MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted Generalized Reed-Solomon Codes

Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon...

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Published inIEEE transactions on information theory Vol. 68; no. 12; pp. 7832 - 7841
Main Authors Sui, Junzhen, Yue, Qin, Li, Xia, Huang, Daitao
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Codecs
Codes
Cryptography
Linear codes
MDS codes
Reed-Solomon codes
Reliability
self-dual codes
Telecommunications
twisted generalized Reed-Solomon codes
Online AccessGet full text
ISSN0018-9448
1557-9654
DOI10.1109/TIT.2022.3190676

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Abstract Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS; give a sufficient and necessary condition that a TGRS code with two twists is self-dual, and present some constructions of self-dual TGRS codes. These self-dual codes are MDS, NMDS or 2-MDS. Furthermore, we study the non-GRS properties of TGRS codes with two twists and prove that these codes are non-GRS in most cases.
AbstractList Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS; give a sufficient and necessary condition that a TGRS code with two twists is self-dual, and present some constructions of self-dual TGRS codes. These self-dual codes are MDS, NMDS or 2-MDS. Furthermore, we study the non-GRS properties of TGRS codes with two twists and prove that these codes are non-GRS in most cases.
Author Huang, Daitao
Li, Xia
Sui, Junzhen
Yue, Qin
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Snippet Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are...
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SubjectTerms Codecs
Codes
Cryptography
Linear codes
MDS codes
Reed-Solomon codes
Reliability
self-dual codes
Telecommunications
twisted generalized Reed-Solomon codes
Title MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted Generalized Reed-Solomon Codes
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