The Hamming distance(HD) between two strings of equal length is
the number of characters that differ between the two strings at
the same position, for example the HD between "gold" and "wolf"
is 2; the minimum Hamming distance(MHD) between k strings of
same length selected out of N strings is equal to the minimum of
the HDs among all possible combinations of size k selected out
of N. My question is: If I randomly select k binary numbers of
length n out of N=2^n numbers, what is the expected value of the
minimum Hamming distance between the k selected numbers? I need
to find a general formula that gives me the expected value of
the MHD from the values of K and N. Below is a table that shows,
for N=8 and all k's, the MHD plus its occurrences frequency
(OF): MHD OF k=2 k=3 k=4 k=5 k=6 k=7 k=8 1 12 48 68 56 28 8 1 2
12 8 2 3 4 Below another table for N=16 MHD OF k=2 k=3 k=4 k=5
k=6 k=7 k=8 k=9 ....... 1 32 352 1592 4240 7952 11424 12868
11440 2 48 208 228 128 56 16 2 3 32 4 8 Appreciate any help,
regards.