On the Secrecy Gain of Formally Unimodular Construction A4 Lattices

Abstract

Lattice coding for the Gaussian wiretap channel is considered, where the goal is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called secrecy gain was proposed as a design criterion to quantify the secrecy-goodness of the applied lattice code. In this paper, the theta series of the so-called formally unimodular lattices obtained by Construction A4 from codes over ${{\mathbb{Z}}_4}$ is derived, and we provide a universal approach to determine their secrecy gains. Initial results indicate that Construction A4 lattices can achieve a higher secrecy gain than the best-known formally unimodular lattices from the literature. Furthermore, a new code construction of formally self-dual ${{\mathbb{Z}}_4}$-linear codes is presented.