An asymptotic formula for the number of irreducible transformation shift registers

June 08, 2015 · The Ethereal · 🏛 arXiv.org

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Authors Stephen D. Cohen, Sartaj Ul Hasan, Daniel Panario, Qiang Wang arXiv ID 1506.02548 Category math.CO: Combinatorics Cross-listed cs.IT Citations 12 Venue arXiv.org Last Checked 2 months ago
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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