Dickson curves
Let kq denote the finite field of order q and odd characteristic p. For a∈kq, let gd(x,a) denote the Dickson polynomial of degree d defined by gd(x,a)=∑i=0[d/2]d/(d−i)(d−ii)(−a)ixd−2i. Let f(x) denote a monic polynomial with coefficients in kq. Assume that f2(x)−4 is not a perfect square and...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/42818 |
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| Summary: | Let kq
denote the finite field of order q
and odd
characteristic p. For a∈kq, let gd(x,a)
denote the
Dickson polynomial of degree d
defined by gd(x,a)=∑i=0[d/2]d/(d−i)(d−ii)(−a)ixd−2i. Let f(x)
denote a monic
polynomial with coefficients in kq. Assume that f2(x)−4
is not a perfect square and gcd(p,d)=1. Also assume that
f(x)
and g2(f(x),1)
are not of the form gd(h(x),c). In this note, we show that the polynomial gd(y,1)−f(x)∈kq[x,y]
is absolutely irreducible. |
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| ISSN: | 0161-1712 1687-0425 |