Associated With Isometric Orthogonal Arrays Of Schematic Orthogonal Arrays

Association scheme is a part of what is now called algebraic combinatorics.It is a combinatorics structure in balance incomplete block designs and it describes the balance of symbols with many associate relations. With the further study of association scheme, it was found to have close relations with group, coding theory, graph theory and com-binatorics. The study of association scheme has developed into an important branch of algebraic combinatorics. Especially it provides a theoretical framework for the coding the-ory, so the study of association scheme has developed into an important branch of algebraic combinatorics.In the theory of orthogonal arrays, an orthogonal array is schematic if its rows form an association scheme with respect to Hamming distances. At present, it is few result about orthogonal arrays of association scheme. Especially, there are very few researches on the orthogonal arrays of strength 2. In this paper we study the Hamming distances of the rows in orthogonal arrays constructed by difference matrix and give the schematic orthogonal arrays with strength 2 and the construction of association schemes orthogonal arrays.Chapter 1 introduces the development and the current research status of orthogonal arrays and association scheme, and contains basic concepts and main lemmas.Chapter 2 gives main theorems and some examples are given to illustrate the appli-cations of the method.Chapter 3 concludes the main content of this paper and puts forward to some sugges-tions and a few unsolved problems.