Generalized Hadamard matrices which are developed modulo a group
type: Item
instance of: scholarly article
title: Generalized Hadamard matrices which are developed modulo a group
zbMATH Open document ID: 0762.05025
DOI: 10.1016/0012-365X(92)90624-O
author: Warwick de Launey
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Let \(N\) and \(G\) be finite groups of orders \(n=| N|\) and \(g=| G|\), respectively, and let \(\text{EA}(q)\) be the elementary abelian group of order \(q\), \(q\) a prime power. Also, let \(\text{EA}(n)\) be the group of order \(n\) which is the direct product of elementary abelian groups. This paper discusses the construction and existence of generalized Hadamard matrices \(\text{GH}(n,G)\) which are developed modulo a group \(N\). In particular, it is shown that the existence of a \(\text{GH}(n,G)\) developed modulo \(N\) is equivalent to the existence of a solution to a certain equation over the group ring of \(G\backslash N\) over the integers. Finally, some remarks on error-correcting coding theory are made. It is shown that every element of \(G\) must appear in any \(\text{GH}(n,G)\) developed modulo a group, if \(n\geq g(g-1)\).
reviewed by: S. S. Agayan
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 94B99
Mathematics Subject Classification ID: 20K99
zbMATH DE Number: 89880
zbMATH Keywords: Hadamard matrices
zbMATH Keywords: abelian group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 89880