# Does there exist a locality sensitive hashing for $\ell_p$-norm distance where $p>2$?

It is well known that the $$p$$-stable distribution can be used to generate locality sensitive hash code for $$\ell_p$$-norm distance measure where $$p \le 2$$. However, it seems that the situation for $$p>2$$ is not clear. Does there exist a locality sensitive hashing for $$\ell_p$$-norm distance where $$p>2$$? If not, what does it happen at the specific value $$p=2$$ that forms a "phase transition"?