Applications and distance measures of subspace codes
Prof. Tuvi Etzion
Technion, Israel
In their seminal paper from 2008, Koetter and Kschischang have shown how
subspace codes can be used for error and erasure correction in random network coding.
It was shown recently that using subspace codes one can show that vector network coding
outperforms scalar linear network coding, on multicast networks, with respect to the alphabet size.
This fact was shown by using a new family of networks which generalizes the well known combination netwoks.
We consider these generalized combination networks and find the optimal network codes
required for their scalar linear solution. Surprisingly, these network codes are subspace codes
on which a new distahce measure can be defined for such a solution. We show that for the orthogonal
complement codes of these subspaces codes another distance measure can be given.
This new distance measure generalizes a common definition for subspace designs. These two distance
measures are equivalent under duality of the subspaces. Finally, we discuss bounds on the sizes of the related codes.
Tuvi Etzion was born in Tel Aviv, Israel, in 1956. He received the B.A., M.Sc., and D.Sc. degrees from the
Technion - Israel Institute of Technology, Haifa, Israel, in 1980, 1982, and 1984, respectively.
From 1984 he held a position in the Department of Computer Science at the Technion, where he now holds the Bernard Elkin Chair in Computer Science. During the years 1985-1987 he was Visiting Research Professor with the Department of Electrical Engineering - Systems at the University
of Southern California, Los Angeles. During the summers of 1990 and 1991 he was visiting Bellcore in Morristown, New Jersey.
During the years 1994-1996 he was a Visiting Research Fellow in the Computer Science Department at Royal Holloway University of London, Egham,
England. He also had several visits to the Coordinated Science Laboratory at University of Illinois in Urbana-Champaign during the years 1995-1998, two visits to HP Bristol during the summers of 1996, 2000, a few visits to the Department of Electrical Engineering, University of California at San Diego during the
years 2000-2017, and several visits to the Mathematics Department at Royal Holloway University of London, during the years 2007-2017.
His research interests include applications of discrete
mathematics to problems in computer science and information theory, coding theory, network coding, and combinatorial designs.
Dr. Etzion was an Associate Editor for Coding Theory for the IEEE Transactions on Information Theory from 2006 till 2009. From 2004 to 2009, he was an Editor for the Journal of Combinatorial Designs.
From 2011 he is an Editor for Designs, Codes, and Cryptography and from 2013 an Editor for Advances of Mathematics in Communications.