Eigenvalues of association schemes of quadratic forms

The duality and primitivity of the association scheme Qua(n,q)Qua(n,q) of quadratic forms in n   variables and the association scheme Sym(n,q)Sym(n,q) of symmetric bilinear forms in n   variables over the finite field FqFq are discussed by Wang et al. [Association schemes of quadratic forms and symmetric bilinear forms, J. Algebraic Combin. 17 (2003) 149–161]. In this paper, eigenvalues of Qua(n,q)Qua(n,q) are computed, where q   is a power of 2. As an application, two fusion schemes of Qua(n,q)Qua(n,q) are discussed and their dual schemes are constructed.