dmtcs:3392 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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https://doi.org/10.46298/dmtcs.3392
Crooked Maps in Finite FieldsConference paper
Authors: Gohar Kyureghyan 1
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Gohar Kyureghyan
1 Institut für Algebra und Geometrie
We consider the maps f:F2n→F2n with the property that the set {f(x+a)+f(x):x∈F2n} is a hyperplane or a complement of hyperplane for every a∈F∗2n. 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.