Wikipedia:Reference desk/Archives/Mathematics/2013 January 16

= January 16 =

How many "non-trivially distinct" Gray codes of a given alphabet size and codeword length exist?
For a given alphabet size n and a codeword length l, is it known how many "non-trivially distinct" Gray codes there are? I consider two codes equivalent if one can be derived from another by: (1) uniformly subtituting one alphabet for the other, (2) consistently reordering the symbols in codewords, (3) rotating the sequence of codewords, and/or (4) reversing the sequence of codewords. (These are some specific superficial differences I can think of; not sure if there's a natural and intuitive way to capture the concept of code equivalence.)

If the answer is known, what is it? — Preceding unsigned comment added by 173.49.12.29 (talk) 04:19, 16 January 2013 (UTC)


 * You're asking I believe for, basically the number of Hamiltonian cycles on a hypercube cut down to ignoring trivial differences, but I might have got the particular sequence wrong for your requirements. Dmcq (talk) 13:47, 16 January 2013 (UTC)


 * Thanks for the reference. addresses a restricted version of the question, in which the alphabet is binary (n=2). Judging from the fact that only bounds are given even for that restricted case, I suppose that the more general version of the question (allowing n>2) is open. --173.49.12.29 (talk) 16:18, 16 January 2013 (UTC)
 * Sorry yes, I hadn't even though of using n > 2. That's me knowing about actual use rather than dealing with it mathematically. ;-) Dmcq (talk) 17:56, 16 January 2013 (UTC)