On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

[EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code pro...

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Autores: Muñoz Castañeda, Ángel Luis, Castro García, Noemí de, Carriegos Vieira, Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/19442
Acceso en línea:https://www.mdpi.com/2227-7390/9/22/2962
https://hdl.handle.net/10612/19442
Access Level:acceso abierto
Palabra clave:Matemáticas
Convolutional codes
Representations
Rings of modular integers
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
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oai_identifier_str oai:buleria.unileon.es:10612/19442
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repository_id_str
spelling On the State Approach Representations of Convolutional Codes over Rings of Modular IntegersMuñoz Castañeda, Ángel LuisCastro García, Noemí deCarriegos Vieira, MiguelMatemáticasConvolutional codesRepresentationsRings of modular integers1201.05 Campos, Anillos, Álgebras1201.10 Álgebra Lineal[EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.SIMDPIAlgebraEscuela de Ingenierias Industrial, Informática y Aeroespacial2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://www.mdpi.com/2227-7390/9/22/2962https://hdl.handle.net/10612/19442reponame:BULERIA. Repositorio Institucional de la Universidad de Leóninstname:Universidad de LeónIngléshttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:buleria.unileon.es:10612/194422026-06-24T12:43:27Z
dc.title.none.fl_str_mv On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
title On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
spellingShingle On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Muñoz Castañeda, Ángel Luis
Matemáticas
Convolutional codes
Representations
Rings of modular integers
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
title_short On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
title_full On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
title_fullStr On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
title_full_unstemmed On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
title_sort On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
dc.creator.none.fl_str_mv Muñoz Castañeda, Ángel Luis
Castro García, Noemí de
Carriegos Vieira, Miguel
author Muñoz Castañeda, Ángel Luis
author_facet Muñoz Castañeda, Ángel Luis
Castro García, Noemí de
Carriegos Vieira, Miguel
author_role author
author2 Castro García, Noemí de
Carriegos Vieira, Miguel
author2_role author
author
dc.contributor.none.fl_str_mv Algebra
Escuela de Ingenierias Industrial, Informática y Aeroespacial
dc.subject.none.fl_str_mv Matemáticas
Convolutional codes
Representations
Rings of modular integers
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
topic Matemáticas
Convolutional codes
Representations
Rings of modular integers
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
description [EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://www.mdpi.com/2227-7390/9/22/2962
https://hdl.handle.net/10612/19442
url https://www.mdpi.com/2227-7390/9/22/2962
https://hdl.handle.net/10612/19442
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:BULERIA. Repositorio Institucional de la Universidad de León
instname:Universidad de León
instname_str Universidad de León
reponame_str BULERIA. Repositorio Institucional de la Universidad de León
collection BULERIA. Repositorio Institucional de la Universidad de León
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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