New Constructions of Permutation Arrays

TL;DR

This paper introduces new methods for constructing permutation arrays using fractional polynomials and permutation groups, resulting in improved lower bounds for permutation array parameters.

Contribution

It presents two novel constructions of permutation arrays from fractional polynomials and a third from permutation groups, enhancing existing bounds.

Findings

New lower bounds for permutation arrays achieved

Two constructions from fractional polynomials over finite fields

One construction from permutation groups with specified degree and minimal degree

Abstract

A permutation array(permutation code, PA) of length $n$ and distance $d$, denoted by $(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$ elements such that the Hamming distance between distinct members $\mathbf{x},\mathbf{y}\in C$ is at least $d$. In this correspondence, we present two constructions of PA from fractional polynomials over finite field, and a construction of $(n,d)$ PA from permutation group with degree $n$ and minimal degree $d$. All these new constructions produces some new lower bounds for PA.