New Results on Self-Dual Generalized Reed-Solomon Codes

Yu Ning; Zuo Ye; Gennian Ge; Fuyou Miao; Yan Xiong; Xiande Zhang

doi:10.1109/TIT.2021.3096934

New Results on Self-Dual Generalized Reed-Solomon Codes

Yu Ning
, Zuo Ye
, Gennian Ge
, Fuyou Miao
, Yan Xiong
, Xiande Zhang

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper focuses on constructions of MDS self-dual codes from (extended) generalized Reed-Solomon (GRS) codes. Let q = r {2} be an odd prime power. We show that, there exists a q -ary self-dual (extended) GRS code for each even length in the range [{2r,3r-3}] , and for each singly even length in the range [3r-1,4r]. This extends the only known consecutive range [2,2r] to [{2,3r-3}] for this case. Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported before.

Original language	English
Pages (from-to)	7240-7252
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	11
DOIs	https://doi.org/10.1109/TIT.2021.3096934
State	Published - 1 Nov 2021
Externally published	Yes

Keywords

MDS codes
generalized Reed-Solomon codes
self-dual codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2021.3096934

Cite this

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title = "New Results on Self-Dual Generalized Reed-Solomon Codes",

abstract = "This paper focuses on constructions of MDS self-dual codes from (extended) generalized Reed-Solomon (GRS) codes. Let q = r \{2\} be an odd prime power. We show that, there exists a q -ary self-dual (extended) GRS code for each even length in the range [\{2r,3r-3\}] , and for each singly even length in the range [3r-1,4r]. This extends the only known consecutive range [2,2r] to [\{2,3r-3\}] for this case. Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported before.",

keywords = "MDS codes, generalized Reed-Solomon codes, self-dual codes",

author = "Yu Ning and Zuo Ye and Gennian Ge and Fuyou Miao and Yan Xiong and Xiande Zhang",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

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doi = "10.1109/TIT.2021.3096934",

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T1 - New Results on Self-Dual Generalized Reed-Solomon Codes

AU - Ning, Yu

AU - Ye, Zuo

AU - Ge, Gennian

AU - Miao, Fuyou

AU - Xiong, Yan

AU - Zhang, Xiande

PY - 2021/11/1

Y1 - 2021/11/1

N2 - This paper focuses on constructions of MDS self-dual codes from (extended) generalized Reed-Solomon (GRS) codes. Let q = r {2} be an odd prime power. We show that, there exists a q -ary self-dual (extended) GRS code for each even length in the range [{2r,3r-3}] , and for each singly even length in the range [3r-1,4r]. This extends the only known consecutive range [2,2r] to [{2,3r-3}] for this case. Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported before.

AB - This paper focuses on constructions of MDS self-dual codes from (extended) generalized Reed-Solomon (GRS) codes. Let q = r {2} be an odd prime power. We show that, there exists a q -ary self-dual (extended) GRS code for each even length in the range [{2r,3r-3}] , and for each singly even length in the range [3r-1,4r]. This extends the only known consecutive range [2,2r] to [{2,3r-3}] for this case. Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported before.

KW - MDS codes

KW - generalized Reed-Solomon codes

KW - self-dual codes

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M3 - Article

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 11

ER -

New Results on Self-Dual Generalized Reed-Solomon Codes

Abstract

Keywords

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