k-Point semidefinite programming bounds for equiangular lines

David de Laat; Fabrício  Caluza Machado; Fernando Mário de Oliveira Filho; Frank Vallentin

doi:10.1007/s10107-021-01638-x

k-Point semidefinite programming bounds for equiangular lines

David de Laat, Fabrício Caluza Machado, Fernando Mário de Oliveira Filho, Frank Vallentin

Discrete Mathematics and Optimization

Research output: Contribution to journal › Article › Scientific › peer-review

5 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	533-567
Number of pages	35
Journal	Mathematical Programming
Volume	194
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-021-01638-x
Publication status	Published - 2021

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Laat2021_Article_K-PointSemidefiniteProgrammingFinal published version, 819 KBLicence: CC BY

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title = "k-Point semidefinite programming bounds for equiangular lines",

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.",

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AU - Caluza Machado, Fabrício

AU - de Oliveira Filho, Fernando Mário

AU - Vallentin, Frank

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85104952812

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DO - 10.1007/s10107-021-01638-x

M3 - Article

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JF - Mathematical Programming

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k-Point semidefinite programming bounds for equiangular lines

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