I will introduce a new class of quantum error correcting codes that can be used to describe the large-N limit of a sequence of quantum theories. The main interest is in studying the large-N limit of quantum field theories with a gravitational dual, where expected features of the gravitational theory emerge from the quantum error correcting code. I will prove various asymptotic versions of well known operator algebra error correcting results, where arbitrary hyperfinite von Neumann algebras can live on the code. This includes an asymptotic information disturbance tradeoff theorem as well as asymptotic constraints on information theoretic quantities such as relative entropy and mutual information.
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