{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I4JPDRLJ7BROMXHDJOUCEEAERU","short_pith_number":"pith:I4JPDRLJ","schema_version":"1.0","canonical_sha256":"4712f1c569f862e65ce34ba82210048d0088cda9cd47891969d4e370650a947c","source":{"kind":"arxiv","id":"1406.0053","version":1},"attestation_state":"computed","paper":{"title":"Fast K\\\"otter-Nielsen-H{\\o}holdt Interpolation in the Guruswami-Sudan Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.IT"],"primary_cat":"cs.IT","authors_text":"Johan S. R. Nielsen","submitted_at":"2014-05-31T07:57:56Z","abstract_excerpt":"The K\\\"otter-Nielsen-H{\\o}holdt algorithm is a popular way to construct the bivariate interpolation polynomial in the Guruswami-Sudan decoding algorithm for Reed-Solomon codes. In this paper, we show how one can use Divide & Conquer techniques to provide an asymptotic speed-up of the algorithm, rendering its complexity quasi-linear in n. Several of our observations can also provide a practical speed-up to the classical version of the algorithm."},"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":"1406.0053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-31T07:57:56Z","cross_cats_sorted":["cs.SC","math.IT"],"title_canon_sha256":"fc9cd0fa16a883a4db33aa6936cf2b9658af442134410ff4634450cd84098427","abstract_canon_sha256":"e46c113407b3456caa440ade6d8edf079a0fba920fe60c893bac47e50a59c5f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.939958Z","signature_b64":"EyB11LyQB6K5ZHz1IxBT8qwwviNhtNMUxkq6E/oCR9olywyx/5dJOKtu4QeD+zcxBWkG1KpsVGOIa+P5Lna4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4712f1c569f862e65ce34ba82210048d0088cda9cd47891969d4e370650a947c","last_reissued_at":"2026-05-18T02:50:41.939289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.939289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast K\\\"otter-Nielsen-H{\\o}holdt Interpolation in the Guruswami-Sudan Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.IT"],"primary_cat":"cs.IT","authors_text":"Johan S. R. Nielsen","submitted_at":"2014-05-31T07:57:56Z","abstract_excerpt":"The K\\\"otter-Nielsen-H{\\o}holdt algorithm is a popular way to construct the bivariate interpolation polynomial in the Guruswami-Sudan decoding algorithm for Reed-Solomon codes. In this paper, we show how one can use Divide & Conquer techniques to provide an asymptotic speed-up of the algorithm, rendering its complexity quasi-linear in n. Several of our observations can also provide a practical speed-up to the classical version of the algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0053","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1406.0053","created_at":"2026-05-18T02:50:41.939399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0053v1","created_at":"2026-05-18T02:50:41.939399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0053","created_at":"2026-05-18T02:50:41.939399+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4JPDRLJ7BRO","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4JPDRLJ7BROMXHD","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4JPDRLJ","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU","json":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU.json","graph_json":"https://pith.science/api/pith-number/I4JPDRLJ7BROMXHDJOUCEEAERU/graph.json","events_json":"https://pith.science/api/pith-number/I4JPDRLJ7BROMXHDJOUCEEAERU/events.json","paper":"https://pith.science/paper/I4JPDRLJ"},"agent_actions":{"view_html":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU","download_json":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU.json","view_paper":"https://pith.science/paper/I4JPDRLJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0053&json=true","fetch_graph":"https://pith.science/api/pith-number/I4JPDRLJ7BROMXHDJOUCEEAERU/graph.json","fetch_events":"https://pith.science/api/pith-number/I4JPDRLJ7BROMXHDJOUCEEAERU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU/action/storage_attestation","attest_author":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU/action/author_attestation","sign_citation":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU/action/citation_signature","submit_replication":"https://pith.science/pith/I4JPDRLJ7BROMXHDJOUCEEAERU/action/replication_record"}},"created_at":"2026-05-18T02:50:41.939399+00:00","updated_at":"2026-05-18T02:50:41.939399+00:00"}