Códigos hiperbólicos

Abstract

In this work we study the so-called hyperbolic codes. We initially present results on finite fields and introduce concepts and results from Gröbner’s Basis theory, such as affine manifolds, the footprint of an ideal, and the relationship between the footprint and the manifold of an ideal. Next, we present the hyperbolic codes and, through Gröbner’s Basis theory, we were able to determine the fundamental parameters (length, dimension, and minimum distance) of the hyperbolic codes and provide a characterization of the hyperbolic codes through duality. Having introduced the generalized Hamming weights and definitions such as dense and optimal sets, it was possible to determine a lower bound for the generalized Hamming weight of these codes.