用Hadamard矩阵构造线性码

Constructing linear codes by Hadamard matrices

作者：秦小二(长江师范学院数学与统计学院)；胡双年(南阳理工学院应用数学系)；姜灏(四川大学数学学院)；鄢丽(西南财经大学经济数学学院)

Author：QIN Xiao Er(School of Mathematics and Statistics, Yangtze Normal University,)；HU Shuang Nian(Department of Applied Mathematics, Nanyang Institute of Technology)；JIANG Hao3(College of Mathematics, Sichuan University)；YAN Li(School of Economic Mathematics, Southwestern University of Finance and Economics)

收稿日期：2013-10-28 年卷（期）页码：2015,52(6):1221-1224

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：.Hadamard矩阵；线性码；自对偶码

Key words：.Hadamard matrix; Linear codes; Self dual codes.

基金项目：基金项目: 重庆市教委科研项目 (KJ15012004); 长江师范学院引进人才科研启动项目(2014KYQD04); 涪陵区科技计划项目(FLKJ2015ABA1031);国家自然科学基金(U1504105,11501387)

中文摘要

Hadamard矩阵在实验设计、编码、网络、逻辑电路等方面都有广泛的应用,并且通过多种方式可以构造Hadamard矩阵.本文主要利用反对称Hadamard矩阵构造出了一类二元和三元自对偶线性纠错码

英文摘要

Hadamard matrices has many applications in design of experiment, coding, network and logic circuit and there are also many ways to construct Hadamard matrices. In this paper, by using the antisymmetric Hadamard matrices, we construct a class of binary self dual linear error correcting codes and a class of ternary self dual linear error correcting codes

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论文摘要

用Hadamard矩阵构造线性码

Constructing linear codes by Hadamard matrices