Códigos Perfeitos Na Métrica De Lee E A Conjectura De Golomb-Welch

Abstract

The Aim Of This Work Is The Study Of The Golomb-Welch Conjecture And The Relations Between Perfect Codes In The Lee Metric In Zn And Znq , Q 2 N, Q 2, And Tilings In Rn. In This Study, We Stress Two Articles: \Perfect Codes In The Lee Metric And The Packing Of Polyominoes", Written By Solomon W. Golomb E Lloyd R. Welch, Which Presents The Conjecture And Some Facts About Tilings Of Zn By Lee Spheres And \A New Approach Towards The Golomb-Welch Conjecture", Written By Peter Horak E Otokar Grosek, Which Gives A Soloution For Some Cases Of The Conjecture Introducing A New Algebraic Invariant Related To Abelian Groups.

O Objetivo Deste Trabalho E O Estudo Da Conjectura De Golomb-Welch E Das Relac~Oes Entre Codigos Perfeitos Na Metrica De Lee Em Zn E Znq , Q 2 N, Q 2, E Ladrilhamentos Em Rn. Neste Estudo, Damos ^Enfase A Dois Artigos: \Perfect Codes In The Lee Metric And The Packing Of Polyominoes", De Solomon W. Golomb E Lloyd R. Welch, Que Apresenta A Conjectura E Enuncia Alguns Fatos Envolvendo Ladrilhamentos Por Esferas De Lee E \A New Approach Towards The Golomb-Welch Conjecture", De Peter Horak E Otokar Grosek, Que Soluciona Alguns Casos Particulares Da Conjectura Por Meio Da Introduc~Ao De Um Invariante Algebrico Relacionado A Grupos Abelianos.