Tópicos de códigos geometricamente uniformes em espaços hiperbólicos

Abstract

This dissertation is an extended text resulting from the study of paper [14] by Lazari & Palazzo Jr. (2005), in which there is the generalization of the concepts of geometrically uniform partitions and geometrically uniform codes, widely used in euclidean spaces, to hyperbolic spaces. The main studied theorem is a characterization of generalized coset codes through the concept of G-linear codes (Theorem 4.3). Besides the detailed study of the paper, we also establish a small contribution: the proof that the fundamental group g of a compact surface S of genus g 2, obtained by quocient of a hyperbolic space by πg, is a normal subgroup of the group generated by re ections at the sides of a hyperbolic right triangle that establishes a symmetric tiling in the fundamental region of πg (Theorem 3.4).