Enumerative coding for Grassmannian space

Natalia Silberstein, Tuvi Etzion

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The Grassmannian space Gq (n,k) is the set of all k-dimensional subspaces of the vector space Fqn. Recently, codes in the Grassmannian have found an application in network coding. The main goal of this paper is to present efficient enumerative encoding and decoding techniques for the Grassmannian. These coding techniques are based on two different orders for the Grassmannian induced by different representations of k -dimensional subspaces of Fqn. One enumerative coding method is based on a Ferrers diagram representation and on an order for Gq (n,k) based on this representation. The complexity of this enumerative coding is O(k5/2 (n-k)5/2) digit operations. Another order of the Grassmannian is based on a combination of an identifying vector and a reduced row echelon form representation of subspaces. The complexity of the enumerative coding, based on this order, is O(nk(n-k)\log n\log \log n) digit operations. A combination of the two methods reduces the complexity on average by a constant factor.

Original languageEnglish
Article number5673705
Pages (from-to)365-374
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - 1 Jan 2011
Externally publishedYes


  • Enumerative coding
  • Ferrers diagram
  • Grassmannian
  • identifying vector
  • partitions
  • reduced row echelon form

ASJC Scopus subject areas

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


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