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#### billobillo

##### New member

- Nov 22, 2012

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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.