Abstract: Firstly, we gave a relatively concise proof concerning the relationship between the length of subspace orbits and the exponent of subspace polynomials. Secondly,  by applying Frobenius shifts to subspaces and merging  cyclic subspace codes, we obtained cyclic subspace codes with a larger size of ((rn(q^N-1)/(q-1)) and a minimum distance of 2k-2. Finally, we gave an example of constructing a cyclic subspace code.

Key words: cyclic subspace code, subspace polynomials, Frobenius shift, orbit