Binary numbers, finite fields and polynomial division, making a QR Code
DOI:
https://doi.org/10.14393/BEJOM-v6-2025-74898Keywords:
Finite field, polynomial, euclidean divisionAbstract
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.
Downloads
References
Silva, A. R. D. A matemática do código de barras e QR Code. Master’s thesis. 2021. URL: http://www.repositorio-bc.unirio.br:8080/xmlui/bitstream/handle/unirio/13368/TCC%20-%20QR%20CODE%20-%20Vers%c3%a3o%20FInal.pdf?sequence=1&isAllowed=y (acesso em 16/08/2024).
Silva, A. R. D. e Fantin, S. A Matemática do QR Code. Em: Revista Ensin@ UFMS 2.Esp. (15 de dez. de 2021), pp. 374–399. URL: https://periodicos.ufms.br/index.php/anacptl/article/view/13902 (acesso em 20/04/2024).
Sousa, D. P. de. Dos hieroglifos ao QR Code: códigos como ferramenta na sala de aula. Master’s thesis. Universidade Estadual do Sudoeste da Bahia, 2016. URL: https://www2.uesb.br/ppg/profmat/wp-content/uploads/2018/11/Dissertacao_DEIVISON_PORTO_DE_SOUSA.pdf (acesso em 16/08/2024).
Souza, R. A. et al. Explorando QR Codes como Recurso Didático na Educação Matemática. Em: Revista Professor de Matemática Online 12.1 (2024), pp. 72–90. DOI: 10.21711/2319023x2024/pmo125.
History of QR Code. 2024. URL: https://www.qrcode.com/en/history/ (acesso em 20/04/2024).
Cornelissen, M. e Moura, R. Códigos de Reed Solomon. Em: Revista de Matemática da UFOP 2 (2021), pp. 1–18. URL: https://periodicos.ufop.br/rmat/article/view/5087 (acesso em 16/08/2024).
Types of QR Code. 2024. URL: https://www.qrcode.com/en/codes/ (acesso em 20/04/2024).
QR Code Tutorial. 2024. URL: https://www.thonky.com/qr-code-tutorial/ (acesso em 20/04/2024).
Gonçalves, A. Introdução à Álgebra. 5ª ed. Rio de Janeiro: IMPA, 2006.
Tabela ASCII. 2024. URL: https://www.ime.usp.br/~kellyrb/mac2166_2015/tabela_ascii.html (acesso em 22/04/2024).
Lidl, R. e Niederreiter, H. Introduction to Finite Fields and Their Applications. Cambridge University Press, 1994.
Mullen, G. L. e Panario, D. Handbook of Finite Fields. Boca Raton: CRC Press, 2013.
Plank, J. S. A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems. Em: Software: Practice & Experience 29.9 (1997), pp. 995–1012. URL: https://web.eecs.utk.edu/~jplank/plank/papers/SPE-9-97.html (acesso em 26/04/2024).
Artizzu, M. Let’s develop a QR Code Generator, part III: error correction. 2021. URL: https://dev.to/maxart2501/let-s-develop-a-qr-code-generator-part-iii-error-correction-1kbm (acesso em 29/04/2024).
Downloads
Published
Issue
Section
License
Copyright (c) 2025 José Laudelino de Menezes Neto

This work is licensed under a Creative Commons Attribution 4.0 International License.
- Articles published from 2025 onwards are licensed under the CC BY 4.0 license. By submitting material for publication, authors automatically agree to the journal’s editorial guidelines and affirm that the text has been properly reviewed. Simultaneous submission of articles to other journals is prohibited, as is the translation of articles published in this journal into another language without proper authorization.
- Articles published prior to 2025 are licensed under the CC BY-NC 4.0 license.






