Research and Simulation of BCH Code Encoding and Decoding Methods

This research focuses on the investigation and simulation of BCH code encoding and decoding methods. In this project, we explore and implement various encoding and decoding techniques, including n-k encoding (systematic code implementation using generator matrices), algebraic encoding (polynomial-based approach using primitive polynomials), Peterson decoding (error location polynomial solver), Berlekamp-Massey (BM) decoding (iterative error-correction algorithm), and group transform decoding methods. Through MATLAB simulations, we implement these algorithms using key functions such as gf() for Galois field operations, bchgenpoly() for BCH polynomial generation, and develop custom algorithms for syndrome calculation and error correction. The simulation evaluates the performance and effectiveness of these methods under various conditions, including different code lengths and error patterns. The objective of this research is to deepen the understanding of BCH code encoding/decoding principles and applications, providing references and foundations for related research and development areas.