k-Point semidefinite programming bounds for equiangular lines

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 m...

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Bibliographic Details
Published inMathematical programming Vol. 194; no. 1-2; pp. 533 - 567
Main Authors de Laat, David, Machado, Fabrício Caluza, Filho, Fernando Mário de Oliveira, Vallentin, Frank
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Springer
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Euclidean geometry
Full Length Paper
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Semidefinite programming
Theoretical
90C22
52C17
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Summary: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01638-x