Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessities and sufficiencies of a class of permutation polynomials over
  finite fields   For the finite field $\mathbb{F}_{2^{3m}}$, permutation polynomials of the
form $(x^{2^m}+x+\delta)^{s}+cx$ are studied. Necessary and sufficient
conditions are given for the polynomials to be permutation polynomials. For
this, the structures and properties of the field elements are analyzed.

20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin