ELUSIVE CODES IN HAMMING GRAPHS

被引：2

作者：

Hawtin, Daniel R. ^{[1
]}

Gillespie, Neil I. ^{[1
]}

Praeger, Cheryl E. ^{[1
,2
]}

机构：

[1] Univ Western Australia, Crawley, WA 6009, Australia

[2] King Abdulaziz Univ, Jeddah 21413, Saudi Arabia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2013年 / 88卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

elusive codes; permutation codes; powerline communication; neighbour transitive codes; automorphism groups; POWERLINE COMMUNICATIONS; PERMUTATION CODES;

D O I：

10.1017/S0004972713000051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In these examples, the alphabet size always divides the length of the code. We show that there is no elusive pair for the smallest set of parameters that does not satisfy this condition. We also pose several questions regarding elusive pairs.

引用

页码：286 / 296

页数：11

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