6 problems

Let $\Lambda$ be a formally unimodular lattice, with secrecy function $\Xi_{\Lambda}(\tau)$, and denote its secrecy gain by $\xi_{\Lambda}$. Formally unimodular secrecy-gain conjec…

Super-activation conjecture. There exist pairs $(\mathfrak W_1,\mathfrak V_1)$ and $(\mathfrak W_2,\mathfrak V_2)$ of finite AVWCs such that

Let $\Lambda$ be an $n$-dimensional unimodular lattice, and let $\Xi_{\Lambda}(y)$ be its secrecy function for $y>0$. The secrecy gain is…

Possible polarization dichotomy. Fix a $0<\delta<1$. There exists a partition of $\mathcal{S}_n$ into two sets $\mathcal{S}'_n$ and…

Two-point convex-hull conjecture. Any point in the convex hull of $\mathscr{C}$ can be expressed as the convex combination of only two points belonging to $\mathscr{C}$. This geome…

Let $U$ be the auxiliary random variable in the feedback-based collaborative secrecy encoding problem over binary symmetric channels. The preceding result establishes that $U$ can…