Construction and secrecy gain of a family of 5-modular lattices

The secrecy gain of a lattice is a lattice invariant used to characterize wiretap lattice codes for Gaussian channels. The secrecy gain has been classified for unimodular lattices up to dimension 23, and so far, a few sparse examples are known for l-modular lattices, with l = 2, 3. We propose some constructions of 5-modular lattices via the Construction A of lattices from linear codes, and study the secrecy gain of the resulting lattices.