- k - bit message is represented by a binary vector of length k

Example, 01001100 --> (0,1,0,0,1,1,0,0)
- k - bit code word is represented by a binary vector of length n

Example, 01001100110 --> (0,1,0,0,1,1,0,0,1,1,0)
- Transformation between message and code vectors.

- In matrix form

where

- G Defines a Linear Systematic (n,k) Code

- Example:

There are 8 unique code words

- Problem: given a received message determine if an error has occurred.
- Model for the received message

- Define a Parity Check Matrix H


- Example:

An error has been detected.