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. We provide constructions of optimal cyclic codes for which their codewords do
not have full length 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, while providing several insights about the connection between subspaces and their subspace polynomials.
Joint work with Prof. Eli Ben-Sasson, Dr. Ariel Gabizon, and Prof. Tuvi Etzion.