Near MDS poset codes and distributions

TL;DR

This paper investigates q-ary codes under poset metrics, focusing on near-MDS codes, their weight distributions, and constructions, especially in the ordered Hamming space, to advance understanding of their properties and applications.

Contribution

It characterizes weight distributions of near-MDS poset codes and provides new constructions in the ordered Hamming space.

Findings

Determined weight distributions for near-MDS poset codes.

Characterized point distributions in the unit cube for ordered metric codes.

Presented new code constructions in ordered Hamming space.

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.