A Linear Algebraic Approach to Orthogonal Arrays and Latin Squares

Abstract

To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi ($1988$ and $1994$) considered some module spaces. Here, using a linear algebraic approach, we define an inclusion matrix and find its rank. In the special case of Latin squares, we show that there is a straightforward algorithm for generating a basis for this matrix using the so-called intercalates. We also extend this last idea.