Asymptotic behaviour of codes in rank metric over finite fields

P Loidreau (1, 2)

1 ALI - Algorithmique, Langage et Information
2 UR - Université de Rennes

In this paper, we rst recall some basic facts about rank metric. We then derive an asymptotic equivalent of the minimum rank distance of codes that reach the rank metric GilbertVarshamov bound. We then derive an asymptotic equivalent of the average minimum rank distance of random codes. We show that random codes reach GV bound. Finally, we show that optimal codes in rank metric have a packing density which is bounded by functions depending only on the base eld and the minimum distance and show the potential interest in cryptographic applications.

Mots clés: Rank metric; Random codes; Gilbert-Varshamov bound; Gabidulin codes

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information et codage [math.IT]

P Loidreau. Asymptotic behaviour of codes in rank metric over finite fields. Designs, Codes and Cryptography, 2014, 71 (1), pp.105-118. ⟨10.1007/s10623-012-9716-0⟩. ⟨hal-01097293⟩