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X-WR-CALNAME;VALUE=TEXT:What's On At UWA
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BEGIN:VEVENT
UID:P-20180716T073657Z-3080-25262@events.uwa.edu.au
DTSTART;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20180720T160000
DTEND;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20180720T170000
CLASS:PUBLIC
CREATED:20180716T073657Z
DESCRIPTION:Speaker: John Sheekey (University College Dublin)\n\nTitle: S
ubspaces of Matrices over Finite Fields with Restricted Rank\n\nTime and p
lace: 4pm Friday 20 Jul 2018\, Weatherburn LT\n\nAbstract: Rank-metric cod
es are codes consisting of matrices over a finite field\, with the distanc
e between two matrices defined as the rank of their difference. Delsarte s
howed that if U is a subspace of m x n matrices in which the rank of every
nonzero element is at least k\, then the dimension of U is at most n(m-k+
1). Linear maximum rank-distance (MRD) codes are subspaces obtaining this
bound. They are the rank-metric analogue of MDS codes. Delsarte showed the
existence of examples for all parameters. Interest in the topic has incre
ased in recent years due to potential applications\, for example in random
network coding\, and in cryptography. \n\nFinite semifields are division
algebras over a finite field\, where multiplication is not assumed to be a
ssociative. Some constructions are known\, but classification remains a di
fficult open problem. They have been studied in part due to their connecti
ons to objects in finite geometry such as projective planes\, spreads\, ov
oids\, and flocks. Semifields also correspond to n-dimensional subspaces o
f n x n matrices where every nonzero element is invertible\; i.e. MRD code
s with minimum distance n. \n\nIn this talk we will give an overview of th
e known constructions and classifications of semifields and MRD codes. We
will present recent algebraic constructions using linearized polynomials a
nd skew-polynomial rings\, which constitutes the largest known family.\n\n
Past and future seminars may be found at\nhttps://www.maths.uwa.edu.au/~gla
sby/GroupsAndCombinatoricsSeminar/S18.html\n\n\n
DTSTAMP:20180716T073657Z
LAST-MODIFIED:20180717T014604Z
ORGANIZER;CN=Stephen Glasby:MAILTO:glasbys@gmail.com
SEQUENCE:2
SUMMARY:Groups and Combinatorics Seminar: John Sheekey\, 4pm Friday 20 Jul
y in Weatherburn LT
URL:https://events.uwa.edu.au/event/20180716T073657Z-3080-25262@events.uwa.
edu.au/whatson/academic
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