Linear Algebra - Help Please or I fail :(

[butterfly4ever]

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[stapel]

Linear Algebra, Help please or I fail

How could one homework exercise possibly determine whether or not you pass the entire course? If this exercise is indeed that crucial, how is it that you have made no apparent attempt on it? :shock:

Eliz.

 

[Deleted member 4993]

Re: Linear Algebra, Help please or I fail

duplicate post:

http://www.mathhelpforum.com/math-help/ ... ction.html

 

[Deleted member 4993]

Given two elements X,Y from a finite field GF(2n ). F is a linear function defined as:
F: GF(2^n) ->C2 or
F: GF(2^n) -> C2 x C2 or
F: GF(2^n) -> C2 x C2 x C2 or
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.
.. and so on maximum C2 x C2 x C2.. n times
So , you can see that the range of F is a group “Cyclic group”, C2={0,1}, C2 x C2={00,10,01,11} .. and so on.

Can we define a linear function F such that F(X) = F(Y), knowing that X, Y are given and they are two elements in the finite field GF(2^n) and F is linear??
How can we define F based on X and Y?

Since butterfly decided to remove the post - I figured I'd copy the post from the other forum and keep it here for posterity.