中文摘要：

代数免疫度是衡量布尔函数抵抗代数攻击的重要指标。最近,Mesnager等研究了布尔函数的零化子与函数所对应循环码最小距离之间的联系,代数免疫度的下界可以由对应的循环码的最小距离得到。解决了Mesnager提出的一个公开问题,给出了一类特定函数的零化子次数的下界,并得到一类布尔函数的代数免疫度的下界。

英文摘要：

Algebraic immunity quantified the resistance of a Boolean function to the algebraic attack. Recently, Mesnager, et al showed that there were direct linked between the annihilators used in algebraic attacks and the coding theory. They showed that the lower bound of the algebraic immunity of Boolean functions could been derived from the minimum distance of the associated cyclic codes. An open problem proposed by Mesnager is settled with a detailed proof. Also, a lower bound of algebraic immunity of a class of Boolean functions will be introduced.