Related papers: Bent functions from triples of permutation polynom…

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…

We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the…

Let $n$ be an even positive integer, and $m<n$ be one of its positive divisors. In this paper, inspired by a nice work of Tang et al. on constructing large classes of bent functions from known bent functions [27, IEEE TIT, 63(10):…

Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…

Bent functions are of great importance in both mathematics and information science. The $\mathcal{P}\mathcal{S}$ class of bent functions was introduced by Dillon in 1974, but functions belonging to this class that can be explicitly…

Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…

We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…

We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei…

We study compositional inverses of permutation polynomials, complete mappings, mutually orthogonal Latin squares, and bent vectorial functions. Recently it was obtained in [33] the compositional inverses of linearized permutation binomials…

Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…

In this paper, we obtain a new class of $p$-ary binomial bent functions which are determined by Kloosterman sums. The bentness of another three classes of functions is characterized by some exponential sums and some results in…

Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs since their duals are also…

In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.

For functions defined on C^n or (R_+)^n we construct a dequantization transform, which is closely related to the Maslov dequantization. The subdifferential at the origin of a dequantized polynomial coincides with its Newton polytope. For…

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating…

In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering…

In this article, we provide the first systematic analysis of bent functions $f$ on $\mathbb{F}_2^{n}$ in the Maiorana-McFarland class $\mathcal{MM}$ regarding the origin and cardinality of their $\mathcal{M}$-subspaces, i.e., vector…