# New quaternary sequences of even length with optimal auto-correlation

## TL;DR

This paper introduces new classes of quaternary sequences of even length with optimal auto-correlation, constructed via interleaving binary sequences from twin-prime, GMW, and cyclotomic class sequences, enhancing applications in communications and cryptography.

## Contribution

The paper presents novel quaternary sequences derived from various binary sequence classes using interleaving, expanding the set of sequences with optimal auto-correlation properties.

## Key findings

- New classes of quaternary sequences with optimal auto-correlation are constructed.
- Sequences are derived from twin-prime, GMW, and cyclotomic class binary sequences.
- The sequences differ from previously known sequences based on their construction methods.

## Abstract

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; two, three or four binary sequences defined by cyclotomic classes of order $4$. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidel'nikov sequences.