Constructions of cyclic constant dimension codes

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.