Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes

Huan Sun; Qin Yue; Xue Jia; Chengju Li

doi:10.1109/TIT.2024.3509895

Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes

Huan Sun
, Qin Yue^*
, Xue Jia
, Chengju Li^*

^*Corresponding author for this work

Software Engineering Institute

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

1 Scopus citations

Abstract

In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters [n, n-t, t+1] over Bbb F_q. For even t, the algorithms can correct t/2 errors with time complexity O(qn). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct t/2 errors, which generalizes a ⌊t-1/2⌋-error-correcting decoding algorithm by Sui and Yue (2023).

Original language	English
Pages (from-to)	1018-1027
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	71
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2024.3509895
State	Published - 2025

Keywords

MDS code
Twisted generalized Reed-Solomon code
decoding algorithm
twisted Goppa code

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10.1109/TIT.2024.3509895

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title = "Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes",

abstract = "In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters [n, n-t, t+1] over Bbb Fq. For even t, the algorithms can correct t/2 errors with time complexity O(qn). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct t/2 errors, which generalizes a ⌊t-1/2⌋-error-correcting decoding algorithm by Sui and Yue (2023).",

keywords = "MDS code, Twisted generalized Reed-Solomon code, decoding algorithm, twisted Goppa code",

author = "Huan Sun and Qin Yue and Xue Jia and Chengju Li",

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

year = "2025",

doi = "10.1109/TIT.2024.3509895",

language = "英语",

volume = "71",

pages = "1018--1027",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

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T1 - Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes

AU - Sun, Huan

AU - Yue, Qin

AU - Jia, Xue

AU - Li, Chengju

PY - 2025

Y1 - 2025

N2 - In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters [n, n-t, t+1] over Bbb Fq. For even t, the algorithms can correct t/2 errors with time complexity O(qn). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct t/2 errors, which generalizes a ⌊t-1/2⌋-error-correcting decoding algorithm by Sui and Yue (2023).

AB - In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters [n, n-t, t+1] over Bbb Fq. For even t, the algorithms can correct t/2 errors with time complexity O(qn). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct t/2 errors, which generalizes a ⌊t-1/2⌋-error-correcting decoding algorithm by Sui and Yue (2023).

KW - MDS code

KW - Twisted generalized Reed-Solomon code

KW - decoding algorithm

KW - twisted Goppa code

UR - https://www.scopus.com/pages/publications/85211481712

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DO - 10.1109/TIT.2024.3509895

M3 - 文章

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SN - 0018-9448

VL - 71

SP - 1018

EP - 1027

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 2

ER -

Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes

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