{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F7DO7R7JD7L5WLMFJQUKYZ4ICL","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":"06283b6e4f682f0413e996a474567fc0492f38217f0c36224db5017bf55f40f9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-29T18:41:24Z","title_canon_sha256":"4903f9252803a13efc2dc381fa1d3a8ed5d5327efe2ab446dd2521e2fc06e6b5"},"schema_version":"1.0","source":{"id":"1603.08878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08878","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08878v1","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08878","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"F7DO7R7JD7L5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F7DO7R7JD7L5WLMF","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F7DO7R7J","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:2fb35c0fd492e012688f6ef160c0c6e0efc3788ecd1a295340d6620c59f34189","target":"graph","created_at":"2026-05-18T00:51:03Z","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":"We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. Inform. Theory, no. 8, 2014). In this paper we focus on optimal cyclic codes that arise from this construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (","authors_text":"Alexander Barg, Itzhak Tamo, Robert Calderbank, Sreechakra Goparaju","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-29T18:41:24Z","title":"Cyclic LRC Codes, binary LRC codes, and upper bounds on the distance of cyclic codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08878","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":"sha256:898fdbc79831269eed8f3b7ad762b6e9b931b124ee6aa321f45822853283f286","target":"record","created_at":"2026-05-18T00:51:03Z","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":"06283b6e4f682f0413e996a474567fc0492f38217f0c36224db5017bf55f40f9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-29T18:41:24Z","title_canon_sha256":"4903f9252803a13efc2dc381fa1d3a8ed5d5327efe2ab446dd2521e2fc06e6b5"},"schema_version":"1.0","source":{"id":"1603.08878","kind":"arxiv","version":1}},"canonical_sha256":"2fc6efc7e91fd7db2d854c28ac678812d86d87211644d0167b41616e791c15d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fc6efc7e91fd7db2d854c28ac678812d86d87211644d0167b41616e791c15d0","first_computed_at":"2026-05-18T00:51:03.286351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:03.286351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOlQ9fYLk4WJLG5kWaSUMlw8zyHHfywIFtfGuJuKXujBvKvG8LbydRWp48YJdMCPa3/X7BeN9FXL0LyT1croCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:03.286796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:898fdbc79831269eed8f3b7ad762b6e9b931b124ee6aa321f45822853283f286","sha256:2fb35c0fd492e012688f6ef160c0c6e0efc3788ecd1a295340d6620c59f34189"],"state_sha256":"c35c4ee501a83db733414bc8c76c7f011ae4cc8a81b2915e6e7f68187137d01b"}