AbstractLet Fq denote the finite field of order q, a power of a prime p, and n be a positive integer. We resolve completely the question of whether there exists a primitive element of Fqn which is such that it and its reciprocal both have zero trace over Fq. Trivially, there is no such element when n<5: we establish existence for all pairs (q, n) (n≥5) except (4, 5), (2, 6), and (3, 6). Equivalently, with the same exceptions, there is always a primitive polynomial P(x) of degree n over Fq whose coefficients of x and of xn-1 are both zero. The method employs Kloosterman sums and a sieving technique
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
AbstractThe object of this paper is to prove the existence of a primitive quadratic of trace 1 over ...
AbstractLet Fq denote the finite field of order q, a power of a prime p, and n be a positive integer...
AbstractWith one non-trivial exception, GF(qn) contains a primitive element of arbitrary trace over ...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a line...
AbstractThe extension field FPq where q is a prime divisor of (P−1), has a unique structure. This pa...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a l...
AbstractA characterization of primitive polynomials, among irreducible polynomials, over a finite fi...
AbstractThe object of this paper is to present a simple proof for the existence of primitive element...
This paper contains a self-contained, minimal computational account of Cohen's 1990 theorem that the...
AbstractLet Fq denote the finite field of q elements, q an odd prime power, and let f(x)=xn+∑i=1nfix...
AbstractThe primitive elements of a finite field are those elements of the field that generate the m...
The existence of a primitive free (normal) cubic x3 - ax2 + cx - b over a finite field F with arbitr...
AbstractLet q be a power of 2, n be a positive integer, and let Fqn be the finite field with qn elem...
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
AbstractThe object of this paper is to prove the existence of a primitive quadratic of trace 1 over ...
AbstractLet Fq denote the finite field of order q, a power of a prime p, and n be a positive integer...
AbstractWith one non-trivial exception, GF(qn) contains a primitive element of arbitrary trace over ...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a line...
AbstractThe extension field FPq where q is a prime divisor of (P−1), has a unique structure. This pa...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a l...
AbstractA characterization of primitive polynomials, among irreducible polynomials, over a finite fi...
AbstractThe object of this paper is to present a simple proof for the existence of primitive element...
This paper contains a self-contained, minimal computational account of Cohen's 1990 theorem that the...
AbstractLet Fq denote the finite field of q elements, q an odd prime power, and let f(x)=xn+∑i=1nfix...
AbstractThe primitive elements of a finite field are those elements of the field that generate the m...
The existence of a primitive free (normal) cubic x3 - ax2 + cx - b over a finite field F with arbitr...
AbstractLet q be a power of 2, n be a positive integer, and let Fqn be the finite field with qn elem...
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbi...
AbstractThe object of this paper is to prove the existence of a primitive quadratic of trace 1 over ...