论文信息 - Dimensional dual hyperovals associated with quadratic APN functions

Dimensional dual hyperovals associated with quadratic APN functions

From each quadratic APN function f on GF(2) with f(0) = 0, we construct a d-dimensional dual hyperoval S[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[f ] is a semidirect product of a normal subgroup acting regularly on the members of S[f ] with the stabilizer of a member. Some methods are provided to analyse the structure of the stabilizer. Based on them, Aut(S[f ]) for an APN function f on GF(2) found in [3] is determined.

Satoshi Yoshiara

[1] Satoshi Yoshiara. A Family of d -dimensional Dual Hyperovals in PG(2d+1, 2) , 1999, Eur. J. Comb..

[2] Claude Carlet,et al. Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems , 1998, Des. Codes Cryptogr..

[3] Hiroaki Taniguchi. On a family of dual hyperovals over GF(q) with q even , 2005, Eur. J. Comb..

[4] Alexander Pott,et al. A new APN function which is not equivalent to a power mapping , 2005, IEEE Transactions on Information Theory.

[6] Claude Carlet,et al. An infinite class of quadratic APN functions which are not equivalent to power mappings , 2006, 2006 IEEE International Symposium on Information Theory.

[7] Antonio Pasini,et al. On a New Family of Flag-transitive Semibiplanes , 2001, Eur. J. Comb..