Jacobi forms over totally real fields and codes over \(\mathbb F_p\)
\textit{M. Broué} and \textit{M. Enguehard} [Ann. Sci. Éc. Norm. Supér. (4) 5, 157-181 (1972; Zbl 0254.94016)] studied a map between the space of invariant polynomials for a certain finite group and the ring of modular forms using the theta constants \(\theta_2(\tau)\) and \(\theta_3(\tau)\). This was generalized to codes over \(\mathbb F_p\) and Hilbert modular forms by \textit{W. Ebeling} [Lattices and codes. Braunschweig: Vieweg (1994; Zbl 0805.11048)]. In the paper under review the authors establish a connection between Hilbert-Jacobi forms over a totally real number field \(\mathbb Q(\zeta +\zeta^{-1})\), \(\zeta=e^{2\pi i/p}\), and codes over \(\mathbb F_p\) for an odd prime \(p\). In particular, they construct a theta series, which is a Jacobi form, from the complete weight enumerator or the Lee weight enumerator of a self-dual code over \(\mathbb F_p\).
scientific article; zbMATH DE number 1839966