Constructing irreducible polynomials with prescribed level curves over finite fields
Mihai Caragiu1,2
Received14 Jan 2001
Revised28 Mar 2001
Abstract
We use Eisenstein's irreducibility criterion to prove that there
exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.