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On the genericity of maximum rank distance and Gabidulin codes

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Neri Alessandro, Horlemann-Trautmann Anna-Lena, Randrianarisoa Tovohery, Rosenthal Joachim,
Project Algebraic Constructions and Decoding of Subspace Codes
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Original article (peer-reviewed)

Journal Designs, Codes and Cryptography
Volume (Issue) 86(2)
Page(s) 341 - 363
Title of proceedings Designs, Codes and Cryptography
DOI 10.1007/s10623-017-0354-4

Open Access

URL https://doi.org/10.1007/s10623-017-0354-4
Type of Open Access Website

Abstract

We consider linear rank-metric codes in $F_{q^m}^n$ . 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.
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