English

Globally optimizing small codes in real projective spaces

Metric Geometry 2019-12-10 v1 Information Theory Combinatorics math.IT

Abstract

For d{5,6}d\in\{5,6\}, we classify arrangements of d+2d + 2 points in RPd1\mathbf{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.

Keywords

Cite

@article{arxiv.1912.03373,
  title  = {Globally optimizing small codes in real projective spaces},
  author = {Dustin G. Mixon and Hans Parshall},
  journal= {arXiv preprint arXiv:1912.03373},
  year   = {2019}
}

Comments

code included in ancillary files

R2 v1 2026-06-23T12:38:37.095Z