Perfect binary arrays and difference sets
type: Item
instance of: scholarly article
title: Perfect binary arrays and difference sets
zbMATH Open document ID: 0801.05013
DOI: 10.1016/0012-365X(94)90165-1
author: Jonathan Jedwab
author: Chris J. Mitchell
author: Fred C. Piper
author: Peter R. Wild
published in: Discrete Mathematics
publication date: 1994-11-27T00:00:00Z
review text: Ingenuous elementary constructions are given to get perfect binary arrays \[ \text{PBA}(2^ y,2^ y),\quad \text{PBA}(2^{y+1}, 2^{y-1}), \quad \text{PBA}(2^ y\cdot 3, 2^ y\cdot 3), \quad \text{and} \quad \text{PBA}(2^{y+1}\cdot 3, 2^{y-1}\cdot 3). \] The basic idea is to use particular compositions of a \(\text{PBA}(s,t)\) and a ``rowwise quasiperfect'' array \(s\times t\) and iterate this or a similar construction. As bonus, the \((4n^ 2, 2n^ 2- n, n^ 2- n)\)-difference sets equivalent to \(\text{PBA}(2^ y, 2^ y)\) \((2^{2y}= 4n^ 2)\) is fixed by the multiplier \(-1\), and quasiperfect arrays with interesting symmetries are obtained. See, e.g., \textit{D. Calabro} and \textit{J. K. Wolf} [On the synthesis of two-dimensional arrays with desirable correlation properties, Inf. Control 11 (1967), 537-560 (1968; Zbl 0157.494)] for sources and motivations (also linked to Singer groups) of the questions involved: unfortunately many of the quoted papers are not so easy to find in a mathematical department.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 562668
zbMATH Keywords: difference sets
zbMATH Keywords: rowwise quasiperfect
zbMATH Keywords: perfect binary arrays
zbMATH Keywords: multiplier
zbMATH Keywords: quasiperfect arrays
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
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full work available at URL: 0012-365x(94)90165-1
OpenAlex ID: W2153150808
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description: scientific article; zbMATH DE number 562668