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As you probably know the public key in McEliece is an $k \times n$ binary matrix, encoding a generator matrix for a randomly permuted Goppa code (i.e. $G_{\mathsf{pub}} = SGP$, where $S$ is any $k \times k$ invertible binary matrix, $G$ a $k \times n$ generator matrix for an $(n, k, t)$ binary Goppa code, and $P$ a $n \times n$ permutation matrix). ...