Weighted Reed–Solomon convolutional codes
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http://hdl.handle.net/10045/141444
Títol: | Weighted Reed–Solomon convolutional codes |
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Autors: | Alfarano, Gianira N. | Napp, Diego | Neri, Alessandro | Requena Arévalo, Verónica |
Grups d'investigació o GITE: | Grupo de Álgebra y Geometría (GAG) |
Centre, Departament o Servei: | Universidad de Alicante. Departamento de Matemáticas |
Paraules clau: | MDP convolutional codes | Vandermonde matrices | Weighted Reed–Solomon convolutional codes |
Data de publicació: | 24-de gener-2023 |
Editor: | Taylor & Francis |
Citació bibliogràfica: | Linear and Multilinear Algebra. 2024, 72(5): 841-874. https://doi.org/10.1080/03081087.2023.2169232 |
Resum: | In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed–Solomon block codes to the context of convolutional codes. For this reason we call them weighted Reed–Solomon (WRS) convolutional codes. We show that under some constraints on the defining parameters these codes are Maximum Distance Profile (MDP), which means that they have the maximal possible growth in their column distance profile. We study the size of the field needed to obtain WRS convolutional codes which are MDP and compare it with the existing general constructions of MDP convolutional codes in the literature, showing that in many cases WRS convolutional codes require significantly smaller fields. |
Patrocinadors: | This work was partially supported by the Swiss National Science Foundation through grants no. 188430 and 187711 and by the Spanish I+D+i project PID2019-108668GB-I00 of MCIN/AEI/10.13039/501100011033 and the I+D+i project VIGROB-287 of the Universitat d’Alacant. |
URI: | http://hdl.handle.net/10045/141444 |
ISSN: | 0308-1087 (Print) | 1563-5139 (Online) |
DOI: | 10.1080/03081087.2023.2169232 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Drets: | © 2023 Informa UK Limited, trading as Taylor & Francis Group |
Revisió científica: | si |
Versió de l'editor: | https://doi.org/10.1080/03081087.2023.2169232 |
Apareix a la col·lecció: | INV - GAG - Artículos de Revistas |
Arxius per aquest ítem:
Arxiu | Descripció | Tamany | Format | |
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Alfarano_etal_2023_LinMultilinAlgebra_final.pdf | Versión final (acceso restringido) | 2,87 MB | Adobe PDF | Obrir Sol·licitar una còpia |
Alfarano_etal_2023_LinMultilinAlgebra_preprint.pdf | Preprint (acceso abierto) | 423,75 kB | Adobe PDF | Obrir Vista prèvia |
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