Let Fq be a field with q elements, where q is a power of a prime number p ≥ 5. For any integer m ≥ 2 and a ∈ F∗q such that the polynomial xm − a is irreducible in Fq [x], we combine two different methods to explicitly construct elements of high order in the field Fq [x]/〈xm − a〉. Namely, we find elements with multiplicative order of at least 53√m/2, which is better than previously obtained bound for such family of extension fields.
- element of high multiplicative order
- finite field
- multiplicative order
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