Cyclic orbit codes and stabilizer subfields

Heide Gluesing-Luerssen, Katherine Morrison, Carolyn Troha

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given subspace is a vector space, the cardinality of the orbit code can be determined, and estimates for its distance can be found. This subfield is closely related to the stabilizer of the generating subspace. Finally, with a linkage construction larger, and longer, constant dimension codes can be derived from cyclic orbit codes without compromising the distance.

Original languageEnglish
Pages (from-to)177-197
Number of pages21
JournalAdvances in Mathematics of Communications
Volume9
Issue number2
DOIs
StatePublished - May 1 2015

Bibliographical note

Publisher Copyright:
© 2015 AIMS.

Keywords

  • Constant dimension subspace codes
  • Cyclic orbit codes
  • Group actions
  • Random network coding

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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