New Constructions of Locally Perfect Nonlinear Functions and Their Application to Sequence Sets With Low Ambiguity Zone

Low Ambiguity Zone (LAZ) sequences are essential in modern integrated sensing and communication (ISAC) systems. Recently, locally perfect nonlinear functions (LPNFs) have been employed to design LAZ sequences with flexible parameters. In this work, we propose three new classes of LPNFs and use them to construct LAZ sequences that offer additional flexible parameters. Notably, all the proposed LAZ sequences are asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang bounds derived in [IEEE J. Sel. Areas Commun. 40(6), pp. 1809-1822, 2022].