{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4P5ASM57KPHDV6XEUOIQQIEHNM","short_pith_number":"pith:4P5ASM57","schema_version":"1.0","canonical_sha256":"e3fa0933bf53ce3afae4a3910820876b1a45baf81908745b151eaf82ffaffa09","source":{"kind":"arxiv","id":"1712.00137","version":1},"attestation_state":"computed","paper":{"title":"Maximal arcs and extended cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cunsheng Ding, Stefaan De Winter, Vladimir D. Tonchev","submitted_at":"2017-12-01T00:35:41Z","abstract_excerpt":"It is proved that for every $d\\ge 2$ such that $d-1$ divides $q-1$, where $q$ is a power of 2, there exists a Denniston maximal arc $A$ of degree $d$ in $\\PG(2,q)$, being invariant under a cyclic linear group that fixes one point of $A$ and acts regularly on the set of the remaining points of ${A}$. Two alternative proofs are given, one geometric proof based on Abatangelo-Larato's characterization of Denniston arcs, and a second coding-theoretical proof based on cyclotomy and the link between maximal arcs and two-weight codes."},"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":"1712.00137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-01T00:35:41Z","cross_cats_sorted":[],"title_canon_sha256":"a86a937d11b7fd454e8ba8942a5df4f59b553ec5a399fd75480d6b592bfa69c9","abstract_canon_sha256":"4fb694c2f57dee6bf8da3420cb21227ec9049701e2687677fac514915a90239d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:07.203631Z","signature_b64":"RSs5pD6+gPI9SIjDdNQV1k/MWrI101AjLQIVBwgMjembixj1rwiLcHrumo0DPvzFwL4vHYPLQet2x4/NhmADAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3fa0933bf53ce3afae4a3910820876b1a45baf81908745b151eaf82ffaffa09","last_reissued_at":"2026-05-18T00:29:07.202927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:07.202927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal arcs and extended cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cunsheng Ding, Stefaan De Winter, Vladimir D. Tonchev","submitted_at":"2017-12-01T00:35:41Z","abstract_excerpt":"It is proved that for every $d\\ge 2$ such that $d-1$ divides $q-1$, where $q$ is a power of 2, there exists a Denniston maximal arc $A$ of degree $d$ in $\\PG(2,q)$, being invariant under a cyclic linear group that fixes one point of $A$ and acts regularly on the set of the remaining points of ${A}$. Two alternative proofs are given, one geometric proof based on Abatangelo-Larato's characterization of Denniston arcs, and a second coding-theoretical proof based on cyclotomy and the link between maximal arcs and two-weight codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00137","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":"1712.00137","created_at":"2026-05-18T00:29:07.203054+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00137v1","created_at":"2026-05-18T00:29:07.203054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00137","created_at":"2026-05-18T00:29:07.203054+00:00"},{"alias_kind":"pith_short_12","alias_value":"4P5ASM57KPHD","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4P5ASM57KPHDV6XE","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4P5ASM57","created_at":"2026-05-18T12:31:00.734936+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/4P5ASM57KPHDV6XEUOIQQIEHNM","json":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM.json","graph_json":"https://pith.science/api/pith-number/4P5ASM57KPHDV6XEUOIQQIEHNM/graph.json","events_json":"https://pith.science/api/pith-number/4P5ASM57KPHDV6XEUOIQQIEHNM/events.json","paper":"https://pith.science/paper/4P5ASM57"},"agent_actions":{"view_html":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM","download_json":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM.json","view_paper":"https://pith.science/paper/4P5ASM57","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00137&json=true","fetch_graph":"https://pith.science/api/pith-number/4P5ASM57KPHDV6XEUOIQQIEHNM/graph.json","fetch_events":"https://pith.science/api/pith-number/4P5ASM57KPHDV6XEUOIQQIEHNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM/action/storage_attestation","attest_author":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM/action/author_attestation","sign_citation":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM/action/citation_signature","submit_replication":"https://pith.science/pith/4P5ASM57KPHDV6XEUOIQQIEHNM/action/replication_record"}},"created_at":"2026-05-18T00:29:07.203054+00:00","updated_at":"2026-05-18T00:29:07.203054+00:00"}