{
  "annotation_id": "0de34163-ea98-414e-925a-720a4bf25f77",
  "date_created": "2026-02-17T05:53:19.852000Z",
  "date_modified": "2026-02-17T05:53:19.852000Z",
  "file_hash": "106205aaa78e883da0b13c1bbe9a7d5c9bd9c52206ba1f10fe29526bf9de3398",
  "private": false,
  "record": {
    "abstract": "Polynomials and elements over finite fields exhibit closely related algebraic structures, and many properties defined for elements extend naturally to polynomials. The concepts of order and $\\mathbb{F}_q$-Order for elements have been extensively studied. In this paper, we investigate several properties of $r$-primitive and $k$-normal elements. Furthermore, by using the concept of the $\\mathbb{F}_q$-Order of a polynomial, we explore properties of $k$-normal polynomials.",
    "arxiv_id": "2601.09201",
    "authors": [
      "Maithri K.",
      "Vadiraja Bhatta G. R.",
      "Indira K. P.",
      "Prasanna Poojary"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On \\(\\mathbb{F}_q\\)-Order of Polynomials and Properties of \\(r\\)-Primitive and \\(k\\)-Normal Elements over Finite Fields",
    "url": "https://arxiv.org/abs/2601.09201",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1bb75d92-38a5-43b1-bab3-c4725e82c3d7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}