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

Authors:
Maura B. Paterson;Douglas R. Stinson
Affiliations:
Department of Economics, Mathematics and Statistics, Birkbeck, University of London, London, UK WC1E 7HX;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Cryptography and Communications
Year:
2013

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Abstract

We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance.