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<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Assoc. Prof. Dr. Wilfried Meidl<o:p></o:p></span></font></b></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;margin-bottom:
12.0pt;text-align:center'><font size=3 face=Tahoma><span style='font-size:12.0pt;
font-family:Tahoma'>(Sabancı University)<br>
30 April Friday, at <font color=blue><span style='color:blue'>14:00</span></font>;<br>
Bilgi Üniversitesi Dolapdere Kampüsü, Room:<font color=blue><span
style='color:blue'>135.</span></font></span></font><o:p></o:p></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Title: </span></font></b><o:p></o:p></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'>Sequences
with favourable properties obtained from cyclotomy:<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'> Legendre
Sequences, Sidel'nikov Sequences<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Abstract:<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='text-align:justify;text-indent:42.55pt;text-autospace:
none'><font size=2 face=F17><span style='font-size:11.0pt;font-family:F17'>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.<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-align:justify;text-indent:42.55pt;text-autospace:
none'><font size=2 face=F17><span style='font-size:11.0pt;font-family:F17'>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.<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><font size=3 face=F16><span style='font-size:12.0pt;
font-family:F16'>1</span></font><b><font face=Arial><span style='font-family:
Arial;font-weight:bold'><o:p></o:p></span></font></b></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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