Group algebras and coding theory: a short survey

Abstract

espanolEstudiamos codigos construidos a partir de ideales de algebras de grupo y estamos particularmente interesados en sus dimensiones y pesos. Introducimos inicialmente un tipo especial de idempotentes y estudiamos los ideales que generan. Usamos esta informacion para mostrar que existen grupos abelianos no ciclicos que son mas convenientes que los ciclicos. Finalmente, discutimos brevemente algunos resultados sobre codigos no abelianos. EnglishWe study codes constructed from ideals in group algebras and we are particularly interested in their dimensions and weights. First we introduced a special kind of idempotents and study the ideals they generate.We use this information to show that there exist abelian non-cyclic groups that give codes which are more convenient than the cyclic ones. Finally, we discuss briefly some facts about non-abelian codes.