Optimal Check Digit Systems Based on Modular Arithmetic

Detalhes bibliográficos
Autor(a) principal: FARIA,L.
Data de Publicação: 2017
Outros Autores: PINTO,P.E.D., PEDROZA,N.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000100105
Resumo: ABSTRACT In this article, we discuss check digits systems based on modular arithmetic, which are used worldwide. Check digits were created to eliminate most errors in data input of computational systems. Though old, a discussion about the optimality of the systems used is not found in the literature. We describe the main existing systems worldwide and highlight those adopted in Brazil. We present the necessary improvements in order to make all systems optimal. We also propose a new optimal system with 3 permutations for systems with modular base 10.
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spelling Optimal Check Digit Systems Based on Modular ArithmeticCheck digitserror detectionmodular arithmeticABSTRACT In this article, we discuss check digits systems based on modular arithmetic, which are used worldwide. Check digits were created to eliminate most errors in data input of computational systems. Though old, a discussion about the optimality of the systems used is not found in the literature. We describe the main existing systems worldwide and highlight those adopted in Brazil. We present the necessary improvements in order to make all systems optimal. We also propose a new optimal system with 3 permutations for systems with modular base 10.Sociedade Brasileira de Matemática Aplicada e Computacional2017-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000100105TEMA (São Carlos) v.18 n.1 2017reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2017.018.01.0105info:eu-repo/semantics/openAccessFARIA,L.PINTO,P.E.D.PEDROZA,N.eng2017-06-12T00:00:00Zoai:scielo:S2179-84512017000100105Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2017-06-12T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Optimal Check Digit Systems Based on Modular Arithmetic
title Optimal Check Digit Systems Based on Modular Arithmetic
spellingShingle Optimal Check Digit Systems Based on Modular Arithmetic
FARIA,L.
Check digits
error detection
modular arithmetic
title_short Optimal Check Digit Systems Based on Modular Arithmetic
title_full Optimal Check Digit Systems Based on Modular Arithmetic
title_fullStr Optimal Check Digit Systems Based on Modular Arithmetic
title_full_unstemmed Optimal Check Digit Systems Based on Modular Arithmetic
title_sort Optimal Check Digit Systems Based on Modular Arithmetic
author FARIA,L.
author_facet FARIA,L.
PINTO,P.E.D.
PEDROZA,N.
author_role author
author2 PINTO,P.E.D.
PEDROZA,N.
author2_role author
author
dc.contributor.author.fl_str_mv FARIA,L.
PINTO,P.E.D.
PEDROZA,N.
dc.subject.por.fl_str_mv Check digits
error detection
modular arithmetic
topic Check digits
error detection
modular arithmetic
description ABSTRACT In this article, we discuss check digits systems based on modular arithmetic, which are used worldwide. Check digits were created to eliminate most errors in data input of computational systems. Though old, a discussion about the optimality of the systems used is not found in the literature. We describe the main existing systems worldwide and highlight those adopted in Brazil. We present the necessary improvements in order to make all systems optimal. We also propose a new optimal system with 3 permutations for systems with modular base 10.
publishDate 2017
dc.date.none.fl_str_mv 2017-04-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000100105
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000100105
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2017.018.01.0105
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.18 n.1 2017
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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