New optimal binary sequences with period 4p via interleaving Ding–Helleseth–Lam sequences

Binary sequences play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation value/magnitude 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≡1(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 1(\bmod ~4)$$\end{document}. The objective of this paper 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 magnitude, which can not be produced by earlier ones.