Runlength-limited codes for single error detection in the magnetic recording channel

An arithmetic function that assigns the value 0, 1, or 2 to each binary sequence is introduced. The authors call this function the error-check value. Two sequences that differ by a single symmetric error or a single shift error are shown to have different error-check values. Runlength-limited codes for detecting single-errors are designed by taking a set of the constrained sequences such that each code sequence has the same error-check value. Systematic runlength-limited codes that detect single errors are constructed, based on the error-check value. It is shown that these systematic runlength-limited codes have the shortest parity length possible for a single error-detecting code