{"paper":{"title":"Triple cyclic codes over $\\mathbb{Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hojjat Mostafanasab","submitted_at":"2015-09-17T18:09:40Z","abstract_excerpt":"Let $r,s,t$ be three positive integers and $\\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\\mathbb{Z}_2$ if the set of coordinates can be partitioned into three parts that any cyclic shift of the coordinates of the parts leaves invariant the code. These codes can be considered as $\\mathbb{Z}_2[x]$-submodules of $\\frac{\\mathbb{Z}_2[x]}{\\langle x^r-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^s-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^t-1\\rangle}$. We give the minimal generating sets of this kind of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05351","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"}