{"paper":{"title":"Near-Optimal List-Recovery of Linear Code Families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Nikhil Shagrithaya, Ray Li","submitted_at":"2025-02-19T17:02:36Z","abstract_excerpt":"We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets of size at least $\\ell^{\\Omega(1/\\varepsilon)}$, random linear codes of rate $R$ are $(1-R-\\varepsilon, \\ell, (\\ell/\\varepsilon)^{O(\\ell/\\varepsilon)})$-list-recoverable for all $R\\in(0,1)$ and $\\ell$. Together with a result of Levi, Mosheiff, and Shagrithaya, this implies that randomly punctured Reed-Solomon codes also achieve list-recovery capacity. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13877","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.13877/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}