  Subspace codes and particularly constant dimension codes have attracted much
attention in recent years due to their applications in random network coding.
As a particular subclass of subspace codes, cyclic subspace codes have
additional properties that can be applied efficiently in encoding and decoding
algorithms. It is desirable to find cyclic constant dimension codes such that
both the code sizes and the minimum distances are as large as possible. In this
paper, we explore the ideas of constructing cyclic constant dimension codes
proposed in \big([2], IEEE Trans. Inf. Theory, 2016\big) and \big([17], Des.
Codes Cryptogr., 2016\big) to obtain further results. Consequently, new code
constructions are provided and several previously known results in [2] and [17]
are extended.
