相关论文: Design and analysis of bent functions using $\math…
In this article, we study bent functions on $\mathbb{F}_2^{2m}$ of the form $f(x,y) = x \cdot \phi(y) + h(y)$, where $x \in \mathbb{F}_2^{m-1} $ and $ y \in \mathbb{F}_2^{m+1}$, which form the generalized Maiorana-McFarland class (denoted…
An important classification of permutations over $\mathbb{F}_2^m$, suitable for constructing Maiorana-McFarland bent functions on $\mathbb{F}_2^m \times \mathbb{F}_2^m$ with the unique $M$-subspace of maximal dimension, was recently…
The concatenation of four Boolean bent functions $f=f_1||f_2||f_3||f_4$ is bent if and only if the dual bent condition $f_1^* + f_2^* + f_3^* + f_4^* =1$ is satisfied. However, to specify four bent functions satisfying this duality…
We study generalizations of two classical primary constructions of Boolean bent functions, namely the Maiorana-McFarland ($MM$) class and the (Desarguesian) partial spread ($\mathcal{PS}_{ap}$) class. The construction of bent functions…
Bent functions are balanced by restricting their domains to vectors with either even or odd Hamming weights, which ensures an equal number of pre-images for both, 0 and 1. Using the previous fact, we can construct bent functions on two…
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…
Every Boolean bent function $f$ can be written either as a concatenation $f=f_1||f_2$ of two complementary semi-bent functions $f_1,f_2$; or as a concatenation $f=f_1||f_2||f_3||f_4$ of four Boolean functions $f_1,f_2,f_3,f_4$, all of which…
Generalized bent (gbent) functions is a class of functions $f: \mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot…
The closure $\mathcal{M}_{m}^{\#}$ and the extension $\widehat{\mathcal{M}}_{m}$ of the Maiorana--McFarland class $\mathcal{M}_{m}$ in $m = 2n$ variables relative to the extended-affine equivalence and the bent function construction $f…
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…
In this article a procedure to construct bent functions from $\F_{p^n}$ to $\F_p$ by merging plateaued functions which are bent on ($n-2$)-dimensional subspaces of $\F_{p^n}$ is presented. Taking advantage of such classes of plateaued…
In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ variables for all $n\ge 10$. Moreover, we show that for almost…
It is known that partial spreads is a class of bent partitions. In \cite{AM2022Be,MP2021Be}, two classes of bent partitions whose forms are similar to partial spreads were presented. In \cite{AKM2022Ge}, more bent partitions $\Gamma_{1},…
Bent functions $f: V_{n}\rightarrow \mathbb{F}_{p}$ with certain additional properties play an important role in constructing partial difference sets, where $V_{n}$ denotes an $n$-dimensional vector space over $\mathbb{F}_{p}$, $p$ is an…
A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on…
Drawing inspiration from Nyberg's paper~\cite{Nyb91} on perfect nonlinearity and the $c$-differential notion we defined in~\cite{EFRST20}, in this paper we introduce the concept of $c$-differential bent functions in two different ways (thus…
Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are…
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…
Bent functions from a vector space $V_n$ over $\mathbb F_2$ of even dimension $n=2m$ into the cyclic group $\mathbb Z_{2^k}$, or equivalently, relative difference sets in $V_n\times\mathbb Z_{2^k}$ with forbidden subgroup $\mathbb Z_{2^k}$,…
In difference to many recent articles that deal with generalized bent (gbent) functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$ for certain small valued $q\in \{4,8,16 \}$, we give a complete description of these functions for both $n$…