disclosed are signal generators for developing multilevel output signal sequences of a preselected period of repetition . in their general form , the generators comprise a shift register capable of storing multilevel signals , and feedback means . the feedback means multiply the output signal of prescribed shift register stages by selected integers , add the multiplied signals in nonmodulo arithmetic , and apply the added signals to the first stage of the shift register . the multiplying integers within the feedback means are selected to cause the characteristic functions of the signal generator to be a cyclotomic polynomial . for descriptive convenience , the disclosed generator is termed a &# 34 ; cyclotomic circuit .&# 34 ; the disclosed cyclotomic circuits are particularly useful in a minimum memory , prescribed - period , signal generator applications . the minimum memory is achieved by separating the prescribed period into power - of - prime factors , and by associating with each factor a cyclotomic circuit . each cyclotomic circuit develops a subsequence signal of a period equal to the power - of - prime factor , and the subsequence signals are combined in a transversal network , responsive to the cyclotomic circuits , to form the desired prescribed period sequence signal . advantageously , the multiplying feedback integers of cyclotomic circuits of power - of - prime periods are limited to 0 , 1 , and - 1 .