Automorphisms of the quadratic forms graph over a finite field of characteristic two II

Let Xn denote the set of quadratic forms in n variables over a finite field Fq. We define the quadratic forms graph Quad(n,q,2+), which has Xn as the vertex set, two vertices X and Y are adjacent whenever the type of X−Y is 2+. Then every automorphism of Quad(n,q,2+) is of the form (1) (see the text), unless n=3 and q=2. When n=3 and q=2, every automorphism of Quad(n,q,2+) is either of the form (1) or a product of the forms (1) and (2) (see the text). In the present paper, this result is proved when n⩾3 and q=2.