Under mild conditions on n,p, we give a lower bound on the number of n-variable balanced aymmetric polynomials over finite fields (GF(p), where p is a prime number. The existence of nonlinear balanced symmetrc polynomials is an immediate corollary of this bound. Furthermore, we prove that X(2t,2t+1l-1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF92), where X(D,n) = {equation).
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