Finding Valid v in Z2 for d(v;11011) = 3 | Error Correcting Codes HW

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Homework Statement



Find all vE(Z2)5 for which d(v;11011) = 3

Homework Equations



I'm sure this one isn't too difficult, I'm just unsure how to go about attempting it
 
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Don't worry guys, I've figured it out!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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