{"paper":{"title":"C-Codes: Cyclic Lowest-Density MDS Array Codes Constructed Using Starters for RAID 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Jiwu Shu, Mingqiang Li","submitted_at":"2011-04-13T16:51:36Z","abstract_excerpt":"The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying connections between C-Codes (or quasi-C-Codes) and starters in group theory are revealed. It is shown that each C-Code (or quasi-C-Code) of length $2n$ can be constructed using an even starter (or even multi-starter) in $(Z_{2n},+)$. It is also shown that each C-Code (or quasi-C-Code) has a twin C-Code (or quasi-C-Code). Then, four infinite families (three o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2547","kind":"arxiv","version":5},"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"}