Improved generalized block inserting construction of constant dimension codes
Improved generalized block inserting construction of constant dimension codes
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DOI：
10.1007/s10623-022-01117-0
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Xiaoqin Hong;X. Cao
中科院分区：
文献类型：
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作者：
Xiaoqin Hong;X. Cao
恒维码因其在随机网络编码中的应用而受到广泛关注。CDC的基本问题是确定给定参数q，n，dandk的CDC的最大可能基数。在这篇文章中，我们给出了广义块插入法的一些变种。这些结构通过改变参数和移动一些小矩阵的位置，将更多的子空间从并联结构引入到CDC中。我们的构造帮助我们得到了具有更大基数的CDC和一些新的CDC的下界，这些新的下界比以前最著名的CDC更好。
Constant dimension codes (CDCs) have received extensive attention due to their applications in random network coding. The basic problem for CDCs is to determine the maximal possible cardinalityof CDC for given parametersq,n,dandk. In this paper, we present some variations on the generalized block inserting construction method. These constructions insert more subspaces into the CDC from the parallel linkage construction via changing the parameters and shifting the positions of some small matrices. Our constructions help us to obtain CDCs with larger cardinalities and some new lower bounds for CDCs which are better than the previously best known ones.