  In recent years quantum error correction(QEC) has become an important part of
AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC
holds in known holographic systems. The purpose of this paper is to fill this
gap by studying the error correcting properties of the fermionic sector of
various large $N$ theories. Specifically we examine $SU(N)$ matrix quantum
mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain
large gauge groups. We argue that gauge singlet states indeed form a quantum
error correcting code. Our considerations are based purely on large $N$
analysis and do not appeal to a particular form of Hamiltonian or holography.
