Error correcting method and device

Abstract

In an error correcting method for correcting three or fewer errors or six or fewer erasures, syndromes S.sub.0 to S.sub.5 from a received codeword are calculated. If the calculated syndromes S.sub.0 to S.sub.5 are all zeros, it is determined that there is no error. If syndromes S.sub.0, S.sub.1, and S.sub.2 are zeros and at least one of the calculated syndromes S.sub.3, S.sub.4, and S.sub.5 is not zero, it is determined that error correction is impossible. Subsequently, if exactly two of syndromes S.sub.0, S.sub.1, and S.sub.2 are zeros, coefficients .sigma.1, .sigma.2, and .sigma.3 of an error-location polynomial are differently calculated depending on which of syndromes S.sub.0, S.sub.1, and S.sub.2 is not zero. The calculated coefficients are used to determine error locations, an error type, the possibility of error correction, and if error correction is possible error values. If more or fewer than two of syndromes S.sub.0, S.sub.1, and S.sub.2 are not zero, an error type and the possibility of error correction are determined using the syndromes S.sub.0 to S.sub.4 and the coefficients of the error location polynomial calculated depending on whether first and second syndrome equations obtained using syndromes S.sub.0 to S.sub.3 which are calculated according to the values of syndrome S.sub.0 and S.sub.1 are zeros, and error locations and values are calculated.