Dimensional dual hyperovals associated with quadratic APN functions
Satoshi Yoshiara · Innovations in incidence geometry · 2008
From each quadratic APN function f on GF(2 d+1 ) with f (0) = 0, we construct a d-dimensional dual hyperoval S d+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 S d+1 [f ] is a semidirect product of a normal subgroup acting regularly on the members of S d+1 [f ] with the stabilizer of a member.Some methods are provided to analyse the structure of the stabilizer.Based on them, Aut(S 10 [f ]) for an APN function f on GF(2 10 ) found in [3] is determined.