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Specifically, I have a generator matrix $$G=\begin{bmatrix} 1&0&0&0&0&1&1 \\ 0&1&0&0&1&0&1 \\ 0&0&1&0&1&1&0 \\ 0&0&0&1&1&1&1 \\ \end{bmatrix}$$ and I must find all 16 codewords that are in this code. I am told this can be done by taking all possible sums of the rows of G, but I am struggling on how.

febasnatt
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  • Your question is phrased as an isolated problem, and I am afraid that some users believe it should get closed. To prevent that, please tell us (in the question body) what you have tried. – fantasie Apr 22 '22 at 16:47

1 Answers1

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We have a binary linear code with generator the matrix you mentioned. In order to find explicitly the code we have to multiply the generator with all the vectors $[a,b,c,d]$, where $a,b,c,d$ are $0$ or $1$. The last means that all the words should be of the form $ae_1+be_2+ce_3+de_4$, where $e_i$ are the rows of the matrix.

dmtri
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