This paper introduces a noiseless quantum code based on a quantum register R composed of N replicas of a finite-dimensional quantum system S. When all cells are symmetrically coupled to a common environment, a subspace C_N of the Hilbert space of R is dynamically decoupled from the environment. States in C_N evolve unitarily and are thus immune to decoherence and dissipation, allowing for the storage of information without error. This approach, termed "Error Avoiding," is complementary to traditional error-correcting codes (ECC) and relies on the intrinsic symmetry of the system-bath coupling. The subspace C_N corresponds to the singlet sector of the dynamical algebra of S, consisting of one-dimensional representations. The paper demonstrates that for sufficiently large N, C_N remains unaffected by environmental interactions, enabling the construction of noiseless quantum codes. The result is generalizable to various algebraic structures and has implications for quantum information processing, particularly in preserving quantum coherence. The study also highlights the potential for extending these results to infinite-dimensional systems and discusses practical challenges in implementing such codes.This paper introduces a noiseless quantum code based on a quantum register R composed of N replicas of a finite-dimensional quantum system S. When all cells are symmetrically coupled to a common environment, a subspace C_N of the Hilbert space of R is dynamically decoupled from the environment. States in C_N evolve unitarily and are thus immune to decoherence and dissipation, allowing for the storage of information without error. This approach, termed "Error Avoiding," is complementary to traditional error-correcting codes (ECC) and relies on the intrinsic symmetry of the system-bath coupling. The subspace C_N corresponds to the singlet sector of the dynamical algebra of S, consisting of one-dimensional representations. The paper demonstrates that for sufficiently large N, C_N remains unaffected by environmental interactions, enabling the construction of noiseless quantum codes. The result is generalizable to various algebraic structures and has implications for quantum information processing, particularly in preserving quantum coherence. The study also highlights the potential for extending these results to infinite-dimensional systems and discusses practical challenges in implementing such codes.