Abstract: Nowadays, orthogonal arrays
play important roles in statistics, computer science, coding theory and
cryptography. The usual difference matrices are essential for the construction
of many mixed orthogonal arrays. But there are also orthogonal arrays which
cannot be obtained by the usual difference matrices. In order to construct these
mixed orthogonal arrays, a class of special matrices so-called generalized
difference matrices were discovered by Zhang [7-12] from the orthogonal
decompositions of projection matrices. In this paper, an interesting equivalent
relationship between orthogonal arrays and the generalized difference matrices
is presented. As an application, a family of mixed orthogonal arrays with run
sizes has been constructed.
