Association schemes of conjugate matrices

Let  f  be a monic, irreducible polynomial of degree n  in Fq[x] and let CM(f,q) be the set of all roots of the polynomial f  in the algebra M(n,q) of all n×n matrices over Fq. The action of the general linear group GL(n,q) on CM(f,q)×CM(f,q) by inner automorphisms defines an association scheme. For given q all association schemes CM(f,q) determined by irreducible polynomials of degree n are isomorphic. When degf=2, then the association scheme CM(f,q) is symmetric and in this case we determine the intersection numbers.