Abstract: A decoding method is presented for error-correcting codes based on the syndrome decoding scheme, which means the set of all syndromes is one-to-one corresponding to the set of all correctable error patterns. The improvement in the high-speed error-correcting capability is achieved by searching a syndrome-error table, which is built upon the mathematical basis: there is a one-to-one correspondence between the set of all syndromes and the set of all correctable error patterns. Two embodiments of the present invention are described. The first embodiment uses a full syndrome-error table, whereas the second uses a partial syndrome-error table. The method includes the following steps: calculating a syndrome corresponding to the received bit string; determining whether the syndrome is a zero bit string; when the syndrome is not a zero bit string, determining an error pattern from the syndrome-error table; and correcting the corrupted codeword using the error pattern.

Abstract: A decoding method is presented for error-correcting codes based on the syndrome decoding scheme, which means the set of all syndromes is one-to-one corresponding to the set of all correctable error patterns. The improvement in the high-speed error-correcting capability is achieved by searching a syndrome-error table, which is built upon the mathematical basis: there is a one-to-one correspondence between the set of all syndromes and the set of all correctable error patterns. Two embodiments of the present invention are described. The first embodiment uses a full syndrome-error table, whereas the second uses a partial syndrome-error table. The method includes the following steps: calculating a syndrome corresponding to the received bit string; determining whether the syndrome is a zero bit string; when the syndrome is not a zero bit string, determining an error pattern from the syndrome-error table; and correcting the corrupted codeword using the error pattern.