Abstract
In this paper we discuss some variations of the notion of separating code for alphabets of arbitrary size. We show how the original definition can be relaxed in two different ways, namely almost separating and almost secure frameproof codes, yielding two different concepts. The new definitions enable us to obtain codes of higher rate, at the expense of satisfying the separating property partially. These new definitions become useful when complete separation is only required with high probability, rather than unconditionally. We also show how the codes proposed can be used to improve the rate of existing constructions of families of fingerprinting codes.
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Acknowledgments
We would like to thank the anonymous Reviewers, whose insightful comments and observations helped to improve the contents and presentation of the paper. J. Moreira and M. Fernández have been supported in part by the Spanish Government through Projects Consolider-Ingenio 2010 CSD2007-00004 “ARES” and TEC2011-26491 “COPPI”, and by the Catalan Government through Grant 2014 SGR-1504. G. Kabatiansky has been supported in part by the Russian Foundation for Basic Research through Grants RFBR 13-01-12458, RFBR 13-07-00978, and RFBR 14-01-93108.
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Communicated by C. J. Colbourn.
The material in this work was presented in part at the 2011 IEEE International Symposium on Information Theory [10].
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Moreira, J., Fernández, M. & Kabatiansky, G. Almost separating and almost secure frameproof codes over \(q\)-ary alphabets. Des. Codes Cryptogr. 80, 11–28 (2016). https://doi.org/10.1007/s10623-015-0060-z
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DOI: https://doi.org/10.1007/s10623-015-0060-z