{"paper":{"title":"Optimal few-weight codes from simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Qin Yue, Xiaomeng Zhu, Yansheng Wu","submitted_at":"2019-10-10T02:31:09Z","abstract_excerpt":"Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\\Bbb F_2+u\\Bbb F_2$ by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over $\\Bbb F_2+u\\Bbb F_2$. Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.04334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.04334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}