On the Genericity of Maximum Rank Distance and Gabidulin Codes
  We consider linear rank-metric codes in $\mathbb F_{q^m}^n$. 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 $m$. 
Alessandro Neri, Anna-Lena Horlemann-Trautmann, Tovohery   Randrianarisoa and Joachim Rosenthal
cs.IT math.IT