Códigos de Grupo Gerado por Grupos de Reflexões Finitos

Abstract

The main objective of this work is the construction of codes of optimal groups generated by groups of finite reflections or groups of Irreducible Coxeter. One group is called the Coxeter Group, in homage to H. S. M. Coxeter (1934), who classified all reflection groups completely and deduced several of his properties using mainly geometric methods. THE construction is based on the analysis of the initial vector problem. This one The problem is solved by using a vectors with their own characteristics, called the roots. The classic group code results are generalizations of the already well-known modulation codes of permutations introduced by Slepian over 42 years ago, where it turns out that the problem of the initial vector restricted to groups of Coxeter has a solution that can be easily calculated. Like objective of better understanding of the theory, an approach is given algebraic at the end of the book giving some examples for the determination of the initial vector.