Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01184348
Contributor : Coordination Episciences Iam <>
Submitted on : Friday, August 14, 2015 - 11:36:40 AM
Last modification on : Saturday, March 3, 2018 - 1:04:57 AM
Long-term archiving on: : Sunday, November 15, 2015 - 10:57:39 AM

File

dmAE0133.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01184348, version 1

Collections

Citation

Gohar Kyureghyan. Crooked Maps in Finite Fields. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.167-170. ⟨hal-01184348⟩

Share