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Question

A $(6,3)$ systematic block code has the following generator matrix: $$ A = \begin{pmatrix} 1 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 \end{pmatrix} $$ When a message is encoded by this block code, the code-word $\mathbf{U}=(0,1,1,1,0,1)$ is obained. Suppose the receiver obtains $\mathbf{r}=(0, 0, 1, 1, 0, 1)$, show how $\mathbf{r}$ is decoded by the receiver and also how the errors is corrected by computing its syndrome.

I was given this question in the exams. I listed all the possibilities for the codewords and I think the codeword $\mathbf{U}$ is wrong or am I doing something wrong?

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  • $\begingroup$ You should type in your problem in text instead of image. You are also expected to show your search and research. $\endgroup$ Commented Nov 24 at 11:48
  • $\begingroup$ I want to know if the U given in the question is correct. I tried to multiply all the different combinations of 3 bits message and the generator matrix. I could not get U. $\endgroup$ Commented Nov 24 at 11:56

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