This problem is addressed by Mascagni, et al.\
[41],
where
they describe a canonical form for initializing Fibonacci generators. This
canonical form is determined by and **k**, but is independent of **M**. To
understand the use of this canonical form, consider a second view of the
register shown in Figure 11. The L-shaped region along the left
column and the bottom row is fixed with all zeros, except for a one in the
least
significant bit of word 7 (the word associated with ). The remaining
bits, those in the -bit rectangular region filled with z's, are
free to be chosen in any combination. Each combination of bits in the area will generate a distinct cycle of pseudo-random numbers. In
other words, every possible bit pattern that can be put in the canonical form
will occur in one and only one full period cycle.

Figure 11: Canonical Form for LFG(10,7,4).