{"paper":{"title":"Optimal Equi-difference Conflict-avoiding Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Derong Xie, Jinquan Luo","submitted_at":"2018-09-25T03:17:02Z","abstract_excerpt":"An equi-differece conflict-avoiding code $(CAC^{e})\\ \\mathcal{C}$ of length $n$ and weight $\\omega$ is a collection of $\\omega$-subsets (called codewords) which has the form $\\{0,i,2i,\\cdots,(\\omega-1)i\\}$ of $\\mathbb{Z}_{n}$ such that $\\Delta(c_{1})\\cap\\Delta(c_{2})=\\emptyset$ holds for any $c_{1},\\ c_{2}\\in\\mathcal{C}$, $c_{1}\\neq c_{2}$ where $\\Delta(c)=\\{j-i \\ (\\mbox{mod}\\ n) \\; | \\; i,j\\in c,i\\neq j\\}.$ A code $\\mathcal{C}\\in CAC^{e}s$ with maximum code size for given $n$ and $\\omega$ is called optimal and is said to be perfect if $\\cup_{c\\in \\mathcal{C}}\\Delta(c)=\\mathbb{Z}_{n}\\backslash"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09300","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"}