Abstract: A method for correcting an error of a received signal is provided. The method includes: determining a target degree based upon a length of the received signal; obtaining plural primitive polynomials each having a degree equal to the target degree; selecting one of the primitive polynomials as a target polynomial; defining plural syndromes according to the received signal; generating a group of product values based on the syndromes; obtaining plural coefficient polynomials based on the product values; obtaining monomial trace coefficients based on the coefficient polynomials; generating an error correction value based on the monomial trace coefficients; and correcting the error based on the error correction value.

Abstract: A method for correcting an error of a received signal is provided. The method includes: determining a target degree based upon a length of the received signal; obtaining plural primitive polynomials each having a degree equal to the target degree; selecting one of the primitive polynomials as a target polynomial; defining plural syndromes according to the received signal; generating a group of product values based on the syndromes; obtaining plural coefficient polynomials based on the product values; obtaining monomial trace coefficients based on the coefficient polynomials; generating an error correction value based on the monomial trace coefficients; and correcting the error based on the error correction value.

Abstract: 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.

Abstract: 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.