To be a maximal-period LFSR
Polynomial formed from a tap sequence (the bits that are XORed) plus the constant 1 must be a primitive polynomial mod 2. (degree = length of shift register)
Example: (32,7,5,3,2,1,0)
Primitive polynomial of degree n is an irreducible polynomial that divides x^(2^(n-1)) + 1, but not x^d+1 for any d that divides 2^(n-1).