Question

I am trying to understand why the polynomial x⁴+x³+x²+x+1 generates 5 periods in LFSR. If we start with 0 0 0 1 it will generate 1 0 0 0, 1 1 0 0, 0 1 1 0, and 0 0 1 1 before repeating itself again. My question is, why does it go from 1 0 0 0 to 1 1 0 0? Shouldn't it go from 1 0 0 0 to 0 1 0 0? Thanks.

Answer 1

Here is the answer.

Every polynomial f(x) in Z₂ having f(0)=1 divides xⁿ+1 for some n. The smallest n for which this is true is called period of f(x).

Hence it go from 1 0 0 0 to 0 0 0 1 and then repeat.