Primitive normal polynomials over finite fields

Ilene H. Morgan, Gary L. Mullen
1994 Mathematics of Computation  
In this note we significantly extend the range of published tables of primitive normal polynomials over finite fields. For each p" < 1050 with P < 97, we provide a primitive normal polynomial of degree n over Fp. Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree n over Fp. The roots of such a polynomial generate a primitive normal basis of Fpn over Fp , and so are of importance in many computational problems. We also raise
more » ... everal conjectures concerning the distribution of such primitive normal polynomials, including a refinement of the primitive normal basis theorem.
doi:10.1090/s0025-5718-1994-1257578-3 fatcat:judndyyw4rgbvfcz4sl7iwzp34