Optimality and uniqueness of the (4,10,1/6) spherical code
Journal of Combinatorial Theory - Series A , Volume 116 - Issue 1 p. 195- 204
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.
|Linear programming, Semidefinite programming, Spherical codes, Spherical designs, Petersen graph|
|dimensions (msc 52C17), Semidefinite programming (msc 90C22)|
|Logistics (theme 3)|
|Journal of Combinatorial Theory - Series A|
|Organisation||Networks and Optimization|
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.