{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LRMP7VX4475RCOQZVIVK7YMAEZ","short_pith_number":"pith:LRMP7VX4","schema_version":"1.0","canonical_sha256":"5c58ffd6fce7fb113a19aa2aafe18026487503a7f1df29a4d96855ce35f51c06","source":{"kind":"arxiv","id":"1701.05965","version":1},"attestation_state":"computed","paper":{"title":"An infinite family of Steiner systems $S(2, 4, 2^m)$ from cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding","submitted_at":"2017-01-21T01:40:57Z","abstract_excerpt":"Steiner systems are a fascinating topic of combinatorics. The most studied Steiner systems are $S(2, 3, v)$ (Steiner triple systems), $S(3, 4, v)$ (Steiner quadruple systems), and $S(2, 4, v)$. There are a few infinite families of Steiner systems $S(2, 4, v)$ in the literature. The objective of this paper is to present an infinite family of Steiner systems $S(2, 4, 2^m)$ for all $m \\equiv 2 \\pmod{4} \\geq 6$ from cyclic codes. This may be the first coding-theoretic construction of an infinite family of Steiner systems $S(2, 4, v)$. As a by-product, many infinite families of $2$-designs are also"},"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":"1701.05965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-21T01:40:57Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"f00413d9af3a1e65c36d629850b654bef6c5710e711dbbb287544ef701d3ed90","abstract_canon_sha256":"6f65036705110743c33a0fe58ea925e1fdeeaed0ed6e1e7ac48ca51895331c03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.013953Z","signature_b64":"9rHD4bIfx1tlIA8PSt3ORfCgvlv8E2++T1gsd6UifGh7a8H5CvqPCZ2BaSTrN2/IDZ6/SM3kuFYQEX76dvFGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c58ffd6fce7fb113a19aa2aafe18026487503a7f1df29a4d96855ce35f51c06","last_reissued_at":"2026-05-18T00:43:18.013342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.013342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An infinite family of Steiner systems $S(2, 4, 2^m)$ from cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding","submitted_at":"2017-01-21T01:40:57Z","abstract_excerpt":"Steiner systems are a fascinating topic of combinatorics. The most studied Steiner systems are $S(2, 3, v)$ (Steiner triple systems), $S(3, 4, v)$ (Steiner quadruple systems), and $S(2, 4, v)$. There are a few infinite families of Steiner systems $S(2, 4, v)$ in the literature. The objective of this paper is to present an infinite family of Steiner systems $S(2, 4, 2^m)$ for all $m \\equiv 2 \\pmod{4} \\geq 6$ from cyclic codes. This may be the first coding-theoretic construction of an infinite family of Steiner systems $S(2, 4, v)$. As a by-product, many infinite families of $2$-designs are also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05965","kind":"arxiv","version":1},"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":"1701.05965","created_at":"2026-05-18T00:43:18.013420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05965v1","created_at":"2026-05-18T00:43:18.013420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05965","created_at":"2026-05-18T00:43:18.013420+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRMP7VX4475R","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRMP7VX4475RCOQZ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRMP7VX4","created_at":"2026-05-18T12:31:28.150371+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/LRMP7VX4475RCOQZVIVK7YMAEZ","json":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ.json","graph_json":"https://pith.science/api/pith-number/LRMP7VX4475RCOQZVIVK7YMAEZ/graph.json","events_json":"https://pith.science/api/pith-number/LRMP7VX4475RCOQZVIVK7YMAEZ/events.json","paper":"https://pith.science/paper/LRMP7VX4"},"agent_actions":{"view_html":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ","download_json":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ.json","view_paper":"https://pith.science/paper/LRMP7VX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05965&json=true","fetch_graph":"https://pith.science/api/pith-number/LRMP7VX4475RCOQZVIVK7YMAEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LRMP7VX4475RCOQZVIVK7YMAEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ/action/storage_attestation","attest_author":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ/action/author_attestation","sign_citation":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ/action/citation_signature","submit_replication":"https://pith.science/pith/LRMP7VX4475RCOQZVIVK7YMAEZ/action/replication_record"}},"created_at":"2026-05-18T00:43:18.013420+00:00","updated_at":"2026-05-18T00:43:18.013420+00:00"}