  We give the parameters of any evaluation code on a smooth quadric surface.
For hyperbolic quadrics the approach uses elementary results on product codes
and the parameters of codes on elliptic quadrics are obtained by detecting a
BCH structure of these codes and using the BCH bound. The elliptic quadric is a
twist of the surface P^1 x P^1 and we detect a similar BCH structure on twists
of the Segre embedding of a product of any d copies of the projective line.
