{"paper":{"title":"Bounds for the $l_1$-distance of $q$-ary lattices obtained via Constructions D, D$^{'}$ and $\\overline{D}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Eleonesio Strey, Sueli I. R. Costa","submitted_at":"2016-11-02T01:08:11Z","abstract_excerpt":"Lattices have been used in several problems in coding theory and cryptography. In this paper we approach $q$-ary lattices obtained via Constructions D, $\\D'$ and $\\overline{D}$. It is shown connections between Constructions D and $\\D'$. Bounds for the minimum $l_1$-distance of lattices $\\Lambda_{D}$, $\\Lambda_{D'}$ and $\\Lambda_{\\overline{D}}$ and, under certain conditions, a generator matrix for $\\Lambda_{D'}$ are presented. In addition, when the chain of codes used is closed under the zero-one addition, we derive explicit expressions for the minimum $l_1$-distances of the lattices $\\Lambda_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00435","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"}