Conjecture on the secrecy gain of formally unimodular lattices

Let Λ\Lambda be a formally unimodular lattice, with secrecy function ΞΛ(τ)\Xi_{\Lambda}(\tau), and denote its secrecy gain by ξΛ\xi_{\Lambda}. Formally unimodular secrecy-gain conjecture. The secrecy function of Λ\Lambda achieves its maximum at τ=1\tau=1, namely

ξΛ=ΞΛ(1).\xi_{\Lambda}=\Xi_{\Lambda}(1).

The conjecture concerns whether the symmetry point remains the maximizing point for formally unimodular lattices, extending the preceding question beyond unimodular lattices; the source gives no resolution status.

Sources & referencesView supporting material

Primary source

Maiara F. Bollauf, Hsuan-Yin Lin and Øyvind Ytrehus, “The Secrecy Gain of Formally Unimodular Lattices on the Gaussian Wiretap Channel”, arXiv:2111.01439 (2021).

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