{"paper":{"title":"New Bounds For Frameproof Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Chong Shangguan, Gennian Ge, Xin Wang, Ying Miao","submitted_at":"2014-11-21T07:47:09Z","abstract_excerpt":"Frameproof codes are used to fingerprint digital data. It can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for $w$-frameproof codes of length $N$ over an alphabet of size $q$. The upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction. Both bounds can improve previous results when $q$ is small compared to $w$, say $cq\\leq w$ for some constant $c\\leq q$. Furthermore, we pay special attention to binary frameproof codes. We show a binary $w$-frameproof code of length $N$ can not have more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5782","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"}