  We study general maps from the space of rational CFTs with a fixed chiral
algebra and associated Chern-Simons (CS) theories to the space of qudit
stabilizer codes with a fixed generalized Pauli group. We consider certain
natural constraints on such a map and show that the map can be described as a
graph homomorphism from an orbifold graph, which captures the orbifold
structure of CFTs, to a code graph, which captures the structure of self-dual
stabilizer codes. By studying explicit examples, we show that this graph
homomorphism cannot always be a graph embedding. However, we construct a
physically motivated map from universal orbifold subgraphs of CFTs to operators
in a generalized Pauli group. We show that this map results in a self-dual
stabilizer code if and only if the surface operators in the bulk CS theories
corresponding to the CFTs in question are self-dual. For CFTs admitting a
stabilizer code description, we show that the full abelianized generalized
Pauli group can be obtained from twisted sectors of certain 0-form symmetries
of the CFT. Finally, we connect our construction with SymTFTs, and we argue
that many equivalences between codes that arise in our setup correspond to
equivalence classes of bulk topological surfaces under fusion with invertible
surfaces.
