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.

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.