Posted by: atri | January 27, 2011

Lecture 4: Hamming Code

In Wednesday’s lecture, we first proved the equivalence of a code having a distance $d$ and the code being $\lfloor \frac{d-1}{2}\rfloor$-error correcting. Then we looked at the Hamming code with dimension $4$ and proved that it had distance $3$. The distance characterization is from Lecture 3 and the Hamming code stuff is from Lecture 4 from Fall 2007.

Next lecture, we are going to look at a negative result called the Hamming bound, which present us with a limit to the rate of a code with a particular distance.