a hard sequence worthy of attention

[Jon Awbrey]

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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


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