3 papers
math.NT2026
Proof of a Conjecture on Primitive Quartic Polynomials over Finite Fields
Rod Gow, Gary McGuire
We present a proof of a conjecture we made about primitive polynomials, for sufficiently large. The argument follows a standard route, however a deeper result than usual with a…
math.NT2024
Linearization of polynomials in prime characteristic, with applications to the Golay code and Steiner system
Rod Gow, Gary McGuire
Let be any field containing the finite field of order . A -polynomial over is an element of the polynomial ring with the property that all powers of th…
math.NT2023
Realizing cyclic linear transformations as Frobenius elements in the Galois groups of -polynomials over function fields
Rod Gow, Gary McGuire
We realize Frobenius conjugacy classes in Galois groups of certain -polynomials over using specific degree 1 ideals. We combine this with methods from elementa…