There is something intriguing me about this cryptosystem. That is :
Let $(S, G, P)$ be the secret key:
$S$ : invertible matrix
$G$ : generator matrix for some linear code $C$
$P$ : permutation matrix
And let $G'= SGP$ be the public key.
To encrypt $m$, we compute $Enc(m) = mG'+e$, with $e$ an error vector
The thing is, the basic idea about structural attacks, is that we brute-force the family of codes used (most likely, the code used is a binary Goppa code, but there are attempts to use other families, which are not yet broken).
So my question is, do we really need to reveal which family of code was used? wouldn't be more secure if we keep it hidden?