Lesson 10

Problem. The parity-check matrix for the code \(C \subseteq \{ 0, 1 \}^{6}\) is defined as follows: \[H = \begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1\end{pmatrix}\] Enter the following seven values, separated by commas.

1. The number \(k\) for this code,
2. The number \(d\) for this code,
3. The codeword for the message \(011\),
4. The message \(m \in \{0,1\}^{3}\) if the codeword is \(010100\) (the code can be corrupted),
5. Is this code linear (\(1\) if yes, \(0\) if no),
6. Is this code perfect (\(1\) if yes, \(0\) if no),
7. Is this code systematic (\(1\) if yes, \(0\) if no).