{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PRKWJEAZ2L7BUVV3OS4VLEOBM7","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":"7025bb56de0277c8dbd8e3c4e8fbb9969ac2059cb6a2037c8a6492310fe0ab73","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-18T15:59:08Z","title_canon_sha256":"e95c5202b9b77139d0992d17d0f5e0555d2f2f08a93c6c180221b539d1588928"},"schema_version":"1.0","source":{"id":"1707.05716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05716","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05716v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05716","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"PRKWJEAZ2L7B","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PRKWJEAZ2L7BUVV3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PRKWJEAZ","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:4048df087d9c308246406ce300ac52aea91fb69ff6af1cc0ed2fd7f69dfc700c","target":"graph","created_at":"2026-05-18T00:40:01Z","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":"Self-dual cyclic codes form an important class of linear codes. It has been shown that there exists a self-dual cyclic code of length $n$ over a finite field if and only if $n$ and the field characteristic are even. The enumeration of such codes has been given under both the Euclidean and Hermitian products. However, in each case, the formula for self-dual cyclic codes of length $n$ over a finite field contains a characteristic function which is not easily computed. In this paper, we focus on more efficient ways to enumerate self-dual cyclic codes of lengths $2^\\nu p^r$ and $2^\\nu p^rq^s$, whe","authors_text":"Somphong Jitman, Supawadee Prugsapitak","cross_cats":["math.IT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-18T15:59:08Z","title":"Enumeration of Self-Dual Cyclic Codes of some Specific Lengths over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05716","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":"sha256:6d03305d300e86eff6f1ec9a6b1a1ec0c4c0b1911fd37c978f62e4373e129f59","target":"record","created_at":"2026-05-18T00:40:01Z","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":"7025bb56de0277c8dbd8e3c4e8fbb9969ac2059cb6a2037c8a6492310fe0ab73","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-18T15:59:08Z","title_canon_sha256":"e95c5202b9b77139d0992d17d0f5e0555d2f2f08a93c6c180221b539d1588928"},"schema_version":"1.0","source":{"id":"1707.05716","kind":"arxiv","version":1}},"canonical_sha256":"7c55649019d2fe1a56bb74b95591c167d95b88730ed45789b08719b551fefbe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c55649019d2fe1a56bb74b95591c167d95b88730ed45789b08719b551fefbe2","first_computed_at":"2026-05-18T00:40:01.636820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.636820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zsvfTS4i4DLBcrt/OPY+TRXbkpJedekBdWleMUL8ZtwfjnbZDmr22vM2MABt4JGm5AQs9ZomWoq1xFs7+up+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.637326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d03305d300e86eff6f1ec9a6b1a1ec0c4c0b1911fd37c978f62e4373e129f59","sha256:4048df087d9c308246406ce300ac52aea91fb69ff6af1cc0ed2fd7f69dfc700c"],"state_sha256":"0c7ff8f463fd23456f1b5144511896e3d5a99c2c7c620f8eb2397fefd01432fe"}