{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TTIVIW5FK4LWZMFWMM3HMVIA2F","short_pith_number":"pith:TTIVIW5F","canonical_record":{"source":{"id":"1604.03774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-13T13:55:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1147f721e6debf2aa41140c8d8088c8d15bddd6d9bb0b6dccb7856dd05bcf4f9","abstract_canon_sha256":"0cee01c566e313590017079e791ced42d73c911be2cae284fbb4c4d7b617f0b4"},"schema_version":"1.0"},"canonical_sha256":"9cd1545ba557176cb0b66336765500d16d0cbd16f24de2bb835b2b2c742aaaaf","source":{"kind":"arxiv","id":"1604.03774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03774","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03774v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03774","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"TTIVIW5FK4LW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TTIVIW5FK4LWZMFW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TTIVIW5F","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TTIVIW5FK4LWZMFWMM3HMVIA2F","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-13T13:55:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1147f721e6debf2aa41140c8d8088c8d15bddd6d9bb0b6dccb7856dd05bcf4f9","abstract_canon_sha256":"0cee01c566e313590017079e791ced42d73c911be2cae284fbb4c4d7b617f0b4"},"schema_version":"1.0"},"canonical_sha256":"9cd1545ba557176cb0b66336765500d16d0cbd16f24de2bb835b2b2c742aaaaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:11.113208Z","signature_b64":"f1fZsha0sC4Yh9Gw7K1kjRnV2HKzzWCW81GBYMG6IXW+ygfnnXuujaC6lXcwey+fBZNFz3EQ4ZcFlCH77fVwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd1545ba557176cb0b66336765500d16d0cbd16f24de2bb835b2b2c742aaaaf","last_reissued_at":"2026-05-18T01:17:11.112431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:11.112431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03774","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFwg60AyemJRSNKsp4K5jWCl9DwAlTdwwL+wi26x4EVSF7iaPH2f4zA5z9MmuvSXMBVDcYYGQiORx4/DaGnIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:38:37.195209Z"},"content_sha256":"de828ba885d24cbdacebbd0039744480687b245039f6c44b6faa07393893be44","schema_version":"1.0","event_id":"sha256:de828ba885d24cbdacebbd0039744480687b245039f6c44b6faa07393893be44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TTIVIW5FK4LWZMFWMM3HMVIA2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix-Product Complementary dual Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hualu Liu, Xiusheng Liu","submitted_at":"2016-04-13T13:55:40Z","abstract_excerpt":"Linear complementary dual codes (LCD) are linear codes satisfying $C\\cap C^{\\perp}=\\{0\\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some asymptotic results are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03774","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkLsJJSq/XhoZLYbZFC/7LhD6H0JLR/VajInGWz+y4TCXttB+AcA5/+u5xcWqoXp7PrQWDbmDHCWIhYdSSQtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:38:37.195564Z"},"content_sha256":"7f5cc294c0e34b61d919bad23544d70af6d626564a42fd2a0a98c7ec72add117","schema_version":"1.0","event_id":"sha256:7f5cc294c0e34b61d919bad23544d70af6d626564a42fd2a0a98c7ec72add117"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/bundle.json","state_url":"https://pith.science/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/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":"2026-06-05T11:38:37Z","links":{"resolver":"https://pith.science/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F","bundle":"https://pith.science/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/bundle.json","state":"https://pith.science/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTIVIW5FK4LWZMFWMM3HMVIA2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TTIVIW5FK4LWZMFWMM3HMVIA2F","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":"0cee01c566e313590017079e791ced42d73c911be2cae284fbb4c4d7b617f0b4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-13T13:55:40Z","title_canon_sha256":"1147f721e6debf2aa41140c8d8088c8d15bddd6d9bb0b6dccb7856dd05bcf4f9"},"schema_version":"1.0","source":{"id":"1604.03774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03774","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03774v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03774","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"TTIVIW5FK4LW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TTIVIW5FK4LWZMFW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TTIVIW5F","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:7f5cc294c0e34b61d919bad23544d70af6d626564a42fd2a0a98c7ec72add117","target":"graph","created_at":"2026-05-18T01:17:11Z","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":"Linear complementary dual codes (LCD) are linear codes satisfying $C\\cap C^{\\perp}=\\{0\\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some asymptotic results are derived.","authors_text":"Hualu Liu, Xiusheng Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-13T13:55:40Z","title":"Matrix-Product Complementary dual Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03774","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:de828ba885d24cbdacebbd0039744480687b245039f6c44b6faa07393893be44","target":"record","created_at":"2026-05-18T01:17:11Z","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":"0cee01c566e313590017079e791ced42d73c911be2cae284fbb4c4d7b617f0b4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-13T13:55:40Z","title_canon_sha256":"1147f721e6debf2aa41140c8d8088c8d15bddd6d9bb0b6dccb7856dd05bcf4f9"},"schema_version":"1.0","source":{"id":"1604.03774","kind":"arxiv","version":1}},"canonical_sha256":"9cd1545ba557176cb0b66336765500d16d0cbd16f24de2bb835b2b2c742aaaaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cd1545ba557176cb0b66336765500d16d0cbd16f24de2bb835b2b2c742aaaaf","first_computed_at":"2026-05-18T01:17:11.112431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:11.112431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1fZsha0sC4Yh9Gw7K1kjRnV2HKzzWCW81GBYMG6IXW+ygfnnXuujaC6lXcwey+fBZNFz3EQ4ZcFlCH77fVwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:11.113208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de828ba885d24cbdacebbd0039744480687b245039f6c44b6faa07393893be44","sha256:7f5cc294c0e34b61d919bad23544d70af6d626564a42fd2a0a98c7ec72add117"],"state_sha256":"89f7453f891348d2bdfda9c5928124b1f3d31f602134b723037b2548469a540d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O423x8GpppO0O5zI4KQe5FmwvRf2PhoSdBn7+CS49VsXjYibHfPpNvssmga7EyjJc4Fln1V1o+U8NE+ykWXUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:38:37.197505Z","bundle_sha256":"9233457bbb0041d397b06ab987849c4d577e62377b76d52c3a2b44fcbbb22937"}}