Hamming code sample problem 5 solution

Solution: consider all pairs of 2 codes from the set:

(a) 0 0 0 0 1 1 1 1 0 0 0

(b) 0 0 1 1 0 0 1 1 0 0 1

(a^b) 0 0 1 1 1 1 0 0 0 0 1

Hamming distance = 5

(a) 0 0 0 0 1 1 1 1 0 0 0

(c) 0 1 0 1 0 1 0 1 0 1 0

(a^c) 0 1 0 1 1 0 1 0 0 1 0

Hamming distance = 5

b 0 0 1 1 0 0 1 1 0 0 1

c 0 1 0 1 0 1 0 1 0 1 0

(b^c) 0 1 1 0 0 1 1 0 0 1 1

Hamming distance = 6

The Hamming distance for a set of codes is the smallest distance for any pair of its members. In this case, the Hamming distance for the set is 5.