Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code, which consists of the midpoints of the edges of the regular simplex in dimension 4, is the unique (4,10,1/6) spherical code.
Additional Metadata
Keywords Linear programming, Semidefinite programming, Spherical codes, Spherical designs, Petersen graph
MSC dimensions (msc 52C17), Semidefinite programming (msc 90C22)
THEME Logistics (theme 3)
Publisher Academic Press
Journal Journal of Combinatorial Theory - Series A
Citation
Bachoc, C, & Vallentin, F. (2009). Optimality and uniqueness of the (4,10,1/6) spherical code. Journal of Combinatorial Theory - Series A, 116(1), 195–204.