Specs - Hamming Code
Our Hamming Code
You can find general information about Hamming Codes and how to use them here and in the lecture slides.
The given generator matrix here is used for Assignment 2 and further, not the first one!
For this course we have input words of length 6.
Since we want to have SEC-DED features the resulting notation for our Hamming Code is $(11, 6)$.
The non-systematic generator matrix $G'_{6,10}$ to start with is provided by us.
\[ G' = \left( \begin{matrix} 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\ \end{matrix} \right) \]
Transformation
Steps - Transform non-systematic to systematic
- Subtract row 1 from: row 3, row 5, row 6
- Subtract row 2 from: row 1, row 3, row 6
- Subtract row 3 from: row 1, row 5, row 6
- Subtract row 4 from: row 1, row 3
- Subtract row 5 from: row 2, row 3
- Subtract row 6 from: row 1, row 2, row 5