{"paper":{"title":"Three-weight codes and the quintic construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Patrick Sol\\'e, Yan Liu","submitted_at":"2016-12-01T03:26:09Z","abstract_excerpt":"We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\\mathbb{F}_2 +v\\mathbb{F}_2 +v^2\\mathbb{F}_2 +v^3\\mathbb{F}_2 +v^4\\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic construction of binary quasi-cyclic codes. %The length of these codes depends on the degree $m$ of ring extension. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Given a linear Gray map, we obtain three families of binary abelian codes with few weights. In particular, we obtain a class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00126","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"}