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 $\text{A}_4$ from codes over $\mathbb{Z}_4$ is derived, and we provide a universal approach to determine their secrecy gains. Initial results indicate that Construction $\text{A}_4$ 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.

翻译：Gaussian 窃听频道的Lattice 编码是考虑的,其目的是确保两个被授权方之间的可靠通信,同时防止窃听者学习发送的信息。 最近,提出了称为保密收益的措施,作为量化应用的 Lattice 代码的保密性的设计标准。 本文介绍了建筑公司从$\ text{A ⁇ 4$以上代码中获取的所谓正式单式拖拉机系列,我们提供了一种通用的方法来确定其保密收益。 初步结果表明, 建筑公司 $\ text{A ⁇ 4$ lattices 能够实现比文献中最著名的正式的单式隐性拉特克的保密收益更高的保密收益。 此外,还介绍了一套正式的自定义$\mathbb ⁇ 4$线性代码。