Kronecker sum of binary orthogonal arrays

Abstract

Kronecker sum of binary orthogonal arrays have been introduced. It is well known that for any t ≥ 2, O A(2^t,t + 1,2, t) exists. We give conditions under which OA(2^t, t+1,2, t) is self-conjugate, and show the existence of mixed OA(2^t,n x 2^t+1,2). Also, we prove that the existence of O A(N, k, 2, t^′), t′ ≥ 2, implies the existence of OA(N2^t k(t+l), 2, p), which is a-resolvable, and obtain mixed OA(N2^t,n × 2^4k(t+1), p) therefrom, where p = 2 if max(t, t^′) = 2, and p = 3 if max(t, t ^′) > 3, where t corresponds to the trivial OA(2^t, t + 1,2, t).