Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A Note on the Tight Spherical 7-Design in$${\mathbb R}^{23}$$ and 5-Design in$${\mathbb R}^{7*}$$
Designs, Codes and Cryptography
Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
European Journal of Combinatorics
A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
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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.