 Although the binary reflected Gray code is useful in many scenarios, it is not optimal in certain cases because of a lack of "uniformity".In balanced Gray codes, the number of changes in different coordinate positions are as close as possible.To make this more precise, let "G" be an "R"-ary complete Gray cycle having transition sequence formula_26; the "transition counts" ("spectrum") of "G" are the collection of integers defined by

A Gray code is "uniform" or "uniformly balanced" if its transition counts are all equal, in which case we have formula_28
for all "k".