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arXiv · 1506.02548

An asymptotic formula for the number of irreducible transformation shift registers

Stephen D. Cohen·Sartaj Ul Hasan·Daniel Panario·Qiang Wang
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Abstract

We consider the problem of enumerating the number of irreducible transformation shift registers. We give an asymptotic formula for the number of irreducible transformation shift registers in some special cases. Moreover, we derive a short proof for the exact number of irreducible transformation shift registers of order two using a recent generalization of a theorem of Carlitz.

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Stephen D. Cohen, Sartaj Ul Hasan, Daniel Panario, Qiang Wang. 2015-06-08. An asymptotic formula for the number of irreducible transformation shift registers. https://doi.org/10.1016/j.laa.2015.06.020

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