{"paper":{"title":"Neighbour transitivity on codes in Hamming graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cheryl E. Praeger, Neil I. Gillespie","submitted_at":"2011-12-06T11:59:03Z","abstract_excerpt":"We consider a \\emph{code} to be a subset of the vertex set of a \\emph{Hamming graph}. In this setting a \\emph{neighbour} of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the property that some group of automorphisms acts transitively on the \\emph{set of neighbours} of the code. We call these codes \\emph{neighbour transitive}. We obtain sufficient conditions for a neighbour transitive group to fix the code setwise. Moreover, we construct an infinite family of neighbour transitive codes, with \\emph{minimum distance} $\\delta=4$, where t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1244","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"}