{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T6ZPRPURWK7JUSOW2ZIRWDIRLV","short_pith_number":"pith:T6ZPRPUR","schema_version":"1.0","canonical_sha256":"9fb2f8be91b2be9a49d6d6511b0d115d7c182ee1fae75787353f1db6359a95da","source":{"kind":"arxiv","id":"1505.05041","version":2},"attestation_state":"computed","paper":{"title":"Higher Hamming weights for locally recoverable codes on algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.AC","authors_text":"Chiara Marcolla, Edoardo Ballico","submitted_at":"2015-05-19T15:20:53Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.05041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T15:20:53Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"e9eaaac75a616e3c9d129a0d18575d65fd82c7e563dee205a197b1c1cba44d78","abstract_canon_sha256":"10eeb6bcfa5354615a25ad43e7cda97abf7e05f677ec11e78bce5de4ca1cb94c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:04.292255Z","signature_b64":"NGj+y2ONn10w/i27MEEKLkzyATg6WUd0SaPaCqmPRB7rBMtvk0gMq4JA4OnNfmSR/er/HBOiIC2mp8LZQr05DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb2f8be91b2be9a49d6d6511b0d115d7c182ee1fae75787353f1db6359a95da","last_reissued_at":"2026-05-18T01:14:04.291689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:04.291689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Hamming weights for locally recoverable codes on algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.AC","authors_text":"Chiara Marcolla, Edoardo Ballico","submitted_at":"2015-05-19T15:20:53Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05041","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.05041","created_at":"2026-05-18T01:14:04.291783+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05041v2","created_at":"2026-05-18T01:14:04.291783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05041","created_at":"2026-05-18T01:14:04.291783+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6ZPRPURWK7J","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6ZPRPURWK7JUSOW","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6ZPRPUR","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV","json":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV.json","graph_json":"https://pith.science/api/pith-number/T6ZPRPURWK7JUSOW2ZIRWDIRLV/graph.json","events_json":"https://pith.science/api/pith-number/T6ZPRPURWK7JUSOW2ZIRWDIRLV/events.json","paper":"https://pith.science/paper/T6ZPRPUR"},"agent_actions":{"view_html":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV","download_json":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV.json","view_paper":"https://pith.science/paper/T6ZPRPUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05041&json=true","fetch_graph":"https://pith.science/api/pith-number/T6ZPRPURWK7JUSOW2ZIRWDIRLV/graph.json","fetch_events":"https://pith.science/api/pith-number/T6ZPRPURWK7JUSOW2ZIRWDIRLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV/action/storage_attestation","attest_author":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV/action/author_attestation","sign_citation":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV/action/citation_signature","submit_replication":"https://pith.science/pith/T6ZPRPURWK7JUSOW2ZIRWDIRLV/action/replication_record"}},"created_at":"2026-05-18T01:14:04.291783+00:00","updated_at":"2026-05-18T01:14:04.291783+00:00"}