Transitive q-Ary Functions over Finite Fields or Finite Sets: Counts, Properties and Applications
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Improved lower bound on the number of balanced symmetric functions over GF(p)
Information Sciences: an International Journal
Enumeration of balanced symmetric functions over GF(p)
Information Processing Letters
Enhanced count of balanced symmetric functions and balanced alternating functions
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On the algebraic normal form and walsh spectrum of symmetric functions over finite rings
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
| Hi-index | 754.84 |
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) = Sigma1lesi 1