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A Construction of Orbit Codes

  • Joan-Josep Climent
  • Verónica Requena
  • Xaro Soler-Escrivà
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10495)

Abstract

Given a finite field \(\mathbb {F}_{q}\), a constant dimension code is a set of k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\). Orbit codes are constant dimension codes which are defined as orbits when the action of a subgroup of the general linear group on the set of all subspaces of \(\mathbb {F}_{q}^{n}\) is considered. In this paper we present a construction of an Abelian non-cyclic orbit code whose minimum subspace distance is maximal.

Keywords

Random linear network coding Subspace codes Grassmannian Group action General linear group 

Notes

Acknowledgements

The first author was supported by grants MIMECO MTM2015-68805-REDT and MTM2015-69138-REDT.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Joan-Josep Climent
    • 1
  • Verónica Requena
    • 2
  • Xaro Soler-Escrivà
    • 1
  1. 1.Departament de MatemàtiquesUniversitat d’AlacantAlacantSpain
  2. 2.Departamento de Estadística, Matemáticas e InformáticaUniversidad Miguel Hernández de ElcheAlicanteSpain

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