Technion
 
Mathematics Colloquium
 
Speaker: Alex Lubotzky (Hebrew University)
 
Title: Arithmetic groups, Ramanujan graphs and error correcting
codes 
 
Time: March 19, 3:30pm
 
Place: Amado 232
 
 <Homepage: http://www.technion.ac.il/~yehuday/colloquium/colloq.html>
 
Abstract: While many of the classical codes are cyclic, a long standing
conjecture asserts that there are no 'good' cyclic codes.  In recent years
the intrest in symmetric codes has been promoted by Kaufman, Sudan,
Wigderson and others (where symmetric means that the acting group can be
any group). Answering their main question (and in contrary to the common
expectation), we show that there DO exist symmetric good codes. In fact,
our codes satisfy all the "golden standards" of coding theory. Our
construction is based on the Ramanujan graphs contsructed by
Lubotzky-Samuels-Vishne as a special case of Ramanujan complexes. The
crucial point is that these graphs are edge transitive and not just vertex
transitive as in  previous constructions of Ramanujan graphs.   
 
All notions will be explained.   
 
Joint work with Tali Kaufman.
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Amir Yehudayoff   <amir.yehudayoff@gmail.com>