自正交矩阵乘积线性码  

Self-orthogonal Matrix-product Linear Codes

作　　者：程子昂 CHENG Zi-ang(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

机构地区：[1]合肥工业大学数学学院

出　　处：《大学数学》2019年第3期5-11,共7页College Mathematics

基　　金：国家自然科学基金资助项目(61772168)

摘　　要：基于矩阵乘积结构构造自正交码,给出了矩阵乘积线性码是自正交码的一个必要条件.指出了在输入码是嵌套结构时,自正交矩阵乘积线性码的基本矩阵与其转置矩阵的乘积不必是对角矩阵,并给出了一些例子.此外,还研究了自对偶矩阵乘积线性码.The matrix-product construction is applied to construct self-orthogonal codes. A necessary condition for constructing self-orthogonal matrix-product codes is given. It is pointed out that under the condition that the input codes are nested, the product of the underlying matrix and its transposed matrix need not be a diagonal matrix. Some illustrative examples are given. In addition, self-dual matrix-product codes are also studied.

关 键 词：矩阵积码 线性码 自正交码 自对偶码 矩阵 

分 类 号：O157.4[理学—数学]