{"paper":{"title":"Fast list-decoding of univariate multiplicity and folded Reed-Solomon codes","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CC","math.IT"],"primary_cat":"cs.IT","authors_text":"Ashutosh Shankar, Mrinal Kumar, Prahladh Harsha, Rohan Goyal","submitted_at":"2023-11-29T17:46:17Z","abstract_excerpt":"We show that the known list-decoding algorithms for univariate multiplicity and folded Reed-Solomon codes can be made to run in $\\tilde{O}(n)$ time. Univariate multiplicity codes and FRS codes are natural variants of Reed-Solomon codes that were discovered and studied for their applications to list decoding. It is known that for every $\\epsilon>0$, and rate $r \\in (0,1)$, there exist explicit families of these codes that have rate $r$ and can be list decoded from a $(1-r-\\epsilon)$ fraction of errors with constant list size in polynomial time (Guruswami & Wang (IEEE Trans. Inform. Theory 2013)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17841","kind":"arxiv","version":4},"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/2311.17841/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"}