The authors of [7, 19] explored the \({{\,\mathrm{(\textbf{C}_1,\textbf{C}_1+\textbf{C}_2)}\,}}\) variation of the McEliece cryptosystem, but its large key size and lack of semantic security make it impractical for applications. In this paper, we adapt the Niederreiter framework over \({{\,\mathrm{(\textbf{C}_1,\textbf{C}_1+\textbf{C}_2)}\,}}\) linear code and propose a hard-decision syndrome decoding algorithm, which allows us to employ the systematic form of the public key that reduces its size. We have developed a key encapsulation mechanism that achieves IND-CPA and IND-CCA security for both the random and quantum random oracle models. By incorporating generalized Reed-Solomon codes as components of \({{\,\mathrm{(\textbf{C}_1,\textbf{C}_1+\textbf{C}_2)}\,}}\) , our scheme reduces the public key size by \(15\%\) compared to the classic McEliece parameters while maintaining a 256-bit security level.