{"paper":{"title":"Symmetric Disjunctive List-Decoding Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Arkadii D'yachkov, Ilya Vorobyev, Nikita Polyanskii, Vladislav Shchukin","submitted_at":"2014-10-30T14:48:58Z","abstract_excerpt":"A binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \\ge 2$, $L \\ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets can cover not more than $L-1$ other sets of the family. In this paper, we consider a similar class of binary codes which are based on a {\\em symmetric disjunctive sum} (SDS) of binary symbols. By definition, the symmetric disjunctive sum (SDS) takes values from the ternary alphabet $\\{0, 1, *\\}$, where the symbol~$*$ denotes \"erasure\". Namely: SDS is equal to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8385","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"}