Gray codes and enumerative coding for vector spaces

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Abstract

Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones.

Original languageEnglish
Article number6642070
Pages (from-to)271-281
Number of pages11
JournalIEEE Transactions on Information Theory
Volume60
Issue number1
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Enumerative coding
  • Grassmannian
  • Gray codes
  • projective-space graph

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