  When approximating binary similarity using the hamming distance between short
binary hashes, we show that even if the similarity is symmetric, we can have
shorter and more accurate hashes by using two distinct code maps. I.e. by
approximating the similarity between $x$ and $x'$ as the hamming distance
between $f(x)$ and $g(x')$, for two distinct binary codes $f,g$, rather than as
the hamming distance between $f(x)$ and $f(x')$.
