This has been an undertaking, I present to you, a very very tunable Gaussian elimination unit in GF(2). This is essentially a state machine that copies over a partial permutated matrix from the other permutation unit, then it finds a non-zero coordinate for the current column, swaps, eliminates, and repeats. Afterwards, it does a hamming weight calculation to see if it’s equal to our needed weight, if yes then it stalls, otherwise it requests another matrix and restarts. The hardest part of this was making every parameter tunable, because doing so allows us to later use something like an evolutionary algorithm to reach a theoretical optimal design for a given dimension.