Association schemes of quadratic forms
نویسندگان
چکیده
منابع مشابه
Eigenvalues of association schemes of quadratic forms
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 Fq 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, ...
متن کاملOn the Association Schemes of Quadratic Forms
The association scheme of quadratic forms (or the quadratic forms scheme, for short) is one of the known Pand Q-polynomial schemes and its first eigenmatrix is represented by using the Askey-Wilson polynomials. We consider two fission schemes of the quadratic forms scheme in characteristic 2 and describe the first eigenmatrix of one of these fission schemes, and compute some intersection number...
متن کاملAssociation Schemes of Quadratic Forms and Symmetric Bilinear Forms
Let Xn and Yn be the sets of quadratic forms and symmetric bilinear forms on an n-dimensional vector space V over Fq , respectively. The orbits of GLn(Fq ) on Xn × Xn define an association scheme Qua(n, q). The orbits of GLn(Fq ) on Yn × Yn also define an association scheme Sym(n, q). Our main results are: Qua(n, q) and Sym(n, q) are formally dual. When q is odd, Qua(n, q) and Sym(n, q) are iso...
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In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملQuadratic and symmetric bilinear forms over finite fields and their association schemes
Let $\mathscr{Q}(m,q)$ and $\mathscr{S}(m,q)$ be the sets of quadratic forms and symmetric bilinear forms on an $m$-dimensional vector space over $\mathbb{F}_q$, respectively. The orbits of $\mathscr{Q}(m,q)$ and $\mathscr{S}(m,q)$ under a natural group action induce two translation association schemes, which are known to be dual to each other. We give explicit expressions for the eigenvalues o...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1985
ISSN: 0097-3165
DOI: 10.1016/0097-3165(85)90016-0