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