Representation and manipulation of message blocks

- 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.

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