We consider linear rank-metric codes in Fqmn. 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.
On the genericity of maximum rank distance and Gabidulin codes / Neri, A.; Horlemann-Trautmann, A. -L.; Randrianarisoa, T.; Rosenthal, J.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 86:2(2018), pp. 341-363. [10.1007/s10623-017-0354-4]
On the genericity of maximum rank distance and Gabidulin codes
Neri A.;
2018
Abstract
We consider linear rank-metric codes in Fqmn. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
