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I am trying implement the McEliece crytosystem in SAGE. My question is How I will be able to choose the appropriate matrix $S$ and $P$?. I ask this because when I trying obtain the vector $\hat{m}=mS$ in $\hat{G}\hat{m} = Decoding(c)$ I get: matrix equation has no solutions, even after verify that $G$ is full rank.

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As per your own Wikipedia link: $S$ is simply any invertible binary $k \times k$ matrix, and $P$ is any $n \times n$ permutation matrix. What is it that you find unclear? –  hakoja Apr 19 '13 at 21:17
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closed as unclear what you're asking by e-sushi, Ilmari Karonen, Gilles, archie, rath Feb 1 at 16:07

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