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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...

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    $\begingroup$ seems like this is not a primitive polynomial so how can I figure out what the max period could be? $\endgroup$
    – cyborg_681
    Feb 28, 2018 at 19:31

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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.

There is more information in answer

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