[Comouter networks] Error detection Policy

Question

Consider the following set of codewords(Last bit is even parity of the first two  bits)

000

011

101

110

Now here min. hamming distance is 2 and if i apply formulae

Min. hamming distance =d+1,then d errors can be detected

2=d+1

d=1

Means 1 error can be detected.

But in these set  codewords if there is any 3 bit error,that will also be detected as parity will become odd.

So 3 bit error can also be detected,but by formula it says 1 bit error can be detected.

Please tell what did i miss?

Comments

if any doubt then please tell :)