Códigos abelianos minimais

Abstract

The purpose of this work is to study the articles of Arora-Pruthi and Ferraz-Milies about Error Correcting Codes endowed with certain algebraic structures. Precisely, we study the minimal abelian codes seen as ideals of a group algebra FG; where F is a finite field and G is a finite abelian group. Under these conditions, the primitive idempotents of the algebra FG; characterizing the minimal abelian codes of this algebra, are found. Furthermore, the minimum distance, the dimension, the weight and the generator polynomial of these minimal codes are also obtained. Finally, the number of simple components of the semisimple group algebra is calculated and it is shown that this number corresponds to the number of primitive idempotents of this group algebra