Codes and designs related to lifted MRD codes

Tuvi Etzion, Natalia Silberstein

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly different representation of this design makes it similar to a q -analog of a transversal design. The structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain a lifted MRD code. Codes that attain these bounds are constructed. These codes are the largest known constant dimension codes for the given parameters. These transversal designs can also be used to derive a new family of linear codes in the Hamming space. Bounds on the minimum distance and the dimension of such codes are given.

Original languageEnglish
Article number6336824
Pages (from-to)1004-1017
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - 28 Jan 2013
Externally publishedYes


  • Constant dimension codes
  • Grassmannian space
  • lifted maximum rank distance (MRD) codes
  • rank-metric codes
  • transversal designs

ASJC Scopus subject areas

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

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