{
  "id": "2411.16559",
  "version": "v2",
  "published": "2024-11-25T16:46:06.000Z",
  "updated": "2024-12-23T17:32:22.000Z",
  "title": "Generalizing the Bierbrauer-Friedman bound for orthogonal arrays",
  "authors": [
    "Denis S. Krotov",
    "Ferruh Özbudak",
    "Vladimir N. Potapov"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We characterize mixed-level orthogonal arrays it terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer--Friedman (BF) bound for pure-level orthogonal arrays and show that arrays attaining it are radius-$1$ completely regular codes (equivalently, intriguing sets, equitable $2$-partitions, perfect $2$-colorings) in the corresponding multigraph. For the case when the numbers of levels are powers of the same prime number, we characterize, in terms of multispreads, additive mixed-level orthogonal arrays attaining the BF bound. For pure-level orthogonal arrays, we consider versions of the BF bound obtained by replacing the Hamming graph by its polynomial generalization and show that in some cases this gives a new bound. Keywords: orthogonal array, algebraic $t$-design, mixed orthogonal array, completely-regular code, equitable partition, intriguing set, Hamming graph, Bierbrauer-Friedman bound, additive code.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-23T17:32:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15",
      "51E23",
      "05E30",
      "94B05"
    ],
    "keywords": [
      "bierbrauer-friedman bound",
      "pure-level orthogonal arrays",
      "mixed-level orthogonal arrays attaining",
      "bf bound",
      "characterize mixed-level orthogonal arrays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}