{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:W7CJET36OD34KG5XVZDCX4NHAW","short_pith_number":"pith:W7CJET36","schema_version":"1.0","canonical_sha256":"b7c4924f7e70f7c51bb7ae462bf1a705bd5fa8cbaec0233aae1c7fc58c683714","source":{"kind":"arxiv","id":"1605.07827","version":2},"attestation_state":"computed","paper":{"title":"Minimum-weight codewords of the Hermitian codes are supported on complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Chiara Marcolla, Margherita Roggero","submitted_at":"2016-05-25T11:11:55Z","abstract_excerpt":"Let $\\mathcal{H}$ be the Hermitian curve defined over a finite field $\\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over $\\mathcal{H}$, started in [1]: if $d$ is the distance of the code, the supports are all the sets of $d$ distinct $\\mathbb{F}_{q^2}$-points on $\\mathcal{H}$ complete intersection of two curves defined by polynomials with prescribed initial monomials w.r.t. \\texttt{DegRevLex}.\n  For most Hermitian codes, and especially for all those with distance $d\\geq q^2-q$ studie"},"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":"1605.07827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-25T11:11:55Z","cross_cats_sorted":[],"title_canon_sha256":"4d455335d8485840982feff7735e55a46fa2523137621f5bfde6d282c7ff9d67","abstract_canon_sha256":"ff715af743954d7885a6d9fe0d8a0897287be5ebd49656493b041217f9c8a07d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:15.252292Z","signature_b64":"LhwvBIO9f619ATpu/9qaTYRZSN8fh4+pfsnyew/1lHAyBdbxc7Ml6i1UteDwVS74+lMxoqxQxTyQL82VizsZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c4924f7e70f7c51bb7ae462bf1a705bd5fa8cbaec0233aae1c7fc58c683714","last_reissued_at":"2026-05-17T23:58:15.251834Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:15.251834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum-weight codewords of the Hermitian codes are supported on complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Chiara Marcolla, Margherita Roggero","submitted_at":"2016-05-25T11:11:55Z","abstract_excerpt":"Let $\\mathcal{H}$ be the Hermitian curve defined over a finite field $\\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over $\\mathcal{H}$, started in [1]: if $d$ is the distance of the code, the supports are all the sets of $d$ distinct $\\mathbb{F}_{q^2}$-points on $\\mathcal{H}$ complete intersection of two curves defined by polynomials with prescribed initial monomials w.r.t. \\texttt{DegRevLex}.\n  For most Hermitian codes, and especially for all those with distance $d\\geq q^2-q$ studie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07827","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":"1605.07827","created_at":"2026-05-17T23:58:15.251902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.07827v2","created_at":"2026-05-17T23:58:15.251902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07827","created_at":"2026-05-17T23:58:15.251902+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7CJET36OD34","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7CJET36OD34KG5X","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7CJET36","created_at":"2026-05-18T12:30:48.956258+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/W7CJET36OD34KG5XVZDCX4NHAW","json":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW.json","graph_json":"https://pith.science/api/pith-number/W7CJET36OD34KG5XVZDCX4NHAW/graph.json","events_json":"https://pith.science/api/pith-number/W7CJET36OD34KG5XVZDCX4NHAW/events.json","paper":"https://pith.science/paper/W7CJET36"},"agent_actions":{"view_html":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW","download_json":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW.json","view_paper":"https://pith.science/paper/W7CJET36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.07827&json=true","fetch_graph":"https://pith.science/api/pith-number/W7CJET36OD34KG5XVZDCX4NHAW/graph.json","fetch_events":"https://pith.science/api/pith-number/W7CJET36OD34KG5XVZDCX4NHAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW/action/storage_attestation","attest_author":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW/action/author_attestation","sign_citation":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW/action/citation_signature","submit_replication":"https://pith.science/pith/W7CJET36OD34KG5XVZDCX4NHAW/action/replication_record"}},"created_at":"2026-05-17T23:58:15.251902+00:00","updated_at":"2026-05-17T23:58:15.251902+00:00"}