{
  "id": "2304.07906",
  "version": "v1",
  "published": "2023-04-16T22:02:57.000Z",
  "updated": "2023-04-16T22:02:57.000Z",
  "title": "Sidon sets, sum-free sets and linear codes",
  "authors": [
    "Ingo Czerwinski",
    "Alexander Pott"
  ],
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Finding the maximum size of a Sidon set in $\\mathbb{F}_2^t$ is of research interest for more than 40 years. In order to tackle this problem we recall a one-to-one correspondence between sum-free Sidon sets and linear codes with minimum distance greater or equal 5. Our main contribution about codes is a new non-existence result for linear codes with minimum distance 5 based on a sharpening of the Johnson bound. This gives, on the Sidon set side, an improvement of the general upper bound for the maximum size of a Sidon set. Additionally, we characterise maximal Sidon sets, that are those Sidon sets which can not be extended by adding elements without loosing the Sidon property, up to dimension 6 and give all possible sizes for dimension 7 and 8 determined by computer calculations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-16T22:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "94B05",
      "94B65"
    ],
    "keywords": [
      "linear codes",
      "sum-free sets",
      "characterise maximal sidon sets",
      "sum-free sidon sets",
      "minimum distance greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}