On a Conjecture by Belfiore and Solé on Some Lattices

The point of this paper is to show that the secrecy function attains its maximum at $y=1$ on all known extremal unimodular lattices and on some possibly existing even extremal unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Furthermore, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.