FOURIER GAME

A function from ${\bf F}^{m}_2$ into ${\bf C}$ represents as a vector of length $2^m$.
 
 
 
 

$$f(0,\ldots,0,0)$$

$$f(0,\ldots,0,1)$$

.

$$f(1,\ldots, 1, 1)$$

The computation of the Fourier coefficients can be done in $\Theta(m2^m)$.

   The Fourier Game : which entries minimize the out put  ?

    Idem with balanced functions ?