{
  "id": "2207.10911",
  "version": "v1",
  "published": "2022-07-22T07:10:40.000Z",
  "updated": "2022-07-22T07:10:40.000Z",
  "title": "Jacobi polynomials and design theory I",
  "authors": [
    "Himadri Shekhar Chakraborty",
    "Tsuyoshi Miezaki",
    "Manabu Oura",
    "Yuuho Tanaka"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.GR",
    "math.IT",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In this paper, we introduce the notion of Jacobi polynomials with multiple reference vectors of a code, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-22T07:10:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T71",
      "94B05",
      "11F11"
    ],
    "keywords": [
      "jacobi polynomials",
      "design theory",
      "multiple reference vectors",
      "macwilliams type identity",
      "aronhold polarization operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}