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

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.

References in corpus (1)

• Algebraic structures of MRD Codes

Cited by in corpus (11)

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• Identifiers for MRD-codes
• Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants
• Constructions for optimal Ferrers diagram rank-metric codes
• On the number of inequivalent Gabidulin codes
• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• Nuclei and automorphism groups of generalized twisted Gabidulin codes
• A geometric invariant of linear rank-metric codes