  Stabilizer states are a prime resource for a number of applications in
quantum information science, such as secret-sharing and measurement-based
quantum computation. This motivates us to study the entanglement of noisy
stabilizer states across a bipartition. We show that the spectra of the
corresponding reduced states can be expressed in terms of properties of an
associated stabilizer code. In particular, this allows us to show that the
coherent information is related to the so-called syndrome entropy of the
underlying code. We use this viewpoint to find stabilizer states that are
resilient against noise, allowing for more robust entanglement distribution in
near-term quantum networks. We specialize our results to the case of graph
states, where the found connections with stabilizer codes reduces back to
classical linear codes for dephasing noise. On our way we provide an
alternative proof of the fact that every qubit stabilizer code is equivalent up
to single-qubit Clifford gates to a graph code.
