Every set of \(k\) columns in any generator matrix of an MDS code are linearly
independent.
Every set of \(n-k\) columns in any parity check matrix of an MDS code are linearly
independent.
Procedure:
Choose one of the options from the drop-down and click on Submit.
The correctness of the chosen option will be displayed in Observations.
If the matrix given is a generator matrix of an MDS code proceed to the next example.
If the matrix given is not a generator matrix of an MDS code, a message prompting the
selection of the linearly dependent columns will be displayed in Observations.
Clicking on a column changes its color to yellow indicating that the column has been selected.
To deselect a column, click on it again.
Select all the linearly dependent columns and click on Submit.
The correctness of the answer is displayed in Observations.
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Consider a linear block code \(\mathcal{C}\) defined over \(\mathbb{F}_{7}\).
\(G = \)
1
0
0
0
1
0
0
0
1
1
4
3
3
6
6
6
6
3
3
4
1
Observations
Consider a linear block code \(\mathcal{C}\) defined over \(\mathbb{F}_{5}\).
\(G = \)
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
3
2
Observations
Consider a linear block code \(\mathcal{C}\) defined over \(\mathbb{F}_{7}\).
\(H = \)
1
4
3
2
2
1
4
3
3
2
1
4
4
3
2
1
3
3
3
3
0
3
0
0
Observations
Consider a linear block code \(\mathcal{C}\) defined over \(\mathbb{F}_{11}\).