We consider chiral fermionic conformal field theories constructed from classical error-correcting codes and provide a systematic way of computing their elliptic genera. We exploit the $\mathrm{ U}(1)$ current of the $\mathcal{ N}=2$ superconformal algebra to obtain the $\mathrm{ U}(1)$-graded partition function that is invariant under the modular transformation and the spectral flow. We demonstrate our method by constructing extremal $\mathcal{ N}=2$ elliptic genera from classical codes for relatively small central charges. Also, we give near-extremal elliptic genera and decompose them into $\mathcal{ N}=2$ superconformal characters.
Categories: hep-th