Integral automorphisms of affine spaces over finite fields

TL;DR

This paper classifies all integral automorphisms of affine spaces over finite fields for dimensions three and higher, expanding understanding of symmetries preserving integral distances.

Contribution

It completes the classification of integral automorphisms of affine spaces over finite fields for dimensions n ≥ 3.

Findings

Complete classification of integral automorphisms for n ≥ 3

Identification of symmetries preserving integral distances

Extension of previous partial results

Abstract

A permutation of the point set of the affine space $AG(n,q)$ is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of $AG(n,q)$ for $n\ge 3$.