Four families of minimal binary linear codes with wmin/wmax≤1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_{\min
Four families of minimal binary linear codes with wmin/wmax≤1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_{\min
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DOI：
10.1007/s00200-018-0367-x
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发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
Wenqin Zhang;Haode Yan;Honglei Wei
中科院分区：
文献类型：
--
作者：
Wenqin Zhang;Haode Yan;Honglei Wei
极小线性码作为一类特殊的线性码，在秘密共享中有着重要的应用。到目前为止，文献中只报道了少数几类具有极大值的极小二元线性码，而对于具有极大值的极小二元线性码却有着丰富的知识。这里，和分别表示线性码中的最小和最大非零汉明重量。最近，Zhou等人从一般的构造出发，构造了几类具有某些性质的线性码。本文的目的是从周等人提出的线性码中获得四类极小二元线性码，我们的极小线性码的参数与已知的极小线性码有很大不同。基于Krawtchouk多项式的性质，建立了这四类二元线性码的重量分布。
As a special type of linear codes, minimal linear codes have important applications in secret sharing. Up to now, only a few infinite families of minimal binary linear codes withwere reported in the literature, while vast knowledge exists on the ones with. Herein,andrespectively denote the minimum and maximum nonzero Hamming weights in a linear code. Recently, several classes of linear codes with certain properties were constructed byZhou et al.from a generic construction. The objective of this paper is to obtain four families of minimal binary linear codes withfrom those linear codes proposed byZhou et al.The parameters of our minimal linear codes are quite different from known ones. Based on the properties of Krawtchouk polynomials, the weight distributions of all these four families of binary linear codes are established.