We address the task of switching off the Hamiltonian of a system by removing all internal and system-environment couplings. We propose dynamical decoupling schemes, that use only bounded strength controls, for quantum many-body systems with local system Hamiltonians and local environmental couplings. To do so, we introduce the combinatorial concept of balanced-cycle orthogonal arrays (BOAs) and show how to construct them from classical error-correcting codes. The derived decoupling schemes may be useful as a primitive for more complex schemes, e.g., for Hamiltonian simulation. For the case of n qubits and a 2-local Hamiltonian, the length of the resulting decoupling scheme scales as O(nlogn), improving over the previously best-known schemes that scaled quadratically with n. More generally, using balanced-cycle orthogonal arrays constructed from families of BCH codes, we show that bounded-strength decoupling for any `-local Hamiltonian, where ` > 2, can be achieved using decoupling schemes of length at most O(n`−1 logn).