DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 167-170

DMTCS

2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 167-170


author: Gohar Kyureghyan
title: Crooked Maps in Finite Fields
keywords: almost perfect maps, Gold power function, quadrics
abstract: We consider the maps
f:
2
n
→
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 ∈
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 ⊂
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.
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reference: Gohar Kyureghyan (2005), Crooked Maps in Finite Fields, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 167-170
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