A mass formula for self-dual permutation codes
type: Item
instance of: scholarly article
title: A mass formula for self-dual permutation codes
zbMATH Open document ID: 1187.94041
author: Annika Günther
published in: Finite Fields and their Applications
publication date: 2009-09-15T00:00:00Z
review text: Let \(V\) be a right \(A\)-module, where \(A\) is a finite semisimple algebra over a finite field \(\mathbb F\). Assume that \(V\) carries a non-degenerate equivariant form \(\varphi\). In the paper the author gives the total number \(M_{(V,\varphi)}\) of self-dual codes in an \(A\)-module \(V\), provided that there exists at least one such code. The number \(M_{(V,\varphi)}\) is determined via a Morita equivalence. The mass formula relates the ratio \(M_{(V,\varphi)}/|\Gamma|\) to the stabilizer orders of \(\Gamma\)-orbits, where \(\Gamma\) is a subgroup of the weak isometries group \(\text{Aut}_{\text{weak}}(V)\).
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 5603989
zbMATH Keywords: permutation code
zbMATH Keywords: enumeration of self-dual codes
zbMATH Keywords: mass formula
zbMATH Keywords: group ring codes
zbMATH Keywords: Morita theory
reviewed by: Štefan Porubský
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.ffa.2009.04.001
OpenAlex ID: W2076988767
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DOI: 10.1016/J.FFA.2009.04.001
description: scientific article; zbMATH DE number 5603989