论文标题
关于$ 2 $维度线性最大排名距离距离的等效问题
On the equivalence issue of a class of $2$-dimensional linear Maximum Rank Distance codes
论文作者
论文摘要
在[A。 Neri，P。Santonastaso，F。Zullo。延长了两个最高等级距离代码的家族]，作者扩大了$ 2 $ - 维的$ \ mathbb {f} _ {q^{2t}} $ - 最近在[G. Longobardi，G。Marino，R。Trombetti，Y。Zhou。 $ \ mathrm {pg}（1，q^n）$及其关联的MRD代码的大型最大散射线性套件。另外，对于$ t \ geq 5 $，他们确定了这个新家庭中元素的等效类别，并提供了其中的不等代码。在本文中，我们完成了对等效问题的研究，删除了限制$ t \ geq 5 $。此外，我们证明，在$ t = 4 $的情况下，射影线$ \ mathrm {pg}的线性集（1，q^{8}）$从相关家族的代码中随之而来，并不等于到目前为止的任何一个已知的人。
In [A. Neri, P. Santonastaso, F. Zullo. Extending two families of maximum rank distance codes], the authors extended the family of $2$-dimensional $\mathbb{F}_{q^{2t}}$-linear MRD codes recently found in [G. Longobardi, G. Marino, R. Trombetti, Y. Zhou. A large family of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$ and their associated MRD codes]. Also, for $t \geq 5$ they determined equivalence classes of the elements in this new family and provided the exact number of inequivalent codes in it. In this article, we complete the study of the equivalence issue removing the restriction $t \geq 5$. Moreover, we prove that in the case when $t=4$, the linear sets of the projective line $\mathrm{PG}(1,q^{8})$ ensuing from codes in the relevant family, are not equivalent to any one known so far.
