let GF(2^n) be the extension of the binary field.Let " F " be a linear function, which means F(X+Y)=F(X)+F(Y) and F(0)=0.

Assume that X,Y are any two elements in the GF(2^n) -the finite field- . The question is can we define a linear function "F" such that F(X)=F(Y), for any X,Y belong to GF(2^n)?? in another word "what kind of function that will look like this?? will do this F(X)=F(Y)???