Posted by: atri | September 5, 2007

Lecture 4: Hamming code and Hamming bound

In today’s lecture we looked at the Hamming code $C_H$ with $n=7, k=4$. We also saw the Hamming bound for distance $3$: $k\le n-\log_2(n+1)$. This implies that $C_H$ is the best possible for $n=7$ and $d=3$.

We also (somewhat informally) defined binary linear codes. Next lecture, we will look at the general family of Hamming codes, the general version of the Hamming bound and formally define linear codes (over general alphabets).