by	ADP
ejpam-890	162	7	the	the	DET
ejpam-890	162	8	following	follow	VERB
ejpam-890	162	9	theorems	theorem	NOUN
ejpam-890	162	10	.	.	PUNCT
ejpam-890	163	1	let	let	VERB
ejpam-890	163	2	z̃	z̃	PROPN
ejpam-890	163	3	=	=	SYM
ejpam-890	163	4	(	(	PUNCT
ejpam-890	163	5	z1	z1	PROPN
ejpam-890	163	6	,	,	PUNCT
ejpam-890	163	7	.	.	PUNCT
ejpam-890	163	8	.	.	PUNCT
ejpam-890	164	1	.	.	PUNCT
ejpam-890	165	1	,	,	PUNCT
ejpam-890	165	2	zp	zp	PROPN
ejpam-890	165	3	)	)	PUNCT
ejpam-890	165	4	,	,	PUNCT
ejpam-890	165	5	x̃	x̃	PROPN
ejpam-890	165	6	=	=	PUNCT
ejpam-890	165	7	(	(	PUNCT
ejpam-890	165	8	x1	x1	PROPN
ejpam-890	165	9	,	,	PUNCT
ejpam-890	165	10	.	.	PUNCT
ejpam-890	165	11	.	.	PUNCT
ejpam-890	166	1	.	.	PUNCT
ejpam-890	167	1	,	,	PUNCT
ejpam-890	167	2	xp	xp	ADJ
ejpam-890	167	3	)	)	PUNCT
ejpam-890	167	4	,	,	PUNCT
ejpam-890	167	5	ỹ	ỹ	PROPN
ejpam-890	167	6	=	=	SYM
ejpam-890	167	7	(	(	PUNCT
ejpam-890	167	8	y1	y1	PROPN
ejpam-890	167	9	,	,	PUNCT
ejpam-890	167	10	.	.	PUNCT
ejpam-890	167	11	.	.	PUNCT
ejpam-890	168	1	.	.	PUNCT
ejpam-890	169	1	,	,	PUNCT
ejpam-890	169	2	yp	yp	X
ejpam-890	169	3	)	)	PUNCT
ejpam-890	169	4	and	and	CCONJ
ejpam-890	169	5	x̃	x̃	PROPN
ejpam-890	169	6	=	=	PUNCT
ejpam-890	169	7	(	(	PUNCT
ejpam-890	169	8	x1	x1	PROPN
ejpam-890	169	9	,	,	PUNCT
ejpam-890	169	10	.	.	PUNCT
ejpam-890	169	11	.	.	PUNCT
ejpam-890	169	12	.	.	PUNCT
ejpam-890	170	1	,	,	PUNCT
ejpam-890	170	2	x	x	X
ejpam-890	170	3	p	p	X
ejpam-890	170	4	)	)	PUNCT
ejpam-890	170	5	.	.	PUNCT
ejpam-890	171	1	definition	definition	NOUN
ejpam-890	171	2	7	7	NUM
ejpam-890	171	3	.	.	PUNCT
ejpam-890	172	1	let	let	VERB
ejpam-890	172	2	kp×r	kp×r	PROPN
ejpam-890	172	3	be	be	AUX
ejpam-890	172	4	the	the	DET
ejpam-890	172	5	set	set	NOUN
ejpam-890	172	6	of	of	ADP
ejpam-890	172	7	all	all	DET
ejpam-890	172	8	generic	generic	ADJ
ejpam-890	172	9	burst	burst	ADJ
ejpam-890	172	10	errors	error	NOUN
ejpam-890	172	11	of	of	ADP
ejpam-890	172	12	size	size	NOUN
ejpam-890	172	13	p	p	PROPN
ejpam-890	172	14	×	×	PROPN
ejpam-890	172	15	r.	r.	NOUN
ejpam-890	172	16	let	let	VERB
ejpam-890	172	17	g(z̃	g(z̃	PROPN
ejpam-890	172	18	,	,	PUNCT
ejpam-890	172	19	x̃	x̃	PROPN
ejpam-890	172	20	,	,	PUNCT
ejpam-890	172	21	x̃	x̃	PROPN
ejpam-890	172	22	,	,	PUNCT
ejpam-890	172	23	ỹ	ỹ	PROPN
ejpam-890	172	24	)	)	PUNCT
ejpam-890	173	1	=	=	SYM
ejpam-890	173	2	∑	∑	PUNCT
ejpam-890	173	3	a∈k	a∈k	PROPN
ejpam-890	173	4	∏p	∏p	NOUN
ejpam-890	173	5	j=1µ(a	j=1µ(a	PROPN
ejpam-890	173	6	j	j	PROPN
ejpam-890	173	7	)	)	PUNCT
ejpam-890	173	8	be	be	VERB
ejpam-890	173	9	the	the	DET
ejpam-890	173	10	multivariable	multivariable	ADJ
ejpam-890	173	11	polynomial	polynomial	NOUN
ejpam-890	173	12	whose	whose	DET
ejpam-890	173	13	terms	term	NOUN
ejpam-890	173	14	represent	represent	VERB
ejpam-890	173	15	generic	generic	ADJ
ejpam-890	173	16	burst	burst	ADJ
ejpam-890	173	17	errors	error	NOUN
ejpam-890	173	18	.	.	PUNCT
ejpam-890	174	1	i̇.	i̇.	PROPN
ejpam-890	174	2	siap	siap	PROPN
ejpam-890	174	3	/	/	SYM
ejpam-890	174	4	eur	eur	PROPN
ejpam-890	174	5	.	.	PUNCT
ejpam-890	175	1	j.	j.	PROPN
ejpam-890	175	2	pure	pure	PROPN
ejpam-890	175	3	appl	appl	PROPN
ejpam-890	175	4	.	.	PROPN
ejpam-890	175	5	math	math	PROPN
ejpam-890	175	6	,	,	PUNCT
ejpam-890	175	7	3	3	NUM
ejpam-890	175	8	(	(	PUNCT
ejpam-890	175	9	2010	2010	NUM
ejpam-890	175	10	)	)	PUNCT
ejpam-890	175	11	,	,	PUNCT
ejpam-890	175	12	653	653	NUM
ejpam-890	175	13	-	-	SYM
ejpam-890	175	14	669	669	NUM
ejpam-890	175	15	659	659	NUM
ejpam-890	175	16	(	(	PUNCT
ejpam-890	175	17	a11	a11	PROPN
ejpam-890	175	18	,	,	PUNCT
ejpam-890	175	19	a1r	a1r	PROPN
ejpam-890	175	20	,	,	PUNCT
ejpam-890	175	21	ap1	ap1	PROPN
ejpam-890	175	22	,	,	PUNCT
ejpam-890	175	23	apl	apl	PROPN
ejpam-890	175	24	)	)	PUNCT
ejpam-890	175	25	term	term	NOUN
ejpam-890	175	26	(	(	PUNCT
ejpam-890	175	27	a11	a11	PROPN
ejpam-890	175	28	,	,	PUNCT
ejpam-890	175	29	a1r	a1r	PROPN
ejpam-890	175	30	,	,	PUNCT
ejpam-890	175	31	ap1	ap1	PROPN
ejpam-890	175	32	,	,	PUNCT
ejpam-890	175	33	apl	apl	PROPN
ejpam-890	175	34	)	)	PUNCT
ejpam-890	175	35	term	term	NOUN
ejpam-890	175	36	(	(	PUNCT
ejpam-890	175	37	0,0,0,0	0,0,0,0	NOUN
ejpam-890	175	38	)	)	SYM
ejpam-890	175	39	1	1	NUM
ejpam-890	175	40	(	(	PUNCT
ejpam-890	175	41	0,1,1,0	0,1,1,0	NUM
ejpam-890	175	42	)	)	PUNCT
ejpam-890	175	43	y1zp	y1zp	X
ejpam-890	175	44	(	(	PUNCT
ejpam-890	175	45	1,0,0,0	1,0,0,0	NUM
ejpam-890	175	46	)	)	PUNCT
ejpam-890	175	47	z1	z1	NOUN
ejpam-890	175	48	(	(	PUNCT
ejpam-890	175	49	0,1,0,1	0,1,0,1	NOUN
ejpam-890	175	50	)	)	PUNCT
ejpam-890	176	1	y1	y1	NOUN
ejpam-890	176	2	yp	yp	PROPN
ejpam-890	176	3	(	(	PUNCT
ejpam-890	176	4	0,1,0,0	0,1,0,0	NOUN
ejpam-890	176	5	)	)	PUNCT
ejpam-890	176	6	y1	y1	NOUN
ejpam-890	176	7	(	(	PUNCT
ejpam-890	176	8	0,0,1,1	0,0,1,1	NUM
ejpam-890	176	9	)	)	PUNCT
ejpam-890	176	10	zp	zp	NOUN
ejpam-890	176	11	yp	yp	PROPN
ejpam-890	176	12	(	(	PUNCT
ejpam-890	176	13	0,0,1,0	0,0,1,0	NUM
ejpam-890	176	14	)	)	PUNCT
ejpam-890	176	15	zp	zp	NOUN
ejpam-890	176	16	(	(	PUNCT
ejpam-890	176	17	1,1,1,0	1,1,1,0	NUM
ejpam-890	176	18	)	)	PUNCT
ejpam-890	176	19	z1	z1	NOUN
ejpam-890	176	20	y1zp	y1zp	X
ejpam-890	176	21	(	(	PUNCT
ejpam-890	176	22	0,0,0,1	0,0,0,1	NOUN
ejpam-890	176	23	)	)	PUNCT
ejpam-890	176	24	yp	yp	PROPN
ejpam-890	176	25	(	(	PUNCT
ejpam-890	176	26	1,1,0,1	1,1,0,1	NUM
ejpam-890	176	27	)	)	PUNCT
ejpam-890	176	28	z1	z1	PROPN
ejpam-890	176	29	y1	y1	NOUN
ejpam-890	176	30	yp	yp	PROPN
ejpam-890	176	31	(	(	PUNCT
ejpam-890	176	32	1,1,0,0	1,1,0,0	NUM
ejpam-890	176	33	)	)	PUNCT
ejpam-890	176	34	z1	z1	ADJ
ejpam-890	176	35	y1	y1	NOUN
ejpam-890	176	36	(	(	PUNCT
ejpam-890	176	37	1,0,1,1	1,0,1,1	NUM
ejpam-890	176	38	)	)	PUNCT
ejpam-890	176	39	z1zp	z1zp	NUM
ejpam-890	176	40	yp	yp	PROPN
ejpam-890	176	41	(	(	PUNCT
ejpam-890	176	42	1,0,1,0	1,0,1,0	NUM
ejpam-890	176	43	)	)	PUNCT
ejpam-890	176	44	z1zp	z1zp	NOUN
ejpam-890	176	45	(	(	PUNCT
ejpam-890	176	46	0,1,1,1	0,1,1,1	NUM
ejpam-890	176	47	)	)	PUNCT
ejpam-890	176	48	y1zp	y1zp	PUNCT
ejpam-890	177	1	yp	yp	PROPN
ejpam-890	177	2	(	(	PUNCT
ejpam-890	177	3	1,0,0,1	1,0,0,1	NUM
ejpam-890	177	4	)	)	PUNCT
ejpam-890	177	5	z1	z1	NOUN
ejpam-890	177	6	yp	yp	X
ejpam-890	177	7	(	(	PUNCT
ejpam-890	177	8	1,1,1,1	1,1,1,1	NUM
ejpam-890	177	9	)	)	PUNCT
ejpam-890	177	10	z1	z1	NOUN
ejpam-890	177	11	y1zp	y1zp	X
ejpam-890	177	12	yptable	yptable	ADJ
ejpam-890	177	13	1	1	NUM
ejpam-890	177	14	:	:	PUNCT
ejpam-890	177	15	terms	term	NOUN
ejpam-890	177	16	with	with	ADP
ejpam-890	177	17	respe	respe	NOUN
ejpam-890	177	18	t	t	PROPN
ejpam-890	177	19	to	to	ADP
ejpam-890	177	20	the	the	DET
ejpam-890	177	21	orners	orner	NOUN
ejpam-890	177	22	in	in	ADP
ejpam-890	177	23	the	the	DET
ejpam-890	177	24	following	follow	VERB
ejpam-890	177	25	theorem	theorem	NOUN
ejpam-890	177	26	we	we	PRON
ejpam-890	177	27	first	first	ADV
ejpam-890	177	28	determine	determine	VERB
ejpam-890	177	29	multivariable	multivariable	ADJ
ejpam-890	177	30	polynomial	polynomial	PROPN
ejpam-890	177	31	g	g	PROPN
ejpam-890	177	32	that	that	PRON
ejpam-890	177	33	gives	give	VERB
ejpam-890	177	34	the	the	DET
ejpam-890	177	35	terms	term	NOUN
ejpam-890	177	36	of	of	ADP
ejpam-890	177	37	generic	generic	ADJ
ejpam-890	177	38	burst	burst	ADJ
ejpam-890	177	39	errors	error	NOUN
ejpam-890	177	40	of	of	ADP
ejpam-890	177	41	size	size	NOUN
ejpam-890	177	42	p	p	NOUN
ejpam-890	177	43	≤	≤	NOUN
ejpam-890	177	44	2	2	NUM
ejpam-890	177	45	and	and	CCONJ
ejpam-890	177	46	r	r	NOUN
ejpam-890	177	47	≤	≤	NUM
ejpam-890	177	48	2	2	NUM
ejpam-890	177	49	.	.	PUNCT
ejpam-890	178	1	the	the	DET
ejpam-890	178	2	remaining	remain	VERB
ejpam-890	178	3	case	case	NOUN
ejpam-890	178	4	is	be	AUX
ejpam-890	178	5	treated	treat	VERB
ejpam-890	178	6	separately	separately	ADV
ejpam-890	178	7	in	in	ADP
ejpam-890	178	8	the	the	DET
ejpam-890	178	9	next	next	ADJ
ejpam-890	178	10	theorem	theorem	PROPN
ejpam-890	178	11	.	.	PUNCT
ejpam-890	178	12	theorem	theorem	VERB
ejpam-890	178	13	3	3	NUM
ejpam-890	178	14	.	.	NOUN
ejpam-890	178	15	1	1	NUM
ejpam-890	178	16	.	.	X
ejpam-890	179	1	let	let	VERB
ejpam-890	179	2	p	p	NOUN
ejpam-890	179	3	=	=	NOUN
ejpam-890	179	4	1	1	NUM
ejpam-890	179	5	and	and	CCONJ
ejpam-890	179	6	r	r	NOUN
ejpam-890	179	7	≥	≥	NUM
ejpam-890	179	8	2	2	NUM
ejpam-890	179	9	.	.	PUNCT
ejpam-890	180	1	then	then	ADV
ejpam-890	180	2	,	,	PUNCT
ejpam-890	180	3	g(z̃	g(z̃	PROPN
ejpam-890	180	4	,	,	PUNCT
ejpam-890	180	5	x̃	x̃	PROPN
ejpam-890	180	6	,	,	PUNCT
ejpam-890	180	7	x̃	x̃	PROPN
ejpam-890	180	8	,	,	PUNCT
ejpam-890	180	9	ỹ	ỹ	PROPN
ejpam-890	180	10	)	)	PUNCT
ejpam-890	180	11	=	=	SYM
ejpam-890	180	12	z1	z1	NUM
ejpam-890	180	13	y1	y1	NOUN
ejpam-890	180	14	.	.	PUNCT
ejpam-890	181	1	2	2	X
ejpam-890	181	2	.	.	X
ejpam-890	181	3	let	let	VERB
ejpam-890	181	4	p	p	PRON
ejpam-890	181	5	≥	≥	NUM
ejpam-890	181	6	2	2	NUM
ejpam-890	181	7	and	and	CCONJ
ejpam-890	181	8	r	r	NOUN
ejpam-890	181	9	=	=	SYM
ejpam-890	181	10	1	1	NUM
ejpam-890	181	11	.	.	PUNCT
ejpam-890	182	1	then	then	ADV
ejpam-890	182	2	,	,	PUNCT
ejpam-890	182	3	g(z̃	g(z̃	PROPN
ejpam-890	182	4	)	)	PUNCT
ejpam-890	182	5	=	=	PUNCT
ejpam-890	182	6	z1zp	z1zp	X
ejpam-890	182	7	.	.	X
ejpam-890	183	1	3	3	X
ejpam-890	183	2	.	.	X
ejpam-890	183	3	let	let	VERB
ejpam-890	183	4	p	p	NOUN
ejpam-890	183	5	=	=	NOUN
ejpam-890	183	6	2	2	NUM
ejpam-890	183	7	and	and	CCONJ
ejpam-890	183	8	r	r	NOUN
ejpam-890	183	9	≥	≥	NOUN
ejpam-890	183	10	2	2	NUM
ejpam-890	183	11	.	.	PUNCT
ejpam-890	184	1	let	let	VERB
ejpam-890	184	2	s	s	PRON
ejpam-890	184	3	=	=	VERB
ejpam-890	184	4	{	{	PUNCT
ejpam-890	184	5	(	(	PUNCT
ejpam-890	184	6	i	i	PROPN
ejpam-890	184	7	,	,	PUNCT
ejpam-890	184	8	j	j	PROPN
ejpam-890	184	9	,	,	PUNCT
ejpam-890	184	10	k	k	PROPN
ejpam-890	184	11	,	,	PUNCT
ejpam-890	184	12	l	l	NOUN
ejpam-890	184	13	)	)	PUNCT
ejpam-890	184	14	∈	∈	PROPN
ejpam-890	184	15	z4	z4	PROPN
ejpam-890	184	16	2	2	NUM
ejpam-890	184	17	|(i	|(i	PROPN
ejpam-890	184	18	,	,	PUNCT
ejpam-890	184	19	k	k	NOUN
ejpam-890	184	20	)	)	PUNCT
ejpam-890	184	21	6=	6=	ADP
ejpam-890	184	22	(	(	PUNCT
ejpam-890	184	23	0,0	0,0	NOUN
ejpam-890	184	24	)	)	PUNCT
ejpam-890	184	25	,	,	PUNCT
ejpam-890	184	26	(	(	PUNCT
ejpam-890	184	27	j	j	PROPN
ejpam-890	184	28	,	,	PUNCT
ejpam-890	184	29	l	l	NOUN
ejpam-890	184	30	)	)	PUNCT
ejpam-890	184	31	6=	6=	ADP
ejpam-890	184	32	(	(	PUNCT
ejpam-890	184	33	0,0	0,0	NOUN
ejpam-890	184	34	)	)	PUNCT
ejpam-890	184	35	}	}	PUNCT
ejpam-890	184	36	.	.	PUNCT
ejpam-890	185	1	then	then	ADV
ejpam-890	185	2	,	,	PUNCT
ejpam-890	185	3	g(z̃	g(z̃	PROPN
ejpam-890	185	4	,	,	PUNCT
ejpam-890	185	5	x̃	x̃	PROPN
ejpam-890	185	6	,	,	PUNCT
ejpam-890	185	7	x̃	x̃	PROPN
ejpam-890	185	8	,	,	PUNCT
ejpam-890	185	9	ỹ	ỹ	PROPN
ejpam-890	185	10	)	)	PUNCT
ejpam-890	185	11	=	=	PUNCT
ejpam-890	185	12	∑	∑	PUNCT
ejpam-890	185	13	(	(	PUNCT
ejpam-890	185	14	i	i	PROPN
ejpam-890	185	15	,	,	PUNCT
ejpam-890	185	16	j	j	PROPN
ejpam-890	185	17	,	,	PUNCT
ejpam-890	185	18	k	k	PROPN
ejpam-890	185	19	,	,	PUNCT
ejpam-890	185	20	l)∈s	l)∈s	X
ejpam-890	186	1	z	z	PROPN
ejpam-890	186	2	i	i	PRON
ejpam-890	186	3	1	1	NUM
ejpam-890	186	4	y	y	PROPN
ejpam-890	186	5	j	j	PROPN
ejpam-890	186	6	1zk	1zk	ADJ
ejpam-890	186	7	2	2	NUM
ejpam-890	186	8	y	y	NOUN
ejpam-890	186	9	l	l	NOUN
ejpam-890	186	10	2γi	2γi	NOUN
ejpam-890	186	11	j(x1)γkl(x	j(x1)γkl(x	PROPN
ejpam-890	186	12	p	p	PROPN
ejpam-890	186	13	)	)	PUNCT
ejpam-890	186	14	.	.	PUNCT
ejpam-890	187	1	4	4	X
ejpam-890	187	2	.	.	X
ejpam-890	187	3	let	let	VERB
ejpam-890	187	4	p	p	PRON
ejpam-890	187	5	≥	≥	NUM
ejpam-890	187	6	2	2	NUM
ejpam-890	187	7	and	and	CCONJ
ejpam-890	187	8	r	r	NOUN
ejpam-890	187	9	=	=	SYM
ejpam-890	187	10	2	2	X
ejpam-890	187	11	.	.	PUNCT
ejpam-890	188	1	let	let	VERB
ejpam-890	188	2	t	t	NOUN
ejpam-890	188	3	=	=	PRON
ejpam-890	188	4	{	{	PUNCT
ejpam-890	188	5	(	(	PUNCT
ejpam-890	188	6	i	i	PROPN
ejpam-890	188	7	,	,	PUNCT
ejpam-890	188	8	j	j	PROPN
ejpam-890	188	9	,	,	PUNCT
ejpam-890	188	10	k	k	PROPN
ejpam-890	188	11	,	,	PUNCT
ejpam-890	188	12	l	l	NOUN
ejpam-890	188	13	)	)	PUNCT
ejpam-890	188	14	∈	∈	PROPN
ejpam-890	188	15	{	{	PUNCT
ejpam-890	188	16	0,1}4|(i	0,1}4|(i	NOUN
ejpam-890	188	17	,	,	PUNCT
ejpam-890	188	18	j	j	PROPN
ejpam-890	188	19	)	)	PUNCT
ejpam-890	188	20	6=	6=	ADP
ejpam-890	188	21	(	(	PUNCT
ejpam-890	188	22	0,0	0,0	NOUN
ejpam-890	188	23	)	)	PUNCT
ejpam-890	188	24	,	,	PUNCT
ejpam-890	188	25	(	(	PUNCT
ejpam-890	188	26	k	k	X
ejpam-890	188	27	,	,	PUNCT
ejpam-890	188	28	l	l	NOUN
ejpam-890	188	29	)	)	PUNCT
ejpam-890	188	30	6=	6=	ADP
ejpam-890	188	31	(	(	PUNCT
ejpam-890	188	32	0,0	0,0	NOUN
ejpam-890	188	33	)	)	PUNCT
ejpam-890	188	34	}	}	PUNCT
ejpam-890	188	35	.	.	PUNCT
ejpam-890	189	1	then	then	ADV
ejpam-890	189	2	,	,	PUNCT
ejpam-890	189	3	g(z̃	g(z̃	PROPN
ejpam-890	189	4	,	,	PUNCT
ejpam-890	189	5	x̃	x̃	PROPN
ejpam-890	189	6	,	,	PUNCT
ejpam-890	189	7	x̃	x̃	PROPN
ejpam-890	189	8	,	,	PUNCT
ejpam-890	189	9	ỹ	ỹ	PROPN
ejpam-890	189	10	)	)	PUNCT
ejpam-890	189	11	=	=	PUNCT
ejpam-890	189	12	∑	∑	PUNCT
ejpam-890	189	13	(	(	PUNCT
ejpam-890	189	14	i	i	PROPN
ejpam-890	189	15	,	,	PUNCT
ejpam-890	189	16	j	j	PROPN
ejpam-890	189	17	,	,	PUNCT
ejpam-890	189	18	k	k	PROPN
ejpam-890	189	19	,	,	PUNCT
ejpam-890	189	20	l)∈t	l)∈t	PROPN
ejpam-890	189	21	z	z	NOUN
ejpam-890	189	22	i	i	NOUN
ejpam-890	189	23	1	1	NUM
ejpam-890	189	24	y	y	PROPN
ejpam-890	189	25	j	j	PROPN
ejpam-890	189	26	1zk	1zk	PROPN
ejpam-890	189	27	p	p	PROPN
ejpam-890	189	28	y	y	PROPN
ejpam-890	189	29	l	l	NOUN
ejpam-890	189	30	pz	pz	NOUN
ejpam-890	190	1	iky	iky	PROPN
ejpam-890	190	2	jl	jl	PROPN
ejpam-890	190	3	.	.	PUNCT
ejpam-890	191	1	where	where	SCONJ
ejpam-890	191	2	z	z	NOUN
ejpam-890	191	3	st	st	PROPN
ejpam-890	191	4	=	=	PUNCT
ejpam-890	191	5	¨	¨	NOUN
ejpam-890	191	6	−1	−1	NOUN
ejpam-890	191	7	+	+	CCONJ
ejpam-890	191	8	∏p−1	∏p−1	PROPN
ejpam-890	191	9	i=2	i=2	PROPN
ejpam-890	191	10	(	(	PUNCT
ejpam-890	191	11	1	1	NUM
ejpam-890	191	12	+	+	NUM
ejpam-890	191	13	zi	zi	NOUN
ejpam-890	191	14	)	)	PUNCT
ejpam-890	191	15	,	,	PUNCT
ejpam-890	191	16	(	(	PUNCT
ejpam-890	191	17	s	s	X
ejpam-890	191	18	,	,	PUNCT
ejpam-890	191	19	t	t	PROPN
ejpam-890	191	20	)	)	PUNCT
ejpam-890	191	21	=	=	SYM
ejpam-890	191	22	(	(	PUNCT
ejpam-890	191	23	0,0	0,0	NOUN
ejpam-890	191	24	)	)	PUNCT
ejpam-890	191	25	∏p−1	∏p−1	PROPN
ejpam-890	191	26	i=2	i=2	PROPN
ejpam-890	191	27	(	(	PUNCT
ejpam-890	191	28	1	1	NUM
ejpam-890	191	29	+	+	NUM
ejpam-890	191	30	zi	zi	NOUN
ejpam-890	191	31	)	)	PUNCT
ejpam-890	191	32	,	,	PUNCT
ejpam-890	191	33	otherwise	otherwise	ADV
ejpam-890	191	34	y	y	PROPN
ejpam-890	191	35	st	st	PROPN
ejpam-890	191	36	=	=	NOUN
ejpam-890	191	37	¨	¨	NOUN
ejpam-890	191	38	−1	−1	NOUN
ejpam-890	191	39	+	+	CCONJ
ejpam-890	191	40	∏p−1	∏p−1	PROPN
ejpam-890	191	41	i=2	i=2	PROPN
ejpam-890	191	42	(	(	PUNCT
ejpam-890	191	43	1	1	NUM
ejpam-890	191	44	+	+	NUM
ejpam-890	191	45	yi	yi	NOUN
ejpam-890	191	46	)	)	PUNCT
ejpam-890	191	47	,	,	PUNCT
ejpam-890	191	48	(	(	PUNCT
ejpam-890	191	49	s	s	X
ejpam-890	191	50	,	,	PUNCT
ejpam-890	191	51	t	t	PROPN
ejpam-890	191	52	)	)	PUNCT
ejpam-890	191	53	=	=	SYM
ejpam-890	191	54	(	(	PUNCT
ejpam-890	191	55	0,0	0,0	NOUN
ejpam-890	191	56	)	)	PUNCT
ejpam-890	191	57	∏p−1	∏p−1	PROPN
ejpam-890	191	58	i=2	i=2	PROPN
ejpam-890	191	59	(	(	PUNCT
ejpam-890	191	60	1	1	NUM
ejpam-890	191	61	+	+	NUM
ejpam-890	191	62	yi	yi	NOUN
ejpam-890	191	63	)	)	PUNCT
ejpam-890	191	64	,	,	PUNCT
ejpam-890	191	65	otherwise	otherwise	ADV
ejpam-890	191	66	γst(xk	γst(xk	PUNCT
ejpam-890	191	67	)	)	PUNCT
ejpam-890	191	68	=	=	SYM
ejpam-890	191	69			PROPN
ejpam-890	191	70			PROPN
ejpam-890	191	71			PROPN
ejpam-890	191	72			NOUN
ejpam-890	191	73			PROPN
ejpam-890	191	74			PROPN
ejpam-890	191	75			NOUN
ejpam-890	191	76	∑r−2	∑r−2	NOUN
ejpam-890	192	1	i=2	i=2	PROPN
ejpam-890	192	2	x	x	PUNCT
ejpam-890	192	3	i	i	PRON
ejpam-890	192	4	k	k	PROPN
ejpam-890	192	5	�	�	PROPN
ejpam-890	192	6	1	1	NUM
ejpam-890	192	7	+	+	NUM
ejpam-890	192	8	∑r−1	∑r−1	PROPN
ejpam-890	192	9	j	j	X
ejpam-890	192	10	=	=	NOUN
ejpam-890	192	11	i+1	i+1	NOUN
ejpam-890	192	12	x	x	SYM
ejpam-890	192	13	j	j	PROPN
ejpam-890	192	14	k	k	PROPN
ejpam-890	192	15	�	�	PROPN
ejpam-890	193	1	+	+	CCONJ
ejpam-890	193	2	x	x	PUNCT
ejpam-890	193	3	r−1	r−1	PROPN
ejpam-890	193	4	k	k	NOUN
ejpam-890	193	5	,	,	PUNCT
ejpam-890	193	6	(	(	PUNCT
ejpam-890	193	7	s	s	X
ejpam-890	193	8	,	,	PUNCT
ejpam-890	193	9	t	t	PROPN
ejpam-890	193	10	)	)	PUNCT
ejpam-890	193	11	=	=	SYM
ejpam-890	193	12	(	(	PUNCT
ejpam-890	193	13	0,0	0,0	NOUN
ejpam-890	193	14	)	)	PUNCT
ejpam-890	193	15	1	1	NUM
ejpam-890	193	16	+	+	NUM
ejpam-890	193	17	∑r−1	∑r−1	ADJ
ejpam-890	193	18	i=2	i=2	PROPN
ejpam-890	194	1	x	x	PUNCT
ejpam-890	195	1	i	i	PRON
ejpam-890	195	2	k	k	NOUN
ejpam-890	195	3	,	,	PUNCT
ejpam-890	195	4	(	(	PUNCT
ejpam-890	195	5	s	s	X
ejpam-890	195	6	,	,	PUNCT
ejpam-890	195	7	t	t	PROPN
ejpam-890	195	8	)	)	PUNCT
ejpam-890	195	9	=	=	SYM
ejpam-890	195	10	(	(	PUNCT
ejpam-890	195	11	0,1	0,1	NUM
ejpam-890	195	12	)	)	PUNCT
ejpam-890	195	13	1	1	NUM
ejpam-890	195	14	+	+	NUM
ejpam-890	195	15	∑r−1	∑r−1	ADJ
ejpam-890	195	16	i=2	i=2	PROPN
ejpam-890	195	17	x	x	PUNCT
ejpam-890	196	1	i	i	PRON
ejpam-890	196	2	k	k	NOUN
ejpam-890	196	3	,	,	PUNCT
ejpam-890	196	4	(	(	PUNCT
ejpam-890	196	5	s	s	X
ejpam-890	196	6	,	,	PUNCT
ejpam-890	196	7	t	t	PROPN
ejpam-890	196	8	)	)	PUNCT
ejpam-890	196	9	=	=	PUNCT
ejpam-890	196	10	(	(	PUNCT
ejpam-890	196	11	1,0	1,0	NUM
ejpam-890	196	12	)	)	PUNCT
ejpam-890	196	13	1	1	NUM
ejpam-890	196	14	,	,	PUNCT
ejpam-890	196	15	(	(	PUNCT
ejpam-890	196	16	s	s	X
ejpam-890	196	17	,	,	PUNCT
ejpam-890	196	18	t	t	PROPN
ejpam-890	196	19	)	)	PUNCT
ejpam-890	196	20	=	=	PUNCT
ejpam-890	196	21	(	(	PUNCT
ejpam-890	196	22	1,1	1,1	NUM
ejpam-890	196	23	)	)	PUNCT
ejpam-890	196	24	.	.	PUNCT
ejpam-890	197	1	i̇.	i̇.	PROPN
ejpam-890	197	2	siap	siap	PROPN
ejpam-890	197	3	/	/	SYM
ejpam-890	197	4	eur	eur	PROPN
ejpam-890	197	5	.	.	PUNCT
ejpam-890	198	1	j.	j.	PROPN
ejpam-890	198	2	pure	pure	PROPN
ejpam-890	198	3	appl	appl	PROPN
ejpam-890	198	4	.	.	PROPN
ejpam-890	198	5	math	math	PROPN
ejpam-890	198	6	,	,	PUNCT
ejpam-890	198	7	3	3	NUM
ejpam-890	198	8	(	(	PUNCT
ejpam-890	198	9	2010	2010	NUM
ejpam-890	198	10	)	)	PUNCT
ejpam-890	198	11	,	,	PUNCT
ejpam-890	198	12	653	653	NUM
ejpam-890	198	13	-	-	SYM
ejpam-890	198	14	669	669	NUM
ejpam-890	198	15	660	660	NUM
ejpam-890	198	16	proof	proof	NOUN
ejpam-890	198	17	.	.	PUNCT
ejpam-890	199	1	the	the	DET
ejpam-890	199	2	cases	case	NOUN
ejpam-890	199	3	1	1	NUM
ejpam-890	199	4	and	and	CCONJ
ejpam-890	199	5	2	2	NUM
ejpam-890	199	6	follow	follow	VERB
ejpam-890	199	7	directly	directly	ADV
ejpam-890	199	8	from	from	ADP
ejpam-890	199	9	the	the	DET
ejpam-890	199	10	definitions	definition	NOUN
ejpam-890	199	11	.	.	PUNCT
ejpam-890	200	1	we	we	PRON
ejpam-890	200	2	give	give	VERB
ejpam-890	200	3	the	the	DET
ejpam-890	200	4	proof	proof	NOUN
ejpam-890	200	5	of	of	ADP
ejpam-890	200	6	case	case	NOUN
ejpam-890	200	7	3	3	NUM
ejpam-890	200	8	and	and	CCONJ
ejpam-890	200	9	the	the	DET
ejpam-890	200	10	proof	proof	NOUN
ejpam-890	200	11	of	of	ADP
ejpam-890	200	12	the	the	DET
ejpam-890	200	13	case	case	NOUN
ejpam-890	200	14	4	4	NUM
ejpam-890	200	15	also	also	ADV
ejpam-890	200	16	can	can	AUX
ejpam-890	200	17	be	be	AUX
ejpam-890	200	18	shown	show	VERB
ejpam-890	200	19	by	by	ADP
ejpam-890	200	20	using	use	VERB
ejpam-890	200	21	similar	similar	ADJ
ejpam-890	200	22	arguments	argument	NOUN
ejpam-890	200	23	.	.	PUNCT
ejpam-890	201	1	let	let	VERB
ejpam-890	201	2	p	p	NOUN
ejpam-890	201	3	=	=	NOUN
ejpam-890	201	4	2	2	NUM
ejpam-890	201	5	and	and	CCONJ
ejpam-890	201	6	r	r	NOUN
ejpam-890	201	7	≥	≥	NOUN
ejpam-890	201	8	2	2	NUM
ejpam-890	201	9	and	and	CCONJ
ejpam-890	201	10	a=	a=	VERB
ejpam-890	201	11	(	(	PUNCT
ejpam-890	201	12	ai	ai	VERB
ejpam-890	201	13	j	j	PROPN
ejpam-890	201	14	)	)	PUNCT
ejpam-890	201	15	∈	∈	PROPN
ejpam-890	201	16	m2×r	m2×r	NOUN
ejpam-890	201	17	(	(	PUNCT
ejpam-890	201	18	r	r	NOUN
ejpam-890	201	19	)	)	PUNCT
ejpam-890	201	20	be	be	AUX
ejpam-890	201	21	a	a	DET
ejpam-890	201	22	generic	generic	ADJ
ejpam-890	201	23	burst	burst	NOUN
ejpam-890	201	24	error	error	NOUN
ejpam-890	201	25	.	.	PUNCT
ejpam-890	202	1	hence	hence	ADV
ejpam-890	202	2	the	the	DET
ejpam-890	202	3	matrix	matrix	NOUN
ejpam-890	202	4	a	a	PRON
ejpam-890	202	5	has	have	VERB
ejpam-890	202	6	only	only	ADV
ejpam-890	202	7	two	two	NUM
ejpam-890	202	8	rows	row	NOUN
ejpam-890	202	9	and	and	CCONJ
ejpam-890	202	10	r	r	NOUN
ejpam-890	202	11	≥	≥	NUM
ejpam-890	202	12	2	2	NUM
ejpam-890	202	13	columns	column	NOUN
ejpam-890	202	14	.	.	PUNCT
ejpam-890	203	1	there	there	PRON
ejpam-890	203	2	are	be	VERB
ejpam-890	203	3	24	24	NUM
ejpam-890	203	4	=	=	SYM
ejpam-890	203	5	16	16	NUM
ejpam-890	203	6	possible	possible	ADJ
ejpam-890	203	7	values	value	NOUN
ejpam-890	203	8	(	(	PUNCT
ejpam-890	203	9	as	as	ADP
ejpam-890	203	10	zero	zero	NUM
ejpam-890	203	11	and	and	CCONJ
ejpam-890	203	12	none	none	NOUN
ejpam-890	203	13	zero	zero	NUM
ejpam-890	203	14	)	)	PUNCT
ejpam-890	203	15	for	for	ADP
ejpam-890	203	16	the	the	DET
ejpam-890	203	17	corners	corner	NOUN
ejpam-890	203	18	of	of	ADP
ejpam-890	203	19	a.	a.	NOUN
ejpam-890	203	20	since	since	SCONJ
ejpam-890	203	21	the	the	DET
ejpam-890	203	22	matrix	matrix	NOUN
ejpam-890	203	23	a	a	PRON
ejpam-890	203	24	is	be	AUX
ejpam-890	203	25	a	a	DET
ejpam-890	203	26	burst	burst	ADJ
ejpam-890	203	27	error	error	NOUN
ejpam-890	203	28	,	,	PUNCT
ejpam-890	203	29	the	the	DET
ejpam-890	203	30	first	first	ADJ
ejpam-890	203	31	and	and	CCONJ
ejpam-890	203	32	last	last	ADJ
ejpam-890	203	33	column	column	NOUN
ejpam-890	203	34	must	must	AUX
ejpam-890	203	35	be	be	AUX
ejpam-890	203	36	nonzero	nonzero	ADJ
ejpam-890	203	37	.	.	PUNCT
ejpam-890	204	1	the	the	DET
ejpam-890	204	2	first	first	ADJ
ejpam-890	204	3	column	column	NOUN
ejpam-890	204	4	is	be	AUX
ejpam-890	204	5	equal	equal	ADJ
ejpam-890	204	6	to	to	ADP
ejpam-890	204	7	zero	zero	NUM
ejpam-890	204	8	if	if	SCONJ
ejpam-890	204	9	(	(	PUNCT
ejpam-890	204	10	i	i	PRON
ejpam-890	204	11	,	,	PUNCT
ejpam-890	204	12	k	k	NOUN
ejpam-890	204	13	)	)	PUNCT
ejpam-890	204	14	=	=	SYM
ejpam-890	204	15	(	(	PUNCT
ejpam-890	204	16	0,0	0,0	NOUN
ejpam-890	204	17	)	)	PUNCT
ejpam-890	204	18	and	and	CCONJ
ejpam-890	204	19	the	the	DET
ejpam-890	204	20	last	last	ADJ
ejpam-890	204	21	column	column	NOUN
ejpam-890	204	22	is	be	AUX
ejpam-890	204	23	equal	equal	ADJ
ejpam-890	204	24	to	to	ADP
ejpam-890	204	25	zero	zero	NUM
ejpam-890	204	26	if	if	SCONJ
ejpam-890	204	27	(	(	PUNCT
ejpam-890	204	28	j	j	PROPN
ejpam-890	204	29	,	,	PUNCT
ejpam-890	204	30	l	l	NOUN
ejpam-890	204	31	)	)	PUNCT
ejpam-890	204	32	=	=	SYM
ejpam-890	204	33	(	(	PUNCT
ejpam-890	204	34	0,0	0,0	NOUN
ejpam-890	204	35	)	)	PUNCT
ejpam-890	204	36	.	.	PUNCT
ejpam-890	205	1	excluding	exclude	VERB
ejpam-890	205	2	these	these	DET
ejpam-890	205	3	seven	seven	NUM
ejpam-890	205	4	cases	case	NOUN
ejpam-890	205	5	the	the	DET
ejpam-890	205	6	possible	possible	ADJ
ejpam-890	205	7	values	value	NOUN
ejpam-890	205	8	for	for	ADP
ejpam-890	205	9	the	the	DET
ejpam-890	205	10	corners	corner	NOUN
ejpam-890	205	11	are	be	AUX
ejpam-890	205	12	all	all	PRON
ejpam-890	205	13	values	value	NOUN
ejpam-890	205	14	of	of	ADP
ejpam-890	205	15	the	the	DET
ejpam-890	205	16	set	set	NOUN
ejpam-890	205	17	s.	s.	PROPN
ejpam-890	205	18	if	if	SCONJ
ejpam-890	205	19	both	both	DET
ejpam-890	205	20	corners	corner	NOUN
ejpam-890	205	21	of	of	ADP
ejpam-890	205	22	the	the	DET
ejpam-890	205	23	first	first	ADJ
ejpam-890	205	24	row	row	NOUN
ejpam-890	205	25	are	be	AUX
ejpam-890	205	26	equal	equal	ADJ
ejpam-890	205	27	to	to	ADP
ejpam-890	205	28	zero	zero	NUM
ejpam-890	205	29	,	,	PUNCT
ejpam-890	205	30	then	then	ADV
ejpam-890	205	31	the	the	DET
ejpam-890	205	32	term	term	NOUN
ejpam-890	205	33	that	that	PRON
ejpam-890	205	34	corresponds	correspond	VERB
ejpam-890	205	35	to	to	ADP
ejpam-890	205	36	a	a	PRON
ejpam-890	205	37	must	must	AUX
ejpam-890	205	38	consist	consist	VERB
ejpam-890	205	39	of	of	ADP
ejpam-890	205	40	β	β	X
ejpam-890	205	41	=	=	SYM
ejpam-890	205	42	x2	x2	PROPN
ejpam-890	205	43	1(x	1(x	NUM
ejpam-890	205	44	2	2	NUM
ejpam-890	205	45	1	1	NUM
ejpam-890	205	46	+	+	NUM
ejpam-890	205	47	·	·	PUNCT
ejpam-890	205	48	·	·	PUNCT
ejpam-890	205	49	·	·	PUNCT
ejpam-890	206	1	+	+	NUM
ejpam-890	206	2	x	x	PUNCT
ejpam-890	206	3	r−1	r−1	PROPN
ejpam-890	206	4	1	1	NUM
ejpam-890	206	5	)	)	PUNCT
ejpam-890	207	1	+	+	CCONJ
ejpam-890	208	1	x3	x3	NUM
ejpam-890	208	2	1(x	1(x	NUM
ejpam-890	208	3	4	4	NUM
ejpam-890	208	4	1	1	NUM
ejpam-890	208	5	+	+	NUM
ejpam-890	208	6	·	·	PUNCT
ejpam-890	208	7	·	·	PUNCT
ejpam-890	208	8	·	·	PUNCT
ejpam-890	208	9	+	+	NUM
ejpam-890	208	10	x	x	PUNCT
ejpam-890	208	11	r−1	r−1	PROPN
ejpam-890	208	12	1	1	NUM
ejpam-890	208	13	)	)	PUNCT
ejpam-890	208	14	+	+	CCONJ
ejpam-890	208	15	·	·	PUNCT
ejpam-890	208	16	·	·	PUNCT
ejpam-890	208	17	·	·	PUNCT
ejpam-890	208	18	+	+	NUM
ejpam-890	208	19	x	x	SYM
ejpam-890	208	20	r−1	r−1	PROPN
ejpam-890	208	21	.	.	PUNCT
ejpam-890	209	1	otherwise	otherwise	ADV
ejpam-890	209	2	,	,	PUNCT
ejpam-890	209	3	the	the	DET
ejpam-890	209	4	term	term	NOUN
ejpam-890	209	5	that	that	PRON
ejpam-890	209	6	corresponds	correspond	VERB
ejpam-890	209	7	to	to	ADP
ejpam-890	209	8	a	a	PRON
ejpam-890	209	9	must	must	AUX
ejpam-890	209	10	consist	consist	VERB
ejpam-890	209	11	of	of	ADP
ejpam-890	209	12	1	1	NUM
ejpam-890	209	13	+	+	NUM
ejpam-890	209	14	β	β	NOUN
ejpam-890	209	15	.	.	PUNCT
ejpam-890	210	1	these	these	DET
ejpam-890	210	2	two	two	NUM
ejpam-890	210	3	cases	case	NOUN
ejpam-890	210	4	are	be	AUX
ejpam-890	210	5	represented	represent	VERB
ejpam-890	210	6	by	by	ADP
ejpam-890	210	7	the	the	DET
ejpam-890	210	8	multiple	multiple	ADJ
ejpam-890	210	9	γi	γi	NOUN
ejpam-890	210	10	j(x1	j(x1	NOUN
ejpam-890	210	11	)	)	PUNCT
ejpam-890	210	12	.	.	PUNCT
ejpam-890	211	1	in	in	ADP
ejpam-890	211	2	a	a	DET
ejpam-890	211	3	similar	similar	ADJ
ejpam-890	211	4	way	way	NOUN
ejpam-890	211	5	we	we	PRON
ejpam-890	211	6	can	can	AUX
ejpam-890	211	7	argue	argue	VERB
ejpam-890	211	8	for	for	ADP
ejpam-890	211	9	the	the	DET
ejpam-890	211	10	last	last	ADJ
ejpam-890	211	11	row	row	NOUN
ejpam-890	211	12	.	.	PUNCT
ejpam-890	212	1	example	example	NOUN
ejpam-890	213	1	3	3	NUM
ejpam-890	213	2	.	.	PUNCT
ejpam-890	214	1	the	the	DET
ejpam-890	214	2	following	follow	VERB
ejpam-890	214	3	generic	generic	ADJ
ejpam-890	214	4	multivariable	multivariable	ADJ
ejpam-890	214	5	polynomial	polynomial	ADJ
ejpam-890	214	6	g	g	PROPN
ejpam-890	214	7	gives	give	VERB
ejpam-890	214	8	the	the	DET
ejpam-890	214	9	term	term	NOUN
ejpam-890	214	10	representation	representation	NOUN
ejpam-890	214	11	of	of	ADP
ejpam-890	214	12	a∈	a∈	PROPN
ejpam-890	214	13	m2×3(f2	m2×3(f2	PROPN
ejpam-890	214	14	)	)	PUNCT
ejpam-890	214	15	generic	generic	ADJ
ejpam-890	214	16	burst	burst	ADJ
ejpam-890	214	17	errors	error	NOUN
ejpam-890	214	18	of	of	ADP
ejpam-890	214	19	order	order	NOUN
ejpam-890	214	20	2×	2×	NUM
ejpam-890	214	21	3	3	NUM
ejpam-890	214	22	.	.	PUNCT
ejpam-890	214	23	by	by	ADP
ejpam-890	214	24	theorem	theorem	NOUN
ejpam-890	214	25	3	3	NUM
ejpam-890	214	26	part	part	NOUN
ejpam-890	214	27	3	3	NUM
ejpam-890	214	28	,	,	PUNCT
ejpam-890	214	29	we	we	PRON
ejpam-890	214	30	have	have	VERB
ejpam-890	214	31	g(z̃	g(z̃	NOUN
ejpam-890	214	32	,	,	PUNCT
ejpam-890	214	33	x̃	x̃	PROPN
ejpam-890	214	34	,	,	PUNCT
ejpam-890	214	35	x̃	x̃	PROPN
ejpam-890	214	36	,	,	PUNCT
ejpam-890	214	37	ỹ	ỹ	PROPN
ejpam-890	214	38	)	)	PUNCT
ejpam-890	214	39	=	=	PUNCT
ejpam-890	215	1	∑	∑	PUNCT
ejpam-890	215	2	(	(	PUNCT
ejpam-890	215	3	i	i	PROPN
ejpam-890	215	4	,	,	PUNCT
ejpam-890	215	5	j	j	PROPN
ejpam-890	215	6	,	,	PUNCT
ejpam-890	215	7	k	k	PROPN
ejpam-890	215	8	,	,	PUNCT
ejpam-890	215	9	l)∈s	l)∈s	X
ejpam-890	216	1	z	z	PROPN
ejpam-890	216	2	i	i	PRON
ejpam-890	216	3	1	1	NUM
ejpam-890	216	4	y	y	PROPN
ejpam-890	216	5	j	j	PROPN
ejpam-890	216	6	1	1	NUM
ejpam-890	216	7	zk	zk	PROPN
ejpam-890	216	8	2	2	NUM
ejpam-890	216	9	y	y	PROPN
ejpam-890	216	10	l	l	NOUN
ejpam-890	216	11	2γi	2γi	PROPN
ejpam-890	216	12	j(x1)γkl(x2	j(x1)γkl(x2	PROPN
ejpam-890	216	13	)	)	PUNCT
ejpam-890	217	1	=	=	PUNCT
ejpam-890	217	2	z1	z1	VERB
ejpam-890	217	3	y1x	y1x	NOUN
ejpam-890	217	4	2	2	NUM
ejpam-890	217	5	2	2	NUM
ejpam-890	217	6	+	+	SYM
ejpam-890	217	7	z2	z2	PROPN
ejpam-890	217	8	y2x	y2x	ADJ
ejpam-890	217	9	2	2	NUM
ejpam-890	217	10	1	1	NUM
ejpam-890	217	11	+	+	CCONJ
ejpam-890	217	12	z1	z1	ADJ
ejpam-890	217	13	y2(1	y2(1	NOUN
ejpam-890	217	14	+	+	CCONJ
ejpam-890	217	15	x	x	SYM
ejpam-890	217	16	2	2	NUM
ejpam-890	217	17	1)(1	1)(1	NUM
ejpam-890	217	18	+	+	NOUN
ejpam-890	217	19	x2	x2	PROPN
ejpam-890	217	20	2	2	NUM
ejpam-890	217	21	)	)	PUNCT
ejpam-890	217	22	+	+	CCONJ
ejpam-890	217	23	z2	z2	PROPN
ejpam-890	217	24	y1(1	y1(1	PROPN
ejpam-890	217	25	+	+	X
ejpam-890	217	26	x2	x2	PROPN
ejpam-890	217	27	1)(1	1)(1	NUM
ejpam-890	217	28	+	+	NOUN
ejpam-890	217	29	x	x	SYM
ejpam-890	217	30	2	2	NUM
ejpam-890	217	31	2	2	NUM
ejpam-890	217	32	)	)	PUNCT
ejpam-890	217	33	+	+	CCONJ
ejpam-890	217	34	z1	z1	PROPN
ejpam-890	217	35	y1	y1	NOUN
ejpam-890	217	36	y2(1	y2(1	NOUN
ejpam-890	217	37	+	+	CCONJ
ejpam-890	217	38	x2	x2	PROPN
ejpam-890	217	39	2	2	NUM
ejpam-890	217	40	)	)	PUNCT
ejpam-890	217	41	+	+	NUM
ejpam-890	217	42	y1z2	y1z2	PROPN
ejpam-890	217	43	y2(1	y2(1	NOUN
ejpam-890	217	44	+	+	CCONJ
ejpam-890	217	45	x	x	SYM
ejpam-890	217	46	2	2	NUM
ejpam-890	217	47	1	1	NUM
ejpam-890	217	48	)	)	PUNCT
ejpam-890	217	49	+	+	CCONJ
ejpam-890	217	50	z1z2	z1z2	NUM
ejpam-890	217	51	y1(1	y1(1	PROPN
ejpam-890	217	52	+	+	NOUN
ejpam-890	217	53	x	x	SYM
ejpam-890	217	54	2	2	NUM
ejpam-890	217	55	2	2	NUM
ejpam-890	217	56	)	)	PUNCT
ejpam-890	217	57	+	+	CCONJ
ejpam-890	217	58	z1z2	z1z2	X
ejpam-890	217	59	y2(1	y2(1	NOUN
ejpam-890	217	60	+	+	CCONJ
ejpam-890	217	61	x	x	SYM
ejpam-890	217	62	2	2	NUM
ejpam-890	217	63	1	1	NUM
ejpam-890	217	64	)	)	PUNCT
ejpam-890	217	65	+	+	CCONJ
ejpam-890	217	66	z1	z1	NUM
ejpam-890	217	67	y1z2	y1z2	PROPN
ejpam-890	217	68	y2	y2	NOUN
ejpam-890	217	69	=	=	SYM
ejpam-890	217	70	z1	z1	PROPN
ejpam-890	217	71	y1x	y1x	NOUN
ejpam-890	217	72	2	2	NUM
ejpam-890	217	73	2	2	NUM
ejpam-890	217	74	+	+	SYM
ejpam-890	218	1	z2	z2	ADJ
ejpam-890	218	2	y2	y2	NOUN
ejpam-890	218	3	x2	x2	NOUN
ejpam-890	218	4	1	1	NUM
ejpam-890	218	5	+	+	NUM
ejpam-890	218	6	z1	z1	ADJ
ejpam-890	218	7	y2	y2	PROPN
ejpam-890	218	8	+	+	CCONJ
ejpam-890	218	9	z1	z1	VERB
ejpam-890	218	10	y2	y2	NOUN
ejpam-890	218	11	x2	x2	NOUN
ejpam-890	218	12	2	2	NUM
ejpam-890	218	13	+	+	CCONJ
ejpam-890	218	14	z1	z1	PROPN
ejpam-890	218	15	y2x	y2x	ADJ
ejpam-890	218	16	2	2	NUM
ejpam-890	218	17	1	1	NUM
ejpam-890	218	18	+	+	CCONJ
ejpam-890	218	19	z1	z1	PROPN
ejpam-890	218	20	y2x	y2x	ADJ
ejpam-890	218	21	2	2	NUM
ejpam-890	218	22	1	1	NUM
ejpam-890	218	23	x2	x2	SYM
ejpam-890	218	24	2	2	NUM
ejpam-890	218	25	+	+	NOUN
ejpam-890	218	26	z2	z2	PROPN
ejpam-890	218	27	y1	y1	NOUN
ejpam-890	218	28	+	+	X
ejpam-890	218	29	z2	z2	PROPN
ejpam-890	218	30	y1	y1	NOUN
ejpam-890	218	31	x2	x2	NOUN
ejpam-890	218	32	2	2	NUM
ejpam-890	218	33	+	+	NOUN
ejpam-890	218	34	z2	z2	NUM
ejpam-890	218	35	y1x	y1x	NOUN
ejpam-890	218	36	2	2	NUM
ejpam-890	218	37	1	1	NUM
ejpam-890	218	38	+	+	SYM
ejpam-890	218	39	z2	z2	NUM
ejpam-890	218	40	y1x	y1x	NOUN
ejpam-890	218	41	2	2	NUM
ejpam-890	218	42	1	1	NUM
ejpam-890	218	43	x2	x2	SYM
ejpam-890	218	44	2	2	NUM
ejpam-890	218	45	+	+	NOUN
ejpam-890	218	46	z1	z1	ADJ
ejpam-890	218	47	y1	y1	NOUN
ejpam-890	218	48	y2	y2	NOUN
ejpam-890	218	49	+	+	CCONJ
ejpam-890	218	50	z1	z1	PROPN
ejpam-890	218	51	y1	y1	PROPN
ejpam-890	218	52	y2x	y2x	ADJ
ejpam-890	218	53	2	2	NUM
ejpam-890	218	54	2	2	NUM
ejpam-890	218	55	+	+	NUM
ejpam-890	218	56	y1z2	y1z2	NOUN
ejpam-890	218	57	y2	y2	PROPN
ejpam-890	219	1	+	+	CCONJ
ejpam-890	219	2	y1z2	y1z2	NOUN
ejpam-890	220	1	y2	y2	NOUN
ejpam-890	220	2	x2	x2	NOUN
ejpam-890	220	3	1	1	NUM
ejpam-890	220	4	+	+	NUM
ejpam-890	220	5	z1z2	z1z2	PROPN
ejpam-890	220	6	y1	y1	NOUN
ejpam-890	221	1	+	+	CCONJ
ejpam-890	221	2	z1z2	z1z2	SYM
ejpam-890	221	3	y1x	y1x	NOUN
ejpam-890	221	4	2	2	NUM
ejpam-890	221	5	2	2	NUM
ejpam-890	221	6	+	+	CCONJ
ejpam-890	221	7	z1z2	z1z2	ADJ
ejpam-890	221	8	y2	y2	NOUN
ejpam-890	222	1	+	+	CCONJ
ejpam-890	222	2	z1z2	z1z2	PROPN
ejpam-890	222	3	y2x	y2x	ADJ
ejpam-890	222	4	2	2	NUM
ejpam-890	222	5	1	1	NUM
ejpam-890	222	6	+	+	NUM
ejpam-890	222	7	z1	z1	PROPN
ejpam-890	222	8	y1z2	y1z2	PROPN
ejpam-890	222	9	y2	y2	PROPN
ejpam-890	222	10	.	.	PUNCT
ejpam-890	223	1	using	use	VERB
ejpam-890	223	2	the	the	DET
ejpam-890	223	3	generic	generic	ADJ
ejpam-890	223	4	multivariable	multivariable	ADJ
ejpam-890	223	5	polynomial	polynomial	NOUN
ejpam-890	223	6	,	,	PUNCT
ejpam-890	223	7	we	we	PRON
ejpam-890	223	8	can	can	AUX
ejpam-890	223	9	list	list	VERB
ejpam-890	223	10	all	all	DET
ejpam-890	223	11	generic	generic	ADJ
ejpam-890	223	12	burst	burst	ADJ
ejpam-890	223	13	errors	error	NOUN
ejpam-890	223	14	of	of	ADP
ejpam-890	223	15	size	size	NOUN
ejpam-890	223	16	2×	2×	NUM
ejpam-890	223	17	3	3	NUM
ejpam-890	223	18	.	.	PUNCT
ejpam-890	223	19	�	�	PROPN
ejpam-890	223	20	1	1	NUM
ejpam-890	223	21	0	0	NUM
ejpam-890	223	22	1	1	NUM
ejpam-890	223	23	0	0	NUM
ejpam-890	223	24	1	1	NUM
ejpam-890	223	25	0	0	NUM
ejpam-890	223	26	�	�	PROPN
ejpam-890	223	27	,	,	PUNCT
ejpam-890	223	28	�	�	PROPN
ejpam-890	223	29	0	0	NUM
ejpam-890	223	30	1	1	NUM
ejpam-890	223	31	0	0	NUM
ejpam-890	223	32	1	1	NUM
ejpam-890	223	33	0	0	NUM
ejpam-890	223	34	1	1	NUM
ejpam-890	223	35	�	�	PROPN
ejpam-890	223	36	,	,	PUNCT
ejpam-890	223	37	�	�	PROPN
ejpam-890	223	38	1	1	NUM
ejpam-890	223	39	0	0	NUM
ejpam-890	223	40	0	0	NUM
ejpam-890	223	41	0	0	NUM
ejpam-890	223	42	0	0	NUM
ejpam-890	223	43	1	1	NUM
ejpam-890	223	44	�	�	PROPN
ejpam-890	223	45	,	,	PUNCT
ejpam-890	223	46	�	�	PROPN
ejpam-890	223	47	1	1	NUM
ejpam-890	223	48	0	0	NUM
ejpam-890	223	49	0	0	NUM
ejpam-890	223	50	0	0	NUM
ejpam-890	223	51	1	1	NUM
ejpam-890	223	52	1	1	NUM
ejpam-890	223	53	�	�	PROPN
ejpam-890	223	54	,	,	PUNCT
ejpam-890	223	55	�	�	PROPN
ejpam-890	223	56	1	1	NUM
ejpam-890	223	57	1	1	NUM
ejpam-890	223	58	0	0	NUM
ejpam-890	223	59	0	0	NUM
ejpam-890	223	60	0	0	NUM
ejpam-890	223	61	1	1	NUM
ejpam-890	223	62	�	�	PROPN
ejpam-890	223	63	,	,	PUNCT
ejpam-890	223	64	�	�	PROPN
ejpam-890	223	65	1	1	NUM
ejpam-890	223	66	1	1	NUM
ejpam-890	223	67	0	0	NUM
ejpam-890	223	68	0	0	NUM
ejpam-890	223	69	1	1	NUM
ejpam-890	223	70	1	1	NUM
ejpam-890	223	71	�	�	PROPN
ejpam-890	223	72	,	,	PUNCT
ejpam-890	223	73	�	�	PROPN
ejpam-890	223	74	0	0	NUM
ejpam-890	223	75	0	0	NUM
ejpam-890	223	76	1	1	NUM
ejpam-890	223	77	1	1	NUM
ejpam-890	223	78	0	0	NUM
ejpam-890	223	79	0	0	NUM
ejpam-890	223	80	�	�	PROPN
ejpam-890	223	81	,	,	PUNCT
ejpam-890	223	82	�	�	PROPN
ejpam-890	223	83	0	0	NUM
ejpam-890	223	84	0	0	NUM
ejpam-890	223	85	1	1	NUM
ejpam-890	223	86	1	1	NUM
ejpam-890	223	87	1	1	NUM
ejpam-890	223	88	0	0	NUM
ejpam-890	223	89	�	�	PROPN
ejpam-890	223	90	,	,	PUNCT
ejpam-890	223	91	�	�	PROPN
ejpam-890	223	92	0	0	NUM
ejpam-890	223	93	1	1	NUM
ejpam-890	223	94	1	1	NUM
ejpam-890	223	95	1	1	NUM
ejpam-890	223	96	0	0	NUM
ejpam-890	223	97	0	0	NUM
ejpam-890	223	98	�	�	PROPN
ejpam-890	223	99	,	,	PUNCT
ejpam-890	223	100	�	�	PROPN
ejpam-890	223	101	0	0	NUM
ejpam-890	223	102	1	1	NUM
ejpam-890	223	103	1	1	NUM
ejpam-890	223	104	1	1	NUM
ejpam-890	223	105	1	1	NUM
ejpam-890	223	106	0	0	NUM
ejpam-890	223	107	�	�	PROPN
ejpam-890	223	108	,	,	PUNCT
ejpam-890	223	109	�	�	PROPN
ejpam-890	223	110	1	1	NUM
ejpam-890	223	111	0	0	NUM
ejpam-890	223	112	1	1	NUM
ejpam-890	223	113	0	0	NUM
ejpam-890	223	114	0	0	NUM
ejpam-890	223	115	1	1	NUM
ejpam-890	223	116	�	�	PROPN
ejpam-890	223	117	,	,	PUNCT
ejpam-890	223	118	�	�	PROPN
ejpam-890	223	119	1	1	NUM
ejpam-890	223	120	0	0	NUM
ejpam-890	223	121	1	1	NUM
ejpam-890	223	122	0	0	NUM
ejpam-890	223	123	1	1	NUM
ejpam-890	223	124	1	1	NUM
ejpam-890	223	125	�	�	PROPN
ejpam-890	223	126	,	,	PUNCT
ejpam-890	223	127	�	�	PROPN
ejpam-890	223	128	0	0	NUM
ejpam-890	223	129	0	0	NUM
ejpam-890	223	130	1	1	NUM
ejpam-890	223	131	1	1	NUM
ejpam-890	223	132	0	0	NUM
ejpam-890	223	133	1	1	NUM
ejpam-890	223	134	�	�	PROPN
ejpam-890	223	135	,	,	PUNCT
ejpam-890	223	136	�	�	PROPN
ejpam-890	223	137	0	0	NUM
ejpam-890	223	138	1	1	NUM
ejpam-890	223	139	1	1	NUM
ejpam-890	223	140	1	1	NUM
ejpam-890	223	141	0	0	NUM
ejpam-890	223	142	1	1	NUM
ejpam-890	223	143	�	�	PROPN
ejpam-890	223	144	,	,	PUNCT
ejpam-890	223	145	�	�	PROPN
ejpam-890	223	146	1	1	NUM
ejpam-890	223	147	0	0	NUM
ejpam-890	223	148	1	1	NUM
ejpam-890	223	149	1	1	NUM
ejpam-890	223	150	0	0	NUM
ejpam-890	223	151	0	0	NUM
ejpam-890	223	152	�	�	PROPN
ejpam-890	223	153	,	,	PUNCT
ejpam-890	223	154	�	�	PROPN
ejpam-890	223	155	1	1	NUM
ejpam-890	223	156	0	0	NUM
ejpam-890	223	157	1	1	NUM
ejpam-890	223	158	1	1	NUM
ejpam-890	223	159	1	1	NUM
ejpam-890	223	160	0	0	NUM
ejpam-890	223	161	�	�	PROPN
ejpam-890	223	162	,	,	PUNCT
ejpam-890	223	163	�	�	PROPN
ejpam-890	223	164	1	1	NUM
ejpam-890	223	165	0	0	NUM
ejpam-890	223	166	0	0	NUM
ejpam-890	223	167	1	1	NUM
ejpam-890	223	168	0	0	NUM
ejpam-890	223	169	1	1	NUM
ejpam-890	223	170	�	�	PROPN
ejpam-890	223	171	,	,	PUNCT
ejpam-890	223	172	�	�	PROPN
ejpam-890	223	173	1	1	NUM
ejpam-890	223	174	1	1	NUM
ejpam-890	223	175	0	0	NUM
ejpam-890	223	176	1	1	NUM
ejpam-890	223	177	0	0	NUM
ejpam-890	223	178	1	1	NUM
ejpam-890	223	179	�	�	PROPN
ejpam-890	223	180	,	,	PUNCT
ejpam-890	223	181	�	�	PROPN
ejpam-890	223	182	1	1	NUM
ejpam-890	223	183	0	0	NUM
ejpam-890	223	184	1	1	NUM
ejpam-890	223	185	1	1	NUM
ejpam-890	223	186	0	0	NUM
ejpam-890	223	187	1	1	NUM
ejpam-890	223	188	�	�	PROPN
ejpam-890	223	189	.	.	PUNCT
ejpam-890	224	1	theorem	theorem	VERB
ejpam-890	224	2	4	4	NUM
ejpam-890	224	3	.	.	PUNCT
ejpam-890	225	1	all	all	DET
ejpam-890	225	2	generic	generic	ADJ
ejpam-890	225	3	bursts	burst	NOUN
ejpam-890	225	4	of	of	ADP
ejpam-890	225	5	order	order	NOUN
ejpam-890	225	6	p	p	X
ejpam-890	225	7	×	×	NOUN
ejpam-890	225	8	r	r	NOUN
ejpam-890	225	9	(	(	PUNCT
ejpam-890	225	10	p	p	X
ejpam-890	225	11	,	,	PUNCT
ejpam-890	225	12	r	r	NOUN
ejpam-890	225	13	≥	≥	NOUN
ejpam-890	225	14	3	3	NUM
ejpam-890	225	15	)	)	PUNCT
ejpam-890	225	16	are	be	AUX
ejpam-890	225	17	obtained	obtain	VERB
ejpam-890	225	18	as	as	ADP
ejpam-890	225	19	terms	term	NOUN
ejpam-890	225	20	of	of	ADP
ejpam-890	225	21	the	the	DET
ejpam-890	225	22	following	follow	VERB
ejpam-890	225	23	multi	multi	ADJ
ejpam-890	225	24	variable	variable	ADJ
ejpam-890	225	25	polynomial	polynomial	NOUN
ejpam-890	225	26	,	,	PUNCT
ejpam-890	225	27	say	say	VERB
ejpam-890	225	28	generic	generic	ADJ
ejpam-890	225	29	multivariable	multivariable	ADJ
ejpam-890	225	30	polynomial	polynomial	NOUN
ejpam-890	225	31	:	:	PUNCT
ejpam-890	226	1	g	g	PROPN
ejpam-890	226	2	(	(	PUNCT
ejpam-890	226	3	x̃	x̃	PROPN
ejpam-890	226	4	,	,	PUNCT
ejpam-890	226	5	z̃	z̃	PROPN
ejpam-890	226	6	,	,	PUNCT
ejpam-890	226	7	x̃	x̃	PROPN
ejpam-890	226	8	,	,	PUNCT
ejpam-890	226	9	ỹ	ỹ	PROPN
ejpam-890	226	10	)	)	PUNCT
ejpam-890	226	11	=	=	PUNCT
ejpam-890	226	12	∑	∑	PUNCT
ejpam-890	226	13	(	(	PUNCT
ejpam-890	226	14	i	i	PROPN
ejpam-890	226	15	,	,	PUNCT
ejpam-890	226	16	j	j	PROPN
ejpam-890	226	17	,	,	PUNCT
ejpam-890	226	18	k	k	PROPN
ejpam-890	226	19	,	,	PUNCT
ejpam-890	226	20	l)∈z4	l)∈z4	NOUN
ejpam-890	226	21	2	2	NUM
ejpam-890	226	22	z	z	NOUN
ejpam-890	226	23	i	i	NOUN
ejpam-890	226	24	1	1	NUM
ejpam-890	226	25	y	y	PROPN
ejpam-890	226	26	j	j	PROPN
ejpam-890	226	27	1zk	1zk	PROPN
ejpam-890	226	28	p	p	PROPN
ejpam-890	226	29	y	y	PROPN
ejpam-890	226	30	l	l	NOUN
ejpam-890	226	31	pz	pz	PROPN
ejpam-890	226	32	iky	iky	PROPN
ejpam-890	226	33	jlγi	jlγi	PROPN
ejpam-890	226	34	j(x1)γkl(x	j(x1)γkl(x	PROPN
ejpam-890	226	35	p	p	PROPN
ejpam-890	226	36	)	)	PUNCT
ejpam-890	226	37	.	.	PUNCT
ejpam-890	227	1	i̇.	i̇.	PROPN
ejpam-890	227	2	siap	siap	PROPN
ejpam-890	227	3	/	/	SYM
ejpam-890	227	4	eur	eur	PROPN
ejpam-890	227	5	.	.	PUNCT
ejpam-890	228	1	j.	j.	PROPN
ejpam-890	228	2	pure	pure	PROPN
ejpam-890	228	3	appl	appl	PROPN
ejpam-890	228	4	.	.	PROPN
ejpam-890	228	5	math	math	PROPN
ejpam-890	228	6	,	,	PUNCT
ejpam-890	228	7	3	3	NUM
ejpam-890	228	8	(	(	PUNCT
ejpam-890	228	9	2010	2010	NUM
ejpam-890	228	10	)	)	PUNCT
ejpam-890	228	11	,	,	PUNCT
ejpam-890	228	12	653	653	NUM
ejpam-890	228	13	-	-	SYM
ejpam-890	228	14	669	669	NUM
ejpam-890	228	15	661	661	NUM
ejpam-890	228	16	proof	proof	NOUN
ejpam-890	228	17	.	.	PUNCT
ejpam-890	229	1	let	let	VERB
ejpam-890	229	2	a=	a=	VERB
ejpam-890	229	3	(	(	PUNCT
ejpam-890	229	4	ai	ai	VERB
ejpam-890	229	5	j	j	PROPN
ejpam-890	229	6	)	)	PUNCT
ejpam-890	229	7	∈	∈	PROPN
ejpam-890	229	8	mp×r(r	mp×r(r	NOUN
ejpam-890	229	9	)	)	PUNCT
ejpam-890	229	10	be	be	VERB
ejpam-890	229	11	a	a	DET
ejpam-890	229	12	generic	generic	ADJ
ejpam-890	229	13	burst	burst	NOUN
ejpam-890	229	14	error	error	NOUN
ejpam-890	229	15	.	.	PUNCT
ejpam-890	230	1	a=	a=	PROPN
ejpam-890	230	2	a11	a11	X
ejpam-890	230	3	·	·	PUNCT
ejpam-890	230	4	·	·	PUNCT
ejpam-890	230	5	·	·	PUNCT
ejpam-890	230	6	a1r	a1r	NOUN
ejpam-890	230	7	...	...	PUNCT
ejpam-890	230	8	zero	zero	NUM
ejpam-890	230	9	submatrix	submatrix	NOUN
ejpam-890	230	10	...	...	PUNCT
ejpam-890	230	11	ap1	ap1	PROPN
ejpam-890	230	12	·	·	PUNCT
ejpam-890	230	13	·	·	PUNCT
ejpam-890	230	14	·	·	PUNCT
ejpam-890	230	15	apr	apr	INTJ
ejpam-890	230	16	.	.	PUNCT
ejpam-890	231	1	we	we	PRON
ejpam-890	231	2	consider	consider	VERB
ejpam-890	231	3	the	the	DET
ejpam-890	231	4	corners	corner	NOUN
ejpam-890	231	5	of	of	ADP
ejpam-890	231	6	a.	a.	NOUN
ejpam-890	231	7	there	there	PRON
ejpam-890	231	8	are	be	VERB
ejpam-890	231	9	16	16	NUM
ejpam-890	231	10	cases	case	NOUN
ejpam-890	231	11	depending	depend	VERB
ejpam-890	231	12	on	on	ADP
ejpam-890	231	13	the	the	DET
ejpam-890	231	14	corner	corner	NOUN
ejpam-890	231	15	’s	’s	PART
ejpam-890	231	16	values	value	NOUN
ejpam-890	231	17	as	as	ADP
ejpam-890	231	18	whether	whether	SCONJ
ejpam-890	231	19	they	they	PRON
ejpam-890	231	20	are	be	AUX
ejpam-890	231	21	equal	equal	ADJ
ejpam-890	231	22	to	to	ADP
ejpam-890	231	23	one	one	NUM
ejpam-890	231	24	or	or	CCONJ
ejpam-890	231	25	zero	zero	NUM
ejpam-890	231	26	.	.	PUNCT
ejpam-890	232	1	if	if	SCONJ
ejpam-890	232	2	any	any	DET
ejpam-890	232	3	pair	pair	NOUN
ejpam-890	232	4	of	of	ADP
ejpam-890	232	5	adjacent	adjacent	ADJ
ejpam-890	232	6	corners	corner	NOUN
ejpam-890	232	7	corresponding	correspond	VERB
ejpam-890	232	8	to	to	ADP
ejpam-890	232	9	the	the	DET
ejpam-890	232	10	first	first	ADJ
ejpam-890	232	11	row	row	NOUN
ejpam-890	232	12	,	,	PUNCT
ejpam-890	232	13	column	column	NOUN
ejpam-890	232	14	or	or	CCONJ
ejpam-890	232	15	last	last	ADJ
ejpam-890	232	16	row	row	NOUN
ejpam-890	232	17	or	or	CCONJ
ejpam-890	232	18	column	column	NOUN
ejpam-890	232	19	both	both	CCONJ
ejpam-890	232	20	equal	equal	ADJ
ejpam-890	232	21	to	to	ADP
ejpam-890	232	22	zero	zero	NUM
ejpam-890	232	23	,	,	PUNCT
ejpam-890	232	24	then	then	ADV
ejpam-890	232	25	at	at	ADP
ejpam-890	232	26	least	least	ADJ
ejpam-890	232	27	one	one	NUM
ejpam-890	232	28	of	of	ADP
ejpam-890	232	29	the	the	DET
ejpam-890	232	30	entries	entry	NOUN
ejpam-890	232	31	between	between	ADP
ejpam-890	232	32	the	the	DET
ejpam-890	232	33	corners	corner	NOUN
ejpam-890	232	34	must	must	AUX
ejpam-890	232	35	equal	equal	VERB
ejpam-890	232	36	to	to	ADP
ejpam-890	232	37	one	one	NUM
ejpam-890	232	38	.	.	PUNCT
ejpam-890	233	1	as	as	SCONJ
ejpam-890	233	2	argued	argue	VERB
ejpam-890	233	3	in	in	ADP
ejpam-890	233	4	the	the	DET
ejpam-890	233	5	proof	proof	NOUN
ejpam-890	233	6	of	of	ADP
ejpam-890	233	7	theorem	theorem	ADJ
ejpam-890	233	8	3	3	NUM
ejpam-890	233	9	,	,	PUNCT
ejpam-890	233	10	γi	γi	X
ejpam-890	233	11	j(x1	j(x1	NOUN
ejpam-890	233	12	)	)	PUNCT
ejpam-890	233	13	represents	represent	VERB
ejpam-890	233	14	the	the	DET
ejpam-890	233	15	term	term	NOUN
ejpam-890	233	16	that	that	PRON
ejpam-890	233	17	corresponds	correspond	VERB
ejpam-890	233	18	to	to	ADP
ejpam-890	233	19	the	the	DET
ejpam-890	233	20	first	first	ADJ
ejpam-890	233	21	row	row	NOUN
ejpam-890	233	22	.	.	PUNCT
ejpam-890	234	1	similarly	similarly	ADV
ejpam-890	234	2	,	,	PUNCT
ejpam-890	234	3	γkl(x	γkl(x	PROPN
ejpam-890	234	4	p	p	NOUN
ejpam-890	234	5	)	)	PUNCT
ejpam-890	234	6	represents	represent	VERB
ejpam-890	234	7	the	the	DET
ejpam-890	234	8	term	term	NOUN
ejpam-890	234	9	that	that	PRON
ejpam-890	234	10	corresponds	correspond	VERB
ejpam-890	234	11	to	to	ADP
ejpam-890	234	12	the	the	DET
ejpam-890	234	13	last	last	ADJ
ejpam-890	234	14	row	row	NOUN
ejpam-890	234	15	.	.	PUNCT
ejpam-890	235	1	again	again	ADV
ejpam-890	235	2	,	,	PUNCT
ejpam-890	235	3	if	if	SCONJ
ejpam-890	235	4	the	the	DET
ejpam-890	235	5	first	first	ADJ
ejpam-890	235	6	and	and	CCONJ
ejpam-890	235	7	the	the	DET
ejpam-890	235	8	last	last	ADJ
ejpam-890	235	9	entry	entry	NOUN
ejpam-890	235	10	of	of	ADP
ejpam-890	235	11	the	the	DET
ejpam-890	235	12	first	first	ADJ
ejpam-890	235	13	column	column	NOUN
ejpam-890	235	14	both	both	CCONJ
ejpam-890	235	15	equal	equal	ADJ
ejpam-890	235	16	to	to	ADP
ejpam-890	235	17	zero	zero	NUM
ejpam-890	235	18	,	,	PUNCT
ejpam-890	235	19	then	then	ADV
ejpam-890	235	20	the	the	DET
ejpam-890	235	21	term	term	NOUN
ejpam-890	235	22	corresponding	correspond	VERB
ejpam-890	235	23	to	to	ADP
ejpam-890	235	24	the	the	DET
ejpam-890	235	25	matrix	matrix	NOUN
ejpam-890	235	26	has	have	VERB
ejpam-890	235	27	to	to	PART
ejpam-890	235	28	include	include	VERB
ejpam-890	235	29	the	the	DET
ejpam-890	235	30	factor	factor	NOUN
ejpam-890	235	31	−1	−1	NOUN
ejpam-890	235	32	+	+	CCONJ
ejpam-890	235	33	∏p−1	∏p−1	PROPN
ejpam-890	235	34	i=2	i=2	PROPN
ejpam-890	235	35	(	(	PUNCT
ejpam-890	235	36	1+zi	1+zi	NUM
ejpam-890	235	37	)	)	PUNCT
ejpam-890	235	38	since	since	SCONJ
ejpam-890	235	39	at	at	ADV
ejpam-890	235	40	least	least	ADV
ejpam-890	235	41	one	one	NUM
ejpam-890	235	42	of	of	ADP
ejpam-890	235	43	the	the	DET
ejpam-890	235	44	entries	entry	NOUN
ejpam-890	235	45	must	must	AUX
ejpam-890	235	46	equal	equal	VERB
ejpam-890	235	47	to	to	ADP
ejpam-890	235	48	one	one	NUM
ejpam-890	235	49	excluding	exclude	VERB
ejpam-890	235	50	the	the	DET
ejpam-890	235	51	zero	zero	NUM
ejpam-890	235	52	column	column	NOUN
ejpam-890	235	53	.	.	PUNCT
ejpam-890	236	1	in	in	ADP
ejpam-890	236	2	other	other	ADJ
ejpam-890	236	3	cases	case	NOUN
ejpam-890	236	4	,	,	PUNCT
ejpam-890	236	5	∏p−1	∏p−1	PROPN
ejpam-890	236	6	i=2	i=2	PROPN
ejpam-890	236	7	(	(	PUNCT
ejpam-890	236	8	1	1	NUM
ejpam-890	236	9	+	+	NUM
ejpam-890	236	10	zi	zi	NOUN
ejpam-890	236	11	)	)	PUNCT
ejpam-890	236	12	represents	represent	VERB
ejpam-890	236	13	the	the	DET
ejpam-890	236	14	first	first	ADJ
ejpam-890	236	15	column	column	NOUN
ejpam-890	236	16	.	.	PUNCT
ejpam-890	237	1	arguing	argue	VERB
ejpam-890	237	2	similarly	similarly	ADV
ejpam-890	237	3	for	for	ADP
ejpam-890	237	4	the	the	DET
ejpam-890	237	5	last	last	ADJ
ejpam-890	237	6	column	column	NOUN
ejpam-890	237	7	,	,	PUNCT
ejpam-890	237	8	we	we	PRON
ejpam-890	237	9	get	get	VERB
ejpam-890	237	10	the	the	DET
ejpam-890	237	11	result	result	NOUN
ejpam-890	237	12	.	.	PUNCT
ejpam-890	238	1	example	example	NOUN
ejpam-890	238	2	4	4	NUM
ejpam-890	238	3	.	.	PUNCT
ejpam-890	239	1	the	the	DET
ejpam-890	239	2	following	follow	VERB
ejpam-890	239	3	generic	generic	ADJ
ejpam-890	239	4	multivariable	multivariable	ADJ
ejpam-890	239	5	polynomial	polynomial	ADJ
ejpam-890	239	6	g	g	PROPN
ejpam-890	239	7	gives	give	VERB
ejpam-890	239	8	the	the	DET
ejpam-890	239	9	term	term	NOUN
ejpam-890	239	10	representation	representation	NOUN
ejpam-890	239	11	of	of	ADP
ejpam-890	239	12	a∈	a∈	PROPN
ejpam-890	239	13	m3×3(f2	m3×3(f2	PROPN
ejpam-890	239	14	)	)	PUNCT
ejpam-890	239	15	generic	generic	ADJ
ejpam-890	239	16	burst	burst	ADJ
ejpam-890	239	17	errors	error	NOUN
ejpam-890	239	18	of	of	ADP
ejpam-890	239	19	order	order	NOUN
ejpam-890	239	20	3×	3×	NUM
ejpam-890	239	21	3	3	NUM
ejpam-890	239	22	:	:	PUNCT
ejpam-890	239	23	g(z̃	g(z̃	NOUN
ejpam-890	239	24	,	,	PUNCT
ejpam-890	239	25	x̃	x̃	PROPN
ejpam-890	239	26	,	,	PUNCT
ejpam-890	239	27	x̃	x̃	PROPN
ejpam-890	239	28	,	,	PUNCT
ejpam-890	239	29	ỹ	ỹ	PROPN
ejpam-890	239	30	)	)	PUNCT
ejpam-890	239	31	=	=	PUNCT
ejpam-890	240	1	∑	∑	PUNCT
ejpam-890	240	2	(	(	PUNCT
ejpam-890	240	3	i	i	PROPN
ejpam-890	240	4	,	,	PUNCT
ejpam-890	240	5	j	j	PROPN
ejpam-890	240	6	,	,	PUNCT
ejpam-890	240	7	k	k	PROPN
ejpam-890	240	8	,	,	PUNCT
ejpam-890	240	9	l)∈{0,1}4	l)∈{0,1}4	NOUN
ejpam-890	241	1	z	z	NOUN
ejpam-890	241	2	i	i	VERB
ejpam-890	241	3	1	1	NUM
ejpam-890	241	4	y	y	PROPN
ejpam-890	241	5	j	j	PROPN
ejpam-890	241	6	1	1	NUM
ejpam-890	241	7	x	x	SYM
ejpam-890	241	8	k	k	PROPN
ejpam-890	241	9	3	3	NUM
ejpam-890	241	10	y	y	NOUN
ejpam-890	241	11	l	l	NOUN
ejpam-890	241	12	3y	3y	NUM
ejpam-890	241	13	jl(α)γi	jl(α)γi	NOUN
ejpam-890	241	14	j(x1)γkl(x3	j(x1)γkl(x3	X
ejpam-890	241	15	)	)	PUNCT
ejpam-890	241	16	.	.	PUNCT
ejpam-890	242	1	now	now	ADV
ejpam-890	242	2	,	,	PUNCT
ejpam-890	242	3	we	we	PRON
ejpam-890	242	4	shall	shall	AUX
ejpam-890	242	5	make	make	VERB
ejpam-890	242	6	use	use	NOUN
ejpam-890	242	7	of	of	ADP
ejpam-890	242	8	generic	generic	ADJ
ejpam-890	242	9	burst	burst	ADJ
ejpam-890	242	10	errors	error	NOUN
ejpam-890	242	11	to	to	PART
ejpam-890	242	12	determine	determine	VERB
ejpam-890	242	13	all	all	DET
ejpam-890	242	14	burst	burst	ADJ
ejpam-890	242	15	errors	error	NOUN
ejpam-890	242	16	especially	especially	ADV
ejpam-890	242	17	the	the	DET
ejpam-890	242	18	number	number	NOUN
ejpam-890	242	19	of	of	ADP
ejpam-890	242	20	burst	burst	ADJ
ejpam-890	242	21	errors	error	NOUN
ejpam-890	242	22	.	.	PUNCT
ejpam-890	243	1	first	first	ADV
ejpam-890	243	2	,	,	PUNCT
ejpam-890	243	3	we	we	PRON
ejpam-890	243	4	introduce	introduce	VERB
ejpam-890	243	5	a	a	DET
ejpam-890	243	6	relation	relation	NOUN
ejpam-890	243	7	on	on	ADP
ejpam-890	243	8	burst	burst	ADJ
ejpam-890	243	9	errors	error	NOUN
ejpam-890	243	10	that	that	PRON
ejpam-890	243	11	is	be	AUX
ejpam-890	243	12	based	base	VERB
ejpam-890	243	13	on	on	ADP
ejpam-890	243	14	the	the	DET
ejpam-890	243	15	frames	frame	NOUN
ejpam-890	243	16	of	of	ADP
ejpam-890	243	17	matrices	matrix	NOUN
ejpam-890	243	18	.	.	PUNCT
ejpam-890	244	1	definition	definition	NOUN
ejpam-890	244	2	8	8	NUM
ejpam-890	244	3	.	.	PUNCT
ejpam-890	245	1	let	let	VERB
ejpam-890	245	2	b	b	X
ejpam-890	245	3	be	be	AUX
ejpam-890	245	4	the	the	DET
ejpam-890	245	5	set	set	NOUN
ejpam-890	245	6	of	of	ADP
ejpam-890	245	7	all	all	DET
ejpam-890	245	8	burst	burst	ADJ
ejpam-890	245	9	errors	error	NOUN
ejpam-890	245	10	of	of	ADP
ejpam-890	245	11	order	order	NOUN
ejpam-890	245	12	p×	p×	PROPN
ejpam-890	245	13	r.	r.	PROPN
ejpam-890	245	14	let	let	VERB
ejpam-890	245	15	a	a	DET
ejpam-890	245	16	,	,	PUNCT
ejpam-890	245	17	b	b	PROPN
ejpam-890	245	18	∈	∈	PROPN
ejpam-890	245	19	b⊂	b⊂	PROPN
ejpam-890	245	20	mp×r(r	mp×r(r	NOUN
ejpam-890	245	21	)	)	PUNCT
ejpam-890	245	22	.	.	PUNCT
ejpam-890	246	1	it	it	PRON
ejpam-890	246	2	is	be	AUX
ejpam-890	246	3	said	say	VERB
ejpam-890	246	4	that	that	SCONJ
ejpam-890	246	5	the	the	DET
ejpam-890	246	6	matrix	matrix	NOUN
ejpam-890	246	7	a	a	NOUN
ejpam-890	246	8	is	be	AUX
ejpam-890	246	9	related	relate	VERB
ejpam-890	246	10	to	to	ADP
ejpam-890	246	11	the	the	DET
ejpam-890	246	12	matrix	matrix	NOUN
ejpam-890	246	13	b	b	NOUN
ejpam-890	246	14	,	,	PUNCT
ejpam-890	246	15	i.e	i.e	X
ejpam-890	246	16	at	at	ADP
ejpam-890	246	17	b	b	NOUN
ejpam-890	246	18	,	,	PUNCT
ejpam-890	246	19	in	in	ADP
ejpam-890	246	20	the	the	DET
ejpam-890	246	21	set	set	NOUN
ejpam-890	246	22	b	b	NOUN
ejpam-890	246	23	if	if	SCONJ
ejpam-890	247	1	and	and	CCONJ
ejpam-890	247	2	only	only	ADV
ejpam-890	247	3	if	if	SCONJ
ejpam-890	247	4	µ(a	µ(a	PROPN
ejpam-890	247	5	j	j	PROPN
ejpam-890	247	6	)	)	PUNCT
ejpam-890	247	7	=	=	PUNCT
ejpam-890	248	1	µ(b	µ(b	PROPN
ejpam-890	248	2	j	j	PROPN
ejpam-890	248	3	)	)	PUNCT
ejpam-890	248	4	for	for	ADP
ejpam-890	248	5	j	j	PROPN
ejpam-890	248	6	=	=	SYM
ejpam-890	248	7	1	1	NUM
ejpam-890	248	8	,	,	PUNCT
ejpam-890	248	9	p	p	NOUN
ejpam-890	248	10	and	and	CCONJ
ejpam-890	248	11	µ(a	µ(a	PROPN
ejpam-890	248	12	j)|x	j)|x	NOUN
ejpam-890	248	13	j	j	NOUN
ejpam-890	248	14	=	=	NOUN
ejpam-890	248	15	x	x	NOUN
ejpam-890	248	16	j=1	j=1	NOUN
ejpam-890	248	17	=	=	PUNCT
ejpam-890	248	18	µ(b	µ(b	PROPN
ejpam-890	248	19	j)|x	j)|x	VERB
ejpam-890	248	20	j	j	NOUN
ejpam-890	248	21	=	=	NOUN
ejpam-890	248	22	x	x	SYM
ejpam-890	248	23	j=1	j=1	PROPN
ejpam-890	248	24	for	for	ADP
ejpam-890	248	25	j	j	PROPN
ejpam-890	248	26	6=	6=	PROPN
ejpam-890	248	27	1	1	NUM
ejpam-890	248	28	,	,	PUNCT
ejpam-890	248	29	p.	p.	NOUN
ejpam-890	248	30	the	the	DET
ejpam-890	248	31	proof	proof	NOUN
ejpam-890	248	32	of	of	ADP
ejpam-890	248	33	the	the	DET
ejpam-890	248	34	following	follow	VERB
ejpam-890	248	35	lemma	lemma	PROPN
ejpam-890	248	36	follows	follow	VERB
ejpam-890	248	37	from	from	ADP
ejpam-890	248	38	the	the	DET
ejpam-890	248	39	definitions	definition	NOUN
ejpam-890	248	40	.	.	PUNCT
ejpam-890	249	1	lemma	lemma	PROPN
ejpam-890	249	2	1	1	NUM
ejpam-890	249	3	.	.	PUNCT
ejpam-890	250	1	the	the	DET
ejpam-890	250	2	relation	relation	NOUN
ejpam-890	250	3	“	"	PUNCT
ejpam-890	250	4	≈	≈	PROPN
ejpam-890	250	5	”	"	PUNCT
ejpam-890	250	6	defined	define	VERB
ejpam-890	250	7	on	on	ADP
ejpam-890	250	8	the	the	DET
ejpam-890	250	9	set	set	PROPN
ejpam-890	250	10	b	b	PROPN
ejpam-890	250	11	is	be	AUX
ejpam-890	250	12	an	an	DET
ejpam-890	250	13	equivalence	equivalence	NOUN
ejpam-890	250	14	relation	relation	NOUN
ejpam-890	250	15	.	.	PUNCT
ejpam-890	251	1	now	now	ADV
ejpam-890	251	2	we	we	PRON
ejpam-890	251	3	have	have	VERB
ejpam-890	251	4	a	a	DET
ejpam-890	251	5	partition	partition	NOUN
ejpam-890	251	6	of	of	ADP
ejpam-890	251	7	the	the	DET
ejpam-890	251	8	space	space	NOUN
ejpam-890	251	9	of	of	ADP
ejpam-890	251	10	burst	burst	ADJ
ejpam-890	251	11	errors	error	NOUN
ejpam-890	251	12	into	into	ADP
ejpam-890	251	13	disjoint	disjoint	NOUN
ejpam-890	251	14	classes	class	NOUN
ejpam-890	251	15	which	which	PRON
ejpam-890	251	16	are	be	AUX
ejpam-890	251	17	generic	generic	ADJ
ejpam-890	251	18	burst	burst	ADJ
ejpam-890	251	19	errors	error	NOUN
ejpam-890	251	20	.	.	PUNCT
ejpam-890	252	1	let	let	VERB
ejpam-890	252	2	ca	can	AUX
ejpam-890	252	3	represent	represent	VERB
ejpam-890	252	4	the	the	DET
ejpam-890	252	5	set	set	NOUN
ejpam-890	252	6	of	of	ADP
ejpam-890	252	7	equivalence	equivalence	NOUN
ejpam-890	252	8	class	class	NOUN
ejpam-890	252	9	of	of	ADP
ejpam-890	252	10	matrix	matrix	NOUN
ejpam-890	252	11	a.	a.	NOUN
ejpam-890	252	12	we	we	PRON
ejpam-890	252	13	determine	determine	VERB
ejpam-890	252	14	the	the	DET
ejpam-890	252	15	representative	representative	NOUN
ejpam-890	252	16	set	set	NOUN
ejpam-890	252	17	ca	ca	NOUN
ejpam-890	252	18	in	in	ADP
ejpam-890	252	19	the	the	DET
ejpam-890	252	20	following	following	ADJ
ejpam-890	252	21	way	way	NOUN
ejpam-890	252	22	:	:	PUNCT
ejpam-890	252	23	let	let	VERB
ejpam-890	252	24	a1	a1	NOUN
ejpam-890	252	25	be	be	AUX
ejpam-890	252	26	the	the	DET
ejpam-890	252	27	first	first	ADJ
ejpam-890	252	28	row	row	NOUN
ejpam-890	252	29	of	of	ADP
ejpam-890	252	30	a	a	DET
ejpam-890	252	31	generic	generic	ADJ
ejpam-890	252	32	burst	burst	NOUN
ejpam-890	252	33	error	error	NOUN
ejpam-890	252	34	matrix	matrix	NOUN
ejpam-890	252	35	a.	a.	NOUN
ejpam-890	252	36	if	if	SCONJ
ejpam-890	252	37	the	the	DET
ejpam-890	252	38	weight	weight	NOUN
ejpam-890	252	39	of	of	ADP
ejpam-890	252	40	the	the	DET
ejpam-890	252	41	row	row	NOUN
ejpam-890	252	42	is	be	AUX
ejpam-890	252	43	two	two	NUM
ejpam-890	252	44	(	(	PUNCT
ejpam-890	252	45	the	the	DET
ejpam-890	252	46	term	term	NOUN
ejpam-890	252	47	consists	consist	VERB
ejpam-890	252	48	of	of	ADP
ejpam-890	252	49	z1	z1	ADJ
ejpam-890	252	50	y1	y1	NOUN
ejpam-890	252	51	,	,	PUNCT
ejpam-890	252	52	z1x	z1x	PROPN
ejpam-890	252	53	l1	l1	PROPN
ejpam-890	252	54	1	1	NUM
ejpam-890	252	55	,	,	PUNCT
ejpam-890	252	56	x	x	SYM
ejpam-890	252	57	k1	k1	NOUN
ejpam-890	252	58	1	1	NUM
ejpam-890	252	59	x	x	SYM
ejpam-890	252	60	l1	l1	PROPN
ejpam-890	252	61	1	1	NUM
ejpam-890	252	62	or	or	CCONJ
ejpam-890	252	63	x	x	ADJ
ejpam-890	252	64	k1	k1	PROPN
ejpam-890	252	65	1	1	NUM
ejpam-890	252	66	y1	y1	NOUN
ejpam-890	252	67	)	)	PUNCT
ejpam-890	252	68	,	,	PUNCT
ejpam-890	252	69	then	then	ADV
ejpam-890	252	70	these	these	DET
ejpam-890	252	71	two	two	NUM
ejpam-890	252	72	entries	entry	NOUN
ejpam-890	252	73	are	be	AUX
ejpam-890	252	74	nonzero	nonzero	NOUN
ejpam-890	252	75	and	and	CCONJ
ejpam-890	252	76	the	the	DET
ejpam-890	252	77	choices	choice	NOUN
ejpam-890	252	78	for	for	ADP
ejpam-890	252	79	the	the	DET
ejpam-890	252	80	entries	entry	NOUN
ejpam-890	252	81	in	in	ADP
ejpam-890	252	82	between	between	ADP
ejpam-890	252	83	run	run	NOUN
ejpam-890	252	84	through	through	ADP
ejpam-890	252	85	all	all	DET
ejpam-890	252	86	nonzero	nonzero	ADJ
ejpam-890	252	87	elements	element	NOUN
ejpam-890	252	88	of	of	ADP
ejpam-890	252	89	the	the	DET
ejpam-890	252	90	ring	ring	NOUN
ejpam-890	252	91	r.	r.	PROPN
ejpam-890	252	92	if	if	SCONJ
ejpam-890	252	93	the	the	DET
ejpam-890	252	94	weight	weight	NOUN
ejpam-890	252	95	is	be	AUX
ejpam-890	252	96	equal	equal	ADJ
ejpam-890	252	97	to	to	ADP
ejpam-890	252	98	one	one	NUM
ejpam-890	252	99	(	(	PUNCT
ejpam-890	252	100	the	the	DET
ejpam-890	252	101	term	term	NOUN
ejpam-890	252	102	consists	consist	VERB
ejpam-890	252	103	of	of	ADP
ejpam-890	252	104	y1	y1	NOUN
ejpam-890	252	105	,	,	PUNCT
ejpam-890	252	106	z1	z1	NOUN
ejpam-890	252	107	or	or	CCONJ
ejpam-890	252	108	x	x	ADJ
ejpam-890	252	109	k1	k1	PROPN
ejpam-890	252	110	1	1	NUM
ejpam-890	252	111	only	only	ADV
ejpam-890	252	112	)	)	PUNCT
ejpam-890	252	113	,	,	PUNCT
ejpam-890	252	114	then	then	ADV
ejpam-890	252	115	a	a	DET
ejpam-890	252	116	nonzero	nonzero	ADJ
ejpam-890	252	117	choice	choice	NOUN
ejpam-890	252	118	for	for	ADP
ejpam-890	252	119	this	this	DET
ejpam-890	252	120	entry	entry	NOUN
ejpam-890	252	121	from	from	ADP
ejpam-890	252	122	r\{0	r\{0	PROPN
ejpam-890	252	123	}	}	PUNCT
ejpam-890	252	124	.	.	PUNCT
ejpam-890	253	1	in	in	ADP
ejpam-890	253	2	a	a	DET
ejpam-890	253	3	similar	similar	ADJ
ejpam-890	253	4	way	way	NOUN
ejpam-890	253	5	we	we	PRON
ejpam-890	253	6	can	can	AUX
ejpam-890	253	7	argue	argue	VERB
ejpam-890	253	8	for	for	ADP
ejpam-890	253	9	the	the	DET
ejpam-890	253	10	last	last	ADJ
ejpam-890	253	11	row	row	NOUN
ejpam-890	253	12	of	of	ADP
ejpam-890	253	13	the	the	DET
ejpam-890	253	14	matrix	matrix	NOUN
ejpam-890	253	15	.	.	PUNCT
ejpam-890	254	1	also	also	ADV
ejpam-890	254	2	we	we	PRON
ejpam-890	254	3	note	note	VERB
ejpam-890	254	4	that	that	SCONJ
ejpam-890	254	5	the	the	DET
ejpam-890	254	6	entries	entry	NOUN
ejpam-890	254	7	that	that	PRON
ejpam-890	254	8	fall	fall	VERB
ejpam-890	254	9	out	out	ADP
ejpam-890	254	10	off	off	ADP
ejpam-890	254	11	the	the	DET
ejpam-890	254	12	frame	frame	NOUN
ejpam-890	254	13	can	can	AUX
ejpam-890	254	14	take	take	VERB
ejpam-890	254	15	any	any	DET
ejpam-890	254	16	value	value	NOUN
ejpam-890	254	17	without	without	ADP
ejpam-890	254	18	any	any	DET
ejpam-890	254	19	restriction	restriction	NOUN
ejpam-890	254	20	.	.	PUNCT
ejpam-890	255	1	i̇.	i̇.	PROPN
ejpam-890	255	2	siap	siap	PROPN
ejpam-890	255	3	/	/	SYM
ejpam-890	255	4	eur	eur	PROPN
ejpam-890	255	5	.	.	PUNCT
ejpam-890	256	1	j.	j.	PROPN
ejpam-890	256	2	pure	pure	PROPN
ejpam-890	256	3	appl	appl	PROPN
ejpam-890	256	4	.	.	PROPN
ejpam-890	256	5	math	math	PROPN
ejpam-890	256	6	,	,	PUNCT
ejpam-890	256	7	3	3	NUM
ejpam-890	256	8	(	(	PUNCT
ejpam-890	256	9	2010	2010	NUM
ejpam-890	256	10	)	)	PUNCT
ejpam-890	256	11	,	,	PUNCT
ejpam-890	256	12	653	653	NUM
ejpam-890	256	13	-	-	SYM
ejpam-890	256	14	669	669	NUM
ejpam-890	256	15	662	662	NUM
ejpam-890	256	16	now	now	ADV
ejpam-890	256	17	we	we	PRON
ejpam-890	256	18	use	use	VERB
ejpam-890	256	19	generic	generic	ADJ
ejpam-890	256	20	burst	burst	NOUN
ejpam-890	256	21	error	error	NOUN
ejpam-890	256	22	matrices	matrix	NOUN
ejpam-890	256	23	in	in	ADP
ejpam-890	256	24	example	example	NOUN
ejpam-890	256	25	3	3	NUM
ejpam-890	256	26	,	,	PUNCT
ejpam-890	256	27	to	to	PART
ejpam-890	256	28	find	find	VERB
ejpam-890	256	29	all	all	DET
ejpam-890	256	30	burst	burst	ADJ
ejpam-890	256	31	errors	error	NOUN
ejpam-890	256	32	of	of	ADP
ejpam-890	256	33	size	size	NOUN
ejpam-890	256	34	2×3	2×3	NOUN
ejpam-890	256	35	over	over	ADP
ejpam-890	256	36	f2	f2	PROPN
ejpam-890	256	37	.	.	PUNCT
ejpam-890	257	1	we	we	PRON
ejpam-890	257	2	list	list	VERB
ejpam-890	257	3	the	the	DET
ejpam-890	257	4	equivalency	equivalency	NOUN
ejpam-890	257	5	classes	class	NOUN
ejpam-890	257	6	with	with	ADP
ejpam-890	257	7	respect	respect	NOUN
ejpam-890	257	8	to	to	ADP
ejpam-890	257	9	the	the	DET
ejpam-890	257	10	relation	relation	NOUN
ejpam-890	257	11	:	:	PUNCT
ejpam-890	257	12	¨	¨	NOUN
ejpam-890	257	13	�	�	PROPN
ejpam-890	257	14	1	1	NUM
ejpam-890	257	15	0	0	NUM
ejpam-890	257	16	1	1	NUM
ejpam-890	257	17	0	0	NUM
ejpam-890	257	18	1	1	NUM
ejpam-890	257	19	0	0	NUM
ejpam-890	257	20	�	�	PROPN
ejpam-890	257	21	,	,	PUNCT
ejpam-890	257	22	�	�	PROPN
ejpam-890	257	23	1	1	NUM
ejpam-890	257	24	1	1	NUM
ejpam-890	257	25	1	1	NUM
ejpam-890	257	26	0	0	NUM
ejpam-890	257	27	1	1	NUM
ejpam-890	257	28	0	0	NUM
ejpam-890	257	29	�	�	PROPN
ejpam-890	257	30	«	«	PUNCT
ejpam-890	257	31	,	,	PUNCT
ejpam-890	257	32	¨	¨	NOUN
ejpam-890	257	33	�	�	NOUN
ejpam-890	257	34	0	0	NUM
ejpam-890	257	35	1	1	NUM
ejpam-890	257	36	0	0	NUM
ejpam-890	257	37	1	1	NUM
ejpam-890	257	38	0	0	NUM
ejpam-890	257	39	1	1	NUM
ejpam-890	257	40	�	�	PROPN
ejpam-890	257	41	,	,	PUNCT
ejpam-890	257	42	�	�	PROPN
ejpam-890	257	43	0	0	NUM
ejpam-890	257	44	1	1	NUM
ejpam-890	257	45	0	0	NUM
ejpam-890	257	46	1	1	NUM
ejpam-890	257	47	1	1	NUM
ejpam-890	257	48	1	1	NUM
ejpam-890	257	49	�	�	PROPN
ejpam-890	257	50	«	«	PUNCT
ejpam-890	257	51	,	,	PUNCT
ejpam-890	257	52	¨	¨	NOUN
ejpam-890	257	53	�	�	PROPN
ejpam-890	257	54	1	1	NUM
ejpam-890	257	55	0	0	NUM
ejpam-890	257	56	0	0	NUM
ejpam-890	257	57	0	0	NUM
ejpam-890	257	58	0	0	NUM
ejpam-890	257	59	1	1	NUM
ejpam-890	257	60	�	�	PROPN
ejpam-890	257	61	«	«	PUNCT
ejpam-890	257	62	,	,	PUNCT
ejpam-890	257	63	¨	¨	NOUN
ejpam-890	257	64	�	�	PROPN
ejpam-890	257	65	1	1	NUM
ejpam-890	257	66	0	0	NUM
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ejpam-890	257	68	0	0	NUM
ejpam-890	257	69	1	1	NUM
ejpam-890	257	70	1	1	NUM
ejpam-890	257	71	�	�	PROPN
ejpam-890	257	72	«	«	PUNCT
ejpam-890	257	73	,	,	PUNCT
ejpam-890	257	74	¨	¨	NOUN
ejpam-890	257	75	�	�	PROPN
ejpam-890	257	76	1	1	NUM
ejpam-890	257	77	1	1	NUM
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ejpam-890	257	80	0	0	NUM
ejpam-890	257	81	1	1	NUM
ejpam-890	257	82	�	�	PROPN
ejpam-890	257	83	«	«	PUNCT
ejpam-890	257	84	,	,	PUNCT
ejpam-890	257	85	¨	¨	NOUN
ejpam-890	257	86	�	�	PROPN
ejpam-890	257	87	1	1	NUM
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ejpam-890	257	91	1	1	NUM
ejpam-890	257	92	1	1	NUM
ejpam-890	257	93	�	�	PROPN
ejpam-890	257	94	«	«	PUNCT
ejpam-890	257	95	,	,	PUNCT
ejpam-890	257	96	¨	¨	NOUN
ejpam-890	257	97	�	�	PROPN
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ejpam-890	257	100	1	1	NUM
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ejpam-890	257	103	0	0	NUM
ejpam-890	257	104	�	�	PROPN
ejpam-890	257	105	«	«	PUNCT
ejpam-890	257	106	,	,	PUNCT
ejpam-890	257	107	¨	¨	NOUN
ejpam-890	257	108	�	�	PROPN
ejpam-890	257	109	0	0	NUM
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ejpam-890	257	111	1	1	NUM
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ejpam-890	257	113	1	1	NUM
ejpam-890	257	114	0	0	NUM
ejpam-890	257	115	�	�	PROPN
ejpam-890	257	116	«	«	PUNCT
ejpam-890	257	117	,	,	PUNCT
ejpam-890	257	118	¨	¨	NOUN
ejpam-890	257	119	�	�	NOUN
ejpam-890	257	120	0	0	NUM
ejpam-890	257	121	1	1	NUM
ejpam-890	257	122	1	1	NUM
ejpam-890	257	123	1	1	NUM
ejpam-890	257	124	0	0	NUM
ejpam-890	257	125	0	0	NUM
ejpam-890	257	126	�	�	PROPN
ejpam-890	257	127	«	«	PUNCT
ejpam-890	257	128	,	,	PUNCT
ejpam-890	257	129	¨	¨	NOUN
ejpam-890	257	130	�	�	NOUN
ejpam-890	257	131	0	0	NUM
ejpam-890	257	132	1	1	NUM
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ejpam-890	257	134	1	1	NUM
ejpam-890	257	135	1	1	NUM
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ejpam-890	257	137	�	�	PROPN
ejpam-890	257	138	«	«	PUNCT
ejpam-890	257	139	,	,	PUNCT
ejpam-890	257	140	¨	¨	NOUN
ejpam-890	257	141	�	�	PROPN
ejpam-890	257	142	1	1	NUM
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ejpam-890	257	147	1	1	NUM
ejpam-890	257	148	�	�	PROPN
ejpam-890	257	149	,	,	PUNCT
ejpam-890	257	150	�	�	PROPN
ejpam-890	257	151	1	1	NUM
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ejpam-890	257	153	1	1	NUM
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ejpam-890	257	156	1	1	NUM
ejpam-890	257	157	�	�	PROPN
ejpam-890	257	158	«	«	PUNCT
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ejpam-890	257	160	¨	¨	NOUN
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ejpam-890	257	162	1	1	NUM
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ejpam-890	257	168	�	�	PROPN
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ejpam-890	257	177	�	�	PROPN
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ejpam-890	257	179	,	,	PUNCT
ejpam-890	257	180	¨	¨	NOUN
ejpam-890	257	181	�	�	PROPN
ejpam-890	257	182	0	0	NUM
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ejpam-890	257	188	�	�	PROPN
ejpam-890	257	189	,	,	PUNCT
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ejpam-890	257	196	1	1	NUM
ejpam-890	257	197	�	�	PROPN
ejpam-890	257	198	«	«	PUNCT
ejpam-890	257	199	,	,	PUNCT
ejpam-890	257	200	¨	¨	NOUN
ejpam-890	257	201	�	�	NOUN
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ejpam-890	257	207	1	1	NUM
ejpam-890	257	208	�	�	PROPN
ejpam-890	257	209	,	,	PUNCT
ejpam-890	257	210	�	�	PROPN
ejpam-890	257	211	0	0	NUM
ejpam-890	257	212	1	1	NUM
ejpam-890	257	213	1	1	NUM
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ejpam-890	257	215	1	1	NUM
ejpam-890	257	216	1	1	NUM
ejpam-890	257	217	�	�	PROPN
ejpam-890	257	218	«	«	PUNCT
ejpam-890	257	219	,	,	PUNCT
ejpam-890	257	220	¨	¨	NOUN
ejpam-890	257	221	�	�	PROPN
ejpam-890	257	222	1	1	NUM
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ejpam-890	257	224	1	1	NUM
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ejpam-890	257	227	0	0	NUM
ejpam-890	257	228	�	�	PROPN
ejpam-890	257	229	,	,	PUNCT
ejpam-890	257	230	�	�	PROPN
ejpam-890	257	231	1	1	NUM
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ejpam-890	257	233	1	1	NUM
ejpam-890	257	234	1	1	NUM
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ejpam-890	257	236	0	0	NUM
ejpam-890	257	237	�	�	PROPN
ejpam-890	257	238	«	«	PUNCT
ejpam-890	257	239	,	,	PUNCT
ejpam-890	257	240	¨	¨	NOUN
ejpam-890	257	241	�	�	PROPN
ejpam-890	257	242	1	1	NUM
ejpam-890	257	243	0	0	NUM
ejpam-890	257	244	1	1	NUM
ejpam-890	257	245	1	1	NUM
ejpam-890	257	246	1	1	NUM
ejpam-890	257	247	0	0	NUM
ejpam-890	257	248	�	�	PROPN
ejpam-890	257	249	,	,	PUNCT
ejpam-890	257	250	�	�	PROPN
ejpam-890	257	251	1	1	NUM
ejpam-890	257	252	1	1	NUM
ejpam-890	257	253	1	1	NUM
ejpam-890	257	254	1	1	NUM
ejpam-890	257	255	1	1	NUM
ejpam-890	257	256	0	0	NUM
ejpam-890	257	257	�	�	PROPN
ejpam-890	257	258	«	«	PUNCT
ejpam-890	257	259	,	,	PUNCT
ejpam-890	257	260	¨	¨	NOUN
ejpam-890	257	261	�	�	PROPN
ejpam-890	257	262	1	1	NUM
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ejpam-890	257	265	1	1	NUM
ejpam-890	257	266	0	0	NUM
ejpam-890	257	267	1	1	NUM
ejpam-890	257	268	�	�	PROPN
ejpam-890	257	269	,	,	PUNCT
ejpam-890	257	270	�	�	PROPN
ejpam-890	257	271	1	1	NUM
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ejpam-890	257	274	1	1	NUM
ejpam-890	257	275	1	1	NUM
ejpam-890	257	276	1	1	NUM
ejpam-890	257	277	�	�	PROPN
ejpam-890	257	278	«	«	PUNCT
ejpam-890	257	279	,	,	PUNCT
ejpam-890	257	280	¨	¨	NOUN
ejpam-890	257	281	�	�	PROPN
ejpam-890	257	282	1	1	NUM
ejpam-890	257	283	1	1	NUM
ejpam-890	257	284	0	0	NUM
ejpam-890	257	285	1	1	NUM
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ejpam-890	257	287	1	1	NUM
ejpam-890	257	288	�	�	PROPN
ejpam-890	257	289	,	,	PUNCT
ejpam-890	257	290	�	�	PROPN
ejpam-890	257	291	1	1	NUM
ejpam-890	257	292	1	1	NUM
ejpam-890	257	293	0	0	NUM
ejpam-890	257	294	1	1	NUM
ejpam-890	257	295	1	1	NUM
ejpam-890	257	296	1	1	NUM
ejpam-890	257	297	�	�	PROPN
ejpam-890	257	298	«	«	PUNCT
ejpam-890	257	299	,	,	PUNCT
ejpam-890	257	300	¨	¨	NOUN
ejpam-890	257	301	�	�	PROPN
ejpam-890	257	302	1	1	NUM
ejpam-890	257	303	0	0	NUM
ejpam-890	257	304	1	1	NUM
ejpam-890	257	305	1	1	NUM
ejpam-890	257	306	0	0	NUM
ejpam-890	257	307	1	1	NUM
ejpam-890	257	308	�	�	PROPN
ejpam-890	257	309	,	,	PUNCT
ejpam-890	257	310	�	�	PROPN
ejpam-890	257	311	1	1	NUM
ejpam-890	257	312	1	1	NUM
ejpam-890	257	313	1	1	NUM
ejpam-890	257	314	1	1	NUM
ejpam-890	257	315	0	0	NUM
ejpam-890	257	316	1	1	NUM
ejpam-890	257	317	�	�	PROPN
ejpam-890	257	318	,	,	PUNCT
ejpam-890	257	319	�	�	PROPN
ejpam-890	257	320	1	1	NUM
ejpam-890	257	321	0	0	NUM
ejpam-890	257	322	1	1	NUM
ejpam-890	257	323	1	1	NUM
ejpam-890	257	324	1	1	NUM
ejpam-890	257	325	1	1	NUM
ejpam-890	257	326	�	�	PROPN
ejpam-890	257	327	,	,	PUNCT
ejpam-890	257	328	�	�	PROPN
ejpam-890	257	329	1	1	NUM
ejpam-890	257	330	1	1	NUM
ejpam-890	257	331	1	1	NUM
ejpam-890	257	332	1	1	NUM
ejpam-890	257	333	1	1	NUM
ejpam-890	257	334	1	1	NUM
ejpam-890	257	335	�	�	NOUN
ejpam-890	257	336	«	«	PUNCT
ejpam-890	257	337	.	.	PUNCT
ejpam-890	258	1	the	the	DET
ejpam-890	258	2	sets	set	NOUN
ejpam-890	258	3	are	be	AUX
ejpam-890	258	4	classes	class	NOUN
ejpam-890	258	5	that	that	PRON
ejpam-890	258	6	correspond	correspond	VERB
ejpam-890	258	7	to	to	ADP
ejpam-890	258	8	a	a	DET
ejpam-890	258	9	generic	generic	ADJ
ejpam-890	258	10	burst	burst	NOUN
ejpam-890	258	11	error	error	NOUN
ejpam-890	258	12	.	.	PUNCT
ejpam-890	259	1	altogether	altogether	ADV
ejpam-890	259	2	,	,	PUNCT
ejpam-890	259	3	they	they	PRON
ejpam-890	259	4	add	add	VERB
ejpam-890	259	5	up	up	ADP
ejpam-890	259	6	to	to	PART
ejpam-890	259	7	32	32	NUM
ejpam-890	259	8	burst	burst	ADJ
ejpam-890	259	9	errors	error	NOUN
ejpam-890	259	10	of	of	ADP
ejpam-890	259	11	order	order	NOUN
ejpam-890	259	12	2×	2×	NUM
ejpam-890	259	13	3	3	NUM
ejpam-890	259	14	over	over	ADP
ejpam-890	259	15	f2	f2	PROPN
ejpam-890	259	16	.	.	PUNCT
ejpam-890	260	1	if	if	SCONJ
ejpam-890	260	2	we	we	PRON
ejpam-890	260	3	were	be	AUX
ejpam-890	260	4	working	work	VERB
ejpam-890	260	5	over	over	ADP
ejpam-890	260	6	the	the	DET
ejpam-890	260	7	field	field	NOUN
ejpam-890	260	8	f3	f3	NOUN
ejpam-890	260	9	,	,	PUNCT
ejpam-890	260	10	then	then	ADV
ejpam-890	260	11	,	,	PUNCT
ejpam-890	260	12	for	for	ADP
ejpam-890	260	13	example	example	NOUN
ejpam-890	260	14	,	,	PUNCT
ejpam-890	260	15	the	the	DET
ejpam-890	260	16	generic	generic	ADJ
ejpam-890	260	17	burst	burst	NOUN
ejpam-890	260	18	error	error	NOUN
ejpam-890	260	19	class	class	NOUN
ejpam-890	260	20	that	that	PRON
ejpam-890	260	21	correspond	correspond	VERB
ejpam-890	260	22	to	to	ADP
ejpam-890	260	23	the	the	DET
ejpam-890	260	24	generic	generic	ADJ
ejpam-890	260	25	matrix	matrix	NOUN
ejpam-890	260	26	z	z	NOUN
ejpam-890	260	27	=	=	SYM
ejpam-890	260	28	�	�	PROPN
ejpam-890	260	29	1	1	NUM
ejpam-890	260	30	0	0	NUM
ejpam-890	260	31	1	1	NUM
ejpam-890	260	32	0	0	NUM
ejpam-890	260	33	1	1	NUM
ejpam-890	260	34	0	0	NUM
ejpam-890	260	35	�	�	PROPN
ejpam-890	260	36	would	would	AUX
ejpam-890	260	37	be	be	AUX
ejpam-890	260	38	;	;	PUNCT
ejpam-890	260	39	cz	cz	NOUN
ejpam-890	260	40	=	=	PUNCT
ejpam-890	260	41	¨	¨	NOUN
ejpam-890	260	42	�	�	PROPN
ejpam-890	260	43	a	a	PRON
ejpam-890	260	44	b	b	NOUN
ejpam-890	260	45	c	c	NOUN
ejpam-890	260	46	0	0	PUNCT
ejpam-890	260	47	d	d	NOUN
ejpam-890	260	48	0	0	NUM
ejpam-890	260	49	�	�	PROPN
ejpam-890	260	50	|a	|a	NOUN
ejpam-890	260	51	,	,	PUNCT
ejpam-890	260	52	c	c	X
ejpam-890	260	53	,	,	PUNCT
ejpam-890	260	54	d	d	PROPN
ejpam-890	260	55	∈	∈	PROPN
ejpam-890	260	56	f3\{0	f3\{0	PROPN
ejpam-890	260	57	}	}	PUNCT
ejpam-890	260	58	and	and	CCONJ
ejpam-890	260	59	b	b	PROPN
ejpam-890	260	60	∈	∈	PROPN
ejpam-890	260	61	f3	f3	NOUN
ejpam-890	260	62	«	«	PUNCT
ejpam-890	260	63	and	and	CCONJ
ejpam-890	261	1	|cz	|cz	X
ejpam-890	261	2	|	|	ADV
ejpam-890	261	3	=	=	SYM
ejpam-890	261	4	23	23	NUM
ejpam-890	261	5	·	·	SYM
ejpam-890	261	6	3	3	NUM
ejpam-890	261	7	=	=	SYM
ejpam-890	261	8	24	24	NUM
ejpam-890	261	9	.	.	PUNCT
ejpam-890	262	1	in	in	ADP
ejpam-890	262	2	general	general	ADJ
ejpam-890	262	3	,	,	PUNCT
ejpam-890	262	4	over	over	ADP
ejpam-890	262	5	a	a	DET
ejpam-890	262	6	ring	ring	NOUN
ejpam-890	262	7	r	r	NOUN
ejpam-890	262	8	,	,	PUNCT
ejpam-890	262	9	the	the	DET
ejpam-890	262	10	generic	generic	ADJ
ejpam-890	262	11	matrix	matrix	NOUN
ejpam-890	262	12	z	z	PROPN
ejpam-890	262	13	∈	∈	PROPN
ejpam-890	262	14	m2×3(r	m2×3(r	PROPN
ejpam-890	262	15	)	)	PUNCT
ejpam-890	262	16	represented	represent	VERB
ejpam-890	262	17	by	by	ADP
ejpam-890	262	18	the	the	DET
ejpam-890	262	19	term	term	NOUN
ejpam-890	262	20	x1	x1	PRON
ejpam-890	262	21	y1x	y1x	NOUN
ejpam-890	262	22	2	2	NUM
ejpam-890	262	23	2	2	NUM
ejpam-890	262	24	will	will	AUX
ejpam-890	262	25	have	have	VERB
ejpam-890	262	26	a	a	DET
ejpam-890	262	27	burst	burst	ADJ
ejpam-890	262	28	error	error	NOUN
ejpam-890	262	29	class	class	NOUN
ejpam-890	262	30	of	of	ADP
ejpam-890	262	31	size	size	NOUN
ejpam-890	262	32	(	(	PUNCT
ejpam-890	262	33	q−	q−	PROPN
ejpam-890	262	34	1)3q	1)3q	NUM
ejpam-890	262	35	.	.	PUNCT
ejpam-890	263	1	i̇.	i̇.	PROPN
ejpam-890	263	2	siap	siap	PROPN
ejpam-890	263	3	/	/	SYM
ejpam-890	263	4	eur	eur	PROPN
ejpam-890	263	5	.	.	PUNCT
ejpam-890	264	1	j.	j.	PROPN
ejpam-890	264	2	pure	pure	PROPN
ejpam-890	264	3	appl	appl	PROPN
ejpam-890	264	4	.	.	PROPN
ejpam-890	264	5	math	math	PROPN
ejpam-890	264	6	,	,	PUNCT
ejpam-890	264	7	3	3	NUM
ejpam-890	264	8	(	(	PUNCT
ejpam-890	264	9	2010	2010	NUM
ejpam-890	264	10	)	)	PUNCT
ejpam-890	264	11	,	,	PUNCT
ejpam-890	264	12	653	653	NUM
ejpam-890	264	13	-	-	SYM
ejpam-890	264	14	669	669	NUM
ejpam-890	264	15	663	663	NUM
ejpam-890	264	16	corollary	corollary	ADJ
ejpam-890	264	17	1	1	NUM
ejpam-890	264	18	.	.	PUNCT
ejpam-890	265	1	the	the	DET
ejpam-890	265	2	number	number	NOUN
ejpam-890	265	3	of	of	ADP
ejpam-890	265	4	terms	term	NOUN
ejpam-890	265	5	of	of	ADP
ejpam-890	265	6	generic	generic	ADJ
ejpam-890	265	7	polynomial	polynomial	ADJ
ejpam-890	265	8	g	g	NOUN
ejpam-890	265	9	,	,	PUNCT
ejpam-890	265	10	gives	give	VERB
ejpam-890	265	11	the	the	DET
ejpam-890	265	12	number	number	NOUN
ejpam-890	265	13	of	of	ADP
ejpam-890	265	14	equivalence	equivalence	NOUN
ejpam-890	265	15	classes	class	NOUN
ejpam-890	265	16	of	of	ADP
ejpam-890	265	17	equivalence	equivalence	NOUN
ejpam-890	265	18	relation	relation	NOUN
ejpam-890	265	19	“	"	PUNCT
ejpam-890	265	20	≈	≈	PROPN
ejpam-890	265	21	”	"	PUNCT
ejpam-890	265	22	which	which	PRON
ejpam-890	265	23	are	be	AUX
ejpam-890	265	24	generic	generic	ADJ
ejpam-890	265	25	burst	burst	ADJ
ejpam-890	265	26	errors	error	NOUN
ejpam-890	265	27	.	.	PUNCT
ejpam-890	266	1	under	under	ADP
ejpam-890	266	2	this	this	DET
ejpam-890	266	3	observation	observation	NOUN
ejpam-890	266	4	,	,	PUNCT
ejpam-890	266	5	we	we	PRON
ejpam-890	266	6	can	can	AUX
ejpam-890	266	7	make	make	VERB
ejpam-890	266	8	use	use	NOUN
ejpam-890	266	9	of	of	ADP
ejpam-890	266	10	generic	generic	ADJ
ejpam-890	266	11	burst	burst	ADJ
ejpam-890	266	12	terms	term	NOUN
ejpam-890	266	13	and	and	CCONJ
ejpam-890	266	14	hence	hence	ADV
ejpam-890	266	15	generic	generic	ADJ
ejpam-890	266	16	multi	multi	ADJ
ejpam-890	266	17	variable	variable	ADJ
ejpam-890	266	18	polynomial	polynomial	NOUN
ejpam-890	266	19	to	to	PART
ejpam-890	266	20	obtain	obtain	VERB
ejpam-890	266	21	the	the	DET
ejpam-890	266	22	number	number	NOUN
ejpam-890	266	23	of	of	ADP
ejpam-890	266	24	burst	burst	ADJ
ejpam-890	266	25	errors	error	NOUN
ejpam-890	266	26	.	.	PUNCT
ejpam-890	267	1	definition	definition	NOUN
ejpam-890	267	2	9	9	NUM
ejpam-890	267	3	.	.	PUNCT
ejpam-890	268	1	let	let	VERB
ejpam-890	268	2	a∈	a∈	PROPN
ejpam-890	268	3	b	b	PROPN
ejpam-890	268	4	⊂	⊂	PROPN
ejpam-890	268	5	mp×r(r	mp×r(r	PROPN
ejpam-890	268	6	)	)	PUNCT
ejpam-890	268	7	.	.	PUNCT
ejpam-890	269	1	assume	assume	VERB
ejpam-890	269	2	that	that	SCONJ
ejpam-890	269	3	a	a	PRON
ejpam-890	269	4	has	have	VERB
ejpam-890	269	5	a	a	DET
ejpam-890	269	6	weight	weight	NOUN
ejpam-890	269	7	distribution	distribution	NOUN
ejpam-890	269	8	of	of	ADP
ejpam-890	269	9	type	type	NOUN
ejpam-890	269	10	(	(	PUNCT
ejpam-890	269	11	α1,α2	α1,α2	PROPN
ejpam-890	269	12	,	,	PUNCT
ejpam-890	269	13	.	.	PUNCT
ejpam-890	269	14	.	.	PUNCT
ejpam-890	269	15	.	.	PUNCT
ejpam-890	270	1	,	,	PUNCT
ejpam-890	270	2	αp	αp	NOUN
ejpam-890	270	3	)	)	PUNCT
ejpam-890	270	4	.	.	PUNCT
ejpam-890	271	1	we	we	PRON
ejpam-890	271	2	associate	associate	VERB
ejpam-890	271	3	a	a	DET
ejpam-890	271	4	term	term	NOUN
ejpam-890	271	5	x	x	PUNCT
ejpam-890	271	6	α1	α1	PROPN
ejpam-890	271	7	1	1	NUM
ejpam-890	271	8	x	x	SYM
ejpam-890	271	9	α2	α2	ADJ
ejpam-890	271	10	2	2	NUM
ejpam-890	271	11	·	·	PUNCT
ejpam-890	271	12	·	·	PUNCT
ejpam-890	272	1	·	·	PUNCT
ejpam-890	272	2	x	x	SYM
ejpam-890	272	3	αp	αp	NOUN
ejpam-890	272	4	p	p	NOUN
ejpam-890	272	5	to	to	ADP
ejpam-890	272	6	the	the	DET
ejpam-890	272	7	matrix	matrix	NOUN
ejpam-890	272	8	a.	a.	NOUN
ejpam-890	272	9	then	then	ADV
ejpam-890	272	10	,	,	PUNCT
ejpam-890	272	11	the	the	DET
ejpam-890	272	12	p	p	ADJ
ejpam-890	272	13	-	-	PUNCT
ejpam-890	272	14	variable	variable	ADJ
ejpam-890	272	15	polynomial	polynomial	NOUN
ejpam-890	272	16	hp×r(x̃	hp×r(x̃	NOUN
ejpam-890	272	17	)	)	PUNCT
ejpam-890	272	18	=	=	PUNCT
ejpam-890	273	1	∑	∑	PROPN
ejpam-890	273	2	a∈b	a∈b	NOUN
ejpam-890	273	3	x	x	SYM
ejpam-890	273	4	α1	α1	PROPN
ejpam-890	273	5	1	1	NUM
ejpam-890	273	6	x	x	SYM
ejpam-890	273	7	α2	α2	ADJ
ejpam-890	273	8	2	2	NUM
ejpam-890	273	9	·	·	PUNCT
ejpam-890	273	10	·	·	PUNCT
ejpam-890	273	11	·	·	PUNCT
ejpam-890	273	12	x	x	SYM
ejpam-890	273	13	αp	αp	NOUN
ejpam-890	273	14	p	p	NOUN
ejpam-890	273	15	is	be	AUX
ejpam-890	273	16	said	say	VERB
ejpam-890	273	17	to	to	PART
ejpam-890	273	18	be	be	AUX
ejpam-890	273	19	the	the	DET
ejpam-890	273	20	weight	weight	NOUN
ejpam-890	273	21	spectra	spectra	NOUN
ejpam-890	273	22	polynomial	polynomial	NOUN
ejpam-890	273	23	of	of	ADP
ejpam-890	273	24	the	the	DET
ejpam-890	273	25	burst	burst	ADJ
ejpam-890	273	26	errors	error	NOUN
ejpam-890	273	27	in	in	ADP
ejpam-890	273	28	mp×r(r	mp×r(r	NOUN
ejpam-890	273	29	)	)	PUNCT
ejpam-890	273	30	.	.	PUNCT
ejpam-890	274	1	now	now	ADV
ejpam-890	274	2	we	we	PRON
ejpam-890	274	3	shall	shall	AUX
ejpam-890	274	4	make	make	VERB
ejpam-890	274	5	use	use	NOUN
ejpam-890	274	6	of	of	ADP
ejpam-890	274	7	generic	generic	ADJ
ejpam-890	274	8	polynomial	polynomial	NOUN
ejpam-890	274	9	in	in	ADP
ejpam-890	274	10	order	order	NOUN
ejpam-890	274	11	to	to	PART
ejpam-890	274	12	compute	compute	VERB
ejpam-890	274	13	the	the	DET
ejpam-890	274	14	weight	weight	NOUN
ejpam-890	274	15	spectra	spectra	NOUN
ejpam-890	274	16	polynomial	polynomial	NOUN
ejpam-890	274	17	of	of	ADP
ejpam-890	274	18	burst	burst	ADJ
ejpam-890	274	19	errors	error	NOUN
ejpam-890	274	20	.	.	PUNCT
ejpam-890	275	1	here	here	ADV
ejpam-890	275	2	,	,	PUNCT
ejpam-890	275	3	we	we	PRON
ejpam-890	275	4	point	point	VERB
ejpam-890	275	5	out	out	ADP
ejpam-890	275	6	that	that	SCONJ
ejpam-890	275	7	the	the	DET
ejpam-890	275	8	frame	frame	NOUN
ejpam-890	275	9	of	of	ADP
ejpam-890	275	10	the	the	DET
ejpam-890	275	11	arrays	array	NOUN
ejpam-890	275	12	hence	hence	ADV
ejpam-890	275	13	generic	generic	ADJ
ejpam-890	275	14	bursts	burst	NOUN
ejpam-890	275	15	lead	lead	VERB
ejpam-890	275	16	to	to	ADP
ejpam-890	275	17	construction	construction	NOUN
ejpam-890	275	18	of	of	ADP
ejpam-890	275	19	burst	burst	ADJ
ejpam-890	275	20	errors	error	NOUN
ejpam-890	275	21	.	.	PUNCT
ejpam-890	276	1	so	so	ADV
ejpam-890	276	2	,	,	PUNCT
ejpam-890	276	3	if	if	SCONJ
ejpam-890	276	4	we	we	PRON
ejpam-890	276	5	have	have	VERB
ejpam-890	276	6	for	for	ADP
ejpam-890	276	7	instance	instance	NOUN
ejpam-890	276	8	a	a	DET
ejpam-890	276	9	term	term	NOUN
ejpam-890	276	10	z	z	NOUN
ejpam-890	276	11	a1	a1	NOUN
ejpam-890	276	12	1	1	NUM
ejpam-890	276	13	x	x	NOUN
ejpam-890	276	14	b1	b1	NOUN
ejpam-890	276	15	1	1	NUM
ejpam-890	276	16	x	x	SYM
ejpam-890	276	17	c1	c1	NOUN
ejpam-890	276	18	1	1	NUM
ejpam-890	276	19	y	y	PROPN
ejpam-890	276	20	d1	d1	PROPN
ejpam-890	276	21	1	1	NUM
ejpam-890	276	22	for	for	ADP
ejpam-890	276	23	the	the	DET
ejpam-890	276	24	first	first	ADJ
ejpam-890	276	25	row	row	NOUN
ejpam-890	276	26	,	,	PUNCT
ejpam-890	276	27	then	then	ADV
ejpam-890	276	28	the	the	DET
ejpam-890	276	29	first	first	ADJ
ejpam-890	276	30	and	and	CCONJ
ejpam-890	276	31	the	the	DET
ejpam-890	276	32	last	last	ADJ
ejpam-890	276	33	if	if	SCONJ
ejpam-890	276	34	any	any	DET
ejpam-890	276	35	nonzero	nonzero	NOUN
ejpam-890	276	36	entry	entry	NOUN
ejpam-890	276	37	will	will	AUX
ejpam-890	276	38	lead	lead	VERB
ejpam-890	276	39	to	to	ADP
ejpam-890	276	40	(	(	PUNCT
ejpam-890	276	41	q−	q−	PROPN
ejpam-890	276	42	1)2	1)2	NUM
ejpam-890	276	43	choices	choice	NOUN
ejpam-890	276	44	and	and	CCONJ
ejpam-890	276	45	there	there	PRON
ejpam-890	276	46	is	be	VERB
ejpam-890	276	47	no	no	DET
ejpam-890	276	48	restriction	restriction	NOUN
ejpam-890	276	49	in	in	ADP
ejpam-890	276	50	between	between	ADP
ejpam-890	276	51	with	with	ADP
ejpam-890	276	52	q	q	NOUN
ejpam-890	276	53	choices	choice	NOUN
ejpam-890	276	54	for	for	ADP
ejpam-890	276	55	each	each	DET
ejpam-890	276	56	entry	entry	NOUN
ejpam-890	276	57	.	.	PUNCT
ejpam-890	277	1	however	however	ADV
ejpam-890	277	2	,	,	PUNCT
ejpam-890	277	3	if	if	SCONJ
ejpam-890	277	4	this	this	DET
ejpam-890	277	5	row	row	NOUN
ejpam-890	277	6	consists	consist	VERB
ejpam-890	277	7	of	of	ADP
ejpam-890	277	8	a	a	DET
ejpam-890	277	9	single	single	ADJ
ejpam-890	277	10	nonzero	nonzero	NOUN
ejpam-890	277	11	entry	entry	NOUN
ejpam-890	277	12	then	then	ADV
ejpam-890	277	13	the	the	DET
ejpam-890	277	14	total	total	ADJ
ejpam-890	277	15	number	number	NOUN
ejpam-890	277	16	of	of	ADP
ejpam-890	277	17	choices	choice	NOUN
ejpam-890	277	18	is	be	AUX
ejpam-890	277	19	equal	equal	ADJ
ejpam-890	277	20	to	to	ADP
ejpam-890	277	21	q−	q−	PROPN
ejpam-890	277	22	1	1	NUM
ejpam-890	277	23	.	.	PUNCT
ejpam-890	278	1	in	in	ADP
ejpam-890	278	2	order	order	NOUN
ejpam-890	278	3	to	to	PART
ejpam-890	278	4	accommodate	accommodate	VERB
ejpam-890	278	5	all	all	DET
ejpam-890	278	6	cases	case	NOUN
ejpam-890	278	7	we	we	PRON
ejpam-890	278	8	will	will	AUX
ejpam-890	278	9	invent	invent	VERB
ejpam-890	278	10	the	the	DET
ejpam-890	278	11	following	follow	VERB
ejpam-890	278	12	compact	compact	ADJ
ejpam-890	278	13	substitution	substitution	NOUN
ejpam-890	278	14	.	.	PUNCT
ejpam-890	279	1	assume	assume	VERB
ejpam-890	279	2	that	that	SCONJ
ejpam-890	279	3	the	the	DET
ejpam-890	279	4	term	term	NOUN
ejpam-890	279	5	z	z	NOUN
ejpam-890	279	6	a1	a1	NOUN
ejpam-890	279	7	1	1	NUM
ejpam-890	279	8	x	x	NOUN
ejpam-890	279	9	b1	b1	NOUN
ejpam-890	279	10	1	1	NUM
ejpam-890	279	11	x	x	SYM
ejpam-890	279	12	c1	c1	NOUN
ejpam-890	279	13	1	1	NUM
ejpam-890	279	14	y	y	PROPN
ejpam-890	279	15	d1	d1	PROPN
ejpam-890	279	16	1	1	NUM
ejpam-890	279	17	is	be	AUX
ejpam-890	279	18	related	relate	VERB
ejpam-890	279	19	to	to	ADP
ejpam-890	279	20	the	the	DET
ejpam-890	279	21	first	first	ADJ
ejpam-890	279	22	row	row	NOUN
ejpam-890	279	23	of	of	ADP
ejpam-890	279	24	a	a	DET
ejpam-890	279	25	generic	generic	ADJ
ejpam-890	279	26	burst	burst	NOUN
ejpam-890	279	27	error	error	NOUN
ejpam-890	279	28	with	with	ADP
ejpam-890	279	29	the	the	DET
ejpam-890	279	30	convention	convention	NOUN
ejpam-890	279	31	that	that	PRON
ejpam-890	279	32	the	the	DET
ejpam-890	279	33	powers	power	NOUN
ejpam-890	279	34	may	may	AUX
ejpam-890	279	35	equal	equal	VERB
ejpam-890	279	36	to	to	ADP
ejpam-890	279	37	zero	zero	NUM
ejpam-890	279	38	in	in	ADP
ejpam-890	279	39	generic	generic	ADJ
ejpam-890	279	40	polynomial	polynomial	NOUN
ejpam-890	279	41	.	.	PUNCT
ejpam-890	280	1	the	the	DET
ejpam-890	280	2	term	term	NOUN
ejpam-890	280	3	z	z	NOUN
ejpam-890	280	4	a1	a1	NOUN
ejpam-890	280	5	1	1	NUM
ejpam-890	280	6	x	x	NOUN
ejpam-890	280	7	b1	b1	NOUN
ejpam-890	280	8	1	1	NUM
ejpam-890	280	9	x	x	SYM
ejpam-890	280	10	c1	c1	NOUN
ejpam-890	280	11	1	1	NUM
ejpam-890	280	12	y	y	PROPN
ejpam-890	280	13	d1	d1	PROPN
ejpam-890	280	14	1	1	NUM
ejpam-890	280	15	that	that	PRON
ejpam-890	280	16	corresponds	correspond	VERB
ejpam-890	280	17	to	to	ADP
ejpam-890	280	18	the	the	DET
ejpam-890	280	19	first	first	ADJ
ejpam-890	280	20	row	row	NOUN
ejpam-890	280	21	of	of	ADP
ejpam-890	280	22	the	the	DET
ejpam-890	280	23	generic	generic	ADJ
ejpam-890	280	24	matrix	matrix	NOUN
ejpam-890	280	25	leads	lead	VERB
ejpam-890	280	26	to	to	ADP
ejpam-890	280	27	(	(	PUNCT
ejpam-890	280	28	q−	q−	PROPN
ejpam-890	280	29	1)2[w(a1d1)+w(a1c1)+w(b1d1)]+w(b1)qw(a1d1)(r−2)+w(a1	1)2[w(a1d1)+w(a1c1)+w(b1d1)]+w(b1)qw(a1d1)(r−2)+w(a1	NOUN
ejpam-890	280	30	c1)(c1−2)+w(b1d1)(r−b1−1	c1)(c1−2)+w(b1d1)(r−b1−1	NOUN
ejpam-890	280	31	)	)	PUNCT
ejpam-890	280	32	number	number	NOUN
ejpam-890	280	33	of	of	ADP
ejpam-890	280	34	possibilities	possibility	NOUN
ejpam-890	280	35	for	for	ADP
ejpam-890	280	36	the	the	DET
ejpam-890	280	37	first	first	ADJ
ejpam-890	280	38	row	row	NOUN
ejpam-890	280	39	of	of	ADP
ejpam-890	280	40	burst	burst	ADJ
ejpam-890	280	41	error	error	NOUN
ejpam-890	280	42	that	that	PRON
ejpam-890	280	43	falls	fall	VERB
ejpam-890	280	44	into	into	ADP
ejpam-890	280	45	the	the	DET
ejpam-890	280	46	generic	generic	ADJ
ejpam-890	280	47	class	class	NOUN
ejpam-890	280	48	where	where	SCONJ
ejpam-890	280	49	w(a	w(a	VERB
ejpam-890	280	50	)	)	PUNCT
ejpam-890	281	1	=	=	SYM
ejpam-890	281	2	0	0	PUNCT
ejpam-890	282	1	if	if	SCONJ
ejpam-890	282	2	a	a	DET
ejpam-890	282	3	=	=	NOUN
ejpam-890	282	4	0	0	NUM
ejpam-890	282	5	and	and	CCONJ
ejpam-890	282	6	otherwise	otherwise	ADV
ejpam-890	282	7	w(a	w(a	VERB
ejpam-890	282	8	)	)	PUNCT
ejpam-890	283	1	=	=	SYM
ejpam-890	283	2	1	1	X
ejpam-890	283	3	.	.	PUNCT
ejpam-890	283	4	the	the	DET
ejpam-890	283	5	same	same	ADJ
ejpam-890	283	6	argument	argument	NOUN
ejpam-890	283	7	is	be	AUX
ejpam-890	283	8	still	still	ADV
ejpam-890	283	9	valid	valid	ADJ
ejpam-890	283	10	for	for	ADP
ejpam-890	283	11	the	the	DET
ejpam-890	283	12	last	last	ADJ
ejpam-890	283	13	row	row	NOUN
ejpam-890	283	14	.	.	PUNCT
ejpam-890	284	1	thus	thus	ADV
ejpam-890	284	2	,	,	PUNCT
ejpam-890	284	3	for	for	ADP
ejpam-890	284	4	j	j	PROPN
ejpam-890	284	5	=	=	SYM
ejpam-890	284	6	1	1	NUM
ejpam-890	284	7	and	and	CCONJ
ejpam-890	284	8	j	j	PROPN
ejpam-890	284	9	=	=	SYM
ejpam-890	284	10	p	p	X
ejpam-890	284	11	,	,	PUNCT
ejpam-890	284	12	if	if	SCONJ
ejpam-890	284	13	γ(x	γ(x	PROPN
ejpam-890	284	14	j	j	PROPN
ejpam-890	284	15	)	)	PUNCT
ejpam-890	284	16	=	=	PUNCT
ejpam-890	284	17	(	(	PUNCT
ejpam-890	284	18	q−	q−	PROPN
ejpam-890	284	19	1)2[w(a1d1)+w(a1c1)+w(b1d1)]+w(b1	1)2[w(a1d1)+w(a1c1)+w(b1d1)]+w(b1	NOUN
ejpam-890	284	20	)	)	PUNCT
ejpam-890	284	21	·	·	PUNCT
ejpam-890	284	22	qw(a1d1)(r−2)+w(a1	qw(a1d1)(r−2)+w(a1	NOUN
ejpam-890	284	23	c1)(c1−2)+w(b1d1)(r−b1−1	c1)(c1−2)+w(b1d1)(r−b1−1	NUM
ejpam-890	284	24	)	)	PUNCT
ejpam-890	284	25	·	·	PUNCT
ejpam-890	285	1	x	x	SYM
ejpam-890	285	2	max{rd	max{rd	X
ejpam-890	285	3	j	j	NOUN
ejpam-890	285	4	,	,	PUNCT
ejpam-890	285	5	c	c	PROPN
ejpam-890	285	6	j	j	PROPN
ejpam-890	285	7	,	,	PUNCT
ejpam-890	285	8	b	b	PROPN
ejpam-890	285	9	j	j	PROPN
ejpam-890	285	10	,	,	PUNCT
ejpam-890	285	11	a	a	DET
ejpam-890	285	12	j	j	PROPN
ejpam-890	285	13	}	}	PUNCT
ejpam-890	285	14	j	j	PROPN
ejpam-890	285	15	is	be	AUX
ejpam-890	285	16	substituted	substitute	VERB
ejpam-890	285	17	for	for	ADP
ejpam-890	285	18	the	the	DET
ejpam-890	285	19	term	term	NOUN
ejpam-890	285	20	z	z	PROPN
ejpam-890	286	1	a	a	DET
ejpam-890	286	2	j	j	PROPN
ejpam-890	286	3	j	j	PROPN
ejpam-890	286	4	x	x	PROPN
ejpam-890	286	5	b	b	PROPN
ejpam-890	286	6	j	j	PROPN
ejpam-890	286	7	j	j	PROPN
ejpam-890	286	8	x	x	X
ejpam-890	286	9	c	c	PROPN
ejpam-890	286	10	j	j	PROPN
ejpam-890	286	11	j	j	PROPN
ejpam-890	286	12	y	y	PROPN
ejpam-890	286	13	d	d	PROPN
ejpam-890	286	14	j	j	PROPN
ejpam-890	286	15	j	j	PROPN
ejpam-890	286	16	in	in	ADP
ejpam-890	286	17	the	the	DET
ejpam-890	286	18	generic	generic	ADJ
ejpam-890	286	19	polynomial	polynomial	NOUN
ejpam-890	286	20	,	,	PUNCT
ejpam-890	286	21	then	then	ADV
ejpam-890	286	22	the	the	DET
ejpam-890	286	23	new	new	ADJ
ejpam-890	286	24	term	term	NOUN
ejpam-890	286	25	expression	expression	NOUN
ejpam-890	286	26	gives	give	VERB
ejpam-890	286	27	all	all	DET
ejpam-890	286	28	possible	possible	ADJ
ejpam-890	286	29	weight	weight	NOUN
ejpam-890	286	30	distributions	distribution	NOUN
ejpam-890	286	31	for	for	ADP
ejpam-890	286	32	the	the	DET
ejpam-890	286	33	jth	jth	PROPN
ejpam-890	286	34	row	row	NOUN
ejpam-890	286	35	.	.	PUNCT
ejpam-890	287	1	for	for	ADP
ejpam-890	287	2	j	j	PROPN
ejpam-890	287	3	=	=	SYM
ejpam-890	287	4	2	2	NUM
ejpam-890	287	5	,	,	PUNCT
ejpam-890	287	6	.	.	PUNCT
ejpam-890	287	7	.	.	PUNCT
ejpam-890	287	8	.	.	PUNCT
ejpam-890	288	1	p	p	NOUN
ejpam-890	289	1	−	−	PROPN
ejpam-890	289	2	1	1	NUM
ejpam-890	289	3	,	,	PUNCT
ejpam-890	289	4	there	there	PRON
ejpam-890	289	5	are	be	VERB
ejpam-890	289	6	four	four	NUM
ejpam-890	289	7	cases	case	NOUN
ejpam-890	289	8	to	to	PART
ejpam-890	289	9	be	be	AUX
ejpam-890	289	10	considered	consider	VERB
ejpam-890	289	11	.	.	PUNCT
ejpam-890	290	1	if	if	SCONJ
ejpam-890	290	2	the	the	DET
ejpam-890	290	3	term	term	NOUN
ejpam-890	290	4	z	z	PROPN
ejpam-890	290	5	j	j	PROPN
ejpam-890	290	6	y	y	PROPN
ejpam-890	290	7	j	j	PROPN
ejpam-890	290	8	exists	exist	VERB
ejpam-890	290	9	then	then	ADV
ejpam-890	290	10	,	,	PUNCT
ejpam-890	290	11	we	we	PRON
ejpam-890	290	12	substitute	substitute	VERB
ejpam-890	290	13	(	(	PUNCT
ejpam-890	290	14	q−	q−	PROPN
ejpam-890	290	15	1)2qr−2x	1)2qr−2x	NUM
ejpam-890	290	16	r	r	NOUN
ejpam-890	290	17	j	j	PROPN
ejpam-890	290	18	.	.	PUNCT
ejpam-890	291	1	if	if	SCONJ
ejpam-890	291	2	the	the	DET
ejpam-890	291	3	term	term	NOUN
ejpam-890	291	4	y	y	PROPN
ejpam-890	291	5	j	j	PROPN
ejpam-890	291	6	exists	exist	VERB
ejpam-890	291	7	only	only	ADV
ejpam-890	291	8	,	,	PUNCT
ejpam-890	291	9	then	then	ADV
ejpam-890	291	10	we	we	PRON
ejpam-890	291	11	substitute	substitute	VERB
ejpam-890	291	12	(	(	PUNCT
ejpam-890	291	13	q−	q−	PROPN
ejpam-890	291	14	1)qr−2x	1)qr−2x	NOUN
ejpam-890	291	15	r	r	NOUN
ejpam-890	291	16	j	j	PROPN
ejpam-890	291	17	.	.	PUNCT
ejpam-890	292	1	if	if	SCONJ
ejpam-890	292	2	the	the	DET
ejpam-890	292	3	term	term	NOUN
ejpam-890	292	4	z	z	PROPN
ejpam-890	292	5	j	j	PROPN
ejpam-890	292	6	exists	exist	VERB
ejpam-890	292	7	only	only	ADV
ejpam-890	292	8	,	,	PUNCT
ejpam-890	292	9	then	then	ADV
ejpam-890	292	10	we	we	PRON
ejpam-890	292	11	substitute	substitute	VERB
ejpam-890	292	12	(	(	PUNCT
ejpam-890	292	13	q	q	PROPN
ejpam-890	292	14	−	−	PROPN
ejpam-890	292	15	1)x	1)x	NUM
ejpam-890	292	16	j	j	NOUN
ejpam-890	292	17	+	+	CCONJ
ejpam-890	292	18	∑r−1	∑r−1	ADJ
ejpam-890	292	19	i=2	i=2	NOUN
ejpam-890	293	1	qi−2(q	qi−2(q	ADP
ejpam-890	293	2	−	−	PROPN
ejpam-890	293	3	1)2x	1)2x	INTJ
ejpam-890	294	1	i	i	PRON
ejpam-890	294	2	j	j	PROPN
ejpam-890	294	3	.	.	PUNCT
ejpam-890	295	1	finally	finally	ADV
ejpam-890	295	2	,	,	PUNCT
ejpam-890	295	3	if	if	SCONJ
ejpam-890	295	4	none	none	NOUN
ejpam-890	295	5	of	of	ADP
ejpam-890	295	6	z	z	PROPN
ejpam-890	295	7	j	j	PROPN
ejpam-890	295	8	or	or	CCONJ
ejpam-890	295	9	y	y	PROPN
ejpam-890	295	10	j	j	PROPN
ejpam-890	295	11	exist	exist	VERB
ejpam-890	295	12	,	,	PUNCT
ejpam-890	295	13	then	then	ADV
ejpam-890	295	14	we	we	PRON
ejpam-890	295	15	substitute	substitute	VERB
ejpam-890	295	16	the	the	DET
ejpam-890	295	17	term	term	NOUN
ejpam-890	295	18	1	1	NUM
ejpam-890	295	19	+	+	NUM
ejpam-890	295	20	∑r−1	∑r−1	ADJ
ejpam-890	295	21	i=2	i=2	PROPN
ejpam-890	295	22	qi−1(q	qi−1(q	ADJ
ejpam-890	295	23	−	−	NUM
ejpam-890	295	24	1)x	1)x	NUM
ejpam-890	296	1	i	i	PRON
ejpam-890	296	2	j	j	PROPN
ejpam-890	296	3	.	.	PUNCT
ejpam-890	297	1	hence	hence	ADV
ejpam-890	297	2	,	,	PUNCT
ejpam-890	297	3	we	we	PRON
ejpam-890	297	4	obtain	obtain	VERB
ejpam-890	297	5	the	the	DET
ejpam-890	297	6	multivariable	multivariable	ADJ
ejpam-890	297	7	polynomial	polynomial	ADJ
ejpam-890	297	8	hp×r	hp×r	PROPN
ejpam-890	297	9	which	which	PRON
ejpam-890	297	10	is	be	AUX
ejpam-890	297	11	the	the	DET
ejpam-890	297	12	spectra	spectra	ADJ
ejpam-890	297	13	weight	weight	NOUN
ejpam-890	297	14	enumerator	enumerator	NOUN
ejpam-890	297	15	of	of	ADP
ejpam-890	297	16	burst	burst	ADJ
ejpam-890	297	17	error	error	NOUN
ejpam-890	297	18	arrays	array	NOUN
ejpam-890	297	19	of	of	ADP
ejpam-890	297	20	order	order	NOUN
ejpam-890	297	21	p×	p×	NOUN
ejpam-890	297	22	r	r	NOUN
ejpam-890	297	23	in	in	ADP
ejpam-890	297	24	mp×r(r	mp×r(r	NOUN
ejpam-890	297	25	)	)	PUNCT
ejpam-890	297	26	.	.	PUNCT
ejpam-890	298	1	thus	thus	ADV
ejpam-890	298	2	we	we	PRON
ejpam-890	298	3	obtain	obtain	VERB
ejpam-890	298	4	the	the	DET
ejpam-890	298	5	following	following	NOUN
ejpam-890	298	6	theorem	theorem	NOUN
ejpam-890	298	7	:	:	PUNCT
ejpam-890	298	8	i̇.	i̇.	PROPN
ejpam-890	298	9	siap	siap	PROPN
ejpam-890	298	10	/	/	SYM
ejpam-890	298	11	eur	eur	PROPN
ejpam-890	298	12	.	.	PUNCT
ejpam-890	299	1	j.	j.	PROPN
ejpam-890	299	2	pure	pure	PROPN
ejpam-890	299	3	appl	appl	PROPN
ejpam-890	299	4	.	.	PROPN
ejpam-890	299	5	math	math	PROPN
ejpam-890	299	6	,	,	PUNCT
ejpam-890	299	7	3	3	NUM
ejpam-890	299	8	(	(	PUNCT
ejpam-890	299	9	2010	2010	NUM
ejpam-890	299	10	)	)	PUNCT
ejpam-890	299	11	,	,	PUNCT
ejpam-890	299	12	653	653	NUM
ejpam-890	299	13	-	-	SYM
ejpam-890	299	14	669	669	NUM
ejpam-890	299	15	664	664	NUM
ejpam-890	299	16	theorem	theorem	NOUN
ejpam-890	299	17	5	5	NUM
ejpam-890	299	18	.	.	PUNCT
ejpam-890	300	1	let	let	VERB
ejpam-890	300	2	g(z̃	g(z̃	PROPN
ejpam-890	300	3	,	,	PUNCT
ejpam-890	300	4	x̃	x̃	PROPN
ejpam-890	300	5	,	,	PUNCT
ejpam-890	300	6	x̃	x̃	PROPN
ejpam-890	300	7	,	,	PUNCT
ejpam-890	300	8	ỹ	ỹ	PROPN
ejpam-890	300	9	)	)	PUNCT
ejpam-890	300	10	be	be	VERB
ejpam-890	300	11	the	the	DET
ejpam-890	300	12	generic	generic	ADJ
ejpam-890	300	13	polynomial	polynomial	NOUN
ejpam-890	300	14	.	.	PUNCT
ejpam-890	301	1	then	then	ADV
ejpam-890	301	2	,	,	PUNCT
ejpam-890	301	3	for	for	ADP
ejpam-890	301	4	j	j	PROPN
ejpam-890	301	5	=	=	SYM
ejpam-890	301	6	1	1	NUM
ejpam-890	301	7	and	and	CCONJ
ejpam-890	301	8	j	j	PROPN
ejpam-890	301	9	=	=	SYM
ejpam-890	301	10	p	p	X
ejpam-890	301	11	,	,	PUNCT
ejpam-890	301	12	by	by	ADP
ejpam-890	301	13	substituting	substitute	VERB
ejpam-890	301	14	γ(x	γ(x	PROPN
ejpam-890	301	15	j	j	PROPN
ejpam-890	301	16	)	)	PUNCT
ejpam-890	301	17	for	for	ADP
ejpam-890	301	18	z	z	PROPN
ejpam-890	301	19	a	a	DET
ejpam-890	301	20	j	j	PROPN
ejpam-890	302	1	j	j	PROPN
ejpam-890	302	2	x	x	PROPN
ejpam-890	302	3	b	b	PROPN
ejpam-890	302	4	j	j	PROPN
ejpam-890	302	5	j	j	PROPN
ejpam-890	302	6	x	x	X
ejpam-890	302	7	c	c	PROPN
ejpam-890	302	8	j	j	PROPN
ejpam-890	302	9	j	j	PROPN
ejpam-890	302	10	y	y	PROPN
ejpam-890	302	11	d	d	PROPN
ejpam-890	302	12	j	j	PROPN
ejpam-890	302	13	j	j	PROPN
ejpam-890	302	14	in	in	ADP
ejpam-890	302	15	g	g	PROPN
ejpam-890	302	16	,	,	PUNCT
ejpam-890	302	17	and	and	CCONJ
ejpam-890	302	18	further	far	ADV
ejpam-890	302	19	substituting	substitute	VERB
ejpam-890	302	20	(	(	PUNCT
ejpam-890	302	21	q−	q−	PROPN
ejpam-890	302	22	1)2qr−2x	1)2qr−2x	NUM
ejpam-890	302	23	r	r	NOUN
ejpam-890	302	24	j	j	PROPN
ejpam-890	302	25	,	,	PUNCT
ejpam-890	302	26	(	(	PUNCT
ejpam-890	302	27	q−	q−	PROPN
ejpam-890	302	28	1)qr−2x	1)qr−2x	NOUN
ejpam-890	302	29	r	r	NOUN
ejpam-890	302	30	j	j	PROPN
ejpam-890	302	31	,	,	PUNCT
ejpam-890	302	32	and	and	CCONJ
ejpam-890	302	33	(	(	PUNCT
ejpam-890	302	34	q−	q−	PROPN
ejpam-890	302	35	1)x	1)x	NUM
ejpam-890	302	36	j	j	NOUN
ejpam-890	302	37	+	+	CCONJ
ejpam-890	302	38	∑r−1	∑r−1	ADJ
ejpam-890	303	1	i=2	i=2	PROPN
ejpam-890	303	2	qi−2(q−	qi−2(q−	PROPN
ejpam-890	303	3	1)2x	1)2x	PROPN
ejpam-890	303	4	i	i	PRON
ejpam-890	303	5	j	j	PROPN
ejpam-890	303	6	for	for	ADP
ejpam-890	303	7	z	z	PROPN
ejpam-890	303	8	j	j	PROPN
ejpam-890	303	9	y	y	PROPN
ejpam-890	303	10	j	j	PROPN
ejpam-890	303	11	,	,	PUNCT
ejpam-890	303	12	y	y	PROPN
ejpam-890	303	13	j	j	PROPN
ejpam-890	303	14	,	,	PUNCT
ejpam-890	303	15	and	and	CCONJ
ejpam-890	303	16	z	z	PROPN
ejpam-890	303	17	j	j	PROPN
ejpam-890	303	18	and	and	CCONJ
ejpam-890	303	19	multiplying	multiply	VERB
ejpam-890	303	20	the	the	DET
ejpam-890	303	21	terms	term	NOUN
ejpam-890	303	22	that	that	PRON
ejpam-890	303	23	do	do	AUX
ejpam-890	303	24	not	not	PART
ejpam-890	303	25	include	include	VERB
ejpam-890	303	26	the	the	DET
ejpam-890	303	27	factors	factor	NOUN
ejpam-890	303	28	z	z	PROPN
ejpam-890	303	29	j	j	PROPN
ejpam-890	303	30	and	and	CCONJ
ejpam-890	303	31	y	y	PROPN
ejpam-890	303	32	j	j	PROPN
ejpam-890	303	33	by	by	ADP
ejpam-890	303	34	1	1	NUM
ejpam-890	303	35	+	+	NUM
ejpam-890	303	36	∑r−1	∑r−1	ADJ
ejpam-890	303	37	i=2	i=2	PROPN
ejpam-890	303	38	qi−1(q−1)x	qi−1(q−1)x	PROPN
ejpam-890	303	39	i	i	PRON
ejpam-890	303	40	j	j	PROPN
ejpam-890	303	41	for	for	ADP
ejpam-890	303	42	j	j	PROPN
ejpam-890	303	43	6=	6=	ADP
ejpam-890	303	44	1	1	NUM
ejpam-890	303	45	and	and	CCONJ
ejpam-890	303	46	j	j	PROPN
ejpam-890	304	1	6=	6=	PROPN
ejpam-890	304	2	p	p	X
ejpam-890	304	3	,	,	PUNCT
ejpam-890	304	4	we	we	PRON
ejpam-890	304	5	obtain	obtain	VERB
ejpam-890	304	6	the	the	DET
ejpam-890	304	7	spectra	spectra	ADJ
ejpam-890	304	8	weight	weight	NOUN
ejpam-890	304	9	enumerator	enumerator	NOUN
ejpam-890	304	10	polynomial	polynomial	ADJ
ejpam-890	304	11	hp×r(x̃	hp×r(x̃	NOUN
ejpam-890	304	12	)	)	PUNCT
ejpam-890	304	13	in	in	ADP
ejpam-890	304	14	the	the	DET
ejpam-890	304	15	space	space	NOUN
ejpam-890	304	16	of	of	ADP
ejpam-890	304	17	burst	burst	ADJ
ejpam-890	304	18	errors	error	NOUN
ejpam-890	304	19	of	of	ADP
ejpam-890	304	20	order	order	NOUN
ejpam-890	304	21	p×	p×	PROPN
ejpam-890	304	22	r.	r.	PROPN
ejpam-890	304	23	example	example	NOUN
ejpam-890	304	24	5	5	NUM
ejpam-890	304	25	.	.	PUNCT
ejpam-890	305	1	let	let	VERB
ejpam-890	305	2	g	g	NOUN
ejpam-890	305	3	be	be	AUX
ejpam-890	305	4	given	give	VERB
ejpam-890	305	5	as	as	ADP
ejpam-890	305	6	in	in	ADP
ejpam-890	305	7	example	example	NOUN
ejpam-890	305	8	3	3	NUM
ejpam-890	305	9	.	.	X
ejpam-890	306	1	for	for	ADP
ejpam-890	306	2	instance	instance	NOUN
ejpam-890	306	3	,	,	PUNCT
ejpam-890	306	4	for	for	ADP
ejpam-890	306	5	z1	z1	PROPN
ejpam-890	306	6	y1x	y1x	PROPN
ejpam-890	306	7	2	2	NUM
ejpam-890	306	8	2	2	NUM
ejpam-890	306	9	and	and	CCONJ
ejpam-890	306	10	z2	z2	PROPN
ejpam-890	306	11	y2x	y2x	ADJ
ejpam-890	306	12	2	2	NUM
ejpam-890	306	13	1	1	NUM
ejpam-890	306	14	we	we	PRON
ejpam-890	306	15	substitute	substitute	VERB
ejpam-890	306	16	2x	2x	NUM
ejpam-890	306	17	3	3	NUM
ejpam-890	306	18	2	2	NUM
ejpam-890	306	19	x	x	SYM
ejpam-890	306	20	2	2	NUM
ejpam-890	306	21	1	1	NUM
ejpam-890	306	22	respectively	respectively	ADV
ejpam-890	306	23	.	.	PUNCT
ejpam-890	307	1	hence	hence	ADV
ejpam-890	307	2	,	,	PUNCT
ejpam-890	307	3	by	by	ADP
ejpam-890	307	4	applying	apply	VERB
ejpam-890	307	5	the	the	DET
ejpam-890	307	6	necessary	necessary	ADJ
ejpam-890	307	7	substitutions	substitution	NOUN
ejpam-890	307	8	,	,	PUNCT
ejpam-890	307	9	we	we	PRON
ejpam-890	307	10	have	have	VERB
ejpam-890	307	11	h(x1	h(x1	NOUN
ejpam-890	307	12	,	,	PUNCT
ejpam-890	307	13	x2	x2	PROPN
ejpam-890	307	14	)	)	PUNCT
ejpam-890	308	1	=	=	SYM
ejpam-890	308	2	4x	4x	NOUN
ejpam-890	308	3	3	3	NUM
ejpam-890	308	4	1	1	NUM
ejpam-890	308	5	x2	x2	NOUN
ejpam-890	308	6	+	+	NOUN
ejpam-890	308	7	6x	6x	NUM
ejpam-890	308	8	3	3	NUM
ejpam-890	308	9	1	1	NUM
ejpam-890	308	10	x	x	SYM
ejpam-890	308	11	2	2	NUM
ejpam-890	308	12	2	2	NUM
ejpam-890	308	13	+	+	NUM
ejpam-890	308	14	12x	12x	NOUN
ejpam-890	308	15	3	3	NUM
ejpam-890	308	16	2x	2x	NUM
ejpam-890	308	17	3	3	NUM
ejpam-890	308	18	1	1	NUM
ejpam-890	308	19	+	+	CCONJ
ejpam-890	308	20	6x	6x	NUM
ejpam-890	308	21	3	3	NUM
ejpam-890	308	22	2	2	NUM
ejpam-890	308	23	x	x	SYM
ejpam-890	308	24	2	2	NUM
ejpam-890	308	25	1	1	NUM
ejpam-890	308	26	+	+	NUM
ejpam-890	308	27	4x	4x	NUM
ejpam-890	308	28	3	3	NUM
ejpam-890	308	29	2	2	NUM
ejpam-890	308	30	x1	x1	PROPN
ejpam-890	308	31	.	.	PUNCT
ejpam-890	309	1	now	now	ADV
ejpam-890	309	2	,	,	PUNCT
ejpam-890	309	3	we	we	PRON
ejpam-890	309	4	can	can	AUX
ejpam-890	309	5	compare	compare	VERB
ejpam-890	309	6	the	the	DET
ejpam-890	309	7	terms	term	NOUN
ejpam-890	309	8	of	of	ADP
ejpam-890	309	9	h(x1	h(x1	NOUN
ejpam-890	309	10	,	,	PUNCT
ejpam-890	309	11	x2	x2	PROPN
ejpam-890	309	12	)	)	PUNCT
ejpam-890	309	13	with	with	ADP
ejpam-890	309	14	the	the	DET
ejpam-890	309	15	list	list	NOUN
ejpam-890	309	16	in	in	ADP
ejpam-890	309	17	the	the	DET
ejpam-890	309	18	example	example	NOUN
ejpam-890	310	1	3	3	NUM
ejpam-890	310	2	.	.	X
ejpam-890	311	1	for	for	ADP
ejpam-890	311	2	instance	instance	NOUN
ejpam-890	311	3	,	,	PUNCT
ejpam-890	311	4	the	the	DET
ejpam-890	311	5	term	term	NOUN
ejpam-890	311	6	12x	12x	NUM
ejpam-890	311	7	3	3	NUM
ejpam-890	311	8	2	2	NUM
ejpam-890	311	9	x	x	SYM
ejpam-890	311	10	3	3	NUM
ejpam-890	311	11	1	1	NUM
ejpam-890	311	12	indicates	indicate	VERB
ejpam-890	311	13	that	that	SCONJ
ejpam-890	311	14	there	there	PRON
ejpam-890	311	15	are	be	VERB
ejpam-890	311	16	12	12	NUM
ejpam-890	311	17	burst	burst	ADJ
ejpam-890	311	18	errors	error	NOUN
ejpam-890	311	19	of	of	ADP
ejpam-890	311	20	weight	weight	NOUN
ejpam-890	311	21	distribution	distribution	NOUN
ejpam-890	311	22	(	(	PUNCT
ejpam-890	311	23	3,3	3,3	NUM
ejpam-890	311	24	)	)	PUNCT
ejpam-890	311	25	.	.	PUNCT
ejpam-890	312	1	example	example	NOUN
ejpam-890	313	1	6	6	NUM
ejpam-890	313	2	.	.	PUNCT
ejpam-890	314	1	let	let	VERB
ejpam-890	314	2	g	g	NOUN
ejpam-890	314	3	be	be	AUX
ejpam-890	314	4	given	give	VERB
ejpam-890	314	5	as	as	ADP
ejpam-890	314	6	in	in	ADP
ejpam-890	314	7	example	example	NOUN
ejpam-890	314	8	4	4	NUM
ejpam-890	314	9	.	.	PUNCT
ejpam-890	314	10	by	by	ADP
ejpam-890	314	11	applying	apply	VERB
ejpam-890	314	12	theorem	theorem	NOUN
ejpam-890	314	13	5	5	NUM
ejpam-890	314	14	,	,	PUNCT
ejpam-890	314	15	we	we	PRON
ejpam-890	314	16	get	get	VERB
ejpam-890	314	17	h(x1	h(x1	ADJ
ejpam-890	314	18	,	,	PUNCT
ejpam-890	314	19	x2	x2	PROPN
ejpam-890	314	20	,	,	PUNCT
ejpam-890	314	21	x3	x3	ADJ
ejpam-890	314	22	)	)	PUNCT
ejpam-890	315	1	=	=	NOUN
ejpam-890	315	2	28x	28x	NOUN
ejpam-890	315	3	2	2	NUM
ejpam-890	315	4	1x	1x	NUM
ejpam-890	315	5	3	3	NUM
ejpam-890	315	6	2	2	NUM
ejpam-890	315	7	x	x	SYM
ejpam-890	315	8	3	3	NUM
ejpam-890	315	9	3	3	NUM
ejpam-890	315	10	+	+	NOUN
ejpam-890	315	11	6x	6x	NUM
ejpam-890	315	12	2	2	NUM
ejpam-890	315	13	1	1	NUM
ejpam-890	315	14	x	x	SYM
ejpam-890	315	15	3	3	NUM
ejpam-890	315	16	3	3	NUM
ejpam-890	315	17	+	+	NUM
ejpam-890	315	18	12x	12x	NUM
ejpam-890	315	19	3	3	NUM
ejpam-890	315	20	1x	1x	NUM
ejpam-890	315	21	3	3	NUM
ejpam-890	315	22	3	3	NUM
ejpam-890	315	23	+	+	CCONJ
ejpam-890	315	24	14x	14x	NUM
ejpam-890	315	25	2	2	NUM
ejpam-890	315	26	1	1	NUM
ejpam-890	315	27	x	x	SYM
ejpam-890	315	28	2	2	NUM
ejpam-890	315	29	2	2	NUM
ejpam-890	315	30	x	x	SYM
ejpam-890	315	31	3	3	NUM
ejpam-890	315	32	3	3	NUM
ejpam-890	315	33	+	+	NUM
ejpam-890	315	34	28x	28x	NOUN
ejpam-890	315	35	3	3	NUM
ejpam-890	315	36	1x	1x	NUM
ejpam-890	315	37	2	2	NUM
ejpam-890	315	38	2	2	NUM
ejpam-890	315	39	x	x	SYM
ejpam-890	315	40	3	3	NUM
ejpam-890	315	41	3	3	NUM
ejpam-890	315	42	+	+	CCONJ
ejpam-890	315	43	8x	8x	PROPN
ejpam-890	315	44	2	2	NUM
ejpam-890	315	45	1	1	NUM
ejpam-890	315	46	x2x	x2x	NUM
ejpam-890	315	47	3	3	NUM
ejpam-890	315	48	3	3	NUM
ejpam-890	315	49	+	+	SYM
ejpam-890	315	50	4x1x2x	4x1x2x	NUM
ejpam-890	315	51	3	3	NUM
ejpam-890	315	52	3	3	NUM
ejpam-890	315	53	+	+	NUM
ejpam-890	315	54	8x1x	8x1x	NOUN
ejpam-890	315	55	2	2	NUM
ejpam-890	315	56	2	2	NUM
ejpam-890	315	57	x	x	SYM
ejpam-890	315	58	3	3	NUM
ejpam-890	315	59	3	3	NUM
ejpam-890	315	60	+	+	CCONJ
ejpam-890	315	61	16x1x	16x1x	NOUN
ejpam-890	315	62	3	3	NUM
ejpam-890	315	63	2	2	NUM
ejpam-890	315	64	x	x	SYM
ejpam-890	315	65	3	3	NUM
ejpam-890	315	66	3	3	NUM
ejpam-890	315	67	+	+	NUM
ejpam-890	315	68	4x1x	4x1x	NOUN
ejpam-890	315	69	3	3	NUM
ejpam-890	315	70	3	3	NUM
ejpam-890	315	71	+	+	NUM
ejpam-890	315	72	56x	56x	NOUN
ejpam-890	315	73	3	3	NUM
ejpam-890	315	74	1	1	NUM
ejpam-890	315	75	x	x	SYM
ejpam-890	315	76	3	3	NUM
ejpam-890	315	77	2	2	NUM
ejpam-890	315	78	x	x	SYM
ejpam-890	315	79	3	3	NUM
ejpam-890	315	80	3	3	NUM
ejpam-890	315	81	+	+	NOUN
ejpam-890	315	82	16x	16x	NOUN
ejpam-890	315	83	3	3	NUM
ejpam-890	315	84	1x2x	1x2x	NUM
ejpam-890	315	85	3	3	NUM
ejpam-890	315	86	3	3	NUM
ejpam-890	315	87	+	+	CCONJ
ejpam-890	315	88	14x	14x	X
ejpam-890	315	89	2	2	NUM
ejpam-890	315	90	1x	1x	NUM
ejpam-890	315	91	2	2	NUM
ejpam-890	315	92	3	3	NUM
ejpam-890	315	93	x	x	SYM
ejpam-890	315	94	3	3	NUM
ejpam-890	315	95	2	2	NUM
ejpam-890	315	96	+	+	NUM
ejpam-890	315	97	28x	28x	NOUN
ejpam-890	315	98	3	3	NUM
ejpam-890	315	99	1	1	NUM
ejpam-890	315	100	x	x	SYM
ejpam-890	315	101	2	2	NUM
ejpam-890	315	102	3	3	NUM
ejpam-890	315	103	x	x	SYM
ejpam-890	315	104	3	3	NUM
ejpam-890	315	105	2	2	NUM
ejpam-890	315	106	+	+	CCONJ
ejpam-890	315	107	8x	8x	PROPN
ejpam-890	315	108	3	3	NUM
ejpam-890	315	109	1	1	NUM
ejpam-890	315	110	x	x	SYM
ejpam-890	315	111	2	2	NUM
ejpam-890	315	112	3	3	NUM
ejpam-890	315	113	x2	x2	PROPN
ejpam-890	315	114	+	+	X
ejpam-890	315	115	14x	14x	PROPN
ejpam-890	315	116	3	3	NUM
ejpam-890	315	117	1x	1x	NUM
ejpam-890	315	118	2	2	NUM
ejpam-890	315	119	3	3	NUM
ejpam-890	315	120	x	x	SYM
ejpam-890	315	121	2	2	NUM
ejpam-890	315	122	2	2	NUM
ejpam-890	315	123	+	+	NUM
ejpam-890	315	124	8x1x	8x1x	NOUN
ejpam-890	315	125	2	2	NUM
ejpam-890	315	126	3	3	NUM
ejpam-890	315	127	x	x	SYM
ejpam-890	315	128	3	3	NUM
ejpam-890	315	129	2	2	NUM
ejpam-890	315	130	+	+	NOUN
ejpam-890	315	131	6x	6x	NUM
ejpam-890	315	132	3	3	NUM
ejpam-890	315	133	1	1	NUM
ejpam-890	315	134	x	x	SYM
ejpam-890	315	135	2	2	NUM
ejpam-890	315	136	3	3	NUM
ejpam-890	315	137	+	+	NUM
ejpam-890	315	138	4x1x	4x1x	NOUN
ejpam-890	315	139	3	3	NUM
ejpam-890	315	140	2	2	NUM
ejpam-890	315	141	x3	x3	NOUN
ejpam-890	315	142	+	+	CCONJ
ejpam-890	315	143	4x	4x	NUM
ejpam-890	315	144	3	3	NUM
ejpam-890	315	145	1	1	NUM
ejpam-890	315	146	x2x3	x2x3	NOUN
ejpam-890	315	147	+	+	NOUN
ejpam-890	315	148	4x	4x	NUM
ejpam-890	315	149	3	3	NUM
ejpam-890	315	150	1	1	NUM
ejpam-890	315	151	x3	x3	NOUN
ejpam-890	315	152	+	+	CCONJ
ejpam-890	315	153	8x	8x	PROPN
ejpam-890	315	154	2	2	NUM
ejpam-890	315	155	1	1	NUM
ejpam-890	315	156	x	x	SYM
ejpam-890	315	157	3	3	NUM
ejpam-890	315	158	2	2	NUM
ejpam-890	315	159	x3	x3	NOUN
ejpam-890	315	160	+	+	CCONJ
ejpam-890	315	161	8x	8x	PROPN
ejpam-890	315	162	3	3	NUM
ejpam-890	315	163	1	1	NUM
ejpam-890	315	164	x	x	SYM
ejpam-890	315	165	2	2	NUM
ejpam-890	315	166	2	2	NUM
ejpam-890	315	167	x3	x3	NOUN
ejpam-890	315	168	+	+	NUM
ejpam-890	315	169	16x	16x	NOUN
ejpam-890	316	1	3	3	NUM
ejpam-890	316	2	1	1	NUM
ejpam-890	316	3	x	x	SYM
ejpam-890	316	4	3	3	NUM
ejpam-890	316	5	2	2	NUM
ejpam-890	316	6	x3	x3	ADJ
ejpam-890	316	7	.	.	PUNCT
ejpam-890	317	1	definition	definition	NOUN
ejpam-890	317	2	10	10	NUM
ejpam-890	317	3	.	.	PUNCT
ejpam-890	318	1	the	the	DET
ejpam-890	318	2	polynomial	polynomial	ADJ
ejpam-890	318	3	,	,	PUNCT
ejpam-890	318	4	bp×r	bp×r	PROPN
ejpam-890	318	5	(	(	PUNCT
ejpam-890	318	6	t	t	PROPN
ejpam-890	318	7	)	)	PUNCT
ejpam-890	318	8	=	=	SYM
ejpam-890	318	9	∑	∑	PROPN
ejpam-890	318	10	a∈b	a∈b	NOUN
ejpam-890	318	11	twn	twn	X
ejpam-890	318	12	(	(	PUNCT
ejpam-890	318	13	a	a	NOUN
ejpam-890	318	14	)	)	PUNCT
ejpam-890	318	15	=	=	SYM
ejpam-890	318	16	∑p·r	∑p·r	PROPN
ejpam-890	319	1	i=1	i=1	PRON
ejpam-890	320	1	bi	bi	PROPN
ejpam-890	321	1	t	t	PROPN
ejpam-890	322	1	i	i	PRON
ejpam-890	322	2	is	be	AUX
ejpam-890	322	3	said	say	VERB
ejpam-890	322	4	to	to	PART
ejpam-890	322	5	be	be	AUX
ejpam-890	322	6	the	the	DET
ejpam-890	322	7	weight	weight	NOUN
ejpam-890	322	8	enumerator	enumerator	NOUN
ejpam-890	322	9	of	of	ADP
ejpam-890	322	10	bursts	burst	NOUN
ejpam-890	322	11	of	of	ADP
ejpam-890	322	12	order	order	NOUN
ejpam-890	322	13	p×	p×	NOUN
ejpam-890	322	14	r	r	NOUN
ejpam-890	322	15	in	in	ADP
ejpam-890	322	16	the	the	DET
ejpam-890	322	17	space	space	NOUN
ejpam-890	322	18	mp×r(r	mp×r(r	NOUN
ejpam-890	322	19	)	)	PUNCT
ejpam-890	322	20	.	.	PUNCT
ejpam-890	323	1	corollary	corollary	ADJ
ejpam-890	323	2	2	2	NUM
ejpam-890	323	3	.	.	PUNCT
ejpam-890	324	1	by	by	ADP
ejpam-890	324	2	substituting	substitute	VERB
ejpam-890	324	3	x	x	PUNCT
ejpam-890	324	4	i	i	PROPN
ejpam-890	324	5	=	=	SYM
ejpam-890	324	6	t	t	PROPN
ejpam-890	324	7	in	in	ADP
ejpam-890	324	8	h(x̃	h(x̃	PROPN
ejpam-890	324	9	)	)	PUNCT
ejpam-890	324	10	,	,	PUNCT
ejpam-890	324	11	we	we	PRON
ejpam-890	324	12	obtain	obtain	VERB
ejpam-890	324	13	bp×r(t	bp×r(t	NOUN
ejpam-890	324	14	)	)	PUNCT
ejpam-890	324	15	which	which	PRON
ejpam-890	324	16	is	be	AUX
ejpam-890	324	17	the	the	DET
ejpam-890	324	18	weight	weight	NOUN
ejpam-890	324	19	enumerator	enumerator	NOUN
ejpam-890	324	20	of	of	ADP
ejpam-890	324	21	bursts	burst	NOUN
ejpam-890	324	22	of	of	ADP
ejpam-890	324	23	order	order	NOUN
ejpam-890	324	24	p	p	X
ejpam-890	324	25	×	×	PROPN
ejpam-890	324	26	r.	r.	PROPN
ejpam-890	324	27	further	far	ADV
ejpam-890	324	28	,	,	PUNCT
ejpam-890	324	29	the	the	DET
ejpam-890	324	30	bp×r(r	bp×r(r	NOUN
ejpam-890	324	31	,	,	PUNCT
ejpam-890	324	32	w	w	NOUN
ejpam-890	324	33	)	)	PUNCT
ejpam-890	324	34	numbers	number	NOUN
ejpam-890	324	35	formulated	formulate	VERB
ejpam-890	324	36	in	in	ADP
ejpam-890	324	37	theorem	theorem	NOUN
ejpam-890	324	38	2	2	NUM
ejpam-890	324	39	by	by	ADP
ejpam-890	324	40	[	[	X
ejpam-890	324	41	5	5	NUM
ejpam-890	324	42	]	]	PUNCT
ejpam-890	324	43	are	be	AUX
ejpam-890	324	44	reobtained	reobtaine	VERB
ejpam-890	324	45	as	as	SCONJ
ejpam-890	324	46	follows	follow	VERB
ejpam-890	324	47	:	:	PUNCT
ejpam-890	324	48	bp×r(r	bp×r(r	NOUN
ejpam-890	324	49	,	,	PUNCT
ejpam-890	324	50	w	w	NOUN
ejpam-890	324	51	)	)	PUNCT
ejpam-890	324	52	=	=	SYM
ejpam-890	325	1	w	w	PROPN
ejpam-890	325	2	∑	∑	PUNCT
ejpam-890	325	3	i=1	i=1	PROPN
ejpam-890	325	4	bi	bi	NOUN
ejpam-890	325	5	where	where	SCONJ
ejpam-890	325	6	bi	bi	PROPN
ejpam-890	325	7	’s	’	VERB
ejpam-890	325	8	are	be	AUX
ejpam-890	325	9	coefficients	coefficient	NOUN
ejpam-890	325	10	of	of	ADP
ejpam-890	325	11	bp×r(t	bp×r(t	NOUN
ejpam-890	325	12	)	)	PUNCT
ejpam-890	325	13	.	.	PUNCT
ejpam-890	326	1	we	we	PRON
ejpam-890	326	2	would	would	AUX
ejpam-890	326	3	like	like	VERB
ejpam-890	326	4	to	to	PART
ejpam-890	326	5	emphasize	emphasize	VERB
ejpam-890	326	6	that	that	SCONJ
ejpam-890	326	7	by	by	ADP
ejpam-890	326	8	applying	apply	VERB
ejpam-890	326	9	corollary	corollary	ADJ
ejpam-890	326	10	2	2	NUM
ejpam-890	326	11	,	,	PUNCT
ejpam-890	326	12	we	we	PRON
ejpam-890	326	13	are	be	AUX
ejpam-890	326	14	able	able	ADJ
ejpam-890	326	15	to	to	PART
ejpam-890	326	16	compute	compute	VERB
ejpam-890	326	17	bp×r(r	bp×r(r	NOUN
ejpam-890	326	18	,	,	PUNCT
ejpam-890	326	19	w	w	NOUN
ejpam-890	326	20	)	)	PUNCT
ejpam-890	326	21	quite	quite	ADV
ejpam-890	326	22	easily	easily	ADV
ejpam-890	326	23	.	.	PUNCT
ejpam-890	327	1	in	in	ADP
ejpam-890	327	2	[	[	X
ejpam-890	327	3	5	5	NUM
ejpam-890	327	4	]	]	PUNCT
ejpam-890	327	5	,	,	PUNCT
ejpam-890	327	6	for	for	ADP
ejpam-890	327	7	each	each	DET
ejpam-890	327	8	weight	weight	NOUN
ejpam-890	327	9	w	w	ADP
ejpam-890	327	10	where	where	SCONJ
ejpam-890	327	11	1	1	NUM
ejpam-890	327	12	≤	≤	NOUN
ejpam-890	327	13	w	w	NOUN
ejpam-890	327	14	≤	≤	ADJ
ejpam-890	327	15	pr	pr	NOUN
ejpam-890	327	16	,	,	PUNCT
ejpam-890	327	17	the	the	DET
ejpam-890	327	18	computation	computation	NOUN
ejpam-890	327	19	of	of	ADP
ejpam-890	327	20	bp×r(r	bp×r(r	NOUN
ejpam-890	327	21	,	,	PUNCT
ejpam-890	327	22	w	w	PROPN
ejpam-890	327	23	)	)	PUNCT
ejpam-890	327	24	has	have	AUX
ejpam-890	327	25	to	to	PART
ejpam-890	327	26	be	be	AUX
ejpam-890	327	27	carried	carry	VERB
ejpam-890	327	28	out	out	ADP
ejpam-890	327	29	separately	separately	ADV
ejpam-890	327	30	by	by	ADP
ejpam-890	327	31	solving	solve	VERB
ejpam-890	327	32	the	the	DET
ejpam-890	327	33	necessary	necessary	ADJ
ejpam-890	327	34	diophantine	diophantine	NOUN
ejpam-890	327	35	inequalities	inequality	NOUN
ejpam-890	327	36	(	(	PUNCT
ejpam-890	327	37	see	see	VERB
ejpam-890	327	38	eq.(2	eq.(2	ADJ
ejpam-890	327	39	)	)	PUNCT
ejpam-890	327	40	)	)	PUNCT
ejpam-890	327	41	and	and	CCONJ
ejpam-890	327	42	then	then	ADV
ejpam-890	327	43	applying	apply	VERB
ejpam-890	327	44	the	the	DET
ejpam-890	327	45	formula	formula	NOUN
ejpam-890	327	46	(	(	PUNCT
ejpam-890	327	47	see	see	VERB
ejpam-890	327	48	eq	eq	NOUN
ejpam-890	327	49	.	.	PUNCT
ejpam-890	328	1	(	(	PUNCT
ejpam-890	328	2	1	1	NUM
ejpam-890	328	3	)	)	PUNCT
ejpam-890	328	4	)	)	PUNCT
ejpam-890	328	5	.	.	PUNCT
ejpam-890	329	1	example	example	NOUN
ejpam-890	330	1	7	7	NUM
ejpam-890	330	2	.	.	PUNCT
ejpam-890	331	1	the	the	DET
ejpam-890	331	2	following	follow	VERB
ejpam-890	331	3	generic	generic	ADJ
ejpam-890	331	4	polynomial	polynomial	ADJ
ejpam-890	331	5	g	g	PROPN
ejpam-890	331	6	gives	give	VERB
ejpam-890	331	7	the	the	DET
ejpam-890	331	8	term	term	NOUN
ejpam-890	331	9	representation	representation	NOUN
ejpam-890	331	10	of	of	ADP
ejpam-890	331	11	a	a	DET
ejpam-890	331	12	∈	∈	PROPN
ejpam-890	331	13	m4×4(f2	m4×4(f2	NOUN
ejpam-890	331	14	)	)	PUNCT
ejpam-890	331	15	generic	generic	ADJ
ejpam-890	331	16	burst	burst	ADJ
ejpam-890	331	17	errors	error	NOUN
ejpam-890	331	18	of	of	ADP
ejpam-890	331	19	order	order	NOUN
ejpam-890	331	20	4×	4×	NOUN
ejpam-890	331	21	4	4	NUM
ejpam-890	331	22	:	:	PUNCT
ejpam-890	331	23	g(z̃	g(z̃	NOUN
ejpam-890	331	24	,	,	PUNCT
ejpam-890	331	25	x̃	x̃	PROPN
ejpam-890	331	26	,	,	PUNCT
ejpam-890	331	27	x̃	x̃	PROPN
ejpam-890	331	28	,	,	PUNCT
ejpam-890	331	29	ỹ	ỹ	PROPN
ejpam-890	331	30	)	)	PUNCT
ejpam-890	331	31	=	=	PUNCT
ejpam-890	332	1	∑	∑	PUNCT
ejpam-890	332	2	(	(	PUNCT
ejpam-890	332	3	i	i	PROPN
ejpam-890	332	4	,	,	PUNCT
ejpam-890	332	5	j	j	PROPN
ejpam-890	332	6	,	,	PUNCT
ejpam-890	332	7	k	k	PROPN
ejpam-890	332	8	,	,	PUNCT
ejpam-890	332	9	l)∈{0,1}4	l)∈{0,1}4	NOUN
ejpam-890	333	1	z	z	NOUN
ejpam-890	333	2	i	i	VERB
ejpam-890	333	3	1	1	NUM
ejpam-890	333	4	y	y	PROPN
ejpam-890	333	5	j	j	PROPN
ejpam-890	333	6	1zk	1zk	ADJ
ejpam-890	333	7	4	4	NUM
ejpam-890	333	8	y	y	PROPN
ejpam-890	333	9	l	l	NOUN
ejpam-890	333	10	4z	4z	NOUN
ejpam-890	333	11	ik(α)y	ik(α)y	PROPN
ejpam-890	333	12	jl(α)γi	jl(α)γi	PROPN
ejpam-890	333	13	j(x1)γkl(x4	j(x1)γkl(x4	NOUN
ejpam-890	333	14	)	)	PUNCT
ejpam-890	333	15	.	.	PUNCT
ejpam-890	334	1	i̇.	i̇.	PROPN
ejpam-890	334	2	siap	siap	PROPN
ejpam-890	334	3	/	/	SYM
ejpam-890	334	4	eur	eur	PROPN
ejpam-890	334	5	.	.	PUNCT
ejpam-890	335	1	j.	j.	PROPN
ejpam-890	335	2	pure	pure	PROPN
ejpam-890	335	3	appl	appl	PROPN
ejpam-890	335	4	.	.	PROPN
ejpam-890	335	5	math	math	PROPN
ejpam-890	335	6	,	,	PUNCT
ejpam-890	335	7	3	3	NUM
ejpam-890	335	8	(	(	PUNCT
ejpam-890	335	9	2010	2010	NUM
ejpam-890	335	10	)	)	PUNCT
ejpam-890	335	11	,	,	PUNCT
ejpam-890	335	12	653	653	NUM
ejpam-890	335	13	-	-	SYM
ejpam-890	335	14	669	669	NUM
ejpam-890	335	15	665	665	NUM
ejpam-890	335	16	applying	apply	VERB
ejpam-890	335	17	necessary	necessary	ADJ
ejpam-890	335	18	substitutions	substitution	NOUN
ejpam-890	335	19	given	give	VERB
ejpam-890	335	20	in	in	ADP
ejpam-890	335	21	corollary	corollary	ADJ
ejpam-890	335	22	2	2	NUM
ejpam-890	335	23	,	,	PUNCT
ejpam-890	335	24	we	we	PRON
ejpam-890	335	25	obtain	obtain	VERB
ejpam-890	335	26	the	the	DET
ejpam-890	335	27	weight	weight	NOUN
ejpam-890	335	28	enumerator	enumerator	NOUN
ejpam-890	335	29	of	of	ADP
ejpam-890	335	30	burst	burst	ADJ
ejpam-890	335	31	errors	error	NOUN
ejpam-890	335	32	:	:	PUNCT
ejpam-890	335	33	b4×4(t	b4×4(t	NOUN
ejpam-890	335	34	)	)	PUNCT
ejpam-890	336	1	=	=	NOUN
ejpam-890	336	2	3840t16	3840t16	NOUN
ejpam-890	336	3	+	+	CCONJ
ejpam-890	336	4	7680t15	7680t15	ADJ
ejpam-890	336	5	+	+	NUM
ejpam-890	336	6	9600t14	9600t14	NOUN
ejpam-890	336	7	+	+	NOUN
ejpam-890	336	8	9728t13	9728t13	PROPN
ejpam-890	336	9	+	+	CCONJ
ejpam-890	336	10	8288t12	8288t12	NOUN
ejpam-890	336	11	+	+	SYM
ejpam-890	336	12	5856t11	5856t11	NUM
ejpam-890	336	13	+	+	SYM
ejpam-890	336	14	3504t10	3504t10	ADJ
ejpam-890	336	15	+	+	NOUN
ejpam-890	336	16	1824t9	1824t9	ADJ
ejpam-890	336	17	+	+	NOUN
ejpam-890	336	18	792t8	792t8	NUM
ejpam-890	336	19	+	+	NOUN
ejpam-890	336	20	272t7	272t7	NUM
ejpam-890	336	21	+	+	CCONJ
ejpam-890	336	22	72t6	72t6	NUM
ejpam-890	336	23	+	+	CCONJ
ejpam-890	336	24	16t5	16t5	NUM
ejpam-890	336	25	.	.	PUNCT
ejpam-890	336	26	letting	let	VERB
ejpam-890	336	27	t	t	NOUN
ejpam-890	336	28	=	=	SYM
ejpam-890	336	29	1	1	NUM
ejpam-890	336	30	,	,	PUNCT
ejpam-890	336	31	in	in	ADP
ejpam-890	336	32	b4×4(t	b4×4(t	PROPN
ejpam-890	336	33	)	)	PUNCT
ejpam-890	336	34	we	we	PRON
ejpam-890	336	35	have	have	VERB
ejpam-890	336	36	b4×4(1	b4×4(1	X
ejpam-890	336	37	)	)	PUNCT
ejpam-890	336	38	=	=	SYM
ejpam-890	336	39	51472	51472	NUM
ejpam-890	336	40	.	.	PUNCT
ejpam-890	337	1	further	far	ADV
ejpam-890	337	2	,	,	PUNCT
ejpam-890	337	3	b4×4(f2	b4×4(f2	ADJ
ejpam-890	337	4	,	,	PUNCT
ejpam-890	337	5	7	7	NUM
ejpam-890	337	6	)	)	PUNCT
ejpam-890	337	7	=	=	SYM
ejpam-890	337	8	16	16	NUM
ejpam-890	338	1	+	+	NUM
ejpam-890	338	2	72	72	NUM
ejpam-890	338	3	+	+	NOUN
ejpam-890	338	4	272=	272=	NOUN
ejpam-890	338	5	360	360	NUM
ejpam-890	338	6	which	which	PRON
ejpam-890	338	7	is	be	AUX
ejpam-890	338	8	the	the	DET
ejpam-890	338	9	number	number	NOUN
ejpam-890	338	10	of	of	ADP
ejpam-890	338	11	burst	burst	ADJ
ejpam-890	338	12	errors	error	NOUN
ejpam-890	338	13	of	of	ADP
ejpam-890	338	14	type	type	NOUN
ejpam-890	338	15	4×	4×	NOUN
ejpam-890	338	16	4	4	NUM
ejpam-890	338	17	of	of	ADP
ejpam-890	338	18	weight	weight	NOUN
ejpam-890	338	19	7	7	NUM
ejpam-890	338	20	or	or	CCONJ
ejpam-890	338	21	less	less	ADJ
ejpam-890	338	22	.	.	PUNCT
ejpam-890	339	1	3	3	X
ejpam-890	339	2	.	.	X
ejpam-890	339	3	enumerating	enumerate	VERB
ejpam-890	339	4	bursts	burst	NOUN
ejpam-890	339	5	in	in	ADP
ejpam-890	339	6	larger	large	ADJ
ejpam-890	339	7	space	space	NOUN
ejpam-890	339	8	in	in	ADP
ejpam-890	339	9	this	this	DET
ejpam-890	339	10	section	section	NOUN
ejpam-890	339	11	we	we	PRON
ejpam-890	339	12	consider	consider	VERB
ejpam-890	339	13	burst	burst	NOUN
ejpam-890	339	14	of	of	ADP
ejpam-890	339	15	errors	error	NOUN
ejpam-890	339	16	of	of	ADP
ejpam-890	339	17	order	order	NOUN
ejpam-890	339	18	p	p	X
ejpam-890	339	19	×	×	NOUN
ejpam-890	339	20	r	r	NOUN
ejpam-890	339	21	in	in	ADP
ejpam-890	339	22	the	the	DET
ejpam-890	339	23	space	space	NOUN
ejpam-890	339	24	mm×s(r	mm×s(r	NOUN
ejpam-890	339	25	)	)	PUNCT
ejpam-890	339	26	where	where	SCONJ
ejpam-890	339	27	1≤	1≤	X
ejpam-890	339	28	p	p	X
ejpam-890	339	29	<	<	X
ejpam-890	339	30	m	m	NOUN
ejpam-890	339	31	and	and	CCONJ
ejpam-890	339	32	1≤	1≤	NUM
ejpam-890	339	33	r	r	NOUN
ejpam-890	339	34	<	<	X
ejpam-890	339	35	s.	s.	PROPN
ejpam-890	339	36	example	example	NOUN
ejpam-890	339	37	8	8	NUM
ejpam-890	339	38	.	.	PUNCT
ejpam-890	340	1	we	we	PRON
ejpam-890	340	2	list	list	VERB
ejpam-890	340	3	two	two	NUM
ejpam-890	340	4	burst	burst	ADJ
ejpam-890	340	5	errors	error	NOUN
ejpam-890	340	6	of	of	ADP
ejpam-890	340	7	order	order	NOUN
ejpam-890	340	8	3×	3×	NUM
ejpam-890	340	9	3	3	NUM
ejpam-890	340	10	in	in	ADP
ejpam-890	340	11	the	the	DET
ejpam-890	340	12	space	space	NOUN
ejpam-890	340	13	m4×4(f2	m4×4(f2	PROPN
ejpam-890	340	14	)	)	PUNCT
ejpam-890	340	15	.	.	PUNCT
ejpam-890	341	1	a=	a=	PROPN
ejpam-890	341	2			PROPN
ejpam-890	341	3			ADJ
ejpam-890	341	4			ADJ
ejpam-890	341	5			ADJ
ejpam-890	341	6			NOUN
ejpam-890	341	7	0	0	NUM
ejpam-890	341	8	0	0	NUM
ejpam-890	341	9	0	0	NUM
ejpam-890	341	10	0	0	NUM
ejpam-890	341	11	0	0	NUM
ejpam-890	341	12	0	0	NUM
ejpam-890	341	13	1	1	NUM
ejpam-890	341	14	0	0	NUM
ejpam-890	341	15	0	0	NUM
ejpam-890	341	16	1	1	NUM
ejpam-890	341	17	0	0	NUM
ejpam-890	341	18	0	0	NUM
ejpam-890	341	19	0	0	NUM
ejpam-890	341	20	0	0	NUM
ejpam-890	341	21	0	0	NUM
ejpam-890	341	22	1	1	NUM
ejpam-890	341	23			PROPN
ejpam-890	341	24			PROPN
ejpam-890	341	25			PROPN
ejpam-890	341	26			PROPN
ejpam-890	341	27			PROPN
ejpam-890	341	28	,	,	PUNCT
ejpam-890	341	29	b	b	X
ejpam-890	341	30	=	=	PUNCT
ejpam-890	341	31			X
ejpam-890	341	32			ADJ
ejpam-890	341	33			ADJ
ejpam-890	341	34			ADJ
ejpam-890	341	35			NOUN
ejpam-890	341	36	0	0	SYM
ejpam-890	341	37	0	0	NUM
ejpam-890	341	38	1	1	NUM
ejpam-890	341	39	1	1	NUM
ejpam-890	341	40	0	0	NUM
ejpam-890	341	41	1	1	NUM
ejpam-890	341	42	1	1	NUM
ejpam-890	341	43	0	0	NUM
ejpam-890	341	44	0	0	NUM
ejpam-890	341	45	1	1	NUM
ejpam-890	341	46	0	0	NUM
ejpam-890	341	47	0	0	NUM
ejpam-890	341	48	0	0	NUM
ejpam-890	341	49	0	0	NUM
ejpam-890	341	50	0	0	NUM
ejpam-890	341	51	0	0	NUM
ejpam-890	341	52			PROPN
ejpam-890	341	53			PROPN
ejpam-890	341	54			PROPN
ejpam-890	341	55			PROPN
ejpam-890	341	56			PROPN
ejpam-890	341	57	.	.	PUNCT
ejpam-890	342	1	lemma	lemma	PROPN
ejpam-890	342	2	2	2	X
ejpam-890	342	3	.	.	PUNCT
ejpam-890	342	4	let	let	VERB
ejpam-890	342	5	a	a	PRON
ejpam-890	342	6	be	be	AUX
ejpam-890	342	7	a	a	DET
ejpam-890	342	8	burst	burst	NOUN
ejpam-890	342	9	of	of	ADP
ejpam-890	342	10	order	order	NOUN
ejpam-890	342	11	p×	p×	NOUN
ejpam-890	342	12	r	r	NOUN
ejpam-890	342	13	in	in	ADP
ejpam-890	342	14	the	the	DET
ejpam-890	342	15	space	space	NOUN
ejpam-890	342	16	mm×s(r	mm×s(r	NOUN
ejpam-890	342	17	)	)	PUNCT
ejpam-890	343	1	where	where	SCONJ
ejpam-890	343	2	1≤	1≤	X
ejpam-890	343	3	p	p	X
ejpam-890	343	4	<	<	X
ejpam-890	343	5	m	m	NOUN
ejpam-890	343	6	and	and	CCONJ
ejpam-890	343	7	1≤	1≤	NUM
ejpam-890	343	8	r	r	NOUN
ejpam-890	343	9	<	<	X
ejpam-890	343	10	s.	s.	PROPN
ejpam-890	343	11	if	if	SCONJ
ejpam-890	343	12	t	t	PROPN
ejpam-890	343	13	p×r	p×r	PROPN
ejpam-890	343	14	p×r	p×r	PROPN
ejpam-890	343	15	(	(	PUNCT
ejpam-890	343	16	r	r	NOUN
ejpam-890	343	17	)	)	PUNCT
ejpam-890	343	18	is	be	AUX
ejpam-890	343	19	the	the	DET
ejpam-890	343	20	number	number	NOUN
ejpam-890	343	21	of	of	ADP
ejpam-890	343	22	burst	burst	ADJ
ejpam-890	343	23	errors	error	NOUN
ejpam-890	343	24	of	of	ADP
ejpam-890	343	25	order	order	NOUN
ejpam-890	343	26	p×	p×	NOUN
ejpam-890	343	27	r	r	NOUN
ejpam-890	343	28	in	in	ADP
ejpam-890	343	29	the	the	DET
ejpam-890	343	30	space	space	NOUN
ejpam-890	343	31	mp×r(r	mp×r(r	NOUN
ejpam-890	343	32	)	)	PUNCT
ejpam-890	343	33	,	,	PUNCT
ejpam-890	343	34	then	then	ADV
ejpam-890	343	35	t	t	PROPN
ejpam-890	343	36	p×r	p×r	PROPN
ejpam-890	343	37	m×s	m×s	PROPN
ejpam-890	343	38	(	(	PUNCT
ejpam-890	343	39	r	r	NOUN
ejpam-890	343	40	)	)	PUNCT
ejpam-890	343	41	=	=	SYM
ejpam-890	343	42	(	(	PUNCT
ejpam-890	343	43	s−	s−	PROPN
ejpam-890	343	44	r	r	PROPN
ejpam-890	343	45	+	+	NUM
ejpam-890	343	46	1)(m−	1)(m−	PROPN
ejpam-890	343	47	p+	p+	VERB
ejpam-890	343	48	1)t	1)t	PROPN
ejpam-890	343	49	p×r	p×r	PROPN
ejpam-890	343	50	p×r	p×r	PROPN
ejpam-890	343	51	(	(	PUNCT
ejpam-890	343	52	r	r	NOUN
ejpam-890	343	53	)	)	PUNCT
ejpam-890	343	54	gives	give	VERB
ejpam-890	343	55	the	the	DET
ejpam-890	343	56	number	number	NOUN
ejpam-890	343	57	of	of	ADP
ejpam-890	343	58	burst	burst	NOUN
ejpam-890	343	59	of	of	ADP
ejpam-890	343	60	order	order	NOUN
ejpam-890	343	61	p×	p×	NOUN
ejpam-890	343	62	r	r	NOUN
ejpam-890	343	63	in	in	ADP
ejpam-890	343	64	the	the	DET
ejpam-890	343	65	space	space	NOUN
ejpam-890	343	66	mm×s(r	mm×s(r	NOUN
ejpam-890	343	67	)	)	PUNCT
ejpam-890	343	68	.	.	PUNCT
ejpam-890	344	1	proof	proof	NOUN
ejpam-890	344	2	.	.	PUNCT
ejpam-890	345	1	by	by	ADP
ejpam-890	345	2	definition	definition	NOUN
ejpam-890	345	3	,	,	PUNCT
ejpam-890	345	4	a	a	DET
ejpam-890	345	5	burst	burst	NOUN
ejpam-890	345	6	of	of	ADP
ejpam-890	345	7	order	order	NOUN
ejpam-890	345	8	p×	p×	NOUN
ejpam-890	345	9	r	r	NOUN
ejpam-890	345	10	in	in	ADP
ejpam-890	345	11	the	the	DET
ejpam-890	345	12	space	space	NOUN
ejpam-890	345	13	mm×s(r	mm×s(r	NOUN
ejpam-890	345	14	)	)	PUNCT
ejpam-890	345	15	is	be	AUX
ejpam-890	345	16	a	a	DET
ejpam-890	345	17	matrix	matrix	NOUN
ejpam-890	345	18	of	of	ADP
ejpam-890	345	19	order	order	NOUN
ejpam-890	345	20	m×	m×	PROPN
ejpam-890	345	21	s	s	VERB
ejpam-890	345	22	that	that	PRON
ejpam-890	345	23	includes	include	VERB
ejpam-890	345	24	a	a	DET
ejpam-890	345	25	submatrix	submatrix	NOUN
ejpam-890	345	26	a	a	PRON
ejpam-890	345	27	which	which	PRON
ejpam-890	345	28	is	be	AUX
ejpam-890	345	29	a	a	DET
ejpam-890	345	30	burst	burst	ADJ
ejpam-890	345	31	error	error	NOUN
ejpam-890	345	32	of	of	ADP
ejpam-890	345	33	order	order	NOUN
ejpam-890	345	34	p×	p×	NOUN
ejpam-890	345	35	r	r	NOUN
ejpam-890	345	36	itself	itself	PRON
ejpam-890	345	37	in	in	ADP
ejpam-890	345	38	the	the	DET
ejpam-890	345	39	space	space	NOUN
ejpam-890	345	40	mp×r(r	mp×r(r	NOUN
ejpam-890	345	41	)	)	PUNCT
ejpam-890	345	42	and	and	CCONJ
ejpam-890	345	43	the	the	DET
ejpam-890	345	44	entries	entry	NOUN
ejpam-890	345	45	that	that	PRON
ejpam-890	345	46	fall	fall	VERB
ejpam-890	345	47	out	out	ADP
ejpam-890	345	48	of	of	ADP
ejpam-890	345	49	this	this	DET
ejpam-890	345	50	submatrix	submatrix	NOUN
ejpam-890	345	51	are	be	AUX
ejpam-890	345	52	all	all	PRON
ejpam-890	345	53	zeroes	zero	NOUN
ejpam-890	345	54	.	.	PUNCT
ejpam-890	346	1	hence	hence	ADV
ejpam-890	346	2	,	,	PUNCT
ejpam-890	346	3	placing	place	VERB
ejpam-890	346	4	a	a	PRON
ejpam-890	346	5	as	as	ADP
ejpam-890	346	6	a	a	DET
ejpam-890	346	7	submatrix	submatrix	NOUN
ejpam-890	346	8	of	of	ADP
ejpam-890	346	9	a	a	DET
ejpam-890	346	10	matrix	matrix	NOUN
ejpam-890	346	11	of	of	ADP
ejpam-890	346	12	size	size	NOUN
ejpam-890	346	13	m×	m×	PROPN
ejpam-890	346	14	s	s	PART
ejpam-890	346	15	is	be	AUX
ejpam-890	346	16	possible	possible	ADJ
ejpam-890	346	17	in	in	ADP
ejpam-890	346	18	s−	s−	PROPN
ejpam-890	346	19	r+1	r+1	PROPN
ejpam-890	346	20	ways	way	NOUN
ejpam-890	346	21	moving	move	VERB
ejpam-890	346	22	from	from	ADP
ejpam-890	346	23	the	the	DET
ejpam-890	346	24	left	left	NOUN
ejpam-890	346	25	to	to	ADP
ejpam-890	346	26	the	the	DET
ejpam-890	346	27	right	right	ADJ
ejpam-890	346	28	starting	starting	NOUN
ejpam-890	346	29	from	from	ADP
ejpam-890	346	30	the	the	DET
ejpam-890	346	31	position	position	NOUN
ejpam-890	346	32	(	(	PUNCT
ejpam-890	346	33	1,1	1,1	NUM
ejpam-890	346	34	)	)	PUNCT
ejpam-890	346	35	for	for	ADP
ejpam-890	346	36	both	both	CCONJ
ejpam-890	346	37	the	the	DET
ejpam-890	346	38	matrix	matrix	NOUN
ejpam-890	346	39	and	and	CCONJ
ejpam-890	346	40	the	the	DET
ejpam-890	346	41	submatrix	submatrix	NOUN
ejpam-890	346	42	.	.	PUNCT
ejpam-890	347	1	also	also	ADV
ejpam-890	347	2	,	,	PUNCT
ejpam-890	347	3	for	for	ADP
ejpam-890	347	4	a	a	DET
ejpam-890	347	5	given	give	VERB
ejpam-890	347	6	possible	possible	ADJ
ejpam-890	347	7	position	position	NOUN
ejpam-890	347	8	obtained	obtain	VERB
ejpam-890	347	9	above	above	ADV
ejpam-890	347	10	,	,	PUNCT
ejpam-890	347	11	there	there	PRON
ejpam-890	347	12	exist	exist	VERB
ejpam-890	347	13	also	also	ADV
ejpam-890	347	14	m−	m−	PROPN
ejpam-890	347	15	p+	p+	VERB
ejpam-890	347	16	1	1	NUM
ejpam-890	347	17	movements	movement	NOUN
ejpam-890	347	18	downwards	downwards	ADV
ejpam-890	347	19	for	for	ADP
ejpam-890	347	20	obtaining	obtain	VERB
ejpam-890	347	21	submatrices	submatrice	NOUN
ejpam-890	347	22	.	.	PUNCT
ejpam-890	348	1	thus	thus	ADV
ejpam-890	348	2	,	,	PUNCT
ejpam-890	348	3	there	there	PRON
ejpam-890	348	4	exist	exist	VERB
ejpam-890	348	5	(	(	PUNCT
ejpam-890	348	6	s−	s−	PROPN
ejpam-890	348	7	r+1)(m−	r+1)(m−	NUM
ejpam-890	348	8	p+1	p+1	NOUN
ejpam-890	348	9	)	)	PUNCT
ejpam-890	348	10	ways	way	NOUN
ejpam-890	348	11	that	that	PRON
ejpam-890	348	12	give	give	VERB
ejpam-890	348	13	raise	raise	NOUN
ejpam-890	348	14	to	to	ADP
ejpam-890	348	15	new	new	ADJ
ejpam-890	348	16	submatrices	submatrice	NOUN
ejpam-890	348	17	for	for	ADP
ejpam-890	348	18	each	each	DET
ejpam-890	348	19	burst	burst	ADJ
ejpam-890	348	20	error	error	NOUN
ejpam-890	348	21	of	of	ADP
ejpam-890	348	22	order	order	NOUN
ejpam-890	348	23	p	p	X
ejpam-890	348	24	×	×	NOUN
ejpam-890	348	25	r	r	NOUN
ejpam-890	348	26	in	in	ADP
ejpam-890	348	27	the	the	DET
ejpam-890	348	28	space	space	NOUN
ejpam-890	348	29	mm×s(r	mm×s(r	NOUN
ejpam-890	348	30	)	)	PUNCT
ejpam-890	348	31	.	.	PUNCT
ejpam-890	349	1	therefore	therefore	ADV
ejpam-890	349	2	,	,	PUNCT
ejpam-890	349	3	the	the	DET
ejpam-890	349	4	number	number	NOUN
ejpam-890	349	5	of	of	ADP
ejpam-890	349	6	burst	burst	NOUN
ejpam-890	349	7	of	of	ADP
ejpam-890	349	8	order	order	NOUN
ejpam-890	349	9	p	p	X
ejpam-890	349	10	×	×	NOUN
ejpam-890	349	11	r	r	NOUN
ejpam-890	349	12	in	in	ADP
ejpam-890	349	13	the	the	DET
ejpam-890	349	14	space	space	NOUN
ejpam-890	349	15	mm×s(r	mm×s(r	NOUN
ejpam-890	349	16	)	)	PUNCT
ejpam-890	349	17	is	be	AUX
ejpam-890	349	18	(	(	PUNCT
ejpam-890	349	19	s−	s−	PROPN
ejpam-890	349	20	r	r	PROPN
ejpam-890	349	21	+	+	NUM
ejpam-890	349	22	1)(m−	1)(m−	PROPN
ejpam-890	349	23	p+	p+	VERB
ejpam-890	349	24	1)t	1)t	PROPN
ejpam-890	349	25	p×r	p×r	PROPN
ejpam-890	349	26	p×r	p×r	PROPN
ejpam-890	349	27	(	(	PUNCT
ejpam-890	349	28	r	r	NOUN
ejpam-890	349	29	)	)	PUNCT
ejpam-890	349	30	.	.	PUNCT
ejpam-890	350	1	hence	hence	ADV
ejpam-890	350	2	,	,	PUNCT
ejpam-890	350	3	it	it	PRON
ejpam-890	350	4	is	be	AUX
ejpam-890	350	5	possible	possible	ADJ
ejpam-890	350	6	to	to	PART
ejpam-890	350	7	construct	construct	VERB
ejpam-890	350	8	all	all	DET
ejpam-890	350	9	burst	burst	ADJ
ejpam-890	350	10	errors	error	NOUN
ejpam-890	350	11	of	of	ADP
ejpam-890	350	12	size	size	NOUN
ejpam-890	350	13	p×	p×	NOUN
ejpam-890	350	14	r	r	NOUN
ejpam-890	350	15	in	in	ADP
ejpam-890	350	16	mm×s(r	mm×s(r	PROPN
ejpam-890	350	17	)	)	PUNCT
ejpam-890	350	18	knowing	know	VERB
ejpam-890	350	19	all	all	DET
ejpam-890	350	20	burst	burst	ADJ
ejpam-890	350	21	errors	error	NOUN
ejpam-890	350	22	of	of	ADP
ejpam-890	350	23	size	size	NOUN
ejpam-890	350	24	p	p	X
ejpam-890	350	25	×	×	NOUN
ejpam-890	350	26	r	r	NOUN
ejpam-890	350	27	in	in	ADP
ejpam-890	350	28	mp×r(r	mp×r(r	NOUN
ejpam-890	350	29	)	)	PUNCT
ejpam-890	350	30	.	.	PUNCT
ejpam-890	351	1	this	this	PRON
ejpam-890	351	2	can	can	AUX
ejpam-890	351	3	be	be	AUX
ejpam-890	351	4	done	do	VERB
ejpam-890	351	5	easily	easily	ADV
ejpam-890	351	6	by	by	ADP
ejpam-890	351	7	positioning	position	VERB
ejpam-890	351	8	the	the	DET
ejpam-890	351	9	matrices	matrix	NOUN
ejpam-890	351	10	of	of	ADP
ejpam-890	351	11	size	size	NOUN
ejpam-890	351	12	p×	p×	NOUN
ejpam-890	351	13	r	r	NOUN
ejpam-890	351	14	as	as	ADP
ejpam-890	351	15	sub	sub	NOUN
ejpam-890	351	16	matrices	matrix	NOUN
ejpam-890	351	17	of	of	ADP
ejpam-890	351	18	matrices	matrix	NOUN
ejpam-890	351	19	of	of	ADP
ejpam-890	351	20	size	size	NOUN
ejpam-890	351	21	m×	m×	PROPN
ejpam-890	351	22	s.	s.	PROPN
ejpam-890	351	23	since	since	SCONJ
ejpam-890	351	24	after	after	ADP
ejpam-890	351	25	repositioning	reposition	VERB
ejpam-890	351	26	,	,	PUNCT
ejpam-890	351	27	the	the	DET
ejpam-890	351	28	rt	rt	PROPN
ejpam-890	351	29	weights	weight	NOUN
ejpam-890	351	30	will	will	AUX
ejpam-890	351	31	change	change	VERB
ejpam-890	351	32	,	,	PUNCT
ejpam-890	351	33	the	the	DET
ejpam-890	351	34	main	main	ADJ
ejpam-890	351	35	problem	problem	NOUN
ejpam-890	351	36	is	be	AUX
ejpam-890	351	37	to	to	PART
ejpam-890	351	38	control	control	VERB
ejpam-890	351	39	the	the	DET
ejpam-890	351	40	weights	weight	NOUN
ejpam-890	351	41	of	of	ADP
ejpam-890	351	42	burst	burst	ADJ
ejpam-890	351	43	errors	error	NOUN
ejpam-890	351	44	when	when	SCONJ
ejpam-890	351	45	repositioning	repositioning	NOUN
ejpam-890	351	46	is	be	AUX
ejpam-890	351	47	done	do	VERB
ejpam-890	351	48	.	.	PUNCT
ejpam-890	352	1	if	if	SCONJ
ejpam-890	352	2	we	we	PRON
ejpam-890	352	3	know	know	VERB
ejpam-890	352	4	the	the	DET
ejpam-890	352	5	weight	weight	NOUN
ejpam-890	352	6	spectra	spectra	NOUN
ejpam-890	352	7	polynomial	polynomial	PROPN
ejpam-890	352	8	h(x	h(x	PROPN
ejpam-890	352	9	)	)	PUNCT
ejpam-890	352	10	of	of	ADP
ejpam-890	352	11	burst	burst	ADJ
ejpam-890	352	12	errors	error	NOUN
ejpam-890	352	13	of	of	ADP
ejpam-890	352	14	size	size	NOUN
ejpam-890	352	15	p×	p×	NOUN
ejpam-890	352	16	r	r	NOUN
ejpam-890	352	17	in	in	ADP
ejpam-890	352	18	mp×r(r	mp×r(r	NOUN
ejpam-890	352	19	)	)	PUNCT
ejpam-890	352	20	,	,	PUNCT
ejpam-890	352	21	then	then	ADV
ejpam-890	352	22	by	by	ADP
ejpam-890	352	23	multiplying	multiply	VERB
ejpam-890	352	24	h(x	h(x	PROPN
ejpam-890	352	25	)	)	PUNCT
ejpam-890	352	26	with	with	ADP
ejpam-890	352	27	suitable	suitable	ADJ
ejpam-890	352	28	variables	variable	NOUN
ejpam-890	352	29	or	or	CCONJ
ejpam-890	352	30	in	in	ADP
ejpam-890	352	31	other	other	ADJ
ejpam-890	352	32	words	word	NOUN
ejpam-890	352	33	applying	apply	VERB
ejpam-890	352	34	a	a	DET
ejpam-890	352	35	translation	translation	NOUN
ejpam-890	352	36	map	map	NOUN
ejpam-890	352	37	,	,	PUNCT
ejpam-890	352	38	we	we	PRON
ejpam-890	352	39	can	can	AUX
ejpam-890	352	40	obtain	obtain	VERB
ejpam-890	352	41	the	the	DET
ejpam-890	352	42	weight	weight	NOUN
ejpam-890	352	43	spectra	spectra	NOUN
ejpam-890	352	44	of	of	ADP
ejpam-890	352	45	burst	burst	ADJ
ejpam-890	352	46	errors	error	NOUN
ejpam-890	352	47	of	of	ADP
ejpam-890	352	48	size	size	NOUN
ejpam-890	352	49	p×	p×	NOUN
ejpam-890	352	50	r	r	NOUN
ejpam-890	352	51	in	in	ADP
ejpam-890	352	52	mp×r(r	mp×r(r	NOUN
ejpam-890	352	53	)	)	PUNCT
ejpam-890	352	54	as	as	SCONJ
ejpam-890	352	55	explained	explain	VERB
ejpam-890	352	56	below	below	ADV
ejpam-890	352	57	.	.	PUNCT
ejpam-890	353	1	i̇.	i̇.	PROPN
ejpam-890	353	2	siap	siap	PROPN
ejpam-890	353	3	/	/	SYM
ejpam-890	353	4	eur	eur	PROPN
ejpam-890	353	5	.	.	PUNCT
ejpam-890	354	1	j.	j.	PROPN
ejpam-890	354	2	pure	pure	PROPN
ejpam-890	354	3	appl	appl	PROPN
ejpam-890	354	4	.	.	PROPN
ejpam-890	354	5	math	math	PROPN
ejpam-890	354	6	,	,	PUNCT
ejpam-890	354	7	3	3	NUM
ejpam-890	354	8	(	(	PUNCT
ejpam-890	354	9	2010	2010	NUM
ejpam-890	354	10	)	)	PUNCT
ejpam-890	354	11	,	,	PUNCT
ejpam-890	354	12	653	653	NUM
ejpam-890	354	13	-	-	SYM
ejpam-890	354	14	669	669	NUM
ejpam-890	354	15	666	666	NUM
ejpam-890	354	16	definition	definition	NOUN
ejpam-890	354	17	11	11	NUM
ejpam-890	354	18	.	.	PUNCT
ejpam-890	355	1	let	let	VERB
ejpam-890	355	2	h(x1	h(x1	NOUN
ejpam-890	355	3	,	,	PUNCT
ejpam-890	355	4	x2	x2	PROPN
ejpam-890	355	5	,	,	PUNCT
ejpam-890	355	6	.	.	PUNCT
ejpam-890	355	7	.	.	PUNCT
ejpam-890	356	1	.	.	PUNCT
ejpam-890	357	1	,	,	PUNCT
ejpam-890	357	2	x	x	X
ejpam-890	357	3	p	p	X
ejpam-890	357	4	)	)	PUNCT
ejpam-890	357	5	=	=	SYM
ejpam-890	357	6	∑	∑	PUNCT
ejpam-890	357	7	(	(	PUNCT
ejpam-890	357	8	i1,i2,	i1,i2,	PROPN
ejpam-890	357	9	...	...	PUNCT
ejpam-890	357	10	,ip)∈np	,ip)∈np	PUNCT
ejpam-890	357	11	h(i1	h(i1	NOUN
ejpam-890	357	12	,	,	PUNCT
ejpam-890	357	13	i2	i2	PROPN
ejpam-890	357	14	,	,	PUNCT
ejpam-890	357	15	.	.	PUNCT
ejpam-890	357	16	.	.	PUNCT
ejpam-890	358	1	.	.	PUNCT
ejpam-890	359	1	,	,	PUNCT
ejpam-890	359	2	ip)x	ip)x	PROPN
ejpam-890	359	3	i1	i1	PROPN
ejpam-890	359	4	1	1	NUM
ejpam-890	359	5	x	x	PROPN
ejpam-890	359	6	i2	i2	PROPN
ejpam-890	359	7	2	2	NUM
ejpam-890	359	8	·	·	PUNCT
ejpam-890	359	9	·	·	PUNCT
ejpam-890	359	10	·	·	PUNCT
ejpam-890	359	11	x	x	SYM
ejpam-890	359	12	ip	ip	PROPN
ejpam-890	359	13	p	p	NOUN
ejpam-890	359	14	be	be	VERB
ejpam-890	359	15	the	the	DET
ejpam-890	359	16	weight	weight	NOUN
ejpam-890	359	17	spectra	spectra	NOUN
ejpam-890	359	18	polynomial	polynomial	NOUN
ejpam-890	359	19	where	where	SCONJ
ejpam-890	359	20	h(i1	h(i1	NOUN
ejpam-890	359	21	,	,	PUNCT
ejpam-890	359	22	i2	i2	PROPN
ejpam-890	359	23	,	,	PUNCT
ejpam-890	359	24	.	.	PUNCT
ejpam-890	359	25	.	.	PUNCT
ejpam-890	360	1	.	.	PUNCT
ejpam-890	361	1	,	,	PUNCT
ejpam-890	361	2	ip	ip	NOUN
ejpam-890	361	3	)	)	PUNCT
ejpam-890	361	4	∈	∈	PROPN
ejpam-890	361	5	n	n	NOUN
ejpam-890	361	6	and	and	CCONJ
ejpam-890	361	7	n	n	PROPN
ejpam-890	361	8	is	be	AUX
ejpam-890	361	9	the	the	DET
ejpam-890	361	10	set	set	NOUN
ejpam-890	361	11	of	of	ADP
ejpam-890	361	12	natural	natural	ADJ
ejpam-890	361	13	numbers	number	NOUN
ejpam-890	361	14	.	.	PUNCT
ejpam-890	362	1	then	then	ADV
ejpam-890	362	2	,	,	PUNCT
ejpam-890	362	3	we	we	PRON
ejpam-890	362	4	define	define	VERB
ejpam-890	362	5	a	a	DET
ejpam-890	362	6	translation	translation	NOUN
ejpam-890	362	7	map	map	NOUN
ejpam-890	362	8	t	t	PROPN
ejpam-890	362	9	(	(	PUNCT
ejpam-890	362	10	h	h	NOUN
ejpam-890	362	11	)	)	PUNCT
ejpam-890	362	12	=	=	SYM
ejpam-890	362	13	∑	∑	PUNCT
ejpam-890	362	14	(	(	PUNCT
ejpam-890	362	15	i1,i2,	i1,i2,	PROPN
ejpam-890	362	16	...	...	PUNCT
ejpam-890	362	17	,ip)∈np	,ip)∈np	PUNCT
ejpam-890	362	18	h(i1	h(i1	NOUN
ejpam-890	362	19	,	,	PUNCT
ejpam-890	362	20	i2	i2	PROPN
ejpam-890	362	21	,	,	PUNCT
ejpam-890	362	22	.	.	PUNCT
ejpam-890	362	23	.	.	PUNCT
ejpam-890	363	1	.	.	PUNCT
ejpam-890	364	1	,	,	PUNCT
ejpam-890	364	2	ip)x	ip)x	PROPN
ejpam-890	364	3	w(i1)(i1	w(i1)(i1	NOUN
ejpam-890	364	4	+	+	NOUN
ejpam-890	364	5	1	1	NUM
ejpam-890	364	6	)	)	SYM
ejpam-890	364	7	1	1	NUM
ejpam-890	364	8	x	x	SYM
ejpam-890	364	9	w(i2)(i2	w(i2)(i2	NUM
ejpam-890	364	10	+	+	NOUN
ejpam-890	364	11	1	1	NUM
ejpam-890	364	12	)	)	PUNCT
ejpam-890	364	13	2	2	NUM
ejpam-890	364	14	·	·	PUNCT
ejpam-890	364	15	·	·	PUNCT
ejpam-890	364	16	·	·	PUNCT
ejpam-890	364	17	x	x	SYM
ejpam-890	364	18	w(ip)(ip+1	w(ip)(ip+1	NOUN
ejpam-890	364	19	)	)	PUNCT
ejpam-890	364	20	p	p	NOUN
ejpam-890	364	21	.	.	PUNCT
ejpam-890	365	1	lemma	lemma	PROPN
ejpam-890	365	2	3	3	X
ejpam-890	365	3	.	.	PUNCT
ejpam-890	366	1	let	let	VERB
ejpam-890	366	2	h(x	h(x	PROPN
ejpam-890	366	3	)	)	PUNCT
ejpam-890	366	4	be	be	AUX
ejpam-890	366	5	the	the	DET
ejpam-890	366	6	weight	weight	NOUN
ejpam-890	366	7	spectra	spectra	NOUN
ejpam-890	366	8	polynomial	polynomial	NOUN
ejpam-890	366	9	of	of	ADP
ejpam-890	366	10	burst	burst	NOUN
ejpam-890	366	11	of	of	ADP
ejpam-890	366	12	errors	error	NOUN
ejpam-890	366	13	of	of	ADP
ejpam-890	366	14	order	order	NOUN
ejpam-890	366	15	p×r	p×r	PROPN
ejpam-890	366	16	in	in	ADP
ejpam-890	366	17	the	the	DET
ejpam-890	366	18	space	space	NOUN
ejpam-890	366	19	mp×r(r	mp×r(r	NOUN
ejpam-890	366	20	)	)	PUNCT
ejpam-890	366	21	.	.	PUNCT
ejpam-890	367	1	the	the	DET
ejpam-890	367	2	weight	weight	NOUN
ejpam-890	367	3	spectra	spectra	NOUN
ejpam-890	367	4	polynomial	polynomial	NOUN
ejpam-890	367	5	of	of	ADP
ejpam-890	367	6	burst	burst	NOUN
ejpam-890	367	7	of	of	ADP
ejpam-890	367	8	errors	error	NOUN
ejpam-890	367	9	of	of	ADP
ejpam-890	367	10	order	order	NOUN
ejpam-890	367	11	p×	p×	NOUN
ejpam-890	367	12	r	r	NOUN
ejpam-890	367	13	in	in	ADP
ejpam-890	367	14	the	the	DET
ejpam-890	367	15	space	space	NOUN
ejpam-890	367	16	mm×s(r	mm×s(r	NOUN
ejpam-890	367	17	)	)	PUNCT
ejpam-890	367	18	is	be	AUX
ejpam-890	367	19	given	give	VERB
ejpam-890	367	20	by	by	ADP
ejpam-890	367	21	w	w	PROPN
ejpam-890	367	22	(	(	PUNCT
ejpam-890	367	23	x̃	x̃	PROPN
ejpam-890	367	24	)	)	PUNCT
ejpam-890	367	25	=	=	SYM
ejpam-890	368	1	(	(	PUNCT
ejpam-890	368	2	m−	m−	PROPN
ejpam-890	368	3	p+	p+	ADJ
ejpam-890	368	4	1	1	NUM
ejpam-890	368	5	)	)	PUNCT
ejpam-890	368	6	s−r+1	s−r+1	PROPN
ejpam-890	368	7	∑	∑	PUNCT
ejpam-890	368	8	i=0	i=0	PROPN
ejpam-890	368	9	t	t	PROPN
ejpam-890	368	10	i(h	i(h	NOUN
ejpam-890	368	11	)	)	PUNCT
ejpam-890	368	12	.	.	PUNCT
ejpam-890	369	1	proof	proof	NOUN
ejpam-890	369	2	.	.	PUNCT
ejpam-890	370	1	polynomial	polynomial	ADJ
ejpam-890	370	2	h	h	PROPN
ejpam-890	370	3	gives	give	VERB
ejpam-890	370	4	the	the	DET
ejpam-890	370	5	terms	term	NOUN
ejpam-890	370	6	that	that	PRON
ejpam-890	370	7	correspond	correspond	VERB
ejpam-890	370	8	to	to	PART
ejpam-890	370	9	burst	burst	VERB
ejpam-890	370	10	errors	error	NOUN
ejpam-890	370	11	of	of	ADP
ejpam-890	370	12	order	order	NOUN
ejpam-890	370	13	p×	p×	NOUN
ejpam-890	370	14	r	r	NOUN
ejpam-890	370	15	whose	whose	DET
ejpam-890	370	16	(	(	PUNCT
ejpam-890	370	17	1,1	1,1	NUM
ejpam-890	370	18	)	)	PUNCT
ejpam-890	370	19	entry	entry	NOUN
ejpam-890	370	20	position	position	NOUN
ejpam-890	370	21	is	be	AUX
ejpam-890	370	22	located	locate	VERB
ejpam-890	370	23	at	at	ADP
ejpam-890	370	24	(	(	PUNCT
ejpam-890	370	25	1,1	1,1	NUM
ejpam-890	370	26	)	)	PUNCT
ejpam-890	370	27	.	.	PUNCT
ejpam-890	371	1	the	the	DET
ejpam-890	371	2	polynomial	polynomial	PROPN
ejpam-890	371	3	t	t	PROPN
ejpam-890	371	4	(	(	PUNCT
ejpam-890	371	5	h	h	NOUN
ejpam-890	371	6	)	)	PUNCT
ejpam-890	371	7	gives	give	VERB
ejpam-890	371	8	the	the	DET
ejpam-890	371	9	terms	term	NOUN
ejpam-890	371	10	that	that	PRON
ejpam-890	371	11	correspond	correspond	VERB
ejpam-890	371	12	to	to	PART
ejpam-890	371	13	burst	burst	VERB
ejpam-890	371	14	errors	error	NOUN
ejpam-890	371	15	whose	whose	DET
ejpam-890	371	16	(	(	PUNCT
ejpam-890	371	17	1,1	1,1	NUM
ejpam-890	371	18	)	)	PUNCT
ejpam-890	371	19	entry	entry	NOUN
ejpam-890	371	20	position	position	NOUN
ejpam-890	371	21	is	be	AUX
ejpam-890	371	22	located	locate	VERB
ejpam-890	371	23	at	at	ADP
ejpam-890	371	24	(	(	PUNCT
ejpam-890	371	25	1,2	1,2	NUM
ejpam-890	371	26	)	)	PUNCT
ejpam-890	371	27	.	.	PUNCT
ejpam-890	372	1	there	there	PRON
ejpam-890	372	2	are	be	VERB
ejpam-890	372	3	s−	s−	PROPN
ejpam-890	372	4	r	r	NOUN
ejpam-890	372	5	+	+	CCONJ
ejpam-890	372	6	1	1	NUM
ejpam-890	372	7	translations	translation	NOUN
ejpam-890	372	8	possible	possible	ADJ
ejpam-890	372	9	for	for	ADP
ejpam-890	372	10	a	a	DET
ejpam-890	372	11	submatrix	submatrix	NOUN
ejpam-890	372	12	of	of	ADP
ejpam-890	372	13	order	order	NOUN
ejpam-890	372	14	p×	p×	NOUN
ejpam-890	372	15	r	r	NOUN
ejpam-890	372	16	in	in	ADP
ejpam-890	372	17	the	the	DET
ejpam-890	372	18	space	space	NOUN
ejpam-890	372	19	of	of	ADP
ejpam-890	372	20	matrices	matrix	NOUN
ejpam-890	372	21	of	of	ADP
ejpam-890	372	22	order	order	NOUN
ejpam-890	372	23	m×	m×	PROPN
ejpam-890	372	24	s.	s.	PROPN
ejpam-890	372	25	the	the	DET
ejpam-890	372	26	sum	sum	NOUN
ejpam-890	372	27	of	of	ADP
ejpam-890	372	28	all	all	DET
ejpam-890	372	29	these	these	PRON
ejpam-890	372	30	give	give	VERB
ejpam-890	372	31	all	all	DET
ejpam-890	372	32	possible	possible	ADJ
ejpam-890	372	33	submatrices	submatrice	NOUN
ejpam-890	372	34	as	as	ADP
ejpam-890	372	35	burst	burst	ADJ
ejpam-890	372	36	errors	error	NOUN
ejpam-890	372	37	of	of	ADP
ejpam-890	372	38	order	order	NOUN
ejpam-890	372	39	p×	p×	NOUN
ejpam-890	372	40	r	r	NOUN
ejpam-890	372	41	whose	whose	DET
ejpam-890	372	42	first	first	ADJ
ejpam-890	372	43	rows	row	NOUN
ejpam-890	372	44	are	be	AUX
ejpam-890	372	45	situated	situate	VERB
ejpam-890	372	46	as	as	ADP
ejpam-890	372	47	first	first	ADJ
ejpam-890	372	48	rows	row	NOUN
ejpam-890	372	49	of	of	ADP
ejpam-890	372	50	burst	burst	ADJ
ejpam-890	372	51	error	error	NOUN
ejpam-890	372	52	of	of	ADP
ejpam-890	372	53	order	order	NOUN
ejpam-890	372	54	m×	m×	PROPN
ejpam-890	372	55	s.	s.	PROPN
ejpam-890	372	56	for	for	ADP
ejpam-890	372	57	each	each	DET
ejpam-890	372	58	submatrix	submatrix	NOUN
ejpam-890	372	59	obtained	obtain	VERB
ejpam-890	372	60	above	above	ADV
ejpam-890	372	61	,	,	PUNCT
ejpam-890	372	62	we	we	PRON
ejpam-890	372	63	can	can	AUX
ejpam-890	372	64	move	move	VERB
ejpam-890	372	65	it	it	PRON
ejpam-890	372	66	downwards	downwards	ADV
ejpam-890	372	67	to	to	PART
ejpam-890	372	68	obtain	obtain	VERB
ejpam-890	372	69	all	all	DET
ejpam-890	372	70	possible	possible	ADJ
ejpam-890	372	71	burst	burst	ADJ
ejpam-890	372	72	errors	error	NOUN
ejpam-890	372	73	.	.	PUNCT
ejpam-890	373	1	this	this	PRON
ejpam-890	373	2	is	be	AUX
ejpam-890	373	3	possible	possible	ADJ
ejpam-890	373	4	in	in	ADP
ejpam-890	373	5	m−	m−	PROPN
ejpam-890	373	6	p	p	PROPN
ejpam-890	373	7	+	+	CCONJ
ejpam-890	373	8	1	1	NUM
ejpam-890	373	9	ways	way	NOUN
ejpam-890	373	10	for	for	ADP
ejpam-890	373	11	each	each	DET
ejpam-890	373	12	case	case	NOUN
ejpam-890	373	13	.	.	PUNCT
ejpam-890	374	1	definition	definition	NOUN
ejpam-890	374	2	12	12	NUM
ejpam-890	374	3	.	.	PUNCT
ejpam-890	375	1	w	w	PROPN
ejpam-890	375	2	p×r	p×r	PROPN
ejpam-890	375	3	m×s	m×s	PROPN
ejpam-890	375	4	(	(	PUNCT
ejpam-890	375	5	t	t	PROPN
ejpam-890	375	6	)	)	PUNCT
ejpam-890	375	7	=	=	NOUN
ejpam-890	376	1	ms	ms	PROPN
ejpam-890	376	2	∑	∑	PROPN
ejpam-890	376	3	i=0	i=0	PROPN
ejpam-890	376	4	wi	wi	PROPN
ejpam-890	376	5	t	t	PROPN
ejpam-890	377	1	i	i	PRON
ejpam-890	377	2	is	be	AUX
ejpam-890	377	3	called	call	VERB
ejpam-890	377	4	the	the	DET
ejpam-890	377	5	burst	burst	ADJ
ejpam-890	377	6	weight	weight	NOUN
ejpam-890	377	7	enumerator	enumerator	NOUN
ejpam-890	377	8	of	of	ADP
ejpam-890	377	9	burst	burst	ADJ
ejpam-890	377	10	errors	error	NOUN
ejpam-890	377	11	of	of	ADP
ejpam-890	377	12	order	order	NOUN
ejpam-890	377	13	p×	p×	NOUN
ejpam-890	377	14	r	r	NOUN
ejpam-890	377	15	in	in	ADP
ejpam-890	377	16	the	the	DET
ejpam-890	377	17	space	space	NOUN
ejpam-890	377	18	mm×s(r	mm×s(r	NOUN
ejpam-890	377	19	)	)	PUNCT
ejpam-890	377	20	.	.	PUNCT
ejpam-890	378	1	now	now	ADV
ejpam-890	378	2	,	,	PUNCT
ejpam-890	378	3	it	it	PRON
ejpam-890	378	4	is	be	AUX
ejpam-890	378	5	clear	clear	ADJ
ejpam-890	378	6	that	that	SCONJ
ejpam-890	378	7	by	by	ADP
ejpam-890	378	8	setting	set	VERB
ejpam-890	378	9	x1	x1	PROPN
ejpam-890	378	10	=	=	PUNCT
ejpam-890	378	11	x2	x2	PROPN
ejpam-890	378	12	=	=	PUNCT
ejpam-890	378	13	·	·	PUNCT
ejpam-890	378	14	·	·	PUNCT
ejpam-890	378	15	·	·	PUNCT
ejpam-890	378	16	=	=	PUNCT
ejpam-890	378	17	x	x	PUNCT
ejpam-890	378	18	p	p	X
ejpam-890	378	19	=	=	X
ejpam-890	378	20	t	t	PROPN
ejpam-890	378	21	in	in	ADP
ejpam-890	378	22	w	w	PROPN
ejpam-890	378	23	(	(	PUNCT
ejpam-890	378	24	x̃	x̃	PROPN
ejpam-890	378	25	)	)	PUNCT
ejpam-890	378	26	we	we	PRON
ejpam-890	378	27	obtain	obtain	VERB
ejpam-890	378	28	the	the	DET
ejpam-890	378	29	burst	burst	ADJ
ejpam-890	378	30	weight	weight	NOUN
ejpam-890	378	31	enumerator	enumerator	NOUN
ejpam-890	378	32	w	w	PROPN
ejpam-890	378	33	p×r	p×r	PROPN
ejpam-890	378	34	m×s	m×s	PROPN
ejpam-890	378	35	(	(	PUNCT
ejpam-890	378	36	t	t	PROPN
ejpam-890	378	37	)	)	PUNCT
ejpam-890	378	38	=	=	SYM
ejpam-890	378	39	∑ms	∑ms	X
ejpam-890	379	1	i=0	i=0	PROPN
ejpam-890	379	2	wi	wi	PROPN
ejpam-890	379	3	t	t	PROPN
ejpam-890	379	4	i	i	PRON
ejpam-890	379	5	.	.	PUNCT
ejpam-890	380	1	example	example	NOUN
ejpam-890	381	1	9	9	NUM
ejpam-890	381	2	.	.	PUNCT
ejpam-890	382	1	the	the	DET
ejpam-890	382	2	weight	weight	NOUN
ejpam-890	382	3	spectra	spectra	NOUN
ejpam-890	382	4	polynomial	polynomial	NOUN
ejpam-890	382	5	of	of	ADP
ejpam-890	382	6	burst	burst	ADJ
ejpam-890	382	7	errors	error	NOUN
ejpam-890	382	8	of	of	ADP
ejpam-890	382	9	order	order	NOUN
ejpam-890	382	10	2×3	2×3	NOUN
ejpam-890	382	11	in	in	ADP
ejpam-890	382	12	the	the	DET
ejpam-890	382	13	space	space	NOUN
ejpam-890	382	14	of	of	ADP
ejpam-890	382	15	matrices	matrix	NOUN
ejpam-890	382	16	m3×5(f2	m3×5(f2	X
ejpam-890	382	17	)	)	PUNCT
ejpam-890	382	18	is	be	AUX
ejpam-890	382	19	computed	compute	VERB
ejpam-890	382	20	in	in	ADP
ejpam-890	382	21	the	the	DET
ejpam-890	382	22	following	following	ADJ
ejpam-890	382	23	way	way	NOUN
ejpam-890	382	24	.	.	PUNCT
ejpam-890	383	1	first	first	ADV
ejpam-890	383	2	,	,	PUNCT
ejpam-890	383	3	the	the	DET
ejpam-890	383	4	weight	weight	NOUN
ejpam-890	383	5	spectra	spectra	NOUN
ejpam-890	383	6	polynomial	polynomial	NOUN
ejpam-890	383	7	of	of	ADP
ejpam-890	383	8	burst	burst	NOUN
ejpam-890	383	9	of	of	ADP
ejpam-890	383	10	errors	error	NOUN
ejpam-890	383	11	of	of	ADP
ejpam-890	383	12	order	order	NOUN
ejpam-890	383	13	2×	2×	NUM
ejpam-890	383	14	3	3	NUM
ejpam-890	383	15	in	in	ADP
ejpam-890	383	16	the	the	DET
ejpam-890	383	17	space	space	NOUN
ejpam-890	383	18	of	of	ADP
ejpam-890	383	19	matrices	matrix	NOUN
ejpam-890	383	20	m2×3(f2	m2×3(f2	NUM
ejpam-890	383	21	)	)	PUNCT
ejpam-890	383	22	is	be	AUX
ejpam-890	383	23	already	already	ADV
ejpam-890	383	24	computed	compute	VERB
ejpam-890	383	25	in	in	ADP
ejpam-890	383	26	example	example	NOUN
ejpam-890	383	27	3	3	NUM
ejpam-890	383	28	.	.	PUNCT
ejpam-890	384	1	next	next	ADV
ejpam-890	384	2	,	,	PUNCT
ejpam-890	384	3	by	by	ADP
ejpam-890	384	4	lemma	lemma	PROPN
ejpam-890	384	5	3	3	NUM
ejpam-890	384	6	by	by	ADP
ejpam-890	384	7	applying	apply	VERB
ejpam-890	384	8	t	t	PROPN
ejpam-890	384	9	(	(	PUNCT
ejpam-890	384	10	h	h	NOUN
ejpam-890	384	11	)	)	PUNCT
ejpam-890	384	12	and	and	CCONJ
ejpam-890	384	13	t	t	PROPN
ejpam-890	384	14	2(h	2(h	NUM
ejpam-890	384	15	)	)	PUNCT
ejpam-890	384	16	,	,	PUNCT
ejpam-890	384	17	we	we	PRON
ejpam-890	384	18	get	get	VERB
ejpam-890	384	19	all	all	DET
ejpam-890	384	20	possible	possible	ADJ
ejpam-890	384	21	weight	weight	NOUN
ejpam-890	384	22	distributions	distribution	NOUN
ejpam-890	384	23	of	of	ADP
ejpam-890	384	24	the	the	DET
ejpam-890	384	25	terms	term	NOUN
ejpam-890	384	26	that	that	PRON
ejpam-890	384	27	correspond	correspond	VERB
ejpam-890	384	28	to	to	PART
ejpam-890	384	29	burst	burst	VERB
ejpam-890	384	30	errors	error	NOUN
ejpam-890	384	31	.	.	PUNCT
ejpam-890	385	1	h	h	PROPN
ejpam-890	386	1	+	+	PROPN
ejpam-890	386	2	t	t	PROPN
ejpam-890	386	3	(	(	PUNCT
ejpam-890	386	4	h	h	NOUN
ejpam-890	386	5	)	)	PUNCT
ejpam-890	387	1	+	+	NUM
ejpam-890	387	2	t	t	NOUN
ejpam-890	387	3	2(h	2(h	NUM
ejpam-890	387	4	)	)	PUNCT
ejpam-890	387	5	=	=	PUNCT
ejpam-890	388	1	3x	3x	NUM
ejpam-890	389	1	3	3	NUM
ejpam-890	389	2	1	1	NUM
ejpam-890	389	3	x	x	SYM
ejpam-890	389	4	5	5	NUM
ejpam-890	389	5	2	2	NUM
ejpam-890	389	6	+	+	NUM
ejpam-890	389	7	4x	4x	NUM
ejpam-890	389	8	5	5	NUM
ejpam-890	389	9	1	1	NUM
ejpam-890	389	10	x	x	SYM
ejpam-890	389	11	4	4	NUM
ejpam-890	389	12	2	2	NUM
ejpam-890	389	13	+	+	NUM
ejpam-890	389	14	12x	12x	NUM
ejpam-890	389	15	5	5	NUM
ejpam-890	389	16	1x	1x	NUM
ejpam-890	389	17	5	5	NUM
ejpam-890	389	18	2	2	NUM
ejpam-890	389	19	+	+	NUM
ejpam-890	389	20	5x	5x	NUM
ejpam-890	389	21	4	4	NUM
ejpam-890	389	22	1	1	NUM
ejpam-890	389	23	x	x	SYM
ejpam-890	389	24	5	5	NUM
ejpam-890	389	25	2	2	NUM
ejpam-890	389	26	+	+	NOUN
ejpam-890	389	27	6x	6x	NUM
ejpam-890	389	28	5	5	NUM
ejpam-890	389	29	1	1	NUM
ejpam-890	389	30	x	x	SYM
ejpam-890	389	31	3	3	NUM
ejpam-890	389	32	2	2	NUM
ejpam-890	389	33	+	+	CCONJ
ejpam-890	389	34	x	x	SYM
ejpam-890	389	35	3	3	NUM
ejpam-890	389	36	1	1	NUM
ejpam-890	389	37	x	x	SYM
ejpam-890	389	38	7	7	NUM
ejpam-890	389	39	2	2	NUM
ejpam-890	389	40	+	+	NUM
ejpam-890	389	41	2x	2x	NUM
ejpam-890	389	42	7	7	NUM
ejpam-890	389	43	1	1	NUM
ejpam-890	389	44	x	x	SYM
ejpam-890	389	45	5	5	NUM
ejpam-890	389	46	2	2	NUM
ejpam-890	389	47	+	+	CCONJ
ejpam-890	389	48	x	x	SYM
ejpam-890	389	49	4	4	NUM
ejpam-890	389	50	1	1	NUM
ejpam-890	389	51	x	x	SYM
ejpam-890	389	52	7	7	NUM
ejpam-890	389	53	2	2	NUM
ejpam-890	389	54	+	+	CCONJ
ejpam-890	389	55	3x	3x	NUM
ejpam-890	389	56	2	2	NUM
ejpam-890	389	57	1	1	NUM
ejpam-890	389	58	x	x	SYM
ejpam-890	389	59	4	4	NUM
ejpam-890	389	60	2	2	NUM
ejpam-890	389	61	+	+	NUM
ejpam-890	389	62	4x	4x	NUM
ejpam-890	389	63	4	4	NUM
ejpam-890	389	64	1	1	NUM
ejpam-890	389	65	x	x	SYM
ejpam-890	389	66	3	3	NUM
ejpam-890	389	67	2	2	NUM
ejpam-890	389	68	+	+	NUM
ejpam-890	389	69	12x	12x	NUM
ejpam-890	389	70	4	4	NUM
ejpam-890	389	71	1	1	NUM
ejpam-890	389	72	x	x	SYM
ejpam-890	389	73	4	4	NUM
ejpam-890	389	74	2	2	NUM
ejpam-890	389	75	+	+	NUM
ejpam-890	389	76	5x	5x	NUM
ejpam-890	389	77	3	3	NUM
ejpam-890	389	78	1	1	NUM
ejpam-890	389	79	x	x	SYM
ejpam-890	389	80	4	4	NUM
ejpam-890	389	81	2	2	NUM
ejpam-890	389	82	+	+	NUM
ejpam-890	389	83	4x	4x	NUM
ejpam-890	389	84	4	4	NUM
ejpam-890	389	85	1	1	NUM
ejpam-890	389	86	x	x	SYM
ejpam-890	389	87	2	2	NUM
ejpam-890	389	88	2	2	NUM
ejpam-890	389	89	+	+	CCONJ
ejpam-890	389	90	x	x	SYM
ejpam-890	389	91	2	2	NUM
ejpam-890	389	92	1	1	NUM
ejpam-890	389	93	x	x	SYM
ejpam-890	389	94	6	6	NUM
ejpam-890	389	95	2	2	NUM
ejpam-890	389	96	+	+	NUM
ejpam-890	389	97	2x	2x	NUM
ejpam-890	389	98	6	6	NUM
ejpam-890	389	99	1	1	NUM
ejpam-890	389	100	x	x	SYM
ejpam-890	389	101	4	4	NUM
ejpam-890	389	102	2	2	NUM
ejpam-890	389	103	i̇.	i̇.	NOUN
ejpam-890	389	104	siap	siap	PROPN
ejpam-890	389	105	/	/	SYM
ejpam-890	389	106	eur	eur	PROPN
ejpam-890	389	107	.	.	PUNCT
ejpam-890	390	1	j.	j.	PROPN
ejpam-890	390	2	pure	pure	PROPN
ejpam-890	390	3	appl	appl	PROPN
ejpam-890	390	4	.	.	PROPN
ejpam-890	390	5	math	math	PROPN
ejpam-890	390	6	,	,	PUNCT
ejpam-890	390	7	3	3	NUM
ejpam-890	390	8	(	(	PUNCT
ejpam-890	390	9	2010	2010	NUM
ejpam-890	390	10	)	)	PUNCT
ejpam-890	390	11	,	,	PUNCT
ejpam-890	390	12	653	653	NUM
ejpam-890	390	13	-	-	SYM
ejpam-890	390	14	669	669	NUM
ejpam-890	390	15	667	667	NUM
ejpam-890	390	16	+	+	CCONJ
ejpam-890	390	17	x	x	SYM
ejpam-890	390	18	3	3	NUM
ejpam-890	390	19	1	1	NUM
ejpam-890	390	20	x	x	SYM
ejpam-890	390	21	6	6	NUM
ejpam-890	390	22	2	2	NUM
ejpam-890	390	23	+	+	NUM
ejpam-890	390	24	3x1x	3x1x	NOUN
ejpam-890	390	25	3	3	NUM
ejpam-890	390	26	2	2	NUM
ejpam-890	391	1	+	+	CCONJ
ejpam-890	391	2	4x	4x	NUM
ejpam-890	391	3	2	2	NUM
ejpam-890	391	4	2	2	NUM
ejpam-890	391	5	x	x	SYM
ejpam-890	391	6	3	3	NUM
ejpam-890	391	7	1	1	NUM
ejpam-890	391	8	+	+	NUM
ejpam-890	391	9	12x	12x	NUM
ejpam-890	391	10	3	3	NUM
ejpam-890	391	11	1	1	NUM
ejpam-890	391	12	x	x	SYM
ejpam-890	391	13	3	3	NUM
ejpam-890	391	14	2	2	NUM
ejpam-890	391	15	+	+	NUM
ejpam-890	391	16	5x	5x	NUM
ejpam-890	391	17	3	3	NUM
ejpam-890	391	18	2	2	NUM
ejpam-890	391	19	x	x	SYM
ejpam-890	391	20	2	2	NUM
ejpam-890	391	21	1	1	NUM
ejpam-890	391	22	+	+	NUM
ejpam-890	391	23	4x2x	4x2x	NOUN
ejpam-890	391	24	3	3	NUM
ejpam-890	391	25	1	1	NUM
ejpam-890	391	26	+	+	CCONJ
ejpam-890	391	27	x1x	x1x	PROPN
ejpam-890	391	28	5	5	NUM
ejpam-890	391	29	2	2	NUM
ejpam-890	391	30	+	+	CCONJ
ejpam-890	391	31	x	x	SYM
ejpam-890	391	32	5	5	NUM
ejpam-890	391	33	2	2	NUM
ejpam-890	391	34	x	x	SYM
ejpam-890	391	35	2	2	NUM
ejpam-890	391	36	1	1	NUM
ejpam-890	391	37	.	.	PUNCT
ejpam-890	392	1	setting	set	VERB
ejpam-890	392	2	x	x	PUNCT
ejpam-890	392	3	=	=	PUNCT
ejpam-890	392	4	y	y	PROPN
ejpam-890	392	5	=	=	SYM
ejpam-890	392	6	t	t	PROPN
ejpam-890	392	7	and	and	CCONJ
ejpam-890	392	8	multiplying	multiply	VERB
ejpam-890	392	9	by	by	ADP
ejpam-890	392	10	p−	p−	NOUN
ejpam-890	392	11	r	r	NOUN
ejpam-890	392	12	+	+	CCONJ
ejpam-890	392	13	1	1	NUM
ejpam-890	392	14	in	in	ADP
ejpam-890	392	15	w	w	PROPN
ejpam-890	392	16	(	(	PUNCT
ejpam-890	392	17	x̃	x̃	PROPN
ejpam-890	392	18	)	)	PUNCT
ejpam-890	392	19	=	=	SYM
ejpam-890	393	1	2(h	2(h	NUM
ejpam-890	393	2	+	+	CCONJ
ejpam-890	393	3	t	t	PROPN
ejpam-890	393	4	(	(	PUNCT
ejpam-890	393	5	h	h	NOUN
ejpam-890	393	6	)	)	PUNCT
ejpam-890	394	1	+	+	NUM
ejpam-890	394	2	t	t	NOUN
ejpam-890	394	3	2(h	2(h	NUM
ejpam-890	394	4	)	)	PUNCT
ejpam-890	394	5	)	)	PUNCT
ejpam-890	394	6	,	,	PUNCT
ejpam-890	394	7	we	we	PRON
ejpam-890	394	8	obtain	obtain	VERB
ejpam-890	394	9	w	w	ADP
ejpam-890	394	10	2×3	2×3	NUM
ejpam-890	394	11	3×5	3×5	NUM
ejpam-890	394	12	(	(	PUNCT
ejpam-890	394	13	t	t	PROPN
ejpam-890	394	14	)	)	PUNCT
ejpam-890	394	15	=	=	SYM
ejpam-890	394	16	4t12	4t12	NOUN
ejpam-890	394	17	+	+	CCONJ
ejpam-890	394	18	2t11	2t11	NOUN
ejpam-890	394	19	+	+	CCONJ
ejpam-890	394	20	30t10	30t10	NUM
ejpam-890	394	21	+	+	SYM
ejpam-890	394	22	20t9	20t9	NUM
ejpam-890	394	23	+	+	SYM
ejpam-890	394	24	44t8	44t8	NUM
ejpam-890	395	1	+	+	CCONJ
ejpam-890	396	1	20t7	20t7	NUM
ejpam-890	396	2	+	+	SYM
ejpam-890	396	3	40t6	40t6	NUM
ejpam-890	397	1	+	+	SYM
ejpam-890	397	2	18t5	18t5	NUM
ejpam-890	397	3	+	+	NUM
ejpam-890	398	1	14t4	14t4	NUM
ejpam-890	398	2	.	.	PUNCT
ejpam-890	399	1	hence	hence	ADV
ejpam-890	399	2	,	,	PUNCT
ejpam-890	399	3	the	the	DET
ejpam-890	399	4	number	number	NOUN
ejpam-890	399	5	of	of	ADP
ejpam-890	399	6	burst	burst	ADJ
ejpam-890	399	7	errors	error	NOUN
ejpam-890	399	8	of	of	ADP
ejpam-890	399	9	ρ	ρ	NOUN
ejpam-890	399	10	-	-	PUNCT
ejpam-890	399	11	weight	weight	NOUN
ejpam-890	399	12	3	3	NUM
ejpam-890	399	13	or	or	CCONJ
ejpam-890	399	14	less	less	ADV
ejpam-890	399	15	is	be	AUX
ejpam-890	399	16	equal	equal	ADJ
ejpam-890	399	17	to	to	ADP
ejpam-890	399	18	t	t	PROPN
ejpam-890	399	19	2×2	2×2	NUM
ejpam-890	399	20	3×3	3×3	NUM
ejpam-890	399	21	(	(	PUNCT
ejpam-890	399	22	f2	f2	PROPN
ejpam-890	399	23	,	,	PUNCT
ejpam-890	399	24	3	3	NUM
ejpam-890	399	25	)	)	PUNCT
ejpam-890	399	26	=	=	SYM
ejpam-890	400	1	10	10	NUM
ejpam-890	400	2	+	+	NUM
ejpam-890	400	3	6	6	NUM
ejpam-890	400	4	+	+	SYM
ejpam-890	400	5	2	2	NUM
ejpam-890	400	6	.	.	PUNCT
ejpam-890	400	7	corollary	corollary	ADJ
ejpam-890	400	8	3	3	NUM
ejpam-890	400	9	.	.	PUNCT
ejpam-890	401	1	by	by	ADP
ejpam-890	401	2	substituting	substitute	VERB
ejpam-890	401	3	x	x	PUNCT
ejpam-890	401	4	i	i	PROPN
ejpam-890	401	5	=	=	SYM
ejpam-890	401	6	t	t	PROPN
ejpam-890	401	7	in	in	ADP
ejpam-890	401	8	w	w	PROPN
ejpam-890	401	9	(	(	PUNCT
ejpam-890	401	10	x̃	x̃	PROPN
ejpam-890	401	11	)	)	PUNCT
ejpam-890	401	12	,	,	PUNCT
ejpam-890	401	13	we	we	PRON
ejpam-890	401	14	obtain	obtain	VERB
ejpam-890	401	15	w	w	ADP
ejpam-890	401	16	p×r	p×r	PROPN
ejpam-890	401	17	m×s	m×s	PROPN
ejpam-890	401	18	(	(	PUNCT
ejpam-890	401	19	t	t	PROPN
ejpam-890	401	20	)	)	PUNCT
ejpam-890	401	21	which	which	PRON
ejpam-890	401	22	is	be	AUX
ejpam-890	401	23	the	the	DET
ejpam-890	401	24	weight	weight	NOUN
ejpam-890	401	25	enumerator	enumerator	NOUN
ejpam-890	401	26	of	of	ADP
ejpam-890	401	27	bursts	burst	NOUN
ejpam-890	401	28	of	of	ADP
ejpam-890	401	29	order	order	NOUN
ejpam-890	401	30	p×	p×	NOUN
ejpam-890	401	31	r	r	NOUN
ejpam-890	401	32	in	in	ADP
ejpam-890	401	33	mm×s(r	mm×s(r	PROPN
ejpam-890	401	34	)	)	PUNCT
ejpam-890	401	35	.	.	PUNCT
ejpam-890	402	1	further	far	ADV
ejpam-890	402	2	,	,	PUNCT
ejpam-890	402	3	b	b	PROPN
ejpam-890	402	4	p×r	p×r	PROPN
ejpam-890	402	5	m×s(r	m×s(r	PROPN
ejpam-890	402	6	,	,	PUNCT
ejpam-890	402	7	w	w	PROPN
ejpam-890	402	8	)	)	PUNCT
ejpam-890	402	9	=	=	SYM
ejpam-890	402	10	w	w	PROPN
ejpam-890	402	11	∑	∑	PROPN
ejpam-890	402	12	i=1	i=1	PROPN
ejpam-890	402	13	wi	wi	PROPN
ejpam-890	402	14	where	where	SCONJ
ejpam-890	402	15	wi	wi	PROPN
ejpam-890	402	16	’s	’	VERB
ejpam-890	402	17	are	be	AUX
ejpam-890	402	18	the	the	DET
ejpam-890	402	19	coefficients	coefficient	NOUN
ejpam-890	402	20	of	of	ADP
ejpam-890	402	21	w	w	PROPN
ejpam-890	402	22	p×r	p×r	PROPN
ejpam-890	402	23	m×s	m×s	PROPN
ejpam-890	402	24	(	(	PUNCT
ejpam-890	402	25	t	t	PROPN
ejpam-890	402	26	)	)	PUNCT
ejpam-890	402	27	.	.	PUNCT
ejpam-890	403	1	4	4	X
ejpam-890	403	2	.	.	X
ejpam-890	404	1	some	some	DET
ejpam-890	404	2	applications	application	NOUN
ejpam-890	404	3	from	from	ADP
ejpam-890	404	4	previous	previous	ADJ
ejpam-890	404	5	sections	section	NOUN
ejpam-890	404	6	we	we	PRON
ejpam-890	404	7	have	have	AUX
ejpam-890	404	8	presented	present	VERB
ejpam-890	404	9	a	a	DET
ejpam-890	404	10	constructive	constructive	ADJ
ejpam-890	404	11	method	method	NOUN
ejpam-890	404	12	for	for	ADP
ejpam-890	404	13	computing	compute	VERB
ejpam-890	404	14	b	b	PROPN
ejpam-890	404	15	p×r	p×r	PROPN
ejpam-890	404	16	m×s(r	m×s(r	PROPN
ejpam-890	404	17	)	)	PUNCT
ejpam-890	404	18	and	and	CCONJ
ejpam-890	404	19	b	b	PROPN
ejpam-890	404	20	p×r	p×r	PROPN
ejpam-890	404	21	m×s(r	m×s(r	PROPN
ejpam-890	404	22	,	,	PUNCT
ejpam-890	404	23	w	w	PROPN
ejpam-890	404	24	)	)	PUNCT
ejpam-890	404	25	.	.	PUNCT
ejpam-890	405	1	by	by	ADP
ejpam-890	405	2	making	make	VERB
ejpam-890	405	3	use	use	NOUN
ejpam-890	405	4	of	of	ADP
ejpam-890	405	5	these	these	DET
ejpam-890	405	6	results	result	NOUN
ejpam-890	405	7	we	we	PRON
ejpam-890	405	8	have	have	VERB
ejpam-890	405	9	the	the	DET
ejpam-890	405	10	following	follow	VERB
ejpam-890	405	11	theorems	theorem	NOUN
ejpam-890	405	12	:	:	PUNCT
ejpam-890	405	13	theorem	theorem	NOUN
ejpam-890	405	14	6	6	NUM
ejpam-890	405	15	.	.	PUNCT
ejpam-890	406	1	let	let	VERB
ejpam-890	406	2	c	c	PRON
ejpam-890	406	3	be	be	AUX
ejpam-890	406	4	an	an	DET
ejpam-890	406	5	array	array	NOUN
ejpam-890	406	6	code	code	NOUN
ejpam-890	406	7	over	over	ADP
ejpam-890	406	8	r.	r.	PROPN
ejpam-890	406	9	if	if	SCONJ
ejpam-890	406	10	c	c	PROPN
ejpam-890	406	11	corrects	correct	VERB
ejpam-890	406	12	all	all	DET
ejpam-890	406	13	burst	burst	ADJ
ejpam-890	406	14	errors	error	NOUN
ejpam-890	406	15	of	of	ADP
ejpam-890	406	16	type	type	NOUN
ejpam-890	406	17	p×	p×	PROPN
ejpam-890	406	18	r	r	NOUN
ejpam-890	406	19	,	,	PUNCT
ejpam-890	406	20	then	then	ADV
ejpam-890	406	21	|r|ms	|r|ms	PROPN
ejpam-890	406	22	|c	|c	VERB
ejpam-890	406	23	|	|	CCONJ
ejpam-890	406	24	≥	≥	NOUN
ejpam-890	406	25	1	1	NUM
ejpam-890	407	1	+	+	SYM
ejpam-890	407	2	b	b	PROPN
ejpam-890	407	3	p×r	p×r	PROPN
ejpam-890	407	4	m×s(r	m×s(r	PROPN
ejpam-890	407	5	)	)	PUNCT
ejpam-890	407	6	(	(	PUNCT
ejpam-890	407	7	3	3	X
ejpam-890	407	8	)	)	PUNCT
ejpam-890	407	9	where	where	SCONJ
ejpam-890	407	10	“	"	PUNCT
ejpam-890	407	11	|	|	NOUN
ejpam-890	407	12	·	·	PUNCT
ejpam-890	407	13	|	|	ADV
ejpam-890	407	14	”	"	PUNCT
ejpam-890	407	15	stands	stand	VERB
ejpam-890	407	16	for	for	ADP
ejpam-890	407	17	the	the	DET
ejpam-890	407	18	cardinality	cardinality	NOUN
ejpam-890	407	19	of	of	ADP
ejpam-890	407	20	the	the	DET
ejpam-890	407	21	set	set	NOUN
ejpam-890	407	22	.	.	PUNCT
ejpam-890	408	1	proof	proof	NOUN
ejpam-890	408	2	.	.	PUNCT
ejpam-890	409	1	c	c	PROPN
ejpam-890	409	2	is	be	AUX
ejpam-890	409	3	an	an	DET
ejpam-890	409	4	abelian	abelian	ADJ
ejpam-890	409	5	additive	additive	NOUN
ejpam-890	409	6	group	group	NOUN
ejpam-890	409	7	.	.	PUNCT
ejpam-890	410	1	if	if	SCONJ
ejpam-890	410	2	c	c	PROPN
ejpam-890	410	3	corrects	correct	VERB
ejpam-890	410	4	all	all	DET
ejpam-890	410	5	burst	burst	ADJ
ejpam-890	410	6	errors	error	NOUN
ejpam-890	410	7	of	of	ADP
ejpam-890	410	8	type	type	NOUN
ejpam-890	410	9	p×	p×	PROPN
ejpam-890	410	10	r	r	NOUN
ejpam-890	410	11	,	,	PUNCT
ejpam-890	410	12	then	then	ADV
ejpam-890	410	13	all	all	DET
ejpam-890	410	14	these	these	DET
ejpam-890	410	15	bursts	burst	NOUN
ejpam-890	410	16	must	must	AUX
ejpam-890	410	17	fall	fall	VERB
ejpam-890	410	18	into	into	ADP
ejpam-890	410	19	different	different	ADJ
ejpam-890	410	20	cosets	coset	NOUN
ejpam-890	410	21	.	.	PUNCT
ejpam-890	411	1	so	so	ADV
ejpam-890	411	2	the	the	DET
ejpam-890	411	3	number	number	NOUN
ejpam-890	411	4	of	of	ADP
ejpam-890	411	5	cosets	coset	NOUN
ejpam-890	411	6	including	include	VERB
ejpam-890	411	7	c	c	NOUN
ejpam-890	411	8	itself	itself	PRON
ejpam-890	411	9	should	should	AUX
ejpam-890	411	10	be	be	AUX
ejpam-890	411	11	larger	large	ADJ
ejpam-890	411	12	or	or	CCONJ
ejpam-890	411	13	equal	equal	ADJ
ejpam-890	411	14	to	to	ADP
ejpam-890	411	15	the	the	DET
ejpam-890	411	16	number	number	NOUN
ejpam-890	411	17	of	of	ADP
ejpam-890	411	18	burst	burst	ADJ
ejpam-890	411	19	errors	error	NOUN
ejpam-890	411	20	plus	plus	CCONJ
ejpam-890	411	21	one	one	NUM
ejpam-890	411	22	which	which	PRON
ejpam-890	411	23	stands	stand	VERB
ejpam-890	411	24	for	for	ADP
ejpam-890	411	25	zero	zero	NUM
ejpam-890	411	26	codeword	codeword	NOUN
ejpam-890	411	27	.	.	PUNCT
ejpam-890	412	1	a	a	DET
ejpam-890	412	2	similar	similar	ADJ
ejpam-890	412	3	argument	argument	NOUN
ejpam-890	412	4	that	that	PRON
ejpam-890	412	5	depends	depend	VERB
ejpam-890	412	6	on	on	ADP
ejpam-890	412	7	syndrome	syndrome	NOUN
ejpam-890	412	8	decoding	decoding	NOUN
ejpam-890	412	9	leads	lead	NOUN
ejpam-890	412	10	to	to	ADP
ejpam-890	412	11	the	the	DET
ejpam-890	412	12	following	follow	VERB
ejpam-890	412	13	theorem	theorem	NOUN
ejpam-890	412	14	:	:	PUNCT
ejpam-890	412	15	theorem	theorem	NOUN
ejpam-890	412	16	7	7	NUM
ejpam-890	412	17	.	.	PUNCT
ejpam-890	413	1	let	let	VERB
ejpam-890	413	2	c	c	PRON
ejpam-890	413	3	be	be	AUX
ejpam-890	413	4	an	an	DET
ejpam-890	413	5	array	array	NOUN
ejpam-890	413	6	code	code	NOUN
ejpam-890	413	7	over	over	ADP
ejpam-890	413	8	r.	r.	PROPN
ejpam-890	413	9	if	if	SCONJ
ejpam-890	413	10	c	c	PROPN
ejpam-890	413	11	corrects	correct	VERB
ejpam-890	413	12	all	all	DET
ejpam-890	413	13	burst	burst	ADJ
ejpam-890	413	14	errors	error	NOUN
ejpam-890	413	15	of	of	ADP
ejpam-890	413	16	type	type	NOUN
ejpam-890	413	17	p	p	NOUN
ejpam-890	413	18	×	×	NOUN
ejpam-890	413	19	r	r	NOUN
ejpam-890	413	20	and	and	CCONJ
ejpam-890	413	21	rt	rt	NOUN
ejpam-890	413	22	-	-	PUNCT
ejpam-890	413	23	weight	weight	NOUN
ejpam-890	413	24	equal	equal	ADJ
ejpam-890	413	25	to	to	ADP
ejpam-890	413	26	w	w	ADP
ejpam-890	413	27	or	or	CCONJ
ejpam-890	413	28	less	less	ADJ
ejpam-890	413	29	,	,	PUNCT
ejpam-890	413	30	then	then	ADV
ejpam-890	413	31	|r|ms	|r|ms	PROPN
ejpam-890	413	32	|c	|c	VERB
ejpam-890	413	33	|	|	CCONJ
ejpam-890	413	34	≥	≥	NOUN
ejpam-890	413	35	1	1	NUM
ejpam-890	414	1	+	+	CCONJ
ejpam-890	414	2	p	p	NOUN
ejpam-890	414	3	∑	∑	PROPN
ejpam-890	414	4	i=1	i=1	PROPN
ejpam-890	414	5	r	r	NOUN
ejpam-890	414	6	∑	∑	PUNCT
ejpam-890	414	7	j=1	j=1	PROPN
ejpam-890	414	8	b	b	PROPN
ejpam-890	415	1	i×	i×	PROPN
ejpam-890	415	2	j	j	PROPN
ejpam-890	415	3	m×s(r	m×s(r	PROPN
ejpam-890	415	4	,	,	PUNCT
ejpam-890	415	5	w	w	PROPN
ejpam-890	415	6	)	)	PUNCT
ejpam-890	415	7	.	.	PUNCT
ejpam-890	416	1	(	(	PUNCT
ejpam-890	416	2	4	4	X
ejpam-890	416	3	)	)	PUNCT
ejpam-890	416	4	burst	burst	ADJ
ejpam-890	416	5	error	error	NOUN
ejpam-890	416	6	correction	correction	NOUN
ejpam-890	416	7	is	be	AUX
ejpam-890	416	8	based	base	VERB
ejpam-890	416	9	on	on	ADP
ejpam-890	416	10	assumption	assumption	NOUN
ejpam-890	416	11	of	of	ADP
ejpam-890	416	12	errors	error	NOUN
ejpam-890	416	13	occurring	occur	VERB
ejpam-890	416	14	nearby	nearby	ADV
ejpam-890	416	15	and	and	CCONJ
ejpam-890	416	16	sometimes	sometimes	ADV
ejpam-890	416	17	in	in	ADP
ejpam-890	416	18	particular	particular	ADJ
ejpam-890	416	19	predesigned	predesigned	ADJ
ejpam-890	416	20	places	place	NOUN
ejpam-890	416	21	.	.	PUNCT
ejpam-890	417	1	reiger	reiger	NOUN
ejpam-890	418	1	[	[	X
ejpam-890	418	2	6	6	NUM
ejpam-890	418	3	]	]	PUNCT
ejpam-890	418	4	proved	prove	VERB
ejpam-890	418	5	an	an	DET
ejpam-890	418	6	inequality	inequality	NOUN
ejpam-890	418	7	by	by	ADP
ejpam-890	418	8	assuming	assume	VERB
ejpam-890	418	9	predesigned	predesigned	ADJ
ejpam-890	418	10	burst	burst	ADJ
ejpam-890	418	11	errors	error	NOUN
ejpam-890	418	12	(	(	PUNCT
ejpam-890	418	13	burst	burst	ADJ
ejpam-890	418	14	errors	error	NOUN
ejpam-890	418	15	occurring	occur	VERB
ejpam-890	418	16	in	in	ADP
ejpam-890	418	17	the	the	DET
ejpam-890	418	18	last	last	ADJ
ejpam-890	418	19	consecutive	consecutive	ADJ
ejpam-890	418	20	digits	digit	NOUN
ejpam-890	418	21	)	)	PUNCT
ejpam-890	418	22	for	for	ADP
ejpam-890	418	23	block	block	NOUN
ejpam-890	418	24	codes	code	NOUN
ejpam-890	418	25	over	over	ADP
ejpam-890	418	26	fields	field	NOUN
ejpam-890	418	27	.	.	PUNCT
ejpam-890	419	1	later	later	ADV
ejpam-890	419	2	,	,	PUNCT
ejpam-890	419	3	jain	jain	NOUN
ejpam-890	419	4	in	in	ADP
ejpam-890	419	5	[	[	X
ejpam-890	419	6	5	5	NUM
ejpam-890	419	7	]	]	PUNCT
ejpam-890	419	8	extended	extend	VERB
ejpam-890	419	9	these	these	DET
ejpam-890	419	10	results	result	NOUN
ejpam-890	419	11	for	for	ADP
ejpam-890	419	12	array	array	NOUN
ejpam-890	419	13	codes	code	NOUN
ejpam-890	419	14	over	over	ADP
ejpam-890	419	15	finite	finite	ADJ
ejpam-890	419	16	fields	field	NOUN
ejpam-890	419	17	.	.	PUNCT
ejpam-890	420	1	here	here	ADV
ejpam-890	420	2	,	,	PUNCT
ejpam-890	420	3	we	we	PRON
ejpam-890	420	4	extend	extend	VERB
ejpam-890	420	5	them	they	PRON
ejpam-890	420	6	further	far	ADV
ejpam-890	420	7	for	for	ADP
ejpam-890	420	8	array	array	NOUN
ejpam-890	420	9	codes	code	NOUN
ejpam-890	420	10	over	over	ADP
ejpam-890	420	11	finite	finite	PROPN
ejpam-890	420	12	commutative	commutative	ADJ
ejpam-890	420	13	rings	ring	NOUN
ejpam-890	420	14	.	.	PUNCT
ejpam-890	421	1	references	reference	NOUN
ejpam-890	421	2	668	668	NUM
ejpam-890	421	3	theorem	theorem	NOUN
ejpam-890	421	4	8	8	NUM
ejpam-890	421	5	(	(	PUNCT
ejpam-890	421	6	(	(	PUNCT
ejpam-890	421	7	a	a	DET
ejpam-890	421	8	reiger	reiger	NOUN
ejpam-890	421	9	’s	’s	PART
ejpam-890	421	10	type	type	NOUN
ejpam-890	421	11	bound	bind	VERB
ejpam-890	421	12	)	)	PUNCT
ejpam-890	421	13	)	)	PUNCT
ejpam-890	421	14	.	.	PUNCT
ejpam-890	422	1	let	let	VERB
ejpam-890	422	2	c	c	PRON
ejpam-890	422	3	be	be	AUX
ejpam-890	422	4	an	an	DET
ejpam-890	422	5	array	array	NOUN
ejpam-890	422	6	code	code	NOUN
ejpam-890	422	7	over	over	ADP
ejpam-890	422	8	r	r	NOUN
ejpam-890	422	9	with	with	ADP
ejpam-890	422	10	no	no	DET
ejpam-890	422	11	burst	burst	ADJ
ejpam-890	422	12	errors	error	NOUN
ejpam-890	422	13	of	of	ADP
ejpam-890	422	14	type	type	NOUN
ejpam-890	422	15	p×	p×	NOUN
ejpam-890	422	16	r	r	NOUN
ejpam-890	422	17	or	or	CCONJ
ejpam-890	422	18	smaller	small	ADJ
ejpam-890	422	19	in	in	ADP
ejpam-890	422	20	a	a	DET
ejpam-890	422	21	predesigned	predesigned	ADJ
ejpam-890	422	22	place	place	NOUN
ejpam-890	422	23	of	of	ADP
ejpam-890	422	24	size	size	NOUN
ejpam-890	422	25	p×	p×	PROPN
ejpam-890	422	26	r.	r.	PROPN
ejpam-890	422	27	then	then	ADV
ejpam-890	422	28	,	,	PUNCT
ejpam-890	422	29	|r|ms	|r|ms	PROPN
ejpam-890	422	30	|c	|c	VERB
ejpam-890	423	1	|	|	ADV
ejpam-890	423	2	≥	≥	NOUN
ejpam-890	423	3	qpr	qpr	NOUN
ejpam-890	423	4	.	.	PUNCT
ejpam-890	424	1	(	(	PUNCT
ejpam-890	424	2	5	5	X
ejpam-890	424	3	)	)	PUNCT
ejpam-890	424	4	proof	proof	NOUN
ejpam-890	424	5	.	.	PUNCT
ejpam-890	425	1	without	without	ADP
ejpam-890	425	2	loss	loss	NOUN
ejpam-890	425	3	of	of	ADP
ejpam-890	425	4	generality	generality	NOUN
ejpam-890	425	5	,	,	PUNCT
ejpam-890	425	6	we	we	PRON
ejpam-890	425	7	may	may	AUX
ejpam-890	425	8	assume	assume	VERB
ejpam-890	425	9	that	that	SCONJ
ejpam-890	425	10	the	the	DET
ejpam-890	425	11	predesigned	predesigned	ADJ
ejpam-890	425	12	place	place	NOUN
ejpam-890	425	13	is	be	AUX
ejpam-890	425	14	the	the	DET
ejpam-890	425	15	first	first	ADJ
ejpam-890	425	16	p	p	NOUN
ejpam-890	425	17	rows	row	NOUN
ejpam-890	425	18	and	and	CCONJ
ejpam-890	425	19	the	the	DET
ejpam-890	425	20	first	first	ADJ
ejpam-890	425	21	r	r	NOUN
ejpam-890	425	22	columns	column	NOUN
ejpam-890	425	23	of	of	ADP
ejpam-890	425	24	size	size	NOUN
ejpam-890	425	25	p×	p×	PROPN
ejpam-890	425	26	r.	r.	PROPN
ejpam-890	425	27	in	in	ADP
ejpam-890	425	28	other	other	ADJ
ejpam-890	425	29	words	word	NOUN
ejpam-890	425	30	we	we	PRON
ejpam-890	425	31	assume	assume	VERB
ejpam-890	425	32	that	that	SCONJ
ejpam-890	425	33	the	the	DET
ejpam-890	425	34	burst	burst	ADJ
ejpam-890	425	35	errors	error	NOUN
ejpam-890	425	36	of	of	ADP
ejpam-890	425	37	size	size	NOUN
ejpam-890	425	38	may	may	AUX
ejpam-890	425	39	appear	appear	VERB
ejpam-890	425	40	only	only	ADV
ejpam-890	425	41	in	in	ADP
ejpam-890	425	42	this	this	DET
ejpam-890	425	43	place	place	NOUN
ejpam-890	425	44	.	.	PUNCT
ejpam-890	426	1	two	two	NUM
ejpam-890	426	2	different	different	ADJ
ejpam-890	426	3	bursts	burst	NOUN
ejpam-890	426	4	of	of	ADP
ejpam-890	426	5	this	this	DET
ejpam-890	426	6	type	type	NOUN
ejpam-890	426	7	does	do	AUX
ejpam-890	426	8	not	not	PART
ejpam-890	426	9	fall	fall	VERB
ejpam-890	426	10	into	into	ADP
ejpam-890	426	11	the	the	DET
ejpam-890	426	12	same	same	ADJ
ejpam-890	426	13	coset	coset	NOUN
ejpam-890	426	14	.	.	PUNCT
ejpam-890	427	1	otherwise	otherwise	ADV
ejpam-890	427	2	,	,	PUNCT
ejpam-890	427	3	if	if	SCONJ
ejpam-890	427	4	two	two	NUM
ejpam-890	427	5	different	different	ADJ
ejpam-890	427	6	burst	burst	ADJ
ejpam-890	427	7	errors	error	NOUN
ejpam-890	427	8	of	of	ADP
ejpam-890	427	9	this	this	DET
ejpam-890	427	10	type	type	NOUN
ejpam-890	427	11	fall	fall	NOUN
ejpam-890	427	12	into	into	ADP
ejpam-890	427	13	the	the	DET
ejpam-890	427	14	same	same	ADJ
ejpam-890	427	15	coset	coset	NOUN
ejpam-890	427	16	,	,	PUNCT
ejpam-890	427	17	then	then	ADV
ejpam-890	427	18	their	their	PRON
ejpam-890	427	19	the	the	DET
ejpam-890	427	20	difference	difference	NOUN
ejpam-890	427	21	will	will	AUX
ejpam-890	427	22	be	be	AUX
ejpam-890	427	23	a	a	DET
ejpam-890	427	24	codeword	codeword	NOUN
ejpam-890	427	25	in	in	ADP
ejpam-890	427	26	the	the	DET
ejpam-890	427	27	code	code	NOUN
ejpam-890	427	28	.	.	PUNCT
ejpam-890	428	1	this	this	PRON
ejpam-890	428	2	will	will	AUX
ejpam-890	428	3	lead	lead	VERB
ejpam-890	428	4	to	to	ADP
ejpam-890	428	5	a	a	DET
ejpam-890	428	6	contradiction	contradiction	NOUN
ejpam-890	428	7	since	since	SCONJ
ejpam-890	428	8	the	the	DET
ejpam-890	428	9	array	array	NOUN
ejpam-890	428	10	code	code	NOUN
ejpam-890	428	11	does	do	AUX
ejpam-890	428	12	not	not	PART
ejpam-890	428	13	contain	contain	VERB
ejpam-890	428	14	such	such	ADJ
ejpam-890	428	15	burst	burst	ADJ
ejpam-890	428	16	errors	error	NOUN
ejpam-890	428	17	.	.	PUNCT
ejpam-890	429	1	hence	hence	ADV
ejpam-890	429	2	,	,	PUNCT
ejpam-890	429	3	the	the	DET
ejpam-890	429	4	number	number	NOUN
ejpam-890	429	5	of	of	ADP
ejpam-890	429	6	cosets	coset	NOUN
ejpam-890	429	7	must	must	AUX
ejpam-890	429	8	be	be	AUX
ejpam-890	429	9	larger	large	ADJ
ejpam-890	429	10	or	or	CCONJ
ejpam-890	429	11	equal	equal	ADJ
ejpam-890	429	12	to	to	ADP
ejpam-890	429	13	the	the	DET
ejpam-890	429	14	number	number	NOUN
ejpam-890	429	15	of	of	ADP
ejpam-890	429	16	all	all	DET
ejpam-890	429	17	possible	possible	ADJ
ejpam-890	429	18	burst	burst	ADJ
ejpam-890	429	19	errors	error	NOUN
ejpam-890	429	20	of	of	ADP
ejpam-890	429	21	type	type	NOUN
ejpam-890	429	22	p×	p×	NOUN
ejpam-890	429	23	r	r	NOUN
ejpam-890	429	24	which	which	PRON
ejpam-890	429	25	equals	equal	VERB
ejpam-890	429	26	to	to	PART
ejpam-890	429	27	qpr	qpr	VERB
ejpam-890	429	28	.	.	PUNCT
ejpam-890	430	1	5	5	X
ejpam-890	430	2	.	.	X
ejpam-890	430	3	conclusion	conclusion	NOUN
ejpam-890	430	4	a	a	DET
ejpam-890	430	5	new	new	ADJ
ejpam-890	430	6	approach	approach	NOUN
ejpam-890	430	7	that	that	PRON
ejpam-890	430	8	avoids	avoid	VERB
ejpam-890	430	9	solving	solve	VERB
ejpam-890	430	10	integer	integer	NOUN
ejpam-890	430	11	inequalities	inequality	NOUN
ejpam-890	430	12	on	on	ADP
ejpam-890	430	13	enumerating	enumerate	VERB
ejpam-890	430	14	burst	burst	ADJ
ejpam-890	430	15	errors	error	NOUN
ejpam-890	430	16	of	of	ADP
ejpam-890	430	17	arrays	array	NOUN
ejpam-890	430	18	is	be	AUX
ejpam-890	430	19	presented	present	VERB
ejpam-890	430	20	.	.	PUNCT
ejpam-890	431	1	this	this	DET
ejpam-890	431	2	method	method	NOUN
ejpam-890	431	3	is	be	AUX
ejpam-890	431	4	applied	apply	VERB
ejpam-890	431	5	to	to	PART
ejpam-890	431	6	array	array	VERB
ejpam-890	431	7	codes	code	NOUN
ejpam-890	431	8	over	over	ADP
ejpam-890	431	9	finite	finite	ADJ
ejpam-890	431	10	rings	ring	NOUN
ejpam-890	431	11	which	which	PRON
ejpam-890	431	12	is	be	AUX
ejpam-890	431	13	a	a	DET
ejpam-890	431	14	generalization	generalization	NOUN
ejpam-890	431	15	of	of	ADP
ejpam-890	431	16	previous	previous	ADJ
ejpam-890	431	17	results	result	NOUN
ejpam-890	431	18	.	.	PUNCT
ejpam-890	432	1	finally	finally	ADV
ejpam-890	432	2	,	,	PUNCT
ejpam-890	432	3	some	some	DET
ejpam-890	432	4	applications	application	NOUN
ejpam-890	432	5	of	of	ADP
ejpam-890	432	6	the	the	DET
ejpam-890	432	7	results	result	NOUN
ejpam-890	432	8	are	be	AUX
ejpam-890	432	9	presented	present	VERB
ejpam-890	432	10	.	.	PUNCT
ejpam-890	433	1	acknowledgements	acknowledgement	NOUN
ejpam-890	433	2	the	the	DET
ejpam-890	433	3	author	author	NOUN
ejpam-890	433	4	is	be	AUX
ejpam-890	433	5	thankful	thankful	ADJ
ejpam-890	433	6	to	to	ADP
ejpam-890	433	7	the	the	DET
ejpam-890	433	8	referee(s	referee(s	NOUN
ejpam-890	433	9	)	)	PUNCT
ejpam-890	433	10	for	for	ADP
ejpam-890	433	11	their	their	PRON
ejpam-890	433	12	valuable	valuable	ADJ
ejpam-890	433	13	remarks	remark	NOUN
ejpam-890	433	14	that	that	PRON
ejpam-890	433	15	helped	help	VERB
ejpam-890	433	16	on	on	ADP
ejpam-890	433	17	improving	improve	VERB
ejpam-890	433	18	the	the	DET
ejpam-890	433	19	presentation	presentation	NOUN
ejpam-890	433	20	of	of	ADP
ejpam-890	433	21	the	the	DET
ejpam-890	433	22	paper	paper	NOUN
ejpam-890	433	23	.	.	PUNCT
ejpam-890	434	1	references	reference	NOUN
ejpam-890	434	2	[	[	X
ejpam-890	434	3	1	1	NUM
ejpam-890	434	4	]	]	X
ejpam-890	434	5	k.a.s	k.a.s	PROPN
ejpam-890	434	6	.	.	PROPN
ejpam-890	434	7	abdel	abdel	PROPN
ejpam-890	434	8	-	-	PUNCT
ejpam-890	434	9	ghaffar	ghaffar	PROPN
ejpam-890	434	10	,	,	PUNCT
ejpam-890	434	11	r.j	r.j	PROPN
ejpam-890	434	12	.	.	PROPN
ejpam-890	434	13	mceliece	mceliece	PROPN
ejpam-890	434	14	,	,	PUNCT
ejpam-890	434	15	and	and	CCONJ
ejpam-890	434	16	h.c.a	h.c.a	NOUN
ejpam-890	434	17	.	.	PUNCT
ejpam-890	435	1	van	van	PROPN
ejpam-890	435	2	tilborg	tilborg	NOUN
ejpam-890	435	3	,	,	PUNCT
ejpam-890	435	4	two	two	NUM
ejpam-890	435	5	dimensional	dimensional	ADJ
ejpam-890	435	6	burst	burst	ADJ
ejpam-890	435	7	identification	identification	NOUN
ejpam-890	435	8	codes	code	NOUN
ejpam-890	435	9	and	and	CCONJ
ejpam-890	435	10	their	their	PRON
ejpam-890	435	11	use	use	NOUN
ejpam-890	435	12	in	in	ADP
ejpam-890	435	13	burst	burst	ADJ
ejpam-890	435	14	correction	correction	NOUN
ejpam-890	435	15	,	,	PUNCT
ejpam-890	435	16	ieee	ieee	PROPN
ejpam-890	435	17	trans	trans	PROPN
ejpam-890	435	18	.	.	PROPN
ejpam-890	435	19	inf	inf	PROPN
ejpam-890	435	20	.	.	PUNCT
ejpam-890	436	1	theory	theory	NOUN
ejpam-890	436	2	,	,	PUNCT
ejpam-890	436	3	vol	vol	NOUN
ejpam-890	436	4	.	.	PROPN
ejpam-890	437	1	34	34	NUM
ejpam-890	437	2	,	,	PUNCT
ejpam-890	437	3	no	no	INTJ
ejpam-890	437	4	.	.	NOUN
ejpam-890	437	5	3	3	NUM
ejpam-890	437	6	,	,	PUNCT
ejpam-890	437	7	pp	pp	ADJ
ejpam-890	437	8	.	.	PUNCT
ejpam-890	438	1	494	494	NUM
ejpam-890	438	2	-	-	SYM
ejpam-890	438	3	504	504	NUM
ejpam-890	438	4	,	,	PUNCT
ejpam-890	438	5	may	may	AUX
ejpam-890	438	6	1998	1998	NUM
ejpam-890	438	7	.	.	PUNCT
ejpam-890	439	1	[	[	X
ejpam-890	439	2	2	2	NUM
ejpam-890	439	3	]	]	PUNCT
ejpam-890	439	4	m.	m.	NOUN
ejpam-890	439	5	blaum	blaum	NOUN
ejpam-890	439	6	and	and	CCONJ
ejpam-890	439	7	p.g	p.g	PROPN
ejpam-890	439	8	.	.	PROPN
ejpam-890	439	9	farell	farell	PROPN
ejpam-890	439	10	,	,	PUNCT
ejpam-890	439	11	array	array	VERB
ejpam-890	439	12	codes	code	NOUN
ejpam-890	439	13	for	for	ADP
ejpam-890	439	14	cluster	cluster	NOUN
ejpam-890	439	15	error	error	NOUN
ejpam-890	439	16	correction	correction	NOUN
ejpam-890	439	17	,	,	PUNCT
ejpam-890	439	18	elec	elec	PROPN
ejpam-890	439	19	.	.	PUNCT
ejpam-890	440	1	letters	letter	NOUN
ejpam-890	440	2	,	,	PUNCT
ejpam-890	440	3	vol	vol	NOUN
ejpam-890	440	4	.	.	PROPN
ejpam-890	440	5	30	30	NUM
ejpam-890	440	6	,	,	PUNCT
ejpam-890	440	7	no	no	INTJ
ejpam-890	440	8	.	.	NOUN
ejpam-890	440	9	21	21	NUM
ejpam-890	440	10	,	,	PUNCT
ejpam-890	440	11	pp.1752	pp.1752	PROPN
ejpam-890	440	12	-	-	SYM
ejpam-890	440	13	1753	1753	NUM
ejpam-890	440	14	,	,	PUNCT
ejpam-890	440	15	oct	oct	PROPN
ejpam-890	440	16	.	.	PROPN
ejpam-890	440	17	1994	1994	NUM
ejpam-890	440	18	.	.	PUNCT
ejpam-890	441	1	[	[	X
ejpam-890	441	2	3	3	X
ejpam-890	441	3	]	]	X
ejpam-890	441	4	steven	steven	PROPN
ejpam-890	441	5	t.	t.	PROPN
ejpam-890	441	6	dougherty	dougherty	PROPN
ejpam-890	441	7	and	and	CCONJ
ejpam-890	441	8	maxim	maxim	NOUN
ejpam-890	441	9	m.	m.	NOUN
ejpam-890	441	10	skriganov	skriganov	PROPN
ejpam-890	441	11	,	,	PUNCT
ejpam-890	441	12	macwilliams	macwilliam	NOUN
ejpam-890	441	13	duality	duality	NOUN
ejpam-890	441	14	and	and	CCONJ
ejpam-890	441	15	the	the	DET
ejpam-890	441	16	rosenbloomtsfasman	rosenbloomtsfasman	NOUN
ejpam-890	441	17	metric	metric	NOUN
ejpam-890	441	18	,	,	PUNCT
ejpam-890	441	19	moscow	moscow	PROPN
ejpam-890	441	20	mathematical	mathematical	ADJ
ejpam-890	441	21	journal	journal	NOUN
ejpam-890	441	22	,	,	PUNCT
ejpam-890	441	23	vol	vol	NOUN
ejpam-890	441	24	.	.	NOUN
ejpam-890	441	25	2	2	NUM
ejpam-890	441	26	number	number	NOUN
ejpam-890	441	27	1	1	NUM
ejpam-890	441	28	,	,	PUNCT
ejpam-890	441	29	p.	p.	NOUN
ejpam-890	441	30	83	83	NUM
ejpam-890	441	31	-	-	SYM
ejpam-890	441	32	89	89	NUM
ejpam-890	441	33	,	,	PUNCT
ejpam-890	441	34	2002	2002	NUM
ejpam-890	441	35	.	.	PUNCT
ejpam-890	442	1	[	[	X
ejpam-890	442	2	4	4	X
ejpam-890	442	3	]	]	PUNCT
ejpam-890	442	4	p.	p.	NOUN
ejpam-890	442	5	fire	fire	NOUN
ejpam-890	442	6	,	,	PUNCT
ejpam-890	442	7	a	a	DET
ejpam-890	442	8	class	class	NOUN
ejpam-890	442	9	of	of	ADP
ejpam-890	442	10	multiple	multiple	ADJ
ejpam-890	442	11	error	error	NOUN
ejpam-890	442	12	correcting	correct	VERB
ejpam-890	442	13	binary	binary	ADJ
ejpam-890	442	14	codes	code	NOUN
ejpam-890	442	15	for	for	ADP
ejpam-890	442	16	non	non	ADJ
ejpam-890	442	17	-	-	ADJ
ejpam-890	442	18	independent	independent	ADJ
ejpam-890	442	19	errors	error	NOUN
ejpam-890	442	20	,	,	PUNCT
ejpam-890	442	21	sylvania	sylvania	PROPN
ejpam-890	442	22	reports	report	VERB
ejpam-890	442	23	rsl	rsl	PROPN
ejpam-890	442	24	-	-	PUNCT
ejpam-890	442	25	e-2	e-2	PROPN
ejpam-890	442	26	,	,	PUNCT
ejpam-890	442	27	sylvania	sylvania	PROPN
ejpam-890	442	28	reconnaissance	reconnaissance	NOUN
ejpam-890	442	29	systems	system	NOUN
ejpam-890	442	30	,	,	PUNCT
ejpam-890	442	31	mountain	mountain	NOUN
ejpam-890	442	32	view	view	NOUN
ejpam-890	442	33	,	,	PUNCT
ejpam-890	442	34	california	california	PROPN
ejpam-890	442	35	,	,	PUNCT
ejpam-890	442	36	1959	1959	NUM
ejpam-890	442	37	.	.	PUNCT
ejpam-890	443	1	[	[	X
ejpam-890	443	2	5	5	NUM
ejpam-890	443	3	]	]	PUNCT
ejpam-890	443	4	sapna	sapna	ADJ
ejpam-890	443	5	jain	jain	PROPN
ejpam-890	443	6	,	,	PUNCT
ejpam-890	443	7	bursts	burst	NOUN
ejpam-890	443	8	in	in	ADP
ejpam-890	443	9	mmetric	mmetric	ADJ
ejpam-890	443	10	array	array	NOUN
ejpam-890	443	11	codes	code	NOUN
ejpam-890	443	12	,	,	PUNCT
ejpam-890	443	13	linear	linear	ADJ
ejpam-890	443	14	algebra	algebra	NOUN
ejpam-890	443	15	and	and	CCONJ
ejpam-890	443	16	its	its	PRON
ejpam-890	443	17	applications	application	NOUN
ejpam-890	443	18	,	,	PUNCT
ejpam-890	443	19	vol	vol	NOUN
ejpam-890	443	20	.	.	PROPN
ejpam-890	443	21	418	418	NUM
ejpam-890	443	22	,	,	PUNCT
ejpam-890	443	23	p.130	p.130	NOUN
ejpam-890	443	24	-	-	PUNCT
ejpam-890	443	25	141	141	NUM
ejpam-890	443	26	,	,	PUNCT
ejpam-890	443	27	2006	2006	NUM
ejpam-890	443	28	.	.	PUNCT
ejpam-890	444	1	[	[	X
ejpam-890	444	2	6	6	NUM
ejpam-890	444	3	]	]	X
ejpam-890	444	4	s.h	s.h	PROPN
ejpam-890	444	5	.	.	PROPN
ejpam-890	444	6	reiger	reiger	NOUN
ejpam-890	444	7	,	,	PUNCT
ejpam-890	444	8	codes	code	NOUN
ejpam-890	444	9	for	for	ADP
ejpam-890	444	10	the	the	DET
ejpam-890	444	11	correction	correction	NOUN
ejpam-890	444	12	of	of	ADP
ejpam-890	444	13	clustered	clustered	ADJ
ejpam-890	444	14	errors	error	NOUN
ejpam-890	444	15	,	,	PUNCT
ejpam-890	444	16	ire	ire	VERB
ejpam-890	444	17	transc	transc	ADP
ejpam-890	444	18	.	.	PUNCT
ejpam-890	445	1	on	on	ADP
ejpam-890	445	2	information	information	NOUN
ejpam-890	445	3	theory	theory	NOUN
ejpam-890	445	4	,	,	PUNCT
ejpam-890	445	5	vol	vol	NOUN
ejpam-890	445	6	.	.	PROPN
ejpam-890	445	7	6	6	NUM
ejpam-890	445	8	,	,	PUNCT
ejpam-890	445	9	pp	pp	ADJ
ejpam-890	445	10	.	.	PUNCT
ejpam-890	446	1	16	16	NUM
ejpam-890	446	2	-	-	SYM
ejpam-890	446	3	21	21	NUM
ejpam-890	446	4	,	,	PUNCT
ejpam-890	446	5	1960	1960	NUM
ejpam-890	446	6	.	.	PUNCT
ejpam-890	447	1	references	reference	NOUN
ejpam-890	447	2	669	669	NUM
ejpam-890	447	3	[	[	X
ejpam-890	447	4	7	7	NUM
ejpam-890	447	5	]	]	PUNCT
ejpam-890	447	6	m.	m.	NOUN
ejpam-890	447	7	yu	yu	PROPN
ejpam-890	447	8	rosenbloom	rosenbloom	PROPN
ejpam-890	447	9	and	and	CCONJ
ejpam-890	447	10	m.	m.	NOUN
ejpam-890	447	11	a.	a.	PROPN
ejpam-890	447	12	tsfasman	tsfasman	PROPN
ejpam-890	447	13	,	,	PUNCT
ejpam-890	447	14	codes	code	NOUN
ejpam-890	447	15	for	for	ADP
ejpam-890	447	16	the	the	DET
ejpam-890	447	17	m	m	NOUN
ejpam-890	447	18	-	-	ADJ
ejpam-890	447	19	metric	metric	ADJ
ejpam-890	447	20	,	,	PUNCT
ejpam-890	447	21	problems	problem	NOUN
ejpam-890	447	22	of	of	ADP
ejpam-890	447	23	information	information	NOUN
ejpam-890	447	24	transmission	transmission	NOUN
ejpam-890	447	25	,	,	PUNCT
ejpam-890	447	26	vol	vol	NOUN
ejpam-890	447	27	.	.	PUNCT
ejpam-890	448	1	33	33	NUM
ejpam-890	448	2	.	.	PUNCT
ejpam-890	449	1	no	no	INTJ
ejpam-890	449	2	.	.	NOUN
ejpam-890	449	3	1	1	NUM
ejpam-890	449	4	,	,	PUNCT
ejpam-890	449	5	pp	pp	ADJ
ejpam-890	449	6	.	.	PUNCT
ejpam-890	450	1	45	45	NUM
ejpam-890	450	2	-	-	SYM
ejpam-890	450	3	52	52	NUM
ejpam-890	450	4	,	,	PUNCT
ejpam-890	450	5	1997	1997	NUM
ejpam-890	450	6	.	.	PUNCT
ejpam-890	451	1	[	[	X
ejpam-890	451	2	8	8	NUM
ejpam-890	451	3	]	]	X
ejpam-890	451	4	m.m	m.m	PROPN
ejpam-890	451	5	.	.	PROPN
ejpam-890	451	6	skriganov	skriganov	PROPN
ejpam-890	451	7	,	,	PUNCT
ejpam-890	451	8	coding	code	VERB
ejpam-890	451	9	theory	theory	NOUN
ejpam-890	451	10	and	and	CCONJ
ejpam-890	451	11	uniform	uniform	ADJ
ejpam-890	451	12	distributions	distribution	NOUN
ejpam-890	451	13	,	,	PUNCT
ejpam-890	451	14	st	st	PROPN
ejpam-890	451	15	.	.	PROPN
ejpam-890	451	16	petersburg	petersburg	PROPN
ejpam-890	451	17	math	math	PROPN
ejpam-890	451	18	.	.	PUNCT
ejpam-890	452	1	j.	j.	PROPN
ejpam-890	452	2	vol	vol	PROPN
ejpam-890	452	3	143	143	NUM
ejpam-890	452	4	,	,	PUNCT
ejpam-890	452	5	no	no	INTJ
ejpam-890	452	6	.	.	NOUN
ejpam-890	452	7	2	2	NUM
ejpam-890	452	8	,	,	PUNCT
ejpam-890	452	9	2002	2002	NUM
ejpam-890	452	10	.	.	PUNCT
ejpam-890	453	1	[	[	X
ejpam-890	453	2	9	9	NUM
ejpam-890	453	3	]	]	X
ejpam-890	453	4	irfan	irfan	PROPN
ejpam-890	453	5	siap	siap	PROPN
ejpam-890	453	6	,	,	PUNCT
ejpam-890	453	7	the	the	DET
ejpam-890	453	8	complete	complete	ADJ
ejpam-890	453	9	weight	weight	NOUN
ejpam-890	453	10	enumerator	enumerator	NOUN
ejpam-890	453	11	for	for	ADP
ejpam-890	453	12	codes	code	NOUN
ejpam-890	453	13	overm	overm	NOUN
ejpam-890	453	14	n×s(fq	n×s(fq	PROPN
ejpam-890	453	15	)	)	PUNCT
ejpam-890	453	16	,	,	PUNCT
ejpam-890	453	17	lecture	lecture	NOUN
ejpam-890	453	18	notes	note	NOUN
ejpam-890	453	19	on	on	ADP
ejpam-890	453	20	computer	computer	NOUN
ejpam-890	453	21	sciences	science	NOUN
ejpam-890	453	22	2260	2260	NUM
ejpam-890	453	23	,	,	PUNCT
ejpam-890	453	24	pp	pp	ADV
ejpam-890	453	25	.	.	PUNCT
ejpam-890	454	1	20	20	NUM
ejpam-890	454	2	-	-	SYM
ejpam-890	454	3	26	26	NUM
ejpam-890	454	4	,	,	PUNCT
ejpam-890	454	5	2001	2001	NUM
ejpam-890	454	6	.	.	PUNCT
ejpam-890	455	1	[	[	X
ejpam-890	455	2	10	10	NUM
ejpam-890	455	3	]	]	X
ejpam-890	455	4	irfan	irfan	PROPN
ejpam-890	455	5	siap	siap	PROPN
ejpam-890	455	6	,	,	PUNCT
ejpam-890	455	7	ct	ct	PROPN
ejpam-890	455	8	burst	burst	NOUN
ejpam-890	455	9	error	error	NOUN
ejpam-890	455	10	weight	weight	NOUN
ejpam-890	455	11	enumerator	enumerator	NOUN
ejpam-890	455	12	of	of	ADP
ejpam-890	455	13	array	array	NOUN
ejpam-890	455	14	codes	code	NOUN
ejpam-890	455	15	,	,	PUNCT
ejpam-890	455	16	albanian	albanian	ADJ
ejpam-890	455	17	journal	journal	NOUN
ejpam-890	455	18	of	of	ADP
ejpam-890	455	19	mathematics	mathematics	PROPN
ejpam-890	455	20	,	,	PUNCT
ejpam-890	455	21	vol	vol	NOUN
ejpam-890	455	22	.	.	PROPN
ejpam-890	455	23	2	2	NUM
ejpam-890	455	24	,	,	PUNCT
ejpam-890	455	25	no	no	INTJ
ejpam-890	455	26	.	.	NOUN
ejpam-890	455	27	3	3	NUM
ejpam-890	455	28	,	,	PUNCT
ejpam-890	455	29	pp	pp	ADJ
ejpam-890	455	30	.	.	PUNCT
ejpam-890	456	1	171	171	NUM
ejpam-890	456	2	-	-	SYM
ejpam-890	456	3	178	178	NUM
ejpam-890	456	4	,	,	PUNCT
ejpam-890	456	5	2008	2008	NUM
ejpam-890	456	6	.	.	PUNCT
ejpam-890	457	1	[	[	X
ejpam-890	457	2	11	11	NUM
ejpam-890	457	3	]	]	X
ejpam-890	457	4	moshe	moshe	PROPN
ejpam-890	457	5	shwartz	shwartz	PROPN
ejpam-890	457	6	and	and	CCONJ
ejpam-890	457	7	tuvi	tuvi	PROPN
ejpam-890	457	8	etzion	etzion	NOUN
ejpam-890	457	9	,	,	PUNCT
ejpam-890	457	10	two	two	NUM
ejpam-890	457	11	dimensional	dimensional	ADJ
ejpam-890	457	12	cluster	cluster	NOUN
ejpam-890	457	13	-	-	PUNCT
ejpam-890	457	14	correcting	correct	VERB
ejpam-890	457	15	codes	code	NOUN
ejpam-890	457	16	,	,	PUNCT
ejpam-890	457	17	ieee	ieee	NOUN
ejpam-890	457	18	trans	tran	NOUN
ejpam-890	457	19	.	.	PUNCT
ejpam-890	458	1	on	on	ADP
ejpam-890	458	2	info	info	NOUN
ejpam-890	458	3	.	.	PUNCT
ejpam-890	459	1	theory	theory	NOUN
ejpam-890	459	2	,	,	PUNCT
ejpam-890	459	3	vol	vol	NOUN
ejpam-890	459	4	.	.	PROPN
ejpam-890	460	1	51	51	NUM
ejpam-890	460	2	,	,	PUNCT
ejpam-890	460	3	no	no	INTJ
ejpam-890	460	4	.	.	NOUN
ejpam-890	460	5	6	6	NUM
ejpam-890	460	6	,	,	PUNCT
ejpam-890	460	7	pp	pp	ADJ
ejpam-890	460	8	.	.	PUNCT
ejpam-890	461	1	2121	2121	NUM
ejpam-890	461	2	-	-	SYM
ejpam-890	461	3	2132	2132	NUM
ejpam-890	461	4	june	june	PROPN
ejpam-890	461	5	2005	2005	NUM
ejpam-890	461	6	.	.	PUNCT