{
  "abstract": "In this article, we study polynomials over $\\mathbb{F}_{q^2}$ that do not permute $\\mathbb{F}_{q^2}$. More precisely, we characterize polynomials of the forms $x^q + b x^2 + c x + d$ and $x^{q+1} + b x^q + c x + d$ over $\\mathbb{F}_{q^2}$ according to whether they are permutation or non-permutation polynomials. To this end, we determine the exact number of zeros of these polynomials using existing results on certain special Weil sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.14529",
  "author_total": 2,
  "authors": [
    {
      "name": "Bidushi Sharma"
    },
    {
      "name": "Dhiren Kumar Basnet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21wqx8280j34b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.14529",
  "fulltext_url": null,
  "id": "21wqx8280j34b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.14529",
  "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.NT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7164815543",
  "pdf_url": "https://arxiv.org/pdf/2606.14529",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21wqx8280j34b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2606.14529",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.14529"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On some Non-Permutations of Quadratic Extension of Finite Field",
  "title_text": "On some Non-Permutations of Quadratic Extension of Finite Field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/21wqx8280j34b",
  "venue": "arXiv",
  "versions": []
}