有限非链环上的自对偶常循环码及其应用  

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

作　　者：高健 王永康 GAO Jian;WANG Yong-kang(School of Mathematics and Statistics,Shandong University of Technology,Zibo,Shandong 255000,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255000

出　　处：《电子学报》2020年第2期296-302,共7页Acta Electronica Sinica

基　　金：国家自然科学基金(No.11701336,No.11626144,No.11671235)。

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Fq[v]/(v^m-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Fq[v]/(v^m-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Fq上一些参数较好的自对偶码.特别地,本文得到了有限域F192上一个新的参数为[16,8,6]的Hermitian自对偶码.Error-correcting codes are important for the improvement of efficiency and security in information trans-mission.Constructing codes with good parameters is a fundamental problem in error-correcting codes.In this paper,we main-ly study self-dual constacyclic codes over the finite nonchain ring Fq[v]/(v^m-v),including Euclidean self-dual constacy-clic codes,Hermitian self-dual constacyclic codes and maximal distance separable(MDS)codes of Hermitian self-dual con-stacyclic codes.We give a necessary condition for constacyclic codes to be Euclidean self-dual and give a necessary and suf-ficient condition for constacyclic codes to be Hermitian self-dual over the ring Fq[v]/(v^m-v).Further,some good self-dual codes are constructed by the Gray map.Especially,a Hermitian self-dual code over F192 with parameters[16,8,6]is con-structed.

关 键 词：纠错码 自对偶常循环码 GRAY映射 新的Hermitian自对偶码 

分 类 号：TN911.22[电子电信—通信与信息系统]