Decoder and decoding method

(Amended) A decoding device for receiving a received word made of an extended Reed-Solomon code as input data, the device comprising:

• an error correction section for determining first corrected data based on the input data;
• a syndrome computation section for computing syndromes for the input data as input data syndromes and outputting a first flag signal indicating whether or not the input data has an error that is determined based on the input data syndromes, while computing syndromes for the first corrected data obtained by the error correction section as corrected data syndromes and outputting a second flag signal indicating whether or not the first corrected data has an error that is determined based on the corrected data syndromes;
• an evaluator/locator polynomial deriving section for computing coefficients at each order of an error evaluator polynomial and an error locator polynomial based on the input data syndromes, and computing error magnitudes based on error evaluation values and corresponding error locator polynomial differential values both obtained from the coefficients;
• and
• a Chien search section for determining roots of the error locator polynomial based on the coefficients, and computing the error evaluation values by substituting the roots in the error evaluator polynomial and the error locator polynomial differential values by substituting the roots in a derivative of the error locator polynomial,
• wherein the error correction section outputs data obtained by performing the error correction for the input data based on the roots and the corresponding error magnitudes as the first corrected data when the first flag signal indicates that the input data has an error, and outputs the input data as the first corrected data when the first flag signal indicates that the input data has no error, to the syndrome computation section, while the error correction section outputs data obtained by performing restoration for the first corrected data to restore the data before the error correction as second corrected data when the second flag signal indicates that the first corrected data has an error, and outputs the first corrected data as the second corrected data when the second flag signal indicates that the first corrected data has no error.