Eigenvalues of association schemes of quadratic forms

Abstract

The duality and primitivity of the association scheme Qua ( n , q ) of quadratic forms in n variables and the association scheme Sym ( n , q ) of symmetric bilinear forms in n variables over the finite field F q 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 ) are computed, where q is a power of 2. As an application, two fusion schemes of Qua ( n , q ) are discussed and their dual schemes are constructed.