Codes over rings, complex lattices and Hermitian modular forms (Q1765600)

The authors develop a theory of codes over the finite ring \(S_{2m} = {\mathbb Z}_{2m} + i{\mathbb Z}_{2m}\). They consider complete, symmetrized and complete joint weight enumerators of these codes and their duals. A connection between self-dual codes and complex unimodular lattices over the Gaussian integers \({\mathbb Z}[i]\) is studied. A theory of shadows for lattices and codes over \(S_{2m}\) is developed. A set of weight enumerators is used to construct Hermitian Jacobi forms and Hermitian modular forms.