I was solving this problem https://www.codechef.com/problems/COVERING and sort of came with a subproblem which I am not sure if it helps to solve the original problem but seems very interesting anyways.

Given an array A and array B with size (2^N) . Compute another array X of size (2^N) such that

X[mask] = sum of (A[i] * B[j]) such that ( (i&j) == mask ) .

How can one solve this for N <= 20 .