p-adic Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender Bound

We introduce the notion of p-adic spherical codes (in particular, p-adic kissing number problem). We show that the one-line proof for a variant of the Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein upper bound for spherical codes, obtained by Pfender $\mathit{\text{[J.}}\mathit{\text{Combin.}}\mathit{\text{Theory}}\mathit{\text{Ser.}}\mathit{\text{A,}}\mathit{\text{2007]}}$, extends to p-adic Hilbert spaces.