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

Abstract

Let X _n denote the set of quadratic forms in n variables over a finite field F _q of characteristic 2, and X _n the association scheme on X _n by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of X _n is of the form X ↦ P^tX^σP + Y for all X ∈ X _n , where P ∈ GL _n (F _q ), σ is an automorphism of F _q , and Y ∈ X _n .