On the secrecy gain of $\ell$-modular lattices
Information Theory
2017-09-12 v3 math.IT
Number Theory
Abstract
We show that for every , there is a counterexample to the -modular secrecy function conjecture by Oggier, Sol\'e and Belfiore. These counterexamples all satisfy the modified conjecture by Ernvall-Hyt\"onen and Sethuraman. Furthermore, we provide a method to prove or disprove the modified conjecture for any given -modular lattice rationally equivalent to a suitable amount of copies of with . We also provide a variant of the method for strongly -modular lattices when .
Keywords
Cite
@article{arxiv.1708.09239,
title = {On the secrecy gain of $\ell$-modular lattices},
author = {Esa V. Vesalainen and Anne-Maria Ernvall-Hytönen},
journal= {arXiv preprint arXiv:1708.09239},
year = {2017}
}