{
  "abstract": "Function-correcting codes, recently introduced by Lenz et al.\\ (2023), provide a framework for the receiver to provide a higher level of protection against channel errors than the level of protection for messages. In this paper, we derive a generalised Plotkin-type bound on the redundancy of FCCs under the Hamming metric for arbitrary functions over finite fields. The proposed bound recovers the classical Plotkin bound for classical error-correcting codes as a special case. We further obtain explicit Plotkin-type bounds for linear functions, Hamming-weight functions, and Hamming-weight threshold functions. In addition, we study FCCs for monomial mappings $f(x)=x^n$ over $\\mathbb{F}_{q^k}$, which are widely utilised in coding theory, cryptography, and finite geometry, and derive an explicit Plotkin-type redundancy bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04546",
  "author_total": 2,
  "authors": [
    {
      "name": "Kanchana Lokshmii Jagatti"
    },
    {
      "name": "B. Sundar Rajan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atbnr5fj679wc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04546",
  "fulltext_url": null,
  "id": "atbnr5fj679wc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04546",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7220708544",
  "pdf_url": "https://arxiv.org/pdf/2610.04546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atbnr5fj679wc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings",
  "title_text": "Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/atbnr5fj679wc",
  "venue": "arXiv",
  "versions": []
}