Ectremal binary matrices without constant 2-squares
type: Item
instance of: scholarly article
title: Ectremal binary matrices without constant 2-squares
zbMATH Open document ID: 1231.05268
author: Roland Bacher
author: Shalom Eliajou
published in: Journal of Combinatorics
publication date: 2010-08-30T00:00:00Z
review text: A binary matrix is a matrix with entries taken from the 2-element field \({\mathbb{F}}_2\). A 2-square in a matrix \(A\) is a \(2 \times 2\) submatrix \(S\) with row indices \(\{i,i+t\}\) and column indices \(\{j,j+t\}\) for some \(t \geq 1\). An Erickson matrix is a binary matrix containing no constant 2-square. By computer search, the authors obtain the following result. There exist no Erickson matrices of size \(m \times n\) with \(m \geq 14\) and \(n \geq 15\) and these bounds are sharp.
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 5776206
zbMATH Keywords: binary matrix
zbMATH Keywords: Erickson matrix
MaRDI profile type: Publication
DOI: 10.4310/JOC.2010.V1.N1.A6
description: scientific article; zbMATH DE number 5776206