Optimal Ferrers Diagram Rank-Metric Codes

Tuvi Etzion, Elisa Gorla, Alberto Ravagnani, Antonia Wachter-Zeh

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

Abstract

Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space. First, we consider rank-metric anticodes and prove a code-anticode bound for Ferrers diagram rank-metric codes. The size of optimal linear anticodes is given. Four techniques and constructions of Ferrers diagram rank-metric codes are presented, each providing optimal codes for different diagrams and parameters for which no optimal solution was known before. The first construction uses maximum distance separable codes on the diagonals of the matrices, the second one takes a subcode of a maximum rank distance code, and the last two combine codes in small diagrams to a code in a larger diagram. The constructions are analyzed and compared, and unsolved diagrams are identified.

Original languageEnglish
Article number7394177
Pages (from-to)1616-1630
Number of pages15
JournalIEEE Transactions on Information Theory
Volume62
Issue number4
DOIs
Publication statusPublished - Apr 2016
Externally publishedYes

Keywords

  • anticodes
  • Ferrers diagrams
  • Gabidulin codes
  • rank-metric codes
  • subspace codes

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