k-Point semidefinite programming bounds for equiangular lines

• 成果类型: Article
• 署名作者: de Laat, David; Machado, Fabricio Caluza; de Oliveira Filho, Fernando Mario; Vallentin, Frank
• 署名单位: Delft University of Technology; Universidade de Sao Paulo; University of Cologne
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01638-x
• 发表日期: 2022
• 页码: 533-567
• 关键词: sets

摘要

We propose a hierarchy of k-point bounds extending the Delsarte-Goethals-Seidel linear programming 2-point bound and the Bachoc-Vallentin semidefinite programming 3-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute 4, 5, and 6-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.