Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on depth-$b$ normal elements   In this paper we study elements $\beta \in \mathbb{F}_{q^n}$ having normal
$\alpha$-depth $b$; that is, elements for which $\beta, \beta - \alpha, \ldots,
\beta-(b-1)\alpha$ 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 $\alpha$-depth for some
fixed normal element $\alpha \in \mathbb{F}_{q^n}$. 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].

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int