Nonexistence of certain perfect arrays
type: Item
instance of: scholarly article
title: Nonexistence of certain perfect arrays
zbMATH Open document ID: 0796.05010
DOI: 10.1016/0012-365X(94)90150-3
author: Man-Keung Siu
author: Siu Lun Ma
author: Wai Kiu Chan
published in: Discrete Mathematics
publication date: 1994-05-05T00:00:00Z
review text: The authors show that if an abelian group \(G=H \times Z_ a \times Z_ b\), where \(| H |\) is even and \(ab\) is an even power of an odd prime \(p\) that is self-conjugate modulo exp \(H\) and does not divide \(| H |\), contains a Menon difference set, then \(a=b\) and \(p<| H |\). This result, together with the equivalence between perfect binary arrays and Menon difference sets in certain groups, is then exploited to establish the nonexistence of certain perfect binary arrays.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 562653
zbMATH Keywords: Menon difference set
zbMATH Keywords: perfect binary arrays
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
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full work available at URL: 0012-365x(94)90150-3
OpenAlex ID: W2043865674
description: scientific article; zbMATH DE number 562653