The Cool
This was cool for me to read because I understood everything but the last two pages. I didn't do very well in Abstract Algebra, but a lot of the concepts they were talking about were at least familiar.
The Hard
How do we know that polynomials are irreducible in mod2. For instance, on page 98, why do we know that x^8 + x ^4 + x ^3 + x + 1 is irreducible? Is there some quick way of noticing that by just looking?
Also, the entire section on LFSR Sequences was over my head (and a little bit of the end of GF(2^8)). In the GF part, what is a analog of a primitive root and why does it matter that a polynomial is irreducible. In LFSR, what was the point?
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