On projections of arbitrary lattices

Abstract

In this paper we prove that given any two point lattices ${\Lambda }_1\subset {\mathbb{R}}^n$ and ${\Lambda }_2\subset {\mathbb{R}}^{n-k}$, there is a set of $k$ vectors ${\mathbf{v}}_i\in {\Lambda }_1$ such that ${\Lambda }_2$ is, up to similarity, arbitrarily close to the projection of ${\Lambda }_1$ onto the orthogonal complement of the subspace spanned by ${\mathbf{v}}_1,\dots ,{\mathbf{v}}_k$. This result extends the main theorem of \cite{Sloane2} and has applications in communication theory.

11 pages

References in corpus (2)

• New upper bounds on sphere packings I
• Curves on torus layers and coding for continuous alphabet sources

Cited by in corpus (1)

• Well-Rounded Lattices via Polynomials