Structural Insights and Decoding Strategies for BCH Codes over Quasi-Galois Rings

Authors

  • Muhammad Sajjad NUTECH School of Applied Science and Humanities, National University of Technology Islamabad 44000 Pakistan https://orcid.org/0000-0003-0006-1156
  • Muhammad Shoaib Abid Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
  • Maha Alammari Department of Mathematics, College of Science, King Saud University, P.O. Box 22452 10 Riyadh 11495, Saudi Arabia
  • Robinson Julian Serna Escuela de Matemáticas y Estadística, Universidad Pedagógica y Tecnológica de Colombia, Tunja, Colombia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6414

Keywords:

Quasi-Galois Rings; BCH Codes; Error Correction; Code Rate; Ring-Based Coding Theory; Cyclic Subgroups

Abstract

Robust data disclosure constitutes an essential problem for contemporary system communication, and the theory of coding becomes the key to maintaining data integrity. This paper discusses constructions and decoding of Bose–Chaudhuri–Hocquenghem (BCH) codes over Quasi-Galois Rings (QGRs) – generalization of classical Galois rings. The QGRs provide richer algebraic structures that lead to improved error correction capabilities, greater codes rates, and more codewords than their Galois counterparts. We provide an all-rounding theory of construction for BCH codes over QGRs, describe them in their construction process, and walk through an efficient decoding technique. Our findings demonstrate the ability of BCH codes under QGR to provide high reliability and performance for the communication systems which will make them a candidate for future use in data transmission and storage.

Author Biography

  • Muhammad Sajjad, NUTECH School of Applied Science and Humanities, National University of Technology Islamabad 44000 Pakistan

    Dr. Muhammad Sajjad is a dedicated mathematician from Pakistan, currently serving as an Assistant Professor at the National University of Technology (NUTECH), Islamabad. He earned his PhD from Quaid-i-Azam University Islamabad, Pakistan, in 2024 and is an esteemed member of the American Mathematical Society (AMS). Recognised for his outstanding contributions to cybersecurity and cryptography, Dr. Sajjad has received several prestigious accolades, including two international research awards in cybersecurity and cryptography, the Computer Scientist Award from China, and the National Cryptology Award from NCCS Pakistan. His research spans multiple disciplines, including mathematics, electrical engineering, and computer science, with a strong emphasis on vector algebras, non-commutative and non-associative algebras, number theory, coding theory, channel coding, cryptography, cryptology, post-quantum cryptography, graph theory, and elliptic curves. His work is particularly focused on designing efficient error-correcting codes, advancing data security, and exploring complex algebraic structures. Dr. Sajjad is an active contributor to the global academic community, having delivered talks at prestigious international conferences. His research collaborations extend to leading universities in South America, Denmark, and Saudi Arabia, further strengthening his impact on the field. He has undergone professional training in various aspects of academic management and possesses strong programming skills in Python, MATLAB, C++, and more. Over his academic career, he has taught 21 bachelor and master's courses and published 13 research papers. Through his dedication to teaching, research, and innovation, Dr. Muhammad Sajjad continues to shape the future of mathematical sciences and information security.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Coding Theory and Cryptology

License

Copyright (c) 2025 Muhammad Sajjad, Muhammad Shoaib Abid, Maha Alammari, Robinson Julian Serna

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How to Cite

Structural Insights and Decoding Strategies for BCH Codes over Quasi-Galois Rings. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6414. https://doi.org/10.29020/nybg.ejpam.v18i3.6414