On duals and parity-checks of convolutional codes over Z p r

Bibliographic Details
Main Author: El Oued, Mohamed
Publication Date: 2019
Other Authors: Napp, Diego, Pinto, Raquel, Toste, Marisa
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/25975
Summary: 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.
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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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:20:12Zoai:ria.ua.pt:10773/25975Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:05:08.397993Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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