广义防诬陷码的改进上界
Improved upper bounds for wide-sense frameproof codes
AI总结：
本文通过Sperner理论和覆盖自由族关系，改进了广义防诬陷码的基数上界，并在码长受限时证明了最优码的唯一性。
摘要：
防诬陷码因其在版权保护中的应用以及与极值集合论的联系，多年来被广泛研究。本文研究了广义$t$-防诬陷码的基数上界。对于$t=2$，我们应用Sperner理论的结果给出了更好的上界，显著改进了Zhou和Zhou最近的一个界。对于$t\geq 3$，我们通过建立广义防诬陷码与覆盖自由族之间的关系，给出了一个一般上界。最后，当码长$n$至多为$\frac{15+\sqrt{33}}{24}(t-1)^2$时，我们证明广义$t$-防诬陷码至多有$n$个码字，且唯一的最优码由所有重量为1的码字组成。作为副产品，我们的结果改进了二元$t$-防诬陷码的几个已知最优结果。
英文摘要：
Frameproof codes have been extensively studied for many years due to their application in copyright protection and their connection to extremal set theory. In this paper, we investigate upper bounds on the cardinality of wide-sense $t$-frameproof codes. For $t=2$, we apply results from Sperner theory to give a better upper bound, which significantly improves a recent bound by Zhou and Zhou. For $t\geq 3$, we provide a general upper bound by establishing a relation between wide-sense frameproof codes and cover-free families. Finally, when the code length $n$ is at most $\frac{15+\sqrt{33}}{24}(t-1)^2$, we show that a wide-sense $t$-frameproof code has at most $n$ codewords, and the unique optimal code consists of all weight-one codewords. As byproducts, our results improve several best known results on binary $t$-frameproof codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
