A construction of non-isomorphic amorphous association schemes from pseudo-cyclic association schemes

As a continuation of my paper [T. Fujisaki, A construction of amorphous association scheme from a pseudo-cyclic association scheme, Discrete Math. 285(1–3) (2004) 307–311], we show a construction of amorphous association scheme which is a fusion scheme of a direct product of two pseudo-cyclic association schemes with same first eigenmatrix. By using this construction, we can get at most three amorphous association scheme. We prove that if two pseudo-cyclic association scheme are non-isomorphic, then these three amorphous association schemes are mutually non-isomorphic.