Related papers: On minimal distance between q-ary bent functions

Using a sieve-theoretic argument, we show that almost all gaps $(p_n, p_{n+1})$ between consecutive primes $p_n, p_{n+1}$ contain a natural number $m$ whose least prime factor $p(m)$ is at least the length $p_{n+1} - p_n$ of the gap,…

New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.

We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of R^k, assuming that P is positive on the simplex. This bound depends only on the number…

Define the height function h(a) = min{k+(ka\mod p): k=1,2,...,p-1} for a = 0,1,...,p-1. It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a= [p/3], (p-3)/2, (p-1)/2, [2p/3], p-3,p-2, and p-1, and…

How to quantify the distance between any two partitions of a finite set is an important issue in statistical classification, whenever different clustering results need to be compared. Developing from the traditional Hamming distance between…

In this paper we compare approximation properties of degree $p$ spline spaces with different numbers of continuous derivatives. We prove that, for a given space dimension, $\smooth {p-1}$ splines provide better a priori error bounds for the…

Many real-world machine learning problems involve inherently hierarchical data, yet traditional approaches rely on Euclidean metrics that fail to capture the discrete, branching nature of hierarchical relationships. We present a theoretical…

It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only ``few" vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, ``few" means n…

A function $F:\mathbb{F}_{p^n}\rightarrow \mathbb{F}_{p^m},$ is a vectorial $s$-plateaued function if for each component function $F_{b}(\mu)=Tr_n(\alpha F(x)), b\in \mathbb{F}_{p^m}^*$ and $\mu \in \mathbb{F}_{p^n}$, the Walsh transform…

In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.

In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…

We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…

In this paper, we establish hybrid results on Diophantine approximation with primes from short intervals. In particular, we prove the following result in a slightly modified form: If $\alpha$ is an irrational number having a continued…

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space $X$ having a minimal separating function set in $C_p(X)$ is equivalent to having a minimal…

We prove a formula for the minimum distance of two-point codes on a Hermitian curve.

Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $\mathbb{Z}$. With elementary techniques one sees that the minimal periodicity of $P$ is at most $2$. Recently we proved a generalization of…

Given a set $P$ of points and a set $U$ of axis-parallel unit squares in the Euclidean plane, a minimum ply cover of $P$ with $U$ is a subset of $U$ that covers $P$ and minimizes the number of squares that share a common intersection,…

We establish asymptotic upper and lower bounds for the Wasserstein distance of any order $p\ge 1$ between the empirical measure of a fractional Brownian motion on a flat torus and the uniform Lebesgue measure. Our inequalities reveal an…

We prove estimates of a $p$-harmonic measure, $p \in (n-m, \infty]$, for sets in $\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $\Lambda \subset \mathbf{R}^n$, $m \in [0,n-1]$. Using these estimates, we derive results of…

We study the total variation distance (TV) between two $n$-fold Bernoulli product measures parametrized by $\vec p=(p_1,\ldots,p_n)$ and $\vec q=(q_1,\ldots,q_n)$, respectively, in the \emph{tiny} and \emph{small} regimes. In the tiny…