Perfect and Almost Perfect Sequences

13 years 4 months ago

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The autocorrelation function of a sequence is a measure for how much the given sequence di ers from its translates. Periodic binary sequences with good correlation properties have important applications in various areas of engineering. In particular, one needs sequences with a two-level autocorrelation function, that is, all nontrivial autocorrelation coe cients equal some constant . The case where is as small as theoretically possible in absolute value has turned out to be especially useful; such sequences are called perfect. Unfortunately, in many cases perfect sequences cannot exist, and so one has also considered "almost perfect" sequences, where one allows one nontrivial autocorrelation coe cient to be di erent from . In this paper, we concentrate on the existence problem for perfect and almost perfect binary periodic sequences; such sequences are actually equivalent to certain cyclic di erence sets and cyclic divisible di erence sets, respectively, structures which hav...

Dieter Jungnickel, Alexander Pott

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