k-Point semidefinite programming bounds for equiangular lines

Journal article (2021)

Authors

D. de Laat Discrete Mathematics and Optimization - EEMCS
Fabrício Caluza Machado Universidade de São Paulo
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS
Frank Vallentin Universität zu Köln
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2021 D. de Laat, Fabrício Caluza Machado, F.M. de Oliveira Filho, Frank Vallentin
DOI: https://doi.org/10.1007/s10107-021-01638-x
More Info
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Published Date

2021

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

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.