Hi,
I'm not sure, but I guess if you check on one single value, then this might be sufficient.
My idea:
If one single value repeats, then the whole sequence will repeat.
If I'm not mistaken then with LFSR you get 2^n -1 different values, but they repeat, they are in a strong order.
So start with any seed, and clock by clock compare the output with your seed. If there is a match before 2^n, then this indicates that there are some redundant codes that are not used in your sequence.
You should be able to verify if this is true for your algorithm.
But one requirement still remains: for any number of "n" the whole test should last 2^n steps.
This may be long time.
Klaus