论文标题
非最低张量秩加宾素代码
Non-minimum tensor rank Gabidulin codes
论文作者
论文摘要
研究了一些小尺寸的Gabidulin代码的张量等级。特别是，我们确定等同于$ 8 $二维$ \ mathbb {f} _q $ - linear grenderal grentarized gabidulin代码的任何等级度量代码的张量排名。这表明这样的代码永远不会是最小张量排名。通过这种方式，我们检测到不是最小张量等级的第一个无限的Gabidulin代码家族。
The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an $8$-dimensional $\mathbb{F}_q$-linear generalized Gabidulin code in $\mathbb{F}_{q}^{4\times4}$. This shows that such a code is never minimum tensor rank. In this way, we detect the first infinite family of Gabidulin codes which are not minimum tensor rank.
