论文标题
分散的子空间和相关代码
Scattered subspaces and related codes
论文作者
论文摘要
在Shekeey（2016）的开创性论文之后，在极端情况$ H = 1 $和$ H = R-1 $之间建立了$ V（R，Q^n）$的最大$ h $ scatered $ \ mathbb {f} _q $ -subspaces的连接。在本文中，我们提出了任何$ h \ in \ {1，\ ldots，r-1 \} $的连接，扩展并统一了所有先前已知的连接。结果，我们获得了非方形MRD代码的示例，这些示例不等于通用的Gabidulin或扭曲的Gabidulin代码。直到等效性，我们将MRD代码与连接中具有相同参数相同的MRD代码进行了分类。此外，我们确定与最大$ h $散布子空间的几何对应物相关的代码的重量分布。
After a seminal paper by Shekeey (2016), a connection between maximum $h$-scattered $\mathbb{F}_q$-subspaces of $V(r,q^n)$ and maximum rank distance (MRD) codes has been established in the extremal cases $h=1$ and $h=r-1$. In this paper, we propose a connection for any $h\in\{1,\ldots,r-1\}$, extending and unifying all the previously known ones. As a consequence, we obtain examples of non-square MRD codes which are not equivalent to generalized Gabidulin or twisted Gabidulin codes. Up to equivalence, we classify MRD codes having the same parameters as the ones in our connection. Also, we determine the weight distribution of codes related to the geometric counterpart of maximum $h$-scattered subspaces.
