{"paper":{"title":"Lower Bound on the Redundancy of PIR Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Vardy, Sankeerth Rao","submitted_at":"2016-05-06T09:23:53Z","abstract_excerpt":"We prove that the redundancy of a $k$-server PIR code of dimension $s$ is $\\Omega(\\sqrt{s})$ for all $k \\ge 3$. This coincides with a known upper bound of $O(\\sqrt{s})$ on the redundancy of PIR codes. Moreover, for $k=3$ and $k = 4$, we determine the lowest possible redundancy of $k$-server PIR codes exactly. Similar results were proved independently by Mary Wootters using a different method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01869","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"}