Equidistant subspace codes

Elisa Gorla, Alberto Ravagnani

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

In this paper we study equidistant subspace codes, i.e. subspace codes with the property that each two distinct codewords have the same distance. We provide an almost complete classification of such codes, under the assumption that the cardinality of the ground field is large enough. More precisely we prove that, for most values of the parameters, an equidistant code of maximum cardinality is either a sunflower or the orthogonal of a sunflower. We also study equidistant codes with extremal parameters, and establish general properties of equidistant codes that are not sunflowers. Finally, we propose a construction of equidistant codes based on our previous construction of partial spread codes, and provide an efficient decoding algorithm.

Original languageEnglish
Pages (from-to)48-65
Number of pages18
JournalLinear Algebra and Its Applications
Volume490
DOIs
Publication statusPublished - 1 Feb 2016
Externally publishedYes

Keywords

  • Equidistant subspace codes
  • Network coding
  • Spreads and partial spreads
  • Sunflowers

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