In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, Abelian orbit codes are defined and a construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As a consequence, a substantial reduction in the number of computations needed to obtain the minimum subspace distance of these codes is achieved and established.An application of orbit codes to multishot subspace codes obtained according to a multi-level construction is provided.

中文翻译：

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阿贝尔非循环轨道码和多重子空间码

在本文中，我们将轨道代码表征为几何上统一的代码。此表征基于投影几何上所有等距的描述。此外，定义了Abelian轨道码，并提出了Abelian非循环轨道码的构造。为了分析其结构，必须重新解释几何均匀分区的概念。结果，实现并建立了显着减少获得这些代码的最小子空间距离所需的计算数量的方法。提供了将轨道代码应用于根据多级构造而获得的多子空间代码的应用。