{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GIZUO5ERA7GWQFKOLBBRUQ6HE6","short_pith_number":"pith:GIZUO5ER","canonical_record":{"source":{"id":"1804.05516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-16T06:22:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"32553315d4356bf5363109944e6dee281848fc9cf3b0f48bc278b8c708ba6483","abstract_canon_sha256":"65995d66670109e71ce321a12e968738be4d486f10061949ed2bf4e9f1275681"},"schema_version":"1.0"},"canonical_sha256":"323347749107cd68154e58431a43c7278ad3016994aafb708008c44b119d247b","source":{"kind":"arxiv","id":"1804.05516","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05516","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05516v1","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05516","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"GIZUO5ERA7GW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GIZUO5ERA7GWQFKO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GIZUO5ER","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GIZUO5ERA7GWQFKOLBBRUQ6HE6","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-16T06:22:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"32553315d4356bf5363109944e6dee281848fc9cf3b0f48bc278b8c708ba6483","abstract_canon_sha256":"65995d66670109e71ce321a12e968738be4d486f10061949ed2bf4e9f1275681"},"schema_version":"1.0"},"canonical_sha256":"323347749107cd68154e58431a43c7278ad3016994aafb708008c44b119d247b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:27.963681Z","signature_b64":"AGOfDiA1EQViZXORhhYKr4HKOlc9rT7Bk0WobwLyUcGDEBCFHY2AT7F53VRLOhJ4k0AEc1mcDc3S73aEtlUQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"323347749107cd68154e58431a43c7278ad3016994aafb708008c44b119d247b","last_reissued_at":"2026-05-18T00:18:27.963291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:27.963291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05516","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlInUwxAiM6uPmJkuWJaAr56JcGv/P5atjx8Nb/ym5dC64Z24eAZZp7KeEHUFmfkRO+8PosYdTGXuEsniTAkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:19:32.953982Z"},"content_sha256":"b08e302c40f8f19861b43064e60b354f4fcda69ce111cc97d08e6cd51f3f6223","schema_version":"1.0","event_id":"sha256:b08e302c40f8f19861b43064e60b354f4fcda69ce111cc97d08e6cd51f3f6223"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GIZUO5ERA7GWQFKOLBBRUQ6HE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Subfield Codes of Ovoid Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Ziling Heng","submitted_at":"2018-04-16T06:22:25Z","abstract_excerpt":"Ovoids in $\\PG(3, \\gf(q))$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families of ovoids are known. The first is the elliptic quadratics and the second is the Tits ovoids. It is known that an ovoid in $\\PG(3, \\gf(q))$ corresponds to a $[q^2+1, 4, q^2-q]$ code over $\\gf(q)$, which is called an ovoid code. The objectives of this paper is to study the subfield codes of the two families of ovoid codes. The dimensions, minimum weights, and the weight distributions of the subfield codes of the elliptic quadric codes and Tits o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05516","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcQWlq8UuZh/+Sra9pSmUTff6L9iDWifIXDD0/T1Xhp4LDS9vsuxDEaaQ8lVxrkzQdvrrJsy/9Uif7RoYdJ5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:19:32.954606Z"},"content_sha256":"c2eda4afd80e0eeef3cf55091ecadf83ea08da42192c1796ed7a63e197fc819b","schema_version":"1.0","event_id":"sha256:c2eda4afd80e0eeef3cf55091ecadf83ea08da42192c1796ed7a63e197fc819b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/bundle.json","state_url":"https://pith.science/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T04:19:32Z","links":{"resolver":"https://pith.science/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6","bundle":"https://pith.science/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/bundle.json","state":"https://pith.science/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIZUO5ERA7GWQFKOLBBRUQ6HE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GIZUO5ERA7GWQFKOLBBRUQ6HE6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"65995d66670109e71ce321a12e968738be4d486f10061949ed2bf4e9f1275681","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-16T06:22:25Z","title_canon_sha256":"32553315d4356bf5363109944e6dee281848fc9cf3b0f48bc278b8c708ba6483"},"schema_version":"1.0","source":{"id":"1804.05516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05516","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05516v1","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05516","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"GIZUO5ERA7GW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GIZUO5ERA7GWQFKO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GIZUO5ER","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:c2eda4afd80e0eeef3cf55091ecadf83ea08da42192c1796ed7a63e197fc819b","target":"graph","created_at":"2026-05-18T00:18:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Ovoids in $\\PG(3, \\gf(q))$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families of ovoids are known. The first is the elliptic quadratics and the second is the Tits ovoids. It is known that an ovoid in $\\PG(3, \\gf(q))$ corresponds to a $[q^2+1, 4, q^2-q]$ code over $\\gf(q)$, which is called an ovoid code. The objectives of this paper is to study the subfield codes of the two families of ovoid codes. The dimensions, minimum weights, and the weight distributions of the subfield codes of the elliptic quadric codes and Tits o","authors_text":"Cunsheng Ding, Ziling Heng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-16T06:22:25Z","title":"The Subfield Codes of Ovoid Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05516","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b08e302c40f8f19861b43064e60b354f4fcda69ce111cc97d08e6cd51f3f6223","target":"record","created_at":"2026-05-18T00:18:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"65995d66670109e71ce321a12e968738be4d486f10061949ed2bf4e9f1275681","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-16T06:22:25Z","title_canon_sha256":"32553315d4356bf5363109944e6dee281848fc9cf3b0f48bc278b8c708ba6483"},"schema_version":"1.0","source":{"id":"1804.05516","kind":"arxiv","version":1}},"canonical_sha256":"323347749107cd68154e58431a43c7278ad3016994aafb708008c44b119d247b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"323347749107cd68154e58431a43c7278ad3016994aafb708008c44b119d247b","first_computed_at":"2026-05-18T00:18:27.963291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:27.963291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AGOfDiA1EQViZXORhhYKr4HKOlc9rT7Bk0WobwLyUcGDEBCFHY2AT7F53VRLOhJ4k0AEc1mcDc3S73aEtlUQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:27.963681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b08e302c40f8f19861b43064e60b354f4fcda69ce111cc97d08e6cd51f3f6223","sha256:c2eda4afd80e0eeef3cf55091ecadf83ea08da42192c1796ed7a63e197fc819b"],"state_sha256":"7a3cf122ea42631658593c4189048988b311a65c739526ef1c0c456b696cfff4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srKWfsahtVSYk6aHazpiiTc/d/mlnLueuVmbjag7t5V6a5Tz4thty3V7mQy2sGVbz8RwjCS4/uzbI/1oA/9tDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T04:19:32.958100Z","bundle_sha256":"10b05ab35e0d6e14b46ff949602ff8e4f9567ab245f42e547ff73f8fdd8b3252"}}