Related papers: Some observations on bent and planar functions

Bent functions, which are maximally nonlinear Boolean functions with even numbers of variables and whose Hamming distance to the set of all affine functions equals $2^{n-1}\pm 2^{\frac{n}{2}-1}$, were introduced by Rothaus in 1976 when he…

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 a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…

Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the…

We give a new simple construction for known binary quadratic symmetric bent and almost bent functions. In particular, for even number of variables, they are self-dual and anti-self-dual quadratic bent functions, respectively, which are not…

A metric space (X,d) is monotone if there is a linear order < on X and a constant c>0 such that d(x,y) < c d(x,z) for all x<y<z in X. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It…

We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials. We show that for m odd such functions have rather good nonlinearity properties.…

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…

In the literature, few constructions of $n$-variable rotation symmetric bent functions have been presented, which either have restriction on $n$ or have algebraic degree no more than $4$. In this paper, for any even integer $n=2m\ge2$, a…

Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $, be a rational function that simultaneously interpolates $ f_0 $ at the origin with order $…

For each non-constant $q$ in the set of $n$-variable Boolean functions, the {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of…

If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of secant planes of a two-variable smooth function is a plane…

We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this…

Two classes of ternary bent functions of degree four with two and three terms in the univariate representation that belong to the completed Maiorana-McFarland class are found. Binomials are mappings $\F_{3^{4k}}\mapsto\fthree$ given by…

Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance…

For function of one variable, differentiability is equivalent to the existence of tangent line as the limit of secant line. The genuine counterpart of this equivalence for function of several variables is obtained for the first time.

In this paper, we study a part of approximation theory that presents the conditions under which a \Ceby\sev set in a Banach space is convex. To do so, we use Gateaux differentiability of the distance function.

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…

We prove that for a homogeneous linear partial differential operator $\mathcal A$ of order $k \le 2$ and an integrable map $f$ taking values in the essential range of that operator, there exists a function $u$ of special bounded variation…

We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real normed linear space X under a proximinality condition on K. We do not assume the uniform…