Globally optimizing small codes in real projective spaces

12/06/2019

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by   Dustin G. Mixon, et al.

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For d∈{5,6}, we classify arrangements of d + 2 points in RP^d-1 for which the minimum distance is as large as possible. To do so, we leverage ideas from matrix and convex analysis to determine the best possible codes that contain equiangular lines, and we introduce a notion of approximate Positivstellensatz certificates that promotes numerical approximations of Stengle's Positivstellensatz certificates to honest certificates.