{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EFJKMLYEBY3K5ZJZK4QYEJI7FE","short_pith_number":"pith:EFJKMLYE","schema_version":"1.0","canonical_sha256":"2152a62f040e36aee539572182251f291db066aa9e47cf0cf444549ee57f438e","source":{"kind":"arxiv","id":"1707.02315","version":1},"attestation_state":"computed","paper":{"title":"Optimal Binary Constant Weight Codes and Affine Linear Groups over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiang-dong Hou","submitted_at":"2017-07-07T18:02:34Z","abstract_excerpt":"Let $\\text{AGL}(1,\\Bbb F_q)$ be the affine linear group of dimension $1$ over a finite field $\\Bbb F_q$. $\\text{AGL}(1,\\Bbb F_q)$ acts sharply 2-transitively on $\\Bbb F_q$. Given $S<\\text{AGL}(1,\\Bbb F_q)$ and an integer $k$ with $1\\le k\\le q$, does there exist a subset $B\\subset\\Bbb F_q$ with $|B|=k$ such that $S=\\text{AGL}(1,\\Bbb F_q)_B$? ($\\text{AGL}(1,\\Bbb F_q)_B=\\{\\sigma\\in\\text{AGL}(1,\\Bbb F_q):\\sigma(B)=B\\}$ is the stabilizer of $B$ in $\\text{AGL}(1,\\Bbb F_q)$.) We derive a sum that holds the answer to this question. This result determines all possible parameters of binary constant weig"},"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":"1707.02315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-07T18:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"bdc2a9889bb982a6de70e1a2a8697332c90c7228a862172bfee395cb3d0c0cbd","abstract_canon_sha256":"65a8d1d0f94755b08bf1d94404204fe8a96ef9fca6aca62b0e86e904696f2243"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:39.548075Z","signature_b64":"1jlWX7mmSfdzDtKF/TPG59MYwC/cbEmLZhBgGyoIbuYK49hR+7VHJHoTe17WMa+m0Mu2vYHhMBJr1DAIwbPpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2152a62f040e36aee539572182251f291db066aa9e47cf0cf444549ee57f438e","last_reissued_at":"2026-05-18T00:40:39.547412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:39.547412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Binary Constant Weight Codes and Affine Linear Groups over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiang-dong Hou","submitted_at":"2017-07-07T18:02:34Z","abstract_excerpt":"Let $\\text{AGL}(1,\\Bbb F_q)$ be the affine linear group of dimension $1$ over a finite field $\\Bbb F_q$. $\\text{AGL}(1,\\Bbb F_q)$ acts sharply 2-transitively on $\\Bbb F_q$. Given $S<\\text{AGL}(1,\\Bbb F_q)$ and an integer $k$ with $1\\le k\\le q$, does there exist a subset $B\\subset\\Bbb F_q$ with $|B|=k$ such that $S=\\text{AGL}(1,\\Bbb F_q)_B$? ($\\text{AGL}(1,\\Bbb F_q)_B=\\{\\sigma\\in\\text{AGL}(1,\\Bbb F_q):\\sigma(B)=B\\}$ is the stabilizer of $B$ in $\\text{AGL}(1,\\Bbb F_q)$.) We derive a sum that holds the answer to this question. This result determines all possible parameters of binary constant weig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02315","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":"1707.02315","created_at":"2026-05-18T00:40:39.547502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02315v1","created_at":"2026-05-18T00:40:39.547502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02315","created_at":"2026-05-18T00:40:39.547502+00:00"},{"alias_kind":"pith_short_12","alias_value":"EFJKMLYEBY3K","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EFJKMLYEBY3K5ZJZ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EFJKMLYE","created_at":"2026-05-18T12:31:12.930513+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/EFJKMLYEBY3K5ZJZK4QYEJI7FE","json":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE.json","graph_json":"https://pith.science/api/pith-number/EFJKMLYEBY3K5ZJZK4QYEJI7FE/graph.json","events_json":"https://pith.science/api/pith-number/EFJKMLYEBY3K5ZJZK4QYEJI7FE/events.json","paper":"https://pith.science/paper/EFJKMLYE"},"agent_actions":{"view_html":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE","download_json":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE.json","view_paper":"https://pith.science/paper/EFJKMLYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02315&json=true","fetch_graph":"https://pith.science/api/pith-number/EFJKMLYEBY3K5ZJZK4QYEJI7FE/graph.json","fetch_events":"https://pith.science/api/pith-number/EFJKMLYEBY3K5ZJZK4QYEJI7FE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE/action/storage_attestation","attest_author":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE/action/author_attestation","sign_citation":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE/action/citation_signature","submit_replication":"https://pith.science/pith/EFJKMLYEBY3K5ZJZK4QYEJI7FE/action/replication_record"}},"created_at":"2026-05-18T00:40:39.547502+00:00","updated_at":"2026-05-18T00:40:39.547502+00:00"}