[Turkmath:2693] Sabancı Univ Mathematics Colloquia - 6 & 7 December

[Kağan Kurşungöz]

Değerli Liste Üyeleri, detayları aşağıda verilen seminerlere sizleri 
davet etmek isteriz.  İyi çalışmalar,

kağan


*MATHEMATICS COLLOQUIA*
*
*
You are cordially invited to attend *two* colloquia this week given by 
Nurdagül Anbar (RICAM, Austria) on *Wednesday, 6 December 2017, in 
FENS-G055 at 11 am*, and by John Sheekey (UCD, Ireland) on *Thursday, 7 
December 2017, in FENS-L063 **at 11 am.*

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*Nurdagül Anbar*

Title: Modified planar functions, bent4 functions and their relative 
difference sets

Abstract: Modified planar functions are introduced to 
describe (2n,2n,2n,1) relative difference sets (RDS) R as a graph of a 
function on the finite field F2n.  These are analogs of planar functions 
in odd characteristic q to describe (qn, qn, qn, 1) RDSs. We point out 
that the projections of R are (2n, 2, 2n, 2n−1) RDS that can be 
described by bent4 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 bent4 functions whose 
corresponding RDSs are inequivalent.

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*John Sheekey*

Title: Algebraic constructions of semifields and maximum rank distance codes
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.

(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.

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.


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Kind regards,

Yasemin



p.s. Sabancı Üniv kampüsüne ulaşım için 
http://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri adresine bakınız.

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