In literature, all I am seeing is Hamming code with minimum Hamming distance $3$. Theoretically a Hamming code with minimum distance d can detect $d-1$ errors and can correct $(d-1)/2$ error. So minimum distance of $3$ can detect $2$ errors and correct $1$ error.
So here is my question: Is it possible to generate a code with minimum Hamming distance of (let's say) $5$ which can correct $2$-bit errors in each block of coded bits?
If yes, could anyone please give me suggestion about that?
If not, then please give me an explanation.