ar X iv : m at h . C O / 0 60 83 69 v 1 1 5 A ug 2 00 6 BALANCED SYMMETRIC FUNCTIONS OVER GF ( p )
نویسندگان
چکیده
Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF (p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we conjecture that X(2, 2t+1l− 1) are the only nonlinear balanced elementary symmetric polynomials over GF (2), where X(d, n) = ∑ i1<i2<···<id xi1xi2 · · ·xid , and we prove various results in support of this conjecture.
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