Jacobi forms over totally real fields and codes over ${\mathbb F}_p$

Abstract

In this paper we establish a connection between Jacobi forms over a totally real field $k=\mathbb{Q}(\zeta+\zeta^{-1}) $, $\zeta=e^{2 \pi i/p}$, and codes over the field ${\mathbb F}_p$. In particular, we derive a theta series, which is a Jacobi form, from the complete weight enumerator or the Lee weight enumerator of a self-dual code over ${\mathbb F}_p$.