Hamming distance

Question

I have some difficulties in computing Hamming distance in following example:

11100000
00011100
10010010
01001001

I know the definition of Hamming distance (in case of two codewords) but how to proceed in above example. Can someone shed some light on how to compute d_min in above example?

Regards

Answer 1

Denote the codewords as $a_1,...a_4$. Remember that the hamming distance is the number of different bits between two codewords.

1. $d(a_1,a_2) = 6$
2. $d(a_1,a_3) = 4$
3. $d(a_1,a_4) = 4$
4. $d(a_2,a_3) = 4$
5. $d(a_2,a_4) = 4$
6. $d(a_3,a_4) = 6$

Thus $d=4$.