Irreducible polynomials from a cubic transformation |
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Affiliation: | 1. Charlotte Scott Centre for Algebra, University of Lincoln, Brayford Pool, Lincoln, LN6 7TS, United Kingdom;2. Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38123 Povo (Trento), Italy |
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Abstract: | Let be a rational expression of degree three over the finite field . We count the irreducible polynomials in , of a given degree, that have the form for some . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017. |
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Keywords: | Irreducible polynomial Cubic transformation |
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