Ectremal binary matrices without constant 2-squares
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.
scientific article; zbMATH DE number 5776206