Further results on complete permutation monomials over finite fields
Further results on complete permutation monomials over finite fields
复制标题
有限域上完全置换单项式的进一步结果
DOI：
10.1016/j.ffa.2019.01.003
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发表时间：
2019
影响因子：
1
通讯作者：
Qiang Wang
中科院分区：
文献类型：
--
作者：
Xiutao Feng;Dongdai Lin;Liping Wang;Qiang Wang
In this paper, we construct several new classes of complete permutation monomials a− 1 x d over a finite field F q n with exponents d= q n− 1 q− 1+ 1, q p− 1− 1 q− 1+ 1, and q q− 1− 1 q− 1+ 1, respectively, where q= p k is a power of a prime number p. Our approach uses the AGW criterion (the multiplicative case) together with Dickson permutation polynomials and a class of exceptional polynomials respectively. One of our results confirms Conjecture 4.18 by G. Wu, N. Li, T. Helleseth, Y. Zhang in [42] under the assumption that the characteristic p is primitive modulo a prime number n+ 1. Moreover, we show that Conjecture 4.18 is false in general using our approach and a counterexample is provided. We also re-confirm Conjecture 4.20 in [42] that was proved recently in [24], and extend some of these recent results to more general n's and more general a's.
