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The generator matrix is made out of that code word and all the possibilities for the code words.

The number of rows of the generator matrix are the number of message bits and the number of columns are equal to the total number of bits i.e parity bits + message bits.

The only necessary condition is that each row of generator matrix is linearly independent of the other row.

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Q: How do you generate generator matrix in linear block code when a code word is given?
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