# Introduction to coding theory (CMU, Spr 2010)

## February 12, 2010

### Lecture 9 summary

Filed under: Lecture summary — Venkat Guruswami @ 3:31 pm

We finished the proof of the first MRRW bound. We compared the Gilbert-Varshamov, Elias-Bassalygo, and MRRW bounds for the regime $\delta \to 1/2$, specifically that they give rate bounds of $\Omega(\epsilon^2)$, $O(\epsilon)$ and $O(\epsilon^2 \log (1/\epsilon))$ for $\delta = 1/2-\epsilon$. We stated the second MRRW bound.

In preparation for the next segment of the course on constructions of good algebraic codes, we reviewed some basic facts about finite fields. We proved that a univariate polynomial of degree $d$ over any field ${\mathbb F}$ has at most $d$ roots in ${\mathbb F}$. We concluded with a definition of Reed-Solomon codes as polynomial evaluation codes.