A new invariant for cyclic orbit flag codes
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http://hdl.handle.net/10045/141484
Título: | A new invariant for cyclic orbit flag codes |
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Autor/es: | Alonso-González, Clementa | Navarro-Pérez, Miguel Ángel |
Grupo/s de investigación o GITE: | Grupo de Álgebra y Geometría (GAG) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Vector spaces over different fields | Best friend of a vector space | Flags | Flag codes |
Fecha de publicación: | 22-ene-2024 |
Editor: | Taylor & Francis |
Cita bibliográfica: | Linear and Multilinear Algebra. 2024. https://doi.org/10.1080/03081087.2024.2304148 |
Resumen: | In the network coding framework, given a prime power q and the vector space Fnq, a constant type flag code is a set of nested sequences of Fq-subspaces (flags) with the same increasing sequence of dimensions (the type of the flag). If a flag code arises as the orbit under the action of a cyclic subgroup of the general linear group over a flag, we say that it is a cyclic orbit flag code. Among the parameters of such a family of codes, we have its best friend, that is the largest field over which all the subspaces in the generating flag are vector spaces. This object permits to compute the cardinality of the code and estimate its minimum distance. However, as it occurs with other absolute parameters of a flag code, the information given by the best friend is not complete in many cases due to the fact that it can be obtained in different ways. In this work, we present a new invariant, the best friend vector, that captures the specific way the best friend can be unfolded. Furthermore, throughout the paper we analyse the strong underlying interaction between this invariant and other parameters such as the cardinality, the flag distance, or the type vector, and how it conditions them. Finally, we investigate the realizability of a prescribed best friend vector in a vector space. |
Patrocinador/es: | The authors receive financial support from Ministerio de Ciencia e Innovación (Spain) [PID2022-142159OB-I00] and Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital (Generalitat Valenciana, Spain) [CIAICO/2022/167]. |
URI: | http://hdl.handle.net/10045/141484 |
ISSN: | 0308-1087 (Print) | 1563-5139 (Online) |
DOI: | 10.1080/03081087.2024.2304148 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2024 Informa UK Limited, trading as Taylor & Francis Group |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1080/03081087.2024.2304148 |
Aparece en las colecciones: | INV - GAG - Artículos de Revistas |
Archivos en este ítem:
Archivo | Descripción | Tamaño | Formato | |
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Alonso-Gonzalez_Navarro-Perez_2024_LinearMultilinearAlgebra_final.pdf | Versión final (acceso restringido) | 2 MB | Adobe PDF | Abrir Solicitar una copia |
Alonso-Gonzalez_Navarro-Perez_2024_LinearMultilinearAlgebra_preprint.pdf | Preprint (acceso abierto) | 323,08 kB | Adobe PDF | Abrir Vista previa |
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