On the 2-adic complexity of a class of binary sequences of period $4p$ with optimal autocorrelation magnitude

TL;DR

This paper precisely determines the 2-adic complexity of a class of binary sequences with optimal autocorrelation, showing it is nearly maximal, which is important for cryptographic applications.

Contribution

It provides the exact 2-adic complexity values for sequences previously studied, advancing understanding of their cryptographic strength.

Findings

2-adic complexity is close to maximum for the sequences

Exact values of 2-adic complexity are established

Supports the sequences' suitability for cryptography

Abstract

Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequences of period $4p$ with optimal autocorrelation magnitude was constructed in \cite{W. Su}. Later, Fan showed that the linear complexity of this class of sequences is quite good \cite{C. Fan}. Recently, Sun et al. determined the upper and lower bounds of the 2-adic complexity of such sequences \cite{Y. Sun3}. We determine the exact value of the 2-adic complexity of this class of sequences. The results show that the 2-adic complexity of this class of binary sequences is close to the maximum.