A construction of Abelian non-cyclic orbit codes
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Title: | A construction of Abelian non-cyclic orbit codes |
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Authors: | Climent, Joan-Josep | Requena Arévalo, Verónica | Soler-Escrivà, Xaro |
Research Group/s: | Grupo de Álgebra y Geometría (GAG) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Random linear network coding | Subspace codes | Grassmannian | Group action | General linear group | Abelian group |
Knowledge Area: | Álgebra |
Issue Date: | Sep-2019 |
Publisher: | Springer US |
Citation: | Cryptography and Communications. 2019, 11(5): 839-852. doi:10.1007/s12095-018-0306-5 |
Abstract: | A constant dimension code consists of a set of k-dimensional subspaces of Fnq, where Fq 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 Fnq. 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. |
Sponsor: | This work was partially supported by Spanish grants AICO/2017/128 of the Generalitat Valenciana and VIGROB287 of the Universitat d’Alacant. |
URI: | http://hdl.handle.net/10045/95511 |
ISSN: | 1936-2447 (Print) | 1936-2455 (Online) |
DOI: | 10.1007/s12095-018-0306-5 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s12095-018-0306-5 |
Appears in Collections: | INV - GAG - Artículos de Revistas |
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2019_Climent_etal_CryptogrCommun_final.pdf | Versión final (acceso restringido) | 567,09 kB | Adobe PDF | Open Request a copy |
2019_Climent_etal_CryptogrCommun_preprint.pdf | Preprint (acceso abierto) | 310,39 kB | Adobe PDF | Open Preview |
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