{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PKC4HX5TZNQLLUSZRYZ64OWRCV","short_pith_number":"pith:PKC4HX5T","canonical_record":{"source":{"id":"1704.04083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-13T12:00:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ad094c0e7664fd359e243299df8be1113fbfb2dee289fb8d0fc4c54937984af7","abstract_canon_sha256":"6034582321906176a8f354d84e339c803dba846f6cd858922266a2e7df7e3ef8"},"schema_version":"1.0"},"canonical_sha256":"7a85c3dfb3cb60b5d2598e33ee3ad115551441d2473632ea8913009e79a5ae1f","source":{"kind":"arxiv","id":"1704.04083","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PKC4HX5TZNQLLUSZRYZ64OWRCV","target":"record","payload":{"canonical_record":{"source":{"id":"1704.04083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-13T12:00:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ad094c0e7664fd359e243299df8be1113fbfb2dee289fb8d0fc4c54937984af7","abstract_canon_sha256":"6034582321906176a8f354d84e339c803dba846f6cd858922266a2e7df7e3ef8"},"schema_version":"1.0"},"canonical_sha256":"7a85c3dfb3cb60b5d2598e33ee3ad115551441d2473632ea8913009e79a5ae1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:25.428446Z","signature_b64":"y+iUYrwpQueRxKS8ehlytqn8tOYl2olmZHFFSBcGsKacZiakfidjJvDxvkH7Nc7KvoDQ1CW8C1daosSN8Cu5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a85c3dfb3cb60b5d2598e33ee3ad115551441d2473632ea8913009e79a5ae1f","last_reissued_at":"2026-05-18T00:46:25.427909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:25.427909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.04083","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":"2026-05-18T00:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mfQVo+Zh+bf3hKHS9pI34vO4jXy4S8XVC5XP814DKvYhbvMvYh67gCj702I09bQOznCdAxcIxC+ui0dQdAIQCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T00:54:02.757840Z"},"content_sha256":"b199bc08421764cb429a54adafe45ff6c598bcdbc3a294b0d6e545e26d71d29d","schema_version":"1.0","event_id":"sha256:b199bc08421764cb429a54adafe45ff6c598bcdbc3a294b0d6e545e26d71d29d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PKC4HX5TZNQLLUSZRYZ64OWRCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructions of optimal LCD codes over large finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Lin Sok, Minjia Shi, Patrick Sol\\'e","submitted_at":"2017-04-13T12:00:13Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04083","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":"2026-05-18T00:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yctgMPyWHhT94Tbc0QAgpk701g+DzIRTfm+Vl9fmzehuZ/TfRz9ccifntVelEU0wv0uymdLSoLwyKC34a/dGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T00:54:02.758414Z"},"content_sha256":"0f8e703516694f13daae45a3006d7cd06c1a728171e6cb48e212dd625b693628","schema_version":"1.0","event_id":"sha256:0f8e703516694f13daae45a3006d7cd06c1a728171e6cb48e212dd625b693628"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/bundle.json","state_url":"https://pith.science/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/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":"2026-05-19T00:54:02Z","links":{"resolver":"https://pith.science/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV","bundle":"https://pith.science/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/bundle.json","state":"https://pith.science/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKC4HX5TZNQLLUSZRYZ64OWRCV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jdVuKTGORJUcwoQLGSZ4l/z9xK7c62e7VRL45AjXxJpfkB4WV/HEGzCnxCUSf7q5g3edmHBeluoezAM73gkUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T00:54:02.760244Z","bundle_sha256":"208eac0eaaf407c818b2d226ea98bcde1289be4da93e2f990d84e37a44fa5b41"}}