Counting sequences

A Gray sequence is a counter sequence where the Hamming distance between successive states is one. A construction for any fixed odd distance between successive states is given based on error-correcting codes. Such sequences could be used in testing and fault diagnosis when sequencing through all possible input combinations. Sequences with the maximum possible difference between successive states, alternately n and n-1, are given. A characterization of such maximal change sequences is given. The most nearly uniform even difference sequences are described. The distribution of bit changes or transition counts for individual variables for a counting sequence is considered.