The Linear Complexity of a Class of Binary Sequences With Optimal Autocorrelation

TL;DR

This paper determines the minimal polynomial and linear complexity of a class of binary sequences with optimal autocorrelation, which are constructed via interleaving Ding-Helleseth-Lam sequences, highlighting their suitability for cryptographic applications.

Contribution

It provides the first analysis of the linear complexity of these sequences, showing they possess high linear complexity suitable for cryptography.

Findings

Sequences have high linear complexity.

Sequences exhibit optimal autocorrelation.

Linear complexity is suitable for cryptographic use.

Abstract

Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed via interleaving four suitable Ding-Helleseth-Lam sequences (Des. Codes Cryptogr., DOI 10.1007/s10623-017-0398-5), where $p$ is an odd prime with $p\equiv 1(\bmod~4)$. The objective of this paper is to determine the minimal polynomial and the linear complexity of this class of binary optimal sequences via sequence polynomial approach. It turns out that this class of sequences has quite good linear complexity.