# Subset of numbers whose XOR has least Hamming weight

I'm given $n$ numbers (let's say of some 100 bits or so). Is there a way to find a non-empty subset xor of these $n$ numbers which has the least Hamming weight (no. of set bits) in better than $O(2^n)$ complexity? I was thinking of some trie based implementation but don't think that will work at all. Would a dynamic programming approach work by any chance? If possible, a hint would be nice!

• Just making sure here - calculating the minimal distance of a (binary) linear code is finding the minimum no. of set bits in the XORs of each nonempty subset of the binary representations? – Indo Ubt May 20 '17 at 21:09