In this paper a new class of single error-correcting fixed block-length (d, k) codes has been proposed. The correctable error types are peak-shift error, insertion or deletion error, symmetric error, etc. The basic technique to construct codes is a systematic construction algorithm of multilevel sequences with a constant Lee weight (TALG algorithm). The coding rate and efficiency are considerably good, and hence the proposed new codes will be very useful for improving the reliability of high density magnetic recording.