Posted by: atri | October 17, 2007

## Lecture 22: Majority logic decoding of RM codes

In today’s lecture we first showed that the binary Reed-Muller code $RM_2(t,v)$ is a ${[}2^v,\sum_{i=0}^t \binom{v}{i},2^{v-t}{]}_2$ code. Then we saw an unique decoding algorithm (the so called majority logic decoding algorithm) for $RM_2(t,v)$ that can correct $< 2^{v-t-1}$ many errors.

In the next lecture, we see the formal statement of the algorithm and the proof of the key lemma that proves the correctness of the majority logic decoding algorithm.