Translates of completely normal elements and the Morgan–Mullen conjecture
Theodoulos Garefalakis, Giorgos Kapetanakis · Canadian Mathematical Bulletin · 2026
Abstract Denote by F q $\mathbb F_q$ double struck upper F Subscript q the finite field of order q and by F q n $\mathbb F_{q^n}$ double struck upper F Subscript q Sub Superscript n its extension of degree n . Some a ∈ F q n $a\in \mathbb F_{q^n}$ a element of double struck upper F Subscript q Sub Superscript n is called primitive if it generates the multiplicative group F q n ∗ $\mathbb F_{q^n}^*$ double struck upper F Subscript q Sub Superscript n Superscript asterisk , and it is called q n / q $q^n/q$ q Superscript n Baseline divided by q -normal if its F q $\mathbb F_q$ double struck upper F Subscript q -conjugates form an F q $\mathbb F_q$