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 50 条

[21] 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
[22] ON SYMBOL-PAIR DISTANCE DISTRIBUTIONS OF REPEATED-ROOT CONSTACYCLIC CODES OF LENGTH 4ps AND MDS CODES
Dinh, Hai q.
Singh, Abhay kumar
Thakur, Madhu kant
ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2025,
[23] 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
[24] On symbol-pair weight distribution of MDS codes and simplex codes over finite fields
Junru Ma
Jinquan Luo
Cryptography and Communications, 2021, 13 : 101 - 115
[25] Codes for Symbol-Pair Read Channels
Cassuto, Yuval
Blaum, Mario
IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) : 8011 - 8020
[26] AMDS symbol-pair codes from repeated-root cyclic codes
Ma, Junru
Luo, Jinquan
DISCRETE MATHEMATICS, 2023, 346 (07)
[27] List Decodability of Symbol-Pair Codes
Liu, Shu
Xing, Chaoping
Yuan, Chen
IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (08) : 4815 - 4821
[28] Syndrome Decoding of Symbol-Pair Codes
Takita, Makoto
Hirotomo, Masanori
Morii, Masakatu
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2015, E98A (12): : 2423 - 2428
[29] The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes
Liang, Yinghao
Liu, Zihui
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (07) : 4990 - 5001
[30] Codes for Symbol-Pair Read Channels
Cassuto, Yuval
Blaum, Mario
2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, : 988 - 992

← 1 2 3 4 5 →