A linear algebraic approach to orthogonal arrays and Latin squares

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.