Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations

Jared Antrobus, Heide Gluesing-Luerssen

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension of a rank-metric code with given specified Ferrers diagram shape and rank distance. While the conjecture in its generality is wide open, several cases have been established in the literature. This paper contributes further cases of Ferrers diagrams and ranks for which the conjecture holds true. In addition, the proportion of maximal Ferrers diagram codes within the space of all rank-metric codes with the same shape and dimension is investigated. Special attention is being paid to MRD codes. It is shown that for growing field size the limiting proportion depends highly on the Ferrers diagram. For instance, for [m\times 2] -MRD codes with rank 2 this limiting proportion is close to 1/e.

Original languageEnglish
Article number8752375
Pages (from-to)6204-6223
Number of pages20
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2019

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Ferrers diagrams
  • Gabidulin codes
  • Rank-metric codes
  • subspace codes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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