论文标题
分散的线性组与MRD代码之间的连接
Connections between scattered linear sets and MRD-codes
论文作者
论文摘要
本文的目的是对最大散射线性组和MRD代码的已知结果进行调查。特别是，我们研究了这两个领域之间的联系。在“线性最大等级距离代码的新家族”（2016年）中，Sheekey显示了$ \ mathrm {pg} $ \ mathrm {pg}（1，q^n）$定义Square MRD-codes的最大散射线性集。后来，在$ \ mathrm {pg}（r-1，q^n）$，$ r> 2 $中以$ \ mathrm {pg}中的最大散射线性集在“最大散射线性集和MRD-codes”（2017）中用于构造非平方MRD-MRD-codes。在这里，我们指出了有关另一个方向的新关系。我们还提供了众所周知的Blokhuis-lavrauw的替代证明，即“散布空间相对于$ \ Mathrm {pg}（n，q）$中的扩散相对于散布的最大散射线性组的等级。”（2000年）。
The aim of this paper is to survey on the known results on maximum scattered linear sets and MRD-codes. In particular, we investigate the link between these two areas. In "A new family of linear maximum rank distance codes" (2016) Sheekey showed how maximum scattered linear sets of $\mathrm{PG}(1,q^n)$ define square MRD-codes. Later in "Maximum scattered linear sets and MRD-codes" (2017) maximum scattered linear sets in $\mathrm{PG}(r-1,q^n)$, $r>2$, were used to construct non square MRD-codes. Here, we point out a new relation regarding the other direction. We also provide an alternative proof of the well-known Blokhuis-Lavrauw's bound for the rank of maximum scattered linear sets shown in "Scattered spaces with respect to a spread in $\mathrm{PG}(n,q)$" (2000).
