Isomorphism classes of association schemes induced by Hadamard matrices

Abstract

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 deal with 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.

12 pages