Cyclic codes of length 5p with MDS symbol-pair

被引：1

作者：

Li, Fengwei ^{[1
,2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Peoples R China

[2] Zaozhuang Univ, Sch Math & Stat, Zaozhuang 277160, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Symbol-pair code; MDS symbol-pair code; Cyclic code; ROOT CONSTACYCLIC CODES; DISTANCE SEPARABLE CODES; CONSTRUCTIONS;

D O I：

10.1007/s10623-023-01184-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let p be a prime with 5|(p - 1). Let S be a set of all repeated-root cyclic codes C = (g(x)), (x(5) - 1)|g(x), of length 5p over a field field F-p, whose Hamming distances are at most 7. In this paper, we present a method to find all maximum distance separable (MDS) symbol-pair codes in S. By this method we can easily obtain the results in Ma and Luo (Des Codes Cryptogr 90:121-137, 2022) and new MDS symbol-pair codes, so we remain two possible MDS symbol-pair codes for readers.

引用

页码：1873 / 1888

页数：16

共 32 条

[1] Cyclic codes of length 5p with MDS symbol-pair
Fengwei Li
Designs, Codes and Cryptography, 2023, 91 : 1873 - 1888
[2] MDS symbol-pair codes from repeated-root cyclic codes
Ma, Junru
Luo, Jinquan
DESIGNS CODES AND CRYPTOGRAPHY, 2022, 90 (01) : 121 - 137
[3] MDS Symbol-Pair Cyclic Codes of Length 2ps over Fpm
Dinh, Hai Q.
Nguyen, Bac T.
Sriboonchitta, Songsak
IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (01) : 240 - 262
[4] MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes
Dinh, Hai Q.
Nguyen, Bac T.
Singh, Abhay Kumar
Yamaka, Woraphon
IEEE ACCESS, 2021, 9 : 137970 - 137990
[5] Two New Classes of MDS Symbol-Pair Codes
Kai, Xiaoshan
Zhou, Yajing
Zhu, Shixin
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (11) : 7701 - 7710
[6] On symbol-pair weight distribution of MDS codes and simplex codes over finite fields
Ma, Junru
Luo, Jinquan
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2021, 13 (01): : 101 - 115
[7] New Families of MDS Symbol-Pair Codes From Matrix-Product Codes
Luo, Gaojun
Ezerman, Martianus Frederic
Ling, San
Pan, Xu
IEEE TRANSACTIONS ON INFORMATION THEORY, 2023, 69 (03) : 1567 - 1587
[8] A new family of AMDS symbol-pair constacyclic codes of length 4p and symbol-pair distance 9
Dinh, Hai Q.
Ha, Hieu V.
Nguyen, Bac T.
Vo, Thieu N.
DESIGNS CODES AND CRYPTOGRAPHY, 2025,
[9] Two new classes of AMDS symbol-pair cyclic codes of length 4p
Dinh, Hai Q.
Ha, Hieu V.
Nguyen, Bac T.
Vo, Thieu N.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, 70 (05) : 4117 - 4131
[10] New MDS Symbol-Pair Codes From Repeated-Root Codes
Kai, Xiaoshan
Zhu, Shixin
Zhao, Yusen
Luo, Huarong
Chen, Zhe
IEEE COMMUNICATIONS LETTERS, 2018, 22 (03) : 462 - 465

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