On cocyclic weighing matrices and the regular group actions of certain Paley matrices
type: Item
instance of: scholarly article
title: On cocyclic weighing matrices and the regular group actions of certain Paley matrices
zbMATH Open document ID: 0961.05068
DOI: 10.1016/S0166-218X(99)00231-0
author: Warwick de Launey
author: Richard M. Stafford
published in: Discrete Applied Mathematics
publication date: 2001-01-30T00:00:00Z
review text: By definition a weighing matrix \(W= W(x,t)\) is an \(n\times n\) matrix with entries in \(\{0,\mp 1\}\) satisfying \(WW^T= W^TW= tI_n\) where \(T\) denotes the transposition and \(I_n\) is the identity matrix of degree \(n\). An automorphism of \(W\) is a pair of signed permutations \((P,Q)\) such that \(PMQ^T= M\), and the set of all automorphisms of \(W\) forms a group which is called the group of automorphisms of \(W\) and is denoted by \(\Aut(W)\). Since Paley conference matrices are weighing matrices a study of the group of automorphisms of such matrices is set up in the paper. The study is also carried out for certain Paley Hadamard matrices. The authors determine all regular group actions obtained from these Paley matrices.
Mathematics Subject Classification ID: 05E20
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1436245
zbMATH Keywords: weighing matrix
zbMATH Keywords: group of automorphisms
zbMATH Keywords: regular group actions
zbMATH Keywords: Paley matrices
reviewed by: M. R. Darafsheh
describes a project that uses: Magma
MaRDI profile type: Publication
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Wikidata QID: Q126771293
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description: scientific article; zbMATH DE number 1436245