{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RDBKMNKWYXTF5BH4SQGRLA4KQK","short_pith_number":"pith:RDBKMNKW","schema_version":"1.0","canonical_sha256":"88c2a63556c5e65e84fc940d15838a828dc79f7559aa5319ffef17404bfdb1d3","source":{"kind":"arxiv","id":"2408.15925","version":3},"attestation_state":"computed","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 $L\\in[s]$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.15925","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-08-28T16:39:58Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"9d091ec7566238af51e171898170fe5e3f0e7c35d95f228164c426c60d0fbd79","abstract_canon_sha256":"9ed98eb625482779d77c84b880f5a7ac9c551e57633b0f154e449f82b55777b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:18.906251Z","signature_b64":"SZarFvvhg8g6NKgojuIsdXpa+NMTczvESyrhmEB2iSAeqOGbbj2WiS9JhoSrmEzEQ22qxZXvROaC4beSwpMbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88c2a63556c5e65e84fc940d15838a828dc79f7559aa5319ffef17404bfdb1d3","last_reissued_at":"2026-07-05T10:48:18.905806Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:18.905806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.15925","created_at":"2026-07-05T10:48:18.905855+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.15925v3","created_at":"2026-07-05T10:48:18.905855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.15925","created_at":"2026-07-05T10:48:18.905855+00:00"},{"alias_kind":"pith_short_12","alias_value":"RDBKMNKWYXTF","created_at":"2026-07-05T10:48:18.905855+00:00"},{"alias_kind":"pith_short_16","alias_value":"RDBKMNKWYXTF5BH4","created_at":"2026-07-05T10:48:18.905855+00:00"},{"alias_kind":"pith_short_8","alias_value":"RDBKMNKW","created_at":"2026-07-05T10:48:18.905855+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07308","citing_title":"Explicit Codes approaching Generalized Singleton Bound using Expanders","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK","json":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK.json","graph_json":"https://pith.science/api/pith-number/RDBKMNKWYXTF5BH4SQGRLA4KQK/graph.json","events_json":"https://pith.science/api/pith-number/RDBKMNKWYXTF5BH4SQGRLA4KQK/events.json","paper":"https://pith.science/paper/RDBKMNKW"},"agent_actions":{"view_html":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK","download_json":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK.json","view_paper":"https://pith.science/paper/RDBKMNKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.15925&json=true","fetch_graph":"https://pith.science/api/pith-number/RDBKMNKWYXTF5BH4SQGRLA4KQK/graph.json","fetch_events":"https://pith.science/api/pith-number/RDBKMNKWYXTF5BH4SQGRLA4KQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK/action/storage_attestation","attest_author":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK/action/author_attestation","sign_citation":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK/action/citation_signature","submit_replication":"https://pith.science/pith/RDBKMNKWYXTF5BH4SQGRLA4KQK/action/replication_record"}},"created_at":"2026-07-05T10:48:18.905855+00:00","updated_at":"2026-07-05T10:48:18.905855+00:00"}