© 1973 by British Computer Society
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Nonlinear ternary feedback shift registers
Digital Processes Research Laboratories, Department of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology, P.O. Box No 88, Sackville Street, Manchester, UK
A flexible theory of the general nonlinear ternary feedback shift register (fsr) is presented so that the inherent advantages of the ternary domain may be fully exploited in the fields of digital computers, communications, coding theory, and other areas where the device finds application. The authors show that the description afforded by the modulo-3 arithmetic functions may be adapted to provide a polynomial domain representation of these devices which is more flexible than other ternary operations. Methods of transforming the sequence domain behaviour of the device into this polynomial form, and vice-versa, are presented. Certain properties are isolated and the theory is extended by deriving the transforms required to produce certain related polynomial forms which correspond to simple operations in the sequence domain of the original fsr. The mechanism whereby two factor polynomials may be combined algebraically to produce a composite polynomial with exactly the same cycle set as a cascade connection of the two factors is fully investigated. Results concerning the related forms of these composite types are presented together with certain identities under the polynomial transforms.
Received August 1972.
* Digital Processes Research Laboratories, Department of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology, P.O. Box No 88, Sackville Street, Manchester M60 1QD