论文标题
常数尺寸子空间代码的参数控制的插入结构
Parameter-controlled inserting constructions of constant dimension subspace codes
论文作者
论文摘要
恒定尺寸子空间编码中的一个基本问题是确定一组$ k $ - 二维子空间的最大尺寸$ {\ bf a} _q（n，d，k）$ in $ {\ bf f} _q^n $中的一个$ k $ - 二维子空间D $对于任何两个不同的$ k $二维子空间$ u $和$ v $。在本文中，我们提出了恒定尺寸子空间代码的新参数控制的插入结构。这些插入结构是灵活的，因为它们是由参数控制的。比以前所有建设性的下限更好的新的更好的下限可以从我们的灵活插入构造中得出。 $ 141 $构建的新常数尺寸子空间距离$ 4,6,8 $比以前最知名的代码更好。
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.
