{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ADYN7UJIHJM5Y34OW356M5BH7R","short_pith_number":"pith:ADYN7UJI","schema_version":"1.0","canonical_sha256":"00f0dfd1283a59dc6f8eb6fbe67427fc4c913f4eb5c0664b859e8e033bf95c87","source":{"kind":"arxiv","id":"1810.11757","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Chen Yuan, Xianhua Niu","submitted_at":"2018-10-28T03:34:54Z","abstract_excerpt":"Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$ with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper bound on the size of a code from coding theory gives an upper bound on the size of a frequency hopping sequence set. Indeed, all upper bounds from coding theory have been converted to upper bounds on frequency hopping sequence sets (\\cite{Ding09}). On the other hand, a lower bound from coding theory does not automatically produce a lower bound for frequency hopping sequ"},"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":"1810.11757","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-28T03:34:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a40b7bda791ad95b1e66e7d963555fbce6d1ec894d505660eae15f7f1d6f0822","abstract_canon_sha256":"4b427dac8380548674d5af6b46da677a5ad04786c8fe16543ef0879205ff4d6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:03.028422Z","signature_b64":"XnUEWf2z5cxZNDiwIGUBIlCvrN3tMFk7290/L+uhruzGY/BEGq9GeyV9vNarOctyTaOSKBp1UCIcjTUtypiICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f0dfd1283a59dc6f8eb6fbe67427fc4c913f4eb5c0664b859e8e033bf95c87","last_reissued_at":"2026-05-18T00:02:03.027821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:03.027821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Chen Yuan, Xianhua Niu","submitted_at":"2018-10-28T03:34:54Z","abstract_excerpt":"Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$ with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper bound on the size of a code from coding theory gives an upper bound on the size of a frequency hopping sequence set. Indeed, all upper bounds from coding theory have been converted to upper bounds on frequency hopping sequence sets (\\cite{Ding09}). On the other hand, a lower bound from coding theory does not automatically produce a lower bound for frequency hopping sequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11757","kind":"arxiv","version":2},"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":"1810.11757","created_at":"2026-05-18T00:02:03.027910+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11757v2","created_at":"2026-05-18T00:02:03.027910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11757","created_at":"2026-05-18T00:02:03.027910+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADYN7UJIHJM5","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADYN7UJIHJM5Y34O","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADYN7UJI","created_at":"2026-05-18T12:32:13.499390+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/ADYN7UJIHJM5Y34OW356M5BH7R","json":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R.json","graph_json":"https://pith.science/api/pith-number/ADYN7UJIHJM5Y34OW356M5BH7R/graph.json","events_json":"https://pith.science/api/pith-number/ADYN7UJIHJM5Y34OW356M5BH7R/events.json","paper":"https://pith.science/paper/ADYN7UJI"},"agent_actions":{"view_html":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R","download_json":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R.json","view_paper":"https://pith.science/paper/ADYN7UJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11757&json=true","fetch_graph":"https://pith.science/api/pith-number/ADYN7UJIHJM5Y34OW356M5BH7R/graph.json","fetch_events":"https://pith.science/api/pith-number/ADYN7UJIHJM5Y34OW356M5BH7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R/action/storage_attestation","attest_author":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R/action/author_attestation","sign_citation":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R/action/citation_signature","submit_replication":"https://pith.science/pith/ADYN7UJIHJM5Y34OW356M5BH7R/action/replication_record"}},"created_at":"2026-05-18T00:02:03.027910+00:00","updated_at":"2026-05-18T00:02:03.027910+00:00"}