$k$-point semidefinite programming bounds for equiangular lines

Abstract

We give 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.

arXiv comment26 pages, 4 figures. New introduction and references updated

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• Potential theory with multivariate kernels
• An extension the semidefinite programming bound for spherical codes
• Semidefinite programming bounds for error-correcting codes