Association schemes in which the thin residue is an elementary abelian $p$-group of rank $2$

In this article, we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian $p$-group of rank $2$.

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 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.