  We investigate quantum repeater protocols that rely on three-qubit repetition
codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV
centers offer a two-qubit register, corresponding to their electron and nuclear
spins, which makes it possible to perform deterministic two-qubit operations
within one NV center. For quantum repeater applications, we, however, need to
do joint operations on two separate NV centers. Here, we study two NV-center
based repeater structures that enable such deterministic joint operations. One
structure offers less consumption of classical communication, at the cost of
more computation overhead, whereas the other one relies on a fewer number of
physical resources and operations. We assess and compare their performance for
the task of secret key generation under the influence of noise and decoherence
with current and near-term experimental parameters. We quantify the regimes of
operation, where one structure outperforms the other, and find the regions
where encoded quantum repeaters offer practical advantages over their
non-encoded counterparts.
