Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new class of permutation trinomials constructed from Niho exponents   Permutation polynomials over finite fields are an interesting subject due to
their important applications in the areas of mathematics and engineering. In
this paper we investigate the trinomial $f(x)=x^{(p-1)q+1}+x^{pq}-x^{q+(p-1)}$
over the finite field $\mathbb{F}_{q^2}$, where $p$ is an odd prime and $q=p^k$
with $k$ being a positive integer. It is shown that when $p=3$ or $5$, $f(x)$
is a permutation trinomial of $\mathbb{F}_{q^2}$ if and only if $k$ is even.
This property is also true for more general class of polynomials
$g(x)=x^{(q+1)l+(p-1)q+1}+x^{(q+1)l+pq}-x^{(q+1)l+q+(p-1)}$, where $l$ is a
nonnegative integer and $\gcd(2l+p,q-1)=1$. Moreover, we also show that for
$p=5$ the permutation trinomials $f(x)$ proposed here are new in the sense that
they are not multiplicative equivalent to previously known ones of similar
form.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess