COMP 165  Fall 2016  Homework 2
Due Wednesday, 28 September, 2016 in class
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Write out a list of all fourthdegree polynomials with binary coefficients.
For each polynomial, show how it factors into lowerdegree irreducible
polynomials or write "irreducible".

Sorting the polynomials in the standard order (x^{4}, x^{4}+1,
x^{4}+x, ...) call the first irreducible polynomial m(x). Use this to define the
multiplication of a finite field of size 16 by calculating a "log table" corresponding
to Table 5.5 on page 148.

Using this table, calculate (x^{2}+x) * (x^{3}+x+1),
x^{10} * x^{11}, and the inverse of x^{3}+x
mod m(x).

Note that the powers of x may not generate all the elements of the
finite field. What happens if you use the last irreducible polynomial
in your list as m(x)?