{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NHKYLFXWT4ELETU3QSE3DWEKBO","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":"c5074df04415bc0dcf94718129f75cce80c08267eafae37cb4eff9682933c328","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-22T11:41:18Z","title_canon_sha256":"bf089fd167d1d3d0d7f3e6d411ca1e771882ffb13f4c91e3462a8e0893d03fe6"},"schema_version":"1.0","source":{"id":"1903.09458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09458","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09458v1","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09458","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"NHKYLFXWT4EL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NHKYLFXWT4ELETU3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NHKYLFXW","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:c78c4498e305f9304b3309990d89697bd86e621673889ec1a89169846195a33f","target":"graph","created_at":"2026-05-17T23:50:39Z","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":"In 1970 Delsarte, Goethals and Mac Williams published a seminal paper on generalized Reed-Muller codes where, among many important results, they proved that the minimal weight codewords of these codes are obtained through the evaluation of certain polynomials which are a specific product of linear factors, which they describe. In the present paper we extend this result to a class of Reed-Muller type codes defined on a product of (possibly distinct) finite fields of the same characteristic. The paper also brings an expository section on the study of the structure of low weight codewords, not on","authors_text":"Cicero Carvalho, Victor G.L. Neumann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-22T11:41:18Z","title":"An extension of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords to a class of Reed-Muller type codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09458","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":"sha256:3c5a05c3833c10fb4487eee6ed7c1d8893ec1e2a61dfc636337f6af99ed76de2","target":"record","created_at":"2026-05-17T23:50:39Z","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":"c5074df04415bc0dcf94718129f75cce80c08267eafae37cb4eff9682933c328","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-22T11:41:18Z","title_canon_sha256":"bf089fd167d1d3d0d7f3e6d411ca1e771882ffb13f4c91e3462a8e0893d03fe6"},"schema_version":"1.0","source":{"id":"1903.09458","kind":"arxiv","version":1}},"canonical_sha256":"69d58596f69f08b24e9b8489b1d88a0bb673de4ba848014f7e7b738b6f28b0dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69d58596f69f08b24e9b8489b1d88a0bb673de4ba848014f7e7b738b6f28b0dd","first_computed_at":"2026-05-17T23:50:39.579593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:39.579593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xLVT87R9b3j5QtamOxC+rp0+Te92GUbH4jMhK0V3zUQzt9ts2zY1FybjPaD9evQuuBUU42KemnEVWLIfuz9aAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:39.580051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c5a05c3833c10fb4487eee6ed7c1d8893ec1e2a61dfc636337f6af99ed76de2","sha256:c78c4498e305f9304b3309990d89697bd86e621673889ec1a89169846195a33f"],"state_sha256":"b662438ab9bdaa6afe642cd1c70dd6657807cbb91421ab496dbae5622bdad2e6"}