282 research outputs found
Bent functions of maximal degree
In this article a technique for constructing p-ary bent functions
from plateaued functions is presented. This generalizes earlier techniques
of constructing bent from near-bent functions. The Fourier spectrum of quadratic
monomials is analysed, examples of quadratic functions with highest possible
absolute values in their Fourier spectrum are given. Applying the construction of
bent functions to the latter class of functions yields bent functions attaining
upper bounds for the algebraic degree when . Until now no construction
of bent functions attaining these bounds was known
A Generalization of APN Functions for Odd Characteristic
Almost perfect nonlinear (APN) functions on finite fields of characteristic
two have been studied by many researchers. Such functions have useful
properties and applications in cryptography, finite geometries and so on.
However APN functions on finite fields of odd characteristic do not satisfy
desired properties. In this paper, we modify the definition of APN function in
the case of odd characteristic, and study its properties
Proofs of two conjectures on ternary weakly regular bent functions
We study ternary monomial functions of the form f(x)=\Tr_n(ax^d), where
x\in \Ff_{3^n} and \Tr_n: \Ff_{3^n}\to \Ff_3 is the absolute trace
function. Using a lemma of Hou \cite{hou}, Stickelberger's theorem on Gauss
sums, and certain ternary weight inequalities, we show that certain ternary
monomial functions arising from \cite{hk1} are weakly regular bent, settling a
conjecture of Helleseth and Kholosha \cite{hk1}. We also prove that the
Coulter-Matthews bent functions are weakly regular.Comment: 20 page
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