{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FAJTOYMZI6LXSFJPKJV4CRZ67F","short_pith_number":"pith:FAJTOYMZ","canonical_record":{"source":{"id":"1505.05576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-21T01:23:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"638fde72092c5410fde536ad0be3a1813c32134fbff457b32bde5b3bae1047fb","abstract_canon_sha256":"40c96d0d07df84836c382cc6df4a1090ea97b083877a347c03758ac286f60c62"},"schema_version":"1.0"},"canonical_sha256":"2813376199479779152f526bc1473ef94c20e2fbdf09b7e7863ddf48e5d2184a","source":{"kind":"arxiv","id":"1505.05576","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05576","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05576v3","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05576","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"FAJTOYMZI6LX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FAJTOYMZI6LXSFJP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FAJTOYMZ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FAJTOYMZI6LXSFJPKJV4CRZ67F","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-21T01:23:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"638fde72092c5410fde536ad0be3a1813c32134fbff457b32bde5b3bae1047fb","abstract_canon_sha256":"40c96d0d07df84836c382cc6df4a1090ea97b083877a347c03758ac286f60c62"},"schema_version":"1.0"},"canonical_sha256":"2813376199479779152f526bc1473ef94c20e2fbdf09b7e7863ddf48e5d2184a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.863902Z","signature_b64":"QiWJpxkgpT0BN3ZxyrQpQFlZ5RMkj4uFKyi+OTEYaOUyiUpwdIkdWnQE3AFTUTEksQrF97/eqH9srNaTyGm5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2813376199479779152f526bc1473ef94c20e2fbdf09b7e7863ddf48e5d2184a","last_reissued_at":"2026-05-18T01:19:53.863486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.863486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05576","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49edelpujAmtndT5I2gVMGMaqSIfgVTIPDYJ1cHDUQcok1pyOeeotx2P62GVZQCw383mhPE2cwQB7hWMZxx7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:21:23.429957Z"},"content_sha256":"e7bbd221f136315b1759e86dd2faedd3c40431b11f4bdbd25ff1ce509e33a207","schema_version":"1.0","event_id":"sha256:e7bbd221f136315b1759e86dd2faedd3c40431b11f4bdbd25ff1ce509e33a207"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FAJTOYMZI6LXSFJPKJV4CRZ67F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complete Weight Enumerator of Several Cyclic Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shudi Yang, Zheng-an Yao","submitted_at":"2015-05-21T01:23:49Z","abstract_excerpt":"Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime $p$, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding exponential sums. As applications of this general strategy, we determine the complete weight enumerator of several $p$-ary cyclic codes and give some examples to illustrate our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05576","kind":"arxiv","version":3},"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":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0tL3gTItfJvTs18oYW5ZpL+pqXteWuC6PsNuHAh8lm4RrVwVERKqeH1J76FD1uR6G1TN/e7twEBWwiQl0HKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:21:23.430380Z"},"content_sha256":"9084de907334344557a2ea7ca1f3797e40815e83005e06a975b1ef0b309b8373","schema_version":"1.0","event_id":"sha256:9084de907334344557a2ea7ca1f3797e40815e83005e06a975b1ef0b309b8373"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/bundle.json","state_url":"https://pith.science/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/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":"2026-05-27T16:21:23Z","links":{"resolver":"https://pith.science/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F","bundle":"https://pith.science/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/bundle.json","state":"https://pith.science/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FAJTOYMZI6LXSFJPKJV4CRZ67F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FAJTOYMZI6LXSFJPKJV4CRZ67F","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":"40c96d0d07df84836c382cc6df4a1090ea97b083877a347c03758ac286f60c62","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-21T01:23:49Z","title_canon_sha256":"638fde72092c5410fde536ad0be3a1813c32134fbff457b32bde5b3bae1047fb"},"schema_version":"1.0","source":{"id":"1505.05576","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05576","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05576v3","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05576","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"FAJTOYMZI6LX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FAJTOYMZI6LXSFJP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FAJTOYMZ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:9084de907334344557a2ea7ca1f3797e40815e83005e06a975b1ef0b309b8373","target":"graph","created_at":"2026-05-18T01:19:53Z","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 have attracted a lot of research interest for decades. In this paper, for an odd prime $p$, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding exponential sums. As applications of this general strategy, we determine the complete weight enumerator of several $p$-ary cyclic codes and give some examples to illustrate our results.","authors_text":"Shudi Yang, Zheng-an Yao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-21T01:23:49Z","title":"The Complete Weight Enumerator of Several Cyclic Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05576","kind":"arxiv","version":3},"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:e7bbd221f136315b1759e86dd2faedd3c40431b11f4bdbd25ff1ce509e33a207","target":"record","created_at":"2026-05-18T01:19:53Z","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":"40c96d0d07df84836c382cc6df4a1090ea97b083877a347c03758ac286f60c62","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-21T01:23:49Z","title_canon_sha256":"638fde72092c5410fde536ad0be3a1813c32134fbff457b32bde5b3bae1047fb"},"schema_version":"1.0","source":{"id":"1505.05576","kind":"arxiv","version":3}},"canonical_sha256":"2813376199479779152f526bc1473ef94c20e2fbdf09b7e7863ddf48e5d2184a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2813376199479779152f526bc1473ef94c20e2fbdf09b7e7863ddf48e5d2184a","first_computed_at":"2026-05-18T01:19:53.863486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.863486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QiWJpxkgpT0BN3ZxyrQpQFlZ5RMkj4uFKyi+OTEYaOUyiUpwdIkdWnQE3AFTUTEksQrF97/eqH9srNaTyGm5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.863902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05576","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7bbd221f136315b1759e86dd2faedd3c40431b11f4bdbd25ff1ce509e33a207","sha256:9084de907334344557a2ea7ca1f3797e40815e83005e06a975b1ef0b309b8373"],"state_sha256":"b4be9ad633f607551f1a07eefb60c4b276934785b8d21be0af9e3d8471c9234f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lag36O/yP9YZdsPgE81JAWi9Ea/6F2GcVv88JuYelaLngBtCFhFOR+HBBLoF5GVd0yObm5Ii4bHctvAmM7ZuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:21:23.433275Z","bundle_sha256":"a543a0dbc25a1dcbc180f2ba58cc1a50da3aeaabb66ca5b0c0bbf3b4353ff204"}}