On duals and parity-checks of convolutional codes over Z p r
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/25975 |
Resumo: | A convolutional code C over Z_{p^r}((D)) is a Z_{p^r}((D))-submodule of Z_{p^r}^n((D)) that admits a polynomial set of generators, where Z_{p^r}((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C^{\perp} . We use these results to provide a constructive algorithm to build an explicit generator matrix of C^{\perp}. Moreover, we show that the transpose of such a matrix is a parity-check matrix (also called syndrome former) of C. |
id |
RCAP_2b808f41419e943e2ca4edb8e51e5a62 |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/25975 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
On duals and parity-checks of convolutional codes over Z p rFinite ringsConvolutional codes over finite ringsDual codesMatrix representationsA convolutional code C over Z_{p^r}((D)) is a Z_{p^r}((D))-submodule of Z_{p^r}^n((D)) that admits a polynomial set of generators, where Z_{p^r}((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C^{\perp} . We use these results to provide a constructive algorithm to build an explicit generator matrix of C^{\perp}. Moreover, we show that the transpose of such a matrix is a parity-check matrix (also called syndrome former) of C.Elsevier2019-05-08T15:29:05Z2019-01-01T00:00:00Z2019-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/25975eng1071-579710.1016/j.ffa.2018.08.012El Oued, MohamedNapp, DiegoPinto, RaquelToste, Marisainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:50:14Zoai:ria.ua.pt:10773/25975Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:03.488099Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On duals and parity-checks of convolutional codes over Z p r |
title |
On duals and parity-checks of convolutional codes over Z p r |
spellingShingle |
On duals and parity-checks of convolutional codes over Z p r El Oued, Mohamed Finite rings Convolutional codes over finite rings Dual codes Matrix representations |
title_short |
On duals and parity-checks of convolutional codes over Z p r |
title_full |
On duals and parity-checks of convolutional codes over Z p r |
title_fullStr |
On duals and parity-checks of convolutional codes over Z p r |
title_full_unstemmed |
On duals and parity-checks of convolutional codes over Z p r |
title_sort |
On duals and parity-checks of convolutional codes over Z p r |
author |
El Oued, Mohamed |
author_facet |
El Oued, Mohamed Napp, Diego Pinto, Raquel Toste, Marisa |
author_role |
author |
author2 |
Napp, Diego Pinto, Raquel Toste, Marisa |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
El Oued, Mohamed Napp, Diego Pinto, Raquel Toste, Marisa |
dc.subject.por.fl_str_mv |
Finite rings Convolutional codes over finite rings Dual codes Matrix representations |
topic |
Finite rings Convolutional codes over finite rings Dual codes Matrix representations |
description |
A convolutional code C over Z_{p^r}((D)) is a Z_{p^r}((D))-submodule of Z_{p^r}^n((D)) that admits a polynomial set of generators, where Z_{p^r}((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C^{\perp} . We use these results to provide a constructive algorithm to build an explicit generator matrix of C^{\perp}. Moreover, we show that the transpose of such a matrix is a parity-check matrix (also called syndrome former) of C. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-05-08T15:29:05Z 2019-01-01T00:00:00Z 2019-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/25975 |
url |
http://hdl.handle.net/10773/25975 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1071-5797 10.1016/j.ffa.2018.08.012 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799137644715704320 |