key size of public key in McEliece
Let $G$ be the public key matrix. With Gaussian elimination, you can find a Matrix $G'$ with $G = (E_k | G')$, where $E_k$ is the identity matrix with dimension $k$. Then, you only have to store $G'$. And $G'$ has the dimension $(n-k) \times k$. 

Source: German Wikipedia (https://de.wikipedia.org/wiki/McEliece-Kryptosystem)