The Belfiore-Sole ́ Conjecture and a Certain Technique for Verifying it for a Given Lattice

Abstract—We discuss a technique provided by Ernvall-Hytónen for verifying the Belfiore-Sole ́ conjecture for unimodular lattices, a conjecture that arises in the theory of wiretap lattice codes for the Gaussian channel. We provide an alternative proof of a key lemma of Ernvall-Hytónen that avoids dependence on a machine for verification, and as a further example of the technique, we verify the Belfiore-Sole ́ conjecture for unimodular lattices in dimension 34 that arise from certain binary [34, 17, 6] codes, which includes some with trivial automorphism group. I