{
  "id": "2408.08472",
  "version": "v1",
  "published": "2024-08-16T01:15:20.000Z",
  "updated": "2024-08-16T01:15:20.000Z",
  "title": "Two constructions of quaternary Legendre pairs of even length",
  "authors": [
    "Jonathan Jedwab",
    "Thomas Pender"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give the first general constructions of even length quaternary Legendre pairs: there is a quaternary Legendre pair of length $(q-1)/2$ for every prime power $q$ congruent to $1$ modulo $4$, and there is a quaternary Legendre pair of length $2p$ for every odd prime $p$ for which $2p-1$ is a prime power.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-16T01:15:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "05B30"
    ],
    "keywords": [
      "prime power",
      "length quaternary legendre pairs",
      "first general constructions",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}