电子学报 ›› 2021, Vol. 49 ›› Issue (11): 2284-2288.DOI: 10.12263/DZXB.20200588

• 科研通信 • 上一篇    下一篇

4上LCD循环码及其二元像

开晓山, 廖文敬   

  1. 合肥工业大学数学学院,安徽 合肥 230601
  • 收稿日期:2020-06-17 修回日期:2021-05-23 出版日期:2021-11-25 发布日期:2021-11-25
  • 作者简介:开晓山(通信作者) 男,1975年生,安徽青阳人. 合肥工业大学数学学院教授,博士生导师,研究方向为编码理论与信息安全.E-mail:kxs6@sina.com
    廖文敬 女,1996年生,安徽宿州人. 合肥工业大学硕士研究生,主要研究方向为代数编码. E-mail:1846755441@qq.com
  • 基金资助:
    国家自然科学基金(61972126);中央高校基本科研业务费专项资金(PA2019GDZC0097)

LCD Cyclic Codes over ℤ4 and Binary Images

Xiao-shan KAI, Wen-jing LIAO   

  1. School of Mathematics,Hefei University of Technology,Hefei,Anhui 230601,China
  • Received:2020-06-17 Revised:2021-05-23 Online:2021-11-25 Published:2021-11-25

摘要:

循环码和线性互补对偶(LCD)码是两类重要的线性码,在数据存储、通信系统和密码等领域有着广泛的应用. 本文研究了?4上奇长度的LCD循环码,给出了?4上奇长度的循环码为LCD码的一个充要条件,证明了?4上LCD循环码的二元像是可逆码;构造了?4上长为2m+1的LCD循环码,得到了参数较好的二元非线性可逆码.

关键词: 线性码, 线性互补对偶(LCD)码, 循环码, 二元像, 可逆码

Abstract:

Cyclic codes and linear complementary dual (LCD) codes are two important classes of linear codes which have been extensively used in data storage systems, communication systems and cryptography. In this paper, LCD cyclic codes over ?4 of odd length are explored. A sufficient and necessary condition is given for cyclic codes over ?4 of odd length to be LCD. It is proved that the binary images of LCD cyclic codes over ?4 are reversible codes. LCD cyclic codes over ?4 of length 2m+1 are constructed. And binary nonlinear reversible codes with good parameters are obtained.

Key words: linear code, linear complementary dual (LCD) code, cyclic code, binary image, reversible code

中图分类号: