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/* 
  The database entry:
  "type" is one of the following: phd theses, phd semester, master thesis, master semester, bachelor semester
  "state" is one of the following: available, taken, completed (please upgrade accordingly!!!!!!!!!!) 
  "by" should be filled as soon as the project is taken/completed
  "completed_dt" is the date when the project was completed (YYYY-MM-DD). 
  "output_media" is the link to the pdf of the project (wiki syntax)
  "table" must be "projects" => don't touch it!
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---- dataentry project ----
title : Witness sets
contactname: Bertrand Meyer
contactmail_mail: bertrand dot meyet at epfl dot ch
contactroom: BC 128
type : master thesis 
state :  taken 
created_dt : 2010-08-01
taken_dt : 2010-09-01
completed_dt : YYYY-MM-DD
by : Nikolaos Makriyannis
output_media : 
table : projects
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template:datatemplates:project
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/* Description of the project */

Consider a set A of words of length n. If a is a word from A, we say that a subset W set of [n] is a witness for a if a can be distinguished from any other word of A by looking only at the coordinate positions in W. Now for any integer w, a w-witness set is a set A such that any word of A has a witness of length w. One of the open question regarding w-witness sets is to compute the maximal size of a w-witness set when n and w are given. 

In recent years, many  upper bounds on the size of codes have been improved using the technique of semi-definite programming in the spirit of Delsarte's linear programming bound. You will be asked to learn about these methods (optimisation, group theory, representations and harmonic analysis) and apply it to witness sets.

Pre-requisites : Good command in mathematics and in particular group theory and representation theory. Taste for experimental mathematics.