A new step-by-step decoding algorithm for decoding Reed-Solomon codes over
GF(2(m)) is presented. Based on several properties of the syndrome matrices
, the new step-by-step decoding algorithm can directly determine whether ev
ery received symbol is an error locator, The detection of error location is
based only on the determinant of a v x v syndrome matrix, where v is the n
umber of errors. When an error location is found, its corresponding error v
alue 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.