New construction of Locally Perfect Nonlinear Functions with Application to Sequences Sets with Low Ambiguity Zone

Abstract: Low Ambiguity Zone (LAZ) sequences play a pivotal role in modern integrated sensing and communication (ISAC) systems. Recently, Wang et al.\cite{WangZhou2025} proposed a definition of locally perfect nonlinear functions (LPNFs) and constructed three classes of both periodic and aperiodic LAZ sequence sets with flexible parameters by applying such functions and interleaving method. Some of these LAZ sequence sets are asymptotically optimal with respect to the Ye-Zhou-Liu-Fan-Lei-Tang bounds under certain conditions. In this paper, we proceed with the constructions of the three new classes of LPNFs with new parameters. By using these LPNFs, we also present a series of LAZ sequence sets with more flexible parameters, addressing the limitations of existing parameter choices. Furthermore, our results show that one of these classes is asymptotically optimal in both the periodic and aperiodic cases, respectively.