Characters and the equivalence of codes
type: Item
instance of: scholarly article
title: Characters and the equivalence of codes
zbMATH Open document ID: 0849.94019
DOI: 10.1016/S0097-3165(96)80011-2
author: Harold N. Ward
author: Jay A. Wood
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-05-13T00:00:00Z
review text: Let \(K\) be a finite field. A linear code of dimension \(k\) and block length \(n\) is a \(k\)-dimensional \(K\)-linear subspace \(C\) of the \(n\)-dimensional vector space \(K^n\) over \(K\). Two linear codes \(C_1\) and \(C_2\) in \(K^n\) are equivalent if there exists a monomial transformation \(T: K^n\to K^n\) such that \(T(C_1)= C_2\). MacWilliams proved that two linear codes are equivalent if and only if there is a weight-preserving linear isomorphism between them. In this paper the authors present a new proof based on the linear independence of group characters. As an application, the authors also give another proof of a theorem of Bonisoli characterizing constant weight linear codes.
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 842856
zbMATH Keywords: equivalence
zbMATH Keywords: linear code
zbMATH Keywords: group characters
zbMATH Keywords: constant weight linear codes
MaRDI profile type: Publication
cites work: An elementary proof of the MacWilliams theorem on equivalence of codes
cites work: Q5187201
cites work: Q3216750
cites work: Binary Codes Which Are Ideals in the Group Algebra of an Abelian Group
cites work: Q4126536
cites work: A bound for divisible codes
full work available at URL: s0097-3165(96)80011-2
OpenAlex ID: W4213125419
description: scientific article; zbMATH DE number 842856