论文标题
关于组代数和组代码的理想维度
On the dimension of ideals in group algebras, and group codes
论文作者
论文摘要
通过分析常规表示的最小多项式来确定组代数中主理想维度的几个关系和界限。这些结果用于最后两个部分。首先，在半神经群代数的背景下，以计算任何阿贝尔代码，这是锤击重量等于其尺寸的元素。最后，要在某些MDS组代码的最小距离上获得界限。提出了一类组代码和MDS代码之间的关系。提供了说明主要结果的示例。
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of semisimple group algebras, to compute, for any abelian code, an element with Hamming weight equal to its dimension. Finally, to get bounds on the minimum distance of certain MDS group codes. A relation between a class of group codes and MDS codes is presented. Examples illustrating the main results are provided.
