A maximum likelihood decoder creates a decoding target data string and provides error candidates that are effective for an error correction circuit. The decoder has a detector for creating a decoding target data string, and an error candidate extractor for extracting the bit positions of which likelihood of each bit shows a high probability of error as the error candidates of the decoding target data string based on the likelihood information from the detector. Since only the bit positions of which error probability is high are extracted as error candidates, a correction circuit can extract the error candidates in the sequence of the lower likelihood, and the number of times of sorting in the sequence of likelihood can be decreased.