 To do this, we consider partitions of formula_34 into an even number "L" of non-empty blocks of the form

where formula_36, and formula_37).This partition induces an formula_38-digit Gray code given by

If we define the "transition multiplicities" formula_43 to be the number of times the digit in position "i" changes between consecutive blocks in a partition, then for the ("n" + 2)-digit Gray code induced by this partition the transition spectrum formula_44 is

The delicate part of this construction is to find an adequate partitioning of a balanced "n"-digit Gray code such that the code induced by it remains balanced, but for this only the transition multiplicities matter; joining two consecutive blocks over a digit formula_4 transition and splitting another block at another digit formula_4 transition produces a different Gray code with exactly the same transition spectrum formula_44, so one may for example designate the first formula_49 transitions at digit formula_4 as those that fall between two blocks.Uniform codes can be found when formula_51 and formula_52, and this construction can be extended to the "R"-ary case as well.