{
  "id": "2312.16908",
  "version": "v1",
  "published": "2023-12-28T08:59:24.000Z",
  "updated": "2023-12-28T08:59:24.000Z",
  "title": "A classification of permutation binomials of the form $x^i+ax$ over $\\mathbb{F}_{2^n}$ for dimensions up to 8",
  "authors": [
    "Yi Li",
    "Xiutao Feng",
    "Qiang Wang"
  ],
  "categories": [
    "math.NT",
    "cs.IT",
    "math.CO",
    "math.IT"
  ],
  "abstract": "Permutation polynomials with few terms (especially permutation binomials) attract many people due to their simple algebraic structure. Despite the great interests in the study of permutation binomials, a complete characterization of permutation binomials is still unknown. In this paper, we give a classification of permutation binomials of the form $x^i+ax$ over $\\mathbb{F}_{2^n}$, where $n\\leq 8$ by characterizing three new classes of permutation binomials. In particular one of them has relatively large index $\\frac{q^2+q+1}{3}$ over $\\mathbb{F}_{q^3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-28T08:59:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55"
    ],
    "keywords": [
      "permutation binomials",
      "classification",
      "dimensions",
      "simple algebraic structure",
      "permutation polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}