{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ITTQ7K4DH33U55SRPG5ZLUPRD3","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":"193d90d00c84b7470e15f2dba096b25c330e89bcb83f4d3da9c50f1ece1f3098","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-02T19:26:54Z","title_canon_sha256":"00e4ab8625c2a15a4e3ebf5c1af06f96ee80e146aefd8c0900ca686e576cfb54"},"schema_version":"1.0","source":{"id":"1606.00815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00815","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00815v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00815","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"ITTQ7K4DH33U","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ITTQ7K4DH33U55SR","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ITTQ7K4D","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:9631d2c242db64b8e9fbfa0c9869a3dff57f701bbc11f74cb07e4df8928d3793","target":"graph","created_at":"2026-05-18T01:13:00Z","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":"Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. Exact counting formulae are derived for DN codes. The special class of length a power of two is studied by means of Dickson polynomials, and is shown to contain families of codes with relative distances satisfying a modified Gilbert-Varshamov bound.","authors_text":"Adel Alahmadi, Hatoon Shohaib, Patrick Sol\\'e","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-02T19:26:54Z","title":"On self-dual double negacirculant codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00815","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":"sha256:27b10a9e6a5357c9a430785a456ac52b946a46494bf9783dce662c83569505bb","target":"record","created_at":"2026-05-18T01:13:00Z","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":"193d90d00c84b7470e15f2dba096b25c330e89bcb83f4d3da9c50f1ece1f3098","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-02T19:26:54Z","title_canon_sha256":"00e4ab8625c2a15a4e3ebf5c1af06f96ee80e146aefd8c0900ca686e576cfb54"},"schema_version":"1.0","source":{"id":"1606.00815","kind":"arxiv","version":1}},"canonical_sha256":"44e70fab833ef74ef65179bb95d1f11ed97ba587e8d4496efd6b78e942f349b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44e70fab833ef74ef65179bb95d1f11ed97ba587e8d4496efd6b78e942f349b1","first_computed_at":"2026-05-18T01:13:00.515919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.515919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9+42dVgBqbNYH5LpdLd9yxtaCem+k8vqQCB7a1wkl6DNse42DfKOtQTHTr0HIcu8+tMmEk5c5sV5+zej0dquAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.516290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27b10a9e6a5357c9a430785a456ac52b946a46494bf9783dce662c83569505bb","sha256:9631d2c242db64b8e9fbfa0c9869a3dff57f701bbc11f74cb07e4df8928d3793"],"state_sha256":"6515eed5a2d22ef2c85a70c946412713950df49a5f8ceeaa8be687ddce2b3d34"}