# New Optimal Binary Sequences with Period $4p$ via Interleaving Ding-Helleseth-Lam Sequences

## TL;DR

This paper introduces a novel method to construct binary sequences of period 4p with optimal autocorrelation by interleaving four Ding-Helleseth-Lam sequences, expanding the set of sequences useful in radar, communication, and cryptography.

## Contribution

The paper presents a new construction technique for binary sequences of period 4p with optimal autocorrelation using interleaving, which was not achievable with previous methods.

## Key findings

- Successfully constructed new binary sequences with optimal autocorrelation.
- Sequences cannot be generated by earlier methods.
- The construction enhances sequence options for practical applications.

## Abstract

Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design. Ding-Helleseth-Lam sequences are such a class of binary sequences of period $p$, where $p$ is an odd prime with $p\equiv 1(\bmod~4)$. The objective of this letter is to present a construction of binary sequences of period $4p$ via interleaving four suitable Ding-Helleseth-Lam sequences. This construction generates new binary sequences with optimal autocorrelation which can not be produced by earlier ones.