Niederreiter cryptosystem
In the Niederreiter system, the plaintext is mapped to some error vector of weight $t$, where the code correction capability is $d=2t+1.$ 

With the trapdoor information (permutation) this can be decoded by the legitimate receiver by syndrome decoding.

Without the trapdoor information, this is equivalent to decoding a random vector, which is hard, as in the McEliece cryptosystem.