Related papers: New nonexistence results on $(m,n)$-generalized be…

In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{\pi m}{b}\right)\sin^{3}\left(2\pi m\frac{a}{b}\right)\:$$ and associate the distribution of its values to a…

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\frac{m}{2}-1} Tr^n_1(c_ix^{1+2^{ei}})+ Tr_1^{n/2}(c_{m/2}x^{1+2^{n/2}}) ,$ where $n=me$, $m$ is even and $c_i\in…

For any positive integers $n=2k$ and $m$ such that $m\geq k$, in this paper we show the maximal number of bent components of any $(n,m)$-functions is equal to $2^{m}-2^{m-k}$, and for those attaining the equality, their algebraic degree is…

In this paper, we further investigate properties of generalized bent Boolean functions from $\Z_{p}^n$ to $\Z_{p^k}$, where $p$ is an odd prime and $k$ is a positive integer. For various kinds of representations, sufficient and necessary…

The number of $n$-ary bent functions is less than $2^{3\cdot2^{n-3}(1+o(1))}$ as $n$ is even and $n\rightarrow\infty$. Keywords: Boolean function, bent function, upper bound

This note presents generalizations of the partial spread bent functions introduced by Dillon, as well as the corresponding relative difference sets in nonabelian groups.

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 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…

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…

In this paper, we investigate properties of functions from $\mathbb{Z}_{p}^n$ to $\mathbb{Z}_q$, where $p$ is an odd prime and $q$ is a positive integer divided by $p$. we present the sufficient and necessary conditions for bent-ness of…

We prove generalized ABC theorems for vanishing sums of non-Archimedean entire functions of several variables in arbitrary characteristic.

Let $m,r\in\mathbb{Z}$ and $\omega\in\mathbb{R}$ satisfy $0\leqslant r\leqslant m$ and $\omega\geqslant1$. Our main result is a generalized continued fraction for an expression involving the partial binomial sum $s_m(r) =…

In this paper we consider further applications of $(n,m)$-functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson theorem, by showing that linear codes of APN functions with the…

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…

The notion of a descent polynomial, a function in enumerative combinatorics that counts permutations with specific properties, enjoys a revived recent research interest due to its connection with other important notions in combinatorics,…

In the literature, few $n$-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on $\mathbb{F}_2^{n}$ of the two forms: {\rm (i)}…

Let $m,n\in \Bbb{N}$. We represent the additive subgroups of the ring $\Bbb{Z}_m \times \Bbb{Z}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of…

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…

We obtain asymptotic formulas with remainder terms for the hyperbolic summations $\sum_{mn\le x} f((m,n))$ and $\sum_{mn\le x} f([m,n])$, where $f$ belongs to certain classes of arithmetic functions, $(m,n)$ and $[m,n]$ denoting the gcd and…

We prove that if M, N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of Ext^n_R(M,N) for n\gg 0 is equivalent to the vanishing of Ext^n_R(N,M) for n\gg 0. Furthermore, if the completion of $R$…