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Comp Sci Math; Hamming Distance
I have been set a task:
What is the maxium possble Hamming distace between two noes from level i in an n-cube? Provide an explanation for your answer!
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Asked and answered here – Dilip Sarwate Oct 07 '11 at 12:48
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Well spotted, @Dilip. Voting to close as a dup. – Jyrki Lahtonen Oct 07 '11 at 12:54
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The discription fore homework says "show sufficient effort". Well I don't think that this is the case... ;)
Anyway I think it would help yourself if you draw a square (which is a 2-cube) and try to find out the distance between the nodes (don't forget the diagonale). Afterwords try to generalize it to a n-cube.
lumbric
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@David, The word level is in the statement of the homework. Presumably the homework is given in the frame of a course. But level was not defined in the course? – Did Oct 07 '11 at 12:49
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@David Don't you think that you should tell us, what a "level" is? Hardly anything standard! If coerced to answer, I would hazard a guess that level $i$ consists of the nodes at Hamming distance $i$ from a given reference node, but that is just a guess. Think "triangle inequality", but also remember that there is a maximum to the Hamming distance on an $n$-cube. Or that "level" $i$ is (if I guessed correctly) the same set of points that forms "level" $n-i$ when viewed from the exact opposite reference point. – Jyrki Lahtonen Oct 07 '11 at 12:50