Balanced Symmetric Functions over $GF(p)$
| dc.creator | Cusick, Thomas W. | |
| dc.creator | Li, Yuan | |
| dc.creator | Stanica, Pantelimon | |
| dc.date | 2006-08-15 | |
| dc.date.accessioned | 2026-07-07T07:21:47Z | |
| dc.date.available | 2026-07-07T07:21:47Z | |
| dc.description | 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 $X(2^t,2^{t+1}l-1)$ are the only nonlinear balanced elementary symmetric polynomials over GF(2), where $X(d,n)=\sum_{i_1<i_2<...<i_d}x_{i_1} x_{i_2}... x_{i_d}$, and we prove various results in support of this conjecture. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608369 | |
| dc.identifier | http://arxiv.org/abs/math/0608369 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115427 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A10; 05A16; 11T71 | |
| dc.title | Balanced Symmetric Functions over $GF(p)$ | |
| dc.type | text |