Latin square code dimension

Question

I am need to understand what is the dimension of the code generated by the Olderogge Encoding:

Given two mutually orthogonal latin squares, the encoding of a message of $m^2$ bits is:

• the message itself ($m^2$ bits);
• the parity checks of the rows of the matrix $M$ having $m$ rows and $m$ columns obtained by partitioning the original message ($m$ bits);
• the parity checks of the columns of $M$ ($m$ bits);
• the parity checks of the rows of the matrix obtained remapping $M$ using the MOLS - let it be $N$ ($m$ bits);
• the parity checks of the columns of $N$ ($m$ bits);
• an overall parity bit.

Any ideas?

Thanks