New Criteria for MRD and Gabidulin Codes and some Rank-Metric Code Constructions

TL;DR

This paper introduces new criteria to identify MRD and Gabidulin codes in rank-metric coding theory, and presents novel constructions of MRD codes that are not Gabidulin codes.

Contribution

It provides new methods to verify MRD and Gabidulin codes and constructs linear MRD codes of dimension 2 that are distinct from Gabidulin codes.

Findings

New criteria for MRD code verification

Criteria for identifying generalized Gabidulin codes

Construction of non-Gabidulin MRD codes of dimension 2

Abstract

In this work we present a new criterion to check if a given rank-metric code is a maximum rank distance (MRD) code. Moreover, we derive a criterion to check if a given MRD code is a generalized Gabidulin code. We then use these results to come up with constructions of linear MRD codes of dimension 2 that are not generalized Gabidulin codes.