# Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings

## TL;DR

This paper investigates the automorphisms and isomorphisms of Jha-Johnson semifields derived from skew polynomial rings, focusing on inner automorphisms and specific classes like Sandler, Hughes-Kleinfeld, and Knuth semifields.

## Contribution

It provides a detailed analysis of automorphisms of Jha-Johnson semifields, including those not originating from skew polynomial rings, and explores their isomorphism classes.

## Key findings

- Characterization of automorphisms of Jha-Johnson semifields
- Identification of automorphisms of Sandler and Hughes-Kleinfeld semifields
- Analysis of isomorphism conditions for these semifields

## Abstract

We study the automorphisms of Jha-Johnson semifields obtained from an invariant irreducible twisted polynomial $f\in K[t;\sigma]$, where $K=\mathbb{F}_{q^n}$ is a finite field and $\sigma$ an automorphism of $K$ of order $n$, with a particualr emphasis on inner automorphisms and the automorphisms of Sandler and Hughes-Kleinfeld semifields. We include the automorphisms of some Knuth semifields (which do not arise from skew polynomial rings). Isomorphism between Jha-Johnson semifields are considered as well.