<p style='text-indent:20px;'>A basic problem for constant dimension codes is to determine the maximum possible size <inline-formula><tex-math>\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> of a set of <inline-formula><tex-math>\begin{document}$ k $\end{document}</tex-math></inline-formula>-dimensional subspaces in <inline-formula><tex-math>\begin{document}$ \mathbb{F}_q^n $\end{document}</tex-math></inline-formula>, called codewords, such that the subspace distance satisfies <inline-formula><tex-math>\begin{document}$ d_S(U,W): = 2k-2\dim(U\cap W)\ge d $\end{document}</tex-math></inline-formula> for all pairs of different codewords <inline-formula><tex-math>\begin{document}$ U $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math>\begin{document}$ W $\end{document}</tex-math></inline-formula>. Constant dimension codes have applications in e.g. random linear network coding, cryptography, and distributed storage. Bounds for <inline-formula><tex-math>\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show the potential for further improvements. As examples we give improved constructions for the cases <inline-formula><tex-math>\begin{document}$ A_q(10,4;5) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math>\begin{document}$ A_q(11,4;4) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math>\begin{document}$ A_q(12,6;6) $\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math>\begin{document}$ A_q(15,4;4) $\end{document}</tex-math></inline-formula>. We also derive general upper bounds for subcodes arising in those constructions.</p>

中文翻译：

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构建恒定维度代码的不同指标的相互作用

/tex-math></inline-formula>, <inline-formula><tex-math>\begin{document}$ W $\end{document}</tex-math></inline-formula>。恒定维码在例如随机线性网络编码、密码学和分布式存储中具有应用。<inline-formula><tex-math>\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> 的界限是许多最近的主题调查报告。我们提供了一个通用框架，调查了许多最新的建筑，并展示了进一步改进的潜力。作为示例，我们为案例 <inline-formula><tex-math>\begin{document}$ A_q(10,4;5) $\end{document}</tex-math></inline-formula 提供了改进的结构>, <inline-formula><tex-math>\begin{document}$ A_q(11,4;4) $\end{document}</tex-math> </inline-formula>, <inline-formula><tex-math>\begin{document}$ A_q(12,6;6) $\end{document}</tex-math></inline-formula>,和 <inline-formula><tex-math>\begin{document}$ A_q(15,4;4) $\end{document}</tex-math></inline-formula>。我们还推导出这些结构中出现的子码的一般上限。</p>