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Eigenvalues of association schemes of quadratic forms

Authors:	Rongquan Feng Yangxian Wang Changli Ma Jianmin Ma

Institution:	^aLMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China ^bState Key Laboratory of Information Security (Graduate School of CAS), Beijing 100039, PR China ^cCollege of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, PR China ^dDepartment of Mathematics, Colorado State University, Fort Collins, CO 80523, USA

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 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.

Keywords:	Association scheme Quadratic form Eigenvalue
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