{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3BKXKSKBZIYHJIUNNHV3GTNBWF","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":"631c18f03b57d25cb26b2f7908f1b6b16ed97f365b4370216fb5d1bdb108be8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-27T07:59:04Z","title_canon_sha256":"ea525a4d0f4579cf7ad79df41702148b74940594640edfb3dc6fdde31b80c1f5"},"schema_version":"1.0","source":{"id":"1404.6723","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6723","created_at":"2026-05-18T02:16:41Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6723v2","created_at":"2026-05-18T02:16:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6723","created_at":"2026-05-18T02:16:41Z"},{"alias_kind":"pith_short_12","alias_value":"3BKXKSKBZIYH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3BKXKSKBZIYHJIUN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3BKXKSKB","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:0f62462db6a273da140fcc7bbfbdac268b2cccb65f186605e56460f2ad5fbac6","target":"graph","created_at":"2026-05-18T02:16:41Z","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":"This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We present different constructions for constant dimension codes with minimum injection distance $2$ or $k-1$, where $k$ is the constant dimension. Furthermore, we present a construction of new codes from old codes for any minimum distance. Then we construct non-constant dimension codes from these codes. The examples of codes obtained by these constructions are the largest known codes for the given parameters.","authors_text":"Anna-Lena Trautmann, Natalia Silberstein","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-27T07:59:04Z","title":"Subspace Codes based on Graph Matchings, Ferrers Diagrams and Pending Blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6723","kind":"arxiv","version":2},"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:dffc794c9e92f56c70167bae44e50793abe2b0eb7de994cf2b1a4d6f6236006b","target":"record","created_at":"2026-05-18T02:16:41Z","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":"631c18f03b57d25cb26b2f7908f1b6b16ed97f365b4370216fb5d1bdb108be8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-27T07:59:04Z","title_canon_sha256":"ea525a4d0f4579cf7ad79df41702148b74940594640edfb3dc6fdde31b80c1f5"},"schema_version":"1.0","source":{"id":"1404.6723","kind":"arxiv","version":2}},"canonical_sha256":"d855754941ca3074a28d69ebb34da1b1419ea59fa9c782e86fc65b701fcdb3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d855754941ca3074a28d69ebb34da1b1419ea59fa9c782e86fc65b701fcdb3ea","first_computed_at":"2026-05-18T02:16:41.287148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:41.287148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8R1B0bZQ1c3DlALCF/khF9+K0++R6ucE7P6D3mJXGKET61peXy1xOBr07sW5Y1vW32T4ABjI9F//FaPJ08ENBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:41.287870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6723","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dffc794c9e92f56c70167bae44e50793abe2b0eb7de994cf2b1a4d6f6236006b","sha256:0f62462db6a273da140fcc7bbfbdac268b2cccb65f186605e56460f2ad5fbac6"],"state_sha256":"3ed4631716c0230d7ea5f797dbac4a04daf4582fa1970c0e9d4edd8da2037a89"}