Ayça Çeşmelioğlu

A construction of bent functions from plateaued functions

In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analyzed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent functions having some additional properties that enable the construction of strongly regular graphs are formed, and explicit expressions for bent functions with maximal degree are presented.

A construction of weakly and non-weakly regular bent functions

In this article a technique for constructing p-ary bent functions from near-bent functions is presented. This technique is then used to obtain both weakly regular and non-weakly regular bent functions. In particular we present the first known infinite class of non-weakly regular bent functions.

Bent Functions of Maximal Degree

In this paper, 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 analyzed, and 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 p= 3,5. Until now, no construction of bent functions attaining these bounds was known.

Generalized Maiorana–McFarland class and normality of p-ary bent functions

Abstract A class of bent functions which contains bent functions with various properties like regular, weakly regular and not weakly regular bent functions in even and in odd dimension, is analyzed. It is shown that this class includes the Maiorana–McFarland class as a special case. Known classes and examples of bent functions in odd characteristic are examined for their relation to this class. In the second part, normality for bent functions in odd characteristic is analyzed. It turns out that differently to Boolean bent functions, many – also quadratic – bent functions in odd characteristic and even dimension are not normal. It is shown that regular Coulter–Matthews bent functions are normal.

On the dual of (non)-weakly regular bent functions and self-dual bent functions

For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of non-weakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality for bent functions in odd characteristic, and characterize quadratic self-dual bent functions. We construct non-weakly regular bent functions with and without a bent dual, and bent functions with a dual bent function of a different algebraic degree.

BENT FUNCTIONS, SPREADS, AND o-POLYNOMIALS ∗

We show that bent functions

A general approach to construction and determination of the linear complexity of sequences based on cosets

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On some permutation binomials of the form x 2 n -1/ k +1 + ax over f 2 n : existence and count

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Bent and vectorial bent functions, partial difference sets, and strongly regular graphs

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On the cycle structure of permutation polynomials

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