M can be realized as a (very large!) set of
196882 X 196882 matrices with nothing more than entries of 1's and 0's, so long as we compute arithmetic as follows:
I have two simple questions for the reader. What is the minimum amount of bytes needed to store a single matrix? What is the computational cost (i.e., in FLOPS) of a single matrix multiplication in the most efficient implementation (i.e., taking into account that the entries are binary, not taking into account mathematical properties about the Monster)?
This is a question purely at the computational side of the problem. In other words, treat the matrices as general
196882 x 196882 matrices with binary entries. This is not a question about the Monster. That was just added as motivation.