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Designs, Codes and Cryptography

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31-10-2017

On the number of inequivalent Gabidulin codes

Authors: Kai-Uwe Schmidt, Yue Zhou

Published in: Designs, Codes and Cryptography | Issue 9/2018

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Abstract

Maximum rank-distance (MRD) codes are extremal codes in the space of \(m\times n\) matrices over a finite field, equipped with the rank metric. Up to generalizations, the classical examples of such codes were constructed in the 1970s and are today known as Gabidulin codes. Motivated by several recent approaches to construct MRD codes that are inequivalent to Gabidulin codes, we study the equivalence issue for Gabidulin codes themselves. This shows in particular that the family of Gabidulin codes already contains a huge subset of MRD codes that are pairwise inequivalent, provided that \(2\leqslant m\leqslant n-2\).

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Title: On the number of inequivalent Gabidulin codes
Authors: Kai-Uwe Schmidt
Yue Zhou
Publication date: 31-10-2017
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 9/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0433-6

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