LINEAR COMPLEMENTARY DUAL CODES AND DOUBLE CIRCULANT CODES OVER A SEMI-LOCAL RING

被引：3
|
作者：
Cheng, X. I. A. N. G. D. O. N. G. [1 ]
Cao, X. I. W. A. N. G. [1 ,2 ]
Qian, L. I. Q. I. N. [1 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut Nanjing, Sch Math, Nanjing 211106, Jiangsu, Peoples R China
[2] Key Lab Math Modelling NUAA & High Performance Com, Nanjing 211106, Jiangsu, Peoples R China
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2024年 / 18卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Cyclic code; Gray map; LCD code; LCD double circulant code; CYCLIC CODES; LCD CODES;
D O I：
10.3934/amc.2022055
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let q be an odd prime power and F-q be the finite field with q elements. In this paper, suppose ring R = F-q + mu F-q + nu F-q + mu nu F-q, where mu nu = nu mu, mu(2) =mu, nu(2) = nu. We first give a Gray map from R onto F4q and consider a decomposition of the ring R. Additionally, we investigate linear complementary dual (LCD) codes over the ring R. Some conditions for such linear codes over R to be linear complementary dual are given. Furthermore, based on the Artin conjecture, we get a class of good codes by calculating the total number of LCD double circulant codes over R.
引用
收藏
页码：1010 / 1021
页数：12
相关论文
共 50 条
  • [31] Quaternary Hermitian Linear Complementary Dual Codes
    Araya, Makoto
    Harada, Masaaki
    Saito, Ken
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (05) : 2751 - 2759
  • [32] Remark on subcodes of linear complementary dual codes
    Harada, Masaaki
    Saito, Ken
    INFORMATION PROCESSING LETTERS, 2020, 159
  • [33] DOUBLE-CIRCULANT AND BORDERED-DOUBLE-CIRCULANT CONSTRUCTIONS FOR SELF-DUAL CODES OVER R2
    Karadeniz, Suat
    Yildiz, Bahattin
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2012, 6 (02) : 193 - 202
  • [34] Self-dual and LCD double circulant and double negacirculant codes over Fq + uFq + vFq
    Yadav, Shikha
    Islam, Habibul
    Prakash, Om
    Sole, Patrick
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 67 (1-2) : 689 - 705
  • [35] On self-dual and LCD double circulant and double negacirculant codes over Fq+ uFq
    Shi, Minjia
    Zhu, Hongwei
    Qian, Liqin
    Sok, Lin
    Sole, Patrick
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2020, 12 (01): : 53 - 70
  • [36] Linear complementary pairs of codes over rings
    Peng Hu
    Xiusheng Liu
    Designs, Codes and Cryptography, 2021, 89 : 2495 - 2509
  • [37] Linear complementary pairs of codes over rings
    Hu, Peng
    Liu, Xiusheng
    DESIGNS CODES AND CRYPTOGRAPHY, 2021, 89 (11) : 2495 - 2509
  • [38] On circulant self-dual codes over small fields
    Markus Grassl
    T. Aaron Gulliver
    Designs, Codes and Cryptography, 2009, 52
  • [39] On circulant self-dual codes over small fields
    Grassl, Markus
    Gulliver, T. Aaron
    DESIGNS CODES AND CRYPTOGRAPHY, 2009, 52 (01) : 57 - 81
  • [40] Double circulant LCD codes over Z4
    Shi, Minjia
    Huang, Daitao
    Sok, Lin
    Sole, Patrick
    FINITE FIELDS AND THEIR APPLICATIONS, 2019, 58 : 133 - 144
12345