{"paper":{"title":"Quantizing Using Lattice Intersections","license":"","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"B. Beferull-Lozano, N. J. A. Sloane","submitted_at":"2002-07-17T18:52:22Z","abstract_excerpt":"The usual quantizer based on an n-dimensional lattice L maps a point x in R^n to a closest lattice point. Suppose L is the intersection of lattices L_1, ..., L_r. Then one may instead combine the information obtained by simultaneously quantizing x with respect to each of the L_i. This corresponds to decomposing R^n into a honeycomb of cells which are the intersections of the Voronoi cells for the L_i, and identifying the cell to which x belongs. This paper shows how to write several standard lattices (the face-centered and body-centered cubic lattices, the root lattices D_4, E_6*, E_8, the Cox"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207147","kind":"arxiv","version":1},"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"}