English

On a conjecture by Belfiore and Sol\'e on some lattices

Information Theory 2011-04-22 v2 math.IT Number Theory

Abstract

The point of this note is to prove that the secrecy function attains its maximum at y=1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Sol\'e. Further, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.

Cite

@article{arxiv.1104.3739,
  title  = {On a conjecture by Belfiore and Sol\'e on some lattices},
  author = {Anne-Maria Ernvall-Hytönen},
  journal= {arXiv preprint arXiv:1104.3739},
  year   = {2011}
}

Comments

Abstract corrected, the case of a 16-dimensional lattice added, and several typos corrected

R2 v1 2026-06-21T17:56:07.439Z