{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SN2OK635UYTXRGJLVBZI32QDW2","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":"37a9f65b76bf8dc895e5e7cf5ab5ac3cfa0d091fc9160a339a4e33aeca456248","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T13:47:16Z","title_canon_sha256":"49727c269a1b18ba208e8cb434598de8e2f43274d01824b410716a1afaccd43f"},"schema_version":"1.0","source":{"id":"1210.0776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0776","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0776v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0776","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"SN2OK635UYTX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SN2OK635UYTXRGJL","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SN2OK635","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:6b56a068fc94b3077ea69e26b78e726e81b8b32f251c470c06cf26025aeddc69","target":"graph","created_at":"2026-05-18T03:44:14Z","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 this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams type identity for such digital nets. This identity can be used to compute the strict $t$-value of a digital net over finite abelian groups. If the digital net has $N$ points in the $s$ dimensional unit cube $[0,1]^s$, then the $t$-value can be computed in $\\mathcal{O}(N s \\log N)$ operations and the weight enumerator polynomial can be computed in $\\mathcal{O}(N s (\\log N)^2)$ operations, where operations mean arithmetic of ","authors_text":"Josef Dick, Makoto Matsumoto","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T13:47:16Z","title":"On the fast computation of the weight enumerator polynomial and the $t$ value of digital nets over finite abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0776","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":"sha256:617d97fb9ec62e00097f162f0fa8c806f727255c8a88ca87f8153f06c634a250","target":"record","created_at":"2026-05-18T03:44:14Z","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":"37a9f65b76bf8dc895e5e7cf5ab5ac3cfa0d091fc9160a339a4e33aeca456248","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T13:47:16Z","title_canon_sha256":"49727c269a1b18ba208e8cb434598de8e2f43274d01824b410716a1afaccd43f"},"schema_version":"1.0","source":{"id":"1210.0776","kind":"arxiv","version":1}},"canonical_sha256":"9374e57b7da62778992ba8728dea03b6bde32258666936b438c537b8fa55e941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9374e57b7da62778992ba8728dea03b6bde32258666936b438c537b8fa55e941","first_computed_at":"2026-05-18T03:44:14.263467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:14.263467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6E5L5xT8cyMhys8TfZJT75ZqLA9meGT3ZOHCFD+GcZaaDHTWj2YHwoL0m+TOWsB0gw7j7QNCrEdVOj/UJPx5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:14.263877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:617d97fb9ec62e00097f162f0fa8c806f727255c8a88ca87f8153f06c634a250","sha256:6b56a068fc94b3077ea69e26b78e726e81b8b32f251c470c06cf26025aeddc69"],"state_sha256":"4ae429d2ccd0c92214922de022c3f60fd9fac529275b5503a53407b0a6b99f45"}