We investigate perfect codes in Zn in the `p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Zn presented here imply non-existence results for codes over finite alphabets Zq, w...

We investigate the Lp-spectrum of linear operators defined consistently on Lp(Ω) for p0 ≤ p ≤ p1, where (Ω, μ) is an arbitrary σ-finite measure space and 1 ≤ p0 < p1 ≤ ∞. We prove p-independence of the Lp-spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω, μ); the balls with respect to this semi-metric are required to satisfy a...

There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces Lp(μ), we get their coarse embeddability into a Hilbert space for 0 < p < 2. This together with a theorem by Banach and Mazur yields that coarse embeddability into l2 and into L...

In this paper, we consider a facility location problem to find a minimum-sum coverage of n points by disks centered at a fixed line. The cost of a disk with radius r has a form of a non-decreasing function f(r) = r for any α ≥ 1. The goal is to find a set of disks under Lp metric such that the disks are centered on the x-axis, their union covers the points, and the sum of the cost of the disks ...

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The metric can be used, e.g., to compare estimates from algorithms with the ground truth. It includes intuitive costs associated to localization, missed and false targets and track switches. The metric computation is based on multi-dimensio...

New text independent speaker identification method is presented. Phase spectrum of allpole linear prediction (LP) model is used to derive the speech features. The features are represented by pairs of numbers that are calculated from group delay extremums of LP model spectrum. The first component of the pair is an argument of maximum of group delay of all pole LP model spectrum and the second is...

Invented in the 1960’s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications. In 2011 a decoding method called LP (linear programming) decoding was introduced for a class of permutation codes with a Euclidean distance induced metric. In this paper we comparatively analyze the Eucl...