Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications

GAO Jian; WANG Yong-kang

doi:10.3969/j.issn.0372-2112.2020.02.011

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Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications

更新时间：2025-07-16

- Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications
- Acta Electronica Sinica Vol. 48, Issue 2, Pages: 296-302(2020)
- 作者机构：
  
  山东理工大学数学与统计学院,山东,淄博,255000
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11701336, No.11626144, No.11671235)
- DOI：10.3969/j.issn.0372-2112.2020.02.011
  CLC： TN911.22
- Published Online：25 February 2020，
  
  Published：2020
- 稿件说明：
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GAO Jian, WANG Yong-kang. Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications[J]. Acta Electronica Sinica, 2020, 48(2): 296-302.
DOI：

GAO Jian, WANG Yong-kang. Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications[J]. Acta Electronica Sinica, 2020, 48(2): 296-302. DOI： 10.3969/j.issn.0372-2112.2020.02.011.

摘要

纠错码是提高信息传输效率与可靠性的重要手段.构造性能良好的线性码类是纠错码研究中的一个基本问题.本文主要讨论了有限非链环

[

]

/（v

－

）上自对偶常循环码的代数结构，包括Euclidean自对偶常循环码、Hermitian自对偶常循环码以及Hermitian自对偶常循环码的极大距离可分（MDS）码.本文给出了环

[

]

/（v

－

）上常循环码是Euclidean自对偶码的充分条件，以及是Hermitian自对偶码的充要条件，并利用Gray映射构造了有限域

上一些参数较好的自对偶码.特别地，本文得到了有限域

上一个新的参数为[16，8，6

]

的Hermitian自对偶码.

Abstract

Error-correcting codes are important for the improvement of efficiency and security in information transmission. Constructing codes with good parameters is a fundamental problem in error-correcting codes. In this paper

we mainly study self-dual constacyclic codes over the finite nonchain ring

[

]

/(v

－

)

including Euclidean self-dual constacyclic codes

Hermitian self-dual constacyclic codes and maximal distance separable (MDS) codes of Hermitian se

lf-dual constacyclic codes. We give a necessary condition for constacyclic codes to be Euclidean self-dual and give a necessary and sufficient condition for constacyclic codes to be Hermitian self-dual over the ring

[

]

/(v

－

). Further

some good self-dual codes are constructed by the Gray map. Especially

a Hermitian self-dual code over

with parameters [16

]

is constructed.

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