Association schemes of symmetric matrices over a finite field of characteristic two

Abstract Let Xn be the set of all n × n symmetric matrices over a finite field with q elements, where q is a power of 2. For X, Y ϵ Xn, we define (X, Y) ϵ R0 if and only if X = Y; and (X, Y) ϵ R(2i + τ, τ) if and only if X − Y is congruent to Then Xn = (Xn, {R0, R(2i + τ, τ) | 1 ⩽ 2i + τ ⩽ n, τ = 0, 1 or 2}) is a symmetric association scheme of class n + [ n 2 ] on Xn. The parameters of χn have been computed. Furthermore, we have discussed its imprimitivity, association subschemes and related quotient association scheme, etc.