两类最大秩距离码的推广
Extending two families of maximum rank distance codes
摘要：
本文给出了一个大的秩度量码族，它适当地包含了Longobardi和Zanella（2021）以及Longobardi，Marino，Trombetti和Zhou（2021）最近发现的码。这些码在$\mathbb{F}_{q^{2t}}$上的线性化多项式空间中是维数为$2$的$\mathbb{F}_{q^{2t}}$ -线性的，其中$t$是大于$2$的任意整数，并且我们证明了它们是最大秩距离码.对于$t\ge 5$，我们确定了它们的等价类，这些码与迄今为止已知的任何其他构造都是不等价的，因此它们是真正新的。
英文摘要：
In this paper we provide a large family of rank-metric codes, which contains properly the codes recently found by Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021). These codes are $\mathbb{F}_{q^{2t}}$-linear of dimension $2$ in the space of linearized polynomials over $\mathbb{F}_{q^{2t}}$, where $t$ is any integer greater than $2$, and we prove that they are maximum rank distance codes. For $t\ge 5$, we determine their equivalence classes and these codes turn out to be inequivalent to any other construction known so far, and hence they are really new.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
