Expected value of minimum Hamming distance

[billobillo]

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 MHD is between N strings and is equal to the minimum of HD's among all possible combinations of size k.
My question is: If I randomly select k binary strings of length n out of N=2^n strings , what is the expected value of minimum Hamming distance(MHD) between the k selected strings?
I need to find a general formula that gives me the expected value of the MHD between k random strings of size n selected out of N where (N =2^n)


Below is a table that shows, for N=8 and all k's, the MHD plus its occurrences frequency:

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

There are more results if you need, I appreciate any help from you.
Regards.

 

[Valkarie]

The expected value of the MHD between k random strings of size n selected out of N (N=2^n) is given by the formula:ExpectedMHD = (1/N) ∑ i=1 to N (min[HD(s1,si), HD(s2,si), ..., HD(sk,si)]) where s1, s2, ..., sk are the k randomly selected strings.