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.