电子学报 ›› 2022, Vol. 50 ›› Issue (1): 142-148.DOI: 10.12263/DZXB.20200739

• 学术论文 • 上一篇    下一篇

几类最优重根循环码的构造

黄素娟1,2, 孙中华1,2, 朱士信1,2   

  1. 1.合肥工业大学数学学院, 安徽 合肥 230601
    2.智能互联系统安徽省实验室, 安徽 合肥 230009
  • 收稿日期:2020-07-16 修回日期:2021-01-05 出版日期:2022-01-25
    • 通讯作者:
    • 孙中华
    • 作者简介:
    • 黄素娟 女,1989年生,安徽无为人.合肥工业大学计算机与信息学院博士研究生.研究方向为代数编码.E-mail:huangsujuan1019@163.com
      孙中华(通信作者) 男,1989年生,安徽肥西人.合肥工业大学数学学院讲师,硕士生导师. 研究方向为代数编码.
      朱士信 男,1962年生,安徽枞阳人.合肥工业大学数学学院教授,博士生导师. 研究方向为代数编码、序列密码与信息安全研究.
    • 基金资助:
    • 国家自然科学基金 (62002093); 中央高校基本科研业务费专项资金资助 (JZ2020HGQA0154)

On the Construction of Several Classes of Optimal Repeated-Root Cyclic Codes

HUANG Su-juan1,2, SUN Zhong-hua1,2, ZHU Shi-xin1,2   

  1. 1.School of Mathematics, Hefei University of Technology, Hefei, Anhui 230601, China
    2.Intelligent Interconnected Systems Laboratory of Anhui Province (Hefei University of Technology), Hefei, Anhui 230009, China
  • Received:2020-07-16 Revised:2021-01-05 Online:2022-01-25 Published:2022-01-25
    • Corresponding author:
    • SUN Zhong-hua
    • Supported by:
    • National Natural Science Foundation of China (62002093); Fundamental Research Funds for the Central Universities (JZ2020HGQA0154)

摘要:

本文分析了重根循环码的纠错能力.利用循环码的代数结构,构造了几类最优的循环码.构造了一类距离最优的二元重根循环码,并由此派生出一类距离和维数都是最优的二元重根循环码;构造了一类距离和维数都是最优的非二元重根循环码;构造了两类距离最优的非二元循环码.

关键词: 重根循环码, 最优码, Hamming距离

Abstract:

This paper analyzes the error-correction ability of repeated-root cyclic codes. By using the algebraic structure of cyclic codes, several classes of optimal cyclic codes are constructed. A class of binary repeated-root cyclic codes with optimal distances is constructed, and then a class of binary repeated-root cyclic codes with optimal distances and dimensions is derived; A class of non-binary repeated-root cyclic codes with optimal distances and dimensions is constructed; Two classes of non-binary cyclic codes with optimal distances are constructed.

Key words: repeated-root cyclic codes, optimal codes, Hamming distances

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