Whether the `odd-even check` only can check the data correctness within limits?

Question

The length of DES arithmetic Secret Key is 64 bit, the valid secret key length is 56, the other 8 bit use as odd-even check.

I have a question, whether the odd-even check only can check the data correctness within limits?

such as the quote, I use below image to explain my thought:

the first line, the odd check value is 0, if I switch the row 2 and row 3, the odd check value still is the 0, so the odd-even check can not check this issue.

so the odd-even check can only check the count of 1 and 0, but can not decide the data whether is correct, right?

Answer 1

That is correct. The odd-even check catches a change in one bit, but swapping a 1 and a 0 involves changing two bits. There are methods that can catch a change of two bits, but they require more than one check bit.