Covering Radius of Matrix Codes Endowed with the Rank Metric
Eimear Byrne, Alberto Ravagnani
TL;DR
This paper investigates the properties and invariants of matrix codes with the rank metric, focusing on their covering radius, and introduces new analytical tools and bounds for these codes.
Contribution
It introduces novel tools like puncturing and shortening for analyzing rank-metric codes and provides new upper bounds on their covering radius.
Findings
Derived upper bounds on covering radius using combinatorial methods
Applied bounds to maximal and quasi maximal rank distance codes
Enhanced understanding of matrix codes with the rank metric
Abstract
In this paper we study properties and invariants of matrix codes endowed with the rank metric, and relate them to the covering radius. We introduce new tools for the analysis of rank-metric codes, such as puncturing and shortening constructions. We give upper bounds on the covering radius of a code by applying different combinatorial methods. We apply the various bounds to the classes of maximal rank distance and quasi maximal rank distance codes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.