Related papers: Perfect Mannheim, Lipschitz and Hurwitz weight cod…
We use a method of translation to recover Borweins' quadratic and quartic iterations. Then, by using the WZ-method, we obtain some initial values which lead to the limit $1/\pi$. We will not use the modular theory nor either the Gauss'…
We characterize metric spaces whose Lipschitz free space is isometric to $\ell_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(\Gamma)$ for any set $\Gamma$. We give a lower bound for the…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
Etzion et al. introduced metrics on $\mathbb{F}_2^n$ based on directed graphs on $n$ vertices and developed some basic coding theory on directed graph metric spaces. In this paper, we consider the problem of classifying directed graphs…
In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
Maximum Hermitian rank metric codes were introduced by Schmidt in 2018 and in this paper we propose both interpolation-based encoding and decoding algorithms for this family of codes when the length and the minimum distance of the code are…
In this work we investigate codes in $\mathbb{Z}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
Here we study what we call bounded rough Riemannian metrics $(M,g)$, which are positive definite, symmetric tensors on each tangent space, $T_pM$, which are bounded and measurable as functions in coordinates. This is enough structure to…
We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…
Recently, double Toeplitz codes have been introduced as a generalization of double circulant codes. In this paper, we study the average weight enumerators of double Toeplitz codes. As an application, we consider the existence of double…
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bounds we derive via the linear programming (LP) techniques of…
We show that $b$-Hurwitz numbers with a rational weight are obtained by taking an explicit limit of a Whittaker vector for the $\mathcal{W}$-algebra of type $A$. Our result is a vast generalization of several previous results that treated…
In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…