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On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers

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1 Author(s)
Lempel, A. ; IEEE

A homomorphism of the de Bruijn graph that maps a graph of order n onto one of order n-1 and its applications to the design of nonsingular feedback shift registers are discussed. The properties preserved under this mapping suggest a new design technique whose main advantage is due to the fact that the problem of designing a desired n-stage shift register may be reduced to a problem of order n-1 or less. Among the results obtained is a recursive formula for a feedback function that generates a cycle of maximum length.

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Computers, IEEE Transactions on  (Volume:C-19 ,  Issue: 12 )