  Inspired by holographic codes and tensor-network decoders, we introduce
tensor-network stabilizer codes which come with a natural tensor-network
decoder. These codes can correspond to any geometry, but, as a special case, we
generalize holographic codes beyond those constructed from perfect or
block-perfect isometries, and we give an example that corresponds to neither.
Using the tensor-network decoder, we find a threshold of 18.8% for this code
under depolarizing noise. We also show that for holographic codes the exact
tensor-network decoder (with no bond-dimension truncation) is efficient with a
complexity that is polynomial in the number of physical qubits, even for
locally correlated noise.
