{
  "abstract": "In recent years, simplicial complexes have gained considerable attention as a useful tool for constructing distance-optimal codes over finite fields. In this article, we construct four infinite families of linear codes over the ring $\\mathcal{R}=\\mathbb{F}_{q}+u\\mathbb{F}_{q}$ with $u^2=0$ using simplicial complexes with one or two maximal elements, and completely determine their Lee weight distributions via exponential-sum techniques. By employing a Gray map on $\\mathcal{R}$, we obtain infinite families of distance-optimal codes over $\\mathbb{F}_{q}$, including a near-Griesmer family, and establish sufficient conditions for their minimality. Furthermore, we investigate the corresponding subfield codes and derive sufficient conditions for their distance-optimality and minimality, yielding infinite families of Griesmer and near-Griesmer codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11783",
  "author_total": 3,
  "authors": [
    {
      "name": "Ankit Yadav"
    },
    {
      "name": "Akanksha Tiwari"
    },
    {
      "name": "Ritumoni Sarma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmbt2cf6zkffn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11783",
  "fulltext_url": null,
  "id": "cmbt2cf6zkffn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11783",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7212267021",
  "pdf_url": "https://arxiv.org/pdf/2609.11783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmbt2cf6zkffn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Linear Codes over $\\mathbb{F}_{q}+u\\mathbb{F}_{q}$ associated with Simplicial Complexes, Their Gray Images, and Subfield Codes",
  "title_text": "Linear Codes over 𝔽_q+u𝔽_q associated with Simplicial Complexes, Their Gray Images, and Subfield Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cmbt2cf6zkffn",
  "venue": "arXiv",
  "versions": []
}