Vol. 8, No. 1, 2008

Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
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