Perfect and almost perfect sequences
type: Item
instance of: scholarly article
title: Perfect and almost perfect sequences
zbMATH Open document ID: 0941.05013
DOI: 10.1016/S0166-218X(99)00085-2
author: Alexander Pott
author: Dieter Jungnickel
published in: Discrete Applied Mathematics
publication date: 2000-07-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 94A55
zbMATH DE Number: 1340646
zbMATH Keywords: autocorrelation
zbMATH Keywords: difference set
reviewed by: Jürgen Bierbrauer
MaRDI profile type: Publication
full work available at URL: s0166-218x(99)00085-2
OpenAlex ID: W2045043420
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description: scientific article; zbMATH DE number 1340646