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Irreducible polynomials over finite fields produced by composition of quadratics

Abstract:
For a set S of quadratic polynomials over a finite field, let C be the (infinite) set of arbitrary compositions of elements in S. In this paper we show that there are examples with arbitrarily large S such that every polynomial in C is irreducible. As a second result, when #S>1, we give an algorithm to determine whether all the elements in C are irreducible, using only O(#S(logq)3q1/2) operations.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/RMI/1072

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
European Mathematical Society Publisher's website
Journal:
Revista Matemática Iberoamericana Journal website
Volume:
35
Issue:
3
Pages:
847-855
Publication date:
2019-04-15
Acceptance date:
2017-07-31
DOI:
ISSN:
0213-2230
Language:
English
Keywords:
Pubs id:
1028195
Local pid:
pubs:1028195
Deposit date:
2020-03-25

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