2.8. In this problem we will study LFSRs in somewhat more detail. LFSRs come in three flavors: LFSRs which generate a maximum-length sequence. These LFSRs are based on primitive polynomials. LFSRs which do not generate a maximum-length sequence but whose sequence length is independent of the initial value of the register. These LFSRs are based on irreducible polynomials that are not primitive. Note that all primitive polyno- mials are also irreducible. LFSRs which do not generate a maximum-length sequence and whose sequence length depends on the initial values of the register. These LFSRs are based on reducible polynomials. We will study examples in the following. Determine all sequences generated by 1. x4+x+1 2. x4 + x2 +1 3. x4 + x3 + x2 +x+1 Draw the corresponding LFSR for each of the three polynomials. Which of the polynomials is primitive, which is only irreducible, and which one is reducible? Note that the lengths of all sequences generated by each of the LFSRs should add up to 2m 1. 2.8. In this problem we will study LFSRs in somewhat more detail. LFSRs come in three flavors: LFSRs which generate a maximum-length sequence. These LFSRs are based on primitive polynomials. LFSRs which do not generate a maximum-length sequence but whose sequence length is independent of the initial value of the register. These LFSRs are based on irreducible polynomials that are not primitive. Note that all primitive polyno- mials are also irreducible. LFSRs which do not generate a maximum-length sequence and whose sequence length depends on the initial values of the register. These LFSRs are based on reducible polynomials. We will study examples in the following. Determine all sequences generated by 1. x4+x+1 2. x4 + x2 +1 3. x4 + x3 + x2 +x+1 Draw the corresponding LFSR for each of the three polynomials. Which of the polynomials is primitive, which is only irreducible, and which one is reducible? Note that the lengths of all sequences generated by each of the LFSRs should add up to 2m 1