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I'm working on a proof and I would like some help. I need to show that any set of 6 distinct 5-bit binary numbers must have at least 5 distinct pairs of elements with Hamming distance less than or equal to 2.

Hamming distance is the sum of the absolute value of each pair of coordinates: the distance between 000 and 111 is

[itex]|0-1|+|0-1|+|0-1|=3[/itex]

Any help would be appreciated.

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# Hamming Distance

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