{"paper":{"title":"Linear Sketching over $\\mathbb F_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Elchanan Mossel, Grigory Yaroslavtsev, Sampath Kannan","submitted_at":"2016-11-07T02:47:12Z","abstract_excerpt":"We initiate a systematic study of linear sketching over $\\mathbb F_2$. For a given Boolean function $f \\colon \\{0,1\\}^n \\to \\{0,1\\}$ a randomized $\\mathbb F_2$-sketch is a distribution $\\mathcal M$ over $d \\times n$ matrices with elements over $\\mathbb F_2$ such that $\\mathcal Mx$ suffices for computing $f(x)$ with high probability. We study a connection between $\\mathbb F_2$-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show that this communication game characterizes $\\mathbb F_2$-sketching under the uniform distribution (up to dependenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01879","kind":"arxiv","version":2},"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"}