One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) = \dim(U+V)-\dim(U\cap V) \geq d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper, we propose a construction for constant dimension subspace codes by inserting a composite structure composing of an MRD code and its sub-codes. Its vast advantage over the previous constructions has been confirmed through extensive examples. At least $49$ new constant dimension subspace codes which exceeds the currently best codes are constructed.
翻译：子空间编码的最根本议题之一是探索$\bf A ⁇ q(n,d,k) 中一套美元维次空间的最大可能值$\mathb{F ⁇ q ⁇ n$,这样子空间距离就能够满足$\operatorname{d_S}(U,V) =\dim(U+V)-dim(U\cap V)\geq d$,用于任何两种不同的美元维次空间。在本文中,我们建议为恒定维次空间代码建造一个结构,组成一个MRD代码及其子代码。它与以往构造相比的巨大优势已经通过大量实例得到证实。至少建造了超过目前最佳代码的49美元新的恒定维次空间代码。
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