{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PKC4HX5TZNQLLUSZRYZ64OWRCV","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":"6034582321906176a8f354d84e339c803dba846f6cd858922266a2e7df7e3ef8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-13T12:00:13Z","title_canon_sha256":"ad094c0e7664fd359e243299df8be1113fbfb2dee289fb8d0fc4c54937984af7"},"schema_version":"1.0","source":{"id":"1704.04083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.04083","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.04083v1","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04083","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"PKC4HX5TZNQL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PKC4HX5TZNQLLUSZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PKC4HX5T","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0f8e703516694f13daae45a3006d7cd06c1a728171e6cb48e212dd625b693628","target":"graph","created_at":"2026-05-18T00:46:25Z","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":"In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.","authors_text":"Lin Sok, Minjia Shi, Patrick Sol\\'e","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-13T12:00:13Z","title":"Constructions of optimal LCD codes over large finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04083","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:b199bc08421764cb429a54adafe45ff6c598bcdbc3a294b0d6e545e26d71d29d","target":"record","created_at":"2026-05-18T00:46:25Z","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":"6034582321906176a8f354d84e339c803dba846f6cd858922266a2e7df7e3ef8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-13T12:00:13Z","title_canon_sha256":"ad094c0e7664fd359e243299df8be1113fbfb2dee289fb8d0fc4c54937984af7"},"schema_version":"1.0","source":{"id":"1704.04083","kind":"arxiv","version":1}},"canonical_sha256":"7a85c3dfb3cb60b5d2598e33ee3ad115551441d2473632ea8913009e79a5ae1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a85c3dfb3cb60b5d2598e33ee3ad115551441d2473632ea8913009e79a5ae1f","first_computed_at":"2026-05-18T00:46:25.427909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:25.427909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+iUYrwpQueRxKS8ehlytqn8tOYl2olmZHFFSBcGsKacZiakfidjJvDxvkH7Nc7KvoDQ1CW8C1daosSN8Cu5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:25.428446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.04083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b199bc08421764cb429a54adafe45ff6c598bcdbc3a294b0d6e545e26d71d29d","sha256:0f8e703516694f13daae45a3006d7cd06c1a728171e6cb48e212dd625b693628"],"state_sha256":"dfb67ed96c2721ee21d9d6b8cde3f47436104ad15222c6e55cdd9b1761e54203"}