Primitive and irreducible polynomials are well tabulated. Example 1: 5-bit LFSR with feedback polynomial x5 + x2 + 1. 1+1=0, 0-1=1, etcĪll primitive polynomials are irreducible but the converse is not true!

Note the above polynomials are in GF(2) so the only elements are 0,1. Irreducible: Cannot be factored, see example: If the generator is not primitive, possible states (combinations of the register values) will be skipped and the sequence will be less than $2^N-1$ in length before repeating. Primitive: Repeated multiplying by x (representing a shift of one position in the shift register) will generate every possible state (except for the all 0 state). This is assuming that you are using a maximum length sequence in the implementation of your shift register, which means the generator polynomial is both primitive and irreducible in GF(2). The duration of the linear feedback shift register (LFSR) in number of 'chips' is $2^N-1$ where N is the number of states in the shift register (and order of the generator polynomial), and chips refers to each unique output that is generated in the sequence.

12 bit linear feedback shift register