indice, relative degree and normality of Boolean function
We report the numerical experiments related to the degree of restriction of Boolean function on affine subspace
Let m be a positive integer a Boolean function f in B(m) is said to be normal if it is constant on some affine subspace V of dimension [(m+1)/2].
Normal Boolean functions Pascale Charpin Journal of Complexity 20 (2004) 245–265
And it is said r-normal if it is constant on some affine subspace V of dimension r.
Let m be a positive integer a Boolean function f in B(m) is said to be weakly normal if it is affine on some affine subspace V of dimension [(m+1)/2].
> relative degree in dimension 5 : 4 : - 0 2 2 3 2 3 : - 0 1 1 1 1 2 : - 0 0 0 0 0
relative degree in dimension 6 5 : - 0 2 3 4 3 4 4 : - 0 2 2 2 2 2 3 : - 0 0 0 0 0 0 2 : - 0 0 0 0 0 0
relative degree in dimension 7 ---- random ---- 6 : - 0 2 3 4? 4? 5? 4? 5 : - 0 2 3 3? 3? 3? 3? 4 : - 0 1 1 1? 1? 1? 1? 3 : - 0 0 0 0 0 0 0