The Kissing Number in 48 Dimensions for Codes with Certain Forbidden Distances is 52 416 000

We prove that the kissing number in 48 dimensions among antipodal spherical codes with certain forbidden inner products is 52 416 000. Constructions of attaining codes as kissing configurations of minimum vectors in even unimodular extremal lattices are well known since the 1970’s. We also prove that corresponding spherical 11-designs with the same cardinality are minimal. We use appropriate modifications of the linear programming bounds for spherical codes and designs introduced by Delsarte, Goethals and Seidel in 1977.

• Publication year

  2023

• Venue

  Results in Mathematics

• Publication date

  2023-12-08

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1007/s00025-024-02322-0arXiv 2312.05121
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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