{
  "abstract": "It is known that all group codes of dimension at most $3$ are permutation equivalent to abelian group codes. We prove that twisted group codes of dimension at most $3$ are monomially equivalent either to an abelian group code or to an irreducible constacyclic code, and in the second case we describe the code explicitly by means of a trace map. Monomial equivalence cannot be replaced by permutation equivalence, and the second case cannot be avoided: the ternary tetracode is an ideal of $\\mathbb F_3[x]/(x^4+1)$ but it is not monomially equivalent to any group code. More generally, we give two infinite families, in dimensions $2$ and $3$, of irreducible constacyclic codes which attain the Griesmer bound, whereas every group code with the same length and dimension has smaller minimum distance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28297",
  "author_total": 1,
  "authors": [
    {
      "name": "Alvaro Otero Sanchez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx2hzq0nyee53.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28297",
  "fulltext_url": null,
  "id": "fx2hzq0nyee53",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28297",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7223105271",
  "pdf_url": "https://arxiv.org/pdf/2610.28297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx2hzq0nyee53.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.28297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Twisted group codes of dimension 2 and 3",
  "title_text": "Twisted group codes of dimension 2 and 3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fx2hzq0nyee53",
  "venue": "arXiv",
  "versions": []
}