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.

Keywords

• code
• Hamming distance
• weight
• group algebra
• ideal
• group code