Implement the reverse encoding to compute the Hamming distance

[emmorais]

This is an exploration of bit extraction.

In order to compute the Hamming distance between 2 polynomials a and b, we can encode one of those polynomials in the reverse order and then use polynomial multiplication to obtain the Hamming distance.

Let a_vec and b_vec be the 2 input vectors and we want to compute their Hamming distance. Assume their length is the same, and it is equal to SIZE.

• Reverse the order of vector elements from b_vec (the choice of second input instead of first is arbitrary).
• Encode both vectors as usual into cyclotomic polynomials.
• Polynomial multiplication gives another polynomial whose coefficient at position SIZE is the Hamming distance.