Generalized block inserting for constructing new constant dimension codes
Generalized block inserting for constructing new constant dimension codes
复制标题
DOI：
10.1007/s12095-022-00590-7
复制
发表时间：
2022-05
期刊：
影响因子：
--
通讯作者：
Xiaoqin Hong;X. Cao
中科院分区：
文献类型：
--
作者：
Xiaoqin Hong;X. Cao
恒维码在随机网络编码中的应用引起了人们的广泛关注。CDC的一个基本问题是探索K维子空间集合的最大可能基数Aq(n，d，k)，使得对于该集合中所有不同的子空间对U和V，子空间距离满足dis(U，V)= 2k− 2dim(U∩V)≥d。本文利用秩度量码和小CDC的矩阵块的适当组合，在Niu等人的广义块插入构造的基础上，给出了三种CDC的构造方法。在2021年。根据我们的构造，我们得到了28个新的CDC下界，这些下界好于已知的下界。
Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. A fundamental problem for CDCs is to explore the maximum possible cardinalityAq(n,d,k) of a set ofk-dimensional subspaces insuch that the subspace distance statisfies dis(U,V) = 2k− 2 dim(U∩V) ≥dfor all pairs of distinct subspacesUandVin this set. In this paper, by means of an appropriate combination of the matrix blocks from rank metric codes and small CDCs, we present three constructions of CDCs based on the generalized block inserting construction by Niu et al. in 2021. According to our constructions, we obtain 28 new lower bounds for CDCs which are better than the previously known lower bounds.