On the genericity of maximum rank distance and Gabidulin codes

نویسندگان

  • Alessandro Neri
  • Anna-Lena Horlemann-Trautmann
  • Tovohery Randrianarisoa
  • Joachim Rosenthal
چکیده

We consider linear rank-metric codes in Fqm . We show that the properties of being MRD (maximum rank distance) 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.

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عنوان ژورنال:
  • Des. Codes Cryptography

دوره 86  شماره 

صفحات  -

تاریخ انتشار 2018