Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the constructions of $n$-cycle permutations   Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a
specific small positive integer, one can obtain efficient permutations, such as
involutions, triple-cycle permutations and quadruple-cycle permutations. These
permutations have important applications in cryptography and coding theory.
Inspired by the AGW Criterion, we propose criteria for $ n $-cycle
permutations, which mainly are of the form $ x^rh(x^s) $. We then propose
unified constructing methods including recursive ways and a cyclotomic way for
$ n $-cycle permutations of such form. We demonstrate our approaches by
constructing three classes of explicit triple-cycle permutations with high
index and two classes of $ n $-cycle permutations with low index.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph