A class of DC free, synchronization error correcting codes

The authors present a class of binary codes that combine spectral shaping properties with additive error and synchronization error correcting capabilities, provided that only one of the above classes of errors occurs in a word. These codes are constructed by finding certain balanced subcodes of the single synchronization error correcting Levenshtein block codes. These subcodes have a minimum Hamming distance of four, and thus single additive errors can be detected. By further constraining the codes, the authors obtain codes for which the second derivative of the power spectrum at 0 Hz is zero and the power spectrum has a spectral null at half the normalized frequency. The rates of these codes are determined and presented for word lengths of less than 25 bits