关于形式幺模构造$\text{A}_4$格的秘密增益
On the Secrecy Gain of Formally Unimodular Construction $\text{A}_4$ Lattices
摘要：
被认为是高斯窃听信道的格编码，其目标是确保两个授权方之间的可靠通信，同时防止窃听者从学习传输的消息。最近，一种称为保密增益的措施被提出作为设计准则来量化所应用的格码的保密性。本文推导了由$\mathbb{Z}_4$上的码构造$\text{A}_4$得到的所谓形式幺模格的θ级数，并给出了确定其保密增益的一种通用方法.初步结果表明，构造$\text{A}_4$格可以实现更高的保密增益比最有名的形式么模格从文献中。此外，还提出了一种新的形式自对偶$\mathbb{Z}_4$ -线性码的构造方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
