MATLAB Code for Generating Generator Polynomials and Minimal Polynomials of BCH Codes

Below is MATLAB code for generating BCH codes, including computational methods for generator polynomials and minimal polynomials, accompanied by syndrome calculation expressions. Initially, we need to define appropriate parameters and variables. During codeword generation, we utilize both generator polynomials and minimal polynomials. The generator polynomial is obtained by multiplying the information polynomial with the parity-check polynomial, where the information polynomial is user-defined while the parity-check polynomial is derived through successive division by the generator polynomial. The minimal polynomial represents the lowest-degree polynomial that can divide the information polynomial. For syndrome computation, we employ concepts of determinants and cofactors. These computational approaches enable us to generate BCH codes and implement error correction capabilities. Implementation Note: The MATLAB code typically involves using communication toolbox functions like bchgenpoly() for generator polynomial calculation, while minimal polynomials can be derived using gfminpol() for Galois field operations. Syndrome calculation often employs matrix operations or recursive algorithms based on received codeword evaluation.