Codes from affine permutation groups
type: Item
instance of: scholarly article
title: Codes from affine permutation groups
zbMATH Open document ID: 0917.94016
DOI: 10.1023/A:1008315701179
author: Markku K. Kaikkonen
published in: Designs, Codes and Cryptography
publication date: 1999-07-28T00:00:00Z
review text: The maximum cardinality of a (linear or nonlinear) binary code of length \(n\) and minimum Hamming distance \(d\) is denoted by \(A(n,d)\). The author constructs codes that lead to improved lower bounds on \(A(n,d)\). The codes are found by stochastic computer search. A permutation group under which a code is invariant is prescribed before the search. The permutation groups used are mainly affine groups. The new bounds are: \(A(22,10) \geq 50\), \(A(23,10) \geq 76\), \(A(25,10) \geq 166\), \(A(26,10) \geq 270\), \(A(29,10) \geq 1460\), and \(A(28,12) \geq 178\).
reviewed by: Patric R. J. Östergård
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1230695
zbMATH Keywords: affine permutation group
zbMATH Keywords: binary code
zbMATH Keywords: minimum distance
MaRDI profile type: Publication
full work available at URL: a:1008315701179
OpenAlex ID: W1588052294
Recommended article: Q4868134
Recommended article: Q3838668
Recommended article: Q4718154
Recommended article: The permutation group of affine-invariant extended cyclic codes
Recommended article: Affine Reflection Group Codes
Recommended article: Permutation groups and binary self-orthogonal codes
Recommended article: On the permutation groups of cyclic codes
Recommended article: Group code structures of affine-invariant codes
Recommended article: Representing group codes as permutation codes
Recommended article: Error-correcting codes from permutation groups
description: scientific article; zbMATH DE number 1230695