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SUMMARY:Subspace Codes for Adversarial Error-Correction in Network Coding 
 - Azadeh Khaleghi (University of Toronto)
DTSTART:20100310T113000Z
DTEND:20100310T120000Z
UID:TALK23686@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:In the context of error control in random linear network codin
 g\, it is useful to construct codes that comprise well-separated collectio
 ns of subspaces of a vector space over a finite field. \n\nThis work conce
 rns the construction of non-constant-dimension projective space codes for 
 adversarial error-correction in random linear network coding. The metric u
 sed is the so-called injection distance introduced by Silva and Kschischan
 g\, which perfectly reflects the adversarial nature of the channel. \n\nA 
 Gilbert-Varshamov-type bound for such codes is derived and its asymptotic 
 behavior is analyzed. It is shown that in the limit as the ambient space d
 imension approaches infinity\, the Gilbert-Varshamov bound on the size of 
 non-constant-dimension codes behaves similar to the Gilbert-Varshamov boun
 d on the size of constant-dimension codes contained within the largest Gra
 ssmannians in the projective space.\n\nUsing a multi-level scheme\, new no
 n-constant-dimension codes are constructed\;  these codes contain more cod
 ewords than comparable codes designed for the subspace metric. To our know
 ledge this work is the first to address the construction of non-constant-d
 imension codes designed for the injection metric.
LOCATION:Engineering Department\, CBL Room 438
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