Cross-correlation properties of cyclotomic sequences

TL;DR

This paper thoroughly analyzes the cross-correlation properties of cyclotomic sequences, which are important in communication systems, by establishing their cross-correlation functions and related algebraic structures.

Contribution

It provides a complete determination of the cross-correlation function for known cyclotomic sequences and explores the relationship between multiplier groups and sequence decimations.

Findings

Complete cross-correlation functions derived for cyclotomic sequences

Relations established between multiplier groups and sequence decimations

Enhanced understanding of sequence correlation properties in communication applications

Abstract

Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we decide the cross-correlation function of the known cyclotomic sequences completely. Moreover, to get our results, the relations between the multiplier group and the decimations of the characteristic sequence are also established for an arbitrary difference set.