New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions

Anna-Lena Horlemann-Trautmann; Kyle Marshall

doi:10.3934/amc.2017042

Article Contents

2017, Volume 11, Issue 3: 533-548. Doi: 10.3934/amc.2017042

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New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions

Anna-Lena Horlemann-Trautmann and
Kyle Marshall^2,

1.
Faculty of Mathematics and Statistics, University of St. Gallen, St. Gallen, Switzerland
2.
Institute of Mathematics, University of Zurich, Zurich, Switzerland

Received: August 31, 2015

Revised: October 31, 2016

Published: September 2017

The authors were partially supported by SNF grant no. 149716.

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Abstract

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.

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Mathematics Subject Classification: Primary: 11T71, 94B05.

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References

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