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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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closed as unclear what you're asking by e-sushi, Ilmari Karonen, Gilles, archie, rath Feb 1 '14 at 16:07

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

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