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A simplified combinatorial treatment of constructions and threshold gaps of ramp schemes

  • Speaker: Dr Maura Paterson, Department of Economics, Mathematics and Statistics, Birkbeck, University of London.
  • Date: Wednesday, 23 October 2013 from 16:30 to 17:30
  • Location: Room 160, Birkbeck Main Building

A (t_1,t_2,n)-ramp scheme is a method for a dealer to distribute shares to n players such that any subset of t_2 players can combine their shares to recover a unique secret, whereas the shares belonging to any set of t_1 or fewer players reveal no information about the secret. In this talk we describe how a combinatorial approach yields straightforward proofs of recent results involving the threshold gap t_2-t_1, and we exploit the connection between error-correcting codes and ramp schemes to derive a new explicit bound on the minimum length of a code having a specified distance and dual distance.