有限域上置换多项式的进一步研究

Further study on permutation polynomials over finite fields

摘要:构造新的置换多项式是Lidl和Mullen在1988年提出的一个公开问题.当q^k≡2(mod 3)时,本文作者曾利用线性化多项式得到了有限域■上一类形如■的置换多项式.本文进一步得到了有限域■上形如■的置换多项式.

Constructing new classes of permutation polynomials is an open problem raised by Lidl and Mullen in 1988.By using linearized polynomials,we constructed the permutation polynomials over F q 2k of the form(x q k-x+δ)q m-1/3+1+x q k+x,where q k≡2(mod 3).In this paper,we further study the permutation polynomials of F q 3k having the form(x q 2k+x q k+x+δ)q 3k-1/3+1+(x q 2k+x q k+x+δ)2 q 3k-1/3+1-x.