# Introduction to coding theory (CMU, Spr 2010)

## March 31, 2010

### Lecture 18 summary

Filed under: Lecture summary — Venkat Guruswami @ 3:07 pm

We discussed a method for distance amplification using expander graphs, and how the resulting codes can be decoded via a majority logic algorithm. We discussed how to get near-MDS codes of rate $R$ that enable linear-time correction of a fraction $(1-R-\epsilon)/2$ of errors.

We motivated list decoding as a primitive to bridge between the Shannon random errors model and the Hamming worst-case error model. We stated and proved the existence of list-decodable codes that achieve a rate vs error-correction radius trade-off similar to the Shannon capacity for the $q$-ary symmetric channel. We commented on why the proof does not work as such for linear codes.