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 $$I_2(4,v)$$ I 2 ( 4 , v ) and prove an exact bound when $$w\le \lfloor \frac{t^2}{4}\rfloor +t$$ w ≤ ⌊ t 2 4 ⌋ + 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.

中文翻译：

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改进了父标识集系统和可分离代码的上限

父母识别集系统和可分离代码是有用的组合结构，它们分别被引入用于广播加密中的叛徒追踪和用于版权保护的抗合谋指纹。确定此类结构的最大尺寸是主要研究目标。本文提出了新的上限。具体来说，对于双亲识别集合系统，我们确定了 $$I_2(4,v)$$I 2 ( 4 , v ) 的数量级，并证明了当 $$w\le \lfloor \frac{t ^2}{4}\rfloor +t$$ w ≤ ⌊ t 2 4 ⌋ + t 。对于 q 元可分离码，我们通过估计此类码的距离分布给出一个新的上限，当 q 相对较小时改进现有的上限。