NEW CRITERIA FOR MRD AND GABIDULIN CODES AND SOME RANK-METRIC CODE CONSTRUCTIONS

摘要

It is well-known that maximum rank distance (MRD) codes can be constructed as generalized Gabidulin codes. However, it was unknown until recently whether other constructions of linear MRD codes exist. In this paper, we derive a new criterion for linear MRD codes as well as an algebraic criterion for testing whether a given linear MRD code is a generalized Gabidulin code. We then use the criteria to construct examples of linear MRD codes which are not generalized Gabidulin codes.