2 Point WHT

Two Point Walsh Hadamard transform.

X and Y are the 2 point Walsh Hadamard transform of A and B.

You can replace the final scaling by 1/2 with a scaling factor of 1/sqr(2) at each step.

Already the 2 point transform has some properties such as the non-uniform probability distribution of the sum of 2 thrown dice and the difference, and the fact that it is self-inverse.  It also leaves vector length unchanged if you take the scaling factor into account.