Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

摘要

Let Xn denote the set of quadratic forms in n variables over a finite field Fq of characteristic 2, and Xn the association scheme on Xn by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of Xn is of the form X(→) PtXσP + Y for all X ∈Xn, where P ∈ GLn(Fq), σ is an automorphism of Fq, and Y ∈ Xn.