{"paper":{"title":"Encoding and Indexing of Lattice Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brian M. Kurkoski","submitted_at":"2016-07-13T03:08:25Z","abstract_excerpt":"Encoding and indexing of lattice codes is generalized from self-similar lattice codes to a broader class of lattices. If coding lattice $\\Lambda_{\\textrm{c}}$ and shaping lattice $\\Lambda_{\\textrm{s}}$ satisfy $\\Lambda_{\\textrm{s}} \\subseteq \\Lambda_{\\textrm{c}}$, then $\\Lambda_{\\textrm{c}} / \\Lambda_{\\textrm{s}}$ is a quotient group that can be used to form a (nested) lattice code $\\mathcal{C}$. Conway and Sloane's method of encoding and indexing does not apply when the lattices are not self-similar. Results are provided for two classes of lattices. (1) If $\\Lambda_{\\textrm{c}}$ and $\\Lambda_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03581","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"}