The Hamming distance between two equal-length bit strings is the number of positions in which they differ.
For example, the distance between 0001 and 0101 is 1.
Suppose that, for some integer n, there are K n-bit strings
such that every pair has Hamming distance at least 101.
Prove that there are K n+1-bit strings such that every pair has Hamming distance at least 102.