In encoding digital data, scrambling is executed after error correction encoding is completed. In decoding digital data, error correction processing is executed after descrambling is completed. In the error correction processing, after syndrome calculation is performed, syndrome s.sub.0 is used to determine the location and value of an error; the error value is subtracted from each syndrome value; and the result is divided by a fixed value. This process realizes a digital data encoding and decoding system providing substantially the same correcting ability as a conventional process except that error propagation occurs through descrambling.