相关论文: Minimum distance of Hermitian two-point codes

We prove that knowing the length of geodesics joining points on the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.

Given a Riemannian metric on the 2-sphere, sweep the 2-sphere out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as…

We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…

Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product…

The Lorentzian distance formula, conjectured several years ago by Parfionov and Zapatrin, has been recently proved by the second author. In this work we focus on the derivation of an equivalent expression in terms of the geometry of…

We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.

In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily…

We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus,…

We prove the existence of immersed closed curves of constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we develop a min-max scheme for a weighted length functional.

Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider across the center of the box). Without loss of generality, we…

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…

We consider the coding problem in the Stiefel manifold with chordal distance. After considering various low-dimensional instances of this problem, we use Rankin's bounds on spherical codes to prove upper bounds on the minimum distance of a…

An upper bound for Zolotarev distances between probability measures on multidimensional Euclidean spaces is given in terms of similar distances between one dimensional projections.

We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by M. Bertola, B. Dubrovin, D. Yang and by P. Zograf.

We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…

Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves…

We prove the ACC for minimal log discrepancies on an arbitrary fixed threefold.

In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time…

The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where…

In this note we prove a sharp bound for the number of 2-torsion points on a theta divisor and show that this is achieved only in the case of products of elliptic curves. This settles in the affirmative a conjecture of Marcucci and Pirola.