Characterization of metrics induced by hierarchical posets

TL;DR

This paper explores metrics derived from hierarchical posets, providing explicit formulas for key code parameters and offering new characterizations and proofs of these metrics.

Contribution

It introduces explicit formulas for code parameters under hierarchical poset metrics and presents ten new characterizations, including simplified proofs.

Findings

Explicit formulas for minimum distance, packing, covering, and Chebyshev radii.

Ten characterizations of hierarchical poset metrics, with new insights.

Simplified proofs for known properties of hierarchical poset metrics.

Abstract

In this paper we consider metrics determined by hierarchical posets and give explicit formulae for the main parameters of a linear code: the minimum distance and the packing, covering and Chebyshev radii of a code. We also present ten characterizations of hierarchical poset metrics, including new characterizations and simple new proofs to the known ones.