Balanced coding with Lehmer code

We propose two balanced coding schemes based on the Lehmer code. The first one is very efficient because it is essentially an enumerative coding without any loss. However, it needs an arithmetic device with very long precision proportional to the output block length. The redundancy of the second coding scheme is almost log n, where n is the length of the output block. The scheme needs a list of numbers with length n and lists of numbers with length n/2 in encoding.