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.

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