等维子空间码的参数控制插入构造
Parameter-controlled inserting constructions of constant dimension subspace codes
摘要：
恒定维度子空间编码中的基本问题是确定${\bf F}_q^n$中的一组$k$维度子空间的最大可能大小${\bf A}_q(n,d,k)$，使得对于该组中的任何两个不同的$k$维度子空间$U$和$V$，子空间距离满足$\operatorname{dis}(U,V)=2k-2\dim(U \cap V) \geq d$.本文提出了一种新的参数控制的常维子空间码的插入构造。这些插入结构是灵活的，因为它们受参数控制。从我们的灵活插入构造中可以导出几个新的更好的下界，它们比以前所有的构造性下界都要好。$141$构造了距离$4,6,8$优于以前最好的已知码的新的常维子空间码。
英文摘要：
A basic problem in constant dimension subspace coding is to determine the maximal possible size ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in ${\bf F}_q^n$ such that the subspace distance satisfies $\operatorname{dis}(U,V)=2k-2\dim(U \cap V) \geq d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper we propose new parameter-controlled inserting constructions of constant dimension subspace codes. These inserting constructions are flexible because they are controlled by parameters. Several new better lower bounds which are better than all previously constructive lower bounds can be derived from our flexible inserting constructions. $141$ new constant dimension subspace codes of distances $4,6,8$ better than previously best known codes are constructed.
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。
