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

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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.

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Notes

  1. After this paper was submitted for publication, Ronald Cramer informed us (private communication) that he also had a specialised proof of the combinatorial bound; this proof is presented in the updated version of [4].

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Acknowledgements

We would like to thank Ignacio Cascudo, Ronald Cramer, Ryutaroh Matsumoto and Ruizhong Wei for helpful comments.

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Authors and Affiliations

  1. Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK

    Maura B. Paterson

  2. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Douglas R. Stinson

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  1. Maura B. Paterson
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  2. Douglas R. Stinson
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Corresponding author

Correspondence to Douglas R. Stinson.

Additional information

D. Stinson’s research is supported by NSERC discovery grant 203114-11.

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Paterson, M.B., Stinson, D.R. A simple combinatorial treatment of constructions and threshold gaps of ramp schemes . Cryptogr. Commun. 5, 229–240 (2013). https://doi.org/10.1007/s12095-013-0082-1

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