REED-SOLOMON CODES IN EDUCATION: FROM THEORY TO PRACTICAL APPLICATIONS IN DIGITAL TECHNOLOGIES

Dimitar Stoyanov, PhD

Department of Telecommunications University of Ruse “Angel Kanchev” Ruse, Bulgaria

E-mail: 7673@email.com

Assoc. Prof. Adriana Borodzhieva, PhD

Department of Telecommunications University of Ruse “Angel Kanchev” Ruse, Bulgaria

ORCID: 0000-0001-5330-4153

E-mail: aborodzhieva@uni-ruse.bg

Abstract

This paper examines Reed-Solomon codes as a key tool for error correction in digital technologies and their place in the educational process. The basic mathematical principles of codes based on polynomials over finite fields are presented, as well as examples of their wide application - from compact discs and QR codes to space communications. Special attention is paid to the connection with education - how the study of these codes supports the understanding of algebra, computer science, and information technology, as well as what educational examples and exercises can be used in the classroom. The advantages for the educational process are emphasized - motivating students through real-world applications, building cross-curricular connections, and developing analytical thinking. The paper shows that Reed-Solomon codes are not only a mathematical achievement but also a valuable resource for modern education.

Keywords

Reed-Solomon codes, Error correction, Data redundancy, Polynomials, Interpolation, Digital communication, Computer science, Education, Learning process, CD, DVD, Media, QR codes, Digital video broadcasting (DVB), Information reliability, Mathematical modelling, Practical applications

REFERENCES

A Little Bit about Reed-Solomon Codes (2025). https://www.math.columbia.edu/~dejong/courses/RS.pdf (Accessed on 30.11.2025).
Geisel, W.A. (1990). Tutorial on Reed-Solomon Error Correction Coding, https://ntrs. nasa.gov/api/citations/19900019023/downloads/19900019023.pdf (Accessed on 30.11.2025).
Hagenauer, J., Offer, E., & Papke, L. (1993). Improving the Standard Coding System for Deep Space Missions, Proceedings of ICC'93 - IEEE International Conference on Communications, Geneva, Switzerland, vol. 2, pp. 1092-1097, doi: 10.1109/ICC.1993.397446, https://ieeexplore.ieee.org/document/397446?signout=success (Accessed on 30.11.2025). QR code, https://en.wikipedia.org/wiki/QR_code (Accessed on 30.11.2025).
Reed, I. S., & Solomon, G. (1960). Polynomial Codes over Certain Finite Fields, SIAM Journal of Applied Mathematics, vol. 8, pp. 300-304.
Reed-Solomon error correction, https://en.wikipedia.org/wiki/Reed-Solomon_error_ correction (Accessed on 30.11.2025).
Sachs, J. (2018). Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed- Solomon Error Correction. https://www.embeddedrelated.com/showarticle/1182.php (Accessed on 30.11.2025).
Wicker, S., & Bhargava, V. (2009). An Introduction to Reed-Solomon Codes. DOI: 10.1109/9780470546345.ch1, https://catalogimages.wiley.com/images/db/pdf/0780353919. excerpt.pdf (Accessed on 23.11.2024).
Wicker, S., & Bhargava, V. (1999). Reed-Solomon Codes and Their Applications. Wiley- IEEE Press, 336 pages, ISBN: 978-0-780-35391-6, https://www.wiley.com/en-ca/Reed+ Solomon+Codes+and+Their+Applications-p-9780780353916 (Accessed on 23.11.2024). 20 Copyrights© 2025 ISBN 978-954-712-978-8 (Print); e-ISBN 978-954-712-979-5