{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EONBJLC5TLYRQCDDY4UWAD2JLD","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":"5f2b52ecc9dc4fe902c6b54ce2dcd46159871471e90e86dd464042171a24f72e","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-09-15T07:19:42Z","title_canon_sha256":"0f89330147253e0ae722984d0fb757c6ff598fd24d714973f3535ac562669253"},"schema_version":"1.0","source":{"id":"2109.07128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07128","created_at":"2026-07-05T05:27:16Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07128v2","created_at":"2026-07-05T05:27:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07128","created_at":"2026-07-05T05:27:16Z"},{"alias_kind":"pith_short_12","alias_value":"EONBJLC5TLYR","created_at":"2026-07-05T05:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"EONBJLC5TLYRQCDD","created_at":"2026-07-05T05:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"EONBJLC5","created_at":"2026-07-05T05:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:2f05e29e45337fb4fd9fb42e424210fd69a63902798cf993f9a81de2b4087b6c","target":"graph","created_at":"2026-07-05T05:27:16Z","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/2109.07128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies $d_S(U,W):=2k-2\\dim(U\\cap W)\\ge d$ for all pairs of different codewords $U$, $W$. Constant dimension codes have applications in e.g.\\ random linear network coding, cryptography, and distributed storage. Bounds for $A_q(n,d;k)$ are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show up the potential for furth","authors_text":"Sascha Kurz","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-09-15T07:19:42Z","title":"The interplay of different metrics for the construction of constant dimension codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07128","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":"sha256:26de2cdc8ac42d8212520f9864cc01acfdb19e94953b0e9734bc0454539186af","target":"record","created_at":"2026-07-05T05:27:16Z","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":"5f2b52ecc9dc4fe902c6b54ce2dcd46159871471e90e86dd464042171a24f72e","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-09-15T07:19:42Z","title_canon_sha256":"0f89330147253e0ae722984d0fb757c6ff598fd24d714973f3535ac562669253"},"schema_version":"1.0","source":{"id":"2109.07128","kind":"arxiv","version":2}},"canonical_sha256":"239a14ac5d9af1180863c729600f4958d9be8fe2c13b8413fde281dbbdab27b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"239a14ac5d9af1180863c729600f4958d9be8fe2c13b8413fde281dbbdab27b6","first_computed_at":"2026-07-05T05:27:16.336596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:27:16.336596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6T+Jh76XVEbLv4dTVUk3b5z5ltFQkVpGL9QHcZypKyg4So20qiv87wwZgjTsjbW2Xp+PQeK0PG3dZqL5CK9RAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:27:16.337180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.07128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26de2cdc8ac42d8212520f9864cc01acfdb19e94953b0e9734bc0454539186af","sha256:2f05e29e45337fb4fd9fb42e424210fd69a63902798cf993f9a81de2b4087b6c"],"state_sha256":"4565ab0ca37f0358639f0706f4ec11ded6bdcbf545f55f8ca463a1a1847f49d4"}