Narain CFTs and error-correcting codes on finite fields

TL;DR

This paper establishes a novel connection between Narain conformal field theories and self-dual error-correcting codes over finite fields, enabling the analysis of spectral gaps via code properties.

Contribution

It introduces a method to construct Narain CFTs from self-dual codes over finite fields and relates their spectral properties to code characteristics.

Findings

Calculated spectral gaps for CFTs from codes

Compared code-based spectral gaps with the maximum among all Narain CFTs

Linked partition functions to code enumerator polynomials

Abstract

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.