Structural Insights and Decoding Strategies for BCH Codes over Quasi-Galois Rings (European Journal of Pure and Applied Mathematics, 2025)
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.
Keywords: Quasi-Galois Rings; BCH Codes; Error Correction; Code Rate; Ring-Based Coding Theory; Cyclic Subgroups