Binary numbers, finite fields and polynomial division, making a QR Code

Authors

DOI:

https://doi.org/10.14393/BEJOM-v6-2025-74898

Keywords:

Finite field, polynomial, euclidean division

Abstract

Through a bibliographical review, we present all the processes of how a QR Code model 1, version 1, is made and the mathematical theories involved, making it possible to create a functional QR Code. We comment on how to write the data in the form of binary numbers, the correspondence between writing a number in base ten and in base two (binary). We emphasize the subject of finite fields, with a polynomial view, this subject being necessary to write the error correcting code data into a QR Code.

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Author Biography

  • José Laudelino de Menezes Neto, Universidade Federal da Paraíba

    Bachelor in Mathematics from the Federal University of Paraíba (2006), Master in Mathematics from the Federal University of Pernambuco (2008), and Doctor in Mathematics from the Federal University of Pernambuco (2016). Currently an associate professor at the Federal University of Paraíba, based at campus IV, located in the cities of Rio Tinto and Mamanguape. Professor in the Professional Master's Program in Mathematics (PROFMAT/UFPB). Has experience in the field of Mathematics with an emphasis on Hamiltonian Systems, Applied Mathematics, and Cryptography. Full member of the Brazilian Mathematical Society (SBM) and the Brazilian Society of Applied and Computational Mathematics (SBMAC). Has published works with researchers from the following universities: UFS (Sergipe - Brazil), UFPE (Pernambuco - Brazil), UFMA (Maranhão - Brazil), Unesp (São Paulo - Brazil), University of Bío-Bío (Chile).

References

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Published

2025-05-28

How to Cite

DE MENEZES NETO, José Laudelino. Binary numbers, finite fields and polynomial division, making a QR Code. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, Minas Gerais, v. 6, p. 1–21, 2025. DOI: 10.14393/BEJOM-v6-2025-74898. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/74898. Acesso em: 23 nov. 2025.