Suppose, there is a primary set with 2 binary strings: {0000,0011}.
I want to know the number of elements in a set that has all the elements that are an HD of 2,4 away from each of the elements in the primary set.
For 0011, there are $(4C_2+4C_3+4C_4)$= 11 elements that are HD of 2,3,4 away.
However, only 8 of the strings as shown below satisfy both these strings: 0000,0011.
{0101, 0110, 1001, 1010, 1100, 1110, 1101, 1111}