o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o please be gentle, as i'm not really in my math mode today ... B = GF(2) = {0, 1} there are 2^(2^n) functions f : B^n -> B. check. but only 2^n linear functions L = {linear v : B^n -> B}, if those are the ones that you mean. so f = g mod L if f - g is in L? but i don't know what you are counting as usual symmetries here. ja N. J. A. Sloane wrote:
J.A. said: just to check, do you mean the 2^n boolean functions that are linear over B = GF(2), i.e., viewing B^n as a finite dimensional vector space, their number is equal to |B^n|?
Me: I am talking about the 2^2^n Boolean functions of n variables, counting them mod addition of linear functions together with all the usual symmetries. NJAS
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o