On the genericity of maximum rank distance and Gabidulin codes

2016/05/19 by Alessandro Neri, Anna-Lena Horlemann-Trautmann, Tovohery Randrianarisoa +1 · 39 citations
Computer Science · Mathematics · #Algebraic number #Closure (psychology) #Code (set theory) #Coding theory and cryptography #Cooperative Communication and Network Coding #Extension (predicate logic) #Finite Group Theory Research #Finite field #Generator (circuit theory) #Generator matrix #Matrix (chemical analysis) #Rank (graph theory) #cs.IT #math.IT

paper · pdf · doi:10.1007/s10623-017-0354-4

published in Designs Codes and Cryptography 86(2), 341-363 (Springer Nature)

arxiv created 2016/05/19 · openalex created_date 2016/06/24 · openalex publication_date 2017/04/08 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05

Abstract

We consider linear rank-metric codes in \mathbb Fqmn. 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.

Citations

• Fast Probabilistic Algorithms for Verification of Polynomial Identities

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