{"paper":{"title":"On projections of arbitrary lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CG","authors_text":"Antonio Campello, Jo\\~ao Strapasson, Sueli Costa","submitted_at":"2012-05-04T10:36:13Z","abstract_excerpt":"In this paper we prove that given any two point lattices $\\Lambda_1 \\subset \\mathbb{R}^n$ and $ \\Lambda_2 \\subset \\nobreak \\mathbb{R}^{n-k}$, there is a set of $k$ vectors $\\bm{v}_i \\in \\Lambda_1$ 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 $\\bm{v}_1, \\ldots, \\bm{v}_k$. This result extends the main theorem of \\cite{Sloane2} and has applications in communication theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0910","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}