New constructions of constant dimension subspace codes with large sizes

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 \(2k-2\) $2k-2$ and 2k. These codes are contained in \(\mathscr {G}_q(n, k)\) ${\mathcal{G}}_q(n,k)$ , where \(\mathscr {G}_q(n, k)\) ${\mathcal{G}}_q(n,k)$ denotes the set of all k-dimensional subspaces of the finite filed \(\mathbb {F}_{q^n}\) ${\mathbb{F}}_{q^n}$ of \(q^n\) $q^n$ elements (q a prime power). Consequently, some results in [7, 15], and [23] are extended.