On the existence of primitive completely normal bases of finite fields

2017/09/10 by Garefalakis, Theodoulos, Kapetanakis, Giorgos · 1 citation
#11T24 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.03141

Abstract

Let \mathbbF_q be the finite field of characteristic p with q elements and \mathbbF_qⁿ its extension of degree n. We prove that there exists a primitive element of \mathbbF_qⁿ that produces a completely normal basis of \mathbbF_qⁿ over \mathbbF_q, provided that n=p^ℓm with (m,p)=1 and q>m.

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