Optimality and uniqueness of the spherical code

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.