Posted by: atri | November 26, 2007

## Lecture 37: List Decoding of RS codes

In today’s lecture we saw our first non-trivial list decoding algorithm. We saw how to correct $1-2\sqrt{R}$ fraction of errors for Reed-Solomon codes of rate $R$. This gives an improvement over the unqiue decoding regime of $\frac{1-R}{2}$ for rates $R<\frac{14-\sqrt{192}}{2}\approx 0.072$. In the next lecture, we will see another algorithm that can correct up to $1-2\sqrt{R}$ fraction of errors. Then we will see an algorithm that achives the Johnson bound.

In class today I mentioned that factoring of bivariate polynomials can be done in polynomial. In fact the following three independent work gave efficient algorithms to factor polynomials over constant many variables: