Question 17.97

67. Suppose that , , and are binary code words of the same length. Using the method of summing binary strings as shown in Example 21, explain why the distance from to is the same as the distance from to .

67.

Recall that the distance between two strings is the number of positions by which they differ. Observe that everywhere and agree, so do . Conversely, in every position that and disagree, so do .