If it's periodic, it's something orbiting something. If it's powerful enough to be seen 500 million ly away, one of the two orbiting objects is going to be a black hole.
I don't think either needs to be a black hole though. What I consider the most plausible candidate for emission is probably magnetars (i.e. neutron stars with extremely strong magnetic fields), and there's no reason the companion would need to be a black hole either, you just need a companion that gives a 16 day orbit and that's very easy to do with another star or neutron star.