  A hyperbolic code is an evaluation code that improves a Reed-Muller because
the dimension increases while the minimum distance is not penalized. We give
the necessary and sufficient conditions, based on the basic parameters of the
Reed-Muller, to determine whether a Reed-Muller coincides with a hyperbolic
code. Given a hyperbolic code, we find the largest Reed-Muller containing the
hyperbolic code and the smallest Reed-Muller in the hyperbolic code. We then
prove that similarly to Reed-Muller and Cartesian codes, the $r$-th generalized
Hamming weight and the $r$-th footprint of the hyperbolic code coincide. Unlike
Reed-Muller and Cartesian, determining the $r$-th footprint of a hyperbolic
code is still an open problem. We give upper and lower bounds for the $r$-th
footprint of a hyperbolic code that, sometimes, are sharp.
