Abel非循环轨道码与多重子空间码
Abelian Noncyclic Orbit Codes and Multishot Subspace Codes
摘要：
本文将轨道码刻画为几何一致码。这种刻画是基于对射影几何上所有等距的描述。定义了Abel轨道码，给出了Abel非循环轨道码的一种新的构造方法。为了分析它们的结构，必须重新解释几何均匀分区的概念。因此，实现并建立了获得这些代码的最小子空间距离所需的计算数量的大幅减少。给出了轨道码在多级构造的多激发子空间码中的应用。
英文摘要：
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, the Abelian orbit codes are defined and a new 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.
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