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teach me Primitive Polynomials of Field Theory? Links provided!

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Thank you for trying to help me!


Okay, so I need to understand primitive polynomials, but I haven't got much in the way of math.
Good brain and willing to learn but no school, really.


Please help me understand {this page explaining primitive polynomials}!

Also {this other page of the same}, which seems more basic but is still difficult.

{The easiest one of all}, but again, I don't get it! :'[


The only kind I need to understand is the {kind which is used in LFSRs}, which is called GF(2), right?


I need to be able to generate every primitive polynomial in GF(2) of a given degree.

{This paper discusses what must be the fastest way to test if a polynomial is primitive} - I don't understand what he's saying though.  Probably because I don't understand the definition of a primitive polynomial.



That's all I need to do.  But I also need to understand /why/ it works, or /how/ it works, or anything!

I don't want code, I just want to understand the properties required to make a polynomial "primitive".

The point is that I need to understand it enough to write the code for it.

Sorry if that's confusing.  Simply put, all I need to do is find every primitive polynomial of degree n for GF(2) using one of the algorithms provided, and in order to do that I need to understand what makes a polynomial primitive.

Edited by MyNameIs

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