Posted by: atri | January 29, 2010

## Lecture 7: Linear Codes

Today we saw a few properties of linear codes. The material is from Lecture 5 from Fall 2007. (The equivalence of distance of a linear code and the minimum Hamming weight of a non-zero codeword is from Lecture 6.)

We saw two ways of representing an $[n,k,d]_q$ linear codes: one based on the generator matrix which stores $kn$ $\mathbb{F}_q$ symbols while the other based on parity check matrix which stores $(n-k)n$ $\mathbb{F}_q$ symbols. The first one is better when $k\le n/2$ and the second one is better for larger $k$. Depending on how much time we have this semester, we will also see that certain parity-check matrix imply very nice decoding algorithms.