  Steane code is one of the most widely studied quantum error-correction codes,
which is a natural choice for fault-tolerant quantum computation (FTQC).
However, the original Steane code is not fault-tolerant because the CNOT gates
in an encoded block may cause error propagation. In this paper, we first
propose a fault-tolerant encoding and decoding scheme, which analyzes all
possible errors caused by each quantum gate in an error-correction period. In
this scheme, we combine the results of measuring redundant qubits with those of
syndrome measurements to identify specific errors for different types of
errors. But due to the error propagation, there may be cases where different
errors produce the same measurement results. Therefore, we introduce the "flag
qubits" scheme (providing its usage conditions) to reduce error interference as
much as possible, and we consider the errors caused by the introduced quantum
gates, realizing the truly fault-tolerant Steane code. Afterwards, we provide
the fault-tolerant scheme of the universal quantum gate set, including
fault-tolerant preparation and verification of ancillary states. This is the
first time that fault tolerance has been considered for every process of FTQC.
Finally, We propose an algorithm for a more accurate estimation of thresholds
and optimal error-correction period selection. Our simulation results based on
this entire scheme demonstrate the effectiveness of this algorithm, satisfying
the threshold theorem and the currently widely recognized threshold. We analyze
the relationship among the maximum threshold, concatenated levels, and quantum
logical depth, showing that quantum operations play a crucial role in
increasing the threshold. Furthermore, we analyze the computational theoretical
limits of quantum computers from the perspectives of attack and active defense
based on our FTQC scheme, thereby assessing the security of a system.
