  Subspace codes have received an increasing interest recently due to their
application in error-correction for random network coding. In particular,
cyclic subspace codes are possible candidates for large codes with efficient
encoding and decoding algorithms. In this paper we consider such cyclic codes
and provide constructions of optimal codes for which their codewords do not
have full orbits. We further introduce a new way to represent subspace codes by
a class of polynomials called subspace polynomials. We present some
constructions of such codes which are cyclic and analyze their parameters.
