{
  "id": "1801.07334",
  "version": "v1",
  "published": "2018-01-22T21:54:04.000Z",
  "updated": "2018-01-22T21:54:04.000Z",
  "title": "On spherical codes with inner products in a prescribed interval",
  "authors": [
    "P. G. Boyvalenkov",
    "P. D. Dragnev",
    "D. P. Hardin",
    "E. B. Saff",
    "M. M. Stoyanova"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.MG"
  ],
  "abstract": "We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on cardinality of codes with inner products in $[\\ell,s]$ and lower bounds on the potential energy (for absolutely monotone interactions) for codes with inner products in $[\\ell,1)$ (when the cardinality of the code is kept fixed) is revealed and explained. Thereby, we obtain a new extension of Levenshtein bounds for such codes. The universality of our bounds is exhibited by a unified derivation and their validity for a wide range of codes and potential functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T21:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B65",
      "52A40",
      "74G65"
    ],
    "keywords": [
      "spherical codes",
      "prescribed interval",
      "inner products belong",
      "levenshtein-type upper bounds",
      "potential functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}