On defining generalized rank weights

Abstract

This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over $L$, where $L$ is a finite Galois extension of a field $K$. This is a generalization of the case where $K={\mathbb{F}}_q$ and $L={\mathbb{F}}_{q^m}$ of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu, Oggier-Sboui and Ducoat. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect to the rank metric.

15 pages; extended abstract accepted for presentation at ACA2015 (http://www.usthb.dz/spip.php?article1039)

References in corpus (1)

• New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding

Cited by in corpus (3)

• Rank-Metric Codes and $q$-Polymatroids
• Relative generalized matrix weights of matrix codes for universal security on wire-tap networks
• New MRD codes from linear cutting blocking sets