Abstract
Parent-identifying set systems and separable codes are useful combinatorial structures which were introduced, respectively, for traitor tracing in broadcast encryption and collusion-resistant fingerprints for copyright protection. Determining the maximum size of such structures is the main research objective. New upper bounds are presented in this paper. Specifically, for parent-identifying set systems, we determine the order of magnitude of \(I_2(4,v)\) and prove an exact bound when \(w\le \lfloor \frac{t^2}{4}\rfloor +t\). For q-ary separable codes, we give a new upper bound by estimating the distance distribution of such codes, improving the existing upper bound when q is relatively small.
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Communicated by C. Padro.
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Research supported by National Natural Science Foundation of China under Grant 11801392 and the Natural Science Foundation of Jiangsu Province under Grant BK20180833.
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Wang, X. Improved upper bounds for parent-identifying set systems and separable codes. Des. Codes Cryptogr. 89, 91–104 (2021). https://doi.org/10.1007/s10623-020-00809-9
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DOI: https://doi.org/10.1007/s10623-020-00809-9