For α ∈ Fq the finite field of order q and β ∈ Fq(α), let Fq(α, β) = Fq(γ). We obtain an explicit formula for the minimal polynomial hγ(x) of γ in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials fα(x) of α and gβ(x) of β. We also give an application of this result to linear recurring arrays.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics