科研之友
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摘要
In this note, we go further on the "basis exchange" idea presented in [2] by using Mobious inversion. We show that the matrix S-1(f)S-0(f)(-1) has a nice form when f is chosen lobe the majority function, where S-1(f) is the matrix with row vectors upsilon(k)(alpha) for all alpha is an element of 1(f) and S-0(f) = S-1(f circle plus 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in offset of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
- 出版日期2011-9
- 单位复旦大学
