Are LAS codes a miracle?

Large area synchronized (LAS)-CDMA has been proposed to enhance third generation and fourth generation wireless systems. LAS-CDMA is based on multiple access codes that result from a combination of LA codes and pulse compressing LS codes. To reduce multiple access interference and intersymbol interference in time dispersive channels, LS codes have perfect auto-correlation and cross-correlation functions in a certain vicinity of the zero shift. In this paper, we provide systematic methods and the underlying theory for the construction of such codes that go far beyond the examples revealed by LinkAir (2000).