Posted by: atri | January 27, 2009

## Lecture 6: Linear Codes

In today’s lecture, we started with a quick recap of the main results we will use from linear algebra, in particular, linear subspaces over finite fields. We then introduced the notion of linear codes and saw its advantages in terms of $O(n^2)$ space representation and $O(n^2)$ time error-detection. For more details, see the notes for lecture 5 from the fall 07 offering.

At the end of the class, I asked you to think about some specific linear code, for which we can do error correction in time $O(n^2)$ time by doing just one multiplication of the received word with the parity check matrix. (The “naive” algorithm takes time $O(n^3)$ and performs $O(n)$ matrix vector multiplication.)