Year: 2010
Type: preprint
Abstract: We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close to MDS codes by the value of their minimum distance. For such codes, we determine their weight distribution, and in the particular case of the "ordered metric" characterize distributions of points in the unit cube defined by the codes. We also give some constructions of codes in the ordered Hamming space.
Source: arXiv (Cornell University)
Authors: Barg, Alexander, Purkayastha, Punarbasu
Institution: University of Maryland, College Park
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: CIF: Small: New Approaches to the Design and Analysis of Graphical Models for Linear Codes and Secret Sharing Schemes, Collaborative Research: Digital Fingerprinting: Information-Theoretic Analysis and Code Design, Collaborative Research: Coding for Nano-Devices, Flash Memories, and VLSI Circuits, Collaborative Research: Multivariate positive definite polynomials and their applications via SDP
OpenAlex ID: W4301470677