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5
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Efficient decoding of irreducible binary Goppa codes and the role of matrix P in McEliece cryptosystem

If we assume that the support for an irreducible binary Goppa code $\gamma_1, ..., \gamma_n$ is publicly known, when is it possible to efficiently decode the code? I know it's possible if one knows ...
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PKC McEliece + $S$ + $P$

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 $\hat{m}=mS$ ...