Optimality and uniqueness of the (4,10,1/6) spherical code

Christine Bachoc (1) , Frank Vallentin

1 IMB - Institut de Mathématiques de Bordeaux

Traditionally, optimality and uniqueness of an (n,N,t) spherical code is proved using linear programming bounds. However, this approach does not apply to the parameter (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code (which are the vertices of the 4-dimensional second hypersimplex or the midpoints of the edges of the regular simplex in dimension 4) is the unique (4,10,1/6) spherical code.

Domaines: Géométrie métrique [math.MG]; Combinatoire [math.CO]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Christine Bachoc, Frank Vallentin. Optimality and uniqueness of the (4,10,1/6) spherical code. Journal of Combinatorial Theory, Series A, 2009, 116, pp.195-204. ⟨10.1016/j.jcta.2008.05.001⟩. ⟨hal-00196165⟩