[Turkmath:6996] İSTANBUL BİLGİ ÜNİVERSİTESİ SEMİNERLERİ

[Oya Cesur Demir]

Assoc. Prof. Dr. Wilfried Meidl
(Sabancı University)
30 April Friday, at 14:00;
Bilgi Üniversitesi Dolapdere Kampüsü, Room:135.
Title:
Sequences with favourable properties obtained from cyclotomy:
 Legendre Sequences, Sidel'nikov Sequences
Abstract:
Sequences over finite fields have applications in cryptology, wire-less communication, etc. Depending on the application different quality measures for sequences are applied. A primary quality measure in particular for sequences used in cryptology is the linear complexity, which is the length of the shortest linear recurrence relation the sequence satisfies. Thus the linear complexity can be seen as a measure for the predictability of a sequence. Another measure estimating the similarity between sequences or the similarity of a sequence with a shifted version of itself is the crosscorrelation respectively autocorrelation. In several applications sequences with low correlation are desired.
In this presentation properties of Legendre sequences and Sidel'nikov sequences, which both are obtained using cyclotomic classes, are analysed. First of all it is shown that these classes of sequences exhibit excellent autocorrelation properties which is the main reason for the general interest in these sequences. Then methods to obtain results on their linear complexity are discussed. The results confirm that Legendre and Sidel'nikov sequences are interesting for applications also under this point of view. Finally it is pointed out that these two classes of sequences provide a useful tool to construct families of sequences with low maximal correlation.
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