{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FDVUKMURVKNRA3SXHFMDCYI2C4","short_pith_number":"pith:FDVUKMUR","canonical_record":{"source":{"id":"1109.0628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-03T15:30:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5a358a05f039d529630a9b4abbacabc6c3b870140b52e4ca0b24b3e806f77ec5","abstract_canon_sha256":"7d98dbd0d5e6cd0a63c7748f6fd9b4e1a460346ee55c501c4df7835fec0e423a"},"schema_version":"1.0"},"canonical_sha256":"28eb453291aa9b106e57395831611a1726d8cc990e74f103592403c648a255f9","source":{"kind":"arxiv","id":"1109.0628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0628","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0628v1","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0628","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"FDVUKMURVKNR","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FDVUKMURVKNRA3SX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FDVUKMUR","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FDVUKMURVKNRA3SXHFMDCYI2C4","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-03T15:30:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5a358a05f039d529630a9b4abbacabc6c3b870140b52e4ca0b24b3e806f77ec5","abstract_canon_sha256":"7d98dbd0d5e6cd0a63c7748f6fd9b4e1a460346ee55c501c4df7835fec0e423a"},"schema_version":"1.0"},"canonical_sha256":"28eb453291aa9b106e57395831611a1726d8cc990e74f103592403c648a255f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:36.965704Z","signature_b64":"Ac4oELjaZNAJ51Y8ynNOx/VfFFeqG3dlhZdaA873+ytlkKxi0PP1vA4bC5CjSXHQpysH6J4mtdCGHaENdmNzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28eb453291aa9b106e57395831611a1726d8cc990e74f103592403c648a255f9","last_reissued_at":"2026-05-18T02:21:36.965168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:36.965168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0628","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrRx01ox13kAay9yOoSwAgLkRHwjepcBV9AmVbKFp/VAeBO327fy4TrQtGqEgWWQ2/SWeCipjhFoLIHSTcGtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:56:13.541066Z"},"content_sha256":"81317fe2b540497ed35e264b23c56e93e4f9f301ca98f8ea9af377c2c0202b3b","schema_version":"1.0","event_id":"sha256:81317fe2b540497ed35e264b23c56e93e4f9f301ca98f8ea9af377c2c0202b3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FDVUKMURVKNRA3SXHFMDCYI2C4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Weight Distributions of Cyclic Codes and Elliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Baocheng Wang, Chunming Tang, Maozhi Xu, Yanfeng Qi, Yixian Yang","submitted_at":"2011-09-03T15:30:25Z","abstract_excerpt":"Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From elliptic curves, this paper determines the weight distributions of dual codes of cyclic codes with two zeros for a few more cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0628","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"am6adaitXL0ngoXfwd4niS/ZD7r4xNqN9h0Aaj0J5tI36G1gJmRgl1uz76prffUFHwKtduak7klvvEFH4zVGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:56:13.541434Z"},"content_sha256":"6e68e35d402b910e304daf35a7a70477054ee3b31946d2926456b00417354d70","schema_version":"1.0","event_id":"sha256:6e68e35d402b910e304daf35a7a70477054ee3b31946d2926456b00417354d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/bundle.json","state_url":"https://pith.science/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/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":"2026-06-03T09:56:13Z","links":{"resolver":"https://pith.science/pith/FDVUKMURVKNRA3SXHFMDCYI2C4","bundle":"https://pith.science/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/bundle.json","state":"https://pith.science/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FDVUKMURVKNRA3SXHFMDCYI2C4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FDVUKMURVKNRA3SXHFMDCYI2C4","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":"7d98dbd0d5e6cd0a63c7748f6fd9b4e1a460346ee55c501c4df7835fec0e423a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-03T15:30:25Z","title_canon_sha256":"5a358a05f039d529630a9b4abbacabc6c3b870140b52e4ca0b24b3e806f77ec5"},"schema_version":"1.0","source":{"id":"1109.0628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0628","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0628v1","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0628","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"FDVUKMURVKNR","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FDVUKMURVKNRA3SX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FDVUKMUR","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:6e68e35d402b910e304daf35a7a70477054ee3b31946d2926456b00417354d70","target":"graph","created_at":"2026-05-18T02:21:36Z","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":"Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From elliptic curves, this paper determines the weight distributions of dual codes of cyclic codes with two zeros for a few more cases.","authors_text":"Baocheng Wang, Chunming Tang, Maozhi Xu, Yanfeng Qi, Yixian Yang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-03T15:30:25Z","title":"The Weight Distributions of Cyclic Codes and Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0628","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":"sha256:81317fe2b540497ed35e264b23c56e93e4f9f301ca98f8ea9af377c2c0202b3b","target":"record","created_at":"2026-05-18T02:21:36Z","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":"7d98dbd0d5e6cd0a63c7748f6fd9b4e1a460346ee55c501c4df7835fec0e423a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-03T15:30:25Z","title_canon_sha256":"5a358a05f039d529630a9b4abbacabc6c3b870140b52e4ca0b24b3e806f77ec5"},"schema_version":"1.0","source":{"id":"1109.0628","kind":"arxiv","version":1}},"canonical_sha256":"28eb453291aa9b106e57395831611a1726d8cc990e74f103592403c648a255f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28eb453291aa9b106e57395831611a1726d8cc990e74f103592403c648a255f9","first_computed_at":"2026-05-18T02:21:36.965168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:36.965168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ac4oELjaZNAJ51Y8ynNOx/VfFFeqG3dlhZdaA873+ytlkKxi0PP1vA4bC5CjSXHQpysH6J4mtdCGHaENdmNzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:36.965704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81317fe2b540497ed35e264b23c56e93e4f9f301ca98f8ea9af377c2c0202b3b","sha256:6e68e35d402b910e304daf35a7a70477054ee3b31946d2926456b00417354d70"],"state_sha256":"13e04cd177af190af9fc931e3d89cc5e5b11d19ba857074193edf6b08261da8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9/jkZ2NdQM0hmbeoOP9fV4S1/8tZajSA2JOq0SN1Wnycg7i4suEjelFMaU64a1fetQWbKFGIUZFoL9NbZ9GAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:56:13.543400Z","bundle_sha256":"21614850b175ea5ceb0dfd0dd3c0d1013d5097f4a8e11ad4bbb44607507cafd9"}}