A Simple Combinatorial Treatment of Constructions and Threshold Gaps of Ramp Schemes

Maura B.  Paterson; Douglas R.  Stinson

Paper 2012/534

A Simple Combinatorial Treatment of Constructions and Threshold Gaps of Ramp Schemes

Maura B. Paterson and Douglas R. Stinson

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 the minimum length of a code having a specified distance and dual distance.

Note: In this version, we have added some additional references and discussion to clarify various aspects of the paper.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. submitted for publication
Keywords: secret sharing
Contact author(s): dstinson @ uwaterloo ca
History: 2012-11-07: last of 2 revisions; 2012-09-20: received; See all versions
Short URL: https://ia.cr/2012/534
License: CC BY

BibTeX

@misc{cryptoeprint:2012/534,
      author = {Maura B.  Paterson and Douglas R.  Stinson},
      title = {A Simple Combinatorial Treatment of Constructions and Threshold Gaps of Ramp Schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/534},
      year = {2012},
      url = {https://eprint.iacr.org/2012/534}
}