A data storage device comprising a disk storage medium containing user data in a plurality of sectors wherein each of the plurality of sectors comprises a subdivision of a track, a head for writing or reading the user data and error correcting means for correcting an error that occurs in the user data during the reading process. The error correcting means comprises a syndrome generator for generating syndromes on the basis of the user data, a Euclid circuit, a chien search circuit and a verification circuit, and makes the error correction using a first error correcting code appended to each of a plurality of sectors and a second error correcting code appended to said sector for every block composed of a predetermined number of sectors.