{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T6ZPRPURWK7JUSOW2ZIRWDIRLV","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":"10eeb6bcfa5354615a25ad43e7cda97abf7e05f677ec11e78bce5de4ca1cb94c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T15:20:53Z","title_canon_sha256":"e9eaaac75a616e3c9d129a0d18575d65fd82c7e563dee205a197b1c1cba44d78"},"schema_version":"1.0","source":{"id":"1505.05041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05041","created_at":"2026-05-18T01:14:04Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05041v2","created_at":"2026-05-18T01:14:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05041","created_at":"2026-05-18T01:14:04Z"},{"alias_kind":"pith_short_12","alias_value":"T6ZPRPURWK7J","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T6ZPRPURWK7JUSOW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T6ZPRPUR","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:f58a060e2a537245b1b9083e0d06c6d70eeb8567b382dfdc6fe7673d4cdfa162","target":"graph","created_at":"2026-05-18T01:14:04Z","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 study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC codes, that are LRC codes from Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds of distance proposed in [1] for some Hermitian LRC codes.\n  [1] A. Barg, I. Tamo, and S. Vlladut. Locally recoverable codes on algebraic curves. arXiv preprint arXiv:1501.04904, 2015.","authors_text":"Chiara Marcolla, Edoardo Ballico","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T15:20:53Z","title":"Higher Hamming weights for locally recoverable codes on algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05041","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:dd21bdcc4575aef46f359519221668cee4afb0bd7fe0072797f76011c5b10225","target":"record","created_at":"2026-05-18T01:14:04Z","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":"10eeb6bcfa5354615a25ad43e7cda97abf7e05f677ec11e78bce5de4ca1cb94c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T15:20:53Z","title_canon_sha256":"e9eaaac75a616e3c9d129a0d18575d65fd82c7e563dee205a197b1c1cba44d78"},"schema_version":"1.0","source":{"id":"1505.05041","kind":"arxiv","version":2}},"canonical_sha256":"9fb2f8be91b2be9a49d6d6511b0d115d7c182ee1fae75787353f1db6359a95da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fb2f8be91b2be9a49d6d6511b0d115d7c182ee1fae75787353f1db6359a95da","first_computed_at":"2026-05-18T01:14:04.291689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:04.291689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGj+y2ONn10w/i27MEEKLkzyATg6WUd0SaPaCqmPRB7rBMtvk0gMq4JA4OnNfmSR/er/HBOiIC2mp8LZQr05DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:04.292255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd21bdcc4575aef46f359519221668cee4afb0bd7fe0072797f76011c5b10225","sha256:f58a060e2a537245b1b9083e0d06c6d70eeb8567b382dfdc6fe7673d4cdfa162"],"state_sha256":"14edaa14624a30bbf7abe82762681219b183af36f1a5500cae9d46bbf7c06514"}