arXiv subjects

João Strapasson

Publications and source records attributed to João Strapasson.

2 recordsLinked to original sources

arXiv2013

On projections of arbitrary lattices

In this paper we prove that given any two point lattices $Λ_1 \subset \mathbb{R}^n$ and $ Λ_2 \subset \nobreak \mathbb{R}^{n-k}$, there is a set of $k$ vectors $\bm{v}_i \in Λ_1$ such that $Λ_2$ is, up to similarity, arbitrarily close to the projection of $Λ_1$ onto the orthogonal complement of the subspace spanned by $\bm{v}_1, \ldots, \bm{v}_k$. This result extends the main theorem of \cite{Sloane2} and has applications in communication theory.

cs.CG↗

arXiv2013

On sequences of projections of the cubic lattice

In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}^{n+1}$ onto a hyperplane $\bm{v}^{\perp}$, with $\bm{v} \in \mathbb{Z}^{n+1}$ and converge to a target lattice $Λ$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices.

math.CO↗