Isomorphism classes of association schemes induced by Hadamard matrices

Every Hadamard matrix H of order n > 1 induces a graph with 4n vertices, called the Hadamard graph Gamma(H) of H. Since Gamma(H) is a distance-regular graph with diameter 4, it induces a 4-class association scheme (Omega, S) of order 4n. In this article we show a way to construct fission schemes of (Omega, S) under certain conditions, and for such a fission scheme we estimate the number of isomorphism classes with the same intersection numbers as the fission scheme. (C) 2015 Elsevier Ltd. All rights reserved.