Narain CFTs and error-correcting codes on finite fields

We construct Narain CFTs from self-dual codes on the finite field F-p through even self-dual lattices for any prime p > 2. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error correction capability and the extended enumerator polynomial of the code. In particular, we calculate specific spectral gaps of CFTs constructed from codes and compare them with the largest spectral gap among all Narain CFTs.

Automated summary

This study constructs Narain CFTs using even self-dual lattices and self-dual codes, and examines the relationship between spectral gaps and partition functions of the CFTs and the error correction capability of the codes.