{
  "abstract": "We give a higher unit-torus lift from q-linearized permutation polynomials over Fqn to generally nonlinear sparse permutation polynomials over Fqns. The construction preserves compositional inverses: if a linearized polynomials and its inverse have coefficients (ai) and (Ai), then the lifted polynomial and its inverse have the same coefficients. As a consequence, we obtain nonlinear binomial lifts whose inverses are again binomials in the two-dimensional case, including an explicit inverse for a binomial family over Fq4. The three dimensional specialization yields permutation trinomials whose compositional inverses are again trinomials, together with explicit involution criteria and examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16619",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckyzh1zfdj1kk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16619",
  "fulltext_url": null,
  "id": "ckyzh1zfdj1kk",
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  "landing_url": "https://arxiv.org/abs/2610.16619",
  "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.NT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7221787310",
  "pdf_url": "https://arxiv.org/pdf/2610.16619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckyzh1zfdj1kk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16619"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses",
  "title_text": "Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ckyzh1zfdj1kk",
  "venue": "arXiv",
  "versions": []
}