Local permutation polynomials and the action of e-Klenian groups

TL;DR

This paper introduces a new family of local permutation polynomials derived from e-Klenian groups and explores their applications in constructing Mutually Orthogonal Latin Squares, advancing combinatorial design theory.

Contribution

It presents a novel class of local permutation polynomials based on e-Klenian groups and demonstrates their use in constructing new MOLS on prime power sizes.

Findings

New family of local permutation polynomials based on e-Klenian groups

Construction of MOLS on size a prime power using these polynomials

Enhanced methods for combinatorial designs in finite fields

Abstract

Permutation polynomials of finite fields have many applications in Coding Theory, Cryptography and Combinatorics. In the first part of this paper we present a new family of local permutation polynomials based on a class of symmetric subgroups without fixed points, the so called e-Klenian groups. In the second part we use the fact that bivariate local permutation polynomials define Latin Squares, to discuss several constructions of Mutually Orthogonal Latin Squares (MOLS) and, in particular, we provide a new family of MOLS on size a prime power.