Bit errors and hamming distance I'm trying to learn for my exam and had the following practice question:

Take a code with the following code words.


101100010111
110001001001
101110111011


Errors of how many bits can be corrected?



The answer i received was:

The hamming distance is: 4.

Therefore only single bit errors can be corrected.



How did they conclude that only single bit errors can be corrected just by looking at the hamming distance?
If you need four bit changes to change from A to B, then you can make two bit changes from A to some A' followed by two more bit changes from A' to B. If you receive A' then you don't know whether it is a double bit error coming from A, or a double bit error coming from B. Therefore, you cannot fix double bit errors. 

Since four bit errors are needed to go from one valid code to another, you can detect double bit errors. 

You also have the choice of either fixing single bit errors and detecting double bit errors at the same time (assuming that there will be no triple bit errors), or detecting triple bit errors. You cannot both fix single bit errors and detect triple bit errors, since I can get the same result by changing a single bit in A and changing three bits in B.