Balanced Symmetric Functions over $GF(p)$

dc.creatorCusick, Thomas W.
dc.creatorLi, Yuan
dc.creatorStanica, Pantelimon
dc.date2006-08-15
dc.date.accessioned2026-07-07T07:21:47Z
dc.date.available2026-07-07T07:21:47Z
dc.descriptionUnder 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.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0608369
dc.identifierhttp://arxiv.org/abs/math/0608369
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115427
dc.subjectCombinatorics
dc.subject05A10; 05A16; 11T71
dc.titleBalanced Symmetric Functions over $GF(p)$
dc.typetext

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