{"paper":{"title":"Linear $(2,p,p)$-AONTs do Exist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Jie Cui, Lijun Ji, Xin Wang","submitted_at":"2018-04-26T05:11:37Z","abstract_excerpt":"A $(t,s,v)$-all-or-nothing transform (AONT) is a bijective mapping defined on $s$-tuples over an alphabet of size $v$, which satisfies that if any $s-t$ of the $s$ outputs are given, then the values of any $t$ inputs are completely undetermined. When $t$ and $v$ are fixed, to determine the maximum integer $s$ such that a $(t,s,v)$-AONT exists is the main research objective. In this paper, we solve three open problems proposed in [IEEE Trans. Inform. Theory 64 (2018), 3136-3143.] and show that there do exist linear $(2,p,p)$-AONTs. Then for the size of the alphabet being a prime power, we give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10491","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"}