Vol. 8, No. 1, 2008

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Dimensional dual hyperovals associated with quadratic APN functions

Satoshi Yoshiara

Vol. 8 (2008), No. 1, 147–169
DOI: 10.2140/iig.2008.8.147
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.

Keywords
dimensional dual hyperoval, APN function
Milestones
Received: 3 September 2007
Accepted: 6 November 2007
Authors
Satoshi Yoshiara