Modular Invariance of the Character Table of the Hamming Association Scheme H(d, q) Original Research Article

It is known that the entries of the character table (the first eigenmatrix) P of the Hamming association scheme H(d, q) are expressed by using the Krawtchouk polynomials. In this paper we show that there exist six diagonal matrices T that satisfy (PT)3 = q3d/2I. This implies that the matrix S of the fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) satisfies the modular invariance property, namely (ST)3 = S2 = I, for the diagonal matrices T.