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