Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the lower bounds for secure codes and their related structures. First, we give some improved lower bounds for the rates of $2$-frameproof codes and $\overline{2}$-separable codes for slightly large alphabet size. Then we improve the lower bounds for the rate of some related structures, i.e., strongly $2$-separable matrices and $2$-cancellative set families. Finally, we give a general method to derive new lower bounds for strongly $t$-separable matrices and $t$-cancellative set families for $t\ge 3.$
翻译：安全代码是广泛研究的组合式结构,用于在广播加密中追踪叛徒。确定此类结构的最大尺寸是主要研究目标。在本文中,我们调查安全代码及其相关结构的下限。首先,我们为2美元防框架代码和美元/线{2}小字母大小的可分离代码的下限提供了一些改进的下限。然后,我们改进了某些相关结构的下限,即可分离基体和可分离基体的最大值为$2美元和2美元取消型家庭。最后,我们给出了一种一般方法,为强度可分离基体和3美元可分离基体的新下限得出新的下限。
相关内容
微信扫码咨询专知VIP会员