Possible Duplicate:
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!


marked as duplicate by J. M. is a poor mathematician, Jyrki Lahtonen, Asaf Karagila, t.b., Did Oct 9 '11 at 9:27

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Asked and answered here $\endgroup$ – Dilip Sarwate Oct 7 '11 at 12:48
  • $\begingroup$ Well spotted, @Dilip. Voting to close as a dup. $\endgroup$ – Jyrki Lahtonen Oct 7 '11 at 12:54

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.

  • $\begingroup$ What exactly is a "level"? $\endgroup$ – user17262 Oct 7 '11 at 12:46
  • $\begingroup$ @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? $\endgroup$ – Did Oct 7 '11 at 12:49
  • $\begingroup$ @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. $\endgroup$ – Jyrki Lahtonen Oct 7 '11 at 12:50