Abstract
The paper explores conditions to be satisfied by feedback shift registers (FSRs) to generate a permutation (alternatively a nonsingular map) of the state space over various fields. Such a condition is well known over the binary field \(\mathbb {F}_{2}\). This is extended to small finite fields and a simple sufficient condition is stated for larger fields. Permutations with cycles or periodic sequences generated by their action of lengths which are of exponential order of the register length are attractive for construction of pseudorandom sequences which have many applications.
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Kammadanam, V.K., Sule, V., Hong, Y. (2021). Conditions for Feedback Shift Registers to Generate Permutations. In: Giri, D., Ho, A.T.S., Ponnusamy, S., Lo, NW. (eds) Proceedings of the Fifth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-15-5411-7_9
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DOI: https://doi.org/10.1007/978-981-15-5411-7_9
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