Perfect and almost perfect sequences
This is essentially a survey article concerning periodic \(\pm 1-\)sequences whose out-of phase (or off-peak) autocorrelation function has extremal properties. Such a binary sequence is perfect if the out-of-phase autocorrelation function has only two different values and these values are as small as possible. There is an equivalent translation into the language of cyclic difference sets for designs (equivalently: designs with a cyclic group of automorphisms acting regularly on the points). The paper surveys the state of the art concerning existence of such objects. Certain generalizations are also considered: non-cyclic difference sets, ternary sequences, almost perfect sequences, non-periodic sequences. The paper closes with an interesting description of an application in optics related to a technique called coded aperture imaging.
scientific article; zbMATH DE number 1340646