Crooked Maps in Finite Fields

Abstract : We consider the maps $f:\mathbb{F}_{2^n} →\mathbb{F}_{2^n}$ with the property that the set $\{ f(x+a)+ f(x): x ∈F_{2^n}\}$ is a hyperplane or a complement of hyperplane for every $a ∈\mathbb{F}_{2^n}^*$. The main goal of the talk is to show that almost all maps $f(x) = Σ_{b ∈B}c_b(x+b)^d$, where $B ⊂\mathbb{F}_{2^n}$ and $Σ_{b ∈B}c_b ≠0$, are not of that type. In particular, the only such power maps have exponents $2^i+2^j$ with $gcd(n, i-j)=1$. We give also a geometrical characterization of this maps.
Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.167-170, 2005, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01184348
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 14 août 2015 - 11:36:40
Dernière modification le : samedi 3 mars 2018 - 01:04:57
Document(s) archivé(s) le : dimanche 15 novembre 2015 - 10:57:39

Fichier

dmAE0133.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01184348, version 1

Collections

Citation

Gohar Kyureghyan. Crooked Maps in Finite Fields. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.167-170, 2005, DMTCS Proceedings. 〈hal-01184348〉

Partager

Métriques

Consultations de la notice

39

Téléchargements de fichiers

125