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On the genericity of maximum rank distance and Gabidulin codes


Neri, Alessandro; Horlemann-Trautmann, Anna-Lena; Randrianarisoa, Tovohery; Rosenthal, Joachim (2018). On the genericity of maximum rank distance and Gabidulin codes. Designs, Codes and Cryptography, 86(2):341-363.

Abstract

We consider linear rank-metric codes in Fnqm. 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.

Abstract

We consider linear rank-metric codes in Fnqm. 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2018
Deposited On:08 Mar 2018 08:14
Last Modified:18 Apr 2018 11:49
Publisher:Springer
ISSN:0925-1022
Funders:Schweizerischer Nationalfonds
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s10623-017-0354-4

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