Linear Code

A Binary Code is linear if

2. if then

Rank of a Linear Code A code of length and rank is called an code. If a linear code has minimum distance then it is a code

Say has a basis Then so i.e. an code is an code

The Information Rate is

We define

Ring over binary words

Hamming weight Parity Check Code Dual Code Generator Matrix Parity Check Matrix Syndrome Syndrome Decoding

Hamming Codes Reed-Muller Codes

Cyclic Code Defining Set (wasn’t done in lectures) Cyclic Code with Defining Set BCH Code