Perfect Codes for Uniform Chains Poset Metrics

TL;DR

This paper investigates perfect single-error-correcting codes within a specific class of poset metrics formed by disjoint uniform chains, establishing a precise condition for their existence.

Contribution

It provides a necessary and sufficient condition for the existence of perfect codes in uniform chains poset metrics, advancing understanding of poset metric coding theory.

Findings

Characterization of perfect codes in uniform chains poset metrics

Necessary and sufficient condition for code existence

Extension of poset metric coding theory

Abstract

The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same size, is examined. A necessary and sufficient condition, for the existence of perfect single-error-correcting codes for such poset metrics, is proved.