On the construction of MRD convolutional codes
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http://hdl.handle.net/10045/140459
Título: | On the construction of MRD convolutional codes |
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Autor/es: | Napp, Diego | Pinto, Raquel | Santana, Filipa | Vela, Carlos |
Grupo/s de investigación o GITE: | Grupo de Álgebra y Geometría (GAG) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Coding theory | Polynomial matrices | Finite fields | Convolutional codes | Rank metric codes |
Fecha de publicación: | 22-ene-2024 |
Editor: | Taylor & Francis |
Cita bibliográfica: | Linear and Multilinear Algebra. 2024. https://doi.org/10.1080/03081087.2023.2300673 |
Resumen: | The problem of building optimal block codes, such as MDS codes, over small fields has been an active area of research that led to several interesting conjectures. In the context of convolutional codes, optimal constructions, such as MDS or MDP, are very rare and all require very large finite fields. In this work, we focus on the problem of constructing optimal convolutional codes with respect to the rank distance, i.e. we study the construction of Maximum Rank Distance (MRD) convolutional codes. Considering convolutional codes within a very general framework, we present concrete novel classes of MRD convolutional codes for a large set of given parameters. |
Patrocinador/es: | This work was supported by The Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e Tecnologia), references UIDB/04106/2020. The first author was supported by Spanish grants PID2019-108668GB-I00 of the Ministerio de Ciencia e Innovación of the Gobierno de España. |
URI: | http://hdl.handle.net/10045/140459 |
ISSN: | 0308-1087 (Print) | 1563-5139 (Online) |
DOI: | 10.1080/03081087.2023.2300673 |
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/10.1080/03081087.2023.2300673 |
Aparece en las colecciones: | INV - GAG - Artículos de Revistas |
Archivos en este ítem:
Archivo | Descripción | Tamaño | Formato | |
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Napp_etal_2024_LinearMultilinearAlgebra_final.pdf | Versión final (acceso restringido) | 1,78 MB | Adobe PDF | Abrir Solicitar una copia |
Napp_etal_2024_LinearMultilinearAlgebra_preprint.pdf | Preprint (acceso abierto) | 392,22 kB | Adobe PDF | Abrir Vista previa |
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