▁In ▁general , ▁for ▁a ▁primitive ▁polynomial ▁of ▁degree ▁m ▁over ▁G F ( 2 ), ▁this ▁process ▁will ▁generate ▁ ▁pseudo - random ▁bits ▁before ▁repeating ▁the ▁same ▁sequence . ▁ ▁C RC ▁codes ▁▁ ▁The ▁cy clic ▁redund ancy ▁check ▁( C RC ) ▁is ▁an ▁error - d ete ction ▁code ▁that ▁oper ates ▁by ▁interpre ting ▁the ▁message ▁bit string ▁as ▁the ▁coefficients ▁of ▁a ▁polynomial ▁over ▁G F ( 2 ) ▁and ▁div iding ▁it ▁by ▁a ▁fixed ▁generator ▁polynomial ▁also ▁over ▁G F ( 2 ); ▁see ▁Mathemat ics ▁of ▁C RC . ▁Prim itive ▁polynomials , ▁or ▁multi ples ▁of ▁them , ▁are ▁sometimes ▁a ▁good ▁choice ▁for ▁generator ▁polynomials ▁because ▁they ▁can ▁reli ably ▁detect ▁two ▁bit ▁errors ▁that ▁occur ▁far ▁apart ▁in ▁the ▁message ▁bit string , ▁up ▁to ▁a ▁distance ▁of ▁ ▁for ▁a ▁degree ▁n ▁primitive ▁polynomial . ▁ ▁Prim itive ▁tr in omial s ▁ ▁A ▁useful ▁class ▁of ▁primitive ▁polynomials ▁is ▁the ▁primitive ▁tr in omial s , ▁those ▁having ▁only ▁three ▁non zero ▁terms : ▁. ▁ ▁Their ▁simplicity ▁makes ▁for ▁particularly ▁small ▁and ▁fast ▁linear ▁feedback ▁shift ▁registers . ▁ ▁A ▁number ▁of ▁results ▁give ▁techniques ▁for ▁loc ating ▁and ▁testing ▁primit iveness ▁of ▁tr in omial s . ▁ ▁For ▁polynomials ▁over ▁G F ( 2 ), ▁where ▁ ▁is ▁a ▁M ers enne ▁prime , ▁a ▁polynomial ▁of ▁degree ▁r ▁is ▁primitive ▁if ▁and ▁only ▁if ▁it ▁is ▁ir reducible . ▁ ▁( G iven ▁an