On Schematic Orthogonal Arrays of Strength Two

Abstract

In the theory of orthogonal arrays, an orthogonal array is called schematic if its rows form an association scheme with respect to Hamming distances. Which orthogonal arrays are schematic orthogonal arrays and how to classify them is an open problem proposed by Hedayat et al. $[12]$. In this paper, we study the Hamming distances of the rows in orthogonal arrays and construct association schemes according to the distances. The paper gives the partial solution of the problem by Hedayat et al. for symmetric and some asymmetric orthogonal arrays of strength two.