Códigos parametrizados afins

Abstract

In this work, we present a special class of linear codes: parameterized affine codes. We show that these codes are easy to construct and that given a parameterized affine code one can easily obtain an equivalent projective parameterized code equivalent to it. We also studied some topics which served as the theoretical foundations for the work, such as the theory of Groebner Bases, the footprint of an ideal and some topics of algebraic geometry and commutative algebra. This work has as main goal to obtain the basic parameters (length, dimension and minimum distance) of parameterized codes related and also to relate them to the projective parameterized codes, as done in [7]. We finish by applying the theory of Groebner Bases to the footprint of a certain ideal in order to obtain the basic parameters of the parameterized code over an affine torus.