  A set $C$ of unit vectors in $\mathbb{R}^d$ is called an $L$-spherical code
if $x \cdot y \in L$ for any distinct $x,y$ in $C$. Spherical codes have been
extensively studied since their introduction in the 1970's by Delsarte,
Goethals and Seidel. In this note we prove a conjecture of Bukh on the maximum
size of spherical codes. In particular, we show that for any set of $k$ fixed
angles, one can choose at most $O(d^k)$ lines in $\mathbb{R}^d$ such that any
pair of them forms one of these angles.
