16 research outputs found
Systematic Constructions of Bent-Negabent Functions, 2-Rotation Symmetric Bent-Negabent Functions and Their Duals
Bent-negabent functions have many important properties for their application
in cryptography since they have the flat absolute spectrum under the both
Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present
four new systematic constructions of bent-negabent functions on
and variables, respectively, by modifying the truth tables of two
classes of quadratic bent-negabent functions with simple form. The algebraic
normal forms and duals of these constructed functions are also determined. We
further identify necessary and sufficient conditions for those bent-negabent
functions which have the maximum algebraic degree. At last, by modifying the
truth tables of a class of quadratic 2-rotation symmetric bent-negabent
functions, we present a construction of 2-rotation symmetric bent-negabent
functions with any possible algebraic degrees. Considering that there are
probably no bent-negabent functions in the rotation symmetric class, it is the
first significant attempt to construct bent-negabent functions in the
generalized rotation symmetric class
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
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
The connection between quadratic bent-negabent functions and the Kerdock code
In this paper we prove that all bent functions in the Kerdock code, except for the coset of the symmetric quadratic bent function, are bent–negabent. In this direction, we characterize the set of quadratic bent–negabent functions and show some results connecting quadratic bent–negabent functions and the Kerdock code. Further, we note that there are bent–negabent preserving nonsingular transformations outside the well known class of orthogonal ones that might provide additional functions in the bent– negabent set. This is the first time we could identify non-orthogonal (nonsingular) linear transformations that preserve bent–negabent property for a special subset