# Some New Balanced and Almost Balanced Quaternary Sequences with Low Autocorrelation

## TL;DR

This paper introduces new balanced and almost balanced quaternary sequences with low autocorrelation, constructed using cyclotomic classes, and analyzes their linear complexity to enhance sequence design for communication systems.

## Contribution

It presents novel constructions of balanced quaternary sequences using cyclotomic classes and refines existing methods for sequences with low autocorrelation.

## Key findings

- New families of balanced quaternary sequences with low autocorrelation
- Simplified construction methods for even period sequences
- Analysis of linear complexity of the sequences

## Abstract

Quaternary sequences of both even and odd period having low autocorrelation are studied. We construct new families of balanced quaternary sequences of odd period and low autocorrelation using cyclotomic classes of order eight, as well as investigate the linear complexity of some known quaternary sequences of odd period. We discuss a construction given by Chung et al. in "New Quaternary Sequences with Even Period and Three-Valued Autocorrelation" [IEICE Trans. Fundamentals Vol. E93-A, No. 1 (2010)] first by pointing out a slight modification (thereby obtaining new families of balanced and almost balanced quaternary sequences of even period and low autocorrelation), then by showing that, in certain cases, this slight modification greatly simplifies the construction given by Shen et al. in "New Families of Balanced Quaternary Sequences of Even Period with Three-level Optimal Autocorrelation" [IEEE Comm. Letters DOI10.1109/LCOMM.2017.26611750 (2017)]. We investigate the linear complexity of these sequences as well.