Let $C$ be a code over the finite field $GF(2)$ with generator matrix $G$ and parity matrix $H$. Let $e+C=C'$ be a coset of code $C$. Let $S$ be a non-singular matrix and $H'=H\times S$. Finally, let ...
I like know: Is possible that any adversary PPT will be able to find the generator matrix $G$ of Goppa code $GC$, if given $SH$ matrix, where $H$ is a parity check matrix of $GC$ and $S$ is a random ...