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This paper presents a derivation of a linear feedback function for an r-stage feedback shift register that results in branchless less cycles of equal length. The linear recurrence relationship and generating function, which characterize the r-stage feedback shift register's behavior, are used to prove that each of the 2r states lie in cycles of equal length.
Characteristic polynomial, feedback shift register, generating function, linear recurrence relationship.

M. Perlman, "The Decomposition of the States of a Linear Feedback Shift Register Into Cycles of Equal Length," in IEEE Transactions on Computers, vol. 19, no. , pp. 1029-1035, 1970.
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