{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:N6C4WEYQTTDVEJV44R3JCEENI3","short_pith_number":"pith:N6C4WEYQ","schema_version":"1.0","canonical_sha256":"6f85cb13109cc75226bce47691108d46d7890471db836626a0aae27a8b7181de","source":{"kind":"arxiv","id":"2206.05256","version":4},"attestation_state":"computed","paper":{"title":"Generic Reed-Solomon Codes Achieve List-decoding Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Joshua Brakensiek, Sivakanth Gopi, Visu Makam","submitted_at":"2022-06-10T17:54:02Z","abstract_excerpt":"In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-$\\ell$ MDS code, denoted by $\\operatorname{MDS}(\\ell)$, has the property that any $\\ell$ subspaces formed from columns of its generator matrix intersect as minimally as possible. An independent work by Roth defined a different notion of higher order MDS codes as those achieving a generalized singleton bound for list-decoding. In this work, we show that these two notions of higher order MDS codes are (nearly) equivalent.\n  We also show that generic Reed-Solomon codes are $\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2206.05256","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-06-10T17:54:02Z","cross_cats_sorted":["cs.CC","math.CO","math.IT"],"title_canon_sha256":"c998df8a8508a292cc33f5e5f3ec1b90250ec75308907d764948d57537ece699","abstract_canon_sha256":"611966fccab67dedf27a0813ebaeeabf9ef9843744c4e0fe538e5bfce2384736"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:00:20.617263Z","signature_b64":"i16Y1YjXRmQi2ZsYE5uEvi9nsBF4nijZb05JjHBaqytrg+ae4tB0KMI2AcQD2HQd63GeG1Pekf4sFi2nsIJ0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f85cb13109cc75226bce47691108d46d7890471db836626a0aae27a8b7181de","last_reissued_at":"2026-07-05T09:00:20.616697Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:00:20.616697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic Reed-Solomon Codes Achieve List-decoding Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Joshua Brakensiek, Sivakanth Gopi, Visu Makam","submitted_at":"2022-06-10T17:54:02Z","abstract_excerpt":"In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-$\\ell$ MDS code, denoted by $\\operatorname{MDS}(\\ell)$, has the property that any $\\ell$ subspaces formed from columns of its generator matrix intersect as minimally as possible. An independent work by Roth defined a different notion of higher order MDS codes as those achieving a generalized singleton bound for list-decoding. In this work, we show that these two notions of higher order MDS codes are (nearly) equivalent.\n  We also show that generic Reed-Solomon codes are $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.05256","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/2206.05256/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":"2206.05256","created_at":"2026-07-05T09:00:20.616758+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.05256v4","created_at":"2026-07-05T09:00:20.616758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.05256","created_at":"2026-07-05T09:00:20.616758+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6C4WEYQTTDV","created_at":"2026-07-05T09:00:20.616758+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6C4WEYQTTDVEJV4","created_at":"2026-07-05T09:00:20.616758+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6C4WEYQ","created_at":"2026-07-05T09:00:20.616758+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":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3","json":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3.json","graph_json":"https://pith.science/api/pith-number/N6C4WEYQTTDVEJV44R3JCEENI3/graph.json","events_json":"https://pith.science/api/pith-number/N6C4WEYQTTDVEJV44R3JCEENI3/events.json","paper":"https://pith.science/paper/N6C4WEYQ"},"agent_actions":{"view_html":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3","download_json":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3.json","view_paper":"https://pith.science/paper/N6C4WEYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.05256&json=true","fetch_graph":"https://pith.science/api/pith-number/N6C4WEYQTTDVEJV44R3JCEENI3/graph.json","fetch_events":"https://pith.science/api/pith-number/N6C4WEYQTTDVEJV44R3JCEENI3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3/action/storage_attestation","attest_author":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3/action/author_attestation","sign_citation":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3/action/citation_signature","submit_replication":"https://pith.science/pith/N6C4WEYQTTDVEJV44R3JCEENI3/action/replication_record"}},"created_at":"2026-07-05T09:00:20.616758+00:00","updated_at":"2026-07-05T09:00:20.616758+00:00"}