On the number of inequivalent Gabidulin codes

Maximum rank-distance (MRD) codes are extremal codes in the space of m × 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 approa...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2018-09, Vol.86 (9), p.1973-1982
Main Authors: Schmidt, Kai-Uwe, Zhou, Yue
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
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Summary:Maximum rank-distance (MRD) codes are extremal codes in the space of m × 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 ⩽ m ⩽ n - 2 .
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-017-0433-6