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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330928" target="_blank" >RIV/00216208:11320/16:10330928 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ffa.2016.07.009" target="_blank" >http://dx.doi.org/10.1016/j.ffa.2016.07.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ffa.2016.07.009" target="_blank" >10.1016/j.ffa.2016.07.009</a>

Result language
angličtina
Original language name
Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients
Original language description
For any positive integers n >= 3, r >= 1 we present formulae for the number of irreducible polynomials of degree n over the finite field F(2)r where the coefficients of x(n-1), z(n-2) and x(n-3) are zero. Our proofs involve counting the number of points on certain algebraic curves over finite fields, a technique which arose from Fourier-analysing the known formulae for the F-2 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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