{"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"}