Primitive Normal Polynomials Over Finite Fields
In this note we significantly extend the range of published tables of primitive normal polynomials over finite fields. For each with , we provide a primitive normal polynomial of degree n over . Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree n over . The roots of such a polynomial generate a primitive normal basis of over , and so are of importance in many computational problems. We also raise several conjectures concerning the distribution of such primitive normal polynomials, including a refinement of the primitive normal basis theorem.
I. H. Morgan and G. L. Mullen, "Primitive Normal Polynomials Over Finite Fields," Mathematics of Computation, American Mathematical Society, Jan 1994.
The definitive version is available at https://doi.org/10.1090/S0025-5718-1994-1257578-3
Mathematics and Statistics
Keywords and Phrases
finite field; primitive normal basis
Article - Journal
© 1994 American Mathematical Society, All rights reserved.