Hamming distance for conjugates

Abstract: Let be strings of equal length. The Hamming distance between and is the number of positions in which and differ. If is a cyclic shift of , we say and are conjugates. We consider , the Hamming distance between the conjugates and . Over a binary alphabet is always even, and must satisfy a further technical condition. By contrast, over an alphabet of size 3 or greater, can take any value between 0 and , except 1; furthermore, we can always assume that the smaller string has only one type of letter. [Copyright &y& Elsevier]