Decoding binary BCH codes

BCH codes are powerful error-correcting codes. Algorithms used for decoding must be able to find the error locations, and for nonbinary codes, the error magnitudes. One of the most efficient algorithms for decoding BCH codes is Berlekamp's algorithm. To find the error locations the algorithm must solve a set of t equations in t unknowns. This paper explores, for binary BCH codes, a new method that uses half of the unknowns to determine the other unknowns, thus solving t/2 equations in t/2 unknowns. However, because of the reduced number of equations, the algorithm only iterates half the number of times. The performance of the new algorithm is shown to be superior to both Berlekamp's algorithm and a simplified algorithm in terms of execution times, which includes the field multiplications and additions and required memory.