On the genericity of maximum rank distance and Gabidulin codes
Journal
Designs, codes and cryptography : an international journal
ISSN
0925-1022
ISSN-Digital
1573-7586
Type
journal article
Date Issued
2017-04-08
Author(s)
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.
Language
English
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
Kluwer
Publisher place
Boston, Mass. [u.a.]
Volume
86
Number
2
Start page
341
End page
363
Subject(s)
Division(s)
Eprints ID
251159