Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions

It is known that the dual of a weakly regular bent function is again weakly regular. On the other hand, the dual of a nonweakly regular bent function may not even be a bent function. In 2013, cesmelioglu, Meidl and Pott pointed out that the existence of a non-weakly regular bent function having weakly regular bent dual is an open problem. In this paper, we prove that for an odd prime p and n is an element of Z+, if f : F-p(n)-> F-p is a non-weakly regular bent function such that its dual f* is bent, then f**(-x) = f(x), and f* is non-weakly regular, which solves the open problem. We also generalize our results to plateaued functions.


Bent and semibent functions via linear translators
Koçak, Neşe; Mesnager, Sihem; Özbudak, Ferruh (null; 2015-12-17)
The paper is dealing with two important subclasses of plateaued functions: bent and semi-bent functions. In the first part of the paper, we construct mainly bent and semi-bent functions in the Maiorana-McFarland class using Boolean functions having linear structures (linear translators) systematically. Although most of these results are rather direct applications of some recent results, using linear structures (linear translators) allows us to have certain flexibilities to control extra properties of these ...
Some maximal function fields and additive polynomials
GARCİA, Arnaldo; Özbudak, Ferruh (Informa UK Limited, 2007-01-01)
We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).
On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
Monotone positive solutions for a class of second-order nonlinear differential equations
Ertem, T.; Zafer, Ağacık (Elsevier BV, 2014-03-15)
It is shown that the second-order nonlinear differential equation
Curves with many points and configurations of hyperplanes over finite fields
Özbudak, Ferruh (Elsevier BV, 1999-10-01)
We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
Citation Formats
F. Özbudak, “Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34526.