A decoding algorithm for DEC RS codes

A step-by-step decoding algorithm is proposed for double-error-correcting (DEC) Reed-Solomon (RS) codes of length n=2^m-1. Since the decoding algorithm can directly find the error value at the highest-order position in a received vector without determining the error location polynomial, the decoding procedure is very simple and regular, and therefore it is suitable for hardware implementation. Moreover, the new algorithm can also be used for decoding DEC binary BCH codes and DEC nonbinary BCH codes. Finally, based on the decoding algorithm a hardware decoder is also presented