In this paper we study a model quantum register \(\cal R\) made of \(N\) replicas (cells) of a given finite-dimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for \(N\) large enough, in the Hilbert space of \(\cal R\) there exists a linear subspace \({\cal C}_N\) which is dynamically decoupled from the environment. The states in \({\cal C}_N\) evolve unitarily and are therefore decoherence-dissipation free. The space \({\cal C}_N\) realizes a noiseless quantum code in which information can be stored, in principle, for arbitrarily long time without being affected by errors.