Abstract: According to definition of algebraic thickness of Boolean functions, the relationship between addition of two Boolean functions and their algebraic thickness is given. Limitation property of upper bound on algebraic thickness is descripted. Meanwhile, the restrictive relationship of algebraic thickness between Boolean function and complement Boolean function is derived. By these results, the upper bounds on algebraic thickness of Boolean functions with small hamming weights and their complement functions are deduced. The probability value of Boolean functions with some algebraic thickness is estimated.

Key words: Boolean functions, algebraic thickness, Hamming weight, algebraic normal form, algebraic immunity

摘要： 根据布尔函数代数厚度的定义，总结变量不交布尔函数的组合函数代数厚度与各布尔函数代数厚度的联系，指出代数厚度上界证明的局限性，得到布尔函数与其补布尔函数代数厚度的限制关系式。利用该关系式得到汉明重量为2和3的布尔函数及其补布尔函数的代数厚度上界，计算满足一定代数厚度的布尔函数的概率值。

关键词: 布尔函数, 代数厚度, 汉明重量, 代数正规型, 代数免疫

CLC Number: 

• TN918.1