两类有限非链环上线性码及其MacWilliams恒等式的研究
发布时间：2018-08-18 10:14
【摘要】：本文主要研究了两类有限非链环上的线性码及其MacWilliamss恒等式,具体内容如下：(1)研究了环R=Z4+vZ4(v2v)上的线性码及其MacWilliams恒等式.首先给出了环R上线性码的Gray映射及其投影映射的性质,得到了环R上线性码与通过投影映射得到的线性码的极小Lee重量的关系,然后给出了环R上线性码的Gray重量计数多项式和对称重量计数多项式的定义,进一步地确定了环R上线性码和其对偶码之间基于Gray重量计数多项式,对称重量计数多项式和Lee重量计数多项式的MacWilliams恒等式.(2)研究了环Rk,m=Fq[u,v]/k;,vm,uv-vu上的线性码及其MacWilliams恒等式,其中q是素数p的方幂且k≥m≥1.首先定义了Lee重量并给出了Rk,m到Fkmq的Gray映射,此映射关于Lee重量具有保距性和保对偶性,然后证明了环Rk,m上线性码相应重量计数多项式的MacWilliams恒等式,特别地给出了环Rk,。上线性码关于Lee重量计数多项式的MacWilliams恒等式.
[Abstract]:In this paper, we study two kinds of linear codes and their MacWilliamss identities over finite nonlinked rings. The main contents are as follows: (1) the linear codes and their MacWilliams identities on the ring R=Z4 vZ4 (v2v) are studied. Firstly, the properties of Gray mapping and projection mapping of linear codes over ring R are given, and the relation between linear codes on ring R and minimal Lee weights of linear codes obtained by projection mapping is obtained. Then, the definitions of Gray weight counting polynomial and symmetric weight counting polynomial of linear codes over ring R are given, and the Gray weight counting polynomials between linear codes and their dual codes over ring R are further determined. The MacWilliams identities of symmetric weight counting polynomials and Lee weight counting polynomials. (2) We study the linear codes and their MacWilliams identities on the ring RKN mq [UV] / KV / VMU, where Q is the power of the prime p and k 鈮，
本文编号：2189157
[Abstract]:In this paper, we study two kinds of linear codes and their MacWilliamss identities over finite nonlinked rings. The main contents are as follows: (1) the linear codes and their MacWilliams identities on the ring R=Z4 vZ4 (v2v) are studied. Firstly, the properties of Gray mapping and projection mapping of linear codes over ring R are given, and the relation between linear codes on ring R and minimal Lee weights of linear codes obtained by projection mapping is obtained. Then, the definitions of Gray weight counting polynomial and symmetric weight counting polynomial of linear codes over ring R are given, and the Gray weight counting polynomials between linear codes and their dual codes over ring R are further determined. The MacWilliams identities of symmetric weight counting polynomials and Lee weight counting polynomials. (2) We study the linear codes and their MacWilliams identities on the ring RKN mq [UV] / KV / VMU, where Q is the power of the prime p and k 鈮，
本文编号：2189157
本文链接：https://www.wllwen.com/kejilunwen/yysx/2189157.html
