  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
$O(n \log n)$, 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 $\ell$-local Hamiltonian, where $\ell \geq 2$, can be
achieved using decoupling schemes of length at most $O(n^{\ell-1} \log n)$.
