COMP 165 - Fall 2016 - Homework 2
Due Wednesday, 28 September, 2016 in class
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Write out a list of all fourth-degree polynomials with binary coefficients.
For each polynomial, show how it factors into lower-degree irreducible
polynomials or write "irreducible".
Sorting the polynomials in the standard order (x4, x4+1,
x4+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 (x2+x) * (x3+x+1),
x10 * x11, and the inverse of x3+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)?