{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J47PA5G7C3TCWLI3TYIXVJDVBZ","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":"66d37cf8364634ae1fbe47770e844a1680ca2ff57313fa44f5cf8e5485b0c8c8","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-24T08:36:11Z","title_canon_sha256":"d91514d4361d77215c15e5d6b8571f2116a7cbb42d280a713429e1aa4d174aa8"},"schema_version":"1.0","source":{"id":"1906.09780","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09780","created_at":"2026-07-05T01:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09780v5","created_at":"2026-07-05T01:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09780","created_at":"2026-07-05T01:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"J47PA5G7C3TC","created_at":"2026-07-05T01:00:12Z"},{"alias_kind":"pith_short_16","alias_value":"J47PA5G7C3TCWLI3","created_at":"2026-07-05T01:00:12Z"},{"alias_kind":"pith_short_8","alias_value":"J47PA5G7","created_at":"2026-07-05T01:00:12Z"}],"graph_snapshots":[{"event_id":"sha256:18354a4b0939b73da67099c8641db905a434f28dbd0eadbe15cf8d4e288f6647","target":"graph","created_at":"2026-07-05T01:00:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1906.09780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Constant dimension codes are used for error control in random linear network coding, so that constructions for these codes with large cardinality have achieved wide attention in the last decade. Here, we improve the so-called linkage construction. Known upper bounds for constant dimension codes containing lifted MRD codes are generalized.","authors_text":"Sascha Kurz","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-24T08:36:11Z","title":"A note on the linkage construction for constant dimension codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09780","kind":"arxiv","version":5},"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":"sha256:3e7802bf2b63ee3cb10d11a59d90bae30a1f8bd9bc53216f290fd5d5600b635c","target":"record","created_at":"2026-07-05T01:00:12Z","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":"66d37cf8364634ae1fbe47770e844a1680ca2ff57313fa44f5cf8e5485b0c8c8","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-24T08:36:11Z","title_canon_sha256":"d91514d4361d77215c15e5d6b8571f2116a7cbb42d280a713429e1aa4d174aa8"},"schema_version":"1.0","source":{"id":"1906.09780","kind":"arxiv","version":5}},"canonical_sha256":"4f3ef074df16e62b2d1b9e117aa4750e57d01729e4b16048ea14d209e70a784c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f3ef074df16e62b2d1b9e117aa4750e57d01729e4b16048ea14d209e70a784c","first_computed_at":"2026-07-05T01:00:12.589788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:00:12.589788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3lKLqG0yvLfi5G3+PlsRklXhv5jMJniQf+w9lbaF2N3+QXu+Y4B/fE1aFGa5UDtDT+I3fXySxDtfRcn0zh3RDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:00:12.590288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09780","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e7802bf2b63ee3cb10d11a59d90bae30a1f8bd9bc53216f290fd5d5600b635c","sha256:18354a4b0939b73da67099c8641db905a434f28dbd0eadbe15cf8d4e288f6647"],"state_sha256":"012b3e6f8cb8ae6cc1ab7fe48cfdcffb753ddc2198e26eee1b9dfd66d6778c7e"}