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Değerli Liste Üyeleri, detayları aşağıda verilen seminerlere sizleri
davet etmek isteriz. İyi çalışmalar,<br>
<br>
kağan<br>
<br>
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<div class="gmail-"><b class="gmail-">MATHEMATICS COLLOQUIA</b></div>
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</b></div>
<div class="gmail-">You are cordially invited to attend <b
class="gmail-">two</b> colloquia this week given by Nurdagül
Anbar (RICAM, Austria) on <b class="gmail-">Wednesday, 6
December 2017, in FENS-G055 at 11 am</b>, and by John
Sheekey (UCD, Ireland) on <b class="gmail-">Thursday, 7
December 2017, in FENS-L063 </b><b class="gmail-">at 11 am.</b></div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;"><b
class="gmail-">Nurdagül Anbar</b></div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Title:
Modified planar functions, bent<span style="vertical-align:
-2pt;" class="">4</span> functions and their relative
difference sets</div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Abstract: Modified
planar functions are introduced to describe (2<span
style="vertical-align: 4pt;" class="">n</span>,2<span
style="vertical-align: 4pt;" class="">n</span>,2<span
style="vertical-align: 4pt;" class="">n</span>,1) relative
difference sets (RDS) R as a graph of a function on the
finite field F<span style="vertical-align: -2pt;" class="">2</span><span
style="vertical-align: 1pt;" class="">n.</span> These are
analogs of planar functions in odd characteristic q to
describe (q<span style="vertical-align: 4pt;" class="">n</span>,
q<span style="vertical-align: 4pt;" class="">n</span>, q<span
style="vertical-align: 4pt;" class="">n</span>, 1) RDSs.
We point out that the projections of R are (2<span
style="vertical-align: 4pt;" class="">n</span>, 2, 2<span
style="vertical-align: 4pt;" class="">n</span>, 2<span
style="vertical-align: 4pt;" class="">n</span><span
style="vertical-align: 4pt;" class="">−</span><span
style="vertical-align: 4pt;" class="">1</span>) RDS that
can be described by bent<span style="vertical-align: -2pt;"
class="">4</span> functions, and we investigate the
equivalence of their relative difference sets. In
particular, we show that two extended affine equivalent bent
functions may give rise to bent<span style="vertical-align:
-2pt;" class="">4</span> functions whose corresponding
RDSs are inequivalent.</div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;"><b
class="gmail-">John Sheekey</b></div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Title: Algebraic
constructions of semifields and maximum rank distance
codes</div>
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class="gmail-" style="font-size:
12.800000190734863px;"> </span></div>
<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Abstract: Rank-metric
codes are codes consisting of matrices, with the
distance between two matrices being the rank of their
difference. Codes with maximum size for a fixed minimum
distance are called Maximum Rank Distance (MRD) codes.
These have received increased attention in recent years,
in part due to their applications in Random Linear
Network Coding.</div>
<br class="">
<span class="">(Finite) semifields are nonassociative
division algebras over a field. Existence of non-trivial
examples was established by Dickson in 1906. They have
many connections with interesting objects in finite
geometry, such as projective planes, spreads, flocks.
The number of equivalence classes of semifields remains
an open problem. By considering the maps defined by
multiplication, there is a correspondence between
semifields and MRD codes of a certain type.</span><br
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<span class="">In this talk we will review the known
constructions for semifields and MRD codes, focusing in
particular on those constructed using linearized
polynomials and skew-polynomial rings. We will introduce
a new family, which contains new examples of semifields
and MRD codes, and incorporates previously distinct
constructions into one family</span><span class=""
style="font-size: 12.8px;">.</span>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Kind
regards,</div>
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<div class="gmail-" style="margin: 0cm 0cm 0.0001pt;">Yasemin </div>
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p.s. Sabancı Üniv kampüsüne ulaşım için <a
class="moz-txt-link-freetext"
href="http://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri">http://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri</a>
adresine bakınız.<br>
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