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The Decomposition of the States of a Linear Feedback Shift Register Into Cycles of Equal Length
November 1970 (vol. 19 no. 11)
pp. 1029-1035
M. Perlman, IEEE
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.
Index Terms:
Characteristic polynomial, feedback shift register, generating function, linear recurrence relationship.
Citation:
M. Perlman, "The Decomposition of the States of a Linear Feedback Shift Register Into Cycles of Equal Length," IEEE Transactions on Computers, vol. 19, no. 11, pp. 1029-1035, Nov. 1970, doi:10.1109/T-C.1970.222828
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