What Is the Maximum Possible Hamming Distance Between Two Nodes in an n-Cube?

[koko20]

Hey

Homework Statement

can someone please help me with this question as i have no idea how to go about it to make a formula for this question.

What is the maximum possible Hamming distance between
two nodes from level i in an n-cube?

If a node in an n-cube has i 1s and n-i 0s in its coordinate, we say that
it is from level i.

Homework Equations

i don't know what the equation is as the question is asking to come up with the equation as an answer.

The Attempt at a Solution

this is what i know:
Hamming distance = (100,011)=3
but i don't know how to make a formula for this

many thankx for your help.
koko20

 

[LCKurtz]

I'm no expert on Hamming distances, but I would play around with n = 5 and n = 6 and try various values for i to see how large you can make the Hamming distance. I think the answer and how to prove it will become clear.

 

[Mark44]

Hey

Homework Statement

can someone please help me with this question as i have no idea how to go about it to make a formula for this question.

What is the maximum possible Hamming distance between
two nodes from level i in an n-cube?

If a node in an n-cube has i 1s and n-i 0s in its coordinate, we say that
it is from level i.

Homework Equations

i don't know what the equation is as the question is asking to come up with the equation as an answer.

The Attempt at a Solution

this is what i know:
Hamming distance = (100,011)=3
but i don't know how to make a formula for this

many thankx for your help.
koko20

You have given the Hamming distance for the strings 100 and 011. These are strings in a 3-cube, but from your description, they are from different nodes, and are at different levels.

Two strings at the same level would be 101 and 011. They both have two 1's and one 0.

How does your book define Hamming distance? (You can also do a search on wikipedia for this term.)

I don't think you'll need a formula for the maximum possible Hamming distance. If you understand what this term means, you'll be able to come up with the answer.