2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 167170
author:  Gohar Kyureghyan 

title:  Crooked Maps in Finite Fields 
keywords:  almost perfect maps, Gold power function, quadrics 
abstract: 
We consider the maps
f:
with the property that the set
2
→
n
2
n
{ f(x+a)+ f(x): x ∈F
is a hyperplane or a complement of hyperplane for
every
2
}
n
a ∈
. The main goal of the talk is to show that almost
all maps
2
n
*
f(x) = Σ
, where
b ∈B
c
b
(x+b)
d
B ⊂
and
2
n
Σ
, are not of that type. In particular, the only such
power maps have exponents
b ∈B
c
b
≠0
2
with gcd
i
+2
j
(n, ij)=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. 167170 
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