Dimensional dual hyperovals associated with quadratic APN functions

Abstract

From each quadratic APN function f on GF(2d+1) with f(0)=0, we construct a d-dimensional dual hyperoval Sd+1[f] over GF(2). This provides many new examples of d-dual hyperovals over GF(2) with ambient spaces of dimension 2d+2. The automorphism group of Sd+1[f] is a semidirect product of a normal subgroup acting regularly on the members of Sd+1[f] with the stabilizer of a member. Some methods are provided to analyse the structure of the stabilizer. Based on them, Aut(S10[f]) for an APN function f on GF(210) found in by Edel, Kyureghyan and Pott is determined.