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On the Secrecy Gain of Formally Unimodular Construction A_4 Lattices

02/18/2022
by   Maiara F. Bollauf, et al.
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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 A_4 from codes over ℤ_4 is derived, and we provide a universal approach to determine their secrecy gains. Initial results indicate that Construction 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 ℤ_4-linear codes is presented.

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