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Given polynomial $P(x)=x^6+x^3+1$ belonging to $\mathbb{Z}_2[x]$. Build an $LFSR$ corresponding to $P(x)$. Then find the maximal period of its output sequence and the initial state that could lead to the maximal period output sequence.

Could someone help me?

maximal period=2^n-1 63 if its primitive polynomial initial state=?

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You are (presumably) receiving downvotes (and no attention to your question) because you do not show any effort of your own. Please show what you have done so far and try to explain precisely where you are having difficulty. – Austin Mohr Nov 5 '12 at 6:56
Also, please make sure that I have not mistakenly changed the meaning of your question. – Austin Mohr Nov 5 '12 at 6:58
WHY IS THE TITLE SHOUTING?! – kahen Nov 5 '12 at 7:12
@kahen I fixed it. – Ted Nov 5 '12 at 7:17
Search for more questions on LFSRs on this site for examples. Dilip Sarwate has given some IMHO very illuminative answers here. – Jyrki Lahtonen Nov 5 '12 at 10:50

Hint: $x^9+1=(x^3+1)(x^6+x^3+1)$ so your feedback polynomial is not primitive.

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