{"paper":{"title":"On transitive uniform partitions of F^n into binary Hamming codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Faina I. Solov'eva","submitted_at":"2019-04-02T08:40:59Z","abstract_excerpt":"We investigate transitive uniform partitions of the vector space $F^n$ of dimension $n$ over the Galois field $GF(2)$ into cosets of Hamming codes. A partition $P^n= \\{H_0,H_1+e_1,\\ldots,H_n+e_n\\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\\ldots,H_n$ of length $n$ is said to be uniform if the intersection of any two codes $H_i$ and $H_j$, $i,j\\in \\{0,1,\\ldots,n \\}$ is constant, here $e_i$ is a binary vector in $F^n$ of weight $1$ with one in the $i$th coordinate position.\n  For any $n=2^m-1$, $m>4$ we found a class of nonequivalent $2$-transitive uniform partitions of $F^n$ into cosets o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01282","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"}