1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show the following properties of Hamming weight

  1. Nov 10, 2008 #1
    hi,

    I have to show the following properties of the Hamming weight for binary words x and y of equal lenght:

    a)w(x+y)=w(x)+w(y)-2w(x*y)

    b)w(x+y)>=w(x)-w(y)

    c) For w(y) even, w(x+y) is even iff w(x) is even

    d) For w(y) odd, w(x+y) is odd iff w(x) is even

    can anybody help me,

    thanks

    lenti
     
    Last edited: Nov 10, 2008
  2. jcsd
  3. Nov 10, 2008 #2

    Mark44

    Staff: Mentor

    You probably won't get much help if you don't at least provide us the formula for Hamming weight.
     
  4. Nov 10, 2008 #3
    Well the Hamming weight of a length-N word x denoted w(x) is defined as the number of components (symbols) of x that are nonzero.

    Well there is no special formula about the hamming weight it can be formulated as


    w(x)= [tex]\sum[/tex]I{x[tex]\neq[/tex]0}

    where I{x[tex]\neq[/tex]0}, the indicator of event {x[tex]\neq[/tex]0}, is 1 if x[tex]\neq[/tex]0 and 0 if x=0

    thanks
     
    Last edited: Nov 10, 2008
  5. Nov 10, 2008 #4

    Mark44

    Staff: Mentor

    a) I'm not sure what x*y means, but I suspect it is the dot product of the two words treated as vectors. If so, w(x*y) gives a measure of how many bits in x are 1 at the same place they are in y. If each bit in x is different from the corresponding bit in y, w(x*y) = 0. Is this correct?

    For example, if
    x = 1011
    y = 0111

    then x*y = 0011.

    Also, x + y seems to be a new word of the same length as x (and as y), where a given bit is 1 in x + y if the corresponding bit in x or in y (or in both) is set.

    For example, if
    x = 1011
    y = 0111
    then x + y = 1111.

    If I'm on the right track here, it seems that the formula should be w(x + y) = w(x) + w(y) - w(x*y), without the factor of 2 that you showed. Of course, I might not be on the right track, since I'm not sure what w(x*y) means.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Show the following properties of Hamming weight
Loading...