Related papers: Bent functions using Maiorana-McFarland secondary …
We study combinatorial properties of plateaued functions $F \colon \mathbb{F}_p^n \rightarrow \mathbb{F}_p^m$. All quadratic functions, bent functions and most known APN functions are plateaued, so many cryptographic primitives rely on…
We consider the light-front wave function for the valence quark state of mesons using the AdS/CFT correspondence, as has been suggested by Brodsky and Teramond. Two kinds of wave functions, obtained in different holographic Soft-Wall…
In this paper we prove that generalized bent (gbent) functions defined on $\mathbb{Z}_2^n$ with values in $\mathbb{Z}_{2^k}$ are regular, and find connections between the (generalized) Walsh spectrum of these functions and their components.…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
Semi-inner-products in the sense of Lumer are extended to convex functionals. This yields a Hilbert-space like structure to convex functionals in Banach spaces. In particular, a general expression for semi-inner-products with respect to one…
We study a new method of constructing Boolean bent functions from cyclotomic mappings. Three generic constructions are obtained by considering different branch functions such as Dillon functions, Niho functions and Kasami functions over…
The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…
The design of plateaued functions over $GF(2)^n$, also known as 3-valued Walsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil \frac{n+s}{2} \rceil}\}$), has been commonly approached by specifying a suitable algebraic…
We consider spaces of trial wavefunctions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground…
We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…
In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This paper describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions,…
Let $n=2m$. In the present paper, we study the binomial Boolean functions of the form $$f_{a,b}(x) = \mathrm{Tr}_1^{n}(a x^{2^m-1 }) +\mathrm{Tr}_1^{2}(bx^{\frac{2^n-1}{3} }), $$ where $m$ is an even positive integer, $a\in…
Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using…
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…
Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$, and let $\phi$ be a strictly plurisubharmonic function on $\Omega$. For each $k\in\mathbb{N}$, we consider determinantal point process $\Lambda_k$ with kernel $K_{k\phi}$,…
Bent partitions of $V_{n}^{(p)}$ play an important role in constructing (vectorial) bent functions, partial difference sets, and association schemes, where $V_{n}^{(p)}$ denotes an $n$-dimensional vector space over the finite field…