On the Number of Balanced Even-Variable Boolean Functions with Maximum Algebraic Immunity
Enumeration of Boolean functions with maximum algebraic immunity (MAI) is investigated in this paper. The even-variable Boolean functions with maximum AI were divided into 3 classes. First, we can obtain the number of the first two classes, and then we give a construction which provides large number of Boolean functions with maximum AI belong to the third classes. As a result, the lower bound on the number of balanced even-variable Boolean functions with maximum AI was improved.
H. Xin et al., "On the Number of Balanced Even-Variable Boolean Functions with Maximum Algebraic Immunity", Applied Mechanics and Materials, Vols. 58-60, pp. 1647-1650, 2011