Globally Optimizing Small Codes in Real Projective Spaces
Dustin G. Mixon, Hans Parshall · SIAM Journal on Discrete Mathematics · 2021
For $d\in\{5,6\}$, 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.