Gary McGuire

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math.NT2024

Linearization of polynomials in prime characteristic, with applications to the Golay code and Steiner system

Rod Gow, Gary McGuire

Let $F$ be any field containing the finite field of order $q$ . A $q$ -polynomial $L$ over $F$ is an element of the polynomial ring $F [x]$ with the property that all powers of $x$ th…

math.NT2024

Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$ -polynomials over function fields

Rod Gow, Gary McGuire

We realize Frobenius conjugacy classes in Galois groups of certain $q$ -polynomials over $F_{q} (t)$ using specific degree 1 ideals. We combine this with methods from elementa…

Linearization of polynomials in prime characteristic, with applications to the Golay code and Steiner system

Realizing cyclic linear transformations as Frobenius elements in the Galois groups of q-polynomials over function fields

Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$ -polynomials over function fields