Optimal Check Digit Systems Based on Modular Arithmetic

Luerbio Faria, Paulo Eustáquio Duarte Pinto, Natália Pedroza


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.


Check digits; Error detection; Modular arithmetic

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DOI: http://dx.doi.org/10.5540/tema.2017.018.01.0105

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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