Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension subspace codes with minimum distances $2k-2$ and $2k$. These codes are contained in $\mathcal{G}_q(n, k)$, where $\mathcal{G}_q(n, k)$ denotes the set of all $k$-dimensional subspaces of $\mathbb{F}_{q^n}$. Consequently, some results in \cite{FW}, \cite{NXG}, and \cite{ZT} are extended.

翻译：子空间码在随机网络编码中具有重要应用。构造同时具有较大码本尺寸且最小距离尽可能大的子空间码具有重要意义。特别地，循环常维子空间码具有额外的性质，可用于提高编码与解码效率。本文构造了最小距离为$2k-2$和$2k$的大尺寸循环常维子空间码。这些码包含于$\mathcal{G}_q(n, k)$中，其中$\mathcal{G}_q(n, k)$表示$\mathbb{F}_{q^n}$上所有$k$维子空间构成的集合。由此，文献\cite{FW}、\cite{NXG}和\cite{ZT}中的部分结果得到了推广。