Constructing covering codes with given automorphisms
type: Item
instance of: scholarly article
title: Constructing covering codes with given automorphisms
zbMATH Open document ID: 0927.94020
DOI: 10.1023/A:1008326409439
author: Patric R. J. Östergård
author: William D. Weakley
published in: Designs, Codes and Cryptography
publication date: 1999-12-17T00:00:00Z
review text: The authors consider the problem of finding upper bounds on \(K(n,r)\), the minimum number of words in a binary code of length \(n\) and covering radius \(r\). Constructions of covering codes give these bounds on \(K(n,r)\). It is shown how computer searches for covering codes can be speed up by requiring that the code has a given (not necessarily full) automorphism group. The optimization method used is tabu search. A new code is presented which proves a new record \(K(13,1)\leq 704\). This code has a very large full automorphism group and several other interesting properties.
Mathematics Subject Classification ID: 94B75
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 1275104
zbMATH Keywords: upper bounds
zbMATH Keywords: binary code
zbMATH Keywords: covering radius
zbMATH Keywords: covering codes
zbMATH Keywords: automorphism group
zbMATH Keywords: tabu search
MaRDI profile type: Publication
full work available at URL: a:1008326409439
OpenAlex ID: W1585940209
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description: scientific article; zbMATH DE number 1275104