Can anyone give me a shor explanation why in this picture, they started of the last 0 from first vector and why what is noted with a is 8?
C = {01010101, 10101010, 00000000, 11111111}
And the question was to:
compute d(C) = min ({Hd(v,w) / v, w belongs to C});
The hamming distance is the number of bits that are different between two vectors (or, equivalently, the number of $1$s in the XOR sum). I think that they didn't mean "we start from this particular zero bit" but rather that arrows are between the wole vectors, to say that the hamming distance between the first and the second one is $8$ since each bits are different, the distance between the first vector and the third is $4$ (one half of the $0$ bits are the same), and so on. The arrow could have start from any other bit as well, this is not significant.