Flag codes from planar spreads in network coding
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http://hdl.handle.net/10045/109622
| Título: | Flag codes from planar spreads in network coding |
|---|---|
| Autor/es: | Alonso-González, Clementa | Navarro-Pérez, Miguel Ángel | Soler-Escrivà, Xaro |
| Grupo/s de investigación o GITE: | Grupo de Álgebra y Geometría (GAG) |
| Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
| Palabras clave: | Network coding | Subspace codes | Projective space | Spreads | Flag codes |
| Área/s de conocimiento: | Geometría y Topología | Álgebra |
| Fecha de publicación: | dic-2020 |
| Editor: | Elsevier |
| Cita bibliográfica: | Finite Fields and Their Applications. 2020, 68: 101745. https://doi.org/10.1016/j.ffa.2020.101745 |
| Resumen: | In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space Fnq, being qa prime power and Fqthe finite field of qelements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For n =2k, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm. |
| Patrocinador/es: | The first and third authors are partially supported by Projecte AICO/2017/128 of Generalitat Valenciana. The second author is supported by Generalitat Valenciana and Fondo Social Europeo. Grants: ACIF/2018/196 and BEFPI/2019/070. The third author is also supported by the grant BEST/2019/192 of Generalitat Valenciana. |
| URI: | http://hdl.handle.net/10045/109622 |
| ISSN: | 1071-5797 (Print) | 1090-2465 (Online) |
| DOI: | 10.1016/j.ffa.2020.101745 |
| Idioma: | eng |
| Tipo: | info:eu-repo/semantics/article |
| Derechos: | © 2020 Elsevier Inc. |
| Revisión científica: | si |
| Versión del editor: | https://doi.org/10.1016/j.ffa.2020.101745 |
| Aparece en las colecciones: | INV - GAG - Artículos de Revistas |
Archivos en este ítem:
| Archivo | Descripción | Tamaño | Formato | |
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 Alonso-Gonzalez_etal_2020_FiniteFieldsTheirApplicat_final.pdf | Versión final (acceso restringido) | 360,7 kB | Adobe PDF | Abrir Solicitar una copia |
 Alonso-Gonzalez_etal_2020_FiniteFieldsTheirApplicat_preprint.pdf | Preprint (acceso abierto) | 1,49 MB | Adobe PDF | Abrir Vista previa |
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