An Introduction to Association Schemes and Coding Theory

Abstract

Association schemes originated in statistics, but have recently been used in coding theory and combinatorics by Delsarte, McEliece and others to obtain strong upper bounds on the size of codes and other combinatorial objects, and to characterize those objects (such as perfect codes) which meet these bounds. A central role is played by the eigenvalues of the association scheme, which in many cases come from a family of orthogonal polynomials. In the most important case these are the Krawtchouk polynomials. This paper gives an introduction to association schemes and the way they are used in coding theory and combinatorics.