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Cryptography and Communications

, Volume 11, Issue 5, pp 839–852 | Cite as

A construction of Abelian non-cyclic orbit codes

  • Joan-Josep ClimentEmail author
  • Verónica Requena
  • Xaro Soler-Escrivà
Article
  • 186 Downloads
Part of the following topical collections:
  1. Special Issue on Coding Theory and Applications

Abstract

A constant dimension code consists of a set of k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\), where \(\mathbb {F}_{q}\) is a finite field of q elements. Orbit codes are constant dimension codes which are defined as orbits under the action of a subgroup of the general linear group on the set of all k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\). If the acting group is Abelian, we call the corresponding orbit code Abelian orbit code. In this paper we present a construction of an Abelian non-cyclic orbit code for which we compute its cardinality and its minimum subspace distance. Our code is a partial spread and consequently its minimum subspace distance is maximal.

Keywords

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

Notes

Acknowledgments

This work was partially supported by Spanish grants AICO/2017/128 of the Generalitat Valenciana and VIGROB287 of the Universitat d’Alacant.

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Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat d’AlacantAlacantSpain

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