Balanced Symmetric Functions Over ${\hbox{GF}}(p)$
Thomas W. Cusick, Yuan Li, Pantelimon Stănică · IEEE Transactions on Information Theory · 2008
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 prove that X(2t, 2t+1lscr-1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF(2), where X(d, n) = Sigma1lesi1<i2<hellip