Minimal ideals in finite abelian group algebras and coding theory

Abstract

We consider abelian groups of order \(p^nq^m\) where p and q are prime rational integers under some restrictive hypotheses and determine the set of primitive idempotents of the group algebra \({{\mathbb {F}}}G\) for a finite field \({{\mathbb {F}}}\). The minimal ideals they generate can be considered as minimal codes and we determine either the respective minimum weights or bounds of these weights. We give examples showing that these bounds are actually attained in some cases.