Elliptic genera from classical error-correcting codes

Abstract

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 U(1) current of the $$ \mathcal{N} $$ N = 2 superconformal algebra to obtain the U(1)-graded partition function that is invariant under the modular transformation and the spectral flow. We demonstrate our method by constructing extremal $$ \mathcal{N} $$ N = 2 elliptic genera from classical codes for relatively small central charges. Also, we give near-extremal elliptic genera and decompose them into $$ \mathcal{N} $$ N = 2 superconformal characters.