Posted by: atri | February 24, 2011

## Lecture 15: Polynomials over Finite Fields

In Wednesday’s lecture, we looked at polynomials over finite fields. We spent some time discussing how one can use polynomials to represent fields $\mathbb{F}_q$ for prime powers $q$. I ended up talking about more stuff than I had planned. Some of the stuff can be found in draft notes for Lecture 5 from Spring 2009. Dan will be scribing the notes for the lecture.

At the end of the lecture, we also defined Reed-Solomon codes. Next lecture, we will show that the Reed-Solomon codes meet the Singleton bound and then we will move on to Shannon’s results on stochastic channels.

P.S. Some of you asked for a source to read up more on polynomial representations of finite fields: take a look at the pointers in my post on an earlier lecture this semester.