Divisible designs from twisted dual numbers

TL;DR

This paper explores the structure and properties of divisible designs derived from twisted dual numbers over finite fields, using group actions and geometric models in four-dimensional space.

Contribution

It introduces a new class of divisible designs from twisted dual numbers and analyzes their combinatorial and geometric properties.

Findings

Divisible designs are constructed from twisted dual numbers over finite fields.

The paper provides a geometric model of these designs in 4-space.

Key combinatorial properties of the designs are characterized.

Abstract

The generalized chain geometry over the local ring $K(\epsilon;\sigma)$ of twisted dual numbers, where $K$ is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated.