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Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients

Ahmadi, Omran, Göloğlu, Faruk, Granger, Robert, McGuire, Gary and Yilmaz, Emrah Sercan (2016) Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients Finite Fields and Their Applications, 42. pp. 128-164.

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Abstract

For any positive integers n≥3, r≥1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero. Our proofs involve counting the number of points on certain algebraic curvesover finite fields, a technique which arose from Fourier-analysing the known formulae for the F2 base field cases, reverse-engineering an economical new proof and then extending it. This approach gives rise to fibre products of supersingular curves and makes explicit why the formulae have period 24 in n.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Ahmadi, Omran
Göloğlu, Faruk
Granger, Robertr.granger@surrey.ac.uk
McGuire, Gary
Yilmaz, Emrah Sercan
Date : November 2016
DOI : 10.1016/j.ffa.2016.07.009
Copyright Disclaimer : © 2016 Elsevier Inc. All rights reserved.
Uncontrolled Keywords : Supersingular curves; Irreducible polynomials; Prescribed coefficients; Binary fields; Characteristic polynomial of Frobenius
Depositing User : Clive Harris
Date Deposited : 06 Feb 2019 15:33
Last Modified : 17 Apr 2019 08:47
URI: http://epubs.surrey.ac.uk/id/eprint/850388

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