Some Schematic Orthogonal Arrays Constructed By The Kronecker Sum

In the study of the relationship between the orthogonal array’s rows, we have already putted forward a lot of open questions. One of them is whether they can form an asso-ciation scheme and how to classify them. Also much of the questions are discuss about the schematic of the orthogonal arrays constructed by kronecker sum. In this paper we according to hamming distance determine whether the orthogonal arrays constructed by kronecker sum are association scheme or schematic. Mainly to solve the questions that whether these orthogonal arrays constructed by orthogonal arrays and intersection matrix in different conditions according to kronecker sum are association scheme or schematic.This paper is divided into two chapters:In chapter 1, we introduce the development and the current research status of associ-ation schemes and orthogonal arrays, and contains some basic concepts and main lemmas.In chapter 2, according to hamming distance, we determine whether the orthogonal arrays constructed by kronecker sum are association scheme or schematic. Mainly to solve the questions that whether these orthogonal arrays constructed by orthogonal arrays in different conditions according to kronecker sum are association scheme or schematic. And gives the parameters of the association scheme, while the conditions are given when the orthogonal arrays are schematic orthogonal arrays, and use some examples illustrate the application of the theorem.