Polynomial representation of nonlinear feedback shift registers

A technique is described which enables the feedback logic of a nonlinear feedback shift register to be represented as a nonlinear polynomial, using simple operations on a Karnaugh map. The polynomial form of a nonlinear feedback shift register is capable of furnishing information on the sequential operation of these devices which is not readily apparent from the minterm expansion of the feedback logic. Further manipulations employing the polynomial representation are described which enable a nonlinear polynomial, representing a feedback shift register, to be converted into polynomials which, when mechanised, result in the dual and time reverse of the sequence generated by the original polynomial.