On the Main Parameters of Parameterized Codes

In this paper we will estimate the main parameters of some evaluation codes which are known as parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert function associated to the vanishing ideal of the projective torus. Also we will find an upper bound for the minimum distance and, in some cases, we will give some lower bounds for the regularity index and the minimum distance. These lower bounds work in several cases, particularly for any parameterized code associated to the incidence matrix of uniform clutters and then they work in the case of graphs.