- Find all the primitive binary polynomials
of degree 4.
- Prove that all the irreducible binary polynomials of
degree 5 are primitive.
- What is the period of the Linear Feedback Shift Register
which has the characteristic polynomial
x

^{5}+ x^{4}+ x^{2}+ x + 1? - Find a non-primitive irreducible binary polynomial of
degree 6. Construct a LFSR with this polynomial as its
characteristic polynomial and determine the statistics of the
runs of this LFSR (i.e., how many runs of what lengths are
there?)
- Find the linear equivalence and an LFSR which produces
the period 7 sequence that starts 1 0 1 0 0 0 1 .... What
starting state will give this sequence?
- Construct a multiplexed FSR by the Jennings method with
(m,n)1 and determine
its periods (i.e., the periods of the sequences for each of its
starting states).