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I'm going to assume you are using binary Goppa codes. That means, that you take a support $\mathbf{L} \in \mathbb{F}_{2^m}$, a Goppa polynomial $\Gamma$ of degree t with coefficients in $\mathbb{F}_{2^m}$ and build all codewords of a GRS code, and then intersect these with $\mathbb{F}_2^n$, resulting in a code that is actually a subset of $\mathbb{F}_2^n$ ...



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