有限非链环上的自对偶常循环码及其应用

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F_qv]/（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F_qv]/（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F_q上一些参数较好的自对偶码.特别地，本文得到了有限域F_19²上一个新的参数为16，8，6]的Hermitian自对偶码.

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

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 F_qv]/(v^m－v), including Euclidean self-dual constacyclic codes, Hermitian self-dual constacyclic codes and maximal distance separable (MDS) codes of Hermitian self-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 F_qv]/(v^m－v).Further, some good self-dual codes are constructed by the Gray map.Especially, a Hermitian self-dual code over F_19² with parameters 16, 8, 6] is constructed.