  We prove that the kissing number in 48 dimensions among antipodal spherical
codes with certain forbidden inner products is 52\,416\,000. Constructions of
attaining codes as kissing configurations of minimum vectors in even unimodular
extremal lattices are well known since the 1970's. We also prove that
corresponding spherical 11-designs with the same cardinality are minimal. We
use appropriate modifications of the linear programming bounds for spherical
codes and designs introduced by Delsarte, Goethals and Seidel in 1977.
