On the modified Niederreiter cryptosystem

In the classical Niederreiter cryptosystem a public key is the r×N matrix H_cr=SH=S[z_jxⁱ_j ], where S is a scrambling r×r matrix, distinct x_j∈GF(q)U(∞), and z_j∈GF(q)(0). Anyone who wants to send a secret message chooses a plaintext m, ω _H(m)⩽t=[(d-1)/2]=[r/2], and calculates the cyphertext as the syndrome c of the code with the parity check matrix H_cr: c=mH^T_cr. Upon receiving the ciphertext c, the legal user multiplies it by (S^T)^-1 and applies a fast decoding algorithm to obtain the plaintext m