New Class of Optimal Frequency-Hopping Sequences by Polynomial Residue Class Rings

TL;DR

This paper introduces a novel construction of frequency hopping sequences using polynomial residue class rings, achieving optimal autocorrelation and creating new, flexible families of sequences with improved parameters.

Contribution

It presents a new method for constructing frequency hopping sequences with optimal autocorrelation using polynomial residue class rings, expanding the set of available sequence parameters.

Findings

Sequences achieve optimal Hamming autocorrelation

New families of frequency hopping sequences are constructed

Sequences have flexible and improved parameters

Abstract

In this paper, using the theory of polynomial residue class rings, a new construction is proposed for frequency hopping patterns having optimal Hamming autocorrelation with respect to the well-known $Lempel$-$Greenberger$ bound. Based on the proposed construction, many new $Peng$-$Fan$ optimal families of frequency hopping sequences are obtained. The parameters of these sets of frequency hopping sequences are new and flexible.