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.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Computer Science Applications
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 2018 |
| Deposited On: | 08 Mar 2018 08:14 |
| Last Modified: | 26 Jan 2022 16:19 |
| Publisher: | Springer |
| ISSN: | 0925-1022 |
| Funders: | Schweizerischer Nationalfonds |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/s10623-017-0354-4 |
Neri, Alessandro