On defining generalized rank weights

R. Jurrius, G.R. Pellikaan (Corresponding author)

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10 Citations (Scopus)


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 extension of a field K. This is a generalization of the case where K = Fq and L = Fqm of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu [12, 13], Oggier-Sboui [16] and Ducoat [6]. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect to the rank metric.

Original languageEnglish
Pages (from-to)225-235
Number of pages11
JournalAdvances in Mathematics of Communications
Issue number1
Publication statusPublished - 1 Feb 2017


  • Coding theory
  • Degenerate codes
  • Generalized rank weights
  • Network coding
  • Rank metric codes


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