# Finding max period of 8-bit LFSR

I am a bit stuck there and trying to figure out the approach for given problem.

What is the maximim period of a pseudo-random sequence generated by the 8-bit LFSR with connection polynomial C(X) = 1+X^2 +X^4 +X^5 +X^6 +X^7 +X^8?

Any help would be highly apreciated...

• seems like this is not a primitive polynomial so how can I figure out what the max period could be? – cyborg_681 Feb 28 '18 at 19:31

If a connection polynomial of degree $d$ is primitive, i.e., it is irreducible and has a root of order $2^d-1,$ then the period is $2^d-1,$ for any nonzero loading.