Some polynomial compositions of nonlinear feedback shift registers and their sequence-domain consequences

The polynomial representation of the cyclic nonlinear feedback shift register is investigated for its behaviour under the application of the dual and reverse operators. The concepts derived are extended to include composite polynomial structures. Invariances under either or both of the operators reveal some special types of feedback shift register (f.s.r.), and the sequence-domain consequences of these are explored. Palindromic, dual-symmetric, reverse-dual-symmetric, and skew-symmetric f.s.r.s are described, together with the conditions for existence, the numbers avaiable for a given register length and methods for their synthesis.