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By modifying the functions with good cryptographic properties constructed by Jin et al., we construct two classes of balanced Boolean functions which have optimal algebraic immunity assuming the correctness of the generalized Tu-Deng conjecture. Considering concatenations of functions from these two classes, we obtain a class of 1-resilient Boolean functions which have suboptimal algebraic immunity assuming the correctness of the generalized Tu-Deng conjecture, and have optimal algebraic degree and high nonlinearity. For some special instances of parameters, functions belonging to this class have suboptimal algebraic immunity without assumption of the correctness of any combinatorial conjectures.
