Flag Codes: Distance Vectors and Cardinality Bounds
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http://hdl.handle.net/10045/127517
Título: | Flag Codes: Distance Vectors and Cardinality Bounds |
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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 | Flag codes | Flag distance | Bounds |
Fecha de publicación: | 21-sep-2022 |
Editor: | Elsevier |
Cita bibliográfica: | Linear Algebra and its Applications. 2023, 656: 27-62. https://doi.org/10.1016/j.laa.2022.09.016 |
Resumen: | Given Fq the finite field with q elements and an integer n > 2, a flag is a sequence of nested subspaces of Fnq and a flag code is a nonempty set of flags. In this context, the distance between flags is the sum of the corresponding subspace distances. Hence, a given flag distance value might be obtained by many different combinations. To capture such a variability, in the paper at hand, we introduce the notion of distance vector as an algebraic object intrinsically associated to a flag code that encloses much more information than the distance parameter itself. Our study of the flag distance by using this new tool allows us to provide a fine description of the structure of flag codes as well as to derive bounds for their maximum possible size once the minimum distance and dimensions are fixed. |
Patrocinador/es: | The authors received financial support of Ministerio de Ciencia e Innovación (PID2019-108668GB-I00). The second author is supported by Generalitat Valenciana and Fondo Social Europeo (ACIF/2018/196). |
URI: | http://hdl.handle.net/10045/127517 |
ISSN: | 0024-3795 (Print) | 1873-1856 (Online) |
DOI: | 10.1016/j.laa.2022.09.016 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1016/j.laa.2022.09.016 |
Aparece en las colecciones: | INV - GAG - Artículos de Revistas |
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Alonso-Gonzalez_etal_2022_LinearAlgebraAppl.pdf | 602,43 kB | Adobe PDF | Abrir Vista previa | |
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