  We propose a fault-tolerant quantum computation scheme in a measurement-based
manner with finite-sized entangled resource states and encoded fusion scheme
with linear optics. The encoded-fusion is an entangled measurement devised to
enhance the fusion success probability in the presence of losses and errors
based on a quantum error-correcting code. We apply an encoded-fusion scheme,
which can be performed with linear optics and active feedforwards to implement
the generalized Shor code, to construct a fault-tolerant network configuration
in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the
surface code. Numerical simulations show that our scheme allows us to achieve
up to 10 times higher loss thresholds than nonencoded fusion approaches with
limited numbers of photons used in fusion. Our scheme paves an efficient route
toward fault-tolerant quantum computing with finite-sized entangled resource
states and linear optics.
