For example, let's say I am given an element α in a field of characteristic 2. Further, I am given the minimal polynomial of α with respect to GF(2). Let's say that minimal polynomial is f(x)=x9+x+1. How would I then deduce the order of α?
This is for a coding theory assignment, but I cannot deduce from the literature how to go in this direction. Most things I have read seem to indicate how to find a minimal polynomial, but don't seem to take that any further.
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