Abstract: A class of Boolean functions f with suboptimal（or optimal） algebraic immunity is presented，by means of the second construction methods，a new class of Boolean functions h with optimal immunity is gotten.The h is different from what have been constructed before.The number of the functions f is given，the nonlinearity of the function h is discussed in the case of even number variables.Finally，the nonlinearity is discussed and that the nonlinearity of the function h constructed by means of the majority function F_n can make the Lobanov bound tight is found.

摘要： 构造了一类至少具有次优代数免疫阶的布尔函数f，并利用级联的方法构造了一类具有最优代数免疫阶的布尔函数h。这类函数h不同于以前相关文献中所提出的最优代数免疫的布尔函数，给出了f的数目，并进一步讨论了h（偶数个变元的情况下）的非线性度，发现利用择多函数F_n构造的一类函数h非线性度达到Lobanov界。