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

摘要

In this work we present a new criterion to check if a given rank-metric codeis a maximum rank distance (MRD) code. Moreover, we derive a criterion to checkif a given MRD code is a generalized Gabidulin code. We then use these resultsto come up with constructions of linear MRD codes of dimension 2 that are notgeneralized Gabidulin codes.