  Stabilizer states are extensively studied in quantum information theory for
their structures based on the Pauli group. Calderbank-Shor-Steane (CSS)
stabilizer states are of particular importance in their application to
fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly
prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is
still unknown, and their preparation can be highly costly in computational
resources. In this paper, we show how to prepare a large class of CSS
stabilizer states useful for FTQC. We propose distillation protocols using
syndrome encoding by classical codes or quantum CSS codes. Along the same
lines, we show that classical coding techniques can reduce the ancilla
consumption in Steane syndrome extraction by using additional transversal
controlled-NOT gates and classical computing power. In the scenario of a fixed
ancilla consumption rate, we can increase the frequency of quantum error
correction and effectively lower the error rate.
