Abstract
Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra \({\mathbb F}G\) for a large class of groups \(G\). As an illustration of our methods, alternative constructions to some best linear codes over \({\mathbb F}_2\) and \({\mathbb F}_3\) are given. Furthermore, we give constructions of non-abelian left group codes.
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