{
  "abstract": "In this article, we show that, for the symmetric group $S_n$, the Young subgroup $S_λ$, with $l(λ)\\geq 3$, is not a code with respect to a conjugacy class of $S_n$. This provides a partial answer to \\cite[Problem 4.1]{FL26}. We then provide a characterization of conjugacy classes $X_i$, such that subgroups $S_{(n-2,1,1)}$, $S_{(n-3,2,1)}$, and $Y_k$ for $k\\leq 3$ are codes for $X_1 \\cup X_2$. Furthermore, we describe some codes in the finite Coxeter groups of type $B_n$, $C_n$, $D_n$, and in the generalized symmetric group $C_m \\wr S_n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21928",
  "author_total": 2,
  "authors": [
    {
      "name": "Subrata Barman"
    },
    {
      "name": "Pushpendra Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90bsye0hdgt2w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21928",
  "fulltext_url": null,
  "id": "90bsye0hdgt2w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21928",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7165675453",
  "pdf_url": "https://arxiv.org/pdf/2606.21928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90bsye0hdgt2w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.21928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Codes in (Generalized) Symmetric Groups",
  "title_text": "On Codes in (Generalized) Symmetric Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/90bsye0hdgt2w",
  "venue": "arXiv",
  "versions": []
}