We classify, in terms of the structure of the finite group G, all group algebras KG for which all right ideals are right annihilators of principal left ideals. This means in the language of coding theory that we classify code-checkable group algebras KG which have been considered so far only for abelian groups G. Optimality of checkable codes and asymptotic results are discussed.

中文翻译：

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关于群代数中的可校验码

我们根据有限群G的结构对所有右理想都是左主理想的右湮灭的群代数KG进行分类。这意味着在编码理论的语言中，我们对迄今为止只考虑用于阿贝尔群G的可代码检查群代数KG进行分类。讨论了可校验码的最优性和渐近结果。