Functional Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender Bound

Pfender $\mathit{\text{[J.}}\mathit{\text{Combin.}}\mathit{\text{Theory}}\mathit{\text{Ser.}}\mathit{\text{A,}}\mathit{\text{2007]}}$ provided a one-line proof for a variant of the Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein upper bound for spherical codes, which offers an upper bound for the celebrated (Newton-Gregory) kissing number problem. Motivated by this proof, we introduce the notion of codes in pointed metric spaces (in particular on Banach spaces) and derive a nonlinear (functional) Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender upper bound for spherical codes. We also introduce nonlinear (functional) Kissing Number Problem.