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.

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