{"paper":{"title":"Bounds and Constructions for $\\overline{3}$-Separable Codes with Length $3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haiyan Li, Jing Jiang, Minquan Cheng, Xiaohu Tang, Ying Miao","submitted_at":"2015-07-03T15:46:31Z","abstract_excerpt":"Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let $\\mathcal{C}$ be a code of length $n$ over an alphabet of $q$ letters. The descendant code ${\\sf desc}(\\mathcal{C}_0)$ of $\\mathcal{C}_0 = \\{{\\bf c}_1, {\\bf c}_2, \\ldots, {\\bf c}_t\\} \\subseteq {\\mathcal{C}}$ is defined to be the set of words ${\\bf x} = (x_1, x_2, \\ldots,x_n)^T$ such that $x_i \\in \\{c_{1,i}, c_{2,i}, \\ldots, c_{t,i}\\}$ for all $i=1, \\ldots, n$, where ${\\bf c}_j=(c_{j,1},c_{j,2},\\ldots,c_{j,n})^T$. $\\mathcal{C}$ is a $\\overline{t}$-separable code if for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00954","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"}