Question

Explain why d(x,y) ≤ d(x,z)+d(z,y) where x,y,z are binary words of length n and d is the Hamming distance.

Answer 1

The Hamming distance inequality for binary words

Step-by-step explanation:

The Hamming distance measures the number of positions at which two binary words of the same length differ. Let's consider three binary words x, y, and z of length n. To prove that the inequality d(x, y) ≤ d(x, z) + d(z, y) holds, we can use the fact that the Hamming distance between x and y is equal to the sum of the Hamming distances between x and z and between z and y. Since the Hamming distance cannot be negative, it follows that d(x, y) ≤ d(x, z) + d(z, y).