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arXiv · 2309.10265

Wreath products and cascaded FSRs

Alexander Bors·Farzad Maghsoudi·Qiang Wang
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Abstract

We show that the transition function of the cascaded connection of two FSRs can be viewed as a wreath product element. This allows us to study periods of cascaded connections with algebraic methods, obtaining both a general, nontrivial upper bound on the maximum period of a cascaded connection and a complete, explicit understanding of the periods in the important case of the cascaded connection of an $n$-dimensional De Bruijn sequence into an $m$-dimensional linear FSR.

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Alexander Bors, Farzad Maghsoudi, Qiang Wang. 2023-09-19. Wreath products and cascaded FSRs. https://arxiv.org/abs/2309.10265

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