According to one embodiment, a Reed-Solomon decoder comprises an analyzer and a calculator. The analyzer analyzes a data frame and calculates a size of a last code word located at an end of a data portion, using information included in a header portion. The calculator calculates correction coefficients, using the size of the last code word, for correcting coefficients of an error locator polynomial and coefficients of an error value polynomial for the last code word in accordance with a difference between a base size of Reed-Solomon code words and the size of the last code word, before error detection for a code word located immediately before the last code word in the data portion begins.