Formally unimodular packings for the Gaussian wiretap channel
This paper introduces the family of lattice-like packings, which generalizes lattices,
consisting of packings possessing periodicity and geometric uniformity. The subfamily of …
consisting of packings possessing periodicity and geometric uniformity. The subfamily of …
On LCD codes and lattices
LCD (linear complimentary dual) codes are linear codes that trivially intersect their duals.
We address the question of an equivalent concept for lattices. We observe basic properties …
We address the question of an equivalent concept for lattices. We observe basic properties …
On the Secrecy Gain of Extremal Even l-modular Lattices
The secrecy gain is a lattice invariant that appears in the context of wiretap lattice coding. It
has been studied for unimodular lattices, for 2−, 3−, and 5− modular lattices. This paper …
has been studied for unimodular lattices, for 2−, 3−, and 5− modular lattices. This paper …
Modular lattices from a variation of construction a over number fields
We consider a variation of Construction A of lattices from linear codes based on two classes
of number fields, totally real and CM Galois number fields. We propose a generic …
of number fields, totally real and CM Galois number fields. We propose a generic …
On the Secrecy Gain of -Modular Lattices
AM Ernvall-Hytonen, EV Vesalainen - SIAM Journal on Discrete Mathematics, 2018 - SIAM
We show that for every ℓ>1, there is a counterexample to the ℓ-modular secrecy function
conjecture by Oggier, Solé, and Belfiore IEEE Trans. Inform. Theory, 62 (2016), pp. 5690 …
conjecture by Oggier, Solé, and Belfiore IEEE Trans. Inform. Theory, 62 (2016), pp. 5690 …
On the secrecy gain of -modular lattices
EV Vesalainen, AM Ernvall-Hytönen - arxiv preprint arxiv:1708.09239, 2017 - arxiv.org
We show that for every $\ell> 1$, there is a counterexample to the $\ell $-modular secrecy
function conjecture by Oggier, Sol\'e and Belfiore. These counterexamples all satisfy the …
function conjecture by Oggier, Sol\'e and Belfiore. These counterexamples all satisfy the …
Construction of Arakelov-modular Lattices from Number Fields
X Hou - arxiv preprint arxiv:1609.03134, 2016 - arxiv.org
An Arakelov-modular lattice of level $\ell $, where $\ell $ is a positive integer, is an $\ell-$
modular lattice constructed from a fractional ideal of a CM field such that the lattice can be …
modular lattice constructed from a fractional ideal of a CM field such that the lattice can be …