Local permutation polynomials and the action of e-Klenian groups

2022/04/30 by Jaime Gutiérrez, Gutierrez, Jaime, Jorge Jiménez Urroz +1 · 1 citation
Computer Science · Engineering · Mathematics · #05b15 #11T06 #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #G.2.1 #Group Theory (math.GR) #Number Theory (math.NT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2205.00151

openalex publication_date 2022/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• An algebraic approach to Latin squares of prime power order by local permutation polynomials

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• Local permutation polynomials and their companions
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