On the minimality of Hamming compatible metrics
  A Hamming compatible metric is an integer-valued metric on the words of a finite alphabet which agrees with the usual Hamming distance for words of equal length. We define a new Hamming compatible metric, compute the cardinality of a sphere with respect to this metric, and show this metric is minimal in the class of all "well-behaved" Hamming compatible metrics. 
Parsa Bakhtary, Othman Echi
cs.IT math.IT