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en:projects:details:bfm03 [2010/11/16 13:28]
en:projects:details:bfm03 [2016/06/23 11:26]
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-/* This is the template for project details pages */ 
-  The database entry: 
-  "​type"​ is one of the following: phd theses, phd semester, master thesis, master semester, bachelor semester 
-  "​status"​ 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! 
----- dataentry project ---- 
-title : Witness sets 
-contactname:​ Bertrand Meyer 
-contactmail_mail:​ bertrand dot meyet at epfl dot ch 
-contactroom:​ BC 128 
-type : master thesis ​ 
-status :  taken  
-created_dt : 2010-08-01 
-taken_dt : 2010-09-01 
-completed_dt : YYYY-MM-DD 
-by : Nikolaos Makriyannis 
-output_media :  
-table : projects 
-/* 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.