Binary Codes and Partial Permutation Decoding Sets from Biadjacency Matrices of the Bipartite Graphs Γ (2k+1, k, k+2, 1)

被引：0

作者：

Fish, W. ^{[1
]}

Mumba, N. B. ^{[1
]}

Mwambene, E. ^{[1
]}

Rodrigues, B. G. ^{[2
]}

机构：

[1] Univ Western Cape, Dept Math & Appl Math, Private Bag X17, ZA-7535 Bellville, South Africa

[2] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-4041 Durban, South Africa

来源：

GRAPHS AND COMBINATORICS | 2017年 / 33卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Bipartite graphs; Biadjacency matrices; Binary codes; Automorphism group; Permutation decoding;

D O I：

10.1007/s00373-017-1765-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be an integer and a set of size We examine the binary codes generated by the row span of biadjacency matrices of the bipartite graphs Adjacency in these graphs is defined by two vertices as k-subsets and -subsets of being adjacent if and only if they have one element in common. We show that is contained in the automorphism group of the graphs and the codes. In addition, we determine the duals of the codes, and by identifying suitable information sets, we construct 2-PD sets for the dual codes.

引用

页码：357 / 368

页数：12

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[2] Binary Codes and Partial Permutation Decoding Sets from Biadjacency Matrices of the Bipartite Graphs Γ(2k+1,k,k+2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma (2k+1,k,k+2,1)$$\end{document}
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