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arXiv · 1605.05972

On the Genericity of Maximum Rank Distance and Gabidulin Codes

Alessandro Neri·Anna-Lena Horlemann-Trautmann·Tovohery Randrianarisoa·Joachim Rosenthal
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Abstract

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 $m$.

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Alessandro Neri, Anna-Lena Horlemann-Trautmann, Tovohery Randrianarisoa, Joachim Rosenthal. 2016-05-19. On the Genericity of Maximum Rank Distance and Gabidulin Codes. https://doi.org/10.1007/s10623-017-0354-4

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