  Almheiri, Dong, and Harlow [arXiv:1411.7041] proposed a highly illuminating
connection between the AdS/CFT holographic correspondence and operator algebra
quantum error correction (OAQEC). Here we explore this connection further. We
derive some general results about OAQEC, as well as results that apply
specifically to quantum codes which admit a holographic interpretation. We
introduce a new quantity called `price', which characterizes the support of a
protected logical system, and find constraints on the price and the distance
for logical subalgebras of quantum codes. We show that holographic codes
defined on bulk manifolds with asymptotically negative curvature exhibit
`uberholography', meaning that a bulk logical algebra can be supported on a
boundary region with a fractal structure. We argue that, for holographic codes
defined on bulk manifolds with asymptotically flat or positive curvature, the
boundary physics must be highly nonlocal, an observation with potential
implications for black holes and for quantum gravity in AdS space at distance
scales small compared to the AdS curvature radius.
