Enumerative source encoding

LetSbe a given subset of binary n-sequences. We provide an explicit scheme for calculating the index of any sequence inSaccording to its position in the lexicographic ordering ofS. A simple inverse algorithm is also given. Particularly nice formulas arise whenSis the set of alln-sequences of weightkand also whenSis the set of all sequences having a given empirical Markov property. Schalkwijk and Lynch have investigated the former case. The envisioned use of this indexing scheme is to transmit or store the index rather than the sequence, thus resulting in a data compression of(\log\midS\mid)/n.