A note on a conjecture concerning symmetric resilient functions
Information Processing Letters
Correlation immunity and resiliency of symmetric Boolean functions
Theoretical Computer Science
Improved lower bound on the number of balanced symmetric functions over GF(p)
Information Sciences: an International Journal
Constructing symmetric boolean functions with maximum algebraic immunity
IEEE Transactions on Information Theory
Linear structures of symmetric functions over finite fields
Information Processing Letters
On the algebraic immunity of symmetric boolean functions
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Correlation-immune functions over finite fields
IEEE Transactions on Information Theory
Maximum nonlinearity of symmetric Boolean functions on odd number of variables
IEEE Transactions on Information Theory
Resilient functions over finite fields
IEEE Transactions on Information Theory
New results on the nonexistence of generalized bent functions
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity
IEEE Transactions on Information Theory
A Note on Symmetric Boolean Functions With Maximum Algebraic Immunity in Odd Number of Variables
IEEE Transactions on Information Theory
Balanced Symmetric Functions Over
IEEE Transactions on Information Theory
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Symmetric functions display some interesting properties since this class of functions are invariant under permutation of indices. In this paper, we prove that the construction and enumeration of the number of balanced symmetric functions over GF(p) are equivalent to solving an equation system and enumerating the solutions, as a result we obtain the exact number of n-variable balanced symmetric functions by searching the solutions of the equation system. When n and p become large, we give a lower bound on number of balanced symmetric functions over GF(p), and the lower bound provides best known result.