Mathematics desk
< January 15	<< Dec \| January \| Feb >>	January 17 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

January 16[edit]

How many "non-trivially distinct" Gray codes of a given alphabet size and codeword length exist?[edit]

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)[reply]

You're asking I believe for (sequence A159344 in the OEIS), 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)[reply]

Thanks for the reference. (sequence A159344 in the OEIS) 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)[reply]

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)[reply]