The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

被引：0

作者：

Liang, Yinghao ^{[1
]}

Liu, Zihui ^{[1
,2
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Key Lab Math Theory & Computat Informat Secur, Beijing 100081, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2024年 / 70卷 / 07期

基金：

北京市自然科学基金;

关键词：

Codes; Vectors; Measurement; Graph theory; Generators; Linear programming; Linear codes; Symbol-pair weight; generalized value assignment; Plotkin-type bound; block intersection graph; Hamilton cycle; HAMMING WEIGHTS;

D O I：

10.1109/TIT.2024.3392744

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.

引用

页码：4990 / 5001

页数：12

共 50 条

[31] 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
[32] MDS symbol-pair codes from repeated-root cyclic codes
Ma, Junru
Luo, Jinquan
DESIGNS CODES AND CRYPTOGRAPHY, 2022, 90 (01) : 121 - 137
[33] Cyclic codes of length 5p with MDS symbol-pair
Li, Fengwei
DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (05) : 1873 - 1888
[34] 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
[35] Constructions of MDS symbol-pair codes with minimum distance seven or eight
Junru Ma
Jinquan Luo
Designs, Codes and Cryptography, 2022, 90 : 2337 - 2359
[36] Constructions of MDS symbol-pair codes with minimum distance seven or eight
Ma, Junru
Luo, Jinquan
DESIGNS CODES AND CRYPTOGRAPHY, 2022, 90 (10) : 2337 - 2359
[37] A Decoding Algorithm for Cyclic Codes over Symbol-Pair Read Channels
Takita, Makoto
Hirotomo, Masanori
Morii, Masakatu
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2015, E98A (12): : 2415 - 2422
[38] AMDS symbol-pair codes from repeated-root cyclic codes
Ma, Junru
Luo, Jinquan
DISCRETE MATHEMATICS, 2023, 346 (07)
[39] MDS symbol-pair codes from repeated-root cyclic codes
Junru Ma
Jinquan Luo
Designs, Codes and Cryptography, 2022, 90 : 121 - 137
[40] Cyclic codes of length 5p with MDS symbol-pair
Fengwei Li
Designs, Codes and Cryptography, 2023, 91 : 1873 - 1888

← 1 2 3 4 5 →