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

HUANG Su-juan; SUN Zhong-hua; ZHU Shi-xin

doi:10.12263/DZXB.20200739

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

PAPERS | 更新时间：2025-12-08

- On the Construction of Several Classes of Optimal Repeated-Root Cyclic Codes
- ACTA ELECTRONICA SINICA Vol. 50, Issue 1, Pages: 142-148(2022)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20200739
  CLC： TN911.22;
- Received：16 July 2020，
  
  Revised：2021-01-05，
  
  Published：25 January 2022
- 稿件说明：
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黄素娟,孙中华,朱士信.几类最优重根循环码的构造[J].电子学报,2022,50(01):142-148.

HUANG Su-juan,SUN Zhong-hua,ZHU Shi-xin.On the Construction of Several Classes of Optimal Repeated-Root Cyclic Codes[J].ACTA ELECTRONICA SINICA,2022,50(01):142-148.
黄素娟,孙中华,朱士信.几类最优重根循环码的构造[J].电子学报,2022,50(01):142-148. DOI： 10.12263/DZXB.20200739.

HUANG Su-juan,SUN Zhong-hua,ZHU Shi-xin.On the Construction of Several Classes of Optimal Repeated-Root Cyclic Codes[J].ACTA ELECTRONICA SINICA,2022,50(01):142-148. DOI： 10.12263/DZXB.20200739.

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.

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.

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references

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