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We consider lattice coding for the Gaussian wiretap channel, where thechallenge is to ensure reliable communication between two authorized partieswhile preventing an eavesdropper from learning the transmitted messages.Recently, a measure called the secrecy function of a lattice coding scheme wasproposed as a design criterion to characterize the eavesdropper's probabilityof correct decision. In this paper, the family of formally unimodular latticesis presented and shown to possess the same secrecy function behavior asunimodular and isodual lattices. Based on Construction A, we provide auniversal approach to determine the secrecy gain, i.e., the maximum value ofthe secrecy function, for formally unimodular lattices obtained from formallyself-dual codes. Furthermore, we show that formally unimodular lattices canachieve higher secrecy gain than the best-known unimodular lattices from theliterature.

The Secrecy Gain of Formally Unimodular Lattices on the Gaussian Wiretap Channel