论文标题
可划分的线性等级公制代码
Divisible linear rank metric codes
论文作者
论文摘要
超过$ \ mathbb {f} _ {q^e}^{m \ times n} $的子空间自然可以嵌入为矩阵的子空间中的$ \ mathbb {f} _q^_q^{em \ times en} $与其任何Mottrix的等级$ e $ $ e $ $ e $ $ e $。询问具有这种特性的矩阵的所有子空间是很自然的，这是由较大场上的矩阵子空间引起的。在本文中，我们探讨了这个问题，该问题与研究等级度量的可划分代码相对应。我们确定了这个问题成立的某些情况，并通过使用该属性构建子空间来描述反例，而该子空间不是由较大字段上的矩阵子空间产生的。
A subspace of matrices over $\mathbb{F}_{q^e}^{m\times n}$ can be naturally embedded as a subspace of matrices in $\mathbb{F}_q^{em\times en}$ with the property that the rank of any of its matrix is a multiple of $e$. It is quite natural to ask whether or not all subspaces of matrices with such a property arise from a subspace of matrices over a larger field. In this paper we explore this question, which corresponds to studying divisible codes in the rank metric. We determine some cases for which this question holds true, and describe counterexamples by constructing subspaces with this property which do not arise from a subspace of matrices over a larger field.
