{"paper":{"title":"Explicit Folded Reed-Solomon and Multiplicity Codes Achieve Relaxed Generalized Singleton Bounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Yeyuan Chen, Zihan Zhang","submitted_at":"2024-08-28T16:39:58Z","abstract_excerpt":"In this paper, we prove that explicit FRS codes and multiplicity codes achieve relaxed generalized Singleton bounds for list size $L\\ge1.$ Specifically, we show the following: (1) FRS code of length $n$ and rate $R$ over the alphabet $\\mathbb{F}_q^s$ with distinct evaluation points is $\\left(\\frac{L}{L+1}\\left(1-\\frac{sR}{s-L+1}\\right),L\\right)$ list-decodable (LD) for list size $L\\in[s]$. (2) Multiplicity code of length $n$ and rate $R$ over the alphabet $\\mathbb{F}_p^s$ with distinct evaluation points is $\\left(\\frac{L}{L+1}\\left(1-\\frac{sR}{s-L+1}\\right),L\\right)$ LD for list size $L\\in[s]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15925","kind":"arxiv","version":3},"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/2408.15925/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"}