16 research outputs found
A new class of negabent functions
Negabent functions were introduced as a generalization of bent functions,
which have applications in coding theory and cryptography. In this paper, we
have extended the notion of negabent functions to the functions defined from
to (-negabent), where is a
positive integer and is the ring of integers modulo . For
this, a new unitary transform (the nega-Hadamard transform) is introduced in
the current set up, and some of its properties are discussed. Some results
related to -negabent functions are presented. We present two constructions
of -negabent functions. In the first construction, -negabent functions
on variables are constructed when is an even positive integer. In the
second construction, -negabent functions on two variables are constructed
for arbitrary positive integer . Some examples of -negabent
functions for different values of and are also presented
Semifields, relative difference sets, and bent functions
Recently, the interest in semifields has increased due to the discovery of
several new families and progress in the classification problem. Commutative
semifields play an important role since they are equivalent to certain planar
functions (in the case of odd characteristic) and to modified planar functions
in even characteristic. Similarly, commutative semifields are equivalent to
relative difference sets. The goal of this survey is to describe the connection
between these concepts. Moreover, we shall discuss power mappings that are
planar and consider component functions of planar mappings, which may be also
viewed as projections of relative difference sets. It turns out that the
component functions in the even characteristic case are related to negabent
functions as well as to -valued bent functions.Comment: Survey paper for the RICAM workshop "Emerging applications of finite
fields", 09-13 December 2013, Linz, Austria. This article will appear in the
proceedings volume for this workshop, published as part of the "Radon Series
on Computational and Applied Mathematics" by DeGruyte
A NOTE ON SEMI-BENT BOOLEAN FUNCTIONS
We show how to construct semi-bent Boolean functions from PSap-
like bent functions. We derive innite classes of semi-bent functions in even
dimension having multiple trace terms
On Negabent Functions and Nega-Hadamard Transform
The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement on f1∥f2 which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed as f(Ax⊕a)⊕b·x⊕c is discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained
A New Class of Bent--Negabent Boolean Functions
In this paper we develop a technique of constructing bent--negabent
Boolean functions by using complete mapping polynomials. Using this
technique we demonstrate that for each there exits
bent--negabent functions on variables with algebraic degree
. It is also demonstrated that there exist
bent--negabent functions on variables with algebraic degrees
, and