Show that extended Golay code $G_{24}$ and $G_{12}$ are self dual.
To show it have to show that any two rows of $G_{12}$ and $G_{24}$ are orthogonal, that is inner product of any two rows are zero.
In this way we get $G_{24} \subset G_{24}^\perp$ and $G_{12}\subset G_{12}^\perp$ and as they are of same dimension so $G_{24}= G_{24}^\perp$ and $G_{12}= G_{12}^\perp$.
But I cannot understand how to prove that any two rows of both the codes are orthogonal.
Can anyone help me?
Thanks in advance.