Some Zero-Difference Functions Over $\mathbb{Z}_n$ Using Cyclotomies

TL;DR

This paper introduces a generic method for constructing zero-difference functions over algebraic rings, specifically applied to rings like rac{p^k}{ ext{where } p ext{ is prime and } k ext{ is an integer}}, expanding the toolkit for algebraic combinatorics.

Contribution

It proposes a new generic construction method for zero-difference functions and applies it to specific rings such as rac{p^k}{, offering novel algebraic structures.

Findings

New zero-difference functions constructed for rac{p^k}{ rings.

Method applicable to various algebraic rings beyond initial cases.

Potential applications in combinatorics and coding theory.

Abstract

A generic method to construct zero-difference functions (ZDFs) on algebraic rings is proposed in this paper. Then this method is used over some rings $\mathbb{Z}_{p^k}$, where $p$ is a prime number and $k\ge 2$ is a positive integer, and for some other special rings.