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Gohar Kyureghyan - Crooked Maps in Finite Fields

dmtcs:3392 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3392
Crooked Maps in Finite FieldsConference paper

Authors: Gohar Kyureghyan 1

  • 1 Institut für Algebra und Geometrie

We consider the maps f:F2nF2n with the property that the set {f(x+a)+f(x):xF2n} is a hyperplane or a complement of hyperplane for every aF2n. 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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: almost perfect maps,Gold power function,quadrics,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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