In this paper we introduce a code-based cryptosystem using quasi-cyclic generalized subspace subcodes of Generalized Reed-Solomon codes in order to reduce the public key size. In our scheme the underlying Generalized Reed-Solomon code is not secret, so the classical attacks such as square code or folding attacks have no more purpose against it. In addition one part of the security of this scheme is based on hard problems in coding theory like Equivalence Subcodes (ES) Problem. We propose some parameters to reach at least a security level of 128 and 192 bits. We make a public key size comparison with some well established code-based public key encryption schemes. We also see that for the 128 bits security level the key size of our proposals are often better than the code-based schemes in competition for NIST’s second round.