Narain CFTs from nonbinary stabilizer codes
Abstract: We generalize the construction of Narain conformal field theories (CFTs) from qudit stabilizer codes to the construction from quantum stabilizer codes over the finite field of prime power order ($\mathbb{F}_{pm}$ with $p$ prime and $m\geq 1$) or over the ring $\mathbb{Z}_k$ with $k>1$. Our construction results in rational CFTs, which cover a larger set of points in the moduli space of Narain CFTs than the previous one. We also propose a correspondence between a quantum stabilizer code with non-zero logical qubits and a finite set of Narain CFTs. We illustrate the correspondence with well-known stabilizer codes.
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