- To Know: I will post the next assessment either late tonight or early on the weekend. I will make it due Monday the 26th. I hope to have the 2nd assessment back to you this weekend.
- To Do: Practice with finite fields!
- Please create a finite field of size 9. To do this, you will need to find an irreducible polynomial of degree 2 in F3[X]. To do this, just try some polynomials. One way to check if something that has degree 2 is irreducible is to check if it has any roots (since if it factors, it will have to have a linear root, i.e. factor). There are only 3 possible roots (namely 0,1,2) because we are working in F3. Hint: choosing a polynomial without a linear coefficient will simplify your computations later on.
- Next, make a complete multiplication table for your finite field of 9 elements. Take advantage of symmetry to speed this up. Practice makes perfect!
- Use the Finite Field Tools to check your work (figure out what the tools do, then check your polynomial is irreducible and at least spot check some items on your multiplication table).
- Hand that all in on canvas.