An error correction decoder includes a syndrome generator and an error correction value generator. The syndrome generator is operable to generate a plurality of syndromes based upon a received signal generated according to a generator polynomial. The error correction value generator is operable to generate a plurality of product values. Each of the product values is generated for one of the syndromes based upon a respective power of the roots of the generator polynomial. The respective power is determined based upon a respective index corresponding to one of the syndromes to be considered and unit positions of the received signal. The error correction value generator is further operable to generate an error correction value according to the product values, and to provide an error correcting device coupled thereto with the error correction value for correcting an error of the received signal.