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Designs, Codes and Cryptography

, Volume 86, Issue 2, pp 341–363 | Cite as

On the genericity of maximum rank distance and Gabidulin codes

  • Alessandro Neri
  • Anna-Lena Horlemann-Trautmann
  • Tovohery Randrianarisoa
  • Joachim Rosenthal
Article
Part of the following topical collections:
  1. Special Issue on Network Coding and Designs

Abstract

We consider linear rank-metric codes in \({\mathbb {F}}_{q^m}^n\). We show that the properties of being maximum rank distance (MRD) and non-Gabidulin are generic over the algebraic closure of the underlying field, which implies that over a large extension field a randomly chosen generator matrix generates an MRD and a non-Gabidulin code with high probability. Moreover, we give upper bounds on the respective probabilities in dependence on the extension degree m.

Keywords

Rank-metric codes Finite fields MRD codes Gabidulin codes 

Mathematics Subject Classification

11T71 

Notes

Acknowledgements

This work was partially supported by SNF Grants Nos. 149716 and 169510.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.University of ZurichZurichSwitzerland
  2. 2.University of St. GallenSt. GallenSwitzerland

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