Asymptotically Good Hermitian LCD 2-Quasi-Abelian Codes

ZHANG Guang-hui

doi:10.12263/DZXB.20240157

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Asymptotically Good Hermitian LCD 2-Quasi-Abelian Codes

PAPERS | 更新时间：2025-10-16

- Asymptotically Good Hermitian LCD 2-Quasi-Abelian Codes
- ACTA ELECTRONICA SINICA Vol. 53, Issue 6, Pages: 1923-1931(2025)
- 作者机构：
  
  宿迁学院数理学院，江苏宿迁 223800
- 作者简介：
- 基金信息：
  
  Open Research Fund of Key Laboratory of Nonlinear Analysis & Applications (Central China Normal University), Ministry of Education, China;Suqian Sci & Tech Program(Z2023130)
- DOI：10.12263/DZXB.20240157
  CLC： TN914;O236.2
- Received：17 February 2024，
  
  Revised：2024-12-09，
  
  Published：25 June 2025
- 稿件说明：
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张光辉. Hermitian LCD 2-拟交换群码的渐近性研究[J]. 电子学报, 2025, 53(06): 1923-1931.

ZHANG Guang-hui. Asymptotically Good Hermitian LCD 2-Quasi-Abelian Codes[J]. Acta Electronica Sinica, 2025, 53(06): 1923-1931.
张光辉. Hermitian LCD 2-拟交换群码的渐近性研究[J]. 电子学报, 2025, 53(06): 1923-1931. DOI：10.12263/DZXB.20240157

ZHANG Guang-hui. Asymptotically Good Hermitian LCD 2-Quasi-Abelian Codes[J]. Acta Electronica Sinica, 2025, 53(06): 1923-1931. DOI：10.12263/DZXB.20240157

摘要

利用有限域上群代数的性质构造了一类Hermitian LCD（Hermitian Linear Complementary Dual）2-拟交换群码.基于有限域上群代数的结构定理精确计算出了此类码的个数.通过探讨相对最小距离较小的此类码的计数问题，本文证明了有限域上的Hermitian LCD 2-拟交换群码是渐近好码.

Abstract

Utilizing properties of group algebras over finite fields

we construct a class of Hermitian linear complementary dual (LCD) 2-quasi-abelian codes. Employing the structure theorem for group algebras over finite fields

we explicitly determine the number of such codes. By investigating the enumeration of codes within this class that possess small relative minimum weights

we demonstrate that the class of Hermitian LCD 2-quasi-abelian codes over any finite field is asymptotically good.

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references

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