A COMPREHENSIVE SURVEY ON RECENT ADVANCES IN CYCLIC CODES: ANALYSIS OF ALGEBRAIC CODING THEORY (۲۰۲۰-۲۰۲۵)

Cyclic codes, as one of the most important algebraic structures in coding theory, are critical for error detection and correction in communication and data storage systems. This survey reviews advancements in cyclic codes from ۲۰۲۰ to ۲۰۲۵, drawing on several scientific papers from reputable databases. It covers theoretical and practical progress, including quasi-cyclic low-density parity-check (QC-LDPC) codes, cyclic codes over finite fields, and their applications in ۵G technologies and quantum computing. Notable achievements include codes with larger minimum distances and more efficient decoding algorithms. However, challenges like high computational complexity in decoding and adaptation to dynamic channels persist. The paper discusses research challenges, opportunities, and key theorems, supported by a comparative analysis of cyclic code performance. Future research directions include developing quantum noise-resistant cyclic codes and optimizing decoding algorithms for real-time applications. This review offers valuable insights for researchers and engineers exploring the current state and future of cyclic codes.

کلیدواژه ها:

Cyclic Codes ، Algebraic Coding Theory ، Error Correction ، Finite Fields ، QC-LDPC