Yeah the paper uses O notation for complexity, but never when N is constant. For constant N and M, the paper uses the number of scalar multiplication operations

Yeah the paper uses O notation for complexity, but never when N is constant. For constant N and M, the paper uses the number of scalar multiplication operations performed as complexity measure. According to Figure 3, their algorithm has decreased the best known value from 49 to 47 for 4x4 matrices, and from 98 to 96 for 5x5 matrices (as well as some further state of the art improvements).