# Efficient Algorithms for Permutation Arrays from Permutation Polynomials

## TL;DR

This paper presents efficient algorithms for computing permutation polynomials, improving the calculation of permutations with specific distance properties.

## Contribution

The paper introduces new algorithms using normalization, F-maps, G-maps, and the Hermite criterion for computing permutation polynomials.

## Key findings

- The algorithms enable efficient computation of permutation polynomials for larger degrees and finite fields.
- Improved lower bounds for M(n,D) are achieved using the new methods.

## Abstract

We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds for M(n,D), the maximum number of permutations on n symbols with a pairwise Hamming distance of D.