A reviewed lookup table turns a measured syndrome into a correction index, then tests whether the code word is restored. The repair is exact only for the stated table and single-error assumptions; real correction circuits must handle noisy syndrome bits, feedback latency, reset errors, crosstalk, and readout uncertainty.
The correction index is computed from the reviewed syndrome table. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Syndrome zero zero uses the no-correction index
The word 111 has syndrome 00 and correction index -1.
s=00c=−1
The lookup correction restores the code word
The word 101 has syndrome 11, so correction index 1 restores 111.