Dimensional dual hyperovals associated with quadratic APN functions
From each quadratic APN function \(f\) on \(\mathrm{GF}(2^{d+1})\) with \(f(0) = 0\), the author constructs a \(d\)-dimensional dual hyperoval \(S^{d+1}[f]\) over \(\mathrm{GF}(2)\). This provides many new examples of \(d\)-dual hyperovals over \(\mathrm{GF}(2)\) 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 \(\mathrm{GF}(2^{10})\) found in [\textit{Y. Edel, G. Kyureghyan} and \textit{A. Pott}, IEEE Trans. Inform. Theory 52, 744--747 (2006; Zbl 1246.11185)] is determined.
scientific article; zbMATH DE number 5788614