Practical methods for de Bruijn sequences generation using non-linear feedback shift registers

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Abstract

In this paper, a practical method for constructing de Bruijn sequence generators on shift registers with nonlinear feedback function is proposed. The proposed algorithm allows to implement the recursive procedure for the formation of Hamiltonian cycles in the graph of the η-bit shift register based on the homomorphic mapping of its states with the (n-l)-bit shift register state graph and the use of finite state machine models of spanning tree graphs of shift register states. The effectiveness of the proposed method is proved by practical implementation of universal generator with an option to choose nonlinear feedback function arbitrary for built-in NLFSR.

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