Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace 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 \(\mathscr {G}_q(n, k)\), where \(\mathscr {G}_q(n, k)\) denotes the set of all k-dimensional subspaces of the finite filed \(\mathbb {F}_{q^n}\) of \(q^n\) elements (q a prime power). Consequently, some results in [7, 15], and [23] are extended.

子空间码在随机网络编码中具有重要的应用。构造子空间码是一个经典问题，其中子空间码的大小和最小距离都尽可能大。特别地，循环恒定维度子空间码具有可用于使编码和解码更高效的附加属性。在本文中，我们构造具有最小距离\(2k-2\)和 2 k的大循环常维子空间码。这些代码包含在\(\mathscr {G}_q(n, k)\)中，其中\(\mathscr {G}_q(n, k)\)表示有限域的所有k维子空间的集合\(\mathbb {F}_{q^n}\)个\(q^n\)个元素（q为素数幂）。因此，[7、15]和[23]中的一些结果得到了扩展。