Step-by-step decoding algorithm for Reed–Solomon codes

A new step-by-step decoding algorithm for decoding Reed–Solomon codes over GF(2m) is presented. Based on several properties of the syndrome matrices, the new step-by-step decoding algorithm can directly determine whether every received symbol is an error locator. The detection of error location is based only on the determinant of a v × v syndrome matrix, where v is the number of errors. When an error location is found, its corresponding error value can also be determined by performing a determinant division operation between two syndrome matrices. The new decoding algorithm can significantly reduce computation complexity and improve the decoding speed compared with the conventional step-by-step decoding algorithm.