Construction of Distance-Separated Gray Codes

We propose new systematic constructions of Gray codes that improve reliability of the track identification field in the servo portion of a magnetic recording disk. In this application, it is beneficial to obtain good distance properties within a certain range of neighboring Gray codewords, because the servo positioning system typically gives a good estimate of the range of interest. With proposed Gray codes, we provide a high separation range between non-adjacent Gray codewords at Hamming distance one, which guarantees error detection within this range. In addition, we provide a certain level of separation between Gray codewords at Hamming distance two, which can be utilized for error correction.