{
  "id": "2103.00827",
  "version": "v1",
  "published": "2021-03-01T07:49:52.000Z",
  "updated": "2021-03-01T07:49:52.000Z",
  "title": "Linear Recurrences over a Finite Field with Exactly Two Periods",
  "authors": [
    "Ghurumuruhan Ganesan"
  ],
  "comment": "Accepted for publication in Advances in Applied Mathematics",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\\(f\\) to have exactly two periods in the sense that the period of any sequence generated by~\\(f\\) is either one or a unique integer greater than one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-01T07:49:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear recurrences",
      "finite field linear recurring sequences",
      "unique integer greater",
      "sufficient conditions",
      "periodicity structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}