Error correction apparatus

One set of syndromes is calculated from a first data string from among a plurality thereof including at least 2t+1 pieces of symbols as a parity string, and coefficients of an error locator polynomial from the one set of the syndromes. Whether or not a correction is successful is judged by using the coefficients of the error locator polynomial and the same calculation is performed for a second data string if a correction failure is judged. Contrarily, if a correction success is judged, an error of the first data string is corrected by using the aforementioned set of the syndromes and the coefficients of the error locator polynomial.