Help with gaussian elimination in problem RECIPES

Im trying to do the RECIPES problem from November '18 long challenge.
I got the basic idea, that if I can find a subsequence with XORsum 0 I’m done, but looking for an algorithm to determine if such a sum exists, I was led to something called gaussian elimination.
I’m not aware of this method, and though perhaps I can myself google some articles on this, I would appreciate it if someone shared their solution/ideas on this problem.