A note on depth-$b$ normal elements Article Swipe

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John Sheekey , David J. Thomson ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1912.00883 · OA: W4288000219

In this paper we study elements $β\in \mathbb{F}_{q^n}$ having normal $α$-depth $b$; that is, elements for which $β, β- α, \ldots, β-(b-1)α$ are simultaneously normal elements of $\mathbb{F}_{q^n}$ over $\mathbb{F}_{q}$. In [1], the authors present the definition of normal $1$-depth but mistakenly present results for normal $α$-depth for some fixed normal element $α\in \mathbb{F}_{q^n}$. We explain this discrepancy and generalize the given definition of normal $(1-)$depth from [1] as well as answer some open questions presented in [1].