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 deal with 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.

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