{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:NNWALOF5COBT6DC2GWMBZNQYMX","short_pith_number":"pith:NNWALOF5","schema_version":"1.0","canonical_sha256":"6b6c05b8bd13833f0c5a35981cb61865d3e7b2765c6ecb7d697dd0eb8ce98fba","source":{"kind":"arxiv","id":"1010.5291","version":1},"attestation_state":"computed","paper":{"title":"New Class of Optimal Frequency-Hopping Sequences by Polynomial Residue Class Rings","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shaohui Sun, Wenping Ma","submitted_at":"2010-10-26T00:44:54Z","abstract_excerpt":"In this paper, using the theory of polynomial residue class rings, a new construction is proposed for frequency hopping patterns having optimal Hamming autocorrelation with respect to the well-known $Lempel$-$Greenberger$ bound. Based on the proposed construction, many new $Peng$-$Fan$ optimal families of frequency hopping sequences are obtained. The parameters of these sets of frequency hopping sequences are new and flexible."},"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":"1010.5291","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2010-10-26T00:44:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e7d3aae93cb5e3acd177a439d94fa270b87a1f818b60c781ff430c1966b7044a","abstract_canon_sha256":"b28feaac4688fee318688090be98a4268a0c26ca111cfa811016950a236515f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:39.081277Z","signature_b64":"RAizWh2+/20rdeS8gHwJU8WbZE/iIpy7xE7cAbCicXBrLXDp3UEtFV55s1ynaI2W5ddan7lQOXEgxsgmpP2PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b6c05b8bd13833f0c5a35981cb61865d3e7b2765c6ecb7d697dd0eb8ce98fba","last_reissued_at":"2026-05-18T04:38:39.080590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:39.080590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Class of Optimal Frequency-Hopping Sequences by Polynomial Residue Class Rings","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shaohui Sun, Wenping Ma","submitted_at":"2010-10-26T00:44:54Z","abstract_excerpt":"In this paper, using the theory of polynomial residue class rings, a new construction is proposed for frequency hopping patterns having optimal Hamming autocorrelation with respect to the well-known $Lempel$-$Greenberger$ bound. Based on the proposed construction, many new $Peng$-$Fan$ optimal families of frequency hopping sequences are obtained. The parameters of these sets of frequency hopping sequences are new and flexible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5291","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":"1010.5291","created_at":"2026-05-18T04:38:39.080687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5291v1","created_at":"2026-05-18T04:38:39.080687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5291","created_at":"2026-05-18T04:38:39.080687+00:00"},{"alias_kind":"pith_short_12","alias_value":"NNWALOF5COBT","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"NNWALOF5COBT6DC2","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"NNWALOF5","created_at":"2026-05-18T12:26:10.704358+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/NNWALOF5COBT6DC2GWMBZNQYMX","json":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX.json","graph_json":"https://pith.science/api/pith-number/NNWALOF5COBT6DC2GWMBZNQYMX/graph.json","events_json":"https://pith.science/api/pith-number/NNWALOF5COBT6DC2GWMBZNQYMX/events.json","paper":"https://pith.science/paper/NNWALOF5"},"agent_actions":{"view_html":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX","download_json":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX.json","view_paper":"https://pith.science/paper/NNWALOF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5291&json=true","fetch_graph":"https://pith.science/api/pith-number/NNWALOF5COBT6DC2GWMBZNQYMX/graph.json","fetch_events":"https://pith.science/api/pith-number/NNWALOF5COBT6DC2GWMBZNQYMX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX/action/storage_attestation","attest_author":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX/action/author_attestation","sign_citation":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX/action/citation_signature","submit_replication":"https://pith.science/pith/NNWALOF5COBT6DC2GWMBZNQYMX/action/replication_record"}},"created_at":"2026-05-18T04:38:39.080687+00:00","updated_at":"2026-05-18T04:38:39.080687+00:00"}