An encoder divides the data in which sector data is adjacently connected to a first RS parity generated in Reed Solomon encoding into blocks to and subjects each of the blocks to cyclic Hamming encoding so as to generate Hamming parities. Subsequently, the data in which the Hamming parities are aligned in a row is subjected to Reed Solomon encoding so as to generate a second RS parity, and encoded data in which the first RS parity and the second RS parity are adjacently connected to the sector data is output. A decoder s divides the sector data and the first RS parity into n blockes and cyclic Hamming encoding, aligns the parities thereof, corrects errors in the parities by Reed Solomon decoding by the second RS parity, then corrects 1-bit errors in blockes by cyclic Hamming decoding, and further corrects errors of 2 or more bits by Reed Solomon decoding by the first RS parity.