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 Γ(H) of H. Since Γ(H) is a distance-regular graph with diameter 4, it induces a 4-class association scheme (Ω,S) of order 4n. In this article we show a way to construct fission schemes of (Ω,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.