Group algebras and coding theory: a short survey

Abstract

We 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. Álgebras de grupo y teoría de códigos: una breve reseñaResumen. Estudiamos códigos construidos a partir de ideales de álgebras 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 información para mostrar que existen grupos abelianos no cíclicos que son más convenientes que los cíclicos. Finalmente, discutimos brevemente algunos resultados sobre códigos no abelianos.

On the number of non-G-equivalent minimal abelian codes

“…Group codes have been of interest for many researchers. For an extensive literature on group codes, see the survey [17]. For some recent works in the field of group codes, see [1, 4-6, 8, 9, 15, 16].…”